aabacdadaccddbdcbbbdbbcacadcbcccbcaccabcacacbddbadbddcadbbaddddcdcdbccacbddbcbbbaadabbddccabbcacddaabcdcdcdaaadddbddbacbdcbdaacabdcbacdaccbcbcaddcaccdbbcaabdabdabdcdbcdbadddddaabadaaabacbabcacabddacadbddcbbcbacaaabbdbcbccabdcadcbbdababdcddacaddadbdbbabbaacacabcbdcdcbbdcaadcdbbcaddbbcccaacbaabbabaddcbcaccabddcddcccadcbcabacdddabbbdabaababdbddabcddcaddbcadaacccaababcdacddcaadababcacbdbcdcbdaaacddbccbdcdaadababbbddbbaadcbbadadabddddcdbbcaccdbdccaddacccbabadadddbbbabdaaddcacbbcbbcbadddbbddabdacbdaddbcccbdbddaaaddddbdbcddacdadbabaccdbaccacaababbccbbdbabaccdadaacadbcdbaddacbdcddabcbbdbaabadcbaadccaddcbccabdbddbacbdcaaaccbaabccdcaaddacddccddbaddbdcacabdbababbbccbddadcadcaccbabccaacbdcdbdbacbbdcddbadbdcdcbbbdddbddabcbaaacdbcdddbacddddcacddababbbbccbadbddadcdabbbaaacabbcaddcbccbbcdadabddcdcbbbddbadbcddccababbcbcccabcbccddabbdacbacdabcacbdcdaaacccdacdddbbaabaaadcdcbddbdadbcdccdaddddcdcbccbbcbcacbdcadabdcdccadbcbbbbddaddabdbbabbadabdbaaabcbdabbccadaaddacadcacbcdbbbdadaaabbadadbadbabdacaddcaddcababbdbaabbaddabcadddaddddddddbccdddacbddbcdadacdcabbddccddddbdadcbbbbcadabdaaabaaaddddaabdadbacbdacdbaddccdccddaaccbddcaadbabaadcadccdabadacacdbaabcaaabdbababaabbdaaabbcbccabdabacdbcdccbdbcbcacdadbccdddccdcdbcbccabcddaadbaccaccaabdcacbcdcdbdbdaaadbbcbbdabaccdbabcbbbdbabbccbdabcbbabddaabdcdbadddcdbbdbdccdbcbabbadbabbaaabbdcdbbbdbcaaaaddbbdddbdbddccdcccdcdabbcaadabdabdabdadcabcbdbacbdcbcadcbcabdabdcdbcdddabdaaccaacbdbddcdddcaccbabddaaccbbbcaadaccbadbadcadaaadbadccaaccadadbadbbacdcaabadadaccbcbadbcbaccacaccdbcadacbdaddcaccbadcccbadbdadbaccaaddbabcacddbbcbbbdbccdbcbadccdadaabdcabbccbbdcabaccaabaaacccbcabddbbcbcbbbdbbadbcbbaddcdcdabdaababbcadbcadbcbaabbbaacdbbccbcbcacdcaaacaddbadbaabdbdbcbcdcddacddddcdacaaaabcbaddacbadbccdcddcabaddcacadcbdcaabacaaaacbbacadbabdcbccaabddbcaadbdacbcccbdbccdabcbbbbccccadbbaabcdbcdbdcabbcdadbabdbdaabadbdcbccbbdcdcddbcbbbcdddccbdaacaacccbadabccacbccaacdbbaaaaabdccbaabaddcbdcbbaaccaaadcadcbcdbbbcbbccdbbddbddaaddadacadaaccbbbcdbcbdcdadacddbcadbbcaacbccbdaddccbbaaaccacdbcbccabbaccddadcdaabbcadbcabaaadaddbdbccaabdcdabbacbbadcbabbcbaaccccdabdcabcbccddcbdcacdaadaaccaddadbbddadcaacddcbabccaccdbacbbddacbcadabcdbdbaaaabadccabacddabbdddcbabadcbdabdcacdcccdcdcbacbdcbbbdcbcbacccabbccbdbcdccabcaadccabbdbddcaacbadccdacdccbccdcaaadcbaacccbaadcdaaadbcbabbbccdbcabbbcabdbbbadadabddaaadbbcacaccccccdccbbbdbdbddbcdbbabcdacbbdddacaccbddcdbdabcacacadddadbcbbdaabdabaacccaacacbacacdccabbadbaccccddabdaadcabbbbddaacdddbabdadacaacbaaabdadaaaacbabbbcaabcaadbdcdbcacdacdcabcbabbaabdcacacabcdacdbcddccdadbbbcbcbdabdbbccbcdcacdbbbabbaddbacdaddcdacadbdddbcccbcacbbccbcdbabbbddbaacdcdcbcacbdbcbdddabccabcacbdbdbdbbdbcabaaadcdaccdccdaddacdddabddccadcacdcacdabbabcadabdbabbcdadbdaabcdaabbccddbbcacadaabbdcbacabdbaaddaadbbdbcaccbdacbbcbabaccdccdbbbddcdcccbccabdbccdabbbdcbbdbcadacccbcdbdababbdaabcdaacdcddbadaaaccdccaddadbaccaabcbbbbbcacbbdbadbcbbbbbbaaaddacdcaaabddcdccddbacbdbaaddaadcdccadcadabddadcddbdaabbddbddcacddacabbbcdcadcbdadcadbcdabbbaddbbcbbdcddcdcdaaaadadaacaccdcaccbccbbcdcdbaddccabdbdcadbbdddbccacdacabbcbaccadbaadbbbdcabbcaaacdbdbdcddabcdabadcadbbddcbadaaadbcacbdbdcaababacdbcbbdcccbabdbaadcdbadcbadbdabacabdbdbdadbabdcadcdbbbaabaaacadaddadadbcdcaaddaabcccaaccdcaadbabbcddaabcccaccbababadcbabadaacbccdcababbbbbdcbdbdaadcbaddacabaacaccbcccbcacaccbcbadabdcacbbbdccacdcbcabccaabccabacbcbaaacdaddcdadbcbdaadbacdbdadcbadcccbbcbaddadadacdaaaaacdbdadbccdbbdccabdbbabbdddcdaacadbacbacbdcbaadadcdcbdcdcbaacbcabbcadbbcabcbbaaddaddbbddcccdabbbaccadbbcdbbbbaabbdbadabcbbacbcbdccabaccdbaaabbaadaddacaccbabaddbdabcacbdbbcddbadaddccbbdacdaccbccaacccccbdcddcddddccaadbdcdaabcbdaaaccababbacbacacdddcbadbdbaccdadcdaccddabbaabcacadcddbbaabbbcadbdacadcadbdbbdaddbdcdaabbcaaddccbcbdbcdcaabdadbddaaacabcbbddcddaddacdcdacbabdacddbacaaadbbdcbadcdccddbaaadbabdcbddbadbdaacbbcbadcbadbadbbdcabbcdacdccabdabdbbdbbaccacaaacadcaddcbbbcccbcdcdaabaadaabaacdcaacabcaddcbbacdbdbbbbbbdadbbabdcdddcabbdbbbdbccbadccbbdccdcacbcccbabdacccdbcabdddbbaadcddbbdbdcdbbbdbdcdcdabbabbacaccaacbddddbcdbbdababacbbabbbcdbbbccbddbcdcddabccabcbadbaacabaddbcabcabcadadbacdabdcdcbccbbcbddcddcababcdbbdbaaacbaaadccacddabaaacbdadbbbaddbdbdadccbbbbbbcbcdbccbaadbddaccaabdbabccddbbdcaaacacbcdcdcadbbdaddbdacadcddadcbddbdbaabccccbccacdddcacdacdabcdbadadbcbdbcaadcbcabacccdddadcaaaacabcdbbddbbdddaaaaccccdcababbbbbcccacbabcddaaccadbcdacaaaabddcbdaabaadaadabbabdbbcadcdcbcbcbaaacabbaacaacbdbddabaacacccaadbdacdcaaaddaaabbcbdddbdadcdddaccbaddbdddcabaacccadaabccdacdcbabbbdbcdddbbdaabbbadacbbdbbcaccbbbcadaacbdbcdcdabdacdaccbdadadabadbaaddadddadbbcababcddddabaaadccabacccacdcabdcbaccabbdaccdddccdcbdacabdaaacbbbcacabdbacabbddaadbdabdccaddbbcdcbbcbdadbdcddccbabaccbcdbbcbbaccdbddbcbdcddbbddaacaddbacacacacadbbacabaaddbaaacdabcbbbacbbcdaddabbddacbacbccdabbdbcbcbbddcbadaabdbdabdbcbccbccbdbaccacbdcacdbbcbcdadcdadbababbdcaddcddadabdcddcadabbbaddbccccddbabcdcbdcdadbacaaabdcdadbacccbadcbdccbaccccddacdbccdbcbdccaaddabaddaacbbbdacbbcbbddcbcdbaccbbdcabbadccdbbabbddbccddadadcbbdbacadbcabbddacabdabdcbcadcaaacbcacbbaccdaacccbabcadabdcbbbdaadbddbbaadcdbdcdaabcbbcddcabbcbadbbbcaadccaaadbdddbccaabbcbcabcaaabcddaacbbbcbcaadbdbadcbadadbcabaabcdcccdcadcbbddddaabcbabdadbbaddabacadabbadabadababbdcdbddcbadddcbdbcbdababdddadbcccbccddaabadabcbdbabdbdbabadbbbccabbccbbdddbbdbbbdbbdbabaaacbdcaaabcadbabadbaabadabdcdddcadadbbbcaababdacbabacbdbcadadacbdcadccccdcccddaccbcabcabacdbbacadaabadddacccdababbaabdcadcbddbbdaabbcadbdaadaaddbbcddaccabdaaaaadddbcaaaaaaabbcbcacccaacdcacabdaabdbbcdbddbaddbacbacdbdbccccbacaddcddaddbdaccddadbbcaacacababdddabbddabbdbddbadbacaabcaccbcddabdbbdbabbcbbbcadbaccabbadbaaddbdaaddadbaaccbadcbccabaababbbdbbbbdcdbdbdbdacbddaccacdcabdbcaabcddbbddccddcaadbabdbbbbdaddbbabdbcbcdabccababadbacbbaaaddbdabbbadddbacdbbaaacbbcdbcaababacbdddcdacccbacbdbdadcdadbababaaadcbddcdbaabcdadbdcacbcddaccbcacacddcdaaabacdbbcbcbabbcacbbdcccddacabadbacdabbbdccdcbcdaabcbbdaadacddbaaaacdadcabdcddcabdcadbcdadadbdbbdccabacadaabaadabddaadacbcbacccabbaacbacdabaacccacadbccacabbbaababddaaccdbadcbbccaddaddcbbcdcdcdabcbabdacccccacadabbcbaccbadbadbdbacdbcbabbaacbdbaccdbbbbccaacbccbacbbbdbabbdacdddcbcdcdadabbcdccaababcacbbdcbdbbbaaabcabddcabbbbdbbcccbdbadcadcbbacadaabcdcabadcdcdbadbbcaacddbbcaddbadaadbcbbcaabdcbcdbbdcbaacadababadbddabcccdcbbcadadbbdaabdccddadababaacbbcddccaacdcaacbbcbdccabdbcbdbbbdbaaabdbabdcabdcaabaabaaddbdbccdbbdaadbdbbaacbcababcbbbdbcdccdcabcbbccdabadbbddcababbadcaadbacaacbdbddadbadadcabdaacdbdddbddadcccbabbccaaacdbcbacabcaaddabacdbdcdccdcbdbbacbdaaddcaaddaccadbdbaccabccdcdadbddbbadbddcbabacabaddbabcdadbdcbcdbbbdaabbacaadbacacbacddacaacccdcbcdcdabddadddbbaacbadadbdccbddbcbdaabadbdaccbdbbacdcbadaaccacaccadaaddbcbbbdadddadbbacbccbadbaadcbadcabbdccdcbbcdbcdddaacbcaaddddbabddadcbdadbabbcdacdadccdabbcdbbacacdaaccbaaacddaaaddcadbbdacaddbdabdaacadbccabbbabddbaadbdadaabddbbacabbbbddaadbcaadabadbbbccaabddcbbbadbcbdbbababbaacbccddadbbbabdcbddaabaaabacbdbccbacaccacaacabadcbbaacacdabcccaabdddacdddcdbbacdbadddadaddbbdddcaaaaabbcbabcccddbbddccddadbbcadaacadcadbccabadcdcccdddacaddbbbdabdbccddcccabbdabccdbaadaddbcadcdcbcbcbcdcdabcaddccaddacbddbddbbbdddbcbadbddadcccaaaababcabbdcdcbccacbbdabcabdacbadcdcccacdabababbaabbabadccbcdccbbcabcccaabdddccaabcdbdbdbdbadbdcdbcbcdbbdcaabaadabccaabdaadcdcbadbcadcdcaabacbadbddcccdabdddabccadcabcabdbabbdadaacbccaaadbaadaaabbabbcbadcdbcbdacbcbcaacdccabbabccabdcadbdcdbbbcbacdbbcbbbdbaacbcabbdbdcbcdaccadaaaadcbaccdbcadcbacbcccbbcbdadddcdbbcbacbbdbcdccddbbacdccbbbacbbabcdbdcbbcddbcabdcaacddddcbccbdacdcdcbcdbdddbcaacbabadccddcabbbaabdbadbaacbacbdbbbcdbddcbcddabccdaadaccabdadcadccbbaabbdaabdcbccacdbbaaddcbadbcbccdcdadacccbdaccccaadcddbbacbbadcbdcadbbcdabbddabbacddccddcbaaaabbcabadbbccddaabddbdadccacdacdadcbdbcbcdcbcbacccdbaabdcdadacddcaaaddcddabdaacbddcbdbacdcdbcaadbcbbdddcdadbbacbdabbabdbdcabbcccddcbbdcaaccadcababccddccbdacddacdaccadaabdbdbdacbcdccdcdcabacadcddacaaaacdabdbccaccddbbbabaabcdacbcabcaccdbdcdabaddacdddbbbcabdacbbdacddcaadcbacccadcdabdcadacbdcadaddabaccadcabbdbadcdabdacbdabcaccabcddbbcbabcabaccadccccbcdcaccbbcaccbaccabbbbbcbcbcacdcdddccdadcbdadbccdcbbccbadcccbbadadbcccdbcbddbaaaaccddbddccadddcbcdcaaacdcbccdacabccdccbcbddcccacadadddbacccaddaddabcbdcaaabdaadcbcadbdbbdaccccddabdbdbdbdbcdadcdaddcaacacdbcaadbaddacdaabdbccdabadacdbaaaddbbcabaadbccaadbcacbabbcbadddbccbbcacacdbbaaadbcacabddbacacdaaddaacdccbabcbbcdbaaddbbbadadddbccbcdcdbcccabbccddcccbbbbcacacadadcccacaddcbacdabdaaabddbbcbdabdbabaacdadbbccadcdccaadbadacaccadbabacdddbcadaaccdccababcadbabbbacbabbcbdacbbcbabdcacbcacaabdbbccddaabbbaabbdbaddcbadbdadbbcbdcacabaadabdcadbbbdcabdccdbcdabcadbadcdbcbccdaaadbdbbbcccddbbbbaaaccbbbacdcddaabddddbcdabcbcddcabcbbbdaacbdaacacadbdbbaaccbbadbddbaaadbcadbacdbbccddbdadcbcaacacbcccdcabcbacbdbcbdcdbdcbcbaaddaddcbabadcdaabaaaaccacbcdcbabdcacacbdbdacccbbacbbcbacbdadbbdaababdcccaabbdbcabbdcabcaccabbcadcbaabadcadbdacdaaaccabcbaddadabbadadaaaadaacdcddcccbcabaacdcabacbcbcaabddadbaaacbdbadccdbadabaccaadaaaabacdccdbbbbadbcdcccabadcabcaadbbdbabdcacabccabccacddcbcdaabcddddaddbddccbcbdaadbbccadbabababacbbdbbadcbccddacadbdadabcdbdcabbccadddccdddcdcdaccbcdaaccbcdcddccddaddacbabcddaccbaddcaddadaccbddccabbaadbacddbcdadcddbddbcddaddadbdbacabdddccbacdacdbcdbdbcadadbabbbabadaaadaadcdbabdcacbddcdcdaddacccbcdcdacaabbacbcbbacaccdadcbbdacccdaabadaaadbccaccdbcccadaadbacdbacbadbddcccddaadabbcddadcabbabacdbabcbaadacbdaccadabdcccdbaaccaddadcdcccabcccacadcaaccdaddbaacbadddcbbccaddbcabddcbadbadccbcacbcbddccbaadadbbbdadcdddccacccbadcddbbcbbcdcbccaabdacbcdbbdbadbacddccbaccdacacdabccbcacdbaabbadddcaddaddcbacbcaacbbbbbbdaadcbcbdaddbabaabadaabdbccddacabcbcccbacbacdabdcbacdcddbcacaabdbdaaaadaaabddbdadccadabdacbbbadadbcaacddbadcbbaaaadbdbdbcdcddacbadacbdbbacabddccdabbabbbcccadbabcddadcdcdcddacaabbcdabddccbacdcbcabbacddabbccbaacabacadcdbcdcbbbbbccacccbaacbbaacbcacdacccacccadbbaaacbbacadaddcadbadbddbbbdcbcccbaacaaadacdddbacbdabdccbdcbdbcccbbdbaacbccabaddbbcdabcdccbcccdabddbddcdbcbdcdbccbadddcbbdbaadbdacabadacabbaadbacbcccddbbdacdadcaadbbccadcdccbdbdacccacdcddbdbadcdacbcbbababaccdbdadddbbcdabcaacdaabdbbaadbcadacdccadcabdbcadcbabdbbacadddbdbcddaadadabbacddcdbaccdbdadcadadcbcabaaccadccabbcdbcbbbddcaddbbbddcbabbbdbacdabbadbbaabdccdcacacddcbadcccbbccdcabdcbdddccabcccdcaccbbbcdcddbabbcdabdadacccccbaadcdbacdaddbdaacccbbccaacbbccccbbabbccbbccddbaddbbaabacdcbbabdcddbdcbabbaabdbaaaccddddbdccdbdabbbbccbbcbdbcdadcbccdbacdbbacabdaabcadddcdddbbdabdbbbbcddbacccaadaddcdadcdaadbadccabcadaadaacdabbbdcbdbaddbdddaddbbbbcbbdadddcabbaaaacbbaccbddcaaadaccaddaacdbcddccdbdabacccdccaaacbbbabcbcdbccacdcaaabbcbbddbcacdcdcbacddbaabbabdbadaddcacdbbccacdaacdbccdcbbbdcdabcdadcabbaabaddbbccddbddacdbdbcbcaaddaccaccdadaccbabacaddbacadcdcdbcdcdaaddcdbcbbccbdcacccdbcbddabdabacbaababcbbbbbdacdcbcdddacabaccdbbdccbbdaadcccdccbcdbcbdbddbbaabaacdbadbdbdccddacddbaccbbdacbdabdcbccadacbaadcacdcbdcdccaadadcbaaabbcbbddabddbbacddcaddcdcbddcbadacdaaadcccbdbbdaacdddabcbdaaaadccdadcbdaadbcdcbabcdaaaddbacbcdbdbcdcaacaaacbdaaddcbbbcdcccadcaccacacbdaaaccbbdabbcacdbdddddcaacbcbdacacdbbdcdbdabbcbdcdcdddcbaadddbcbcbcdaabbcddadcbbacbaabacdcdbbbbdccaaacaccdabcccacbcbbbcdcabbabbbaaaaccaccabbcaacddddaaacaabdaacabbbbdabaccbcddcaabadccdddcaddbaabadcaacabdcbcddbddcdbacbccbbbcdcaabacaddbabdccbdcabcaaaddcdabbccacccbcacdadbcccdaacbbbcdcdccdacaccaddcdabddbadaadabcbdababdcddcaadcdbddbbdbaacabaaadddacabcdaabcbccdcacccdcdbbbbdcaacbbbdaabbdcacabacadbbaabdababbdcccaddadaabacbbbcddabcbcddbbddddddaacdbbcdacccdddaabbcadadbdbccacbbddcdcbcabaccbcbddbabcbddaaabdbdadbbadbbdbacdccbcdacaccccaaadbacbaabcacaabbbaccdccabcadadbbcdcdcbcdcaaacbadbcdadddabaaaaadcbcdcdbacbbdbdbddbcddcaaadbddaabacddbccbabbccdabaddabbacdaddabbdacccddccccbcbdbbababbdddaabcbdddacbbbaacabcbbadcbaadbbccdddadddddadaaabbbdadbdcbcdababdadcbbbbbadadcdcacbcbdcdddbabbcaadbdadaadbacbbcddadaddcbcabdcabdabcbacbdadbcddcaccdbbdbbdadbbdadaaccbaabdddccddbbabdcddbdaaacbbbaadcaabcccaaaacccdaadcacdabcccbbadbabacadacdcadcbdaccbbcabbbbcabbcccdaaabbdaacbdddabccddbbccacbadccbbbdabcbdbcdcadbccadacdaaacccdaccdbaddcdcacdccbabdaadbacccdadcaaaabbaaadbdcdadacbbccdabdbdabbbbddbdbbaacddaccbadbcadbcbcababbaadaacaabaaddcdbadcdccacbabbddcaddbbcccacbbbacccddbbcbcbddaabcaaccdbbadddcdddbaccbbcccdcddacabddbbcabaacccdbcbbdccabaddadabbcdaabbdcddaaddcbbdcaabcaaacdccbcdcacbabdccaacacdadcbdbdaacaccdbddcdcaccadabdcdbbbaaacdabcabdbaadabddbadcdcdbcabcacbbdbcbbadcdcbbbdaaaaddddadbbbccabbdcaaabbbaadaaaaddaaabbabcbcbabbaabddcbacbacdabadcccbdadaddcadcdbdbbbbcccadacbcdabcadbacdccdaadbbbaacddabdcccbcdcbdbbcddabaddadaabdbcdaabbaaaacdcbdccdacdaaccbbdacccbccdaaaccbcbbbbcbbcdccabcbdbaddbbabacbcdaaaadcadbaaaccccdaccddbbaabcccadcbdcaabddacabadbcbcaddacbadaacbbaabadddabadbbaabcdcdacbcbacccaacdccadacbcdadcddcadbdcbaddbbcddbadbcbdabdddbbdbbdccaaaccbabccdbdcaadcbadadcccadaddcbabacddddddbcaacdbddbdabbdadaacacccadbabbcccacdcbbabacbbabbcbdcdababaccaadbdbaadccbdcbaaaaaccaaadcdaccbdaddabdbdddacdcbdacdddbbbacacadacccaabbccaddbabccbdcbbcabcbdcadcdbddcdbabddabbadabcbacccdcbdbadaadababccbbdcaaccbadcdcbbbbcdccabadbdddcbcddbcbcbbbdaaddbdbabcbbbdacdbcdddccdbabdbdaaabbcdaaabdccbbbcbdbdbcccdbccbadcdaadaaadacdbcbbaabddccbdbadbcaddddbcacdbbabcbbbacbbdcaacdddacccdccbbdaadbabdcbcbdbaccbbcbdccdaacabddcddddccccbdbbdcabdadccdcdbbbbcbcdddabaabacddbabdacbdaccabdbbcbcabbabdadbbccabcaaddbbcccbccdaacabcdddababadbcbbabbcaadbdacbbacbbdbbbddaabdcabdccbbcacdcacaaddcccbcacdaabacadaabadcadbbbbccaadacdbdcdbdcabbcabcbcbccbbacdbcadbadbadaadcdcdbdacbbddcbdadacdbaccccaabbdabbcbdaccdabbddaabbdadddbadabadbdadcadbdccdacbccbdccbcbabbdcccacdbdaaacdbacabbabbcdbbcacbaabccbccbadbcadddaaacdbdcdcdcbbadadaacbdadbdcaccadacadcbdcccacbdcbccdcacdbccdcbcbacaadaaccddaaccbdbbbbcacacababdacacdbcacabaccdadadcbbcbdbdacaddddbdacadbbdddbdabdaabbaabccbddcaccaadddaadcdaadacdabbabdabbacabbbdddcabddadccbcbabcbdcabbcdbcccadccadcabbdcdcaccdadcabcabbbabcdabaaaccabbccaccadaccccbacabbbcaaabbbdbdacdbddbdaaaaddcbdccadbcaaaccbbbccbaadbcacbaabcbbabcdabaaadabcabcbcaccaacabbbdabcdadadadbbcddbddcabbdabaccbcdcbaaacdcbdacccdccbbdbdddabcdadcababbbddbbacdabaddcbccdadcbbabcccabdaabcaabbddcdbdacbacdbdbadbbcdaabbccacaaddcccdabdabccaaacccacbdddbbbddcccdacaabbdbbddaddcbaddbacabdacdbcdaaaabddaaaabbdddaadaacddcdbbabdccbbcccbcddcbccdcddadccdacdddbcbadadabaacdbccbbdacabbbcccbaadaaacbccccabdaacabcacabbaadbcbbaadaaccdddaacbcccdabbcbccabbccbdabadccadaabdbddcdbcbccacacadaccabcaccaacbccdccaadabccbcabbbcbdaddcaaccdbbcbdcabacacaaabdbbbbbbccacbbdbbdbadcdbabddbdabcdaaaaadbdbdaabdbcdcbbaaabddcccdbdcbdcdcdbddbcabdaadacbddacabcacabacdbbcdaabdcaadbbddbdadaadbdacddbbddccdaccaacadbdaaabbddbbabbdaacadcaddaaaaccccddbcacbdaacadcdddacaccccabdacddddcabcaacddbcdcaacadbaccbccbaadadcdadcdaaadaabdddadbacaaabbcbaacbddcbcbdcacdabdcdbdccacdbcccddbdacadacbacdbbccbbcdddcaacacdaadccabdbabdccbaccccdbabddabacdcbddadabaabdcbcddbddcdddcaddcdbdddadcdabdccdbbcdcbbbcdaadbdaccddabcdddcdbdccccacadcccbdddabcbbddcbcccacdbbccbababbdddbdcdbdcaacdddbabadcadbdbadbdbbcdacadbdbbbdbbcbcdbcadcddcaccdcacbdbcaaddbbbdadbbcdaadcadacccbbdbdbccdcbdaadcbdaabdddadbbcdbdddcbccaccddabadbbdabaadbdaadadacdabbcaabddbacbdcbabdabcdccaaccadcddbbdcbddcaccaaacabbbcabdadadbbaabbbcddccaadcbdcdcabdbdadbcadacbbdcddbadaabcdaccaddadcbcdbcbabadbbabdbddcdbaddccdcdbccacbadabaadacdbbbbcbbbacbaadcccddcacdadbbdbdbdcbdcaacbddcddccbddcdbbcdcbbbbdadddbbdbbbbcdacaddddcacbdccddbabbadddbadaddaacdddcdcddcbdadaabdcabdbdacdbdbbbbdaabbbccaabacacbbacabbaabcddccdadadaccddadadcdcbddcaaaaddbdbcdbabcdadcccdbcddbbacaccbacdbbabccdaaaddcbdcddaddacdcbabddababacbddaaaadabbbbacacccbadbdcbbdaabdaabbccbbddaaacabcdbcbcddbcadacdadccadbcbadcadcdcccacdbadbabadbbaaacdcabbaabcbcdbacbdcbddbbdcacdbcdcabdcabbababacdcbccaaabdcccdddaddccacadcbcddcddbdbddcaabaccaaacdcdbcdbdddcacccaaddaaddcabcddaabaaacdbacddabcddcbcbabadbadcaccbcdabdcdcbadcbadabccaabbcaabcaccaacdcbdbaabcbbabdccdbbbcabbdcbdccbbbbdcdbcbcbcadcaabdbaacabacdddacabdbbccabbcacdccacacdbaaaabcdcdaacaaaadcbdbaccdcddcdbaaddbccbddbccbbbbdacbbadbdaacabcccbaadcdbcbbadaabcacadcdaaddbbdbdbdabcdcabadbacacbdacbacaaccabaddccddbccbbdcdaabcdcbcbdbccdabcbddccabacacbaaccdbbbbcdcbddbbdccbcadcbddacaadbdacadbcccaaabdddababbbdbbdccbbbabacbbddcacddcdccdbababbaabddbcdaccdccdcaccbadaabacbacddacbadbbcddbdddcabbcdbcddadaacccabbdcbacabddbbdccdcddcbadbccdbaaacacbccbddbbddcadcabbbadcdbcdccdddadadbdabbadbacbadacadaabaddadbbdacbccbcabdcabcbdadcbcaadabdddabcccdabcbadcddadcdddbacddbdbbbdbacbdcbbdbbddcbdcaaccdcadcbcbdbcbddbdbcdbdabacddddbbccdbdddddddcbcabcddadcddadcbbaddabcaaddacabbbdaaacabbacbdbcacaacdccbabbbaadabdcacdbcbcddcbbcccbdadbcabcadbcdcbbdbbdcaddacadcaddacdcdaccdacdadbcdbaaabcbbdbdbbbbadaacaacbbdbbaadadbbaadbcdaddbadcccabddbdbcaabcdabbcdccdaaabbadcbcdbadabddbadcacbccbbcddbdaabcdcbadbbcbcdbdacbbbacddaddacdcbdbcbbbddacababbaacbcbabccdddcbddabbcadbcaabacdabbdabddcabaadcdbadabcdbccbccbcdbcbbbacbadacddcdacdbcaaccdaaacaababbdaabcaabbaabcdcabaaccacdbabaddbbddbbcadddbcbadcabacaddbdbbbbccccbbacadacbcacdddddbaaadaccbdacdcababcbcadbdabdbacccdbabdbdccdbcbdacbdbbddbabacbddbdcdcbcbbbabccdacacadddababdccccbddabccdaabaddccadcadabbdddcdbcaccaabaddcddcbaaddbdccdbbbadcacabddaccbabcdacacbadbdabacdbdbcccdbcbacbcacbaaaadcbbccacbaaaaccbbcacccdbcbdcdccadccdbccabacdaabbbdabcdcaddadccbbdbdabcccccaacccacabbabcadddbcbacadbccdbbdccacabdbbabcdbcdcdbbddbdbabcdadacccdcbddbaaabcabdacdbadadddccadaaddcddbdcdadbbbcabadbdbacccbdcadbbbbcbbcdcdababccadbdacbbbdcadddacbcbbbdccbbdbcbdaaabaccdaccabadbdcbbcbccacbbaabdbadcabddacbddaddbcbbadcaabbcabdbcdaaaabbcddbdcadcbdabcdcddcaabbddbbdbcaabdaabbddacaddccdcaabbdcccadaabcadaddcdcaadabbacbcdaacbaddaddcabddcacbbabadacddbdbcbaaddbcaacdbacdaacbdbcaddccdcacabababddbadadbdbdcbdabcacacdccdacddcbbcbdacbadcaaaaddadabbaddcdcababccdbbaaccabbcaaccccbadbcddaacccdaadadadacbacbcacbddaacccdbcbadcdcacabbbadcdbcddbaaacdaaacdacdccdcbdbcdabdbdbcbbabcdbcbddcdaaabbcbabadadddaadaabcbbbccbdcccccdabaadddcbbcccccbbdaccdcbdcdbbaaaacbacbbadabddbddcddddbcdcaccabdaccbccdbccdbaddabcbbcaddadbbcabbdbdbaccbdabddccbbdacbcdcbaaccbcddcbccccccbcdddabcdbbccdaaaaabbcdcdbabcbcacddadbbdddaaacbdaaaacccadccbdaaabdbaaadbbcbdaabacdaadcdadbbacaddabdddcaaabcbcdccddddbcddbbdbbdbaadcbbddacbbacbbccbbbcbcdacbabbacccabcbabbbaccdbacbbbadcddabadcdabaaaadbbccbacbccbcdcaabdbbbbdcbaaacbccbbccbdbbaaccadacdcbddaabaacddcabdccaaadbcbbbaacaabcdaaccdadbbdbacbaccdbdddacacdbbbaccbdbcdacbadbdcbbbadbdaadcbdcccccddcdbdddddcdadadbdacbbaaccdddaacaaaccaddccbaacddcadcbcddacadaaddacabcdadcdcdcdbdacbacbbdbacddbddbdadddacbaaddddddcdabacbdccdbcacbcaabaccbaddbacbacadcadabbbccbbddaccbddbbdddaaabcccbaacadcdabdccbaccbdbadcabadabacccdadcdcabaabaabbddbcddacbdacbababadabbccdacbdabacacaacabdbaadabcbacbdaccbacbbbcacaacbcccbacbaaaaabdadbbaddacacddbbcddacabadadadddbbacdcdaabdcbcdadaaaabcbadbcbaacbdbcbcbbdacdddbbadbdbadddbadbbcdbccbadabaacbbadcdbcabccdaadbdddcbdbaaabcdadcdaaacddaacddbccdccdabcadbaaabdcbbadbdcabdbbbbabaadacdabddcdcdddbcaadddbdaacdccadddaddcbbadcbcbdcddaacbabbdcbbacbdadddbbadbcaacacabbdbacbbbcdcacdcdbcacadadaccccaaccadccdadbddcdbcbbaaabcdbabcadcbacabdddaadbddcbccdddbdaaacbaddabdaadabbcbcdbbbccadddabbdaddbbbbddcdacdcbaacacaaaabaacdccbcdbdabccadddacbdbccaadabbbdbcbdbbadaacabacbdacacaadbddddabcddacbcdcbadcacacaaacaddbbdacadadaccaadcbabbdcbacbdcadcbdadcabbcaacabbaaacddbdcdaaabaabdcbaacbaaddddacbacbcdcddccabaccacddabbaddcbcabcbbcdabcdbadcbdddcddcbaddbbabdbdcdacaaabdcbaccdccacdbcaadcabdbcbbbdcacddadbbacaaaadbcdcbcdbdcbbababaababbdddbabadacacbadddddbccbcbccadabcdacacddbbbaacbddcadabcbaacbbcadaccdcddddcaccbdacccbdbbbddbcbbacabdaadbadccbdaddbcabaccaabaccccdbbdaaabbcaddbadbbbdccdbcacaadbaabbadddacbacabbddbaddbabdbacbbdaddadbadacbbbbdaaabddadadcdacbcabccdaccaabcbdaadddaacddbacadacddbacbddacacddcdccccddccbaadadbdbcdbcbddcadcdacbddddbcdbacccbabddbddcccaddccabacbbdaabddbdabbacbcbaacacbbacacabdbdaabbaddcccbbbcbdaabcbbddddbddbdbbabdcdadddaddcbcbabdaccadbaabdaddaadaabadcadcbddcccddcaddbbdbcacddcadbdaadbaacaadcbcaabcbddaabddbaccdbbcaddcabcadadcdcabcbacddaddbdbaddadabbdcdcacdabcbbcacadacadacbccdbdcacacadbddacacadaddddcabdcaddaddcaaadadadaadbaacbdddccccbdccabbbccbbcbdcbcaadddaabbbacdaabdadbcabaaacaccdbdbcdccabddcaaabacabaaabdacaaddbadcaacbbdbbbaccbccdbddacccdaabcaacbcacbdcacdcdbbdcadcbabaaacacacaccaadcacabcadbdbbdbcccbadbbacaaacbcabcdbddbbbbdaabaadbdcabbcddcdadbbcbdcdcdccabddcabbcbcaadcaabbbddacddbdbabaaacdcabdccbbbbccdccdcdbbdcdaaabcdacbacbbbaaadcdbbbcaddddbcccdaacbdcdabbadabbcbabdddbddadadabdcacababdaacdacabcbdbbccdbdaaaaccbabadccbcdcdaaadbdbccddccbbddddcdbababdcbadaccaadaaddddabccbabaaadcbbdcabbcbbbbbaacdbcdbdadbcddcdbcabdcaaacdaddacadbaabaddcbcbddaadccddaabccdacdbbdababdccbcdcdcdabbadddadddbadacababcdddcdcddbabbbbbacaaaacdbacddccbcbcacacdbbbadbdcbaabbbaaaddbcabdbaabbddabbcadbdbdbbacccdbdabcaaabdbcacacaccbbaaaddcbddcdcbcdcabbdcdbbcccabcbbacdaddccdbbaabdaabddaacadccddacacbcbddcaabadbaccbadcdcbcbdbacdbabcbdcabbccbaaccaadbdabcbcabcbcccbbdadadbabdcabdadbbbbdcdaabadcadacdbdbcbadccbaadbcddcbacddcacababaccbaadaacdbaccbacbdadaadbadcacbdddadbbbddddabbbcbccbccacabddcdcabbbbaaddcdacadbbdbbdacaaaddadccdbaddabcadccdadccbcccacbcdadcbdccacdabcccbadcdadbcbddddadbbbcaaccbbaadddaabadbacbabccdcbbcddcbadbcddabbdcbddbdbddccabbaacbdccacbaddadaddddacbcaddcbaacaabbacccdbbccccbabbabddbdadaabcdcdcddbbccbccaaacdcdaaccbbcdadcccdccaacbcbacdbcddcbbbaccddaabbdcccbbdabddbcaaacbcccabdcbbbbdaccaadbaddbaaaadadcdcbbcccbcbadbdbcddcadaccacaaabcacbadcabdcdcbbdcdbddaddaabddbdbdabdacbdacbcccbcdbccbbddbdcaacbdaaddcdcddcccdcdbadbbbbddccbccbacbdcadbbbcdacbbcbabdcadccdabbdaddcccaddcdbaccbccacbbacccaadbacccbdddccbbbabdbdadbcbacddabacabdccbdabcabaaaccbdbabcbbcbadcadaacddbddcadadcccccabbdcbcaacbdbcdbdabaadbddaadacbadbbcccbcacbdaddabddbcbcdbdccdbcabcbdcaadddabccabdbcccdbaddabcacbdccacdababcbacddbadbddbbbcbaabcbcabbbcddbaaacbaddcdbbadbbaadbccccdaadddcbbcdabbbbccdbddccdacbbaacacadabaaaacdccabacbaddbacbdcbbbdccbcdcbdbbaabbbddbcbadcbdbbaadbcbcbcddcdddcbcadcdbbbbbdccadcdaadbccccaadadadcdaaacabdccbabaacadccdbabddcacbcccdcbdacdbdccddbbaacdcabcdcaaaaddbacdbbdcbbcdcdbcadcdbddadbaabdabdbcbdbcacacbcdbbaccaadbdaadbcccaaadbdbbdbdacdcccbbbcabbbcbdddbcbcccdaadccaacbbbcacdddbdccaabdddaddcdaaddccadabddacabaaadbacbbbbbadadbcdadbcbbbadaacacacdadcbbaababcbaddcdabacbacbbdddcbccbaaccadbbddbccabdbbccbcadcbabccaabaaccaaadcbbcdddddbdbaaccdcddccbcccadabcbcdddaabaabbbddaabdbcdddddccbbbccdddbdcbaaacbbabbccbddcabcbcccbadadcccbddbddbccdaaddcadccbcadccbccddabdcbaacacddcbbdcaadacbcbddcbcbcbbccddabccdcbadcadcbcacbcbbbdccbcaccccabcbbddddcacadddddabcdabcdbaaaadadabaadacadbbbdcbdacaaacdcadbbaddaaacaccaadbbcdaccdbbdbbababbdcccccaadadcacbddbaccadccbbdcdddbddadcbaacaabaddcbbabaabdabacdabdbaacacbdabdaccdbcbcaaccdbbabdabddaddbbddacabbadcbbcacbcdbaccbabbbdbbaacbbbbaabddcbaddbdbabbbbbaabddbdbbdacadaccabaabbcbadabbdaabbbdddbdbadbbbdcddbabaadccddbcbabdddcdbadcbabdddaabccaccdbdbabddbdadcabaaadbbcbaccabdcaaabddadbbbdccbabdcbbbacbccddcccaabccbabcbdacaadccccdaddbdaadcdacabbdcbacabacbdcbbabbcbaddcdaddabacaacaacaaabccddabbbacbcaaaccbdcababdbbbabdabccbabdbcacacdabbcaaddbbbcaddacdacdbaaaccacabcbbaaaadaccbdcbacccacdcdbabbaaacbcabcaddababcacdadaccdddadcdadcaabbbaaaaaddadadadbdabbadddaaabcacbbdbcdbdddbcbcadaddaacaddcaccbaccadbdbabbbcdbcccbbdadcbacbddabaaacbcccaaabbbbbdbabbbcaabdddbacccabacbadaaaadaacadcdaccbbcbcdabdbcdcddbbaadbbaaaadbbcacaddaaababdbcabdccdbdabcbaabaddccbddcbadaaadccbbdccacbcaabdbacbcdbbcabadacbddcbdbddcccdabcbdcbabdcadbaacacadcdbaaaaddcdcaddddbbcccabcacabadacaaaaabcbbacddbbbdbacbcccbbcbdaaaaadbabdcacaccabccbbbcbaaaddcdabcbbadacbbdddcadbdddaccdbdbbbbabcaadaabddadbbdddaccdbcbcbadcdcdaaaabcabdddcdabcaaccaddaccdcccaddabdaaacabcabddbcaaaabbddcadbbcbbdacbacbbbcabcddbcddcbcabcbddacdcabbbbcbbadcdbdddcccbaadbccdaccbdccbdccddadaacbcbacbcacdaaacdbabadbbbdcdbcdabcdadddcccdadbbdcacdaddadadbddabbcbcbdcacacdaaaadabbacbabaaacadacaccbdcccbdabbbbdbbbcbacbacdbbdcdacadbcddcddbcbbacacccddccdccbdbbabcabbbadbcaadddbcbdacaaddabccddbdabdbdbdbdacbddcdbcddabcdabaabbbccdacaccbaaadbcabcabdccbdddccdbccbcaccbaadcabaacccabdddccbadbaaaccbacbadaabcbcacacacbcdbcdacaabbcbacaccacbbccacaacdcbccbabdbdadadbdcacdccbbabaccdbdcdabbdbaddaaadbcdadaadcbcddacbdccdbcaccabacbcccabbdaaaaabaabbdadcbbcdbdbdbabdccdacdbdabaacdbbaddbbbdaaabbbdbbbbbdcadcddaddaaadcadcbdcabcadabdcabbaabddcaccbcbadacdbbbbdddcccdbbbbaaaccbccdcaabaaacdbdcbcabaadbdbccabadbabdcdacdbbbaabdcabcdbadcaadbadaddaddbdbccbdacbcbdbcaadccbcdbdcdcbcaddccccddbadcccabbbbddacdcabadbcaaabcdcdbaddaaadbdbcbbbddddabdbdcdaacadbaccbbaadbcbdaddbaddcbcbbababbdbcaabdbcadabcdabbdaabbccddccccbdbdddbaaccccbaddadabcaacacdbccaccbabaaddaacdaccaaacccaccbdbacadcaccdccddddbdbcbcabaacdaadabbadbaabaaaabdccdbaabcddabaaaadbcbccaaabdbdcccaccababadacccaadaccbbdddabdbacacddcdadbacbcbbbcbabadcbdccddacdcbcaaabcabaaacadccbbdcbbaabacbdbabbdbcaccdabacdbacadccbdbddcbdcbacdddcdbccbacbcccadaacbbccacbbaaccbdabcadadbdbaabbbdbbcaabcdacccbddabddacdaaaabadbdcaadbddbbaaacccdabbdddaaacbdbccaabbbdaabbcdcaacbcacdcdaadcbcdacbcadabdbbbbbdcaaaaccddcbdcdcbcdbcadbabcaabcbbbbabdabddcadcacadbaaabcbcacdaaababcaadacadcbccadabcccdbcbdabbaaaabacaaadcbddcbddcadbdcbccccadbbdbaadaacdabadaddabdbccbdbdacaddcbabbccbccbacacdbcabcdacbadbcddbddcdabdbdccbcacbaddcadbdcdcddadcbbdbcdddadcababdbbcddbaacaddbdcaaabacdcaabbcbadcbcdbccdcdcdacbbcdcccdcaabacbbadabacbcabbadbcabaadcdbbbadbaadcccbdacdacaaadbbcbcdcbadbabcaaccbbcbbadadabaacdcbcdbdbdddaaccccddabbcaabdadbccbcccccdcbcadbdaadbbacbcaacbbcbaabaddbdaabadcdabadbcdaccaaaccdddcbcdccccccbbdabbcbdadadbbdccdcabddadadabbacacbccccbbdcbbbbdcabdacbaaddaadcaabacbccdcababbbbcbaccbdbadcbdacbdbbbdccbcdccbbacabadcdadddbaaacbdbccbbcdabbdaccaddadbabcdddcdaabcaaccdbcbbccadcbaddcaaadddbcabbdabcddaccdbbcbabbbbdabdbdcacaacbbcbdccdccbbcacaadcddcdadabbadcbabdcbcbbddbadbaccbbdadacbdadccadcbacbcbadcabcbbccdbbaddabdadaaacbdddbbacccbddaccbccaddccdacdaaaabdcadcddabcdaadaadbadaadcabdcccadcdcdbabbccccadcadcacbabbcababcaabababaacbdcbabddbbdabdcadcbadacabccacadbddcccdacbdbbdccdadacbcbcbdbacdbababddcdcccccbccbbbbddddbbaaccaccddcbaaaacbcdabbdcbcbcbdcdbacaadaadbacdbdcacaacbadbadcccdcdbcabbddacdbddbbaadccaddbaacbcbccdbbbacdcaaddabadddcdccaaccadadcbabbcbdddbcdbdcbababaabacabccddadbdbabaaaccabddbdcbbcdcccabdadbcdcdcdacabbdcbccbcababbcaccdbccdcbcddabddacdcaacdcbcdbdbbbbcabaabdaabcddaabdcddddcabcddbdabdbcdcddcbaaaddacdbddddabbccbbcdadacabcdccdaacbacdaccbdaaddacdccdccabbdcadbaaddaacccabbabcdaabdbdcbddbadcbdbaddaccbcaaadcbdbcdddbdbdcdadccdabaabbcabdcbdacbcacbbabcabdbccddcabbbdbcaaadabbddbdadbaabdcbcadaabdabccbdadadaddbdcdbccaaacdabccabaacadcacdabbddcacacaabdaabbaabddbbcabacaaabcbbdcddbcdaddacdaadbdcabacdbababdacdaaabdccadbcbabcaccddbbcdcbcbcaddcadaaabacbcccaacacbddacccbdcbbbcddadcddcaddacccddbbcdcddabadabdbadddccadbdcdbbddacbdabdddcccdbdcdadacadcaccbbcdaaacbccdcacbadaccbacacdcbcdadcaddaadbcbcbbaabacbbadbccacaacaacbcbddabaddccadbddbbbdbcdcbdaacaacaacccaacdbcccaaadcccdacccdacbdadbcbbbcbdbaccbaadaabdbbbabbbdddaddbcadbccdacbaabbbdaabccacaadddbdbcbccaaacddbddcbbaaccaacccabcbbbacbabbdcaabbbbcbbccbdbcbdddcbacabbdadbbdcacbadbadadcaadcdacbbdababaaaaddabdbcbdbddcaabcbadbacddcccbcaaabdcbcdabcbdaababccdbddacdcabbddbcbaccabbbbdbdccadbdcacdbcacacacdddcccccccdcbcbaabcbcbdaabaaadabacddcccaadccaadddadaccdddbbbbbadbcabbacdbaddaccccdaaaccaccbaccdacdaaddaaacacabcbacdcbccccadaccdcabbcacabbcdacdcbdbcdbdabcccaaaccacdbcbdabbddbcccbbdbabcbaaddaaacbdccdcbabccbadbcdcdcddbddabddddbbcaabacdbaaabacdcdbbbddcdaadbbdbbbdbcdaaabaacccadadbaaaccbccbaabcabbdccaaadacbadcbdcbbabcbbdcbdccddbdbbbadcbdacddbddbbcadabccdddadbbbdbbdacdbbabdaccddaadccdaddbddbbaacdddcbbadbadcdacbbcdaacddbdcccadcbcaacadbbaadbcdabcccddbbaaabdacababadabadcdacbdddacddccccdbcbdaaccababcdddabacdaacdbadcdbabbdabaaabaccccddddcccccabacaccdcdbdbcbcdccbdbadadaccadaccadbcaadaadbbadbacbcbababcaacdaadbadddccdccbbdabdababbbcbddccdcdcbaacdadcadabdbdabbddbdcbdadadcbacaccaacaabbaaacaddbbaacdcdbcadccbcccbacbbbddaccdcddbaacdbcbaccbbbbabcaddccbcabcbcbccacddbdbbbbcaabaadbbaadabcccababdccbddcbcaccbccaaccbdcdddaabadccaabdabbaacdbcbdbcaacbaadaaadaacbcacbccccaaddcbbbbcbbdbadddbcbbbccdcbdcaccbabaaaacdadddddbdcbccdbabaabbcadaabdccccaaacdccbbaacdacabccaadcdbacbaddbcbbdcdacdadcabbccbacbcddbdcddbcaababdbddabdbbacccabcaddbcddcbadaacbdcacbaacaacacdcabdaabdcaddccccaacbadadcbbbbdabbcccdaaaccbbbadaabaacaccdcdababbadbdbacaccabcaddbcddbabcaadadacbdacbabbadccdbcccbbdccbaddaadcabcdabcbdbcddcdbbdaddadcabaaabbbbaabcdbdbdbaddbcbbdddacbcabaccbdbbccadbabbcabcdabbcbdcbabcbbacaabddbcbcbbbddccadcbcaabbbcbcdbcabccabcdcbcbcaaabcddabdcadcaabccdaddbabbbdaddbbdbcdbdcbcadbadbcacccdaabaacdacaacadaababccacdcbdbcbadccbabbabdbacaacdbabadabcadaaaccbaaaabbabbaacbbcbaaddbabbdadbacdbcadcbaddccddcddbdbcdbbdddabacdbbcbbddabdbbbbdcbdccdcadddbabddabdaacaabcdbccadaaabbdbbcdadbbaacccddbabdababddabcbcabdabcddcddbcaddcbacadacdcbdacbabbdcddbcbaaadcccddbdcbdbcdbaaddbcaabbccabdaadaccccabddddcacaadcdddabddcbccabdabcdddccbbbdbcadacadcbdadbaadbbadddaccacdbacbbabddccacddadddcabcbcdcbaabacbcdabbccbbcaccaacababccbadcbdcdbaddadabccaadbabbbabcbbcaadbbaadbccdcbdbbddcacaadbcaadccdadcacccaaadbcaaabdabdcadbdcbdadacbcdadbddbbbbbdddcbbcacabbcadbcbcdcdcabadddabbbbbccdccbacaddbaadbabccbacdadbdaaacdadbccdddbcaabccbadcdbdcabcabbdbddbabbcbbccacdbdcdcdabbacbadcadcdabbdcadcaaccbcadbaaccbaaacbcaadbbadcdcacbcbccbdbdaabadacbadacccbcbbcccdaabbadddbdabbaacddccdacdaaaddbcddaabddaccddcddcdcabcdaacbabdbcabcbabbaabddcdbdbbabaacbbbacdaddcddaaabbcaddadccaaabddcbdabccacbbacbcbabdacbdbcaddadacbbbcdbaadbbbbacbadacbbcbddbbcaddbcdcddcdcdbdbaacdcbddbadadabddaaddacddbbbccbdadaccbaabdcabcccccdacbabcdccbcdccdaddbabcccaacdbbbadbbadbbdadacadcbdbaacbaacdaaccbaacddddaaaaaccbadacccababcdcdcbbddcdaaccaadbddabbdbabcadaaaabbbbdccccdcdadcccacccacbccdbaadcbadcacccadccbacbbbaccbcddddccdcababbbbdcddbacdcbadcdacbcbbbadcdbddcbcacaabbbaddaddcbcdadbbadcadbdbaaacdbacdbdacbbbdcacbcddaabbbcaccadcacaccdacbbabddbaacbcbbccbbdccddcaacbaabcdbdabcddabdcadaaabbdcbddcddacbacaaaadacadbcdcacbccdcdadccdabacccdbccbbdbdcabdbaaaccaacacadbbdcbaacbdbcbdbbbbddabcdbcbcacadbdaccccbbccccdbabbcccddbbdbdcadaacdbcdaddbacaacccbccbcdcababbdcabbaaacbdadcbddcbccdbcccababacadadccabdbcdcdbcdcabdbdccabcbbcaddcccaddaadccadbbdadaabaddbddccacadcaccbcdaabbbdbbaccdcdbdcddbacdcaaabbdbaccdbaaabddcbbbadabbcdacbacdacadaabbaacdbbabcbbadabdadbbccdbbcdacdaacdacdbaacdabdaccacbcaadacdabaadaacadbbcddaadcabbaadabcadadcbddaadbcddacabdcaacdcbaabddcbcddddbcdadbbbcdabbabbdbdadacbbcadcdbccdbbdbcadaabcbdccddacccddaaccbabcabbcdcddcbcadbddcbdbbabdbddcaaaaddcacdadcbdddcbddabacbbaaaddadddddbaaadbcddbdaaddcabbcddcaddcaaaadbbaccabcdcccddbbcaaddabcacbdccbcbaccdabcdbdbcacadddadcbbabbaccccbcdbadbacbddbaccabcaccbbacacbdcddddadbabaadadcdbdcdbbbbaaabccababbabdbdaabbcbadaadadacdaabcccbadddcbbbdccabaacbcbbddbbdacdcccbcbaadbcbcabbbddbbaccbcadcdcaddbbabbddcaabdcccdabcdacdcbcdbdccdddbabdcaabbbacaaddcaddccbbdaaaabdaaacbdbddacccdacdabbdddcdbadcabdcbadadbbccbadaddabbbadbccababdadbcdccaabdbdaccbdcdabbbdaacbccdcbadbbadcadcbadadabbdbccbcbdcabbdbbbaccbcdacdccdbdcccddbbbdbabbacdcaddcaaaacbbddbaddcbaadbcaabcadbbbbbbcbcbbdbcaabdbabcdcbcccdcddccdabdcbcccbdbdcdcccbacddbbbbdcadbcbdadbadbaadbbadacddcbbacaaadadcbcdbbaaadbbcacddcdbcaacbbaddaabddaadddddadcbacdddbbbbcbbbccacbdcdacbbbacdcdacdaabcadcdacbacaaabcbdacccabbacadbbdbaacaddbbabdcacdbdddcbcadbacdadcdddddcdbadcdaddcdcbbddcddbcbdcdcacddacadbdbabcacdcdcdaabacacbdbacabcccdbaaadacbadadaaadcbbbcdbdadbccccbaadabbcbdaccacccbbbbabadddcbcdcbaabddcbcddbadcbcabbbabcbbcabbcccbccddadcbddabbadadabdacbcdbbdadbcdbdddaddcbbccdccadcaddbbaccbdcdbcbcddbccddcbcadccdcccbdbccabbdcaabbccaacccaccccdadbbccddabbbbbbbacddcbdcdcdaaaaddcccddbdaabbdabdadbbaaabddbdbdabcdbdadabdacdcbcbdbbdcbbadcabababbdcadabdbdbddabcccbbdacdddacdbabbaddcadacdbdbcacaadcbbacdaadbabcbbbcbccbacbdbdbabdaacadcdaaacdbbddaddbababbbddabcbccadbbabacadaaadddcaacabaaabbbbbdcabcaccacdccdcbdcaaddbdaaadabaaabcddacaacaccdabaadbcbcbabbccccabcaaaabbbaaccdcdbadbcbbcaadbacadcddabbaaaadddbbdbbbabcdaccdcbdcbcccdbcaccdcadbdbcdcabdddcbaacbcdabbadbdacabcbccdbadbcbddacadacaabdcacaccbdbcdbaacbdbccdabdcbbdccaabcccabbbaccbbcbdcdabccbadadbcbacaabddadacddabdbddddcadaacdbcbcabcbdcdaadcadbcdbbaabaabbcccadddbbddacbcadbacbcabdcdaccbabdabbbbadadbcbabcdccddddbdbbadcbcadcdbbddcdbbdabbcaaacaabcdabdbbddbbababcbbaaccbdbbdbcdccccbdadccbabcbaddcbbcddbcaaddbbbcbdcbacadddaccdaccaccabdadacdcaadddbdddcacbbaddadddacdabbcbbaaadcbdcccbaaaaabbbaddabbabadbbbcbcbccaccbbdcdaadaabbcdddadaaddabcbdbbbcbbccdadaacdcbbcbaddcdaccabcbabbbcdcabcbdbcababaaccabaacadaaadcdccbabcddaccbcccacadcaacbabcaccddbbcbcdaddcbddbaccdccdabdadcdbdbbaabdaacbadadcbcabdadbadcdaacabcddbbbbddcacddadcbbaaadcdbcabbabddcadabbbcbdcccbacccbcdbbbbbbddbabdccbadcadbaadcabaacdcabdabdbaababcdabcbaaaaaaaddddccdcccaddcdadcdccbdbbcccacabccaddcccadcbcdbbbdcbccdcbdcbcdcbbadabbdddcccbbddadbdbdcbccbcbadaadcdacddaabbbbcdccddccadbbbcbcadccbaaacbcdddcdaddcdaacbdbddabcdacccaacddadadcabbadccbcdcddbddbcddccdbbcdadadcdbaacdcbacdcccaabcdcbcbcbdbaaddadbddbadabccaadddbdcabddbcadccbdbcdbbdcbcbdddbdcdabccbccbbabbbbdcdcdaadabcaaababcabbcadddddbdbbabbcadbccccacbbbabbbccaddbbabababcaaabbbbaacbadacacabbaabbdbbcaddbabacbdcddbdbcbddaababbbbbaaddcdbbddbbabbdaacbaddcadabcdadacdbbabbaacabaadcbdacaaadadbddbcaaadddcdaacdbcbaabbbccbadacacbcabacabbcccabbacddabbabadcbdcccaabcdaaabaaaccbbaacbabcabdbbdccbcbadacdbbddccacccbbbacccbbdbcddddbcdcbcbcdabddbdcadadaaaccbdbadbbbaabcdddabcbddacababccdbdddacacbacbcdbdccbcaaccdadabdddcccdacabaabbdcbadabbdbbabbdcaddcccdaabcdcdbadbcbcdcdcdbcbdbbdbdbdbabddbadcabcdbbddbbbcabaaaccbadbaabadadcadadacadccacbbaadcaadabdcbdaacbdcdacbcccccccbbdcabbddaabcabbacaacccbaabddabbabbabdbcadbacabdaacdbbaadacccbcccbbdaabddadbcccdddcdabcccdbaabddccaccabdabcacbdccadadcadcbbcdacaadacacaddabcbbbdbcbbddaddccabcacbacacabdbcaabbcbabcdacbcdbdabcadaccbddcaddbbaccccbcbdcbbbcbddcaaacadacbddcccbdbccbadacacbabbbbcbbbbcbcadddadbbccabbddccadaccdbbaaddadaadcdcccddbddcddcdacbdbbaacdbadbaabdcadcacbdcadbddbacadbaadaccbddbdaaccdacdcdaccabaaaddcadabbbdbbacacbcdbbbcaabbbbdcaadbcbddddaddbacddccddabcbaadddaaccdcbcddddbdbbccacddadbbbcdbcbbbbaaacbddaddddbbdcacbabadddcdaadadddacdbabaccccbaabdaaccdacaddaddabbbacdaaacbbdbaadbacaaabcbdbabccaadabaddcbdadcaddabcadddbacaacdadcabaacdcdcadddabbdaadacabbbcdcdadbadababbcbabacadccbdbcddddbdbaabaccbbcddcbabbcdadababacccadcbaaacccdcbddabacccaddabadbcbdcdddcadbbdabcddbbaccabcbadbabaaadacbddbaadaaaacaadcccbcbbabacaadccdcbcabccabdaddcaabbcbdbbadcaadcdaccccddddcacdaddaacbababdcccbddbbacdcbaacdcbbbdcdadcdcdcbddbbcbadabaaabcadaaacbcabddccddcdaaacbcabadbadddbadddcdacbdabccdabbcacdacbbccbbaadababdaddabcabbcbbdabbcbabbcbdabcbddcaddacacdbcbddabacccddddbccdacdadaaadadadbabbababaddcdbbdbadddababdcbcacabbdbdccadcccbaadacbbdbbbaddbbdcabccdabcdcdbbbddbabcbbcbdadaabcdcaddabdbdaabbddbacdcdddbbbbdccdbbbacaaababdbddcdcadbccaccccbaabcbbcdabbbadbcabbadcaacbddccbcdcacdbacaacadcccdaddaddbcaacbbdbccdbcdaadcdadcbadabdcdaadabdddaabcdbbcbbbccddabbbcadabbddccbcabbbdbdbcadbabcbcbcccdcaaddddddccbdaccbcdcbcbdbbbbddddddccbcadbcabbacbddaccdcbbbdbbbcbbcbbdccddbbbbcbccdaddaccacdbcabddcbcdccaaaadccdddadbcdbababbbcbbaaaadddcadbdcbcbadbbdcbabdcacddcdacbcdbacdaaddcdbcdbbdaccbbdcdddbdacddcdccbacaccdbdcbbcbbbdcdccadbdccaacabacdddbaddadbbdcdaccbbabddbccbdcbccdbdbbcdabbabaadbddaccbacbbbaabaddbcabbacacddcddcabbdaacaaaccbccbdcbbabadcbaddbccacaaaccadcbabacccaabbbdcaccbddcacaddbdcadacdadccabbcbdbadcaadaacdbcbdbbbcaabbcacdaddcacaacaabbdaadcddbbcaacbbcdabddbacadddcbdabaaddbbcccabdaadacbbbbadcbaabbaabdbdccdcabcdadcccacbdbcdacadadbccbdbaddcaadbbcbcdcbcacdadccdabcdcccdcaccdcdcddbdcaaadcddcbcbcccdbbdaccdabccabbdccddaadcccbdabcbbbdaabaaadcccabdccdabcbbdcbbbbcaabcabcdadcdbbdbdbcbbbbdcaacdcdaddaacacaabbcaccaabdccacbddcbbaccbbddbaadabaadbabdcdabdacdbddacabcbbacccbddacbcbacaaadbaadbcdcdcaccccbccadddbbaccbbaacdddbcdccdabdbabdaaaabcaabbacbbcccbabbacdbabbcbcdaddaddcdbddccdddaabadbabdabcdcbacccbaaacbccddcdacccbdcccbccdbcdddcbaacbbdbccbaaabaababbcabacbbdbcbdbcbdadbdababdadbcdbbddccdadacaaddccaccabbaacbabcacbcacdaaaddbbcdddabadccdcadbcdadccbacbdbdbaccacdbcddabbbadaacbcbcbbbabccccdcdbbdcabdccccccdcdccbbbcdadbdcacbcbcdcbbdbabacaddbbababcaddadbabcbabcccabcbbdcccbcbddbbaabdabbccbcccadabaaddbaadbacabacadadabbddcdddcdcdacccbbdadbcbcddacdaacaacbaccdddabbdddbbabcdbadacbcbabbbdacdadbcdbbaadabbaaaaccdaacacdcaadcddccaabcbccdbcbddcabdbcdccabdccbbbcbbaacacddbdcdbdaccadbcacacaadcbbabcacaccacaddabddabddcabdaaabbccbdddacdabdddddccbbaaabdabdcdcddacacdbaaadaabaadcabcdcbbabaadbdcbaabadbccdadadcdbcadccaacddbabccabbacbbccddabdabaccdaccbabcdadbadcdcdcbacaaddcbcbdcccdaaacddcdbddadbadbcaadcdbbccacbdbdcdacabddbbbdacbcadccadccaababcbccdbcdabaaaacbccaccbddcbabbaabddcdbacddabbdabbadcdcddcadcbbadccadcdcbbcacbbcacbdbccabbbabbaaccdcdaacccadddbabcbadaccacbaadcaabbcadccadcaacaadbbadbacbaaaaddacddacdadbbacdacadaccdbdcbdaaddabcdcacbaabbbdaddaadabccaadcbdadaaabaddbaadbcdbcadbdcbcbadccddcbcdaabcddacbaadbbdaabacbcdacddcaccabbcdabdabaacaacbadbdcdbcdaadbbdcbdadcabadcdaaccbcbbdcabaadbbdacdcbcdddbccdabaacbacacadcbbbdcdabaadbbcbbdadbacccbadbbcdaaddcccdbdbddcccbbcdaccddadbdcadbbadaaccabcbdabbdabcadcccbacdcdaadbbdaccccadbdddcadcacacbbdcadddcddaaacdabbbadbbbbabadcdcbacaabdbdcbbccbacbdbdbadcbbaccddbacdcbabbcadbccabccdbadaddcdcbaaadbdddacbabcacabdcdbaccbcacbcdcbdbcbbbcddbdcdbbacacbbccccbaacdcbabcaddacbdbdcadacddbabbddccdabadbabccbbacdaabcaddcbbddabbdabdadbcbaccbacddbbabaadcacbabbcdcccbcadcabbbddbaaaccdccdbddaadacadbadcacbdddcbbcbbdcbbcbcaccbbddbcabbdabbbadbcbccdcdcdaaccdbcbbacbcbabcccbbbcbdddbcbcbadbbbabadcbcdbbcdbdaabdadcddcdcdabbdbcbccacdddabdacadbacaaabbdabcbadabcdbcddbaacabbccbaccbacbabddbddcbabdcdbaabbbcaacaaccaddbbdacdaabbddbacaadcacdabcbbcdbdbbcbbbdacbdadbbddcbaacbdccddcbdcbccbdcbdbcacccdbdcdacddabdaaaccbddcddcbadbadcdbdcdacacdaadcdbcbcdbadddadabaaacbaaadaababccbdccdadcccbddbcbabcaccbbbcadbdcccbbccacbbaddcaddaddaaaddabbdcccacadbbadcdaacddddaabbcaabccdcabcabddcbccddbdbadabbaddcbadacbccbbbbacdadabbdabcacbdacbccccacabcbcddadbcbabaaccbadbdbcccaabbbbadbddcdccbabbcdccbcbaccadadbabaaccbbccbcdadaaaaabbdbaddababaadaccbdbdbcaccbbdcaddadddbdadcbabcddbbadadbcbabdcbbdbdbadcdbdabbbbccbcdcdcdbadcbcccdaaaaacbddcccacadcadddbaabcacaddddcbcabbbddcdbbddbacadaddcabbcdcbdadacdcbaaadbbaacdddaacdbcaddaccadbdcabcdababdccdddaaaabdcacdbcdcbdaddadabccccdaadcbddbdcccaadabdaccaabbcacabacaaccdddddccaabacaadabadaaababccdbaadbdcdcacdddcdbadcadcbcdbcacabbdbdcabadbadabaadbbcabcbbbcbccbccdabaadccabddabdbcdbcdaddcbbcaadbbaaadababacdbdcaccddddbbabbbcdadadbdacadaacdbbbddbcaddddbbdbbabaaadcbbababdcbbbbcddbdbacdadbacabdcdbbacbcccacddcddcbabadcbcbddccccadcacccabdcbabbbabdaadadaccbbadddcaadccdbdcdbdbbbabcbdbbbbadabdbdbdaaddbcabdadaaabdbbdacddaccbabaaabddbbbbadbcabadaadaadcbbaadccdbbdbdbdbbadadbcdbbcacdabdbbbbcbadbdcabadddabbcddbacbbabdabacacadbcabdbcbaaaccccbdacdcbdcaaaaacbcddbbbbbdbbbadaabbdbbdccdcdcddccacbbdacdbdbdacdadbcbbbdbccbaacdcdadcdcaadddbcbacadbaaacaacabbbccbcdbdbaadabdccbdaaaccacbbacdbadabcaddaacbdabaaaababcbaabcbaacbcccaddabbaddddaaccbabbccbabbcadaaccabdacbdcdacabcbdcadaddabbbdcdadaccadbbcbbaaacadbdddcaaacadcddaaaccbaacdccccbcddaaaacbaacbaacdbccadacabbbcccdcaaccccbcbaacabbbcdccdbababcdadcddaacabdbacbcaabddbccbadcbabadcccbccdcdadcdabbccacbcccdbcbbcabbbbbdadacabcabbcbbcabbacacbdbdbddcaaccbadabdbdaaabdbdddbdddbcccbaadcbcbcdbcdcbdbacbbacadadbccdddcbadbaccbaccbcbabcbacabcaaaccdddbababbbacbcbdddbaadcbccbccdcbdaaaaaccbbbabcadaadbcdcadccbbcabadabddabccbadadcbddccbaaddddaaabbdacdaddacadabdbbacabccdbcbadbbbaabccaaaabdbdddaacbddcadcaabacdabaadcbabbbdaabdbdbbdddabcdbcdaaccbbcacacddcaaaabbaacacaaabcadbcbcdcbdbadbbdbcdaabaabbabadccbdddccacadaaadbbacaadddccbbccbabcdadcdcbcdcaaacabcbcacdcddbabdbaccbddaccccdcbdcdacaccdddacbcadaddcbbdccbaaccdccadaabbcdbdcbcbccbdaaaabcaabddbbabbabbbccabbdadacadccddadcbaacdbcdacadbbccdadacbabadaccdaadbaddbdbddcdacbcccddbdacdaabcbdbdbdccbcaabbcddadccbdbbcdaccccdccdbbabbdcdccdbadcaaadcabdaabdcccabdbdccaaacacbddbbadcdbbbaabacddadcababcbaccaccbcbcdacbdcabccabcbcccbcccbddbbbbcacbdbbaccbdcdaaabaaabdbcbddaccacddabddbbabbabacbddcbccabaddccabaaddaadcbcbadbcaabadabdabcacccabdddacccdbbaacccddccdcadccacbcbaaaaddcccdaaaacdbdbbcddacdcdbbccbbbbddcacbadbddddddbcabaacaddccdbccdbbbdcaadacaabcbdcabbbabbddaabcabbdcbadbcbadacadcbddadbcbbcccaacdbdadadacccabcdadbbaadbaabdbababbccaddbbbbdabcbccdacbcdbbbaaabdcdcbbaadabcbdbdadbcbdbbdbbcdaddddacaacdadcbdcaaadaabcdddadccacaacccccabcaaaddcdbaddbddcbbccdbcadadcaddcdccdccbaccbadddcabbdddccdddcdaadcddcddddcabcbadcdcaddcdcdcbbcdbacacdacbacbadaccbbccbcaabccdaabbbccddcaaaadcaadbdcadbbbbaddbdcccaddcbbcddadcdacbbbdbabdcabcddacdcaddadddbccbccbadcdadcabccaacdcdddbaacdcaddaadbdcaccabcaaaddbdadbbbcbbcdbaccacddbbdabdccbcdddddbcdccdacdcadabccbdbccbccaddccbcaabcaacacdddddabcbdaccbadddbccaccccdcddbbaddcdcdacdddcbabbccdabaccdcdcbacdaaccaccaabbbadabaadadcabacbcbbdcccadbaccadadaaddbcacbbbbaabadaadddbbddadbbddacbcbabacdabcdddcbddbabcabbcbcdabbdcacabbabacbacabccdddabdbdaadacacdccdbccddbdacbccbbabadacddabbdbdcaddbccaaccabcbbccdbacbcdddbdddcccbdabdcaacdbdacdcbaccbbabdcddaaacbcaddcddccacacadbdacbacbaabababcaabdbaccccababbaaaccadcacacdbdbbaaaadabbbcddddcdacaacacabadbdbbdbacabdababcbdabbbcbdddabdabbcddababbbbadddccccdddcadddbdcbbcbdaaaddaccaacdaddbdbcacabcbbadddcdbadabbaddacbbcaadabbcddbdccadacbbcdaaaabacddabcbacacdbccbcdbbcdcdadcbdbabbbbddccdcbabbabbccaaabcccbcdaacdaddbcbcacbbbdddcdbbbcdbdcdbcaccaabcbdcacabbadacbddbbcbbcadcddaadbbbabacccccbadcbbabdbdbbacdbcdbccaacabdddcadbbabdccdcdacdbadcdbacabbacababacbddbcacbbcccdabccbaadddacadbcdbcdddabaacacddbdbcbdabbdcabdbdaabadbcbaaadadabcdcaacaaaddbadcbaabbadbacaddabcacbcbdcaabbbcaabbdbaaddcbcddabaadcaaabbbbdcadcbaddabacbdbabdbdaaadbcdbddabccccddcdccbaadcaabbaccbddaabcbcdddacabaadddcaadabccdcbbaccdcbccdcdccbbdccbcaddddbdbbcbdbdcacddddaccaacdbdbdabcddaacadbcdbbadadabbdcbabccbdadacccbbddbaaddacdbcddbbbccbcbcbccadbbabcbbbadbcbabdbbbaadbddbbccdacccdbacbadcbdbbddaabbadccbbcdacdbabaadcaddcbbcbbadacacccbdaddbccbcdbbabbbddbabadccdcbaaddbabaabbdadaacbaddbaadcdabbdddabaaacbdabdbbadbbbdadbdacbbbacbbbdcbaaddccccdbaddbadbcabacdbaabcacaacdaaccdbdbadacaadccabcdcbabbabccddbcacbacbadbbbdabbdacbbdbdadaaabcdcdacaddacbbbdbdbdccadcbcadbbbdccdaddcadcdbadcddaaacbccabcabbbcbdcbbdbcbcabdcbabbccccbdbbdccddbddcbbcbcbabbcdcdaacdcbbaabdbcbcacbaaddcbabbadabcbacbabbacabbaddbcdccbcddcdbbabcdbadadacbcaadbabaacdabbbbaadacbcbbbdbcadcabddaabaaaaaacaddbaccbcdaacacbacbcbbccdacddacdcacbbdabdcbabcddcaccccdbaadcabcbaadccdbabdddcbbdbccaddcdbaccdbddbdbcbdcabbbccacbdcbbccaddadbddacbcdcdacaabddccbbadccadadcdacbcbaaadbaccddabbdbcbdbdcbabbdbaabdaaacacbdcaddcdcbcacddacdccabacdbaaaaccccdbcdbdccaaaddddaacbcdcaadbabacacccccbcbbcbaacaacdacdadadcbaacdcdcacdbacdabdabbaacdcdccccdddaddabbacbdcbbdcbdbbddabdbbadadaccbdbbddcdccbbcdcdbbccacdcdbcabdcdbadacdcccbcdcddcaccdcddcbdcbcbdbbccbdbbcccacaacbcabdbdbcbddaacbdccabbddcdccdbcbadbbdccdddbbabcbcadadcdcbbbcbddadbbacbdabbbbbcdbbbbbbadcbcbcacabcdbabbacbaacbbbbdbcbbcdacadadaaccadacacbdcbbabdbaadbcbdcdcaddbabbdcabdbadadadbcabddadcacbbaccbcdbccabcccadddccdbaabddcbdcbabdcbbcabbadadddadbcabdacaabbcbcbabbbddbabbdcdbdbcadccaccaacadcccabcbbabcbcccababaababcaddbbaabdbbccacbbddbdadabbdbccbbcbdabcabaaccabdcbadcbacbdacabacdaddbbbdddaddcdacacdddcccddccaccdaabccacbdcccaccadaaabcbcccacbacbbbdccbaaabbcbdbadcacdcbbacaacacbdddadaabadcddadccdbbbdbcababacddcddbbccbacddcadbcbbabadbdbdbdccccbddaccacddcadadacbddaaddcbacaaadbcdbaadaddbcaabdacbcddabdbdcdcdcccadacabaabbcbacbacaccabcbdcdccaaaacadabacdbdbccbdddbadcdadbccabaaacadddddaaaddcdacbbbdbdbdabbbbbdcaccdcdddccdbccdcbadbbcccdbbdbbdbacbdbaccddccbbabadacdabdabdadabdbaaacaccdacdbcdccbdcbcbacdbbbcacabcdcddbbddcdaabadadcaaddcddcccdcbdadbbadbdabacbddcaccacdaadadbaddddadbbccbddddbbdacabaacbbdbcbbadbbcbdaacaaacbbdbdbacaadbbdaccacbcccbcbadbccbacabddbdbbdadbcdadbcadabbbdddadddcbccacdaadadbcccdbdcacbaadcbdbbdcddccddbdbabcacccdcdbadddcbbbbaadcabbdcdbbdcdcdbbcbabddccaaabcdcaddbadbdcdddcbacccccabadacabbbacaacacddaaadbcabbcacdaababbadacbaddcbcaabcdbbdbaabddabdbdabdcdcdcdcbcccbbddacbdbdacbccdcbabcbbadadcdcbadbaccddbbdccaabdaabccccbadaaccabcbaaadddcabbcdabdbcacbbbccabaddbdbabbbacccbbdcbbccaddcbddacddcddcacdcbdcbcdccdccccbdccadbcbbbaadbccabdcbacaadacdcacadcdcddbdaaaccbccadcaadcbcabbbcbbbacdddcacdbaccadccadbdcdccbdbabbcbbbaabdaacaddbdaacddabdcadcaadcbacbcaadddbabaaddbcdcbbaadaaddaaacbacacacdccacccbbcacccadacdccccadabadbabddadbdadcbaaccadcaadbbddddcdaabdccdadbbcdaaccacbdbadbabcacabcaaabbbcddaddbdcabdcbaccdcdbbccddcdbdacbabaccddbabababdabadacbcdbbbbcdcbccaacabdcdcdccadbbbcbdaddcdcbccbbdbbdabdcaabbcaabbbcdababddaaadabcbdbbdacbcdbcbcabbcbcbbbccbdadbbcbacbdcadcdabbbbbddaccaaadacdcbcdaaabddccddcadcbaaccacaadbbcdbaadccbbbccaccdacdadcbdbbcdbdcbcbdcccaabadabcaccbabcadbacaccbbcbbbbdcadcacbdcbaabbddadcbbdacbdccacbcbaddcabbdcbdacadaddadbcabcdcdbcdbabbdccdddaaaddaadaccbbdbadddbacaaabacacabbabcaadbaabddcaadabacabadccdadcbacaddaddbddbccbdddbbdacabdccdcddbdadcdacddabdccbdddbdbacccbacdbaadcdacabbaabdbbaadcbbaadacdccacccdbcadcbcdbcddbbaaadcbbbcbadbcadddcbdbcdcdddcabcaaabadddbcccdcaaabcbdacccddcbadacdcbdcdabcbbbdddabaacbcbadcccddcaccabbdcbddcdaaaddadbadbbbadaabccddccdaacbadadbdbcdbadcacbabdbaaadbdbcabdcabbdaccacbbbdbbadbbdcdcbbdbcdcccddcdddabddaaacaadbcbbbaccdabccbadcdccaacababdbdbdaacaaababccbbdacbaccdbabcabadbdadbcdbbcacbbbaaadcbdcbadbcaacdabccdadddacdcbcdacaaacbbbadddccbcdcaacaaadcbdabccdababdbddacbbbcbaacbacbcddadaabdacddcbacaabbddbccabbaaabccbdbcbcdbcbbcabbdbcaccbdbccccabcddacdbccbbccdabccadaaccdcdacadbaddcddcbbdddacddccaadbacbabbdbbddabbcabaaadabadbbbaccdabbbcdaddbbccaabbcadaddccbabcddacaccaabdbdddbcdaccaaccacdbcdbaabaadcdcbdaabaadaabcdccddbcdbcbbbacdacaccbabddacbdddaabcdbddbcaaabacbacdbcbbcadbbccdcbcadccabbddddbadbddbdcccbdcaadcdbcadbcbaabdddbabcadbdbdbaaaabdcbcbbcaaadaaddacdbddadcaaadbbbdddaddccdcbbddacaadbccbbbadccdbcadcababdbcbbbabdddcbbbdabbabadacbdcccbdcbdccacbacaadbbccadbccaabdcaccaddbdabcadcdcabacbaddddacdcdabddcbbadccddcdcadccdbccbdaaaabcbabccabddacdacbdaabbabbcbbccaddbdcaddcbadbccbddbaaadddadacbbcbacadbbddcaaaabcaacaadbcacacbbddbcadcddadcbcbbcdaadbccaabdacbbbbcadcccdacddbaadaabcacbaadddcbabcdcbbccddaabdbcbabdbccddbccaddabdcbcacccdcbaaadddadcddaddddcaddaaccacdacbdcddddbdbdcdcbddadaccaccdaddbaddcaddbbdababdbcccaadadcacaaadabbcaacddcbcddadcdbacaabddaabcdcbcacddaaacdadbcbcdccdbbdbcbabbbaccdbddccccadcacdbbcdcbcabcacdddbcbddbdbcbadbadccbddcccbcacbaaddcbddbcdaddadbaccbdcddaaccddbdbcabaabddaacbdaddbcbadacaadabbdbbacdbcbdcbaccaaacbacdabbbcbddbdbacccbaadbbbdcccdcaadcabaacddadacbcabddaccddaacccdcbbbcaaaacccacdcbdddadaccddccadcbbaadbdbccddbaaaaaaddccaccbcaaadcbaabadabbaddbaccdaaddabdcddccbcbaabdcabcaddcbaaabdddddccabaaacddaaabcdadadcadccddaaadddacdcbbaddddacbbcdabdcbababbadccabdadaddccccadaaadabdccbcadbcbbdccdbbdbabbbcaddccacccabacccacaacaaabddaccdbcacdbddcdcbcaaccabaaabacccbcaaadbdaabcdddaadabcabadabdadbcdcbbddbcbddcbddbcacddababddddaacddabcbcdbdabacadcddaaadddadbcdadcdcdacdaccadbaccccbbcdbadbaaccbcccbccdbbaaacadcddbcacbcdccbdbbabbbabdaacdcddbbacdccddcbcbddddbddccbbddccadbccbddccdacbcbddbaabdcdbdddbdbabdabbccaddbdcacadddcbbcbcdccbcbcabcadaaabccaacbcdbaaaddaabcdbaaabcbacadcbdbddddbadbaddcdbdcadabcadbadbbcdbddcddcabadbadcdadabdcacccbaadbcabaacaacababbcdbdbabbbbaadcdcdddbdddadbaadaabdadcccdddaddababcabaaaaddcdadcadaaccdbcdbdcbdcbccaccbabbdccadbbcbacddabaadddcabacbabbcdacadadadcabbccddbacaccbcccccdabbbcacdbcbabbdacaabdbcabccdbabcccabdcadcacdbbbbddcbcbcbbbbadcdbbdccdcdaacabbcbdadcaccdcadbdbcdcdabbbadbcacbbbdddcacdacbcadaccadadddbbaaabaacbdcacadccccddcbcccddbddcadbdaccdcacdcbacadddbadbdbdbdcbcaabbabcdccacaabbacbbacbaadadbaccddcbdadadacbbbcdbdbcccaccbbcbabbcdbdbbcbcbcacabbcddcbcccdacabbbabbbdcacbabdcbdcaadcdbabdaabbaacabaacdcbbbadbdaaddbcaabccacddaacdadabbcaadaadcdaabcabbddabbadadddbbbccabcaaddcddddddcbaaabcadddbccadbcccddccccddcbcdacacadaaabcddcbdbaadcabcacbcaabccaaadbcacbacdcaaaaddcbbcccbcbccaaabaacbaccdbbacdacabcaadacdcadcaadbbadaabddbcdabbdbbddabbcbddbdacdbcbacabdbbbdcacbcddbdbdbcabdaabcdbbdabbddacdcbcddcdbbdbdbddadbdaddbdddacccdbbcddbbbdcdbbccdbcbbbcdcdbcacaaddadcabdcabaaaabcacccbccbdabbcdcccddbadcdbbcbbbbddcbbaacccccddbdcccdcbcbabdcdbdbdbcdbbcdadbaaaaccccadccdcdbabbcdbbaaddadccbdbdabddddcaadacddbdcbdbbbbcbaadbbddadbbdccdbadabadcaadbcabacbddcbbbabbbdbbcaccdbbcdbddbbccaadacbccccdcacdcbbcddbdacaacbbadabcbbadaccadadbbccacacaaddccbaaabcccabdbbddbbbcbbbcccdcaadadbacdccdcacdcbacabbbabbdddbadcbaaccabdcccdabddbbaabcaddcbcdaabbcaadcdacbccddcddbdcbdbccdccdbcbdadacdacadccddacaddcdcdbcddabdbdcdccbccbddaccdbcadbcdacaaabdcdbacdccbaaacadabddbdcbcbddbbbadcabacdccaaabbaabcccccbcacaaaabdaddbdddcabcdadcdbbaabdaabbbcacdadddbcdbabcacdabbddcaacadbabbccaadcaacdccabaccacbadccbdcaabbdcabbdbbabdccdaabccbdcdabbbdbdddbaddbaccacabddacaaddabaccaacdadccdbddabccdddcabbbaadcdaccaabadbddcbcdccabcaccabbabacadbacbbabcdbbdbcdcaadaaadddaacdaaaacdbcabccaddbaadaaaabdcacbcbabddaddcddbdccacbbabaacadbdabcacbddcadabcbbabbacadacddcacddcadacbcdccbdbbadbdadcbaaaaddddcdaddbcdddabcbbbaabdbbcbaacdacabcacbaadbbccddaaccaabccaaccdcbdabcbdccdabbcccddddaaadaddcbaccdacbdcdcbaacdddaabbbbdbbbbddcbadbdcacbbdbccbabbdbaaaaaccddcdcbabbdacaaabdbcddaaddbbbdbcadacddcbbbbddaccbdcaaaaaabbbdcaaccbbdadcadaaacbbdadcbacacdbcbaccccdbbdbabdacaaacaabdcaabbddcabbabcdcaccbbbdbcddccccdccacdcdadcadaacadcddcdaaadbbbaabddbcbcdaacddddcbabbacbaaccabbbbaaacbcaaaaaacbcdbaabdbdccdbcdcddcdabdaaacbcddbbbacbcaaaccddcaadbbdbabbaaadbcbcbbddaacadddcdcbbdadbbdadcddccdaccdacbddacddadbbbbabcababcdbdabdbcacddabcbcdbaaccdddacabbacdaaaadccccacddddbdbdbaaabccabbcaddaacbcbccbcdcaabddbadabbcbadabacdcddcdddbddaaaccbbaaccaaabccaddbbdbadddbbcddabddaabbdbcadcaabbdcbcdabbcbcacbcbbdbcbcccdaccbcabddccdbbdbcacaadadbdcbbccdcbcbaacaabdbbdcbcccbbcccbcacbdbcacacbbbbcdbabadaaddabddabbacdccdcabdcadabdccdaaddadcbddcddabddbcbccbcabccdbcdabdbbbaddabdbdccadbdcdacdacbadadcbcccaabccacdccdddadacdadcacbdcaaaabacdbabaadbacbdbadacbbaddababdcaaaccdaadcdcbaadacdbaabbbadaccdbcbadbbdbdbcaaaadbdddcdcadcbcdabdadcdbddccccbdadccccbcbabdddabccabcccdddaadccbaadcbabaabddcbaaaaaccdabbdbacdacabdcabdcbacbcbbbcabdbaadcbaadaaccaddcbabdddccabcddbdbdccabaaddaddaababddaabcbdacdbaabdadbdbcdddcaddabbddbccabacaddaabaabcdaacabcdadcaaccccddcbdbaacddcdbbdbdaddcabbbdcdcdbcccdaacadbcddabbdcbaabdabbbdddcadcbbadcdbcbaacabdadbbdddcdddadabdaabcbccddddcdccdbdadadbbdacbcdcaacacabacbadccaaacbcdcabddabcbddbdcadccaaaabadacbbcbaadbcacbcbdccbacdcdccbaacbbbdaaaacdddcdbbcacbbdacdddbbdddadadbcadbbaaadacccbdbacbcbdcbdaadcbddbcabcdcbcbbcdabdbdbdbdcabddbbabcbccbdcddcdaadcbcdaccdcadcadcdadacddddbdbbccabdbbdbdaabcabaaacdbabcbbaabbcbabdaaabcacabddbacadaccdbbadcbbcbdabdabcacdbdadacacbaaadacabdddbccdbababbcdbccabbbdbcdccddcabbdcdcaaacadbbcdacbadabcdcdccadadbcbaaaccaadddabadbacacdaabdcaccdcbdcacccdacdadaddbbcdcacbabbbcaaaaacbdbccdcacabccadbdbdcbddddcacdaaacaccbccdddddcacdcbbbcacdcdadadddccdbcccbbacaadddbabddcdddadcbdbdaacbadabacdcaccbddbdbcaabadcbdccbdaaacabdbdcaabcdabdcabcbbbabcadcddbdddbaddcadddbadadcadcdddbbbdcccababcccadcbddcdcbdcacddcbbddccbbddaaabdbdaaccbdadabbbbddcdbdbdcabbbaccdddbccdacccbcdbbcccdbabddcddbbbcdccddadacccddbbdabbbdcacdcbacbbdcbccacadbdcadbcbdaacbcdabbddccbacdbbacdbbcdaacbcddcbdcbbbdbcdccdbcaacabcbbcdbbbddcdbdbbddbcdcddadddccbddbabccabacbbcdcddddcdbdddacacddaabccaddbcdacdacbaadbddbcacaadabbcbacadadbccacbbacdabbacbdbabadbaabadbcbadacadbbddddbbbcadbbbccbdbdcdbadbacdbdddbbbdaccbddacadaaabadbdaddcbddbdbdacaabdccbaddbcbacabcddacbccadbaacccbadbbbadcadbdcaddcbadadcdbdaddaddacaaaaacacbabcadcbbabcabdabcaabbbdccbcdacaccdcdccbdcacdbbabaadbcdcbdabbdbbbbdcabddcdbbadbadcdabdcbbdacbaccaddddddbddaccacddcaabacbadcdababcbaaacacbcadaaccbcabdddacacdbdacbbdaddcbbbbadbbbaacaccabdaabdcabdccccbdcbadbcabaacadabcdccbbdbdbadcaddababadaabcdabbccbcbcbdadcacdbacdddbbcdadcccbabcddcdbacdaadadacccbaddbddbcaddabbaccbdbdadbacdbdddcbcacabbbcbbcdabacddacdacbacdccdcdbaccbcbcaabaaddabadaaacddabbabaddbabcdaadbbccdcdcbacbddcabdbbababaddbccbcaaddbddacdadddcbbdabaccdbcbccaaccbadaccbcabadababbdcdadbbacbcabbcbcccdcbdacddbcdbcbdbbddcdbdbccdadaabcdabdcbcdaaccbbdcddcdabbccbbbcaabdccdbcbdbccaaadaaaaaddbdcdcadbdadbdbbbbcbcbcdccaccbcdacbbdabadddcbcdbdaccbaabdcbcbcacdabdbbcbbdcbcacbcbbcdabadbcdbdaacacacdcbcbbcccdbcddccaccadddaaddcaaaaaccbccdaccbbcccabaadcccdaccdddacbaaacbdacaabbbbcbbaccabbdaaccbaabdbdacbbcdadcdacbbbbdbbbbdcdcdabaabdcbbbcaaddadaabddadaadccdabbcbbacbbbbacaaadbacadcadaccbccddaadbdacdabcbcccaccaabacadaacaaacadbbcdcdcabdccacbbabbcbaddbadcdcccaaacbbddcdbabcccbcdadcddccadbbddbbdbddcbbabccdcababbbadbcabaabddaccbbbbdadccccbaaacaaacaabcddcabcaadccdbbdddcbbacadcddbbdbcbacaacddbdbbccdbbcccdaadbbbdddcbddaddcbddcbcaccacdcbcbbdacbbbadaadbdbabcdcabacbdbdbacddcbabcddbaabbbcabaddcaccaccdddbcdbaccdcadaacabbcaabcbbdcadacdccaaadabacbadbaaccaadcdcccabaadcabdadcabcdabbadaccababaaddbabbccdabddbcbdacbacbdbddbcbdacaaacbbddbbcacdccdbacbcacadaddcdabccccdacacbcadcbadcbdddddcdaacacdadcabbaacddaaadcbbabdaabadbcbcbbabcdaacccaadbbbdbabbabacddccdccadbababcaddcdbbcadabcbdabccadcdcccababdbadcacddbaabdacbddaddbabccddaccacdccabcbbacdadaccdbcaddcccacbadcbbbcaaaacabdabbbbbadcabdcbbdcccdbacdcbaaadcdabbcbadccbadccadcacdcdbcbcbaabcaadbbcadbcacbbdaaaddbaabccbcdacddccbabdcbaccbcabcbcbacadcccdabccbacddcaaddbdcadbcaacdcbddbbabdbcdbaaacccacabcbccbdaadaccbabcbccabbdbdbbaaaadbccacaacbcdcdccdaddaaaacaddbdbdacbddddccbdcccdbdabbbccdcccaabbcccccbddabbbcbccdbcccbdbbdacaabcdcadbaacacdddadadccbbdbdaaaabbdbdbcdcbadcccddbccbbccdcddabacaadcbdaacccdccaaccadaddaadacaacdccaacbbdcbacbdbbbbdbcdbddbdacccddaaaabcdcdcaadadacdcdacdabdcccbbdabdaabbcccbbdbdccddbbbbcacaacabbcdccbddbccaddbcddbcbdbcccbadabadcdcbbccdbddbdabcdadbbddacacdcaccdbcccadddbadbccaaabbbdbccacabcadbccbabadadbadbcacacddddaaccccacacadcabbacbabbddcabadcdaddccaabdabbadbcdacbbabdbbdadcdacccdcbabbcdcaddbadbdccdcccadcabcabddaabddbddcbbbccadcaadacabcbcddaabaaacccbdccadbdcdcdadbcaccacabdcadadabcacabbaaadcccdccdabdccbbbdccbdcbccdbbbbdcccacbadcadcdbcacabdcaaadccabccdcdddabcaabadbdcbcdabcbddcdbadabadcccbccbccbbbddcccbcdccbcdaacaaacccaddbcbbdbadbaaaabdadbdbbdababccdacbcacadcdbcdbbccddabdddacacdacbbadaabdbbcbdcbbbbdbbbdbacbcadbbdcabccddccdaacbdcaddbdccadbaaabbbacaddcbacbbccdbbabbccccbcdbaadcdbaccdbbaabbcddadbddadcabdaadadccbcbcdcadadcaadbdcbababcbbccbddcaabdcbdcbabacacbbdbcdacaccacdbaabdbcbdbbddbadacdbbacabcbddabbcadabcbcbdcbbddcdddccbadcdcdabddcbcbcbcabbacccadcbadbbacbadadddbdbabcaababdddcadadbadccbbacdbbdabdcbbbcdadbaaaaaacaadbaccdddbcdddbdbdcbaddbcacdccacdaadbbabdabcadaabbbddcddbdbdbadcacdbabdddcaabadcdccdcdddccbbbdddaabaaaadacccadcbaabbdbadbacacdbccabcbaadaaccacdbbbbaaadabbcccaacbdbabdaaaabdcdddaabddbdbdcbabddbaaaddbdaaddbbcdbdbbccccddbcaccbcaaabdbdcccabbbabdcaabaacdbbacacbbcdbdaacaccccbaddaadabccbdbcdaabcadbdbcddcbcabdacdddbcacbccacbbdbbcbccccdcbddbaaabccbcdbaaadbbbbcbaacaaabbadabcccabccbcaabccbcbbacbcaccbdcdaadbcabddabadcddbcbaacbaaacaacaabadbabaaddbabaaccbcbbbdcdaaccccababddcadbdbdadbccbdadbccdadacaabccacacccbacaccdaaabcbbaababccbccbcabbabcdaabdddcdabcdabbbbddabdcddbcdadaaabadbcaadbbbdacddcaddddacddabddbccdcdbdaddacbbaccdacccdaabdbbabcdaaddabacdccdcaaccbdbbcbcdddccabbcddabdabcddddadbbdadccabdbdacbacccaacbdaaaadccaabdccbbbcdaddadbddaadbccdcddbcbadcdadcdbaddddcccccacaccabacdaaabcdababdacccbcbabcbaadaadaabbcdacbabbabdbacbaacccbaacccccccaadcbbbabbddcdacdcaacdcddaabbdacccdacaadbcdabbdacadadacbcadbddbdccbacbdaabadaabdcdbacdbcabddcdbdaaacbcbbaacbcdabdcddbddaaabbdcadcddacbdbbdcdbcddabdabadababbddabcdbcdcaacdcbdddbdabbdcdabcbbcdadcbaabdbabbadbabcbcdbbcadacbdaadddacaaababababaadaccabacadabdacccccbabdadcaddabcadabccddddcdaaddcdccdbaacddbcbadababddbdbcdaabdbdaccdbdccaaddbaadbaaadddabddcddaddacacacdacaacadbcacdbbabccbcdcabdcaadccabcbddacaacbacdabbddccdbcacbccccadbcdaaadddbadacaacbcdabaabbaadadacaadaddadbbddbadbbcdccaabdbbcbdbacaacdaacbadadaabcacccadbadccabaaaaabadbbbdccbddbabacadadbcaabcbbdcdaddaacbdccbabccbadbccacdcacaccacdbbcdcbdcacadccdddddcacaacbaddcbaadcaccaaabcaabaadbdccdcccaadadcaaccdbcccbbadacbdcdabbbadaababbdbcabcbabaddccccccddbbbdcacbaaadcdbabbdccabcdabccdcabdcabaadacbcaccaccbdcbcbcbdababcaddbbdabcccdaccabacbabdcbbbbcdaacbcaacbaddaccacbadccadacbaddaddcdabdaccccdcbbdaadadbaaddadcbacddabccddbcdbaadaacdaccbacbbccbcbaadbbcaccdaddbdabdabadbdbbdbcadbbadcbaaaaabbaaacabdbabbbbdaadabddacbddbccaaccdabbaadbcbdcbbccdbdddbbbdadddbccadbdddbcbbdbabcacbbdbdbbacbcddcdbaddbccacccddbaddcbccdaccdbdacadadacdaadbaacdbaddbcacaabcbbcdabaaddccbdbcbbbdcabddbcdcbddcdcbbccbddcbddabcbadbacacacddcbacbaccacdabdcbdadacddddbdcaccddccdcbcaabacbacbdadabcbcabddccacccadbdcabbdbbbdbdadaadacdcdbddcbdccdddbabbbabadabdcdadaacbaddbacbacabbabdcbccbddddbabcbccccadadaaccabdcbabcacaaabdadcbdcadadcabacacadbcbbdaaadbaadcdaccccabcdbdcbdaccabadcbaddcdacccbbdaaacabacddbcddddadccccdaacbcddccdcdcbcaadbddaaadbdcbbddbbdbbcdddabccbdcdadadcaabaaadcdaccadbbcabccbbbbadadacbbbabbaddbbacdbaaddcaacbccdacaadcbdadadcaabaddbdbacbcbcbddbaaaacbaccadcdddcacdcadbdaddaaacaaadcaabdccdcadcaccddcccabaccdadaacbbbcbdaadccdacbaaabccdaacbadbacaacbccbcacaddcdccccdaccbbcbababdccacabdbabddabccadbdaabcbdccabbacdcbbbddcddadcddbdcacdbdadddbcdcacbcbdccabddbacbcaaaacbaccabbbadbdbacbcabbaddacaccdbbcadadabdccdccddcdcbdddabbdacdcaabbdccdadbaaccbccbbbbbabacbcabadbcbdcaacadccadaacddcaaabbddcacbcdcadcbdaadaadacddccdbcdbbccacdbbabaadbbdbcaaaddddcadaadbccbdadcdacdbcaacacdbaabbcbdacbdbbbbaabbddbbacbdabbcaabccbdbcdcddcbaabddbacaabcbbabdcccbaadccacbacdbabcdadcbcaabbbabbbdbcbbdbcabbccdcabcbcdcabcddaacabcccbbcdbaaabcdcdbbcbbddcadbbcabcdabbcdcabaddcdabadcbdaddddcdbcacbbdcbbabcabbdcbcbdbddacdccbcadddadbaacadcbdbbccbbdacababdccdcbaaaccaadacddbbcbbaacbadbdddcadaadcacabdcacdbbcbdacababacbddcabcdbbacabbacdddadadbdbbbbadcdddcccbadaabdcadddddbddddbbdbbcbdabbabadcacadcbbabbaacacbacdbaabaccddadaabbadbacaabbbabdbccbdadbcaabcaababaddbdbbaccadabdbcbbabaaacccababbadbbbdbaaacddabaacaaadaddabdbcbdacbbdcdacbaabbcaccbadcbbcbbadddabdaddbbabdadbbbdaabcccdddcadcabbcccdddbddbacaadbcdcdadcbdbcdaccddcbdbbadabbaadbbadbdbddccbdaadcabcbadddbaadcadababbcadbadcdbcacaddbbbccccddcacbcbabdabbbaaccbbdabdddabadddbcacdbdbdddadadaddddbbaaacadcdadbbccbbdadcdbbdbbabcbbcbdcacabadacabdbdcbdbbbdaadbbdcdbddccddacbbddacabadaaababcbdaadbabbabbcadcaadadcccadbdabdbcbcadbbbcbdbcddcbaadcbddaccabdcacacaaabacabababadabbdbddbdcaaaccbadaddbdcdddcabcabbdaddcbcbbbcddddaddbbdccababdaddcbaaaddbdadcaabbabddabbcccabcababddaabacaaddccbbdbbcccbddcbabccdbcdadbaadbcaaaaddbdacccbcddcddbdbddaaaabbddccaacacbdadcdbcdbccabaabdaadddadaadcbcdcbddabbcaadcbbccbbacddcdbcbaccbacaacbcdbbaacbdddaaccaaddcdcdcdbacccdcaddcdadaaaaabcaaddaabdbdabcbccdaacdbbddbbbcbdbcdbcdcdcddbcadbdcdacbbadbddddcbaadbdbadcccbacbbbdbdddbdaabadabaadcdabdacaddbcaadcbbcaaadbaccbbbcdabbabadacacdbbaddbbacaabddcddbbbcdcdababdcadccbbadcbcbcacabdccccadcdbadbbbadabcbadcdcabdacddbdacbddccaddddaacbbcbacddddabcdbabdcaabaddbbccacbabbbdbaaadaabdcccccdbbbcbbcdbcdabddcaacbabadabddbcddbbddcbbaabddcaaccacdabdbbdacbcdccbcddadaadccddcadabcdbdcddccaabbabaacdaabaaddabcdbdbbcabbadbccdcbcbaccdddbccaccaacabbacdddaddcdabccacdcdcbcccbdcbaccdaacccacdcacdbbcadabbdcaacadacabdbbbcbdbbdbdacaccccdabddadaadccbdadbaabacacdbbbcababdccaacdbcaddcddbdbdacdbdcaacbabcacadbabbddcbcddabaaaaddaadadababcaaaaacbaabacacbdbaaddddccaaaabdbbaabddaaababbdddccbdddcddddddbbabccacccdcccdabbadbadcdccccdaaddacddadcbadbaccdaaacdacdbbbbcbaaaacbbdbbacbadddbdcbcddcdabccbbdcacadacaaabcdbdacdadbccadbabbacaddbbdddcbdabddbdcbaaadabcdaaacdaabcccacddcabcdbbaabadcadcbdcbcbcacacdbdcaaadaaabaccbcddbcbcdbaaabdcbdddabdcbaccbaacbbbaacddabbadaadbaddaacbdabddaaadcddbdcaadbbaaccacbcdbcdccdaabaaaaddacadadbdccdbbcbcabbcadcdaabdaccbbcddcabbbccccdbbdcbcdbadacdabdaaddabdcdccbadacbacabcddcdcdcbcdbacdcdacddcccacacdcbbbccbbbdbcbbabcbaabdaddaadaddbaabbbaabbddabaddacbccacbccadbdacbccdbaacdcbcabadcacbbbbdabacaababdbccabcaabbbbabcadddabbbcbabcdbbcbbbadcacacbdbaababacccaaabdbdbcbbbabbcdacbbaddddaaddacbadcadccbdbccaaadaacaadccbddbdcbcacbbdbcadbaabbddbbcbcdbaabddabdddadcbdbdaabbbbaaaddaaabcaccccdcaccaaaadacaaddbbdcabccaaabaccddcaabcccadadddabbbdddaabacadcaddabddcdccddaacbacdacccbdcbbabdcaadabcddbaadbdaababbccddcccddbaadaadcdbcbbbddaadbdcdccadccdaacdadbcdbacaaabbacbdbabaddcddabadbdbdcbaccadcbcccadaaaabdbabaabbbcabdadaaabbcbcadadbcbdabadcabcbccbaddddacaaaabcbbbddbabccddbddabadcadacccbcbcaacbbbaabdababaadbdcaaadbdcdadbcbddacdbacabbccbbadbaccbbbbcadccbddbacbbdbaccbdcbcadabcbcdccaadbbbabbdbdbdcccabccbcaabdcbabaadacaabaadcbbcbacaddadbddabcddcbbdcbdcbcdbabccddaccbcadbaccbbbbccbacaaabcdcddbaadbaaddcababcbaccdbaaabdabbdacaaacccccbaabdcaccbcaabdbbcaddabadcacdcbdcbcdbaaaccbccaabaddabaaabdcbcbbdbdbbddacdadcbaddabcddadbbcdbbdaaadbccaccbbdacbddaabdcbdbbdbdcbdadbaddddccbcabbdbdcdbbabcccbccabcbdcdbcaaaabacdbccddaadabbdbcbdcabaadddbabddbadacbaddbcaccddbdabdbbcbcdbabacdbaadcbcdcddbcdabdaaddddcdddbbdabacbcabcbadbabbdbbcddbcbdbdddbbcbacbccbdddcbbcddacdddbcadadcbbcccbadadbcaababdbacddabcbcbbcabdbdabccadcacdadbdcaadbcddddcaccdaaababaaadccbcdccaadbbddabdcccdabbbdcdcccddaaabddadcacabcddbdcaabddcbabdabdcccccbacabccddbccbdddbcccbddddcbccdcbccbcdacadaddccbdacdcadbcccaddacadaaddcbcdaddaaadcccaddbbdccdbcbdadabdddbcabacbcccddbdccaaaabcdbdbacadbcddbcbddbbbdbabcaabbdcbdcdddbcccccdbccaddbcdacadaaacdacadcddacbcdbacbcddaabdbbbccdaabacbabbccdcddacabddbcdcaccacbddacbabccbbbddcaadbaadddbbdcdcdccdcacbcdbcaaabaabbbdabcbdcaabcbbacbabbbcaddabddddbdacbaaaaadacdcaadcbadcadcdddcbbbbbcbdccabaddadaabacddacbccdbbcadcccbaddaabdbbcbbadcbdbabdcbaccadbcdaadabdbbaabddabddbcccddadcaddccacdddbaabaabdcadddcbcddaacabaabbadcbdbabaacbacacbdcacacdaabcbccbdbdbaadbaabbabbadaacbcbdbaacdcdbcabaadbdadccdcabbbcdabbcababacaccdccdabcbcbacddcadabadccbbdbdbddacababbbdadddabbacbaacdddabaabacadcaddccdcddcabaadadacbbadcdbbbbdabccbbcbdbdcaccbbabbcbadbddcdcacbadddcddaacbdcbaaaadcdbacbbcddcdcabbdaddaaabdcadbaacabdcaccccdabaacddccdbdcbdbbbaadcacdcabcdaccddcbabbdcdcabbbdadcaadccdccbacbdabcbaaadacdddbbabcbcaaacdaadbbcccdacababacbcbdcdbccddcabaadbdccddacaccadddcadcbaddbabbdcbddbcacbbabdadcaddcdccadacddacddaccacacbdccaaabacabcacadcbdddbddbbcdcbddcaabccdacbabadcbaabcbccaaccdbacddbbdbdbdaaabbcbabdbdabdaacdbcadcabacddacbbadcadadccabadbcadcbcbdbadbaccdbadbbbdbabcbbaccccdbcbcdccaaacdbbdabdaabaababacadadccbdcbbacbacacacdadcaaadadccabcacaacdaadcbbbccdaadccdbacaccdbadddcbbdacccbaacbacbdddccaadcbbacabbccabbaabacbbacccddccbaabdbabbbbdcdbccbdacabcdadbccaadcdaaaadbbcbdcadcdcccacdadcbcdbaccbcabbddcdbdcddbcdaddacbaccabdbacdcdcdcaadaacdacbadacccdbdbabacddbccdbabbcbbbddadacddddacddabbdadabccacadaabdcbbbacacbbbdaaaabddaacadbcdaabcadabdbbdadacddbdcacadabcbbacccbcddbacdaabacbddacbcdacabadacdccccacbaaacbbaadacaaaccbcabbdbadddcaaaccbcacdcaaacdcdcbcdbbcddbbcbacdaaababdabbcddcbcaadabbcbbccbacbcbddbddbddacdcadbcbdbbdbcdcccaccbacacdadcddadabadbbbadaadcaccaabbccdaacbcdccdcdcdacdbbbbbdadacadddacdbabbcdbcdbaadacdcaccadddcadbdbaabbdabbddadabbacdacdabdadaccacdbaddbcbadddadbcdabbdcbbbdddcdbcdcbbabbcbabccddbbdadbadcbcadcbbaaaddddbcdbbcdbcacaccbdcbddbacadaadcacacbbcabdbdbcadddccbadcbacadcdddcdbdcddcbcabccdbcccbdaacddcbccdaaaaadaabcdcaadabccaaddcbabbccbbadccaddcbccdbcaaddbdacadbabbbcbaadcccadcdbacbbbcccddaadaabadbcddcbaaacbddcacbdadcacbabcbcdaddbdadadbaacbdbacddcbdbcbcadcdaaadccbadcccdcdacbdbbcbdccddabbddcdbbbccabaadcacbbddbcdacdbababdaccbccdbaccdcbcbdbacdbbdcabdaaddaabbadbcbacdccbcbccabbccbcacdcabbcbadcccaacccdcdaaccbccbdbaabbbabbdaadaadaadcdbdbaabddcbcbcaddbaabdddacbacddabbddadddcadbabcbbdddbdaaacdadcdadddbcccacaddabbbbdcaabcdbdacccccdacdadcdcabacccacadaabbbdbabadcaccdbacbbbaddcbdcbdcadccccbadccaccbabaccdcccaccdaadddccdbbabcbccbbabaaaacbaaddabdadabcaadbdbddaccaadbdccbcaccacbdcacaacccbbbcddacddbbdbdbacdbcacaaadccbcacbcaadbbaccddddaccacdbdccbcadbaadcabbcccdadacdaccccbcccdabdcaddabadcdaddcdbaaddaccdcbbbababbcbdabacdabababcddcdcadbddcbcdcddabbbcaaddbdaabbadcbbbadcbbbbdcccbababddbdbcbddbdabbbaabccbadbdcbcabdbdccabbbddbadbbdaadabaccdabdaaadbbadcbadbddaacaacbbbbadbdbbcbbdbaacbaccaaabdbcbaacdbdbcdaccacaddddbcabbccadddaadbbaccadcbdabdaddaacbccdbadccbbaaddcdacbdabbdabacbdbadabaabddcaaddabbaabcaaddcbddbccaccbacbabbdbadddaccacdaabbccdccbbdcbcbccaccaccbdcdbbcbdccabbdbdcaabcccbadadaccadbbdcddacbababbdabcdccbccacdbcaabaaccabaccccbbacadbacadaddcacbccdccdbaaccaddcacbbdbbaacdcacacbbaadbdbccacabadbccbbdcabccaabcddbbaacbacabccccdccbbcbcaddaddaabbddcbcabdbacabdccbddabadbaabdcdcacbaabadadbdabdcabdacdaaaaccbabdbaadddddcadaacacaddaabbadccbcabbbabaccbaddbabcdcccbdddccccbbccbdcbbdababdcdcbcabacbcabacbbaadbcbdadbdaabbbbbaacabbcbbddbddabbdadbabccbbacbdbddbabdcaccbdabddaabacbdaaaaadcdcccdaadabadbcdccadbaaacddacdadcbdbabcabbddbcbcbabccdbbcdbbbcabaddbdbbdaaaccdaddabbcdbadcadaccaaabdcddbbbdaabbbdbdbbddacbbadcccaabaddabcdbddbdddccbaabccccabcddababcbdbdacacbdcbaaadcacccdddbcaaaababddacacdacdcdaddcbdcadacbcbddccdbdadbbdadbacddccbcbadaadddcbbbdbadbccabadacadacacdcdcaaccbabadbcdabbcddcbadabcdddcbdadadccdbabaaaabddbdcacadbdcbcbaadcdbbaabcdcccdacbbaaababdbcddcbbdcbbcabdaaaadadbcaaaabbcadabbbcbdbdcdcaaddbcadabbbdbbbddbcbacbbcddddcbadacacbcddbccbcbdccdbdbddaabaadbabadadbbbccccaccbbcbcdcbccadaddbbadadabbaaadacdcacaccdabdbbddddbdaccdbadcbaaadcbdcdabbdaddcbdbbcaadadadbacbbbcbdcddcbddaccdbdaccddddabcccdaaaabdcbaadbadcccaabadcaababdacdbddacbbcbccbdbcdababddadbdbdbddaabbbdaadbccbbdbddaacbacbbbccdaacbccacbcdbcbbccbcaabbdabbbacddddbddcbaabddaddddaacaacadddbdabdddaaddccadbcabddccbbdcbdccaabbdbccddbbabccdbaccdacdadcbcdccbccbcbabbcbdbaabccbaccabccaaaccdaabcdadddbbacaaccbbcbabbdcdadccabbbcaddbacbbdbcccbdbbaaaadccbdbacadcbdbddadbcbcbcadccadbaaaaaababcddbbbdabccbdabdbadaadbbacacbbcbbadcddbcadacabaccacbbcbaabdcdcbccdbcbdddbbbbadcdaddcaabbcaddcbbbccadddacbbdcadadddcadadddbdcbbbbabdbdcaabaaddabdaacadddddbabdacbcccdbcabcacddbadbdbadaadccaabddbbbbdbdbcdddbcbacdabbdddbcbcdabcdadccbababbddcddbabbabcbcabcdbdccdcaadbbcdabacdcbcdacacdcbabbdcbccadadacabdbcbcdabcccaaabadabbccbcccdacabaaacbbbbcadcabdabcbccbaaadbbcdddbccdbaccbdcbaddccbadbdbadabccdcdcbaabbaccadaccdcdcadaccbabaddbbadabaacbadcbdbdaabbddddadcaacdabdbccbbcabdcdaacdaaaccdaccdabccdaabbcaabcddbcaacdcabdbbdbbaaccdcadcdcddbbdcddbbccacbaaadcaabbbcdacabbccaaaabacdadaddccdcdcbcddddcaadbcdacccdccddddcdcababbcaddbdaccbcacaddddabccadbddcabadbdddccdcdddaadacdaddcbbbcaaccacbdbcdcadaabcbcadcadbacadabddaacdaacacdabbcaadabacbadccabdddcbdacccacbcbadbcdadbbbddacccaddcdadaddcddbbbaabbdcbbcaddbccbbdcdacaacacadacdbddbbabadcbdacaaaddddcbccacbbbcbadabdaabaaadcaccadbdbdadaabadbccccacbbbcdbcbdacddbbcabdaccadccbaacddcbccadbdaabdcdbcccaacdcbdbbcbcbabccacccbddcaaabbaacacccbcaabdbbcadadaadbadccaadbbadcdaadbabbddcaabdaadcaddcbdbbacddbdcdaadddcbaddcdcadbdbdcdcbbbcaadbbddbdddbbdcdcbcbcadacbdbcaddcbddbbcdacaccacdbbdbbbaadbbdbbdcccdddccadcaddddcacdddbabcbdcccccbdaccdaabbccbbbdbacbcccbdcbabddadcdadcdcabcacdbbaddabdddabdadbacdcaabbaccbaddabcbbdcdcddabdbbacbbddbcbdabdbdbcdcdbcdbdcddababbddabadbbcdbccdaddcbbbdcdcbccdbdbdbdaccaaabdbcacaabbacdbdbbbbdacccbccbcdabacadaaaadacccbaddbcbaddacdcdcbabdbccccdcbdcacdabbcddabaccdbcdacdaabbcddabdbbaabdcbcabcbcccadadbcdcaacdbabbdadaadadcacbacbababadaabbbcddabaccaadddaacdbbbdbacaacbbaccddddaacbbcacacbccabcabacddbcbacabbabaacadadbcabadbdbccbbcbdbddcdaccaaabbaccaaabbadaabbbcacdcacabcbaddccbcbbbaadddddaaacbbacadccacababccdadabdaacdbacbccbacacbadbdcaaacdddddbdacdbcdddcdcbbcbadbcbddcabbaaaccbcdcadddabacbcadccbdaaddadacdcadbbdcbabcaaaccaadaabdcdabcbddacdcbddcdddbcdbcdcbcbaacbcadcdbbadcbcdcabdbcaabacdcbdddbdadcdaaabbccdbddbdcacddbabbbacdabcbccbbdbacbbcbccbcbcadbbdbbcdbcccccbdaaadcbcdbacbddbacbadbddbcbdaaadccccbacababcbdbbdbbabdadcbdcadacbcccbccccaaabbdcbbdbacdcabbaabadabacbaacabdcddcdaacbdccbccbddcdbadadccacddbcbcaacbddcdddccdbcdcacccbdaaadcbdaddccdbcddbbabdddcbdbdabadcddcccddaabdcabadccdbdabacbadbbdacabcadcdddaabdbbaabadaadbdbacaabdcabaccabbbabdbdaabbddadcabbadbdbbddadbcacadbaaddaaaddbccababcbcdbcdbddadcadacddbadbdaabaabccdddaddacaacbaadddcaabcbbdbddcccbbccdaabcbbaccbaabbcabdcddcacdbccbadbcaabddbbabcadbddaaddadbabacdccabadccdabdbaabbdcdbcadaadcdaaabcddbcbdaabcbcdbaaaddbcbbcadaaabcbdacbbdaddbcdabddaaddcbccbcdcdabdbbcbcaacaabcaaccccdbbaaacaacbaacaacbcdaccbaaddbbcdaaadcbababadcdbabadcbcbdaddabadcccacbabcccabadadabcbdbbdabdbacdbaaccacbddddabcbdbbdadaaadcdaaddabdcdacdaabadccdbcccbdcbabaaabdcaccbcccacbacdddbcddbaaacdabccbbbbdcccdcaadababcdcabbbdcbdaacadbcbacbbacbcccbbbddbacaabddadaabbaabcccacbcaabdddcbbbdcabbbbaddaaacbbaacdcddcabbbcccbaaabbdcabbdbdbadccddadccdcdbdcbadabccaaabcbaccbcdacdabdbdbdcbbcccbbdbccbabacbbcdddbcbcaadddbaabbddcbaddbbbbdbdbddbacccabadbdbbddbadbbccdbacbbacccbbbcbdaabadbbbabcdcdabdccbddbddbcbcaaadabccbbbcddcdcadaabdcccbccaacbbbdbadacdadabbcbcccdaaddddcdcddbaabcaaadbbcadbbcadaccbdbabccdaadcdbccbabdcdddcaaabdbdaabbbabbccccdbbacbaddbdaacbdcccdcbacaaadcdadaccabdacbbadadcbdaacbabbcbccbacddabdabbcdcddaaadddbddbabcddadbcacabaccdccdcbabddbbdacbabdcabccadbbcbcadcbdbbddcdacbcbccdbcdddacabddaadcdcaccabaadcadcabcbdcadadaadbbcbabddabddbdbbcdcaabddaaadbbdabadadaaaccaaacbbaccdbdcdaddccbadbabbdbdcbbdbbdbcabcacacbdddabbcbbdccaadccabddadaaccdabccabadabaadbbdaacbacdbdccabccddcbdbdccbddbacccbabbacaacacdcdcaabbaacdddcaaabddcbcdaddaabdaadbcabacddcbbcddaadbcaccaaccdabcaacdaccbaccdcdabacabbcdacddabdbccaaabccabbcadcacaacccabcdbdbabcdbcacaaaabdbcbbacdbcddbccbabcbbadbdadbcadccdddccabcdadaabcdcbcaddbbaccccaaddadaaddcaadaccddccbbabdadcaacadddbdccdbcaccaabcccccdcdbdbbdcdabbaacddcacbbcdbbaadabcbabdaabdcbacacbabccdcbbcdbcacbcdcaacccadacbacbbdcbcddbcbcabacdcabccacbdbacbbccdbddaaadbabbbaaaaacadbabbdcdbdbbcbaaabbbdbcacadaadcaaadddbcdaacdbcadcbaddbdaccbabcbbcdacbdadcbaacdabbcdacbcaacdadbbcabbaaacaddcccadcddbbdbdbdcacaadaacdcdcaabcabddcbddcacccddbbdaddbcbaacdbbadcccacaccbadbcbdabbcaddabacbdbbabddddbaacccdcaaadcdbaacabcbacccccabbcccacbcbbaacbbaabaccdccddddcccbdbdbacbcdbcaabbcbdcdcdbadaccbadbcbacabcbaaabcdcdbdbbdbdbdddbdcdaddccdbbdbdbdcaabcdddbccbacdbacaaacddbddabdcbadaddacacaacadabcbdccddbaddaddcbcddaaccdcbaaaabcddabddbdddcdaccddddabbccdbbaacccbabccccaadbdacaacbbddcdcaccdaadbcdababdaccbbdacbbbcbdaabaadcacdcaacdcaccabbacbbcbaddadcbaadcaaccccbadbbbadababbcccadabcaacbdbbbcbdadabcacdbddbaadbaadbccbbbdaccbdabcabbdabccacbcabccdbacbdadddcbdabaacbbddbbaadabadccdccaabacbdadbbdcdaadbcacbdbdcbbaaabdbcbddbccdbcacbdaaaddabcaacbdabcabcccdcdbbbaacbabacdabdddcaabdcddabdaadbcbacabccacbaaddaddbadcdcaccddbcdbabdabcabbbcbcdaababadacadcbcbbadcbdaccaadaabdcbddcaccbbcbaccbadcccbddacdcdbdcaaabbcabdcabbcdbbdabdadbdabbaaaacaaababdbcabcccccbbbbdabddccdadcbbdadacadabacbddbadabccabbdaccbcbcbcabbbbcdabdbacbdbbacbcacbcaccdcaadcbcbdcabbdddbccdacddbacaccddabcaadcdcabaababddcbadbbbccbcabbcdcbbbadcbacaabcbbbcbcabadbdddcbacddaaddadddaadabcdcaaccaabccdacaacbbcaacdcbbbbaccbaddcdabadcababbbdaacabbdbdaacdadcdacbdadaddadcabccabbcbddaacdcbbcbadcdcbbabaaaabacaccaacddbbccaddabbdadccacabdcdddcbadbcdbababaaabdcbbddcaababdabbdabaabacbbdaadbbadbacaacbcacdbdcbdcdadaddaddcddcdcccddddcadbaaacabbbaddaacdcdcbdcbdddddcdaabacdadcdaadcbadbbdadcaadbaaabddddcacbcabcdbbdaaabdbbacbcbccaacdaadddbbdaabadcddbccdddacdcddbaacbcbdaaaaadbcbbccbaadabbcbcddccbbabbadbcabaddacdddddaabcbabcddbbcabbdacbccadccadbacccdbccddcaaabbdcdbdbdcaaacacbdadbadabbccaaacacabdbdcbdcbababdadadadbadacaaccdccddabcbbdbdaacbadccaacdcacbcbbaacadcadbcbcddadaabbcbacacbbccaddaacadadadabdcacbadacbcadbaabdabbcbdaabaccbbabbbdbbddcabcaaaacaacccbbccadcbbadbaddcacdabbdaaabcdabbcdacdcddcbdbbacadaaaccdddddaadadddcbcacdbbbdcaabcaaddbccbadacddadbbdbaacadccadaacadacbbcabccdbdaadaabbbcabaadbabbbbdadadbdadccdabcdaccacddcbcabbbabcdabcbbddcccabbcbcaacacdcdaacbacbbbcdaccdbcbbbcbbdbbacaadacbbbacdbbabaccbdabbbdacbadcacdccacacdbcdccdcdbcdddaabbdddbcbcdcbadcdccdabcbdbccdbbaaacbbabddacbdcabbbccaaabdbcbcaadabcbaccbcaadbbccdbcddabacdabbabcbbbacadabcaacabcaddbcbbbbaaaacadabcbabaddadadcdddaddccdddaddcdaabbaabbbadaadacbacaabacdabdabdabbcacacaadcdbcdcddadbcdbbacbaabbdbbaabbdbdaccbbcdbaabbcbbcbcbbbcdcabadbbbaadabdcdcaadadacaadcacdadbcbcdaacddbabcabcbcdccdccdccadaccdbdacbaaacdddabbacbdcacaccbcbabbabbdcaccdddddbcabdcddcacbaccbdbdcbdacdbaaccbddddddcdcadbbabacbddaaadbbddbcddddacadcccccbcdddaccbdcccdbaddababcddddaaaaadcaaabbcddcdccbacadadabcdcccccdcbaaaaccbccbabdcccddacbdbbacbbababdaddbbcbbacdbbacddacabbadbcababdcbcaacccdbddbabcacdbabacbaaadaaddcdcbabddaaacbccaadcaadbcbdddbbdaacadbddbacacdddbbcaacdbccdbdcadddbcbcbaddbccddbbadacbbadcdcdcbdacddabcdddcdccbdcbddccabddcbbcbdbddbcabccbbbaaacdabdcadccaccdccbcdcacdccabbbacdccddababcccdbccadaabdcbbaddddaaacdcababbbbadcbdcbadabddcdbcaaccbcbdaaacaacbbcaacacaacdcacddcacbcdadabdacbadabcbcccdbbabdaabdccbcaaacadaadabacdacbbbcbbdabbabbdadaccdaccaaaadadacaaabcccdbadcbccdcdbbdaaddbaccabcbbbadccabdcdbdbcaacbdbccdacaddadcaaaddbbbabadcabcaacababdacbabbccbacacdcbadabcaaacdccaaccacccbcdbcacdaddcabcababcdcbcddccbccaabccbbbbadccbbdacbacdaddbdacbaadabcddacdabaabcacacbabdababddbadbcdbcdddabacbaadbcdadaaaabcbadddcdbdacbdddcddbbcbabddcdbabbadcbbdadbbbccdcbdbbbbcdcdcacccdacaacbdaccaacbdddadadaddabdbadabcdcaadbacbcabbbbcababacadaabbddcaabacccaccabddcacdaadbddabcddaabacabdbaaabbadcbcbadbddabadddcdbccdbaddabaaddcbbdbcbdcdddcaadbdbbacabcbdddaccbbbdcbcacdddcacdaaacddccdcbcddabaacacbccadacbdccccdcbbdddddbdaaacaccdcdabdaabadbbcaacddbacdabbdadadacabbddbbcbbcddcabdaacdcdbbbddadddcadaaabacbcdbccabdacaaacddbddbdcadbadcaccdddbbbcbaaabddcccdbaadbdcbbacdacbabacbcbdbdbcbdbdcdcaacdbbdccadbcdcdbdbdacadaccdcccacaacdbadcddbcbdabcbdddcabbdabdbbadadbbbcdcbdbaaabbcddddddaabbacacddccbacbdcadbdcaaacbaddacdadbcadccdcdcdbdcccdaccadccbbacdabbadabbddbddbbbcdbccddadabadadcddaadcabdbbacddabcdadddbbccddbaccadaaaacadbadbddacdddbadadadccccaacccccbadcbdccadcddaacccbbacccbcdababcdacdbabacdbadcbbdcaabacbabcaaabbcadaccdbddddbdcdacadabbcdbdbaadccaabbaaddabaabcacdbccccdaaddcabbddbdaadcbdcacdbbcddcadbaacadacabbcccbaabbddcddbadbbbadbdcacddcdcabbcbdccccacacdabdbbabadadaaccaccbadcccbcddddabdadddddbcccaaccbdbcadabbdadcbadbcaacadadddbddacbbabadacabaaabadadcbaddcaaaabadcdcaaadccdabdabacaddcbadcdddbdbbdccdadccccddbbcbccdbadbadcdddbdbbbbdddcdbaadbabbdacbbcbbbabcdadcaaadaaacbcabbacdccddaccaccbaadabdaccbddadcdacbbdccacdaadbbdacddbbabcbadbbbacddccbdbbabbadbdaabadccabcaaacdaddaabcbbaabdbabdcdabbbcbbcaabcddbdabdccababbcbabcbcddddbdbccadbbcadacdaccbcadabdbdcaaadbddbaaacaabcaacbadddabccbdccdcacbabddcdaacbbabbcaacbcccbabcbdcdaccacdccaabbbbabdbaddcccaabaacbbdcbcdcabcddbbaacbdabcbdbdadcdcdacdacdbaaadabadcbbabdbdbcbbdbabccddbdcdbaaccbcbdccaabccdbcdadbcbdbdcbbdbdabcdcbccdcbbdbcabbadaadcbaccbbabbbcccbadbbbdcccacaadbdcccbbdacaadbbaabacdcaabbbcdbadcbdbaacaddbaddcbbbabaabaaaacbadaaccdaccdbbbbcccbbddddadaadcbcabadbcbcddaabdbaddabcadcbddbbadcadbdcdcaaddbaaababadacadcdaaadaddabadbdbaccccdbdabdaadbddddcdabacaddaaaacccdbbbbcbdbbdaabdccccdddcacdddbccdacdccddddcdaccbbcddcadddbcddacaaacdadbcdbaddcccaddccbcbbccdbabbcdbbddbccdbdbbaaadcdbbbcacacbdacbaacbccbbacbcacaaccddadabdcccabdabbbbbcccbcccbabadbdadcadacbbcdaacdbbcdadcbccdabddbbcbcdcaaabaacdadadabbbbdbdabcacabbadbcaadaaccbcdbbcbabcbacbbcdbccadbbbccdccdcdcbccadadaccccbcddadcbddcbaaccccdacbbccbaacabdabcaddbdcddaacdbccbaabccbccbdbbbccbabdadcaaadaccaddcdcdcbcbbdbcbbcbddbbccdbababcbbbcbcccdcdbcaabbadadabcbabcadccbbcacacbbacbdbcdbabbcabdabddbabcaddbbcddcccccddbabaaccaaccaacbadcdbdcddddaabbcaabccdbddabdcbccbdacdccaacabaddccdabccbbbbdcbbdddddaaccbabdddbdbcbdcddcbcdbbabcabccadaddbcbcbbbacaaadddcadbaacbdbadbaddddcdcccbbaccbdbaabcaaabcccdaacbadcdacbcbadabdacbadbdbdadbccacccdabcbdccacbccdcaadcbbbacadadabcdbdbbdcaccbbcbbbbbaacdacdcabdbbcdbacdcbbdccaacabcbadaccddbdddbdcabbadbabdddacdccddcdbdbabcbaccbabacbadadaaddabbbcacbacdcbdacddcdadadabdacbadaccadccbcccdcdbcddaaabcdbddcdcaabacabadcadbbccddbdcdabdbdcbbccabcadabccabaabacccdaadaaacbdacdabbbadbbdbddcdcbcbdaabbaccbbdacbbabbcdcaadabcccbcddbcdcacdbabcccbbccadbdaabdadaaaabcbdbacddbbaacabbbdccbbbcadcdcbdccbdaaadbcbcbaddbdcdcccadcdbbbcdadcdcbddddaddcddccdaddcacdbdbbcbcdcbaddadbcdababaadccbadbbccbbbcaccaddbcdacdccdbdbabadbbdbccdddcacabddabbacadaaaadaabaaccdcaaddcaccacdabcbbbddadddbaadcdddddddaacdbaddaacdbcabcbbbdbadddcccacccdadabccdaadaddccdcbcddacabbccadcacbcccccacbcbbdccaadbaadaaddaaaaabbcbbbabbdcacabbdabaccacddbbccabdcadcbbbbaccbddadbcccbdcaccccbdbcabdcdbbaaabdbbaadccdcddcbcaadbbccbcccccdbbdacaaaadddabcdabbdadcbaccbbddccbddccacbbdacaabccbccbdbddabbadbcccccbddadaacbcbbcbccadddacbabdbbddcccdbbcbaaddddbdbbcaabadbaacddcdaddacbdcccddaaccdacdadcacddbdabbcdaacdaccbabddacdcccbdabbbdadadcdcbacacbbbdcaadcacbbbbbcaacdbadaadaddbdcccbbcbaaddbaadddcabdbabbcdccdbacabccddcbaddddbccadaadabccdcccacababcbcbdcdcdccbbdaccbddcddbdbdcddaaadabbcabcdbccccadacdccdaaaaddbaaaadddddcaababaacbcacbbcaddbccacccbcaadaccbaabcddacacbdcacbdcbbcdcdaaccddacddbbdadbdcaccdddcdaccbcabbccaadbdcadbccaabcccacbbbccbdabcccaaaacdcbaddddaacacbbabbdbaadbcdabbcccadbaabcddacbcddcadbcabadaadcdabdddcdaaadbbbdcdcbaccdcbccdcdbcaadbbcbdddbaadcbadbbdbabaddcdcdddcaadcbbccaaddaaacccbddabdccaadabcdcbdcddacabadcbcacbdbaaacdacbcadcccbdccbbcdadbdacddccadadbbbbbbcdbcdaaddbcbaabdbdaaccbacdaacbabddcbdadaadcdabaaddbcbadddababdcbbdaadcadcabdadadabcbadbbdbadbddcbdaacdbabaaabbcbaccacdadcacbdcdbbbdcdbabcabdabddaadbbcdbbbcbdcccacdcbcaaccacbcbcaddaddccdccdcbccacbaaacddadbbbabdccadcdbbadacdbddaaaaddddcadaacdbcbaaacdacaaadccdddcccccadccacdcbbabbacaaabbcabadddbbcbdcbbdbaacadcbbabdbccbacdbbcaccdaccdddaadbbdcbdccccaabcbaddbcdccaacbdbacbcdcdabacdadabdaabccaacbdcddbadbabbcabdcabdabdaabadabdccbccbdbdcdababdcbdcabbdbbbdcccdaabbaababdccabdbbdcdcbbabdbcadabadbabdbcdaadadbcabaddacabcaaaaabbaacbbccdccdbbccacacadbbdcdbcbbcbccdaadbbcbddccdddcabaaaacaababdacaddbbbccbdcdccaadaabaacacdbaabccbbddaccabaadbcccdcdbaabacacbcdcadddcbdadcacbadccbbdcbbcadaaaabacaddaaabdacabcdcbdddcdcbadabbabacacaadaabcdddbcaadbccddbdcdddcbcddabbddbadcbbdccdbadbcbbcdbabbadbabcacbcadcbdcbaaaaabddbcbdacbddabddccbbbbddbbabcbbcbbdaccacbddcdbccaacdacbbddcaaadcacdcbacabdbccbbdabcdaddcaddcadbaccabadccbbccbbbabdcaabcdbddddcbbccbdbbdccbcdadcbcdbacbccdbdcdcccdaabbdaabddcbbbccadcadbbcabbcbdbadabacaddabacacabbbaacdacdcbbabbadbbdcdadadcbcbbadacddcbbbbcbbabbddabbaadababbacdcbbadbdabbcdbacbcbaacacbdcbdcdbbbbcbddccaabdbacbaccaaccccccbacbbcccdcabacbdacdcabaadaacbbcadbddcaaadabcbcdaacadbddcdcaabcdaccdaddcdcbbadacddcdbcbcbabbdccdbdbcabaaabadddbdbbddcdcdabaaabcdcbaddababacdbbcdbdcdaabaabcbccdbaccddcddadcdcdabcdbacdbcbbabdddbddddababdcaccabcccbccdbbaddadbcadcdbcdabdddccdadddaadadcdccbdddbbaacadadbaacbddbdcbcbdddcaccaadcadbcadbbddaaccacbbcddbadbcabaacaddcbdabdaaccbaadbcbbccdbcdaaaccaabdcdcbbcbdcadaabdbbbdbbcdbacbcbbcabdbaddacaccadacdcdbbcccbbbcdbaaaadaddcbddaddbbdbdcabcbabdbdcacbddccdcbbbaccbacaabdadabddccabbbccdbabccdbddbbacbdabddaadccadadcabbbdbbccabdadcdaabdaaccbdacadaddcdddcabcbcbdbddcdadccdadbadbadbabdccaabccabbdddaaddccddbaadccaddcadadabcdcbbbbccddacdaccdbbacabbaaccacaacdbaddaccbaaddacbcddcbcadcadddbadcabadacabdccaabccbbacabddbbdbbcbadbcddabaabbdabccaacabdaabbaabbcaadbbbcacaddabdbcbabcaddbaaddccbccbbccbcdddabcdadcaaaabacabbcbbaccaacabccdbbcbbadaaddbdadaadbcdaddbdbdbbdbaaaabadcabacccabcbbabddaacaadccadddbdbdbadbcbbcddacbaddacbbdbcaddadadcdaadabdababcacabcdbbaadcdadabcadaacddbdadbccdabdacccdabbabdbcbdccbcadbbbdbcbbccdbdadbdabacbbacabdbcbcaacacdddcbbbaccbdadbadccdadddacdbacdcaddbdbcabadcccddcabbcaaabbadbbddcbcddbddccbadbaabdacdbcacbddbaadaabcddbaabdbcaaabdbaabccbdbbdabcbaaacbadcbcdadbdaabaadcbadcbcaddadbacdcdadbaacabacdacdbcaddbadbccddaabdbadcbdccaabbcdddccadcddbcdccddccdddadaccdabdaaacacbcbbdcaadbdccddcddacbcdbcdabcccdcbdbcaddcddcdadbabbbbccccbdadbdbccadbcbdadbadcdbbbacdbdbdadbcbdcadbadbdabbdaabbbdccadccadbcdbaccdbbadacddccbbbccbcdaacaaaabcbacacdcbcbbabbbacbacbdaadadcddacbabaacabbcbcdbcddbccbbbbcbabacadddbbabbaaddbaddcaaadabaabdcdddcbaadcdabdcacbadcdabbadccbddabbdcbbbaaddccbcdcccabcacacccbaccbdadabbcdbbdddaddcadbbbadcdddadcddbbbaacaddbdccccadbadcdbaacbabadbcddccdcdaadbacccdadddcddaaccaaddbdcdbabcbcabcbddbaacadabdbddbacccccaccbcbcabbdbaaacdadaabdddbdbddbdccdcbcacaabaacbbdabdddcdbaacdbabcaccccaabdaacaacdcddcdacaadabccdadaacdccbccdcbaddbacbdcbadabbacacbabdadbdbdadccbbdcbcdbbbacbbcdbdddbddbbcbbadabddbccbbbbbdddcacddadddcddcccadcdacdbcadbadcdddccbaadccbbbdabdbbccaacabbbdcbccdbadcdaaababddbbccaadaddcdacbcbddbcbcbccbdbbcacbbbcccddadbbcadbccbdbccdcbddcabddcaaaadcaacdadbcdadbdbaaaabaaabdcbcacdbcdbcaccbddddadbcadaddacadbdbcbdbaaccccdcccaabdbcdaabdaaadacdbadbcabadbabcccbdbadbcdbcacdccccbadadbdcabcbcaacbbaabbbadddbcaacaaccaddddbcdddbdccdacbbadaaabccadcacbbcabbadccdbbbcadbcaddbcabdcddccdacadddbadabdbcdcaaaccbcacccbdddaaccbbddababcaddddccdbcbacadccdababcdbdddbbaaacacacdaccadabcccaaacabdcdcacbccccabbdbddbdcdbbbaddababddaddabacdadcdacaaacbbadbbdbaadccacaadadacccbcaddbdaabacbddbbbcabccabdabbcddadbdcdbdabbdccacbaaacacaaddccdabdbcbdddacaaccbccccdcababaabdabcdbdcbdddadcacacbaccdacdcddabaadbcacadabddabadacaaaacabcaaadcaaadccccaddaacdbbacdcdcaaaaadcddcaabcbbbbdaddbdcbccdaaddcacaacccbcababadaaabbaaddcbbacadcaddcaccbdddacbccacbdadbbcaadbccabaabbacdacaccdcdcdcbcacadddcadaddcdadbadcdbcbdbcccdbaddbdccabbbcdcabbdbccddabccdadcbbdacdbdaabadcdcdadcbddaadbdbcdbddcabacdbcddbacbadaadbccbdbdacdccdbbcbcdcacbcbadcaaacddcacaacccadcaacdaacaaacaacbadbcadadbbaabcadacbaaabacccbbdadacdaddabaaabcddabcdacacdaccccbaacdcdbcddaabdbbcbdbcccdadbbcdcddcbbbbcbdccdddaabadccbadabcbdcdabcabbbadcbcbcbaccdccdccbbbabbbadcbdbbdacbadacbadbcdaacccdcdabdddaaacadcdccdabbaadbbdaabbdbddadbbcdcbdacaccddbdcccbaccdcacbcbcbbdacabddccaadabbccacacddbadacddbcacdcababcabacabbccaabbabcbcddbcbdddbcbdbbcdddcabaadbddbbdcacbdbcccbcacabddadadaacaaddcbccdaaadbcacbcaabdbabcbdabaadabcdabbbbddbbdabaddbbdcdcccacacbbdadcddabbbbdccabaacaaddddadaddaccccbdbbcdaadcbacbcbbcaccddbabaccdcdcdbaabdabdbadabaddaccadbdaddbcbababdcdcbdcdcbcdadabdbcbabccbacccaadadcdbdadacdccdbddddcaddcdbaabdabbbccdabcccbdaccbadaacacdbdbbaacdaddabcaddcccbddbcbacbdbcaccacbbbddccbccbaddaabaaddaccadbbcbbbbdbaaadadbdbdbaacaccbcacdcabaabbcadabdacbaabdddaadcccddaccaddbcaacbdcdabdbabcbbccadcababdabacadabbbbaabcacabdacdcbacdacababacdccabbcadbbdddacbcacbcadddabacaacbadbccbbadcabccbaabbddbaadddaaabcaadabccbbccbdbbdacbaadaddbbdccdaadaccaccccacdbdaddcbbbcdcbbdacbcbdbcbcbdcacdabbbbbbdacbaaddcabbdacddcdccdbdcdbbcbcbccdacadacaccdadacbbccccbbdcddabdbbbadaddcccdacbccadacddcadccbdabdaddacaddcbaaacdabacbbcccabacadaabaadaadcaaaccaadcaccbadbcadcadabdccdcbbadbcdddbababadbaacaccaadadcaadcdaddcdabdcdadddcbbdbabcbdadbadcdbabcacbddbbbcdcaadcababacdddcadcddbdbbcddaadaadbbacaddcdddcbbacbbbdcadcaccdddcdcbcadcabcbdddbbbdccdbccbcbbbaacaaddaabbacdcbdcdcbcadaacadccbbcddaacbaccacdabcdcddabdaddaddaddbbddacadbdcaabccbdaaddcbcacbaccbcdcaddcadcdabddbcdcbaadbdabdcabaccdbccbddbbbadabadccbdcabccbccdcccadbcdaddbadbccdbcdabcdccdababbcaacacdcbccabccbbaabcddbdabbbcaacccadccabbdcbdadabbdbbbbaaabacabdadbddaaadddcbacacbcbbaddcadcbdbbacdbbaddbbbcaaacbbbbdccbbcadacbadbccbadcbaccbaccdbadadcdcbdcbdcbaacdaddaacddcdbbcabcacdbaabcdacaabacaddcdcabcddcbabdbcdabaacaccddcbcbdaaddcbcdcadaacdabbdadccaabcdcdbdaaaccacdcdcdddbcbdddbbcdbcbdccbabdcadabdaaaccdabbcccabaddabcbcbadcccbddbcdcbbcaaacdbddbccdccdbbadaaaabddcbdadddddddabcdadaaaadbbdbccbcabcabbbabdbcdcdccbbbabaccacbcbbcbcdacbadacbbacaadbcddcbdabbacaadbddadbbbcdccdcacccaadbcdcabdababcbabdcaabdacbaadbaccdacaaddadbddbadadbaaacbbcabdcdbbcdbadbcdddadcaccadbcbbcacadbbacadabcbcaabaddaacbbdddadddcacdbaadddcdbaddacacdadacdbbccbdadaadcdcdcbbdddbcababbdcdcbbcacaddadacbdaadacbadcacabddbcccadbddccacbacbbbddcdddbbdbbddbcabbbadcdbabcaddcddcdbadddddacccbcccabdcbcdaccbbbbcbbabbbdadccadbdadddbcbcbcaddcabdbababdaaadadbbdcbadcdbcccaccbccadbdcadcaddaabbadabcbacdabcddbdbddcbcbddcdabbaccaccdcbbcccabbcbcddcdbabbccccdabbcacbabdacaaadcacbdcaacaabaadadddbdcaaacccbbcdccadddcbbacdbcbcdbbabadbadccdcbbcacdcbbdbbabbbbadccaaadaacdccaddacaadddcacddabaacbacbcbabcaccbbabccbcacccaadcaadabbbbcdbdabdbadcaacaacdacbadacacaacdabcccbbcbcacddaaddabccacacdaaadababbaccbbcddbaacaabdbaacbbadaabcbcdcbdacddacdcdbbccbccbbacbabadcadcccdbcbdcddaabadcadbadaddcaadacccbcdccadbcaadadcaaacabadbdaccbadaaadccccbbbccbaacabcadcaaccbdbcaddbabaacdcbbacbccddbbacbdbbbbcdacddcbbaddcbaadaccaaaaacaacbccdbbadadbbaaddcccdcbdbadabdcaccdaaacabbabdaaacdbdccbaaadcbaaddbbcaacaadaaacdbdcbcdadbadccadccaabcabbcdcbabdbcddcdaaacdbbcdcadaadadaadcbbcabdaaabbcdcbddaddaabaccbdbacbbdbabccddadaaadbabbcadcbcdbcdaacddbabbbdbabaadbbcbacdbabacacddddabdccccbaadddbadbdadaaacdddcbdcaaadaadccccdbabcdbdbacaccdabdcadddcabdaabbcdccbdabcabdadccdbdbcbababbcdcbdabacdcbaaadcdccdbbcdcbdbdbcdbbcadabaadddbbaacaacdcbddbacdbdcdbbcbdacabacabcccadacdcbbdcaddddcaabbcaadcbaddadddcbaddbabbccbadaaabbcaadddccbbbcbabcbdbaadcaddadbbadddaabccdcdcaaaccacbcadccdaacacccdbabcabccbbbddbdddaaddbdbadbdcaadbaaccacbcddcbdcaddaacaabaddddbccaccadccdbbbacbccadbbcaddcdbacccdaadbdcaccdddacbdcddcccacccddcaaccabbdabacadcdbbacdababadcabbaaaaadccabadabddacdbdbadccaadacbacadadddccbbaacbadacbccaacdbabbcddaabcbbbbbbbabacddcccdadbbaacabddbccadcccccbadbdaabcbddaccbbabcbdbddbaaaccdbbbcdbdbaacdacbadcbaddccadaadaddbaaabbbcdddccbbddccdcddbabbbddbadbabdcdcdcbdabdbdddaaacccdcbadcbacddcddbbddabdbcbbcadddcdcccdccbbcbbadacabcccabaadbcdabcdbdcdbbdcccdcaabbbccdadaddbbdcbcbdababdbddbbaabaadadaadabbbaddcbaaabaacacbddcdabadadadddadabdbbbdcdbdbacbadbbbadcdccbadbbccdcccadccccccbbabaabadcaadabbabdcbaacdcabadbbddbbddddbacddbcbaccdcbdbddaadbbdbcabaababadabdadcacddcadaadddccaacacbbaadacabcaacbaadaacdbdaaaaaccbdcabacabadddaaadbdacccabccddabdcabdbaabdcabbadacadccdaacdacbcbaadccddaccabaadbacddcbdacbdbcbcbbdadbccdcadabaaddccbbcabadccbdcacdbcccbdcabbcaacbdbccbaddccdcdadddadbdaabdcacaacdbbcbcdcbdaaabdbaacddbacadadababbaacbaadaaadadbabbccdbbddbcbaaccbdddabdbcbdbbadbacabdbcdbbcadbaaacbdadbbcdaabbdbbabddbdacdacbcabadacabadbdbadadabacdbdcadabdbdbccdabbcdccddadccccdccddcbaabaddaadddacadbdaadcddccdadbabaabdbbabddccccaccaddcacabdccbcaaaacbbabddddacdcbdcdcbbcccdddaadabacbddbaabdacbacabdacbaabacbcdbaacbbdabaaaccdcbdabddbcdbdbbccdcaaccdcadbccbdbcbccacccdbdccdaccbbbbdccabdbbcccaaaacdabccdaabdaadcdbdcacaaadcdcddbdbbcbddaaddbccabcbcdabaacbcdccbaccacccabdacaddccdaacdcccdccaaabdcadbbccaaddcababddccddcccdcbcaccdbbdbccdacdbdaccaadaaadadcbcadbddadaacccbbbdadcbbbaaaabbabcadbbbdabdccadbbbcccdcacacddaaacaddcddcacbbaacacdaabadcbddadbbaadcccbacbbabbcacaaddacaaacdabdaabdacdcdacdacacadbddabdbbabcaabbaccaccbdabaabdaabcadcabbbdcbbcbbdaccdbabdcadccaadddaacddddaabdacdbdacdcdaacddadcbabacbbdbccadaabaacbcccccabdaccdacddbddcdccacacacdddaadcbadcabdddbadbddacdadacaabbcdadacaabcdbbccbbacdcdcbaadabddbdccaaccdaacdbabdcbbdbccacadbcadacccdcaccabcccaaacbdcbbacacdadcadaabbddaddbbaacacadccbbbababbdcababbbacbdadcbdbacbbdcababddabcccbdadaabadbdbbacddbaadacbdccdadbabbcddcbbcddbcaacccaaaabcdcdcbcdbabacabccbbbccbcdcddacdacadabddddcdcabccdcddbccacadadcbbaaacdadddcacdaacadbddcccdcbbaadacbadbaacbbdbcaccbddbbaddcbaadccdccdcdcaddbccddbcdaaaaccbbcccbacdbdabbbabbdaccdcadcdabbacadbbaabddbdaabddcddbbbbddcadcacadbacbcaccccdbabccdadbbadbaccbbddcbddcaababaadaabbccdadabccbcabcbdbadccdacdccbabcbadbababbddccadbdbaaddbbbbccaccccdbdaaddcbcaacaabbadaccbdccbabcadadbcdcddccdbdbdcdccbdadbdcdddcabbdcdbbcdadcacbbaabdcaccaaadbbddcbdbacdcadbcbbcddddcccdbcdddbacaabbbcbdbadaacbcaddabdcacbcbccdcbacadbadadaaccacadcdccbccaaaabacaaccababcdbadaadcdcbdddbdadcadacbccbcabcabcbdbabddbaacdbdcdadaddbddabacdbcaccaddaccbadbaabbcbabcbaabaaaccbccbcdcbbaaccaddbdbbdcddcbdcdaddcdddcadcdbbbacdcbcbcdbbdbbbcdddcbbabddccccdbbcdacbdcdbdbcdabbcadcdbababcdcccaabadbcbadaacdbacaabacbbcddacdddadbdadbbacbcacbcdbbabdbbccbadcbdcbabcdacdbdbbaaaddddccbdcbbdcbdbbaaadddcddbccbdadabcaadaddaccbbcccacabdbadbdaacddbaabacabbabaabacdddbcdaccbacbcdaabbbcbbaddcbdabbcadcdbacabcdbadbbaadccdcddbabdabacbbbcdddcbbddaaddcaaccdadbdadbcbcaabcaadccaabcaabaabcbddabbddcccbcbabbbdbccabddcdbabbadabdbaaadabdbcdacbabadadbbdcdcbbdacddaaabbbdcbbcbcdcadacacaabbacbbaacdaacdbbbaccbbabccddccdaaccacbbbdcacbdddadbbcdabccbbcddadcbacaaabcbcaccdaacddadadadbdbcddcadbbbcccaaadddbaacdddaddccaadaddddabccccbdcaaabdbdbdabbcbdcbbbbcaabdadbadabdacdcaadadcadaddaaccabbacdbbbdacadcdccbddabddadbdcdbabacaaacadcbbcbccacdbbcdcdaacdcbcdccbaadccbdccdaaabccaabcbcdcbdcdcbddddbcbccbadddadaccdbcabdcadabaaabcbbacbbaabbacabdcccbdaddcdbcdcdbbdbccdcadaddcdadbcbacdbccaaaddbbdacabaccbaddadddbcbcdadacdcdbbbbbccbdbccbcddadcdbcbdabcdcdbaacdabaabdcabdbbaacdacdaaccccacbadcccbcadaababbbbcdcccdccaddadabbbaccbddcaadadddddacdccdbaabcbccbcbdadbdcaddbcbdccdaddacccdbbccccdcadcdcaaaabbdcdbabbcbbbdacdadbcbdcadcdcbcbcacaadbdbbadcccacccbaabbcbdbdcadccbaaadcabdcbdcdbaabcdcddbccadbcdabcadadbbdbacabaccabcadbbacdccaaaaddadaddaaaddcbbccdcbacddabaccddbacdbcddabcbbdbccddacdacbbcddbdbbadadddcaabbabccbdbcdccabacbcacccccddbaaccbdababbbdddadddcccdddcdabbbabdbbabbcbacdacadcaaccdccabadddbddcaacacaadbdbdaadcddcdababbdccdbdccabbbcbadbaddddcacabadbabbaadadbcdccbbcddddccdbbaaadabbdcacbacaccdcbdbdbdcbabcaacabacdacdcdbbbbadcbccbbbdcaabdabcbbbcddacbbbcaadcbccdcadbbbbdabadabcdbbabaabcbcbbdabdaadccbdaccaddabdbadbbaabddcbdacabcbdbdaadabcdbbcabacbdaaccbbadcaddbbddabcacdaabdadcbcdcdbcbabadabbdcaacbdaaaabdcbcabbadbcaaddcbdbababcaccadaacbcbcbcdbbcbaddbcdcbaddaddbbbaaaabccdbcdbccbdabccdddbdaabacdcacbdcccccddbddbacccbabdabcbbcdbbdacdddcccabaadbcdbcdbddbdbdcadbccbbccbacdabbdddaccccddcaadacaddadbbdabdddabaabacdcbbaacadcbcbacdadbbcbaadbddacdacbaadbaddbadabbdcbdcabadddcaabddcbabbdabcdacbacbacbbacbbdddbbdaacddacbbbccacccadcabbcdbbadbbdabadbbdccbdbbabcdddcdcaacabcdabddaacbdcccddbcdcdbbbdcbadccabaaacabdacaaaacbdabcbcdadaabaccadbcddcdbbaacadaccbdbcabbdbacaabaacbccdccaaacacdbcdadccddbacacbdcbbaabbcdacadbaccbbabcbdcbccbdbdccababadbcdcadccccdcbdcbacbadcdbababcdddccdabaddbcdabccdbddddbdbdaccdbacdaadaabcbddccccaaddcaabcbacadaccddcbcaacccdadbcbabacddbacaddbababbcbbadacdbddbdddbdcccccbacbcbbddcbcccabbcdbbabdddadbadddbbacabdbdcadbabdaaaadadccadbadaccacdcaaadccccadbbbbcdbcbcdacbccaabdaadddbcdbcacddadbabdbdddacdddddbcdbbadcacaaaddbccddbdaddcdcadacbddadaddacbbddbaddddddcabcacbdbbddabcacdadadabdbcbadcaaaccdcacbcdabdbdbcbbaccdbbdaddbdcdadbababcadadcaabadadddbbbddbbbcdaabbbabcbaaabbdaabbbbbdaaddcdabdcdddbcbbccaaaddabdaacbdbcccdcdccbdaabcdaabaacaddabcababdbbdbcdccaadccbcacdcddcaddaadbbbcdcbcabdbdcdbbbaabdaccccacdabbdbccdcadccdabbbbdcbccdacdbadaddaddacbadcbcdcdbcdbaadcdaddaaaaadabdacababcaabbbaabaaccdbdbbcbaaddabbddbbbbbadbbbababbcbdcbbbbadddcacdaacdabbbbaaaaddadcddbdbdbccdbaacadacadccdbcdbababcddcabccbacbdcabdcaaabdcacdbddbbcccaadcaccdacdbdddbddbdbbacadbcabaaddaabdababacdbacabbdddabdcddbdbdbdaddddabdabbddbcddbddbdcbbdadcbcdbdbdbacadddbbcccbcdddddababdddaaaacaddbbbabaabdcabdbcbbcdcbabacdacababacaabdaadcdbbdbdcaccbddbadbbaccdbbacababccccdcdabccadcddabacdbdbcbcbdddcccbadbabbcdaaacbbbdbbdccdcaaabdcabbbcddcbabbcdcccddcbddcbccadcbbcbccaaaabbddcbbacbaacccdcccbcaddcddddaacccdbaaacbcadacdcbbcccaacbaabaadbbbdcbbcaaaccaaacadacadcbacbccabddacdcdcbbacbbcbccabbbcacbaabddabdcabbcaccdcabdbdabadcbcdcbaccbdbbbcbaddbcbdbbbccdadadadadbbbadbcddacaacdbadddbccacbbabcbbbcdbcaacdcadbaababccdbacacccbbcbdacaaaddcbabaddbdadcbccbccccadbbababcdccdabdbccadabadbabbdadcddddddbdadcddcccdbcbacacbadabbcddcdcbcddddcdbbcdbdccbdcaabbbababcbabbdcccbabdaabbbbbdacbbcbacbcccdbcccaacacdaabbcbdadcdabddbcdaacbbddbbbbdcbababccbccbdbaacddbdbaddbbacbadadddbabcdabacbdbacddcdbcdccacdacdcaaddcdcadccbbabbbbccdbbaadbadabdbdbacbdddbaabdcbbbbbbbbcdbadcbbcbbddbdccccdcdddbdbcccdbcdccaacdbdbcdabdacdcabadcccdbcbdabadacbbaabcdaabbdcbbabdcbadcbdabbbdacdbdcabdbdadbbadadddaadccacacdbcdbcbcabdbdacbcccdcadccbcaadddadadcbdbadbcdbbdcdddaaadacabadbbdacbaabbbcdddbaadadadbccbdccaacacbcbdadacbbddbbacbbaddaabdaadbbbcbbccdbadcbbccbbdadbadddbadaccacdccdbadbacdbddabbabaccbadaacaacdabdcacbacdaddbaaddcdcccdbabadcccaaadaaddbccabdbccdabadadaaabdbcbbccbadddcadaaaccbddcacdcabbcabbaabdcaddbdccbadababdcccbbccdddaadcbaddabccadcbdabcccaabdacccbcddbbcdcaddaaadaadccddbdbcdacccbadcccdddaddccccdabaddcddbbbadccdadbdaadcbaaacdacbbdbdadbbabdbbadbabdcbaccadaaaabadbcbcdbbddadcbdbccdaaabcacbdbaddabbccdaacbbacaacadccccdccbaadacadccdbdcbbadaabdabccddcaaadbdccacabdbaaacdbbabdacabdccaababbdcbadbacdabdcacdddacbbbbbdabbaacbcbababbdddbdcabdbdcbcccabdbdccadcbdbabcbcbcdabcdcacdadbbadbcaccabbcdcacaccbbcbbabdcbbdabdabaacccacddccbbccddccddaaabdbbbbcbadbcdaacdbaaccddcbaaabdcdaacaabbcdabccdbdcdccaddddcabccbcbcddacadabbbaabcadadbcbabcbaadaadddbaabddcdcaaaabbccacbcdaabddacddaabcababdacaabbccabcddccbcbcdbcaaaaccbaddcdbdccdcacbdcbabbdaddbbbaddbcdcbdabcbdddadcdccdabaacbacdabbbbcabadbddadbddddbddcaadadaabdcbbdddcdbbbcabbcddbaabcbaddacdaacdbccdbaccbacabcbbaaadcbaaacdccbacadacdcaadccdaaacaacdcdcbabbadaaccdcddabcdcbdcbbcbbaadbadcbcaaaadaadbcbbcdcdaacdcdbaadcdaadbabbcbacaabccbbbcdaadcaddccacbaaccdaabdcaaacdccbaadaaaccaaaaccbbcdcdaccccdaababaabdcaaabcbccacbaadddacdbbaccacadcccaddbacbcdaccdadacddbcabdbdcccbaabaadaaabccdbccadacbcdadcacbbcbdddbaddbcdcdddaccabacdbdcacddcbbbbbacdbcbcbbbdccdddaddaadabbcccbbcdccdaadacabdadaaaabcdbbabcbaaaccbdbbababbaadccbdbdcbcdabaacdcbabcbccadcbbacbbacbcccadddaccaddadaaddbadabddacddddababcdbabdcdcbaabbbcbcadbdcbacdbcdabaabbbcdbadcdddcddbbadcbdbcbccbccbaaababbcbaaaaccdaddacaaadaadbcbbcdabcbcaabbaaabcbacdabcbabdacdaddbbcbacbccbddadcabdadbcdbbacabbadcddbaacacdbdddddbddbdbdbbddcaccccabcaaccbbaddbcbccaaccbaadbaaccabdcbbdbdcddcaabcdcaadbbbabadddabacdbbbdbcababacdccdcadccdbdbdddbcdacbacccacdabadcdadccccacbdccabccdbdabccabadaabaadcdcddadbdbadadaacddbacdbcadbadacabdabcdcdbddaadcdbccabbcadcaccaadbdccacabcaabaaccdaaccbaacadbaddddaacbbbabbddacbadcddcdadbcddddbddcdaabaabbaccaaccbabcdddbbdcdcdbcaacbcdcbdaddadbdaacbddcdbbaaacabcbadaaabcabbdddabddcbccadcbaaacdcbdacbdadaaadccaabadadcdcdadbbcbdbbdabadbaadcdcdacadbdadadbbababaddbcccbbcbbcbcbbcbadcaadbdcbabbdaccddaacbabbbacacbcccdcbaadcdaccbcadaaadadbdbcabaacbdabaabdcbabdcdbcdbaacccadabdbbdbdbbbdddccbccadbaabbadabcadbcbaccccdbbdabdcbbcddddcbbacaaabaaddabacddaaaacadbddabaddcccbbbbdcbadcddcadbacdcbcadacccddcdadcbabddcbddadddacccadbcacacdcdccabdbadcccbbcadbdabaccabbbaacabbcacbadcdbdadbadcccdaccbcbcddbbdacddbbbbaddddadabbddbccabcdacbbbaacacdcacdaddcdddddcadcdcbbadcccacdcccbccacbcbabbbbddaddcdccadaacbbcadddacdcaadaddbbabbacbadddabdacbddcdabcccacacbccaaacdcabbcdcdbdabbdbaacbbdcccbacdbccabbaccbaaabdabaddcbaccbbdaadadacdabaccaaaabbbbcdaadccddcaabbcaccbdabdcabbdbaaabccbcabaadaccbbacdbbbcacbdbddbcbcdbadcbadaadddaacaccbbdbaaacbacdbdacdbadddbbdaaccbcddaccbbadcbaacaddbadaadcaabbbdbdbcbcdbddbcbaaddcbbbdbcaddccabadddbbdaaccacbacaaddccdbbadacadabdaacbddabbabbddacaddccadaabcccdababcbcdaadccddbcacacbaacccacbdcabcdbbabcabcacabcddcbaccacbadbdcaadddabccdcdccbdcacbdbaababacabdddaaddbdcabcaacccbbaccddccddcaadbbcbacddcaddcccabcabbcdbabbdcbaadaaaccbabadcbabadbcbcdccdbabbdaacccbaadadccdbcdbbaaccaccadaccacddadcdcbbccddcdbdaabbbabbabbcacccabbbdbccbadbdcadbdcaabbcabaabaabaacadaddbaddcdcddcccdacdabdbdbadbcaadadccddddbacbbadddcaabddcdbdbcdaccadcbacacccdbcabcbaddcdcabcdaaaadbddbabadbcaabcbacbcacdbdabadcdabcbdacdcdbabbccbcddadcbabccacadabbbbabaaddaaaadabbcbddbdacabadbacddacbcabdaadccbcdaddcccdaabcdddbdabdbccddabbbdbcccbabaddcdccdbccaabdaaddbddcbdcbbaaacbaaababccdabcacadabcdddbddacbcbbdacbcdadaacdabbbaddbbaacbbdbccacdcdddcababdacadbbbbaaacbcabbcbcddaacaaaabdaaababaaddcacacacdbddcadacdbbbbbcdbddbcbcbcdbbadcbccabdccadbcccadbbdbdcdbacabcdddacabcbdacdadccbdbccadacadbacdbbaabbddabadbcacbabccbbcaddabcdacbaaccdaaccbbabcccadcacbbbddaccabbbccccccaaacccbaabbddbabccdbaddbcddabcaaabddacbabddcaadbddcbbcbadcbaaccbccbadadacbcaddaaccbadcbbddadaabccabbcaaaddbbacdbddcdccddaaccccdacdacbdabdbcdcdaaccbaadcddccadccbcbdbbdbadbbdbacaacdaabddcdbadccdacacbadcdccadcbdacadcbaaaacdbbbbbadbacabcabdbaadbbbaacaacccddcccaccdabcdbdadaacabddcabcccaaacaccdbaadbacadaacdadddddbabacddadacdacaadaaccadaadcacccddbddabbbdacbccccddcdbbbaabbacccbcdacadccccaccbcccaabaddbbdcccdacacbaadaadbcabcaddadcadbcdcbcdabbabdcabadddcccbcabaccddacddbcaadbbcbccaaaacbbcdabbbccddccbccbcbcabcdabcddccadabdcdcabbdbdbddaacaddbccbcddadadcddbcaccccdccdabbaabdacdadccddddacbdcbadaaacaaabdbdccaaaddbccccbcabcbbdbdcddbaadbacdbbdcccdbcdabaadabbcadabdcdadddadbbdaadaaddcddbcdacadbbddbdabddadabddcdabdadddccacddacaacccacccdaddabcadcdbacddcdcaaacadabaaacdbabaccaacbaadaddcbbbdabacbcdcccbbdddbddbbcaadaccbbadbadbdbddacdcdddadaababdaadbbcdcccaadcdabbbbdcacccbdccdacbbddbcbbdabaccadcdadabbcadbcaacbaadddadbdddadcbadccabbbbcccaaacdddbbbcdcbcdbddbaacaddadbdcccadadcbddcacaddcdbaddcddbddcadcaadcacdacdbbadcdababbbccaaacbbbbccccbcdbbacddddccdacdccbdddddabadaaadbabcddcbdcbbaacbbcaccddaadadcdbadddbdcaaaabccbcddccddbabbdabcdadcbbadcdcabbdbaacbdbddddbcacbbadccdbadcabbcdcabcdcddbadadddbaccaabcdcaaadcaacdbadccdaabacbcacabaabacdddaaddacbdcbdaabbccabadacaddcacdcbbaabddcadadbbaaddcdcdbbacbaccbadabbdbbbacabdbcbabbdbbbbdaabbcccbbcddcdcdccadbcdabccbbcdcddaabdbdbcdabcbdddbdbcbdbbdddabdadccabccacacabbcbbbdcddabaabcbbddcdbcdadabadaacadcdabcdcbcbababcaaacabbbdcbaabdbdcaacddcdcdadcbcdbdacaaaabcccdbbcbbcbcbbbcddcbdaabbabccabaaaccbbdbaaccccbbadbbcdadbbbadabcddbdaddbdabdbcacbcccccaddbdcdddcbbdbddbdddbcaadaccdcabdcaaddcbabdaabbdadbdddddccbbaccaaacdcbbbbcbcdbabdcddbdadadbcccdbaccdadccddcdddbbbdcacadcadaadabaddbbcbccddbbcabdbdddcccdcbbcbadcabcabdcccbaabdababccacdbbabacddbdbddaddaabdcaccaaccacbccaacbcccacdadadacbcaacccddaabaabbaccadbbacadacbdbbcbdbabddadacabcbcccaaadcabbdcadabdbccddaabaacdcdcdbdbbadccdcdbacbdbaaccacddbdacabddddadadccdabddaaacaadabbaabacdccbddddcdcadbdaddacabcadcbccbcbcbbdacbbcdaccccdbdbcdcadcbdacadacacbbddcdcbdaccaacdadaabcbccdcdcdabacccadbccdbcddacccbcdcdcabcbbadcccabadbaababbabadcbaccadbcdddccacccdbbcbacaddbababddcaccccabbbbccdcbaaccddccaccacbdabdbaabdcdcdbbccdacaabbdcabdabbcddbcadcbbbcadcbccabbabcbcabdddadcbaabdbbcdacbacbbcaabccacabcbbadddbcbbadabbacccdadacbbbcabcbdabbcdcabadabdbddddbddddababcbacadbaaabdacdbbbadcadadcacdbbacadadbbcdacdabcbadbddcdadccdabccacabdcddbcdddadcabadcacaabbbdabdddbaabbdbcccccadadadcbadbdabdddbbaaddbbbacacbcccbdddccbcbbbbbdcbdadadcbcddbccacacaacccbabcdaccadacadbddbcaddabdcddcabbdcbaddbccacadbbcadbabbaacabdcaabcaadcbcdcbabdcbcddcbdaabdaacaaadcaacdacaccadabdbcacbdababdcaacaccbddcbcdbbbccabdcbbbcabdabddccdadacacaaddcddbcdbdbbaabdcbddddccccdadbbcacddcbaccccdbaccbaabbadcabacacacddccabcbbcacdcbdcabdbccccbddaaaddbcdccabacbacaddccdadbbcbcbbcadcbbaaccbbddaddcbaacbacdcccbdbbbabddabbccacbbaabbdcddbccacdbacdacccabbccdbdcdacdddacdbbacaabdadbbcaaadadcdbbcabdccaccbcbcbbbabbdcabccdabcadbcccdcdbacdaaddbdbbdaacdbddbcdaddccabdacbbbdaacbacadcbcbcabbdacbcdddbcbacaaddbacaadbabbababdacccbadddacbdddccccbabbdcdaacbabbdbccdddbacaddddcbbddccbbddacbccbacadaabbcdabaccbbbabcaabbbabbbcdccdbcccbdabbcbcdbcdacbbccaccdababcbddcbcbbaddaabaccbdaabbdddcadddaddcddccacdccbbcbdddacdbacaaabdbdbcddbcbbdddacdbcaaabaadaadcbcbcddacccacaaddcaabbabbbcabaadaacbbddcbdbdacdabddcacdbcccbcbaabdabccdcbaddbdcabbaadbbddbddbcbbdbbddbbdbbcdaabbcddbbbbbacdbacbcabacabbdcaccbacabaccaacdcbcdccbcbcdcaacdadbccddaacbbcaaabbcaadaadacdbadbcddbccddcaaadcdcdabaacabccbadabdccaaddcbacaddcbcdaaaaacbbcaaaaaaaccbdcddddbdcaabccacbbbbdbbaccdcbaadadaaddbcabacddcaccdcbadadddccadaddaaaddaadbbadcbcbbbbdddbabbbcbdcbbaaadbdbbdcbddacabdddcdbdacbaacbaddcaccacbcabbdadabbdcbaabdaddbabdadddabaacabdcaaabdbbacacbccdddcaaaddcdccdbdacaaaadaddcddaddaabdaddddadbdabacbabddabdbbbcbddcbadbadbbaabcbbababdcbdaaabadddbaaadbbcabcbaacaabdadbccaddabaccbcbdadadbbadaabcaccccbcdcbcbaabbccdadcdbbbbdccdbccdabbccbbbaabbcddccdbbbacdcadcbcdcadcadacdbadccacdccacbcbbdbbcacbdacaddccccdbbdcbaaccacdddcddcbcccbcbacbacaadacbdbcbddbdcaabdbabbccdbbdddccdaacdcbadadbbddabacdaabccaadcdccdbacdadadacbcdbdcbcadcbcabbddabdcaadcabdabbccdabaaabbbcbbbbabcdbbabccdbbbdaadcdbabaddddabaaddadcccbbaaabacbddbabbdcddaaabdbabaddcadbaadbcdbabadacbcabcddaccabbaccdadcabbdbabddadaaabaadcadbdbdcbdcdbbbddacadbabaccaacbbbdadbaddbaacdccdbdbcbdbdaddcacdccdcadcdabbccacabdbddacadccccabcabbbcdaaddbccadddadacbabbcdcbbbbcaacaaaabaccaacdcdbcbdacdcbcdadccaabdddadccbdaccccaddbcdbcaacaacadbacbaadbccaadcacaabbadcbaddaadabccaaaacbabdbbcacdacdccbdbbccbaddabaacccacbaaadbdcccaabdadbccdadcadcaabddbcaaabccdbbdbbcbccdcdddcaddcaabacadcdbadcabcacbaacddbabbabcddacacbcbabdcbdaccdcbaabaccacabdddbcbdbdbbbabadcdcdacdcabaacddbddbcbccbaaadbcddabdbdddddbbdacbdddadbbdcdbdddaababcdcdbcdddadcacbbadbcabdcdbbadccdccbcbbcbadcacdabbcbabddacbbbbbadaaccaacaddadbdabdaaaabbdaadbdcdbdcabbadbbdcabddcbbdacaddcabccbcbabbdbcbccabaddcdbabcacabdbacbadbdbcdaadbddbdacacccdcaacdccbabbcbbdaaacbcabcddddbbcabddcbbbdaacbbddbabdaddabbccabbacadcdacaaaabdbaccccacabdcbcccaddbadbaccabbbaadaaddccbbabbccaccbcbcbcdcdcabcccadbbcccddcbdadbbaddbbbbcaadbaabbcdacddccdbcccbbbaaccacadbaacbcbabcbaddaadcdbbdabcaacbababdbacdadccbdbbbdadaabddabcaaabdddccddbcaddbabaddabdbccdbacabcbabcbccdbbabbcdbdbbbdbdddccccbcbdaadbabaaadbaacdbcdbdcabddddaddccadcdaaddabddadcbcaccabadadbabdadcacaadbbdadaddacddbbdddbdbccaddbdacbccdabbbaaacdcdadacbcacadabdaadbbdcacacbbbcdbbcbbdcaaaaadcababaaddbabcddbadbddbcbdaabbbdbcadadcddcdcbcddddaaabcccccdbbbaabbdcbbdbccdabccaabaccbabdddccddcaaadcccaaaaadadaadcbadcbbdcaabcadcbacbcadccbcacaccdcbdbbbcdcbcdabdbcdbacddabdccbbdadcccdacddcabadbdbdbacddabcdbadcabcaacabbdbddbdcccabacdacddbdbcbdbdaaacadbdaaadabbcadccabdabbbaadbcadcabccbbdddabddbbddacaabacaccdacacbbcbcccccdbbacbdbbaadacdbaccbaccaabccddbabccacbcbdabbcacbbbdddcdbcddabdbdcbbbcbcccdbbccbcdcddadcdaaaccaabbcccccbbbdbdcdaddbcadcacbadcdcddacbdbacbbbaccdaaccdddadcabcddabbddcdacddcacbcddbbccdbcdabadddbdcdcadcdbcbdabcccacddcabaacbabbacabaaacadabbbcdbabdbbccaabdaaabacaadbacadcadaccbabbbaaabdbdaadbbacabdcdbabdbbcddadbabaddcdabdaddabbacbcddacdcdbbdddaddccbadbbcbaaadaadbabbdbccacabdbadbccadddadadddabbacdbdbcabccddaddabaadccccdbaadbaabdbcbdbbbccbddddccacbbaabbacaaccdbcbabadcbadcbbdbbaabcaacacddcdddcbcaddcbdcaaccbacbdadcdbbdacdcdbdbabdbccbcdbdabbadbabdbbaaaabbcdbdacabbaadcabcabbddaddcdacdcdabbaccbcadabcdacbdaabbababaadaaccbaacbdabbbbbacadcdbcbcadccccaaddabdbcbcdacaccababdcdacdbbdbdbbbcddbddaadbddccbbbdcddbcacaddbdacabaabbcadbaadbdcdccdbabbcaabadcbbdcadbacbdcddbadcbcdccbbbdcbcbcbbbbdbccbadbbddcdcbdbcdaacdabdadcccdbcdabaaaccbbcaaadbddbadacbdadabddcbacadaadaadabdabaaadddbcccdadcccddadcdadcddbbbbccdacaccaaacbabacdcdbdabddcdcabdbacbcabaccbbbbacbacaabadbccbdbbacdccbabccabcaabcbddbccdddbdbbbabadaaddcdabacacdcddcabdacababbbadbbbdcadacdadcbdcbdabccbaaccaddbaccbbabbccbdbcbcbbccadaddcccacbcddaaacabcaccaacdbcadcabcddccdccaabbcdbbdacbbbadbdccabbadcdadbdbccadbbadcabbccccbdccaabdaccbbabaaddbaadabdaacdbbdccddcccbcddbacdddcbacdbaddcbccdddcaabddacddbacadabadacbcbaadcacacaccccaabbaacdcadbbddcbadaacbdbdadddccdcbcbcdbddddcccbabbcaddbcbbdbaacdbdbdcbadbddcbccdcaaaddddbaadabbbbbbabcccbbcadbdbcbbbbbcabbddcdccdbdbbdcbdadcdccbcbccabbaabdcdcccdadaacabbcdcacdbadddbddbadcabccdbcddbddbaccbaabaddbbdacaaabccadacdbdabbacabdbacbbcbdbaaaacbbddadbdcadcddaaadcbcdddcbbabcddbaadcbaddbaabcdddadcbccdadadccbbacabaccddbacbabadcbacaabdabadbdbcbdadadbdaddbbaccccaadbbcabcdcdbdacbbcbaccdacbbbacbbdcbacbccbbccdbddcaadaabcbbcbbbdddbddcdddbdddbcbabdcacadddadababbbdccddbdcddcbabbcdacabbcabacacbdbbcbbabccadadddcdbdcacacbacbddddbadbbdbacadbbbcdbabbdabcacbbcddcacdbabdcacbcbaadbdcbcbadacddbdcabaadaacdadddddcccdbcddcacbabcacdbcbbbadcccbbdbdbcbdaacddadddcbbadbadcaaaccbbddaddddabbdcbcbcaddaccddacdbadadbdbacdddcaadbcbbbcddbbaadbcbcacdcdbbabaddcabcccdacbadbababbbcddbdddbadbdadcdcdcdadcddbcbbbcdcdbcccdabbabbddcbdcbaccacbcddbdabbbaabcbccdaddbbcaadddbbadbdcacbbbdacbccadbadcccdabbaadcbaabbcbbcbddcccaaaabddcbbcbadacbcbcddaaababbcdacccbdbaacbcdcaaddcdbcacbdcdccaaacabcbcbcadcbdbbabdbdbbdacaabdbddddcbbabcbbdcbdbcdbadccdbdbbadabdddabbdccaabcdcdbacacdcdddbcdcabdbdbadbadcccbcbdacbbacbacdaacabbadbdabbacbcadacacdcaddbbacabdbcbbbbdbbcabddbdcccbcaccacdaddadaddabbbacbdcacddbbbadacababaadcdbccdacadbaccabaaddddacbdccddaabccdddaddcbdbcccdacdabcadcbabccdcbdaacadbaaacdadbcbbdcdcdcabaddbbdcdddcacdbacdabadbcdcabacacddadbbbcaddcdababbabccaacdccadacaacacdddadabcbddbbccbbcbbbdaabdbddbbdcccdcbdcccacdbdbcabdcbabcdcdacbaaccbbacdabcaccbcbccbddabbbcccacadacbacdbdaacbddbacbcaccbbbdcaddddbababdcadaacabdbccbbdadcdddccacbbacdacacbcbcbdacabbcdabadabbdbccccdbdbdcbddbbddcaabacccbcdadabddbbaaddcbbaddbacbcaccdbdcaaaaacdbcacbaaadddcbaaadbcabcccbadaddaabcbcaacccdacaacaabdbacdabdcbbddabcabbcbdcabcbdbabacccbddcacdddbbccdcbdabdbacdacdbcbccbcaabaaddbcbcadcbabdbabbcdbbcbbbcaaddbccbabdbbaddbbccbadabaccababadbbadcdbccdbccbbadcdbadacddbbbddbabdcbcabdadadbacaacabdbadbcabbdcbbdbbdcabaabbcacdcddcaaacdddcaabdadacaaabaacacbccddcbcabcbbbdabdcaabbcaaddcbacbbccabbbcaaacccdaadbbdbdbbdaabccbbcadaccddaddcbaccbaddaddaacbbbdbacccdddaababbdcdaacbbbdbbcbdbacbdddacaddbacabdbcdbcaababdddcdbcbabddcddcbadabbdbababacddcaacaacddbcbaccdcacacddccbdcaabcabdbbaacadacbbbacbdbccbcabbcabcababaabbddadacbabcababbcddcddcdcaddbcdcaadbadacabdabcccbdaabdababddabdbcabbacbcbbcbcaabdbbcccccaacdaddcbbadcdbccbbdcaabbdaaccabbbbaccaabbbdbcdabdbadaadcbbbaddbdddacbdbabaadbdbbabccabbcddcbdabcdbddbcacdbbccabcbbcbbdbccadcddbadddcabdcdadbcbcbadbaabadcaaadcdaadbdcbcbbccdaacdaccabacaadbabbaddadacaadcbbaccddabdcdddcaacdcacdbdbadcdbdabdadbbbbbcadcdadbaccdacaddcacddddbacbcdaaddbacdcabbcccbbaadbacabdabdbcaddcbbbbbbcdcabaddddcaabddbcdcbadddbbdddcdddcabddacbaaccbabaabddcaabdacadbccbdbddadbcabcacbddddcbdaddddcdbaccbadbccdcacddcaabaaaacacdcdcdcdacbcdcbabddaddccbbcdbbbcdbccbcaabbbddabadcdcbdbacdcdcbdbddababdaddbdabcaaadcbbabbccaccbbcdbbdddccacaaddcacadbaacdbacccbbcbcddccdcadcccbabbddacbbabdbdadcbacdaddabdabbcaacbdaadacbabccadbddabdabdbcbadadcdbbdadacddbcbdabbaddaddddadbcbdaabbdddcaccabcdcabcbbcbdbbaadabdcadbddadabbadcdbadcbbaddbccaddacdaadddbbacbcabddbacbcdbdddbaccbdbabbdccabcdaadbbddbacacabdcdadcdbbdcabadccbacbddbbcaadbbbdccadbabbbdaaadbdcacacddbacbbabdcabdcaccbccadbbcdbcbadbbbcbdbbadcdcdabcdccaabaacbccdcccdaddbccdbdbaccacdccbcaabbdcbdcaddbcbcbbcdcdcdbabcacacacddcacdabdbadbbcbddacdbccaacccdabbbdbadcbdddccdddacbccabcacacdccbaddadadcdddcddddbcbcdbaccdcacdccdcbdaaaccbdaadaacbabaccaabcbadbadbdaadcddbbcdacacbbdccbaddddcadbcccadbbbabbabaaaddaaaddcbbcbbcccaddbaccadbdbbaabbacdbddbbacdcbbdcdaaabddacbbaaadabbcbbdacadaccddcabddcdcadaccacdadabbbdaacdaddbcbccaababbcaacdccacbabbadcacdbacadcdadddaabdabdbdbbabdddbbddadbbaccccdbddaaaaddccccadbaadacaacbadccadcccccacbaadaacdcddcdcbccccdbacbaabacbbacbbcbbabcadbbdabbddadaaccbdccbdcddcacdcbdbdddbacdbbadcbccbcabbcadcdacddaaddbbaabdabcddbdddccdbdbddddbaacbdbabbbdbadaadadcaddccbbaadbadadadabadcacabcadbaabdadabccdddadaaddabdcdaabcddacdaccddbacbaddacadddbabdcabcbaaaddabbcbacdbbbdbbcdcdcabccdabcdcbdddadbdaabdccdacadcbadbdcaadcdbabdaaacdcbcbbdcadcbddbccccbacaaccaacabccdadddcacbccabbbabacbbabddacbacacabaaccadcbdcbdccacaddababdbacbdaadacabbbddacdaddabdabbcabdccdadccdbbdbbcdcadcdadabbbbcccdbbadcaacbccdbbcddacbbdababcdacbbcaadddbaacdddabaababbbaacbccbcaabdabaaabdbdaacbaccdadbcdadaddcacbddabdacccbcdcbcadbbbbcccdbbdbbbaaccdcabbacdddadaacddacccaaccbadcabcababbbaacacbacaabbcccadadbcacccdaaddddaddddabadaacbdadacdbbdcaadbbdabbdaacdbcdbabdddbcabacdbadcddbbbddabbaccacdbbdbdabdcbbbacdcdddacaddcbabdbdcabaabdabacdbacaddcadbdacabacdbaaaabdadbbbbddbcbcdbaaaabbcccddabcabbadacbadcbbdcbacacdabccdddccbcdbbbadadaccaaacddadbabaacccdddadcadabddacbcbadbdbdcccadacdbdccaaadbbccbabcaaccdddbdbbcdcdbcbadcddcaaacdcacbaccbbabddcaaadaddccaabaaaabcadbbbabbcbadabcdddbcccccdcabaacdcdcdbbcddddabcbddbbbcabaabcaadbcbcacadcaaadbcdbbcddaaddacaccbccadbdcddcdaaccaabbbdccbcaaaacccabbcbcdacbcdaadadddcbccacdbbddcabaacadcbddcbbcbdcbabbccccacbabaddccddbaaccdadabbcdbabcadabdaabadbcccddabdbcbcbcdbabcaabddadaccbaabbabcbdcdaacdabbccbabababbcdcdabcbcabcaddadccddcacaccaacdddabcddbbbcddababaadababbcbbbdbaaaadcdacbcdddbdccbacbdcadcccadddbadadbdcbbcdaabcdcadadbadccbacabcabbaacacbdaacbccbdbddacdcbadbbbbddcbdbcacadabaabaabcbcbcbdddadddabaababbbabdabcbbdadddbbcccbdaaccccabcabcccbdaaddbbbccdcddcaabadcdacbcacbdddbbcccdbcdabdbccdadddacccaccacaaccbadbdabbcabddadbdadcdbababdcddbadabdcaabbadcbabbadbcbcbbcaddbbbcbcacdcadddbabddcbbbcbddbcacacaccabdddacacdbbacdadbacccadccbbbddaabcadabacbacdaccddddbbdbddadabbbdbcccaccaadbcdccbdcbbbbaccddacadcaacdacbacdddbbacbabccccdcddcbacbbdabbbadadabbaaccacbbcdacccdbcccbcbccccbbccbabdbddaacadbdbacccaccccbadabccdacaadddbdcdaacbcddcbdbcbcabbcadbdcbccbdaaaddbacbbcccabbcbaddbcdadbabababbadcdcbbabaddbaddbcdaabbdbdbdcbbccababdadbabdbdbdddaabdbbdcdccaaacdddddacbdbabbbccdabcadaddbadbccddaacaddcbaccbbcbccabaaccbbbddcdacbbdaaccdcadcbcddbdadddabddbdabcccbdccbccddccabacabcdacbadbcadbcdaddccdcdcdaccabcdcdccaacdccdabcaaddccdcbbdbdaddccbdbcacbcddbaccbbbbabdbddaadacdcbaaccbcbaacccabdcddaacbbccdcbcdadbbbbadbaadccdcdcaacbbabdacadbacaddabcacacabadbcdbdcacddcbcadbaacdcdacadccbddbbcaadbdaacbbacbadcdcbddbbaabacbbccbccbbabbbdcaaddbaccadcddcaabdaacccddcbbbdcbdabbcaacdcbbdcadbcdddccbbdbadabbbbddbcddcbcdbdbbbdbcdaaddcadddbcdddcadacaaaadbdbdccbcdbbacbdabbcacabaaddbbabaaabbdaacbcacdbabbcdcdaadbaacdccdcdcbcbdbdaadaacbdaccdacaadbbcacadcccabaadcbdabcabdbdaccaddbdcbcbcdbbcabccaabcbacbaadacabcaabddaabdccccdcbcbbacadbdddcddaabbaacbccddaabdbcdadccdcdcdbaaabbcdbaccaccbadcdbadcabdbaacbacbaddcddbaddbbccccbadbbabacbcdaabaacdcadbdcbcabbacbcacbdccabacbbbdcdabcddcccabcdddadacdccbcbbadccccbcbbddccbdaaabbcbcccdddbccabddccddcdbdaadcacadccddcddabcbbacbcdccbddbdaddccacbdcbdacdacbbcccdaadaaacdaddacdacbacaaddbaadabdbccacdcacddadadadbabbaccccdccbbaddbcbbaccdbccbacdacabcacdbaddddcbbddabcbdadaadbaacaccdbcddbbcbdcdccadacbcaaadbdabbddcdbcaabaabbabcaabadbddaabaccbbbbccdacadabadcbddbbddcbcdbddcddcaacdaccdbbabccddcbccaddcdbcdaabababaacaccbcdbbacbacadcabbcacbdcddaaddaaabbcdcbdcccaddcbbacbdbbaddbacddbdccddcdababdcbacdacdcadddccbacacaacddbcabddbddbbcdddabbbbabbdcccdddabaaccbaddacdbbcacbdcbccbcdacdbaddbabacdbcdbbdbdbadaddcbdaaddbbcbbabcdbaccbadabdadbccadaddddaddaacbcdbdbaaaddbcbccaaccbddaadddbcdaadaacdaccddaaababdddcaaadbdbabddddaabaadbaccddcdcabbaccbaddcddabcccaaabddbbcacabbbbabaddcacadbdcbdccdbaccdccacdcbaadbddccaadabaddbbdcacabaaadaacbbabbbbdacdaddcaadbacaacaacbbcdbcabcdaadbadaccbcaccaabcbdccaccacbabbadcbbadbaccacbdbaaababccdcbdaabcadaacabdadbbddadcdcbacccdbdacbdabcddbadbdbaddbacaadcbabcaadcbbadaacbbccdacbbacdbbabdbcbbcaadbaadaaaaadccbcbccadccccbbdcbcdbbdcbdbbbaaadbddddacbcadcdaaddbcabcbcbbdbbbcacbababaabcaccacdccddcccadddcbddababacbabddabcccbbacaabccadabbddaaaabcddbdcdbaaaddbddcacacdcbaddbcbdaabdabcabcbdcababaddcaccdbbbccdcadaacdcdcaacbdcdabcdbbbcacdabbbaaaabccddbcbddcbdcdaccacdbbccbcdddabbdbabcadddccdaddddaaaaccaddbcacaacbdaccadadaadcdcccabbcbcdadbbaabacaababbabdbdabccbdcaddaacaadbbccdbaabcaddbccabbacdbcaabbabbabbcbdaadbcaadbdabddbbbdcaabaadabbcccaddcbacdaababdabcbaabdcababbacdadccbadddcbcabcacddababdaadccabbbdcdadabcadbbaccadcacaccabcdddbcdddcaaddccbdaabdbdbcdcdcaacacdadcabddddcacbdabbcdcdacabbcccdccaadbbdddabcddbcddabaaddacdacbdbcbcacdadacdccacddbdbcbcadbaabbccbadbabaaaaaccdaadbbbddbabaaacaaabcbdabdbbdddadabadbdcdabccbccaddaabbabbbcadbddbcdaacddbbcdbdadcdcacaccbcdaaaabbcadbbcacbbccdbdcbddbbcacccdaadaabbbaaadccadaaababcbadcccbacbacaddbbddbdcdbbdaccccdcdbadacbddabdbcbaaaabadddaadaddcccbcabcbcdbacbbcbdacdcbcacbacabaadcddbcdaaacacccabdbadcacbbbabdabdcabcdabbdbcabaacccaabacbbadabbaadacdcdccdbaadbcabbcbbacdccdadaabadccdbaddcbabbbbbbadaaabdcdaacbbcabbcdddddabcddcdbcacccaccbddddbccbcbcbadcaadbdbccbacdddcddccbabbcbcdaaadbcdcdbaaaaaabaddbadccbcdddccbbabbaadccbbdaadacadaacbadabcdcdccbbabacadababcdbabacbddcdcdabcbadbbabddddbbcaaccaaacbbdbcbddbdaaadddcccccddddaadbadabbdcabbaadddbbbaacadbdbcbcaadccccdcbdbccccddcddbddbcdbcadaccaadaccbdddbcbabbadbcdcbdaddccdbcccddbbcdcccdaabcadbbdbcccdaabccaabdcccbbacbcdabbcaacdaddadbadbbddccadcddbddbacdadcdcacacbacbbdcdbacbaadccdadddbcbdacbabcbabbaadaaacddbbccccbabbcabdaacccdccccccbcacbaabbddcdbdcdcdacbddbccdcadacbbbdbaacaaabdaacabcacabbabcbdbabbcdcaacbbddaacadadcaadddabdbdaacdbbadddbadaacccacdcacdbdaddcbdacaaacbdbddccddabbbdbadacccadbbcdcdacaaddadbadbdbcbddbcbbacbaacdddaccadadabbccdcdcbdddcdddcaddbadaaaadcddaaddcabadbbbabbddbbbbccbbcbaccbddaaabcccdccbdbaacdaaacadaccdbcdbccbbbcacddddadaccadcaabbbadccdbdabddccdcbdbccadcaacdcdcbcdcddbcbcddbaaabaacdaaaacaacdccdbdbcbacdadaacddcacdbbccadbacdbadabbbcdabadbbccbcbacbdbdccabacbdcddbaddbddabcbddaccaabbbaabcdbdbadbdcaabccaabbaaddaccddabbbcaddbabbabbbcdaccdaacbacdbabdbcddcabbacadbabccdddbbbcbaaabadacaadcaccabcdcdbbdaabcabbacadcddbbaccccadbcccbbabccdaaaabbacbcccacaaccdabcdccdbbccbabaddcadddacdcacddbbdabdbbabadaadbaabacbbdddacbadbababbdbdadcacbbcbddcddacddadcdccbbcddacbcbdcabccdcbcbdcbccdccbcaacdbbcadbaabdbdccdbadcdcabacbcbcbbbbaaddbbabdcacbdbcddababcbaaabccbdbcadbcccaaaccbdadbdcbadddaadacaddbbcbcddddddaabddbbcaaadcadcccddcdccaabacbacdaaacaadabdcadcdcdbdbabccbccaabadcbaabaddaabcacbcadacabbcbabdcadabcddacadcadbacbcaddadcbbdbdadddbcbadcabcdaababbdbcccddcddabaadcbcdaaccdbcabaaaadacdabcbdacdaababbcbddccacdacddccdaacabbccbaaaabbdccccddadaaaadbdbbcacaddaddacbddacbacccbbbdcadddadacbadaadbaccdabcbbbcccccdaabddadcddaadaccaddccdddcaddabbbaccbcdbdcbabbaddcddacbcaaddacbddcdbdbcddbdcadabadbcadbdbaaccbdbacbbabdaadbaaaaadbbdabdbacbcdbbadccacdbabccabdbacdbdbdcbcaaacacccaabcaaddbdcacdacdddccaadddddcccadbbadbbcbdccbdacbacddbbccbcdcbabbcddabcccdadbcabaaaddbcabbaabdbcbdddabadbbcabccdbdcdbdbbddadbcdbccadbddabddcbcbdcdcdcabcdcbadbbacbbcbcbdddcdbacdbccbbaccddcbcbcdcbabaadcccacbdcabcdbacdacabbcadacddccddbadddacbdcdbababbbadabbabbbadbadbaccbcccdaacddbaccccdcdcdccdcbadcbadacbaddabbbbbcaccadddaadbcbccdbdacddacaadbcbcbdddaaadabdadaadbbbaabcdcdbabcbacbdadbbdabdabaccbabdbaaadaddcadbdadbcdaddbdcbdddddaaaaaccdbabacdcbaddcabdadbacdaddbabbabdabaabdcbcabcddadbabdcdababccddacccbbadbacbdbbbaacbdcdbddbdacccaccaccabbdbbabdadbbbccaaadcaaddabdadcbbdadadbcacbcabcaaaddbcaacdcaaacdbbacbaadadcddbbcadcacdccbdacaadacbcddacdadbaddcbcacdadbacacbdddcdbaacccdcccdaaccdcacabccaddbbcadbaaaadadcbddbaaabdacbadddaccddabbbcacadabbaddaabdddbaaababcdbccdcaaadcabbbbcdcbdbbdbcaaccdcabdddbddabcbadbdacdaddccabaacbbbccabbddcadcdcdddaabcbdbcdbaabdcaccbdbcccdcabddbbcabdbbdcadcdcccdddcbcdbdabdadccccadcdcdbaabccbddbbacdaacccdddabdbacdbcdbddbbdddbcacbdccacaadadcdbcdbdaaddcddbdcbcacdaacddcdddcdaaadbaaacccdbdaabccccaddbcaacdcdbbbccacddaaacdbdbacacadaabddabdadcaccbaaadaccdbccacbcaabddccdcadbdcbbccdcbcdccdbdadcccbdbdddbddcabdbbddbccbdcdadbabaadddaadbabbadabdccacbaaabaabdbacdccbdbbbdbcccddbcccbcddacdcbcdddcbdaabadbdbadbcaccbbbdcdabdbaaadbabbddaaabbbdddcccaacaadbcabdaacbdbcbbccbbaadbabddabbacbacbbdbddbabbcddbababadbcccabbbabccdaccabadbcdadddbaddcbbdacaacbcdccdcddaabdbacadcddbaabbbacddddababcdaaadbccbcaadcdbdadbadabbadabdddaccbbacdbbbcdcdbdbccddccbdcbcbcbacaddbddcabddacddcadbbccdcbccddbaddaadbdaacccdddacbbacacbdaaccdbdabbbbaddbcaacacbcdcdaaccaadacbaaadbdbbdbcddcdaccbddbdadcadbdbdbddacbdddccdcadccbabbcdbdcbcbdaaabcbcabbccdaddaabbcbdbbcbaacbaaaacbadddcbdbdcddddccccbcaadcbddbdcdadadaadbdadbabaabcdbbaabdbbadddcaaabcacdbaddccddadbdbccdaadbcddcbabbbcbdddcbcbddcbdadbcadbddddcadbcdcbcdcaaaddabcbaddddcdbdcccdddbcbbbdcdaddaacbccbbdabdbadaacdacdcaccbcdbaaabdddcabacaadaaaadadbbcbbabaacbcbccbadadadbaabbbbbccdbaadbddccdcbdadaacbcddbaccdcaccdcdbacdbbbdadaccccbaaadddbcabcdaabbccdcdcacdbcaccbcaccdcdaacdcdaacdabcabbabddcbcabdabdccdadbcbdbcdababdbcaaabadbbcbcdbbcadccbcbbbbbabacbaaddcadbdbbbaabddbabdcbdbbccccddcacbcdcacdaaaaadabadcaaadcbddbbdcdbbdaadbcadbdcadccdabdadaacbabbcdacabdcaacbadbcbbcbcaadcbccddcababdbbabbbadbbbaabdbadacbcccadcbdacdcaacadbcdcbbacabdcdbbadbcdcdbaacdacdbdbaaabaabadbbaaabcaccdacbdadaaaaabdacbdcbaddaddbdbcbccaccacacddcbaacaccadccddaccdbcdbbadbbcacdcacdcbaacbadbabbdcdbabdabcccadbdacbbcaaaabddbdddacdbbcdcbacbabcbbaaaaacdbbcdaabdcaaadbdabaabbbcbcdbcddadbcbcadadcaaabcaaacbbaadadaddbccdabcacaadcaaadcbadbcbadaabbcacccdaacddabdddaaacdbbbbaadadaadabdaabdcabcddbccbbabccdbbccbcbadcabddcadbdccbabdcbaaaadacdbccdcaaabaadaaadbdcaaaaabacddbabbcdacdbdcbdcadabcaddcdaacdaacbcbcdcbbbbabdbaccccccbaddcdaaccabbbdbcccdcbabcacbbbbccadbcddcababcccaaaddbadcdaaaddbbaddccddbbdbbabcccaccbcacbcaadcaacbcbdbabdcbdcddbbccdbdcddaaacdbdbbadcddcbbdcbbaccaaaadddacdaabbacabbdddbdcdcbdcbcbdabbddbcbccdbbddacdadbcbddbddabddcadcbcaacbcccaddabcacaccaccadaaadcaddacbbbaabdbcabacaabaadabccdacbbaadabcccbbabddacdaaacdbbbaadddcbdcdacaccadccbbbdacddbcabdacbbaadbbdacadacdabbbbacacdbabdcbccbdabdcbbbadcaabbbbbaaaacdccdcbbdcbacdbbdcabcbacdcbaaaacdacdbdccbddcbadbddadcaabcacaabbdccdadbbbbbcdbbcbcddbccbcbccdcbcbbdcabadcddddbccdccaacacdbcdbdcdbcaacbcdcbdadcbcaaadadabdbacbacacbdcccacabdadabbdcdbdbcbbdbccbcaccadcccbaabdabcdabadbcbabbbddcbdcdbaddbdbbccdbddcdacbddccaaadcdbacdbdcadadaccbcdcdbcdacaacbcdaaacdacdbadbcbabddacbcaacbdcdcaddbaacbaacbdaabcbaddccdbaaccbaadbbcbcdcadacacaaadccbdbbabaaacddcaacaaacbbddcbcdbbdaacabbddddccbcbccdcccdddcbabaccbcbdcddcccbcaacaadaccccbbbbddcadabcbabdaabacbccacdbaaabbcbcbbcaadbcdbcbdacbadbbaaccdaabbddcddbdddabcbbcabbaccddaadaadacbabcbcaabaabcadccaddbacaaadbdbaddcadccccdacbbacbaabccabbdacaaddbdabacbbbcddddacddbdaddaacadabcccdbddcddaadcccacbcbcacadcabcbdbbddadccdddaccbcbcdbccdbbcbcccabaaacdaadbbbccdaddcaddabdcdadaccdbaadbbccdaccccbabaaacbadaccbcaacbbcaaaacbdbcdbcadcadccbacbbbdcbcddbbcbddcdabbbccaabdbdacdaccddadddddaddabbccdccacbdddacbabdddadcddccbbbbdbcaddaccbbdabdacbcccdaccbdacdabbbcabcdbbbdbcbcacadacaacaabaacbdbabacadcbcdcbaabccacdbddbbcadbaabccbcbbcbacbcaaadcdcccddacadcabbccbbdaddbbdcacaaddbabacddddaaaddddcbaccaddbdbaacdccbbbcdabcabcccbddcaadabdbdbabddbdcabdbaccbdbbbddacaaddbbdacaabddacddaabdccdadbccdcdbaacbcaccdbcbccacadddbbbdacaccaccaddabdcdabcdaccbdbdcdcacabbdadccbaccdbbdcdbbaddccbdcacdabdbadabaddcccaaaadcbbdaddbaacbbacdacbadccbaaacbccccddcaccdababdaadabccbabdcbcbdcccdddaaddcadbadccbbccbaabdcdbbabdcdabadadbcbababcabacacbaccaacbccabdaddaabadabbaabdcdbcddaaacacbddbbcbbcccdabdaabbaddcabbcdacbdcaaddddbbbbccdadccccbabbadabbacadadcaabcccdbcccdcbdbbaabadcadadddbddddcadadbaacdcbcdaddbcadddbdadccdccbbbacdbcbadbdabdadccdbcdbababccbdcacbdabbbcdcddabbdcdcddbdccadddaccdcaddbbbddacadbbcbabcdbcdcacbdbdaaacdbbacdbbadaabcbcbaaadbdbabcaccbbaabdddbdcbadcbaaccdccdadbdacdddbaacbacdabbcbdadbbdcadbcccdddcaabcaadccbbdcdddcabbacdccabdcccdbaccdcaabcaccbcdadabccccaaacddbacdaabcbddddbbcdddcaaacbdbbdaabcbdcaddabbbbbdabaccccbdadbadcdccabbaadcbdcdbabacbbdddabcccaddcbacacbababbdcdbcaccbadccbccadabbbdcdcdacadcdabacbcabbdbacdddabadbbbbaadcabcadabddabcaccbcaddbcadbdadcabbaccdbdcdabbcdcbaddcaaaabccdbacccccdadddaabdcaddbddbabcdacbcccbaabcbabbacbacaccbdccbabbdddcbdabcbcdcaaabdddccccbbdaccdddbbcdbbaaabbcdaaadcbcdadabadddcaccbacaadcaaccdbbdabcadcdcbdabbaacaabacbcadaabbadcacaababbdbcacbdbadbbabbbdadabbdadcabdbcbaabdcdcbdaddbddbbcaccaaadadbacdaacbacaaddbabddbacdbaccabcabdbcaddcddddadabbdcbdbdbbdabddbdcdcddddbbabacccdcbaccdaababbdabacacbdacbdcacdbcaddbdabbccbaaabaadacacacddaabbbadadaadacacaacaabcaadabcddddddcadddcbaabacdabcbcaabdddbddbdcdaadabbdadbdbcaaacccddbaacaddbccacdcddaaadadbacdcdacdbddcbbcbbabdbdadabcaabbdbaadbcdacccacdaccacaaabcdcddbcccbbdbacbcbcddbccbaadcadcdadadabddaaadadaadacdddbabdcccddccacbdbddaddaaccbbdacdcacbaddcbcaabbcddccdaacccbcdcaaababacdcacdddacdcdacbaabbaccbaadddacaacdcbcdbcaacdbabccabcbbabccdbadcbcdddddabcbcbcccbadbdaddacdaccdccaabaaddbdabdbaabbbcddacadabdccdbdddadcdbaadcbbbaccbcdbbcbcddaabcbbcddbabcaaddbabacaccccabacbabacbaaabdabbcbcacabbbccdacbdbadddadddbdabcaaddcbdddddccdabdacddbddcadacaacabcdbddbbaacddaddddaaddcdcdcdddcdabcbacdbbcbadcbababbacccdcddaddbcbbbdabbadccaabaccbbcaccabbabacbdaddbdcbbddcbcacddccacbdabddadaccadccbbdcbdbdbbdbddababacbccdbdccdbdbacabcbbdaadbaadacddbdbabcbdbbadabbbabccdaabbccccccadadbbadbddbdbdbbdbadddbcdbddabbddcadbdbccdbcdaacdbaddcadbcbaddbcabbdaabdbccadbdbddcabbaacaaddaabadbaadcbdbabbbabdcbadddccadbccadbdccbdddddaccacddadcccdbddadbabcccaaddaacaadabdbdaccbaacbcccbdadcacbdcadccdbcbddbccccadcdcbccbaadbbccdcaaacacdcdcaadcbcadababdaccbbdcbcccabdbbabcaccbbacccdbdbdaabddcdcddbbdbabddbdaadbdddbdacddaacdcdccadabcbacbaaccacbcdbaddadcabccaadcadccddaccacbbdcbbaccaddaaaaabddbacbaccdcaacabdacbdccbcaadaacabbdccbaaccccaccaddaabadbdccaaabaadccbbccbdcdacdaaaabdcaadccbabcbcdccdaacdcddbcabaddcacbbdacbbbaaabcbdbddadcaacbdbdcbcbacbbcadcdbcddbdbccacaabacdaabdbacabbccccabaadcbcbbddadaacdadcacbcbbadabbaaddabcbdbbcacbbcdabacccbdddbbaabbadddbdcdccdbbadbcabdbdbcddbadcadbdaaacbcbbbbcbabbdaaccabdccbaadaaacbcddbaabdbadcddcbbcbcadcdcbdcacabadbaabbabaddaadabbbcbadcacadabcbabbdbbcaadadadacdbdaacbdabdcccabadcbdcabddcbacadbccaadccbccbbdcaadacdcdaaddabdbcdcdddbaadcadadbdacdbbddadbdacaccbbbabdbacdddccaaaabcddcadbadbdbbbddcdccdacdacbaccadaacbcadabadaaaabbcabaccaacacdcaddbdaabcdbadacacdadbaababbddcdcbccdcdbaddcababacbaacbdddccdbbddcdbbbccdabdbbcdddabdabdbcbccbbcdcabaabdaabcaaaddcacbccdbdaaaacaabdbbbababcdbddadcbcdadcdbdaccacacaabbadbaccdccdcadabcbbcbadddddacaaddcbddacdcdcdcbabcbbdbbdacdadacbabdbaacdccbbdadcbdaaaacaadcbcbdcadaccabdadcddabdbcddbacadaabcccdabbdbdcdabcabdbdbcacaadaadaacddcbacdcaadabcdadbbacddbdacbcacdabdcbdcbbbddcdccbbcaabdcdacdbbbadcbdcccaacddcadaddaadcacbbabcaccccaacdcbccddaabdbbcacabddaaabadcaaddadcdcaabcdbcaacdcdddadcdbbcbcadbaabdcadcdcbadcaaddcadbbbccadcdbadbbcabdaccbccbdbbbdbbcaaacdaabbaccbcdcacdcbcdadadaaacbdbcdcaddbdbacacdadbcbcbddcaacccbaddcbcbbcdaadcbbccbbdadbdaccdbcdccadaabcdaadbadbbbaacdbccdbbabdadccbaabccdbbaacaadbdbaacccacdbdcdabbcdcbabadccddcaccdccbabdacbbacdcdcccbaabaaacbcacdddcaabbdbbbdcbadcdbddbdaaacacaddadccdbbacbbdcdbbbbdbbcacddcddacdacbbbaacbaccdbdaaccdbdbbbbaacaccccdbacaadaccddacdcaccdabaccbcbcbbaacbcababdddadaaaacaabbbbddccabddbacbbaabbabadbbacddcddbadbcdcccbdbbdcacaababcacbacddbacddddbabdbbaccacadbabddabdbdacbadaababbcbadaacccbdaaaaacccadaacdabcbdcbbcacbbbbcbccdcdadbbddcddbbddaaddcdbdacaaaaabdadcbbdaababcdabacdbabababdaabddadcdcaabaabdabbaabcddcadccaadcbbcabbacbddacadacdcdbdaadcabbcdbabcacadacbccadbaabacdbcddbdbdccbabddaadbacaaabdbcbaccaddcbaaaaadbbbcbdabcadbabbadbbcbcbccacbabbcccccddbdaababddbadcbaacbccdbddbbcccbbbcddddabdcacabaaaaddcbdcdddadacbccaacddcbccaddadcbadcdaaacddccbadadacbdabbbcdbbbcbacbbbabddadacdacaccccccddbdcaddaacbdddbcaaacdcbcbbdaddbdaabaaddaccccbcdbabbcddabdcbbccdcdabcbaacccdaabadcabccacadcbcbdddbcbbcacbacdaadcccacdbdcbacdcbccccbcdacaabcccaadcbddcccadcdbcbdbadbddabcabacaddccddcbacbcbcabacaacbabacdccddcacbbaadcbabaabbdccbccdbccabcbbcdacbabbdccaacadddadadbbbcdcaaccacbbaadacaaaacbaacccaccdbdcbaabbcccacbdcaabbbddbddcadbdadbcdcacddddbbddcbddadaddaccacddcbaabbccdbabbbbbdbcdbabcdaccbdcccbaddccddadcabddaccaacbadcdbdbadbacddcccaadccdcbdcaccbdcbdacadbbbddcbabcdacbacabbabdbcabcbdcbaddbbacabcadaabbddcdbadbdbdacdcaccadddadabcdcacdcbdcdadacbdcdccbcaabdaddadbdabadbdccccabdaaccacbcbcdcddabddaadbdcabcaaaacddaccccbdabadddaaccccbaccdbbcdacbdcdaccaddccabbacccdaadacdcabacababadcdacdccccacaabdbbcdddacbabaadbadcbcdadcbabdcbcccdaaccbbcacccdddbddcaabaddbadddaccdbbcdaadcdaacddcbdbadccdaaddcabaaaccdcdcbbaadadbdcbcddccbaccabaddbcacdbdccbbadcaccdbddababadabdbbdaabadddbdcabcddbbcbdabdbadbcbbccaddbaabadabaddcbdccdbcacbdcacbcabdbadcdccddddbbcaccdcccdacabdacbaabcaddbdcdbcdddcdcddadbccaddcaaaddbabbaabcddabaabcbcadcccdabacddbcaddbdcbbaccbaabcbddadddcdacadadaabbcabdaabcabbababdaacacdcaddabcdcbccddbdddccaaaddbcdccdabadbdabcbbacaadddbcbcaaacccbdcccdacddccbdaacdccdbbcaabbaaccbdbadadccdcacbdabadcbbccdbcbaadbbdcdcbcdaddbadcddcbdbcaaccbcbadadabbcababbdbcabbbbdaacbbbcbcbdbdaacdbcaacdbaabbbbcdccbcdcbbddbbacadccddbcacbddbcdcdadbaabddacdabcbdabcacdadddabdacabcddcdaaabdcbdbbbcbabdcdcacbcbcacddcaccbdbdabcacdcdabbddbcbaadbdcbbaaacdcccddacddccbbbabaddccbdcaabdccbcbdbaaaabdddabbddbbbcdbcdacabcddaaaddccdbdcbcdabccbdabcabcdaacaaaaabacaacbbadcdabadbbbbccdcbddbbacdcdabdbbbacbadccbabcacabbabcbbbdcdcccaacdcbcbbcbbcdccbbdbacaadcadcbbdbdcbcadaddddcdbcdadbddaccbacdbdaadddbddadbbcbcdbddbdccdccabbcaccacdcccbbdccaabdadbcadbbbbbacdbdbbdabcaddadddbabadabdbbdccccadbccddbcacabaddbdcdabcbcccaacbdccdabdadbdbdaacadccdcddadcdbacbdadbcaacabacbcadcdbbbdbaddadccdaddbcabbbdcbdddaaccbaaddbadccadacbcbcaddaddccbcaabbdbdabddddbbdabccabcbbccadbcbbcacabbccddcadddccddddaacbbdcbcacccddddaddccbabbdcaadccdbabdccdbddaddddabcccbddcccdadcaaadddcddcdaccbaaadbbdcdaaaacbdbdcaccabbdabaabcbcadccbaddbabcdacdcdadacdadabcdccaacbccdaccaaacacbcccbaacaabddccdadacbbccadbcabdccbdcadabadadcbacdacdbcdbbbadacdacddbaccabbabacaccbabccdbccbaaacacadcdddcccaccabcccabaddddaabcbacbdcbdbaaadabcbcdbadbbbddadcabcbddadabdabacdbdbcddddbbdcdcdcadccbbaddcbcbaabdabdacbaadccdbdcddcccddbcdbbcbdddcbdaacdacdbdbdcdcdcbbaccbcbcdacdabdacdacdbdbacdbbcabaabdabcbaaadddcabcdccacbcabccdbcbabadcbbcbddcabdbacaaaacbcbcdabbdabaadccabbbacdbdbbddadaaddacdbaabbbbacddccdbdcccddcbbcacddacbcabbdacbdbacabbaacdccbaadacdaccbcacccbdadddacdccbaccdadddcdcacccdcddccccbdabacbaaaadbddacdcbbaddbccabbbaaddadcdaaccbbaddbcabcbbdadabccdadcdabadbbbbbddcbddcabbdbbcdacddbcbadbbbadaabcccadacbcaadcdbaccabcdddcaaddbbaddcbccacacbdcbabcbcddabacdbcddbdcdcbabbbcbadaaaaaaabaabcbbcdbbcbddaadacddcaaabbcaacabcadccbccabcdadcbdacccdadbaddacdaaacdcbdddbdcaddcdcababbbabbcdbcadcccdbcdddcccbcaccadbdcbbdcbaddacadbdddccabcbbbdbacbdaddaabdadcbbdabddacdccadcacddcdcadbaadcbdbabbaabdccabcdcccdcdababbbdddbcddaabaddadbdacdacaadaddccccdcbbccbcdabbcccaddabbabcabddabcdbcbbbcdacbbcdacdbadcacbbddccbdddbbaacbbcbcdbdbccacabaabbababdbaaaadbcbcaddbbdacbdadadaddbbbaccddadbdaaabbcaadbddcbdaabbabddbdbcbaadaacadabcaccabaabcabacbacbbaaaacaaabccaccdcaadcaaaaaaabdbdadccdabccbcddcacdcccccabddabcacbbcaaddddbcdddaabbbbbddbcccbbcdbaabaabdaabcbcbbddccacaacddcbabaabbaddddccbacaccdbbabdacbdcaadaaddbcdacabdcbcbcbddcbadaacacabaccabdddbccddbadbbaadbacacbbdcabcddccbcdcadabcdbbdddacbbbdbddbdddbdadaacdcbacbccbdbcdbcbcdcabcdbbcbbaabaaaccdbabacbbddacbcdadbcbbddacccadcadabaaaacabbdbbabababdabdcadbbbbbcadcadadbcadcaabcbcdccdbbabdcdadaadbacdcccbddbbacdbcdcadabaddabbacaabbcbbacddcbadbdabccdaaacbcabadcaccacbabcbacbdcddbbccbcbabcddbabcbdbcbdcdddbdbcbbadbacbdabcddaabacbabadbbcbdddbabdbccdaccbaaccadcabacddadbabbaacabacddbabbbdcdaddcdaddcbbbbbadbcacadbabcacbcacaaadacbabcbaacbbbcbccbbbadacdbcaababccdbbccbabbcddbbdcdabdacadacabdabdaaddccdaddcadccbdbdaaacdbcaadcdbaaacdcdaaadddacbdcbacbababababddccadabacbacacaaabbbbdcdddadbbbddbaadabdacbcabaaabccccadacbaabcbbddcbbcdabcddddbbcdaaddbaacbbdbbdcbacddcaabbbcdbdbababbaabcccbbabbadabdaabadbadccacbbadaabbbdccaaccaacadaadaadcadbbcbabbddacacbbbbaddcabdcaacdbaccbbbabacdcdbcdcbdddbbcaaacbcaacbacadcbbbddbdcaccbbcddaacccaddddabbbdaabdcbcaccadbacabccbdacdddcaaacbddadbccabbdbabacadbbaabcabbdacacbcddbddccdaadbbdbdadbbdcbaabbbccdbbbbdadbcbbbdacaabcdbcccbabdaabdbcadcadadddabaabbddccbcdadcdacddcdaabddbbdddaaaadbcadcaddaacbbbdbbcdcddcbcdcacbccaadddcbcabdabdbcbbbcabadcacabddcbbacdddcdbaddcacbaacaaabadccdcadbbcbbbcbbbabdbcdddadadbbddbadbcacabadccbdacbbddabbaddadbdddccdcadcddcdaaabacbcbcddcdccdbdbbaadcbbabcdccdcabcbacdccdbaabbadbcaacdbdabaaaccabbddbdddacdbaabbbdcaaabcaddaaaabdddcabaaddbacdbdcbdaddcdacddadddcbadbaabbcbbbdaaccdbbbacadbabdbbcbdcaabcaaacabaacaddcdcdabcaddaddbaddbddcbbcdbdacccabdddcccdcddaadccbacdbbacaaaacaacdaabcabbaadbadbccadacadcbacaadacbbdbaadabcddbcbbcdaacacadbcaddbdacbccabadcbcdcabddaccdacbbbbacaacbcdaaabbbdadaaacadbadbddcbccaabbdcaaacdbcbdbdcbcabccdaddbccabcbbbbdcbddaacabacbcbadddddcdbdacbccaddcaabadbccdbbaacbacaddacdddcccdbdaabaaccdddddbabadcabcbbdddcaccdbacbacbaacdabdcbbabbaddbcbbcacacbabcaaccabaaacaaadbcdbcdcdcdbdcacdcaabcaadbadabcdaacabcbbdadcadbbcbdbacaacdcdcdcaadccdbddaadaacacddbcaaacacbabccbbcbababbbbcdcdabbabbcababaabdbbdadbbabdbcdbabbbddbddddacabdddbbcccabccaacddbcbdbbdcbbddddbbcccbcdcadcacabcdbbabcaaacaaacbabdaacadddccdbcaddcacbabbcbddaaacadabadcabddcbcbcadcaddbdcdccdacbbcacddbdadccbbacbacbdbbbdbcaabbcadccdddbcdbaacdbcdabddcbcdacaabccdbbbacdddaddcdcaccadccacdbdddbcadddbdbacbdbbcabbddbdadcabbcbaccaccacacdcbaabdccccdcdccdacdaabcdcdbddadbdcabacdaacbaddcabdcdcdabbbdadbccbbcabaaaabcccbbabacdaddcbdaabadaddbabbccbdcadabdccaacaadbacaaababcbbdaacadadddaaabadadccaaaddbbccbddcabdadcacdaadcdaccbcbdaacdabdbcdbacdcdbbbdcbcabccbdabcbdcacccbaaacbdccccabdcccbcdcbdbdacbdcaccacbaabbbdabacccaacdbdbcaadddadcaacbbbcacbbbadcddcabbcdbcbdababdabccabdcacdabcdadddddbdcaaaccdbdddcacdcddccacacbbddcbddddccdacacdcbadbdadcbdbdddddacdccbcdabbaabccbaaddbbaaaaccacbadbccaaaccdddabbadddccadaabccdcadbadbdbccbacdbccbbaddcadabdbabbdacddbabdcacaccbdbdaacdacacdabccccbaabbccabacadbddbccdcdcaacdcbcbddaccabbadabbaacdcbbbdbdcddbbabbbadccdabcddbbbdaabadbabaacbbcbdddbacbacaddabcbbadaabdbadcabdbadaaadadccaaadabbabcddddcbaabbaaabbdabcdbbbadabcbbccaccababdaaddcadccddcdabadbdcabcbbcccdacccbaacdddcdaddbabbdbbdbcdcbcbbcabbdaccdcbbdcbbacabaddcdaadbccbbcdccdcacdbdcabbbccdddcdbdbdcdbabcdccbadbcdbbddbbabcaaccccbacbcdccdcadcbdccbdacaaaddcdbcbacaacccbcbaadddbcdaaacbdbaddbabcdaadbdbdcdcadaadbbbaddaddaccbbcabbaaaacdaadabdbcabdbaddcbbddaddcdaddcbcaaddcaccbcbbbddbddbbccccddaababaccbbdcccdbddbacacdcbdaabdabbbaaadccacacdabccbbbcadcccaabddbcacdadabdbdbdaccacaacdbcdcdddbcbbaaadaacbccbcddaaddcbadbcbbbbcdcaabdacacbbaadbaaddbbbaabdcacadaadcadcbbdbbbadbacadabbabbaddaaabdddbdcbbababcbabbabbbddabaaabdbcdbababacbddbbddcacaacaaccdabcbdbabdddabaabbaccdbaabddbbabdcdbdbdbbbddacaacccdcaabbacdacbdaabcabbcbbbdbccccdbadcddbbcadcdbcdbccbcadaaddcbdddbdddcabbadbddadcbdaabccbcacddacabcbaaabbcbdcbcddddbdddacccbdabcdacbbbdbbdacdbcabbbcbcaddbdddcabcbbdabbbacdbcdbbddcdaddabcabcbadabaadcbcbbcdacdbadaaabacadbbadccbdddbaaadaccbccabdaadbaacaccacbacacaadcbacbacbcbdadcabbadabdaacdaabdcacccddaddacdddcdabacddcddacbddaddbbbcdbcbddbddaadddccccaabccdcddacbacadddaccbabddaababcbddbdcacdbabdccabcadbdabadadabadabbbdccbccbdabbcaadacdbabddcbaaccbadadaddddaaadbaddabcbdddbaddbcccdcbbaccdbcadcdadbbbcdddcccdbbcaaabaabdcadbdcaaaadadaadadaabcbbdcccbaddbcadccabcbbcccdbbcacaaccdbdbbadbcbcbbadbdcadbabbcbaccbaddacbbdbbdbdcbcaadadcbbabbbddadadabcccccbadaabccaccbcdbacdacdcdccccbadcabaddcccddbccadddaadbabaaaabbcbdbddaadddaacadbbdadaaccbccaadacaabccabccbaadadbcbbacccabaabacdcddddccdcbcbbcdbcdadbdbbbbdbdcdbcdcddcacacbadacbdaaaaddcbbcbbdcdccabcacccdcbbcbacbadcaabcdacdbaadadcdcddcabdccbabacbadccababbdbccbddcadabdaddadabcccbbccdacabcbaccadcdddacddcbaddbbadbbdaccbaaabdbaabaddabaddccaddaabcdacdbcddcdaabcbbadadcbdbcbddacdbabdabcdacdbdccacabcddbbbddaabbcdbdddbadcbdcdbacbaacbbbbaddcadbaacacddcdbbdbbabaabddbcaadabbbdabccadacabbcccabdbaccbbdcaccbbaddcbadcdcbccccbccaabbacdaccccddccabcccbdcbcabdccbbddabbacdbddbdddacbcbdadaaaccbbadddbcbcacbbddbccdadbbadbcccdcdabcbbbcacdddbdadcadcdbaacbdcddcbbabbadbdcdbcaddabcddacdacdacbbadabadddcaaccaddaddddcddabcabbbdbbcadcdcbdbadbbccddcbdcbbcdcbbaabddccdadcabbacdbaaccdcddcaaacbadabadabbccaccacadaaabbbddddddcbdbdadabdddaaaccdaabcbdcdcbcbdbccdcdbacbaadbcacccaddbbaacdbbcdadbdbaddbddbabdddcdcdadcdbdaddadadddcdddaacbabcdbdbbbcacbbbbdbbacdcccbbbaccbddcabcbbccbcbbbadcccdddcacdadbdddbcdadaccabbbadcddcbccdaabdbdcbdabcdcbbabcdcabacabaadcaaadcacbdcccabaaadbdaabbcbbbcdcdcdbaadabddbbdacbbcdccddcadcdaacdddacacaccbbbcbababcccdbbaacddabcabcbadddbddcdcacadadccbcacaddabcabaadbddadacbbbdbbcdbdcbaddbdccccaabddcbcccbdcabacabdbacdcbacacabaacdbdabcbccacaabbcbbbacccabacadcbacbabbbbdcadcbabbcccdadbdadbdcbbbddcbdddadbabaadcabcbcbacddaadbabccbbdcdbcaadbacaccddadadbcbdabadabdadbbabbddcdabdcccabbabbcddaaacadbcbbabcabcdddbadbadbaaaacdacdccadcbadccaaaaddcabcdaadbaababbdcbcbbcddcdaccbcbacdddbadccabcdbccacdaccadbccdbcacccbdaadbaacccadbaacbdbadacbbabbccccaacdbdccdcdddaaadbdbddcdcacabbbcbaaaccdadbddcbcaacbbaaadadaadadddabcacbcdbadacbbbadcdabdcbcbaaccaabcdaaaabaccbacdccaadcbaadacbdcddaccadaadcddaabaadbccdbdacdddccccdaacdadaadcccaadddcaccdbccaadbbdddddccccddccdccaadabccdbddaddbbccbadcdccbcaadabbbbbbbbabaddbcacdbbcdcbbbabcbdabbcabbadacbdbacbaccacbaabbdbaacdbbbaabddadcdddbdaccacaccdbadaaabaadbbdcbcddadadcbbcddacbdddbbcadddbcdbbbaaccddabccadaaaccbaccbadbcdbddcdcbdcdbbbcadadcbbaaadcacdabbcaabcabddacdddcabdccbaabdabbbbacaabdbdcdbccbbadddcbddaccbaccacbdaccbababbdcddbcdabbadabcbcdcbddaaddaababdbbdcdccdcbdbbdaddddcabbaadaacaaacadacbbdaaadcccbcccdddcaaaaaacbdaaabcbddaaacdcadcbadbdcccbcddcabbcdbbddadcacdcbabbdadccabcbcabcbdcbbcdadcdbbabcdcacacabdbbcccccbaccdbbcdbacdddcbdaddbcaddccadcbccaabdcbdacbddccdcaacadbcabcabbddcbdacccbabadbddcdcdcbbbacaadcadbdccaaacdcbdddbbcadacbdccccbabbdbbdbabbccbaaaabaaddcdbddbcbdbbaadbdcbdbcdbbabddcaccdabdcbbcabccbaddccdcacbbcaabdaddadccaabcdabbbaccbdacabaccbaacadccbdaccddcccabcdddadbbaacbabbdaacdabaabbdadccdbbbddabcbdacbbbbadacbbdbdcdccbacbcacbaddcdccdbdbccadcdddbcdbcbbdbbadbdbbadbacadbbdadcdcddbbbcabbbbbcdbccccaaaadadabdbcdaabccccbdcacabccacbcadbabdcaabcddccdbcccdabcbcabadcadbdbcaddacbbdbbabcccdadbddbbacaccbabaabcdadadaacadacdddcdccdbdabacacdbddacccadadadbbbbcbbaadcddcadbbabadccccadccdcdacbbbbcdbccabdacabbcdabdbcbbbdcbcbacbbcacdcaacddaddbdabbccccdddddbbcacdcbbcdababcadbaacaddaddabbccbdcabbcbadaaabaaaaccddbdbddcdaadacbadbbddcdbdabbabbcccbcdbddbbacbbddacadcdcbbbccbdbdcabbbabbcdcabbabcadaadcdbaaccaadbabbcbcccabcacaccbbcccabbcdaacdccccccabaabbbabaabdacdcbdcdbddcddadadbaadacbbccbdddaaabddaabccbddbcbddcbdabcddabcabdbcdcbbdbcbbbdaaabbccaaacaaccbcbdcbdbddabacaccccaccdddbbbcbacaacddbadadcdbdbccacdacdbcccbadacdaddcaddbccbddbcdcadcdcdcadacbccbaacabcadcdddddaddbcdaacacccdccddacbcbacbaddcdcbbaccbbabadccadddabdaddadcbbcccbddcbbaadadddbdbaddcadcbcbbacdbabbdddabadbbadbabbcdabacdaddabcbadbabddbbcddddcadabddbdabcccbcacabbbaaccdddccddccaddcacddcbdaccaabadcbdcaacdbbdacdcbdbbacbbaccbbbbcccbbdbcbcdccdcacaabbcacbabdddabbdacaadcacccabadbbdddbdccccbcbdaaddbcbcdbcdcdcddcccccaaaadbddbddddbccdcbacaacdabbddbcaaaabdabccddbcaaaddbcadbabbbdacabbddcddbbbdacbcdcbcbcacccbadddbbbbdcbcbbaaddacdbccbaccdcdaabbbabadacbabbcdcabcaccdbaadcbddccdbdcdbacdaaababcdcdbbdccccbcccaaaccdcabdadbdcbadbdddaaababaaccaababdaaddbdbcdccacccbdaabaabdaacddcdbaabdacdcabbcbabaadacdcadbbaacbabdcababbacdcbaccdbcbdadaccabbbbbdbcdbaabaacdaaaccdcacdcdadaadbcdbabaccacbbcbaaabbcaccaddabdaccaddbdcaaccdacbbdcdadacaddcadaddcabbdddaccdbcbdbddcbaccddbadcbdadddcacbbbadabdbadcbddcabcddbccccaaaadcbbdbbbcdcbbaaaabcabbbcadbcdccdbbbdbbdddcdadabbbccccbdcbccdadaaddbddddadcccabdacdadccabdcbadcdaadadccdbcaaaabccababcdddabcdbcccdadbaddbbddcddbbcdbdccbccbbcbcddccbbadadcdadaccbddadababbcabdbbcabacbcbacbbdcabccdbbbdbdbacadadcdccbcdddbdcdacbdbdadadccdabdacabbacbabbcaacdbcadbcbcaacbcbaaaabadcadabdbbaccbdbdbcadccbcbcacccddcbabcbdccadddabacbcaccbadcbabddcdadaadbacbaacdabbaabbdcabcdbccbcbcbadbcdddccccccbcdaaddccbaddabddbdacddcbcabcddaaccaccdddccbacbabbdacaaddaadcccbcbaabdbbbdccacbbaccccbbabdadadaaccdbdcbaaaddbbbbcbdadcbcbcabbaddacabbbcccbdbcddcccabcbacdabdaabdbbbcdbddbaccabdaacbadcddddaacccdaacbabbbccdcbdbcaadbdabaddaddbacdbccbabccbabbdcddbadddddcaadbbdcbccbadadbbdbcdbccbabaacbdacdcddcbbadaddcbcbdcccabdabcccbccbbcbabaccacbabaaababbddcadabbaabccdcdaddddbacdbbaabdaacacadbdbaabccbbbbcbaadbaabcabbaddccbbbabdbaddacbcbabbdcdcabdbaccdaadddccabadcdddccdacbaddcdacbaadaababdaddcbdddbbdadbddcadcddcadabcaddbdaadcdbcadcacdccbcbbbddcbaacdbccdcabbbbdacddbccadaddbddbbdcbdcdacdcddbdaaaccbbcabddadddcadadcacdccdcbadacabacdadacccdaabacbdadbbdacbddbcbccbbdabbaddaacdaabbddaccacbcccdaabdcabdacdcddcbdbbabcadccadcdbbdabbdaadbadccbadbcddcdccdaddadabacaccbabaccccbbaaadbcaccaabcbbadabbccdbdcbccaaaabcabaccdbabdadaacdcadabdbdbbacdaccaccacccddddacbcaccdacdbcbbdaabbcadaaaacbbcbcbabddbaccccbacddcbccdccdcdcdcaadacacacddcbbddbcdbcddbddadaccbcacbacdccbdbadbccdcaadbabaacdcdcdabbabdcdcdbcddadbaddabcdcacaabbbcdbbbccddbcabbcdaddbddadaabacbbaabacbbcdcdaddabcdabdacaaaddbbdabacaaaddbbbabdbcadddddbbacdcddcbddadbbdaadbddabbcdbdcabadddddacaddbdabbddcbbbaddbcbdbbdacbacbacdcabcdddbbddbabdacdaabccdbdaaccabcbbadacaacaadbabdabcbcbcabbdaabddbbcbadcbcddcdacaaabbadcccdaaacabddcadbbdabddabdaabccbdadadcccdcabccccacadadcdacacccacbabbbcabbcbcacdbcbdaadbacaaccbadaadcbabcdcdbdbcbaacdaacbabbacbdbcbaadabcdcababcdbddabadcadddbdacdbacadcaabadcaccddccbbacccdcaabcabbabcaabababcacdbadbaadacdddddbdacabdababbcababdbacbdcadacdbccbacbbddcdbdddddadcbaabacddcdcbbcbacadbbccbdabcccddbdddaadcdcbbccbcabbccddabacdbdacccdcbcbabbbabdbcacdaaadbabdadccabcaadaaacdddbdbccdbbaaaabaadcbabadbacccddadbcbacdcbccaccbdcacddbddbccdaabdbaaddadacccadcdabbadcadcadbcdcdabccdaaabaacabdaccbaaadadcdbddcacbddcbbbbdbaabdbcdacbadcabdddadbbabbadccadbcbbaaabbabbcccaabaacdbddddcbbcddaadbcdcabbbddcdabbbaaabcdbaacbcdcbdcbacaaaaaabddcbaccaaccccccadbabddabcdbcdaacaabddccbdcadbbcabdbadabadabdddbaabcdacccbbcbcdacbccbdbbabacbdcabbdaacabbaadccccbbcaccacccacdbdcdcbdabdbbbdacdcdbabbaabdbcbdcbacdacbcabcacdcbcadcacbdacadbcddbadbdbcbcdabacbbabbdacddadbacadaabbadcbaacaddbbccdbabbdaccccbbbaaabdcccdcdacabbacbaddbbdbcccbddddcbcaccbdddaddbccbdddadcaaaaadadaaddaaacccbadddbccadabbcbcdbcdbbcabaddddbcbbacaccddcadbddddcdddcacaadbbbbadbcabdcddcaccdacadccaacacadaddabdcabacbadbbbddddbadccbacdbbcadcdcacdaabdcdddbbcbcbcabbdacaabdbaaadadacadaddddcacccbdcbdbabdbaddbdadacdddddbdcdcbadabccbbdbcdabbbcddcaadabbadcbddcaabcdccdadddcdcbbadbacdcabbacadcbdcbdbbbbbccacbdadbacbdccdbaaaaabacaabdacdacdacbdabdcacbccdcdcdacbdcbadbcadabcbdaaacacadadcaadcbcabdcaacadbdccdabcdddbdaacaccbadabccacdbcbcbbdddcadbbcabdcbcdcdcbbccacdcbbbbcacbdadddcbdbcdadadaaabccacbabaccaccbddadadcbababcdccdbdbaadccdbbbcddbdddddacdbcbaaabaacdccacaabdadbdcccaacdbddcadcbcaaddcddcbcddcaacdadabbccbadcdcabbbcbdaaccacbcacccdcdaaaddbbdacbbdbddcdbddaaccaccbabdaccaccabaddbbbadabcbbaaacdbcdbaabbbdaadacbacdcbccacaacaddbbccbbbcddacadcddbdccacdcdaddbbcddadcddabacbccbcadddabccacadbbbbddacaddadaccbcccabbdbbaaccccbadddaabddaabbcbbabbbbcbbadbaddbccbbcaccbbccbcabadabaaabaaabbbcbbdbbbabccbacdccdabbcaadbcacdbdcaddbccbaabccbadaccdbabdbcbddbddbdaaaaddcbcbdadabdcdddccabdbddadbdaaabaddcbaaaabaccbdaaddaadacbccbacccdbbbcdcdaaaddddcacdcacdadaaadbdaccacccdcadaddddcacddadaccbadcdbccabdbbcccbdbdabccdaccaacabdacdbbaadddcdbcbdabaabbcbcbccdaaabcdddbacdcadbaddcdddadadabbdababddbccdcbbcccadbbcdbbbcdbcbdaabbbbaaabbbbacaddddddbabacacdacdbdbdadbdbbacacddcddddccacddbbabdcabdacbcdccdabbdadccdcbcbcbcdacaaadccdcadcddabdbbdaccabbadbcdcdbabcbcbdcdbcdcaccaadbcdababbbccbbbdbcbabcbcdddcbaabaacabdcabbaccbabddaddcccacdddaaddcccbabdcddbabdacbaadbcddccabddbacdaaabaabccbbaabdddcacdccdaabdadbabadbcdbdaaccbcbcbcbcbccddacdbadacadaddcddabaccdccaaddccadcabbbdddbbbcbaaacbacccccdcbbccbccaccadabccddcabdaccbdcdbdcacdddcbacbcabdcbbaccbbdcdcbdbbbcbddaababbaabacbaababcdacababddadacdbcbbbdcaccdacadbcbcadacaddddbdaaaabcdbdcdccddbbadcacddacaddbdaacaaabacadbcaccccaaabacabdbbcaacdacbadacacacddabcdbadacddbcaababcdaaacbbdddabaccbcacdccabbbddbcabdddddbdcadcadddbadbbadadddadcccacbcdbcadabaccbccbbaacccbcccbabbddadbbdbcaccbcddbcababbbbbaccaddcddddcaccbdacdbdacddbcdddadbcbaacccdadccdcbcdbcaddcabdcaaddaccdcbdadddabbbbbdbdcddadbdbadaaacaadaccaaababbcddcccadcaabdcbbcbdbbadbbbcbbcabadddabccbaadcbbaddabadadbcbabbcbababbdaabbbacabdcabaaabbbacacdcadcbcdbcbcccccbcdcacdbdbbcacdabcbadcdcacbadaadcbbddbadacaccacaaaaabddcadbdcbcabcaddbddabacbacabaccccaacaacdccbababcaccdcbdbdddbbabbaacdadacdcccacbbbbcbbddccdbbddbcacbabaccbbbdcbdbddcccdaadcacdababacdcccdbdcabdccbbaacbacccbacabcabadcddccabbbbdcbdabbdadccddbccbddcaddadddabbadcbaabaacacbddaccdcdaacddbdcdddbabbacdacdcdcccccdddbabadbcbcbadddcacbbbbadddcaadccbadbcdbdbaddacbdbbabaddbbbdaaabdcddbaadccdabacacadaadacdaabacdbbcdadccddaaddbcddbcacadaabcbbdcbacbbcacbacbdcccbaaaadbbddcababbaaadcdadbddbaabaddcddabcddbaacdbdacbdddddadbcaaccabadcdacbdacdbabdddbcaaadadcabdbcbdcddbbcabccbbaabdbabcdbbaddaadadabcdaadcbbabbbaacaccaddccaadadaddabbbdbdcdabbabdbbcadcadaabcbbbdbdbcccdabbaabcbdddbabdaadaabacdbbdcbbabaccdabacdcdcbaacdcbdbddbacddddddbbacddbbcccbaaacabddbbbadbadbabbcadaccddbaadcdbcacbbcacaadadbacddaddadbcadabddadddbdacabacdccddaadcabacabdbaadabdcadabadacddcdacabcddbdcdbddccccddbcacacccabccaddbdcaaadacbbaaadcbddacbcdcccbaccabcacacaadacaaadcbabccdaacabdcabbacdddbddccddcbbaaddbcbaadbbadcdccdddddabacadbccadcabcddbcabbdddbdcdbcabbbbababdadbbdabccdbcccdcdcbbcabbdabdabcadabacaaccaaddaaaaacdbcdacdbadbcdbdcdabcddaaabcbadabcbbcbadbbddcbdcacbcadcaabcadccdcbdabddbabbbdccadcccddaaabacabbcdacaddccddbadbccdaadcbacdbddcaadbbccdcbaaabdcacbbdbadccbddccbbcddddbbdabcbdccbbbdbbdcaddccddaccbbbbdcabbbdcaddcccbdbaabadbcbaccbdcddcaadddabcdabcacaddcbbbdaaadaabdcadaaaabdaacdbdacddbaabbcaaabbbbbbdbadcdacabcbbddacacbbbbcaadadccdaabccacbaadcbdacbaababcacadbcabaadcadadbbbdcabcdacaaccccaaadbbcbddadcacacbcabdbadcdadabbabcacadbbaddcabcaabbaaaddcdbadaadcbcaaacddacacdabbacabcbdcdaadaaccccbababcbbccabcdbabdcbbcbaabbccbadccacadbbbcabccdbaddcdccacccdbcacdacacbaaaccbcadbddcaaadbbcacdacbcadbcbbddbaaadacdbccbbbaacccddddadbbdaaacbbbadaadddacacbcdccdaccbdcdaacbbddbadabbabababdaaacdccddabcabacbdbddacadaddbccccaabaadbadaabaadacbdbbabadcababccadbdcdaaccccdaacbadacadcddbcdccdbccabddcaddcbacdcacbaadbadcbcbaabacabbcbcaadddacbbdbdadbdaabbdacccdbbbacbacbbadbadacdaddcbcbacabbcbcadacaaabdddcdccaabadacbbccccbccbbdbabacdadcbcbaabacaabbbbdbaacbacdbbbcaccbdcdaaccdccbcacaacccdaadcbdacccccabcccabcacbdadabcbaddbcdcaaaacabbbdbbcababacbdacacbcaadabcaddcdaddbcbcbdbbdccccaddbbdaadaadccdbbdccccaccbdbdabbdcbbbdcccabcbadcbcbacbdaccababdaabbbbdcddaaabdacbddccdbcbababdbdaabaadccbadbcbdbbacbbddabcbbccaaabcdcddbcdadcdbccccbcbbadcddcbcdaddbcdacbacabdcaaacddacdacacaaccbaccadabccadcbccaccdcabccddddddbbcccbcbcdbdaaabadddbaccdbbcbbcaacdcaccdddbbdadcdcacdbaddcbbaadcccbadccdabcbdbbaccdbbadbdcbdbbcbdbddcdabdbaabacdddddbbaabcbaaadddcdadbbcadbcbbcabbabbbabdbcaabadadaddcdbdaaabcaadaaadddacdcdbbdddbbcacabacadbddaddddcdbcdadbcbadbdbdadccaadabcdcadbbcccabdbbbdccaccccdcabaccccbccaccdbaddddbcbdbbacadbcccbadccabbccadbdacbbcbadcbddcacacdbccdaacccadcadbdcddacccacbcddbdccbcbcdcbdccdcbccdabccdabdcccaaddabbdbbdcdaddddadbabbcccaaacdadbccdacddaddadadbadacdbbdcccbbabdbaaaaacaaacddbacaabacdbdbaddbcdddaaadbaaddcaaddaadaccdbccbbccdabaccdddbdabccabbbcccbabbbcaabbadabadbbaaabddbcaabbcbccadaccbabdbbdbcbacbcbdcdbdddbadcabacbabdcacabcccbbdcdacdbbadbbddcadcbdcbccacaaabcadabbaccbcaccddbbcadccacdddddadbbbccbcbdbcbcddbacbcacaaacaccabcaccaabbbdccbcbbbaabcccbdcdaddaaddabcbdaacbbbacaacdacbbdadccdaccbbcdcddbbbbcccdbababdbabadbaddacbbabaacddbdbddbbbabcaadcabcbcdbcadabaaadbaccbcbcadabdbadccbcbadadaddbdddbcbaacaaddcdcdcdadcdaadcccbdabadcdccddadcabdddbcabbcdbcdbbbdddbbadadacaacadbbbccabaddaccaacdadddbddbdabbbbbdcddacabdcdddabbbabbaccbcddcacddbdbdaacdabccbaababaddbbdaddbddccbdcabcaddbbdbccbaabdbdccaddcddbdbdbddbbaccbadbcdcbcbcdbbbdbabdcabbbcbcacaabcbdcbabbcbabaacbbccbddbcbcdbddadabaabcabbbcaabbabbdbabbaaccadcaaacbdbddcddbcbbcbbddaaabcadbbabcaadababaaccdbcbbacccbbdbaaaacbbabdcdadbabcdcaddadaccbdbbcdabccbccccbbdaaccbadcbadadcbbcbacaddcdbbbdcbdabddcbacbddbdbcbccabcbdcdaaccdddaaabbcacbaacdbcbcdcabbdbbbdbcaaabdbcbabcdaccabcaddddabbcdbaacccbbacaddbabacccbbcddcaadcbccadccbdcadacaddcaddaddccdadbcacaddaabbabababddccccacbcddabacbcdbdbdadacbdaddbcbcbadbbabdddbbcbcbaddcbcdccbdcddabbbcbdddcabcacbacbaddabadaaacdbccaacbdacdcabdddcdbcddcdbbacabbaddbbbcdccabdaacacccadcabcbadbaddaabacaaaddccacbadccccbcbbddacaccadacbadbbabbcbbdadcbcbbabadabccccdcbdbbcccccddcbadadbdbaacbabdabacbcdcdbcbcabcdacabaaccabcbdbcbabaabbacbbbbbdabcbdcbccddabdbbddccaaadddcdcdbccaadaccbdbbbcaacbaaabdadcdabbdbdcdacbadccdccddbcdaaabccddacbbabdccbbadbaccdbbcbbdcabaaadcbddcadadaddddddacbbacdddbcabbdaaddadbadbbbcddacaaadbcddaaccbbbbacdabdcbcabacbddbabcbdbabcdabcdbbaccccaccdabdcaabbbdacbbcdaadbbdcdccdcdbbdbbddabdaddabbaadcacbdacdcdcbbbcdabaccbbdabacbbaaddcdbadcbacdddaabcdadddcccbacdcddcdbabcdcacddacbaaaabddabbaacaaccabbcbbaccabbcbcaadcbcdaabacbdbabddccbddcdabddccadabdcddbbdaddabdbdabddadadcacacaccbcdddbcbbbddacdcaddcabbacccdadaaaadcbdacccccddccccdacdacbcaacddaabbdcbbadabdcbbcdbaccadcbcccbbcccdcbbcabccbccdbbbbdcddccdccbbbdbbcdcddadcccdddcdacbbcccaccaabcbcdcbbadaaabbddcabccaccbdccacaabbaacbcabcaccdcdcbacbacbadacbddbdbabcaabddcdbadacadaddadbbbcccccccdaabcdccacabbdccdbbcadccaabbdcaaabddcdbbcbcaacabddaddacbaccabcadcaabbdbbbbdbbacbbcacacabdcbdaacabdccbabddcabdbdcbcddaadbacaabbdcdcdcbcababcccddbabadcbdacddcbbabbbbcbabdacaccbaacabbadaacbcdddabaaccadaaadcbbdadbbdddbccdabcddccadacddabaadcabdcacdbcdcddcbdcaaaaabccdabbadccbabbacdaadbaaccbddadbdadbccaaadacddcadadadddcdaabbaccdaaaabdccccdbbcacdcdaccbccccabdadbddccccbbcbdcccababaadaaabcddacaacbcaababacdacbcbcddabbaddabdbdacbbccbdabbdccccdbccdaacdbaacadbabdcddaacabdcdbdacbdabbcadadbcdcacbdcdccddbccccaddcaccadddcacabdddacbadabddcabbcbbacabdccccbbabcabaaadadabbbbcbddbbbbccbaaaddaddddbdcaadccdccaaadaaddccbcbcaadcbbadbcbadaddcddbbbcacddcabacabaddddccabdcacdbcdccbcadcccbbadabcacbababcdcaaccabbbcadbbbdaacabaacdbbbacaaaaabbdcdcaaabaadaadabcddaaccbaaadabccdbccaddcbbacbdcdccdabababaaabdcbcbabdaddbbbbacabbdadcdadcdccbbdacacddbcaaabccabbbdabcdbbadaacdbddbbdbadcacddcbadabbbbbcacaddbacddaabbdcdabcdddcccbbdbddcccbbcacdaacbabadbacbcdddabddbdcbccdbaabddddacddacccbdaacddcacaaadccdbaacbdccbdbcdabbdadabbbccbcacdbcccbacdbcdaacccaaaddccbadbdbddaacdbddacbdaabccaaacabddddacbdccbbbccccaacdcabaddaabddbdbdbacccccddadddbcdcccdacabdacadbcadabcacdbacaaaddcddbdadabdacddcdadccaadaddabdbabdddcddcdccbbcdddcdbadddcccddaaaacccabbcbcddcccaaccadddaccbacaaabdbccdcdbccaddcbaccbbcdccbaabdaadcadcccbbccacbbdaddbbadaccddabaccdcdcadadddcbcbbdaddbbcbbbccacbaabcbbddacdcbdcdaacbccdbcaaaddbdbcbabbbababcdacdadaaaaaabbdcdccbdadcdbdddaadbdcbdbacacdbbabaddcbcaaddabadaadcccccacccccbacaadbdbabacacbccacbdabaccbbbaabaacdbbadbbadccdcadbdcddaddcbddbbdddcdbdabbdaccaddaadcbadabbbbcaabbcbdddcccdddbcadbccbbccdbcccacdbbaaaccadcbbadccbadcacddcdbbbbdccdaccaadcdcdbbdabaadcddaadabbbcabcccaddbdbbddbcacddbadccbcadcbdcbddcbacaadbaaacaaccabdcbadcaccccacbcddadbcaaaabccdbaaaabccbacabdddbccabdbabcadcbbdbbbdbcabadaddbcbdabcadcadcabbbabcaabcaabcadacabbaccdcbdaacbcdcdcabbabacccbbbccacbcabcccbbdccadaaaacdcbdaaddbaadacbaccabdcbadcbaabccbdbddbdbabacddbdaacdbacadaaabcdbdcbccabdcaddcabdadcbabcdbccabbbdbcaaccbbacdaabcdbaddbbcbdbdbcacbdcdadbcbbdbacabbcbadcdbaabbacacaccaacacaacababaadabdaabccbabdaccdbbdcdacacabdacabaddadbdbdaaacdcdbbccaaacbcddbbddacccddbbcaccbadcacdacaaddbbabdcabccabbacdcaadddaababbcacdbbcadaccbdbaddbcacccdcaddadaaddccdcabdbabbbacbcacaccccabababdcddbdabdcccbacaaababacbacbdbcbbbaacbdcbacdcddaddcdcbbccabbdaabddbbbbbcbdaabbddbaadaabdbccbaccdbbdccbcaaadcabbbadbbbcdacdaddbbaabcbaadacbdcccaddbccbadcdbaccaaacdbbccbbdcccdaccdbccdddaabaadddacadcbcabadaabadbcbbdacabbcbbcdcdcbbcccdccaacaabcadabaccdabbbcaabcbccaddcabdcabadbdcacbdabdaccccaadbdbbacbabaaccbbccbbcccbdcbcccbbdcbbabcbababccdabaaacdaaabdadadcbaccaabbddcbbabbbdcdcbbccccdbbacadbabcbdddacdcdcdbdbabcaaadddccababdaaaccdacabaaddccccabbadddcdcbcaacbaabcdddcadadbccbababcddbccbdadabbbaaadbcddcdbadbdabdddacdcbabbdabdacaccbcaaaacadbbdaabacaaacabccdcacadcacbdddccbdbabadadcdccbbadbbbcccbabbdcaccbdcddbdcccabdaababbcddbddadbaababddcddbbccdbacdbbcdcdbdcabbdaadabbabaaacccddcabdcbaabccacdaadbbddbadbaddacdddcdbdadabcacaabcdacaaddcccabcaabdccdcaacccaaddbccdddcbabdccbbabccccdcccdccaaddccddbddcbbddabadabccccaccdbdaddbadcbaabaabdbccacaccabaaddcdcbbcdacabdcaabdbaacaccbdcaaddddcdcbabbdccdbcaddddaabbbddabacbcccaccadaddabbdbcbabbbbabbabcddbaaaabbabadabcbcbbddbccaacdbcdbbbbbbdabdbcdbcbdacdbdbacaabdabdbbcdccaacbccbbdcdcbdabdbdcdddcbacccdabddcacdcbdbabddbbaacbddcbbdcadabcbcbcdcdaccbababbcbcabaabbaddddaadabccdbcbcccaddbdccaddcabccdbbcacdaacdbaddaddbbdbcadddacbaabbcccaccddbcbbdbbccccccaacdbcabaccbbacdbaddacbdacabdadadaaabdabaaaadaccdabdccbabccddabbaadbbacadcdccccabdabcbaaddbcaccdacccbdaacdadbdddcbadabbbbddbbcacbadbddbbadcddcbadaaadccccccddccabbbcabcdacaabccbccbbadbcadcdadbbdbadacaccbdddbbcabcdabbdcdaacccdaacbaabdbabbbbbcabbbaadbdbdcdcbacaabdadbbbaccbbdbababdadbabcbcdbadadaabdaccbbcadaaacdcddaadbbdcccccadabbaabacaadacdddcdcaaabaddbaadbdccaddbadacbbddabcddabbbddacadadabaacbbbdcbbdcbcbbddcccdbcacabbcaddabccaaacddbcdbcaaccbbaccdacaadcdccbddbabadcdaaacaabaaaacdadabbbacddccacacbccccdbcbdbaddbadcccabddaadadccaddbaacbdabcccbaadcdadacbcdbdcaabdcbaccbabcadbcaabdabdcabaabdcddbdcadbbcbbcbdcdaadabddccccdbbbdcaabadaadaadabaabcddacaaccbadccaaaabcbcbbdaabbcbdcbdddcadbccccabbcdcccaaaddccbaddababcdcdccdccdbdabcabadacbcacadbbdbbabbbcacdcbbacdbdcddbabdaddaabbcbaccbbaabdaccdbacbccdcadacacdcccbbdbbabdbbddaabbbaaddddbcabddcddbdbccadbccbcccadadcadcbdacaccbabaddddbababcabaccbbbccbcacccbaacdaacabcdcbcaccccbbcdaaabcdccabccaaddbbdaaccbcacbccdaddcacbcdbacbbaccdbdddabdcdccbaacbadccbcdacaacadbcdbaccaccdddbdbcbdbbdbcaddbddbcbbbdbdbdbbbdbababadddcababbbdbdacaabcadbdaacbaadbcddbdcccbcacddaddaaadaacdbddbdbdcaaaabbddbccacaadbadcbaadcdcadacdbbbbbdcdcaddaddabaadccadabdcbabdaabdcdadddccdcdacacacdccaddcbbddabcccdababbaccdbbbaacbabcddadacbaccdbbbacdccbdacdaacabbcbdbdddbbaaaaacdcdaacabadcbaaccbddcaababbbcbbbabbadcadddacdbcaabbaddcbdcaccdbbbdaddbcbbcddbbbcadacbcaccbcdddbcababbabcbacbbaacdddabbaaadcccdbcbdabcdcbadccbbbabcbbcddbadabbacdcbcbdddadabaadacddababbcacacbcabccdbbbcbacbcabadcbaccaacadcabadbccaacbbdaabbcbadbacadcacababcbdbbcaacddacbcbdbdccababcbcdbcabcaccdcabdcddaaababbbaabababbbacdcbdbadbacdaaabccaccccdcbcccbababbadabbbccbcdcdcbdccbabcbbbabddadacdddcdbbcaaccadbdabdccadcddaccacbabdaabcbbbdcaadddacbaccdbccadbbdabadbcdcbcbcacbdcaddbbdaadbdaaacbcabbaccdabdcbbdddbabccdbdbcdbcacadcbabacbdcaadabcbcdbaaccdacdcbcbbddddcccdabadadcbddbddcbccadccbcbabbcadaccdcbbccadbdddbaccdbaabadcdadadcacdcbdcdbbdacdabbdcdaacddcdadbcabaacabdaaaaccabbdbbaacdcaaccdcbcadaaaacddddaaddddbcdcbbbadacabbbddcdaaccaccabbaabaccccdcbdaaaaddbabbcddddacdcdbddabadadcdcaaaccdbacbbaadccbcbdbcaaccbabacbabcadacbacbabacaccbbdccadbbdcccbbcbaaccdaabdaaaaabadacdccbacaaddbcbadacbcbbcccbbdbddcbcdbcbddbacaabbcbbcbbabbbadbaaaacabaaddcacdbccdbaadcaacbcdbdccccdcdcbacdbbbacbddacbaabbabbaacbdcdcabdbccadacddccdbccacbdaccbacabcadcbddddbbacaadacddddcbdcadcbaababbbaadaabbbdccadccdbaddccbadadddbacdcdcccadddadbdcabdccddcdacbacbbddcadadcabbaadaabaacaaaabbadcdadcbbccaabbcbbbaccdabccaccadddbdccdccabcacaccbbddacccddaaddbdabbabbcabdacacabdddabdbbdbccacadbabbaadacbaccddccacabcdcbccdadcadacddabacaadabbaabaccacbbdabbddcdbdbbbcdbbbdcabdccbdcbccbabccadbbdbcdaadcbdbbcacdddacbadbdbdacbbbadabbadbaddcbbcccaacbbbaddbcdddcdccdbcccddbcbbbbdcdbaccbbdcbbcbabddbdbaddcaaaaaacbbdabcccdcdccdbdbaabdbbcdacdbbadcacdcccdcbdccadcdbaccdccbaaccbbdcbabbdbdcbbacaccddacccadcbbdbadabadcdbccbbccddacaaccdcacdaacaacbabcadccbbaccbddabdddadacddaddaddaaddaddbacaacadadbbddddbababdcbaacccbbdadcbcccbaabaaccccaadddbacbdbabccabddbcaaadcdaaaccabcbdabababbadbbbcbcbcbadbadaadacdacdbbdbcababacbbcdbbccacbdcaabdbcdabaadbcabdbbbdcadbccddcccadccbbabbdbaabdbbcbdacbddbbbdbcbbdaddbdbdaabaddccdcdddacddaadddccbabcacbbcdbbbabadacbdccdcbadabbccdcccbdacbbbbbbcbabbabbbbdbdcccbdbbbdcdacdcacacadddcacaabbcacabcaaabdccddaccabaaabacacaabbbddcdddddcbccbdaabbacdcdbaddbdcbcddabccdcaddbbaddacdbbaaccaaacbccabaaaccaccbdacadacdcdcdbbaacacdbddbcdbaddcbbccacdbccdbaaadabbbbbcadcccbcbcccbabcddcbdabbbdabbccdccdabadbdcdccabcadbbddacdabaabccdacdadbbddbaaaabcbdadcaddcccdbddadcdbcdabbcadbbdaaabdacbbddbdcddaaaacbdbcdabcabcbcbbbcadbbcdadddcabdbccadbaddbcdaaccbbaccdababbbbadacbabdbbccdacddbbbabccabdcdbdacdbdaaacaddadbabbbaaccdbdadaccddbbcaccbaaadacaacddccadbdabddddadcacbbaddadcbbddbbbdbadbdadddddcadccbbccbdadacbbbccdaadcbacaddcddadacbdadacdccbddadabbbabbdccbadbcdbdadbccacccadcabaadaabbddddadcaacaddbcdadaaadcbdacbbcdccaccbacdbbadacdcbdbdccbdddcbbccdcdddcbccaacbcbcaadacccdcbccccabaccbcbdcabadddcbcbbbbbccbbbbcacdbcaddddcdbdbacadccdcaaddadcbdababbcabdcbdadccdbddabaddacdbcbcabddbbaacbbdcdcadacadcdbbcccdcdaaadbdbddcbbddcabaccdbcaacdabddbadabdbbcdddbcdabddabccaadcdccbbadadbdbcccbdddbbdcdbabccdbddcbddbdacbdaadbdddbdbabdcabdbabdadacddcdbddbbdcbbaccabcdcccbcddbdcbcabdbacaadacacccbabbbaccddcdadcbbccacaaccbdcbbacaddbdbcbaacbdccddbddcbbdbbbcddbddcddbdaccddaccbdcbbdbadbdcbaaabdacbdbbccdadcaaabdbcbdbbdccdabbcccdcdbaadbbdbabdaadcddcbadcabcdadcacbcccaadcbabbadadbcaddbadcbbcacbacbaaccccdadbcacbbccaadcdaaadcddccbcbdcaacdcbcbcdbdacddadcacdabdbdbdccccddcbbdbcccbcccccbbaacddcbddacdcdbacdccaaddadbbdbcbbbcadabddadbcdadaddcdcababddbabcbcccdbaaadcddabbaabcccdbddbbacdbbbabbddaaaaacbcbacacdbbaddaccbddcacbabcccaadcdadaabbbbdcdbddaadbddcbbcdabbbdadacaaaadbdbaaabacabbccccddadbccbabbccccbddcaaddcaabcbdcdadbbbdbaddadbdcbdabbbbdbacddbbdddabdaaabcadcbcbbdaadbaabcddcdbdcaaadcacadcbaccdabaadacbcadcacbdddabcdadbcddccccdacbcdcadabbcababacdcdcdabacdcbaddbacbccbccdcbabcbadbcabbacdccbaccbadbadcdccbcaccdacdddbbccbabdcbddcaaccaadabaaccdbdaaabddccbddcacbdccdbdbabbcdbaaabcacababcbcdbdcdbdacadccccccbdddddaabdddddacbccabcdcaabddbaadbacbdacdccdcaaaabaddbdbddabaccbdddcbbadbdaadcbcddabcabddccacbcdbcaaaabdcadcbddcdbdcbdbcdcdbdbdbdabcdbcbaacbcaaacbdbccaaccdacbadabdcaaaacababbbdadabaccccdccdcaddcccabbdbcbdbaddcbbabccaaddbaabbbbadbcdaaacbdbaddaccbabddbbbabbddacbdabaccbccddacaadaabcbccbadaabbbdbcadabdcadccccccadaddcaccdbcdbcaadddbbbcabdbacabbabadbcdabaabaaacdaabdccbbbcaadabaacaddcaddbabccddcdbcacccbbbbacccbcbbdbbbaccadbcbddddbdbdbcddadaaaddcaabaaaaccddbbbdbcadbadbbdbcbccbbccbcbcdabdabddddbbaddbcadabddccacadbcacacbcddbadabcccadcacacdabccdabcaaacbadaccdbcdcacbdcaddbbabbbdbbbbcccacababbddccdabdbadcddacbdccacdadbccbdcadbdbcaaccdcbbdcabacdccabdabaddbcaccdbaadbdbbbdbcadcbbddadddbaaabadadacacacabdccabadbdaabaacaaacdbdbbbdbbaaacadccaaccdccadabbbdcdabbbccbcdacadadabcccbcbcbadbaddbdccadaabcaaacabccbbacdabadcbbcbddbcbccdddaddbcaaacacaacccdaaabcaadcaabccbdcbcbccddddbadddaacaddadcaaabcdbbadbcbadcacccdcdccacddcdbdccccbbbbddcbdccdddabbabbabbacbbacdaddbabaaabbcdadadbcdabacccbaadadcacbdbcdcdccbccdcbdaacdababccbcdaabaabaccaaabadbddaabdcaccbcbbcdacaccaaadaaacbabbcaaaddbbddadabdccdcbdcadbbcddbbacbddaaacdbabaddcadbcdabddbdbccccbccbabbabcdacabadccdaacdbaaacadabbbcdcabbdcbbdccbdbadcadcdbbcdccdacdcababcadddaddcbcbaaccbdbcdaaaabbdcdacccbdcdddbcbabbcacaabdabaaacccbbbdbbbdbdcaacbaaccdcabcdcccbaddbaaddcccadacdbdccddcaaccbaadadaadbdabdbcadcabcddbcddcdabacbdaabbdcbbdccabcddbcaabcdddbdcccbcdaaaaddbcabbddbddcccaccddbdabcbcdbaddabbdadacddcacaccdcccccbcbbbdbccdcbacddacddaaccabadbdddbabbadddabcccaadbdcddaddcdccaabcaacaabdcbabbcbaabcabdbaadabaaaccbaddddccdaaccdbabddbdccabcbadcdaccbdbddabbdddddddcaaccbabaaadbabcbbccbbbdcccadbbacdcccdaabadbcadaaaabacdcbdaaaadccbaaabcddccaabcdabdadcbcacccdbdcdaaaccdbdaaabddcaabcbaabbbccacbbddddcbabaaadcacbaacbbdadbbbcdadcbacaddacbdddcccbdbadcdbbacbcabacabcbcccaacabbdddcbbdcddccdbdbaadcaacddbaacddccbcddcaadcdbcbabcbcadbaabccadbbdcbaaabcccbdbacadcbdbdaccbcbcbddabcadbcdcccdcbabdbdbdbcadcbcabbaaacacdabaadbcadbbdcdbbdbbdabcddbdbccdacbcabdcbcbcabcbbabacdadcdcdadabbcabcabdaadabccbadcaabcccacccddcbacadadcdcbbccdcabcdddbaaabdbccacbabdbbdaadccbbdabaaddcbbadbbaadbadbabdcbdacbcaacdccadbdadaccdddabdccabcddabdcdcbcdaddbbcdcacabbdcacbaddcaacbdbaadcaacbdcdcddbadddaaadaddbcbbdbcdbcddcadccbcdaddcddaabdcababdccbabbcbcccdabacadcdacdcacdbaabbdbbdcddabdcdaacdaccddabbddadadbbacdabbcdcdbcbdadbaaacbdacdcddbdadbbbcaacaadabbbbcbcabdbbcccbdddadacdddcaacbacbbaaabccddbcdaacbcbddacdcdbadcadbcddcbdadbbacbdacdabdbdabcccbcdcddcbaccbaaabdbacdadacdbbabdcbacbadaadcabdcdcddcbbdcddcbcaaadcaabdbabbcbbabdbbdcdbbbabdddbdaadacdbcadbabdbaaddaabcbbcbcabaadcbcdadccdcdcbbdbccbbaabbccdadcbccccbdcdbabbdbabbadabdcdaacccbcabcadbcacaabbdaccddddcaabccbcddbcbdddabdddadadcbbacdbacccacbabdaaadacbddcbdbbbdbbdcabdaaccdaabdcabcacbbdaaacacdabcddbccdbdadacbcaaaccabcabbddcacbdccbadacacddbabcdcadbaabbaccacbcaabbcdacddacdbbccbadcbcbaacdbbbacccadaabdbdcdaababcdaacdadadbacccccdaacacdadbdaaddcbaddadcbaddabcdcdaacbcdcadbcdcacadbdddadbacbaddbcaccbcccaccaadcdbaaaacaadcdbdccbabcccdbbcbccadbcaddacdadacadaaaddcdbcbcbadaccadcadddadabbcdbacadaacdcbadcdcaadcbdccaabadacdcacadbddcbcdaaaddcbaaaaabcacdaddcbbaaacbbaadbdaccbddadccbaccbdbcacbaaaabcdacbcdacccacacbdcddbadbcccccabdcbaddbdcddcacdacccdddaacaaddcbcdabbacddbbaadbaadccacabccacccabcaaabdbbcaccabbaadcabcabbdcbbbccadbddbcabcdccbcaacbcacdcdbbcccaaddadcddbddaccdbcbddccacaaccdcadbbaccbcddaddcadcdcddadcdbbadcdababcbbdbdcdcaaccbabbbabcdbbcdbbdadbddaabdcdacbabdcdccccbccccaabacbaaabcaadcbdacdbdaacbcdcbdbcdbababddbcacccdabccdbdbdcccacdcbcbbdacdacdcaaabaacdcdbcbdcdacabbcddccabcccabbbadababbbbcbabbbdcabbcaabdddabcddbccdbbcaadbadcbdcbaaddaadacdaabadcdbddbadbdbdcdbdadcccaacaadcdcabdccccbcdaaaaaadcddabbdadacdbaabcbddadccacccdacabaaaaacdabcaaaacacdccbbdbcabdbadaaccbdabcaacdacbdadcddaabdcdbabdabaddccbddaaabaabdccdcaacbadbbdacabdcbbbbaddaaacacbbaacbacacdcccaddadbddccccadbbcdbdbbbccbbcabaacbdcccdccaccaabaabbcddccbcbdbacaadaabbadaadacabbcabcddddbdcaddcbcacaccbacbcacabbadbabaaacabcbccdcbccacddacaadbdbddacbdbdaddbcccdcbcdacbcdcaaaadacddbcbdbdbbcbaabcdaccaadbbaccadabbaadcbcddcbadbdcaababbcbcadcbaacaadacaacaddcbaddbabbccabacbbdccbaddaabaadddbdbdbcdcbddcdcabdbddaaabacadadcbcdacdacdcbbaacababbbdcddcdaabdcdcdddbacddbbccdbaccadaabccbdbbbdcbaddbbdacbbbbcbcdbdaaccacbbaacdaadbddacbabcdaaacacbbbcacbbdcadcdadcacbbddcdabcddbccccabbdacdcbcabcacabcdbacadbabbdaadcccdcdccabddcdadaccbdacdcadbcdbbbdacbcbbdbadbdadddbdabcdacbadabddabbdbcbbabddacdbbdaaaaabdbbcbbcdbdbdddddcdaadababdccadacdaccdbbcbbcabcbdbdbdcccbdbadcbdacdabdcabcaddbcdbdcbadddacadcdcadadccbbdbcdcaadbbdccdaddacddccccdbcacbdcbccbccbcaccddaddddcdcaacddacaaaccddcbcacdddcccbcdcdbcbbbaccabbcdbbabbdbacbacbbdcbbacccbbdabbbbdaaccddddccdababdddbcbbdddacbdccadadbdabbdbddabbaacbccdbbbcaadbbabaacaababcdbacbadcbabbcaaccbcdbaadabdcabbbdadbdcbccacbdcadcbbacdadbcdaabdbccbbdbbcbadbbcabdcbcacdbdaacadcadbabacdbdbcbdaabdbcccbacddccaabadcddcbacbdcccdabdcacccdabdcbdcdbaddbccacbcbaddddabacccdabcbbccbdbbbacacbacbbadddbacdaaccbaaabbbcaacbabcbcccaddccdabbbdbddddcbbdbbcbbcccbddccbadddbcdaccbdbbaaccabaabdbaadbaaddabbacdcdcaddabcbbcdbdcbacadccacbabbdbdddacddcdcdaabadcbcaabcadbcddcddabbbbbcdddaabdaabaddccabbbdbbccccbaadddcbabbbadcddbcdacbcbbbccabdbbadbddbaccdccdcdcddbcdccadbdcacccaabbcccdccbaacabcdbdacadddbcdadcbcacdabacddccaccdddcbdbcccdaccdcbdcaddabbdaadabababdacaaacddaacacadbbdbbadaacdcdbdbcdcaaadcddbdcdbbabdddbaabaacddcbccdaaadbcbdddcacbdcdacccaaccaabaaacbbbadcbbaaaabcbacbcddddabaccccccddcddccadbbcbaabdbabddacdcbccaddccdadbbcdaccabcbabdadbdadabdabbcddbaacdbbbccadaddbcadcbacdcdbabbbadbbaadabdbbaabacadbcaddbadbbaddbcbccdadddabddaddacacdcacddbcbbcabcccbdacaadccbbdccaccdbbcabdcdcdaacaadacccddbdaabdbdcdbcaadbacaadcadbdbbbbbbabacbdbadbcdaccabcbaacbdccbabadcbbacabcbbdbaddbaaabadbdaadaacacbbadddaacddcdddbdacaccbcdbcdabbcadadadbccdbbbabdcbccbcbdcdadcbdcbdadccbbbddccbcddbadbcadbcddcddccabbdbcaabcdadcadcdbdcababbadacacddbcaaaddbddcccacddcdcdcbdabadbcaddccaacacbbdabcdbbcabdddabdaabbcabadccbbddccaaadbdbdadcbdbcabacbcdacccddbbdcccbbddacaacabdddbcddcbcaaadcdcaabdaabdbdababddbabaaacddcabdbbddcbcbadbaddaaabcabbdabbabcabacaabccdabbcadbccbbbadbccbcbdbbbacdcbacabaadabaddddacbbbbadbcddbacdadacccbdbbbbbaadaccbcbccdaacbdbbbdacdacddccbbcababcdcccbcbbdbabdcdddaaadddabccabcdbdabcabacccadbaddacbbbabbadbacabdabbdaccccdadcddcdcacadbbbcabddabddaccabcabbbdcccaccbdcccbbdccadadbabddccadbabbadbdaadaccbdaddccacadddabddbbbcbcdabccacacccbcdbbbbcdadbbbcccadaadcbdcaccbdbbcacdabacbcddbdbadbbccccadbcaccdcbbaacdcbbdbbaabccdadbcaadbbbbdbdacbddcdabdcbcaaacbcacaabccdbadbbcbcaadcadacbacacbabccdbaacdbbaccbbbcadbaddabbdcaabadcdadcdaacddacbaaadbdadcdacaddaabbaadbbbccdccbdcbbacdadbaadcdcbacccaacdcacdcaddcbdbaadadccadbbcaabdccdaddadddcdbbbccdadbadbababdbdcacbcbbbabcacdcdbddaccdbbbbaccabacdadbbbabcabcbcdbabcbcbddcabcdbbaadddcabccbacccbbbacdddddadadbaacadddcaddccaaddccddbbdaacbddbdcdbbaacbbbaaadabddddababcaccbdccdcdbcdaaadbababaadbdbbcbaccddcdbacbaadcccabcdacdabaadcdaddbacdaaddcdbddaaddacdabbaaabccabacbddbdbddcccddccabacbdbcdbbadacacdbcabcdadbbbcadbbbcdcbccbaabaaacddcbacbdbabddbdbcdadcbbdcabddabbacdbbbabdbaaadacbadcdaacdabaddbcbcdacdcabddcbcdbcdbdbaacbcdbddccbcccdddaddcbababbdcaddbdddddbcddbbacdacbbaccdccddccadcbbbbbbdccacacddbdbdacdbaabdadcbcadbcdbadccaddccbdcadaaacbadbbaaadcccbaadabdccdddcdcbcdcccadccbcbacaccdabaacdddcbbccbbccabaabadcbabbadbdabdcbabbdcdcbbcbacacccbaaacdaccbccdbdaabbaadcddcbddddcaccaaacbaadbcaacbadbcdaaadbdcacadaababbbbcccaaddacbbbbbddccababdcaddaabbbdabbacbdadbddbcaabcccdbbcbcccddbbddcacdabbaabbcaadddaaaccbcadbbcabcdcacbdacaadcdcbadcacacccacadbaaacdcdddaaabbccaccabacdabbacbcadbddcdddcdbdcadbdcdbbdbaababbacdbcabaaddbacdcdbdaacabdddbcbacacdacccbacababdbcabdcdcdbddbbdcacbaacdccbbddabdbcacccdbcbbcbadaddcdcadcdccadbcdbdbcdacbbaaabbdcdbaaadbcabbcbbbdaccbaabdcabadbadcbaccbcbadbcccadacddcdbddbabdcdbdbbddabccddccdbbbddddccbcabdaacadbbaadbbdbcaabacbbdbcbdbcdaaaacacccbcccbbdaabbadddababbdbacdbadccabaababcabaaddccccacccbabccccacbccdcdbabdaaddbdccdabaaddcabbcdbbcabccccdabadcbbaccbccccdcccdacadbdabdcbcdddccddbdcaccbacabadaadbccddabcacddbdbdcbcaddcabbaddaccbdaadcbbaaacacddcdcdaabcccaaacbabcdbacaadbbbadcababbcdaccabaddbcbdccbccbacddaddbdcdacadacaabcbbcaaabdbbddabcbcddcbbaabccdbccaccaddcbdcbdcbaccbddbadbdbbaabdbaaababbbddbabaadaadbaaaaacadacdaddddcdcccdbbaaddcbaaacadbcaaacbcbdbbccccdcacbbbddbcacdcccacccadccacccbbacbbdbbadbddccddcdcabddcdccdbcadadcbdccaaadbdbbcddababdacbcbbaddbadabaccdbaacddadbaabacdacbcacccaccdadccddbdabbbdaabaddacccaadaadabacabdcdbddcddaadadbadbaddcacaccaacadadcadbccbaccdbcbcbdaaabadbccbbbcbdcaaddbbdcbadabbbcccadcaacaaccadbaddddcadbdabbbaddacbbcdbcdaacdabdcdcbbbacddcbcbabdabddacdccbdddaccdccddcaccabdbdcdaaadaabdddaddbdbaacbdaddcccbdbdcabaaddbbacdddcbcbccbcabbdadcdcdaccccbccbadcdcbcbdcbddaacbcbabacadbddaacdcdabacccacddbbbdcddaadacbbcdcddbabbcacacdbccbbaacadbacccdddacadcabddadddddcacacaccbdccccdbcdbcbddcdbddcdccdcadacacccbabcbbaccbcbacdabdadadadadbaaccdbdcccccbdaccaaddaaaaadbaadbcacbacadcacaabbcbbdccdbaabadbdddacdbccabdbbdbcadbbbbbabbcdbbdbdbbcaaabbccdcbcbbabbbacccabcdcdacacacdbdabcdbbaadaadbcdcdccbacccbdccdcaccacbbcabbbababaabcbbcbbadbdaaadbccabcdbcccacbadabacbccbabbddcbcdacbccabcaacdbdadbbbaabcbcdcaccbcadabbbbbabdbcbabccacaaaabbbddbcdbcbdbaacaadcbbabcacaccdaaacacaabbddbaaaacdbbadaaddbcaaccbcabbabccbdacdacaccbccabccaacbcadbdddbddcddbddabbabbdbcbaacdabddadadaabdbccccbdcbacdcabdbccaacaadacacaabbdcaadcabacdccabbbadbcacadacddadadabdccbccadbbcaaacadbabcbabdcbbdaaaacbbacadcdbddacccadbcaaaacaaabbaababcadcbbdddcbddabcdcbddbcabdaccabcaababcacaadadabcdcbbabbcbabdadbbddcdadaccccaaacdcccbdccabbcadccbabbddabbacdbdbbdbcdddcdbcdbbcccacbadaccbcdbacdacabcadcdccdadddcdabcadcccdbbadbaddbcbbadadbbaacbdbcbaaabddadcccddcadcabdcdabcbabdcdccbccccdddaadaaacdabbcbdcbccccacaaacddadaacadbdddbacbdcabbbadabaaaddadcaddaabcbdccabcbbcbabbdaacdadcccbddddcdcdbdabbdbccbbcddcabcdccdadbcbacdcabacbbcdacbcadbbdbbaabdbdbdacccabdccdabcdddcaccdbadddaabdaadcddbaacbdabdbadccddccadacadccbdabdbacccbdbbcadacabcdadcbbacdbadccbabadccbcdcddaaaddabdacddbcaaacabadbabcbbcbdbcddddaababdcddcdddaccdacdbcaadadbcaadabbcccbddaacdcddbccadbadccadbacdcbadbcddaabcabadabbccdbbdcdbbbcdabaaddbdaacdcababaabdbdbbddccabdcccaaacaabcbaacbdbcbcadcbddbddacdbdcdabdbcdcdccdababaabcccaabaabadcbcbabadacdcbacaaccadacddadbaccdcacdbdcdbaddcccdcaadddbcbbbbabccdcbccacacacdcabbaddaadcdcddbaccadddccbcccaaacbbddaaaddabdcaabbdbabdccaccbbcaaccabadababddddcbdcbbbdbcaabcbabaacdddbadaaaabbcdcdcbcaaacabbccddadadcadbcaadbbcaabacbabacbbbdcdbabcbbddbccaaccbccddbcbdddadbcccbbaaabadbbdbdddbccdbaaaacddcddaabcdbdbdddabddccabccacbdbaadcabbaddbcdcbdbcaaacddccbbdabbadabadacadbbabaacaacaacacdabbacabdcdbccbcdbaadabbbcbbdccaccbaadcdbacaaabddbbcbddcaabadabdcbaadadcdabcdbbabbbadbbbaddcddcdcdccdbaabcdccdbadcdddbccdbbbdcaddcbdcbcbddccadccbabdbdcbcddadcbadabdccdabaccabcccaddcaaccabaadaadaabaabbcabcbdaaadccadcbbbaacaacacdaaddadbcccdadbadabaddddbacacbdaddbcabcaccbabbcdbdbcacccbbbcaabdbdabdcaadbcdbbabdbcadccddbbabadcbccbacccadaddcbdbcbdcaaddaddaddadcadcbbdadadbcaaabdbaabacbbadaaaaabdddbdbdbcbdddccbaadbaadcccabbbdbbadbaaaccbbcdbaadcccdbddbccdbdbbcbacdcbdabbadcdabdcadbbbbaccdccdccdccdbcbbcadbbdbcabcabadabcabbdccaacaccdacdaabcccaddcddbadacbbabbadbbcdaddbababbcccbdbdbbacacbaddbbdaadddbbbcdbbdcaabbbdabcddcabacaaabdadbdcdbbbadadbccddbdddadcabcdcbcbdbbcdacaaaaabdbdaaddccccccddcdbdbbcaccddaaadaddcddadcccdaacdbcbbcaacdccbccbaabbbcdcacbaddcaababbbaddddddaabdaadaadbaaccadbbaccccbdacaccbabdccbcbdaadcddacdbacbccbbdccccadddaccabaaabcddababdddcbcbbcabaccabaccacbdcacdbcdddcbbcacdbcccddadacdabdbadaadcccbcadabadcbbbdbddbcabacbcabcccdddbcaadcbcacdbdddbcaacaacacbbabdacbccbbadacbacbbadcddbbbbcbaadbbaababacbdbdbdcdcccbddcaadbcdbaccacdabdcdbdbaaaccacadccadbbcddaddbadcbaabcaabacaadaadcaddddcdcddabbdbbcaaabdbbbaaddbccadcbdccdacacabcabadcdabadddbdbdbbddadacdddbcdbadddaadaaaaabbaabbacabaacdaabccdadbcddbcacbacbdbddaccaadaacdddcccccbacbbbbcacadaaabcaaababbcddbcdaacdccdddadaddcdcdabbbcdcbcbcdabacadddcddccdabbbacddcadbacdcdaadbcbabcdbabaccbababcacdabdbbacdccbddbabcccbadbaadcdbddcccdccdaadcabbbcadbdcbabccabddbbabbdcdcacccbbdbbadadbbbdcdaabaadbbdcdbdbbbbbccaadbdbaacabaabbbdaccadbddbbcdbaccdddaddcdcdcbaabbacbbddabcacbdcacdababddadcdcbadbdccbbbdcacdbcccadabdcabdbcaaddaadbcacaadccabbdbcdbcabacbbbbbbdbadbdbcbbaabcacdcbbbdccdabdbcacdaccdbcdaacbcacdbaccbaacabdccaabbbbcbcadabccadaadacbbabbbdacdabcdccadcabcacdcaddabbcbacacdbcaabcbdbddadbdbcaaaadddbdcaadddabaaaddaabcdcbddabbcadbccdbbbaddabacdbabadcdcddaaaddcaadcddaccacdbcdadbccadbcdabdbdaabbacbdabcdcddddbbadcaadcbaccbadadcaababdbdcddabddaacaddbbdddbacbccbdbbabaaddaacdaaaccabddacbccddddcaddddcabdadcbdcbbbdcabaadacccacabbdaccaadadadddcdcaadbacaacdcbcdbacdcddaccccdabcdbaccbabadabcacddbcacddacaabdbcbcbacddbbbbacbabcabbcddabcbddcdacdcbdbcbacbcadbcccdbabcdaaabadbabdadabdabccaaacbaadbcbdcbabcbcddacadaccdabaacadbbcaadbbdcaaddbacdbcbadbdbaadcdadbcaadbbbccdbcadacbdabdddddbbcadbdacbbaddccbaaabccdcccdabaaccccadcbdaddbadacacdbcdacacaccadacabbacbbabdcdbacddcabddaaacdddadbdcddccabdabccabcaabccacccaadbcbdcaaadbcdbbadbcacabcbcdbbbbbcaadddddddcacaaccbabdabdaaaccadabdbddbdbdadacaaaacaccaadbbabdcbacdcdbdacdbbdcdbcadabaccbcdcbddacccaadccccdbdbadccddcdbccbadbbbbaacbdbabcbaaccbabaabdbdaccbacacaabadcabdbccaccbdadcaacbdcbcbcadcaadaacbcbdcdcdcaccdadcbdaadccdabbcdadddabcdbacdcdadaccaabbbbcbaccccdcdacbcbdccbdddbbaacbcbcaddcadcdaddacdccdcbcdabccaccacdbbcccddcdadabdabacbbddababdcbdccbacbbdcacadcbcacbcadcdabcbcdbbbaccaacbbbcaddccdbdcabdcbdadbcdcabbacbcdcddddaacabcdbabdaacdcdddbdcdbbdaadaccbadbacdabcdbcccdaacabaddbbbdbaaadcbbdbbdadcadadcddbddbdadcabcabdaacbaddbbbddcdcdbaddcbadddbdbbdacbcbbacbcadacdbcbbdbcbccaacadcbcbadbdcdabaadbabadabcadbdcabadcbdccccaaababcadcddbccddcbdccbdabddcabcdcacbccccbcaaacbadddcdbcbcdaddbccdbdaabbbbbcbdcddabacbdaabcccabbbababbacbcabddcbcbcababaacbacbddbbadaaddddbaacdddaddabaadabcdadcbadcddbdccbcadbdcbbbdcbabcdabccdaacdbbabaaccdddaadbdaacdcdcdbbbadcbbdbcdadbcaaaabacccabaccbaccadddaddadccdbbbdaaccdaddbbacdaccddddbbadcabcadcbdcdddabbadaccbabbcdbaaaabdddcbdcdccabdbcbddcbccbdcadbaddbcdcbddaaddbcaadabcdbcaabaaacbdbaacccacdabcacdbcaaacbaccaccaaaabacadcaaadccdbacbacddaddcbacdcbdcbccaaaaddcabacbbcabacdcbdddaabbbbcbbbbadcdcbdcddadcbdcaacdbcaadbbdccbccacadcdbbbdcaccabbdbcacbcdabdbcadadaadcbcaaaacbadbcbabddaccbbdcbdccaadbbbaadadcbdcdaacaaabcbddcbcddbbacdbcadbdcbaabaccddcdaddcaddcaddcbabdaabccabaadadcacbccbddbdabdbbbcaaccabcaccdcddadacdcaccdadcdcabdbcbcabdbaddbdacccdddcbddadccbcbcdcddbdabbcaddcddadcaabcdbcaddaccaaaacdcddababacacbdcdcccabdcabcdcbdbbabccacbabbdcacdbbbcadcbdbcdbadcccbabbcbdbcbcbbccddbbcbbdccdabaaaaaaabdacaacadadabccddacbdccbbdbcabddbbcabdcccdcaddabbacabcbbbbcacdabdaacbabcaccaaadcdaadbddcdacaaadccdcdbdccbdadccabbbddacccaabdbbaadcaaaddddadbbabccbaabdcacddcaabdcabbcaddadaacdcaabbabbcaadbacdcdbbbacbcddcadbacaadcacadacaaaaccacdbbbcacababcaccbbcddabdcaaacacbaacabdcdaddcaddbadcbcacabacaaaccadbcbacdaabcaccaacbbabdcddbddbdbdbaacaccbbbbdcabacbaacdcdbddadaaddddcaaccddbccaccbaabcaaadcadddaaddbaddbddcbabacdabbcbdacbccbbacbbbbcadbaccdcaabcadadcaaabcdccacbaaacbddccadcadcdcdbaabdcaabcbadcccbcdacbbcdbbdaadcbbbccbbadbaddcdbbdddacddadadbadacccaaaabbacbdddcccdaabcadcabadcdacdddbbdbbbcccdbcdbddcdcabcdaaccabdbccabbacaacacaccdaddbccdaddcdbaccabbbbbdcbdaccdcddbccdcadadaaddddccddddacbdabbdccddbabaadddbccaabababcddccadcabdadbaacddccdcbdcadcacdbbadaccbdabdabbaacbbacbdaacbbdcbbccdbdbddacbdabadbbcacdabcddbaddaaabddbacadbbccbacacbbcbbdabddbbcaaaccbadbbbaccacbbbcabbbdaacabaadddcaadccdbcacacbccdddbcaaacddabbcacccddadacddaccaccdcabbdbcaabbcdacaaaaadbbddddcdcaabdcaabcadbcaadadcbdbaddbccabdadbaabddbdcabadccbdbcdbddccabaabdacdaccbaabaabcbcdbaccadbdaaabaccdcbccbacbdcbddcabbcccbcacaabdabcadbdcdbdccdabdbbbbaadccadcbdcddccbaaadaddacabcacccdcbdabbdaacdabaddbababbadcccabcbbcdddbbbdbbdbbaccabbddddbacdacdbcadadaccbadcdbaadddbdbccacbbabadabdabbdbdcaaaacbddccbcadbacdaacbdaccaadadacdbbbbabacccdddcbbddacdcbaaabddddbcbddcdcbcbdbadbbabbddbccbdbdbaabbbbaccbbdaccdaacabbbbabdacbbccdaadcadabbccdcbbccccddbdacbdbdbbbacabdabdbacccddcacbccadbccbbbcbddccdcaadbcbcbbcddbdcbacbbccdacaccdcbcdccdbadbbbdacbdccbcccdbcdbddacadaaddbdcbabacdaacddaabbacdbdacdbabdbcbcdccdbbcccbbcabacbadaaabaddbccaddcdaacabccccddbbdbbacdaccbbbbaabdcdcbbcdcbcabaabcaaaadaaacdaccadcdccabbcddabaddccccdbddaadcdabdadabcdbcdaadabcadaabdccacdabaadccdbadbbdbdbbacacaaacbbbcccdbdddbbbcbacdaacbadbbcbcbabbcacbbdcacaacdbadbcabccacdcbacabbacbbaadcbcabadbcaabdddbdabbdadcdbbdacadadacdaadbbbcbacbcaddcacabdbacdccbbbbacdddbcbccbacdacdbdbcdccccababcddababdbdabacdccaababcdcdddabdaccdcadbbacdacccbcdbaccbccccadbaddaadbaacddadbdbbbcddcdbdbaaacbabaabdbbdccadcadbdbcbadccbdcaaaddcbbddaababbaaadcababcccbdbdbbbbdccbccbdbacaccdaaaddcaabadbacccadbdacbaacadcbbcaaabdacdacdbbdbccbbbabcdcdadcabbbcdbadaacbaddadbbbdbbdadbaadcddabadabdaadbcbaaccadcaadddccbabbdcdbcbdabbbcacccacddbcdbdabbcbbcdacaddbcbbdabbaaabbbbcacabbbaccacdccbdbbacaabcbdbcbabbdbacbbbdacbbdbabccdabaccaacbbcbacdccbddbbdabadcadbcbaadabaddbdbdcdddccaacdddacbccaaccdabaabdcaadbcccbdcdbdddbccdadaabdddbcddcccddabbddbbbdcbaaabadcaabdcbbdbdcadbbaddadbcccbdcdbdcdbbdbdccabbdddabbccbdcbaabdbcdcacccbabbaabccdbaacdbcdaaabcdcabaacdabdcccccabbccdcdbcabbdadadcbcdddcdcabaabbcacccdccbcdccbccddcbddadbdbcbaabacdcabccabcdcddccdadbbcbccabcaaababdaaacccaadaddbcdaddbababcbbbabdbdbdccacdaccccbdccbddabaaabcbadbdaabacbbadbbdddbdcddbbcddddadabbcdddcbdcddbbbacaddabdaaabacaaaaccdcdcbccabdbacaddccdabbdbbddcbabcacccdaabbcbcadbabddadddbbdccaddccadacdabbcacbdbdaacdbccaddbcbcbbcbadcbcddcdabadccccbbbdddaaacadaacaadcdabcdaacabcabbccdccddaaddbbadbdcccaaaabaaadabcdddbcadddaadbdbdabbacbdbbcbaaabdbaddbcbccacddbbbddbcabbcbaabddcbddbdddbdadbdbdbdabddbaacbabdcccbacaddabbbccaddadaaaaccbaadbbaaddbbdacbbbccbccabcaaaabadcaaddabababbadccaaaccbbdcabadbdcbdacacadbcdcacdcbbacbbddadacbcdbccacdacdcccadaadcadbcbadcdccaadcdbbcadccdadababccacdadacaabbddcdcbbbcbcbbacddcccddadadbccbbdacabdabbdbadbddacbdaddbddaacbddbabcabaadddadcbacddddcccbbbdadaabbcdccaaabbcaadbcbacddcdadbbacdcacbdbcbbbcbccdbacabdddddadcbdcadbabccacdccaadaabcdcddcdbcddcaabcbadcdaaccdcdabdabdbdacaaadcdddcbddaadccacccacdadaccabcddaacdaaacdcacadbbcabbddbbbabbadbdbdcadccdbbcabbddbadddcccacadaabdbadbdcbccbbbddaddbadcddcdccbbdbdcaabbdccdadadacaddacbdbccbacbcacccaabbadbdbadabbacaddacdbccbdbaaadbacadbcccbbbaaacddaacbabbcdddadbbbbcbdddbddadddcddabdaaaadccdcccbacdbdcdcacdcabbccbabadbbdaadabbcacdaabbddcabcbcacbbbabaabaddacbcdadccdcbcdddcaccdbdababbabdabcbddbbccbcdbcbcadbccbcbadcdbcddcadabacacadcdcbdbadbabddcbaaaabddadbdaddabbaccacbdabadbdadddadccbdaacdcababccdcdabbcbcccdadbcbaadacaccacccdacbbadbbcdacabbdcaddbcdaadcdccaddacbccbcbdbbbabddbbccbcbabadbadbcbcdbcbbdacccabdbccabadbbdabaabccaccdabcabadbbbdcbcadccababdbdcbdcacccbbcadabaddbccaaddcaacbbaabcbbcccaaabcdadbcddbdadaccbdacddbaccdacbdaccadadadddcdcbbcccacbdadbccddbcacccbbadadbcadddbacaaaddadddacccabbccdaccdbaabbdbdbccbaddbbcadbbdcbcddbdadddbbdcdcbccbaacdccabadcadaadbdbcbabbadacddadcbbbcbbcaacdbdbacddbabbbbbaadadbbdcdbbdbbcddaaccbbdbcbbdadbaabcddcbcddccdbadddcdcdbdbdcadaaaadbbbacabbcdcbcdaccbaacdaadadbbbbbcadbdbacabacdbbdadadcbbdcaddacbaddcbcbbabcabcccdaaccdbcaacdccdaadbcdcdbbbaccadbdaadbaabaaaccddbbacaaacdabcccdddbdcbbddacaaadacaddbbbabdacdbbbdcddbbcdadbbabcccbaccaadaccdcbabcdababccaadccbddaaccbdbdacbcdcdbdabcdbbabbbacabbdabdabbdbdcabdccabbaccabdccadbdcbbbdbcdcbbcabaacaabbbcacacdbdcddcacbcadadaadbabbbbcbcbacbbdccdacacbbadcbadbacdbaaaccadbdbcbaadbdddcdacdccbbdababddabbbacccadacdadbddacabbccbabbacdadbaaddcddadacabcaacdcbcbaaddabdadcabdbbbabccbddbddaddbcdcdabdaabbdabaaacdbbadacaccdcabbcbadccdbccabbbdcbcabaadccdcbddadadbccaddbdacdbbddadaabcbbbddbcbbdcbabaabaabddcdbddccddabaacbabacbcdbbdcabbabddbddccdbbcdbccccadabbcdacbcccbabacbdcacdbbabadabbbbbdadbddcdcdcbabcccdbbadbaacaacaacdddddbbcbadbcaadcddddcbdaaccbadaaaacdbaababcbdcdacbddbabccddcadbddcdaccdcbaabbacbdabcdaddcbaaacbbccbbaadcaaccbbcacaaddcbddccbccddacbdcbcccbbdcdaaddbabdcbdbdadbdbbbdcaadcbbaadccdbaabcddbcaaacdadacacdbabcacadaddcbadbadbdcdccacdddcbdcdbcdddbdcdddcaccbbdacdadcdddcadabcaaccabcdabadcbbaaccccccbbbaddcbbaadadbcacbadcaccaadacddcbadbdabadcbddacdbdadcaadcbacbdbddaacbdcddadcddacdcdcbcccbdcbdbbccddcadcdbcccbbccbbccaccdbaacbcababbccabaacabadbccbdaacacababdccabdabbdcbdbdaabaadbbaaaaccbacdbdbcbcdbabddcbbacdbbacbbbcabdcaabbcbbdddcddcbbcccbbdadcbbaadadabdbaaccbdddaaaddbabcdacbbaddabadbaccdddacbccadbdababbbcbdaaccabccdbdadaaadacacbadbcaaaacdaadccabdcbcbcdaddcbaccbbdbcaacabbdadadbadbaababbdccdbbcdcdaababcadabacdabcadcadbbcacdcbaccdcacdcadddccbacbdcaddbdabdbcadcbcbdcbdddabaadcdabdbbabddcdddbabbacbaaaccbacdcdabdabcdcabbdabcabbcadbbabbacdcbacaddcabcacbcddbbaaddbdbadaabcbdddbdbbcdcabbaddbbdabdcdadccabbadadacccbbaaadbbdbbabbccdcccdbdccdbacbccacadcdbabdddbdcacacbacacdcdbaddbdcbdcbbcddcbcbadbabcbbccadabaddcdaaadabacbabadaadddbdccbccaacccacbcbccdcabddccaabcbccabcddbaddbdcdbbcdacdabdccbdbdddaabdcdcaddcabbdabccdbbbccbbdddabdbbaabbbadbbdcbbbacaccdbdbcbbcaccbddbdaacadddcbdcdbbbdabcbccbccabdbbddbaddbcbdcccadbacdbbdbaadcccbdabdcabbdcdcbdddcbabadabcbbcbccdbbacabbcbddacacbdbacbdbcccbcdbcdcbbbdadbacbdcdcacddbacdbcccbaadbcddaadbdcacccbddacccbdccdddbbcacbddcabaacdbdcbcdaacadccbcbcdabbcdbdddccdcbdbbadbdddadbdddaadabbaabbcccbacdccbbcabcabadacdacbacdddbaadbddcbdaccdabcdbcdbacbbacaabaacccbcbaacbcbcbcacccdacbdccdadaccaabbcacdabcacacddbbacccdabbaacddacabbaaddddaddddbbbbdcaadbaacbcaadbadcbadcaabaabdbcdbdcbcdcbabbaabdbbacddccdbcbdadcbbcbbabcacdcccdaddcbbddbadaadabdbadabcaaadddaabcdccabdccadcbbdcbdcbaadcbababadbaaadaabbccaccadabcbbcdbccdacdadadaaaaccbadabdaddccacdadcbcdadcdddbbadabcbbdaddbdcaacddccadbabacbcaaaadbadadbdcbadbccacccbdccaabbcbcbbcacdcbbdabaccabadddadaaaabddbadaacbdadbbcaddcbcacdbcadbcaadacabaaaaddcdccbdbdaaddbbcbacdbbbcbcdcdcaacaddbdbabaabadcdddacaabbbcadaacccccacabcdbdbcabcacdcacdacbabcbddbbcccbdcaacbcccbcadbdbadabccdbccacdbbaabadddacdbddcdcbdddacdbacacacaaadaccbdcbdaddcccccdcbdadadbcddcadaddcbbddcabcadbddaacabbcdaccdadddabcabaadacccdcbcddbbbaaddbabbddbabdcadbaadcacbdbabdcccaaddcbcababbcddccaadadddccacadaabdadbdcabddaadacbadabccbbadaacaabccccdcbdcdabdaabdabacacdcadcdccbbadabbaacbbdccdccabdcadcadadcdccabbbacbccdaacdaadcbccccdcdaabcdbbccdbcbdbdcdcbcbdaaaaadddccbaccbbbbaacdadaaaddcdcbbdabdcabbbcddbbdadacbaaddbabaccdbddabbadcddbdbadacdadbbbdcbcaacaabadaaddbaadbcbddcdccbbcabacacdcbccacccdbaaabcbcabbbbcbabddcddbcaaabcccaacdaccbbabcaddddcddcaadaabddcdcabdcdcbccbdbbbbaabdcbccadcdcbaaabdbcbcaccdccadccdddbcadcdcdabbcdcadbdbcdbbdccdcacdbdbcdaacbccbbbdabadcdacadbcbdccabcabccbbddadadcbbdaababbdbcdbbcabbcdaddcadbabdddacddbbbadaaabdcddaaddcbddbcbdcbadbbbcacdaccdbbaaacbaaadccdaaaacbddbddbabbddadcbdcdbabccabbcbbcbcbbbdaadadcbbababddcadaaaccdbbabcaddbcbcbaaaacaaacbbdccccacddcacaccbdbbaacdadcdabbdcdaddaaabcdbaadadddcccbcbdabbcbcaaaaacacbdbbadcaabaccdbdacbcaaccddbaaaababdcdaddababcdbadaabccadcdcbddcdccabbbbabdcddbacdbcdbaacccadbcccddacabaabbbaadcadcdcbddcdcbdcddcbdabbaddddbbcaabacaacdcdadaacbbaccbdacdabbdcdbabaaaabdccdccddacbbadbdabdaacbbccdbcacbbddcbbdcccabbbbaccdaaaddadcaabdaccdabbdbbbbcdbddccbabacacdaccccdadbacaccbaaabcacbaaaabcbcddacbcbbcaddbcdaccccdcacadddddcdaccadcdaadadccaabcbdcacabcdcbcadbccdcbccbbacddabbabdcccaccbcabbacddbbcbcdddcaaccbccdcbddacaaadddddbbbbdcdcbdddbdcdcbaadabdcbcacdabcbddadbdabcddcdcabcbddbbdaabcddbcdccabaaddcdcbcbcbadccbcadccbdddccbababbccdbababcbcdddbcddcbadabbabbbcccccdcbdaacacacbacadbcdcadaacadabadabbdcbcdacdbbcbdbdcdcadabcbdaddbcddbcbbdaccadbbbdbdcbaaccdcbbcabacadbadcbdbbdbbccaabcaaaabadaaccbaccbbcacbdccdbcbacaadbcbcbdddbdcdaccccdcabacccabbcdacaabcdbabcadbbbabbdcbcbcbbbdbddcbdcaaaadbcadadddcbbcdbdcbdcdaaadddaddbdadddbcdaddacabbdacbadcbbcacccbbdcdadbcddadaaabbadacdccdbcdabdcbcbabbcdbcadccdddddcbdadadabbbadbdcaaabcdaddcaddabdddbaacbdacbabcbbababdddcbdcdabdccabccddbdccbddcaaaabdbacbbccacbbaaccacddacbbacadbdabbdbdbbbacadbcaccaaadcacadbdcaaddcccbddbdccbddbbbccbabddadcbdbbcacaddbcaadcabbbdbdcaacbbdadccbdabcaddbdbbabcdaacbbcabdcaadadbdcbdaaaabaacdcdbbbbadcaccdadbaaaacaadcddaddbbcbabcdaacbaddacadcaaccdcbdddbbdaadadbbbacdbcaccadcddcdaadaacbcdababdddbadbdaaacdbaadcbccbcdcacbaaadbdcabcabbaacdbdccdbdcdbbdbcbbcdddbaabcdcbdadcdacacaddabcdbbdccddbdadbbbabbdcbbacccddcbdcccacbbdccadbbdababaccdcdcdabbdadcbddbadabcbcacdcdcabbabcaddbddaccaddbaddddcdaaadbdababdacbcdbabbadabbdaaadaaabadcbbcddbcabcbacdcccdbdccaddcddaddccaaacddccbacbacaddbdcadcbaaccbbacbdbdbcbbadcdadddadbdbdbdbdaadbbabbddcdababadabddadcdaccacbbcdccddaadadcbdbcbaabaaaabbccbaabbcbbddbbcdcaddaaaaadccdbdaadcbdbdbcdcabdbbcabbdaadbddddcdcbcdbdccdaacbccccdcbbacaddacdcbdcbbddacccbdacadaccbddcbddcacacaaaaccbaacdabcbbccbbcababbbadcbdaabcdcabbabdbbcbcacaddddcdaddcbadaccdcbbdabdaddcacaabccbadadcdbaabadccdbdacbbbdbbcdddbaddadacbcbacbaabbcbbcabaccdcadddcbaabdbdadbcbbacbdbddcadaccdddcddaacddcccccbdcbdadcdcadabbcdccdcbbcddaacaddcbaddbdcdaddbdadbcbcdcbabbaccdbddbcbbbcabbbdbcbbcacbadabaccbcdddccddacbdbcabdcbabcbcccbbaddbbaddacdccbacdbcadbdbabcaaadccabcbdccbbbcbdbccdbadcaadabcacddabdbcdcabbabaabdcdbbacddbcbdccbcddaadcbbaccaddbaaccabaaddababdddabcbbadaccacabdcbcbddddaacadcdbbddcbcaddbacbadcdadbcbadacaddcbcbaddabccaadcbbcbcaaddabacadddbcadabccdccccbccadcbcdadabbababdcbbcdabdacbacbaaaaaacacacbdbbcadacabbbdacdaacdddbdcddbcabbcdcabadbcdbcdabadccdaacdcdacacabbaacaccaaaccccbdbabdadaccdbcbbccccdcccaabcdbdbbdabdbdddcbbccdddbabdabaccbbadcdbccdbaadccccbacbdcbbbbbccbdcbcacddbbbdcbdcabbaacddccbacbcbbcdadbbcaaadaaddcabbacbbbbdaccccccadddadcbbbcdddcdbcaddaaaddccbabdccaaddcbaddcddcbdabacacbacabadddcbdaccbadcabdaacbbdbcbdbddbcabacdaadccbccdbacdcadbabddccdbcadabadbcbcadacbddbbcadbdbdabdadbcdbccbadacbcbdbcbbddbdbbbcdbbcaddddacddbbddabbcbdcdacdcaacdcdadbabcbccbbbaacbabbaabaaadccabbcaddbabbaadaadcbaaacdaadaaddaabbcaddcabacbbcacbdbbdddccbccbabbacabbacaacdccabbdbddcddbdcbacbddadbcbdbdaacdaaabddbaabcaddacabbdccbadbbcaadabbddcadacdccaabdddadaacaadcdbdbbdacacbbaaddabddbddddbbadbadbacacbdcabbdacaabbbcdddcbaaaabadddcbcdabaabdbdacabcabdadddaaadcbbdbcbdddcdbccbadbbbaccccbcddbdcbbcdcdaccabcbadcbddbcbdadbbdcdddabadbddacacccccdacdcbcacdaaccccabbbdbcdbdcdadcababcdaaadabbcadacaaabcddababccbdaddbdbacbaaccdabacbbaaccdbcbcbcaacdaadbdbccdcbccdcbdcbabbdcbcbaaccdacdcabcaddbbdaaabcabaababbcacbdabccdbbbccacbbdcccbdabccabadcbaabccbabbbadcccdcbabcbbdcbbccdbbcaaaabdbbbadaddabbdbdadbbdaaccbacbbcbdacacddccbabccbdcadbbabbbadddabbabddddcaacdacdbbadaabbabddcacdbbaabdbcdcbabbdbdbbbabccadcccddbaddbacbaccaddbadabadabadabdbacdcdcdadacdbacbbabdbcaabbaaddddaacdabbdbcccbabdddacbbacdbcccdbbcdabacdabdddacdddbacacdcabcbacbdbcacddbababcbcdacaccaaadddcccbbdcbabbabbbdacbcabdcdbbcbaaccbbcdcdcadbcbbbaaaaddaaabdcdcdbcdbdddbdbbccccddbdacbcddcbaadabdacddcdbdccdaaddcdcdddabcabdcacdbccccbacdadcddcbcdcdcdcabdadbacccbaccbcbaacadbdcdccbcdadbddddaabddacdbdacbdadabbbacaaaaaacddcbccbbdacbbdccbbbddbddabbbcbbccbadaabaacbbdccbabbbaccbacaadadccdcccdbaadbadaacdbadddcdbdccbdabdaabddacbaaadcbcdcadbdbdbddbadcabbaaccbaacabcbcdadcbbaadbcbdcabdccccccbaddcbccbcdaaccbbbbdabdddcdacdbcbcddabdcaddccaccddcdbdaacccdaaccbbdcdaadaacdadbbbcbdaabcbccddcdacdcdbbcddadbcbabbbbbdccbcbddcdbbdbdccaadccbdbbddbacacccdcddcdddadcdcdcabcdaabdccacbcadabacbbcababaabbcabbacbaccbcdbbadbcbacbabdbbadcaabbdbcacbdabbdbbbdddcadbdbcbacaabdacaddacdccbaacdadaacababbdabccddbbcadddbbaacaadbbbadbcdddccabbcbddabbdcbabbcddcadddbdcadbcaadabdddacadbaadaabbdbacaabaacdbcbcdabaabaaaabbbddbbbadcabddadbbdbddbdabcabbbdcccdcdabaaaccbbcbdddcbbbccacbaccbbcabcbcbdcccacdbdcadaadbcabadabadccaddacbcbdddaccdacdddbdccdbadcbbcacadddbdbbcadcdcaccccbadbdccdbadbaacdacddccbcabaacbaacbdadbbbddadbbdabcaaacbdcaccdaacddbbacdcdcdabadcccddbbccadccacddbdcaacbdccdccadbddbddbbddbdbcacbcbcbaaaacbdccabcacbbcdbabdddbaddbcabcabdbdbdbdbaaaddacaaadbcccdadccdaabbbcbbbbbcaaaddacbbaddbcadabbbccbbdaadcadcdacaabcbaadabccdabcbbbccacddadcaadddadcbbcbcddcaaaddddcdaaaabdcbbcbcbbbddbdbccbaaccddbaddccaabdccbddadbdacdaaadbdcbbacadcdaacdccddadddcdbdbccccbadbccdddcddcbdbbccbcababddbbdbddbcbdcbadccdcaacbaadcaacabccdbdbdbdacdaccdacdbcdbbbbacccadbcccadabbbdaddabcbbbcdcbdcdacbcadcccdadcddbabacacaddabdcbaaaaacbbdaaadadadddcdcadbaabdbcbcaabcbbddbbcdcbbdddbddbaadcbacbdbcbcabccdbbacdadadaacbdcdbccadaadddcabbdbcdadabbdcddadacbabbdcddbbdadabdbbbcdcdabbaadadacabadcddbdbcbddacdabadccaaaccbaabbbdcdcbbadbbbcdccdbabdbbcdabacadaabccabbabbbcccdbbbcccbadcabdacaadbaccbabddcabcdbdadbcbadbcdddccbdacdccbcbadcddcbbbcaaabdddbabdabbbadadbccdaadbbbcddbbaadbdaccbbaccbbbaaacabdcacdbdcbbcddaccddadbcbadcdddaacccadddacdcbababdaddbbcbacdcdaadababbbddbcbbadbaaacabdbabcccaaabbacadcaadacabcdacaadacddaaabcbcaabcdbadabbbadaccdaaacbaacddbdcaaacccbcdddadddadadbdcabaadbabbccdadcacbabbbddadbbcbadbddbcabaadcbadacaabaacadbacdddccdacbacbdbcbbcaabcddbaaddcacccdcbadaabadbdaddddcdaccbabcbabbbcdccdddccaacbccbdbcdaaddacdbddddbbacccbcacccbdcacacdbaaddcccbddccbacadaccdccaaacdbbccddcdaadbddcdcbadadbcabdccbcccbcddacbbdaaabddbcabaadcdcaccccabcccadcaddbbdababaabbdccbabadccccbcbcacdbdaacaccbccdacccbaadcbaadacbddbbcbcdddccdbdcacdcacaddcdbcddacbaadbabbcaddcdaddadabddccbabcabbadabaddcaacdbdabbcddcdbdcaabbcadcbbacbadccbccdbabbbbcdaaccaaccdacaccdcaaddbddaaddaaccacdacccaacddcacbaccbadccaabbcccaccadddabccbcaabaaacdabcaadddadbcbbdcaabbadaccbbddcddcaaccdadcdcdcabacacccadaddacdaaadcbbcacbdbbdbcacdaadcbcbcdbdcdcacacdcaabaaccbbaaccccbacccadabacccdcaddcadcdaabaacddacdabbaadabcaddbcbccbabcbbadccabbcdadcabcddabbabdcdbbdcdbbdddbcbcbbadcadbacbaabdbcdbdcddbbddbadddadcbcdaddcbdbcccbcccbdbdbdbdbabcdaabddccdbdbacaadabddcbadcadaddbddbcdcadabdcccbcddcdccbdbbdacdbccdaadcadcadabdaaaccbadbdbbbdaabaccadbdabdbdddabddccdaacddbbdbcdccbaccadcbabdbcacaaddbcadcadcdcaadbacacddbbcdbacccddabcaddcdadddabbabbbbbcbdddaccadaccabddbdcabacbadbdbcccdbacdadbadcccdabbcccbacbbbddabdbbabaaaddbcbbacdaddaaabadbdddabdbbcbdcbbdddacdbcababdadbcccbbdbdadddcdadcdccddaccdaadcbdbbbddabbaabaccddacbcbcabbcadddcbbdcdbdbccdbdabbdadbcbdadabcbddaddbcdaaaabcccaaadcadadbabdbaabcbcbdbacbbbcaaaaabdddccbccadacaddaccbdcdcbdabacadbbbdbcccdcdbcacadacbaadacbcacdddddaacddcdcdbcbabdbbaddbaababbdcacccbacacabacbabcdaadcbccddcbccdcbacaaadabdacbbbcbaccddcddcddbbacdcaacbadcdbcdadabdaacdadcdcdddbdacddaabddcdbdcbcccbddcccccdacbbabbdabdbacdabcbbcabbbdbcdccdaadcbdcabcbbacbdaaaccaadccddcbcbaccbcaabbcbcaccaaddbcbcbadbbcadccbacbbaaababadbccaddbcdbdaaabadbcdacbdcbbadaccdcabbbddcabcacbdccdbcdcccacddacaabbacdacddddcbbccddcaddaccdaabadbcaccadacccabdaddddadccdbccdcbbbadcbccbcaaccbdadddbbdccabacdaabdcdccccaacdbdabdcbcaabdcdaacbdabdaacaabacddadacabddaacabbdbccaaaabdbdddbbccbaababcddbacacddaddcaddcdcbaadaddbdbcbadddcbbcdbdadcbadabacccbdaaacadddacdacbaccaaadcdabccadbaccbbbabccdabbaddadabcaadaaccacbbcdaaaaddabbabcccdbacddcbcccddaacacdddcadaaaccdcbddcaabcadcdabaaddbabcacaccacdbadbdaacbdccbcddcdccbaddddacdcddaabaadabccadcdbdabcbddacaccccbdbacccbabbbdacccdbddabdcadbabcdacbdcbacdaacddaadcdbdcdababbadcccdbbdacaddcadadbbdccaabdadadcbbdccbcaadacbccacbbdcdbccabaddddaabbababcaaababdadcaccaddaabbdbadcadaaabddcacdbdcbabddacaccdababcccacacadcdbadccdcacbcdcccdaaacbdbaccbcbccdadbdadcbbcdbddbbadbcbcddcbbbddccbdbaaadbbbbdccbaacadaababacbcaaaaaabdbacabbbcabbddddcbdbdadcadbbccbccabcdcbaadbddbdaacaccadabbadccabddcacdadddaacaccccdbcbccdbdbacdadcbabbdddbaccddbdababcaadccccaaccaacacbbcdacbdbdaacadcbbdcbcdacacdbcbcabaabcdbcddcdabaabcadcbcbbdcbdcccacdbcbccbbcbadacddacaccccdacccbaabaabacbbdbadcdaadcbdbcbbcbbbaaddacaabbcaacbdbcbacaddccaadbcdbddbdcdbdbaddaddababdbbdbddddccacddaddddcbbdadadaccacbbbaaabddbacbbdbdaabdddbbccbdccdacccccaccacaaccbacdabbbcdbbcddddaddcbaadaababbdddddbaadaaacdbbabdccbdbddbcdcbdcbacaccaaadcacdcaabcacdaacdcdbcdbcdacbabbcaabdbbadbddaabadbddaaccbcaccacbddccbdcaacaddcaccbbbabaccbcbbcdbdcbaadddabddacbcdadcadabadcdddadadcdabaaaddbbabdbadaccbacbacabddacbbdadbcaadadabdcccdadcbcaadabaaddaaabddabcdaacaadbddbcacdbbbbadabdadbccddcdbbdbcadcaaacdbaabcddacbbdccddaacdabaadccbacbacccbcddddadacadacabaccdcacbbaccdcbacbdacdaaacbbacaaccacbbbbddadbdcadbadcdbdcadabdadabdcdaaaddcbaacbaccddccbbabddacdbdcbbcdcddbadbdadbddbddcccacdcdcdcbbcddcbddaacbddbaccbcbbcbcaccabdaddbbbcabddbdbabaddaabdbbbaccccbbbbbbaaaaabaaaacccacddbbabbcadcddcdbbbcddbbdacabcccacbabcbadcdbbcbcdacddcbbdbcaddbbdbbcdbccbdadadadadcbbaabcabbdcddbdbcbbccabacabbadabcadabdcdbdccccaabbaaadbdabdcadbcaccdbddddcdacacddcaddacbabbddbbdcaccadbdddcaadbbdabcdddbdbdccaabbcccdcbbdaccbdcccdadddacadacbcbcadbcbdacdadbdcbcaccbabbdddaabbabdbccacbacbcabadbdaadbcdbbabcbbbaadaaaadabaccdddbbbdcabcccaccacbdbcabddabbcccbbbdadbaccdcbbbdddacaaaadcddcdcabddcbcdcbcdadcbdbbcdcdacdabdbcbcbddbacccacbbbabdbbdbdcccbcbbbbbddbdcdccbabccbdbabbcdadddcddadddddbadbcaccdcbbacdcaabcabdbadbcccbdbbcaacccaabcdbcddadbbccdabcbccdabbbbaccbcbbbcbdddcbcadcdcdaabdcddcbaabcdccbbbdcbbccccccaacababaadaaabdcccdbdddddaabccddbcdabccbbabbcbbddadadbbcbaddddaadaadbbbddcacbddcdbcabcadaccbbcbcacaccacdcabacbdabaabbaddbacbdaccccdaddabdacdadcbacaacacbdbcbcabcdadcbdabacaaacdcbcbbbcbcbbcbcdaadbaadcbbdcaaababddbcbbacdbbaacbbcbcadcaccbdccbbacabdbabacdcdddbbacbbbabcdbbbabddbaddbcbaaabdcaacbcdbccccadbccdbbcbaddbbbdbcbcabddcdcadddbdadbddddcaccbbbabbabcccdabbdbbdbacaabadaaaddbcabcadbdadbdcdcbbccbacbcccccbdccdcbadadcaabcadbddaaaabaccadadaabcdacdbccdcbdcbdccdaaacdddbdcdacacdbadcbbadbcbabdabbddabadaccabbbbdaccabbcadddbdcdccbaccccbcbaadbddaccddacbdbacadccadcbaddbccbcbdcdddcbdddddcdcdbbbadbdaadacbbbacacadcddabcaabcbdacddccacabcbabdccacbcdacaadaabdcadbcdbbacdddccbcbdaabdccdacdbcbdbdbaacdacabaadccbaddadcacdadbcdabaacadcbdadadcdcbcaddaaaaadcccddadcadadaccccbcdbadcabcabaddacbdddaaddddcbcbcbcbbdcdaabcaaccbabbbacddcbcadacdccacccdacacdabcbccadddbcbacbdadadacabdcdbbdbdcdddabbbdacadacababababacbcacbdacccbbccbcddbbababddccdaaddaacdaabbaabdabbdccddcabcacbcddaaccaadbaaacdaaadcabbbacccadadcccdadcdcdbdbabddbdabcabdcdaaccbadadbbddbdacaacdbadcdbdddbdababbabbaabdccacbcbbdccbbcccdacdbabcbaabadbcccccccbcdaaddcaabaacacbdabcbdadcbbababbdcbaabdabbdcdbbdcdcaccaaadaacbdbdaabbcdbbcbdabbdbdbcccbdcabdcbbccaccddcacdbdaabbdadcbabccbcaaacddbcadcbdcdcdddddacbaccdbacaccacbcccdbcdddddccccaaddbdddcccddcbccbaabdbadaacddbcbbdbbcdbacdacacadbacddccbcaadbdbbcbdcbabbbdccacbddbadbbaadddcbadbacdccdbcbbddbadbcdcadcdcdbdbbadcabbdbbabbdbcdcbbdbdccbbcadaabbdbadcbbddcbadbbbdbdacbababbbcbaacbbccadaccbbadaacbdbddaccddbacaaacccadbdbaababdbbcbdaaddbcbccacccdadbadacdadbcbbcbbdaacadbdbbdacbaadbbdacdadbbaaaaccbabababbdcacbacdbdaddacdadbddbbcbcdcaddabcbdabadacadccddccbdbcabdcabcacdbcdbcdabccdadabdacbcccbbaccabcdbbacaacabccdadacdabbaadcbabdadaddbcabaccaccbcdbcaaddcdcbbcddcddcbbabbaddddacbabbacbdacddabddcabbbabcaacaacacdaadbcacdcaadbcadcbaccbcbcabdbabacbdaabdbbdadccbcbdbdadbadcccacbbaacbddbdacbdccbccdbcdbbdadcbcccadbcdadcbcaabcadcbccccdcbddbdbbcaabaacbddcacaacabdccdbcacdbdcbbbadcacabbbbdccdacdaddaacadcddaadbcdcbbccdddcbbacdccaadbcddcbbdbdadaaaddccccbddbdbbdbbbdaaaabdaadbbbdabbbcbadabbcbdabbcdaabdcdddacbdbbbacbbdbbaaaccbcacbbbccdabcadacbaddbcaddadcdacbcabcbacbcdabcccdcdcdbdcdddcdbcaccdcdcddcadcbcaaabbbabbcbcadbbbddbbdccbdcacdbcdbbcbbbdabbbacaacbdddbbadcdddcbbacaadaaacbcddcdcadcdbdbbaddabbcdabdddbaaadcdaaacdbdaaacbaacadbdcbcacdaabdccdbabdbabbcacbabdbaadddcdbbdcdbbbccacacdddaccabaacdcadaddbdbdaabdbbbccadbcbccddbaadcdadcdcbbdccddadcbcbcdaacccabaacaddadcbccdcdbcbccbdbddbcbaacaddaaabbcaccdbdacbababcbbdcddabddaabdccdcdacdababbcdbbdcacdaaccddcbddbabbcccdbadbbbbcadacaaccacdaddddbbdcccddaccbcdaadacbdcaadcdbcdaddccbccbcbdacddcdaddccdabdcaacbdbcdcadcacdcddcabadddbaabdaccaddccababdbdcaddcacabcbccdcaccdbacdabbcabdabccabdcbcabbabbcbdccdcbaccbcbcbccdcaccabadccbdbccabbabadacccaddbbdccdbbacadadbdbdbbbbbcdcbdacbacadcabbcbdcbabddbcacccdcbbbbccabdaddcbcaabddbccbcbdaaddaaaacccdcdaabcbcbbddbcddcbcbabbccbadddadddbcdabdcbcacdbdbdddbbadbaccbddcdbbacaabdabaddcadddcaadbbcccdccdcbcaccbbabbbabaadbbdaabadacccaddaddcbbcbabcbcbaabdbcbcadcbbaacbddadbcccbbdcabcccaddbddbcbbddbdabcdccadaddbbccdbcacccbbbadaccabddccadccdacbdddbcabdcccdbbdccaccccccabdaaacbbcbcacbcbcbaccadbccbdcbcdaadbcdacbdabdddbaaadbdacbcdccbdccaccccabbdddabddbcabbcdbaccdbbccadadccddccabbababaccbdbaccbbbbcccabaadbaacadcaaacccccbbbaaacbccacadbaadcaacbbaabcacdcdaabdadaabdddacbbdabbadacabcddaccbcacdbbacbcaaacbbaacdabaacbdcbabbbdcddbcacdccbcdddaacaacdccdbccabccbdbabcbaadcccacbdcccbcadcaadccaadbbdcdddcdbcccdadcdcbbcaadadbabbcadacbdcbcaaabdddaddcccaadbbbbbdbcddacaaadacdcaabbddadcadaaccbadcdbdcabccbcaadbcaaacdccbbcbbddcdcabbaddcddccbbcdcccbccccdccdacacdddcbcacaaaaaadcbbbcadddbaacdaaacbbabcbbbbdcdcabddaaaacbabccdadacdcbcdabcbdcdcdcddcbcbcbadddadacaaababdadabdbccccadccddadbbaddcdaccdbcbbbbbbcdbbbaddbbadaadcbdddbadbddbdcabbbccdccdbdabddbdbcbbababccabbdaabcdcccaacbcacdccbaacaabadbdcbcbabccaaabaaadbbcdddbacadcadbbcdabacdcdbbdbbddaadbcabdaacdcdbddacccadbbcbbdadcabaaacdbddacacaddcbdcadcaccabcacdcdacdbdbbccabdddadaccacddababdcaaccabbaababababbdbaaabcdbbabbababccabdccbacbccbbcaddcccdcbbbbaccdcbaabbabdcbabacaddccbdcacccadbcdaccaccaddbdaabcbadaabddadbddbbbddacdacabdbcabbbbacdaccbbaacbdbdaddbaccccdddacbdcddadcdabdabdcacccbdcddcdadbacdcccaccaadbdcacabdbadcbbccbbbcaddccdadccccacccdbdbbdbacdbacdcddacbdabbbaacdbbcdcdbbaaddbcabdcbaadaddbddbaaaadaccccabacbbcaabdcbbabddcbbbcdcaaacbbcbddbbdabacadccbcbdbdcbbbaaacbabcbacccccdbbacbdcadababccaddcbdddbcbdcbbaaaddbbccdbbddcaaaadaaddadcbabcadbccdbadddbdbadacbbdcacccdccbbabadaaabcdbdbabcbcadccdcabbbdadabbabacdaccaacbcdadbabaddacdadaaccbcbcdabddcbddbadbcaccbadbbbdabdbcadcbdacbbabdcabcbacbcddaddddaababccdadadadababdacadddccacabbdabdadacdcbccabcacabcadccabcdbcdddabccabdabbbbadacbabddcccaccdacdccaaadaacccabbbbdacdbadcddbddacddadbdabadcabcbcbccbcbbdbddbaadcbbbadbccaacbddadbbcaababdcdccbdddacbbddacdddbaddabdbacacbdcadbbdcddddddcbbdbacdbdbbdbccccbbacbbccabbbbccdcdccaadcabbddbcadccdabbaccdbbcaaabbbdcccbbadbdcadabccdcbbaaddbdccbdbabdcabaabbbdccddcddacdbbcbbcbcbabcdbbaacadcbbaaababddcdabdbcdcbcddcabdcbadaacdbbbbacadbcbccdcbdcbdcbabdadabccacacbbcdbdbadbdbccabbaccbdaabdbcbdaabddadababcdbadacadbadbcbaaadcddbcaadbdbdbbadbbdcabdacdbdcacbcabcbbcdddcacbabdccdbdddbdbaaabaaabcbbaaabbadbbaaccdbddbcadacbddbbcdcbbdaaacbadccbabaabcabacbccddadcaddcbabdaacbbddcacdadccdcadddaccaabaadddacaabbcaadcccccbbbdbadcadaccdbacaaccaacadbcccadbaabbdacaacbcbabddadaaacbdabcbacbacaacadbbadbcacaacdccdadaadddbcdadbadbaccdaccddaccacbbcdadbdbbacbbaaadddaccbbcbbacacbbcdcdccabadbcadbadbccddbabbaabccaabaadadaadaadadcaddccbdacbcdaddbdbdcacacbbcdbadcadcdaddacbdbdaaacccaabddbbaddcbcbdbdcbcddbdcabacbbcdacadddbabadbcdaccbddbadddbbadbcbaabbaacbddcaccdbbdacdacbbcaacacdcbbcdbadcbdadcdbdacdcbcadcadddabddddaddaddacacaacccadddcaadabbababcbcacaccddbdbdbabdbddbbdaccaaadabaabacbcbdcbccaccaddbccdacdaaabaaabacadddbadadbdabcaacbaabbabaacdbccacaccdbbcdcccbadbbaaadbcdacdcddababbcabadbdddddcacbaabddbbbacbbcdabdabccabcbcabdcacdcbaaaacaabcadbbcbbdcdbbacaaaacdacacadbdcabcacaadbcbbaddcbdccbccdbadabadaabdadbdabddcdaadcacdbccdddddadaccbbababbacdccdccdaabdbdbacaacdabbababcdbbbbbdaaddadcdcbcaabcccbabbbadaaaddbddbccccaddbcdbdaabcbbdcabcbaccdcbcbacabaacaadbbdbabccbbbccdbdbaaacdbbadcdaabcaadabacdcbdbccbdbbdcdacccabbadbddbbaaacabcabcaacbcbabccaccbdbadacdadbdadcdadaabccabbbaaabcdbbadcabcdbbddbacccddaabdbacdbccdbdcabbdbdabacddacacababcabaacacabdbbdbdaaaddbdcddcdbcababddbdaaabcbccbadacddbabccccacbbbdbaaddbbacdabbbcbcbcbaccbccdcadaccddddaacddaabcbabbabacaabcddabdddbdcbbdbddbdbcadbccdbdaccccadcddbcbaaacbdbaccabdaabcdcacdabbcabbdababbdabddcdababddadbbcbadddccabbdadaadbaaadbaccaacadcbaccabcdadcbbacccadccdbbbcccdbbddccabbccaabdcadbcaacccacbabcbcbacbbbdacdbbadccdaccccdddcdaadabdbccbcbcbbbdcbdbdabdcaaabdbcbcadacdbabdbddbbbbdbcaacbaaabbaacbaaadbaabcacbbdbddabbbdcdbdbadbbabaccbcbbdacddbaaccdbcdbbbbdcdbddcdbdbaccdccbaaaadadabdbcdababcacaaacaccbbbacdbcccbadcbaaaddadacacadbabbabdbdcdacccdddbcaacbccccdadadccadbcdcbdcdbcbbaadcbabcbccaaddbbdbacdacdbdbcacddcbdddddbcdcbcabcdcddccbdbcbabbbbbbadddaaaabbacdadabcacbbbbacbcccdadaabbccbdcbadcbdaabccbadcbbdbaaddcacccbbbcabdabaadcdbcadccabbcdcaaabadaacabacdcbabddbbcdbabcabaabaccaddaadbbccabcaddcdddbbbdcdbabcbcbbdcacdadbaadbdadacabaaabcdccacdbbddadadcabbaaadaaccdccacaccdabcbbcacbddcdacabcbdbbcccaccbdadcddbcdbabdaaabdcbdadbdadcccddddbbccdaaccbbdbbdacadacddaabadbbbdcdccbaaadcdabdbdcbbcdcccdcdccbbadcbdcababdacbddcdbaaadccdcbdbcaccdcbcbcadaccbdaabdaccdcbaabddcaabdccabcbbcacbdabdabbbbcbdbbbbcabbbabcabbdcbbadaabdaaccdbaccdddaabdbddcaabaaaaacadcbcdbddbabcaabbcbdcacccbabdabcdbcddbddbacacccadcbabbcdddbdcdbbdbababbbdbbdbcaadbccbbabdacabbaddcbdcdcaaababcadadbbdbbbacdbdbccabdcdbabdabbcacadddccabadabaccdbbcabbbdbadddaddcbaababcccdbdbacddacdcdaacbbabaabcdaccaabdccbcbcadddbccddbcabcacbdddbabcbbbabddcdbdcaadabacbccbcacbabdabbaabbcdbaddccdcbacdbabcccadaccaadcadbcccdcaacdccbaddbbdcacbdbbbabbddddddcadacbbcbaaddbaadbcacabbccdabcbcaadcdbcadbcdccccdacdccabbdaccdbbdaaaaaaabcdadbabbabbcadaaacabccdbccbbacbcaaabdbcdbbdabccbbccdacaacbaabbcddcacdaaccdbdacdcbadbaabdccadbccbaabdcbbddcbcbabbbcbbbaccbcddbbbabdbaacabdadbbbbcdaddaabbcadbbbcaddbacacacdcbababcacbdadcaabcccdaacacdcabbcaccacdadbaddcabcacabcbbadcdadbbcbbbacdadbacbdbccbddcbbddbabcaccadacacbbadcdbaaabbcbabbabbcccdacabcbabddbadbaabdabbabcbbbcbdbdcaaaaabccdbbababacabacdcbdbdcabbbabddbbabbdaaadbcadaabbabbdccbbdcddaddbaccaccbddadcabdcbadbcdaadcbaddccddabbddddcdadadacccccbadcddbbabacabddadddcadabbcccccdaadcacddbaadbbdabcaddddaaddadaabccbbcaabccdccdbaacadabddcdccacbdaaaadacbdcccbdddbbbbccbacadabaaccbbcadaadbacbccdcbdcadcabdaadabdcdbdcbacbcaccddbdccdaaadccacbdbbdbdacaacdddaddaaacbbdadaddcccbcaacdacbacdacbaddbcaaaadababcbdabdbdcbdbcacaddccdddacdbccacbdaaabbcabadcdaadaddaccaaaccbcbdbbaabdbadcabbaddcdaacdbaadcdbaccddbababdbaadbacdddacaacabadacbabdcbaadabddadbdccbdcdabbccacabbabbbbddaddaaaabddcdaccdcbbbbbccdacdacadbcacdadbdbbcbbbdcdccbcbcdaabacadbcdbbdabbbaadbaddbcbaabadccccbadadbcabdddbacbbacdccdbcabbbdaaacacabcbadadbdbbacbdbdcbbddacbbdadcbbabadabddbcbdbbbccacbbdbbcdbcddacddacbcaaddabdbdcaaaddcbacbddbaabbbbabdaaddcbccbbdccbaaaccacabaacaaacbacadbaacddaaccbddccadddbcaccbcdddadbdacbbccccdddddcaadadaabacccbbdbcabcbadccdacacacccbdcadadabdddcacdbcdddbdadaacdabdbacadacdababaadbbccabcdcbbcdcbbcabdbdbccadcabbaddcbadbacadabacdcacabdbbdbccccddaddbadbbaaacdcbaddadaaddacdcdddbcaccbbcadcbcbbdccadaaddbabdbddabdbacddadbbaacdbbccacccccababacaadcacccbcdcdccdcaacaacbcbbccaccdcadcccabbadabdbbcbdbaadabdbbbcabaadabadcbccaddcbbcdcaabbccddabdbddabbbabbdacbcdaccbcbacccccaacbcbddccdccddbcbdccdbadacacddcccdacabdcbdcaabdbbabcbabdbdcaddcccaccccbcbbbacbcaddcccccdacbabadadccbcdcaddbaabbcdacdabdacbadbdcabcbcbcdccaacbbababbcacddaacddcabdababdbabdbbcaacbddbaaaccaddbdcccabdbdadddcbcabbdcdccdbbdccbbdaddcdacdbdcbacbcbaadbbabdccdddbddddbbdbdbcbaccbbdacdaabcbaadcdbbabaccbdcbdcabdccdcabdccabbbdccdccbaabcddcdbcccdcbccdcbdbdaadbaacbcddacbcdcadcdbdcdbccbbdcadddacadbdbaddabadcbaadcdabacbdcdbcabcbcbabddabbbcbacbadddadbaccbacaadcccddadcbdcbdbdbbbaacbcbbbacaaaddcbcdcacabadddccdcbcaaaaddcadacadcbdccaccbaabcccaabdabcdccaacccacdbadabcabbadbabdbbbdbbaccbdadadaaacbcccdcadbcbbdcdbdbdaaccbbbbaadabacdbbcaaddabbbaadbddababcbcddbbdbcccacabadbaaaaaadbcdaabcbdbaadcdbbcbaabddcbcadddbcaddbaccccddcbaacdcdaabbdbbbbddcccbbbbdbdbabcbcbccddcdbddaacbdbcabdcbbccdbaadacadbddccadccdcbdccaacbcaaabbadbaabccbdbddabcabcdbbacdbbaddbdbabadbdbaacdabbbdbcdabbcacbdcccaaccbdbcddcddbbbbaabacdcddbddddacaddbbbacdaaabbbabadabbdcabcabbbbabdbcababdcdcabccccaadbccbdadacacadaacdcbcbacdccdccdccdaaaaacacddcdaaabadacacadbadcabbbabcacababbccbcdcacbdadddcbdabbbbdacbdbcacdbdcbbdccccadcacabacbbcdaacaabdbdccaaaacbbcbbcbddbccbccadabdabbbabacdadbdaabdaababbdcbcbcdabdacdcccbaabaadadacdcbbddcababaddbccdaccdbaccaadacbbcbdcbbddbdbbdcbdabaacccacbbdcadadbcadcadcdbdadaabddcbcdbccaddcaaabcbadbcabdbbccabcabcbacdddaabadadbdddcbaddcddcdbcaabcbddbcaddababdaaccccccaaaacbacabaccddaccbbacccdccbdccacaadadbcbcdcddccdaadbacccaaadbdabdacaccacbddaadcbdccacadcacaabbbdacaaccddcdcdbcdddccabdababcaacbadcbccbaaacdabdccccbaddaaabcbdadccdbddbaaaacdbcbcacdbaadaacdabaacddddcccdbcdccaaacacbbaddabdcccdbcadcccabacbccbccdcccbcdbbbbbddabbdacbdddcbdadaabdbacdacbccaabbbccbaaaddadccbcdacadaccadcdbbbcaaaadbddddbdbddbcddaddcdcacbbdddaadbadacbddbacbcdabaadcabdabbdccdbacadadabadcdcdddacadcdadbcdbabacccdbacadcdcbabdcdbbdbcababaadddcadadaccaabdcacacbcdcbabdddbbbaaadcacacdbccddaccccddcbacbcddbdbaacadcdabccdbcccbddddcdcaddadaadbbbbcbbbdbabadabddbabdcacdcbddabaaabbdcdbddcbddcbcadbbaddcbdadbabcdaacbbaabcabcbabacaccddcadbdbbddbabcabddcbbbaabadabaacbddbccdcdcaccdbaadbacdabbbccbdcccbbbcccbbcbabdabccdadccddbacbbababbbcdcdadbcbdadbcabbbbcbdcddddbaabddaaabdccadaddcadbbbbdcacaaaacadccccdccadaadbdcdbcdabbacdacdacccacddcaddaccccaaaaaadaccbadcdacacabddbbcaaddabdcbaacadabdadcccdbcacbcbcaacaadbddadabcbaabbddbaabddbccdcdcabcabbcbadbccdadaadaddbbdaadccccbbbcdabbddcccaadbcbbccabcbbbbbddcdaadacbbcbccbcaddbacdcbbdcbccddbbccdabadabdaddbbaabbcadcddbabdcadbbbbdabbbadcaaadcadbbcdccabbababdcacaaadcddbcaacbadddaddbbabcbabcbaccdbdacdddcaddbababdcddadbbccdccdaaacdbaddacccbccabcdbbaddaaacccaabcabbddbdadabddbcaaaabdddadddbaadbddddddbbbaddaadadacadbacdbabdcababcdabcdaadadaddadabddacaddbdbdcbacdccacacbddccaaabbdbbbccddcabcdabcadccabaacbcdbdcbaddacdaaabcabbdadccdabbdcdbaacbcabccddcabcbabdacbabcbdaabadccbbdabbabdaadaaddcbaaadccacdddacbccbcdccdddbcbdaadbbadcddabccdcbcaccbcaabbdbdbccbaabcdacdbdbcaadcaabadacbdbbddaacbdbcddcadcacbcbabdbdacadcaaaccbbbbbaaaacbbcccdcbbbaccbcaccdacbcacaddccdaadcbcdcbcadbaccbcddabdaddbbbcddbcdcdbaadbaaccabcadababcdbcaddcbbccddbbdabcaaabdcabccbccdcbcadccabdaccacabdddccccaaadcdbdadbbcabdccbbdabdadbbdcaccaacbdccccccabddcbaccdbcacbbbadddadccdcaaaabdadcdaaacdbccacaacbbdacdadddacbccbcdbdaaabbabacbccadadabbdccdccdacbcbbbdbdddcbaabadacacbbcccdbddaabbbcddbbaccadbddcbacdbdacaabdcccaddaaccacabbcadcadcadbcdaabbdcdcbdbbddbbbabadaaaaabbbabbbddbcdbcccbaaccccdbacaddcdbccdabadbccbbacbbdaaccdabadcccbbdbcbcdcaaccdddcadcccbdadabaddcddcdbbdabccaadcdbcddbcacddddcbbbdbaaabbbbccaabbadbbabadcabadbddbcbadbbbcdcbddbaadbaddbbbddcaabbaddcccbdcacdbaabcbdbdbbcdaadbaaabaabdcdcbadabbdadbdbaaddcbcbabccbbcbdbccbbaccbdbacaacabbbcdcbcdbbacbcdabcdbdcbabddadbabdcddcaaacdbaadddbbbdcbacdaccadacdbdddaadcbccdbcbbbcbbdadbdcbcdacaaacbabdabbaddcbcdacaaacbdacddaccdcbddbcabcaabbdcddbdcadddbdcbcbbadbabbddcbcdcadaacbabcaaaaacbcdccccccbbacbdaddddabcaabadbdaabdabbcdbdbcbadcbdbdcacbddadcbadddcbdddbdbadccccacabddccabcaddaddbdddddaaccacbcbccbacadcacbcdbacadcbbcadcdddbdbbcbcdccabdbabdccccccdaaaadaabdabacbddbaacbcdabacdcbccbaaaabaabbbbacabdacccabaaccbcdbcdbabccdcbacacadddcadbbabaaccccaddacdadabcbcdcbaaccdddabbacdbdaccadaaaaabbbadcbbbdacabdaabbacaaddbbaacdaccbcdabcabbdadbbaddcacadcdbabccbbdaaabbdbccccdcbdccccabccccdddadacadaaabcabbcdadbabbbccccdbaaddbcaabaaabcccaddababcdcaaddbdadcbdaaabbbadaadcacaddbdcbacbddaaadadccdcbcadaadabaaabbddbdabaaadbcbbcbcbcdcddbadaaaacadcadaccbdbbbaadcdccacccbadbadcbdbdaacbaacadddccbddaadcdbddacbabdadadcaddddaabaccaadadcdbbadccadccdaacabababacdcdcdcadcbcdabbacaccdaddcaacdbcadabdbddcadbbaadbcbddcbbdabcadcbbaadabdacaadaacbdaacdcdacdcadccbdaccddcacdcdadcbccacdcabcdacbddcadcccacbcbcbdcadbcdabbbbacbbddcbbcddcbdabbabcddaccbdbdddccabcbbabadccdcdcabdbcacaabbaaabbdbabbbadcacbccaddcdccbacdcdabbbdcccabaaacbbacaacacddcdabdddcbcaaddcccbcbbccadbcbadbaacabacbddbbbcdbdbccbddcaccbcdcddddcacaaddbddccddbbcddaccbadadcdbdbcbbaadcadbddcadddbbdacbaacbddbdadabdbddddaabcbbbadddadbaddabbdbaddacacacbacaadbbacddabddddcdbadbaacbbcdcbbadabbbbddbaacccdbbcabbcccaaaadddbaddabbcaadbabaddbbaabbdcacabbbbabcabbddcbadababdbbacddcbaaccccdddadadbacdbcccccdbabbdcdaaabcdcbdccdbbabcbcddbcccbacccbdbbcaababbdadccdbdbabacbcdacbcdadabbccbdacddbccdcccabbdbaaadcabddcbbacdddaaddacabcddabbdbccabacabadacdacdbbbdbbabdabdddcdaccdadabdbbbcbaacabdaabcadcaaddbddccdaacaaabbabdcaddcabbcdccadbdaaacddbdaadbcdacdbaddbdcacabdcdabdccdaacbabddcacbbaaaccbbdbadbbaababbaaacbbdbacdadaddbbdabcabacaccdcabdbddabccdacdcaacccaccdcdacbaddaacbddabbcaadcccaccbcadcacacacdabccddccbdbcddabcabbbbadcadccbbabadcacbabbaacbcccaadbdacddbcdacbbcbdbbcccacaabdbcaddddbcdcabadcbdcabcbcbcbdabccbadbdbccdabdbaccdddbdacaaaabbbbdbbdaaabdcabcbbdaacccccdcabcbdcababbccadcbabcacdbcacdbdbbbdbacdcabdacbdcddcdabdcaaabdacabcbdddabcadcdbccbccbabdcdaadadbaabbdbcccddaddccaccbbbbdcbaaadddbaaabcbbcccabcbbcacdadcaadcddcdcccbabcddddbbabcbcbcbcbddabdddaddacdaacdadcdcbacdbcbdbbbcccaaadaaaccdaccabcdcdbdbbcbdababcdbabadaabcbabdcdcdcbaaddaadabdaaddaccaaddbacaadcadcbbccccddacccdccdbdcaabddadbadbcaacdddcdcbddbbbcccdcbcadcdacdacdcaadabadbbcacadacaabaddacaadbaccddbbcbcccddcacacadcbbbabcccbdbcdcddcbcabcbbabbbddbdccadccabadaddbcabbacdabbbbaadbadaccadbbdadcaaadacbcccacbbadbbacbbcdcbabbddbadccccbbcbaabaccdadbccbbcaacbcbabccababdcabcddaabbcacddcdacaadbdcdcabdaabcbccadacdbdbaddabadabccacdddccadadcbddadbcacbadacdababdcdcdaabcccbdddccbababcacaccaccdcdcaccdadbbbabccdcaaadaaacbbbaaadbcbbabddacbaddacbddbadabadadaccaccbbaccbbadbacabcabddadbdabdcdaddabcaabcbbbcdcacacacbabdccccccaccdabaaadaaccaaacdddcbcacabaababcbdbabcbdacdbbbddacacadcbdabcbcabbabddaabdaacdbacbdaadbbccaaaaccaccadaacdaadcbabcacddbacdddbdddacbcbbcbdbadcaccdbcccacbccbbcaddbbacabdcacdccdcdcddadbdddacbdadabbccacdbcaaddcbcdcaabdccaccdbacbabcadbdbaaaabbbcccddcdbcbcbcdbccbdbcdbacdcbadadbdbbadbcbaabcbddaccaadbdbaacabbbcbbcdadabccdcaacbcacccdabdcdbcbddadcbaaaaccaaaaaddbdbcaadcbccabdacbbabbacaacdcdbdaccdbcadaababdbcddddaabcaacccbadccababaacdccacbbcdcadcadbcbbbbccddaddbcdddaadccdcdcdaacacdacbbcdbdbcdaccbcbbdcdabbbaacabdddbbcaadcdacbaccbdcadddcaddabddabaddbddcdadaddbdcdadbcddbbaadcbcbddbdadbabcbbcaacbadcddcaccdbdddbaadcaacabbaddbcccabadcdccccddccddbadbddacaaaccaaadaadcccbacbaacddabdbdacbbcbdbacadddacccdabcbcbdbdacadbbcddcbbadbdbbddcddaabcdcbacdcbbbbdbddbacbbbcbaacdaccbbcbadadaddacdddcdacddcabdacacaadccdcdbaddabccbbadaccddbcbaaacacacdcdbdbdabbbcdbdaddcccdcdddbdbdcaaddddcbcacddabbcbadcdbcadddcddbabcbccdaaabbdbbcabadcacddcadbcddbcaaddccbbdaababdbddcdbdbdabcdaadabcdbdcccabdccababbccaaadbdbadaaaaabbaadcaddbbbcccaccdcdbdcabccdbbcddbbaacaabbabadaadbaadcbdaabcbbbadcddacddaacddcbdcbacacdaddabaabdcbaabbcaaacbbcbddbabdbbcbcacdbbddcadadbbccbdcdcabdcccbddabcaabcbccabcdbaabcbcabcdabbbadcdadbadadccbdaaabacacddcacaacacdddabaaacdddadbbabcddbbadcadddccbbabbdbcaadccadcbccdcccccddacbdabbdababddadddcbbcaadbabbadcdbdcdcdcaadcbbadacadbdabcdcddcadbacbcccbcaacbdbbdcbcdabdcdaacadbdcdbbdddaacaaaaccadcbcacdccdabcbbddbcbadbccdddddcbddcadcddddbadddccaacaddbbdccbdccbccadabdddbccabdcbdddcbbbabcabcbabccbbcbbccddcdbbadbbcbacddddadcbbddddddaaccdaaabdbcddaddccabdaaababcbbabaccdbcdcaaccaacbddbacdaddaacaacbabddaabcacbbccadbcbaadccbddcdbbbadccdabacccacddbbcdbdbdcbcdcbaddbadcdaaddbaaabacdccabcadcaddbbaaccbabbdbcdacddccbbadbbaddadccbcbbddddcbabcbcacaddccdcdcccacdcacaadbdcddaacdcadadaaddccadadaccdcdcaabadbbbcddadcdcddcccdbbbbabcbadbbdadaccddabcaddaddbbccdaababbacaaadddcbdcbacbaddadbcdaacccbbbaddcbdbcbccdbcddcacdcccabdddcbcbcbcaacaaacdcbaadadbadbaacdccbcaddbabdbcbbabdbcdcaabaacdaaabddcdccaaccabdbddaccbdccbadabbdcbcabaadadbddcccaddbddbcccbcdcabddbadbacdcdaacbbadaabbbabdccdacdadaccbcddccccbaccdcccdcacddcacacdaabccadbadaccdbccadaddabbbadcdacadbbbdbdbdcdaaaabbaadbbaaddacaacbbbbbcbccbdaccbdcdcbaabcadbbcdbaddcdcabcccbdacdbadaacbbcbbadaaaadcbcdbdbaadddbcbadcccbcddaadccacdaacaaccdcbdabbcbcdbcaacdcddcbdcccdacbdbddaaadbcaacbdbcddcbbccbabcdcdcbaaadbaacbcdadabdbaccccbbcdadbbabdbccddabbbaacdcbadcacadacaacdcdabbdcdddcbdccddbbacbbdddcabdacaacbddadcdccbbcbcbdaababdbcdbcdaacdcabbbddcadaabaaaadacdbbcdccdcbdbbccddbbbaaaabdacbcabbdcbdadaacacdabbbbdccaadcaacdcddbdabccacacdcbbabbdcbadaacbbcbcacbdbbbbacacdbccabdcbbbaacaabccbddcbbcdabdcbbdaccaabaccdbaabbcddccddcccacaababcacdcdcbddaaacbaabcdabdcccbdccccdddddbacbcccbcacabdcdccbbacbdbdbabbdadcbcdbdadddaacababddddabcbcddacbdabadbdccbacccbdbbdcdacdbbcadcabcdbdbdaadadadadddbaababcbddcccdbdbddbbdccadbcadbbadadbadaacbcaacccccababbbdccdabbaaaddabbbbdddcbbaddadabcbdbdabccabbbaddabdbbcbabdaaccdaccdddabbddcadbabadaaaccbbcbacacddaccacdbbdadcdbccbdcbcbdaccdbbaaadabcdcbabbdcbdcdaaabacacaddcbbcbacccbdcbbabacdbccbbcacdcbbcbadbabdbcabacababaadacabaadddcdbcacdcbddbadcbbddadaaaaddacaadadabccaadadcddcdaccbdbccacdcbdcabddbbddbcacdbcbaacbccacbdcdcdbdbbcbddaacbdabccdcccdbbcacbaaccccccbdcbdaaacdbbccccddcadbaaacbbcbccddaaaddaacccadddacdacbdcabdbcdcdaadaddbbcdbbbcbcbcbdaadbbdcbbcadbcbaccdbbdaddbbbbbddbcccabaabadacabadcbacdccbdcccaddadabaccbbadadccdccacbcddbbdddccacddbcbcbdbccaacdacbdabbddabcacaadcdaababdadcaadadcbdbabbdddccdbacdaccadbbbdacdabdbbddadadbbbacdabbbacabdbbcdbbaabcdcacababcbddbbbdbdddacbcddabaaadaaabaabdddcbaabbbacabdcdccaddbacdbccaddcccdabbabbbbcacddbdbdacccdcddabdabbdcaacbabadbdabadacddcacddaccadaadbabacdbddababdaaaddbabcbbaccbcdbccccdacdcacaaadbdbbcbdbababbadbcabacbadbdacdbcabbcddcbbcccddaabdddcaddaabbbdacdbbcccdbdccabdabcdbcdbdbdbcddabbcaaadddbdcbacbdaaddcdcdadadddbdddbdcadcdaadbadcacaaacbbddbadccddbdaabbbacaabcaccaccbabbacdaabdcbbbdbacbbadcccccbccddcaabdaacbdddadacbddbadcbaadcdbbccbbccbadbdccccaddcdccdcdbabdadddcddabbbdcdddadbaccdbcbabbaddbdaaddbabcaccaaabadabddbcbabdcbcbbcbbdbdabadbcaaaacbdddadcdaadbaaacccbdacccddaadbbacccccbdcccacabdcbcccabbcbbdccaddcdbabaccddbccaaaccdcdadbddbcadcbacaddcdcbcddacdddddaadccbccdaacdddddcdbcbaadacccdbabdcccbabddabbdbbbddcddbbcadcdbbadbbdccadaaaaacdddaccdbbdbbdccbbdadcdddcdbaacbbdababcadbdadcaadbcdabcbabdbdbbcdabbadccacbdbcdcabbccbaacddbcaccbcbccdbaccabbbbcdddbcddadbaabdadbadbcbdcaccdcbdbaccdbcbbbacddbaabaaacbbababaadacaaccbbdbcbddacdbadabccdcdaccdccddcdcccbcbbbcddbbcacbbacdbdadbdbddcbcacaabdbbdcddbabcaccdabccddadccbcaccdcacddbdbdcacddbdcbaacacccdcaccbacbcaadadacaadadbcdacacaadacbacabdaabaaadccdbbdddcccbcdabcddcbdbcbcadbcdcacbbbddbcaaabbddaadbdddcaddaccadabaababcabbdbcdabacdbdddadbdddbbcaccbddddbdcbbcddabadcccdaccdcacaaccdccaddacbcbccddddaaddbccadadcddcddcaddaacaaccaabcbbcacddacadaabdcaaccbaabcadcdcbbacbaabcccabadccdabbbadacbacdaadacdbadccccabccbdcdbbadbddbcbbbbdcbdbdcddbcdcaacdacdccacddddbdacacadaccccbddcbabbcdbbddbddbdcccacdbdcaccabcbcdbdbcacbdabcacccaacbaadacaadbcaaacddcdbdabbccabaaacabdcbbacdcdbcdbdcbddcaababbadacbbddaacabbcaaadbcabcbaadbdcdcbabcacdbbcadcaccaabacbbcbbdbacdbdccbbbdbdbbcddacddbdadcccddddcdcadcbaacaabbbabdbdaddddbdcabbddbccaaddabcabdbcbcdbcbaaabbbddbbcdacbcaacdaccdbcdddbcdbbbbcabdadbcacaaabdbadcbabbabbccddbdbdcccbcabdadbddbbacccbcbbacbadcccbdaacadbccacbdabbcacbcbcdacdadadbccabadbcbdaaccbbbcdabdaaddbbabbbdbbcacddaacadbdbdaddabdcdcdbcbdaaadddadddcdaaddbdaaddabddaaacbbabbbcdcdbadbccaaccacddbabadbcaacabadcdbaadcbbbdcbdcbbbdddbcdcadcccbbbcdabacccccbabababadcdbacbdbddcdbcadddaccabdbcabdcdadacbccddbccadddadcdaaabbbaccdddaadddbacabdddddadcdaabbaabbaaddcddacbbaaccbbbabbbababbbddbdacacbcccadaacdddbcdabbcdccbbdcabddccadcbbaadcbaaaacbbacddbdaddddcdacadabcccbdacbadbdbdadbabcdabcbdcdadabbacbabaabddbcdabcddabbaaaacbbcdcabcccabcbaacccccdddcbccaacbddcdcdbbadcdaddabdbbccccacddbbdaccdcbdddcbaddbcabbcddcababdaaacabbcbbbaabcbbbdadcbbadabddadddaddabdaabbbbadcbbbccacbaaadadcacababbbddcdadccbdbccdddbadbabcacbcbdcaddaadabaddaacccaadccaaacccdaabadadcbbcdbdbbabbadcbcdadccbdcabcbcdabdcdcbbbcbbcbbabccdcbbcbdcbdbdbbbccbcbcaddcabadabdcbcdabbbcbbdabdccccaacbabddbabdcaabdacdddcaaaacdbdbddbcbbdddcdbbadbdcdaddccaccdadcdbacbccabdbcaadbcbabbdcdaabdabcdccdadbcdbbcccbdaabcaadbcaacbcbaadbccbbccbdddbdaadacbcabbaddcccbddadcdbbaccdaddddbbdabcdaccbcdccbbbcbcbbabcdbdaddcdcdbdadbdccdcbdbadbdcdacbdcbbcdacaabddbccdaddcacdcdcdbcbadbacbbdcddbcacabdabbaddabdadbadbcbaaaccbbdddabddcbddadaabcbccddcdbaccdaacadabccdadcbdbbbcdadacdcdacdbaccdabdacaadbcdbccabcaadbccadbccbddaaddcadcaaddaaddacaccdcabaabaaaabacbcdbddbcccabccadaacbdaddaacdbadaaaaccccabaabcaadadcddaaabdabcbcbbdddabbdadabcabbdcaabcadabdaadbbaabaadadbcdcbcdcbadacaccdbaaadcacadbabcdbddbcdcdaadacccadbcabacbbcdacdacccabcbadbcbddcbbcacbccacbcabaadaddcdbbcdbbbcdacddddccdbaadcdcbcccdcbacbccabccdcddccbbacdcbcdcabbabbadcbbacbdbaadcddcbcbcbccadabdaaabdbbcaaacabadbbaccbbbccbccdabcdbdcccddcbcbdabbcbdacbbcdaaabdaabcdbbacddccdcbaaadbcbdcdddcdccdbdbbabccbbacbbcaaadcbcabbdbbabcaddacddcbaabadcaadcaddbbadbbbdcdcbacdabdcdbadcccacdcacbacdaddbccbddacadbcccbabbaddccccbcbadadaddbacccdbddabcccacbcacabaabdbcddadbbdbddcddacbaadbbbbababaaccdbbbbcdbcacccdcccaaddaacabbacabaadddaddcccbbcdcadbbbddaccdabadcdabdaadbcdbbccaabcbcbcbabdcaabadcccbbadbbaacdcccbabdcccbabbcbcdacbcadcaddbdbbbcaaccabdaadbaacadbbcdcbcaccacbbdcdbadbacdbdbcddacddbabccaccddbddbadbcacacabbacbdcdadaccbdcddcabdbccacddddacadcacbcbbacbdbcbdccdbcabbaccccdbacdbcaaddaabdacadacaadababadabacabccacbacdcabcccbbbdccdadbcbddbaaadbaccadbdaccacdaabadbbadbbcbcacababcaaabdcbbdbbaccbcdcbacccacbcacaabbddcbabbadacbdcaacbadcdbcddcacbacaacccbbaccbcdacacbcdaaabcdcdddcbddbddbbcbbadaaddaccabcaabdaabadbbbccbadddcbadaaccaccbcbcacadbcbabacdbaabddbcbdacacbdbbbcbacdcdbbacadbddabacabacbacadccbaacadcccaaabdabdbcdddbdacabcdbabbdadaababbddbbdbcdbbbcdcaacbacdbabbdbbabadbadcbcbaadcbcbdcdbccccacdcdcdacbcdbadaabdaadbaaaadaaaaaabcdbbcaacccbdabbbbbdacaddacadbdaacacccdacdbbbbdcabcaabcbaccdaccdccaddacbdccdcaadbbbbcaddacdcbcdacbbabbcbcbcdbadccacababdabadaaacaaaaccabbbbbcdabccdacdbccccabadcabbdbacccbbdddcdddbdddadddaccbdccbcdacaadacbbbdadcbbbadddbacccbacabaccaccabbddbbbbdddccbccacaacaabaabbdaabdbbacabaacaaadaacccbdddadcccdcacabcdabddccccdbdaddcbbcbcbcadccdabbcdaaacbdcdcccddddaaabbaacddbcabcaadcaddaadaaadbbdacbadcaddbcaacccbabcaaaaddbcbadaccdcdbdcbaabcdbabdbaabbacccdbcbbadccadaccaaabcbbacabdcabacaccbcdbabcaccacbabccacaacdbabcccdbcabdadccbbcacbdadadbadabadadbcdbacadcaacdbbadbccabbcaacccdddddbdccdbddbbadcccaaabccdbdbabcbdacddadbaaabdccacbdabbcddcdabdacaacaabaacabcbbaddbacdccaaccbdddcdabdcdccdddabcdcdabdbdddacabdabcadbdacbbcadbcbdbadbbbaccbaaaababcbccadddcbcbababbcdabdbbddbcdcdcddccccbaacbcadcbbdbbaadbbcabcbbccaacaabcbadadadbbadadbcdabbccadadaaabacaddbbbbbdbacdbccccaaabdbdbcdbabaccabdcdccdbbaccccacadabbbaccadaadccdaadaccbaabdaccdabcaabaabbacdbcadcacdddcccbdcabaadcbadbbcadacbaacdcabccaababacccabcaccacabcacdaaccdabdbadcddbdacaccbcbacacdaccacbdccddbbdccbaccacabbcccadcabcdaaaabccbadaabccdbadbadbccaadaabcaaaaadaabadcbcddcbaaccbccbdbdaddacaddcbdbcbcaaaadadbbbbbbcabdabdabddabcbcbaacacabdbaacadbadaadbcdbaacddbbadddbcabbdbddcdbbddbcbbacdbdabbaacbaacabdabcbbacabadcbbdabbddaabbcdbddaadbadabcabcccbabacbaababddccbcadabddbbdcdacbbbaaacdabbabaaadbadbacdacccddbabdccdcdbcddadbbccccdadbacabbabbccbaddaccccdbdadcdbaddabcccacbcdcccbacbdbbdcddacbbbaddadcccdbdaadaddbbdbddbcbddbacacabdccaaccdbacadcabbbdaabdacddbcdaccaabcaccadddcdadbcdccdbdbbaabdadcdbbddbcbcbacdaddcddaadadcdbcdbbaaccaadcccabddadabbabdbbccbcacbddacddaabacccdcbcacdbdaccacdabdadccccddbabbcdbaccababdbccccabcccdbbacbaacccadbadacdbcabdaaaccabcbdaddcadacbcdbcdbdcbdcbdcabadcdabdbbdcccdccbdacdbacdbadcacadbdbbcdcdadbdccddcdabbccdabcaabcdacbaaaadaadcddcadcdadbbcccdbadaddababdacccabaaddaccbbaddaadadcbcdcbdcdbdaadbadacbdbdaabaadbccccbdbbaabcddcddabddcbadbcdaacaacbabadcdbaacbbdbabbdbcbcdbdcbcaadaacaccccdadcbbacacbdbddcddbcdadcabbbbdcbccacbabcbbdaabcacadcbabdbaaccccbcaadccdddbbcbbdbacbcdaccdbbbacaadacbcdddaddacccdcdddccccbcbacadbdadcdbcbcbabcbacbbbacdcddaabccbddbabbcbdcdcbdddbccdbcbaabdcacabdbacbbacccbddbababacbbcdbaacbaccabcbcabaabcccabacbcabaacdbcacbcdabbcdbbcccccddbbcbbbbdccdbdbdddababdcabcccdcdbaacacccadbbbcbdcbaadaabddbbdccbacddadadaaacdcacadbbbbcdacbcbabbdadddaddacaddcabdaaabbbdadbbddbadbccbdcadbdbccdccbabcdcacbacbbcddccdacbcdbabaadabaccbacccccbcaadaaaaadbbbbbddcddbaccacdbbacaddbcdabbbbddcccbacdbabdaaccaacccdbdcdcaabdbaddcccdcaccaabaacdadddabdcacccaacacccadbacbabdbdddbadacdcaddbbabcddccbdcbcccbdacdabcdaddabdccdacbcdcadbdbbbcdaaddcdbdddaabbcacdbcabdadacbdbdbdaccdbacaccadbcdccddddcbcdcbadadcddccaacabbdcdcddccdbbbabcadacddbcbabbdbcddaddccdccbabbbbadcacccaacdadaddbcdcbdaabdaaabbbbcbccdabadbcdbdccbbbdcbdcdcabcacdbdadbbcbbbcbcbaabaccbcaddcbcacdadacabdccdabdcbcadaaccccadcdacacccbdabcacadcbcbcabbbbddacdddabbacabaddccbdcaaaaaaabbdbccbaddcacbdcdbbaaadccbdabcacaabbadccdadaaacddbbacbbccccdabdacdddcdbddccccccdbcdcacadabbddaabbcaccdccabbabddbaccaadbcabaaaccaddddcdaaabcdadcdabbcbdaabadbbbaaadabbdbbabcbcccbbaccdabaabbbadcaadbdaddbbadcbbabadaadcbddadcaccdaaaddbcbbbaacaddcddddccddacbabacaadcdddadbacdbdccddcdbcbacdcacaccdccbdbcdbdcacaaccbbaacbbddaaaaaaaabdaabcbdccdbadccbacbabdacdddadbbcabbbdbddbdcabcdbbbcddcabbaaacdccbcaabbdbdaadadbcbacbadbadcbcabccacbcdaaabcbcdbdddcbdcbadcaaddddacdbcadccbdbcabbdccdbddaaddccbabdcacaaccdbcbdbbcbdcabbaadacccbbcdadaccadddbabbaadadacbdbbaddbdbcadacbbaabbaccaadcbacaabacadcdacbacabcbbdbdbbbcbcbcbdccbcccddccdbcadccbbdadbaaccaabbbddcdcacbdbabcdcaddcdcdaababdbcbcbcadddccadbaacaadbdcdbcbcdbdabbdadbbaacdabaacacacabadaddbcdbaddbdbbdbacbcdadabdcdaabbdcdbaccdacbdcbcccdaddbbdccdbadbcbbadaddcaaaaccddabcacbbbadabcacdddbbbcdadbbbabbcbddabdabbbacdbbaaaacadbbbbccadabaacdcbaabcabddcadbacadacdbadcbbdbcabcbdcbbbcdcadbbbbbaacacbcdbbddadbcdbaabaacadbbcacaccadcbbcdaaadbccaaccadbcbcacacdcdcabadadbcbdccdbcadddcbbadacbdccbcccdaabdbcddddadcdddabccbdcacbdbdacbaadccadcbdaabccdaadcadbddbccabbcdcccadbcaabbddccbaabbcbadaaccdcddddacdccdadbdadbbbcbbbbdccaadcdacbcaabbaadccdcadbccdcdabcbababdbdabbccdddaadbcbdbdcdaadcbcdaccdaacbbacbdbacadbbacbdcbacbcdccdbacbdcbddbccdadbcadbcbdaadaabbcdbddbbdcdaaddabcbbcabbbaacbddadbcdadaaaccbcbcdbdcacaddbcbdabdcbbcbcabbbdadbbdccdadcaaadddacccaadcbdabddcdacbcabdccdbcadadabbabcaadbabdbbdadbdacabbbcbadbdcacbabdbcacddabbabacddaccadadbdaaadabcccccdadcadcababccdbabbaabcccbdccaaabababcbaddaadcacccbbcbcaddbdbcdbdabbcabbbcacddcaaddaacbbabacdabdddcdddccbdadabbdaadaddbabcbcdcaaacbadddbcbbddccbcdcabadcbbacbcddabcbdacaabacbaaccaabacccbadcbdabbccacbcdbaabbcaacadcbdacddadbdcbacddccddabdbbcddbcdcdcabbaabdbcdbbcaaadddcbcadbcadacccaaadcdabcaaccbbdcdbccaadaccadaaccccdbabbabdbbacaaaddabacaabdddbcddbbacbcdbccaacdbcababdcacdddbbdddaadcaaaddcbdacdabccbddccacbbadcbddcdadbaadccdbdccabbbdcaadabbbaabcbbbadcdcdbccabcccbcaadddbdcaadadbcbbbcadcbadbabaabdcbcddbcbbdadbcdccccbdadaaabccbbaabcccbcaddbababdcddbaacabacdbcdaadbcbcbbcbacdbababccadadbadaddbcbcdbcdaacbacbaddaadcabcaddcccaacbdaacaaaaddaadcbbaddababcabbdcacbabcacacdcdbcdabdbccbcccdacbbcaccadbcbacbabcdbbcabbadacddabbcaaabddadadbcdbadccbadddabbaabcdabdbcaccccbdccddddbcababddadccaddbdaacbdaddabadcacddcbdacdacaccbdcdaccbcbcbdbdcbdabcdcabbbbdacdbbccadcdadcdbbbbcddbbbabadbacbbabbbbcdbbaaaaccbbcdcccbbdbbdbcabdcdbdcbdacbccaacbbacaabdaaaccadaddbbdbadabbddcaaccbbcbaaabddbbbddaaaddaddcccbcbcadabcadacabadbddacdddccaadddcbadcbbcccbdcbbddbbccbdcbaccbaccaabbabdddccbaaacdbdcacacdbbcdddbadbcbbdccdadbdaacdcbcbdcdcabdcbbddcbcabcddccddadcdaddbbddbdbcaacbcddbabcbabaccdaabbbbcadaacbabaccdaddbbdddaccbaabddddbdbdccbabacbdbaacabaddbadabddbbaccdacdcbddaccddbbadbcacdabaaaaabdaadbbabbadddadccbbbcdbcbacbccbbcbbdadcdbcbabcbdaddaadbbcadbdabcdcdddcddaccadabbddddaccdcbccccddaabddcaaabacddddabadacabbccbbabbcacdbddccabbcddcdabcdcbcabbacacdccacdddbdabcacbcabdddbadbbdbaadbaacaddbdbbdadbbdddaddbbaabbacbdaccbbbabaadddadabbacbaddbabababdbddddbccddbdabadaacadbbbacacabcbbbbabbacccbdcadddcabbdaabdbcdcdbabccdbbbaaaabcadaaacaadcbdcddcdbddbcdabdacabbbbdcaadaacdbcacadabdcbbdbcccbbcbababbbbdadccabdbccabadcbabcdcbabcdcacacacbbbccaaabbcdbacadadcabacdccbccaccaabbabcabdacbacdbccbddddcabcdabbacdaacdbbacddcdcadbabdbbdbcbdaabccdbcabbcccccaaaacddcccbbcccccdddaacadaddaccabdcbbadacdbcbaaabbcdccccdbaadbabdaccdbabccaaccdcddbbdbddbaabababdbcdadddcaadbbdbabbdbcacddcddaacbdddbdbbaddddbddcabbdbabacadcbccdbbbbdbcdaacbdbbddaaabccbadbcaadaaccbcdbaccabdbdacdaacdddaaabbbdbacbcabbbcbdcbcddcbbbbaadadbddddadccdaadacbabadbbaddaddaadadbaacbcbbbaddabdabaaddadacadcbabbdaddacbbadddcddccbaddbdbacacaaabdcabdcccbbaddbaadabbbbcddccbbcbcccbaaaaadccdbdbcbaaadcbadbdcabbdcbbbdbabdacadabcadcacdddddabaabddbcdcaabcdcdabbacdcadaaaacacbcbbcdaaadbaadabcbcadbbbcbadbbddddabcababbdbdcabacadbcdabbdbaacdccdccccdabacbcadaacdbdddbadbbabddaaaccdcddabbabbcdbdccdbaddddaaadcadddbcacbddadbcaddcacbaddbacbbbcdaccdacccbadccbccdcdcdcabcbabccbcabadcacabdbdbcccdbabdbcdacabdcadbaddaaccbaccbaadccadcbbdacadaddbcbddbbdddccaaabbcacdcdbddbcccdccccbbdbcbcdbddddabcaabbdbbdcccdddcbcabacbadabbdcaddbcddbbabadadddcccabacbbdbdbdbbaadaccdcdbabcdcacacccbaabdcdcddbbcbccbadaacdcdcbacabdcbadacbbadcdacabcccdccaadddadcbbccbbacaddabbabcaccabacdccacaccbaabcddccbcbbdbcddddcaaaabccdbcdaddabbcddacabbcdbdaaadddcdcadddcccdcbcdacbcaadbcdbbdaaaadcdaadaccbacadccadcdbcacdaddbbddbbdacdbbacbcdbbbbaaddacdcbcadddabdcbcdcbcbbacdbccabdaddbbacccdcadbbccabcabcbcacaabacdcadbdaacacadabaaddbcadccaacdaacbddddbcbbbccdcbccabddaadaccbacaaccabbcbababbabbccadbdacbabcccdbacddbacbbaabacdacccacbdcadabbbccadcdabbaadadbcadbbcbcadcbabaddacbbcdacdcbdacbadcaadcababdbcbbbcdcbabcadddccdacccabdbabaabaddcddbdcbdbcaccbaabdbdabcdaacabdbdbabbbdccdabcbacdbcccbacdbaabdbbdbbdadbbcdccdaadccbcdbcbbadbbaaabbdccdbdbbcacddcccacabaacccbdbdaabbbabdaddaddccacdbdcacdbdbdccabccdadbdddaccdcadaacbddbcccdabbcaaadaddbcacbcacbbaaaaadcbdcbbdabddadcdcabddcdaabbccbdcaddbcbcdbbdbdadcddbaadcaccccaaaaabadcaaabcdcaacbdabadabcabcbbaadabbbcdbcbdbbdaaaddadcbbbabbbaaaccadbccdaccdbbbdbbacbaddaddaabdaacccbdcdcddccaaacccccbbabddcbaddadbacbadbdccbcddbbbcbcbaccbabdaccbcbbbbdccacccdbdcbccaccbaddacbbacaddbbdbcdcdbccaadccaabdccaddcbabbababdaababbcabaabadbbcbdccdadcabdcadadcdcaccbadabbaddbbbbdcbcadbdadcacdacabbadbadabdddbcdbcdbabacaccabdbbabbdacababababddcaabbddbbdcacaaacaadcbddddbcacabcccbccabccaadbabdaabcdaadbadcbabcabacdcbdddabbcadbccbccdcbabcaaadcbcbbbacbdaccbcbdddddcabbccbdddbdcddbcbdcbcccaacbabcaddbbbcdaabaccbbcaacabdbdadaacacddaabdcddbdcddacbdaaddcbacbadddcacabaaddbabdbddbcbcdbcccbccacaccabbbdabdbdacbbabbadbdbabcdbabcabaaddaaabbcdabbbccadcadcdaaabbaadbdaccaacacadbdcbcaccaaaddcbdbbccbaaabdbdbdcbdacadaccddddadbbbbadbdddbbcbadccadbadbbbbdbbaadabdddaacbbacdbddddddcabaddaddaaccabdcbddbddbaacdbacddbaacdbadbabbcadcbcbdaaacccccddbcadaaccbccbcbbaaabccccabbdaadbdbbcabbcaaabdbcbccbabbbcccbbcccddbbccbcacadbbdcccaadccadabcdbaacaacddaacadcbcdaadbbadcadcbbbaabccdacccdbccabbcbdcadddbbdbdccadddbbddadadacdcdbcdddddacdbabdcdcadaaacccadbacaaabacbaadaabdbdbadcdbadddaadacdccabcbacbabcdddbabbabbacabdababbcaacbcadadbcbbdaaddbbbdbdccadaacbcccaaccbcccdadabdabbcbcbdbdbccddddcaabbbcbbccaddccabbaabbccbdccaacbacdbabcccadbabdcabcddccaaddabccddabccabbdbdbdabbaabddbdccdbcbbaacbdcdacadcaaabcbdabdbbdaabcdadbbbabcaaacdccdbadcaccaabcadbcbcdadcbbabaccdddbcbbdaccaadbcaccddbbabbacbcbdbadcddbbdcdacdcbacbbaccdbdacddbdaadbccdbdaaadacdddabdbcbcbcbccdbbcadbbaadccdbbbaacbcdaaadabbcabcacababdadccaaadaddadacacadbbacbdcabccbbccaacdacdbdadddaacaccacdcdabacacdcaaabbcaaadbbbcbddcaabaababdabbabccbacaadcbcaddbddbcbdabcdbaaaccadcaadccbccddbdbbcddaadaddbdcbacbdabcdbddddabbaacdbdbadcdadbbccbbabbaccbbbccacbdaddbbacaddbaabacdacaaddbacaaaacdbaaacbcadbdcbbccbcbbcdddabdbbbaccbbbaaaadddcadbcbbcdcaaaddabdadacddcadddcbcdbbbcddaadcdcadcdccbdccaadbdcdbdcddddbaacdbbdaaaaaaaacbabadbbcacaccadcbddbaadcadcbaddaaccaacddcadbaabdccddacdcabaacddbbbbbbdcdbdcadbdcdabdaabdbbddacbccdababaaaddababbcbcccbdbcdddabbccacbdaabdabcdcbadbcdcacadddbacbaabbdcaabccbcccdaaddabddadacccbbbaacacbdaaaacadccbbadbdbcadabbdbdaccaaccacabdcdaaacdadacdbcddaacabcbdaddbadcabdcadaddcddabbcacaadbacbcbdababbdccdddddadcbaaaadabddbbacbdcdacaacbcadadabaddadacabaababddbbcddabdddbdbbdcdadbdbbdcbbcdaaacbcacabcdbdbcdbcbcaaacdccbaabccacdadcacbdcdcacaaadbbdcddbccddcdbdcdddcccbcacdccbbbcaddcbdcdbadabdbacabbacdbbcdbdcdbaadacddbbdaddcadcbdcadabcbabdacbaacccccbdacaaccabcccabdddbbddaabbabbbbcabbcacadacbaacbabcdacdbbccbcdaccacddabbbbbbcdacacbabbaabcbacbbaaadcadcaadccbdbaabdbadaccdbcabbdcbcdbcdabddccabbaacaaacbaaabccbddaaaddaddcabbbccbdbdbdabccabcabacabdbdadabacdcddcbdbadaddacaaaabbdbabaabbacbdaabcbaccbdabdaadabdbdbbdbbaadcabccbccaacdbddacaaabddbccbccddbddacbbdbbcbaaacccbdacbacbcdbbbbacabddcacabbddddaaadbcababacbbdcabacaacbaaaccaccadcdaabcbdccddcdaacabdcdddbbbdabbadacbbbadcdaccabdcaabbddaaacacccdcbdcbdaaaccbccadbdbbdbccbabcddbbdddabdcabcbcdabcbccbbbbdbdbdaabdcbdabdcbccabbdcbbccaddabbaccbbcaaddddaadadbbcadaddaabdddabcaccbccadccccdbddccccabbcbbdccaabaaabbcabddddccacdabcccbbadcdddbbaadbbbdbddbbdadbcdcdbaadadbbbdbababaddcbabcbdbbbaacacbbbbbabcccabbccdcccdbabdcbacddcacadabdaababccaacdadcaddbbbdbcdbaccdcbcbbdcacaaacddcdbbcddaddabdbcbdbaababcbdbbacddbbcccaadbaadbdacbcbcaddaabddabdccdacbbaddddbbcaadddbadbbbabcbccbdcadcdcabbcdcaabcbdaaccccadbbbcbbbaccadddccdbddaccbadbcdbcbcbbdacddabbbcaccaadcacacadcbcabccdbaadbaabcaddddddbadacdbaabbcbabcddbcdcdadddbbadbcbabaaacadadddbdcbcbddadbadccbbbbabaddacbdbcdbddccbacdcadcbabcbdabbcbbaddcbcbbbcdabbccdadbbcddbadbbadbbdbddcddcccacaacbaccccccaaabadadddccadbccddcdcddccadbccacbdbbcacbbaadbcbdcacabdccaccdbbaccbbcdbddacbcbbcddbdcdbcddaadcdadbbacccbacabdcaccbdcaddbdbbbabcdaddabcbdddccbbccabadccdbcdbacadbccacaddcbdaacdacacbbddababccdadbddbcbcccaabbaaccbbdaadbddddbdaacbabacbddcbbbbdabcdcdacbbdcbcdbcadcdaccdddaddaccbcabddcdbbabcabbabcddbcdbbaddadcdcbbcbbacdbdaaaabdccdcbddcabaadbbdcabdabaddbdaaddcabdbaacadcdcddccdcccddabaacdccdddadbbcacadbdabddadabadbabcbacbaacbcabbbacaaadccdcaadbddbcccdabcbbccccccaddcbaaabaddbcdbaacddabaaababdccaaadccbbdacabbaaabaacbaadbadbbcbcaacdcbbdccddcccaccaaaaccadbaaadaaaaaccdabbdddbcdbacadcabcbcabddcbcbcbaadcbdbabaacddccaaadcadddadcddbcacdaabdadbcddaaaabdbbbdccabdbdbbccaccdbaddbbabaccdaadaadddaabbddabcbbbbcaddcbcccbcacdadabaddbaadbdccbcbdcbcbddbdacaaaaabcbbbdbddccdddabcdbdbbbdbdddaadccbcbabdbcbabcccccccacddbbaddacaabddddcacdacbacbdcbacbccbddadcdaaabbbcaabdcbbcdcbddacbbdcbbdcdbcaaacccdabccbaabcabddabbbdbcbccdbccdaadbbcbccaaadddddbdcddbadddcbadcbabddadcadcbcbbbbcdbbbadcdcddddbccdaaabcadacadccbbdbaabcbdbdbbddcbbcdacdbccacdcbacdcccdbdcabcdaccadbcdbbddcbaadacbdadbaacdcddbcdabdacbadccdddccccbacbddbbcbdbbbdabaddcbcaddaddabadbcbaababdbbdcbdabdaadabdbbdccbdacbacbaddcdbaadcccacacbccbcccaccaaccdccdcdadbdcccacbcbddddaddbbabbdcaacdbbbccdbbcbcdadaccdcaacbccacbcabbaaacdddbcabcdcbdbbbcaacdaadcaacccdacccdacdcdbcbbcabaacdddcdadbdbbccbabdacddcbdaaddbccddaadcaaabdcbadbcacddccacaddbabddccbacabdaaabdbbdccacbdaabddbbbabbdacdbcccccbdabdcabaadaaddcacbaaadbdacccdccbabcccbddadaaddcaddbdbcbcccccaadbcdcabdcdddbcdcaaabdaddcddababcbdacabcdccacbddcaddcdcdabbdbcccbadcccabdcbbdacccbdbcdaddbadbdacbaaddbdadbabcabacdbacdcacbdbbcacbaccdcbcdcdaaaaaabdbdddbbbddccaabacaaacadabbabcddcdcdcdacadddcdbccaacdddcaabbcaabdbbdbbadaaabacddcbcaadbcabbbacdcddaadcdaadadccbbbadccaababadbbaaacacabcbbabbadbcdbdacdaaccbbcdcdcaaaadbdbadbdbbdaadadcbdcccccdbabcacbdcdabdbbdbbdccaaabcbbdbddaddacdbbabccbdcacaacdcddaacdcdcababdaccbdacbbbccaaccdadccdccbcabdccbdbcddaddbdcadacabcaabbbaaabbbdcccbadabaadcbddcaddadacacbdaaacddbbabdcdbdaccadcbdbadabdbaaddbbbdadaadbaccbadcbbdccbcddbbbaacadbaabcbddbbaddcabdaaacaccbdcacdacdbbccbdacabbcacbacbddbbacbbadaccadcadaacacdbabadacddadbacccaacccaaababbccaccdccdcccdbdbcacaadcaacdbcddbabacbbbacabdbddbcbccaddbaddcccdccbcbaccadbcdbddcdababbbabccbacbabcabdddcbdabdccbbdddcaacdacdadabbacbbdcbadcdcccaadababcabcdaababbbdbccaaddbbadbdaaaccddbdabbbbbdbddbabbdbcaaaccbadabbbacdbaabcaabccbdbddbdbbcdcbcddcbaadccacadacbdaaacdccadccbcabcdddbdbdacbaddcbbaccccbbacbdaccdbdbcdcbcbbabbbcbcababbabddcdddaabdbcdccbbacdbcdbbccdcbacbccdcabddccadcaaabcdccbdacdadbcadabacddbddbbacbcaabacacdbaadcbcabdcddbbacadaaddcacdaddcacbbcdaabcadbdbdccabbbbbabcaacbadacdcbbcccbacbadaccddaaacacbcbcbddcdaddadbdccdbddcaaadbccdbabdbddcbddcdbcaabccabadaddadccdbddacadcccaabcdcdadadaddbdaacabcbcdbddbbdabdbaacdacbbddccdbdbcdbccdbabadadbbddddccdcacbbddabdbbcddbddccdbbacaaccdccbdcdabbdaacbbdcacbaadbbabcccaaaddbdbcadacacabbdabbaaccaddbaccacababcadbacdddcaaccdccdabcbbababdbcbcbaddcbdaddbbbacbadddbabacdaccaabcabbddacddadadacddcaaabaacdadbddcadaacaabcbddacbddddcabaabaacddcdadadabddcdcacdcaaadbcaaacbbbbdacbcbacdbacacaddbbcdbcbacacccabddbdabccdacddbbaaabdbcddcbaccbcaaacddcdbbbababbcbcbcccccdcbbacbacadccaaccbababbdbdbaadcdbbbbbddbdcdcacaddcabcccdddbcaabdddcaabbcdaccddaaabccdaaadbadacbcbbdcbbbdcdbadbdcbdccaabbbdadcbbbacbdddccdcdababadbdccbcaadcbabdadcddabbdcdbacacadcbcdadacccbaacadacbbabcbacdbccdcbbbdccdadccdbaccbbacccbdcdcbbaacccbcbadbcaaadcdcccabdaaaaabbcccaadabbadccbbdadbcaddbbaddbbdcaababdbacaacdbddcbabbcbadabbdbaacabdadccabbdaaddcdcbdbbbbbcbcbacabdbcacbbacdcacbababbddbcadbdaabaadcbcdcadababbcabcaddccdbbddacbcdacacbbcbdadbddbcabaacdbacddadbcddabaaacdaabadbabddcacddbdabddcbdccbdccbcbbcaabcddacbdcbcacabcbbaaacbbdacddbdbcdbacbcddbaacabcaaadbbcbbccbdcabbcbadaddaacbabdccbcadbcabaddabdaddaaadddaacacccdcdbcbaaccaaddbbbdadddccbccddabadadcbdcacacbdacccbcdbbdabcbaabcbbadcaaacaddcbdcddabdbcdaddaaddabacadbccadccdaddaadbcdcbcdbcacacabcdbbbddcdcbbabcbdadcaccaabdaaacacccbadcaddbacaddbcdcddccacdaabaaddddacbccbbccdcabaddabbacdcacadcccadcbbbdabaacaacdbcddaccdcdddadabbcddcdcabbcdbdcbdabbbabacabbabcdbcbbdbddaababbcbdcbabddaabdcbdaccdabbcddcdbabaccddcbabddacabacddabbcbbcbddbdababaadcdacabbdbbbabcabbaaadcccdaabdacbbccaddaaddbbaaccaabaddabacdbbddccbdbacddbccdaacbadbccdbbcadbadddddcdbbdabcdbdccadacdbbddccabadccdabadadbdcdcccbadbadbbcbcbbbdaaaacdbdbdbdbdbdabddaabdcbdaabcbabcdcdbbdabbccaacbbbbdadbbbcbddbbdcbcddbaccaddbbdbadcdabdbdccabacaacbaacbdabdaacdbadbcdabdcdaabadbdbacdaaddcddbbcacadcdccadddacaadcbbdbabcbabacccbdbabcacadcbabbddbadabdaccaccaaadbabacbdbdbcbaddaaadbbbaaaabdbcdbccadcccabbcabddddabcadacdbbbdaacccbbadabddcdddbcdabbdadbcddcdbcbadacdbacaddaaaacccbdddcddabcdadbccdbdabdadaadcacbadabbccdbbddadcaaaadcaadababaccbbdbbabddbcadcbddaddcabccdbcababdcdcbcadcabcccdaadabdbabcddadacadbaadddccccaabdaadbacbbcaacbccddcddaaaddbcabccabcaabddbbdacbbbaabbcbddadbcbacdaddabacaadadaabcadcdcacdbabdddbddcdcbdbcddacbbbdabcadddbdcddabcccadbbacddcbaccbbbdbccdbdcddaacabadabdcaaadbdbbddbadcdbdadddacbcaaddcbaadacccddcdabadabadbcaccddbdcdadcaabacdbdaaaadbdaaadbcbccbdbbddcdccaddddcbcccabdbabbcacabdcdacabadacbbddabbaddcbdacbbaacadbbccddbaacccacbaaccccaacdaadcddacbcdbbcccabdddbcbbdddbdbdcddbbbdbdacccaddccbdbcbdbbbbcaabddaacbbabcdbbcbcbadacdbcabbddcbddbdcbbcccaccddbcddabdcddccbbadcabdcdcdacdcdbabcbbaadabdacbabadcbacbcdcbddbdacabadaccbdcbacdcbbccccbcdccbadcccdaadbccbbdbbdccbdadabccbaabbadbbcdbcbbbbcdbcaadcbcabababaabddbcacdabbbbccccbddaddabdaabbccddadddaaaacddcdaacdabcbbacdcbbcdbacacadbdadadcacdaabdbccadddcbdbcddccaccccbcdcbbddabdbdbbcbcdabdbbadddddadacadcbcaabcacddddacabcccdaaaaadcdabddbdcabaddaadaacadabccbaadcbaaaddbcdddbaacaaddddbdadbaadbabaaaaadadcbcbcbdcdcaddbdcaaddacabcdabaadccccadadabccadbbcabcdccddadddabaaacdbbcbbacbcbdbdabccdbbcbacdbdcacbaacdccaaaabbcdbaccabddccabcbcbaaadcaaaacaaccdcacbbcddadcccddabdccddddbbadbbbaddbabcdaabccddcdcbadaaaddabcbacbbdddaddcbdcddaadcdcaadaababcabbddcdcadccbcdbbaddddaccaddcdbccbcbbbbbccbabbdccdadabacabacbbddccdbbdabbdaaccddadbbbcabdcaccabbcdbcdcbdcccdabccddaccdccddcaabbaaacdacddbcabaccacbdaddbaccddcabaccbddadddcbcadbacacdacbddbdcdcbddbcaacdcadddccacdbbbaacacbcbdaadadcadabcddaadbccbddaccabaddaabbdababdbabcdcdccbbddccddbbcddcbbbacabbcdbddadabccbdabbddacadacdbcccbaababbadacccbaabdbddabaabdbbdaccdbbdadbcacadaddbdaaadbdcbccadddaddddcadacddcadacacaaacdcacddaacbaddadddbccdcdcbbacddbabaccddbbacaaddcacaddbcbdbaadddbbadbabcdaaabcdcdddccdacbabbcacacbdcbdbbcaccdcddbbadaccaaaacaababcbadcbaccdaaacadcacdbbadccdabbbaccbacccbdddaddcbcbdbdccbacaccbabccbaccdbbccddadbdccbbbccbdabdadccdaaccbadaabaaabdbbccccaadbdbbdacabacdacbcddcbdabdcadccaaabcdbcabcdbdaabddbccadbacbacbcbcacdccccacacdbddabadcdcccddccdacdcacccccbacacddccdbccbadbbccbdcbbdaccdaaaacddcabcdaabccdabbaadccdaddcbccdacbcbcdcbabdbdcccccdccaacddbcbcaabdcacbabddbdcddabbcdccadcaabcabcddaaadcaaddcbbdcbaaddccbcabdcacaadbbdddcabccbcbabdcacacddcaabccbcaabaabdbdadbccdccaccddacdabbccdaaadcddaabcbcbcaddcaacbddbbdbbddaddabbbbbbcbbabdbcdddacbcaabbabadcbcbbcbcdabdbbcddddbbbcccdddbbdcabbddddaddccdadbbaccbcbaccdccacccdbbcdbcadbccbbbadbbdabbaddcbadaaddbbadcddadbbdabacdbacbbcdbdcdaabbacbccbabcdaacbdacbaacddabacaadccddaaaddcbbddbdbbbaccdbacbaadcdcbbaddababdcdbdcdbbccdbbcacddcbcbccacabaacadccbccacbdcbaccaccaaadcbbccbaaacbacacccdccabcbcddaaacccdbccaddbadcadbdbccdddccbdadadadccacadbddaacccabadbcdccdabdcabbcbdddbcdbacbcbadbbdccadcdacdbdbbaccbaadbaadacbbdaaaacdcdcaacadaacbadcdaaaccabacbdbbcdabababccddbabbdbabbccaccbdcaadbcdacacdbbdbdbccbacabdbdccddcdacbcbaadcdddaacbbbbbbdbdddccdccbadcbbdbcabaacaabbcbcddcbcdddacdcdadbddacdccccbdddbdacdababbcadadbcddddcbcabccdacdbcacbbdbcbcaddcaabbddbacbbccdddbbbcdacbcaaacbccdbabdccbcbaaddaddabbcaaddbdbdbdcddaabaccbadbdcaaccaaacbdddbdbdabdbcddbdacddacbddcacdcabdadbbaabdcababaabbcddbcaccaaabdddcadbdbdddcabbdaaccbcbcacbaababbcdbddadbddccbdacbcacdddabdbcaacdbddaadcdbccababdcdcdabdbdbaacacdcbccadbdcaadcbacaddbbbcbadaabcbdabbbbcdbccbcccadcccbaabcddcbcddabcdbbdadaccabadadcdbcdbcbabbbddcdddabcacadddcdbccbbadaddabdcbbacdbdbcbdbcaadddccbababaccabaadbcaccbacdacbbcaaacadcccccbcdcdbcacdaacdadccadcccbbbbadcadbdaaababcabccbdcaabbcaacbcacbbabcacbabbbcadddbadccabcadaccdcbdbadbbbabbbbadbacdccbbdbdddddccdabbabbcbdcdccdcbdddbbdacacadcacdabbcbbdcddcadcadbbccacadcdbacbdcabdbdabdbdddbbcaacdcdcdabcbbaabbdcdcddbcbacbaaacbbbcdcaacbbdadaaccabccaadccaaccccaddccadcbbbbbcccbcabbddcdbdbbadbcaddbadcacbabddcdadaddadabbbcabdaabadaaccdbbaadbddadcadacbabddcddbdbadacccadcbdcaaaacabbdcacbacdcdcacaccbbabccaadadbabdcdddacdbadcabadcbccccccbbacabdbbbbadcdabbaabccdcddbbbdacbaaddcbaadccdbbbadbbabcbcbcbbcbcdcbdbccdbddaddbbacaaaaddbabbabddcdaccbddbbcaddbddbdddadcdddcdcaaccbcccccbcccbbcccbccdaaddadacbbbdccacdabccdacbdabbabbdbabbcbabbdaadcbbabcdbdbcccaacaddccbbbddacdddaaaddadaabcbaddabbddbbacabaadcdabadabdcbcadaabacccadccacdbbbdccaacacdcadcddddcddbdccabcbbdaacdabcbaabcbdbdadddacaccaacacdccdcadcaadcabcbbdaababcadabdbdccababdadddddcdaccbbaccaabcbcbcacaacdaaddcbbabbcddaadccadcbcbbbacaddacbcdccacdbaadabcdaadbbdccbdddcbcaccbdaccaacbcacbabcabdacbccbddadbdcdbbdcdaabbdcabdcabdcbadaabbccbdddacacccbacddcadcbabcabccaacdbccabbbaaabacccdabcdacbaaddacadbcaccbaccdbdacdddbabdbbbdcabdbbbbabcdcdbdbacccaabacdbbdcbcdbdaddbcaabbbdcbcabcaabdbbabaacaacabadabdacbacbdaccbcbcccabbcaddddcdddaabbdccbcbcadcdcdacbcaccaadcbbadcdbdaccccbcbaaabdbdbdbacaaaaddacbaaaaabcddbdddabcdcadccbcaabbcbabacabdacddbdaaaccaddcdbacdbaadbbacccdbaaadaaadcadbcaadcdadcaacababbbcbbaaadcdabcdbacbcdcdadbcaadbbcdcabdaddcbccddbdcadcddabdcaabddacadbcbbacbabccdacdcacdacdddccbdabbcbbbcbacdbbbacbddbdccdadbbccdaadabacbcbcdabcdadcadadbbcbbbdaacdddacccbbdaddcbbbcddbcbdbbdbbbdaaabbccbbcdcacbccaabaccaaabaacaacdacbaaadcbdbacbbabbccccccdcaccddbbbdbbaaddadaddbbbadacaadbdcadddcbddacabdcabaabcabbcabbaadbbdbbcdbccababaaadbadbddaacdabccddcdbaaadcadabacbdddbcdccaabdadcddacdccdadaacbdbdcbcdccbbcddbacdcbaaddcacabbadccdbadcacaccbbbcbaadadadbbadbababbacdddaddcbbabcabcabcbdcbbadbccaddccdbaccdbcbbbdababdbaacdcdbcbcadddbcdadccdadbcdbcaaccaaddccbaaacbacaabaabaadcbbdcccdbcaadabcdadbcdadacadbddbbccdccbcadbcadadabbcadbccccbbaaddbbcdacdcdbcbdcddaccbaaaadbcadbbddabcaabaadbacacaaabaaadbaabaabcaaccbacbbcabbbbdddbcbaccaaaacababdcbacabcadcacbdabccccadbbcacbaddababbbadaccaddcbbacdcdaabbbadbdcdcdcabbdacbcccbcaaaadddaadbaaabddcaababdcbdbdadcaabbabdbbbcddbacacdbcbbdaabbaccbddbddbbaccdbaaadcabcaddcdcdacacaaadaadcaccbbdcbbabdccaabcdbaadabbbacabbcdcaddabdcdbcabdbaacaddabdcccaabbabbaddcadbacacadcbdacacbbbadcdbaadbacaacbbddcbdbbdadaacddabadccccaccadcaabdcaddacabaadcbdbcaaddbdcabccdbcddaacccadccabdbadddbbadacbdcacbacbcaccbbdaccabcaccadaadbdccabddabcacacbbbabdaabdbadcdacacdbccadccabcaadabcbaabaddbacaaabadbabaacccdaadacdadacbaaccdaddbabcadaaccdbccddaaaaddbabadbdaccccddbadccacbdbcbddacadbbccadddddbbbaadbdbcadacbbbcabbcbcadcdbbccaaacbaaabdcbcbbdbdbdabdaaddbbdbaaacccabcccabaabaccadaddcbddbcccddbdabdcdacbccdbddddccabbadbccadbabaaaccacabdbcbdacaddcbdcdaacbcdbbbccccaadabbbcbbbcccbabaacdbcccdbdbaddbdbdbbcbdbdbadbbcaccbaacdacccdcbdacccccbabcbacabdabdbdbbcabacacbaaaaabcdcacccaaabadbaaadbcddacbdacddccacddbbcbbaaacbbdcdbabacbbbcbddacaaadbcdcaddcbaacababbadddbaaacbdaddcababbcaaddddadbdbddaaabbcadaacbdbadaabaaddaccaddbadabdcbbcaccbddcbadddcaaaaabcbbccdadccbaacdbcbcbadcbcacddbabdddaccabbaadabacabccdabcdbbadddddbddbdbcbabcdadababdbbbbaaddabadacadcbcbbbdaccdbcbcdacdbaabbdaacadbccdbcbdbdbdaccadaacabacdcaaabcdcdbaaccddcaccdcbbacadcbabdaaacaacbabcbdcabbcdabacdbcbdcacddbcdbcacccdabcdabbacaabbaaabdbdddbabaadcbadbbbddbbbccbbbcdcabcddadbacbcdddcaccacaacadbcadabcbdacadddddbbcbcaccbbcccdccdbbccaabcadcaddbcdcdcadaabdbccdcdbbbcbbcacdcacababbbbcbcbaccaaabaabadaaadcabbababdcccccddaacdbcddacdcbddcdbddadbdcdaaaabbdddacdddbbdbaddbdcadaabbcbcdddbdcdddddcbcdacccadcacbdcacdaccdbdbcdddacdbaadcbccdacccbcbcccdbdabbcadcacabccdadaaadbdddbccdabbacbcbacaaacdabadddcbabaadbcbabccbcadddcaaccaabaccaadaadabcdacacaccdadacdacaabbbaaddaccbdaabbdabbbbcbdacbcabdbdaabcaabddaacdcaabcbccbbddcaaaabcabdddcbbccbcbbbbbdccdadbabadcdcadacbbccdbbcbbdbbcddabbcdcdbcbdaabdacaddadccdbcdcbbcdcbdaddbabadcddbcbddabccdddbbdbdabadddaabbdbbbcabbdabaadbbdcbbbbcdcacadcbbabdbcbbabccaadabdbdddcabdccdacacacaabbaacacbacbababbbcddadcdabddaaababcbabbcabdcacaacaccabbdcaddacbacbcdccaaaadccadcbadacbdaddbcaadcadbcbddcadadadadcbbdaccdcdbcbdaddbcadaadbcbdbdabbabbbbccdbaabbadabcbacabbcacccacccabcddddadccacaadacdbaaabccccdcaccbbcccacaacabadddbdbabacbdcccbabddaacbdccbdacabdcbcbdadbdbcdacbadabddcbcaaaadabcdccdacbbabdabcbccbbbccabbdabdccdaddbdbdbadbacbcbbccacbcbddcacbaaddbdaddccdbcadbbacdabaaadcdbbdbbcdcacabcbabdcbbcdbbbaaabbcdcbbbbdaccbdcdbbaaaddadcbbaadbcaadabcbdacdabdcbbacaddcdcacbbdcdacdbaacdbabdaabdcbabbabdbbbcabbcdbaadacbbacaacbcbddbddcbaababbcabbdbbcacbcdcbbaddcababababdbcabbcdccbdabacabbdacbdbddcbcccacddccbcdbdaabacbadbaabdadbacdbddcdcadddcbdbcbbbdcdababdbabdcaddccbcdbdcbcdbbbbdbdddcadabccbdccdbbaccbdccacbddcbacdddcaaadabdaddacdbcbcadaccdacbbbdaacbcccbbcdcbddcadbddcaabcdcabaadaacbaabcbcbaadccdcdacabacadbccbcdcbbcadcbacccabcbcdcabdbcadcabbbdcbacdbccbbcbccbcaaacababadadaabcbdbdaadbbccdddcbbabcccbdcacadcdbdbddacaabbbdbcdbcdbdadaadccaddbccdaddaaabaddbddcddacdcddbaadddbcbbabcccabcbbaadcddbdcbdcbdabbbbbabbacbbacbcadccdaccbddbabcdbaabdbdbcdabdccdccabbcdccddaaabbaacddcaccdcdbbddadaaaddaaabbbcdcadcbccdbcdcdadbccadccabadcbbcbacdbbddccababcabdddcbacdbbadcdbbaccbdcddbabaddbcbaacbdcabbbcacdbabbadaaacccacbcabbddabdbdddabcccabbaacacacdcbccccadccddddccbdbcdccddbbaaddbdbaccdcdddcdaaadddddcbcaadcbabbcbdbaaaacdaacadbabaaaaaabccdadaabcbcdbabdaaadabbacaadadcddddcbbcbbaddbdabcdcabbdbcacbacacbdbcbaccbbdacdcacacdaaacdbdabdadcaaabdadabcadadcccbcbbaaacbadbbbdadcccaacacdcdbdadcaabbaccdbdccdbdbbaabcabccacbaadccddbadcdbabaaaacbcaccacdbaabadccbbbcdddabbadaaabbaddddabbcadadcbbbbbaaccababdddccdddccbbdbadabcadaacccdabbaaaccdadbabddcbddaadcbaabdcaadbbabdbcdbaaacadababbaddbaacbcdacdbacbaaadcacaadaacabdaaccadadbccdcdbaaacabddcaddbdabbbacbbddcbbbbdbacbdadacbbdacadabdcbbbbadaddbbcaacdbddcabdccdcacdbdcdcbaccccdaaddaabcabdbdbdbccbccbdbdbadcaadcadcdbadcabbaddccacacaaddccacdaaabbdcbdadcdbadcbbdabddadbdabdcadbcbadcbacabcbdcccabbcdcacdbbabaccbccdbdcddcdacdabaacdbacddddcbdcdabbacdadcacdccccdcdbcbabbbccddadbcbddbcbdcbadbaccbcbdbbbdbcabccadddcbbcabbdccbbdcbaadbababbdabcabbcccbdcdacccdbacabdbaddadabdbcacdbddbaadcacadcacddbddccbcabacbccacacdadccdacacbaacccaddddabcdbbddbdcaaabaaaddacbcacdabbdddcaaadaccddbdbdbacdccadadacbcaddddddddccbadadcabaaacacbaaaacbdbabaccccacdccacbddddbcaaddccdcdccaccaabbdabdcddadadcdddbdaddbdbbdadadcdddacdbcadcccbdadddaddddddbdaccdaaaacccddacbcaacdcbcddcaabaacbaddbdaacccbdaccacbcddcbdccaabaadcbccdadcbcbcbbccaaaddcadaabcadbdbdbaddabacccdbbabdadbcbbdddcabaaabcbbcdddcbbcaadabbdcadbbbccabccbadaccabbaadadcabcbdbcdbdacbcdaaabbcbacbaaacbbacabcbdcbdbbdbabdbcdddcbcabdadcbdbbadabbadccabccbbdabbacaddbddaadadaacdacbbababccaddccdacdbcabbcdacaccdbcbdcccdbbbacbcbadbdbcdaaacdabbcdcbadbdbbdacddcaadbddcabacbcdbddcdbbbcadaccbbbdbbccbaccdadcacccddaaddddadbcdaacdabbcdaaacadabcbabdaacbaaaccccbcacacccbbadaddbddbdbcdcdcadcabdcdbaaddbaaaaabaaacdddbddcbadbdcbbccadaacbacadcadcaddaccacbbcddcddbcccaddaddaadaadbbdbadcacdccbdccbbaaaacbcbabaddcccadcaaacadacddaacdbcdcbaccbbaddddacadcabaddaddbdddadbadbadacbabccccdbcdcacadccbdadbcccbbdcdcbbbccdadbbacacdadcdaabaadbbddadbcdcaabaabcdbbadabbacbdccdadbcbdbdbbddacdadabbdbbdaabdddbdccccbadbddcdcabcccadcbbdcabdccccdacabcabbaaddcccbccaacbbabacdadbbdbcadadbddabbbacacaadbccadaccbccaadbbcddddabdbcbddddddbbdbdccabaddcdbdcbbbacaadddbbcbcdadbbccadaaccbbadcccdcbccddadbcbdcdadaababbbbbaaaacbcdacbbaaadbaaaaddcbbbdbddbbbdcdadbcdbbacadcdcccddaadbdbaddbdbacccacddddddcabadbacddcbccbddccbacacccbcbccdaaabacadcbdddbbcacabdcacddadaadcbbcdbdcabadbbcadbaaddadabbbdcbbcbcbadbacbdaccbccaaacbbacddababbdabbccdaaccdaccadacdbcdcaabadccbcdacbbdcbadbccccbbdbcbcddbcbcbbbcadadcdcdbaabbbccbabaaabaddbcbdddadbadcdacacacabbabdcadbcaabdddbcbbdbbccacacdcdccdcdcaaaacccacdcbdccabacbaaabbcaabacbbdbdccbdbddddaacdbbbcddddddbbacaddadbacdadabdabaababdcddaddbdbdacacdbddbccbabcdaabbbcbccdabacccdacbacccbcbbdadbbbbaadcaadbdadccadcdbbdbdcaaadaabddbaacabbacbbdaddbdbaccdabbaabbddaadbccabacacccbbacababaacdacacdccdddaddcccaacdddbddbbbbabcccabdbbbddcbabdbbccadabaaaddaddcdcbdcadcabdddbbbdccccdaaaaddcaabcccacbbcaabcdbccdccaccbcdbddcdbacbbbcddbaadbccabbcbbdbcaccccabccdabaacacbbcaaccaadcdaccccdddbdcddaccdbcadabcacbaaadaabbcadbbdabcdaaaacdabccbbdcadbcdbcdcddccbcaccaacdcaddbacabbabcdbadaabbcadadbcbdccccbcbdaaaddcbcadcaacbacabadcadbdbacacbdcccdbddbbabdaabacbbdbcccaccabdaabdadccaaaaaacbdcabaabcabcbabccdcccbddbbbcdaccdcbccbdaabcdaaacacaccbacccaabdaabbaaaccbabadbdbaaaadabbbababbbcddcbaacdddcdddabccabcdcaddbbccdccdadccbacadacaacddaabbccbccbbcaacacdbccdababcdddbbbbbabaacbdabbbacbaacccdaccdcaabaddddcdbbbdcbacbabdabbccbbacaabddcbccbbbdddadcacccccaccbcaaaadaaaacdcddcbbdccdaababadaccacbacaaadcbbcdaaaaddbaddbadaabccaccabdaaabbbcdbbaddbacbdbcdcaaaacbdccdcbaadcbbddaccbbcbcdababbbaaccccbaababdbdbbcdccaaadbacdaddcdbadbbddbdbddbabacadadbdaacdcdbcdbcacaababbcbabdcabdbdbcbcabaabcdbbaccabddbdcddbcdcdacccbbdcbdacbaabdabddcccccdacbddbdcbcbcadbdcddaabcdbbdbdbdabbbbbbdbccbcabadddadbbbaabbabccadcdccaadabccdaacbbadcccabacbccbcaaaddabdbcccadbabcbcacddcbcaadacadcadacdacbbcaaacacabcddaccdcbabcabacaabcabbdcbdcdccaadabadbabcccdbcdcabadaaacddbdcbdbcddbcaccaabbdbadaabdabdcbabbadadbdcaddbbddabddbacacdbbadadbbbcdbcdaaabddcdadbcbcaadcabdaccccddcccddacaaacbddadcddbabdbaacbbcbbcdcaabbdaacbdcbdcaaccccdbccbabddcddabbcdcdbddbacbccadbcbbbcbcababbdaabbacbcdadacdacacabddabcdadcdbdbcabbabdccddbaccaddbcababaddddbbacccbcadcaacacbcbababadabdababacbcdcbbadacbccdcccdaabcbcbadcbdaabcacbbcacadddadaabbbdccaaacbbccbcdbaccbbbbdcacdcbcdcddabcbdabbdbccbbbacbbadcbdadacbcbcbdbabbaabdaddccdddaabadaccccdacbdcbcacdbdabcddabbbcbbdcddcadbdbcbcbccbabdbdcabadbbacbbcadccbabdcccbbcbbabacddcbaabbabdbcbaccaacdadaadaaacabbabdadaaabcbcbabacdddbcdbabaaabadcbcbbadbadccdcbcadbabddabbaaccdcdcaaadbcaabbbaaaacbcdddbbbdaddcdabaabdcaaabacbacdbdbbbdccbadbcbcadcbabaadacdadaadbaddabccaadbbdcbbbcbcaddbddbddadbdacbbbddadbadbcddbddbccaccdabcbaaaaabccbbdbbdcaaddddabbdababdadccbabbabaddccccacdcbdbbccbcabdaccadbdddbacddaaacdbbcababbcacddabcbaadaaadbcdcacaabaddabcdbdaabbcccbcbdccdcaaabcacdcabdddcabccdcdddbcbcdaaddbdddbcbbbbddcbdbadbdcdcaaccaaabdcdcbadcaccaacdaacdbabacddddaabadbcadcdbcaddcbaddadcacabbddbcbdcacdcccbbaacdbcbbabbabddccbdabddbcbcdaccdaabdbaabcbbdcaaabbcbbbbdbcdcddbdbbaadaaadbccaccaadccabdcaddbdbababaaadcbbbaddabdbbbdabcccdbcbcdccdbcbbbdcbdddcacbdcdadcbbbbbbacdadbddcbcccbbaddaadcbdbdddabbccabcaacacdbbdbdaadcdaadabbacbbbcdbcdaaadccdcbbadcbaadadbdabaccbdccddcbcbaabbcbccbcbcbbaadbcdcdcacbacdaddbabbcccbabdbbdabcaddadaccccccaaacaaaccbbdcbdaaaaadddbabbcaaaccbcbcdbcbbcccdadbadaaaaaacdddcacacddaaccabbccddccaccdddbbaadbdcabaaabaabccbccddbcbacbadddbdaddabcbbbbaddcddcbccbccabbbbddbcaabbbbcabcabbaabcdbaccdaacccbadaacaadccddadcaacdaabaabddccbcbdadbcdadaccbddbbcabdbbbabbcbbcdacabddddaabaabcdbddbcdaadbbcaddabdccdddbbdddaabbbdbbbdcccbaccbdbdadbaaacbbabcbbbbbccdabbbaadcabbaddbcacbcabacdacabadabaaababbccabdbadcdcbbdbadacbbbaddadbccadcadcaaaabbadbadaaddccbbdbdcddaccdadbccbbbdccaddadcbdacccdcaacaadbdaaacbabadcdbabaaddbddabdddbbdbabbccdadadabaddcdcbbdabdccdadbbcabbabdcbdbbbacadddcdcbcddcbdaacdbdaddcbaccdaaaadaccabcbdaaabbddabaadbddbbbaabbbcaacadddbdbaabdacabcdcccccacbcdcaaddbbaabbdadcaccaabdbcadacbdddabdbdbbbdbbcdcabcbbdbbacdcbbdccadacbcbbdadddbacdaacababbabacadddbdabdcbbbadabdbccdaaababdababbaadbbcdabcbacccdbdbacdbdcddcccbaaaddacaddabcdccbcabacaabbccbbbabbbccdadcbdabbbcdbcbccbbdbadacaabddcccacddcdbcccbbcabcdaaaacdadcadccdabdcadcddddcdaaabcccdccaaacbdcddadccabcadabaabbbdcdaabadccccbcddacdadccabcbccbadbcbabadcddcbdaddacaaabcaabdccdabcdbdddacdbbaabbcbcddadaacccdcaddbbdbbdcacbcbbcaacabbddbdcaabbabbcbacddabbccabbbcdabbcbcbbdcbccbbccbcaddbdbdcdadcdcddcbbdbbbcdbbdcdaaccdbcbaabbdbdcbcdbbcacaccbdaaadcbccbcbbadccbdacaccdddddcdbccabbccbcaddcbdbdbaaddabcddcdcaabadcabdbccadbbcbdcabdcbccdddacbadbcdcbabddbbdadbbcddccdacbcdcaaaadacdcacbbbadbbacaadbdcdadcbaaaaabdddccbadabccdcddbddbaabbdcbdbbabdccdabadadcacbcacbddabcdbdaadacbbbcddaaabbcbddadcaabcbbccccbcaadababcbbabbddcbcbaccddcbccbdadbbccbdddbcdadbbcabcdbbadcccadbbabbaabdbabbdaddaadacdddddbbabacdacddcdcbdcdbddcaccaddabdaabaddadcccaaadabccdabccbcbbdaaacddbccacbaddcbbcdbaaababdbdaadcaaadacddcbacdadadbdadaddcbabacbadddcdbacbaabcbabdabcccbaacccccdacacacccaddbacaaaacbdccddbddcaabadddcdabccbdcbabaadabadddddabbbcabdadabbbadddcbbadbdccdabdddacbadaccadcabbabdddddbbaaabdccdaaabbabbcdaaaaabdacdacbbcbddcbbccbbabdddcaacacdadaddababdcbdadcacacacadaccdbdcbadccbabaaaddacabcbacababddbbcbaddccdbcbabbdadbddabccdacbbccbdaacbabdabdcaabbbcdcbdaccacdbbcbdaacdcbdbacbdaadaabcdbdbddcdccdacacbdccbdabbbddcccdaabcacdaaaaddbabbdbcacbdbcbcddbbbabbbbbbddcbddddbacdbddaacddbadccbcaaaccdadbccdadcbcbbbaccccbaddbdbadcccbacbdbbbacabdcbdbddaacadaaaaadcacbddcccaadbabaacbbbcdcaccccadddbbdabccccccadcadaaccdbadbdcbaaccbcdccacaabaaabddddbacbbbdddbcdcbdccdadcabaabddbcbcccbbdcdcaabdbdbccdcacaccbddaddcdbbadadbdabaddddbbacdccbdaccadababcdcadccbcdcbdaababcdabbacdadaaadaaacbcccaacaccadcdcadbcaccbcccadddabdacbbdbacdcbbbacdcbabdddaadabcbbcbacddcccadccddbbccbaccbcbadbdbcacbaddaaadaabdbdadababaaabaabacdcbacdbcccbcdbabcbbcbadbababadadbaacbdbcdcadbdcccabdabaabdcdcbbabcbabdbdbcbbadbcbbdbbbbbdddcaccdaaacdaaccdacbbcccddccacbcdcdcddddadaddaadabdbcabadccbdacbaccabacddbcdbbbdcbcbdcaaaabdadcaaadbdbadcdbaabcbaddadcacadbbdadacdcdbdbabbbaddccdddbcdabccbbadacbbccbdbcaadcbcbccdbbdbdbcbcadadcdacdababadbacaaadacbdbddbcbdbccccdcccadabadbdbbadbcdbadbabddbcbdcacacdcdcaadabbcbdacaccbcbcddabcacbabccdadcccaaaadbbbdcbbdabdadadddabbbbbabcdacbcddcbbaabcacdcadabbbabdbdadaadbabbbcccdabccaccbcdbbbaabddddbbcdcbbcadbddacaacdabccdcaaabdabdadccdcaacccdccacdcdacdabbdcdbdcdacbddabdccadcddbbcbcddcdbabdaccbadbbbacadcaadcabcbccbaddccadabcddbccdbbcdbabccadaabadabbaadbdbdbabdcbcbccababcbccccbaadaabacaaadcbbadddccddaababbacbcabbacdbdcbadccabcbddaacdcadcbcbbacbdddcbdbbbcbccbdcbbbddabcbcdcadbcbbbcaaacccccbbbdbccbbdaddcdbccaadcbadbdacccdabdbbcddabaadddddbabaacdbbbdbdabbbcbccddcaabcbbcdacacdaddcabbcbaadbbcbaadbcacbacabbabcbcccbbbcadbdbddaddcbaccddaadcabccccbbabacacbabababbbababcbbbcdcdcbcbbacaaccbcdcaacbbdbdcbadabacddacadbdcdacdaadcdaccaadbdabcbbcbbdcacddccddcbcdbddccadddadddaadacccdbbcccdaadadccadccbdbccbcdcdabaadcbbccacaccadbacabddacddabacbaacdcabcbccaaaadcdcacaacdccaddabcacddacdccdcbbabdaddbacbdcbacdbbcabadcaabaabbdabbaaaacbbadcbbccddbcbcbcbdbdabdabadaddacccccccdacdcbcbbcdccdaadbadbdacaabccbabadaadbbacdddddaabdbcacccacbdabaacbacccbdadbabdddbbadbbddaddcacbbadbcdcdcbdbadaaddccbabacdadaaaccbabdccddbbacacccccadbdabbabdcccbbccddddbaabcdbcdabaadacadcdbbbdbcccbdddcccbcaaddadacbbbababbaadcadcacdcbabbbbbcbddcddbdbbbbddaaccdaddbdcadbbaacdcdcbbdcddaacaadbcbdbdddbcccdaadacabadddadaadbdababaaadbadadbcbababcbbbcadcabdcabdbdcabbccdbbbccbabcadbbdcacccabccaccdaadadcacdadaccadbbdcccbbdbaaacadbaaccdbddcbccdaabadbaacbacdadbdbdddbadcabdccddabddabbbcddcaddadbbbbbbdabcccbcdbcbacadacdcbbbbbdbddadbabbadcdbabdacbdbaaaadaaccaacaabcabcadcadbadaaaccdbdcbbdbbadcdcdcdbadbdbbcbbbbbccbdbbadbbbdcbabbddcdcbdbabbbcaaabbbbadadcabacdcbabbdbddcaaddcccddaacbddccdabddacabddbccdbabadabdcdbbbadbaccdadcbcdaabcddcaddbaddaadbddaacaddcdcbbdbccaccacbdccabdacbaadbaadddcddbadabbdccdddcdbdbdcdbacaddbdbccdddbdbcddaaaaabaabbcbdcabacaccbabdaadddbadaccacddbcbbcabdbbbdcbabbbacabacacbbadddddadacbbaccbcacacaaddacbccbdbacacadcbcdadbbdccddbbacacadccaccbacbaddbcddcdbabcbcadbdbadadbcabbbadaaaddcadabbbacbccdcabcbbabccbcdaacbbdcccbcdddcabbccabaadbdacdbaccdabbccadcaccbdabbccdacdadaabcdaccddcabbbbcccbbdbaadaddbabddaccaabcddbdddaccbaaabcacabdbdabacbcaaaccccbadbbbdcbbccdcdaabbaabcaccbbbdddacbcaabdcaddccbccabaaadbbdbcbddbcbddbabcabadacbcacdadbccacaabdcdbcbacdbdbcdcdbdbcaddbddcaabdaddcbbbbbbdcdddadbdbdbcaaabdbcbdddbbccdcdbcddbcbabccdababbbcddccbcdabdbabaaaaccaddbacdbbdddaccbaaddcbbadaddbbbaadbccaadaccbbadddddbddaaadaaadbccccabdddabbacabaacdcabbdbadadcccbccbddcdacddcbbbcdcddcabbabaadcddbadbaadaddaaddcbdaddbdaccbddbcdbaacaddbdcbabbbcaadbbacbcdddcbacaccdadcaacbadbcbcbbabcabbcbddcbaadbcaaaddcacddbcbcacdbbaccdadcbccbabdbdaadcddbaddbccbdbdababcddbdcbaddccdadcdadbbbbadbbadacbcdacaccabbddccbbbacddcbacacdbacacdbcbdbcbccccddbccdaadcdcdaacaddcadbdccccdbbdddbcdddddcbbdcbadadaacbadbdcababbadbcddcdbabdaaadbabdabcacadaddbbacaaabcadcbbbadbabcdbabccbcdadddcbadbddbbbbbadbacdcdbbadddadbcccaccddbcaabaaddcccdaaadcabcbadcacabbcacddabacbcbdadaaaabbbcdccdaacbddcadddacdcddaccadbccdcdaadbcdbbcadcaddacccbbaddbaabadcbbadbadaccacbccbcdcdaaccabacbcbcabadaccabcacaacbddbcabddabbcdbdbdbbbabbccbdaabbabacaadccdcbcadadcaabbbdadaadcccdccdbaaaaaabdccabbbcdbaaaadcdcddaabdadabcaabaaadcddacabccdaaabdbdccadcbdcbbdacdccddbbbbbcdaadacaddabdbddabaccacccdbbabcdacdabcdccdcbacacadbbddbadbccdbbdbdaadddaacbddccadadbddbcacbacbabacddcdabadacdcabdcdbcdcdbdaaaabddcbdabdddbbbdccabdbabbcdaaaaacbacdbbcdcaaabdadbdbbdccaaabddcaacdaacdddcadbddacabbbadbdcacddadbdcbdaadacadadbbadbdbacdcddddbbacabcddbddabddddbabacababbcdaabccdccadbdcdacccbdcadddbdbbbaaadbbcbcbbabaadbdacdbbaddcbacdcddbcdbbaadcbddbaadbbbaacdcdadcabaaadbccddccabdbcbddbddadabbadbccdbccccdbbbacbdbadabbbdcacbbadcacacdacdbbddcabbcbaddaadcbbccaddcdccacdcabcccacaaadddabaaadaccdaddccbadaaabaadccccdcbdaaababcccdcdbacdccbdbdccddbadcbabbabbadccabdcdacadddaddbabaacbbddacbbaacacbcbaadcbcbddbdabdcbaccaaddbcabcccacdbcdbdaabaacddddcdcbacdcccdacbccacacddabcacbdcbcacababcdaddcacadacaabcbbdbacdcbdbadadcabcdcccbbbbdcddddddddcabaaaacabcccbcbacbdabbbaacbbbadddccbcadcaacadbcbbcbcbacddbaacbdbabbadbcbacbadbbcdaabdcaddaadddbbbccaabddcdacdbacadbbacbdaccdbdddacbabacbcdbddcddabddbdcadabcadabcaacbbbdbadddbdabadbadbddaaacaddacaddddadbbdabacbbdcabddbcabdcacdacaabaacdcdbcdaadadbcabcaddbbdbddccdacbdbbacdaabbbdbcdadcbaabdbabdcabbdaaadabdcddaccbaacaabaaccccdbbcadcadcccddaccbabdadcabcddcddbdacbbbcdcbaaddbbddaccddcbcabbccdcababacdaddbbbbacbcbdaabdaabaabbcabcbdabacacbcddbadbaabaaaabbcbcadddccbaddadbaabccdddcbbcaaacdbbaacaaddcaadbcdbbbaaabdbcddaadbcaddbaaabdcabcdacbddbbcaabadcbbbcabcdabbdbcdadbccbccbaacbdccdcbcdddacddbdcadbbdabbccdbccabaabbbccaadccbdbbbbbacbabbaacccdccacadabbdcbaaacadddccbabdabbdddbccbbdcaaabbbbdcdbdbabbabbdabaadadcaddccbbccddaacabcaccdcacddbcbdadcadbcdaccdadcbaddbdadaabbbaaabdbcaaaacbcaddbbcbbcbbdbaddabacccbacdcaddcdbacdcabbdcdcabcabbddbbadcbcbbdbbcdccdddccccacbdcdbbbbccbccddcaddbcacddddbcaadbbcadbdbabbacdcdbdaaaccadcadbabaababbbadacbadddacabbcccbdbdddadbdbacccbdbdabdbaabdbdbddcdcdadbbaabbcacddbaacdbcacbddcacabbddbdcaacbcbbbbcbabcadbbabddbbbacdbcccbcbdadacbadabbdcbdacadaaadccddccabbbadadddcbdcbabaabbacbddddbaaddddbabcbababcccdcacababbaabaddccacdcadddabbcadcbabcccacbabccbccbcccdccdbaadaabbadcbcccdcbdaabacdcdcbcdbcabbacbbdbcdaaacbdabbdcdaadcaddaddbdbbddaadbdacdbcbbbacaaabacacccbbdddacadbbbbdadaaddcbaaabbdddaabacbccccbccdbdcdbaabdabdbbdadbabcabcddaccbbbdadddddbcacccbdbddcbaabcbdcaacabacbcddccbdddccbbabdcccdbcdddcbdbacdaccdcccabacaaaddababccacdcbcaadbbaacbdabccababdbcccdbccaadacbaadcbbdbabbbdcdcdbccbadcacbbddacdbbcdacacccdbdccadcabdcadbdbaacdcdbccaaaddcababdadaabcbadcadcbccabccdbbcdabdabbabccabacccddbabbcaadbcacadaaaacadcdcdbbbcdccbcddbbcacbaccdcabbdbbabbcbbbabcddccdbcacbcaaccdabbcabbcdcaccaccaddbbaaadaadcbcbdddcdbadddcdaaadbacdbcadbbdcbbdcbdcdcdddcbddaababaddaadaacdacdaabccadbdbdbbddbddcacdbdaabbcabddadcaccdaadddaccccbcaccddcdddccccbcadbcbbcbabcbadcbcdcbadcbbccbdacababaacccdacdddaabadcdbddbcdbbdcabcacaaabcaabbbdcdadbcdabadcbabcbbdacccaaabdcddbaadaadadcdcbbdbdbbbabcccacbdcdaabababbccdadccbdacccbdabbaaddbbbcbdddabbbddcccababddbcdacccdbbdadaacaaaadbacabcabcadcbadcccdccbddcbdbdbabbbddbbdbbabcacdccbadbbbdacbaaadbcaaaccdcbccddbababccbddadcbcddcaadcacbcbdbbacbddbcadcbdbdccbdccbcddbbaddbbacbbdddaacccdabdababdcdbddbcaddbbccdbddbdbabcbadadddbcbbddaacabbdcdcdbbcccddcdcaadaabdbbcdabddbbccacbbcaabaccbddccadbaddcbbbacbadbcdddcccadcddacabcbcccbccdcbdbcbadbabcbaaabbdadbbcacbadcccbddacdadcdbdbcdcccbbbbadcbbcacadddccdbacbbacdaabbbbbdddcdacdcbcaabcbddcbdcbddcbcbabacccdaabddaccbcccdcbbdbbbdcacbbdacdaabddbcdabacabbcdaaaacccaadabbddcdbaaccddabdbaadaaccdbcdacccbcdcbcbabbdbcbccaabaccbdcadccccdbbddcbbaadcdaadbcddbbabbccbacddbbddaaabddbcdcbbaababbbacacabdabbbaccbddacbdcacaabbaaadccdddaaababbdcbcbaddddbbdcabcdbccbcaadcaadaacbcdddaabbdaaddddbcadabcabdbbdaddcdbddbdddabccacddbdadcbbcbaddbbdccbadbcadcbaacaabccbabcadbbddbcaacddacbbccbdacadbadddabacbccdadcccdccadadddbbabddabdddbcccabbacdbcbabbaabbccbbadbccbcbbaacaaadddaccdddabbadccdddccacbcdadcaadbaaabbcdbbdadabdcaccbdcdbcaacccbdacddbdabcdbbbaabcdbcdadacddbaaabdadcbaaaadababcacccdabcdddcdccccaaadabdccccbdbcdcaadcaaaaadcdbbbdcbabaccbcccddcabbcaabbaddacddcdcbcbaaaadacabbacdcccdccbbabbcddbcbadddaabbdcdbabbacbcbddbcbdccbbcbaddaadacaaacaadbacaacacbabaacacdbacabccdaabbbaddbdadaaabbcbdaaccbbadacacddbbdcbbdbcadababadbadcdabcbaddcbacbdbcaabacaaaabcabdbcbddbcbcbbcddbadaaddbabadbccbaabadaaadbaddaabbcbaacdcdbdbdbbccaacdadacaaccacaabbadcacbacadcbdcbbaacccbccadcacaddadaaaadccabacaacdbaabcaccababcddcbcababcdadaabdbadbdbddcdaaccaadddcadbdcdabababdddaccbcbbacbdbdcbabcbcdbaabbbddcabbbacacbcbdbdcdcbbabdddcdadabbddcadacbabdddcbccbbccdcbbddadccddcbcabaadccbadbdcadbcadcbcabdbccdbcaabdacddbaaaaadbbccdcabccabdcdcbacbacccdbccbbcbddccbdbaaccabdddbcaccabccacabadabababbcaabbaccbaabcbaccabbbbbdbbcddbaabacadbaddcadbadacdabbdabddacbbcccdadcdabcbcabababcbbdbbbdbadbcbaccddbdaacadbbacdcacbdadacaddbcbdcbbbdcacccbdaddacabbddcabcabbaadcbdcadcbabcbbaacccddbadbccdaaccddcaccdbdbdcccbbbbbbbdccacadbdadcbacdbdbdcacbccdbbdabbadddadcdabacbddcadaabcabbcccbabdbaaadaadaadcbdacbcddccacbdcddddcabacbdacabdbccccdadaddccacaabaccdbcbaddabaabccbcdabccadcccbbbcdbdddaabdacabcbddcbbdbaccccadbaccddcbaacdcbadbcbbcdcadadacdbadacacadadbcadabdabcacaaddadbabcaccbadddaadcadacadabaaadcdcdadddbdaabcccdaabadcbcacadadddadbbababaaddcdbbcccbdccdcaacadabbdabbabadaacbacaaababbcdaaccccbbcbababcbacdaccbdbbccddcbabaccddadddccccaacacabcbccbcadbbccbaacbccccbbacdbbccdbcabcdbacacdbdadcccacaccabdabadddabbcbcdacacbacabdcbccaabdcddaaadbbdcdbadacadcaacaabcdcacbdaddcadaabbddabcaaddbcabcdddbbdcbcdcccbdbabcccbadacadbaaabcccbadbcbdbdabddaacaaaaabdbbdcddbabaaadadcabdbcdbcacdabccdcacaadcdaacabdbddcacbdacbdbbadabcccaaddaccadcadacabdbcdbcababbdcacaddddccdbaadcaabcccbacabdbccbadaaacbcaabbbcdbcabdccadbbcbabaabbacbbabbcbdcaacdcdbbccdbdbcdabbbadccadcbddddbcacbabaabaaaddadcadadbcbabddccdcadbcbccacaacbdddcadaabcaadcbcdcdcabbdacbbbabcacbdabacdaacaaccaadbcacbdbabcbcacccabdcbaaccdcccdcbaabbdcacaababaadcdcbbcbcccacdabddacacacacabcacdcacdbabbadbccadadcbadabcbbdbdbacadcbccaaaabbcacdaabccbdccabdadcccacbbcbbacdadcccacaaaabccccabcacbbddcababcbbaacacaabddcbccbddaccbdccbadaaccbacaacdcabdcbcdabbcdacadbcdbaadaacdadaabdaacacdbcaccbddbdadaaabdabacdaaadcbacaacababbbacbccbacacdbbcbdcbadbdbbadccdbcdbabcbcccdaadbdbdcddcaacadbacabcdaabcdccbaacabdaddadaaddcadaddcccdcabdbcbcddbbccacdabbadbcaccdbababcaadacbbbbadddacdbdbcaddadcbddcbbdbcdbabcbabbdabdababaababbaadaccbabaccbbbcbbdccbccaabcabacdbacabdacabbdbcdbacbdbddaccabbcacccbdbdcacabdadbcaabddaddbccbcccababdccbbbdddbcbddadddaadbcddbcbcbdacdaadcbbbccdbddaabdbbcdccdabbdacaadcccbcdacdbdadbddccbadbcdabadcbacccccbcbdbabbcdcadcbdcccccdaadadabacadacabaccdbacdcbbaabdabccbccbddadbbacaadcbbccababdabacdcccccbaaccbcbbaaabbcabcdabdbadadcbdcddcbabcdcccddabaddadbdcbaadcdabdbadddcadaaaccddbbbbbbbacdacabdaabcaddbadaacaaaddbacabbbdabdbabcabbdccababcddabadbdddcbabddacdbbbaddcdaaabaacccbcabcadcdabdcbcadadcabdbadbcadbaadaadbacaadcabcbcbaccbdabbdccccdbcaacababbdbcabbdbdcabcddcbcacdbccacccdcdabccbabccbbbacdddbccabbbdadbcacddcdcdcbadadbacabbcbdccbbcadacbbcccbbcbdddbaaabbbbbdaccabdcddbbdadabbcdcddcadddaccbbaddcdadcdaccacccddcbdababdabbdbbdaaddccadabbdbdcdaabbdcdccbacbadcccbbcbdaaaddcbcbbcabcdbcacddbcdddcbdbdcdcaccdbdacdcbbadacccccdcacabcccbcccaccaddaabbddbabccddaddaddbdacabdbadacccabdbcaadcadccddbadcbdcbbbcdddabadbaddbdacddadccdadcbdaccddccacddbdbbbacaaaaccdccadcbdbbdabadcabbcdccaacacadadacdcaaadbaacaccdabbbddaaabbbcacabdcaabcaabcdbaddbaddbaadcccadbdcdcdbbdddbdcbdacdbbabaaacdccdcbbabcbcaabaaabbddbcbbcacccaaacabddbadddccaacdcbbdcbcdabbcbbccbcbdadacccdadbadaacdaccdaddabbcdddcaacdacddaabddbacdabadabababcdaabbcbcaccddadccadcaacdbdaccdbacbddbabbccddbaacadcdddbdbbdacacbaabadbdccadbddbabaaacbabbadadcaaacdbdcadbdaddbaddbacadadadaccddaadbdbdbadbdddadddaabbacbcdbbdabcdbaccbcadbcbacbbccccdabdbccbbabcbbcdadbdbbcbdaacdcacbdcdcbcbbbaaddabbbabbdcbcabdbdbabccccccbdcccaccddbdadaabbadccddadacbcbadacdbadbdbaccababddadaacaddacbadcdbaccbbbbabcaacdbcdaabdacbdaabcacacccdbddcbdbabbddbbdadcdcabcddcddacacaacbaccaddbcbbccdcbabadcdbdcbdadabcacacddcbddbcbaaccaaabdccddccbdabdadcbccbabbbccbaadbddbcadabccaadbadbaadadbcaaacacaadcdcdccbdcdaadabaaabbabaabbcdcbbdadbdbbcdccbdcabcaaccdabbcddababacdcacdaddcdcaacdbddcdaaaddabddcaddbcccadcccbdaacababccbbcdbabccbbacccbbbadcbbbabadadcabbccdadaaadadbabcdcdccbbaaadadbaccbcbcdcccbddcaccdcaccaaaadcddadabcacbadbccdabddbdcdccacacdcbabbbdbbdaaaadaccdcbbccbdbadcdbbbbdcaabbbadabaccdabbbbbbaaddbabcdcdbacbadadadbaabdaaccdcbccadabbacaccabbccbaadccdacaaadcacaaddbbabcdabcccacccacbdbcccbddbadddbdcdbdcbabdcaacdcbdbcdcbcadbacacbccadaddcdbcbbacaddbabcaaaadddabbdadbbabacdcaacbcdbcbcdcdabcacbdccaddcbabbccadabdbdaddbcdbbcadccbdbbddadbdbcddabcaadacaadbbacabddaaaccacdcdacbadcbbbaaacbccbcbbddcbadababcbbcbcccddbccbbbdcdcbaccdacdddadbbdbbacadcbaccbcabddbbbdababdabbcbaccabacacdccbbabbbbdadacdcbacbbdddbbbbaaccddadadbaaaacbbadaabaabddddbaddaadaaadbcacddaccacbcdbdaaabbbdddcdcdcbbabdbdcdcaddbdaddbbbdcddcaccbccaadaadbdcabdbcbbbdddbcbcdcccaadacaccbbaccaadccccbdacdbdbbabcddaaddbaccbbdbdabdabaabadaddbacbcddbababcbccaadacbddccddcbbbcbbbabacbccdddbabddddbdbbdacaabcbbaddcccbbdbdcdbbbcabacddaddcabbcadaacaaadaabcabbbcbaccdabadaacdbdcdcbaadcadbbbdcadddddabdbdddbbcabcaddcaaaddcbbadbcccbbcbbbbbbcdddcdcbbdabcadabdcbbcdbaccbccdddadcdadacaabbcdabadbdbdcccbbcdccdccdcdacccbdaabbddababbabadaacdadcacccacabdabcacdacdacadbadaccbacacbbdcdabdaaddaabbbccddaaaccbbddcbbaadacadbbdbaabadacbdacbcbaabacbdabddcabacbacabdddddadcdcacdbbbbbbdacbdcbcdabcbddcbcbccaacdccaddacddddaaaaabccabcdababbaddbcabbdbcbcabccdddaaaccaabccadcbcdbacbabdccacaaccbacdcbbbddaaadccaacddcddcaacbddadbdaadcdaabbdcdddcabacdcdacdcaaaddbacbdcdcabbbbbbaddcdabadcbbcdbacccdbbddababdcadcccadcabcadadddddadbbbabbbacbcccddcdbbdaaacbaadbbaacaabdcadaaacddcbaaadccbdddcbadcdcabacacbabddccacdcadccadadddddcdcbdabccacaaacabbdcabacabbbcbccdccdcacacaabcdaccadbdcdbcabdcadaaabacdabbbaccddacbbddaddbbcdddaaaccaccbaabaccdcdbadcaabbacacbabdcadddbbdbaaadccddbbcbdabcdbccdccdabcdcdabcddcdcaaddaccbacdaaccadccbbcddacccbcadcacddcbabccbcadcbbadcabbccdaadbddcbdaddaaddabbcabcdcdbddaddcdadcabbbaaddabbcdcbcbacadabddbbccddbbccaabcabdddadcdbcbabccdcadabbcbdabdcdcbcbaaacadddcbcbbcdbdaacbdcddbbdbccbcdadbbbcdacdcabacdccdccdcccabcbccaadbbababcddbbccabaacdcddcacdacdbaadbddcbccdbaacbdccbdabaccbcbabcdbbdbdadcccbdabbabbdabdbbdccdddcabbcabaabddadacadacdbdcdabccdcbcbdbadcaccacdcddbadadccbacbddcdbabddbdbbbddcddaabdbcaacdbcbcacbadadddacddcadabcdcccbabbdadcbddaddbcaccabbdadcbbabdcbcabcbcabcbbadaadddaacccddcbbbcdcadaddbacaabbbbdbdadacccdbabccbcacdaaacacbcdabcdadddaddcdcdccdbcabbcbdacaadbdbdbbbdbdacbdabcbcbccccbcbcddaaccbcdadcbddcacbbbbabcddcbcaacccddbaaacabcdcddddcccadbbdadbcdccbabdccbdddaccaaaadcbdcaabbcdbacdbdaacadbdcccbaacccbdcddadbcddbdbdbbdcabbbdabcadaadadadcaccadacdbcabdbbdbabadaaaababccddcbaddbadbadaabacdbadaccbbbdcabadaaaaacbdabadbaaadbcaddddbdacccbdacabdadbadbaacacddbddacadabddaabbdbadbdcaddbacdcbcaacdaaddacabcadaabacdccddabbcdcaaacdababbbcbbbdbadbadaddbdddcadbccbdaccaaacdabbdbbbbddbabddaabccbadbddbaadcdbabddaccdcdaccdcbccaadcbacbbdbccbdbcdadadbddbdbddbcabbbcdbcbacacdcdcbabaabccbbcadadaddbabcaaacadbcbadccccdabaacacadadbdadbaddccabcacddcdaabaaacbbbadbddbdbccababdbabcbbdbcbdadccbcaacadccbccdaadacccdcbdbccddabaccbabacbcaccdddabcbcadbadadbadcaaaaccdbbabcdbacabcdddadbbbbabdaabbadadccdbcdbdadcabaabdbcbbcbaccdccbddbbdbbabddbddbcdbbabbdacddcdadaccadbadcccdcadaacdcadbdcddbccbacbbaabdcbabdcddcccaaabaadcccbababccdbcdcbcaaacacddbdadcaaaccabaadabcbdcddabcaaaccdddcdbbaddacddabbdddcccddcaadbdbdccdbadcbbadbdcdbbdbaabcaacdccbdaaabaccddbccaadacdabdaacdaabaacaaacbbcadccdcbababbcbccdbcbdbadbabbaaaadcacbcabdddccdbbdbacaccabdabbaacbacacacacddccacdcbbddcdadabbccddddabaddcadcaccbaccabdacbadccddaabacbdccdaaaccbcbccccaddddabadacddcbcbbcdabcadadbcbacdddbbababaabaacdcdbddcabdcbdbdcabadbaadbadabcbaabcbddddcdbbadaccadccbbdabcdabccdbabcacdabacaccacccbbccdaacccbcdaaacabcdaabccddcdaaacacbdcbbdcddbbbadbbdbcdadbccdbcbbbbbbbbcddbbdbabacacacdaacbcbbbadcaacdacbbacbcaabacdbdcdcbbcbdcdbcdbdcbbacbcccbcacccdbccbcbacabbdbdabcaadbdabcabbacbdddbbcbaadbadcbdcaccbdacabcbadcaaaddaddbdaabadacccbcbadaacdacbdcdddcbcaddcaabdabaabccdccaccdbbadacbabbbdcbbcddababacabbdcccbadabdbabbbaadcccabdcbdbddbcabdaddddcdacddbcadabddacbadbabccacdbadbdcbaabddccdcaddcdcbdbbcbbbaddbdcbdcaccabdcbbccbabaababbcbcaaccbbcccbadcadcadbbdaaccdaacbacccbaacdbcbabbaddbdbdaaccdddcccbaaadccdcdacdccbdbdbcdabacccdacddaaabdaacaaabbabdbcdaabadbabdaabccadbaccdbdaadacadbddbbaabcdcabdddacddddacabacaadbcaabdcadcaacdbdbaaaabacdcadbbdadbdcbbcdddddababaaadacadacbdabdcadaabbcbddacccccddbdaddacabcaaabbddbacbdbdcdccbdabadaaadcacabdaddbadbabacdadddcddbabdcdcbabacbcccadcadcadddbdddabcadbcdbddbcadcbdddddcdabcddaaaaaadcacabbbcddcbacbaabccbacbcbaacacbbcbaaaddcdcbcacdcdcacdabccbbccacbcabcbbbabbbaaddabdabdcdbbccbdccbddadaacbbcdddcdcadcbdbabdbaaaabaadcdadadadaabbaadbbdbdacdcabbbcddccbbacadddacabddbdbbdbcdaacdddddbcdcdadabbdbcaccbccaadabdddbdcccbccacabddabdbcadadcbccabbbdaacbaaabacbcccdddbaddbdcdaaaccdbbcbdadabdbaacabcbdcaddbacbcdbcbcacaabcbcdddcdbadbdaddbdccdcbbdabbaadcdacddcbdaabddddacaddcbcccaddbbbacadccbbacbdddcddcbbbcacabcddbcbdaaaddadddcaccdbacaabccddcdccaddbddaadbadaabacdbcdcabaabadbdbabbdadcddcbadcabccdcdbaacccdddabbcbbacbcdcbabaabcbdadabcbdabdbdcdddabdbdbdccaccadbadbabddcdaabdbccdddaddabadccacaaccbbddcdacdbcbadddccababdcdcadbccabaacdabcdabdcbbdadccdbacbdadcbacadaabcbdbadbddbcabbcabcdccbcacdbcddccddccbadddcbbadbbbaacbcbaaccababbdddadaaadabbabdbdcbdcdbbcabacccbbdaabcbbcacacdbaacdacaadbcdcaaaadabbbaccaaabdabacccbaaaadbabccbccbbbabaacbdbaacaadabdcbacabbbcccabbbbadccaccbdaadacbacdaabcbdaacccaccaaddadabccdabcadaadacbbcdadaacdbabcbcacabacaaadcdcaddaaccccacacdacddadabcdccdcccdadcabadacaabacdddbdbcdaccccbabdbcbdbaaaadaadbdbcdcccccdaaddccdbbccbabbaaaadbbcdbbcbcbdcbdbcaacdbbbbadcabbdaaccbadccdacbbdcbaacdcbadcaabbbdabdcbaccbbcdbaccccbdcddbcbdaddbdacadcdabbdccdccadabcaddbcabcbbbddccbddabadcbbcdacadaaddabadcddcdadcbcdacdacdccdacbaddcaaacabcacacddcabbbcdabbaadbcbbdcabcaccbadcbcbbabcadcdbbababcddacbbcbacdcdcddccabcdbdcbabdcdcbbbbbbddabdbcccbddadabadbbdaabadadcdadcddbdccbcccdaadbccdcaaccdbdccdddbddbcddaadbdcbadbcbddbbdaacbbbdadbbaaabbdbdcbcddacadbdadbcbbbdabbdabcdbbadadabacbaaabcaadbbdcadcbacdbaacbadccdbbbabdabccbbaaabaacabddacacbbbacbbdadcadcdbcbdccaddcddbcaaabbddacbaadbdbbadbcbcdddbbdcdcaadbaadaabcdbddbcaaacdacbadabacacbdbcbadabbbbdadddcdcccbbaabbaddddabadddaaddbaacaccadbbcaccdddcbbcabaaccbbcdbcbcbaaddcbddaaaddcddaadaddcaacccadadbdcddcaabadabcbbcbdbdbadadbacadddbcaabcbaacccadcddaacbaabcabccbcbaddaabaddddbacadbcbabddccdaaaccdaccadcaabbcddbdbcdbcbdcdcbaddaddccdaddaacccdabaabdcadbdddbbddbacbdbbcddbbcdbbabccadadcddccdbbabbcabacbacaabbcbacddbbacddcacbadacabdbdbdaddbbbadaabbabddbaccdbabcddbacddbbccdcacdacbbacadddcacdbccbcdabcbbcadcccbaadbadbbcadcaaaaaaccdacdcdaacddcbaccaadaaccddabdbacbaabcadbbbbbaadbaabccbbcaddaaabdcdacacadacbbdbdddbccdcabddbcdccadaabbbbdbbacbbcaabcbcacdadccdcabaadacbbbdcaccadadadbbdccdbdaddbcccabaadacbaadcaabbaaaddcdabdaddbaadacdacccabdcdcccbccddacaacadcdccbbbbdbdbcbdaccacccbbdcabddbabccccadbbbdabbabaadbdadcdacbddcdacacbddcaadbcdcaaabcdbacdabcdbcccbccccdcbbaccacbcbadacacdcddabdcdabddccaaadbdddcabcacababbbdddbcdabbcbdccacadcddccacbacccdbabbadbdaadabbaabccccdabacbcbacadcdbbbdccdaddcaabbdadccaadccbdcdcabdddbddcbcadddcdcdbdcbddaacbcdcdbaabcacdbbdacdacabbddcabadcdaaaadbbbbababadaddabcabdcbbbcabcddbbdbaccabccbcdbcbcacadcddbdddbaabaaaccdbbacdbcccbbccbddbbabdacacdbaadcabadabadbbbcdcbdddcadcadadbbbcdbabddabccaadabbbacabdacbddbcbaccabaadbdccccbccabcbcaddbcaabbbcaacaacdacadbcacdbccacdcbdcddbaaadaccacadbaddabcdcbddadabcadcaabccbabcbaccaaccaabbaadadbacbddccdaccaccbadcbbcbcbdaadaacabadcddccbacaccaccdbacdaddbcdccbdbdabaaadacbcbcdbcabbcbcadccdcaaccbabccbcadcdbadcabbdddcbccbbaccbacccbabdbdaaaaccadbcddddcacdcacdadbbcbdcacaacdcddddcbcdacabdaadababbdbcbcaddcdabdcaccdacaadaacdddaaaddbdcddbacbddbbbbcabcacbccabaaababbbcaabaadacdaddcdbacbbcbdaaaaacbdbaccaccabbcbdcaacdbbbcdbdcbdcacdbdcacaadcbccbbbbccacdddccdccaccdacbccbdbdcccadbbbbcadbbbccbdadbacbcddcbabdadbacbabccaacbbadddcbacdccaddbacbdbbbdbcbabaaccdcbbacddaacaabdcaddbdabdaaccccaadcacdcddccabcdacdbadbdcbaadcaaaddcdbaccbbdddcdabcddacbcaabaccddbaabbcdbddcaadacbdaacdcaaccdacddcadcdbbbcbcdabbcadbddcbdadbaddcdaaccabbbdcaadcacdbbdddaddddbaacddbddabcacababccbaacbaddcbabbacaddbccbccaaddabdabdcdbdbaccbcbabbbdacccadcadacbcbdcbcdaaaabcbdcaadaabdddcabbcdbacbbbbabdbaadadbaccabddcbdccdbadcbbbcadbdbdaabddaacddabdcadcdcbcdddadbbbabbcdcdadcddddbdcdacdbcdbbcccbaaabcdccbdccdcddcdaaacdbbdabcdaacdcbbdbcdaababbddbadcdbdbddcddbabaaadbcaaacbbccaccabbbdabbaadacbadccccddbdcacccccbbdbdccdbabcdaaacccddaabacaaccbacdbbbdbdccbbcbddbcbccacadbcdbccbbacdcacbcabdcdcccbcacacacbbcccbcdabbdcccdcbbdbdcbddcbcaddccaaaabcdbcccddcdcacccbabcaddddacadccdbccbcadabacbaccacbbbdacdbbdadbcdcbaabccddacaaabccdcabaadadbabcabbccbcadadacbcacdadcacdbbadcbdadccbabcccdcdaacaacaacabcbabdcdbaadacccdbbdadadcbabdbcaaadbbcabcdcaddddbdbbcdbcaaccdbcccdadbccacddbdcdcccabbaabbaaccbdcbdcdddbdccdbddbdabdbcbdaddbcbbbdbcddabddcaadbdaaacdcdadbacbdbbddacaddbbccbbbbbaadcdaabbaacdadcdddaddadbbbaacbbacdcacacdbddbdbbcaccbbbbaadbbccaccaccbbcbaaabbacacdadcdccacdcbdadbcadabcdbbdacabdbcdbcaccaccbcaaddcbbadbcddbaabdbacbbbbbcddbbaabdabccbbcbabdcbbacbbbbabadddccacabddacdcadbbdccbddbdcccccaccadabacaaddbbacbcacddbacaaabddaacacbcabbccccbdbcdbdbbaaabbbbbaddbcaadacdccadbdddcdcccbcadccadbaaabbabdbbabadbcaaadbaaccbabdaaacaccbcabaaddbccadbcdabccbaadbccaccdbbcbcaddababaacaabccddadacbdcccdddbcdabaaabcbadaaaacbdcdcbcbdbbaddccdaaacdbabddbdbdaacccacccdaababdabccacdccabaccaddbbcdababacdaadbcbadbbcccbaddbabbaaadddccaadaabdcbbadacbadbacdcccddcabdcaabbacbddbacdaddadcaabadcbccdaaccacdbccccbccddaccaabdabaddcddbbcbccddbacbcaacaacbcabaddcccbcaadcabbcbcdaddccddacbcbbdaddcccdddbaddaddbddabdccacadbbacddabcbaabbdaadadacccaabcacabbcbaccaccadbcaabbaabbbcbaabaccbddabdcbbcaabcbccacadbcddcabcbadcccbbccbcadbccadcabacbadcacaaccdadcbccccbcaabbbbdcbbcacbbbaadddaddacdabdddacdbacdcbaaaddacdddadacbbcaadddcccabacbbacaddaaabcddcbbacadabccaaccdddbcacdbccbbdbaaabdcaddcadadabbbadcbdaaabcabdacccbdbdbabddddaccccdabdddabaddcadacdbcadbbabacccddddcaabdcadcddccbaccdccaacccdbdccbbabbbcddcdabbdcddcaaadaaccdccbdabdaaddacbccadddaabdccccaabccaabadcadabbdcdabadcadbcaabbddadddbccddbbcddabbcadcdcdcbaacbabcbbadacddbcdacddabdddbbdcccaaacbdcdbadabcddbddaaadacbdadcacdccddadbcdbbbcaaddbcdbcccccabddabacddaaccdcbaaacccdacaadcbacdcbccbcccaacbabdabcdaaadaaacbadbdbbcbabcccdacdbbbcdabbbccbabbaaaacabbcdcbcbdbcdcdabdcacaabaccbdaaacdabacaddcdabbbacabccbbcddaacacaacbacccbbddbdcdadcacddbdbbdddbadbbcadbbbbbcaaacbdbabbaddbdbbdabcacdbbddddbddadcbdcadacdaddbaadbccddaddbccbcaadadbbcbcadbacccccdbcacdbdcbddcdcdacdbdbacaccabddababdabababacccbacdddddcadacbaaabcadaddcbbdaacbcadbcdcbadbcdacdbbacabdcccdcddbccccbdbcbacaabacdaddddaaddabbcdcdcddbacbddccdbcccbabcdddaaabdccbbcbaacdabdaaccabbddbccdbbddccbbcaccaaacacdabdbcccbdadbaddacbbbcacdcdcacdcbaddcabbbaaaadaddbadcaadbcdacaabcdccbcaaaadcabddccdccddcadbbcbbabddcbbdbcdbdccbcaabbdacdbdbbcdbcaccacbccaadadbadbbacdabbbcaccbcdcbadaabdbabcbdbddcdabbddabcddcbdbbbcadabcbbadbbabbddcddbcddccbcaabadacabccccdbcdbabbaadcbdcddcbdbddcbbdddaabcdcbcbbbdaccdccabdcaccacbcbacdcccbbdaadbcabbaccbacbbcdbdbdccadaccccbabaddcbddabccbacdadccaccccabbcdcbaddadcadcdccacacbbcbdaaccaaadacadccbbcbbdaacaadadbaccbddccccabcacabdababcdcdbdbacbcabdbbbabbbabcdcadacadabdccdddadbcababdcddccccacbacadabbbbcdbbddbbbbdddbdbdacaadbcdcacaadacdaacadacbacdbbdcacacdbdacaddbaccdccccccbcbacdcddacbbcadadaacdbbdacadcdbbbdbdccbadbabacbbaabaaabdccaccabaacabaadcbcbdbcaddabadcbcbdcbbbcabbabdbaabbcaadbdabbabddbcbbbcddaaadbadcdaadccbdcbdbdbdcdccacbbcaccadbdbcbbadbdaaddcbdbbcaccaadabbbdccbbbdddaabdcadbabbcdabddcdddbabbbcabadcbaabbddbacbdbcadacaaadabddccdccbddabaacaabdbbcbaaadddcddddcdbcabadccdbcabccbdabcbbabaaccccadbcdddddbbbaabbddcdacccdbbbdddcacaabaadbcbddbbdaadbbccdbcddbbbcbdddbbdbabdababbcbbddbcacaadcdddbdbccdaddcdacaacccbccbbaddabdccdcaddbdcbbdcaabcaacbddbaadcdabacacbacaadccdccdcaadbbddddcbddcabdaaacadcaccdaddddddccbacacbbabdbabccdddcbccaddcddbcdbbdccacaadabdacbdbbbcaddaababcbcccccdddaaaadcadaabdacbcbadccadddcabacbcbdcccacdbbbbaabbcbbdbcaabcabbbdbaabadbacdabccacdbddbabdbdbccbdcdcacdabbcabbbdcddbbbdbdccaadaaadabcbccccbdaacdcbaadcdccbdddbcdcbccbcdcbcadcccadccaadabdcaacdbcbdbbbbaacacdadadaaddbdcadaadbbdabacacbbcaaacbbcaddcdaabaddbbcbbdcdcabbaabccdbcdcdbaadccdadcacdacdcbbcaddcabccdcbcbbaccddaccadcaccdccddacbcbbcdacaaadabaadddabbbbcbcbcadccaacbbabdaacbaccaabdacaacccdcdaadcababacbabdacadbaadadbbcadcbcbaadcaababdbbaaccbaccdaababadcadabddbdadddccdacddcdccaadbaacbbcdbbabbabadbdacbdcaddbaddcbcdcddabaadcdadbcddaaadddbbaaaabddbbcdcbdccabadcadcdaccabbdbcbcdabbbcccdbbbaccaacaaddccabadacacaaadbbabaddcaccadaacaabaabbbcdabccdbdbbccccdccccbcbcacababdacaaddbbaadadaddcadbabbbcbcbdcbccbdbabbcbddacbabdaddabadabcabdccdacaaddacbaaabccbcacbaacabdddddcdbbccbcdbcccadbcadbaadbcdcdbcbdabdabdabccbbbaabcccadbabbcdccacbbacadbcddadccbdbadcddddbdbdadccbcabdbddacadbdbcddaaaabcbdbcadbccbbdaadaabbccaacdbdacdababacbddcbaccacabdcaacdbbbcdcbbcbdbcabdadddbadcabcbcbbaadbcacabbdddbbabccbcbbdaabdacdcadddcdbbddccbadddaacabdcadaddbcbccacbababbbbcadbcddaccbdacbcaabdaddbabcadabccbbadbddbbadbdccadcddabcdbdaddbbaabdabbaddccabbabbcaacdaddadabddbbbcabbbbcabddddcdadcbdcdaccaabdcaaacdaaaccccddcccaccaaccbdbdcbbdbdcdababadaccccbdbbaddcbbaabbaddbadaddbddaadddadbdccdacdaacbcdccbbdabccbdabacaabbdbdccaabadacabbabcaacddbbbcbdcddcbcaccccbdadbdcbacadbddcdabacdcbddccbcacccbadcbdaacbaaccacccdaadcdccadbbcbcddbdabaadbbadbbcdddccabaddcbbbbadbbcaacdaddabbdabcdbcbccabddbddddbdbcaaadcbbcbccacaccddcdaaccaaacddcacabbcccaaacddccacabcbdabbaabcdbabacdccabcbabdacadcdaabbcaddabaacbadcccbdbcaccdadbdddaacbbcacacdcbccadcabcbdcabccacbbcbcadbdcbdcdbddbdbacbabcccdaaacbdacaaaabbcbdddddcdacddbcdccbdccbcbadaaabdbcddcbcbccccaabdcadcbcbacaabbbcaccababbcddcabddaaddacacabcdbbccbabdaacacdddbbddabcabbcddaaccadbbbaadcbccbabcdababdbacaabcbcaacbbcbbbaadaddadababbbaabccddccbababcdcdabdbcdccadaccbcccbcccddbdccadbbcdbbabbccbbbbccdcbbcdcccbbbdcbcaadabdbbcdadbcdaabbabcdacdaaabbaaaadacaadadbccdcdabadcdcbbdbadbcacdabcdbbaabbcabacbaaaddbccaaabbdadcacaacdadaabacccbcdcbaadcaabbacddaddcaacdcdabdbabcdbbcccabddbbbadcadabcddbacdcdbbcbcabbbbdabdcbdbccbdabdadadadbacdabaccaaadbdabbdacdbbdcaccdcabbcabdaacadcaaadadabdbadbadcdaccbabdbabddbbabbcbacadccdacdbdaddcbabbdaaddabdcdabbacbdbaaabbcdbdadbcbddbbabdaacdbddcbabdbcbadbdcacbdcbaaddbaccdaddabbacddbacaccccadbadadbaddbcaaddbaccabacaaacddbcadcdaacaacbcbdcdaaaacccaabdacaaaaabcdbabaaabcacdddcadcadbccbabbcaccdbbbcaccadcbcadcbdacdaabdbcdbabdddabdaaccddcdacbdaacbdcaadcdadabdacacacbdacbdcabbcbbbacbcacddaaddbdddacbdadabacbbdcdddbabddcdddbbabbdccabbbccaddbdbaaaabdcbddabaadbbcbcdacbdbbdbbabbcbbcabddbbdbbdbbaddbaaaacaadacadbadadcbcadcccbbbaabbbadbcbdcabbccdcbcbcddaadbdcbbdaaacabcbcbcababcdcdcbaacbbcacabcdbcbddcbcddacbcbaabbdbcdcadcbabdddadbbadbbabbbbacdddadcbdcabbbbcbabdccdbcdcacbbddbbbdabaacabdbadabaaaaaabbadcdadcadbbdabbcbcabadbbdcbcbbcdcdbcaccbdabddaadadbadaabacacacacadaabbbbadbdaddbdadbbbbcbacdcabaccbdabdccbbacbccbbdcbcccacdccacbabacbcbdadcadbddcddbdadbdddbcccbbaccccbbadbbccdcbcbaddacdadadbbdabcaddbbdcdbaaccdbddcabaaabbabbaddcbdaabadcaadcdcdbbacacdcdbccbdacccdccbdbdbbdcaaccaaddcddcdbccbddaabcacbadaaabacabacababaadcddccdbbdcdbbdaabcbabcddccccbabcacadbccaacbbaababddcabcaccacbbddbdbbdbbaabadbaaccadbdcbdacacadaacdadabbdbcccacacabcbabcabbdabcddcbadcbdabaccbaacdcaccdcdbdaabbddcbcaabbdacccacacdbaadcaddbbcccdbabdddccacddbcddbddbdcbbbabbdacacdbcabcaddccadddacacadbccacbadbbacbabbcdbaaabcabbccbacddcbbbbbbabcbccabbbacaacbddcdabdcadcccdcdcdbdddadbacbcdcddcbbbacbdbddbdbbacddbcbaacbaccbaaacbaddadadcdacbdabacdcababcbdabdbabcbbcabadabbbcbcccdcbddbdbaabdcccbbbbbacacbabdbbababadacadaabadaddccadacbbbbbacbdabbcddabbdcbadacccbbddcdadbabaaccbaabbccdbccaadaacbbcbdabbdbadcbccbabcbbcdcdaccdaddbcddbcadaabbbbacdabddcdbccacaaaacdadbbbcabcbdbbcbcdadbdbaaacaadabacdcaaaccbbdbcddcccbbaddabaadddddbbadcbbaaabdcaccbccbbcdddaadacccccadbccbcbcdccccabaabcbcdbddbcccadcdccdbdcdcdbcadaddcacbacacabbccdbcbddcabdbccdadcaaacbcbcabacdbcdcabbddcddcbbccbcacdccbadbdcdcbdcdbabacddaccbcdacbdddadabccdacadaddacccaaccadaaddddddcbdbdbbcdcbdaaaaaacbdadabadddbbbddccbdcaacbbcaaacbabdacaacaddcbdadcbdaacdccaccdbdbcddbcddcbcbbaaddcdcabaacbabbbaaaacbbddcccddccbbbbdaadddacccaacdcdbdacdcacacabadacccacbaccbdbcbcbdccbcbcccaacbbbdbccbcbcdaaaacdaaabbcadbcbbdcccdadaaadbcbccadcbacdaadabcccabcdabbadbbaaabadbadcabdaabaccabcabcdacdccbdbcdcbaddaccbbdcadcbabbccbbdbdbdcacdaadccadbdcbcdccdcbdbcacbaabcadcacdcbbddabaacaccbbbdacbbbdbccbcddabcacccdbcdbbbbaddbcbacdabacbbcbbdbdcabbbaacbcbaaaabcbaabdabcdbbddcbccaacadbbadabaadcaaaddcbddcdbbcaabbcbbadbbccdbddaaccacbdbbcbcbabbccbabdcacbcaccabacadadbabbcdbdaacbaacaccadccdaacddaaadcabcccdccabcbdbbdcaadadbbdacacbcdccbdbbcbabddcaddbbbbccbbbaabdbcbbdbbbdccbabadccdbbdcaadbccbdbdccbcaccacddadcbcdbaabcdbccbcababdcbdbbbdcdcbaabaaadbbcdacbadcdababacdaacbbdbacabaccdadbdbaddaadcdbdbaaabaaddaabacdbbbadccccabbbdcbdcbcccdaccbbbdabbbbabddadcbbdabcabaddcbdbbdacccbcdddabdacccabcdbacbddabaaacddacbaaccbdabddabccdcdbadadbcabbbadaabdaadaaadcdaccaadbdcdcdbccbdbbabbbcbdaccdccdcccddcdcbabaaadccadbacaaabdbbddbdddcbdbadabcbdcdccdcadadacccdadbddaaabbdccaaacdcdccacbaaaaaadcacaddcbcbdabcddcacabababdcbdcdcbcabbacbbadacdbaaacaabcadcdbdabcaccdbbaaaccadddaaabbcbcdbbabcdcdcbcabadbaabddbcbbcbdaadddbcdddcbdabbbbbbcaccabdcdcdadaadcabbdcdaadbcccbdbaccacadaddaabbaacabbbcdccbccadbcabbaabadbcabababcbccdbbdcbacddaadbbdbdadccdcdbdcdcbbadbaddbdbcbdcccbdababbaababadbcbdbacddbcbdabdaadcbdcbcdaacadcdbddadcaaaacbddcbaaadaabbbbcbcabbdacacbcbcaaaaccbcbaaccadcaddabadaabcbbcdbaddbcccbcdbabdaccaadabccabcbabdadabbacccaadadddadddddbccacbccbcbdbabbdacdacdaabacbcddaccaccaadadaaaddaadaabdbbacbbacdcdccadbacadddabcadaccdcbddcddbcbddadaacadbdcbbaaaabbbdcadcbadaaadcbacbbcacccaaabccababcbbddbbdcbabaaccdddcadcccddccbacccabddbbaacaaccaccdbdadbabddbdaacacddadaabdabaadcaddcccbadadcbabdcdcacbabacbcbabdbcadbbababcdcaabbddbabcbaaadbcbddaccbadadacacbbccaaadccbbadabbbbdbbabdabdcdabacacddcadccbdbcccaabdcacbbaabdbacccaacccaaaccbbdadaaccabaaaccabcdcdbacbdabcadcadbdbabcacccdbdbdcccaaaabaabbddbaacabcdbcbcbcdaaabdaabbcccdbdbbcaabaccacbdcdaccbbdacabababdcaadbcbdbcccbabcdbdababddacbacababdaacddaaacdabccdcbbcdbcbadaddbbbbabddadaadccbdabdddacdadcbdcbddbdacbddbccdbacbacdccbbacdcacbdcadcaddccbbdaddcacddbacdabdacccdcaddcdacbaddbadcccabddcbcbdbcacccbbbaaacdbdbdacbbaacccdbdbacdaabcbcbacddcdadbbbbabadcaabdaabdcaacacddbbadcddbabbbbadaccabddbadaaadbddbabbbcbcbdcaddcbbacdcacacbbdcadaaacccbbbcdcdaacccccdbbdcbccabbbbccabbcddbdcabcdbdadbcdcccdabdacaaaddcbbdcacccbbacddccabdccdabcbdbaaaacbadcacdbccbacdcadbaaabcddbccbcbdbbbaadcacbadcbaddbbdbdaabcbddbdbcddccadcabcbddbcccbccbcccaadaccacbdcbcbdaacadddcbddcbcddadabdbdcdaccccdcdbbacbcaacaadacacdacabbdddccadbccbcacbcbdadaaccacaabcbddcdadbdacadbdacbbcacddabddbdabbabbcaaddccddcddacabbabaabbabbcddaadcbcbbdbdbcdcabdacccdaacbbaaccdcabcdbdcbaabbbdcccddadaddbdadcbbbaaabbdbdaacabccacabbcccaaacddbbcddcbcabbddddbbadaacdbdcdacdabdccabcdcbdcdbcdccbcddbcaadbcbaaccabbdaabacaccbdacdbdcabbdcbdcbbcaaacbcbbacbacdadadbddbabaacbabbcbccdcbdddcabdcabcbaaddbbddddbdadbdbccbaadacdbabdacbaddbccbbdacdcadadbabbbbdaaddccbcaadddccdbdaaddbddaabcbcbdabbbbaabbaabdddaaaabcddaaabcbacaaaacdcccdabdadaccbadccdadaaddccacddaadadddbcbcadbcdbbcbdacbbccabbaacccbdbacbcdbdbbbdccaccbbbaccdcababdadadbbcabcdbdadaccaabdabacbcabbbaacbcdcaccdbadaaddaccbcbcdddbcbccadaadbdadaabbbdababdaccaadccbcccaaacbbbbacbbdbdcddbbcacbdabdcdbbbcccbddccbadacdccaccbaccdadbbaacccacddabdbaabbbdbcaabaabdabbbaaddbaaaacccabbddbacabbddcbcbbdcdddaacabdbabcaaddccccacbadbdbdbdcdadbababdbbcbdcdcaaacbccbbbaacdddadbbaaacdaabaabdccbbdaddcbbadaadbdbdcbbcdbcabaaaabcbbcaccbbabbdcccbbddbbbbcbcaacddcaacadaacbaabccbddbaccbcabdbbbddabdccaaadabbbbbacbbddacbdbbaccdcdaccaaddaacbbbdaaddccaacaddacbbcbdaacbadccddbadcaaaadaabadcadcdacdbdbccbacaadabaccbbbdccbacadbadddccabccdaacdaccbbbbdcacbbabbdcdcdcbcaccaadbcccbccdbabcbcccbcccaaccadbcdadddcbbdacdacdabbdabcbadbcadaacdbaacccadbdcbabdcdcbaccbdacabbcdcbadaddcddcbbcbcbcadbabbddbbbcdbddbbbadccdccaacacadcdaaacbacbbdadadabadacccdadbcadacbadcccccccddadcabcddabcbbaadbcbddbddcdcbaadbcdcabbbabbcdacdccabcbccdbacbacccdcdcadaddacdbaccaaccdddbcccaababdddbadcbddaabbaaaacadadbbdacbbcdacbcaacbdcbcddbdddabadabaacbdcbccdbddbccbcbacdccaddbbbcdbcaabbdbcbbdbaaccdaabcadaaabdacbabddadcaaddcddbdccbbacbdabbbcdbdccbcccdbdcabdcdbbbbacbcadcaccaacadcbdbbddcbdaddaccbacbaacbdbbcaacadddcdacaadaccacbacbdbbdaadbddddabcbbdaacdacccccabccbbaddcccdcacbcaaadbaddbbcdccabbdcdbaadbaaabccaaddddddcbbccbcdcdbbdbbbdbddbcdabcddbcdbcddcbadbbabdbacabbddaabbacacdbccbaaabbbabcdcbbcacabdbbdcadbddaccbaadcbaadbcaccaccdcbccddabccdabcbbdccaaccbdcbdcdadadddcabacbccdcbccbcaccdccbdbbacbdcbcbcacdbabdbcdadaaaaccdcbaacbdabdbaaabaaaccddcabbadcabbdcaaaaccccabccbbdccbbcccdabacbadbcabbdcdddcdbcbcbaacacddcacaddbcdbdaabacbcbaaabbdabdcaadaabdcdcaacdaadacbddcabbdcadcddaaaadaabdbacaddbadacddbadababcbcbbadaacbbcdaccbadcbbdbacaaaddcadcbcbbaaacdcbbbbcbbcdbdddadbcdbcbdaadcdbcdadbcddabbbdcabdcddbcaaddccbdbaddacdbcadbdaddaacacdbbcddadddabddccbdcddbddcabcaaadacacccddbbccdccddaaaacbcabbdbbbdcaaddaadabbdccccdcdbbdddbbbacaaddcaacbcbbabdcbbccdadddadbccdcccadbabcddbbabacaabcccadccadbbbdbadccbdaccbadbadccdbddcabcbccdcccbcdacdbdbbdadcadcdbaabdbbdbdcaccbaddbccacbcadaacbacdaddaabadcddadccbababbabadcdbacccbcbcccdabadcdcbbacbdabbcdbcdccabcabaccaaaaccbcccddcaccbabbdcbcabdbaacbcbabbacadccadddbcbcdddacacdcddabbdbdcdacacabcdbbadcbcaadabdcbaabbcacccdaabaacadadbdacbacdaabbcadbbcbbddbbcdddcbbcdbcabbaaabaacbcdcbbcbdcdcaadadddcadcbbbaabccccbbddabccccacdbaddddaacacabbcaddcaaaababcdccacacbbcbadbadabddbbddbdbcbbabaddbccbdcbccccabccacddcacdbccaaacadadaadcddcbddcacaabcbdacdbababdcdadbcabacdbadccdbdaadcdcccaccbbadcdbbdddcaccddadacdbbdcdccbbcddddaccadbbbdbadcacdaacbbcccacadbaacbabcdaabbcbdcccaaabbcabbbadabaaadabaccabdddbbaaaccadcadbbabcdddbaccdcdadcacaadabbacccadabadccbcabbadcbdaaacbaccbbbadbcdcabacabbcdbdbaddbadcaaaadbdcdabdadabcacadadabbdccccdabbaababdccdbdbdabbcacaaadaacbccccdcdadbbadaccddbbdcbadbacbbddcbaadccadcbadbdbdaacadcdabaadabbbbcadcbbcabbaacaadbdccbcbcbbaabdaabacbcaccabaabadcdbabaacbbcddacddcdacbcddcbacbcbcbaccbcdbaaddacbdaabaaaccccadacadbbcdbaccbdacabdcdddacbabdbdbabcbcadbbbdbcbcddbcbdaadcdadbabaaddcabddbdcbabccdbdddbabcaccbaddcdddcbdbddbccacdcbddcbcdbaadbbbcddcdcbcdaccbcdbbcddaccdddabcdacdcbbaaabdcbbdadacdaddcdddaabadbacaabdbabcddcacbababaabbccdcdbdbbbddbdbddaacdadcbbaacbcadacacacbbacacdccadbbdcadbdbbbdbbcabdacddddcaddadaccddcccdbcadcddbdcbacdaabdbacdbacacdabdccaaacdabaaacacbddacacbbababbbbddcabacaadccdcccccbcbcbdcddaabdbaaddcdcdcdbdccbddaadbbdcabadbbddccbccdaadaadaaadabcaadbcbaddbcbbaccccadcacbcbbaadaaabacbbbdddddddbaaadddccbacbbcbdbddcdcdbcacddddbdcbddbdcbadcbbbaccddcdbbacbbabaacbbaaaccdcbbaabbaabddcdaaabddbacdcdaccdbabacbdaacbdcbcdacdccdcacacdbdaaddadbcbcaacdacdadcaaaaccabbdccdcdbaaccccddbccaaddcdddddbcbbbcbbaaaddddcabcbdcbaabcabbdddccaacaadacdbaaccddddbcadcddbdaaaccdacadccbccacaccadcadcccccdddccddaccbcddddbbdacbaadbdacbabcacbdbadbdaaababbcdabdaccbbddabbcdbacdbadcbdccbaddcbcbddadbabbaddabdaadacdbbcbdcccccdcbbaadddabcdabaadcbaccaddcbcdbbaacbababcdaccccacbaadaddabdcaabcdbcbaacaccbaaccaaabcccbcacbcccaadccbbbdbbaacaaadbbdbcabddaaccacbadacadbadbaadadcbdddbbdcaaabdcababdcddbcdbdbdcaddadddaabcbdbdbbacbbcdadaddcacadabcccddbcabddbdbdddacddbbcaaacbaccdaacbbdbbdacbbcdbaaacadbabcbaadbadacacdacdbbaccbdbcabbccbaaacdadacacdcabcdcddbddccaddddacddbcbbcddddabadaddadabbcadbccadddacbdcacdcacdcabcadbcbcadccbbabddddcdacbccaacaddaadcbcdbadcadcbadaabcbdadddaccacdcbcbdddccdcbbbcdccacdcaaddccbbccaabbdacbdcacabdababccaddcddaccaddadddccdcdbbaababccbbadacddccbaaacbdabacbaaccbbdbccdbdcaaadcdccadcbbccdcaabdacbccddbdbdbdaaaaacbcaccbacddbdabcccbbdbbaabacbbacbadddbcdadbcabcddacccaccbbcaaadbbcadcddcbadbcddadccbaaabcaaccdcbcaddaacaacbbdbdddbaddccabccaaccdbcadadadcbbcbbcdabdddacadddaabcaaadcddbdbccadbdbbacacddaababbbbacdddbdabdabacddacccbbbbbdddaacacbcccbbdbcbaccbbaacccdabadbbaaadccbbbacddbbdaccbadcabbacabbcaaaddbbbdaddbcdaaadcdcbbbdcdacdddcdcdcabbcabcccbcccadcddaaacaddbcdbcdaadbcdabdddacbddbcbcdcbcbaababccadcbcbadcbcacbabccbdacaaabbbadcaabdacaccdcaadadababddddacdbbdcdcdacdcdbccddcdcdabcbbcadbabbdddddddaabbcbbcacabcbcabbdbaadcdcbccbccbdbacdbcdbabadadbdcccddbaabdcdacacaccaccdcbbddcacadbcdcddaccaaabbdadccbcdccdbaaaadacaddcddadddcbcccadabdcccbabcacadccdbccbdcbcdadbbbdaadacbdacddccbdbcacdaddabdbabccadabbddddccbbbcadbcdcbcdcddaadaadabbacbdbcdccbcaaacdbbabdccdadbdacaaddbcaadcbddbaccbadbdaaacabbadcbadddbccbbbcbddddadcadcbbcbcbcdddddcadccbabddbcadccbdbdaadaabbadaabccbcdcdadbccbddabdddbbdcacabcdbdadcdacaacaadadbabbdcacdaaccdcabbcdcbdadbaaddabaacabbbcddaadaccddadacaadddaccbccccddcbabbaaaacddbbcbadcaccacadbbaadbddbccaaddcccaddccbacccdaacadccccadcacbdbadaccaccdcbbbddddaccccaadddabcadcacbcacbaaaddbcccdbbcbacbadbddadbdcaabdcadaaabddadaadacadaabaccbcdbbddddbcccabcdbccacbbcdcababbdcabdddbcddaabaddbdaabbacbaddbaccbdccdbdddabbbdaaabdacddabbacddacacddcaddbbbadbaddcddcddaddbcaabbbcadbdacacbcbbddbbdadcbaccadbadbcddbbadbbdaaaccdcccdabaddadbaddcbcaaaabaacaaddaaacdbcadcadddcbaabbdbccbcdcccbaadddbadcaccdcdacaacbabbddbacbbddcdabcddacaadbcabadcccbbbaacdbdacadbddabbcacdbddcaccbabbcddddcbcadbaaddddbcaadbbbdabbdcbdabddcacccaacbaaadaaabcaccbcadcabcacbbbabcccbddccbbdcaadcbccabadbadbccdddcbcdccdddcdbdabbbcdabbacaccaabacaabbbcdcadccaaaccdcdcdcdcdccbcbdbbcdccbabdbccddbbbbaaacdcdbcaadbdcdbdbdbddaddbcbbbddaaaadcbbdbadbacaccdbcadabacccadcabdbabacdabbdbacddbdcdcdadaaabccbdddacdaaaabaaacaabddadbdcbbabcdbbbcbddcbcaccadadadddbabddabdaccdabcaccbcaacabadaacdaacdcbcdcadcdacbabaabbbcbadaccdaddadacbbbbcaccbbccabcdddacdbbacacbbabbaccaccdcdccbbabbbccdbcccadadbbadccbaadaacbbadbccadcddadbbcdccabaaacbdcacbabbcbaacbddddcbbabccaaababccdcaaddacdaabbdbbbabcabbdddacbdaabdabbcddadbcbbcbaaaaddaddacadaabcddccdbcadbaccbbbbcabcdadabcdbcdbcbbddacbaadcdccacccacdabadabcbdccbbccaccdabbbbabcabbdaaccadbcaabdcbbbcbdcabaabdddcbcdabacaddbcabcccccbacaacbdccddabdcdcaaccadacbdcdbbcaadbcccddbcadbbbadbbbbbaaaabbcdbbcbddcdbabbbbdaaaacdcbdadacdbddcadcdcccababbbdcdadbbbabdddddabbbbdccddadbddaabdccbaadabcccbadbababcdbdbdacdcddbdaacdcbcbdaabcdddddadbdabbcbdcdcdaccbcbccbccacacbaddbbccdbbbadbacacdadacbbbbcbaccaabccababdcadabdcaaccabcbbbabbaccbbcbccacbcbdadadbdbdacadaacdbdabbaaadccaababadbbdaaddcccacdbacddcddabbadbadadcacddaabcaddddaaaacbddadcddaddadcdbbdaadcbddbbcacadbcbccacbddcacaaadbdcbadddbdbcacdcadddbddccdacadabaabaacbbdcaabdbdcdaacbbbabbbddaaaacbbbbcdcaacbcdbaacdabbdbacbdccbaabccacccbbbdccdabbdccccbaabcdbcbaccaddcaabbababadddbccaadddabaadccbabcdccbdacdbbbdacaddbcdabbadbcbbdbacbdacacacacacaddaaadaadbdcaccdaacddabadccabccdbbdcabbdbdadbacdbbbadcabbbbacdabcdbabbccddaacdaaabddaabbcbcacbcabdbcacddcbcbbccadaaaacccbbacdbdacabbcdbdbbddcddadbbcdbdbdbcdacadcdaabdcddbdbdcccacadaaabaccdbbaabddcddbbabadccdadadbdacadacdaacddbacaabdabbbcbcacdcbbdddddcccdbccdccddacababddbbabddaddddaddcaaacdabccabbcacaabcdbdacacadaabdbdaddddabdbababbbbadabaadbccbbcdabddadccbacbbccbcbbdbddbccdaaaccdbadcdcdaadbdcaaadadaccaaacadcbaddabacacdbacbcabadddcdcccbaadaccbdbccabdbccdbaccbbbddcbcdcaabbbcbaccdadbdadacbdaccadbdcacdbbacbacacacadcbbdcbcabbaabcbcbcbccacabdcaabcbdbdabaabdaaccbacaaacdaadbadddacabdbbbaaddcddcddadcbabacabdabcdaabbdbadacdcdadcacccacbccddaadaaddaaccddacacbbddbdbddcabcccccabbcacdcdbdbbabdcbbcbdcbcbacbcbaadcbbdddadcbdabcabaaaaddcdddababdbccbccbacababdccabbbaabacdbcaccbdadadddabadcdcccbaaacdddcccbacdadbcacacbadcccccdcccbdcbbbddcbbdadbdadbdcabaacdbdbaadbabcbbdaaabbbbaaadacbaabdcdadccdcdcdddbccdcacacdcdaddcdbbbbbddaabdcbddcddbccdacbbdddcddadbbcdaaddcadadbbdcbcdcadccbcdbbddabbbdbdcacaaddbddbbaabcacbaadbbdaccaabddcabddcabaddbaabcbdbdcaaddccabbbbacaadbccdbbcccdcdddaaaccaaadbbbcccadcbdccccaaacdccdcbddabcaacadbcdcbdcbbcbdaadcabcabbbaabbccaaaddaccbcdababbaabbdaaacbbaccdbcbddbadaabcbacdcdbacbaacccbabacbabdcaaabaacdbaaddadcbcadcdccddcadbccdbaaacbdaddcbacdacdaaccaabcbcbadbcbaacadbbccddcdcaadbaccbcacbccdbdcadaabcdbdbabcdacdacabacbdbddabdabcddcbddabdddbbdacdcddddaacccbcdadabcdbdcaabadbabacbccddbdadabacbcbcbabccacdcbdcbacaacabbcddcdacaacbdbcaabdcddabdcddcdcacababbadcabbabdcdaacaadadcbaaadccbcdaaaababcdbdcdccaddadbcdbaabbdddcaabacdddaaadcacabddbabaddcaadbcdbdabdcccddcacbabbabccbcababdbdccbadabcdacbaadbbdbdccbcdbdadacccbddabdadbdbccbcadaddcaddddbabbabadcccaccaacbddcbcadbcbdcaaccbaabadbdbabcdacaacabdbcdaaadddcabdbaddcdcbbbacbdcdaccbbcddadbabdabaabadcaccbbabcabdbcbadcbadcacbcdaabcaaaababdddabcbbcbdcabdacdcbcdaadcdbbbacddcadcdbbcacbdcccacbacbcbacbdbdbcdcbaacdbbccaddaadbcdcaabadcdddbcaababbdbdcbbbbdccadaabbbbdbababaaabbbbdacccbbabdaabddcbdbbabcdcabcdbababcaddaacaadaaabdcaadcccadbbdaaadcaaccbdacaacbbddcacabdbbaaccadbccbddabccaacdadbdcdaabbbabbcdacdddbcaadcacbabbbcbadadcaadbbccabacdbdddbabccdbbccadabadcdaaaabcabdacabaddacbcbbbdcabbdbaaaaacacaaadcdcccccbdadacdcbbbbcbbdddbbddcbaccccbdccaddbcdadcdaababcdcdcbdbcdbaabbabdbbbbcdabcccccbbcccccadaabbacabdbbabdbaccbdcacabaadbbbcbacdddaddcccbcddabbdbdcddbbbddacddcabbcbdadaaabdabdddbcdabbcdaddcbcbbbbabaccaabaddabbcabdaaaabadcadcdaaacdcdcbcbddbababcddcbadabaccaabcbaadddcaabbacbddaaaadacaaadabcddbbbbabcbaaaccaadacdaddaaaccabcaadcbdbacdbcbdccddadcdaadaaadbacaddcddbcacbdbcdcbbbcacddddabdbbddccbbccabdcdcbacbcbcabdaddaddddbacdacacaaadcbdbcdacccbacbddbbddcadbaddcabdcdcdcbdbacacbcaabbdbbbdcaddabaccdbbcbadabccaaacbddbdcdcbaabdbbabddbbaaacacabacbdaaabbdcddadaddccaacdcaaccbddcbbaabacdbbcadcccbbcabbcbdabaaaaaaaddadbaccacddaaabacdbbdabdaccbbdabacdabcbdcacaddbbcbbcddbcacabbcabaabccbbaababaaabcccaabbbabbaaacdabcbdcadcdcbadacbdcbadbdbcbdaaddacadddaadabacbccbbbddddbcdabdbcbbcbaacbaadbaddaadaaabbacbbddcdacbbcdabdddbccccadabdbcadacacbabacdccadccbcddaccdbddcadaaccadcbbcdadddbdbabadbbbabaadcaccbcdaacdbdbddabbbaadcbabbcdbbcabaadcacbaacdccdcddbcddddbcccdacabbdddadbccadddaccbddcddadcdddacdababbacbcdbacbbbabcbdddbdbdbbcddcabdbdddacccbdccdadcbdadbddbcaaccdbcbbbddaacdbbaaddbcaccaaacacbbaadcaadaccdacbacaacabcdbcaaaaabcddccaaacacaadcbabadbcabdccddbdcdcbaacdcdbdcdbdbabaacdaadbdcddaccbcbcbcabbcdaadcdbbddcbccdcbbcbcbdaddbacacdbdddbbddadccabbcabdaabdabbbbbacddadaaaabdbcadacbabddcadbadbcbadbaacbcbccbadaacbabbadadabbdacdbcccababccaddabbbddbdadadbaabcdabcdcdabaabbbbababcccbbbacbcbacccadbcccaaacbbabdbddbaaadacbcacacacaadcccaadcabadaddaaddacdcacdbacdcdadbdcdacbcccabbbdbddccbbabacbbaabbbdaabcbdacbcbbbabddaaddbdbbaaddacbbccacbbccbacdcdbdadcaacdddcbadddacdbbaabbcbcacbbabccddcdbcaadcbbaddaabcacbbacdbcbddcdaabbdcabcdaccbbbcbdbccacbccdbbbdcabcaaaacdcacbacaccabddccddbbccbcdbbacbaadacdcdcbbdacbddbaccabbdbaabacaddabdacacabaccddcbabdabcbbddbadbadddadbadbdccbadabbdabdadacccacaadbdaaaaadbaacdcbbccbaabadbbbbbdcababacdbcaccacddabaaddcccbbaadcdcddaaccbaacddddaddddbbbbbbbcbdbbabbcbdddbdbccdabddaabdbaaaacbaddaddaababdabdacaaaacdbdabcabacbcbabcbacababaddbccadcabcbdabacccacdaccbbdddabcdbdbdaaacbdcbcdbbdacccbdbcbbcdacbcdcaddadbcdbcdbabddaddaccbdcccccddbacabdcaddcbbaadbbaabbbcbbdabddbdbcdaabddbbccccacabaccacadaadbccdbdbcabbddbddbcdbbbdcaccdcadcccbccabaddbcdbddabdbdccbccdbbbbcbddbbadbacbdcdddaabcccdacbcdbdadacaabdbcddababbddcaacacbcbcccddacbadbabddddcbcdacacaabccdabadacabcdddddcaaaaccabaabbdbacdcbcccddddccdcbdbbadddbcbcbbabacbbcadcbddabaabaabbbdbdbddbbadacabaacadcdcadddddddcbcabbbbdccaaaabdcbddabdcacdabcbaccddadcaadaacbcacbacccabdbdaddaccdaccdcccdddadcdaccdadccbaacabbcdbdddcdadadcadcdabacccbbccaacadadbbcabbadccbcadabbdacaddbcdcdcacdddcadddbdddbcbdcccdbbdaaabbbbcdbbcddcbdcddabbacdbcaadcddbcdbcbaddddcbcdcdabcdaddcacbccabbddcdabaddbcdbdaadaddbcacbbcaaaaababcbddcaaaadbcccdbcdcdbadacdabbadcbccccdccaddcbdaaaccbdbacdbdabcabcddbdbcadddcbbbcbabdddbabbacbdddaacbcbcccdbcadaaacddacddcacbacdbcacbcaadacabbacbddacdabcaabbadadbbbcddaccdcaaccbbdcbbcbbbadcadabbacbcbbaacbcaddcbcbadbdbdbcdbcdcccddbddccabababcaaacababdddbaacabbccadbcdccdaccbdcbacbcaaadcaaabacbddaaabcaacaabbbdcaccadddabcdadacabdaddcddabaabbacadcadaabcbccddadaaacacdbacdaacbdbddcacdacddacbdcbcbcadcdadaacaaaddacabddbccddbaccddcbaccbcadcbcdbcaaadbcdddbdbddabbacbbabddcddcacbccddbdddbdabdbadcccccaacabbcbbcabcbdbacdbcabdbcbbaacdabdbcdcbdbdcabdcaacadacadbbdabadbaadbabacacbcdccabddcbcbbdacccdcbcaccacbdaaadcccddadcaabdabdbcadbccdddaccaaadbbacbadddddccadbbacccadaacdcddacdbddabbcaacbcbacdbcadddbbdbbdbcbcadabdadacbacccbaccbbaaaabbbcaccddbbdaacbadadbddaccaaadbccababaddcbbcbbbcabbccabbddbdaabbccaadcdaacbdccdcbbbcacadabacbaadcdbbabbcccbadcacbcccbbbabadddacabddaadccbdabaccbcaddbdcdaccdcacbcadddbddcdcbcabbccbccdccacbccbbbdbbccbbbacbdaadbaabaacbddbbcccaacddaccbddbcadddbbadadaddabaabdaccdbaadaaddcdcdcccaacdadaadcdabcbcabdbbbbcbbddbbbbadbbbbadcdadccddddbdbaabacacdcaabaaddcabcadccacddabcdbdcdadbdbccbdcdbbbaddcddcabbaacdabadbcaaaacbdcdacdcccadcaadbadddacbadbacabaadcaacacaaddbddacbcbcaadbbdacabcbbcaaddbcddbcbbcbcdabaacacdcbddcbacdcdcddccddbdddcabadbbdcdcccbcbdbabbacacdaccddccdabbbdcdddababdcbcacadbabbbddcaadacddbcbdcaabadabbbbccdbadbdacaadaddbabddadbcbdcaacbbadddaddddbabddaacdcdcacbacccbbaabcdcbbddccbdbcdbcdbbdbacaaacadbacacbcacbacdbbaabdaaddddcaccadccbccabaabccbddccdabbbbbccbaabdacdbbbccbaddbabcaadbadbdabdbbbacadcacdcbbcacdabccbdcbadbdcdddadccaabcccdaabdcadacbbbababcbaddddddbcbdbbbbcadabdadbbbabcbdacaadcbdacbdabccbdacacbdbabbabdabadbcdbddbaaacadccabcddbcadabaacbddcdbcadbdcaaabcadaddcdadbbadabbbdbcbcbabaadccbadbcbbcaccabacbacdadbdccaddabbcbaccdaadcccbdadbdadccdcabddcbdccbadccbdddacdacbaabadddbdacbdabcbcdacaadbdcddcbabdddaabddbddccdadacacacdbabdbdbbacbabadaadcdacccadbdddaabaccbcdbddbabadabbcdcbbdccdbddccbdacdbcddccaaabcdbbabaacbaacbbdbcadabcaaaaaaabbcbdcdccbabccbccabbaaddbbbcaacbabdddadaddbdbdcdbbcdccdbdcadccdcbadbbbcabddadaccdbbdacbddddbacbbdbadaabdbcdaccbccacdababcdaadbcaddcdadaabbacbbcbcdaccadaadcdbbbaccbaccccdcdccbcaacdaccddcaabbbaaccbbaadbdcddaadcacabacaabdbbcaadbcbadddabccbaabbacbaaccadcacddbccdbadbdaabaacacbadcddccdadaadabcccaddaabcabbcacadacbcbdacbdddabcdabbdbcccddaaccacaaaacadbcadaddbbcabbccdadaaaaabddacbadcabdbadcadcccacbbccdddbdbcddadbaaddacbaabcaddcbdbdddbbcccdcbabccadbdbdcdcbacdbbcdccaaddbacbbcdccaacaabcaadcdddcaaaaadaadbbaaccdbbdadddbdccdccdacacadbbdacbacddcaaaadbdacbcdabdbcddacdbdbbddbadccacacacacdccbbdccbcbdbdbacdaacddddbbbdbbacabddadcabbcbdcddcbcdcaadabcbcadadcdacaabbcbbbcbbbdccabbcddbadbdbaadcdadcaacbdcccdababcbcbdababbaacbcbbdbbcdbbabbcccdcacaaadadabaabcadbbbddacbcbcaccacdacabaabaaccbcbbcabbbdabbabccaacaccbcaccbddacaababbbdbaaaabbbbdabdacbbdcbddbcbddcbdbccabbaadbadbbbddaaacbaabdaabdbbccdbdacdadccaacdadbdbcdcdbaacbacdcadaadcdaaadbbaadbccaaccbabdbdaddbadabadcaccaaaaadaacaddbdbcacbadadcdacabcdadcbcbadcadbcbdcddaaaabcbcbddacbbcccaabdbcdbcbcccdadacddddbaadaabbaccccccbbadaabcccabbcabcbacbbabbcaacbccaaadbdadbabbacdabbaddcbdabdcbabdccabcbaaddbbbcdbbaaddcabddcbbabdaddadabcbcbacddbcadbdbadddcaacacbcdbbddbcbacaaacdbdbaadccaccbbaadabbbdacbdacdbaabbacacbaabaadddbccabdcbdadddccbdbddbbdccbbacaaddcbddbbccaadbacbaaabdcadbbabcaddbdbccbdccccdccadadbcdaabcbbaabacbccacdcdaabaaabcacaadccbaddcabadbcbcacaadbbbaadaaacbccdaaaadbadcacdddddaddbccbcaacabbadddaaddddabbbccdadabdbcddababdcadccdaaddccbcbcaabbbaacbbadacbcdbdcdabbdbddcacaacbbcdbcbdabadcddbdaccdcacdacccbaadcbddcdaddaaccccadcccabbcbdbddaddaddcbbbadabcabdcbaacbccddcdcdcdbdadcbdbdcaadacdbbdcacbcdacaddcdbdaaadaacbaabcdadcabbbcdacdbdcbcadbcacddcbabcdbdaaacabcbaaaaacdcbaddbbcaacabddbacadbbadcbaacdccbcbcaddaabbaddcbbbacdbbdccaabacdbadcdccbdbbdcccdddbbccbdacdddccbcccccabadbdadccaddbccccccadacddaabaccadbcaccbabbbadcbaccaadcbdbdcbdacddcacbdaccacdbccbccaaccdcddbbdccbcdbcacabbcabbdabacacbdacbddbaccbccabddcbcbacacdbdcbddadbaabdaaaacadcbaadbaadabcdbbacbdcdcbdddadcbbabbbbcdccddabbbcbcccdadbcbdccccbaacaabacaabbaddcdbdcdcabcbbdacbcacadccaccdbbdccdadbcdcadbcbdddccbabdddbbdddcacbbdcadbbbbaaaadacaabadbdabadacaddaccbdadacaddaccddbdbdacdacccdcdcdaabdcbbcbdbccbbabcbcabdcaaddcbcacdbbddbccbacbabbdaaadacddaabdbdbabbbcbadddcadbccccaadbadbcabddbbdbcdacacabcadabbbbcbdbcbbcdacaabacababaadbabbbddbdbabbdccdcbaaddddaaaacbdcddacdaabaaccbdbacdbcdabbdaaaaadadaadaaaccabacbabddbbabddbaaabadaaadcbabdbdcbcddaabcaacccaabbcadacddbbadbdcabbccaccacbbdccbcaaaadcdcdbaadbddacabdbcaadbcadadbadbcbdbcdaaddbdaddcbddbdddadaadaccacbadacacbacacbdcdaaabdaabbcbdcadadddcbaacacdbaaacdbbdbdbadcdaabcdacabbaabbdabcacbddaaabbcadaabacdccdbcdcbcbdabddbacabdcdcbcbcccddbbcbcabbcdbbbdcacabbddcdbcbbaaabcdbcdabcacbabaabcbbcbcacdbccacccabadcddbbdbdddbbccccddbbcabccaabdbabacdaadaacacadbbbabcccdcddbaabbccbbadcbbccdddbdacbbbbbbcabbdaacdcdbbdabdabddabcaccbdbbccbacbcdccdddbcbbadabaddcdccbadcabdccdbbabcabdbabdcbdaacbdcaacbbcaabbcbbbddcaccbaaddbabdbabaccdbacddbaccabdbdacadcadbdcddbdcabcdcdbbdaabacbdbbaadcddabadbdbccdcdacabdccccacdbccbccbcbcaaadabddbbaaacbabccabdbccadacbdacbcccbcdbadbcccadbdcdbdbbcccababaaaacddcabacabdbbcddcadddbbcaabcbdbacaaabaddcabddddcabacdadaddcdadccbadbcdddaaacdcacdaadcbccaccdaabddaaadcbcbadbccdcbacbacddaaabcdaaaaadbdbbabcbcacbabdddbabacccaddcdababacbdaddcadcddbbbababdaccadacccddcaccaddcbcbacdaccdaababbbdbacaacaacbdabccbaabbbacdbaacdbcbababbddccbaacddccdddbbacadbcbcbdcbbabbabbcdbdbbbcdcdcacbacbdababbbbddcbccdcbbccdcccbacbbbddbbddcccaabddabcbdacbcbdaadcacacababcdacbabaaacdacdbbdcbbcddbdbabbacabddddabcbabddbbbdddacabdadcbaaaacabdcdabddaacdccdcbcacddcbbcbbdbdaabbbdadbaabbabaadbddbcabdaddaaadaaaadaabccddabcacadddaddabbaddabbcdccbdbacbbddacdbbbddabbcaccabcaaabddcbbdbcaccdbbcbcadbcaadbbcdbccccbbbaddcadabddcadaabdbaccdabcabaddddbbcdcccabcbabdddacbbbcbacdccccbbdadaadcdcadadbabbbcaadabaccbbbbbdcccaccbcddddadccccccdadcacbcbdacbcbbcadbbbbaabaaaabbbdaddacabadaaacacaacccdcdcadbacbadbcdddbcddcddbcdadaacbbdcddbbaacdbadaacbbcbcddcabdbbadddabbcccdccaaddcddbababbaddcabbbbcdcdabbcdbdcdbaabbbcbaabbaadbdbbdadcadabdcccbaaacbcabbcddabbdcacdadbcacacdcdcaddcabcdadcbbbbdbacabddcaaadbdbdcddbabcbcbacaaadabbbbcbcbccdcddbaabcaccbaabbbcbcacbddbcacddadbbcbbbacdaccbdbdababdcdacbacadcdababacdbccdababbaabcbccdcbabcbbbddccbdbadbaabbcbaabdbccdcdaaddbbdabdbaddacabbbbacaddcadbbacccdcbdbbcacbdabacccbaadacccdbaccdacbbddaacdbdbdabaadacdcabaacdbcbdccabbdccddacbaacadcaccababdcaadbbabddddaddcadccdcdcacacbbbaadccbcbaddbcbcddbbbdcddbbaaaccabdacbabcdcbadddaacdbabcabbbaadccacbcccddabbcbababcccbabaaddaabddaaaabaaacbdbaaddcccdaccdccaccadaadbccdcccabadbcbabaabcdbdbccaacbaabdcdbbdbcacbdaaaacbbdbbcacdbbcdacdbdcddcdaaaaaabccbddcbaacbdbcbdadabdbabccddacaddabccbbadbdbbaaacaaabbcccbabcababddbdcccbcbdbadacdbdddbaaaacacaddcaccbbcddcbdadcdbddbcdbdcbcabbbadccbaacbdcbddadbbcbdbdaaabaadabadbaabbdccacbbbcdacabbbccaacacadaabbababbbadddddacdcdcbdacadcbbaabcadcccbcdcdcccbdaaadcdaacbbcaaabbbbdcaaabcccaacbabbacababcbdcaabacaccacdcbabbaadcacbcdaabdddaaaaacbdcddabaaccabbddbdcabbcacbdbddbaddcdabcdddddcdadcaabdbddbaccdbdadbdcacaccdaaaaccddbbbacbbadbdcbacaacdddbadababbcdbdbdadbbdbdcbcacbbdbcdcccaacbcdabbabdacacdacbacdabbcbcddcdadbacdacabdcabccbdbdddcabdcbcbcbcacbaaaaabcbcddacccdababcccbababbbdabdcccdbddaddcabadaadccdcbccdadbccaccbaabadaabaddaacaabcadbbadcbcbacabbcabbadbcabdadcddbcbccbbadcadccccabdbdcdacbdadbbbdbccabcdbadbaaaabaccacadbaacdbbaaddbdcdccdcdaacacccbaabbbbacacbbdddbacbcadbcbcaaabaccabddcabdcadcacbacddaaacaaccdcbcddacccacacaacacbcbabcccbbddaaccbabccbbdcdaacccadabaaaaaabbcaaadaddcabaabdccacaccaabdcaabcbbccdcacdacabddaddccdadaacaabcacddbdbbcddcbbadbbbacdbbdbcdbdbbdcacabcadcccdbdcdcaccddbdcaccdbaccbacabcabbaaadababacbddccbacdadbbabcdddbcaabcaadbdbcbbacdcbabacadccadbbacdbdbbbadadacacaadabadcdadaabcadbaaacbbbccdaabaaaabddcadcabadddcbcdcbbcbdcbdbcaccdaabdcacaadaddacdacacadbdaaabddadbcdccdcbbddbdabbcabbbbbbabdddbacccaadbaccbabbdadccddadbadbbabcdaaabbdccaaabababbddacbcddaddddccadacadcabbabcbddadcbccdbabacbcbccbddbcacacabcccccbcbbaaadaaccbbddaaaddbbdcbaccadbabbbaabaabcdcdbbddbcadadbccbdadcbdaacdadbbacbcdbccaacababbbcdaabccbccabcadcaaccbcdddcabcaabcdabdacccbdddaabdcbddabcdbaacbcbdacccdcadcdbccdadbcaadacddaabbacadbcdbdcabccbcbbbdbcbbbcaddacadbddcdddabaaacbdddacdabbbbbcaabbbdbaabcadacbddaccdbcbbbdcaaccabbccccdccdccadaacabdbacbaaacdddaacacbcadabbbaabddbbbcddaacbacaaacbabbcabcbbaabcdaabbbdaaccacadabaabdbadaabcbaccdcbcadaacdaabdbbbdcddabbdddbdbabdbdddacbbcbccacbcbabbbacccbbbddaadaaddccbcdddcbaccaaccaddcdaabcbdcaacdcabaadbdbdadddcbdbbbcadcabbcbccbcabadccabdccbbbcbdccbcaacbaacdbdbcdbdadadabcccbbaaadddcadabddddddbcddbaaababbdddaadaaaadddcdadbbbcbccabacaaacdbbbdbabadabbdbcddcabccbadadcadcddabdaadaaabaddabddcadaabaaaaaadcbdcbdbbabcadccdbdccbcaaacbbabddadabcabdcacbbcbbccadbabbdaddaaabdbcbcbcbccccdddcadabccddbbbddabdddcaaddbcbdbbaaabbbadcddbaaabacddaaccadbbbcbacbbadbaabbbabbcabbcacdcddccacabbbbddccaaddaddcacdcbccdbbbdbaadadcabdcdadbdcdccbbdadccdcbcdaacbcdcbbdacbacddbacdcccaccbabccbaaadbbbdabadcbabbacaaccacdbdacbcddadbadabccaaaccabdcbdddccaaaabbabbbdcddbadacbbdaccdcdaabaadddcbcababdbcddcbcabadbdbacdccdaabbaabaaabcabbdbcbdcbaddccaaddcbdddcdababdabcccabcacdcabdacdbaadaaacbbadbadcbbcacadacddcbdabcadbcabbbaaaccabcdaaddcccbcbdddaadcbaacdcaaaaaddbdccacdccbbabcadbacbbbcacabaadbccdabbababbbdabaaccbdbcdddddbbdbbbdcaabacaacbbadadcbbdccbabdadaabcdadacabacacdaaabaacdaabadabbdaacdbccdaabcbbbabbcddddcdbbddcddbbdabbadcbbdcbcbabaccacbdbabaaacccbccaddcbabdcbddcaadbdddabcacabcaaccdaadbcdcbccdaacaabbcdcdabadabcbcddabbbacbadcdbcccbcabddccccbcabbdbacbbdbdaacbabdddbcbcadcabccbacbbcadbbbdbcacaacccadbcadbcbbcaddadbadaccbadabacdacbcbccabddbbbbcadaddcdbcacbcccccdcadcbdaaacdbaadcbccbdbbdcdbbbdadcadacacabdccadddabdccdddccbdbbcccbdaadadddadbcccbdacdadacbadbdabacaaabaddaabacaacdaccacbbdcaabdcbdaaabaacdbababcdddacbaacdcddabaddbdaadbbbbacaadbbcdcbadbbcbabadbbcbbabdaacadcaacaabacddacabcdabaccbccdcbccbbcdaaaacbcbbdbacdaaddbdbbdaabdcadcdccbddcbdadbaacbcaaadbdddcdbdbbdbccbdcbbdcbdbaabcbdcdadcbcdddddabbaccbacbcaccddacccabacddabdadaadaacdcbdcbcccbcacaddbacadaaaadddbbcbaacacbcadddcdbdbaadbcdccbbcbddacbdabdccaccbabdabaadadacbcbdaabdabbaabdcdccdbcaabacbdcaaacdbcccaddddcaccdbabaaccdccabccabbdadcacacccdbcbbdbdbbaaddbabcabdadabadbcdbcdcbbabbaaaaaabdbcdbcdbbdbdabbbccdcdbaacacadacbdcabbadaaabbbbcaddcbaaddbcbbdadbbcacddccababbdabbdccabbacdcabadaadaadcadcacacdccdbbcdccdabacdccbbabaacdbccdccabadbaacacaccdbddacabccbddcdcdbcdaaaabbcaadbbdcaacbdaacbdcadacbdbcbaddacdaddacdaccddadaaaadababaadbcdddbbaaadccbcbadbdbcacdabdbadababacbacdccdabcdcdbddbadacbbdcdaddcdabccbccbaccabdcaddacdbaccabbdadcaccaabacaccacaccccccbadbaaadabddbbbcababdcddaaabbcddabaadbbbcaccabcbbcbcddbddcddbadbddaccaaaddccadbdadabdcaaccaadddddddabbabbcdbdcdbadddbdbdddcaddbbacaaccdadabddcbcdbcdcaabccbcadcababbaccacaaabddaabaadacaadbccabbcacbbbabddbbadcabacabacdddbcdadacbdbdbccbdcaaacdbadbdabbabbdcbcbddbdacccbaccdcbacdbadbbadabdcbaacdbcbbbaaaaaaaadbcbdabadbbacbddbbcdabcbbacacbaabdcbccabdadbbbdcbabadccdbdcddadbbaabacbdddaacbbddddacadcddbdbbaabbdaadbcdabcacbcdcabaadddaddaaacbdcbdadaaacbcdbcbadbbacaccaaabacacdadcaaaadddbacddcacddbdcdcddbcaadabbadbddaddabbaacbbcabaadbaadabaabddacbadcaadaddcdcdaddadbacabdacabbabbdcabdadadaacccabcccacadabbcdabbbabbcccbccacacadcbbaddcdbcabdacadccbabdabbdcbacaaddcddaddbadbbacaaaddacaccbdaabbcbaacbcdacadcbbddcdbcbacdbcccacbcadabbdaccbccbcdbbbcaabcbacdaddcabbbbdacbccdccadbcaabccaaccababaaaacddbadcbcbaaabbabdbcdbcacabaaabaacabcadaccbdbcaadcacacbcbcbadbabaaccdddadbccaddacccdaabdcdddbadbbcbbbdacdcadbbbcaacbbbaccaaaadcdabddacdbcbacbacdbadbcacccbabacddacaaadaddbbbcadbdcccdcbcadccaacaadcabdbdddcaabcaabdabbadddddabbadabbcbdccbbcdbdabdaabbacddbcbbcbacbdabaaaacdbdcdbdaccbccaddbbdbadcdcbbabbcadbbbdcabddaddbdaacbabdcacaabcbbdbbadddbcbbbbaddcbaadacdbcdcddbdbcdacdadabacbadaccdcbaacbbcdabcddaaddbddacbbbababbbcccbddacdaabcabaaaabacabccbcccbaacdccdcaadccbaacbdbcabcacdbabcccabcbaaaddabcacaccbbabdddaabcaaddbadccccacddaaccdadbdaaaadadccbcacabcdbacbaabcddabbdcdbabdddcddcccbcbcabbcbcacdcdbcdbcabacabcdbcbaabddadabcbcdcbbcbcbbbbdcaccadcbbcbccdacacabaadbcaadacacacddbdaacdcadadcdbabacbcccaaabaabbcddbaabbdadbcbacabcadddcbabdcbbadccdacccbcdbaccaddddabcdadccbcccadabcaacdcdccacbbbdadcacdccacbcccacacdaaabbdddaabcbababcadbdbacadddcdbcdbaabddcbcaababdbaadbddcccdacccadcdaccbababaaacacdadaccdcdaabadbddbbbabccbbdbcbdaddddbabbabcdcccacdcabdacbbdaadbdbcbdbaddaacdbcadadaabcacaddabcaadcaacccdccdddccbcabdbaadccbccaccdaacccdddcabbbcdbdcbadcbcbdbcddcaaccbdcbdbcbddddcdcbbbccdcdcbdbadddaaabbdaacadbcdcacaaaccdacbbacdabbcdcbbddbdacbdccacdbabcaddbbbccbdddddabababaacccdcccddaddadcbbccdabdadddcdabbdbabdccdabbdbdcdbdcaaaabcbbbdcbbbaaadbcadadccddcacadaccababaccdabdcadacdcbddaabadcaccaadcbdacbcbdbaacdaadccbaaaadcccbcbcdcccccbbbccdaaccaadacabdaaddbcdcbbbdaadbdbbccadbbbbdadadacacbaaadcacabccdacddcbbcacbadcdbcabcaaddbbbbabdcacaabccdaadbdbdbabadaaadcbacabdabddaddbacbccbdbdbacddacccdbbdddabcdccbbbdcacdadbcccddbaabbaaaacdaacadbdbbddbcdbddacddccddbbaaddadbadacbdcdcbdbbdbbccdddabbbabddbddddbaabcbadadcdbbccdbddcdbbccdbabaacadbcbbcbcdbdaacbccaddbdbaccabcaacbccdcaccbadcaccaadaacadcacbdbaddbbcdbcaadacdcdbadbdcbdbcddddcdddbacbaabddadccacdbcbdadabacdacabbabddaaacaccbccbacacbddaadbbadbcbaaaadbddaddcadbdbaaacbbcccaacbacaaabdabbbaaaaadcdddccabacbdacbbdbaadbbadbcabaccccaccbdaacbabacccbccabbbcccbcbdcadbcccddbacdcbdbbbddbdcbcbacdaccadababdbbbaaaccbdaabddabaabbcdaaaabdbaccacdadbbbaaaacdabbdaabdcabbddcadddbaabddbaadbcaccabcbbbacbcbcbdcaacdabcabacccabcdaabbbabbacbcdacdabddadbdccabcbadabcbacaabcaaccdabdccdcccdcbcbdbcadbdadbabaabdbcbbdcccdbddcddbbbccbbcdddadcabccabbabddddcabbacbdadcbbcbaaacddaddaabcccbadbdaabbdaacdddcdbcdcbdbcadcbbdcbacbdccddccdacddbddbbbddcbdbbbddadddcdddcdbdcdaaabbadbcabacdaaabbdcbbbbaabdccabacdbaabcbddaaadcbbccacabcbcadbcbdaadcccbdcddbdbacccbaddbacccdcadcaacdcbcbbbcccaddaabaadcbacbbcbdcdbdcdabbcbdadcaaaabccdacaaabadbbcdccbcdbcdccdaababccccaabcadbdbbaaabaadcacdacbcbaabbadaddcaabcdcdaddbcadaccccacbdbcdadabcbbcaddcbccdcbcdcdaabcddbaaddddbdccddccbcdcbbbaacabbbddadbcbcdbdaadbbbcbaddaccbaabddaaacbdbdbcccabcbbdbccccbdddcbaacaaacbdaadccbbdaccccdcbaadbacbbcaddcbbddddaaabacbbbddaacabbbccdbdbccbdbcbaaddbbcdbdadcbdadbbbdaaabcbddcddbcbbcdddcdbdddcdcdddbccccacadbcdcccdabadccdbdcccbdabdacacaabadabbabadcbcbabddcdbbcadaabadcdcbbdadcbbcdcbbdaabcadbdcacbbccadddbabcdbddacaddbdbbaacaadbcdadabdccdcccddbbdcbdcacadbbdccbbbcdbdaababdcdbcbcdabbaacbddabcbdcbbdbdbcbdcddccaacabadbcacbcccccdcaaacdacdbcbaaaaadcdbacdddcadcdcbaadabcabaaaadaaabccbcbdccdddaccbbccbadaaaadacdadddbaabaddbdcdbcacacacdbdcbbcbcaccdabddbccccacbdcabadaadcdacbddbdcaacbbabbbabdabaabadacdccbbcbccccaacadcbcdbcbbdbabdaaaadcbbcacdcddccbbcacacdadadbcabdccdadcdabadabccdaadcbcddadacbaabbbadcbcacbbaacdcbbdccbccdcbbcdbbcccabdbbdacbcaaaadbacbdccaadbacbaabbcdabcdbcdcadbcdcaaabbcccdbddbadbbddaadbcaacdaacadcaaacddddaaacabccccbdaabdbaccbabbbccdbbbbabacddcabdddcbdcadcaabdcddbadabacbaddacabcdccadccaaabcbadccacabbabbbacaddadabcaaabdacbbdcddcccabbbbcbbabcccbbddabadaddbaabdbacccdccbaacbaacbacadcadddddbbabbdabbbcddcdadabdbabbcbdcdcbacbdbdadcbaacbdddadbdcdbbddacbdacaddcbbcdcadcbdcaadcacadbacbddddabdcbababcccbcbddcabaaaddcdacddcbabccaaadbacaccbcbddbdaabcdabbacbcbbcacbbdacaccbdaacdccdabcbddacabbabccddccbdbdbbbbddaabdaacadbccbbdbbbabcdbdacbcaabcabcdcbaddabababdbbadbdcadcbcdcbddbdadddbcbabccacdcabacbddcbcbdcacdbaaddababcaaadaccdcadccbacbbdcdbdcbccdccabbcdadadbbdddabcdccdaaacdcddbccccbcbabcadcbcdbacdcbadbbbdcccccacbdbdbadbabaacdbacadbdccdcdcdbbcddcaddddddcaaddcaacdacdbcbbadcbcaacccbcbadbdbbdccdbcdacadbcadadbcabbbcccdbcadddbacadbaddddddabbdddcdbcaccabddbbdcbdcbcdcbbdabbbcccaddbcbdaccacdadbaccacdaaaabacacabdbbbbbdccdbccbbaabacbcdadadaaacdcdacdcacdacbddbbdbadbcdbdaabbcdcadcabbcdbbacbbcdbadbadbcddbdbadacadccdaadaaccdbaabbacbbdaadbbabdcbaabdbbbaadbacaadcdbcbdcddaddbdcababccaadcddaaaaccdcccacaaabbcdabadcddbddcdbbbadaacbbbacadddbccdbabdcdbadaabcddcccbcbdaadaabcccabbcbcadbcbcbbbcbccbcdcbaccbccacdacbadbaacbccaccbdcacabcdbdadaadddacddcbbcddadcbacdaccccadacbbbaaddcbaddbcacbbdcbddacbbabacaacdddbdccdadabaacbbbcbccbbcacacabdcdbdaddddbadadcacddabbcaadaabadcccdbaccadcaccabbdbddbdcbccccacbabbcabdabbbbcccbabccbdcdbdddcadcdaaaaddadacdcddcdbabbbcbbabbaabaaacadbdccccbbccadcccccddcbbcccabcadbbaaddbadabcdccbbbddcdbaaacdaaaaabbddbbbabadbdcbbbbcabdcbcbdcaccabccbbacbbbddccabdcdbdcdccbddccaabdcddbaddcbbcdaaabcdabdaadbcbdbadbdcbbcbaabdbaaaacbcaacacdbdddacccaddbbddddabdbbdcbbdababcaccababbcadbbbaabaacdacaabacaadbcbaabdabdbdbbcbdaabddaddababdaddcbabbadcbcaaaddadcacacccdadddddbbabdbccacccaadbdddcaaacdadcaaadcbbddcdcbdabcdcdcdaaacbcdbdadabcbadaddbccbcbcdbdacbbcdbadacbdadadccbbdcabbcbbabbbabadbbaaddacaacbccbabaabbbdcdadbcdbbcabadcccdaadaccbabbacddaabcbcddcaaaabdbdbaaccaadaacadbacbdabdabcabbadcbbccbdaccbadbbadaccadcddbcabaadcdddddaadcbadbabccbbcacbdcccadddccbbbddddbdacaadcacdbadabacdbcddbcbacdbabaaccbbbbbccacabbcdcbbdbaacabacadaacbbdcddcccadcddcdbdaadabccbcacadabdabaaaccacdcbbbcdaccaddadcbbbaaadcdaaabcbabaadccaacdabcbadccdcaacbabaccdadbdbccaaabbcabccbabcaaaaddaccabacdabacbbdaacabddacacabcbbdddcbdddaadbcdbdadcccaaccbbbadacdcbaddaddbcbacdabcbacadbdcabbdaddbcbdacbacdbabcbabdcdaabbddaabbdccbcddcbdbbbcbddcaadbdbaacabbcbddcacbdacbdabcbddcbdaadcdaaddaaaabacbbacbacbccbbbdbbbccbacdcdacacaccccbcacdccbbcdadbcababadcadbbaccbdaddacbdbdddbcdcaaadcadacbabcbbdccabdcadccbdccdbadddddccddababccacdcdcbddbabcbccbbdbcbdcccaabaccbaadcabbbacdaadddacabcbbbcbdcbaccbabacadddcbcddbbcabacbbaacdbbaaccdbcabaadccbdbcdddcaabbbdbaadbccbdcbdbdbbaabdbabbabcaccbadccbcdcbdabbbdaaddcaacabddcdbccabbdababdacdbdcdbdaaabdcacababdaddaadbdabadcadcadabcbdccddbadbadbdbaccccbcdacbbcbadccbadbdabcacdaabcadcbdbddcdaabcbaccbadabcdbbddcddbdddddadbacbbbbabbbccbbdcccacbdbcdaccababaddcdaabbdabacadaabbaccdccaacacacdcdbdccbabbdddbbacdacabcaaddadbaabacadcbdcbbcdddbbcaaccabccccaabbdbcdddcdbcdcbccacbbadadabbddcdddadaadddbabdbddbdcadbdcabcaabdcddaaacdbbacdcbcbadbddcbaddbbbadaddddbbabbdccddadadcbcddababdcbccdbcdcbbccddaaccbcabdbbcaabccdbdcaacacaccddbbdccdbbcbadbccadbadabadbbdccddccddbccdddcdadcbacabdbdcdaacabaabcacacbbbabbacdacbccddcacabcbbdcddcadadbbacbdbbbaabdcddddbdbbbadcbacccbbacdcbaadababcddaabddbbcdadcccdaadcbdabbbdbdcccabacddcaacbcdbabbaabcbdcaacbddabbdbddaacadcdbbcdabdbdacdacddddaabadbabbdccdbdabaadabbbdcdadadddbcdbbacbcbccadbbdaccbdbacbacadcdaddaaacbddadbbaaaddccbdccdbdcbcccbdccddcaadbacbadbbadcdaabbbdbadbccbddddaccadddcaaccaadccdddaaddadbdacbadacbaadaabddadadbaddcbaabddcacdacbcacbdccbbbbdcccbdbabcddddcdcaaabadbaddabbdcaadadbddbddcaddaacaddaadabdcbcbdbdadbbcdccdcccbbbacbaadacbdcdadacbddbdbadabbbcdcdabdddbabbcdbcabcddcdaccdaadabaddadbbbadcdcdcbdabbdbccaaddcbccdddabdbcbbccdccababdaabcaaacccccbccdcddddcbacabdaaccacddbdcbdccbbbddcbdaacccccaddacdadbbbcbdacdddcdadbbaccccdcdababcbbdaaadbabdacbabbbcdbcddbcdcdacabbdcccdcdcdadbaabdddabccdcbcdddcdaabbbbddcbcadadbccbbccbbccbaaddbcaaaadabcacdbccccccbbaccaacaabdaddddccdbbbbcdabbbbbddbdbdbbcccbabaadccddcbacbbdcddaaabdccbddcaddcadbbcbbbcbdacdbcdbdcaabbadddaacdbaabccaabcccdacbbaadbabcbcdbaabcdbdcdbcdbaccdbbadababdcdbdcbbdadacaccbcccaaaaabdcbcbcbbbdacbcaabbacbaddddbdaabdaccdbbcdcdccdddaabdbcdbddadcdddbbbdbabddddbdadabbccbcbbcacbccccccdcbadddaabcbbdbbacaaadadbcdbacbccdaaacadddabccaacbaddabbccabcbccadccbabccaaaacadadbdccbaaabdccabdccccabacccdccdbcdbcccdcadbababbbdababaaccdbbbdadcccccbccbbaaadcddddaaabaccacdadaaddcdcddbababcbdcabacdcdbabacaaaddbacacbbbadbadcbadccbbbbbaacbbdcdabdaccdcabcacccabbaadbdbbabcbbbacdaabcbcdcbbdbcadbabacdababbbacaccaadbadcdaacacaaabddbddadadacacbcaaadbcddddddccacaddabcdbdadacdcddadacabbbadcdbdcacdacbabcdcbbcbadaadcbbbcbabacbcbaddbccaababddccadbacbcbbdbbbccadcdccdcccdcababaaaccbdbbaabbcaabddddbbdcbaddccbcdbcdaadabaaaacbbbaddbccbccbadbabccdbadddaddabdbdabacdcdbcacddcdadcddbcadcccaadabaabdababdbaaacabbacdcbccccadbaaadccbbcdaacddabbbdaacdaddacccbccccadbddbdbbbbbbadaabbdbccbdccbcadacdcacadccdddbdbbccdbabdbdcbadbcacdacdddddbdbdccabaddcbbdaaacbbcbacdbdaccbaabacccdbbbbbddbcdaccbabbdbacbbaaddacbdcbbbddbcdcaabdbaacddccdddccadbdbdcdaadcdbdbcdbabcbcdaddccbbcabbadcadcdcabdcbbababdaabbcddabdaccdbdcaaaacdadabcbabaabcaccbabbdcccabdbaacbbddcddcbbccbdbdcadbdddbdbcbabccdbbcbbcbddcccdbcbaaababdcdcbbcdcbcbbbcbacdccddccaacaddbadbdccbaabbaaacaaaaaaadbdcdadddabacabcbbcdddacdcbbcdbbbdaddbdadabcccdcbdcaacbbccaaacdbaacbbacccdcbcdbccacadbbaadbabcadadaabbcbaacadcbbdbacabacbcdcdccaadddbacaacdadcabccccabccbcbbabbcddaaaccdabdbdcbbbbacccbadaacacabdadbbadcbbadabddcddbabdcbbcadccddbbdbcdcacbccdcdbbcbcbadadcacbaacbcaddbcccbacdadadabbdbbdacabdcbccdbddabcbbcdaddbcbbbbccbabcacabaadaddcbccbcbaccbadbcacaacccabbcbaaadcabbbdabdbaccccadbabaaacdbadbddccbaacbacacaaabdbabbaaaabbdcbcddbcabbaaaddbbbaabddadacabddbadaddddaacdbaabdcabadbbcbababbccbabaadacabcdaacaadacbadadddaaabbcdacdbdaddadacccdadbdbdaabcbacccdcccdbcddaabcdccdadaaaaacddddaccbacbbaddbbdbddadbadcbbdadaaadacdadcbbcdbbbdcadacacdadabadcaddcbcbcdaabcaaaaaaaadaabbadbacdbdbaaacdadaacccbadbbacbdcdcabcaadabdbbbddcddccddcadcdaddcdbddddcaccdcbdcaaadcbdcddacddabbbaaacbdadbcdadcccbacbbbdbacdbcaacdbdaddbbdcaaccabddabddcdaabacccccdaadcabcaddbdacaaadbcbdcbaadbaacabacddddbaacbbcacbbbccbccbcadadcaabbcccadbbdbcacbcbacbbabaccbcaabdaadacadababdcddcbabaaaddbacdbccdabdadaaadcbddbabdcbcabcdaaccbbdddabdbddbcbaccddabbdcdbabdddccaccbbbaabbdbcdbababbacacdaaaaccddbcbbcbacabbbcbdacccdbddbaaacacbadccbcadabcbbdbacdddbaacabaaabadccdcdababadcdbbdbdbabaacbdbbddaaadcbcccadbadbcadbaadaacabbbdbcaadbcbdaccaddbbbdccccaabbbbdaccaccaabddddcdcbbaaabbdaabddccbdadbbdddcacddaacccadcbaabbdcdbcbacbabcdbdddacdcdaddcbcaaaaabbadbbbddababbcbbdbabcbdbacbaadbdbbbcbcccabdabaaddddbacdabcadccacddacacdccbdbbbcdbdcccbbbdbcdacbcdcddcbbdcaacadddabbcadaaacdcdbcacaacbbacddcccacbbbccccadcccbdbbcbdbbbcacbdccdacaaccddcbcabcdcadabbadbbdbdbdabaabcdabcdadcddadbbcdbaccaccbbacaddcbcbacadacbccccabdacabdcadbdcccdadbbbdcacbcaabaccaaaddccbddabdccdbbadadbbbcabdcbabccbbbcdcdaabacdabdddaddaaaabccadaaadbcbddcbbdacbcdcaabdbcdcddddddbbcaabbadabaadadddadcbdbacabaadcdcabdcabacacdacbbcaccdcbbcbadbbcbdbcdadbbaadbaabcabacbabcabccbbadbbdbbcdcacbacdcbbcdcbacaaacddcbcdadbddbccccbaddacdadccadaacdaadaaccbbdadaaccacddcccbddabcadbacaddbdcbbbdccccdaabddcddcdbadacddbaabcabcaacbcccdbabbbbaddbdaaabddadabababcdbadbacddadbbabadddbaccddbadbddbbdcdcabbdaabaacbdbdbdbcaddcdaddccdbcaaacbbacbabbbbabcbbcdadccdbcdddbbadaaccdaabcccbccaddcbbabdcdcccadcdddabbdcaadabcbbaacdadcacbbabcacdbccdddddacadabbcbddcdaadddabbcacdcbdcdaccdababdccaaadcadaaccddaabccbcbddcbadbdaabaabaabaddbccabcabadbaacdaccbdcdddbdbdbacaacabdabddbccdbdcabcdcddabacbdcbadabbcdbbabbdbbbaacbcbbdcdacaabbdbddcddacabdbcbbdbcdaddbbaadacccbbcababddbcdcacbbdaabaacadaabacaabcbaccdbbdadcabccabcdbbbbadabadaaadbbdcbbacbaabdbcdcbdadbaaddaaddcdaaacbbbdbadbcdcdabdbbbcadbaaddaccdacdbcaaacbbbdbdbbcddaaddcbbddcabdcbbdbdbababcbabdabdcbbadbddccdbbddddacdccbaddbbabccbcaabdaaaacbacdaacdddccbcabcdcbdcadcbdcacaacbbcaaddddddcbadccadbcdddddacbcccadaddbbbcdccddacaaadbabdaddcbcabacabcdbbcaccdbcdcabaadcabbbaccbadbdbbaddddbbccaabdbcbdbbbccadbabbbcccbbabdcbdcccabbdbbddccabcaadaccccbacbabcccbcacccbbbcbdcdcbaacbbbaccbbbacdddabaaaadacdddcaccabdabbcdaddccbaddcdadcddcadbadadabdabdabcbcabccaddcacbccccacabbaacccbaaabdbbbacdddadadccccaadcbacdbbbbcaddcddbdcbcccbaaabddbcaccdbbccdadadccdaabdadaaadadbabdabcbbcadcbddadadbcdccccacddcaaccaaaaccdaccabacbdcbdaadbaccbbcbccabccdcabaccbaacbcddcdbcaccbccbbbcccaaabacbcaabacbaabadaccdbdccbbbbbabcaacaccadacbabbacaacdddcbaaccbcabacdbbbaaddcbadbadddcadababcabcabdbcbbaadbacabbdcbbdbabdcbdacabbaccdcbacdaadcdadadabcbdbbbabadaaadacbddccddabadbabbbdadbadbdabcabdaaccadbacdccdddbacccbbbcbdbbdaccabdbccabdbadbdbdccccdbaaadbcddddadbaaccaabaabdabdcbcabacbadaadbccbddcaddacababdaadbbdbdabadccadcdccacbcbddabdcbaccbcacccadcabccaaaabcbbcddcabccaddadacbcbbabbccbadbcabbabbbbdacddbcacbddbdbccbaabdacbdcaadcddcdacacccddbbccabdbbbbdbcdccaaaaaaadccdbdbcacbbbbcdcaadcdabaddcdabddcdaacddccbabddadabacbcddaabadabbdcbbbbaabbbcabbdbcbaaacccabcdccbccaddcdbbbbabcabcbdccbbbcdabadcdcbacadbdbbbcaaabadbcddaadacadbcaccadcabdbbbbcdbdcbaacdbdbbaccccacacbbcadbaaadbcccccbaadcbdbbcbacddccbaadbcddbabcbbcbcdbaabbdadacbcdbaddbbbaaddcdbcbcacbccdcbccbbdccdadadbcccbbdbdaadddabcbaabcbccbbacaddddacddcabddaddddcdddccccbabcccbcacddbadddccabbaaaaacdbddabbbbabdadcadcdadcdbbdbdacdaaaaacadccdbdcacddabccabdaacdddbbcdabcacccccaaabadcdbdacabaacbaabdabdacdcaadbccdacbabadaccddcaadaccabcdccbadcacaadcddcdddabcbbacbbbaabbcddacadddaaaabadaabccbcadbacbdadcbbcbbdcccabbcbbbbbdbcbcdbadabbbbadabcddabdcdabbdbaaadaddacbbbdcbaaadcabcadccbaccabdaaaccabcdaaccdaaddbdadacacddcddcbbacabbaadbdabdadaacacdbdadaabdddabcbdaabcacaddadbaaabbcdabcdacbccaaddcadaabbcbbbccaadcdaadcdacdadbdadcbddabbbbdabbbaabccbacdabaacccbbddbdccdababddabbadbdbbaddbbbdcaaddccdccbacbddbdccaadccbdbaaadbacaaabdabdbadbcbcbadadbabadcbdaccacdddcccdabbdcdbdaaadccdbacbabaadbdaaabacdbbaaaddcdcbacddcdaccacacaacdbcabacbdccdccadcdaabbdbcaaadcddbdcabadcbbbcacacbddbcddbadcbcdcaddaddbcdabbaaababadbdbcdccbbbddbdbabcbcaadbcdabdaaddadcbdaacbcdbcdbcdbbbaddccdbddabdcaaabaadcdaaabdabdbcccadddbbbdcabdbdcacbbdadabbabccbbcbbaabddccddadcdabaccaaabbacdaabddcbadbacbddbcadabbcadddbbdcbaddabdddcadddcbdcbcccbbdcacccdbbabcacadadabdccbcddbaacdacbdbcdcdcacccbaaacadbbccbadbbdabcdadcacdbcccadacacdcbbccbcbbbcccaadbddadcbbcdbdadbbadbcbbabbcdabbcbbcdaabbbddddcdababbbddbdddaadacacaadabdddbccdabddaadcabbcacdaaadbdddcccbacbddcdccaacdadacbadbcadbaabcdcdcbcbbdbcdccbabcaabcaacaccddbbcabdaaadbdddcddabccdadbabcdabaacaaccbadacccbacdababaddbcbaccbadbbbddbbdbdcacabdbcaacacabcababcccdcbdabcaacbbcbaabdbcaaaaabbbacccdbddabcbcacddbdbdaacbcbcdbccdddcbccadbdddcdddadbbaccaccaacdcccbdbcbabccbccdbcbcdcbcaacdcdbccabdcaccccddaaacadacccabdbcadacaadadcadbbaacabbdcdcbbcbbdbbddcdcbacbacadcbddadbaaddcadddbdccbcbdcbddbbbdcbcdaaabacccbcbadabdcddbdbabadaddaabcbcccddcdabcaabcbcadbcadbdbccbcddcdcaddcccaacabcabccaabababcdddcadaddbbccbbdddddabcbbcdabadadaabccbdaaccdbbadcdcbbaacdcacccaccbaacacadcabcbbcbbcdbcdbcacabaccacacbaaadbcaddbdacddaabbddcdbcbbcbaabcdabbbbdbbabbdacbdaadcadcccbbddabcadbbbddaacdcaabdbdcddddcadccbbcbbbaacaddadcabaacccaccbdbdcacabdbdccbccbbdadaccdcaabdbaccccbcaabcdbadbcbcdacacdbaadddadccabaacaaadbbaadbcadcaaacdddbaddacdbaabcbbcbdabdaddbcddabcbcdcdbbcbccccbbcacabaaaddbcdddbabbcdccdbabbccdccaaddadcbddcabbdaaacaadbaacbcdbacdcbbccbcbbadbbdbaabccaaaabddbaacabdcbcdadabacbbaabbbdadbdabdacacaabbaddbcabbbddaabbcabbdabbbdabcdcacabbbbdbdcdcadaadbcdcdbdbbcddabbadcccabaaacbaccbcbbccbdbccbaaaaccbabccdbadcdcbbadabdbbadaccacbcccbbacddcadcabbcbbbaabbddcdaccbcadabdbbbacadabddbacdaccadbdcaadcacaccbbbdcbadcabdcddbaaadabdcbccbcccbccccdbdbabaddaadcbabdccaccddadbcabddbdddbadbcbcbbdbbdaaadabadcccacbdcddcdcadcdadaaadacdaadddbcbcadacbabaccdbcadabbacdacaaccaddbabacbdbddbcbaabaccabadbbacbddbdabdacccdbcbbbacabcdbcbccbbadaacdcccddbacadadadbbcdadbccddbdadcbacacbabaddbbbdbbabbdbacbcaccbbbdadbdbdbaaaadbbdbbaaacdacbacbdaacacdbacacbaaacbadaadddccabbcabbcaaabdccadbcacdaadacbacabbdbcdacdcdcbcccaccbcbabbabcabadcaacccccaacbcbdbaccbacabcacabdbddbcddabdaaabcadcdcadadcbabbadabddabaadcdcabacadcdccaddbcbbcaacbddcdabdbaadbbcddcabcadbdccdabadbcccbccdadbabcddcabadaadcbaaadbcaababdcabbaddabccdcbaaaacaaacdbddaadbbaabacaddccaaddabbdcacddbdabdadaacbdccdaaadcbbcaaaaadcadcddacdacadddadcacbacbabaabcddcbaacadddbdacbbcaabdccabaccbddadadbbabbdcccdaabdcbacababacdadcabaadbdbcacdcdbacbcccdbdacdbccabdadaabbabaacabdcacadacabddbbdcbaaadacbbcdcbdacdcccaabddccacbabdcaaabdaccdadbbdcabccbbddccdabadcbadcabdaadbbaabcddbcdccbbadcdcdccbdcbbccbcaadbbdacaaccaabaacccadacbbccbcdcddaadccbaadbdbccddddccccaaccbabdbddbcdccddcddcaccbddcacdacbdbcccddbbdcdcadcbccdcdacadcbcadbaccbbacbbcdadcbbbbccbbcdbdaadaaabcacadabdddacabddacacddddcbabbbaabccbbccabbbcaabaabaabddcbdabacdcbdadcbaaacabdbaaacbadccadacadadcbbcbadbcadbcdccccddcbdbadccccbabcdbcdaccaaaaababdcdaddbccbbbcdabbacbccabcbacbaaaacdaadbbcabcbddddddcccabdddcbbacccbacbadcccbcadcdddbdabadbacacccaabcaacdcdbdaadccbaabaddcbdcbccdabbccadcacddbaabcacccdccacbddacbdbcdddacabdbcdddcadcabacaaddccccddbbbcacddcbdbcbaabaadabcbaacdabbabaabacddcabcbbcdbbbddbaacbabaccacdcbaabdbacbabbbbbdbcaddcdaacdabdbabdabcddbaabbbbcadadcbbbbadbbcdabbbbdbcabdacabbccdddcbdcccbdadacdadaabdbcdcadcaccdbbdbbdbcbdabcababacddccbddbdbbaacdcaabddcddabaccdbacbaadccacbdacbaacccbbbadaccbbbcdccbbbabdabddabcbaabaaaacddccbdcccbbdddabbccadbadacbddcacaadbcbdcadbdccbdbaadacccaddabbdcdcbccccdbbbcdbcbddcdccbbbcccbbbadbaddbdaabaabdddaaaaaabacadbcacdbbcdddcdcbcbadbccbcaadacaabddabbbddcdcadbdcddcddbdaabcbcdcbbacdddaacccacbadcddcccdaadccddddccccccaaddcababdbaadcaaaadcacbcdccacdccddaacbddadcddbbbabbcdaadddbadaddcaccbccdddcdacaaabdbcdddbdbdabcbaddabaccaddbbadbbdabacbbadcdccaddbddbcbdddbadbcaaadaaadcbcaabbdccdacdbaccbbcabadacdaadcdadccdbdddbbcdccccbcaddcdccdbdbdabdbcbacbabacacaccabbcaddaaaadaccdcaacadcbcdcbbbdbacdcadabadccdaacdbcbdacabdccbacaaaccdabdbcbcadacdaaddddddabbdabaacbcdaadacaadbbcaadbaababaabcbdbddddadddbcabdabccddbacacacadbdcbbcdaddcddbdcccadccdadacdabbcdddadddcacbdacdccccccddbdbdabbabdacbcdccbccccacbbcbadaccaaaabdadcabbabdaabacddaaacacdbbabccddbaadddadcdbbbbbdbddcacaabcacccdcbabdbcbdcdcdabaacdacbcbabcadcaabbdaacddbbabdacaaccaadadddadddcbadddcaddabdccabdbccabdcaccbccaadddbacbaddaabdddddcdaaccbdadbaaccadccdbaacacacbccbcddabcbbbdccababccaabbababacabcbdcaddcccadddadadcbbabaccdbacaaadaacdcaaababdaadadcdbabcbcadbbacdccddaccdcdcbcdcacbaccdaacbcdadaacbcabdcbdbdbdddacbdbbadcdaabdabdcccbccaaabcadacbbacdbcddbddcdacaacabbcccccbaaabaaadaacabcbcabacbcabbaddacbcddcdbdbaaddadcdccbdcbcccbcabcdbaadcdcbadacdaccdcabdbaddcdddbcadbabcbcbacdadbddabdabbdadcccdcddaabbbbbabaaabdbbddbcbdcacccaadcacdbcccbbadacdcbbcbbcacdbaaabdbdcabdbabdadbcabacbadbaabdcdcbabacbabbdaacaccababbbadccbadbbcabcadbcadddcacbaddcbbdabdcbbddcbccddbbbbcdcdbaccdcccbadbacacaabbacbbddababdbaacbcdbabcadadacbcdcbbbabcdcbbdccdcbbabbadabcdaadcbdcbacacabbbabcddcbbcaccdcabbdadcddbaccabcddcbcbbbdbddacccccbbccbbcbdddddaabbdaadaddbdbabbdaaccbbbcccbdbacbadddaccbdacbbcbcbddcbdbbabdbcadcaacacaddccaadddcbccbbacaddccccdcbaadbdddacbacbaabcbdcbdcbabbadddabdbbbbbcdcdbdbcaddccbbbdacbddbdbcccdaabaaaacdababcbdabcdadbdbcbaddbbbccdcdcdbbcdbcbadbacacddcdcbbcaaabbcbdbbdcddabbdcbbbcdccbdcbcdcdcdcdcdbacadcabdbcdbaddbcbcbdbdacdbabbcdaaaadaccacdabaabcbbbdacaadaddabbdbaabcccccbaddddcbacddadbccbcddcdcbadacacbdabacabbdbbacbddbbbcaccbcdadcdbdabbcbdadddbcbbdaabaabcddcdcdacbbccdadddabbccadbdddbcdbbbdcadbbcbdbbbbadabaadbadabbacbbadbddaadabacacaadcccbcbdaadabacbbabddbbabbbccacacaddbdcddccaadcabdacddaadbabcbccddacccacdabdcdcdbcacbcacabcbadccbacdaacdcadcaccddbadadcaaccadccaddccbacbaabcabbaacbbddcbdccccdabadddacaadbcadadbcdbccbabdbddbcadccdbcdbcbbbacccdabaccccdabddabdbdccddaabadcdbdadbaddbabbbddaaddddbbdddcdccbbcbadadcddddccdbccabbbcbbaabbdbdbaadadaadacdcabcabddbcccacbccdcabdcbaaaadacadbacccbadabcadadcdbbbababdaddacdbdcdccdcddbadcaddbabadabdbcdacaddbbaacaccbacabbcacdabacbaababacabbbddaadccbbdbcaadcdccbbddccdbacdbbdccabcdadabcaddbbcbbbbddddabdaaaacbcdddcddddbddacdcaadcccadbdadbaaaaaadbdacbabbadbddccaaabaacdcdddcadabbadabbabdbbbddcbdccaaacddbdabbcadbaccccbabdcaccbcbcddbcdacacabbdcacbadaacddccbbbddbcabdbacaddaccbadcbccabbbabbbcabcbbccddadaaddadccdbadddbddabcdccaccacbbdaaacaddbcaabadaaaddbbabcccdccbbbbadaccdaacadccbbadbabdcdacdadbdabcbccadbdabaccdabbacddaaaadccadddbcbcbcdbbddbcbbcdcdddcacbdccdacddacbdcadbacbcbddbcddcacadbcbcbdbaadabbbbbcababadcccccdadbdcddcacbaadcdbccababcacdbbaddbaaccadaaabaacbbaabdabbdaaaccaccbcadcdabdadcbdcbabdaaddabaadddcbcbacaacabcdbcddbbdbbbbdcacdcdabcccbbbaadaacdbdbddaacccddcddbdabaccbcbcbdabacbbdcdaaabcadbbbbcddcdaadcccbcbaadcbdcacaaddaadacbdcabdccddcabdddddbbdcddbaccbbbcbbbbaadaadbbccdaabccdaacddcacaabddaddbadcaaadddccababdbccbddcdabbbdaaabcbcbdcacadbcdcdbccccabbbcbacdaacdaddaccabacdbabddbaccccabdabdacbdcddaabdaadaaaadcaadbbcdcaaccaaabbdbabdacdaaaabcaddacbabbbacadaacbccccadbabbddaccbdcbdbccbdbadcbccaacbdcdccabccacbccabdaaaabaacdcdacabcccaaaaaaaccadadcbbdabcbacbbdaccddbabacadcccbddbbdaabddddcadadacaaabdbadacbbdbcccabbcbcbacabdaaaaabbadbbdcabbabdaddaaadaacbcaadccabcbcddbaddacdbbcaaaccccaccdbcdbcdddabadaadabcccbdbbacbccccaadccacadcbbadddcddddcbbbdaacdbaaadacbbdbdcadaabddbcbabdacbdcdccdabbbdadbccddbbaabccadadacddabdaaddabaabdbacbcddbbbdbacdcbcaadddaabdbabcbacbaadcbcdbabddabaadbacabcdbcbdcadccddcbddbccddbbaddbbcabbaccabcccbadbcdcbdccacbddbdaabacbbbaabbaaabcdddbbbadcdaaadddadbacaabdbbbdbbaccdcadcbcbbbbbdbdabbcddcdaadaabbbbcdadcbccbdcacbacdbdabcbcddaddddddcbcadbdbacdbbaaaddcabbacccacdaddadcbbdddddbdadacbdddbddbbdbabcdaabbcdcaaccbcbbbbdabcddadcaabcdcaadcacbcdaababdcbbbcdcbdbaadabbcbcadaabbabcabbbdbbcdacabadbdbadacabcbcbcbccdcaccaccbacccaadcbbcdbcdabadcabdbabbdadbacbbaccddaabbcddcddaadbadbcaababccadaddbddaacacbacbaddcaccbddbaadcaddaabccccacbabcbbbbbbbdacddbcdcccabbcbbbcddabcabbabbbddbccddaddddacbbdabdcbdbadabcdabbbdbbdddacacbcabbdacabcaaddcbccbbcccdddbcbcabaccdddcabdddadbadaccaadbddddaabdbcbaaddbabcbbdddddccaddcaccbacacccbcdbdddacaadcdcbdcddbcbbadcdabdabcbadbabdbbcccdcbcbbdddddcdaababccbcddcbcbdbacdcdcabcdbdacdacbadbbdbbaddabdcdabacdbbbaccdbddbdcbcbaaacbddbacbdaddcbbbcabcbcadcdcacbccdbbdbdddcdccdacbccddacdbbddaccacbbbcdcdbbccadaabdaaacaaadcacaabcbcbddbdbbcddbaaadcdcacbdaccadabcddcdaabadbabadbdbbccaabcbbddaddcadcaacdbccaddababacacbcdbbabcdbcaaaccbdaaadabcdbbbbcbacadacdbbcddbcbccdbccdabdbddaabddbdcdadacabdccabcbdaabccdacadcabccaabbccaccadcaabbbcababcdcadadbbadbdbddccddcbddbbccbcabcbbcdccabaaaabaadabcbcabcbacbdccbbadababcbbdcacbbddcddcbbbdbaadacacaacdcbaacaaaabddacaacbcdbaaddccacbbdabdcdabbdaddcdbccabbdbbdaacacadadccdcabbbddaaabbbcdbaadcacadccaacaacbdadbddcdcadccbdbbbbdadbcbbabddddacbdbaadddccdaddacdbadcddababccadbdcacdadcccdcbcadaaddcccdacbbadcddabdbababbbadddcbacdacacdabacbcddcadacabddcdabcbcabaddcabdcbabdbadccdabbcdbbcaabaaccbcbcadadccbbbcbdcbcccaadddacddcbddadababbbdaccbddbabbbdbadbaaacbdadbadcbadcbdcddaabdadbdbccbaccdabaaacdabaaadcaccbcabccdacadbccdbcddacaacddcbdbaabbdcabdddaddddcabdbacabdaaddcacbbadaddacacadadaddbcdadccbccbaadccdbcddbddaacdaaacabacdbccdbcacdaabbddddabdabcaccdccdcababacccabddccdbcadcadabbdaccdbabdbbbdbcabdccabdbcbddadbcdbadbcddadcacaccabcbdaacdacdbcadabdcbaadcacccbbccaababccaccccbdbaccbcbdcdcdbadbacaaadddaadadbdcaddbacdccbcbaaacaaabacbdbbcbcbbbacccbaadabcaaabadcbabddccdbdaabbddcddbadcbadbdaadcbcbbdddbdabbbdcdbbbcadcddcabcbabcdcbabbcbdcddbbdddbbaadccdbaacdbabbcdcabdaaaabaacacbbabccbdcdcaadbdbcbbadddabdcbbbcdcddbcbdcbdabbcbdadbadaaadbabdcbccdcbccaddbddacaaddbabcdccdbbadccbadbacbcacabdadddbaaaaadabdbbcacadccbabadadddadcaaaadcbabcdcccabbdbcbadcbccaccddabdcddcbdcaaacdcabbbaabdccbbbbbbddbdaccbaccdccccdbaabddcabccbccdccaccbcbdcabccaaacbdbabdbdabbbadacaadadabdacbbbbabbadaababbcdabcaaacdadcdbcaddbcadadddcaddcdbbddccbcabbcdbdadcccabcbcbcdbcabdbcbdacccddcdbdcdbbacaccdaaddcdcbbcdddaacdbbbcbcccbcbcdacbbbaaddcdcccdcdcabcdaddcbadacdbcbaaacddccbdcadcaddbbcddbbabcbdaacbcbcacddcbcaadbbdcddcdcabcdbaaddcddbababbbcbacddbaadcdddaddcbbcaddcdcdcdbadccdbcbacaadbbacddcdbcbddcccbdcabdcbdddcdabadddccabcadcbdddadacbcadccdbacaccacbabccbdbcacbcdadbabcadcabcacbbbadaaaddbdccddbcccdaaccdcadaabaacabbbdbddbdcbdddcdaadaccbbaadbbcdadcdaacddddadcaccaacbababccaabcdbaabdacccaacbabbaacbbcacdbbdbbcbbadabdacdcdacdbdabcdaccdbcbabcacdabbabaddadbcbdccabababddabdbaccababacabbdbddbbdbdaaddcbcaaabaaaaacaaacbccaabdccaadbacdbcbadbaabdcadbdbcaccabacdcbaaddabcbcdaaadcbcdddbbddbbbdccbbabddbdbbccadbcaabbabbdbabbdbdccccadcadddbccddacaddcdbdbbbbabcdcbacadbadadadbcadddcdddbccccabadcabddcddbcccdbbdcdadacdadbdacadcddbccbddcdadbcdadcacabddaaccbbbbcdadaabdadcdccdbbcdcbaababdbdbddcdcddaabdbbbbbccdaaacaadccbadcdcdaacdbddddaacadacbdddbadcdbcacabcdabaacaaacccccbbdddacbdbccabdacaaccbddccadcabaaccabbadaacbbbcddcbdbdabacbbcdcbcccacadabbcdbaabbaddaddcbcaabcaaaacbdbcdcbdcddacaabdaabcbbdbccdcbdcbcadadcdbadbcadacbcbddccaabbcacadcbcccccdcdcdaaaccbdbadbcdbbcdddacaddcbccccacbacadabaadabacbacccdbcabccdbcbddbddadbdcaddddbddaabcdbbabbdadadadcaccbcbacbaabcdacdadccadddacccabbdcbcbbcacddcdaccaabddaccdccddcddacbbbbabcaacadaabcdadccabccccaacbddadacbddadaaabaaacbabdcadaddbccdacaabdacadbccaaddaabbdcbbbadadbbdaacdddadbbdcbcdbddcdcbabdadcaaacddadcdbbdbadcadbcaabbccaaabacbbbcbaddbcddcbcccbbabddbbdadbaaababbbaacbbddddcbdaccacbcbbcaccbadaccccccdabacaaccabcddacaaddcdadcabaacdbcacbccbdbaacbdadcacaccabbdbccaddcbbaacaaadacaaddaadccacddbbadddcacbdcbaadcbbcdcbdbdddabcbcdcadbddcadbccdbadbbcccccbacadabbcaaccaaadbabcaabbadddbcbabbcbdcbcadaababdcdcdcaabcdcacddaadbdbaacbdbabadcdcacdbbdcbaaddcbbbabbdbcaaccbcaaacacbccddccbdcbccaaccaadcaccbcadbdcdaccbbcdaacdccdcbccaadbdddbccbbbcbbbbcbccbcacbbaccdaccaadbbadbdaccbcacabaadcbbbdbacabccccbcdddabbbbdabacbaddccbcdcbcdcdaacbaacccaaccbccdabacdbacbdbbcdcadabbdccbcccaccbaddbdaabdcbdaacadaacdbccdbdaddbdbbbadcbbcbaaaabacadaacdbdcdacdcdbabdccbadababdcbacadccdacccaaabbddbdabbcabbdabadadcabcaaddabcccbcacdcbbbdbbadbdcbcacacbddbdcdbabadadcdbacbcbbdacbbabaddccaadcdbcbddaabccaacccaadccbadbdbaabacaacdbdcdcbdccbabdddbdbdaacabbccdacadbaccbccaccadddddbdabadddcaabcabadacadcbaadbaccabcdcadddbcdccdaccbdcdcbdbbabadcdbccabddccbadbcaaaadbdadadaadbdadbcdaabacddaabbbaadbccaacbbbabcccdcbbadcdcacbacabbdbbbdcdabdabdbddcdbcdbdbadaabaaabcaaccbcbbbbccbbcbcccbdadaaacdcbdadccdbcacbcbbddccdcadbbacdaddddbdadddcbcadddcccdcacbcaabbaadaccbaddadbccddabaddcaddcbaabcbcdbaacacbdcbdcdcbbaabbacdcaadcbadbbddcabababdbcabcdbbdadbbcbadacbcdddcabcdacccdaacdddaabcdacddddddaabcaacabcbbdcbcddddaadbbadbbcbddbcaacbccbbcdadbacabdccbcbbcdbddbaabddacdcdcdaacdcabaaaabbdadabdbbdabdcacdbbdabcadcbcbcdaadaadaadddcadccbbdbddcacacbcacdbadbcbdbbbcbbbbdacdddcccadbaccdacdbdabdcddddbddbbbdbbdacabbadddbacbccbbcddddbdadcbacbaddbcbdaddddcabdbdddcadadaddccdcabacbcbbddbdcabbbabdacdcddabcdcaaadadabdadcaccabababcddcbbdbddccadddacbadacddabacaabcdbcdbabacaddbbdbbaadcbdbcccdbbdbdbbdbabcdaacddbdcadbaabbcccdcadababbadcaccbcddbddaacdadaabdddcbbdccdaaaddbcadcccdbbababcbdacabbcbdaaaadacdaabcddbaaddbadcaaabaddccdddabdadccdccbbbaccbcbcccbaabbbaaccdddbcabbdcaaabccbdbcdccbdbdababccabbababccbdccabccbdaacaabacbddbacddcbbacbcaaddccdaadacadbccbadabcdacaabadcbacbcbdbacddddaddcadcddddbadaaccdaaadbcabdbcdadbcaacddcddcabbabaccacaabbaccdccddabbcbdccddaacadadddcbdabccadacbdbbacddddcdbddaacdabadabdaaaaccababdacdadabacbbbcccbaccdcdabaccbadccddbcadcabbcbccbbbccaaaccbdaacaabcccabbbadabcdbbcbbbcbccabdadddaccadadabccdabddcbabcddcdbbcacdadacdbbbbcacabdbbacdddbacadacbacdaccddcbdcaadbdcabdbddbaacabbdadbaddabbdcbaabaabcbcdbbccadaccbdbdbbccadbdcacadbbdbcdaadadcdccdbaccaadcbdadccbdaccdadaccdbdbcbcbbbbbadcdcbaaadccaaddbdbcacbccccaadbdbadbddbcbbdcccbccacaabbbcaabadbababdbccdaaabaabcabdaaaabcddcdcdbaacdadddbbbbccbccadccbdbadcabcbcdbddcbbdaddaabdabcadcdcccadacaadacbdcacbbacbdbbddacddbdabcdbccabdddbbcaccaaabaadcacccccadcbbcacddcabdcacbbbdbbbbbbdcbcdcacadaacbdabbadccaddcadbdcabccbddacbcadcddbcbabcaabdcdddcabcdbacaccbabcdbabddaadadcdbaacbcabddaababcbacaabdacdadbcdbbcbcdbababadbbbdaaacbbbacbacaabbcbadcbbacaddbbcbadccacccdccbdaccacaccabccaaabdcccdaabcbacdacacccadddacdbbacbdbadbcadcacbbacdcbbaaaddcbacdacddadbdcacccddacaabaabdcadabdabccdddbdcabadccabaccdaccdaabbaabdcccdadcbabddabbdccddcbdcbabddccbdabcadcdcacbcadbcdcacddaacbcbdadcdcbbcaacbdcbadbbbdaaddcaacbdbcaaadddddadccccbbbddbdbdcdddbdacccccaadcbbdcddadbaabdadbdbdcacbadcdabdbcdbabbcdcccabcabdcadadacbbcaabbabdccacaacdaacdbadbccaaacddddccdaaacdbcadcaacdbcaccddcdcbcccbdddbacccacacabbbcbdbdccdbadcdacbbcdabaabcabadacabcdacccacacacbccadabcbddcdacaabacaaccabbcbaacdcdbdbcadcbdaddcdadcdddabdbbbbbbcaccbabbcdbdccbcbbacbcaaaaadbabbacbabbdcdacacacccbcdbcdddabbdcdbccbaabbabdcdcdbddabacadbdbdadabddaaabbbbdbddddaddbbaadbadcdcbcccdbbbbdbcdcbacabbcbbdcdadaadaaaabcbabbbcaacacabdacbccbdbcabddaabdbcbbabddcbcadbcacdbcdabdcbdabbdcbbadadbbacabadbbaadaaddddbabbdbbdcabcdbdaadabdcddcdabcadaadbbcabacdccdcddbbcbccccadddbbaabbdbaccbbcaadacbacddaaccdddabbbaabcdcdadabddcdcadbccaaddabddddacbdaccbbdabadadcbccddacaccadcbcddcdbdacaadcdbbabcbadabcdbabdbacbcabadcbdabdbcddbbdbdacadbcaaacccabadcabbdcbccbbbaabbcbcbcbcaaadcdcbdadcbcbbadcadbadacadacdababbacabaacbdbadadccdadbcdcbdadcadddcdddddbbabacdcbbddbcdadbbbbdbdbdbcdcbcccabaaaabbacabdbcdbbacbdddcbaaddcbcaacbbdadbddabcabdbbacadddacdcbadadcabcacbdbdcabbdabcadcdbdcdcdbdddbacdbbddcadabaddacabdabcccabcaaccbbbdcdbcdcdbabbddbacdcbbabcdbbcaccabcbdbaaabbbccbabbbaacdccdadcdbdcddaadbaccdcbcbbcbababbadaabbbdbcbabbcbabbaaacbbadddaddccabccbbccdccbbacbbcdcabdadabbcccbdbdbbbdbddcddbcacdccdcbacccbababcddbdcaabadbcbdabbbdaadacccccaaacaaaabdcabacccaadcaadbdddabcccacacacddddcdccbcbcabbdcdacadabadcbdbbbbbdbbddabddcbbcaaaddbbbacbdacddbdabbaccccbcdaaccbbbcbcabbdadacdbbcabccaabcaddadaddcddbadbbaadbddabbacadccaddabbbcabdcccaabcbbdcbdccabcbbddcdccadbbccccccabbaddabadddaaadddabaddcbabcccddbbdbdaddaacbabbdddabacdcaaabddaddadbbbaaddcdddbdbbadbcabbcaddbbdbcabdccaacbbdbbcbcdaccadadbdbbcddcbbccdddcdcbbccbbacbbbcbdbcaadcaaabbdddaddacacaacbbcbadcdcdcaadabbabbbadacdabbbbdcadcccdabbaccbdaddbbcababcdcdaabacdaaaaacadbdbacabdcdaddcbaabdcbddaabcabdbcabdbdbddcddadcbadbdaacbdbaccdcdcbccdababbaabdadaabcdbcaccacdddcbcbbaabbaadabacdbacabdbaaddabacbacbbaadcaadbbcbbdaccdacbadccdddbcbbaabbbbddbbcdaaabbbabdcbcbaccbacdabacbaadcbabdbdccababdccacbbcbbadbadabbbadddcbabbcdabdcacadcacccbbaaddbacacbaacbcdbcabddccdabddcbacbdcadbcaddcbcdbdccdabdaadbcbcacacdccbdcaababcccbdbccbdcaaadbdccdddabbbdbcacdcdadddbaddcbbacdbdcdcdabbbcdcdcbbcaaccadbadcabbadacdaaccabddccaddacbccacbbbdadaddbabbadcddbccbdbccbadddcbcbabaabbbbbadccbdaaaabadaacaccbbcacbcbdbcdadddadbcbbcbcbabddadadddddcabacccdddcdadaabaadaccdcdabbababcbabdbacbbdadbbabaacdddabbcdbbbdbccdbacbbcbbdcdcbccdcacbcddcaabddccccaddadbbbadacdbabcaccbddabaabbdcdbdbcdccadbabcdcdacbaaddcbbddaccacadccbdacdaacdcbbbbcbcadccacccabbbbbcbaabaddbcaacbadbcabdadddaacbaddadadbcdcddbcbbdbcbcacddabcbdbdcabcacdbcccdddbcbbdadaaddcdaccddbcacdacdabccaccdaccadddabcaaadabbdbcbabccccbdaccbbccbabbcadcacbbccdddcabdcdbbbcaaabcdddbdbbacdbbbdbbbadbdcbcaadbbdbdadcccdabbbcbdddcbdcbadcabcbdddccddcaddbdbcbadcacccbcdbbbadccdddbccdddcbcbdbdbbdcadaabbdbcdacddaddcddbadaacabacdbcaacacddacbdbcccdbcbcbcaadabbdadddadccaaaccadccbbdaacaaadcdcaaaaacccbccdadbbcbddbcaadadaadabadbaacdaabcabbcaddcabcbcbbaccaaccabacadbabddcababbcabacbcbabbbbccaaabbdbacdaccddcdbabcabacdccdbccdacbbcabacacbacbcdbbcdbaddccbdabbddacbaaddbdddbdabdabbaacabdccdddbaacbadbdababaaaddbcdcccbadaccabaabccbadbbbbbacbdaaccddaadaacabbcabdbddbaabbbbacaaadcbccccbdbaddcabcbbaadadbaabdacbdbcdcabdcdacccdbccadbdcaaabbbaccdcbacbcaddbabaddcbdbccacabbdcacdbaadbddcccdcdcacdcbaccbbddbcccacabacaadddbdcdaabdabcaddabbbbbbbbccabccdcbdddabcddcdbdccaadabacbadadcbacacabcacdcdaabacdaccddcaabaadaddacadcadaacbbdadbbbdbadbbaaadbcdbcbcddacbacabdbccdcadacdbbacccacaaacccbddbcddbddcddcbcabacbdbdbcbbbbbbbbdacabbbbcadbccaadbdbcbabbadcdbaaaaddaccdadbadbdddbccddbbaccdabaaacbabababbacdccbbdaccabbbbadabcaddabccbcadaacbaccccbccdcacbadcccdbbabcbdbdaddadccccaccdadbaabcabdabbdbbbdadabcbcabadadaabadcbdabbbaadccdbacbdcdcacadbccabdadcbdcadbbbcadccbcdaaddbaaaddbabddaabaadcbbacdcdcdbcbcbaacabcdbbcabdcbaaabbcabbdbddaacadababddccbadbaaadbbadcbccdbcbddcbcdcdadcdcbdcabadbaccbdddbddcdbdbbdccbaccdaadcddadacacacddabcbbdbddcbaaaaacbbacadadcbdcaabbbbadbbdbbddacccbdacabbcdbddacdcabadbcdacddacdbcbadaacbcbcbdcabaacccbaadbacdbcdacabccdddbdabcaaadcaadadcdccdccbddaacacbcdacbadabaccdcaddcacbbbbbadbadbbacacbbdaabdbddaaaadcccbdddabbabaaccbcaccbadbadacbdccaacdbdaddccbbabcccacdbcdacdbdabbadcaaaccdabcabbbabbbadbcbcdbbcaccdacccddcbcabbbbbacbaacbbabddbcdbdcbaadacbddbddbccaccbccbaabaccdaddadcaadacdbdccbbaadbddaccbbadcdcbaddabcdabdbbcaacabaccbaababdbcabdbaacabdbccccbcbaadbbbddbcdbdccdbaccdabadcdaccaaadccdbdcdbaaaddbcdccaabcaccdcbcbbdbddacadabaaabcaaaaaacbadbddbadccbacababbbabbdaddacacbccccccdddbddbcbdddbdbdbddcccbaadaddbbbcdbdabcaccdcabacbcbaaacdcdccabdddcaaabadbabbaacdadabcaadbdbdbcdbaaaddcadcbddbacdbbadcacdbccccaccabbcdadaabccacbcbdacdcbcdbbdaadddcdbbdddcccccaaaaacdadadbacdddcbdbbcdcadbdbdddbddbddbabcbbbcdaccaadabccbbdcabbadcaccbaabacacddabaacbbdccddcccdabdabbcdabdaacdcbdaccbdddcdcbaaccdabdbcdbbdcaababdbbdbcacabdccdbddbacbdbddcadcbdddccdccbbcdcabacdcbccacadcdaabccdcddddbbbddaddbbadcadcacbcacaddacdcbbbbaaadaddcbbcdaddcddcabadaccdaaaccbdaadacbaccaddacbabbcaccaadcadaccbadaaacbadbaabdcdcbcacabdaaacdcdbccaabcccbacbdbcbbddadbacbccddacbcbdbccbdddaacaabaadbbabcabdbcadaaadccacadabbaadddbcacbccaccacbbddbbddaddaccdbbbbcbaaaabcdaabdadbdbbbccbbabdbbbadaddbcdbccbbcddbbbabbdbaaabadcbacabdabdadcdabbdcbccdddbdbcabcacccddcbabaccdbbbbbbddbdcbbcdddcdbccaaabaddbaddcbbcaacbccccccdbaaadccbccbdbaaadadddadbcdbbaaaaadaacdbdabbbdadcbabbccaddacdbadbbcdbbcaaaccbaccbccdaccacbdadabddabaaaadbadbdddbccdbacadcdababdaaaddbcaccacbddbabaabbdbbddaadaabadcbbbaadadaacaddabbdbdacccbdcbcadadcbddadccdacdbdcaaabdacbbaddaabbbdcdaacbcacddadacdbbccdbadacaccdcaaabcbdcbbcabdbccdbcdcaabdcbddaabbdaaabcadccdcbbcccbdabddcdbbcaddcaddbadaccaabcccbaaaaacabbcccccccadcbbdbcdaacccdbabababdadcbbbdacadaabacbccbcbbbcaadbcdadaacbcdbdbbbcdacdcacadadddbdbabddbdddbaccbbbbdcbacaabccacdcbdcadadcbcbaaaabdbadbbccdbcdaabaadccdaddaadcaaacaacdccbdccadadbbcdbdbdbbcdacacddcbaddaabadcadbbaddbddddaacbbcddbbcddcdbcbcbddbacacdcaabdbdbdcaadadadabbbadaacadbdcbcbbbbadcdcbadbadcaacdccdacdbdaabdddccbbbbddbaacccacadcabddbacddbcaddaaaacadcdbadcbbdacbcdbaadbcdbbaacdddcabadadccbdbbbadbccacbbbdabbbddaaadcadacbacadabbbaccdddcbaccccddddacaccadbbdadbcdddcbbaadcbdbcabadabbbbaacbbdaccbacacaadccccdcacbcababcdcaacdcbbbdbcdbaadbbdbacacabbcaaaabbbcdbccccbbaaabbabbcabababcddcacaabdcdbcadaadccbcccccaccccbbccbdcbadaddbbaaadddbbbbbcbbcdcacbcacbdcadccbdacbccdcbdadadbbdddcdaabcbddbddcbddadadababadcccccddcaabdbbdcbdaadddadccabccabdddccacdbddadbaacaabcaacacbdabcaaaabdbadccaacaccaadcacbadbbabcbdacbdacddddacccbcacabccaabbdacaaccdbdcbcabbbbbdccbacbddabbbddccacbdabbacaddaabcdbaaabdbdabdacdbabbcbdcdaaddccaaabcdcabdaacaccbdcccdbabcadcccccbcdabddaacaadadccbcbadabcbbdddddacdbadaabcdbbccadbcbddabcccbacbbcadddbaddadddbdcaddcdcaadaaaccbacccdadbacacbbdbcaccddaaacaabcaccbddbdacbdcacbbaabbbabddcddaadaccdadaadaaaddacdbaaabdabbdacaadbadaabdcdcddbbbcbcaadabbddcbaacdbcccbccdbcddcdcbacdbdaddbabadabbabdabcababcaabcdbbdaaadadccbcdcbdbbbababccbbcdcbabdaaabccaaadbcbcaddbbbbdacbbcdbcdadcbbbdaabcbacdcaabdaaddcaccbbccabadaddaabbcdcaacbbcbdcaccdbaaccabcaddaabcbbdbacbbbcacabdbcaadbdbdacdcdbddccdcdbdcdcccdcbbdbaababdcbbbdcdcbcbcbccadaabdcbbcdaaacdbcbdcbbcbbabcadcddbbbabadccdadbbccbadbabdbaccabcabbbddcbaccdabbbdbdbbccbbdcadddabcadabccabddabbcddbdbcbbbbadcacdcccbbcbacaaaadcbdbcaccadabcccabbacddccacdadbcabababbcbcdcccccdaaaadbcdacdcdbcdddbbdcabacdccabaccdcbaaadbdadccabddbccbcbaaddbbcbacdcbcbadccaddabbaaccbdabcccdccddccbdaddcbbbcabbcbcbdcddddbbcccbccacdcdaddcbdbadadcbbaadbbaaaaddbbcdbdbbaddbddbbbdaddbdcaaaadbaabbabbddccacacaccdcabdbadcdbdcdbcaacbbdcccdaaddbbacddadbbdbadacdddadcdcdbbacbdaabbabbccbbcbbbdcacacdbdbdabbcdddaccabdaadccdaccabadbbabbdbacadadbdcbabbcacabdbbcbababbcadadbcabbbacbcadadadacdccdcaaccdcdcccadbcbdccabbdbcbacddbccccaccbbccccaacadbdccbddaaaacaacabababcddbbcbbcaddcdbaaaddbdcaacbdbbdabababacbdbabccbbacaabcacdcdabddcaddcaadbaaaaacdcaccdaacadbaadaaacccaabbcbcbdabdaadcaddbddddcbdbbdbbdbabccaabcccbcbabbbacdbbcccbcbbcaddbcbbdcaadccddddbcbbbbbcdaacdaadabbcaccadbbcbcdacccbdddbbccdbaaadabdbbddddbdacbcdacaaaaacccbbcaaadacbdcacdbcdcacdcabaccccddcadabacadbdabbdbcaacbacacdcdbbccddccdbacbaccadcbcadbccdbcaacbbdbaacdbabcacbcaabcbacbcbabaaacbaabcdcbcccbadaadccdadaadcddbccbabbccdccbabacbaabcdddbabbaacddcbaccbacccadcccdbbccbcddddcaaddadddbaddbcddbccadcdabcbcccdcaaccdadbdbddcdaadddbccdcababbddcbdcccccddcabdbadddcbcadbbccaccadcadccadaaaccbabdbdabcacaccabcadbbaccaabcbabababccbbcbbcabbbadbcdcadbdddabaabbcabdcbabbadbdacadcaacbbbbcbddbcadabbcacbbbcbcdcacadbdcddabdbadadbdaddabdbdaacbacbddcddcbccdadddbbcbaadadddbabbcbcbabcbddcadbddbcbaaadbbdaacddbacbccbdcccccacaddacbbdcbdddcaacddacdcdbadcdabcbcbddaadbdcbcdccacdbccabdbcaacbdcdcdddbdcdadacbddbcaaabcadddabbdaaccbcadbabccbccbbcabaddaadcdadabccddddcaabdbacbaddabdddcabdcaacadaabadcbcabadbddacaddccadbbbbcacacbdadcabbacacddacdabbbbdadbacacdabdbbddabbbcbddacaaccaacddbdbacdcadcbcccacdaabcadcaaaaaacbadddadadccbaacadbadcadaabddcdbadcbbbadababddcdcabcbcbdbcccabbdabbcaaacadaaaaccbdaddddccabcacdbbaaabbdcaccbdcdccacdccaaddaadcbcdcaaadddbbccadbdddcacdccdacabcabacbadacbadbacbcbdccbddccaabccbccbbcbdaabaabddbaadacdbddadadcdacaaabbdadcbcdadabadcbcdabcbcacaaadbaacddabdbbadcccccadabcdddcaacbbbaaacadbdbdbdddacdccdacbccdaaabdccbcdcddbcabbbabcdcbcbccbabcbdbbabddbadbacbacdbcbbdbbadccbdcdcbcdcbcdaabddaccdacaddabbcaacaadabbcabcdacacddbcabcccacacdadbbcaaadabcbbbaccbdbacbabccdcdcbddcbddabdcabcababbbbcbbccbcaacababacbabdbbdbabdbddbbccadcbccbaddbadacddbabcbaaddadddbaddcbbdadcbbdbcdcacbbaabdbddccbaddaaddcdaabbadaadccabcdddccbacdabdaacdbbadcaddcccdabdcbcadabddbaaabcbbbdcabacbadddcaccadccdddabbcabbdaadbbdbaddbbbddbbcccbbcbadcccdbaacccddcaccdccdabcabadccbcddbdcacddcbbcbccddadabaadcdccdacbbdaddcdcddaabbbdaddccdabccadbacccdcadddbdcbdbadbbaadbbaacdddddbbdbdcdaadacacbcacdbbbddaadadbcabacaccbaabbbdacccbbdccdbbadadaaaadddcaacaacbcbccccaadbaababddddabcadacacbddcabbbccccabbdcccaaaccbdbdadabbaccacaadccbcabcbdbdcaadcacdbdaadcbcdccdddadbadbccbccaadddbddbbcdcabdbacdbdbddbaddadcdabccacacdbbdadbbcdacabbaddabababdcdadddaddabcabaadcbaddbabacddbddbcabababdaabbddaadcbabdcbbddadacacacdadbdbdbdddbabbcbdaaddbccccacadbcdcbdddbbcbcaacacccaccbadbbdaccadbbcdacbccaabaacccdbdcacdbddbbdabdadbcadabdbccaddcadcacabcabadcccaccabdcbcdabcabccdcbabddaadbacabacbdcaaaacadddadcadcadcdcbbacdbdbccadbcacdabdacbcddbdcbcabccbdcddbabbaaaccaabccbabaddabbdbbdcadacaaadddbdbbccdcdcadcadbcdcaddaacbabbdcbdbadabccdddcacacdbcbccdbbabaaaabbbcdcbabaccccadccbcbcddccdaccddbaccbaabaacadddaadcddbabdadaadddaaabcaaaaabaacdcdcbbcbcdaccbdbdcbbccabadbabccbbddcabbdbbcabcbcbcbdcccaaadabaddadbcdabdcdbbabbdcbbadcbbbdacbbbcddacdbbbaabbacabbabbddbbcabacddbdddaacaddadcaccdccbdcbbdbdbdcadaadccdaacadabbabaabccbcbcbddcdbaacadbccbbbccdaaddabcbbbbcddbbcbbdbaccdacdaabdcdcdacdcdaccbacbdbbcbdbddacbacbdddbdaccdcbadbddaabbbbabdbcbdbcdcdabaabbcdddcbbbccabdbbacbbcabdababcabdbdbacdcdcdddbbaacdcbccaddbcdabccbadcaaaaacabbcabdacacaabddcbcaacabbaadbcddcbabdcbcbbbcabdbbabcaacccaabbabbaadaaddaaadcddcadbbbcadbadabbadaddaccdcbddadcaadccdadadbbadddacbacddcabbcbcdaaccdcbcccbcbbccaadbbcdadacbbcbccaacbcbcadaabaacdbdbbaaaacbccbcbbcacbdbdbcbdcbcbdbcbbdbddadcbbdccbabbbbcadbbdcdabdbdddbccaabcbbbcdabcddaadbdaddcacbcbacccbaacdacdbbabacddcadbbdccaaaabdbaadaacbaaddcbddbabadabacbcdbbbaaadaabccdbabdadcdbaaadbcaabccccaaaadadcbdadbcccbabacbbccacaddccacabacaaccdbabccdcddbaabbabdbabccdbbcddaadccadacccabadabcbddcabcddbcdcbccddbccabaddcbdbcbdbddbcaadcabddcabadccdbddcddbbdbadacbdbadbdacdacccbbdbdaacdbbbacdcbbadadbaaccdaddcdcddacbddbbdbbabcabbabbcdadbcccbaadaabccdbdbdcdddcddbddcacddbdbdcbdcbaaacacdddbdabcbbbababddacabbabbaadaddcabbccacdbbabcabcacdbcaddaabbbccbcbbdcaadbadabccbbdccbcccbbdaddbaccaaaccddcccbdbdbdbcbdaabdbcdbbcdcbaaaabcdacbbaacccacbbadbdbaddbdccaaddbcdacaaacdcdacadabdbbcdbbcadacaccbababcdbdcababbcacbcbddbaaabaabdcbbdbdcbcdbdaacbbadbdcbaccdabdbcabbcbdbcadabccbbdacbbddbcbbbacbadbcdbbbddbdacbadbbcbadbadccbbcccaacaaacaaacadadcddcbbaddcccacadadbcbcdbcdbbcaccccacbbdcdbcadcaccacdccccabbdddddbdabcaacadbdccddcdadbbcadbaaddaabaccbadaadbcabdccacaabbddabbcbbcddcaabacbdbcccddaaabbdadbdccbcdcdabcbbbbdcadccdaabbbcabbdbacababaabcabbcbaddacacddccacadcabcdcbcdaacdcddabbbcbccdbdcbcacabbddabdacabadbbdcbccaabdbbacbdadaccadbbabdbdadaabcadbbabbadadadbbdbbcddcbdbdcdcadbabdaadadabbddcdcadadccababbbdacaaacdabcacaabcacdabadcbdcaccdadccdbaadadccadaacdadadcaaaacbbdabdbbddbddcbaaccbcbddbcdbcbdbdbaacabcababbaadadcdabdcccaddabcabddcdbbcaaabdadccbbaacdacdaccdccaaccdaaccadcbacadabdbcbaadddbacddcbbddcadcbcdcbabcadadcddccadaabcdabdbbcbdaabbbdbacaccddaadacddccbcdaabddccbdcdbdcacdaaddabacabccccacabdcddbaacdbbdbbdacdbdccdabccdadacbdcbadcabbdacccdcdaaadabcacccaabccdcadacddbdbdadddbbcabbaadbbdbacaadbdbabdbcccbddcbcbbaddaaadbcdaadbdccaaddcdbababcddabcaacadddcadcacbadcadaacbbbdcddadacaadaddadddaabdccacadcdabbcddcacbcddbddddcdddbdbacadadcabbccbaabdabbcccdcaddbaaabccddccdadbddccacbccadacaacacbaddaccaddcdcacbadddccbdaadbabaaccbbcddbdcadaddbadbabcabcbbdcaaacbcbadadcaddadbacddcddadcacbbcaddbcdbaabbdaccbdbdbbaaaaaacbbdbbadccdabaadccdcdbcaaabcbabdaddbbadcbcdcdccadbdaacddcdbcdacbddbbcacadcdbbccddbbdcabcbadbdbaaddccbcbcabdccabdadcdaadccadadaddbcdbdcdcaacdcadabadacbdcdcabcbbbaddbabdadadbbccccdcdaadacccdcdcddbaccbaaacacaacacddcdbcbaabacddbcadadcddccdabbaabcdcccababaadddcdcaddbabaccddcaaabcdcaabaadadacccaacddccdcdddbcadacaaccdacdcccaabdcbadbdaabdbdabbcbbabaddcabdaaadbcccaadcdddaccacabcabbddaadcccdbacdcabbdbaadaaccdabdccdabcdcacbacabdaddaabcacbadcbcdadddadcdcccdbbaaadbcadacaababdddbcddccbdbbbdbccabdddaaabaacdbbddbacacddbbabdccaaabcddaacadbddbadadbbddbbabdbbaaabcbbbddcadaacbcbbcdcbbaccbacacaadddcdddcbbcaddcdaacdbabacbcaddbcbaacaadabcacccdcbbdddbdcababaadcbbbadbbdddadaabbdbddddcdcddcbddbacdcaaacbcaaccabbdbcbdccbcddcdacdadccccdbcddccdbabcbcccbcbddccdaadadaacbcdbbcdaddaadbbbdaadabcbbcabbcbacaadacbbacddcacbdccdcbbacbadbabbddbbacdbdcaaccccbdacdcddadbadcdaaabbdaddbbabbbadbacdbdbdbbbccdbbccacaccbbbabacddbdccdccacaadcaddbdbabccaddacadcbdcdbabbbbbabaabbdabacadddccbcdadadccbdcbddbaddbcdbcbdabddacccadabdacacbabaababbdaacdabccdcabddacabaaaadccabdaccbbdcacbacbabbbbdbabacaccbaccddbbadadbaddcbbcacaabbdcadcaaaccadcccaaaadcbabbbbbcacbabbcadbbcacbaaddaccbbdabdcacdabaacbdbddcccdbadbadbbacddbccddbcdabbbbcacdaabbabbabbbbdacbadcbdddcddcdabdabccaacaddcdcbdacdcbbbbbacbdbaaaabaabbaacbddacccdbbadcdcbccbbcdcdacddbabbcbdcaadcdccdcadcddccbcadbadcaccbcbaccccccdcbbbdbbcbaccaccacbcddadaaabdaaabadbaadabccbdbcbbdcdcabacaccccadbddcbdacbacdbacdaaccaadbbadccbdaadcccaaddbacbdbdaddadcabbdcccaccadbdcacbcadadddbcbbcbcdbcacbbccacabbdcadcccddccaaddcacbbcdccbbadabcbabddbbdcdddbccbbadabcacdbacbcaccaabbdcabbbdbabbcdadbccbaddaccadaadaaabdccaddbbccdabdccdbdadcdbacbbcccbcaadcdaddbcadaaadddadcdabccababdcbdcbabcdcacbbdddbbdddabacadbbbcccbdaadaababacaaacbbdcccbbcacddccbcaddbabdbababcaccbcadcbddadaaddbbdadadaadbbbadddababcbbdbacdbcbbdddadadcddcbdababccbccccadddbdddccbdcadcbbcabdabdbbaaabbbaabdacbadbadddcdaddadddcccddbcbaaccdbdbcabcdcadbccdabdccabbdaabcacdcaaddccababdaaadcddadddcaccccaccabdabaaabbababbcabcaacaaccdcccddabbbabdabdbaadccbcabdacdcbdcddcccabcbddabaabdbdcbbabdabcbdacbccacdbbcbcadcbadcabdcdacabbcbdacaccaabaaadbccddcaddbadcbdbbcdacbcaacbcbbbcdcdddcdccdacacdaacacddcbabbbdcccdcadcaadbabbbdbdbcccabbccbcbdcadcdbcaacabcbaadabbacabcccdcdbbaaacccbdacabbbbacdaadbabddbcdbbabacabdccaaaabcbadbabdbbabdccdcbbdbbdddccacbdbadaaddbacdcbdcbcacdddbabbacabbaccbadacccddcaaaddcacdcbaabaddbdabbaacadaabcdaddbbbbaaabdcadddcadcdabdbcdbdadddaadbbbcdcaacbbadabdccbadccabcbccbcadbabbbbdcadcbdbaaaaacaabadaccaccaadcacacccdbcacbbbdcbbaacccabcdbaabcdadbcaaaacbbbbcbbcadcdbadddbbdddbababdcddaaddbbbadaacdabdbcacabccaabadcdbadddccddcbcbbcbbcdaaccbcbadbddabaacbcdbdaccbcdabcbbabbbdbabbcbaabbbdddbbcbddcdcdddccadcaadaadbcaadbdcbdbbcadddcacbdcdbdbbdbdabcadacaabbadabdadcbbdabcbbccaadbcaadddbddbdcbbaabcbabaacbcbacacabbddbdbdaddbcbcbbdbbadaabdddadcccaadbbccdddddbdccbabdbbacbaacdbcbacdcbbddbdabdddabababccdcababbdacbddccccdbcdaacadaaaabaddcdadbcdbcdbdacdbdbccaabbddbcacbdaccddddabacccaddbdcdbbdbbabcbacacadccdbbaddaccbcaccbccaacabdacbdcdaadadcdcdacccdddaacaccdcdccdddabcadccbaaabdbdaadbaaadbbdccbdddccadbbaaabcacdaacccbbdbdcdccabcdcaddcaadcccacabadadcdcccbbddbcdccccadcadcdadcddadcaabbabccbdbbddadaabccdddabdaabdbdbbcbcbbaacabcdbdaaaddcaddcdcabcbbdcbdababbdcacaacbacadddbbcbacadabdcdbabadcadadaacddcbcacbabdaadadadadcdadcadbbbbbabacadaccbdbbcbaaccacdbacddbcccdadbbcbbbbadbcadccdacbbbcadaacddabcbcdaabadabcacdbbbabbaacadcbbcbacabbbcccadabdbcbdaaadbcbbcbbcacdacbdbdadbbaaccdabcacabbbdcdadacdbaaabaabaccbbaccccbbabccbabbccdbdcdcabdaaaaaadadbcbdbcaddddcdbadaadbbdcaddaabdbabbaccbacdbdddddcabdcdbbcbcdaaddaccdbaddbabadcccbcddcdaccadccdacabadbdadccabaaaabaaddcabbaaadcddaddcbaaabbddcbccacbcbabbcbdbcbadbaadbbabadadabaaddadadbbbcacabbccdcadabddaacdabadcccbddabcdcccaccdabdcbccdaaccbabcdcdaccaaddcdaabbbbdbacdcdcdbadbdaddcabbabaabdbbbbccdbababbdccbdccbadcabbbbbdaadaaddcbbdccaaabbdacaacbcbdcbabadcdacbacbbdcdadddaaacbdacbaddadddcbddddaaaabbccbabddcaadbdaacbbbabcccabbbaadacdcdcbcaabccdccbdaabbcbcaaaccabbccacdaadbdddacacbcabaddacbdbbdbaacacddccddbbcadddbbbdbdaddccabbadabbbcbaadaadddbdaccdbbaabbdcacbdabdddbbcadcdacdbdcbcccbdccaaaccadadbcdabddbddbcaabdbbaacaaabbdcbcdccbddccddabccbbbabacdacdcaaaaadccaaacccccdababddcabaadccbcddbcbbcbdddadbaacdcaddbcbdacacbbbccccbdbbbbdadbdcdabbacbabdcbbcbbdadccddcabdcccaabadcdbdabccacdcbdadaaccccaddaadbbbbddcdcdabadcadacabddbdbdabbdbdcadadcbdbbbbaabaaddbabadcadacabaacdabdddbadcddcbadbaabcccccaacbaabcacaacbddacaccdcccdacacaadddacadbccadbbaabcaadbdcdcccdaacacbccdcbbcaaaaabbcdbdbbabcbbdabcdabaacadcccbacdddabcdacabbcccbdccadddbcabaaddcaadcacbabdbdbdbbdbcabcbdbdacbdbdbdcbccbbbcadbabcadbcadcdcabccdbcbacccddccccccbaadadbcddddbaabbcaabaddbadaddddabdbcdcccacadaabaabccaadacbcbababcabadcacbbdcdabdcdbbaddadcbbcbcaddcacbdcabdadbabddaccdbdbadadabcdbdcdcabdcdcdbdbaacccccccabddcabbdadabdadcaccadaababdbddbcacaadbdaddcaadbdabaaabaabbcdbcadddbbacdbdadbccbcccdacbaaaaccbabddcdadbcbadcaacdbacbaacacdcdcacdaccccbcdccaaacbcadaabaccdbddbdcaddcbaddabaabdaaadabdcbdddcbaadaacbabaddcbcabbabdbabbbbcccbbdabbaadbacdacbdddcbccacaddbbcbaccaacadabcabcabcbadcacabbdbabbabcabccabbaacbddbddcbdbdaacdcbbcabdbaddadabdbbdbdaaadbbddbcbcbdbadabadcdaaddbdbcbcabaaaaaadcccbabaacbabcaaadccdaaccaaaadcacabbdbbbdaabaabbdbdacccdcdddbbbdcbdaacbbdcbdbacadcaddabbdbcaadbabcdbbddbadccbddcdbbcdcbbbddadbbcccaaabcaabdcbdbbbdccccdcddaaabbcdabdcddddacabbdccaacdacdcdcaccbbbbbdadadddadcacddcdadbcdacdacabbacdcaabbdcdadaabbadbccccbabcbcbacaccbbabcbbcabccdaddccadcbdacccbdcdaaabbdbaabacdaddddabacbacbadcccbadaccdadbdbdadaaadbcabdccdacbadcbdccddbaaaaddaaaaabccbababcdadddcdaabbbbcdddbdbcdacbcdbbbcbcccbdcaddbbccadcccdcadaabdcaacacbacbabadbbbbdcccdadaadcabccaddcbaccdacccdaaadddbbcbccddbacadcdbacdbbcaadbdddbbbadadbdaadacdcaaaaccadbdccdcbdbccaddaabcbbddbdccdcddccdcaadbaccdacabddcdbcdadcdaabdbabbcbdadabdddbbcddbabadddddacdccddbacdbcbdadacddbabaacadbbacaaddccaaaacaaacbbcdaabcbdaaddaabaabcaabacbcbbbddcdababdddddcabdcbaaadcaaabaabaacbbbaddbddbcbcbbcdbbdbbbaaabdcbbcbdbacbabbabccdaacbcddcaabdbbddadddabacddabcddcdacdbbcdabdbdbbcdaacddcdabddddcbccbcbcccddabbdcbabbcccadadcabaadadbdacdbaaaacdcaabddaadbaacabaadaabbcdcdbaaaabcaabbacabcacdadccaadcdccdaccdcbcbadadbdcbcdddaccbbbaccbbcddabbbbdcacadbabbdcddcdacdcbbdaddcdbaabccdddcaacbddcadbccdaaabcaadacbdcdccdbdadbdbaccccacaaadbbabaacdcbaabaddbbaaddbdbcbdbdbbdaddddcbabccddadbbabdddcabadddaccbcbabcdccddbdacddacdccbacbcadddabbcdcbdbaabaddcbdccbcabdcabaaddbccdcadbbcdcdaaadacbbadacdacbdadabbddbacdadcdddadbbcaaaabbbdbddaddcbccdcbacbcdcadcaacbacabbbbdcaccdcbddcacbddacdacabaddadcdcbbcbbaaabcbaaacdaccbbccbdbdcabbdabbdbcaabdbaaacaacacadbbadccadabcbdbddcbcabcbcdbaabcdbaadbbadabdbdccabdaddcacbbcacbdaacbaacdaddadbdbbbbadacccaabbbadbabddbccbbccaacbdbadcaccaaaacbddabacdabadbaadddddddbddaaddcbabdcbdcccdbaddcbbcadcddbddbcbccacabcddbbacaabdacdbdbdcbabbabcdcabbcccdadddadaddacdaaacabccdccaabbdbddbdcdddaccbdcacadcbaaadcbaddbdabddaabccbabdddcbabbbaddcacbdccbbcbcdbadcabaadbbdbbdbcdaacabcabbcdbcdbbaaddbbbdcbbdbbcdddbbaddccbbdbcdadbbbcabbcdcbacdacaaacdcbcabbccddbdbbbabacccdcdacbbbadbdbacbdbdbcbcacabcabadcadacbacaddbdcbcadbddacabcbcdabababbbcbcdcbddbdcddbcacbbdbdaaaabaccdcbdbccadbcdaccbadddaaabddcadbcbcdbbdaccbaddabdcaabdaabaabdbbaaaaadcccaddcdcddcacabbaadadbbdbbbcddadacdabcdbaccaccbadaaccbbbabbcaadadcccbcdcaccdbdacdacadbdbabdadbaabaccbaddbbaadcabcbddadacbbdcccbdccdaccacabacbbbacacccaccccbcaddaacccacaabdddbcdcdadbdadaadabbabbbababbbdbacbbbddadddcbbbbbcbcdaadbbbabbaacacaacdaaaacdbcacabdcdbaabdbcdbbbcbdaacbbcdbadccabcbcdabcaccbddaabcddbadcabcdbaadcbdadacabacdbbbdaaabbaadcbcbbcdbacaadcbdaacbbbcadcacdcaabccdbdbbbdcaabcbdadbadaaaddadabdbcacacacdddaacbacdbcdccacaacbddbdbdbadbcadcdbddcdabaacacbaaadddadabadcbadaccdcadccaabacabcbabcbddaabbbbdccbdcddacdbbcdabbcdbacadcbbaacdccdccbaaacaabddaadddbddadacaabbbccbdcdbacbddcabaabbbcabaccdadcaaadbacacdbbccbbabbdabbacdaccdddaadacbaacbdbabbcaccbaacccdcbbccbdbcdddddcbadccdacbaacdaabdbccbaccdcddadcacdabadddbcdbcbcacaccdddaddbdcdcdcbaababacbbaadbddbddacaabaaacaabbaaacbccdcbbbbccadaacdaaabcadcbbcacbcbacbadbbcdadacbdccddbcdcdddbdbaadadcacacbcbbadcadccbabcccccbadcaccbadbdddabcbbaccdcdbbacdbacaddccbddccaaccdcaabbbaabadbbacaccddbadcbddbacddacadbdbbbdcadddcacccbbbccdbaddabddcbdbbcbbddcbadbdabdbbaabbacdabcbaabaddbbaabccbddbbaaacaccbbbddbbadbaaccbbabbdadabaadbcbcbcbcbaacabcdcccbdbbcacbbbbddccbcadabccdcddcabbcacabcacacbacbcccababacdaaabdbabdbacaabcbbdabaaddbadacddbcaaabccbdcbdbccaaabaabbcbbbcdcadbdabaaabaccaccccccaaabaccdbcbcccbdcbadcdabcabcddddcbcbddacdcaaabaacdbbcdcaabbdcaaaaaabcabdcbbdaadcaacdbddcddaacdadbacdacaccabccdacdadbbcdbbdccaacdacaadbdccccbddbabbaaabcabaaddcccbdaccbaacbdacacccacdbacdadadbabbacbdabacbadcbcbccbdadbdbddcdbcdbddbcacadbcacddabdabbcbbabdaabaabdaaabdccbcbdbcdddbadcabaacbcabcccdbdbaacababdaccbcabababdddadaadabcbcbdbcbcddbaaddbcdadbaabacbdcbaabcacdbaccaddccddcaabcadccaaadbcacddddabaabaacbcbdbdcbcbdbddbaabcacdaaaacdaaabbcbcaabbacddbdccdcdaddcccababbddaddaacbdbcddcaacbddcdddcbabaacaacadbddabddddddcabdccdbdbddcbacbdbacaaaddbbddccacbcbabdadadacaabbccbbaaccabacaacbdcddcbbbbdbabbcacbccccacdabddccbaddbcacdadddbcdddbaadabddddbdabdadbdabadcbbdabbadbbdacbdbcbccdbccabaacdbabacaadbabaaddccbcbbcddcbbbacccacaacaacddcadabdcbdccaabbdcbcdaadcacbbddadaccbdddbbdbaccdccbdbcaacbdbbbcabbcaacdbbdbdbbbdcbabbcbbcaaaadbacbddbdcadcaabacadbbcccbdcdcddbbbacbbdcbdaadbaccadadaaccbdbdbcccccbbdaccccbdaacdaddadaaaaddabaddbccadadcaddbccbcaccddcaabdccaabdcdcbcdbadccbaddcaccaacabdbaababcbdaaaaadbcacdbdcccbcbdbccdccbdcbbadbaadbcbbcbcbcabdbacadcaaacdbabaabbacabdabdcdbdbbcbaaaacdacbccdbacdcaabbabdaacbbdbbadaacbacccabaddadddbcacbddbaccbdaaabccdabacdcababaadccabdbcbadbacaabbbdaaddbdccbabbccddbdadccbddbdcbbaabbdcddabdbdcddbbccdcdaaadcdababdaddbacacbaacadbbdbcddbcabbbcddabcdaaaaaadbacbcadbcabcacdabababaaabdbadbadbadabbddbdaccdcbbbcbdbdbdabadbadadbacbdbaacdbadddbcdbddcabbbadaabaabdcccaaaabaacbcccadddbdddbbcdaaaadacccaabcadaabdbcabacbadaadaddaddbddbdadbcaabadbddcbcabbaccaaadcaabbaccddacaacbbbcadcabdccccadbcaadbcacaaacdcdadcaadcabacadccabadbbbdcdcacbccadadacabacbaacdacadadaacddcadacadccadcddbbbacadaddcbdccddbdabcacbaadcaddbabacaccaabadadaaddadabbbadaababbaddaacbcccadacabbcccbbcaaaadaccdacabdbadacaabddcbdadbdcdcbbccabdcccccacdbacbddaaabcaaaccbaddccdabaccabcdcdadaccacaabdabacdbbcbcbbcdabcddbbbaabbabaaacbadbcabccbcabdcbacaaccbdccbcdabcbdbcbdabadbbdddcbdcdcaacbddadaabbdbcbcdcaadcbdabccabbccbcbbcdbccbddaadcddcbbaccccaccdcdcddadacacdbdbdbcdadbbacdddbbdbaddcdccddcabbacdaddacbbdabbbbbbddbcbaddbadacdabbdcadcbcadcaadacbccbcdbbdbdadbbcbabdaacbbdcddbdbdcccddacadadbaccbdbdbcbddabdbdaadadbdcacbcdbccadddddacdccbabdabdcdcdbcdacbddcdabdcbbdacccdcbacbddbdaadacadbdcbdcdcadddddaabbcaababbdbbbccdadbbdacbcdddcbbaacbddbcadddcadacbcccdccdbdcccccdcacdaabadbacdccddabdbbcabddddddabadccdbcbacdaaabccccbcbabaabcaacddaaddbcbccdabadcdadbbcbdbaabbcddbcdbdcbdadbbbbcddccbdbdbabdbccddbbcabcddcbcadcaddccabccadaabbaddabbbbaacdbacbbbaccaadaccbdcbbaabdbbdccacabbcdbaabdaadccaaddacaaadbacdcabcccaddaacddbbaddddaabcadbddacababbcdbbcbbbbbcadbbabbbbbccbbbcadccddcaccdabcbcdccdddcdbacbccbdbbbdcddbbdcbaabccbaaddcdbbbdccadbaccadcdbacaccaaaadccccabcadbdcabcdcdcaccbdddaaabbdacdbbabbaadacadadbccbbcddaadccbbbcdbaabdcdadadbaacaddbbccddddcaaadabdacccdbcaccbabadabbdbcdbaabdddaaccaccadcdcabbdbabbdcbacbbadbbdbccbddabaaabddbcbaacddcaadcccbadcccccaddcabdabcbcdcabbccccbcabadcbdbcbacdbbbdabacbcbbbababdcaaddadbbbbbccabcbdaccaccaacaaddaacaadcbbabaadadccdcdbbcddbdbcbdaccbbabbdadcbdacbacdddaccdbcddccadacddcdcbdbbaadcbbbcdadacabbbbbddaccbbbddbdbabbcdbcaacbddbcbbbacbabccdcbbdbaccddaddbbbbdbaddbaabcaacbdbddabcdabddadcacadccdccdaccbcddcbbcacacbcabbcadadbdbbbdbccaaadccaaddcdadcddbdbaabaadccbbcadabcdaaaabbbbcaadccaadccaddbdcacabbadddacaacdaddcdddcdddcccdbdddbbcabbcaacbccccbbbccbdbcbdddaddbdbcdddabcbbbabbbabaaddcddbbadbbbddbabaccbbbdcacdbacaaccbdcdbdccacbaacbddbdcccbacabccdbbbccbcccaddcbaaacbdbdcdacdadcccdbabdabbdcbacabadcddabdbcbbbddbddbdbadababcaadccddacccadaddddbbbacbbacadbcadcabbadcbcabdcaadaaaabdacaaddabbacddccdbdbdcdcbcccdbadbbbbcdcbbbabbdddacbdadacbdacbcadbabadcaddadadbdabccddccbcbabacbbbccbbdbdabbdaddbacadcbdabcbdabdccbadbbacaaabbbddccabbabbbabacbbdbbcabbdcbbbcbdddcbbdbbbdbcbbdadbddaaccbbbccbbbcbaadbabaabccababadbdadcdadbbadcdcbabbddccbddbccdcbcaabbddddaabadacadcabcabbddbbdcbabbbaacbbdacccadcbdbdadbaaadabaadcddbcdccccbcaccddadadccabaddabdaabcdadcdaddbcbaaabbbbbccabcdbddbbdccabdcbabacbcbcaaabcacacabacbbbcacdbcbdbdaaadaacdddcadaacccdabacadaddbbcbdbacddadabcaabbadddbcbbddcccaababbbacbccbbcadbcabcdbacddaccbddacddcaaabcabaadadcdcadcbacbaaddccbbccaaacbcaadbcaaadabbcddacaacabcbdbacdbdbabbadddaddbbbadcbdbbcacdcacabcbdbabdcdccbcaaadaccaacaabccabbcaabbbadabaaccdbcaadacaabcdcbbcbcabdddccbadacbddbdbbbbddbcabccadbcbccccdbaacadacadddcaabcbaadcdaaabdabddcabbdacccdcbdccacbadbadcbdacacdccbcadadcadcdabbaddbbcbabbccdaabcdbabcbcaacddbcddabcbcaadadbaacabdbdadacdcacabdddbdabbbabadabdccabdcdcacdadbaacadadddaddbbbcbcbdaacdbcdadadacdcdccddbddcbccdacccddcabbdaacbbbabacbadabaddddabadabdddcbdccaddccdadccdccdacbddddccaaabbacbcbbabcdccaaabbacbcabcdabadcbbadbadcbddabbddbbddbadcdcbdbbbdcadbcabbddccdbcdaaaaccbddaadcdddbdcacadccdacbdcacadccbdcbcbcbadbbaacdaaacabbddacadbddcbccdadcddbcacadbdacdbcddddccbddcaacacacdbaaabdcacbbbadccababddacdbdddcadddabacabcddcddaddcbbdbddddaaacbcccccdaacabcdbacdaadbabddcdcbccbcaaddcbcadddddcaaaddadbadbabdaadaddbbbcdcaaaccbcadbdbacadadbddaaccdbbabcbabbbcdbacabacdbbbdcaaccdbdaadcdccdadcaccdabddbacababaabbaabacacbdcdccdbddaadcbccabccacbddabdbdaddcbccdcdabdcddadcddcdcbdacabddcdadbbabddbbdaabdbcccbbccdbacbdaaddbccacacbbdbcdcdcccdbdaacdcdbcddcaadaaadbcdaaaaddbaaacdccadaabcbdbccdcbdccbbddababdaadaacbbdaddacadadcbbbbbcccdcacdccbaddccabdcdcbadacbbbcbaadbbcaccccbbabadaccdadcbddcadbdbcabbbdcaaacbdbdbaddabdcbbdaacbcddddbcccbaddbbcccaabdbcdbbcbcdbabbcbbdcaddcdadbacabadbcdcdcdcdcdcdababbabbbaabbadaabbcdcbadacdcbbabbbdbbadccaaddcddadbcadbdbcacccccabcbdcadbcdddcccdcadbcaddbccbbdddbbdcbaabcadddcbddaccadabcbacccabcaacaaccdbcaaaccbdaadcbadcaaaadaccabaccabbadaadcbadcdacaaccbdadbadbbdddadaabaccdacdddabdacdcccdaccabbdabaddcbacbddbbaadddabaaadbdbdacdbcccaccaccadcdcdaaababdaaccbdccbadcacdaadabaabdcaaaaabdaaadbabbaabccdbaddaaddbdbcbdaaadcdbacccaccbdaabbdcdcaabdbabccabddaddbabcddadccbaaaabbdadbddabaabdcdadabaaddbcbddbdadcbdcbccabbdaaddbcdadbadaddaccbddcddaaccbdaccbbccbdcbcbbacdacdcdbcaccbddbcbbbdbcdadaabccbcabdbdbbbdabbddddbddaaccbbacccaaacacabdddabcbadcbcdcaacabcddaaacccdcdcbcdbabdbbdbbbbccbcbbbbcdcddbddaabaddbbaccbacacabddbccbccbcdbbbabdbcdccdbdadcadcddbbcbbdabacadcabbcbcbaaaaadacadcddcbdadaddcbabccdcbcdbcdcddacddaabdabcbbbccadbbcabaacbbacddacbcddbbbccdbbcbbabbddbbbbbcbdbcbbabbdcdddacbcacaacbddcccababccaaddcbcbdbbbddbbacbbdbcdccacadcababacddbcccbadbddaddbbdcdbbddcdcacabacbcddcbadabaddbdddadcabaaddadccadaaaaccddbaacdadababaaadcdabbbaabaccccdcdcbdacccadbaabcdaadaddbdcddcdaaabababccabadddacdadacabdcddccdcbcbbddbbdcadacddaacaaacbbbdacdabadabddabcaadaddaadadbdbcdccabdabddcbcbbacccdbdddbabcbabbcdbabcbbdcbdbbbbbaadcccddadaaabdcaacdacdbabcaddbbacbdaddddcbaabaaaaabdcaccaacbbcaacdcdacbdabbdaddaccadacadcbbdcbaadaadccbdcacacdaccddcdbdbbcbdbadbcbcbcaccbbacddcddbbabbaacacacbdccccccaabdacdbdddcaaaaadacbbcdabbbcdbaaaaaabcddadadbbbbdbdaabcbbdacdcdadbddaadbbccbdcbdadbcadcbdbbbbddaacacaacbdbcbdbdddbddaccabbacbabadaaccdcbacacccdbaabddabbbcdaaabbbaacbdddbdaabaaabdcadaadccbadddbcbbdabcacadddbddabcaddcccabbbddccbaabbddbbcdabccbccadbbbcbbaaacaddbcbcdbadadccbaabdcabbdcccadddaababdcadcbaaaaabcabaaadacdcacacabaadbbdbdddaaaccdadcdbccddabccdabcdaccadaacdbcccaacbddacaaaabbbdabaacaaabadcbccdddbcbbdaabdacbcdadbcacbbdcdcccaadaaabdbcaabadbbbbbccdbadcddbccbcbddbdcccadddcbddbdddbdabbcaadddbbdddbcaadccacaddadaaddcbdbbdabbdbddbcbdcbdccbadbddbbdbcbdbdcaaabdccdccaaaaadbccaaabcccccddaadaaadbaccdbcbbdcbcdbbddcbbccadbddcbcacdbbcdbbdddbbacdaccbacabdccdaccbdabaadcbaaaaaabbaabacadaaacaddcadaccaadddcbdcdcabadabaaabdcbacbacadcdbdacdadddcdbbbddaadbbdbbadaccbcdaacadbaddaacaababbccadadbacdddbdadcdacabaacbbccbdadaaadcadadcdcdbdddcbdbccdcaabaaadacbcadbdbaacbcabacbcdcccbbddcdacaadcddabbbbcbacbcbbddacaabcdbbccbbcadbbcabcdcbbbabadaabdabbbbdcbcccabcdcbbcdaddbddcbadcaddbcddaadaaccbabcacbaddbcddbbddccababcbdacccadcabaabacdccbbbbbbabbbcaadaaacabdbadabdcaaccddddbacadccbbabcadaddcaaaaddcdacabdbadbaadddbcaabdcddddbcacddccaddbacaabaaacaacbdbbaccbaaccbadadbdbbcabacddcbbaacdccdccdaaacbaabccccccccdaaddbcacbcddabaaaccbdaacadccbcdbcdccaaddbdaddcddbcbbdaacbccdabadcdabbbcdcdccaaaadbbbdabdbdadcdaaacbcabdbcbdbdbabbdbcababcddbbdadbaadbdabbddabacaddcdaadaccbabdacaccbbdababdcabcdbbcccdcddddcddcbcaabcaddabbbdcbbbdacabcdbcabaabbbdbcabddddbbdcacaddbdcbdbcaacaccdbdabbcbdbaaccaaadcacaacdbcbaccbabadcbccacdcbacbbbdabaaabccddcbccbcdcdcdbbacbbccdccdbcbcbbccaababddcdabcdcbdbabcccdaaaaccacacbdaacaacabbdaabcccabcdcbacbcbdcccabdbdaaccdadbbdabadabcdcabbddbcdacccbababcaaacbbcbabadacddacccbcdbdbcbbbdaacabbdcacaddbbdbcadbadbdaacbaaadadcadcacbadddccdcbccbbdbcdbbdaccdcdddadacbadaabbaaacaddbabbbcaabcdaababcddbdbbcadcbaabccbdbcbcabdbbbdcdaaadcdcdddcbccccddcbaccbdaddabdcbdddadcbaabdccabadbadbccbdbaacdaabbcbdacabdbabbabcacdbbabdcaacbbcadddbdbddbdcddcbbaaaaabcabcaddcaddabbbaccddbddbcaaacbbddddcdbaccbabacadacccbdaaacdcdadccdbbbdadadacbcbdabbbdcbdbcaadbbaddcdaaccbaabbadbdcdadddcabbddacdacdbdaaddcacbddaadbbacdbcbaaddaabaaaddabcddddabcccbcbadcabdcadabdaaaaabaaaabdaccdcccaddaacbdcbbcbccdcabcbcccbcbbbcabadadcdbaadbacdabcdabcccbaccdbcbcbabaaacbbcaccaabccbbcacdadadbdadbadbccbcaaacacdbcacaccbccbbbdbbbdadbaadbadadacddccdcadabbbdbaaaccdccadcbbabcabcabbadccbbdcbddabddbaddaaabbdaccdbcdcbbcbdacaddcbaabacdbddcdbcdbbaabddccbddadaddcddbdccadbabbabaccddbbaabbcbabccaabadbccccaabcaacaabbcbcddddcaaabdddadcbdddaadbabbbdacabddbddcbaaaaacadccabdcbbdcaddaaacbddaaaabaccabcbaabadddabaabdbacabdbabbadbacadaabacaaaaadbdcbaadaabaddbaaccdaaadddbdbaacadacccddbbbdaaacddbadcabdadaabbbbbcabcdbddddbabadacdaadcdcadbbbbccbbdbcddaccbbabcccdcbcaadabdabacbccbbddbcbcabcadcccadbcbcdbdddbaaaccbbaabcdabaaaacaacbacadcbadddccddabcacdcadabddaaadadbcbbddadbacbdbaacbcbbddddaddccccdcbabdcbabcacaacabbcadcbdbbbbdabdccacbaddbbdbdbcabbbaadcdcadcdbddbdaacbdcddadbbcbbbdbbdbddcabdddcadcaabbbcbacacbdbadbddbacddaacbcdcacabaacbcbdcccaaacddbbaaccdcadbaabbdadccdbacdddaacdcababbcaccadcadadddbacadbbdcbbcdabdcbabaccdbcabccdbaaccaaaadacbcacaddadadcbccdcbdbacbbddcccabdadaaacacadbbdbcccbcbbacdabcbcccbaabadaabadddddbbadaaccbcbababcabcddbaaabbabbcdadaccbbbcdbdbdcdccadcabbcbbddddccbaadacbbccbbbaadbaccacbcbbdacddccadaccccaccbbaccdddabcbdacccaaaacdbabadadcaccbdddddcaddddddabbacddaaaddbdbcdddbbbaabdadbcbbdcdcbcacaacdbdabdcabaaaabbcaaadcdbbbadddcbbdbacbabaabdbbbbdbcaacdaacbcbbdbbccabbbacbccbbbadcddbadbcbacadbcbddabcdacdabaadbaddbdcacabaaacdabaadcbacaaadbdababaadbdcbadcbaabadcaccbbbacbdcccadcdcccabcdcaaaadddaddbcbbabbbbdaabadddcdabbaabaadaaadaaaababcbcdbbddcbdabdaabbccdcdaccbaaccdcdadddbcbaddaabaccadacddbcabbbdbdccadabbbabdbbdbdacaabaddcdaccabcbacabdcbadddbcacbcdaaaaabcbabdadcbcadbacbccaddddbdcabcbbcbaaababcdbdddcdcccabbdcccababcdcddddacaacaddcacbcdacdadbcaadddaacbdbabaadbcccbbbdbbbbadacdaaaacabbbbaacdaabadcaacbbacccdcbaccdacddcdacccddbdadababdbdccaddcaacbbacdcadacdaccdddadaccccbbcaccdabadcadcdccbccddbdcccdbbacdbbbaadadcdadcbacbabccbcbccccdcddccbccdbcdbbadbbccdddcbacacbadccddcaaaabbcbddbaaadcccccbbdbadcbbdcadddabcabcbbbddcadbdaaddcbaccaacaadccbbdcdcdddacaaddbcdcdddddbacddbdcadbcacccbbdadcbddddbdbbdadabdddbaaaaaccddcbdacddcdbccddcbdaaaabaccabcbccdbacdbaaabdbccaccdbdccbaabcbaddcbadddadcdbaaadbdddcadabdcacbbcabbabbdbbbcbdddcdbddacadbbcbaaabbccacbdccdaaddadccbcddbdccbdcbdaaddabdcbdaacbadcbbadcadcbcacdbbbbacadbbaaadbdbdcddaadadcbacabcaadaadbdcccaadccbddacccddabcdcbdacaaaccdbcddcaacadbcdccdccacbdcbcbabaddcccbbccbcaacadaddbaababdcaadcddaabdadaaabcaccaacdabaaddacabbabbcccacbbbdbbaaaababcadbbbcdbcbcccaadacbcbcccbdccaacaccacbbbcadbbbaaddaadddcbadcccbadddaddadcbbcdadcadabccdbabbcacbaccbddabcbdaadcdbcbaaabcdbacbdccdcbaabdbadadbcabcadaaadbaccbcaaccabaaaccaccbddacbccbddaccabddbbcdacbddacadbacaabacbabacbdcacaacdcaacccdccdcbcabadcbdbcdccdbcbdbabbdaaabbbcacbccbbbdcbbccabbcbcdcccaaadddcaddbbbaccbacbdddbcdbdbcdcdabacdbadacbaacadbcdddaadbacbdcacbabdccccdcbbdabaddcadaddddbdbcddccccbddcbdcadbcbdbaacabcddbacdbbddaabbcdddddddaadbabaabaddbbacbadcabbcabccdaabdbaddabbccaacaadbaddacbccacbbbccbcdadaaadadbbbaccdccabcadaddbccdadaccdbdbddbdbcbdbdbdbcbcaddcadacdccccdbddadacbccdcaaddbbdbbdabacaddbbabbdcbccaaabadababaaccbcbdbbccbbdaccabaababadcddddbadbbaabbdabacaabaccadcdcbdccacccddbcdbadaddddccccbbbccabbacbabaaabacabdbadcadbbcbddbabcdbcbcbccbadccddddcccbcaaaaaaaadcbcbbcbadcadaaadaccbbcaccdcbaacbabccdbdacbbbcadcbaadabcadcbdbabbaddcaccababcdbdbacdbbdbdabcbcaddcdbbbdaccdbcaccabccbdccbacdccbdbdabaaacbbaaccbacccdbcacbbcccbdbaabcddbcbdabccddcddcbcaabddaccdcbbdadabbdacbccacaddbdcabbdcccadbbadccbcacccdbdcabbdacdaaabbdabcbddaabababbababcabdbbdddddcbbcbcabaddbdbacdbdcbcaddcabbccaadaabdcadcbcbccaccacddcaabaaccacbdbddcbbcbadabdaddccdadcadacabbacacdddccaabbdcadcaddaaacbcdaacabacbdbbdddcacadcddcdbddbcaadbbdabccadadacccabbaadcaadadccdcaddabbcbdcbaabbcdbdccdadadbababddcabbdcbdbabdddcdccabcbdbaabaadddccabadccbdccacdbbababbbcdcbbcbbaaadcbbdadbaccaaddbcddadcaddcbdbbccbbdaddabdabcbdcdccacdbdcbddacdcccbbbccbdbacaaccabcbaaadbacccbcbdadcbbcabacacbbcdacccdccbdaacdbdaadccdccbcdbdacdbddccdbababaaadabddddbbbbbabbcdaaaadcdbcbacbadcbabbaadccaccdabcccabcdabdccdcccdacdadddddacdabcdaddbcbabaddabaddcbcdaaabddbcbcdbcbdcccdcdbaaabccbadaccddbdbaaddaadccbccaccbbcadcbaaacaaacbbddadaadcbaadcdcabacacbddcccabbcadbdbbcdaaacbaaaabdcbabcbaadabaccabddbcbcbbbbcdcbcdacbdbacaaaacadaacdddaadacadcaccdbcccbdbdbbadaddbbbaaaabddbcbcddbadadddcbbcccdacdadacbbccccadcccadcbdbadbaabbbcaacbbccdddccbacadbadbbccbcabccadaaddababdcacaddaacdaadbdadccadccaabdaacbacbbddbdbbadbacbddadbbcddacddaabbcbdbdcadbddddcaabdaaddcddadcbacbdaccacbbadbcccabccabcccbdddbddbbbcabdddcbccddcbaadacaaabbaababaadaddaacacbbcddccdcbcadcbbaaaadadddadbaacabababadcdadcadacbbdcbaaaadadcdabbadbccdbcccccccbddbcdbbabbbacbdbdabddcccbcabcbdbaabdaaabaabbcaaaccabcbbcdcbcaddacbdaccddabaaccdabdccadaacdbaacacbcdcadadabcbddcdbcdadcbbaabdddcbbdddabdbacabcbddbdbaacaddbcbbcbabbbdbcabdbccaaabcdbabacbccaaacddaaccdabcbbdadbddddabcdcbcbdadaadbcccddaaacdddccdccacbdabaaaccddcbadaadadcdbabadcdcabbcccddadcccbdcbaddabdbbdcbbdbcabbdbdbabdadddbbccddcdddabdacccdcabcddccaabdbddcbbddcdcabcdcbcddbbcccdbccaddddacdadbbabdbdabdacababbbadcdbddbbdbbcbcbcadbbadddadbcdbddcbabcddabbbbdbbddabcdcabcaaddaccbbbaaacbdcaddbcaccddacbdacdbcbdbbbadccdcaadcbbdabcdbdaaaabbabcbabcbabbdcabddaddabaccacdcddbcbbbbdababbbaaccbddbccbbcccaccbcbbccadccbbacbddbbbdaadbbcacccaaccbdbbacbdbbbbccddababbaababcbddbccddcdabcdcabcaddcabbdbbdbabcdaddaaccbcbabbabdbdabbcbaadcaddacdabcacaccaddccadcabbbabddbdcbaacabaadacddabdcdcdbaccadbbccabadacdadbbddccbaccdabdbcdccbbacbcbdbbbcabadccdacbbbadbdbbadbbbaacbcacdbaaabccbcbddabcdcbdabdabdaccaacbbadbaccbccadaadcbabccaadcbcccbccacdcaddbcabdabcdcbbccbbcddaabddbabdbddaababdbbcccacdadbbbcbbadcdcbdbbdcdcacacbbcbcacbcbabdcdaccddcdaadbdadcbabcacccaccbbcbbcddadcbdbbbaadbacbbabddbbdadcdbbbccaddabbbcaadddddbcacbababcccdcdaadbdbbbdcadbadadcbdbabdadbbbcdaabbbdababbbccccabdaacbadaacdcdcacacccbdaabdcbbbddddbacabaadcddacaabcbbdadccbdcacbcabbbbcdbcdaacadacaaadcbdacdbdccbaabadddcaadbaddcdbbccddaabbacccdabcddadccdaddbdacdbabcadacadddcccabddddaaaaadbdbcddbcbdacbacdaabaacbcbccbadbaacacbcbacbdbbadbacabcbdbbdbcbbbcbccaadcddaccdabdbbbbddddccdbbaddbdbccccaabdbbcdbbaaaddbbbcabbacadbbadaccdcccbcadcbddcbbbacbbdaccdcddcbddbababbcacdadccaabcbbbcdbcccabcacacccdbccdddaddcdbcadddccbadadcdbcadcbdaaaccdddbdacbdcadcbdacbabbbcbbcaddcabcbbaccccbcdabcbbababdcbccdacbccddcaaccbdbcabcccaabacbaaccbabaabcabdacdcbbdcbcccacbddacdcadbdccddadadbbbddcddbddcaaddbdbcccbaacaddcaabdcabdbdabcbdadadadddbaccaddbcbddbddbdbadbacadadbadbbbbabcdcaababddcabbcbaccbdbdbcdaccdccdaaaabdddadaacbdaacdccadddbaacacaaccacacbacddcdddbdbadcdcbbadbadcbdbdbaaaabbcadabaaaacccbdccbaddcbbbababcbdbaaabcbacaadccbabdadacaacdcbdabaacaaadcbcabcbccdbcbbacabaadcbbaccbaddcaacbdccaaddbbadcccacbadacbbbdcdababdabcbddbcbdbaabdcccdbcccbacaccdcbccbabcccbcccacbbbdbccabddaadbccdbbcbdaabcaccdddbbdccbbddccbdbabcaaaabdcdcababacdbbdacdcbccdaaaadbccaadcdbbbabbdaabdcdadbbccbccaddccdbabadbadaccabddbbbdbadcddcbbdddadbbdcbbcbdbbdaaababacdadbacbcababcbbcbcadcbaddadadbbacabaccdaabbcdadbaadbacdcbdbcbaaccadbbdcabbdddcbcddadcaddaccadcbbabacddcabcdcbaabacccabcdaadadcccccdbcdbacdbabbccbdcadadabbbbdcdadcadbbbaddcddcacbddddcbbdbcbcdacaaadcaddcdbaabcacacbccdbbdaabdbcdbbbddbabacbcaadcabcdcccbcddaccbaadaababbbbccadbcbdadbccbaabbadddbdbcaacddabddbbccadccababbcadcdabbcbadabacbbbadcbaadacdccaacdccdaadbbcbadaabcdbadacabadbaaadbbdbacdbcbaacccbdbbdddbccdaaabcdddddaacdaadbabbbbacdbbcadbcdabadaacdcdbdcbaccdaccabcbcaacaadccadcaabadcbbbbdcbaadbabddaddbbcccdbbaccbacbdcccdacbbdacdbbdcbaababaabbacdabbdbbcaccbabdababdbbaacbdbbdadcbbccdcdacddbcacccccaddadbadcdaaabadaabcbaccadddadbadaacaccadacdaddbabbdadcbacbabacbacbdaccadbacbcdbccaadbaaabadbbccbbdcbcdbdcababccacdcbbbabadcdccbcdcbcaadcadaaddbccbabdbaadcabadacadbbcaabbbbcabdbbaabdaacacdbcabadcbbdcddbbccbdaddcccadbbadaadbbabdbacdcdabdbbdaababccdcbaadbdabcaddbddbcabaaabcbdadbcbcabddaadbadbaddaaadabacdcacbbbbbabacadbbccbcdbcccbbdcdbcbbbdcaaabcccbdddcbabcabbcbacacaccddcddccadcaacaabdbbbaadbaccbbcbadccccdcaacaddcdcadcaaddbdababdaabbdbbdbcbdccdbcdadbccbaadadacdaaacdaddbdcccbdcbbcbddccbddcaccbcdbcacacdadaccabdbbdaaaabccdbccdabaacaccacdaccdacdbbcbdccdbbcbdcbacabbcdcbcbcdcadcacaabbaaadaccbbcbccadacdadbaddcaadbdcbbddcacaabcadabcbbaaaacdadbabbcddaacddbcdbacaacdbdbcdbdbbabdbadacbdabbbdababbacdbbabcbacbdcdcbaacdbcddcbdcdbadacabdccdcbcdcbdccdbabbaaaaccacadcccabdabcacdccbdddbbddbacdcaddacdccdbabdcdadacabcdcbbabdcadcabbdaaabddbadcadcadbacaacbaabaaaadccddccddacbbaaccaaabccddabbccbbbccdbbbaadaaaacacbdbabbdbaacdccabccdccbbcacabcddcabacaadacdcdcddbadacdbcadccbcdabcabaabdacccacdcadbcdcdcacacdaccadcccadbaaddbbdcbaabbcadbaadcaabacdbdcdcbcaadbbbacabdbacacbbbcbacdaddccadadbbdaaabcacdbbcadcdabbadabbaaaaddccadadcdddcaaddabaccabaadccabdcbdaadbddbabccdcdbbdbbcadcccaddacbbcbdbacacaaadadbadabaddbddcdccccbccbcbdbabaaabacdcbdcbadbbddddcbcacadcdadbadccbdadbacabcaaddbacccbbabbdcacccccbbcbadbacdbcdccaddaaaaaacdbdadbddabdbccacbdcbabcddbabccdbcddaaccbdcaacababababcaddbbcbaccdaaaaabcdbacadbcaccdcdacbabddcabadaabaccabaccddacacacbdcacdbcbaacdcaccdbccbaccaaabacbdaaddcaacbcaacbbbcbbdcacdcccadcdacbbcdddacaaaadcbcadaacadccddcadabbaddcbdcdadbcabdbdabdaadadacdbbdcbcbdaccbadbbccbdcbdabacbabdcbddabbdccbbababddccdaaabdddcbccabcbdacdbdacdbaaabbbdaadccbdaabdddaabbbdbaacbbcbbcbddbabccdbccabbcaacbdacadbcbcacadcdcddabcadcaadbbcdadbccdcdaddbcccbdbbddcdbdddbdbbabacbcbddaadcacbdccadadadcbacbacddbbdadbadacabcbddaadadbcdabcacadcdddbddcbbdbdadcbabcbbdcddaddcdcbccdbdaaaacdccacbaacdddcbdbaacbaadbcccababbdccdbbdacbdbdacdbbbdacbbdddbcabaddddbdaddbaadacaacadabdbbdbbabccabbcbcabbbbddadaddadaadabaabdbddcbddbacbddbbbbaacdccbdbdcccacbdabdbbcadbdbbabaacacdbcbcadacbccbcdcdbbbcaaabbbdbcbddadcdaadaddbabdcabbdacacdbcdabddabacbdbdccbbbbdbdacdcaacbacabaaacdccacdcdbcbccbcacadbcdcdacbcbcdbcccaddbcbaaaaddaddccdbdcbdaccbccaacaacdbdbbbadcddbdaccaacddcaacbcdabcabdabcddcbbcabbbcbbccdccdcacdcbabddccbbbabadbaddcdddaacdcbddacacdbbacabcadbdabccbbcbccddadccdcdbbddbbbbadcddcacbdadbdcdcdadcadbcbaddccddcdacadbbdbacdaaccdbccaabcdcbdabdadcdbcdaadadaaacddcacbcdccdbcbcbadcaadacdbaaddaabcdabcadabbcaddbcabcbbcddacddacdbbbabbbddacbbbbaadbaacbdcabbdcbabdacbdaacbadaabadcbbadcbcbdcbaadbbcddcdadcadbdbccabbdddcdbddbddaabddaaaddddaddbccabccabacdabcddbadbbadbbadcddcccabbdabdabddcbaaacdbaaadcabddabdddccbccdadcbabbdbcbadbacbddcabdadabbbcdddacbadbaadbbabcdaccbdcaacbbcdcdaccdabbbcdacaaaadbbcccbaacbbadbbbabbacdcacccdbcadcbaddadbbbdbbccacabdababadbcddbdcdcbadbbaadddaabaadcddcadaacbdbbdccbcdbcbdbdbcdbadcabcbacabcdcdacbdbbdcddbbaadbcdcadcddaccdacbbdabbdabadaddbabdadcdccbcdabdbddabccabaacacaabdadadaccbadbbddbbcddbbaadbbcdabacccdaacacdbbbcdcaaabdbdbcacdbdababaccbddcbbcccbbbadbdccaabcbacbcdccccbddabbaabbdbcbbddaccbdbbddabcccccddadaccbbbdaaadbdadbaaaaabaabaabbadcbdcdadacadabbbbbbaabbcaadbcddaccaddbdadccdadbdabcadcbcdbcaacbdcdbbdbcccdbcadddacbdbaadcaabaaabcbaacadccbacccbbbdcaabcbdcbbcdbaccccabdbcbabddbdbbbdadaadabbaaaccbacccddaabdcbabdcbddbcadacccbbadccaddacabcabadacaadcacbbaddaabbcabddbcbdddcacccbbbbdaacddacbdadadaabcaddaddabbbdcdabcacbabddabdcbbabccbcdbddacbcbaccaccadbdabdcdadcdbcadbdcbdcddbcacccaadcbbdbabcdbadabbccabaccdccbbbdcddadcdcddbbccbccaadddbbacbdbbccdbabdcadcccacbdddabdadabcdcdacbaccdacbabacbddabadbbccbbcbacbdaaabccacaaccdccbdcdcadddacabbbaadabdadcabcbdadcdbadcaaacaadaccdbdbccaddbddacbbbcbbaccaddbcbbbdcacaddcadcdaadbccbbccdbddbdaabbbdddcbcaabbddadcbdccacbddddbbdddddabaccdcbbddcaaaaacdbccbadccaabddcabbaddacbdaddaadadbddbdbbdaacacccbcdcbbbbacdcbacdcabbbbabbacdaaccacdaadaacaacbccbcdbadacbbbcacaabacdccacdcbdbccdcaadacbcacbcaaacaabbadacccabaabdbddcbccabdabacabcddcdccadacdbacbbddbaacdacadcddbccccabbdcdadbcdbbcddacdccaadcacdbcdcabbbadbaacdaadacdcbabcdbccacdacbccadadbbabbaaaccadcbadbadbbdddabdbbbbccbdcadbacdddabcabdccadbcacdbcaddbdddaaddddcdabcdacabdcaddbddaaccbbbcbdacdacdabdbcacccaabcdaaddacbcaaaaabcaddbddcbbabacccaddadcbdbaacdaaaabaddbcacbaacbbdccadbbddacaddacbaddcabdadbddcdaadcacbabbcbcccdacaaddccacbbcabdcbacbbacabdaaaddbdcaadcbabaabdaaaabaaadaaccdbdacbdaaccaacababdcdbcaadbbbabdcbacccdcbbdadacccdabccccbabbdcbccadadaaadcbadbdcbabacacbcbbbcaadcbdccbaacbacaccdcccccacbbbccbcbbcacdbdabbdcadbcdcabdccdbacbbacadbdabcbccabdcdcdaddcaabcbcccdbcbbcaabaabccbddbbacbbcbddcaccbbbcdbadcbbbdcccbcaaacdcdacdbbaabbdaabdbbcbdcaaaadcabbbdccddbcbbabaabadbabdbaddcbbdddbccbbcdbdbacdcdcabadabcbdacdcbcadcdcdbdcacbbbbbbcadddaaadaaddaaccbdbccddcdbcbbabbbdbaacdcaabcdacdbcacccdbcaaacbbabdbcdbbaabdaadbaadbabcababcbbdbcababcbdabacacdcddbcbccdbacbdbbddbacbddcadaaccccddaacababbdcddaaacadbcbcdabcbddaadccacdadadaaaadabddbaabcbbabbbcacbddcacaaddbcaadaadbdbaacbbddacaccabcdaabdaadcabaabadadbdbdabdacacccdabccdbbcbaaddcdaadbbcbabbbbbcbbddbacabddcadddcbbcccbbadaadddaddcdbbddccdbdabbadcabbabbaabdccbcccabadaadbcaadddbaddcddcadbdcabcddbccddbaacdacdadacadaddddcddbcbddcdcdbaabcbcddacccdadddcbdbbcbabbbccccaccbcbbbccbbcaccdbadacbbdbcbadaacbcbaacadcdacababadccaadcaaddabbdbccbaabacadcaabbbcdbacdadaadcdcbacbbaabbcbdcbccbacbdbbbcdbcabdaacbdbbabcaadddddcbbcccabdccdbabdcbdccdaacddaddbabddbbaccddcbacdaaacdadcdacbdbbbbacdcaaacabbaaadcacaaddaddcdbcddacddbcddbbdaadabddcabcbaaadbddddacdccdcbcdbdccabdbccbddbcadccacacbbaddbcacbbccccdaddbbadbcadccbabcbdcbdbbbcacccbbccbadcdccbdbbabbcdccdcbdbabdccabbaccbcadaadaddbcdbdbcbadacdadcaacdcbbdacdbbbddacaabbdcccabbbcbbbaaccabdaadaadcdbbbdbdbccaccbdbdcbccdcabcbcdbbbbbdbbbbbbcacabddabddaccadccdabcaacbdcadbcbcbdddbbcddacdbdacabdcadcdccdadddcccbccbdadbacdbbbcdccbdddbcdacdccabaccbadbadcdadbbbdadacbbcbadaacabbaccdcbcadbdcbacbddbdcccdcbaccacddcaacdddcabdacdddaaaaadbbcababdcadbdcbddabcaddabdcadaccbdcbadcdaacacdadaabdbcabbbdcbdabcbabdacbbbddcbadbdbaabbcdaacccbadabccdabadccdabcdcdbddddcdbcbdaabbdbdabadaacddbbcdbbdcbdcbccbbccccdcaacdabbccccadabdccccdcdbbaabaccccaccbaaacdbdbcbbabcacccacbbdaccdcaccbdaccaacccbddcdacabbccbdadcacbdabcadadcacdcaadbbcaadaaaabcbdbdbadadcacadabddbdacbbccbbadabacdbcabdbdddbddddaabbbadbbcccabbcbdddccbbabdabdccbbcabcdccdcddbddddbdcadabcaccdabddbdddcdbcbcbcadacbaacbccabcdbccdddcddbbbbdaccccdbcabdbbadcdadcddcccbbdcdbddccbbacbddbbabcddbdaabcbdaaabddcccbcdbabaabadbaaaabaccbbcdacaadcadcdcbadadcaddbbbbacbdbbdccdcbabdccbadbdddcdcaddabcacbcccdadcadaacbbcbcaddabacaccddddbcacdcdadbacdbcdcddaddabddcdcdbacadccadcdacbdcaacdbabccdbabbcaaadcacbacbdaaabdcadacbcbcaddbdbdcbccaadcddbdcddccacbbbaaacdadccdddcccacabcacddacaccddacaaccabdbdaaccbabacbbacdcbacdabacdbccbdddcbdbbccabbabdacbacbcabbdabddddabcaadbaaacbabcccbcadcccaabdabbabdaadabdbbbbcbdabccbdbbcccdbaabbdaabdccbdcbdbddacdbaddbbcddaddccdabdadaacabdcddbbcaadccbcaaccdcbbadcbdaddcbdbbacddcdaabddcdabdadbbccadbbbbdaadddcccbdddacacbadabbadddacdaccddbcdbddaadbbdddacaaddaaddcababcbdcacacbddbbbdbbdaabcdacabdababdddadadbdbdaadcadbabcabbbcacbcbabcaccdcdcdcdddacccaddccbabacdcadadbabbbabdbbbcaccdcbcbdacccacbccdaccdacacbabcaaddddcbbbcddbdcccbbbcabbdbaaaacbcddaabbaadcbabadccdbdaccabdaddabcccacaccaabddacaadbaaadbababadcbacbdbacbbcbacaadabccddddbabbdbcccaddbccbdcbdcadbdcbbaabbbdabddbddcdbbbcddbcacbcacaaddcaacbaadaaacaddbaadccbdaccddbbdababcbbbcacadbacaabaddabadcaddbcccbdbddbaaadddbcaadbcbddaadccadcadcbcbadbbcbbaadcabcbcabcacddbbaaccbdbccbcbbbbbadcccaadccaadbbacdaabbbadccdcacccbbbdabccabadaabbccdacbaddadccdabcdcdbcbaabaabacbaacaccccddaccabcaaabdbdcaabaacaaddacdabddccadcadcddbbacdadcadcabcbbddadcabcaadbcdcabdcbddbbcbbdcdaacdadcccbaaddaaaccbcccccbbdacdddbdaacbdbccdddacdbccbcadacbacccbcdadddddbdbacabdcbcdcaccdadaaadabcdbdaddccadddadabbcacbabcbbbbabdadcbcdcabdcaacdbdcbcdcdcdacadabaddaddabbdccbdbbaaccadbdadacaabdbdcadaabadddcdadacdcabdbbaacbdadccbadcccadcaaadadabaabcbdadadababcdcbbcdadccbdbcabbacccdbcbacbaacaaabadcddacdaabbbdcbbdbbdbdabaacdadcaadddabdcbddbbbbabccbddabcaddcadddbbcbbdabbdbbdcadccdadaaabdbbdcddaadbccbbcadcbaddcddbcbbcbabacdcbacdbadbbbacadcdacbbcdaaadaabbdbacddaccbbbcbddcccccbccdabcaaaaacdabddcbbacaaabdccbbcbadaadabcbcbcbbaaacbaacadbcdcdababdabccbbdcacdabbaacccbcbbdddadccaaabaadcdbdbbadcdacbbabbcaddaaacdacaacccdaddddbbbbcdcaabcdcdaddbbaababbcbdacaaabbcdccccdbabdaacbbdbbdcaadadaadadcbdcadabdbbbcdadabbdaddcdddccadcbddbaccabcbcbdcaddccdcddaadbbbaabcaadbcaabcdbacabdccaaacdccabcdccabbdddabbddbdbaccdaccabacddcbabcbcbabdadcacddaabbacdcaaaddabbacdabccdddccbabaabcccbdddbacaaaddbbdbcdccbaddcaccaadcbcbadcbcccdcbbbbdaddccddabdbbabacbcddddabacacdababdddcdaabbdccabdabbccadacccbbddccdccabbabbcacdcbbcccabbdcdaccdcdacdbcaddacbdccccdcaddaadcccabbddcabbbbaaabbaddccaabdbbdaccbaadaacdadcdadcadddacdcdbbbacbdcbbdbcbdbbcbdccdabcadbbadabcccdacacddbccccdddbddcaaabcbdaadadbbbccdbbaadbcaccadbbcdabadabbbbdaddcacaddacabddcdbccadccdadabcbadcddcdabbcbbcdcaabcbabcaadadaadcbaddbddbcbcddbcbcabbbcdddccddbacdccbadbaadddddcbdcacccdcbcddccbaacaabcdbddadadbdadcdccaccdddabbccbabcabbbccaddacdbbbbbcdbdbaccadadabdccccddadcacaabcddbdbdbabcacaddaabbbcabbbbcbbdbbcbbdcababbddabcddacbdcbbdbcdcadcacaddbdcabddaaadbdbacbdcccddcacacabdcadadcbbcbbbddcbcdbadbaaaaaddadccddadbcbaaccaddbbbdcdddcbacddcdadbbbbdcdabdbbbadddddbbacadcbbabbccbccdaacdaadaacadccabbabdbbbdcbcddcddbbabdddddcadbcacaddabccbdbbdbacaddbcbdcbcbddcbabacdbcabaaabadbbcabdbcadaadddcbdcdcabaaadbaabbadccbbbddacadaabddcccbbaacaaaaccaddddacdbadcaacdadbdccbcbbbaacddbdbababaddbdbdaadddacbaadcccbccadcdbcaccaccbbcbdabbdcbaddbccbcbcadaddaadbdbaaccdadbcbddcdadcbdcdabbacdddcaddbdabacddaaadbdddadaabbbbdddbddbdcaccddbbdcddadadadbbcabbaaccccbdccbcccbaadcacdddbaccdcbccdcbdaabddcadbdcababdbbaddddddcaccaaabbdcabcddcdaadddcdcddcaadbdabaccddbcaaaadabcbdcdbbbbbbbaccadabaccdbdbddbdddadabcbaccabaaaabccddcaaacaacdacccacdacdaddddcbdcbcaacadbbbcadaccdbccadbdcbcbadbcdaabacbcaaccccdcbbcbcacabbdcccbdcddddbadbdcbabacdbacdaadcbcccccabcbaddddcbadabddbaabbabdccabaddcbbcbaacadddbcaccdcdbbccccadccaaaddbdcadcabdabacbbdbdddbaccbabcbccbadbaddabbcabacdadbaabacaccbdaaaaddbdbbdaccbacdddaabccdadcbbdaccdaaccbaccbccdaacbbddcdcaabddddacbcaadabcbadaddcbbddcddbdbbdbaabccadaabbcdcaccbbdcccddabdaabbcdccdbaaabdcadadcdaaabadacddcbcdacabcbbadcdcaacdbaadcbbcacdccdabdbabacbbcddcaddaaaccdbdabdabbcdbdbbbbdaacbbdcacbbcacbbdacbbdcdbbaadcabdabdbbbcddcdabadcdacbdddabddaadddbaaadaaccbdaabbababcadccadadabcddaddacdabdddaaabdacaabaddabbbccdbcadabcacbbcbacccdacadbdcdbaabacdacdcbdaddcdcbdaddbdbbccddcabbbbdbdadadcdbcdaddbcdcaccdcbdabcbcabccbccdcacdaaabadbdabaadadacbadcdbbccdaacdadbacaabcacddbcddcaddaccdbcbbcdcacbbdbbabbaaacbbaddbbcabcdadbbdcbccadbaadcadddbabbdbacdacdcbbddccadcbbacadaadcaccabdbabcaaaddacbaacaacddcdbcdccdcdaaaccccddbbdbdbaababccbdcacddbcaabadddacacdbcccaabbccdaaadbbbcabaaacdaccadbcbacabbbdbdabaadbbbbbabaabaabbbcdbacdbdbabcaadaccccabcbcbabadabcddccdbdbbaabdacdacdbcabadddccbdcabcddbdcbdcdbccbdbbbcddbcacaacbacdaaddaaabbcddbdcdbdcacbbbcdddbcaabbbdaacbcacaadacdbcbbdddacdaaacbbbdcabcabbcacbbcbabbabbbbdabcdcdbcbabcccdacacbcddabbdacacdcddbbdddcbaadccbaacddcbdbdbcdbcdbacaabdacadabbabaabddbcddcbbdabdadacacaddabccbaabddbdcacdccbcccbbccaddacbdbdacddbadbcdcdbabbccaddbbabdbdcaccbddcbabbabddcbadbdcabdaadaadcbdaddabaaacddaddabbbacdcddcdcabbaaadbbbdaadbdccdbdddadbddccacbbcacdadbadbccaabcccababddcbaabdbdcdbddadcdaaadaacbdcabbaaaadcccddadccaabbdddbdabbacddccbcdcdbbbaddaabcabaddcddbccaadcaadaacdddbbcbcbdacabcdadbccbadcaadbaddacbbbbcdacabcadcddbbabbdccabbbbbccaadbababbbbacddcccbdddbaacbcbdddaddcbbdaacdcbbacddddbbcccddbaabbccbcacbbdaabaacdccbbdacbcaccbabbbcddadabbbcbddaaaabcabbcacbbbccdabdccacaadbcbadabaadbacabdbaaddbbadadcadbcddcacddbabbddcdbacddcbbdddbabdbcabdbdcbcbdbcacccadddccccadaabacdbbcccdbcdabdaaacbcbcddccdbbdccadcdccabbdbdacabcccbabccbcbbbdbdcbaadbcaadcaddabbcaabccdbbddababddbcccaddcddbadbbccbbadacbbdaacdccbaacbdcbdcbbddbdadbaadadaabbbaddadcaadcccabcdcbdcbabccaadbdabbacddbbbbabccdcaaaccbbaaacbcaccacbadaabcbcacbccaabaddccbcdbbabacdbcbabbdacbaaabbadbddbccacbcadacdbacacbbdcccbbabaabbcadaabddaddadabbbdbcdbdbdcdbddbcdbaacdacbccddbcdaadcababcadbcdcdbcacddbdbcccacaabbbcbbdaddbdacaacbccbadddddcbbaddaccdabcdbacccadaacbdbddaacaccbbcbcdddccaadacdbcbcbbbcdbacabcaddabddabddadcbacabcadabadadcccacabdbccbadcabbcdadbdcdbcbacadbbacdbacacadccbddbbacbbbdcabdcbaaccbbcdccdcdbadbcabccdacddabbcdaccbdcbdaadabdaaabbbcabcbdacccbdabddcdaabaadacbabbbccdadbdcacbbdcadaabadccccccccbdbcdabcdcadcaacdcdaabdbdbcdcacadcbcabcbbbdacacadddbcabbaaacddaadaabcbcbaabaaaadccbbaddacadcacbcbbddcddbaacdbabbacdadbacddacaaabcbdaccdabcaabbcacccdbadacaddcdbadaacacdcdbdcbbabdddbbddcccbdddbcdadcddadcbacbdcadcabccabccbaacbadacbcaabddabddacbcacddabbdbbaddcdcaddddcaddccbdadbaadddaabcababdbcbcbddbdadcacbcdbbcbadbdacbbdadcdacadcbbbdbbacaababbacabcaaddddbcccbaacdaabddaaddbdbabbabdbcdadabcbdcaddcacbcdbdcbdaabbcdcbadcaacbaabdcadcbccbdddabbcccbbccaddbbcbbadbbccddbadcdcbddcbcdcbcdcddcbbdcdbcacacdadaacbbbbbbdcabdcdaadaaaccdcbbdbcacdcdcbcbaddbacccbddbacacccaddbdcbdadcddcabadddabaabbbcadadacbcbccdbddddabdabbaddcddbbcaccacdbdbaacdbdadadcdbcbdcacbaacabcbcddddbdbddddaaabbdbdbacababcadaacbddcabbacdacdccabcdcbcadccaaaccdbbdbcbdcbdccccacbdbcdbabdcabaacabacdcdbcddaacabbabbcdccabadcaacbdcacbdaccdacbdaccacbdbdaaccdaacbaaacacbccddbabddcbabaadaadcdcabbccbbbddaaadbdcddaaabcadddcbcbdbbbbdddabcddcccaabddbacbcadadcbaddbcdbcbbababdbbbbddcbddbabdbcdbdbbabcdbcbbdacdbaacacaabdbabaccacacbacbbacdcbbbcddadbbaccdbabcbdcbcaadadbdbabaaabdaaddddadaaaacaadacacbacbcababbcdaabcbbcbdddcaacccdcdadababccdcdcbbcbdaaabdbacdcdaadadcbadcdbddcbcabcdcabbcccdbbbbabaaccacbcbcaddcdbcaacbabbbcddcddccdacbaacabbbdccbdbdabdbadadddbcdaabdaaaaccacdcbbbdbadbddbdaadcaabbcabdbdcabcabdaacabaaacdbaccabaadbadcdcadbbaabdcbbababdbcdbacbdabbcbdaddbdbddbccbdbabacadabbbcdddbdbbdbcbccacdccdaacbddabaabccbccbdabbadcacbccdadaaccacaccbaaddccbaccacccbbdadaaaabaccbddadadbacabcdddacabcccdcbcabbcbadbdbdcbadbabaadaaddabbdacaabbdadaadbdbbadbabbccaabbbbddabcbcddacbdbbcadbcabdabdaabcbaaaacddcccabbacaacddcdddadaddcdcddcbdbdacabcbcacdabdacaddccabbbccccbabcadcabdcbaabdbbdbdcabbbbbacbcdbbbbbaadacbcbbcdaaaddbbdccbdcdcbabacdccdcbdabcadbacbadaabbbadccddababdbdccbcbabadaabcbaaccccdcdddabcdacabcdbbabdddbdacccabcbbbdbdddcccbbadcabbddcdbdccbcdbbaabdadcdcdbbcddbcbdbbcaacbdbabcababcacccabcbbdbdbdccdccbccbdbbcbddbccabccccaacdbcccadbdaaddcdddcddbcaabcacacaaaabcbabbdcabcaabacacaccddcdbabaccbadabdbacccabdbdccdaacaaddbcbacadadbcaaabadaadcabaadbdcddccddbccbdcbdddadbcbcbcdacacbabdddbbadbbcdaadacacdacadaadccbabacddacaddaabdccabacccdcadabdbcddbadadbdbcdcaabdadadcdabdcbcbbdbddbbbacdddbadbbdccacadcbaadddbaacaacbddadabccaaaadddbbbbabdaccccbabdacbaabcdbdcbdbabbbaaddaacccddbbdcaacdcdccdbdaacadddadadccdcdddbbdddacabdcbdcaacbbccacdbdbbdbcdcaccdbbabdaadcabcbdbaddaadcabcbadacdaacaadacacccdabaaadbaaacaacbbadcbaaaaaaddbadddcabdababbcdbadabcdbdcbdacaabcaabcacdccbadbaacacadccaacaabaacadbacbdbbdcacccaaacdcadbcbacbdcbbbdabdbadcdadcaccbabdacddbcbdbacdaabbddcaaccbbdcaadcacbbbaabadaabadcdaadcaaacabdbdccdccddbaababdcbbbcccdbbaadccbadacccdaccccbbacbaccaadbcbabcbacdcadbabacaadcccadacbaccdcdcaaaabccacccdcdabdccabacbccadaadbbdacabbcdcdaaaccdcaddabcacaabbaccbacbdabccbccbabdccdddacdcccbaadabaacabcbbdaaddddddacccadddbccacbcacaaacdcdaddacabcdaaccbcdbadcbcbbabddccbcccbbbadadccbaaabacdddbdbaccdbddaddcbdbcddabdccbcdbbddbbadaddccbabaccbddcdccbcbcddadacccabcabbadbadbdcabddccdabdcccdadbabbaaabcabcccddcaccacadbbadadaabbacdddcbdcdbacccbccdabcacbdabaaaccddcccadaaaaccdcbcacbddacabaababbacabbcabbbbbbabadbdccabdddbdaaacdccdcdcacdbbbdbddabacaaddbadaadaabcbbacadbddbdbbcdbbadaaaadbcbccabccdacbbbddcbbccbdadadaaaaadcaacbccdbdacabcdbdbaddbdbadbcdbaccadadacbcbbcbabcdbcbbadbcaddadcacccccdddccbdadcdabaaacaadddaccdcbdcabcdacbaabacaccaadbdbacaccdcdaacbbaadcdccaadabdcbcaabdbbccbacbcbbcdacbaacbbbcddcdbaaccbacbbbddbacabbdaacabdcaccdbdbbdbbadadabacdbaaadacdcbcaaadabdaccbccbbacbcbabdcdcbcddcabdcbcbbabdbcabdccaccbacdabdcdcddaabaadddddddbbcdadbccdababbabbcabbadbcbabdbbddaabbdbaabcbdbcccbcdbbbacdccdcabbddbbadbcbbadbdadcdbdddcbadabcaadddcbaadadbdbaaddbbbbdbbadddadbacdabbdcaacabcdbccbdacaccdcbdcbaacaadbabbcdabbcadcdacaccadadacdcccbcbadcbbbcadbdbbddbbdaabdbdcccbcabbbbabdcabdaadaccaccaacccbcbaaacbcdcdbacdaacbacbdaabcbbadbdacbcdaccdbbacddddaacadaadccbaaabbbcdabcaddadcaadaabbadddadadababbadbdacbcbaaabcacaadbabbcbbdacddacaddadcdcbaaccccbbdccdbaadadaabbbadcbaccadbabdaabacaccadcddbabcdbadabbcccbcbdabbdcdccdadbdcdbcdcdbccccbdaabbdbccaddabaccacbdbcadcdabcbddccaabcbcdbadbddbbbabddcbcbdcbcddbdaacdabccccdbdbaabacaccbbaababcbdcdcbdbdbcbdaaaddcbcdcbcbcddcdaabbbdcddbbdbbdbbdcddacbaacadbdddbbbcddddadabbbaaacddbcdbcbcbdccacccbcbbbcdccbaaacdbbbdcdbcccddcacbadcaddbbbacbccddcbaddddaabbdbaaaabcdbbcdcabbbcadcaaacdccbbcbaddbacdabccdccdbbccdddadaadcdbcadbadbddabdaacbabccbdbccdccdcaddaaacddbaacbdbabdcbacabbacdbbcaccbaacccddbcdadacadbcabbaaabaabacaacbdbbacbbddccadaacbdbcbaabcbadcbbabcddabadddaddaadaacacadaddbadbbababbdcbbacaadabbaaabbdbbcbbdccdccaccaabdbcbaaccdcbccdadaddcacaaacbdaaddbcbabccaccccdddaaccdbdddaddcdcdbbbbcdcdccccbbacbdbcbacbacddaadbcdbdabaddddacaabbaddccaccdbbacdaaaccbbaaccadbcbaadaabaddabcddbdcadabdcbbbdacbcaabcbdccaddadadbcdbcdaaccbcbadbcbaacbbdbacaddacdaddbbdbabccadaacbbbcddddadbbadcdbdacacbbdadccbcabaaabdcabbcbdbabcbdbccadbaadacdbbcabbbacacbbaaadbbdddddcdaacbcaadcccdabccbabaabababbbcbacbadbcadabcadcbaacadbadbacbccbbbdabbcccccacbcdbcaccbbcbabcbdccddbacccaabadcbacbbccccbdcdabaacaaddbccacabcbdcdaaaabaaddacdaddddaddacddcbdddbaaabccccadbbaaabcbbbbdccdaadccbdcdabbcaddaacacdbababbdacbbdbbbaccdcdabaaccacbdbcbccacabbacbaaccbdacaccbbdacbdcdcdabaadbbbcdddacdaacbbaadbdccaabccaaadaaadddccaaaabacbadacbdabbdbbddabaccdbadcaaadbddacbccdcbccbdcbabccbabaadcabbabaabaacdbcaaddccaddbcdcbacbcddbadccdcdbbadcdccdbadccdbbcabcbacaaddaddcdddcbdcacabcbbcbaadbcdbdcdddacaccdbababcddbbdacdddbadcadccbdbcbcdcbdaacaccdaddabdbadabacddbadcdcbcdabcbbcbcbaabacaddcbbabcabbcacbbdcddbdaccddcabdbbaacdbbcadbbcbcdcbbcbbadcbaabdcbdbabadaadaadbbddbdacdccdcdbbcacbcdbbbbbaabaddbabbabddbccbccaccadcccaadcaddcdccabadddadbbcbdcbcddbbbcdbbabaccccdacaaacdddbbabcaccdcdddcacbadabaadbabadacabaaccbbcaabdaacdcdbdbbdbbcbaaaaadbdccaabcdabbcadcacccabacbabcdcbbdacccccdacaadcccacabdbacbbcccbaaaaabdddcacaabaaaaaaacdabbbcbcbccdbabcbdccbcaacadcdaacadcccbbdcbccadcbabddcaaccaaccdaaababcdbdacbdcacadbbaaacbbcaadbcdcbdacbcaacccbbaddaabbcaabdbabbcbacacdcacabcaabbcdcabaaccaccdbbbcaadcbcaabcaaccddbbddaddbbcccadbabbcaccacbccadacdbcccbabcaaddddaacdbcdbacacddcdaadabaaaccaabcadadcbabbccaacbdddbdbadbbcddaacbadacccdacabccbdddbcacbccbddbabbdbaadddcddbadcdcdaadbbbcdacabddaddccaaddaccddcdacdaacadcbaacbadadbdcbcbadabbbbcadcbaaabaccaacaacdbdadcbdcbcacabdcdccbdcccabdcdbbbdcaacbdccdddbdaccabcddccbccbddaccddcabadbbcccdbbdcddbbacabdbaccbdacccdcadddbbccabccdabdcdaadcacbcbabccbcadbcccaaccbbacdcaadbaacabcbaccdbabdadbccacbdabdcdbbdabbacbddbbacccddabadbcbabdabbacdbbcabdabdbdbdcddaddaaadbbaddcabbabbcdcdcbabbaadacddcaabbdbdaadcaccacbcdbbbcacdcccccbdbbcccbcabdbacdaaabccdbaadcbcbddbabddbdbccdbdcbccbacacdbabccbddcccadbdaacacbcddcbdccbabccacdbbddccadbabbbacbcadbcbcccbdddbccdabbadbcbadcdaadabbcdbcacddacdbdcdacddacdccccbdcaacaaadaaaaabaabbdcacdbbdadcbbaadaabdabcbbccdaaacabcddababcbcadbbacbcccccbcbbbcdbabaaabdcdaabdaaabaadbddbcaddccabbdbadbccddbdbbbbdabaddabbbcddbdacacadbbcaccbcbbbbdcdabdbadccbcbaccdbdcdbdbbbbaabdadcbbcadcaacdabdaccbacbbabbbcbcdacadccaabdbaccaacdbdbdbbcccbbdcccbabcccaacdccdcdbcabbaabacadaccacddbcdaccbadcbcdaadddadacacbadaddbaccbbdcabbadbdaadccddddbccdcbbabdcdcdbdaccbaacbbbddcddabaabccbdbbcadaaaadbbadacccbbdbabbaccacdcdbdacbaabcabcdaaaadbdbbbaaddbcdcdcccddbdbbaaadbacdcbbbcaaccdbadbccbdabcabaabcccbbbcabcadcaabbcacdbdccbbdcbcbdabdbbadacbddbbbadbbccaaadddadbaacbbddacbbccdbddccaaacbabddaabcdddcabbdcdcbbabdbbdabbaccabcdccdaacdbdcdcadcabcdccdcacbdbbbcacaddbdcdaacdcbaaddccdabcccccbadacbccddbcddbbdabbcddadbcbabaccbbddadcabadbbcacbbcbabcaacacacadacdbbcccaccadbacdddadddababcbcdadaabbadbcdbbdcacbdacbacccdbdbdcadbabadcbabadccccdabccbbdcbbdabdbddbbddaacdabcabbbacdcabdbdcaccbdcacdddaddaabbbdbadcacaaadcbccbaaabbbdabacccccddddbcacbcaccdabdbbcbddddccbdadaabdccadbdddbbaaaaaaaaaacbaacababcababbbbdbccbcbbabbdcabbcdabccadbbbacbbabddabcadcacabcacdddaadbbddccbbaadccaabacddaddaddabbdaadacddbbbbabdadcdcccabdcabdcbdbaabbcaccdddbdddaddcacdacbdabddaacbddccbabbcaccababaaddcabdabbadbbbbbbddcabcaaddaaacaddbaaabbddbaacbcbabdbbccdaabdaccbaabbdbbabbaacddbcdbbbcbcaaccdabcdbbabdbbaabcccbdcccabdbdbbcdacdbbdbdaadadcdbccbacadcaaaadcbdbbbcdaacbdadababacbaddbbcacbdcabbcdaabcabcbabcaabaacdbdadabacacaddddacddcaccdccbabdcbacadcabdaadcdacccbaaccdaaccccbaadbdacaaaacdaddbddcabdcbddddcbdaadcabcdcabaadbdcbcbcdadbcdbaadcaacadbaddacaaddcdcacdcdcadcadbdabdaadacdabbadabbbacacbaddbbdacacacaababddcddbdacddaabadbdaaaddbacaccabcddbaabbbddbacaaacddadccacacabbcdcdcdddcdbbdadccababdbdabaaabddadbbbbcaacddaadddcbbaadaabcaacacacbcccadaaaaabcbbabcaabcaaaacbcacaddbbcabccddabdaaabadbccbddabbbadaddcdbcabccadbdabddabcdccadbadcbbdcdabdbabadacbccbbbbadcadcdddcdacbbddcabbcddccdcdacbddbcdabbcabccabbdbcbdbcbbdadcbcddaddcaddbabdbcbbcbdcbbdcaccbaccbaaadcaadbbcdcadbdbdccdaabbdabccababbaccdabddbabdddcbccdddbbbbcbbccdcccaacdaabbddadaadbaadaadccccccaccddaacbacdcaddcbcbaccadcbdcccddcbbdbbbabcbbadccadddadbdadbcadbabdbccaacdcadbaabdbaadaccbbaadbccbbbbcaadddbbbbdddcbbacbaddccdddbaaaabccccbacbcaabdcacbbbcabaddadbdbaddddcbcdbbdcabbcbadcdbcbdbdcbdbbddddabcdbddabbbbabadbdcdddcdbadcadcbdaadaacccbcdabcacbbadaccabbadcccbaadacadbdcccdbabddaaadccbbbcaadcdaccaaddabbccdccdcbaddbccaabadbabbabdaaaaadacaccbbbbaccdcaabcbababccbdbbbadadacccabbdadadbddadccadccbcaabdbcabbbaddbdccbcdddadbddbcbabaacbabaadcaabdcdccbbbdbbddabdaabdbbbbccdbaddadadaaadbcdaadddacabbccacbaccbabaccddacabcdcbcbddacdcbbabcaaccdaabaabbbadbdcddbcbcbddbccabadcdbddaddacaaadcbccbbbcbadbaadccacaaccadcaacacdcbacdbacdbadcbcabbadabbabcbdcaaabdaaacdabadacabdbaccbcabcdcdcaccaaddbcddaaacaddbbbcdacccadbaaabbabcdccacbaabddccdbddaaddadbbbccbbdabcadccabdbccdbbbbaaccbccabdadcdbcdccdabdbdbbdcbccbbadcccccacbddddbdbddcdbcddcbbbdbcccabadbddcbaabdccbdbcbccbbddaaacacaaadddcddabdcdccccddbdbaadccaaddcacccbdbcabdccbdabdacdcddaddddadcccbcaaaaccbcdacbaddcacabcabcaaadccabadcbaacacadbcdbdabccdcccccbcddcaababadadadbbdabbcdcaaabaccbacdbbcdbcacbabaabdbcdaadabdadddcbccaabcdccbdcaaaaddbaccdccbacaccaccbbbccdaddaccdbaccadbabbbccaaadcccabbbdcdabddcdbcdbaaaccbbabccdabaccaacbadccdcabddccaddaabcbddddabbcddddbcbdbddccdabcadacadddbcbbdaaaadaccacbacbdacabcaccbdddcacbaadcbbadbcbabbddcacbbdbaaddddccaacbbdabccadabacccaabaacacadbdabdabcacdbaabbadadcabcbbaacbadbadaaabbdaddbcabddadccccbcbababccddcdbdaabaabbacbaddbccddddaaddbdcacaddcaacdaccdacacdbbdccabcbcbbbbcacdbaadadbacacbbbbaadddcdbccbcaacdccdcdacbccacacbbdbbccadaddacbdaacadcdadaccaccadadaaddccadbaaddaccaddccbabbddcbbcdcdaccdcaaacbdadbbcbdcacbbbcdbbcadddacacdddabaaddcbcbccdadbbccdcbcddcbdddbcdcdccbcbdbbcaabcccdabbacccbdaacdaabcddacbadcbaababbdabbbaacccdbdbadbcbbaaaacacabbadcabbadcbadaccabddacdaaaddadbbaabacadddbcadbdabaabdacbadbcbddbacddacabbbdcdaaacadccdaabbdadacddbcbcabddabbbcadccccdadcbacaddaccaadbbaaadabadcaccdaadccbbccababaabdbbadcacadccbccdacddbabdddabddbbacbdcbdaacabdcadadddaccabacbbabdccdadccaacbdbcccddcdaccbacbcccabcadbbacaaacaadcabcdbdddcadddcbccbadcbddbdcddcbbdcccdbaadccbbdccddddbaddacdddbdbaccacbadccdaadaabbacbdbdabaaaaccabccdaabcbdbbdbbcdabbcbdacdcaaabdcccacddbbbaabadaaacdabdcbdccdbbbdbbdadaacbbadbdddaacadbbbcddbdddbbaaaacabbbccacdaadaaabbaaaadddabbddbcaacbaacacadaadadaacbacddbacddadadbbbdccabaadbdaaabdbabccaacbadcdaccaabbaacadabaadbadbdabbacaddadabbadbddacccacdabdbbbbcabbdcadadabacababaacabbabadcaaabdbddbdcbccbabdabbabdbaacacaacbbddadacdadadddabbccdaabdbaaabdbcadcdaacddacbcababddcadbacdadcccabacbdcaccbaaacdacccbabdacaacbabcdcaacaaacbccaadacdabdacddabdbacbddcccbabddbdbccccacbababaddabbcbcaccbbcbdcbabbcaddcbdcadcdbadbbaaddbccadcdacacbcacbdaabdcabcaddadcdaabcabcbbadcacdbadcccdbdbcabdacdcabdaacdbbadccaaadbcaabbbbdaddbaacacbcbbdbabddaaccdccbbaddcdbbacabcbdccbdaadcddbccbccbbaaabaacbaacdacdaaaddcbbcddacadcbacaabbccdabacbcaabbbbcaaccabdadbacadabbaddbbdaacacdbabdbcaadbbcaddbacdbccdadcabccdacccddbcacadbcaddbbbdcacbccbddaddbadcdbccdacdcdcbddbaccccdaddbaabbddbbcbaccccdcaabcaacdcddbacbdadabbcabddaaaadccadddcbbbadbcdbcdadadbbbbbdddbbccaddbbdcbcdcdcdbcaaaccdcbacaaacaccddcdcccbbddbdccabdbcbbabcbbddadddacddbdbacadcaabcaddacadbbddbacacadccbbcdcaadabbcdcbcacbadacdabdabdcddbdabadcbdcbdcbaaddabcacdddabbbcabdacabccdcbbbbddacdaabcbbccdadccadbdddabdacbcdbbccdccacaacabcbabbbbdcadbdbbddabcbbbbbccadacbbcdddaacdadcccddcdabdcdadbdbacadcbbaaddcbbbcabbcbacbcbbccdbbdcdabcbdcaccaacbdbabbcbbcbadbbbacacdcbacbccacdcdddddcdddbbcadaaadabaabbaccadccccdcdbaddcdcbabdcaccabbaabacadaadddacbbadcdcbdaddbcaadaaccddccdadcacddbbaabaabccbcdcbbbcdbccbadcaabdcbbabaccbaccddbddabdcbabbccccadccdcdddcbaacabaccbcbdaacbccdabacdbaadccdbbdbabbcdddbaabbadaccbacbcdcabcbcabdacaaddaadcaadccadcadddbbbcadabcccdacbccadcdbbbbdadcdbbadbbbbcbccdaaabcddcaaabbaaabccbcdcbddcddacdbbdbbccbcbbabcdccadbbcbcbdabadddaccdcbcbdbccadcbbbaababaaacabccccbddadcaddcbcdadcbccbcbacdadadbcacdbdacabcdadabaacadbdccdadaaddaaddbddcbadbbdbcdbbaabdcbdbbacbaacddadaacacccbaddcbbdacdaacbdadbbabadabbbdabcdcbbccdaaabccdadbdccaccdcadbbaadcaccbdcacaddbadbaaacabbabcbbcababdaddbbcdbaaabbccdcdbcbbdbdbaadcbdacacdcddbaacbbdcbdaccbcabadabacdddcdbcaacdccabbbdddcabccbbcdadabbbacbdbadbabababdacadbcabaccdcbbdbbaddcaddbccdaccddcbbbacdaabcacdbdbcbdbbdbbaabcbdcdcadcddaabcccbcabcbbccdcccdbadaadbbbaddbccbcdbbaacadbcabdccbbccbaabbcbdbabaaddacbdbcccbdddbadbaadaaddccabacabbbdadcacddbdbcbcaabdabbcddccaadbdcaaadacbadbcacacbbddddbcdabdadbbcaaabaaadcccacbcbbdddccdddddddbcdaabdbdacaddddbcbcdbaadabdbdbbababbbaddbabcabaccccccdcddbdaabaaacacaaddcaaabcbddddabcdcdcbccbdbdccacdbbdcdcadaadaaddbbdaadddcbbccbcaaddddcabbdadbcdbbcadcdccccddbacaaaccbcaaabbbdbbccbdbcbccabbdcdbaccccbcdbccddbcaadadabdadbbbbdbdbdcacbbacbadcbabbaccbaaddacdabadcdcddacbdcadcadcccdabaccbdacddabccccdcddbddaadbadcbcbddbdacccdcccdddcbcdbcbbcacacbdbabdabcacdaddcddbccbbacbdbcdbacbcbabdccabcdcaaacbbdbcbcadabbadabaabbcdbabcbbaadcabbaacadabdacabbdccbcccabdddbcbadbbcdbdbdccbacadaaddabdcdabcbbcddddbcccbbacbccaabdbcdcdcaddbdcdbadddbbdddbcdbdbbddccbdacdcdcdcbbbadbbbdadbacdabdacdbbacddccbccbdcddcbdddcacbccabaddcbccabbcbbbabcbadbbadbbccbcccaaabbdbdbddbcdabdccdcdcdaccddcadddabbadcabcadcacbaadabcbabadabacacacbaaadacdacddaaabcccaaaddacdbccdddadccbbdaadaadbbdbabaaccabcbacaacbbbabacdcbbcbabbcdcaabdabdbbbbcbddacbccbbaddcdbcdabacbbbcaaccdbbcddbccacadccbbbbcdacdbdbaddbddaaaaabdabaaadaddcdbccbbacaccbbddaadbdcbbccabcaacddbabbbdddcbbbbcabbbccadadabbdbbcbbdacddbcccdbbaacabbbdcbbadcbdabcabbcdbcbaaccdbbacdaabcaacdabddabbbacdadcbacaaacbbacbbddddcbccacdcbcbabaaddbddcaaaabaaddaabacccabbdaccdabcbdbdcdbbcaccdbdccccddadbcbbbbadcacbcccddcccbbcccdaccabbcbacddadabcccdbdabcbadcbdbbcbaacadabddbbdcaaacbdcbcddccaddbcdbacabcabcbaddcdcacdcccacadabdccabaddcbaabcacbcaaaabddbbdcdabdbcacdcacbbbbadcadcdaccddbcccdbabddddbaacdabddaacbbadbadbddcbadacacaabbaddcabcabdccaacddddacdcabcbcdbacbdaacaccccbddbbcbcabaaaddadcdcccaacddccddadcddcabdacccccbadacbcbbdaacdabacccadbdcadddccbcccbbabcbcbdbbcbbccbabdaadbbdbcdcaacbbcbaddbacabaacacbacdcaddbcdbcdbbccdacccbccbaaadadcdababcbbbabacabaaccbbbdddabaabbadaddbcaacccdadabcdcabddadaabbacbbbcccbabccbcbdaabadccaacabbdcbdbdacbbdbaddcddadaacbbcdddddddaacdabcbcdcbbcbccdbcdcddbacabdacddaababdacddddaadabcaacadbadcdbcdacdaabdccabbcaabccdaaccabcdcdddbbadabddcdaaccbdaacaaccbaaacadadbaaabcccbdaccbbdbdaaabcaaddcbbccccdbabbccdadabbaaccbcbdadabdcaaabddadcaadbbdbbaccdbccbddbdbbdcdcdcbbacadcabdadbbbabacabcbaabcbcacacddcacaddcaabdbcdaddbbcaababccaadabbbaccabbabcbccccadcbdddbaacddcbbcadcdbdacbcbbabddcbaaacdccaacabddacddaadccbaadbaadccdbbcaadcbdcadbbabccbaaaadaaaadadcbcdcbddbdccbccacdadbaacabcccbaaacdacdadbdcadbcbdbbcdccadcdadabcdaadaddddbabbbbbdabdbcddccdbbdcdacacbbdadaaacaabdcbaaabbcdacddabadccbcdcdbbdbdcadcdaaddccbaccbaaacccadacaacbaaddacccacbaddbaabbaddbbcdaadcdccbdbcabcbddbcabdcaaaacbdbdbcbaacbddcaacdababbadaddcdbadccccacccbbccbabbacdadbdcadaaadbdbacbacdcabdbbccdabadadcabddcbcaadcbbdaacbcddacbabaccadbcbcdabaaadbccbacbaadabbbbaabcbcabcddabbaaccccbbcabcccbaadcbcdabcabadcbccabdccbabddcccbcccdcdbacdbddccdcacbcabdaaadcdbcbdbcddcbcddaddadcacadddbbbccbbabbcdbcadbdaaaccddbddbdaddabbbccbdabccccbcdbcdbdbcbcbabdcbccbbccbddbbdaaccaabcbdabdcbbaaaaabddadbdbdbbcbbcaadccadaaadbcdbccdbccabbdbdbdbadcdaacccbbdcdddbcbadbddddaaaccbbddcdcccacdacbacbdadbadcdddbcbabdccbcabcdadcadbccdcdbcaccababadaacbaccbcbbcbabbdcccbdcdacbcdaaccbccccadccbabdaccdbbababbbcbbdcdccbdbaccabbabdddaccdcdbdbdbcddabaaccbcabacdccddbaddcdcdcbcaadbcddabbcaabadaacddbbabcbdacacdbaaacadbbcccbbbcdcdadbbcadaaccddccacddbcbbadbdcbcdddbdbbdbdbbbddbbdbaaabadaddbdcbddbbcbddccbdaacbbdabcdbbccaddbbcbaaabcbbbdaccccdabdbbbbcabdbddaadcbcabdcdbcdbddcddcacdbccdddabbddaadacdcaacdcdddcbdbabcacdabcbabbbccaabaccdcbddcdbcdcadabaaccbaabdccbcaccdbdcacaddddddbcbdbbcdabadbdcccbbdcdbdcacbdbbcccbcdcdcbdbbdcdccdabbddabbaacbcdddcdbaadccdbddbcbbbbbcabcdaaadaadccbdacabacdaccdadaacbcdbcdcccaddccccdccdcdadddacaaaacbdddababcdddbcacdddcccbacdbbddcbaadcbacdabdcdcdcdcdddbcbbbccacacbbacdacaabcbddbbabdbabaaddcccccdbacdaaacaacbbaaddddddadccccdbbcbabdcadcadbdddcaacabdbcdacccbbddbadddadbdaadcddaadbbdcacacadbcbaacacdbbbdbbaabacbdbadcadacabdcadaabacbadbbccddcccdadbdbabacdbadccddadacaddaddddaddccdcccccacababcaaadcbbdcddcaccadcbabbaadccccbcdbbdccabdcbaccdbbccdadddbcdcaacacabdbaaadbadbaaadddabadabacdadbbccacaabcbcdaadcccbbcbdcabbaadbbdcbdcbdccabdaaddcdaaddbabbcddbaaabadaaacdbdccbddbcbadacaadbbdcbaadbcdaccdcdacdbbabcbaabcdadaddcabbdacaccccabccbddccbbbcbababdbddcddbbcadbdaabdcbddddbbdcbbabdadbdadadcaaadcbdbbbcacaacbcaaddbbbbbdbbbcadadacdcdacdabddcdcdacacacddbbbabbcccdaababaccdccabcadcddcdcddddbdabaabdadddbadaaccbdacbddaccbcdacdcdcaaaccbbcdcbddbddbbacbbbacdbaacadacbbdddcadcaaaacabaccbddcdcbabcacdddbadcbbcaabbabdaaddaaaccbcaaaaabacdccbdcccaabdaacaacadcddaaacbdccdcdaddadcdbbadaddadcccacacbdcbadabbbbbdccccdddcbcdbacbccadbcaaacbbdabbbbdacdcddaccdaddccbddabdaccccadbabdcaabbaacabbbbacddaaccddbdddbcbbbcacadcbdcbaaddbbddbccbbacbdaadbabdccabccddbbadacdddabdbbaaccdbadadbabdcdddbdcabdcdabdabddcdccdadacaaadddddbdbdcbbdbacaddadabdabcdaaaaccbcdaccdbadddcbcbadddabcbadbddaccaacdbdcccdadbdddcbddaabbadbcdadcdccdcbacbcdbbadccbdabcdbcccbaadbbaaabdadcaccbaddcabccabcbcdccbabcdbcbabbdbddddabddbdddccaaaccadcabccdbcaacdbbbaabbddcbccaabcddcaadcdbcbcbbabbcacbddbcdbdbcacacbadcbbdbdacabcdcdcddcbddbcdbccbcaabdbccbbadadbbbbcccdaacbcadaababdcabbdabbcccbcbacddbcdcaadabadacdcdcadbcadcdbcdddaabccadccaccabddaababbcaabacadddcaddccaccabbaaadddadcdaccdcccabaacbbcadcbbcdacbbcccdacddabdbbadcbbabccaccbaddcdcbccbdacdaaddddcdacaccbcbadbbdaadbadbcadddabcabddcbddcabdababcbcabccbcadbadbbadddcabbdcadbdbcababacacdcbbcccdbbbddbdabbcbbdaddbbcaacdababbbdcacabababcdccbaacdadcbbcccdbdaadaabaccbbddbbadadaddcbcdacbdddbbbdaabcbaabbaaadbbddbbbacadcaabddcabadabbcbcbbbdccababdcaadcdbdccaccbccacbddadcbcddbbbabccddbddbdcdbdadbccccccdcdacbcdccdcdccdbbdadddbdbdaaacaddbabdbabcbcbacddbcbabaaddacdadcabaaccccdcddcabcccdbcababdbdbdcbabbacccabcaabdbcdaadccacdadccabaadddcabdcdabacbacddadccdbdaaaddbbdacdbbcdbdccadabcdadabdbbadaadcbbcccadddbadcbbdaadaaabaddbdbcdbdcadcdbbdccabbbbdabcaaabddcdcdadbacbddcdcdabdcabcabdcaccbbcdadcdbcbbaddacadbccdbababddbadabadbadddcdcadddcddbbaddaddbbcbadadccadabbddadddaadcbbaddbacccacaacbdbbccdbcbbdbccccabccbbbadddabbbcdcabdcbbdacccabaadbcddabbabcbbbdaacbacbaaabbcbcadbdaabcaacbbcbcdcbdcacbddbbabcacbdbbacdaabbaacdbbdddbdcbdcadbaadcabbbbbcdcddcaaaaaacaddaaababcdbdadbaadcacddcadcbdabddbabaaccdacbcbcccbacccddbbcadbcabbdcdcbaaddaadaacdaabbacddaddcaabbdbadccdacadcabbaaccdcbadcaccbaaacdaaaadcdbcbcaccdacaabadcdcbbabddcbabbaaadabbbacdddbbcddaaaacabcacbaabdababaccccddbdccdcaddbdbaccbcbbddababbaacdadadcdcabdacaadbddbddaadcbbdaabdccbdcccdbdbbabdcacdbccadbcaacbdabcabccbddbadbacbdaaddddacaddacaccaccdbaccdbddbbdacdbcbcaccdbbdacdbcacbbcdddcdabaddadabdcdbacadcbcababbabdcacddbbabcbbaadddcaddcdbcaddbddacaabbdacdbbabccbdbadddaaddabbbddabdbbbbdbadbddaccbbdababcbcdbbaadadcdbdccdadddbdcbdcbdbadaaddbbdabccdacaccccccbbdaccddbbbccbacadcbbdabcbabdbcddabddcdcacddddabccbdabcddcacbabaabccacaaadcdacddcdbddadaaaadcacbddbbbcdcccbabdbbcbaaaaababccddcadbabcddaddccacdcdbacadacbabbbbbbcdbbcaccabdbdcdadcbdccdbdbbbdabbdbdddcdaaadcbdacacaabbccdcbbcbdcdbcdacdbbbbdaabdcdcbaccdbacaaccbcdaaabccbabcbdbddbddbabcbddcccdbcabcadbdcddaaaacababdbacbaadbbdaacbdcbbdcbdadbaaccdcdcaacdbbabdbacbaacccdacbcccdbcbadcddcdbbaaaccdacbccbcdbcddbdaacccbbbdcdccdbcadcdacdcbdbbdabdaadabddaccadcbcadadcbbcaaadabdcdcddbabdbcaaddabbaaacdabcadacdbddbdbaabccabaccccddaadaddcccccddadabbdbbcacbbdbcdcabbabcdcaddaacddaacdcbbbccdddbcdaaadddbdcbccdbccdddddcdbdbdbcbadbcdaaccbacacbcacbcbddbcddbcbdcbdadcbddacadbbbadccaccdabbabdabcacbdcddddacbbbadcbdcddcdacbabacdcadacbaacbdbadcdcadbabbaaddcbddaddbcbaaaabacbcaadccddaadaaccaadcbbcdcddbdbbdbddaaddcbbbadcbcbacdadbcdbcdabbaccaaddabcccdcbcbbcccbadddaaddbddaacbcbdadcdbcaabdabcccdbddcdabbacabcbdcaaddbccadbbdaaabbcdcbaaaaaacdadddacadcaaaccccaacbcabccbbcccacddacddaddccaabcbaaddadbdacdddacdadddcadccdabbbaccbddadcbabaabccdccbaccddddbabcccdbddbaaaaacaddbdbadadadbabbdbcbbcabcbddbadcadbbabcbcbbccbaddabdacaacddacddbbbccaabbcbcacdabcddaadbcadbbccabdabdbbacadccbdbacbcdcabbcaaadbccaacdcdaaccaacddbbdbcacddcbaddbbaddbddbbbddcdbbcccddacdbdcdbabcdddbddddbcbdcaccccacaaaabbdcacccabdbacadaabcacccddcdcdaaccbbcccdbcbdccabdaabbdaaaabcacadbbdddacbbddbacabddcccaadaddabdcbdcbdbabbdcacbadbbabaabaadcaddbdcdcacdbcdccadaaccadcccacbbdabdcabbacaccbdacababcadaddbdbdbaadbccdcbacabbadcaaccdcbcdbdabcaaadcaadddbbddaaccdbbdbcddaabddcddcacbadbbacbdcccaabaaacacbbcacbdbdabbbdadcddabcbdcbbcdcadcdaadadabbbbbdbdaccabcbcabbcaacdacdbdcbdbbbbbacbacbddacadbbabdccdadcbbacabddbaddbcbcaccadbbcbcbbcbcdcdccabcdccbdabdddbbdabdbbacddaccadadcdbcacadddacaacaaabcdbbcadaadcbaaabbcacadabcdcacdcbcdcadcdabbbadddccabddddbbabccccabbdaacbbcdaccadaaadacbcbdcbcbadddadbbacdbbabcacbccdbcdbccccbaccdabdcdcabaccdcbbbbbcbdccbbdcacdcdbbdaadbcbabbcdbaabbcdbbcdbbdabaaaadcdddccdcaadadcdadabdcdcabaabbaacbddacbccdbccacbacbcdcadbabbcabdaaacbbcbccacddacaabcdcabdcbadbdcdccacddadcbdadbacadaabacadcabbbbabccbacddcacccaccbbcccbbbabbddaacccddcbccddacabadcbadbbcddabdcdcdcbcaaaacbadcaacacabbbcdbcbdbbcadaacacdaacbcccaacbbcdcdcacdadbdcaccdcccccbcbdcbbacccbbababdbcccbcbdaabddaadbdbabbbbaadccdbbdabcccdddaccdacdbcdbbdbbdabaacbbcdbbcbacdadddaccacdbdadbcbdddcbdcabcdccdbcabcbdaadaaddcccddbddcbbbdbdbcaacbbcbadcbccdbcbdccabadcadabaccaddcbacddaddadcbcdaddbbdccaccddbdbdbdcdbdcdbabacbdabbbbadbabadbbcbdbaabadbabcbabcaacbcbbdcadcdbcaaddddccbddbabaadaccbdbdaaccccccabccdbabaadbdbccdadaabbccbadcbacdddddcddddcabddaddbdaaacbabaaabdbbdbbbdaddcadcaaccccbcbcccbcbbadbccdcacccdaacbdddcbabadadcbcbddbcadcdccadbbbcbbcaaaddccbaabcadababbcbdbcbabbcacbaddcbcaaabbbaccadcacbcdbdacbdadbdabbcbcccabaabbcbcdaacabbdbabdaacbcdaabccabcadabcbbcacabdabcdbdddbaacdbacdabcbaccddbdaabdadacdcaadcccacddddddddbbbccbdcacbcaadcbdacdacaaddbdaddbbaacbcaaaacccabcdcccdcabdbdbbbdbbcaaddbcdcaccccabcccacaaabbcabddaccbacadbddadcddcbdbcbccadbbdccdcaddaddbacbddacdacdadbbacccaabdadddbbccbccaddabaccaadabaddbadbbbbbcccabccbaadbaacadcdbdcbdddbcbbcacaabadcdacbbdaabacbbdbdcddbbbbdcaccabadcdcbabbaddbbbbdbbabcdaabdacccaccbbbadaabddaccdbbacadbdcaacacbcaabddcbdadaaaaacdcaadbcdacdbcbbbdbaabaaaccaabdcdcccbcbdbddaccbaddbdbdaaaacbcccbdacabdbadaaaddcdaaddaacccbbcbddacdaabdbbaaccababcccbdbaddccbabacabbbbdabccbdcbbddbadacaabdadbcbaddcadabbabbbccdcddabcbaaabdccacacabaddcbcaaccabbcadabbdadacadbcaaaadadcdbcaadbababbbcbbaddcbdadbbbdbcdbcccaccdacaadabbcbacddccdaaadaadcaabdbddbabbadbbbaccaacbdbcbccdbadbbbaabddacadabcaddcdccccdacbccdddaddbdcacabddbbbcbbadccbabdcadbcbbadbcababbdbadcbdbddbdccbcbabcdbbbbcaaaccbaadbccbdaddcdcacbbbbabbbbaacabcddcdbbccdbbbcadaabccbddacbccaadcdcbabbcdbcadadddadbdbdaddbbbcdbbadbdcadaabaacccabaababbbacbcbddaddddbabcacbcdbdccbbddacdbaacadcdbdacdcadddcdaacbdcbadabcbbaaddbbdabaabcaabdddcdcdbdcdabddddcaccaccadcccccbbddccdbadabcbbcabdacabdbaddbdaaaabdcdcbdbdadcccacacdcbaddddaccdcbdbbccccacacadbcdcbbaadcacdaadaababcdcddacccbccdacccdbabbdddcabbabdbbbadbcabcbbcddaabbccaadaaabacacdabbabcdadbacbaacadcdddbdddddbaccdcadbcdaaadabdcdacaadbbcdcbbaacbcabbbccaddadcbcbaadbddadcababbaacdacaabaabcdbbacbbbbbbcbccadcbdcbdaadddcbbbcbdcacddabdbadbabccababbaaaaddaccccdacdaccabcdcaacdbadacccbacabdaaccabacabdddbacacdcbdcdddddbdbabdbabdbccababdddcbdcaddadbcacacdbddcdcaacdbbbbdbccabccdcaabcbaadaaccbaaccbcccaddcabdadbcdcaaacbbcdbcbbddbacdacabbadadbdcaacbdcccdadccbbcaccbcbdbbaabbaaaddbaadbbbacbdabcadddcadbdacccddcacdabcbacadaddbddaadabacbdadcddbcabbacdbdcbabdbaddabdbcbccbbdcdaacabacaadccadcacdadacbcacccbdbbcdaadacdadccbdddcbcabcacdbbadccbdbddbaacaabbdccdcbdddcabcabcbbaadadccacccccdacdacdcbcdcddbdaaaadddbbaccbbbabdddcabcbdbcbaaccddcdbabcbbbcccbbbddccddabaaadacddcbbabdaadadbabbcadbbccbdaaacccbacbcdcadcbdbacbaddbdbaccbabacdadcbabbbbccddbbddccbdcccdaadababbbaaaaddcbdabdbbdbdddbaacbcbddbdaaabbdcdddcdacaababdbacddbccadabdaacdbcbbcaaaabcbacbabacbcbdbccacadbcabcbadcbbbbdcdaaaabdadcbacaccaaabadbadadbdabccbadcbdcdaabbaaaadaadccdddcccdbcdcbbccacddbbccbcbacadacbbacdacabadbacaddaddbdcbcabcadcbdababdcccccdbacbcbbbcbcbacdabdcacabdbacbcbacdbdabaacacabcabbacacacaddbadbbcabdcdddbdbabbdcbaadaacbaabbcacdcabacabbddcadccbaccaabcababcbbddaccccdbbadbbcdbccddbcccbccccacaddcbdacbbabcabccaacacdadbcbbdcbdbbcbbadcbcdacdbdabaddcaacdcccbabccaacbadaacbcbcddaabaaaacdcdbacbcaadbabdabdacdcababdabbdbbbbaaccadccabaccacabcbbdbdcbcccbadcdccbdcdaacdbbdccaccccccaaaccbadcbbbdacdabbdbdaabbbbadddabdcaadbdbbbabdbcacddbddbbcbcaadcadbbdadcccdcbbcccaaacdaabbcddbadcadabbdbabcadcbcabdbaacbcdacdbccddbbcaadaadcadbbcbaccddbbcbcaddbdaadcadabcadbbcdadadbbcbbaabdcccadaccabcbcbccccaaacbdbccbcbddddcccdcaccabdbcaacbddbdcdbcdadddaddaadaddabdbdacacbaddcadadaccddddbaacaabccbddbcccccaacdbbcddcbdbcddadccacacbbdacddddcdaaccddcdbbdbbcdabbcbcdddabcdcddaadadcabbcbbbccdcaacbccacdddcadcbdcdaabcaddacdcdddbcbccccbbcbcaaccdbccbaadaddabbbdbdcccdbbbddbabccbaacdbbaaadabbbcaccccaddbccdcccdaabcacddbcbbccadcdccbbddcbbbbbcbcddadcaabcdbdbababcbbcaaddbbdbdbcabaabccddabcccabbacbbbddabcaaadbcbbcddacacbbcdddbbbccbddadccaccbabbbdadddbcbdbcbccbccccbbbdaadbbdadccdbddaddbddaaabdcbbcccdbbdcbbacaabacbdccaaaacaaadaadbcaaccdcbadbcacaccabdaaddaadcaaadccccdacddaaacbbddbdddbdbddacddcaabcaaddadcaadccacbdbdacdbdcbccabbadbdcdaddaacddcbacddabcbbacacaadacdaadddcaccdabaccacabdaccaacaaadddddabddccacabcadaacdbcbabbcadacaabbdabcdbcbbccadbcddabbddaccbbbccdabaabdcddccaabddbbbcdbbcdcdbbbbcccddbcdadbdadadccaaaaddbbcabdbdaccdbdcabdbbccabdcacabbbbccaaabacacdadcccdccdcdaadcdddcccdcbbdabbacbbabdbdcbcccdacaccccbdacdcabbaacdbbbdadbabbdbcbbcbcccababcbccbaccdbbddcdcdbbcdaadacacbdcdaabbbccccaaadacdcbbbbdddadcbababacbbbbabaabcbaacdcbabacddaaacabbddcddcbdbadadcbbcddaadbdacdddddcacddbccdbbcaacdacadbbaccbadaddccabcbdbabaadccddaabcdaaccbaabbcbadcbacaacbbadbccbcabcdaadcbbbdcbbaccaadccbcaababbaddbcacdbbbccbaccbacbbcbbdbcadbadcdbbacacdaabdadbdabddbdbacbdbbaacdbdcabcacbacacdacdbcaadcbccbcbdbaabadcccadbdcaddcbcbadddabbccacbadcadaabdaacdcaddbbdbbbccbdbccbbcbcaccbcabcdacdacaddcccdbcdcaccdaddcbdaddbabdcbdacdcacbabbbabdbadacdaacdcdaadbccbbcaabccdcbdabcbadccabbabcadabcdcccaabaaabcadbabcdbadabcbddbcbbcacadabbacabcaaddddabcabcdaadacccaadaadcbbabcdaaaacaaccabdddccdcccaaccbdcabdcabcabbdbdacdadddcbcbbabbadcdacdbadaacadbbabaadaadabacdabdbbdaccabbcbdddcacccadabcbdcaddbbcacbcdbcbcdabdbaaadcbdddabbdabacbbacdbcacbacacdadbabcdbdcdddabcdabacdabbaabdbadcdbbdbacdccbdcacacbabbbddcabcdcbddcaabdddbadbddcabcccabccadbbbcdcbabbbaadccdaabbcabcccacaaabdddacaddacdadbbabddababcccdbbcbbccccdcdaacaccacdbddbbcaddbdddaaaabccbbbdaddcbcadcabcadbcabccddcbcbbabbcaaccadcadaaccbacddaaddabdabdccbdacaddbadbdbddbbddddcbbcdadcbdddbdcadcbcbbbbaacbcadaadadbbdcabaacaaabadcaaadcaddaccabbadbcddadaddacadddadbacdaddcdadbbcabcdadddadaccdbdbcaccdddcabdcadabcbdddcddbbbacbddcdcbcbdabbcdabbbaaacdcdaabdcddcccbbcbabddabbdabbbdbdbdcbddbbcabddcdbbdcddcbdcacccdcdaacccccdccdcbadcbdabbcabdcaadcadaacbbabaadbdbaddbdacdaddbbbacbcccdbddaaaccddcaadbadaadccbadaaaaacdddabdacdbaabbabdbcabcdbadcbdcbbcdddaccdbaaacbccdccbcaaaababadcabccacadaaccadadccccbbbddadadbbadacabadaadbcbdacacaaadabbbcadcbaccbcbdcdcddcadcdbccccdddcdcbbcaaaadaaabcaababaaaabccdddbcbddbcadbcdacacadadbbdddabccbbacaadcddbdabcacbbaadbcdabdaaccbdcdcddcdbcabddbbbadbcbaadbcdacacadbccbdbcadddccddbcbadddbcddcacbbbaddbbbaacacbcdadcbbaadcaacadaccbabaddcaacadcbdaccdccaccbdbcadbdcacdadcbaacbadbdcbdcbcbbccdacadabbabcadcadbdacbaadbcaddcabbcabcdcbdbcddcaaabdbabcaaacacdabcbaabaacbcdcbbcbcbdbbccacddddacdbdcdabddbccabadddbaddadacdabaccbbaccabcddadbcdabbcddaababccdabaaccadabaddacbadbcbaddbbaacabdcbdadadbbcabbadcacbcadadddbcacabacbdabccbaabdccdbccabcabcbbdbaccbabddabacadcdbbddcabdaaabcbcdddacdcbcbdcbcbbcbbbaaccabdcbadacaddcbbcdbaadccbddaccaacaccbacbcbadbbacaccccdcdabaadaacaabbccabbdbbbcbcbdabacdcbbbadabcbdaccadaadbabbbbdabbdadbccaacdbbacddaacdbccaadacbccacdddabcaaadbacacaccbdbcdacbcbabcdbbdacdbbdddbbdabddabcbaaacbcddacccadaddacdaaadccbccacabbdcbbdacbbcdaaaabadaadbbcaaaddccdbbcadddababdcbacdbcccdddadcdbcaccdbcbdcbadcabaadacdbcaadcbdcdacabddccbbcabadcccdccdabbbcbaadabddaaaabacdbbcadbbababcaddcbbdddaadbbbdaaabaabcbaccadbdbbdbacaddcbacccddbccdbbbccdabcbdcacdddbdabccbbacddaaaacaabdcbabbcaaaacbadbbbbaccacbccdcaccadbabadabbcdbdcbdddddbbbbdbdbbaaaaddaaccdbacadacccbcacbcaaacbddbbabbcbabbdbcbcadcdbbacabbbbddcabcdddcbbadbcaacccbdaaadaaadbadbcadbbdacadacaccccdcdcdaabbccacdbbdadcbcccbbaaccdcaadaddccdcabbbcaadbbdbdcbdbbaacdcbaaccddacbcdcccccadbcacbabdcabdbcccbdabababcddbbbbdcddbcdaccdaaabbabbdddaadadabbbbdabdaddbadbdacdaddbacabddadadacaaddadcdabbbddbcddbcaccacccaadddcdbbcddbdacbacbdbcccaabbddacbdbadaddcadcaddacdcbaccbabbdaaddddbaadbbabadcbaadaddcdbdcabadadcbccdcabdabddcdcdccaacabcbcbbabccbaaddcacccdaaadcaccaaabdcbaabdcaadbaaacdcccdcddbacdabbadddaadcdcdbbbdabcbcbacaabcaabbddccdcdccadcaddabdaadacbbdbacbddabcdbbbdcaadaccbdcbcbadbacadcacdcaddaccdbacdaabdabcaacabcdcbacdcddaabacbcbddaccbbcddaddaaadbaabdbcbbcaabbcaaacbbdcbacaccddbcdbcbaacbbbccbaccbdbcddabdbbdcdccadadddcbaaccbccbbbcabbacbdbdaadcacdbcdabccacbcdbdbcadabbabbbaaaccddabdccccaaaabbbabbbdcbbadcbdccbabbadbcbbbaabddadbcabdcabadbddbccbcdbbbcdcbacbacaccdadcbaaddcbbbbdadabbaddaabcababdbbbbcadbbdaadaaccadcacddadddbadacbddacccdbcddccaaddbabbbabdcbbabaaaadcbccbabdcbcdcaadbbdaddcbcbbcdabbbcdcdccaaababdddcabbacddaacbcabdbcbabccdddbbcdcbcbabccbabadabccbaacbacdbbddcbabbbabccaacabadbdcaacdcacddddddaacacadbdabbdcddbdbbaddacccbbcacdbdcaaacbbccdcaabdcaabdcbadadcacdcadddaccdbdbddbcabcbbbabacccdbddacabdacccccbacacccbcbadccaabddddcbdcabdbcdddaaccbdadcbcabbbbcaccabcbbddbbcdabbacbddbddcaacdcdaddcccadabdaabbbbddadcdbdbbcdddcdbadbddbcaaabacadbdbbdbbaabcadcbdabccaaabccdccadbbaababadccaddbdbcdaddbcbccdcdbbbbadadddcdddccccbbbaccaddddddadbadcbaccabdbccddddabdbbbbcdbcdaaaddaddcbbbcddcbbbccacdbccaccabcddcbdbbcbbabdcaccdbdccabdcdbabcbddbddadcabddaacababdcdbbaaababccdabcbdbcabbbbbdcbdadadcbcadbabddddbaaaccdcacabbbbdcbddccbbbaccabccddabddcadcbbccccbacbbcdddcaabbaaccbcbabbacdcddddcadccdbaccdaaacdcbbdacdbcbcdbadadcabbcccbcaacdadcabbdaaaabcabcddbaaabaaddccccacaddabcdcbcbaaabcddccbabcdcdcbbbbaadcbdccabccbadbdbbbcbbbddababddccccabacdcaaacbcbadacddbacdcbdcdbccabcddcccabadbdbcdcabdbacbabcbdadddcdabdaadcddbdcacddbcabbbddbddbbacaacbcdddccacdbdbcdaababaaccdcadcbdcbabbaaaddacdddcdcbddadddbcaadadcadcacbdcccdacdbabcaacadacacdbacbdabdabcbbadaadaacaaddbddabcbcccbbbacbbdbbccbbcddaccccadbcddddadaaadadadaacaacabcaababcccabbbbdcdbbaabaabadbdaccbcadbaadbdcbbbdbadbbdbabbdddcdbabadadbcdbbabdacaabdddadbdaabacccbbdbbcbababccddaddbbdcbbccddabbddddddaacdcadbcbacaddbbbdcdddbddbdacddbaababdabdcabacaabaacaadbdbabbbcdccbdacabaddabaabddaacbbabccbccadacdacdcdacaddacadadcabcbdcbbdbaddbdccacdcbbacdaadbbdbddbadbdcdacbbbabdcdccbcbdabdaddaabcbcabdadccabbcacadcddcdcbcddacbbcbcbcabbbcdbbbdbadbcbbdbaaabbabcdbacdcccdbadbbababbaaaacabdbbbcccbbacacddaaadbbcbbcbdddbbcdabddbdadbdcccdcaaacacacaaddcacbbdbaadbdbbbbacdccccabcbcbdaabacbdbdddaadadadabdcccdadabacbccccbdcdcbaabccaadbbcbbdbccdddbcadbdcccabcdadcdccaaaccacaaabbdbbbabcdbdadbdcbdaddcacaacbbdaccadabddbdaadcbbbadbdadadaacabdadbdddaadbbcabdbaaccdbdcbabbcbaaacbbdaccacadabdccbadaadbcaccaccacdbabbbaddcaccccdcdabbdbaccbcdbbdbcdccdbcdbcaaccdcacdaadddcbaabbbaaaccdbcdcddbdadccbdcaaddadbbadcacbbbacabcacbdddaaadaddbcabcbadcacacdbdddadbbaabcbbbabbdcccacbcdbcbdcdccadaccadadaabcbbabacbccddacaacbcdcaddacbbbdccdbdabbabbaacabcadabdcddcadcbcabaaadcdadcadcabadadcabbacbbbaddababbadccbccccbdcbacaabdaacbadcdabadadbadabccbaadaccbaaabcdaccbaadccbdcdddbabbaacaaddcacccdcabadbadddaadcabdbcccbbbaadbcacdadddabaaadaadbcdcdadadabbcbdbcbacbbadcdaaddaddddcaaddabdbcdbadadabcabddcbcaaadcdaccbdaabccbcccdadbdbdbaadcacbaadbccbbccbdddcaccbbaadbddbbbbdaddddcdadabccbddcaaddacaacdcddbadcccdcdaadbbdcbababaddbdbcbcbbdaabbdcbbbadcbacdcccdacadadddbaaabaadcbdcaccccabacdddddadbdbbbdaaccabbabcbbbacddcbbadbaccbbdbddccbddcacbaaccacbadddbbcbadabbbdddababbbadcbdcbbdbdbccdccbdabcadaacdbbacaddbbacdbdbbbdadbbbddcaadaddcbbcdbbabdcbdcadccddbabbadacccabdaadaddcbadcdddbdcadcbdbdcaddadaabbadbabbaabdccbbbbbdddacdcbcdadcbbabadcccacadbabaadbddaddadbcbbacbbaabdcbbbcabbabbaacbddbcccdcbaadaaacacabaddaadcdcccbaccbcadacaabacccdadbccbdadacccbabbadaabbabcdbcaabcacddaccacbdcdddaccbccadcabbaadbbabdcadaacdacadbadddacdcdcadabbdadcadaacaabcdbcabccddbdcbcbbccbbabaddcdbbbcaccabcaddccabdbcbacaaccbddddcaaadadacdbabadcadaadabcbdbadbccddccbbacbaaccbcabcdcbcadcbbdbcbdcadbbabddadbbacbacbadadcbcacddbccbdcdbcaaddacdbcbbddacaabbabdccdcbbbaacbdbbbdaaaabbddcccdbcacbcadccacdacbabcbadbddaadcccbccdbddadbdacdcbbacbabddddaaabbbadcddacbbabcacbaadcbcabdbadddbdcbdbabaccbddabdadcdcbccdadacaddbcdcacdcbaddddabdaabadbcdddbacaacccdabcaabbddddddbacdbbdccaaddaaabaacbbbadbbccaaabbaacbadadcdbdbdbacbabbcbacbbbcaabdabddcadcabacadcdacdddaababbdbdaaaacbbbbdcdaaaccbdddcdcbbcbbbbbbdbabcacbbcbcacddcabcdccaadddaccbcaadccbcbcbbbbcccabbdcdbadbcbabcbcdcbdaddbadcdabdabddcabddaadcabacbcbccacadcbcaabcacaaadbadadcaacdabbbbccbbabddbcdcbdcbccbaadcdccdbbcbbabacdbabadaaaacdbddcdbbdaaabbdaccccbcbcbbaabcbcaabbddbaccdcbabbdcdcabcbaccabacbaaaaaabdccaaacaabcaddbbabccccdbbdbabcaddbaaadccddbccdaadacdcbbccdbcddacdcbdabadbddacbdbaababddaadbaacaadaacddaadaaabdbdbbdbdddcbdcbacabbdcbaaadabbcdadaacacdacababaacdadbdbaaccadbbccaacdacbdbccdcacbbbddcdbabbcbdaadccbcddcabcbbaccbcdaaadacbbbcdbcabbcdcdaddcaaccacbbcaadaaacacbbadadbbadbcabbcadcdcbaadbcbadbddcacdabdbbddbaaadcbdddcadbcbadbadaddcbdccabdbacddcbaddaacbcbbddbadadbabbbddaddbcbbcadbbbbcadcddbddaacdacbdabdaabdbaacdcdbabcdcccdbbbadaacbcddddcaaabbcbacdbcdcaddaacbdbbcacaaddcabacccbddaccdcccbcdbadcbdbbadccddaabccabdcbbcdaacdddddbdcddbddcccbcacbacacdcabcbbccbdbcbccdabadcbcaaabaaacbdddbcbcddacbcbaabcbacbbdbaabbcbbaabbcbcdaabaaccddbbdbaadbadacabdcbabbadcddddcaacddcabaadbbdcdbcacacdbcaabadcbacbdadcbbcddabacbcadadddbbcaddccaadbbdcdbdaccdddbdbbcbcbaacdbabadbccdcacacbcbcdabcabdaddadcbcabcaddadcbaddddccacdcabdcccbcacaabdccdabccaacdbdcdacaadaddcbdbbaacdbadcbadaccbaadbdacbdcdcdabcacbcbabbbcbccbbaabaadcabdcdabddbaaddbdcdcacddababdbabdbcbcaccdbdbddaacacddcbdbbddcbccacbdabdabcdbcbdddcbbbcacdadbcaabaaccbcbdddccbccbbdbddddabdbccbbcdbdaaaababbbcbcdbccdbadabcdabcddcbbdbbbdcddddababccdbaabcaadcaddadabbbcbdbbddadaccadbcbaccabddccacdbbadaaabbbaddcbbdbaadcaacbcbadcdccbcdabccdaccaccdcddacabbddddcaabbbcbccbcdbcdbcbccaddddadcbbbcbacbbdccdbcacbcbbbdaddcdaabbbbabcadbbaabdbdcbaccbaccbbbccbccbcbdaddbdddcdadadcadddadddcbbbcaabdababaaabcdbddbbbacdddbddddbacbcccddddaccaabcccdbaabdcbdaddaaadadddabadadccaaccdbbddaaabcabcbcbdccdaabbacbbaabacbaccccbdbbdbbaddabbbdcbcbacdcaacdbdabacbdcbbabdccaddbddccdcdabadcdaacbacdabdbabdccbadacbccbadcbbdaddbbccdcbccadabbdbadaacababcabbcabcbdbdaabdacbadbdabcddabdbcbcdbdbcaddcccacdbabcaacacaddddacdacdbcaddadbdaddaccaaacdabaaccbdccbaabacdaadcbcdccdbabdcbbbccbabbbccdaadabcababbaccddcbbbdadcaaadbdbbacbccacaadbddacbcdbaabdbbabbbaacdbbdbcbdacddbcdbddcadadcbbdabcbbdccabddcadbdbdbdbcdadbdbccccacdcaddaabadaddcabcddcccabcbcdacccaaadabdaaabdcdadacadcbbbcddbdcbccdbbdbabddaabbdaabbcbcbdabaabaaaaadabdcccaadbcbdadccdaccbccadacddadabcbdaabbaadbcadadcdbaabcabccaabbbcccccacbacdadbdbdcacbccacdccababcbaadabdcaaaacccdacbcdcabbacbcbbdcccacbbabbcdcadadaacbccdcdacabaadbbbbbcaddabbbabadbdcbacaadbaabcadadcdddbbabdbbbccadacbacbdacddccaabcdadcdddbbaccdccdcdddacbadcbccccccccbbcadcbbcdbbaccabdcaacccabdacdddaddcacddcdaaddbddbaddbacddbbdbbdadcacdbabcbabbccacadacadabdbccbddcaccaaaadddbcaddaccdadcdcabcbccddbadbdcbacdccbdbdbabbbdbabcabbddddbdccdcbdcaacbcbddaadbbbcacdacaacaaaccaadcdbcddbdaadcdacacbbcccabacbaddcdcbabdacdcbcabbadcbcbdddacccdabddbabcaaacacbabadbabaccbbbaababababadbccabcbacdcaababaacabaacbbbbbabacdccbcdacdbaccbbcabddabadadadcbcacbcbcabdcccbcaccabadcbbdabccbaddbaccacddabdadbdadbdabbccbadcbbddcbcdbabbbbcbaaacaabbddbadacdccbaadbbdadbcccadcbcabbadcbddccdaabdacccbdabcbabcbcacdcddabaaaacdcccaddcdbbdcacaccccabdccaaccbabcddcdcdabddabcabadcbadbccdbdaccacbabbabbbcdcddcaaaccaaaddcdbcbacdcdacabbdbadbadabbaaddbdabdadcbcbcdddabbdbbcbabadcdddabadbbcdadcdacaaacadadcbbbbdcddbcdbcbdcadccbdadaccbaccaaaaabdddbdcadbcdababbdccacdabaadbcacaabacdcbcccdccdcdbbbdcbdababcdbdddacaabccacabdbdacccbadadbacaabccddbaacdadaccddaabbcdaccbddadbddbdbcadaddbabdcaccaacbaadbddadcaaabadaddddbccdacaacdddacdaababadddaacbaccdabaadcccddbbcbdcdddaacaacccabbcbaadcaaddbdddcadbababbaccbbbbccdcbacdbbacdccdcbcdadaabadadaabbacaacccccacccccaadbbbbbdaaddadadabbbabccaabadbdcdaccacbacbccdddccaabcbbdabdacaaddddabdbbacaddbbbcddcadaaccabccbadddcabcbdbaacdbcabbbbdcaddabdcabbbacabdcdacbbdacaddccddadcdbddbddbbcdcddaacbbdbbddbdccccddcbbdbbcbdbccbcbadcacccbaddcbdadacbcccbcadbbbcbdbaacaaccacbbbdbabdbbddcbdcbccbcdcddabcadcbcbbbadabccdcacabddbcacdadbacabcccbccbbabdbacddcbbbcdcccdaccdabbadacdacaccdcddcbbbbdcddcbadacccaaddccacacaccdadcbacddaaabcacadbbbcaadcbdbabcbdbdbcacacdcdccbcbbdcaabccddaaaabdcccccadbacbdbbcbabbdcbbdbddbaadabdbccbcbcccbbcbbcdabcadbdccbcccbaddccdcbdbaccbbbcdadcdbdcacddadadbccdddcdcbccbbabadbdbdabcabdddbbcddacbddbdadaadbcaadcbaaadcbbaaadbccdcccadddcabdccaaaadddabdcbddacabacbbcadacccdbbdadcdbddbcbccadaddaaabcaacbddbcdbadabcbbadbbbbcddcccddcdbdccbacddcbddacbcbaccdadccdddaaccacaacbabacdccdcccacbcbadacbbdcacbdaacccddbbbbabccacbcbacdcdbdbaddbdaadabbcbacabbcabaaccbbdbddbacbcbabbcbcadcaadbdbdacacdcaaabcdcaabaadbbabcacbcccbabaadcbccdbcabdcaaadcddadaabbbaacaaaaabbccbacccacadcadbaccaaacacbbaaddabaddbcadcdbccbadddbcaacbbccdaadddbbdbabcbcbcbdbcadcddbbbcbcbacbdcdadbbbbbacdacadbbcbbbcdbbbdbdccababadabababadaadadbbdbbddcbcbdaacbabbdbdbcbbcdaadbaaabbacadabaaaacbcaacabcbcacacabaccbcbdcdccabadaddccbbadcbbdcadabdbddddcaccdbbccbdaadadcccbbbbcdcbcabdcdaacddacadbdcaabbccbcbbdcdbacdcdadadcbababcabccbbdbabdcdcdacdbcbdcbcaccbdddaacddbadacbbdaaadaabacadcbccabdaadddadcccdcbcbaaabbaabcbcbbaabbbabcaddbdbcdcabcaccacdddaabcbadccaddcbbdbbcadcbadacabccdcccbabddabccbcadcdccaababcdccdcdcdbdbddbcccabdaaadcacdadbbbabbcbdabbaddcacbaaddbabcdadbbabbbabccbbbbcddddcdccadcbdbbbbdddcbccdcaaabbaacbbcaaddacdbcbcaccaadaccbabcadabbabadcbbddabdababaaddabaaadbdcbcacbcbbabdccddbdacaaaddadaacbdbaadcaccbbbcacdaabddbcaadbabaccdacabcadacbcbbcaadccaacdbaacccaabcabdabdaacaabdccdcabacdbdadccbbacadbcbcadccbacbbacdbacdbacabcccdacdbbbadcabaccabbbbcdadacbbaadbbabdbdbccbbdcaaaabbdabbbabababcbbdabbdadcadadcbbacddacababdadabcabcbbbcadabddcaaaaabbaabdbdacabbbadacddbabdadbbbbcabcbdccdaabcaaccdcacaaddcbcbdbcdbcbbbdbdbadacacbbadcbcbdaddbddcccacbbdccbcddcacabcdbdccaaaadbacbdcdcbbabaaacbbcdbbdccddccacabaaabdcabbcabacacaddacbbcbdcbbdddbddbbabbabdbaaacbcaadcacddacadadcdcdacdaacbdcdacbaccbbccccadbdcbdabbacbcaabbadaaabaccbcddcddbabdbccccbddaabaabdcddcbbcdcaccdbacbbcbaaccaccabcabaacababcdadccdcdaddbbacddcbcacbdcadadccdacacbdacdcccdcbcacdabcbcbbaddacbdaadccbdddccaddacaaaadcbbcbaccdaabccbaddacbaacccadbdcdcccadcddddccccacccdbcbcbaadbabcdcbdabdccbcbaaccdcabaadcdcccbbabcccaabdacbdccdbdbaabacbcbccbdabdbddbdaddbabdacddaddcadabddbdbacddbbbbccbdaadaabbdbcadaccdcdacacacacabddbdaadddbdabababbbcaababbccdbcbaaadabcccbdccbddabcadacbdcccbbbdabdacabbaccdbcaaaaddddcbabdddccadbcbdbbbbabdbaccbbbabaaadcbcababadddddacabcbadaadbaabbdbbccdbadcaddcddcaaadbdadcdabdbadadbccadcddabcccccdcdacabcabdbbdcccdaddcaaacccbdbcdccacdcbdbcbcaaaaadcbadcbbcadadabaaccdbadbcbcabbbcddbbddbcccbcbcccbdbacadaabddabccacdcadbdaacaadbcdbdbcbccbbccaccdabbdadbdbdaabdbbcadcccbcbbcdddcabddcdbbadabaabaacadcbbadcbcbaabdadccbddbcbdacccddbaddacccacbacadbabacddbdcaabddbccbbcccbbbcbbccdbdcbcbdadccddbacaddacabacbbcbcddbddabdbacbbccbbdbcbcbcbacaaaddabdcbcacbbdcabbbdddcbdbbadaadbcbbdcbacdbadbbccadddbddddbddbcdbdaddbaccbdbbadbcaacbdcdddcdacdacbddbdccbcdcdbdaaabcdcaacdcacdcccaaccaacbacdcaccacbbbadddaccdcbadddbaddbdbbbcddacbdabdabccddcdcbacdcdaadcddbcdddcadbaacbbbadccddccacbbcabcbcacbddccabcdbbcbaabbacdbabacbdbcddccaddcddcddabaabdcddbddcabaddbbcbaaaadaadcacbbbacbbbbcbbcbadbaaacdcbbcdbdbbccabaddadbadcccdacbddadaaacaddaacaadbdabcdaaadbccbcadcbdacbdaccdadadaddcbbadaccddabbabbcaabcaacbbdddddcbcdddccbccaacdccbcddcdaadbcdadbbbbdbaaddbcbdcbaaccdabbbbbbbdcbbbacbdddddccabcadcdbddddabdbdcbdbdadbcdacbddddadaabccccaacbcacacdaaadaddddabddcabdaabbcddbcbaacaadcaaccddccbdbbbaaddbabcbaadccddbbadacccccdcdaacdadaddccddbacdcccabaaacbaadbabcccddbdbbbbbdbbbcdadacdbadaacaabbcdcacacacadaabbcbccccaaddacaddcccdbadbbdbbdbabdbbbcadcacadccbacaaccdbbaadbccbaddacbacdcbbbbaabcabcdddcadcadbcbacdbbbcbaadacdbddaaacbbcdcadccbbcbcdcccbadcdddcccaddcccbbababacbcccbdbccaabcbaadcaadbbbdacbacaccbcbadaccbdbcdddccdacddbddcdddaaadbccabcddbabcbaaababdddaddadabdddabdaddcbbaadbcabadadacacdcbccdadaadacbdaacbbbdbadbacbcddadccbcadacccbbcdcbacdacdaacdcabcdaacdaadbaabbcdbdbcdaaaddaccdcddcdabcbbdbccccbdcdadddcbddbaacbccdbabcdcaccdadaabdbdbaacdacabbdbcadddbdbccccadcaabacbbbcdbccabbbddaadcdcadbccbdbcbbbdcbcbcccbccbabdbccddacbcbdaacdacaaabccbaccbbadcbadabccddcbbbcabbbcbccdcccbacdbbddaadddddabcddbaddcabdcdcdcdcdaddbcbcdaabcadaccbbbddadbcbcdbddabcdbccdbabddcaabadbbdbaddababbbadcadcbdcaacaadbcdcaaddaccabadddabddbacdcacbccadadccdabdaaacbabbbbddaabbbaccccccabddcbbaaabbdbcbddadddacdccacaaabaaaacbcbdccbabadddddadaddacacbcdbbabcccaabcbaacbddbdbcdbddddacdbcdbccdaadadacbccdabccacabbcaabccbbcbcbbaadbacbddbcdcabdacbadbbdcdcbaaabcdadbbadadcddbcbcbbccdaccacbaaaddbdcdaccbcadabbaabdbcccbcbcacdadcaaacddccbbcbdbddcadcdbdcbbdbccdaacdcbcdcacccbcdbdcbccdacdbcbcccdaadbdcdbbaadddcbcaccaacaccaabccdbbdadccaadadaacbbddcabaddbaccacdcbcbcdcccbdabaabbaaacccdaaaabbadbcdcabdabcdcdbdcabccbddbdabdcdaccbbbabdaccadcabdbdddcbddbddbcbbaabbabbdbbbbcbcaaddbababdaabdabcbbcbdaacccdcaacdbdbaaaaacbcdddbaccdbabaccddbadbacddcbcbddbcacaabdbaccdaabccddacdddcaaaddaddbabbacbaabdadcadbcaccdabdbddbbbcbacadacbabddccdcbcdacdcaccacbbcaabcbbaaaddadccdbcbddddacdbcaadcdacbbabbabbccadbdbacbbbaaaabacabdadccadacbcabbbcaccbcbabaabbadcaadbcaaabdabacdabcbcbdbbdabdccdabdddcddabddcbddccccacbcddabbadbbdbbdbcbdadbcabaabdaddcddbadadbccdbcbcdcabacaadddbbdcacadcbddaaabbbadddbbaacdbdcaaddaadaadddbcdcbbbadadcbabddbadcabcaaccdbabbbcdacaddabddaabaacadbbbdcdbabcbaaabbcdcaabdacbbdcacaadcbcdadcdcdabadbbcababbcaacabaccddbbadccccdccdccbbcdaacdbcacdbadcaabbddddabbcbdadcbbcbaaccbdbaadabdadabadcdbccdbacccaabddaaacddcbacaadcccbdcdbadbadccdcaadbdbdbbcbcccbbccbdaaacdacaaadcdacdbbdaddccbddbccdbbbbbacabadddddaabbadcdadabdaacccbcabadbbcdacdcbacadbbacabdcacaacbdddcbdabacadbdacaddcdadcacbcdbdbabdababbadcbbcabdaddcabcadaccabdcdbbbcbccadcacaaabbbabadaccddbbbccbabcddddcdbabbaccbadcddbcbcacbdcadbbbaabaddbaadcccbdacccaccdaaacbbcdcbcacbbcbbdbcccdddbababbcbdacccabccabcccdbcdadbabccabdaccdcacddccccaaadddbcdbcbcdadacbcaddcbabbcdabccdabacdbbabddaacdddbdbadbbacdbcdcbbadbccdcbadcddcdabacdacabddcdddacabddabdccacdcdccdaaddcadadbdbdabadbdadcaacccbcaacbbdbcdaadcdacbbdadcacdbdbcdccdabddbdbbaccdbbbbbcdcdacdcabdcdbadbcdacadaadababdbabbacadabaaaaabbdbacbcadabbacbcdcbbbbdbbadbaacabbbbbdbdbadcdbbddbbdabbdabacdcabcdaabcbbdbabcdcccdaddbabaccbacdaccdccaccddbabbddbadddddbddbcacddabbcadcdddabaaabbbcbabbabbaadacdbcaacacaaddcbacdcbccaccccbccbabdbaaccaccdddddabbaadbcbcabbdaaccacbbdcddbddaddbacdddadbcdcabadabcaadbcbcbbbbbabdccbdbabddbaaabdcddbbbcbacbcccddbcaccadacacacbadbbdaabdcbcbdabcacabbaaacbbacdacdbadddccaddddadcaccbcbaaccacaacbcabbacdbcccddbaaacbaabadcdaacccacacabaadcaaaadacdbdabbaabdaabcaaacbbdacaabbdabcadcbcbcbcddddddcadcbaadbbadbbdaadcadadacacbabaacbcbabdcbabcacbbabdcacaaabdcdcdddcddaacaaadcbddabacdcdacbaaddcdadbbcbbcbaddcccccaddaddabbaaaaccdcabcbdaccdbbdbaaddccbbbbdaadacaaacbdababbddaadbcacaabdadacddadaddacbcbdbccadabaadcdadcbdbdcbcbabdbcccdadbbaacbcbbbcccbaccdabcbaabbbacdcabccbabccbccaaabcbddbbcadabcccbabacaddbbacdadcdcbdcbaddbbaacdaccbdcdabdcaabdabdcccdbadcbbcacadaaaacccadbddbadcddcbccdbcacdcadccbdaaaaddccddcacbbacccbbcdcdbbcdcccbddacddcdadabbbaacbcabcdadaaaadadaddabcaaccdbbcaabbaddaadbcbbbbdabddabaabacbcdaaadccdcaaaabcbdccbbcbacdbaadaadababddbdccbadbbbccabcdbccddadbdbdbacdddaacdbaccdacdabadacacbbdcdbdbcadbacccacdbbddccadddbdcddcbacaaaabbcdababdddcddaccdacaaadbbabadacadbacdbdcdaccabddaabaaccbdcdaddddddcbccdbccbdbdbbcbddbbaaababaababadddbbbddcdaaddbbbdccacdbddccdbaadbbdcabdaabdcbddaababbbcabdaddadadccddbcbadcdcbaaababddbddacababbddadcacdccbbaabbcdcdabccdbcadddabbacabaaadcccabbbddbcaadabdcacdddbcaddcdabcbacbdadcddcbbdbbcbcabaadadbcdabbcdbabddcabaadbcdbaadcdadbbcdbbdadaacdadcdabccbaacdbacdbbcdcbdcdadbcbddcdbabbcdbcdaddbdacbdbadddaabdcdababcabcabbdadddaadaacbbcdaaddabcadbacdaddabdbbcbdacbdaaaabcaddaddbcabdaaadcbcdcbdacbcdbcddacaadbbcbddaaadcaccddcdbacdbddabbbdadcacabbcdbadcabccadaabbbcdbdcadadbbcdcdaaaadcbdccacdbadcddbcacdababadcbbccddaddacbcadaadcabcddacccdabdabddbddcccdccdccbaaacaadccabdabaabddddccbbdcbdbddccdacbccdbbdcdbdbdccabddacacdcdacdbcdaaaabadcdddadaccbdccbaadccdaaaccddcbdddcdccdaccbdabbacbccdbccccddacbcabacdbcbcbabbdddcdcbbdcbbadcabdddddaaabbdbdcddbbccaaaacaaabadbabbaacbcddaccabaaaccdcacabcbbbcdcdabcdcadddddaddbddaadbacbcdadbacdcbbcaaadcbbdcacbbbdaaacbadbadaccbabaacbdbacaccacacddbbdcdcdbddcbabdbacbbbbdbbdbdccdccbaacabcaabbbdcabdcabcbbbbcdbababbcabcaabcdcdcbacdcadabdccdbcbbdbdbddabdbcdcbcbbaadcbcbaabccacbdbbdbdacddddbdacddcbdcbdbddccadcbbbaadcbddbcaabacbdcbadbaadaacbbbbdbcacabcbaaadaabdbabcadcbadcadaccaddaadaabadbcdcabdabdbdbbcaaaccdacbcddbbcacdddbccabaadadabcdddabaaccbbbbdccabccbdccaaaddbcaaababdbdcddbdcbbcdbccabbadaddaaacbbabdabbcaabcadabddcbabcddddbcacadcdbdcbacabcababbbaddcbcbdaabdbaabdabcabbbdbdcadcdbddddbcbaacdaaabdcadbbcadbcacbcbcbaaabdccabbccacaddcacdbacaddcdadcdbcacbcadbccadadcaabcbbccdcccaabdbaaaccbcddaadabcbbacbaacddcaabcccacaddaabccbacdbadcdbbbabcbbdbdbdcddabbbccdbddbbacabcdaacbbabbddabcdcdcddcbcdabbbbbcbbdddadaacdcdcaddcddbbdaadbccbbcdcdddbdababbbdacabddcadabcabaccacccbdadddcabadbacacdbbbddadccacbcabcadbaaddabacaddacdcadbdddcbdbbacabdbcdabcabddcadbdcabbcaabaddbcdbdcbcabaccacdadadcbbbcdaabadbbcbbdacaddcccdcbabacdbdddadaaccdaddcbadadacaabdddadddaccbacbadadaacbbcadddddbccbdaddccbcbaaddbabbabbadcaadababcdbbdabbaabcdcabcbbadcbaccbbbcbbaabbbcadddabdbcbbddcbcbaadccdcdabdbbacbdddbdabbabadadabbbabcadbdbccaadadcaddcabdadddbddddcccddcadbdabdcdbbbacacabbcbbdbaaacbcacadabdadacbccaabbcbdbbacaacacadacbcdcdcabbbccdcddcaabcbbbdddddcdaddbabcbdaabccccdaadccccdcdcddacddddcbcdabcccbddcddcaddabdabaddcbaabcdcaabacddaaccdbbdccaaacbddbbadbaaccdcdacddbcadcbbdbaccabdaddaabbdabbdadddadacbccbbbacbdaabadbacbbdaadddcdbbcbdadabaacdcdcdaccbdbbabbcccbdbdddbabddabdacbbdcaccaabcddbacbacdabadbbaddbabddaadabbbadcddbdbbdbbbaccbdbdbbcdacbbcadcdbccabddaadadadadcdacabbadbbabbabbdcddcabbdaadacaaabaddabddbbdddaaacdcdcaacadcccacbccadbdabccbdbabddbdccdbdaccdaadacbbadcccacaabcaabadcdbabaaaaacadaddadbdcccbacddbccdcdaaaacbbaaaaccadbacbbccdadddddcacbbdddbbcaaaabdcbadcdbcacaadccbadccbcdacbbccabdddabbdbddbbbacddabdcaaddcdabddddabccaacdaccaaddcacbbdbdaaacddcdbdbdadbcdcbbbccdbbacabccccadabbababacbddbdddcbbaacbbaaddcbddddcdadcbcacddcacaddabddbaaddbdadbcaccdbbbcacbbbcacbbcdaaccaddbdcacbabcbcddbcbbbccdababcdacdcdcdbcacbddbdcacccaaaddbcbadcadadbbcccaadcaadcaabdbbdaddcbabbdaddbcbacacdaabbcdaaaddddbbabcdcbcddbadccaddaaadabcbcdbccdcabababacbbababcbaddadcbbadbcbbbbacbcadbdabdacabccbaccadbbbcbcdcaddbbddaadadcbcdbbdaababdaaaacccdbcadbacdadaabbbdaaccbbdbcacacbcabdcdcdaaddabbabaaadabbabbbdcdbcdbdcadbabcbbbadadcccabbdaaabccadbbbddcbbdbddcdbdabcccbcddacbbacaaabdadbbbddbdddcdacabacdddbcdadcaccbcacbabdcbaaacaabddcccbabdbbabdaadcaadbcabdacdbdbaccbaabbcdcaadcddadcdcbcdacabcbcaacaaabccaccbdbbbcccbcacacdadbcddbbccdacadacaabadacacddaabaabaadcccbdbcdcdcdcbdddcbbddcbadbdddabacbbcbdcdbdabcadcaddabccbbdacddddbdaaaccadcccbdaaabdbcdccdbbbdabdbdaababbdacabcbccdacbdbdcdbddbbcbcbddaddaacbddaacdaccaabbbacbacbadaccddadbacddbabbadaadbaddabddddddbacdbadcddccccdcbddabddabcaacbabdadbaadbcdaaccccbccddcadccacdbbadabdddcdcddbdcdcacaabdcadaddaddadcaccdbdbcccddcbadbbdbabbcdbcbbacbaacbcddcaacbbcbcbadcaabddddbbcddabccdcaddbbbadcdbcdbcdccacdbdacdbcbddaabcaacbcaadbbaaabcadbbbacbcaaaddaacdccbccbdbaccaddadabdcbddbddadcdccdacdbccbdcacaaaaaadcdcbabdcaabcdabcbaddcbcbbdbcbbbdcdddccdacbcabbcacdbdcdbbcaadaaccccdccbdabbcdadacbcddbadadbcbacddcbcaaccdcccdcdaabaacaccdcaadbbdbccacdbbcaaccadcadabdbabddcadacadccbdcdbaacccaaddbcdaaccbcbccaabbdaadcdaacbdbdabdcdcacbbbadaacdbaaccbbadbadadcaccdddcbcbaaddacaabbcadadadcccccdabcbcdccaccbdcbbbbcbbddbdcbadaaacdcbccdddabdaabdcdaadddddddcabacdaacaddccddbcbaacccbadbcdacbcbababbbdbadcbdddaadccacdddcacdbdcccacdbbbcadbabbccccabdbdcddaadabcbaabbcaaccadcaccddbabddabbaddbbbabacdcbadbbdbcccdcbbdadcaabbccbdbabcaadbcaadcbcaaabbcbaacbdbdcaacdadbbcbbdcbcdababbaadcbbdcbbaadddbcccdcccdddaacaacacaccaddccadcbcbaabaadccbbcbcacdcdaabbbbccdcaadcbadddbccacbabddcccdadaaaaabcbbcdbdadcacbdbcdccabcdbcacbbcbccdddbddddbbabccacccddccdaddcdbbccdabcbbdaaacdaadbcadbddbbbbabcabadbabadbcdcbdacabbaddbcdcddbbbcbadcacadacddddcadabddcabadcaddcbbabbcbcacbbadbddcdacdcacacbddcabdbdacacaadaaaaadadbbccaabadbddcbacbbacdcbdaabbccbccbaaaccddbbccbbcdcdbcdbacdaddaabcabdcbbdcbbbcdbcdcbbcdcacdcdabdcdaabccabdbbadddaacbaabcbccdcbaadbbccbbccbcbbadcbbadadbabadcddaadadcbaacabccbacbddbacdcbdabdabcbadaaccbdaaacbcbddcdacaddadabdcbcbcaccbbbcbabcbbddcdadbcbabbaaabdbddccbcbbdcddaccbaabbaaadcdcbabbcbcbccaadddacccdbdbbabbdaccdaacbabbadcddaddabaacdcaacbcddcbdcabbadcdcaccbadacccbbdcdbdbbcabcababbcbddcdcddbaddbbacccbacbbdcdabccadadcacaddbcddbadbcabacabaaadacdcbdbcdbdcddadcdcaabbdccbccdccbdabcbbbbbbdbcadbdddcbdddbcbcccaadbbccabddabdbddaacdaadbdbbacddbcbbbadbccaadacadbaccdbbdbcdcabcaadababbbcbcbcdbbaadcaacbcdabbddbcbaacbdbbabcacaabcdcbabdcabdacaaddbabdaccdbdcdbababcbabdcacaabcadcccaadacaddaddcacdaddcddaaabdcddbcccdbdccaaadcdcddbccbbbbbcbcadaababcacaaaacbbbbddbbdbaabaaaddadccbddbacacdcccdabbacbabacccdddacbccadbcdcbdadbdaabdcacbbccaacbbddbbcdadaaaaadcbabcccacdccaddbdabbcbacccbabdaccdbacbcabcacdcdbbcacccbadaacabdcdcdaccdcabbacadaaabcacadbadccaaadabaaaaddccbcdbcdbaabaadbcadacdcabbbdabccdbbcbdcadacccaacabcbddacddcdccdcccdcbddbcbaaaddbbaccbabdaabdcdbbdbaddccdadcaccdcdbdddcacdaccbbcdadadaacdaddbdaacdaaddcddaaacacabacccaaaadddaabbaadcbdddcaaadadddcbadbdddbbdbcbcbaaddcdaadbdcddbdadaddbbddabacbcddbbcccddcdbcaccdbacddaddcaadddbcdaddbcdbcdababcbdcbddbbbdbbdcdcdbdbcaddbbcbcbbadadbbcbcccadcdbadabadcccdddabaadbbbcbbacddcabdcbbbddcdccdbcdccbbbbbcbcadcddddababcacbabacacaacadddbadbbbcccdadaddccabcadbcacbaacccaaccbdcddbdbddbcaddccbddcaddccabadadbddaadbdcbcbabbbabaabdabcbcdacbbbcadcadadbdbcbbabadabbcdabdacbcdaaccdcddbbaccaacdaababcaddcddcadbcabdadbbaadbdabaadcdbcadcdbaaadabaadcaabdcbaddccaaabccdaababddbdddbaabcbcbcaabaccdbdcacadbbdddbbbbcacbbabbdcdacdbaccddbdddccbcbbaaadbadccbdddddddddabdabbadbbaabdcbbbdbdbaabdaabcdadbdccdbdcccdccaaccaaabaaccaacdcbbaaababcbdcdbbdcdbcbacdaadacaadaddacbbaddacdadccdbbbdabadcdcdbdbdbbabaadcbcdbbacabccdcaacdcbcdddcabdbcbcddccacdddbbabcbdadcadacbacaaddcaabacaaaabaccaadbbcbabbacaacadbabacadbbcbccbaaacdbcdaacddcabdbdcdccadddccbcdcddabccbbaadadbacdbcadccdacbdabacdbbaadadaabbdabdbcdccaabdbbdaabbdcdaabcdbccadcdbdadcacddaddaabdcbccbadbbadbabbcbcbaadbbaacdbcadbabaddbbbddababaabbdcdaadbdababdbddbbcbdbbdcbcdcadbdcbaabcabbbcbccbbdabcdcabcbbacbddbdbdbdbccabbddbcbccabbaaddaaddddaabccdcbdaddcbbbcbbbbadddddbabdccbdaddbbadbdbaacdacbccacacdbbbdcacbdccaadbbcbdbaaaccacacdddbcbdccaaadbbaabadbcbbbdaaddaaadcabacbaaccabadbdbdbacdbbccbaadbdbcabcbdcaadbddaadcdacdadcaadaccddbdccaaaadacccadbcabdcdbbacbaddaaacdccbbcbbcbdbdaadcbcaaccacaabccdbaacddadadcbbbaddcccaabbdbddaccbbdcacaaaaaababadcdbbdacdbbddbcdcbbcabbcdbccabbdcbacabbbdbabacbdaaddcddcbcdbcbcabcccbabccdbdacddcaadcbbbddcbcacddccccaacabaababbcdddbdbcbbdabcdbaadaadbdaadcdabdbdaccadaabdcacbcdbdbacacaddcbdacdabbcbdbadcbcbddcbdbaaaacbdccdacaaadacbddaacdadbbddbdadccbcdccbdcaaccadbcccbcddbaaadacaabdcbdbcacacadbaddbccbbcbddaddaaacbdbcbdbacdbbbcdaadaddcbdbacbcbabdbccdcdacbdadcbbaaacabcdcdacddaaaccccbabaaccaadbbcaaabdddabbcacbacaaabdbbabadabcbaaaacbaccbaacabbbadccbccdbbdacacbcddabdddadccdbacacbcccbddbbbbcbbbabcbabaaadaacdcbbbabdabbcbddddccdddbabaccabbdabbacdacabaaddabbadbcabdcaadcaaabbcaccbbacccbcbbccbddaadbbdddcccdbccacddbccbdabcbccddcacdadbdccadbcdacbdaabacbbaaabcbcccadbdcbaccaccbacbcddbccbbcabbbabacdcbbaadacdcbbadaacacdddcbbbbcccbcbadbcccdbaddbdaabdcddbbabaddadcddabdbabaabbdabbcbdadcaadbcaaabdbacbcbbcbdcdbacdbadbaccddbbaadccabdaacdacaabddacaaddbdabcadddbddddcacbadccadbccabbccaacacdcdbbadcdcadcadadbccccbdcadabcdddacbaadacdbcdcadcbbaaaccadbadbcaccdacdcaaddadabbadababdabccaccbdcacddbcdcbbdbadbcdbdacdddabccacddbabbddbacaabcbdbbaddbdacdcbdcbcbcaabbdccdaddcaccabdccabcbabbdbbcdbacadcdbccbabbdaddddbcdbbddadbcdbabddadbaadddcadacbdabbbadbcbabadcdcbadbaccbcccdaaccdddbadaaacadadacbbddcbaadbcacddaaababbbccccbcaabdcacccdccabbbccadcdcddcabadbdcabdbdabbbdbaadbacadcbbbcacbadccbacbcbabcbbabdccbcaaadccadccabcbadccacbbabbacacacdccbdcbacdbcacdabbcacbbaadccddbbdaaabdcdcbdcbabdcdcaabcbabbdcbcabaddbbcdadbdddcbcaaadabbdbbbddabcdaddacbcbacdabcddbabdcddcdaaacdbabcdbddccdbccbdbcdadababddccaadcbbddbccacdcacdddadbdaacaddcacbbabdddadcccddbabdbdbcbbdbbbadbacadcbddbddaadbaabbbcccbcabbcadccbadbcdbdbccdcabbbaadbaccdbadccaaacbdabbdbddabbdbdbccbaabcacccbbdbaccbaaccbaadcadaaabbdbbdabbacdcccbddbbaacabadadddbcadbaadcbdbadcbbdcccaccddaaacbcbbbabbacdbbabcdaadcdbbdddbbbdddbcadccbccddddbbbacacdcdccdbdbdccddacccddadcbadadbadbcbdcdbbbadabaccdadbddaddcbaccabbabaadcdbaaddbbddaadaabcdbddbcbcbaccdcacbcabbdcccadbbaadbdacdaccabdcabdbdacddccacbcbacbdbdacbbbacbbaaabbdddccabdddabcadabcabbacdcdcdaccbcbdabbadcbcdcabddbcbabdddcabdcccddcacaccbbcbbbabbaadbcaadcbdcdcdbcacccbbcabadcaaadacbaaacabddadcadcdcbbdccdcccdbacdcdbbccdaaaddabcdbddbbadcbbbaccdcdaaababdacdbbddaabacbddcacdbdbdddabadcddabcacdacbdddcabaadadaacbbbaaadbbadbbadccdbbabbdccdabdccabcdadacadcdabcdddbcacdacbacaccdaacdacbcccaddcbaaacadbcccbaddddbabdadbcbdbaabbccbbadbacbcbdbbbaaaacddadbbadbaaadcddacdbbbbdacaddaddbbcbdbaccabcbbabcbbaacccbdabcddbdadbdaaaaabbdddaabbdcabdababaccabddadddbbadbacbddbaccccadcbddabacbabcaabdacdbaccaccabacdbaaabdacabaaddbcaabccbcbcabcaccaddabcabbacdcbaababbabadbdbbadbdccbbacabaaadcabadcbaddabbbbacccbacabbdcddbddbcdddcccabaadacbaaacbddaabdbbcbbacadbcbcbddcabcddbcbbcdbaadbadcaccbdccbccacbdbdaddddbdcbadcaccdcccbddadbbccdbcbacaaddcbbbdacdbcccbbbbcdbbaadbdbcacbdcadcbabcbcbdbbadcabbcadbacdabbabcbcadccdcddcadbdbcadbabdddcddbcbdcddcbbacdccddacaabbdddbaadbabddbadcbcaabdcadaccdddabcaabdbbbabdaccbbbdadbdacdbddbcacdcddbcdacadacabcdbdcbccbdbbbddbbcdccdbaddadcacdbabbdddacabdcdbdddaabbcccacdbdbddaaadddccbbdbcdacddcbbdccdbbdaddbbaadaacbabcbbdcabbbbbcbacddcbcbdcdddabcdaccdcaccbbccbdcabdbcadbbdacdbacbacbacdbacdadbaaddadddccdcadcaccccdbbccccaddddcdabababbddaadbacadadabdabdccabccddcccbadbbcaaaabdcccbdaddddcadbddcbddbacbcadcadaccadabacdaccdbdacacdaabacdaaadccdabbdaacaacacabccbdabcbdccadcacccbaddabccccaaddcbacaaccddbaaccaaddaadbddcaacccbddbabbabdabdccaddabbabbaacdcddcaccdbcabdaddddbdbaaadaadbcbadcdbdbcadaabdacdaaaccdbbabccbadcddcbbdbcdadddbddccdcacabcadbccdddcbcbaaadddbdcdcdbacdacbcdccdbabdcdbbdabdbbdbcabacbbdadbccdcdaaaccacabddbcdcadddadbdbbaacacddbaabcbdbdbadccdcacbabcbdcadcbadacbbaadcbdaadbacccacaddddcbaccacadabaabbadbaaaacbdabdcaabcbadaabbdbacdddcbcbabadbbcbcdcabddddadbcadcdbbacbbbaaccbccbddcadcbcbbdbccbaacaacdbdbbacddabdbcacccadccccdccabdcbddcbbabaadcbbaaaaaccaaaaddcbcbbacbcdadbadaabccbbbdacdaadadacdcbacbccabaacdbbdbdcaacdbaacdcbbbbcaddcbcddbcdabbdabbadbcdddbcbabcaacbcadabbbddccdddccdbadacbbaccdbadbacbacdddbdbadcbbdccabadbcbbdbababbbdbcddcdddcdbccbdccddcbbcccbdbbacaaddbbdccaddacbaadbdbaabbadbbcddccbdbacacacdbbbadbabbddddbadbdcbaaabacddcbbddacacadaaabcabcaccdaaadbdaacddbbadabaacdacbbdaccdcadddbdadbccdbabbbabbcbcaaadcabdccadcbabcccaacdbaacaccabdacbabcdddddadadcbccacdcabbbaacccaaabaaacaddbcbcaccdabaacdbddbcdcacadcabdbbdcdccbcbcccdadccdbbdabaccccbdbbcbbbcdccdacaacbddcdacdbdaabcdbacaccbaaabbdcbadbddbdcadccabbaddcabbcbddbacaaddabaddabdbbcbcbbadcabbaabbbaccbadccddcbccbcdbbcbcbbdbaadabccdbbaaaadbccadcbccddacddacdbbdcbcdadccbacbdcaccaaccbcabddbadabbaabddcdaaacbcaccaccdaddbaadddaacabbaaccdbdbcaacdadadcbccdbccbdacccbcbcbdabababdcabbcdacabbbcdaacaadaddcacdbdbdaabbddbddaccbdcadcbaccdabcadbdbcdbdbbcbdbcdacbcbabccdcbccdbdddbcacdddccbdadacaccdcdacbdddacacaaddcdcdabcbcccdadabbddbbbcccaaaabbababdcabdabcccaccddcaaaacabaaabcbbddbbcbcccacbbdccabbccccdcabaddcbbcadcdcbdbdcdcbddadbcbcabadabdccacdbbbdbdccbbbbbdcddabbccaccbabbddadaddbabdcabbcdcaaaaadadbcdaaaccdcacacdadccbdbacdbdbbcadacadccbbaabbacdcacbdbcbbbdcaaaacdccabdaaddaddadaadddaabdbdcbdcdbacdadbababbdcaddbabcbbbbabdcdaccccccaccbacdcbbaadbabdcaadcbcbcaacaccbaddccadcdabaadbbbaddcaacbbabddbccccddadbbdbcdcacdacbadabbdccbaaaddbdcbbbcdacbbdacacdbdddabcaddbcdbcadcadcbdabaccdccdcdadccbbbdbabbdcacababddccbaaddccbdbaaacdcbcdaabcacaaccddcdbbadaabccabbdcabcdbcccaabddbbababbbdcdcbbababbbacbcbacdadaddddbcccdabdacbcbbacccccabcacdadacdaaddcccddbdcbbdaabadabacddcacddcbadbbababdadcdcdbcbabdbcdadacaddaaadcbbccccbccbdcabbadacabbdcacacdaabddcddbabcbdadcacaabcbdddbcdcbaddbbbcbbdadbddbcbabddbcbbccbddbbddabdcacbcbdabcccbaaabaccadddabaacbbdadbdaacbacabadcbaacdaabcddbcaacaabbdaacbddcccbcbabbcbbbbbcbbcbcdcdadcbbdcabaaadaadabacbabccadaccdabcaabdccbcdbabbddbdbbbccbbdbbabddcabdcdcbddadadaccabcbcabaadbabcbddacaccbbcbbbbddbdadddaababcdaaaccbccaabdadaddbcbcabcaabacbbdcabdaccccbbaccacdacbadddabbadacbbddbcabdabaadadddbadcabbbddbdadddcbadcabcccabdbbcbbddabdaccabaabccabbbcabbbaccccddaccdcbdbddbbabacbaddcdbdcabacaadbacccaaacdbabbaaabbdbbbaaccdaabdccbccdacdaabcddcbddcbdbcbccaadcbbcdcccbcbdbaccddddcaabcabacbccdcacbaadcdcabcaaaccabbcbdabdcadabbddbadddaaddcdcabcdacdbdcbbdcbdcdbadbdccccddbbcaaddbcdccddccbdcdbbcbdbbabbabacbcccdabcbcdbadbacdcdabdaccdbaccdcdacbcbccbbbbbbcddddddcbaddacadbccadbcaadcbdadbbadbcbbbcbabcbbacbabdbabaddcbdcaaacabdbdcadbcbabbadddccbbbccdbaadcaabccbbaddccbbddababdacbdcdbbabbbbddcaddccbabdccaddcbaccdbcbdaaabcbbabcadbcaabaabaacabcddcdababbabccdcdddabaacaaddbabbcdabbccacadabbcdcbaadbadcbbbacbacbadcdcadcbaadaabacdadccbadabcaccabcacbcaadbcbcbacdbaaaacaccbcdddccbabaddcbdadaadcdcbaaaabddcdcbbbaadbddcabbbdccdacacbdcdcdbbbcbcaabdcdbcababbabcdadcbdcabcbbcbadcadabdcdbbdcaabcbaaadbbadbbcbbbdaadbdadacadddbbcabbbcacbbcdbdcdbdddddcddcacaabcdccbcbcabaccacdadcbbdacdacbdbaaacdacbbabbccabadcdcacdccacadabbbdaaacbccdaaacbcbdcdaacacacdbbabbdaabbdbcabbdbacbbacccddcccdcbcbbcaddcdabdcccdbdaddadadddbdcddcaaccbcdaccccbaccccbdbabbbadbaccdddbaccabaadddcddddbacbcaababbadadbadaccbabadbdbbcbcccadabdccbcbcbdaccdacacabcbaccbbccbddbddabbadbdbabbbcdacccddcdacadcbbaddbbbdccdbbbddccbcbdadddcbabbdbcabdadddadbbdadddacdddaabaddaaaacabbcdccadacbdbdbbcabdbdcdcdccadcabbccacbdacadaddaadddbaaaadddacaddcdcaddbadaababdaabcccbdddbddbbdccadcaaaabadacadbadadcbbddbbddacadbbbdbdbcdcccbbccccdbbbaadacbddaadbcddcbbbcdcbbbdcabacacbabbbbdabcabcacdddddaabcdcdbdbcdbcacadadbdcdbaabdaadcabddccbbadddacbccaddddcbcbdcbcbccaacaaabdbdbbaacbcccacdadcdbdcbadaddcddbbddadacaaddacbccdbccdadcccdbbacaadbcabddcbbdadcdbbdaddcabcbcccabcdcddccdacaaddbbbaadbadadaddcdcacddbdcadaadbacdaaadcbdaaabdacdabbbcddbadaabdcbacccdbcadadbdabcbccaadadbbdabdcdddbdbcabbcdaababacaaccabbcadccdcacaaddacdcdbddababadcbdbdccdbabbbbddbbacbadacabddaabcdaadaddccaccbadbcddcdbcdbbaacbcccbcccabdbaacbccadadccddaaabdbbbdaaddaabbdddcacdadbabcdcdbbbbdaaacccdadcabbcbbacacaaddddaabccabcdacdcbdddccdbbdcdbbbddabbababcddcdacbddddddbddcdcaaacdcdbabbcbcdacdcbccaadbcdddcacadaadcabbadbdbdbdbaadabbaacbaaddabbdaadadbabadbdcbaabaacadababbddbdabacdbdddadcccaaadccacbbdbaacaacddbcdbcbdaacdbcdcdbabdcdbddbbbbcccdbbcdbdadaabccbcccbaacccadddcdaabdcbdadcbacdacddbcbaccbcbdaaabcdbdcddbadcbadbbacddcccdcccdcabdacddbbcbabcbbbcccbcdbbccaddaccdccccdbbbadacbcbbacbacdaaabcbbbdbbadabdddbbcbbbbddbcccabbcaacdbaacddccdcbdbccccdabdacbddaaabacbbccccbbbacadcdbdbdcddbdddcabcbcbdbacdaacdccbbabdcbacddbddabcdcbcbabbdcababdaaaddabaacacccdbdabbbdcbabcbdccadddaabadaccabbcabaaaaadbdacbaabddcbdacbcdcdadcdbbbdbdbcacccdcababbdaccadaddabddbacdcbbadcabaddabcaabbdaadbcabccbbbbacbbabbadccccddddbdccddabbccdcaabbdacabbcacdbcdbdcdcbdaddcabdcadccdbdadbdacaadbccccdbbaddabdabdadabdbbddbabaaaadcdbdddcddbbadaadaccbadacdccdddcdcacaccacacadcdbcbdccaaadaccdccbddadaccbacaddbdbdccdcdadbddcbdcdcbadbddcacacbacaabccbbdddddbccbdbdccdaddadbcccdbbcccadabcaaabccdccbdcdaccdaabcbdcdaabbbaabcaacdcdadbcdcaababbcaabbbbabddbdcbcdaccabadccccacbdddadccccbdbbdbadaabbbacdaacbaabacdcadbbddababaabbadaccbbcadbabddbaadddcbacadbbdddbadbddbbcdadbccdbcddbcdaadcbbbbcbdcddbabaddaacdccbbbaacdbdacbcddbaadddcdaccdacadabcabbbcdddaccdccdaadbccdadaddbcdccaacaabdcacddcdbabaddbbdbccbdaaabacaddcbbbcbcdcbdaacacabaddcdcbcbcaaadcbbccaadaacdabbcdcdddbbbbcadaaccbabacdabadccdcacaaaabbbcadcbabaacbcbccbdcbacddabdccdcbbdacbadbcadababcdaadcabdcbdcacaacbdccaabbaacdbcdbbababbaaaacbbbadcbaaddabacccddbcccdbbbcdbbdacbcaccbccabdbdbddbbdbbbdcbccbbccadcbdbcaadadbdacdbaabdbababcacdabbcaddbababcbcacaabbadbcccddcacadbaaacbbcacbbbdcccbabbbdacbcdbacbacacdcacaabacdbaacbbaaaadbdbcaabdbdaaddbdcdadcdacdcbbccccadabbcbdacabdcbddaacbaccaaccbbcccccadcacaddbcdcacdaccbabbabbcddcaacddbcbaccddaabaaaadbbdaadadcbcacabddccacdbbbcbdddcdacbabadcddaabacabaababdaaabbdbacdcacdbddbcdcabdcbaaaacccdccdbabadabdcabdbbaddbabbbaaddbcaaabddbaabdcabbaadbcbbdcdcddabacbbbaaacaaddbaadbacbddabadacbabccddccdbdcacbacaabddbdacdbadbcadcdcbabdbcaadbbcbdabdaabbddccbddccbaccdbdbcbadccbbbaccbaadbaaaacdcacbaadabcacacacbcabdaaabcabdbccbdbbabcbbdbadabdccccaadcbdbbdccabdbcbabababbcaadbadcbcccdddccacacabdccbdcbbdabdcaabddacbccdcdcdcbbbbdddbcbbabdcdcdbbaccdccbddaadbacdbbaacacbcbdbbdaabcaabdadbcdcddddcaacacddaaadbadadcdccdadcdaadddbccaacacddcaaaccacbddcdcdcbadcbbacdccccbadbaaaabbdaddddabbcbcacaddbcbbbdccadccabbbbbddbcddbdbadccaccbbadabdcbdabcbbbdaddacacbdabbdbadbccbddbcbbdadddbdabaddabaabcaadaddaddaabbcdcbcbaacbdcabadbcbcdabbddccdabacabcbbdaadcbcdbbdbcbdbbddcabdddbbbaabcbbcddacdaacbbcbbdbabbbdbadacaddddabbcbcadbabaabadcdacbdacdcabddadadabaabccdcdcddcbcccdbdcacbdcadabaabbbccddccbccdddaaacddbbbacddbdddbabccaadadccacacbbcdbcbdcdbcdcbadbabacbddbcbdbaddaacddaacbbcaaccaddacbdcbdaddacccadcbcbccbccbbbbadcbbbabbccaddcdddcdcddbccacbcadacacacdcdaaaddbcaccdaaddddddccbbbacdbcbdababbacbcdaacbcaadacabcdddcaacaabdccdcaabdacdbbdddbaaacbaacccbcaacdddaddcbdbdcbcbcacbcdaaadbadadadaddbbcbbcdbdbabdddcaddbdbbbaddbccadddbabaddcddabcdaccbbdbbadacdbbddaacdbddccbbcddccbdcbcccadbdbdcccbbbddddbabbabadcaccdbcdacdcdbacbcdcbabadbcbacdbdabcddabdcbbccdcccabadbccddcacbdbddcbdbdcabdcdcdccbcacacdcaaabbbabcbabcdadddaddbccabbaddcdabdcdaadbcaaccdcbaccaabbaacccdcabaccdbcaacccccabadbbddabbdaddcdbbabccbababcbddddddcadccbbdbcbbdbabbacaaccddacbdddadddbbcacbcbcbbacbdcaadaaadacacdbdddacabcbbaaadddcacbddacdaabadbaaccbddbccbababdacacddacddadccdcdacadadaccdcabbaddbddabaacbacaddcaddacdddacaadbccbdaabbacacaaadaabbdbccccdcbacacdcbbbcbcaabbcbbabddddbcdaacdccddabdcddbcccbddbdbdaccdbdcdcbcbdbcbdcacbbcdbdadaabdddbbbcbcbbbbabaadcabacbdbcdaaacbcbbadadbbcdcadaaddbcdacdbaccdcbcccddcdacdaaccdccbbcdaaabccbcccbbdbbbcadddcbadddcddcddddddbddaabcadabcbdbbbcacacbacbabcbbadbdddcbdbbaadbddbddadaabbcbddcdddacacacdaaabdababbacacadcbdbadccdbcacabcccbdbbaaaaacabdbaaaddcdacacbbaccbabbcdcdddcdccacbbdaacccbbddbdbbbbbaccdbaddcacadadccbaabaaddccadcdcbaaaadacaacaaabbbbbadbababdbddaadcdbbdddcdbdbcbbadcbbcbadddbcbcdbdaadcbccdaacacdabddadadbdbddcaddccccbaadaaacdbccbabadbababbbbdababbbcaccbadcdbcbababadbbcbabdbabcdababddbacaadcddbdacccdaabccacdcbdaccdbdcccdbcdadddbbbdcaccdbbdbcbcdbbacaabcadacacabddcaabdccbcdaacdcbdcbbcbddccbaccddcacadcdaadbacadadaccbaabbbccbcaaaaaadcadbdbaddabadbbcabdaadccabaacbdbdbbaadbccacbabdbaababdbaddadadcbcccbcaccbdcbaadadacaccdbdcbdbbaccdcacbaddcdbcbbcbbcaacacdddcaacabbbcbbbbbbdcdaaccdacdabcdbacddbcbabcdcbadaaccccccbcbbbdbbabdcbcbccdbcbabcdadbabaaacabbccbaabbccdbadaaacaddbcddcabbdbcaabababbbccabdcdaacccbabbbcaddbbbbabdcabcaccdbabaaaadadacdbbdccdabadabacabcbadcddcabdcdaddaccbdabdcaddabbaaacbdcaaacacbcdcaabbbcccbbdadddcacccabacbbccbdddbdcdcdcdbddccbcbcddaadbcccdacabdddbdacdbbddbddcddcaaadabccadcbdcaaaaaddbaddcbcacdbabcbbbacbcbcbdddbadbcbbbcddbbdddcabdaabaadabdcbaccdbcccbcbabddbaaccddccdaadbdbcbaaddbddbbbbacbacdbbcadacddcdaadcddccbaacbbaaddbdabcacdbadaaadbdacacabbddabdcbcdcdaccaaadacabbaccbddbccabbadcadcaacacdcdacaaddbcdccacdcddcaaacccbdbcadacbbbadddbdadaabddabaddccadcacbcddcdabaadddbdbaccdcabcbbccdbdabbcabccddddadbaccacccabcbbdbaabddddbbcbabaccacadcaccdcdbbbacacbaaadacddcabaadcdcaaadabccaccdddacaccbcacccccccbaaccbdcacdbbbaabcdcbccaddaddabaddaddcdabcdabcdbabcdaaaaadcbccabdbdbdabadcaaaabdbbddbbaabcadbcbbbaabbdcccdbdbbcbddbccbaadcaaacdbaaadbcaccbdbacdccdbaadbacdbcccbacdcbbdaaabdbaabbdcdbaabccaadccacdbdcbcdaacbdddabaabbbbdddbdbaacadcaccadddbcacdddcadbcccacadcccaacbcadacdcdcbbabdcbddacddddddcdbcacbcccbddadbddbdddadcaabaabbccddcdaddbbdcbbddccaacdccacdcbabaadcccbabbadbcdabcddaaadbcacabadcaacacbdccadbaabdbbadabcbcbacbcdacacdadaccacbaddabddbdccbaaadccdddbdddcbaadacabbcdbdccdadadabaadbbbbadcacdababdcbbcadaccaabbbccdadddcadcdbabaaacdbbbbdabadcdbdcbdccadddaaaddbadabdbbddbcdbadcbbddcbbbdbcadadddabcbcdbacaaacbcaaabcdcaadbbaadccbcacccdbadcaacdaacdbdddcaccbcabcbabbbbaabbabccaadaaabbbcdabdadadcbbcbcddcbcacdbccbcbdcdcdcbdcadaaabdcbcdabbdbcddbbabaacbdacccdbacdabbccbcabcabbddadcaddcdadcadaabdddbaccaaacddaccaabdbcdacddbbdadbcbbbdcaaccaddaaacbadcaabbdbbbbdcbcddbbddccbcdbdbabccddcabdabdbacbccbcbbdadaddcbdbdbacbcbbbbababdddaabcbccdcdccdcbbbccdbddddadddbcdbacbdbacaabaccdacaabdcdddcadcbbaaaadbcabddcacdddbaaabaaabddccaadaaaadcdacbccacddaababdddddbaaabddcadccbbaacabacccabcdacccaadcaaaaddbddcbdcdbddddcabddabcaaadacccdcdbcccbddbdaccddaadaaacbcaacbdacaaddabaccbcddaadcaadcbdbaaabdaadbcadcdbdadbdaacdbdbabdadbbccddadcabcddaaaabbcbacbaadcacdbbddcbacdaacaccbcdcbbabccbacdaadbcddbbdcaaaccddaadccadddaacdaacbbacacbbbdbacabdadaacacdabcacbdbcadaaaadddcaaddacadadbcbbacadddbabdcaddaadcaddaacbdaaabddacbdcccbadbdbdcdbcbcdddbadabaaacbdcdabdaaabbddcdccdbbbcbdbbdcddcddbbdacdcadcbbadcaabdacacbabbddabcbabbaccddbcbddabcbbbbdacccacdacabbbadccbcbaddacdcdbdccbbcdbcaccbbcaadbbcdcbbbdcbdcdbcbacbbaddbbccbabccdbbccbaaadbdccdaaaccddcbadbcbaacbcacdbddddddcbdcccdbddcaabddababaacaaccbbdadbbdaaaccabdcbabacccabdadbccbabcdacaabdddadcadcdabdcdbabbcaacbadadbadabdcaaccbcdacaacccabbbcacaadbdcddbbdddadcbbcbcaabacbbadcadbcdcccaddaaaddddadddddddbbdbccadddbbddbbabcddbdcccababbacdcaccccbbccbddbdaababbcddddcccaabbbacaadaddbbcacdbabcbdbcdbabcacdddaacddbbcbaaadccdbcacadbcccabcccabcabaaddaaadcbdadbccaadabcbccdabdcccbdaacddbacddbcdabcbcdddabbbbdcdbdbdbcdddddcdbbcdbaccabdcacdbddcacacabacdcaddcbddddcbdbaccacdbadbdcbdaacccaabacadbcbddcdbdabaacddbdabadaadbacbbadcbcabacbacadaacaccdcdbdadabbbcaacccddbaabcadbbadcdcaaddcdcbbabaacdccbbddcadbdbbbddbccddbcbadcddbdadccadbcbcabaaacbbdaddcbacaabbacdddbbcbccbdcddcdbbcbbaabcbaddcccdbbdbdcadcacbbcdbcccdacabddcdddddcbbbdcdbbbccbbbbbabcddcddcbacabbacbbcdddabacbddbcbabbbcbacccbdadcddccdacaacababcaadadacbaccdacacbcddabbcddaacadcdddacbdbbacdcbcddcbcbdbbadadbaaadbbcabccdbacbdbdabcdbdadbdbdddcddaabccaabbacabcaacccaadcbcbbaddaccccabdaaadabccabdaccdaaabacbaacdaabdbcccddbabdaaddacaddcaccbbbdbcaccddbacadabacdaddabaccdabdccdaaacbbabbdbdbcdaacaabcabcabcdcdbbbddadbcbcbdbbbabcdbcabcbbadbcdacbccddbaabbbcccddbaabcadbcbabaccdddbadbbcbcdcddccbccccccdcacacbbaadbaccabbbbacdcdddbcbccbbccdbcdabbaddbdbdacdaddbcacacbbbbccbdcbdddbcbacbcabaadbdaabaabcdaabbdcbcacaaccbcbcdacbbbbdbadcbcbacbbdcbaadcbabcabadccbbadabcacbbbaabacbddabdbbcdcbdddcdbdbaababbdcdabadcccaabcbacadadbddddaacddabdccaccabaabcabcdaacdcddbcbdddcaccddddadbddbbcadcdaabdbbcdbbbabdcbbddddadbdcadcbcaacccbbcbbddadcbcdcadcdbdbadacbacddbbbcacdbadadbdabbadadabcbcbbdcbbbaddbccbdabdcbadabddbdddccdaacdcbbadbcbdacbdaabcbdcddcddbddcacdcdbbbbcccaccccacbdacdbbdadcadbdbababaadcdaccbcbaccaddcbccdcdbaacdaadbccabcdccbbaaaacabbcdddcdbadaccccbcbbcbbacdddcaccbcddcadbacbcccbccdaacbdbbcbbaaccbdccaccddcdaddabddabcbcbbbcacacababdbbadcbbcccabdabcddaccabccdcccddcbdadaadcddddbccbbdcccaaacacbadddddbbbdacdbddbbbdbacbcaabbbbaacaccaaddbdcadbdccbbcaacbdcabadddbcabccbbcacacbacdbcdcabadcacdaddbaaacdccbbcacbddabbdacddcaacbbdbbcdaccaadcdbccacbdbaccaabddbaadcabddbbbdaddcadcbbcbbbabddcaaaddcadabcbbdabddddadbcabdabaaadacbbbbdcdbcccdabbdadcccaddbdbdbbbaacabdbadbcabbcdbccdccaabadbcddbdccbaacacddabdacaaabbddadcbbdcddabdcdacabaddbdbdabbdcdbcbcddacdbdcdbaddccdbbccddbbaccdabbcbcabadaacadcabaabccdabaddadcbcdaabcdcbbdbabbdbbbadacbdaabbbaabdcccbabdcdacbcbccbdbbadccccdbdabcdbddbdacaddccdddcccbadcccbcbadcbabbcbadcaaadddabbdcccabbadabdbddbdbadaaddacbcadcbacdcccbbaccddcadddadacdbcaacacbbcccccbacbabcacabbccbcadadaccbccdaddbbdbdccbcccbbbcbadbbaccbbacdcaadcadacdcbbcacdddadddbaadaccadcbbbacbabdbaacaddaadcabcacdabccddcabacdacddbdbdabbcabccdcaabadbbdadbbddaabcadcbdccbcababcadaaccaabadaabaabcbacdcaaddcacccaabcaccdccbaccdbabaacbaacabcaabbbdbdcccccbbcbccabddabdbbaacdadcbddbcbadaaaabcccccdcdacacddaddaccbadbbcadccbbdbdbcbcaadaaadbaadccbddaaaabbabadcabbbdabcdadbcbbdcadaabcbbcdcdddaaccddbddccaddcbacdcbacbdcddabbddddabacbaaadbbcaddabdaddabadbabbdbddccdccddadcabdcdaccabcbdaccacabbadbbacddaccccaabcbaabcbbcbbabacbcaabdabcacddabcacaabdbdbbbcccdbcbbbbbbbdabddadcccbbcbacaabacacccdbcbbaabaaccbbbdbbbcaaaabdaabdbbdcaaabbdbcbdcddbacdccaddabababdcacaadbcacababccdcadaaddaccacdaddcccbadbcdbabbaaaccbbcddbadadacbdacbcbcaacbdaacbccbcdadcacbdbdaddaaddddbddadadccabaaccbcaaaacbcbcccdbabcbcbbbadbbaacabdabdbbacbacacbcbdacdccddbadcbbcdcddacdabadcccdcbddbddbddacdddadcbbadcccbabadcdbadcdccccbcbdccbdcabcccbdcaccbccddadbacacbabdccacdcdcbdaccdadbdbbdccbaabcddcccccdcdccdcacbcabbdbdcaaacacdbcdabcccdcbddadbcdbaaabdabcdacbdcaadcbcdbbcbacbaadbbbdcbcdbdddbadbaccbadbaabccaccdddadccdccbcbdabdddabbbdcbaacbdcabcdacdcacbabaabaccdbadadbcabdcbbbcbabcdadddaacbbcabcaacadccaaadbcdaaabcdcdddbcadbcbdabdaacbbdaaadcdbdabcbbabbabbcacdcabbabaaabccdbcdcdaaacbabcaabcdabbbcdbcdaadbacdcddbabccdccbaadcbabaccabcbcccacdbaadccbabcbbbacbbddacabaaccdbaaabadcbcadcddcdbaddacbadbcadbadcababbddddcabdacccbbbaccccdabcdcdbbcbbacadbcdddabccbdcabdbbdccabdbabdcbbccdccabdbcbbaabcababbbbaabbdabdccbbbbdabaccaaddaadbdcdbabbcaacdbccbdbcdbcccbadcbbbabadbaaaccbbdbdcbddcbccbccdccbccddbcaacadabaadddcadcddbcbccdcabbacddddbcdadcacaabcbddccdddaccdcbaabddbbacdaaaddcbbcdbddbdadccdccaabadbcdccccbadccbaacdbaddbdadaabbbdacaabddabbdccaaabcbdaaacbcdaabccdbabddccdadbbcccabacbcdcddccbadadbbcaabdadccddbdaddcadadbbabcaacababccadbdbbabddbacbabdcdccccdcbcacdaacbcbcddcccdabaccbacbdacdcdacbadccccddaccbadddadcbccbadadbdbdbabbabbadbabaddbaacdddaccaabcabdbaaddbdacbababbdddaddbcdbaaddacdddcdbdaccbabcacdddcdcbbbddbbbcaaaacdbaadcddcddbdabcaabcccbbdcbcccbaddcdcddbaacbddcaacaccacadaaabaddbdbdbcccbcacdbcdacbaabacdccddabdcbaccbbccbcabbcbcabdbcbaadbbabacabaaacddddcccdaccddacdbbdaccbcdcccccbcddcdbaadbcccbbddbcbccdabdababaccaddbcabbbcbadbddaadbbdcbcaaddddbdadbcdaaabbcdbdccaabbbacdabddbdcdcdbdbdcbbdadcbdadbddcabbacaaacbcaadccabbdddcdabcaadccbaddaaadbcddaabddcdcdadbdbcdbcdaabddababdacadbdbaabababbadcaabbbaabcbdacaddcdabacaaabcdadbbcacdadcbcbbbdcdbdaccbbabdabbbaaccabbdababbddbbbdcbcabbadbcbdaccdddbcbcadcabdddcaaacbdabdbbbbdcddaaacababcbcaadacbddccacaadddbccbabaacacbaadabcacdbdccdcbcbcbccbbdaabcaddaccbcbbdcdcbbcbdacaacaaadabbcaaabbdacbcdaabaacccdabacddbbddaabdaaddabbbcbccdabbccdbbdacdbacacadabacdddabccbdcbddcbcdcaddccbadadacadcbddabbdcbbdbabddabbcbabbcbdbcaaacaacadcdabaabccdacdaaaaaddabbadabdcdcbbbadaabaacaaabcbaabbccabbcaabdcacdcbcbcdabdacbcabdcdadccaaddcdbcabdadbddbaddccdbcbcddcbdbbaaaccdddbcddbcdccbdccbacdddaccdacbabbbbcdcbccadccccdcabadcbcbbbabdcbdccdbddbaddddcaabacbcdddcaadaadaadcadcabaaddbacddbcadacacdaabcddbddaadcbbcbdbcaadcbcdddacdbdbbcdacbbddccabddaaccaabbdddabaddddabcccdcbadaaabcbaabddacaabacbbddbbbaddcaccdaacddddddddcddbbbbbbbadabddacbccbaadbbbbbbbccabdcdcbcdcacdaddccdabdacbabdccabcbbbadddabcccacdacaccbbacdcdabacdaadadbbcbdbdabcaaacbacacbdabcdcddbbdcbdacbbcbadcdbdcbbabdcdccdbdabddddbbbabbbadaddbdbdbccabdabbbabdcababdcaaaacaccddcdcbcadacabacbcbaabdcacabdadbcadcdbcdaaabdcaccaddaabbbccaadbaddcbaaadadaabbdadadbbcddaabddbdbbcddbbdabadaccbabcaabadbdcccbdacdaaabccabadddcccdddabadaaacabddcacabaabbabadbbbccadbddadaddabddbccdbdabadabdacacdbbcbdcadbbcbbcdcabbacabccdcdcaddaacababddabcdbbcbcadcbdccacbcabbccaaadababdcbacccadbcbdccdbbbdbcdabaacaadabbddadaaadbbbaaccbddcabaccacacbbbabdddabcbadcdbbcaccdaaaddcacabcdddddccdcdaababaaacaaaacddababdbacbdccadadcaabdbbaddaccdddcbabdaadcacabcbcddaddbddccaacadcbabdbcadacadbcdbaadaabcddbacdabdbacdcaddabddbbcbdbdbddbacbdddbdcabbdbaddddacbccbdbbbbdbbdabdabbdadcbcacbddaadbaacaccccdbacbcbbcaaaddbccbccacddbdaaacdbbcbdbbbbbdaaaaaddadbccabcccdbacadcbbdcdbbaadcdcddcaddadbaadbdcbdadadccddcabccdadcccadbdbbacdbcdbcdbdaaadccdbbccdcbbcbdacddaadbacbcdccbadcababcdbccdacaabbaccbbbdbcddcdbaadbcbacbddabccbcbacdccbabadaadccdcadcbadcdddcdbbccddbbbaaccadbbacaacbcdbadaccdbdaaaadadbcbcabdabcbaabbbdabddadabdcaaaccbdaacdcbbacdddababcadbcaadbaccdddbadcabaaadabdccabdadbaaaaacccbabdadbcabdccabbaacacdcbdbaadabdbdccdabbdcbcdcacbbbaddbabbaacaacdcacddaacbbcbdbbbaacacdcdabacbcccbacbdabbacacacccbbccaadcaabaabbabccaabadabaaccccccbdacdabacacddbbdcbcdddaacbacabbbccabcbbbbacdcdccbdcadbcdcabbacdbabacadadaababcdbcbccdabbdbabbcdbdcdddaccacababbdbcddcdcccabbaaacaddcadbdbddccbbcacbbddbdbbaabbacbcccabababcbacdcaddadaadbadacccbdbbcddccacbbabbbbdbdaacbcddccbcadbdaccbccbcdaaabdadccaccadbbcddbbdbcaaddbddddbdccbbcddccdacdcdacadddabcccbbdabbabddbabaaababddcacdddcdddaddcacbabccadbabbbcaddaacccccdddacaaaddbabaabdbacadaaaadbdddbdddadbbadbdadcdabccaadcccbdddccabcbcaacadaccdcdbcbbdbccaddaacdabbbbcbbcdcbbcddccbdabdcdcbbbcabacdcddccbcbdacccbdaabbcbcbdbbbbcadbacacabacadbcacbacbcbbbabcddabccaabaadbaadabcdbdcbcdaababcbdbbdbaacdacadccbacaccabcdbbbaaddcbdccddccdabdbdabdddddddcdacdcadadabcddcdbadabcaddaadbaccacbabcaaacbcbbabdabcddbcabccbcdccabcdaabcdbddbbaddbccddcaddbcdaacbdcbaaaddbaacaddaabcdcabcdcdccbcacdbcdacaddcbdcadbacdacacadccbcdaacacdcddbaabcbadbaadacdadbcddbdabdbbdacadcdcdadbcbacacadbccadadcbcdabdcdabbbacddbbbccbcccbcabccccbccbdbacdacdaaaaaddcabbccacabacdbcaabdcadabdcbadcdababcdcadbcdddadbcdddbadccacccbccabbdccccabcdacadabdddacaddcbaabbacabbddacdbcdbaacdcacdbbccaabccdcdcddbaabcabcacdabbacbadcbacdcdcdacaadbabcddadcdbccdaddbdccadbdddbbdcaaabcbbdbbadbddddacaaabdccdcbadbddbbcabbddcdaacacccdacaaadaaaddddcccddcaabaccabbcabbbbbadddadcaabbcbdadddacdcdbdadbcccdbcdbdbbadbbcddbcddadbcbcabdcbbccacadcbdbcbabbaaabddadadcdcbbbdcbdbbcdbdcdacadabdcbaddbcabcdbabcdbadadcbacabbdbccabcaacdbddcadcaabddcadaadacbacbbccaccabaadbcaaabaadcaacddccbbaaaddcacdddacadacbabbcdcadadaabbdbcccdbacbbcdcabdddacdbbcaacadccbcacbaadcccdcbcbabdabcdbccbabcabbadbcdaadbbdcbcdcabcbcbacddcbadbccddcbadcdaabbcadcbabcdbabccddacdbdccaaccddcccbdaabbdaadbbbbaabbbdcccbdcabbbaabddbdaabacdbabbdbdccdcbbdcacaadcbbadacacddbcbbadbbabcdbbdabbcdbcdadacbaadbbbbbddabcbcbbdaadcbbacccacbdbdbababdaaacdbababcaddcbbbdcccbbbbcdcbcdaadbcbdddadbdabbbdbbdbbaadabbccaccdcaccabadcbddabacdbdacccbacdaaddcbaadbdcbadcabacdacdcbbddcdaddacaabbadadcccdabcdbdbaaddabadcdcacddacbabcbaaccaacbbbaabbcabaaaabacbcddccacbdaaabbbbdcabbdccbbccbaabacbcdccdbdcadaaddcbbadccadbadbbcdddacaddbddddaacbabadbdcddaacaadbadddadcdacdbcdbcbcacaaaddcadbacddbaadddacdcbadadacabacabdddcaacddcccadabcdcccbcbcdcbaaacbcdaacadbccbcabbaaabababadddcdddcdccaaaadacdbdaabcbaacddbabdaabcdbabdadaadbbaabcccdcccbddbacbdaddcbccbbcbdddbbadbcaadbdaacaddaddbabcdcddcadbddadbacdddccdbbbbabbdaabacddbbabdcdcccdbcdcddaacadabdbdbddaddadddcbabcbbdccaaadddcaccbcadccadcccaaddabbbcacbcbaacccccacaddbdcccbbdaacccbdddcbbdcbbdaaadcaaccaccdaddcabdbccaaaabbcbbcabacbdacbddcadbbbaaccdcabbbcdddbcbcbdcdaabbaaacbcdbacdabcaadbcdcaadcdcabbbcaabaacbaadcbbcabbcacbcbbdbcbaccaccaacbccdcbbdcacdadbcdcdabcbcdcbccacdadabcbcdbcaadadddddbcbbdbdadcabbdcadcacdcddddbbccbbacddacddbcdbcbaddcaaaacaccbbcbbaabcbcccaaaaacaabbdbbaaaddccadaddbababcbaaccdbbbaaccbccbadccccdcddccbbabacdbbdbacbaddaacabbbdaabccdbcdcaaacddadcabdaccbbdbbbadadddcbacaaabacbcdacabddbdcbbdddcaacbbbdbcdcdbbbbddddadacddddbabbdcddbcbbccabababdbdadbddabaccbcdbcadacbbdcaacadbabbbabcdcacadcddaddbdbaacaadcacbbbdbbddcbbbdcdcbcbbcdccabbadddcddbbcbdcaddcbadbcadaacaacdccbabbabdbcccdabdccbdabddaacdcddcbdacddcaacbdbcbbaccacbdcdbddcaacabcbbadbbdbadbaadaccacdadbbcdcbaabcdabaadbddbbcddcacbbadbabccdaaadcdcccccacacdbacdabccbcdcbdccbbbbddcacadcdcdbbcabdaabcbccbccdadaccacdcabacbdcdbabdabadcbabbbbcbbcddbbcdccadaadacaccbddbdbabdbcacaaadadcccbabcbbbdabdacbccadbcdcbcccbcacbdccdcbaaaccdbdabaccbacddccddcccdbbacdcabdccbccaabcdacbaccbaadddddddbccddabccdaabcdbacbdaaadabbbbcdaaccbbddadcccbbbbbdddcbbbaacdbabdbcdbbdbccdcdaabddcddbbdcbdbabdbbcacadbbdccdbabdcacadcabacbabbcdbbdabacadabacdbdbbdaabcaabaacacacdadcdcbaaaccadcaddcddccdddddcdbdababcbdacdbabcdbdbbdadacacaacacbdbdaddcdaaacacaabadabbdddcacaabbabddacbbcacdbcdbddcbdddbaabcbbbbdcbcddddbabdbdcaabbabaaabbbdaabaccdbdbaccabaabcbbcbbbcadabcabacdcadbdccadbdccbdbacbabbaddbcbacaaccadbadabbdcbdaaababccdddcacbdddabadbaddabcdbdbcbbaaddbacabbaabbddbdbbbdadcdcacaccdbdccabdbabaccbccdadddaacdddbdbcccdcbadcdabacdbcddbaddddbddaaadddcddcdcbcdccccdccadabbddcdbbbcaabcaccdcadbbadcbcbbcbdadbdabdddabaccccadccdccddcadacdbdcaddabacaabbbcdbccbaddadbcbaabccddabddcababccdcddbcddabdbaadbaccbabbdadbcabdcdddacbdbdbccdcdbaddbcddabacbaccabdcbddacccccacbbcaabdabbaacbdbcabbacbbdcadcbadbdbdadcdcdbbadcddddbdcdbacdbdbbacdabcbdacbbcdadbcaabacadaccdbaacabcddddaadcccbdaccacaacccabaacaadcacabdbdccaaccaadabcadcdbadababccacdbbccddcacbdacadcccaccdababaaaaacdcbcdbccbccdadbcccdacbbabaadaccccdbbbcdcdcbbbbbddacddabbccbabbdacbccaacadbdbcbccbcbaadcccacbdcccabdcadcbacbcdbbcabcdcccccccddacabcabcdbabdbadcacdccabcadddcdacbbaadacadddabbbaddbabacdbabbcadadaaccadabaadadaccacdbcbbbdabccacddcdacdcdadbcaccdcaaaddbdddbaaacdbccaccbcaccaabddccddabccdcbdadacaabdadacbcbdcaccdacdccbbaabcdbabaadbddbaadbcaabdcdadccbbbacdaacabcbadddbcdcdaaadddcddaabcddabcdccacabbcadbbccbcaadbacbcaababbcdabadbcbcbccbcdbbbaccaaddbccccbbdcccdcaababadaaaabbbbddaaadccaacadbdbaabbccaccaaacddadabacabbacdadbadcacbacbabcadcccaccdddabdbcbcbbbbddbcaadbdbbdcdbdbdcabcbabcdbdbbdaaaabaaddddbcabbcdcacbdadbabcdcdcadcdbcaadadaadcbccbdbabcbccddbbddaaccaccdcacccadcabdaacabbacdbabddbcccdccbaaadbaddbcabcaaddaaadabcdbdcabdcadcadddadadcddabcdbdbaacacdbdcacccbbccabddbacaaaaaabccaddccadadcbcccbcaaacbdddadaccdcddcdcdbadaddbbadcbacbddadcddadaacdcdcabbdbdacadabbbbcccadadaaabdcccccadbabbcbddddadadcaabdadbcbdbadabbddcbcbbbbbaccadbcdbcbdbccddadbddcadacbacccbcbabaccbddbbdccccdddccabddcdbcbbbaabbdcbbbcdaaaacdabbcccaabccbbdabadaacdacabacdadaddbbbabcbcbadbadbbdcadaabdddbdacddbbabbabcbdcbbcbbbdddccacaddcaacbdcdacdabddbaaabbdacaddbaacdbaddddabaabcacccaccabadabcaaadcadaabacacbaacdbdadbbcdaaddcbdcadbbdbbadcddbbdccddcccacacdbacdcddcdaccbdbcbacdcdabaadbadbcccaaaaacbdcbccbdbdbddacdaaaacadddbdcdaacddbddaadadcadcbcddbcbcbcccbabbdccccaadbbabcdddcabbabdcbccaacdacccbbdcdbbdcddbbddadacbcdbbaaabaadcbacadbacadbdbbcddbbcdbadbbccccbbaccbdbdbdcdccbaadaadbacbdaaabdababadacbdadccaadacdcabdaacadabccccdcaaababaddddbccbbbddbdbccabbadccccddabacbacdcacdccadbcbddddbcacdcdcbcbacaacabbdcabbbbacdcadadacbaccdbaddccbababcbdbaabbabadcabcbbcadbdaaddbcaddcbabaabaabacadcbbdbccbbacbdbcdadbdcdbbcccabdadbdcabcadcaddbcccbabacabddcddaccddbdcbbccbcbbddaabcbaadcbcbcbccdccbcbbcdbbbacbdbdcdddcaacbacbccbdddaadbcbddcdcaaccdddcdcbabacadbdacabcbacacbbaddaaccacabbacacacbbdbabbaccbbcacdaccabdbdcbcaddbbbaaaacddbacacbcccbdddcdaadabcddcbaacdbcccacbcaccaabbdddbdbddabaaaccddadacddacdacddccabdcccdaadddcbcdccbdacdbcbbbadabbbacbabadccaacacbbaddacabcdcbdbcabcbadbabdaaacbaddaadcdbcbbcacbbccabbadaddbcbbbbdcbdbbbddababddabbabddbbdbdacaacadbdabcadabcacabdcaaacaccaabcdcdacadddcaccaaadadbdabaacccdddaabddaccbabcaddbdadaabddaabbaacbdbbbacadaccabddbadbbdadcbcbcbaacdbabadabddbbbaadcdcabdddddabaccccbccdaddcdcabcbaaabdccabadddddcbaccdcaaaabaaadaacbbaccdddccdcdacaabadbbdaadcdbcdcddddaccacadbcdaacacbccdbcbcdbbcaaabcbdccccbdcbccddabcdaaabbbddccaddcdabdbabbbddddddbdbddcaacaacddaadccabadbdabadddcbdacdacacbcdaadadbdcddadddcbacdadbadddbacdabbdcbccaabacabdacbbacababcabccdaadaccdbabaabcdaabadaabbaaaadddbaaddbbddaccdbabddabdcbbcacdddbdbbbddbadcddbaaabaacabbbabdcbcadcdbcbbbdcdcaadbacddabbddabdccccbbdcccbdccdbcbbcacdddadadcadaadbdcdcddcbaacbbbdbacbbbbbdcabcbbdcbbccacadddcbcdddbaaabdcdbcbbcbbbabacddacaabcadabcaaacbbbbbccbbbbcbdcbadadcccbcacaabbcbddbbacbdaccbdbabadddabadabaccadabdadcdabdcdabcbdbddacdadccaacadcaacaaabbdabdbacdacbcdaabcaccdcaadddbcbcdccdcdcabdbbbbcaacddccbdbdbcdbabdcdcadaccddacbcdabdcaadbacbbdddaaacdbcddaabadaacdbdddcbcbdacabbddabbcacdcbadcbabcbcbaadcbcbbadcbabacadbbddbdcbdbbdddacaabccaccbbccccabbddcdddabbdaadbcbbbcdbbdabcaadabadbdbacacdaccaaacdcdadaccbcdddcbabababaabcabcacddabbbcddddcccbbabbcbcddccdcdabaaacdadddaaacbaddcabadbadcaabaadbabbadddbdddcdacbcadaaacbdaacaabdaaaababdbdbbaaaaacabcbbdaacbadacddcdabadddaaccbcaacadcacddbdaadcbaacbacaadcccdaccdabdcccdbccdcdcaccdacdcbccdbcbbbdaabcabadaacadddaacccccccddbbdbcddcbccbbdddaaadacaabaabddacbadbbcbbcaaaaadacbcdccdbddcdbddbbaccacaacdbadbacbbccccdadddbbbcbabbabbcaacddccabdcbbbdbbcdcbcbdacbaabaddadbbbbdadadbccccbcbcdcbdcbdaadcddaacaddbbbcbacdcbacacbddddabacbdaabcccccbabbcccacdbcbddccbaabcddcaaaabccdababbbdacccdadaacdbdacddcacbcdadabdadcabbbddbadadcdbaaccaacbacdcbdaddbbbbcddbbcccaabbdadcbcacbcddbddbbccddbdaabbddcaabddaccaccacccbccaabbacbccabdbbdcbdbbddbbbddbdccdbddcaddbdabacbdaddaadaadadcddcdabcaacadacbcddbaadbbbaccbcddcaddbbbdddcacdddcbacdccbadbababaabdcadaacdbcabdcccddcbacdddddadcddcabaadbdbacdbcdbbabdbbbbdaddccacbcdabadbadcaadccbbabaccdaabcdacadcacbaaccaaaadaabcdcdabadddabdadcbdabbbdcccbbbabdbcdcacbdaddbcbdbacaaacdbcccdbcbcccdbccbacaaacbdabcacbdaaccbdaaabdcabddbdacadbdacddabdacadaddcccdcddaddaadaddbadcddabddcacdbbccdccaadcbbddaadbdcddbbdcaccbaddbbccadcbbbcdcabbcdaddaadacabbdbcbdaaccdbcaddabddcdcdddcbadccadcdbdabaccccaaccbaadaccdabddbaccbdcbddacacdaaacaababcbccdcaaabcddbbcdacddbdcabdbaddbacadacdbddcbdcabdcbdabbbccbddbabdccddccaabcdddbdbbaacdcbbcbbadcbdcaaabacbcdbabdcddccbcdabbcabddcbbdcabaddcdabccadcdcabccdccbbdcaacbabdbdbddcacdcbccbdaaacddabbcdcdaabbbbbbdcbbbbadacdacdbaaabdaacccddcddabccacddbdbddcbadcccacdabcdacdbcababbbcdaacdabadaaadabadbaabbcbadacdacdcadbbcdbbaabcdcbabdbbdbcbcdaddddccddbcaaaacdaaadaddbadacaccbbabaadcdbbddaabdcbdcccddacbddcdccabadacaaadcadcbdbcdadaddaabacaacddbbbaddcdabbcadabdccbdcdaccabddaacdbdbadbbdccaddabccbbacaabdcbacdccaddbddbcacbbaccdaacdaaaadacdbcbbddcddcccdabccadabbabcadabdbbbcacbbbdadbdcbdabadbabdcccdacddcadccbbcccddbcdcaacabbadcddccccadcbadadacbadaaaacccaaabdcadcbcbbacaccddccdaaddcdaacadbcbcacbacbddbabbdbcdbcddcbcadcaccacdbbdcdcccdbcaaadcccbdcdcacbabbdbcdddcaadbbbdcbaccaaacadbcdcabbcabdddcaddababacdcdbabaccddadacaacdbcdaaaaacbadbdaabaacdaadddabcadbaaadbcccbbcbbdaaabcaaaacddbbaabcbcbbddbcaadcbcacabaaaacbbbccdcccccbbdcadddcadacdabbdddbbbabbcdaccdbbdcaaabadabcdbadcaabdbccdbbaacdacbddbabadcdabaaadbdddcbcdcaccbdddcbaacdabccabbcdcbabbcdbbadcccaacadacabdaddaadacdbaccdabbdadaddbcdcddabdcdbbbabccbdcccbcacbadccddbbaaaabbbadcccbddaaccdbbbccaacdbadbcdbdddaacdbdadacbbdbadabbdaadbbdadaabcddccabcccbbaaadacaaddababdccbddadbbcaddcdbabdbacbbbdbcdaaaacbdbcdbadcbddcabcbabdaaabbdbdcabccdcbacdaacddbbaaaabbabcbbbbbcbdbdcacaadddcdbdacbacdaccaacdcbabcadccdbccbcbdaacbaddbbcadcadabaddbbdccdadaabdcdbddcabccaadaaababdbddabcdbcdbbccaddadbadacbdddaadacadabcbabdcdcadddbabacbccbbbbbddcbabaaacbaadbdcaadabcbbbbdbdadccbdadbddbaccabaaacbdaccbbcbbccdabcabdbcbccbbbbcacbbadbbacbdaacacdbcdadbcabcabbbbccccdacbcdacbddbabcbdcbddaddbabcdcacdbbacaaabadabcbdcdaaaddacdccabdabdbabcacaddbbabcbabcaaabbacdbbddbccdccccdabddacaaddabdddbdbbbbdbcdbcdbaddacdacdabbccdccaaaaddbcddddacabbbdcbcbacccdccccdddcaadaccdacabbcccddaabdacbbacdaacabdcddaddcccbbbdabbbcdacbdbdbbcdbdbcbbadddaddbabcccddabdaabddaccbcaabddabcbcdaadaacabbbaddadcccacdbcacdccaaadaddcabbbddabacccbdcbdcdcdcccdcddaadbbacaabccabadbdacdccaaacdbacabbdbbacacdacccdbcbccbccdcbbbaddcdbbdabadaadccadbdbcccbadbacbcbbdcdcdaddddaacdbdaccbdcacadbabaaaaccaaaaaaccccdcddbbddbddacaddabaadacadbcdacbddcaadadcbbacdccaabcccdabbcaadcacdadccbddabddaabdaccccadacadacadcdbdcacdddcbdadbbbcadcbcddababcbcacbcacbadaaddcaaacccacacbaabbdccbcdcdcdabbdbcabcbacdbcdbccabdbadacdcdcbcaabdccdacccbdbabccbdbbbbdcabcbdbbbddadbbdbbadadcadbaddcdbaaddbbabccbdbacadbcaddbdcdcaaacbbaacbbadbaaccccbacccdadcacabddaacacaccbdcccaacbaadabbdbbabccadbcdcbdbbbcdcdbdcacbbacdcbdcaddcdbabbcadacbbbacabcdacccbadadbadddcaaadadbdacacbcbcbcdaccdaaaacbbcdcddddcbcbdcbdbddcbdbaaacdcbadcadbbbdbcadadbcccdcbddcdcbdacacccbcccccaccbdabaacccdbabdcadbcabaabbcbacabbddbbbdbbacbbacaddabacdacdbddcadddcbdcddaccabadcdbaacdcdbbbcbcabdccabadcccbbbaaababbcacaddbcaabccddbdcadbdbddaddadbdacbdddbdbadcbaaadababcdcdadccbbddbcacccdbbdbccbdcabbdabcdcccbbadcacbddcdbbdbbadacddbdbcddaddddadbaddcdaadcbbbccaaaadacbdabaabaccccaadbddccadbdacbdbaccaaaccbadcadcbccdbdacacabcccaccabccbcdcbabdddadbcbdadbccabaccbcabbdccacdadaddaadbcdbcdcddcdbbcaacccccacabcbbaacbcdbcdbbcddbcbcccdbbacdddbadaddaccbaccdbbdcdbbbcbdccccdcadcadcdbcacacdddaddaaadddcdddddaaddacdbccdddaddbaadbdbacdabccbccdbcbaddbbcbdadacacbddbbaacadbcdaaadadbddaadccbbbbcadcbcabbdbddbbbabbcbbcbaabaddcdccbcdacaabbcacaabdcccaacabddadacdabdabbadacacccbdacdcddabccccdadddcaaaabdcaacdccbcacacddbdcabcabaadacbbdbbdbcbabcdcddbdcdbadccbbaccddcbdbacadabdbbccbdabcbdbabbbcbcadaaacddbbacbdaacdddbabbaababcacbabaabcdbbdaaaccaaaaabbbaddadccabbbdbcddbdbbcaaaaaadbabccbdcbbaddadbaacabcadcddaaacadcaaaaaabccadbaabdbabbcadabbadcdadcbbbadbdcbccddbccbaccbbccbbdcbdaddbcbcdadbdabbbdabbbdacbbaccdacadcadbaaadbbadcdcacdcdbdccdcbdadbdabcbadcdbdbbbbcbddcdbcbbcbbbadddcdccdbcdddbbbdccacbdabccbaaccddccbddbbcccbbabbdccaaaccccdbcbcbdbabcdaaabddbbaadcbaadccbaccdbaacbadbadbcddbadababadacaabdaaaaccbaacdcabcbcbacbccbcdbabbacacbcbbcdadcacadbbbbdadbddbcddaabbccdbccbddaaccabbbdbacddcdddbddcccabbdbdcdddbbaaabbbbcbdbbdcabbcccccaaaadbdacbddaabadaccdadcdadcacdcbaabcadbbbcccddabaaccdaabbdbbacbcdbccbabddbccddabcdadadccddabbdaaddcacccdaadabcbaccbbcdbabcaacacddadbabdbacbdbbddadcdbaadbdcadbdbcaccabddaacdddbacacabdcddcccdbdddcadbacbbacdabbadbcbbdabdbbcaccacddacbdcccdbcccabdcdbdcaadadcadacbddbabbadccaddddbdabbdacbadbcbbaccaddcbdadcaccabcbbaaacaccbcccacabcbcdcbddaccbcddddadaababddccbadccaaaadbabaddbabaaadddcbbbadadbbaadbdbbcadbaaabbdccdbccabdaadddadcdcccbbdaababcddbadbadcccabdbcbdcdbdddbcaddabbbbcadcdbbaacddabcaddaccabddcbacdcbbbadddcdacddaabdbdaaacbcbccccddaabbbabcbcdcdbbbaabaacacbbbabaccbcaacaaccaddadaaaabbaaabddbddbbdccbcbacbccbabbcabbdaabdcadabbcddbccccababbbaccbacadbadcdaadbddbcadadbbdaababbdbdcdbbcacacbaabdababddbdbbdacdccacabdcadcdacdabdcabbbacdadcabdccdcaaadbbbcbbadbaacbcbbccddbbddccbaccddbcddbbabaadaccaabacadaccddaacdabcbaadddbbadddabcaacddadaaaadbdbcbadddbcacbbcaccadbbdaabdbdaddadaadccbbdacaaaacdccaacabdddadcbadacccdabacaaabaacccdaddaccbcbcddcbdacaddccdcbaaacccadabdbcaacdabcaddbabddddcadbdbdbdacbbcabccabddccaadacddcdbccbadaaadbcbdcbcaaccaccaadbccadcccdaacbdcdcacbbadacbaaddcbbadddbaabbadbcdcaccdddcacbaddbdbaaaadcccaabcccdacbbbacabdadccbaabadbadbcbbbdaaaccaccdaccccabbcddbbdbdbabdcbcdcbbdaabbadabddbbccbdadaccabbaadaacbbcadabacaddacdabacaccccdddbcbdaadabacbbbbdadabcccccadbdadbcabacbdcacdaaacacbbacadbbadadbdbadaaadbbccadcbabbdaaabbadaccccbbddbaddacbcbbabbaaccbadcadddddbcbcabaaabadddcbccddbacdcdcadcdaaccdddacabcdcadbacabcddddacdadbcadababcddadaddabddabadbaddaabacdbbbdbbddaaabddbddacbccccbddbbdaacdacbabbccdbdaddaddbbaccbcacccddacdbacabbdccaacabbadbcdadbacddbccaddbdaababacbbbdbcadccddabaadaaccdbbaadcabbddcbcddadabbabcadbaaaccdcbcbccdbccbdbccbbaacdaddadbcdbaadbcdbbcccbacbaacbcdddaacdaddadcbcaaaddcbadacbbbacbccabdcbabbbabcadacadbdcbcadaadadacaadbdabcdbdbdbccdabdaaaddbbcaddadacddddccbccabddcbadccdaacbbbcaacdaddacdcccbbbdabacacddaacabaadbaddbbcdbcdccbddcddbcaaddccdaadabacddddacaaccbdbccbdbdbbbbaccbccdaaacaadbbaababdaaadcbcdabccdbcccdabdccbdbcaaaadcdbdaadaaadaccabaaccabdbcaaaadbabcbabaaacbaadcadcdadbbbbdbbbacbabddabccdcbdadbcadaaccbadccbaabaadcbabdcbdabacbbaddbdbcdcdcdbabdbbaacaacbadbcaccbbbbcbbadbbbbcbcacddacdacaddccabbaccabdaadccdddcccbbcadcdbbdbbdbcabcccadbbdaadcbccabaacbdccaddabdbaacdddabcaaadcbddbadadbcbdcbccbaddcdddbcacacdcbdcbcbcbaabccbadcabdaccbdabbaaacbdccdcbacccdcbbaaaaaacddbdabaacabbdbacacdadaaccbccdcbaadaccbdccddccacbcdacdabcadadabdccdaabadbacbacadbccaddcccadadacabcbddbcadcaaccacdaddcdcbadbadcddadabaadacadacbbbdaacccbdadbccdbaccdbcbadbcbcbbdcaadcbbbddaddcacbddcdcdcbacddbdaccbdaaaaabbccddbacdaabadcdbbbddbcccbaabcacadcabdcaccacdcddbccddbabdccccacdcbdcaabbcadcdabdadacddaacabccbccdacbadbacbacabddbadddbbdcabdccccddbcdaabacdadbbbdcadcbdcaababdacabbcccdcabdaaabacdaaabdaccbbddcadaddaacaabcacdabbccbcacbbdccabbccacddaabadddcccdcabaaddabdabacbcdcacacaaddbdddcbcacaabdbcadaabbbbacacadcbdbdaacaccadbcddbbdacbbdacbcaccbbabccdabdbcddbbadbacacdbcdddbbdcddcbddcbdbdccbaaabaaacaabdbddaccadacbcdcddabbbabcabccbaacaabcbabdacadbacdadcbddababcbbbdcacddddbbdbcdbddbdacadcdcaacacaccdcdbababdddcbaaabacabddcacadbddaaccbcdabcaabaacdacaddbdccdadcdbbacabadbccaddbabacbcaacaadddbaaacdcaaabdabaddabcdbadadaaaaacbdbbacabcbdabddaddbdcadddbbaddcdaadadcccdacdcdcacaaabdbcdaaadddbcaaaccdaadcabacdcdacbabbcaaccdcaacbaacbbcbacbdaacbccabddabbbbcacdcbcbdbcdbcdbcadcaacaacbadccabcacbadddbddddcabababcbdabddadacbbbacddddbdabcaacdbcabbccaddbacaabcadddabbaadaaaabadcbcbbdbcadabbbcbccbcbcbaadbaaddbcaabccacbbccccbcadddbddacbdddbdaccabdbbdbacbbdacdbddbdbcccddaddccdccdadaddadaccacabccdadbabdabdcdaddbdaacbdcbbcbdddadaddcdacabaccbdadadaabdccadcdadbadcbcbbcaabbbbadaaccadbdacacadbdbaccccdbbdbddbcbdaacccccbbddbbccdccbcddccbcdddaddddbaccbcddcddabacdcaaadccccaccccaadddddbddacababababccabbadabddcababbcaaabaaccbbdabbccbbabbadbddcacbaccbcdcdcadacbbadbcaccacacaaaacabdacaddcddcdcdbaadbbbbdcddabbbdbbcccbbdcabadbcdaacabcdddadddcabcdbcaaadbdbbddddadbbcbbddaadaddcdadabbcbdabaabaadcadbcabddbccadabdddccadaadbdbcbccdaddabbbcccdbdabbddcbaddcccabccabacbdbdbdbbabdcdbcadddabbcbaacacbcdcdcaddadbabcaddadcbccbccbadaacbddabcccdacddbdacbcdbccaaabadccbcbbbccaaadddddbcaabadcadcbadadccbddcbbbcabdcdccbbbaabadcacacddadbdccdacbdbcdabcddaabcbdacaddbcadcccabcbdcdaacddccdcdcddadaaaabdbbdcaddbadbaabccbbcbddaacadaaccaacdaccbcbbbcdaaabcbabaaccadbbabccababdcdcbccbdccadcbccbbacdcdcaddbabccdccacdadcbabadcddabdcadcaaccdbbacbcbdadaacbaccbdccbaababbadcdaabbbdbdccbbabdaaacdacbaccbababbcdbaadddcbddaaadacadadacbcdbbbaaadbabbadbbababbccdcbdbbcabbaacbcdbddcacbacbdcacadbddaabdddcbcaccaacbcbadcddbbcdcddbabbbbbaabdbadadbdcdcddccdddbabbcbbcddcbcdbcdbcddbcdacbccadabcdadccaacaadbdbdcadcbbdddbababdacddcacbcbaacbdcbdcabbdcbcbbdabdcadccbcbcddcbbcaaaacbbdacbbacbbddbbaacccccdcbdabbbbbddbbcdbabdcaccacbabacdacdddbacbbaaacdadddcccbdccbccbbbccbadaadaddacbbadbcccccbccaabcabcaacdcaadcbdaddacbcddaacddaaadbdbadddbbccaacdddcadcdaddbdaadccdbbbacbacbcbadadabacbddaaaacaaaadcccacdbacaccbbcabcdbccbacadbbdaaabdaaaccbadbdadabacdbdccacaacacabdabdcddaadadddbacbabcbbddcdaccdcbaacdbbbdbdcbdbadbcbaadbdcdcdcabdbbdbcabbbdbdccdaccccddccacadacacddababdacbbbabbdcacbbadbcccdccbbbabdcdcdcbaabbbbababaddabdcdaddcbacbcbbbbbcbaddabaadbdcabdcbdbabdbbdacdadcacaadacdcbcbbaadcddcadcdbdbabbcdccadbbccdabbacdaadaadacccaadddbbccadcccddababbbcaadabcabcbdaacdddabbdadcbdabbcabcadbbdbdcdaaddccdcbccbdaadbabdcaacdcdbababdaddacdcdccbcacddbbadacdcdacbabcaaccbccdbdddabccbbcaaadddabacbacdcdbbcbaabcabaaabaacacdcacbcdacbccacbadcbabcdbaaddbbabbcaccbaaccaababddabbcddccbbbabbcaacacabdabbbcbccbbdaddddaabccccadbabcbdccbacbbdbaaacdabaacbcbcdadabbdbbbabdbbbadcdcbccdbcabcbbdcbdddbbdccbcadaaadddcdacaacbbaadadacbbabcccbcbcadbbaacbdbcbacadccbcbcbaababacbabddccbbbdbdbbbbaddadcadbacaddbcbbaaddaaadddcabccbcaccbacbaadcdaaaaccdbabddcabaabdabccbdabaaaddaccdadcabdbbdacdccdbccdacbcbabccabdaadcdacbabcabcbdababdacaccabdbcaadabcddaccbcbdbcacaabaadbaabbaacabbbdbddbdbbbccbccacddaaccdbcadcbbbacbcccaacbbdccacbcaaaccdcaacbabdddabdbbcdcbbbacddbdbcdabbddbaddbddbdcccadabaabdbbdcdaabdcaabbbddbdbcdbdcbcdaaadbbddabdaaabdabbbbadddccdcccdbaddcacabbbcccabbabbacacbdbdcbbcbdaaadbbcabcbcdcdababdbcccdaccadbdcbaadadbcbddbbbcaababaabcdcbadccdabbdaaddbdbadacaddacbdbbbbddadbdcdabdddbacbaaadbcdcdaddbbbabdcbdbcccdababdbdbabcddcbcbcacbcaddbabdbbadccdbddbacabccabcbbcdacdaabcaddbdbbadbbcbbdacbaabacbdcabcdbcabadbcbdcdbbbaddbddabcdddcadacdbbcaaccadddcadabbbcbdcacacbaccbacbccbdbaabdaabdddaccabdbbbbacadaddbbcdbcababbccddaabbcbdbdadddbdabdaadbcddbdccadbcdcabcaadccbdbbbccbaddcdaabccbdaacbdbbabbdbabdadbccdcaddabddbcbccadbbaacdccabbbaaadbaabbbbcdbdabddcdbacbbbbbcbcdbcbbcaddcdabaaaacbdadaddaccabcadddcabccbaabdadabbbbccdcbbaaccacdacbdbddddabdbabababdbccaadcbcddadddabcaaacdcabdbccbdadbbcbdacabbcbddcbcdbcdcccacacdccbadaabcabbadcacaadbdabbcabbdbababdbccadcaaccaccabbcadbcbdcdbbbcbbadccdacaccabdbbdbbcbaabbcbddcbdddcdbbdcdbbccaaccbabcdbdcadadbabadbcaabaacbcbbabcbadadacbcbabdadbdcdcadcdcbaaabbccccbdcccdcbbccccdbabadaaaaccaaabcccddcbdcccbaaaacdcbaaccbaacddcabdbacbbccbaadcdcdcadddbacbcaddbdcabcbadddbdcbdbcbcabbddbcbcccddcccccbdbbbddacdbadddddabaadccbdcdbdacababcbbabddcdaabbbcdadabdaabcdddddbcccbacbbbbdacaacaddcccbacabadadbaaabbbbbbbbccaadcbdcdadccccaadddcaadbddbcacabddbbaccadaddccbaaabaadabcdbbccbdcdcdcaddbcabdccadddacdcbcadaddcbaadcddbaaccacdadbaaaadccbabbbabadabdcddcdbaabddabcccbdcdbdcdcacacbaacddaaabbdccabadddcbbaadbabddccbbcaaabaaaabacadddcbaddababbcccbdbbbcbdbddbdaaddacccbdcacaadddbbdaadbabddabcaacbabbabcdabdccdcabbbbddcccddcacdbbaadbaadddbdbabdadbbdddcddbbadadacdccbbdaddaabcacbacdcdddadddddbaddbcddcbddcabbdacbadbbbcdbbaadaaddaadcbdcaaccbdcbbcdcbacbdcaabcdcadbbbdcccdbaadddaaddbdbaadcacbcbdccbbcccdabadbbdcdcacdacddcaadaaaacaacdcddacccaaaaddadaddbdadccaccbacdaaacaccdbadabbcacacbbbbabacdbaacadbcddadcbaccdcadbdccdcaababcdbacdcaddabcaadbabdcaacdcbdadbdabdbbccbabadabdbdcdbcddbccaaacddaabcbcaddddadddcbdabcbcbddbdaacabdababbddabdadcaddbbabbdbcdadddabdbccddadbcacaddbbdcbddcbadacbbacbdbcadcacabaddbcabaccbbddbcabcaacaaacaaadacdbcdacbdbcacccdadaccbddcbbddcddddaccdbabcbcdbbddacaddddddaacbcdcadcbdbdaacccdbaacdbdbacbbdcdaacbddbcdbcdaccbbcacbaabaaabddcacdbcbabcbcadcbaaacadbaaacaabbacbadacccabadadabcadabbdabacddabccbbaddaccdabbcbaccbcdcbdcdddaabdddbcbccbddacababadcabcbbdacbdbcbadaddbaabddcdaacadbcbcbcbacdbaccddddbabccddadbabdbbdcbdacbbbdbbbdabcacdbcbdbcaaccabcdbdadbcaabcdddaacbcacaddbddadadaadbbcbabbbbdddabccacddcddcccdbaadcadbbcdcaaacdacaccdacabcdaaadabdbbbbbbcabcbaabddcaabddcbddccdbdbcccbadddbadbbabbdbdbcaabccbdacdbdccacacabbddcdacdccdabbbbaddddadcaadbbdabbdbcabcaccbcdcbacbcdcdcdaaabcbbcdadbbbaccbddabaadbdbdaadbadaddddacadcdddccadbcbbddaacabbcbdcdadccaccabcaaadaaddbaacadbbccdaabadbccabbdcbddbbabccddacdccccadbabddacadcdabccddabbcabbcdabdddadadbcccdaabbadccdbbdccdadaccdcaaacbccdccccacdabbadcbaaddaacdcdcabdddbddaadcabcdcbccccdcbcabbdacaacbdbdacabcbadabacdcddaddddcbccdcccabdababbccdddadbadbbddddbcccacadbabdcddccbbaabbddacbcdcadcbcaaaadbbbabdabaabdcbbbcaadacddbabbcddddcdabddacdadbaddacacdbadadabcbcbbbaccbacdcaadcdddbdbacdbcbadddabcdddbbacddccccabaaabbadbcadbddacaddbddacbbbaacbababbdbaaadbabddaaaabcaaabbcaaabbcbdbabdbcdbabadddcbbaabbdbaababdccdacddcdbadcaacbbadaaabcdbbadcbdbdcdaabcbccdacaccdcbbdcdcbcdacccbddbccbbbccbcddbdaacddaddcbbbadacdbcdcddbcababcbbdacccadcbcbbbbdaccbacaacddcbdabdaabbaabbadababcdbdbbdcdcaabdbddabcbdabbabaaadbbdadbccbadccdbccabbcacbdbbdaabaabbcddababbccddbaadacbadcccdddbdbdadabbbbdaaccadbbddbcdbbadbdcdabaddccaccddcddcadbdaccbaddddabbaadbdcbacbcdaaabdcddcbaacacdbbaaccacbaaacdbbbbbaabccaaaabdbaadbcabcababbdbdabdcacbcadbdbbaabcccaadcdddccaacdcadcbabacabbddabbcabcdadadbccbabdbdbddcaadcbbddbbcbdcaadddaaacaadbdaacdcacdbabadbdcadacbadaaaddabaabbcaabdacbabccbdddbdbacbddbbcdbdadaacdaddaaaacbbcacbbaabbbadcbdbaacaccbacaddcbaaddbbbacdbbdbbdddccaccadcaaaacdcbbbccdcacbcbbbaacdaacacacbbdacadbaaacacabcdbbaccbacbcbbbdbbddcdccbabccbadddaaddccccbbaaacaabcbcdcbaaacccdadbadbcacdaacddaaacccbbdcaacabaacbbdbcabadaabbccaadbbcaabcdddccadcbdadabccbabdacbcdcadbadadbdbabcadddcbccbbbbbbcbababdcdcdcbaddbabdbdddccdacbcccdccabbbabdbdadbbadaccbdddbabcbaaaadaaccccdcbbabaabbdbabdbabcdddbcccabbddaabccabcdcaabddcdabacbcabcbbcdcdcbabddcccbabadcabdbbcabdbcccbdacaabbbaaababddbbdbdbbadbdddccbacccccddddabcdbaddcadbcaacacccadbbdacddcbabdcbacddbbadaabbdbdcddcbaadbbdddbbadabcaaacacccdbbbdabcdaaccabdaadaacccacbbdcbbadabaddbabbdadbccadbdadacbdbdbbbcbaaabcbacaaccabcbaadabacbcddaccadcdbdbadccdccadbcbabdbbbbcaababdcacbbcbadbadadbabdacbaabbacdbddbddcbbbdaabdadddaabacbddabccacdcaaaabdbdddaabdbaabbcbbddbdbadbccbdbbbdcbbadadbbcbaacccdddccaaddbcaddbacacdccbaabccdcbbabcdbcbbbdcdcdbabcbdabcbcccacdbcabcddcdcacdcddcbcbacbaabccbddaadaadaabccdabbbcccbbcdacaaddcbdaadcddaddddadabbbadbcbcaddddcdcdddddcdabdddaccbdccaaddccbdbbbdabbcbadbcdbdbbdbccbdbabdcccaabdabddbbcadabdcdbdcddcbcacddabcddabbdbcacdbdabdccdcdcddcddcddbabdccadaddbddaacaaaadbddddadababddabacbaddddacacdccbadadccdbbbddaadabbbbcbadbcdddddcaaaadbdbbbdbcbddacadacaddccaabdcadccccccdbaaabcacadddcabdaddbdcabcddbdbddabdacbdbdaddabadcddbaddbaccaaabbdcbaabacadccbaabcccadbbcccbbdcdcbccbcdcdddbbcaadbdcbdaccabddbbbdcabccdcbcccacacdbdacdbcdcdcdbbddccccaddcbcbbcaccdddbdbbcdcbcbadccadbabdcacacabaabaddcbccdcbddacbcbacdcdddaabadcccbdacbcaacbacbacbcbcccaccaddcbbdaaabcddbdcdcacaacacbadabdbdadadaaccdaddadabdaabcdaaaaacbbccdcddbddbadcaadbccbabaccbdacdabccdccadacadcaaabdcaddbabadbbbdbdaacaadbcccabcdcaadcaaadbacaccdcbabcccacabbcacbcadbcabcbcbddaccbaabaababaccadccdcbbaccacaaaddbaabbacbddacccdddbbcbadbadccdbddbcbbacdabaccbcbdbcbcbacbaabbccbdadbddabbcbdacdcbacadcbdcdddadacdacbadcdcbbcdbdaaccabadbaabacaccabaacbdbbcbbcdcdcacaaaadabcddaaccdcdaadcbadcbabdcbdbaaccccbcdadcdacbcadbaaaaacccaaadbbcbccababbaaaadcabcdbbacacdccbbaaacdacbdaccbbbacbbcddbdbcbcccddbbaadcbdccabbccbbbaddddcadaabdbbbbcbdccbcbaabbaacabdbdbbbcbcbacabccdabdcdabdabdaadcbccbdaacdacaccbbcbdcdcdacaddbbbdadccdaacdcddbdbccbdbbbdcadcbddaaacdbdbdbabccaacbabcdbcaabcdbbbbcdaaaabcccbcdabbbbabbdcdddbadcabcbbcacdcadadacdccbbdcbcdcddbbcbbdcddacbbbbbcdaddcbbaddacbbcdbccbadcbbaccaddcadabdcdddcdccbaacdcbbdcdbcbbcdbbdabbcccbdadddcdaaddbbabdddccacaaadcadbaaddcbbddcbcddccbadabdabbdcccabbccccdbcbcbbdbacbcabccbdcbdbcbabababaadbabdddccaaaddccbabadcbddcccbdabdcbaddbdbaacbbcbddbaddccacddabbacbcddaabcacccaaccabbdabbbadbccbcbaaaababdaacbabdbdaabcdaaddaabdbaabacdbaddbaacacbcdddbdbdaaacbbbcdbbbcccdcdacbbbadcddabdacdbccaccccbaaaaccbcaadacbcaaabbbbbdbbaadbaabcbbacdbacbccacbdcadabccbababcccaaabcaabbcdbcaddcabbcbaddcbcbcdbbbcacbacccaccabdaaadddbddbdbaadaddadacdaadacaabbccdaddbddbabbdbccbbdacdccabbabbbababdadbaaccdaadadbabadbbadaabdadabcaacdccdaacbacbbababbacdadccdadddddaacbcdcdbcbddaadbacaaccadcbdccabadddaacdcbacadabdacdadbdcdadbdadbddddadbbcdbbcbddadcbcbbdbbbdcbbdbbaabbaccdbacbdddbcdbccbdddcbbdddbacccdcbdadaababcdadcdcadccabddabbddababdccbbbbbbdddbdaadccbdbadbdcccbaccdabcadcbabbbdbbdaddcdccdacdacaaabacdadcdcbddddbbaaaacbdadaccabccabdababaabdcacbadbabaadcdacbcdadadccbbbadbaaddcadbddcbcbaacccbcdcdadabccddabddcddddcdbdbbdadacbcbdccbbacbccababccbbadcaddabbcadbccabdbadcacdcbdbcaadadbcacddaccbbbcddabdabcdacbcdacacdbbcbaacacaddacbbbdadcbadcdcbcbaacaccdcbaacbddcabacbabacddbcdcddbacbcdababcccdaacbccdabbbbcadbdadcddbdddbdbcddadababdcbbcadbaccbadbabbbbbdabbaacbdbcbaaabddcabdacbaacaccababccbcdddbaabbbcbabadbbbababbcbdbabdddaacbcdddabbadbdcaabcbccaddbbcdacbdbcdaacddbddbccdabbbcccdaabacdddbaabaacacbdacbdcddbbddbcbdaabbaddacbbcabcabbacdaaacabaadcdabaacdabcdcaadbaaaccdbaaadbaabbbdbbcdccaacbabaaccdbabdacbdbcdacddcbccbadddabbacdcbdbdbccacaadccadaabbbdbbcbcdccaadbacbcbaccbbcbcbdcbcddbcaabbcbbbdcbaaaccdcbcdcdccbacabaddbaaddacccbddddbdbdaadbddaadddbcdbabcacdcccaacbbccddabbddaaacddacdaaadcacdcacacaababddbccdadccaacddccaabccbbbdacbbbbaaadabccbadbcbdcdddbccdbbbcdcddbddcabcdaadabcaddbbabccadccbabcbdccdbcccddbcddcdcdaaacbdbdabdccdddbbbdbbcbddcddabdbaabbddbdbdaddbbdcddddcbacccabbcddcbaacabbabaacacaccaacbddcabbcddabddababccacdbbdacdaaacbcaaaabbcabbbbbadcbbdcbbabcabadddaddadcbbbbadcaaabccabddbcddcadadcadbabbaaaacccabdbdbabdcdabadaaccabbabcbbddbcdbadcbdcaaddcbadbbbdadaacddbaaadcbbadcdbdabcbdabacddcccddddabacdcdadcadcacdaaabdbbdaccaaacbbdaaabcbdcbdccaccdadadbcccccbcbccabbadbbaccbcacaadbdcbadadaabcddadcdadbabccddabdbacaaabcacabcbacabcaadbbbbbccadbcdbacbbbdadacccaddccaabaaacaaaacbcddcaacdaccabbdbccdcbbbbcadccbcbcaabcbdaccdadaccbabcdaaccdcccccabaacbbdbaabbbcbccdacbbbacdacbcbaddabddacbdcbbddadbcbdddaacdbddbadbabbcaaaaaaaaabaadbcdcddadccbbaabbdabaaacaccdaaccddabbbcadababcbbdddadbbabcbdcaabcbbdacdaabcdbbddbbbabbcaaaaadaaadadcdbbdaaacbdcbbbbbbbcccadbaabcdbaaaadddbcabcddbdabcadccadccdaadbbabdbcaadcdacdadaacbcbcdaabddcbcabbdcbadabcbcddcaaccddbdcacbdabdddbcaaaabacbabacadbcadabaabaacdbcdbadababbbaccbbaabdcdbabbadcaadbadabaaacacaccacdabdbbdacaaaadcadcbbdacbddcadccbcdbbddddcaacbcdbcdddabcaacadccdccbadcacaaaacbcabdccbbddaabccddcccbcbcbdccdaaacbbbdabdcadbadccacaabbcabacababbaaadadbccbbbaddcabcbabadcbddadbbcabcdabddddadbaabbbbbaadbacbbabddcaccbbbabddbcccdcbbacabdbcadbbbcdccaabaadbbbcccdbcaabcddcaadbdbcadbdabadcadcdadcbbbdddadadacbcdbcbbabdabbcdaddaacabbabbadcbdddadaadbbcadccdbbbadbdcadbcdabbdbcaaadadaabbccabcaacbcacaaabccaadcdadacccabaddadcadcdbaacdbddccacabddbbbbcddbbbddbcacaabbbdacabdadbddacdcacddcadccddabddbddcbcaabdadbccbdbabdcbdddddaddbacddaaabccccccdbccdcbdccdbcdccadcacbaabbaadadcaaadaaaabbbcdbadcadcbacabdbcbccabdbcadabababbdcabbdbdcbcbdbaabcabccbadacabdcdaabccbcbabdadaaccdcbbbaaadcbbcdaacbdccacccddbdbcbdcdcbbddaaabdbadcdbdcabcdcabadaadbddbdadcbcdbddcddbbcccaabbdcadcbbababbbdaabadaabaccbddbccbabdccacbbdabddcadadbbddabacdcddcabbbdaabaabdbbbbcdddaabaaadadbdcdccbcbdbcbcbabbdbccdbbcbbacaaabdcdcabbcaaaaaaacdcdbcdbacddbdbaccaacddbaabacaaddadbccdbcbccbcdbcacddabcadbbdaabadcddccaaaabbdbacacbadcdacdbdacdaacbbddcccdabdcabdabaaddcddcbccbdcdbadaddcdcbcbabcdbbddaaadacbbcbadbdacadcacaacacbcccaabcdbcdabbcadbababbddcadadcbaabcdbaaabababaaaaacbbcabaabdddbabbbacaabdcdabababbccacdbdcbaabdaaacacbcbccccccdbdabadcbbcaacadbdbbbadaccdacddbdbdbcaddcccccaacbcbddaccbdaabdabacbbcdbcdaabdcbcbbbddbaccadaabdddbddbacdaacdabbcbabbbbcdbbddddacbabaadadadcbdcadbbdbaddcacdcbcbcaaacbdbcbddaaabbdcdccaabcccccdbdaadcdbacbdddacccbcbccbccbdbababdacdacdccdacdaadccbdbcabadbdbadabbccdadbabbacbccadabbbddbadbdcbcaaacbdadcbdbdcaabcbbdddaccbadcaddcdbaccaababbbcdbccaabddbacdbbacccbbdacdacbaaadcbbcbabbbcdadbdbbbdacdcddddcddcadbdcdbddbbdcbdacdcbdaadbbbcbbcdcaccdccbcbddcbdacddddddccddaccdcbbddabbaaaabbbccdacdbdcdbbaaccdcbcdbbcaabdcdbbaccaadbbcbdbadddddaccdcccccccabbaccbaabdbcaaccaacbdccbbcbcbadccbdcdbbdcddcacacbdcadacddbddcbddccacbccdbdbdacaaaaabaccadcbbadabdbabddbcbaccbdacbbabbdcddbdcdbdbdacddcaaadddbbddcbdddabcddaaaacadacddacdbbbaadacbccddaacabdacbcbbcabacacbdcccdbddabdbcabdbdbbdbcaddbcdccdbbbbadcacbcdccbaaacbbddddbbdddaccadbaddacdbbccddacaadbdbdbdaccacacdbdadbaadcacddadbcbbadcdbdbaabbddbaabbabddbdccbaddcddacbccaadbabbaabcbdaaaaabbcabccdabaabcbbabcabaadccdaacddbdddbddccbbbbcbcbcbcddcacabdabbabcabbcbaaababbbdbbdaddccbacdabdadaccabbdcabbdbccbbadaccdcdbdbaacdcdadcabcabacbacbddbadcacdbdbddadbabacacdcababbaddbccdaaccdddcbcbddcdcbaddadcabaccccaadcbdbbdbaabbdabbbbdbcbddadbaadddcdcdbaadbcddabdcdbcacddadcdabbbbccacadddccdadabccccaccdcabddbbbadddccabbdabacccdcbdcbddaaacccaadbcdadbbabaabaacabdbdbabcaaaabcdacbaabbcdddcbabcbbdaacaabcbccaaadcadabcddbbcabdcbdabacbcdbaaddbddabdbcbbcbcccdbddcbdaaaddabdadbbcbdbdcbdabbadcdddbaaddaadbbbcdadcbcdaddcadacccdadacddacdcbbaaabaabbcabddbcabcadcabadccbdcaadbabdbbbcbbcdbcccdbcbcaadcdacdcbacadbaddacdaccbbddddabdbdbdacdaaddccbaacbacdbccbbcacaadacabdaaccccbbcbcddcabcacccaabbadcbdaadcbdcadaaddcdcabbcbdbacabcbcabaadacbccbcccadaaaacbbcccaddbaccadbcadbaadabadcddbbbbcacbcbcbddcbbdbbaacdcdddacbcacacdadcbccbcadbcbaccdbdccadacbbcdadabbdcabcadaaadcdadccdacababccabadaacbdccacbaadcbbabdaddbdcadabdcbbdadacdccddaabddabcddbcddadcaaacccabdbcdaacbaacadabdcaaccabcdccaabdabdaadacabdcccbcbaccabaddaaaaacbbaaaaaddcbadacbabddbdabdcbcadbcabdddcccccdcbaccdabdcadbcbbcdbadabacdbcadbbbaaaddbbbcccaddbddcacbabaddcbcdbdabddbccaddaaadbcabdbcaaabbadcddcdaddbbbcadacbbbbabbabadcbbcdccdcdbcbdbdabdccccbcdabdbcbbcacabbddcabdabdabddacaddacaccbdbabdaaaaaddaacbbbdcbaacaaaacbdbbcdcababdcabaacaccdbdcccabbabdccdcababcdbadcdcabacddabaabcdaacbbbbdaabcaddcbbaddabbbcbabadcdaacbbbacadcbbbcdbadbddabbdcacbdcddaccbcaddbcdaadddbcbadbbabaddacdcadcccccbbadbdcccddbbabcabcccdbddcadbaabbcadaadaddcaaccdabbbabcaddbabbbabacacacaaacbacbabdbacacdbdcddcbddaadaaccbaccaddcdcbacbdbabccacbbcadcaaabdbdadcdaadcbdaddbbcccbadaaabaacdbcbdabbddcdcadadccccccbacddccacddcacddcacbadadacdbbaabccdbdaadddbbababcbcbbccadaddbcbbcaacdbaacaddbdbcadacdccaccdbdadcbdbbadadddcbddacadbdadbacacabdcbaadcbbcccddbbbbbdbccdcdadadbbcbdbabbdddbbbadbcdcaacdddcdddbcadbdcdbbaddddadcacacdadbcdacdddbdccccdbdccbbbddccdcdabcbcdadcadcadcaccbdacaaccaacccdaadbcadbadddabdacacabbaabddbcbdaacbbbbabaddbaadabccbaabcbaccdaaccdcbddbdaaddbcacbcabcddaddbcadddbbdbadcaacbacdbdabcabdddbcaababdbdddcdbbcadadccccdcabacccbdddcccaddccbccbacadcdcdaddbbcbddcaacbccbcbcaaaaaadddccdcddcbdcacaaabbcbddbbbdbaddacdbbabcdbbbbcdbaacbbcbbadaddbadaaaccaababababcccdaacbbdbddbbbddbaacdacbcacbbbccbadaccabbdaaacadabacbddadcbccbcadbaacbbdabbcbaadddbadadbdaddaddabcbbdcacbdbdabdbaaaaccdccccbdddccbabbdadacabcdaacadacccccbbcdaabdbbcdacbdacdadccbdacbcacdbcbccbdacabaacbbadccdadbdaacadcbabdcbabddaacccbaabadbabacbcdccdbdadcdbdbcdcdadbccddcdbdcdcdcbbacacdbdadbabdbcdaadbbbaddbcbcabbbdccbdbdadbacbddddbbcabbbbbbbaaadabbdbdaabbcdbbbabaddcccddddaabcabbaabcabdaadabbadcbdbcdbbcadbbabdadbcdddccbabcbdcdcccadcabdaccbbbbddbadbccaabacacbdbccabcacacbdddbaaaddcddadbbbaacabcdbdadaccdbcddaacbbccaaadcdbcabbdaadcaaaaacdaabcbbcabbcadcdacbddcccaadbdcacbddccbbdcacacdbcdbaadabadbbdcccaadbdcacdcaaccbacabbacadbcadbccaddaddaadaacdadddccdaaacbcbdcadadadbababdbcccbdbdcbcbccdddcccbcdcacbbdddbcbdaaadbbaccdbacaadddcccbabdabcbbabcdacabadbcbdbdaddacbbcbcccddddcabbcacdcdabacbabaaccbacabbcbccbbdcdcbbccccacaccddcbbaddbabdcbbabdaacbdbabacddbaadadccadaccacbdbdaaddcbacbccadccbdbdadcccdccbbbbdcdbdacbbabdccaccdcddacacaccacbdbbccaddaadbdcbdcaadbbaccddcdcdabdddbadadaccdcbbdabcdabdadbacbccbbbcdcdddcdabadbaaddacdccdcddbccdddbccbadbadddaaacaadbaabaaccbacdacbaaccbbcdbbacaaaccbcbdcbbdbddabbbdabdbccdaaddaabadcddbbddadcbccbadbbdbdabbcbdbacadcbdacdbadcbcddcdbcdcbaacdabbcacddddcdaddadbdcbdbaabacdbdbbdbbdbccdbbaadbbdadbbacdcaaddacaaacccbcdcdcabbacbdaccabdbcccdacbaadaadcccdcbcaacdcbdccbdaddbcbddcadbcbaccbcacbdbbccaddbbdddcdbbddabacccbcbcbdbbacaacbdaacdccdcaabdadaacddadcadddbadcbbccaaabcabcbacaadcaaacabbcddbcbbcdbabbbaaddaabddcdddccdbcdbabacbabcddaacbbdbdcdcbaaacdddbbacbacbdbcdaccdbcdabadcbacbdbbdbdacabdabdadbbcacaaccdcccabddaabdbcabacbaabbcddaabaddbacaadcaadcdcbbbbddddbadddacbcdaabaacadbaacdadcaabbaccbdddddbadddabdadbbdabbdbbababcaddcaaaacabccdaddcdaaabaadddcdcbbccbbbdbbbcaccdccbaabdccdcdcadcccbabcbadabcbbbccdcaccbdababcbdabdbbcdcdacddadddcadbbbdaccadbbcdcbabcddbbccadaccdccccdddcadbbbbddbccaadccddabacdabbbdaadcbacdbcbccbdcadaddcababacbdaddccadaaaabbbcbacbbdcdaaadcdcabdddcdddcaddcbacaccbbddabccbbbcdaacabcaacbdccbdbcdccaacadaaadababacabccaacdabcdbaddbdddbaabaaddddbdbbcacccdaacdcaacadbccbbcaabaccacdabcbadbbbcccadcbacdcdddbbbcbdadadbbdacbdddbacdaaadbcbcdcbdaaccaaacaabaddcacdacdbcdacbaaaccacdcbbbcadbcbdcddcdcdbdccbbcacabcdbbaddcbbdaddadadaacbcadbacaadbbdbbddbbddcccdcbbaddddaaacabdabbbadbbcbcabbcacaaccddcbcdaadbcccbaadbbaadddadbcbaaaaddbcbadbcccaadddabccbcdbadcdcbddabaabbabbcdabacaccddabcadbaadcdaabbbcdaaacdbbaadadaccacbaddcccdcabddcdbcbabccccbcbbcdbabaabcbcadccababbcabaacbdddddaddbbcbbadddbbdaacbbaadbdddadacbdbdbddadacaabdcbbdbacdccacdcbdaddaaabcbdbcccaaadaaaccadabbbaaabbbababaaaabbdbdabccbccbccdcaaadacabcdcdbccacdbaccabbcadddddccbccdcbaadaaaddbcaabcabacdbaacadbaaacccbabbccbcbbacdccbaabdbaadbddbddcaccaddbcbddccabbbdbcdbaacadadbcbddbbadaabcadcdbccadbaadccadaaddccbbddadcdadbbdaaaacccadddcadbcdbdcdbddacdddcabbcbabcdcabdcacbcdaccaddddcacacaacaacdaaacbdbbaddcbdcbbcaccacdacabdacbabadaaddacbcbbdaaddcdcdacadaabaacdbadcacbcdccdcaacdbddcbbcacbdcbbbcabbaccbcbcdcbcdabcdddbbaccbaaabbadaddbbbbdccdcaddddcbdccccdbababccdcbdabbbccacaaabadcbdbaabbabacadddcdcabcaddabcabddddbaaddbcabaabbbabbbdbdcdbababddcccadbdcaccabbddddddaacbdadbcdabababbbbadbabcaacdadbbbddcdcadbacacdcbadbbcbdcabbcdbdabbaabacdadbdaabaddbdaaacacaabaaccdbbcddccaaaddcbbbbaaaddcbbbacadadcdacdaadcbcbbadaccddabcabbcdaabcbdaabdcdbabaadabbccbccbacaacdacbbcccdcddbcacaddaabdbcbbcddcdbdbcccdabdddcabdaaaddaaaacaaabccaaabdbbddbbdcccbbbcdacdadacaddbcaaacdabdbbccaaabdddcbdacbbbbbcabbccbdbdbbbadcacbdaaccadbccbddbdccdbadbdaddacdcddbaacadbcaaccdbaddbadbdaddacdacccdadaddaabacdbbcbccccbdbdaacdddcacdaccccacdacbbadbdadbdacaddaddabbccaadcdcaabddddaabddbacbacaacdbbdadccaabbcabdbcbdbadbddcccbdcacdbbccccbdcbbbdbacccaacddccbbacdaddabbbdcdaabdaabaacddbdaacddcdbbbacabcbabdaccdbddaacdbcadaddbbcbbddcdddcdabacdababbcdbcbbdcddccccdabdccccbcabcaadaddbccbadcabcdbaaddcbddcdaccbddcacadbbdacdacddcadddbcacdacbdaddccbdbbcbdbaabdccaadbbbbbacdccdadadcddacbbcdcdadbadccdcbadccadbdddadaadbaaccbaadddcbcdadacccdbababbadbddcaadcadadddccdbbbabbcadddbdbbdcdadadbcccaabbacbddbbbcaaaabbcccbccadaadbbcbbbdddcbdcdcbcabddaadadacbabdcaaacbcbbcbbdbaaacbdcdcbaabcacdbddccbbcbdbaaccdbcaaabbaddbdadcdbadbcdbdcbabcadbdabcabcbbdadbabccbdbbcdabdbddbdaadbbbaadcdcabbaabaaddcbdcbacccaabdaaabbcaddcababcccdcbbacabbdbdadcdbaddddbdadbabcddaaccacdcbccdbdccbaaaaacddcddaddcbaacdcccdccddcacbcadcbbabddcbcbbcbcddcbadadacccabcadcaadbbbbaccbdcaaccddacdaddcaabacbabdbcbdaabbcaaccddbacbddddcacbcacbdddbdbdcdddcddccaddadddbccaccbdaabdadddbcacbdccdddcdddbaddadddbadcacccadcdbcdcdaabaacccbacccadbcbddcbbcdadcadaccabbbbdaabbdccccbbbcddacacabbadcdbaabaadabcdbdadbdbabcdddcabbdacacdcdbdacdccbddbbccaddacbabadadaadcdacbdadcabcbcadcdcbbdccaaadbbadbacdbbaaaaabcddcacbddaababdccabbdcaddbdadbbcadccadddcdabcbaadabadbbbbcaadcabcdcbccdbadbadbbdadcbccdababdaadcccddcccccdbaacbdbbbbbcdcdcaddacaabdbccdadcccacaadbacccbccbadcddaacbacacddcdbcdadbaacbdabaaaacadccdbdcdabaaabbadacbaddccaccdbcdcbbdcbbdaabbabbccacacbaabdbdcaaddbccaadabaaacacddcbbbdcbdbaccbaccbdbabacdabddbabbcddbaaacddddbdaabddbdcddbbcabcdcacdabddabccacabadccadbdcccbabcddbdcdabccaccbcdbcadacbcdcdbbcacacadadcdcbcbdcbbcdaaadabdbaaabbbdaabdcddcdddadbbcccacdadbbbddccdabddadadbaddcdabdabdbcbdadadbacadabcabbaadccdbcabdbabcbdbdccddcbaddcaccabcbdbadccdcabdacacdddcbddbabcdaacbbbaabaddaacacbdabbcaabddadaddcbbbcbadcaccdacdcddcacdcddbcadbabdcdbbbdaaddaadcdcaadabdabdacdaabcccacddbddabcbdbddbcaababbadabdcdcdadbcbacdacabbbdbcdadaacbdaabcaacadbdabcdcbacdbbcbaacbcdccddaccaabccccbaadcadabdcdaacbdcccccacbdbabdddcaadbabdaccdacddcbdccaaaacbdccddbdbabcbaaabcdcacdbadaadcbbccdcdbababcdcbdbacdccaacdcbcacdcbcaccddabbcccadbddbcdcdaaabbdcccadbbdcbcaabbbababcccbdadbadccbbbaaccddbbbdaabbbdddcdbaaccbdbbccdccabdccbaddadbcbcbbaabbcaccbbdcdabcbccabadabdcaaaadacccacbaabacbadacbccdbbbaadbdabacbbdcdcccabaaccdccabaabbadcabacdbbcdccbcdacdccdbaadacdbbccdcbbbadabacddcabdbababbcddbcabbcadabdacaaaccbbdbdddcbcdadcabddadcadbabddcdabaadcbdccbcccabddddaadcaddbacaaccbbcbcadccdcdcadbcddcabdcddcbbadcbddcdcdccabddcbaadbaacbcdbaacddbcacbcbcdbccdccaccabbaccdaacacdcbcabddddbabbcadbadabdbdababdcdababddcadbcdcccbcddaaaccdbcdbcbccacdcbaabaabdbaccacdcadaaababbacdbcdbdaabaccdabcdbccbbcabcbacbbcdacabcadacccdbababdbdddacadccbdbdbcabcacdccccacabaaccdcbaabdcadcdabdbbdcdcdbaccdacabdaddabaaaccdbcdacbbaabbabcddaaacaaadbacabdcabcadacadcddbdaccdcddcabadaddaacbcbdbcbaccadaacbadabaaaacbbbbbacbddccdccdadbbcbddccbcdccddddacbabbcabadcaabdcdacdacabacccccbcbccabccbcacddcbcccdadcacddbdcabaadcacbccdbbccbccbbbacdbcdbadbdabbdcdabddabbbacbbabbbdaaddabacdaadbcabcdaadcadddabdddbcbcbddaccbcbbaabbabbaacdadabcddcccbccddaacdbcccbcabdaddaabbdddaddcacbccabdaacbbdccacacdccacabacdbdcccbaddadcbcabcdbdbadcdaddbddcbcddadcbcbdcadbbdadbaddddbcddcbbdbdddbbcdadabbdbcaaacccdccdccabaccbcabbdbaccbacabbbcbdbddddbccbcaabbadbaaaadcbdbabbdaadadcbacdbcdddcbdbbbdbddaaccdcdbcdbbcbbdddbadaabcadaaabcccdbacbdbbdaadacacbcbdbcbaacbbddcbbbbabdcaaccabbdcadaddaacbddcbdadcdaacaddacabcbadcaadabdadacacabbaccdcaaaccaddaccbcacdacaaccadadddbbdcdcabdaccadbbacabaabaaaabaaacdcbcdadcbbbbacdaadbacdabdaccabbbdbabdcccbbcdbbdaccbdbcbaabbabbbcdabddbcdabcabcbbacaadabbbbcbaaddcdbdbddadadcdcdadbabccbdadadacdabbcadbdaabbabdaaadbcbcdddadcdccdcbbcdcabdaacacbdcdcddabcacbcbddddbccdccdadbcadabdcdbbddbbdcbbbcbccdcacabaaabcddbdbbddaadbaabbbabcbdabacddbabddccaabacdaddcbacddcdbcbdabadbbacbbbaccdbcbaaacabdadaabadbaacddaaadabcdacddcacadccabcbcbaaaabbcdcaccbddcaabcbaadddbcdbdbdbbaadacbddccddbcdddadadbbbbcbcddcaaadabaaccdddbbcccddaadddcbdaddbabbbbccacdabcbcdbaccccaddbbabacbbcbbddcbcddadddbdadbbdcdcacdbbcbdcbbddcdcabddcdacbddaaacbaccbdbcacacbbadacdbaabbbdddbdbbbdcabbccbcaddacbdddcaabddcbdddddabcdbdbaabbabbadbaadccbbbabdaccacabbbdbababccdddaabdbdddbacdacaadbbacaccddbdccdbdcabaaabdacaacddcacacadbabccababbcbdcbadcabdadbbbdcdaabbaadbcbccbbbacccabaccddcbcbbabdbadacaacbddaabaaabbcbadbddbaddbaadcddbcdbcaccadadbddddabdcacccdcdcccdbadddabcdbcdccacaacccdadbcaaaadacbbcccacabaddbdbaccdabccdbcadacdddbacccacccdcdddacdbccccccacbdcbbbcacbbaddbaaaacdaccbbbbccacdddddbbbabbdbbcdcdbcacbcdaaabbddcaaadcaaacdbbaaaacacaadcbcccbbdcacabbcbdcbabbdcdcddcbcbacadccaabdcccdcdbbbdcabaaccabdadadcddacabaacaaccadbaccaadbbddcabcbcaaacccdbbcddaaacccbadadacbccbdbddbddaddaaabbadbbbdaacbacbbbdbbcdbacccdcabddcbbbccdcaaababcaccaacdcbddbcabcabdadadcccddccdbadacdacddbccddbccdcbccbbbcaddcbbcdbdbbacacabbdbbdbadccadcbacadccdbdbdbbbacdddadacbbcbbccbbcacbaaaaddacdcadaccbcbbdcbdadbbcaaacadaabacdadacbacacdbcabdddbcdcdbbcabaadacdbbadbddacadcddddbcccdbcddcdcccccadadbccdabbcdbcccbabdacabdbcbaccbdcbbbadccdcccbacadbdcdbaacacbaabcabacddbccdccdbbbdcbbdbdbaacddadadcbcdcaccaabacacadadcdadaadbaaabcbbadddddbbbbcdbaaabadbacddbbadddcbacdaaccbcbabccbcabbbdbaacadbcbdaaacadacccdcaaaacdbaddddbcabcaacdcccadccadccbbcacccbccbdadbcbdbdadbbacbabbdadcbccacbdabadacbcadbbbcbbbcacdadcbbdacccbbddbddacbaacdbbddccdcbbcbacadbdacdbbabaccdddbcdaccbdccbccccbabbbabdcacbcbaddacdcabbcdbdbcacdcccdaaaadcacaccbdacccacccababcdacbcbacadaabccacabdccabbcbbbddbcbbabdadadcddbadccddbaadcadabcadbccbbdadcadbaddacbadccbbbbcbaacadbdcbbcbbcddadbbcdcaadddbdcabdbdcabbcdcbbdcdcdccccccdbbdcadadabcaaaddcabadcdbcbacaabcdcbbaacdbbdabbaacacaaacccaabdcbddaadabcccddbccdabbcdadadacabaabcbacdabcaaccacdaadaabdcaaccaadccdadddccbcbdbbdccccbadbabbaaccdbcacbabdcbbdaadbbdbcddacbbacbdaacccbaddaabcabbccdaabcdcacbaccdbcccbcaacbdcacaacbbdcacbbacbccccbaccdacaaacaadbccdaacbdcdcbccdabdacbdabddacccdcbabacaaacbadaaaaaacdbdaabbacdbbcaaccbdddaccdccbadaacdabbabdcdcabbdcabdbbabbcbcdcdddcaabdababcdcaadaddcdabaddbccbcccadbadadccdbcbbbcdcaaccbbdcbbbacddbbadcdbbbbbadbadbccabacbbdaddbbcbbdccbbdadddadbbbaccaabaabbcccdcbaadbcbdbdcdacbbbabaacabddacadddbdadacdbdcadcbadaaddaddaddccbddccdbaccabccdccacbadcccdcacabccbcbbccbbcddcbbbbabbdacabdacddcddbadcdcbdcbdcdaccadbaddbabbdbdcddccabdbaadacdcdadabaabbcababdabbaabbbbdcacadbbbdcccddbbcaaadcdbcbaaadacbbbcddccdacddadcbcaacccdaabdbcdccddbbdddbabaccaabdccbdbdbbbdbbdabcbadbacdcbbbccabbddbaccbaadcbabcacdcbdbcdbbaacdbbaccbaabbabcdbbddaabdaccbadcabccdabbdccabbaddcaaadcabaaaaaacaacbbdbdaddbabdbacdabdacabdcdbbbddcbccdcadadaaadacdacdcaddcadcaccadadbccbbbbadbcddbcbbdbbabacbdaababccbcddbcdccbbdaabadaabadaaddddaaadddcaadbaccacbcddbcaccbbdaabdbacabbcbcabcdaacabdadbcbbdbbccdaabcbdddbabddaddbcacccbcbbacadddacabbdadcbbabccbcadabaabcdbdadcabdbababbacbdadbdadccacbadaabaacddbababcbaccbcddccbaabaacdccaadbddbddbcbbabbabbdbbbddbdbdbcacbbcbbadbacbaddbdacbdbdabababbcdbacaaaaacbcdbbbaababdacabbcaddddacaadbccabccccabdbddbabddbadaaacbaabbabaccccdcddaabbccdcdaadddccabbdcddccbbbabdcdaaadcbbacbcbddcccbcaacabdbcccdcbbcbddaaddccabddbaacadcaddaaddcccbdcaccccdbdcadcbadbdcdbabddbbdbadbcddbcadbbcddcbdbdbbddddcbdabcaaccbcdbcddbdbabccdaaaacadcacaadbcbacdbbdcaaaccbdaadbccbddddcbabbcaccdaaaccaacbddcadcccbacbadcdadadacdccacadbdcbcddbbcaddbddbcaacaabbbbcdbcaddccdadabbabaddddddacbcdacbccccbddaaccbcdacdcdbccbcbdaaaacaaabcddcbaabbaabbbabcdcdadbdcdddcabdbddcabdcdbcbdbdddcaaacadccbdcccaddbabacbcdabaababaddccbaaddaccdbdacacabbccccdaabcddcbcadbccbbddcdaaddaddabbaddadbbbdadacbacdaacccbcdaadaadbdddccabddaacaabdabccdbcbacddbabdccabcddaddbadbdbdbbcbbbddcbacbbcbddccadcccbbbdbddccccabbaddabadbddbbdadcbaddcdccadaccdadbcdccdaddaadaaadadbadcddddbdcbbbaddadaababccccacdabadcaaddddcdddbbbcabbcbcdbadddcddcbdaacbdddbdbbaddbcddbbccdbdbbabdbacacadabbcbccadadcbdcddbabdbdcddaadacbcbddcdacdcdabcdadbdcbccacddadbbabbdaadccdabbdaacaababbddcbbbaabbadccadaabacbcbddcbabbdababdcaadddccacbbbccdbcbcaacddcbdcacdddadaabbaddadadaacdbabdadcdaacacadddcbadcbababcadacdcdbbccadbbbdaadcdbbdacbddabbaadbcdbddabaaabbacabccdbdacbadaababcbaddacbcddddbacbacadaaadbadcaaadabbbcacdadccddbbcdbabadbccdbaadcacabdbccddaaabbcbadabdbdabbacaadcbaccddababddccacbdcbbdabacccabdbdabacdddcadbababdccbababdbaccccdacdabdddacabadaaaaaacbdcadbacbbacdacdadacdadbbaccacaccdbbbaddbcabdbacdaaaccadaddcaddadbbddadddcbacddabbbcdddcdaabaabdabbdacddcbddbcaacabaaccbdabdbacbacdaadbbabababcbdccdcbaacbadadcadaaadaddaaccddaabbdabccaacbddabacaccdcaacbbbddacaaacdccacbdcddbcdbdaabacddabbddbcbbcddbccbcbcbcddacdcacaddbdbbcdcbbcddabddadbdcdcbaaabcabacbaabcbaabbbdaacacdbcbaadaccadcaaaacdcdcbbcaacbcbdaabadaddbaccabdcaacbcbddcbddbbcaaddacbbdaccabcdcbccbbdccbcdbadbcacbddcdbaabdbcdaadaccdbaccddaccdaaddaadadcddccdcacabdabbcccacddacdbbaacaacdcdaacbdaddadacbaadbddcdbacbcdcbdddacbbcaabcbccbdddcdcbdbdcdccbccbbacccccdcacbacbbcadadbdcbcbdbadcabaddacccaacdcbaaaacadacdaaaccbddbcdbaccbcbbadacbcbbbcbacbccbcbbacdcbdccdaabdcbaacaaacdbcadccddddabddcbbccaaaddaaadbdccbaddbdbdbbaccdcbbdcbbcdbcacddcadcbbaadccbacadabdababdddabcbcacccaccdcbaaddadddbdbbcbcacddcdabcbdbdaddbbdcbcbdbbdacdddbabbddcdbcaacadcdcbabbccacdbadbcabcccccaabdaadddccbddadaaabbbbdddbadccaabddaaacbacdddcaabcccbacdacabacdadaddbcbbcdcacbabbbbbaaacbbaadbadddbbadccaccdbcdcccdcbbbcccbbbdadabcddaaadbcbbcddbcdddccdbacdcbbdadbbbdbdbcbaadcbcccaddacdddddddabdaadaabbbaacbdaabcbbccccdabacacbbbdcbddcdacabbbcddadaccccaaacdbbdcccdbbaddaadddacacabcbaddbadacbccabddaddcbcaaabcadbdbdcbccaaaddcaacdadaddadbcbdadbddbdcdabadbbcccbcbcabaddadbcccdbaddbdacaabcdabbbbbbcbcbbcaabcccdaaadbcababbdbaddacbcadbcbddacbcbaaadbcbbbbbdaccbcacdacccccaacccdbcdbdcadadbdadcadacacbbbdaccbcdddaaababbdbabacadadbdbbaabdadbddadcdacdadcdbaadadacdacdcbbacdcdbbabbdddbcadddbdddabbaddabcaaddcaacdaccdccbdadbcbbdccbdacddccaaabcddbcccabcdacadcccabcdbddacdaccbddbddddbadcbbdaaacadbcbadbdbabdcaabccbcaadabccbcddbcabaccbacdddadaaaddccbababdadcbaababdcbcacdddabdbcadcaaaadacccdacbddbabdaccdadcbcbbddabbdbcbccbddcbcdccbdccbbdaabddbbddcdccadcbbdbbbabadadaccdacccdcbcaddccadbbdcaaaacaddbabdabbbccdbcbbdbaaabdadababdbabddbbaadcbbcacbbcaabddacdacbbbddbdacbcaccaaccdacbdbcaccccbaddcbdcaadbaacbdddbdcdbccdbddabbdcdcaaacbdacccdbcdddbbaddcbdddcbcbbdbdcddaabbadddcadcddaacbbdcbbabaddbadacacbddbbddcaadaccadbbdabdcaccdaacdbcabccbbdddbcabdcccdbdddacbabaaabddacacbdbdaaadbaccdccaadcdadadbaacbacdcdadbbcdcbabcabdbacdcaaddbddccadbacddcadbdcdbdbbaacddbacddacabadadbdaabccdbabdaccdadcdabccdcdacbcadbbacadabdbbadadbcaadbdaadaccdabdcbdaacdcdbbdadadccdddccbdabacdaddbcbdacbaaddbcabbdbbbdaacacbdabdabcccadbbccbaadbaababaaddbdcbabadcacbbbcdbcbdaadaaacaabaadbdbaccadaaabdddcbdcadbaaabbadcabdadbdadcccbddabdcbcccbdcacbccdbcdbcccadcbabbadcbabaaacddbcdbaddbcacccbcacbcbadadadabccbdcabcbabddbdadcaaaadacaadbbccbacccbaaaddcbcabaccbdcacabbadcbababaccabbcbacdbbcddbbbadbabaddaaaacccdaaccddbbbdcbaaddaacaabaaddcdbacaccacaacbdaabcacddacbadcacdaccddbdcaaadcdcacdcaabbcacdbbababcadadcdabccdbacaddbbcbcbcaaccdadabadbacbbccbbcdbccdabdaacdabbdbbcdcdccbdbacbcbcdbbdcabcdbadadddcbcabaaddcacdddcaddbbabbcdcbbbcacbaacbbbdcbdbbcdddabcdbcbacaaccaacddabddbbbbbcdbcbdacccbbadbbcdddabdbdabadcbbbcccbdccbcaaaaccdbcadbcadcbbcbacabcbbbdbcbcdbabccdaaacacbacaddcdcccaaacbdbbabacbadcccbaaacaabbcabacbcddbcabdbdcbbcadabccbbbdcaacbbcacbbbbaadddcccdabadbcbddbbddccabbcbdbdbbacaacbddbabcccdbadbcabdcbbbcaadbccaadcdddbddacbdbbbacdccbcdbbdbcdbddadccddacbbcbdccbaadcaadcdbdddcaacdaddcadaaacadabdbdccabdbaccbcdcdcdadbcadacadabcacdbcacbabbcacaacadaaaccddadadabddabbcacaacbdcccdadbdcacbdaaccbdadadccdcdaccbadaacddcabccdadadddabbacbaaacdacbdaabcadadcadbbabcbbacbcaaababccccbddcbdcacddaababababbcbaabdcbbaaabadbbabdadadbdcbadcccddcbddbdabdbcdbcbcaadaaccababcbcdccadbcdbcbaaacbdcdaddbcaadbaabbdcabdcbcdabadadcaabcccbbdbaddcacabbabdcbdaaabdcdbddcaabbdbbdccaacaadccddcadcddbcbadaacbddccbbbadadbccabaacbdaccabaabcddacbabdaaabdccdbbbaaddcdaabdaddcadbadcddacbabcdaaccaadcabcdaaabddbdbdacbaadacbcbbdbbacacdbbddcdddadadacddabcdaadcdbbdbdccabadddabacddababaadbcadbabcdbdaabccccbdbbcbcdaddacdbaaaaabdbcbcadcbadbaadbcabbcadcdadbabbaabaabddcbadacaddbddcddaacababbacacccdbacbccbaddbcccdcadbdccbdcdacadadbccdacbbdcaababadacbbbbababbaacbdcdcdaaaccdcccdbabccbbcbdbddadbbaaadccbabbdcacabcdccbbcbdabacbacabbcccbbbbbaaabcccaadddcddbbaadccbdabacbaaadcbbbbaccbdcccbbbbadbabcabbddacdaddadddabacbcbbababdcbcbbbacdddcdacacbcddddbdccdccadaacaacbaacbacabadabdccbcabaaaadcaadacbdbdbdacdbbbdbaaaaacdabbdbbdbcdbbcdbdcbdbdbbbadadabdbbcbadcdbbabcdadccaabbdaacaccdabbcbcbaccacabbdacdbbacabaacaaacdbddcbbbcdabdacbdbcacdccbdbaacabcdabbdbbadcdacdcaaaddabdcdaddbacaabbddbccbbdacbbbcacbdbbddabdbbbcbddadaddbaabcdbdcddbadaadbcdcacabbcdabccbabcadbbbdbdcbaabbddacbaccdbcdbbadbadabdbdbdcbadbcdacddbdbdcacdcbddcbddddcaadddcbdcdccdbcbddcdacbdcbbdbbbdccabadadbccacccbdaddcaabbddcbbccdbcadadadcbccccdbcbdacdabcbbadbaadabddcbdbbaadcaabbcbdccadadcadcbdaccaaaaddabdddbbdbbcbbdacbdbbabbacdbbbccdacddbbbdaddcbbccbccdcbacbcabacdaaadabaabaabdbcbdddbddddbacaabaddbdbbcbbabbcbbbcbaabdbbdbdccadddcaddddcabaaabacdaacabacaabadddbacdbadbcdbbadcadadbbdbccdcdbcccbbbcbacacddbbcaadbdcabccbcddbcdbaadabddbdaadcccaaacbbbbaacbaabdbabcadbdacaaccadacaccbbdabdabccbdabdbbdcbcabaddbdaabcdadbcbdaabbccbbcbccabccdcdadabdcddcbccdbbccacadbadacbaaabbbdcdddbdbdbabbcbcdcddbbabcaaaadcdbbbbaaccabcdaabacabcaccbaaabcbdacaddabadbdaaccdcbbdcccaabcbcbdaccbccaaaabaddccdacbcdcdaccdadaaabcaccdcddccdcaadabacbbbcccbbababdcdccbbcacabcbacacdbcdcaacbadccddbaabcadacbcbbaddcddbcdabcddcadaacdabaacccdabadcdcbccdccaaddcabcdadabdabcddcbddbcdacbbbddaddcbbbbbbacddbacdbbabaddcadcdaaabbdcadcbcdbadbbadacabbdaadaddaaabadcbaadabdcaacbaaabdcdaacddabdbcdbdadaabcddcddccdadbbbbcabbabdadcdabcccdbcdaadbadcdddbbcccdcaccaaadbbdcdbabdcbcaacadacbdcccbbcdbaadabacdbdaaacddbacddcdcbdddaaaaddcdccdbcabcabbaaadcdcccbdddcadcbcdbddcadccccdbcacadddaaacdaacbbcdbacbcdccdcacadbcdacaaccadbacbcdcdadabcbbbaaacdbbbbcdcdbadcadacbaaaaabdabdccaababdaaadcbcaccadadbacbcddbbdbaacdacdaaaabdbdaabcbaddaddabcbddcbbabccbadccdbcbcaabaabdabccdadbbcdccdbcbbbbccdabbadbcccbccbbacabdaddbbdcbdcbcdaacdaadcdcbccacdccccccadaaabbaacbccccaacadadbadabcdcbcccbccbdadbcbbcbadabbddddddcaaccbdddadcbacaadcdabdadadbbaccbbaadabcaabacbbbacbdbbbdbddacbcbccdbcddcaccddaaddacbaacbbbdbddcbddbdbdcaaaddacacbaaacddaacddcdaaaaadddcacbcaaadadadcadcbcccbbabcdcccbacccddcbdcadccdccccddcadbabbacbcadccacbcdbddbdcbccdbddbacddcbbabdccacbcbbdbdaccbbaacbdcbcacccdcadbdcabbaaddbbacdbdaacbacdadadcaccbcacaaacdcbcadaddbabddcdbbcbcaabcdddddcdcabcdbabcaccbbccddccbddddbcbbcbbacaddbcadcdcaabddbdaccacbdabcbdadbdabaaaadbaccbaadbababadcbcabdbcabbccababdbcccbabdcadcabdacbcccbccbdddbcaacadcabbaaabcddcbdcccdbbccbacbadccccdacdaaabaaacadddacacbbdbcccbcddbcddccccabadbadbadadcbbadccaddacbacccbabdababddbdbbdabbabbccaddadbcdadbccbaadacaacdcbabbccaababcdddbddbacdccddddababadaaadcacabccbdbcccccadabbacbbdbbacabdbcabbbdbabcbcacaabdadbccbcbabdcdcaadbcbdddaacbaaadaddccbbbabccaaddcdddbbbdacaabbabbcaccadbcaabcdbaacaddcacbacdbaccbccddacbabcdcddcadcbbbbddadbadbbcacbbabcdbadacdbbabcaaaadbbbbbdbacdcbadaaaddaddbbbcbaaacdacddcbadccbadcadabcdcdaccdbbbbccbbdbdcddbaadcddabdbcdddaadccaccaaccacaaabdaddadbbdadaabdcbdcccdadbcbbbbbddcccbdbbbdcdaddcbdadbdbaaadddcadaacdbcddbbbaaaaccbddcaabaabbcaabddcbacdadddabcabaaadbcacadaaddabdccacbbcaddcbbdcaccbccdabbdcadcdbaddcaadbccacbbcaddaaabcaaacddaccbbcdbdaaccaaadcadccaadcdaddabdabacdadbbdabadcccdbdaacaaddcccccadaddbabbcadaabcbabdabaddacaadcdddccaddbdaaaaddaaabcbcdbbcdacbadcbbdcdbbdaddcddaaccacbabcdbcaadadcbbaadddabcbbbcdccbbdadbbadbbbdbaadbdcdcbadbdaacdcaccaddbdccccbdcdbddbbaabacddbacbabcaadcaadadbcccbcbadacddacdbdbdbcdcabcacddaacbdacbcdcbcbbdabcaabadddacbbabacadbcbddbbdacacadbbcdabbcddccbdadadccbcaadacaccbddadddbbdadbdacbdacadccbbbdadcbcaabcbabaaccccbcacaccacccababacbdaddcdacdccccdcadbbdbabdddcbbbdbacbddcdbdaaadbdaadbdbddaadbaacbcadcbbdcdadadddacbadaaacbbbbadacdadcbdbbacdcdddcacbcdcdcadcdbabcdadddccabbabacadbdadacccabcdaaccccbadbbbbaaccbdcbabddbcaccabdcdddcdbbbdccaaabdcdcbadbddbdbccaaabbcadbcaadcbdabdcdaaddccddbcddadababcabbabbdbdabdaadbdcaaabdadbdbdcaaabaabbdcdaaccbbdccddcaabcdddbaaccaabdcbddacbdccdbdddadccccdbccdddbddcdabdcccccaaccbcaacaccdabbaacdcbaccaabbacabdcbbaccbdabcaadddabbaccccdbbaababcaddabbadbbacdbabccaacaacadadadadbdadbacadcadbacdddbdddaacbcbddaacbdccbbdcbddbadcabdadbddbacdcddbaaddcbcacabbddbabacababaabdaddbacddbcbdbcccbacbcbbabbabcdcddcbcdddbdbcdcacadbbdcadbabdcdaadabaacbadabbccbbbbcacbaacbcbbaddcbaddcdaabbcbadcabdccbdabcddbbbbcbbdbdaddbabaadccabccdcacbabdcaadbbdbdcabcbaabcdddabbaaacacaadacbacbadcbdbccddddbccbcbabbcaddaddccdcaaadbbbbdcbdbabbbabbbddbabcdccadaaaacbcaabacbaabcccacbadbcbacaabddbadaddcdbacbdccacadaadabbcaaccdabcabbacbdcbbcaadaaaacbbcbacbacdadbbddadcdadbbbcdbbbddcaacacabbcbbcaddaadbbccdbbabdacbcadaccadaadbbdddaabacbbcbaadccacbccdaaddacbbabcbbaabbdbdabaababccbacdddcaaabbdbddcdcbcddbcdddabbaadbadbcccbcadddaddaabdcaaadbbabbaadbaacbbdbcdcabaccbaccabddcabdbabcdacccdbdddaacacccdadddbdccbabbdadadcacbabdcbcccdabdcaddcbabbdabddadacaaaadacbddcbacbbbaadabcddcbbbbddaaadabcbacdcbcddcaddcbaadabcbccdbbcacacaaabdcabaccdcdcaaaddbcaccbcdbbcacddabdbbccacdabacadcdddacbadbadccdaadacccabdabcdadaddddbccccdaadbdccdacadcaaacbacbdacacbabcacbccdbcbdbcdbbdbbddccddccbbbabacbbcbbcaaaccacdbdaabacbbddbadabdaddabaabbccacacacdbccdaacaabbbcdccbbbcbdbcbbdabddbcbacdadaacaddaabadcbacabccccbcdcacdadcddabbaaccbaaaccddbddcdaaddcccdbacbabbbadbdacaaabdcdaaccadadbddccacabbbbccdbbcabdaadbddaccaaddcadabbcddacabbbaddbbdcbbcaabcddaadbcbabddddcbbadadaabaddccddbbdddbaaababbcabadaccbcaacbdabadcbabcccbcbadbccbdbcacdbbcadacdccaaccdadaccaadbcaabdabcdaaadcddcacbbdaadbaabdbbaadddacddaabcccbdabdaddbbdbbaadaccbcacbacdbdbccadbccbdbaacdbdcbccccadadbbabdcbdbbcdcddddabbcbbdcbbbcaaccaccddcbbdddbaaacbccbdcdccddbdcdcccbdbdadbdcaabdcbdbbbbbacbacbabbacdcbbbcdadbddbaadbaadccdcaddcaabcdaadabccaaddacadbdbccddabccabbaadabddcababacdcaacdcadcddabaabadcdbdacdaadcbdadbaaabdadbcbcdcbcbadcaaaacbccddddcbddcadcaaababccccbcbaccbacadcdbadcbcdbbadcadbadbcbbabaabbbcbdccdddacadcdbccdabdacbbcadbcbcdbdaddbacccbabbadbddacabccdcddccacababddbdbbcaababcacacabaadccacacacacaaccbbbadaadddaaadbaccabddbdabbcdbbdbbddbbddddaadacabbaacbadcacacdcbaaaaaabddccbcababbcdccaabcaadbadddbcabaaadcbcbacddcaaccbdbbadadadcdbabbcbbdbaaacbcdcbbcbcacdbcbdaccbbdbbcdbcddbdadaacdadacdacbaaccdaddaababcaaabdcbcabdcaccdcadbbbaaaabdcaccbbdadaadbdcbcaababdbbddadbbbadcabdadcdbadcaadcbcabccacddcdabdacbcabccbdccbacbbbbdacddcbadcbabcbadbaacabcbcacabcbbcdabbacaacdcdcacdabdacbcbcbdbdaabadccabadaddbdaadcaaabdcaaaabdcdaadccacbdbadacccccddccadbddcbbbaaccccdbcbabddcbcaddcbdbbabcdaaacdbcddccadbdddbaaaacbccdddaabaaadaccccdadbbcacbcbbcccbbadbdaaddcadbccbcaaccbbadbacdabdbcbcdbdcaaadbdbbccccccacccddcdadcbddddadcccddcaacdacaabbdbcbbcddccacdacaaaccabbacccdacccadbaddaacbaadcadccabcdbccbadadbbcbbdbcdabccdddbbbacbbabcdbdddccccbcdddcbcccaccdbdaddbdcddadcbbddabddaaddadbadbaabbadcabddbbbacddaaabddcbdabcabcdcdcddacaaacdabccacbccbacaddcbdbbdacbddabdccaacdcdbbcaccdcbdccdcdbcaabacabbcbacdbdbbbabbdacddbbbdadaccbbdddadccbdbcaaaaabcaabbbabbccbabbaababddacababacbbabbbcdabacbcaddbabbccccbbcbbdcaacadbcadadadccadbcaabccdcacddaadcaccdababadbadbadbbbcbccdbcacabddbcbbccbaddcdbbcccaccbdabccbaaddbabcabdaadbaccbdadddbbdcccbccdbbbdaaacabdbbccccdaadbdcdbddaaabbbcabccacaacddcccccbcaadcabaacacdcccadadbbbdbaabbcbdacabaacbbcdcacadacbaabccacaacdbdaacadbadbdcddbbbbbdcbaadadcadcddcbcccdbbabababbcdbdccaaacbdcbcdbddacdcdbccdbacadcccbadcbbdcdcaccdcddbabbbdbdbdcdaddbcdcdcddccddacdcbdaaabbdaddabcddaaabcdbaddbcabcddadaadbbcaacbccbcbbcaccbadbcbdacacccdcdbadddadccbbdddadcddcbdddacacbdddaddcdbaacdcdcaddbaddddddddddbaabcbbdacdbddccdbabdcbcdccadddaccdcbdbcaddccaadcdcabdcdbabcadcbdcadbcbaddbbcacadabbdcbbadadacbdddbccccbbdddbabbaabacddacacdcdbbaabbdcacbbbdaaadccdaddacbacbcadddaabcdbbcaadbdcaacdddcccdacabaacaacccaacccdbdbbacdabccdaaadbbdcbabbbaacbdcbbdadcabadabcbcdbdaacbbbacdcadccbbbcbdbadabcabadacdbabacaaccaabdbaddcadcadbdcdcddbbddadcabcaccbaaaccabdaddabaacbbaabdacaadbabbdaddbacddacacbcdbadbdbacdbcbabbbccabdcdbdaabdcbbadbbdaaaacbaacadaabbbbcdabaacccbadcccdbddbbbbbddcbaadbadddcababcbcbcadabbadaadadccaaaababddccdacdbcacbbabcabcaaadcbabcbadcbcdccdcccdcdbcacccabaccbccacabababacdcbbcdbacdbddababbbdccccbdcdcdbdbdccbacbdcabccacccbacbbdadbdabbbdabcbbbaddcacbcdaddadbccdbdabcaaacddddabbaacbdcdbbacadcacaabcbabddaddbcacdcacbaaabccaabbcdaacdabbdbbbacbbdccccbaadabdabcdcbbbacadadacbbdcdadbcacaccadbdcabcddadacddddadccbbdcadaabddaabdbcbbbbdcbdbdcdbacdbdbcbddbcbbbbbdbccdcbbcbcdbadaaaddacdcbdbbbccddaaddbcacccdabbaaabdccabdddacbbbbcbdcbaccdaaccbbcadbddcaadccaccbcdbadbbbacccdbabdddcbccbbbadaaabcdbadaacacbdcddcacbccbdddcdbccddcadaacdbcdaccdbaaddcadbdacddcdacdbbcccbabdbcdbdabcbdacccdbccdaddbdbabbdcadcccccaccdcdcabbcababcdabacdabcbbabdadaacaadcbcaddbaaabacdcbccbaadbdddadadadddbcccdabbcacbdddaccbbbacdaabbccacabaaddcdabccabddacdbdadbcbaadbbbbabacadbbaacadbcbcabdbbdaacdccaaadcdddbdccbbbbddcaccacadaccddbbbcaaaccdaadaaddadbaacbbabcdcdbcccabdcddaaabadaabddddaabccacbacbcbadcddcbbddacabcddaacdbdcbcacbadacadcddcbccbcbcbbdcdacccbbaccdaababbbcbdbcadcadcdcddbdadccdbcbbaaabacdabaaaaabacaabaabaaabcbdcaaabddbdabdaaccbbbddaddbaaddadbbacddabdbcdbacbdaadaacbaccaacbdacccbacbbabdddbdbabcadcbbbadddcbbbbbacadbbcadcaabacdbbbbcaccacbcbcdabbbabdabbdacabdbacbacabdbaaabcadbadbdbbaddacccaccbbccdcdddbdcbadccddadabddaddccddbbcaaababccdabdcaaacaabaddcdaadccbdacbcdcabbbdbcccbabcaaacbacdbbdbadddbdaddadcdcddbabaacccddacabacadabdcbdcddbbabddbcdbdbadacbbdccbdbaababadadbbbdcdbbbdadddcdbdcadcddbbbbbaaccbbbadaadcacdcbdbabdabcdbbadcbabdbabcdccdcdccadacbbadddacaddcdbdacbdbbaaacccdaababddcbdaadbadbddacbaacbbacaadccbdcdcbabbacacbbdccdadbdbabcdcdcbaabacaadcaadbaabcbcddbaccdddbcdddbcbcdbadadaabbbaabdabbaadbbcddcacdccaacddbccccdabbdbbdcdabbdbdabacdaadacbababdddcaccacdadcdacccabdbbadabdbdcaabccbddadcccdacbbdbccdaaaddccbcabcccacaccacacccbabacbddccdaaddbbbdccdccababbcddcdabbbbdcaaccccdabbbdbccbdacbcdcbbbdadababcdddabccddcadcdbaccabdacbaaaaaabcdcdcacacaccacbacabcadaccdcbdababccbdcddacbdaccadacbaddadbbddcadcbdddcaaadddcddbddccddcadcdbccaccdcaddbbaddaabdbabccaaaaaaccdcadcadcbddaaadacdcddacdbaacdbabbbcbdacccdcadcacbaccdbaaaccaaabbbddcadabcdbcbbdcacddcbcdcdbddbcddaabacbcdcbaddbadddbccabbbadaacddddaaddcaabbaddcadccabdbcaadcabadbcdabcdabddbcdaadddacbadbaaddaaadcdbaddddababbaabdbcbdbadaacdaacacdcabbbaaaabcaacadbcbbbdabbddcbdcbabbcddddabcaacadcdacdbadaadbacdccaaccadcbbdbbaadbdbbcabbaaddbaadabbbdbaadaddcdaaabbdcaacdcdacabaadddbdcaadccbccbcbbdbcbadbbdbccdcbdccbacadabdcdbabbdcbacccbababcdabddacbcdbbdabbbbbabdaadbacdccdccdabbcabdbaabadccdcbcbdbbcadbdbcbcbcbaabacdbdaddabcacbbbccabcaabaccaadcadcabbcdccbcbdadbddcbddaddcddadcbbdbdddacdcdddcdbdcdacabaacbcbddacaaddcaacdaccdbdcaabbacacdaaacbcdcdacabbdaadbbdccaadbadbbabacbcbdadabccddbbaaccdcbbbadcaddddbbdccbaddaacacdcbacccbdbbdbdacddadcdbaacadcaaaacdacdaccabcbccacbbccadbcddbbddbcdcdbabdaaabdadbcabacdcadaccdabdbbabdbcbcdaaadadbaaaccccbacdaabccdccbcbddcacdacbaccbdbdadcccbdbabbbbccbdccadabdbdabbaaaccddcabadacddbcdcabbabcbacbbacaccbdccadadaabadaccbcabbccddddbcbbdbbcbacabcdacbdbabcdbddcbcbdbdbaadcbdddbdabcadaacaabaaddddcdbadcdddccdcccbddabadddccbdcacbaacaadacbcacaddabbbabdbdcbaddcacaadaaaaacaadaddbdbddcbbacacbccbccacbbadcddbacbddddbacdccacdbcccdaaccabbacbdcbbaacbbaddbbaabadbccdbcccaaaadabccbabdcdabcbaacdcbcbccbaccbbcaaddaccbcdccbcbaaaaccdabaddbabcabaccdbbbcaadacaddbabbaaabccbcccabdbbbdbdcbaadaaabdccbcddaabdcddbcdbdcbccabadcbaacdaabdcdcdcdabbbcadbbcabdacbabdccbdbccbccadbbbbdbbdccccdbcbaddacadacaccdbbacbdcdccaacadbabbabdcaaaddacddbbbdbbaaadacdcadbddbbbdddbaacabbddbbdbdabdaddbcabaabbdbcddacaddbaaacbddcbaddddbaadcdaaabccddbcaadbbbddcdacbdcabbcccabbbabbbabaadbbdbdbddadbacbacdbcbdacadbdcabddaaabcadbcdbcacbddbdcabcbabdaacbadbabcadccdcdbaadabdcdaacabbbdcadaccdcbcdcccadddbcbdbcdbcbccaaacadbcadddbaabaadbbbadcbcacbddcddbaaddacbbdadabbcbddbdacdbbabababadacddabaabbdddcbdbcdddcdcbcdaaadacbadbccbbbbdcddbbdddcbccdabaabcbbcbadbbaaddbaacdaddbaacadccddacadadcccaaabccbdddacdcbdabbdcccccabaaccaccabdacabddadaaaabbbbdcbbcdcaddccdddbabaacdcbaddbaddabadbccdbbacbdadbaacbdcbdbdadacadbbcbbbbcaaccbccddccdadabacccdaccdbcddacdcdaddbadccbddbaabcbcdccacacbacdddbacababcdbabaacadccbbccbdacadccddccbcbcbbdaabdddcaacbacaacccccdbbaaaaccccdabdacadbbdbdacadbcdcaccabaaaaacbcbbdbcbdbdbaababaaaaadcbbbcccccacdcadbcdadaddcbcbbaccdaadadcdbbacdcbbbdcbbbadcaaddabcbaccdbdabbcbcbbddbbcbbcabdacbdbbabdaccadcaacdbbcaddccadcbdbcdbaaadddcadaccdcdddccabdddaccadddbdabaacaddcbbbabbdadbbcbcacbbaaddabaadddbbccbbdaccddabcdcabbcbadddcadbbbcbbbdbdbdcccabaaccddbccdaaccbacadcdcabbdbdacaccbdcbcbcacacbdadcdbbdcacabbdbadadaaaddbbbbdcacdddbbdacddcacdddbccdcddcbabcbddbcadcccbccbcdcbbdcbddccccbabacacbbbbdabbccccaadddbadcddcddcdaccaaddcdaabbbadacbacabcddcbacdadbddcdababcbbadbbdabbccaabadaaccdabbbadddcccdddbddbaabcdbdcacbbdadccdbacdabcdbbbdcdaadbddbabbbbacacbabcbddaabbadccccabaacbddabcababdcbcddaadbbbbdadabdbdcbabcdadadcaccbbbdbcbdadcadbbcdcdbaacdabdabdadaaabddcadccbdacbddddccdaadacdaccaadacaddbabcababadaddbaabadbdbaddbddcadacaddbadcaddcbadbdbdcacaabbddbbbbaabcdcddbcdcacbcdbdbacdbcccbabbbbbaadcacbaccaccacbcaccaaacbbababbaacbdccdaadaacdbcddcaacbcbcddabadadbbbcbcdadcbdabccabaacadbaadadcadbbdcbbcaacdcbddadacbaaccaccbbaddcdcaddabbbbdcabbcbcdbcadacdaaadbdcbaddccbadbccbccdcaccabaadccdababacbbccabcabddadcabcbccbcaaabbddddcaaaddcbaabcddababbabcdabcaddccaddccccaadcbdcdacccabaaadcaaccadbcddacbcbbdcbcbdadccabcaadadadbccccdbbdbcacddacaababbbcdbddaaaaccbbdadabcdcbccaacdadcacbddddcccacccddbdcadaaacadadbdaaacbdaabbdbdabcabcabacaccbcbacdaddccbccadcbcdcbbdccddbbadbadaaacbbbcbdccbdaacccbababdbdaaadcbcbaddccbddbdccdaccbaadbbacbaacbcadbabcacdadccbdbabddacaccbcaabddbaabcddbdaaccbbbdbcaddbaadbacdaccbbddaaaacccccdacbdcccadbdcdcbbacbdbdadbbcababbacdacdaccabacbbdcbabcccadacdcdbbddbaaabbdddbcbccbadcdabaacdcbbabbcbcbdcdcccdbbcaadcabdbcccaacbdbadbccbdbbcbddbadbabbdaddbcadaccbddaadcaccbbabcbacaddcbaaaabbbacdaddcaaabcbccacaabdacbaaaddbdbdcabddcccbcdcabccddccabcbdddbabbbbdbdbdabdaaaccaadabaccccdaadaabcacbcacdbdbbbcdbbddaddabdbccdbadaccbccbaaabcabcddbdbcbcacaacaaddadcbdcdbbcbcacabacdccdbdbacccccdbcadbcdddcbccbbacdaadcdcbcdbbadabdadadbabcbbcdcdacdacbabcbddddcbadccccdbbabdabcadbadcbaccacddbdadcbbddbbcdcdbaacbdbdbcbcccabababadcabbdbbbddcaabdacbdcabcaacacabbbdddaccdccabbacdcdcadaaadbcdcbbdcdccbdcabdaaaabcdaacbcaddcddcdabddbacacdbdddaabdacdcbcbbbbddcaabdcbcbadacbbdadadbabddbcdbdbadcbdcaddccdcaaacbcdddbabaccaaacbdbaaddbbdabdbbabaadaaddcaccadcbdabbdacdbaabcbcbdbabbaccababdcbcccddadbbaddcbcdddbdaababbccbadcdaabbadaabcdbdbcbcbcbbaccbaabccdadcacdbbbaddccaccbcadddbbdbabcbbbddabcccbaccbbaddbdabcbcaddacaddbbbabdadaaacbbddcdbbdbacaccdddbbcdacaccccbbbcbdcadaabbcdadbcbbbcabcbaaacacababdccdacdcbcdccdbcdcbccdabbdcddcaddcbdccaccddbccacdabdbdcadacacdabaaadddabbdbddbcbcdcabcbdbdccadccaacddddbbbabbacabbbaacadccbdbaccbcdadadabdcdcccbdadacddabbadabdcdaccadbaddaddccddadadbbbacddbddbcbddcccccacbdbaaaccdddbaccbccbccdcadcbbbbddbcabadcbbbccabdbbbcdaabbcccbdbdddbdabcacdbabbbdbbbcacbbddcbbdcadcbbdddaccacbabcddcddbcdacddbcdabcddabddbcacadddbadabdbddbabddcabdcbbbbbaddbbddbccdacdbdbbdcacaabbcdcdccccabaddccbadbddaabbbdaaaacccdaaadcaabdbbbbbcdacaabbbdadabbdadbcaabdbaadbdadabbaaaccbbdcaabdaaabaacadabbccbbbbacdbcccdbccccabcacdcddbcbdbcdadbdadddbaacabcabaccddabbcabccaccbdaadabdacbdbdbcabbcdcccadddbaaaabbbccdcdabcdabdbccbddccaacdbdbdaaacadcaddbcdabbbdbadbcdcabcddbbbbbaabcdcacddababddbaccabcbcaccacdcddbdcdbdcdddbcdcdadbdbacbdccbdaccdbaabadddaadcddccdcbccabbbdcadddbdbbcadcbaddbdaabbaabccdbcdcbdbbcddcccbbbccddcdccabadbbadbadccabacbdcadccbadcccabadbbacbcdabbcddbddddbbbacbaabcabadcbbaaacaaabddcabacbdcdbabcccaadbbabccddabbadcddccdbbbdbccbbcdccabbcbbadcdbdbacdccdcbbcdacddccddcadabbcbbddddaaaabcdcddddaaaadcbabdcccbacddcbbbccbcbbbaaccccddbaddbdcdcbbccdbdbaabbbccacbcacabbbbbdcabdadbaaadbacbbcadbaabcdcaaddcdcbdbccbbacbbbdaacaaaddcababaaabdbbcaaccaabcbbbabadbddaabbdbdbdadaadbacadacdcdbdabdabaaadbdadbaadbcabccccddcddbbacdbcadcdadabdddcadcccaaccdbccbbccccdbdbacdabbaacbbdbabcdcbcbadbaaaddcdcabdadacccddbdcaccaacdbaaaadbdcbbcccbaacdaccbbcbcdcdadbaadabccdacbacdaadcdbdbcdaddaaaabbabbbadcdadcdbcdccadddcbdcaaaaddcadcacadcddaccadbdbdadaddcbcadacaaabdbacdbbcccbbcadddbdbacacddaadbaadcbbbaacabcbcbabbdccdbcbdbabcaaadddcadbdadcccbdadaabcacaabacbdcbabdacdbcdbcbabdaadbbaccabadbbcbcddcbbabddbbdbccccbcababbacbcdbbcccbaccbbcacdcaddcdbdabdaabacacdaaacbdadcbdadaaddabacbdddacadbbccacddbcbadcaadbdccdcdaacacddddadcdbaadbccacabdbaaabaccabcbbaadabcabddadbbbcdddccabbaabbdaddbcdcadccccbbbabbdcbabdcdbbdbbacabccdcadbbbabdbdabbbacacdcaaaadbcbabdacbabcdaccacbcaabadabaacccaaaccccdbcbcbbcadcdbaabcbaaaccdbdbdaaccaacddadccccabddcbddccccdbbccdccdbcadaccccabcbcbcccbcccdcbdbacdcbdcacaaaaddbccadacbbbcacaabbacabbdaaacdcaccabacdcadcddcadbacadcdcdcdacbabdaccaaccabbcaabbadbaddbdbadbcadcccacacdccbcdbddabadcdcbdaabdacbcaddaaaacababcccababcbccbbaadabdddccdddaadbccbcbaddabaabccbbcdbbcaadbccbdbbcbddaccdbacadcabdbccdccccbaabcbcdcdccdcbccbdbadcaccaddaabcddcbdbbadabcddadadddbacdabdbbaaacababaaaccaaccdaaadcdaabaababadccbccdbdbadbbbcbcababcbbdddbdcbadacbcabcbccbadabaabddcccdbcdadddccadcdaddddaabcabaaccbdccabddbccbabcddcababbbcdaadbbacadbcbbcdbaccdcabdccadbabccbcbcbdabccdaaddbcccaadbcddcdbcccbbdbaadbbdccdcddcbabacacdabdaacbbbdacaaaddadccbadddadcccdbabacbccbaabacbbdacadacdabbabbcbadddbcaacabbbbadbbdddbdbadadaaadbdbccacccacdcddbdcbcacadcdaaaabbbcdaddababcbcbbbdcbbbcdbcbdbbdcdbbaabbaacabdacdbdacbcaadbbddbdcbaaddcbaadadabbdaaaadbadbbbdabdbbdccddcacacddcdbdddcbaaccccbaacbabbbbacbdbdcdbacdacdbcdabddcddaacbcaaacabddcbdccacadcbccbbddbbbddabcaabcdababbcbcadccbadabbacbbacadcdabccacbabbadcdbcddcbbccccdbdccaacdbccbdababaabddddddaadadbaaaaadadbdcadccbdddcaabbbcdabcacabccdaaadabdbacacbbaabcdbcbbcbabadcdcbadccabcdbcbabbbccbaddbaaadbbccccbcbadbcccbaddaaaacbaadadbbdbddaaccbcbdbdccbcbdababaabbaadcaadbdcddbcbbacbbdabddabccdbdacaaadbcaccddcbdaaabcdabddddabdccdbcdaaaabdbddcdcdbaddddbacaacccddbbbbbcbdaaabdbcdbaacbddaaacdbdaccdddadddcbcbaccdcacadbcaadbacdbcadcccaddbadaacbcccbadbbcbdbddadcaddcdadacbcbaccacbadddacbbbbccdbbadbadabdcadcccdacdadcddcbdaadddbddcaabcddadcbaaacdccabcdccbbbdcababcddcbcadacdaababdacbabdcbadbdbbcccdabacadcacbcdaaacdbcbaabbacacddbcdbaaddacccacacccccbdbcdadcbcccabdaacbcdddadabccdabaacccbccbdacacaddbbcdccbbbddccbcdbdadbdddcbdcbacacadcdccadccdbcbadbdaddaddbcddccacddbcabaaacbdbcaadabccdadbbacdacdccaaaabbbabdbbbacbaabbbddccbaddbbbdcbbbdbbacacbdcccaccdcccaddababbbadbdbcdcacbabbdcdbdcacccbddcccbabddcddcddbacaadddaabcbacccaacacadbdaacabdcabadcbadcdcbcbcabacbccbccabadbdcbbabcbdbaaabcbabccaaaacbcabdabddcdaadcdbdacbaddbcbdbcdcdcaccdcadddaaaaaacdcccbabdbcbaabaacdbbacbcaddbccdddbcbaaccdcdaabbcbcbdadcdacdadbbbacdcbcdaddbdbccaddbddbbaddadbdabaabcbaccccdbdabaadbdbabbbaadbcaccdcadaacababccdadcaaaccadcddbabaaadddaccbddadcddcabcaddaaabcacaddabcabdcbaabbcaaadbbbddbdcdaacdbabadcbcddababacbcdcbacccbcbbcababbbdbadbdcbdccadbabdacabbdcacbaddccddbbcaddbdddcdcbdbddaacbcbdcddadcccdcdcaccacccbbcbaaaccbacaaadcaaddbdaadbbdaddcddaddbbbdbcbdcacbbdbcdbdacbcdcadaaaccabbbcbacabbbccabbcacdbbccaadacbaabbddcbbbabbaddbadcbcaaddacaacacddcaddcbcccadbbadaacdbcadcdaadcbcacbdadaaddadbbacdaddddabcaadbadacaaaacaabbaccacdbcccbccbbcddaaddbcbaaabbcacdcdddbcacdcaacbbcdbbcdacadcccdbcaacadabdadacdcdbadcabcdccaaaabababdcbccbabdbabdaaabbadbdcbcbacaccbcdbcbbbccbcddbddcdbacadbaddddabaacccbdacdbdbcdbabbccababbaabcdcdcbaaccbbcccdbcbcdabcacbacadccabdaaccadcaabccadaccdbdccacbcdddbcbadabdaaccaaacbcbbbacbaadccbdcbdbcbcccacdcddcacaaaadabbdccbbbbaabdcadbcbccdcdabdbdddaaadadabcdddacacacacccdccbcdcbcdbcdbaaabbddacacacbcaadcbabacadbcadacbaaacaacddccdadcbcddaacbadbabccdccccbbccccbaccdabcbcdacccbdcbddbdaabdcadacadbdadacadcacaacbccdcadadbbcdbaddacbabdbbabccaadddabaddbdacbddbdaccbbabadacdabdabdaaacaadabdcdcbcdcaaababcdaaaabcdccddbbbadaaabbbcbaccabbaabdbbdccdaaaadadcabaababadadadcbbbdbdadaccaaaaabdbdbdaaaddbdaacbacdddabbcaadbdabcccacdbcadbabcacabdacdcaabcbbbbddddadbdcaadcbdcccddbcacccccaacbcadcdbbdcbdaabadcababbdadaddacadabcbcabbaccacabcacbcccbcbcabcdcdabdaddbbcccbddccaccaacbadbdacbcccbbdbbdbbddbdbabcbcdacddabcabaddbcadcbbbddcadadbbccbbbbadbcbadcaacdddabbcaadcdcbabbbcaadadaadbcbddcaabdaacdbbaddddabccbdbaacabacaaaaddbadcadaccbbdbbbdaadbaddaabbdaaccdcacbcbbdbddabacdadcccccabcddaadbdabbacdbcaacabdbbcddbacadaaddccdbdabbacdddbddcdddacccaacbdcbcbcbcadbacaccbaabcccbbbaabdcabbcddcdddccbacccbbcdbdcbccbbabcbcbddcbbbcdccbdccdcbcbdbdbcdcaddacdaaacaadcadbcabcaaacabdccdacaabbbadacabbcaddacbcbacccdbaabacbbabdbcabccccdccacdcaadaacccbabcaddccddcdcdabcacacbbbcdccbbccadaabccaddcbacdccadccaadcbddcdccacddabbdcacaaaaddaddddcddcbcccdcbadbddaabccbddddaabcdaccbdccabcadddccbdabccdddddccaacadcaccaaadadccbababdcdbddbbbabaccbaccacddbbdccdbaddbbacbaddadcaabdbacccbcccaacdcdadddcdcbbccaccdcbaccaacbcccccdacaccdccbbddbacadbdddadbabcbcabcbbbcbbbacdcdcddcdbacadbcbbcaabdaabdbbddbdcabaddaadddaccadabbdddcbdbbddbcaadcaabaddbcadcacccbacdcabacbddadccbbadbaddacdbccdbccaaacccbcdcbaddcbbdcadbabccbdccbadcccaccbcadcadbcacabccacddadabcddabbdcbcccbbdbbcaaacabadbcacbdbbbdcdddaaaccdcbdcddcbdadacccdccbdcbbbcabcbddaacdababbadcbbcabbcccacbcddbdccdccbdaddacdabbccdccabbccacaddcadccdddacdbccdcddbbbdccccccbddbcdccdbaacaccacdbccbaddbbcccdcaccdadadbbbaaadaabcababaabdcaabbccadaccabaacaccdcdddcdbcdbacbbbadcdadadbacdbaaddcdabbadbcddbdbcccbaccabccccdcacaaadaabcadbadbbacbcacdbaaabbdbabcbdcdcaaccbddacdcbdcbaabdcddbcabbcbacbdccbabbbdccbdadbcaacabdcddbddadcdaddbabacbddaadbdabdcbbddddadaabadbadabcbbaacdaabacacaacaccbbbcdddbddacdbdadbdbcbaacbacbbdcdcbcaaaccdacababccdbabbaacbcdccaccdadcaacbbaacacbdcdcabcadadccbcbbcdbdbdcccddccacdbbbccdcaaaccaacddbdcbdcaaddccddaddcbbadcbbbadbbbdbabadaabdabdadbdbbabcbbaddddadccccdaaccddaccccbdbbdcacbadbaddabddcadbccddabbbacdcabdbdddaacaacadddabbbcacbdadabbabbdadadcbcbabddccadccbdddcbadbacbdaccdbbaacaadbacabacccbbdadcbbabdcddbaabddddbadbadbadbaadaccbccaabadaccabcabdcaaacbdcaaccdddbadcdadaccbcbbabbacacbbcaaadababbcccadadcaacbddadbaccaadbdacbbbbdacddbaddcdccccdcbddaaacaddccdacabdabaadaabbdabaccccabbcddbaabbddbcaaabbabbdccaabdacacadcaacdacdbbcacdcaaadacddcabbacacbadcabdcdbbbddacabcbadabacbdcddacbdbdcbaccacbdcabaccadccbaddacdadddbdabccadbbdcaaadbdacacddcbddcabbccaaaaddcaadddcdbcbdbdbaabccaadcbcdcdacbdbbcddcbdbbdabccacaccabaabdbbccacadcbcacbbabcdcccbcccbcbdaacabcccdbaddcaabcccbacaabaaabcbbbbcadbdadabcdbaaddbcdacbaccbdabddaabaadddbbcaacddcccbbdabbbcabdadccbbdaccabcbcabdcaaddbddacacacaccacdcdaadbdaccacbbcdcdacaabbabadabcdbbdbadcbacaccbbdbdaacdddccbacdbdadddcaacaaacabadaccdbdacacaacadbbbdaabddaacdbbabadccbcbbadbaacdbbbadadcacaacbacdccdabdaccaddbadbddcabaccdaccbdcdcbbbabbcdbcccacabdacdbcadbacdbcbabccabccadaacadbbbdcddddbabcabddadadadacbdbcabaaccdacaaabccadbcaaababccdadcbcbcaaabcdcaabbdcbadbbcccababdccaccdabaccccaaababddbddacbddddabcbcabadcddbaccbcddcbcdddbdccaabdbbbdbabbbbaccacaddbadaccccbbabccbcacbcbbcccdbbcabbcacadbbcbbaadbccccccaabcacbcbdddacddcadbccddbbbdbabbcabddddaabddbcbbdbddbbddacdccabdcbdcdacddbcdbbddacdcdcccbbcaabbacbcabddcccdabcddcbabcccaacaddcbacbcdaaccbdbcbcaadcbdabbbcbbdbbadbbdddcddabacabdbbbdabbbccbbcddaddbbbcdddbbaaabdaccbdccddbcbbddcadaaddddcbbcabdaaacadbcdbadddbbbdbacabbcabbaddadddcbabcccbdcbbdbbdacdaacadcccaabaccdbbdcdadacccabccabccaabaacdaddcabcbaabcdccdcbbcdcadcbbdcccbbaadbdabdcaddcbbbcdbccadcbcdaccccdccbcbbbbdaddbaaabdacbccccbbbbbbcbabaacdccabcdbabbcdababacacdbcdcbdddadccdbddccdaaaaacabcbbadacbcdccbbbabbdbbbcbdbdabddcadcbddadbdadaabccdadddbdcdbacbcaddadcababacaacbccbaccdbbcdbbadabbcddbacadbcbbcbacabdbadabbacccddcabdccdbddbdcaaabcdabcdcccdcabadbdbbcbcbbbbcbadcdbabacabaccaaaadccbdcaabddacadbdccaaadbdbddcdaabddadacbddbccddbbabbddbbbabaadacaaddaacbabdadaddddbbdddaacccaadcccadabbaacbbdacbbcbddbbdbbaddccaaacacbcbdacaabdbdcadabdcacadbcdbcdcabbdacdccabdcbccaddabadbadccacdcccccdbccdabddbbcdbbabbadbcddbaccbbaddbcccbcdccbdaccacbcccaaccaabbddaadadbaacbbdbacbcabadacbacbcdcdabacbaddcaccacbdcbdbdbacadcadcbddddaabadbcdcbbbcdaaacddcaddaabcddcdcdbbdbaacbdadbaadbaaababdddaaccddabdbccbadbdacdacbaddadcdbccdcadddddbabadbcccbcadcbcdadbcbabaccdbdcaaaabddccccbcaabcabdbaccdcdbaaddbdcdcbdbcbbdcdbabbbbacbddbbbcaadacbcdacdaadabdbbdbcdbdbcacacadddbcdcddcdaabbccdabddabccddadabbbcccdcbbaacbcababcddbdacccdcabcbbddaacacaaccddabbabbbcbacaabdbabbdbddccddbcdbcdabcddcdddbccdacdbacdcbaabbacabaadbcddbadaaadcaabbdddaabacdbcbababdbabcadddccbbdbcadbcccbadaaddcadacbbacdcbbdcacabdbadbcabdcdadccacbbdaabdcbcbabcdccbdbabdbbcbaadbaadabacbbbcdbccabdccdcdbcbabccdacabaddaddbaaddcbddccabaaaaaaaccbdcabbcdcadbbadbbbdcdddbbdaadddcabaacadcdbdddcabccbddbadccbcdacbbccbcabdabcccaacbbdaadadbcccaaccdacbbbcbacdbddcdadaabccbabaccccabdaccacacabdccbbbddcdaacabdbddaaadbcdcacbccaccaaaddbdbbdabcadbaaadbbcaccaaccbbadddbacaaadbaccbbabbdbddccbaaccddacaaabcbbaddbdbcdcaccaddbcaddbdaaddbaaaadadacdcbacbabdbcddbcdbdacadaccdcacbdacadbbcbdaadcdaaaadbadddacccadaacccabcdbacbadadbaccdbcdaabaddaaddbaccccbabcbabcdddcacdcdbbcccbaddabaabadccccacacbbcbbbcdddadbdbbdadabcbbdacabccacaabcdcaacbaacaadbbbdadcbdcbaabdcadcaabaacacadacdcdbcbbadcdaabbbaacbbacbbdcabddadaaacaacacccdcbcddabdccadcbacbccaccdacbdabcdbccadaccbbdcabbdddccdaabbacbcadaddbaabddababcbabaacacccdacdaabdcddacbbaddcbabaaccabbcabbcabbadcaaacabacdbadccaddcdddbaaaabbbaddcddaccaacbdddddbbadcdcbaccbabababbbdbddddacccbaacdbbadabbdcbabdadbabbcaacbacdcdadbbadbdcddbdbabcddbadabbaadacbdcbadbadcdcbcadbaacadaaabcaaabdadacbdcdbcdcbbcbadcaadcdcadaacbcdadbcccbdbabccdbbaddcacdcabbdabcdcaabbccbddadcdadccddabdcddaaadbabbcdbaccccdcdbabcbdadcbabdaccacbacaabbbddabcddbbabcbcaadccddabbcbddbbcbaacbdacdbcbdbddccddddabdcdbddbababadadbaaacbbdabbacdcaaddcbaacdcddadcacdcabddbdbdddbbcccdaacbcacacabccbbdaddbdcababbadcddbacabbaccbaccdbcaacdcdbbcaabbabdcdcacaabdacccbbcacbbbcbcccbadcbcdbcabbbabaadcaacbbcadddabdbcdbcaaccdaacbbbcbadbdcbdcbbbbdcbdccdccadddadadcbbaddbcddbbbbdadcababbabdbcaadcdaabadbcacaabaddbaddacbbbccdaabaddbcaacdddaadabbaacddacdacddbbddabccbcdabaabacccaadbccadddbbadcdccdcdbbabaaacdddaccbccacbdbcbcdddbdaacaadbaabdcabccdaaddbcdbbdbdcccdbddbbadababdadcadddabaaadabddcccdbdcdbcdcbcdbdbddbccacacdcbaccddcddbabcdcaaaaddcadcbcaaddaacdddabacdccbccdccbcdbcbbbcccdcdbddacbdababbcbdcadcdcbacacaccddcbdbccabbccbcacccaabacccbcaaabdbabbbbacaddccdbabbbaaabaabdcbaadbaccbdbcbdbbddaacadcdbcaadacbacddddcacabcdacdacbbbdaaabdcdcdccdabbbcbdcaabbbdacdddccabcdcdbaacbdbdcdaabaaadbcddbbccadcacddaacadabcbdaddcdacdcaabcbacacabacbbcadbccacdabaadbadadcbacdadbbdabdaacdbadabdcddacabdccbdccbadbbbabbacabcbaaabdbbcbaadcbbaccbddddabdcaadaccbbdbcadcaacddcbaddddbacaaaacccbdbbadbdaaadaacbcdcccdbbdbdcdbddbbdaccdbbcacddcaaaddbbbdbbcddaacaacabbadcaadcccacdacbdacacabdaacbacddddcadddbdbababacbdbaabadcddbcddaaacbdddaccccabbdcbdbddccabbcdbaabcbccdbbbbabcdbbbcbcccdadcbdcddacbbbcdacdccacbcbcdacbabaddacdcbcacdcabccaaacbaccaabbbddbabacbcbddbddcdcababbcbddbbdbbbdcbaabdbacbaadbcaccdccdcaacccdaccdabdaabdcaddcabdadbaaccccbdccdbdcddbcaddadcbdacbdadcbdcccaadcdaadccbdcaccadccabdaaabbccddcdaadadadcdbdbaccbabcdbdaadddbcdccbbabbbccccbccdbddacdabdbcbbabadcadcadabdbdcbdcabbcaababcdaaddadcabdcbcddcdcddacbdcdbddacdbadbadcbdbcacccabcbadaaddaaabdaaccabbcaabddbbcbbaddabbaccddbcdbbbacbcabccaaadaccdddbcababbacdadbbbcabdbccdbcaaccbabdcccbbcdaadbbbbadcddcbcdaabadadbaaadcdddcaacdcdcdabcaaacbacaadccaaaabccadbdcaacacdcbacbccdadabdbcddbddbabdbdcbbdbadaddcabdcadaabacadbccbcbddacdaaaacbcacccdcbbdadadcbaaacadbcdbaddbccbdbbbadbdcbaccdbbbadadcabbdbbaaacccdbbdcbbbbacbddaadbabcadabadbacdbaaacacdacddaadcacbadacacdcadcaadcbadaacbbbbcaadbcbcccaccbcbcdbcbcccdbbaadabdbaaabcbaccaacaaccdaaddbccadddcbbddbddbbacdabccbcabdbabbacdbbcaacbdddbcbbdaaacaadccdccbdbacdabdabaddabdbcdabdcddcacdcaaaadbbabcdbaabbddabbacabdadadacddbcdbcaaadaaddbbbbdbacbdabbbcaaaacdbdbdabbccbdbdcadcabaddcdbcbccccdbbcaccbcdbbbbcdcdcdcacccdbaaddaacadddcdbbccddbdddabbdddbcddbccdadabbabdccbbdaadbccdbbcbcdadcdcdcaadaadbacaccaabcbcbacdbdcabcbaabcabcadacccaaacacdbcddaabcdadacbbccdaacdababccaaddcadbddccdadccdddabcbbdbcaaabcdbdcacddccaaacdcdbccddaabbbccdcbbdddaadaadadccaabacacbadccacbcacdddcdbbdcbbbddbbcabddddacdcbdaabcbcaababaddaabcadcddcbbbdadbcddccddcadbddaddddaaccccababacaabbbdaadbbaadbccdcccbabbcdcdbcbabaccbcabbabbdacacddadbcaaccbbbdcbacbccccbcdaccaadbcabcccadbdadacbbcdbcccaccbcabdbbacdcbbccddabaccabbccddabcddddbcacdabcdcdaddcbbaddcbcbcdbbcbddbabaccdccaccacaaacababaadbcaacadbdabccacbadbdaabcbbbcabaabddcdacbacbdbdbddbddbcaaaadbabaabababbbcbaaabadbabacacccdbbabccbccdbbbbcdaabcddaadabdcdcbabbbacdbccdaccdaabadacccdbddcddcddbbbcdbdbcddadcabdaccdbabdadaaadaccbdaabccbbbddaabcaaaaaccbaddbcdaddbadbcbdacdabaaabbbbdcbbaadbabdddbdaaaabdbdddbcaccbaddcaaccaaadaacaacdcabbbcabbcadaaacbadcaabbdaacabccddadbddbccccdaddbdccbccdccbcbcabcbddcccbaacbddacbbbbadcbdcbcdcccbdccdacbadddccbbbbdbbbdbcaddaaacdcadbbdbbcaaddaaadbabbbdabbbccbbabdaaddcabdddcbbbdbcaacbcabbcbbadccdacccddcbaddacbbdbcdbcaabccaaadcacacdababcadcddcbdadbdddbabacddbbcdbdadaacdbbddbcbcbcdcdccdacbddaddbdcbddbcabdaaababacdccaccbdbbdbacaabdabdcabadaabccbcaacccdbbddbadbabddadbdbcdaacdabbbadbadbaccaabcbccacbbadbcadcabccdaccccbccbbadababaadaaaccaaacdacaaacaccddacaaabacbaabdbcdbdaccdcaddacdabcacdccbbdaddcbccaabbadaabddbaddcdabbdbbaadbabbbaacdadbccabbdbdbacdcabdbbcacddaccdddcbcdddddbadbccaaacaacadcbdaaabdcbaabbbddbbbcccdddabbcdcbdbdcdabcaabdabadcadcadaccbdcadcacaabddadacdabcdadcdadacdacbbbadbbdccdcacccbcdcbaacbabbaabcaaabccbacbdbdadcdcadcdcbadcbdacabbacadcddaabdcaccabcccccbbcccdcabdadddcdbdcdcdccdcbdadaaabacaaacbbbdaacaabbbddbadcbdcdaadcbbbccacbaddcdacacdddcbdbcaacdcdbdbaacabcccbbcdcacbbbbdcacbcadccbdcdbcbdbcdcacdcccccbadbcacabaaddbabdabbbdabcaccabcabaddddbacbcadbbaaabcbdcdbcbcbcaacbbcabddabcbdabdabccdbabdbcbabdaaabdacdabccbcacbbdddbaaccbadcabadccccadadbdcabadbadbaabaabdccdabdaaddcaccaddcabccdbccbaccaaaababbcdcbabcbcaadbbbdcdccacabababbadbbcbccbccabdcbcdcdbccbabddbddcbddacddbbacdababdabbddaaabaddababcdabaacacabbdabbbbcaadaccdacbdddcccddbabaddacdbccbadbaaacddbabdacabbacbacbacbddacaddccbbbcbdbaddcabacdbcdbdcdbacdbbaaadbcabdccdaddcaadcbadacabbdabaddacdccbccadcdbaadcccddabcdcabdaddbbaadbdbabadabccbcdaacddacccddbcacadbaddcbbbadaddcabbdaabdabcaaadccbcadbadaddabdbdadcdaaabddababacbccbacdcbcadbcaabadaacadddbbbbcccdcdaacbccabbacacdcdcbcccbcaaddacaacccdbcdcbcbccbcbacaccbbdacadbcbcdadabdbbdcddabddcdabbcabbccbcbdaacdbbdcdadcaacccdcbddcdcbacddcbdbadbbcbbddacadddcadadbcdaaccbcaaccddbcdccdbbacacbdbdaacdabdbddcbcbdaccbbbdbccddbbdaacaabccdaabcdaadbacdcddccbbacabccccaacdbdabcbccadcadddcadbdcacccddbbadaabadbabbccacdccaaccbaccbdaddacbbbccdcacdcdacdabdabdacddbbcababcdaccbbcdccaadcabdcbcbadccdaabbabcacaadacbacdaddabadcdcddacbcbabddbaaaaccababaccbcbbbcaabadacacdababcacdadcabdbbcadddcbabcddadbcaabcbacabaaaccbcddbacbdacdbbcccabbbdddddbdbbccdabadddccdababbbbcddbcbdbcbcabccbcbdbdbbddcbcdcaacdadcccccbcbccddcbdddcbcaabbbdbdabbabcdcddcbdcadadbabbdabbbdbabdadddcacabacbdbdbcccbcababdcdabaddbbcbcaddadddccabaaabbbabcacdddbababcbdaddcbbdcdbdccbcbdccbdcaaddacdbaccababadabadaaaacacaccdcbdabadbaacbabdcddbcbdadcbdadbccadbaaddbabaaabccadcdddbcadacccccadcaadcbacccbcdccdbbdbdcdcadbdadddaddcbaaddbaacadcbbbcbddbbcddadcddddcdacbdccddddadbabcbdbddddbaddabdbcbacadbbabdcabdddbddaabbabbcddbbadbbcbccacdbcccdcbcbdbaccddcdbadbdbcabbbdacbbdbbabcdddcccbddbccbdacdadcbdabdbacaabacccbbdbbbdcbdbcabdbdacbccaddabaabbcbbabaddabcbacbdacbcabaaacdcbbbcacbaadadabcadadabccdabdddbaaccbcaacddcbccbaccddacbbdaddbdbadcbabcdadddcbbbcacdddbadbadacbaccaccdbcaabdbbaabddbaadabbbbdadcaaadacdbbddbcaacaaadbbddbbaacaaadadbccaaccbcdababcdbdccabaabbbcacdbddddcbbadbbdabbcdddbbabbddcdbabdacdacdadaadaadbabbcadddabccccaabdcbcbddaadabadbaabccccabbaabcdddadcdbcbabddcdcbbcaaaaadabddacaadcbcdcdaddcaacadaacdcdadaacdbdccccacaaacbacbaccbbcbccbccdbccbcbbbaacdabbbbdadabbadaddddcaaddacabcbbbdaddabdbdbacdcdcdcbbcacaddcdbcbdcbcdccbdacbbbaccbabbaadaadcbabccabababbdbcdcdadacdaaababbdadbcbbccbdcbababdbbccbdadaadbbcdccaabbccbadaacbaaccaddddcbadcbaccbacddadcdadddcaacdbdcadaaaabbabaaaaaabcbabddadbbcdbcdbbcbbdcbdbcdcaddcabcbacaaababccbaddaacddbbdaaacdbabdcadbadacacaabcabbcdcbaabadcddacaccdcccbaacdcdddcadddcadabdddbabbbaaccbbcdacabadbdbcadbadcbbcccbdbabbaaadbbdaacccdcdbcadcaaadddbabdcddaddcadccbdccdaacabddabcdcadddabbbbabaddbdddccadcdaaddababbcacbabbaaabbbcdbbcbabcbcaccdadbaaabbacacadbadcbbbaddaabdbddabbabddbabacadaabaadbaddddbddcbdbcbdaadbacabccdaadaadbcabbadcccbdadbbcddbcbbdccbaabdddabaacdbdabbcccbcbccdcdacbbbbabbabccbdbbbddbddabbdbddbcbabcbbabbddaddabdadbcdbcbcaaccdadbccadaaadbaaaddbbcdbdbdadbddabdcaaaaadabbdbbbdddbdbcbabcabcbaadabdadabbbdacbaddacbbcbbddaacdbcaccabccababbccbbcddbbddabbccccccbdbcbccddbbacdddbabaccabcbdbbbabdccaaccacdaabddcaacbaacbaabcdcccbcdbbbdcbcdaddaacccdbabbbaddbbbdadcacbaabaaabaabdbcdcabcbdddbcaaaaddacddaadacbcabcaadacdcdcbcbbdccdadbccdbaadacacccbbacdcccadbccabbdacddbdaaadbbbbbcdabdbbabbdbcbacaccbdcccdadbbbbcdcdbaccdbaaaadabcabbdbbadbcdbcbdcbdacbdccbcadabcbcacacbaaadadccbabacbaabacadbdbdadbaadbdadababdcdacbcbadbdcdbccddadadbcccadcaacabdbbabbbacabbabacdbdcbacddbadcbbbacdadaaabbcbaacdcbbbaadcabdbcabbadcbdaddaadaccdcaacdcbadbcdaaddcdddacddbadddccccdacadcdcddacbbcbabbdccacddbcdddbaccadbbccdcddbcabcaabaddcadabdaaaadcbabcbcabbccbbabcbacaacaadbcdbabcaadbabaaacadbbcbbdacabdbbcaaccddccbabdccdcadbdbcaacccbdcccdacbaaabadbccaacdaaaadbcabadbdcbcdaacbcdaabdadbddbdabbbcdacbdcddaccdcdcbbcccbcbdbcdbbdbdcbacbacababccabdadcaacbccacdcdacdbbbdbddcaacaaccdabddabbcdcbaabdbbdbbdbabbaddacacabddbabbdadbdbddbcccbbdcbbbbaabdacbbbbddddcbadcddcaacbbadcbccbbcccacadbbadadaacccabbacdbaadddccbcccdaaaadabccacaaadcabcadbdbbcccdbcbdadaddcccdacbbcaacacacdddbaddbcddbadbbbcbdcddacddaadbdccdacaaabcdabbdacacdbadaddbbcdaccdacbcddadcbbcbadddadcaddcdcdcbdcbbbbbcbbabacbaabaccaddbcacccdcbababbdcccaddcdbaabdaacccaccbbccaccdabbcadcaddbcdabbcaaccdaadbbddbcabbbcababcbdbaacdccccdadcbaaaccbccacdacdbcdccbaabaccaaccbacddbcabacddbccbcddbbcbdacbddacddbadcbbaddcdcbbcacccadcacbaabccbdbaddacccddbdadcdcccadaccdaccbbacbcbbbcadbdbacddbbcccaccbdddacbabdabddabcbcaccaaabbdcdbbdadadcbdcacccddbdbcabadcabbdadbacbcaadddbabbdcabbadcbadcdbdccbabdabdaacabaacabaaccaaabdddcdaabadaccabaddccccbdccbccacbdacabbcaabdbcabaacaaddbddadbdcabdccdbaacbaaacccbdcccbddcabadbcacadbdaabbbdbacccaabcbabadcdbaabddaadaadbaaadccccbdbcbaaccbdbdcdddbdabaacbbcdaaaccbbcddadcaacccbdcadcbabbdacdadddbaaabdbccddcdddbabaabbbdccbbdadcabcbabbacdcbbcbcdacdbacadbcbcaadacdbbccddabcbacbccacadddddcdbaaddcaadbcaabddbcabcdaddddbbaacccdcaddcbcdaaadabcbdccdddcadbdcbbdaadbadacbccbdbaaabacabaadcbcdcbbaadaccbcacbcccddbdaadaaaabadbddacbcdaddadcbbdacddbbdbbcccabbdabccbbccccbcbdaacbcadabcddbabdbddcabdddaadcdcbbcdccdcbacadccdbcbdadabcaccacbacabddccaccccadaccccbbabbbaccbbbbbbbccdaaabbbcdcbdcdaaadaadaacdddcababcdcdbadccbadabbadcaaccccbbadcbaaadaaacdbccddcadbacaaaabdabcbcacdcaddcdabdacaddbbaccbccabdbcccbabbbccaccddadccaaddabcadbdaadaaadccabdadddcbdbaddaabdbadccbadcdcaacdbcdcdcdaddcbbdacbdbadbdadaadaabccbbdddcddcbaabaacabcbcdbcddcdadbcdcbcaacbaacbabcaabcabdacbdabdabdcaccaabbbdcbddcaccdbbacaabadcdbbcdaadcaadbdccadbdadbbcaaabbdbacacadacdddbdbcabcddacddcabcacacbcddacabaddbbdcddcbaacadcbabdadcdacabdaaccadbcbccbbdabdccdbbadcccabbabbcbcbcdabcbbaaddccadcbbcbbdbbdcdbbcbbacccdbadaacadcadbbcbbbadbbabaadcddddddacadacbdcadacdccbcdbaaaacdcabaaccddacccdbcacacdddbbcbaaaddabdddccaaacacddbdadbaacdcbcdabcdaccdaacaddabdbbbccbadcaaaacbcdacbbbdcadcdccacadbccacdaadaaddacbadccabbadbaabcdcaabaaabdcbcbdbdabcaacaaabbcaabaddabbdbbddbbaaabdccadbbdacddbcdcbdbaddadaabcabddccbdcbaccbacabbbbaaabaaacabaddbbbdcadcacccdadaccdaddcaabadcbabcbdbdadbdbbaaaabbbadabbdcbdabbdaabdbbbcbbdbadbabcacbcccbcaacaddbddbdbbbbdbdcaccbbbdcdcdabaabcaaacccddcdbdabcdaadbaabcbdcacbccacbbdcdbdacbdddcccacdbbdcdddbdadaddadbbadadaccaabbaccdacaaabdbcdcabaddacabcbccdcddadcdbaadabbcbdcdcdcadddaaaccbbbaacbdacabcdcdcaabbdbbaaddaddcdaabdabcdadaadccccbabdcadcddbacaccdadbcbcacbcbcddbccdcabaacbcbbcaabdcacbdccdcdbbbcbdbddccddbacbddccbaddbacaddbcbadabbbdbccaccdbdcadcacacadcbbbabcdddcdadabcacbabbdccdbcdbbdbcbddcbcccddacbbdcbbcaccdacacdbaddcaadbaadbcdcdacaaaadcdbbaaaabddccbddddccbcdccbdaabdccaadcdcaabddacbcbbcdabcacbbbdcabacbbcbccbcaaaccdcaaacacbaccddbadcaacbddcbdbadaacdccbddddcbcbdabaabcbadcbbdbbbbcddbdddcdddcdbcccdbaacccacabccadcbdbaababbbbddcaacbabaaaabadbbdcacbabbaaacdacdcbdbcddcdccccbbbcbbdccddccdabacdbddccbbbcadabaddaacabaabbbaddacdbdbdabbbbbdaababdacbcdabbccacabaaaadaaacaddcbdddcadbaaadbccdbadccbdbbcbdadacddaabcddddabbccbdbacaddbbcbdbabadaabbaacddbabccaddcaaacabcbacbaabcacadccbacdaabdbcdcdcbcdcacdbddaabbcabbababbbabbddcddaabbdcccbcacaabbcdabbabacdaaaabdbcdbbadbbcddbabdadcababacbbdbbdbdbbdaaabbadabdddaddabcabadabbcccdcbbcadbabdcaacbacbbddababbdbddcaddbcacbaabaccadaccbbbaaddbbacbabdaacbddcbbdccbdddddadcbbaabaaadaabaaddcdcdbbaaabdbadbcdaaabbabbbcccacaddadcadcdcaacbbcbbcaddaababcdcccdccddcadbbaabbcbddacdcadbdbdaacdbccdcbddcacddadbcbdddaadacddabcccdacadacdbdcaabaacbcdaadabbacacccdbabcbaddddabbbdbcacbadababcddabcdddabcdccccabcbdadbdadaddadccddbaabababcbdcadaaaaddbaccacabbbadcccdadadbbccdbbcabdabbcadadbbdbdddbabcbdcadbaddacabaccabbaacddcacdbccbdbaacccddacaaacabdcccddaccbccabbabbbbcacdddabcccddbbaadabaadcbcabacacdbdacbdcccdbbcdbbadbccccbadbaccadaccdbddcbcddccdcbcabdadabbcbaaddbbcddbbcbcababbabdddddaaccdaadbdbccbacddcdbcaabbbaabadcbbbadaacacaaadacadcccbcbadabcaadbbdaddacddcacdbcbdccdbadcabbddcbdbccddbbbacddcadcccccaddddcbbcdaddabcdbdaddbdddccbadadabdbdacbbadbcadacdadaabbcacdbddcdbcacbaddabcccbcbdbcbbaaabbcbbbbbdbabaadbaadccdacaddbdabbcbdbbbacaddbbababbbbccdcbcabbdbaababbdcadadbadcbdabacababcccbbddccddbadddaabbccccacbbcabaaacbddadccbcbacaddacddbaabbddaadabdcadbdabcabcaadbdbbcdcddccacdbbcaacdbdadcbbbaabdbdbbcacdcadddbdadccbaccabacacdadbbcacdbdbbdcccabdacdbabdddacbdccddcbbdabcbcabdbacccabccccbaddddabdbcdbaadcbdbcddabacacacbabbaaadddbbacbbdccccdddcdccdcdcbabcaaabbbbbacdbbcbdccdccaacbccaadcbbabadcdcadddaddddcabbcaacdbdabccdbdbadcaccaaadacccdcdabdaaddcaaaddadddbabacaacadadbbbaacabbaacccacabaaccdcadbabdbadacbbdbbbaddaccdcbcccabadbcdacbcabcaaaacdaacdddbcacbcadbbcddbaddabdbaaacdddccbdbbaacccadadbbdaddddccadcacdbbbaddddbbbcacbcbaadddbccbbabdcdaacccaaaddbaacbbcdcbadcbcaddcacacbcaaacdaaaaaadbdcdbddababcbcadaddcaaabddbadccabbcbbbbdadacbbccacbabccdadbdbdbccddcccacdbbabccdbccdabdaaddadabbdddabdbdacbbbcccbdcdbcbdbbcdaadaacaaacbcaadcdbcdacacbdadcadaadbaddcdcdcdcbdddcdaadddadccaabcbadaabddcbdbccdaddcbbdadcdbaacbbaacdbbabbbdbdbaacaddadacdbdcbdccdadaddabbbddcdaaaccdaacaabdcdadccdbbcabcddcacbcaacaaddbbdbaccdcdaaabcaacdcacddbabbaabbaaaadbdacbdbbcadbddbcabbaabdbadbccbdacadaaddddccdaacbdcdcccdddacaddcdcabdaacdbcaccdaacbbccabacacbbbcccbdabdbbbbbacdbdbadbdcddbdbbbdcccdcbbdaacadbdbbcaabcdcbadcbddcdaadbcabbbbbcbaadaccaaadcbbacbcabdccddcdcacdcbbadadcaabcbbddacaacbddbcccdbdcbabcdbdadbbaadbdababbccbcacbcadabbcdbbbbcbacaaadabcacaabbdbbbcabcabbbbcdbabccdaabddcbbbbdcaadaaddadbcbccaaaacbaabcbccbdabdcbbdabbccbbbadbcbcbbadacbaadadbdabacccbcbcbcbccadadacbcbbaadccbbdcdbddbbbdadcacdccbaddcbcabaccdabdbccadbdddbcadcdbaacacadacaabdbcdcababdbbdbbcdbbbaadccabadccdbdbcbcbaacbbbacdabbaabadcdabbaacccdcbcabdcbabaaddccbadbacbbdadadcacdabcaaadabcdacbcbaacbbcbbdaddbadbabadacdccdacdbcabbbabccacaaaccdaabdcabbcaadcaddcbddabbdacccdaaaccabdaaaacccbcbbcaaddbdcaacbaacacacadbacabbacddcaaadcaadccdacdccaaacbdcadacbbdbddbcbaadacdadbaadabcdccddaacdbaddbcabaccbaaabdcbbdababbddcadaabdababbddcdbcddaabcbdcbccacadddaaccbdbbbbcdbddbdadabbbacadddaaacdddcdddcabbdcdaddaabcdccdccdabaadaacccdcbccdccdbcdcbdcacbbbbccbdbbcccccddbdcbbcaaddaccdcdadcacddbdbdbdacbdbcbacbccadadaadbcacbaadbcbcdbdcacbdadcdbbbbbbdaabccbcccccaababbdbacaadbacddccbddaacabccabcdbcdaadcccadaabcabbbadbdacabcaababaccaabcaacbaadccbddcabadacdbbccddadbbbabaacdbbcbaddaaadcacdccddddccdbbbaaccbcbcadbabddadadcbdaaadaadcbccbcaacbdabdddbdccddaddbbcbabadadccdcaacbdcadadbbdbdcbbcbbdbcdabccbccaaaddddcdcdaaaaddcbcadcaaadcdcabaaaddddacdcdaabbcaaabaabdaadcbdccdccddbbdaccaacaabcababddaabdbddbcbdbadbcaaabaddcdbbdbddbcbcbbaababcbbdcabcbcbcbcdacdbbcbabcbdbcabddabadcdabcbbbacbcbbbacdbcacbdddacdacdbbbdabdacaaacdddadbbcadbdbbbdbbabdcbacdaaddcdaabababcbcacdacccacdbadaacbaadcaaadbdbacbdaddbdabbcbbacdaadaaadacbcdacccdabadcccbdbcadcadaaaadccdbbbdadbadbccacbabdaadccbcabdaaccadbbdddcabbbbbbccbbadacddadbadbbdbccbacdbadbdcddaadaddacbbaadddcccacbabbaaabbddcbdbcbaacbddcbcdaaddbcdbbdbdbddcadacdddbcaacadcbbcabadaaacbdadcdaacabaabbbcccbbaaccabbaacadaaabccabadaacccaadcccbdddadacdadadadbadadacbbddaadadbabbbbdbbaaaabdbccddddbdcccdabcbbddbabbaccacabdbccbcabcdabdadbcaddbacddcdbbadbdaddbcbdddddbdbbdaccaacacbddacbadabccdbdbdbbbcbddcdaaacdddbccbcaacdcbbabdcaddcdccadcdacacccaddbdadccabdbacdbccccbbdccdcbbbdcddcddaacabdcaaccadddccabbbbccccacbbbcbaabbbaadbbcdbdcbacbdbcabaabcbbddcbabdcbbdbaabacaadbbccdbcddbaaabcabdddbabbbcdbcabbcadadabdcbcbcbcbaababdddbdcdddacabdadbddcaccaccdbbdcaaacccbaacbdccacbdbacbaaddddacccaadacbcdabcbabcdcadcbcdddcbcbadcddddcabacaaadcccadaabaacbcdcdaadccadbcbbdbbbbcccdadbcccaaabcadddcbbdcddcbadabdcbcaaaabcdbbabdabddddadbdbdadacdadbcbcdcaccadadcaddadcacacaddacbacdccbddaccaccbabdccbbcacccbaababcaadadbbbdcdccdacdbddcbdccacaacddbbdcbdcbdccacbbdcdbcbccbacadbdacddccbdbdbbbddabbbddcbcaaaccaabbcabaabaadbbabccaacdbcbadabbadbbbccaaccbddddabdbddacdbcdcdbcbbadacacddbdbbadddababccdcadbabcccbcbdaaddcbcaabcdaadddcdbcdacbdddbdcbcadcabaddbaabaabadbadcddcdaddccbccabadbaacaddcbadabbcdacabdbbdabbcdcbdabcbbacddabcbacacbdbccccadbcaaadbddbcbabddbbdccccbcdddcbccbdabbbbbdcdcdadddacbdbddccbbdcaabddbbadcdacacaddbdbbcbdcdcddbdcdbcacdcbdacccdbbbbaacdccbbdcbdadbcdbccbcadaacabacadcbadbccdcdabccbcdcdcbcccadbcadccaadbbddcaaccbadbdcccbdcddabacabaccadcaddabaddcbcdbbcbccdddabacbacccbcaddccadbacbbbbbadbdabdaacbcbcdddddbbdcdcaaadacdbccbbaaabaacbdbcbabaabababddbcacbbbaabbbacadbbdddacadddcbbcabcdcacddadddacabcadbadadbcdbcccaccbcccbaadbbcddddbdcbddaaabddadcbacbbcaaddbccdddbcdcdadcbacbddddbaacbabdadcdacccbbdbbcbdaccdcaddaaabbadbabacdacacaacadbbbbdbcbbabddaccacdddaddcdccacacaabcbabdadccdcbdbbbacbdddbbcbaadbcdccbacccdddcbbdadbbbaabadcaccbbabdbccdddbcadadaccbdbdbdacccdacdbaabcdabcbbddbacadddacbabcacaabbdbcdacddacbbdbacdcbadcbcdaacbaaadcdcccdccccabbabcadcdbabbaacdcadbdbaddaabcbaccaaaadbcabacdddbdacbcdacbdccaddcacdadabadbcccbccbcdbabdcbbabcbadcdacdaccacbdbaabbacaacacaacadaacdbccbbaccbbbcbccabdcbcbaacdccababccdbcbbabccadbcbdccbcadbbdcdbcbabcdadbddccbbbbbadbcdcddbddbabadbdbcbaaaaadbcaacccdccdcbdacbcdbdcaccadcbbcdbbdbcddbdbccdbaacbdaadddabdcbacddcaccddddbaccdbaabccbddaccbccbbabacddaacddabccdcdcbbdbdacaadbbddcabdcdccdbadcaabbdbdddcaccbbbccdcababdbbdaabccdadcaaccadbacbcadbbdddcdcbabccdacbadaabbbbccccccdbdcddbabcbdaabadbbdccbbbaabcabcdbdcbdadddabcacabddcbbcabacbbcadadbdbccddcadacababdccbcacacacddacbdcaabaacdcdcccbbabddcbdcbddaaaddcbcdcbabbcdddccbabaccbacbbdbcbbccdccccbbcbdddbdcabcdaaaacabccaabbabccdcbcadcbcadcaccccccacadadbbcdddbccbdbadbcbcdbcdbbbbdcbbdacaaccadacaabcbdcaddcbaadacacccaadabadcaacbddaddcaadabbcdddcdcdbabcbdbdadcbacbdccbbbdccacaabadaddadcacadbcddacbbcababcddcccbdaacdcbcaaacaabbcaabbcddabdbbbdbcddcabadbcadadcbddddaddcbccdcbaccacaadbdaaaacbcccdcabbadadcadadabcadcabdaddcdddcbdbdccdaccabadadacccbaaccadcaccaaacbdddacabaaabbdbdbadcadaadadbcabcdddadcadaaacdadcaaacbcdaacacddcaabbbacaddbdbddcaadbbccaaabbababaccdabcdbddcacbdbacbbdbabacadacdbacdcabdabdddcabddaadabcdbbdacdacbdcaacadbacabaddddbdbabdbbdbdbaadddabacbbacabcbbbacacaabddcdcdcddccbbdbadcdadbdcdadaadccdbdcdbaaddbddcbdbcdbbccababcabdbaaabbabcdcababadcbdbcaccdbcdbbbcbcccadbaabdcadccaadadaddadbbabddcdcbabdbbcbbdbdaccdcdabbddabdbbbcabcacbcbbbbdbabcaacaacbacadbbacdacbccccabcdadcdabcaaddadbccbcbbcbbcdbcaddbabbccbcdccbcbccaaadbddccaccbbcdaaddacdddaadddaccabdbccdcbbbacccccaaaadcadccdccdadcdacbdacdcccbddbbadbdccdaddbbabadbdaaddaaabdabdcaaaadacadcdacacbcabbbadbdadbbcabbbdbcadaabdaaabcaccabdadbcbbddaaacdabbabaccdabccdbcdddcbbbadcbbacdddbcddccaacbdbadddbbdbdbdccdacbacddbaaddcccdaaabcbdabadcdbadabbbacddcdadadcbbbacdddbddbabbccdcdabcddadadbadcbdcaddabdacacddadccbbcbacdddccdddddddcccbcabaabbcdcabdcacdcbabbcbbcbdadcccdddbdbaaccacbbcdbdaaacaaacbdcddcdcaaabbbcaaaabcacbdaccadcbadbdadacbadaccaabdbcdccacbbababaaaabcbdaacacbcbacbdcbcbadcbddadbbbabadbdadadcdacabbcddcbbdcdbbdddaaaccdacccbbddacabadccbdacbbcadbcadccdcaabcbcabdcaadabcdbbdddcaccbddddbbdcabcaabdbbddaabddcbcdaacacadcabbdcabbddbdabbdaadabbddcadcdcccdabcdcbaddccaccccaaadbdadabdcdbbbbbbdbbdbbddcbdaddadbccdacbddddacbbcaddcbcbbdcdcdacbabbbbabcddacbdccacaaabbbacaccddcdcadcccbcbcdacccabadaabacdcbdabbcdbaaaddacaabdabddbdbaaadacbbdabccacdabddddbbdaaabdcdcadadadcdaddddcbccbabcbbbacacabbbbbcbccbdbdbadacbcdbdaaadcbdcddddbaadcdbbdacddbbacabbcdcacbcbcacadcccccabbddacadddbbcabcdadccadcbbbaabaccddcdbcbdcdbcaabacbdcbbbbabbcccbcbccdcdbdacbbdbabbacbddcdabbcdabccbbaababddbbbcbbdbdbdcccaaabddacaadadadaddccdaaddabdcddbcbbdaddbaacdbadcabaadacadaacbdcaabcbcacdcabdbdcaadbacddbdccaaaddaddadcbcaccdbbaaccacdacdcbdababdbdbcbbcbaabacadbddcbcbbaccabbdcddccbcdbbcdbdddddcbacbcacbccaacaddabcbbacabbacadcaccdbbcaabdddcdadcbcddcbdcaaabbddacdaaccacaddcbcbddabaabaaccdaccdbbccdccadcdcbbddaaacacbdcbdbccbcdadadcdcbacdbadcccbbdcdbaccadbccacacbbdcbcaabccacdddcdbdccdcabcaacdddacdaddcbbabddbcabbbbcabacdaaabaabbdccdccdbdcadbbaccbcdcbbdbdcadcadbaddcaddaababadcbdaddadbdbbcadbdcbdccdaccccdcdbbadcdbaaadcdddcabbbcccdcbbaaccdaaddddddcdbbadaddbcdbaabbaabaccbcabccdbccdbdcbbbaccaddaacdbcddbddcbcaccbbaaddaddbdbabbdcbcdacccacccccaacddabacdddadacdacadcccadacccccccadbcdaacaadcddaacddbcbacadccadcabbcdcabacbaacddbbbdbadadaaacaabdbccbbadbcbbcdabbbcdbdbcddabaaadccbbdbcacbacaacdbadaadbbdbcbdbaabbdbaaababcbbadaadbaddaadbdabdbdbbdbbbdcbccadadadccbaadbbacaacbcccbbbdabaadddbbacadddabcddbbbdcadbbabccbcddadccbbadbcabbdacddcaaacdcbabadcbcaadaaaccdbdcabaccbdaaacadddcacddacadacacabaadddddbdacabbbabbddbbdbbcdcccdcdadbccabcbaadddbaabbdbddbadbbdadbbaddcbaaabccaacccbccdadcddabddabbacbbdccddbddccbddaabbabaccacbacbdadabbabbccbbabddbdadcadadbcbbadbbbcaaccbcdbadcbabaacbdaaddcabadaabacabddddbccccdbcaaacbcabaadcadbdbbddaadbdcadbaaaacdbcaddddadbbbcdbcddaccdccacdadccbcbacbaddccddddcdaccbdcadddddbcbaaccababaaccbdaabdaddacddbcadadcabdbddcdcacdbdccabaacbdbbacdbddabdcbbaacbcbbcdddbcbcccdbcbcaddcbdcddbacdaacabddabbabaabcbabcdabcbddbbddddddabddacbcbbdaabcabdccbbddabadbabbddabbccdaddcbadcabbddaacadbabbaccbcdbbbdcadaddaadbbcacdaabaabcbcabbdaddacaddacababcbdadbaadbadcdadbcbcaabcddadaddcabdadcdcbbbbbabbbcabdccadcddbcbcababacdcdcaabcbbbcbbaccddacccdbadbbabdbccbbdbabbcadcacdadcbbbdccdcdcbdbbcbccadaccadadbaabddaccbccaacacddaacacabbdaabcdaabddaabaaacddbaddddacaabdacbabccdbbbbccdcbbdaddddaacddadbddbbacbbaccdadbcdcdbabcaccdbdbadbdbacdbacbaadcbdcbdccbdabdcddcdcbacbaaacbacacabacaccdcdabadbbddddbadcaddaaadcdbcabccadcaacbcccabbbcbcdaabcabcdabdaaadcadcdcadbdddbdbdcabccbbbcaddbbdddaccccdbbccbbacbaabdbacdcbcdbdddcbcbabdcddbdccddbbaccbbbcdaddcbcbaccbcadbbdaacadacbdbdadbdbaabbbbaacccccaccddcaadccdadbdddadcbdabdaadadddbcacdcabbcdadddccdbdadbdbdbaaabcbaaaccdadbbddddcddbdcbdbdcbdacadaccdbcaabadadcaadcbaabacccbbdbbaacbbaabddccdaaaabdbcbbabdaaaadcabbadabaccbabddccdcabcbcbcdbcdddcabdcbbdddacbbbddbadbcbcbccaaccaabcdddbabbacddccadaadcaababdabaadabdabacdbccbcabccdccabdcacbddabbcbcaabcadcbdcabbbdbcaabadbcadddacccbcacbdaadbbdcccdbbcbadadcddabcdaddcbbcccbccabbabcaccdbaabccddaababdbbbcadcbcdcbbcccaadcbccbbdbbcccbbaacadbcdaadacddabcbbdccbadbacdddcdccbbacbabdcccccadbddadaccbdacadacdddccdcccdccadbadcaadbbadbcbcababdbdcbbdbaccaddcaddaaabbdccbbbcdadcdcdcccdabacdbabbdbddaaabcdccdaddacbcdabdabababcbadbcddcbbdcdcadbaddbcccadadddbbadcbacbdcddcdbadbacadbdabcddddcbbdbccdbadabaacbcdcddcbbbbccdcadaaadbdbdbcbccbdadbccaccdadcdaabcbbaabdbdccdacdbcdadbbbcbbcbacbdcaabcadabadddbabdbcbdbadddbccdbcbbabccbbdddcabbddcadbdbcadbaaacadccbaadddbaabcdcdaadacacbddacaddabdcadaaaabdadccccabacdaaccbdcdcbadbcababdcacadaccbdbacccdccaaacdbcabbdaaaabadaacabdbbaddcabdccaadaaadbddbbbacbbcddcadbacdbdcbcdddcbacbbbcaddbdaaddabdabadbbdbdcaaaccbddaaadabadadddbdaaddcbdbaaddddcccccaaddcdccbdbcbbabbbcdacbcbdaacbadbdadcabdadbbcbaabbadabadbbabbbbbcdbabcabcdbcabddcdadbcdcddadddcaccbacdabbdacacccbcddcabdadbdaaadabcadbcdcbdcabdcacbbbbdacccddccccbdacdcaddaacddbbabcbadbbdcdcadbcdaaabdccacbadabbdbcabaadacbcbdaabcdbcbccabbaddddddaadabbcadbddcbbbbdcdaddbaaddbbcabdaddaccdcabaadbbbbaadcdbccaccbaddacbdccabbcbccdcbdbbbcadbadbccadcbabdacbddaabdcaccdcacccabccbddcabbccbbbcbcdcdbdcbcbacbabcabbcbbdcccbadadadbdbabbccbcdcccdbcbcbaabbbbdaaddbcbcadddadaaaaacaabadcacbaabdacaadbbadcbdababdccddddcaabccbaacbadaaabccbbadcbbacdacdbbdcabbabdccddaabbadddcacbdbcadbdbdcacaabdbbbbabbbbdacadbdbadabbcadddcbbccbccbaaaabbcbddaccccdbdccdaaacacadaabbddddabbbbaabdbcabcdcdabdccdcaaacdbccbdabaaddbccaccddbbbcabdabccdcdddbabbaabcabcbcbcbdcddaabadacccbdbdcdbdbcdddcdbcbbadabadadbdbbadabbcacadabbdbabaaacaaccdbddbabbbccdbaacdacbddbabbdddcacccbaadcbaaabcaacccddadcabacddccdcccadbcdcabddcbbadabdbddcbbdddbbdcdbbbbadcbddaabbbabbddcadbbadbcddcaadcabbbadcbababddabcadcacabacbaabacabcbdddaddadaaddddaccbdcddbaacadcaddcabbdbadcbcccbcaccbbccdcbadcbaacdabadddbdabbcccbdcbbbbbdadabcbddbcbcaacdabcbcbcdbbaccacabdabcaaaddbcdbcabaddcadbacbbadbdddcccdadbbcdbbbaaccddaabacabdbccbaaabacdbdbcbcacbccabdccdabdaddddaabbddbdadcbbacadadcaaacdacdccbcbcbabaccddbddbbbdbadaaacacdcdcdbaddaccbcbacdcdacbdbdbcaadbbbdcababacdadcacdadbabbbaccdcbdaacabccccbcadadacdcaabbcdacbdbacadaabbcdabaccddbdacaabddadcacaaabdcbdbcbadadcadbcbcbabddbabacdccadbaaabddaabcbdacbcdbacadaddabbabcadccdddddacbdddbccdacdabbacaadacbaddcbbbcbdcacbdcddbcbdcdacdbcbbdccddcadaaabcbbadddcccacbdadbcccdbbbcdbdabccdcbddbadadbadbbdadadbbcdbdddaccdcaadabcddcabacabadbdddddcbbdddcdcaccbcdbbccadadadbdbccbadcbcacadcaacabdbbabaabccabbdaddabadcccdcacdccdcacbcababaddcabbdacabcabdddccbaccabcdadcdaacabbdaaabcbadaaaaacabaabdbadacbdabaabacbcacadbcdcadcadcccccdacacccddaadbbbddbbdcacdadbdccddcccaadaaadcabcaddaaabcdbacbbbdbbcdcddddcaccbabdbcbcaccbcddddaabbbbcbaabbcbdddcdbbbdbdccdbaadbdccddaccccacdaaabbdabccccdbcdacdabbbdbaacddbdddabadbbbcbdbaccbabdbdbdbcadaadaacababddadcddabccbcbbaddbacddccbabbbbbcabddddcbcdbddbccaadaaaccdbacaddacdcbbcccdacaccbabcaababbddbdcbdddccbcaabcdacaaadcdcddbbacbbadabaddcdcaddcbcacddaddbcabdbbcadacbdabbaadabaaccacaaadbdabbddabbbaacbcdbbaacdabdabadbaccdabcdcdbcbabadcdcdcdcabacbabddbbdaccdacccdcdabadacbcccacbdabbcdcdccdcdadddcbcdddaaabddbaadbbcbacccccddbdcccbcabbacdadacadcabbccdcdabadcaadcdbbadabcbcaccbacaacbabddcdadaabcacdabacdddcdadddacacdcdadbccccdddcccddccbddbabdccdccacabbabcccaaddadbdaccdcccbbddcadcdadbccaacaaadbdbdcccaaccdcbcaabccaaaddddbbadabbbbabbcbcdaaddcdbdbadddcddbdbdcbbacadaabdbcdcadcadcdaabdcdcbccbddccdcacbabcccddcadcaaabddbdbbbbdcacddcdcccbccadadccbcadcbcabbcbaabdaccdbbdabdccaddbcaabdbadadcdcabdcbbdddacbaccaaacdaddacdaccbddcbcdcbdbaadbbdbcadabbdacdbbcbadacbddbcadcbacbacaddaadccabdbdcdaabbbbddbcdaaaaadabcbbadbbbcdcbbdcdcadcabadccbdbbdcbddcdaaddbccadcaabacbdaacabaabbcdbbbcadaadacdcbbcdabaaaddcdcddbcdddbcccbddcacabaaadaaabddddbcaabcacdbdacdddabcbabdbabdddcacaabadcdddcacaaabddddacbbddbbacdbcaabaccddbccbaadcddbadbbbbbcabbbbcbcddaabcbdccaaddbacdbdaacdbbccccbcabacbbccbbbddbcaccabcadcbcdabadbdaabadcddbbcadbcacdbabacdaaccddbccacadabaacbaccabadacddbcadacbacdbcaddcdddcbacbaadcbadcddbccdcadaabdaaaabadcaabdaaaacdaaabdacdaddcacbdbcbcbaddbbcdddabdbdcdcdabcaadabacccbbdbbbbbcddcbadbaccbdbbbcbabcbddaaaaccadbcdccbcabbcbacddbccacdbacaacddcadccbdaaccddcacacdbacbdacbddcdaaadaabdaabdccabdddcacbdddbaabcadbbbabdcabcbddbaabcbdabccddbaabbabcaaccbdcacddbdbdabddbccdddabccaababddbcdabbbdcacdadbbaadcdacccabacabbbcbbbcdbcddadbdaababdbdcdccaabbdbbdcababbdacddabaccbadbbbdcbdbabcbcdddcbccbddcbdcdcaabbdbbcacbdaccccddbdbccddcbdcbccaabaccdbddcbdddabdbabcbdbaccaaacaaacbddaadcbadcacdabbaddacddcaabdcbbccabcacadbcdccbbaabbabcdacabbcdcdaadbddadcadbbabcbdcdbabccccdbabbbabddcccdbabcddabbadcbcdccbaccbadaaccadbddcaddaabbabbaababdcbdbdcbcbdadbcdabdccdaddabcbbccbcdbcdcacacabaaaabdbbababdbdbbcbcabcddacddcbcbcbcbdbabdcacccbccbdbcabccadacdcdcdbbcbbbaabdabbcdbcbbabbbdccccdbdbdcbbddbadcdcadbcbddacbaaddbdcddcccbdbbbbcdcccdbbbacccdaadbbbacdbcaacdbcbaccbbcacacabacbdbcaabddddadadbabaaaccdcdcdbdcddbcbaacabbdacdbcaadbdaaccadcccdbcaddcbacccbaabacbabbdabadcdbdddaabbbaadbdbdcaacdcbcdadabbdadbbadddcdaaacbbabacacdcacdaaddcbcbbbbabcdccccdbdddabbbcadbcbadccbbadccccdadabdcdcbcabcdcdbcdabcacacaddbbbbbcdcbcdbccdccacabdacaaaccacabbcbabdcacdcddbcdddbcdbadccdcacaabacacdabbbddabddadcdbaacdccbbacdddadadcccabcabbbbaaddcbabbabddabacdbcdcabbcbdcbdadbcdddbdcabadbdaccbadbbbbccacdaddcdcabccddabadcdcbcdbbbadbcbaadbcaddddcdaabbaccbdadacadcccbdcacdbbcbabcbcabbdbdabdbaadcaabdcbbbccbccdcacbcdcbadddabbbcdccaaabdabcabddccbccbdbbdbabccbcddcaacdcbcddacbcaccccdaacddcbcbcaaacbaddbcbbdbcdaccdbcbbbdacdbcccdadddacaacdbbcdacbabdbbdcacbabddadaccacddcddddcacdababddcacbcddacbaaaaccdaabbabdcbbcdbbdaabbcbadabaaaabadbaadacbcacddbadaaccbbcabdccbbccccbdbbcdbdcdacabdbcbcbcbabbaacbcbabbdbddcdcdcdccadacddcabbbdcbccbccabcbcbadbaccccadbbcaabbabcbbbabccddbdaccbcdcbcdbadbdbcadccbabdabdcabadcbbddbbcbacaccacbabbdbbbbcabbabdbdadbddbcbdabbdcdcaacaccadcdabcaacbbccbdddbabbcaaaaaaacbcdbcdbcbcdadacbbcbbcbbcacdacccbbdabdacdcdcddadadadcbdcaccbddddadabdbccdadbbdbaccabcabcbbccccdbaabbadcbbcbccaddadbbdcddaadaaadbcccddabbbbbcbcdcdaddbbdadddaadbacdadacccabbcddacadaabcaadbbbdddddcccdcddcadcbbbdadccbdcccaddbbbacbcddbabacbcacbddacdddaaacccbbacaadaabadcbdbabdddccdddabcddddbbabacbabdbaadacdddbbcadbccabaadccbbcbbbcbabdbddcdabadccbdccacddcaadbbbcacdcdacdacbddabbcababaccdbcaabdacbcddbbcbadbcaacbbcbddbdbccaccdbaacccdacbaabccbbbadbcbdbbacddbddbcabdaabbdacdacaabcbacaabbdbddcdbcbbdbddbadbabdacabaabbdaabdccdcabdcbdbcaccbdadadcdddcbdbdaadcacabdadccaadbcabbadcddbcbbabbbadbdbdaadaccccabaddbadcdbadcddbcbcadaddcbbbabbcbabccadbbadbbcbadbbcdbadcdadbaadbcacbcaabacdbccababababcdbacaadcbdcadcaabdaccbbddaabcbccaaaababcadcdccadacdcabcdbdddacbbbacdabcbacaacbddacaababdcdcccdacabbbdccdccdbccabaacdddabdcdcccdbabadcadacccacdbdbcdcdcdaadbdacacbacdaaaabcababcdbcbaccbcbcdaccaabddbbdcacacdcadcccadccbaabbbcabddbaadbacaacbabdbcdbdacdadabaadcccdacadaababcbcacaaaaddbdcdcbbcbcbbbacbcabbcdbacddaabbacdabccdacccbacadadcdabccdbcdbabdbbdcddcaaadbacbcccdadaacdabbcccbacbbdccdddbacdcaddbbacdcdbcacdbbacabacaaccbacbbadaabadabaadbdbdccdadbcdbadbddcdbbdddcdaadabdcbcadbcbcdaccdccccadbbcddbacaddccbddcbaccdddabcbdcdbbabbababadbbbbcbdbabcddcccddcacbdabbccdccbcbddbabcbdadbdaccdcdcdcbabadcadbaaacccbcacaaddbaacdacabacadbaaaabacdbccbbcbdabadbdadacddcccacbdaacdcbbcdbcbdddcadccdddbaadacbddcdbcddbcabbabccdbadcbabcaaaabbdcaadbdbaddbdbddaccbcabbdaadaabaadadabbcadacdddbbcbbdabacacbbccadbdadbcacaddcbadcddcaaabbaadcdcdbcdcaadbcdbacacdaaabdddcadbbdddddddcdabcbbbbccdacaadabcdadcdacbbcddbdacbcadbbddcabcdadcbddbaadcbdbadababbddccbabcdbaadacbddcacbdddaadaaaddacccaacdcabcdcbaacccbaadbaddcbabcdaabaaabdcbbaabdddbdacbdbcddacdcbbdcacdacbabbcacdbabddabaaaddcbdcdaaaccbbccbcddabaadaadcbdddbbadabdacacbbbabbbdbddbadbcaabcadaabbabbcdaabdbcabaddabacacacbaacabaaccbdadcbbcadacccbbadbccabcbbbcbdddbdcbddbddacdcacddaadbaddcdbccaacabcdcbdccdbcddccdbdacbccddccdcacbdbdabdaaabcadbbbdcbabbabdbcbcbdabbadbcddbbaaaadbbcbbbaccdccaadccbadbddbdcabaabbdbdabbdbadacbdbabddcdadbbbdbadcbaaddbdacbdcacdadadbddaaccccbaacbcbddbbacdadadbadadcddaadacdbadcaddbaabbcdcbdcdddbccdccbcbdddadddcacccdadcdddbadbdcaaaaacbbacbacbbcbbdaabacbccabdbadacddadbaddddccddbbaabcabbbbcacdcbdbcbccddabdbccdbbbcddcaabcabdacccbdacaacbcdabbcadddbccaabbccacdcdaaccbaaccaacbdaacbbdaaaaddbbacaacaaaadddddbbcdbcbbbdacdccadcccbcccdadcdcdccccbaccaccbcbdadabaccbabcbdababacdaddcbbddcaabbdaadddacaacdadcdcccadddddcbbdddddabccbaccccbaacbddbaccdbaabbadadabbbbddbbbcaabcddbdcbbbcbccbbadaadacabaaccbacccbccadbbacbcbacccdaccbdcdcaccadbaaaccabccadbaaddcabacbdbabbadbdacacccbdbacbababaccccdabdbccdabbbbacabbaabbcadbcbbbadbbababbcabdccbdadcacbbaabbcdcacaabdabcdccdbdddadcdbccccabaddbaddabbaaaabcaaaadbaddabcccdcdddabdcddccdaaddccccccdcbcdbbcbacbaaaddbaabdaadbcbbdacccbbacbbcaddaacbdccadbdbdbaddadcccdbabbcdacdaaabdabbaaddbdbaacbbacadaccdadccaccaccdbcbcacdbababcbdcbabdcbadbcbbbaaddabdacccdcddadaadcbbababdabccbcaaaaadbacaabbbadbbdbbdbbcaadcbdcccdcaacbbcdacaabacdcbcbbbdcccbadccabbbdbacabaddcbdcccdacaaccacaddcbcabadbdaacaacbacbaaabbcdcdcbabbdbcdabdcbcccaddbadabddccbdbcaacbbaaddcbadbcacdaacbdacabadddaababcdabbbddbaaacaadbcdadbcbcbbcaadcadccaddabcabccdcacbcabddaccacaaaddcbbacbbdcbcaabacaabcbddbddcadaabbbbcabbbadacbadbbccdaddacdcadcdadddaccdbccaabacddcbddaddaaccbdadbbccbddcbbcadaabdbdbaacdaadcbcccdacacdcdbcdddcbbcdbbaadccdbadddabddbacabcdbbccbcccddbabcabddccbdbdcddbddccabadbcbcccbccabaadadcdbccdccdbbddbadcaaabddcadbaabbabdddbbaabdbbddcdadcabbdbbdcddbddcacdacddbcabdcbddcdccccbaacdbdccbaaabcbdbbdacbcbdbdcbdbdbcdaccbbcbabacaacdabbbdacaccababdacadbbaadddacaacdccbccbabcbccbcdcaaddaddacadcbdabccddccbbaacddbdaadabbcbabbacddcbcdcbacbcbccabddaabaaacacacabdbdcddadcddabdccccbbbbdbcccadadaadbbadbdaccadbbcdcdbbdadbbdacacdcacdddddaccdabaaacbaaccbbadccccdacbbcbabdbcdadbdbbdadaadcdccbdcbcbaaddabcaddcbbadbccbdcbcbaccabbabbacaadddbbdabdbacccacadaaadcdabbbdacdcbbbbacdbcccddbabddddaccdaadcdaccdaaacccbbcdcacabacabdbccdbccabaaabacaaacdccccadcbaabadbadaacdabbadbdadabbddaadbbdababdbdaabdbabccaaabdacbcdbbabcdbbabcaaccaadacdaddadbcadddbacdaaddbcaccdcabcbacdbadccbabbcdaacbccbbacdaabdbbadcbdaadccadbaabcbcadcdcdbdcddbaddcbcdbbbbadadbcbdcbacccccbccabaaaacdcbdabcacccbdabdcbcacbabbabbbdabbcbccbcbdddcbacaaddcccbdcacbccbccdcbcbdacbdcbabcbadbdddcdbbbdadcaacdbcadcbbcbacbcbbcabbccccdccacdcccabdbcdcdbcaaadadcddabbccacdddbbcbdadcadbacabddbcdbcbdddadbaabbcbcbbbdbcacacdbadbbddcbbbbabbddbdcbbbccdbdabbcbcbacddcdddbccabccdbabbdadcccaacadabaabcacbcccbcaaccccacdababccaccadcccdaacaccbcbccbcbadbcabaadbbcdaabbcabccadabdddbdccdacadacabcaadbacbaababcdaadabaacacbcbdbdadbdcdaadcdcdabccaadadccdcbddcddbaadabacccadacadabcabcdacadddbdcbbbdbcbddbaddbaaaddcbadcbcccbaabdadcdaaddabbbcdcddaccadccbccbbacccccddacabbbdadddbdcbbdddabbbaddabccddaabccacaacabddacaaddbdccaccaaaddcdcbcbcbddcacdbacdbdcaddcaaccacbabddcccbcdbabdccdddbdcbbaccbdadccdaaccdacbacacaacabdbaadccaabacdcaabcdcbcbdadcdaadccababcbdacabcbcabdaabacbcadcdbdbcababcdbaacadbdacbcddbcbaadadbacbadbdbabdaaddbccabbccccbaddcdaccaadcadcbbdbacbcbadbabdacbddbadaabacaaadcaddcbdcadddbcaadcdbbcdbbcacdbcacabdaabdabdcccabbcacdacbdacbaadbcccdcbbbbbcdbcbdbaaaabaadcccdccadcabcbbccaabbbdaadbbdbbcccdaaacbddbadadccbcbaccddbbbaacbacdbcacaddcbabddcbaccbaabcdbbdcdacadadddaabbbddcabbdcbcaabdabcbbaaaccaabbadcdadaaaaddacdcddccdcbbbbdcbcdbdbdcbdccaabbddbdabdcbacadaacaabdcaaaddadbabbcbddcdadadbdcaaaaadddadccbbcccdcbcbcdbbbabdacbcbddbacabbadccdcbbacdbdaadbabcbbbcaacbcbdbdbbdaadbdcbdabaacddbdadabbbbacadcdcdadccdababdaaabdcdabbdacdaadccbbcdddacbbccdcacdaacccdcbddcdbbadddadaaddbabcccadadabddbabaacbdbacbaccbcbdcabdbcbacbbbdabdabccbddadaccbccddccaadbdbcbbcbbbdcaadabcaddcbcdaabcbcdccabbabccdbccdbacddbaadddcbcdccbcbbbbacadadabdbadcddaacbcdabaacdbaddbcbcdacadbbbadbdbbbadcddbbdaddbaaaadbbbcbaccbaadbcbcaccabddcacddbdbbcdacadbaccdaccddacdccbddcccdcaccaaaccababdbbcaaadabbacbcdabddbdadbcddbbcdddabcddacdcdddadbaadccccdadbdcbcabdadcabbddcacccbcccdacadbabbbbabdcdbcbdcdbbbadbadbacddadbadccdcadcacbbcabcbdbbdcbaadbcdcbcdcdadbbdadcaaadacabbabbbbaaadaacddddbcadbbcbcccadaddcbdcddddbdcaabbabdacaacadcbaaaacbddcacddbbababdccddacadcbcbdddcbcdbccbcbbaabadaabbbccccdadcbcdcabaabbaaabadcccbacabcaccccccdbbbacdabdbcaaddcddcdbdcdbbaaadddbccccdcaaabaadaacabcbccbbbadcddcbddccddcbdbccbababdcdaacbcbbccaddcadababcbaabbaaadbdccbbabbdadacdbbdddcadcaadbaddaccaabadbadaadbbdabcdcadbbdbaacbccadccacaddddbadcadabbaaccdcbdbddcbcabdcbacabbdaaaaadbdddadbbabcaabaacdadaddacbaddcabcddabbabadaacbaabbcaddabacdbaddccadaadadcbcbaaccacddbdbaddcadbddaabdababcaaddbdacaaacdddccdadcbbcdadcddddadadbadadccbcbaaccadbacacaccbdddddbbcbcdaababdbcbdbddcadbccdcadaccadabddcabbdabdaabdbdcaddbddaddabdacccbdabccbddacccabaaaabdbabbadaacbacacabacdcbdadacdcacadcbcbbabacabbdaacdacbdcdaabbcbbbaccbcbdcaccddddbccabdabadbcbbbbabaccaadccbaaabbbacbdcccabaaaaacabcbbbbccbabaccabbdbabbbccbccaaaabbdcacbdcdaaaabadcdddcccdccabbddcabddcacabcbbbbaccbadbbbbbbcdbabdabdaddacdcdbaaccadcacadacbabcbbacbadaaadabdadcdcbcabbabbabaaccddddacdabdabcacadabbdacbacccccaddccdddcbdabacdbdbdbadbadccadbdabbdbbcbacbdbbacaaadaacddacacdaddadcdbcddcbccddacbdbccaacaababccaaaddcacbcdddbdacadadacbcbadccbaddaaaacdcaddbadddbacadbcccbddadccdbdbbcbadbdaaadadacbaaaccaddddddbaccbbcccdcacdbcbdcabcaaaddcbbadabccbadbdadbbbdabaddbdbaccdacdbbdbdacdcbdcbcccdbcdbdddbcacaaacadaaadbbdcbdccaaadddcdadbdadbbddcbbaabcbaabdbadcbdadcaadbddaadbbbcbcddcdbccadbdacbdbbbaccbbbbbbdaddbcbaddcdbcbacbbbdbcdabbcacadadccaabdccdaccbaddbcdbabaccaadaacbccbcdccdcdbccdadacaddcaccaadacdbbdbdccdbbbacdcbacdaddccdbdbadbadcdccdbdcbdbdadcbbaccbaddddcbcdcbdcbbccdacdbcbacdbbcaadadbbbcacabbcddbaacacacdadbaddcacbdbabaaadcaddabbadaadbcbdcbcccbddbcdcbcabcddacdaaadbbdbdaaaadbdcdbbbccbdaadabcbacdcccbcbbcacdbbccbbdadcadcabbddcbdabddacbbbabdadbdbaccabbadcadbadbbabddccdbccbacbbbddaacbacaacdbabbcadcbddbbacacddbcdacccadbdacdbcbcddaddddaddcbaaadcbcccabcddccbbacacdcdddcbdccdcbacdbbaacabcdbcbcccabbcaccaabbbacbcddaacbccadacbdadabcdaabbbcbaabcaaddabdacddabbcbbacbcddbccaabbaccbadabacddacddcbbcacbbbcbadabdacadbcbadddbddabcacdaabcdddadbdbbcdcddcacdabaabdcaaaccdabadccacbbcddabbcabaadbacbabbbbddabbabbabbccacbacadbdbdcdccccdbbcbdabbcdadbcbdacbcccccbbdbcbdbcbbdadcbabbcbadbbaaacdbdaaabcbcbbcbcbcaabcddccbdcdcbbadbbddcabcdbccaabbcbcbdabacbddcadadbbdcbdbbdcbbdcadccdcbabbcdadacbbcdbbcdcabaddcbdcdcbbbcbcbddcddcbacaccdddbaadcdacdbaacacbbbacbadbabaddbdababcddcadbcbcbcbcdddabdbddbbddcabcbaabbdabcdcacdaabbdcddabdbcacbcbaadacbadcdcbddbaacdcababbdddddcbadabcbcbbcddbcabbccdbddaadacacbacbdccbaaadcdabacbadbdabccdcbcbaaabbadbacabacbdcdddbabdddadabbacbdcdaaaaddbaadabbaadcabccbcacabcaacccabdaadabaaabdacadbccadbbadbdcbdaddddadaabbccccbddcbaadbcbaadaacababcabadabdcaaddddcdddabcccabcbdaddaacdcacbacbabbbdbcbadbbcbdcbabbcbbacabcdddcdcdabaacacdaabbababacccbaddbccccdddccbacdddcdbbbbbadabbdddbdcccdadbcddbcdcdbbcacddcdaccbababdbcbdaabbcacbcaadcbcbbcabddacabdddddcbbdcacabcbadddadcbdabcdcbdbbbdabbbbdaddccdddbcbaddabadbaacacdbcccaddadabdacbbacbdbaadcbbdcacacccbcbaacaadcbbaabcabdbccdcdacdcbdddbbdccccbaddbcaddcbddbcbadbcaadcbdacbaadacaaacdcdcacdcabddbbcbaaaaaacccccaaabadaaabcacbbaaabbcadadcdbaacbdbdddbddbcdbbacadbcbbcdcbddccbadccbcdbaadddbbcddccbcaadabdbdccdbcadaccddabaaadadabaaacaccccaaabbadccdaddabdaaaacacdcbadcccaccbcacbbadacacdbabaddbdbcabbacadcdaddcbdbacadacaacdaadcbabbcaabcbaaadcacaccbbbaacdaabacaaacbbbadaadacccdcbbbdbbcaddabcadbcdbcbdaacbdcdbcddaadbdadcbcccddddcddbbdcdbcdadabaddbaacbacddbcdbadcadadcbccbbdbccbdbdcbcbbbabbaacccdbbaccacabbbabbbccbcbcacddbbdabbbdcdddaaaadcdcacdbccbbdbbdcbdcdcdbbbcacacbccaacbccdcbbbbaddaadddccababbaadcadbacaacccbddcadaaaacbacacaccbdadcbacdacddbdbadabdccacccbddddbcbaadabadbcdabdadacbbcdbddcccdbddcbbcbdbddbbdbaaabaabbaabdddbcdbdabddaadcabdacccccccaadabcdccdcbabdaccdddaaadcdaabdaaabcbbdacbbbacbdbaaccbdabbabccdcadaadbbcdddcbaadbcbabaccadccbdccacbdcbcdcaaaccabcddbabccbdcdcbbdadcccbacacbbbaccbbcabbbadbcbcbaaccdcaacdabcbbabcaacdccbddcbcacbbacadccbacdcbadbcdddbacbccccdbcadaacbdddbdbcbdbcacbcabbdaddddbbdcadddcaabdadbdabcaacadddbdcaaddcabbcdaaadadbcdddaaacdaadcdcdbdaadbdcadbcdaabaacdbbcddacdbcbcdadddcbadadcccbcdccbbcbbbdccdacbcdbcbddcbccbcddbbbbacaacbbdacaacccdabdcdbbcbbddacaadcdbdccbbcbbbbbcbdbcdbdcbbabbdcbdbbacadddbddcbaacdadbbcdbacaacabdcccdbabcdbbabcbdbccaadbccdcbbbcddbadcbdacdccccddcaacabddcdacbdbadcbbaccdcddadaddbdcbdacbaadccabdadcabdcacdacccbcdbcdbbbcbdabaabbcabdbdbabdcbbbbcbdaaaccbdabdcaaddbacacaadbacadcccddaabdcaabdacbcabdddabbcacadaacdaadabdacacabccbdacadbbcdccccdacddbabccccbdacbccabbddccdbbdbababcbabdddddcccaccdabadcdccababbbaccbbdccbdadabdcbcbdcabdcbdaccbccbcbccdbabbadacbdbdabdbcddcacbcdcbcccbddcdaacbadabacabddaccccddcdbddcdadddaccbcbcdbdbddbcdcddbdcdddcbbbbaddaacabccbacabbbcabcadacdadbacacbaacbbaabaacacdababbcaacabcdbadcdabbdcbbccbaacddaddbbabdacabcbadbbcbbccabbabaaccbbcacaddabdcbddcdbcabdddaaaddbddbccdcbcbbcbdacaddcbbcdbcbbadadcabbbdccdcccbabbbabcddcbcdbbddddbcbbacbaacaacdbccbcdbcabccccdabbcdacacaccdacaccbaabbbacdbadaddcbbdbadbcaccbaddbbaddabaabdddadcbbadbdbadcccdbbcbccabdbdcdacdacbabbccdcaabcbcccbbdccbacccbbbddcacbbdcabcbdbccabdcacbbacabdbbcbacadbacacdacaacbdcbbdaddccdcbabdadccccccccbdddcbcdaccbccbabaddbdaacbbbdccabdbddddccdbaabbbadccadbdccdbdabdcaaaddcddcbbccccaacacaaccbadbcdcabadddbbbabbacdbabbadbaadacaadbdcbddddaabdbaacdaabcdccabdbdccaccacbdddbdabaccbacbccdbcccdcccaddbbbcdcdabcccccdcdcdaddcaabbacacbbadbadbbdbbbaaabccbacbabdbdbadadaabcbccbcbbcbcbcdcdcabccadccabcccdcbaacacdbacbbadbdadbacbcbddabdbabbdccccbbabbcbdcaccdaacabbdbcacbcbdacdcadbbacddcdadcababdaaacdccddaabaadbbdbabdcdcddacbbcbbbadcbddbbbddbcdbaccddbbbbdcaaddbdaadabbbaaabccaacdbdacadcadacddccadddadbabcacbaacdabdcbddddcdbbadbbdcdcddbaabcbbcaabdbdabcddcccdccbddcbdacacbaaaacabababaaadcacdacbadbbdcbddccaacbabdccccacbaaadbddadbcbcdcdbbcaaacaaccabcbdaaababddacbdaaadbdbdbdacdbaabbdbbbddddadabddaccddcdacbcdadcdadccbbacdacdbccbbacaadbaabbccdbadaccaccbdaadaabdcbaaaabdbcbaadcadccaadbdbbbcbccbacabbdaabdcdddddbdcdcdbbbddcbbccbdddadadcadbcacbbcadaacbbbdaaddbacadaaaccdcacdcbbdbbbaccccacbbbdbabcbadacdadcaddcbcacccdacdcababbcaadbaadbabdcbbbbbaaccbdbbabbccdacaababbdbbddbcdcabdadbbdaaadbddbadcdabddacbbabcdcadbdbaaacbaabcdacbcddcdcdabcdcbaddbcdbcbcccdbaadcdcaccbdbddddbcabacabbdbacbcdacdabaaacbccccbdadcbaaaccabdcbbadddddaacdaaadaacabcddccbbbbdaaddbabcdddadabdbdbaddadcaaddbbcbdbdddcccaabcabaabcddcbcccbbabdbddcaccabddaabbadaabbbdabcdbacddabacbcabcbdcdbddbcdbadadabbccbbcbaabbadadabdaabaabdaadabadbaccabbbadaaacacacddaccaabcbdddcdabbdcbdcdcddaaabdccbbdabcdddbbddbccddccaaaadcddacbdcbcacabadabcdcbdabbbccbcbbbabdbcabddcdabbdaccdaccdaadcdacccdcdacababbadcaaccabbcccdbdcacbbddcaddbcbadcbdacbabbdcdbaddaacccdcbaacacaccbddccaaaddbdbaccccccabdbbddcbbbbbabcbddbaccccddbabccbaacbcaccbcbdbbccdbbababacccacaddacbcccabddcadccabbddabbcadacdbbcbadcccabdbbadaddcbbbabaacdaadacbdcdcbabbbacbcddcabbbbcdabdaabaacbabdcbcdcbadcbabcbbbcbbdccabaabdcbcdddcbbddcbbcccbadaddadbcdcaaadcdbcbdacbbaadabadacabdcacbcadbdccbabbabdcaacdadddbdcdaadcabccbabacdcdbaccbdccbaaacddcaddbbaadcbadcbdbbbdcadbabcbcaddbdabcbcbbdcbbaabdbdaddbadcddddaccbbadacdddadbbacacacababbdddbbbdbdddcbdbabdcaccadbcccaccdbbbbabadbabdaddcacabbddbcdcaadcbadccccbcaacaacbdcbbddcadcaabcdbaadccdbddbaaddddccabddcadbdcbabdcccbdadccbcccbcbdabdacbbbaacccdcdabaacccddabcbbdcdabcdbcdbbcddddaadabaccbacaadbbddadadcdaaacaddbbdcdccdcbddcdbdaabacacacdcdbdbddadcadbbadbbbadcacbaabccdddcbddbbdbbbbcdaddbcbdaddcbacbdabddcbbacacababbcdcbbbaccccaaabbccdbabbbddddcabdbacdbbbdcccbbdadcccbddacaabacaddcabadabaadbdabadabbcaddaddcaccdddadcdbbddacbadabdbdacaacdaddcdcaaddbadddabcbdcaadbdacccdaddcadabdbcadccdabbccbcaabdbdcadadacaadacbdcbbdcbaacdbbadbbaccddccbddcdcdddcaabbcbadadcccbbaddcccdbcabdbabaccdddccdaabdbdcdbccccbbcadacdcccddadcddbbbcdcabccdabcbadbadabcbbbcdcadcabdcbccdcbbddddaaccbadaabdaadbcdbdbdbadcbbacabdbcdcdddacbdcaaccabdbbbaabaabacadcadccadcbdcdcbbcdbcccbcdaabcbbaddaddbbcbdcbcbccdbbbcabcacccbccdddbbcccdbadbccbdaacadaddcacbbbccabbacbaddcbadddddadbbbccaabadaabaabcbcaaaabbcabacaaacdcaccaaadcacddcaadbcdbbadbdddabaabcdcabccbbaaccacaaadacacbadbbdadbcbdcacbcacbdcddbadcbdcacbdcbddadbcbbccaadabdcacbbcbcbccbcdcdaaacbaacadadcdcbdcabdcbdbdddaddaacbdabbbccbbdcdadaacdbbadccccdbcacccddbadbbdacbccccbdbdcdddcbbcadbdbbadabdcacbadacbbdbabccddbdcaadbdbabcbcadccdbcbbcadbcddaacdcdaacaddbcaacdcbcaccadcccccdacdadbcccddcabaaacbdaacbcbdddbcdadaadcbbbadadddabdbddcbcdbcabdcbcdcbccdcabdabbacdccccacdddbbdccddcdbddbbcddbcbbdbccaaacdbbddaaadddccbaabddadaccddbdacaabbcabadcabddababbddabbcbdccdbbcccaccacdabdcdaadcbaddaccdaddaaddabdbbbcbbbacddbcbccccadaadccddadacddcddaacacdaabcbaccdcadabbbacdbdbcbdcdbdccccddabbabacdccaaacabbdacabbacddaccababacccdcccbcaaccddbdcbdcacdcaaabadcbbcbabcdbcdccdbdbddccabbddbcacccacddaabdccadbdbcacbcaaabdbaadcbacaaddadbdaacadbacccccddaaaabdabcabbcadcdadcabddaaadbbbabdcddbdacacdcdbbabdacacbcdbabdaadacacdbcbaddccacadbcaadbbacacabdcacbbaabbaddbdccddbdbddcbcaddcddccacdbcbddabcdadcabbccdbddbbabcbabdabdbaabdbdbadcdccabcbdbccacadddbaacababaabadbacabbbaddcaaabbabcdcacacabdddcdadcbbadddcddbdbbadcaaaccbcbbbcbbddbaacbdbdddbadbdadbacacdbcdbaccbcbaddaadbbccbdddccbababccabadabcbdbddcddacddbcdbdcabdcbcbdddcdcacdcbbbccbabddadabccadcdabadbcbacacdddacdbbbdbacdccaddbcadaaadcdaccbcabacdcbabbadbbdcadcabaccbaabacbbcaacadaadbdcbdddccaabcaaabddbabbcccdbdcbdbcdbabadadabddcadbdaadbadbabaaaabddbdccbccdbdcabddbcaaaadbcaddcdabacbaddcbbcdcbcbcdbddcbadbabbddacdbbabaabcdbdcbdbdcadacabdbaabccabaadbadbdbbccbdcaadcabaacddcccabaacbcabaadddbadacdcbbbddabdcbdccccccbbbdcbddacddccdaccbacbbcbabcbdbdcacacaacabcdacaacbaadadddaabcabcdbbaccccbbdbcabaccdcdbacaddcadacbadacbccacaccccbddaaadbbbcdccbadbdacdabccaabacabddcdaaddcbcbaabcdccddcdabcdbdcaddcabbdbcbcbcdbcacddddcdbbbbdbaadcdbdabaababddcdaaccddccaabdaabccddadbadabaccbcbaddaacababaaaaabdaaaacdcbccdccddcbabcaadbbcdbdcacdcccabdbdabdcaaabadaabdbbdaccdabbcbdaaabbabbccacbddbddadadcabdbbcbdcbacddbccadaabdddcdccdcbaabaaccacbcbdaadadaabbcccaaabdbbdbaaccaaaaddbdaabcbdbcabdbbcabadbcddcbbdcddbaabdbddbdcdbbcbaabccccddcddcbbbdbcbaccddabbabadbdcdcbaabcdbbcadbacdaccaccbbbcbdddcadbbbcadbccbcaccdccccaddcddaabdddcbbaabdbaddbdcbbdcdcbaccdcacbbbaabbccabaabadbbaacbbaaacdcbbdbabaadbdcaabdacccaaddbdbbdccccbcacdacaababdddccccadaabdacdccdbccacbcadcbacdccadcacbbabcbccacdbbdbcdbbcdcbacbcbacdcaaddcddbbbdacaaadcddacaccddaacdbaaabaccdacddbbcdacbccbadbccbdcddbdacdbbaadbaddcdbadcdacdcababaccbbccccaaabbcbcbcbacadcbddaadbbddbaaccdaadbcccbddbcaaaddcadbdacbababaadcdddbbbcdddabddbacddcdcabddacbaabbcaacbbacccaddacbdacaacbbcccbddabdcdbcacbbbdacbddadbbdcdccddaadcbdacbaabbdaccbcbcbbccbdddacccaccbdacbdacdccbbbbbacdbdcdbcaacbdbbccabccccabadbacbaadbcdcbcccbcdaabdddbdadbdaabddadcccabccdadbaccdbdbbaccbddcabbaacbadadaacbdccdbdabdaabdabbacddcbaccddbdddbdacccbddacbbccdbaddadabdaddcacaccaadabbdabcacacbbccdbcaacccbdacbcabcbccbdbacbdbbacdaaabbbcdaaadbacdcbbdbbccbcadddbadcbabdadaaccabcbcccbdabdccbbdbbbdaccbbbacdabacdbabadaccdcacaadacdaccdbdaaababbcacbdadddabcbcacacbddcabcbcbccbddbdcacdbadddbbcccdbccdbadddddbabdaccdcabdcacbbdadacdcccccdabaddbadcbddacaadbbcaabdbbccbcbbcbdcbabcdbccddbacbcaadbdadaccadacadbcddbbcbaacacbdbbcaccdacabbcbdcbcddcbdbbacbbdabccbcbdbdcbccabcdcadbabdbdabcdcabcdacccddbbbcbcadadccddbdbcddcbcaabaadcbdbddbacbbacadaccbbddcbdaabddcadbbadabccdaacaddddaababccbbbabdbdacbbadccacbcabbdacbaadaadbcbccdcbacacdabdbdaaccdccdcbbbacaaaddadacdcddadacaabbaddacaadabacaabcadbddbaadbcdadbcbcddccbddccaacadadaccdacdabbdccadabbadcaabcabdaaddcbcbbacadbaadaacbdcbbcaacadddaadddcdabcdbccccbbcbcdacacbdbadadacdcacdacbabddbdbcaddbccdadcaadcccdacbdbaacdbbdddddcadbcbdaadaabcdadbbbdbaaddbddacdabbabbcabcccdbbbdcdbbccddcadcabababdddcccdaaabdddbccdcdccdccaadbdbccbadbacadaddadadbaddbaaddabbccadddcaccabaaacdcaaddbabcbabacacccaccdcdacdadadbaadcaabacbdacacdacbcadbbdaccbaabdacdbcaaadcdabdcdbbbaadcdacddabdccbaccdcbdbcadddabdadcdaadccbdabcaabbddadcdbcbbcacadddbcbadcbcbaacbadccbcccdaadccdaaccbcabcbbbacacabcbbccbcbacacbbdababbbbbcacdaacccdbdccbcbbddabcaacaabadcbaacaaaaadbdddacabbbbdacdcdbdadcbcbaabacbaadcdddddabcddcadccacccdbddcdacacadddccdccadacdbdddacabccccddcadbabacdccdbcbdbbbaddcbbddcbdcbaacddddbcdabaaacdaaaadbbdcdaacbcdbbccdabadbcdacadacbbcdbbbdadcddcaddbdcadcbdddbabbdbdaabbcaddbcbaccbdabcdcacdcdcbdadabcbccdccbcaddababbbdbccbcbaadcbbccaaaccbcacaabacbdabdcacbadcacdbdccdcbdcccacdcddbdadacdcbbaacbbcbaadaabbabdadacbaaacacdabcccabdbacbdccadacacdbcdacbdcdccdcddcdcddacdacabdccbdbdabaabbbbcbbacbdccadbcdbcbbbdcdcbdaacdcbbcdccbababdbdaadddcaaaaddaccbbdadaabbdcdcbdadaacdbbddbaacaddaacdacdaabcbaaccdbcaaadccdabacadbdbcacbbdbcdcbdadbcbdbababbdaccbcdccdbadcccbdbacdbbaccaccdadaadbdbccbaababbacdcadbdcdccdbdabbccbdcdbdddbaabacaacbbaaddbbbdcacbbcaaaccddadddcacabcabadbcdbbcbdaadadccdaddddcbbbbcdbdabaccccaacdabddadaaddddcbcaacbacacdcbaadddbcdbccaaccddabdacbacbadcaabcdadacadaadbbaddccbcaacabbccacdcbccdbacbabdabaccabbbdacdadcababaaababaddbcbaacacdcdaacaddbacdcccddcadaadabacbdabacdbbbbaabdaddbacccdaccaacadcaccccadaabcaacacacaabdacdbdcdbccdcbbcdbddaddabddcacaacadabcdaaadcbbbccabcbbccabbabcabacbdaabcbcdbabdbddccaaaaddbdcbbcbaadcabbbdccbddbbdbabbaccdadcddcdaddbacabbabaddbdcddcbcddcddcdbabbbccccdbadccdabccdbcbdcbbbacacadbadbbdcdbdaacdabcdbcdbcdbdcaaabcdddcbddbbbabcddcdddabaccbdbdaaabddddcaabbddcbdbbaccdccdbcdacccbccaadbadacbdcdbbdcdccbccaabbddcddaaacccddddaaddcbbaaacdccddacaacbccbdbdcbccbddbdaccdadadcbbbddbcdacaadccdcbdbabcbcaccdcdcdadcbabbbbcbdadaccacbdcddccddbbbdddaaabccbbbcdddaccabacdbcddbbacbcdaccbbadaadbcacbdaabddcadddcadbbabbadcccadddadbbbbcdccdcbcaddcdaacbadbbcdbcdcadadacdbdcdcbbccddaaababdadcabdadacbdcbabdccdbdbcbcdbcddddcdcdbabaaacbdaaabdaddaadacabdbbbadcbbcddaabbccbdcbdccbdabdcbbbabcaacccaccdbccbcdbbcbbdcddbdbdcbaddbbdadacccadaacccbccddbaabaddadbabdbdcdaccdccaddacaccaabbccaaccdaacdacdddbdbabdbdccdcbabbbbdadaadbddbdddaadbbcbaaddbaaddddadacddaadcaabaadcaaccabaddcabadcbdaadcbdaddcccbbcdddcabaccbaabbcadbadcccdddcdcbbdbcadbddbccaacccabbbdbcbcccbbbbdacbdabacbbbdbdaadbdacddbacabdacccbdcbcadadbbcbcdbdcccadcdbcdddcbadbcbcaaabdcbaabaddadccdaabdbddcbdccbbbaacdccbcabdbbdbacbcbadcbbdcbdabdccdbadaaccbaacdabdbdcbdcccbcdcabdaddaabbcacadbdaaaccacacbbdabacbcadacccdaaabadcbdddbddbdaddcbbacabdcadccdbacaccdddcbdadabccbcacdbacbdcacaddacbdcabddbaccdcdbddabccbdbbdabcbdacddbbbdccaaabdbbaabadbabcbaaabbbcabadbdaadaabcbcdbdadcdabbbcbdccaccbaccbdcdcbabcdadcadccdbdabdadcdaddaddcbaacbacdcbdbacdbcacdabbaacbbddbbbbbadcacdddcbabddbacddccacdadabcabccbcbdddaaacdddaacdbacbabbbdcaaccadccadacccabbdbabadcacadaddccbbccaadbdbdbbcadbddaacaacdbbadaabbcbcdcccdacaddbdbdbaabbdcbbdcbadbaadbbdccaababadbbabbabdbabbcbbbaacabcddddccccacdacaaccccacbbbbaabdadabbbdcaabdcaadcadbbbabacacdbdaacacabbcddbcbbacdbdabaacaddbadadbdbccacadcaccdcababbcbcdcaadbadacbabacbddddbdaabaadcbbcdcbbbcdbbbcdabcdbcabaaaaacbcdabbadacdcddbbbdabdbabbddbdbbbbbacacdbbabdcccaacddaabadddbcbadaccadaabadcaddbabacbacccbcaddccdddaabbccadacaaccdabadbacccacddadccdbaaabbadddccaabcbddbdbdcbcbccaddddbbcdccbbbdbddbadcbaddbcbddcddacaddaaaacacdaacccacdacbbcbabacacbbdcbccbabccdadccbbddbbcabcbdcbaaddaccaaccbbabbdddccacddadaaabcdccddaacaaacdabcddbacdabccdddcaadbbaacccaacddaadaacacdbcccbdcaadabadabcdaadbdbbbccbddabbccaadabadbbdaadadbbdaabaadaaccbabbbabdbbdbbbcdcdabcccccacacabdbacdcacdbbabdbbacbdbcabbddccbcdbdabdabcbbcbcaadcccaddabcbabbdddddbcadcbadabbcbbabccdbcddcdcaabbbdaabdbbabccdabdcaabbbcbdbcabdccadacdaacbbdbdddacbdaabdddccdbdbbcbbbdcbacbddcaaadcacabaaabadabdabdaddbdcbaddadbdcbaccccacacbcacddaadbddbacdcbcaacdbbabdccdcacbaaacadbcbadbacacddddabcdbbcabdccdbbabcdacbcddbddcdbccbadcbddbbccabddcdcccbdacaacbcbdccdacdddccbddaccdbbddbadacabaaddaabcdaddddbbbccadacbadacadabacaaddaccdcabacadabadbbabadcbcbadabaacaaddadcbccbacbcddaabbdadbdabccadccaaadccdbdcbdbbadacaacbbccbbbbdddaadacbbaaaadcddcbbadabbbccbcbbabdbcadadbacddccbdcbdacdbbabdaacdaabbbabbacaadbadcabbddcbcaacbddabbdddddcbccaddddacdaaabddcdadaacaccccadabdadbdacabcbacccaaacddccabdcdcabcbdcaccbbdbdbdabbccdddbbbdcbabddcabaaadcccbccaaaccbacdbcbbbaaadbcbaacccabcbbaaccdbbccabcbdccbcaadbaacbcbdcbbbccccdaacaccbdbcdddadabcabddbcbddabadbccacaadccacdcddbaacdbcbdbabdbacdcbccbbbbcdcbbadbdbcabcaaabaabcacacbbcccaddcacaabcbcccbbcccdcddbbddccdcdcdbaabbacbddbadbbdadaaaaccbbcdaddbcdbcdbdbbdadccddabaaacacddabcabbbcccccbccbddbcbdcbcdadacacccccbdbdacbaadaacadddccdacbddbaccddadabcbdabbdbcdbcacdcaabdaddccbaabdcdddcccdccabcbaddacacdccbcabbacddcacbacadababbcaadbbaacbdccbaddbadadacbdaabbccbcbabdbbaaacdaaddabbadcddbdbbbdddaddcacddbdcbabcaaadcaadbbdbdacacbdbcccbcacbdbaabcadccdacdcbddddcadcbcacabbabcdbdddbccadccaaccbdddbadcdadabbcaacdabddaacaaaddbbbacabdddcaccdadcadcabbcabdaaddbddcacacacbddccccadccdcbbbdcaccbdbaaddaacbabaacabdaccbdcbcacbbcbcbbdbaacbdbdcdccbcdadadcbdaabccbadccbddcdbaabccadbdbddadabbcbcdcddddccaaaacdbcccaabacaaaaaacbcacdccbbbdaaadccddbbaaddbccaddacbabacdcaacdbcacabddcddcddababbacbbbbabcbdcddbaddbccdccacabcaacbcdddaabcbabdccbabbccdbcddbdddcccbccadabbdaacbdcdaabaccdcaaacbccbbbbdccdbcbdbcdcbabdddbccaacabaaadddbcacddbddacbbadcbdbccbbaadcdcbdcbdbccdcadabbdadaabdddcbcccbbbddcdcabbbcdcccbbccdbbcaadacbbdcaddbaaaaccaddcdbcbcadbacbaaacaacababadbcaaadaccdcbcbacaddcdaaabdaabdadccbaababaadcbaaccadcabdaddababbddcddabbddcbbbbbccddabdabcdaaaacbcddbdabdaabcddbdbaadabdabcbaccacabaacdaaccddbcabbcacbdbbbcbbaadddacadbccacbcbcababaadacbdddadacdabcddcbabaacabcacacaddacbccbbbdabbbaabdddaabcdacbbccccbabaccbbdcabbcccdabcdcdcaddcccabcdadcdaddbbdacaaddbcbbbcabdcbdbcbcbdccdbaddbbbbadabdaadddbacbdacbaaccadcacaadcacdbbddddddbaabbaccabdbbbbcdaaacccbbcddbcdcbbddbbaaabadaabdbccbaddbcccddacbcaaabacdadbdabcddccbbddabbabdbcadcbabacdaacabbcccdaccccdacbbabddccadacdbcbdaadbdbacaabccdbdabcbcabdcbaccdbababacbdabccbcdbcbaabacddacbbdabbacdddbabdbccabbdcdbbcbcbdbcbdcdcdbcccbdbccbacabdbcbcaccbccdbbcabbbcccbccabadcccbbcaccbadbcdaaacabbccbcdcbdcccddcccbbcddcabdacdcdabbaaccacdcccdcbadbbdcbbadabbbbbcbadbdcadbddabcbdbcbacbccacbcbabbdbdcbbcaaccbcddcddbbacdcbddcbbcabddadadcaabbbcdcbadaddbbbacccdacdbcddddcaccbcbadcdcdcabdcacdacbcabbddbacbcbbcaaadcabacabdbbdabdddadbadacacadaddaaadbcccadabcacacccdbdcdacdcbcacbbbbbacddccadaadddddbbabbcdddabaaadbcabdbcdbddbbdbcbdcdcdaacdbddadaaadbdbadcaadadaadbddbbcdabdbaadbddcaaadcabaacbccabdbddddacbdbcdaaabddacddcdababbdcbdaadaaabdbacdddbddcdccbbaacbcdbbabdcdddabaccadbbbbaabdacccbbaccdaabcabbaadaadbbbdccbdbadcabdccddbcabbddccbadccdbdcdcddddcdcddddbaadbbcdcdacbaacdaaadcbbadcdcdccdcbcdccbadabccddccadddbddbbcbdabdbdbddbcbaaadbaddbacabcbddcbdccbdcabdccbadccabbddcbababbdbaacadcbbbdcabaddcdcbdabdabcbbbbabadccacdabbbbddddddddbbadbbdacacbdaaddaddccbbccbdcababbdaaaccbdbacbadaadbcddcbdabbccaabdadbbadcbaacbddbaddadcbdcadcdbbadbbadccabcadccdbcacdacbadadadbcdacbcababdcbaddbdbdbcbdacbbddabccadbdcadbddcdbaacccaaccaabcbaabadbacdcaacbadbcbabdbdbaccdbcbccdbacdddcaabdcbadacacbadacdbbaddbcddbaabacadcbbcbdcbbaabcbdaccaddabaddadaccdddbcadacaadbdbacbbcccbdaaaadcbdababcabbdcbbbaadbdabdbcbdddbacdaabdadcaadddabdbbdbddccccdbdbabcdcadaacaddccaaddbdbcadbaccbaacddbacaadbdccccbdbdddccdddcdcabdbabaaadaaaacddacbbbaddbbccdbbdbadaacccbcdbdaddcbcbaaadbababcaaadccabbbabdadcbdccdbbddcbaacaacbadbbaadabbdcbaadabcbbaddacabdddbbcdabdadabcacacbdbccbbbbaacbadccaaaccadcdcaddbbcdcdcccddabcdbaabdbdbaaccbbacbaacdddaabdddcddbcdcbcccbbddbcacadaccaccdcadbacddcddcddccdadcccdcbdbccaaabdddcaccdaacddbbacdddabdcbcdddccbadacacbdaaadbaacadacaaccabddbcdababbcaaacadbbbadcababcbacdacdbcaacadbcdaacccbddcddcaddbaaabaadcdabcabacdbcbddbbadabadcdabdcbaddbdbbcbddbaddcdcbcaadbbaadbbcdbaccbdcdabdbadcdaccbdaaadccbbddacbbdcccaabcbbcbabacccbabcccbcadacbbcccabcccaddaabaacdddacbcbabadabcbbccadddcccbabdaaddbbdddcddccaddaaabcbdddacaacddcbcaaaddcacaddabbaadbdacbaabbbabacadbcddaccbccdaaddddbbcccdcdadaccacabaaccabaacacccdcddbcabcacaadbddcadbbcbddacabbacdaacbbadbddaacacabbbadbbdacbddddabccbddbcaaadbaddbdccabadbddbdbddcabaacdbddbbcaadaaaabbaacddddddcbcaabdadcbdbaccdbaccabddcacadaabbbbdaadbddbccbbddcdbcaabdaacdaaccdccbbababcaaaabbacddaabcbdbdbbbdbdaaaadcacbccdcbbdcbbbdcabdcaadadbbcbbddbcaabacaadcbdabbcbbccddacdbaccaaadbbdbcbbbbacdbadadbccbcdbcaaccbadcdbababcbbbbdabcaaddaaaadcdabcadccaaabbacdaaaacaacccabdcbbabbdddaaddaadccdddacbcaaadbabddbdbcbccbdbcbadbdcbddbdadddbbabbcbdaddabaabcbccdbbaadcdbbabcbcabbbdaaacbcbccacaaabcaacdcbcdccdabdabbcdabbbcddcadabccdabddddbaddacacabbbbaabaaadccacdcdaddacbcabdaaacbacddcadcdadaddbbcacdcbaccdcdadacabcacabddccacdadcbccbddcbaacbdcbdbcbcbcbadbbccadbccabacadccbacbdccdcdabababcbaaaacbbbacbdacdacdadbacdbbbbcdcdcbddccdadcbcbadadbaadbcddabbccdbabccdabcdcdadadccadbaaccbabcccccabccabadadbcadbbdadbbdacddadbadbaadaabbbcacbbacddcdcacaddbdddccddcaaaccccdbcbbbadacbabddddcabdcbbaabcadddabbdcbdbcdadadbcbdcaccdbacbdadcddbddacbbbcacddbcabaabbdabdbbbababddbbbacaadadbcadabbcdbcbdbcbdacbbccbbdabdddbcaabbaadbddcdcadacaaddbbdbdbbddcadcdcdbcabdddcadbbdabccdaabaaacbdbdbbccdbccadcdabbaddcbddcaabacdbaadbdcdabccbaadacbadcbccbabaddccbccdcadaabaccdbdbdabcabcddababdadddcbdccccbbcabbbbbddaaddadadbbbbabdcaadddabcaadabbcdbbdccdaddacbcddacbbcccdccccbccbaabcaaadaacbddbabdcdacddccadabdacbabcaacaabbaabccbbddcbbabccbdcadaaadbaacadaccacccabcbccaccdcbccbabadcdddbdaacabadabbdabcaaaacacabccacbacbaacccadaadcbddddbadadacabcacabbaadbbaddadccddbabaabbcddbaacaaccdddaccbdcaabaddadbddaababdbdcdadcaabaabdbcdbcdcdadccbdbbdbcadccacbccabccdcbccbaacdccdadcbbbccaaaaadcdddaacaacdaacbaddcaabdabdbacbacaababbacbbadaacbddbbbaaabdabcbaaabdcdbccabbccdcbddacddcdcdbcdcdbabdabbadcbccdddaacbcdbddbabbdddbcdaaaacccddbccacaabddbdbcadabbdcdddcdbacacaabacabaacdaacadbcdcdacdbbccaadacdccbdadcddbcdbaadcbbbaaddddaaaadcdcbbdbdcacbcdbaadcbaccadbababdacadccacbdccdccdcaabadccadcabacdadadbbbbbaaccbbbcaaadbbababbbbcdcdaaadadcddabcbabdbdcaaacacccdddcadcacbaccdbabbabbcbbaddbccbdbdbccbdabdcabdaadccbbdddbbdbcbbacdadadbdbccadbcaadbcadbadbaccdaabcaadbaddcbcdcbcbdcacdbbdcbcbbdabbadbbdcbbbadaacaadcbabdabdcbddddaddbdaaaaabdbbbadaaccacccccdcbccbddddbdbdccbbcbbadabacccaaccdcccbaaabbbbacadcbdbaacaddbcbadabacadccdcbbccdcadbbcddcdaacbdcaacbbbbcdaaadadabadbbccadccbdcabbcbcaacdbaddbacadbddbcadabbcccacacadabcdaaaacbaaabbcaadccadaccbcddcaaacdbcdcbdcacabbcccaacbabbbdbbcaddacdabcadbbcdbdadacbbadbcdabccbbdcacabbadcadadcadcbcdbadbccacbbdabaccabddbaabcdbdababcdcbcbbbadaabdbcacacbccddcbccddcaccacbbbdabacdbdddcdbbaaacabaaacababdcbaaababbadadacbcbacaaaabbadbcaaaaadabbbbaccabbdccdbdaadcdaccdcbbdbaabdcdccabccaaaacbcaccbadacbcccbdbaaacabddddacbdcabbbadbbdcdbbacaddcaacdcdcdabddbcadcddacdaacbbbcdacbcbddcbaccccadddadaaacccabcdabbabbbdabacbddcbadbacaccdbbdcadcbadcbbcbcbcbbbdacdaadccbcabdabaddacbddbbcbadbaabdbbcbbcdddaabdbbdddcdccccddabccddbbdcdcdbdcdacdabcdadaabbbaabbbadbdaddbbadcdcbbadccaabbbcbadddacdacabdcbccdadadddbbaddbdaadcbacbaadbbddbcaaccccbdbdacdacbcccdddadbcbdcbacdcdaaabdbabaddbaddabcbbdadacacaadabacbacbcabbbdbdcabcbdddcccccbadbacbbccbdadcdacababadddbccaacbababbddcccccacbcdcdaaabdcbabaadcbcaabbcaaccacbdbbaadbaddaadcbacdcdabdddaaacbdaacaacadcdcabbdadaabaabbdadacbacadacccdacddaabadaaaabccdacbdccddadbcbabbadcdcacccbabbddabbbccdcbbacddaddbdabdabaaaacadcbbacbbacccacbddabcccdbcbbcabdcbbcdaaccbaaddbbbcaacacddcbddbacbddbcaddaabcbaacbdacccbaaccbdcbbdababbbadcabbbdbaabddccdcbacadcadabbadcbccdaabdadadaacdaaaaacadbbbdacabcbadbcdbabbaabbddaadcccdbdabadcaddbbcabbcbaaadbcddabbaccadbdcdddccadaacdddaccacdacbdadcdbcdcbccadbdbcadadababbcddacbbbcaacabadacddcbdcdcbbbddabbacadcadddaddddabbdbccdaaaadababaadabcbdbbbdabcbbaaaabbbabdbbbcbbbdddbbbddcbcdbaabddacdbccdcdcacaadbabccabcabdaaddbdddbdcbbaaaabacbaacbaababdbdbdbccdddacccbcdccbcbbbacaacbabbcbdaadcbcbcddccbbbcbcacadacacdddddddcaabbbbddabbbadcccabddbabdaaccaacaaadaccdcdbddbbadccabccddacadccdddcbcdcdcddbcdaaadabbadcaddbcbbbcaddacacdcacdbcdadcadcdcaabbcdcaddadbadbbdbccbdcbbccbbdbaabcdcaaaacaadabcadadababdacdbdcbcadaddbadbbbdaacaccbdbbdbbdbbdabcadaaaabcacacdacadabccadbacaabcbbbbcdacbbbadaaabababcddcdacccdacccbcbbabbcbbabddcbdabcabdacccdbdcccdadcdddcbbcdabacdcbbcdbdcaaaaccbcbaadcaaabbcccaabbaaacccacdaaaacdbabbddcbcddaacddcdccdbdbdbdcbdcbbbcacbdbdcadaaabcaaabadccaaabcadbbadddabdacabbbddbcdadcacdccadadbcddddcbbddbddddccabdbccccccddbdadbaacabcdadadddcbdbabbdabcacadadbcaccccbabaddadbaddadbdaddaabacacbcbbccbaabaadbbaadadcddadcacdcdbacbdadacccdbabdaabbbdbdcaaaabbdadcbacdbdaacacdcacdacbcdababdcccbbcbddbacdbaddcaacabcccabdaddccacadbddbdbbccdacbcaddbbadcbbccbaddaacbcacdaadbdbbadbddaccbdaadacbcbccbcdbcbcadacdaddacadccdaaaacddbcdaadbababcbacbbcadbccbbdbcabcbccdbbbccbddaacadabdccaadbdbddcccbdbcbbcdaacadccababcddbbaaddbdbbdcaccdacabcadbabbabcaddbcdaccdccaacbbdabcabcabbbccccaadbacddbddadaddaaaddbdcabccbdabbdbbbcaccacccbbdbaadbdbaaacaaacddbcacaabddccbcdaaabddabcaacaddbbabcabbabdbdbbbcabdcdcbddcbcabdcbacdbdccacacbadadbaaabcacdbcdaccbbbabbdbbbaadabbacdabbccddcbdcdbbaabbcddbcccbdddacacdcbbccacbaccaccbdaabacaccbdcbcddadaabacbbbbddabdbaaacbacccacbbbccccdddbaaaaadbaaadaaacbdcabdccdbbddcbaacaccacaccadbabcdccdaaddbaccdbbadbcdaddababaaabadccaaacbacbbcbcaacdcabbbcbcdaaadadadbdbcbadcdabcbcacbdcaaabdbccadadaaccddbcbacbdbdddbcacbccacdbcddbdbcaaadcddddadbbcdaccabcbbdbcdacaaabadbdadbcaaccadaadcccbdcdcbdcbcdaaacddabdadbacbdcdbcbaabbabdbbaabdcacccdadbcaddbdcdbbdbddbcbbddaaaabbacbbdccacbabbadcadaaabcbacdbaadacadcdbcccbdccbddbbcbddcbdddcdbadbdbaadcdbbccaabdbbaaaddadbcbbbdbabdcacbabaddcccdbabdcaaabddaacbcdaabbabaabbcdaacbdcacccdaaaabadadbbaaccdcddbcbbabdddbcdcdcaadacdbdabaaaacdbddcabbcabccdaaaadcbcdcbdadcccdacaccacbcacdccdaabadacacddabaccdbbcadacdbbbacdabddbaadbccbccbccacabdcdccdacacbacbbacdbccbcdcdabdcdabbcbddbbbacdddcbacabcbabbbaccbabacdadaaaabaaababbddaaacddacaddaaadcdcdaddbaacdadddcbcdabbdadbcbbcabacdadaacdbddbaaacdadbddbdccbaddbbaaadacdcdcbcabcddcaabbccbbccaaacabbccaadbdaccbaccbdabacdacacdbaddabdddbbddbcbabadccbdbdbbacbdacbcdabdcbcacddaccbaaddbcbddbaabbcdbcdadccadbdabcbbadcaabadcddcbccbbdddbdacbbcaacbbacacccaabcbdbbcbccccddccccdcabacdccdacabbacabccabcaddcccdbbddbadadccabbcbbabddaadbcacaabbdddacadcaccdacdcbdadbdbacdcbdcddababbabdaadbcadabcadcabccdaacdaaaacdcbbbdccaabaddcbbcccddcadacbcddccddcddcccdcbcacabbaccbbcbbbdbdcabacaccacdacbdabcdbddccacbbacdbaacddbcbcaacadbddadccdbddbcababddbbdcbadabbbbbadcbdccbbbbacacadbcbdcbbcbaabbdbabbbcbccadbaccacbdbcdaabbdbcbbacdabcadddbcdabcdcdaccbbbbddadbaaccbcbaabbbdcbaacabcdcdadbdcbadadbbbbddcadbaddddccccaddbddddcbccddccacaccacaccdcbadbcdbbcddaccdacacbdadddabaddddbacccccdaddcbddbbcabcbabdaaddbccadbadcabddaaccaaaadacabdabcacbacbddbdccddbadccbcdbccacdcdacdbcbbdcccabaaacbccbbaddbccacbdbbadadcadaddcdbdcbcdaaccddadddadcadcabbdbaaccbbbbbbcdbdbdcdaddadcdcdbcaadaddaaadccccdabcdcccdabcbadababbbabacbcbbddcddaacbbacccbcaccadcacbcbabbdbabbcdabbabdacbdaacbacdacccaaddaadbaddadadabaabbbbcabadadbddcacbdadbababcabcdcdbbccccaabccbcabbbaacdbbccaadacdacbcbbacdabcddabbaabcdccddbdddaabbabaadbcbacdbdaababbdaddcbbacddbcadddbbcdacccbbbdaddcdabdcdabddbcaadbcdadabaccaacbcadddaacdadccdbdcccddcbbcdcacbdcdbacacccbdccbddabbcbbdcdbcbdbddadabdaabcdcacbbccdccdabadaccacdaddccbddacaddbcacbabaacaccbbcbcdbaacdabddbbcadbdccbddadcbabadcccdaacdcaabaaaccbddbddcaacdabccdabcbdbdbbbdccadbaaadccdbbdddcabcdbcbddcccbcaadbccddbabdddcccadcabcaacbabcadccdcaccdaabdcdacabccadcdccdbcacadcacabdbdbbaaababbdbabdccdaacacdbdcaddadbacacacbddbbccdbccabdaabdddaaababbdbabdbaabddcdcbddadccccdcbcdabcabcdcccdcddcccacbccccadabcdbcddddaacaaacdaaaacdcadadbbddbbadacbdcdbdacbaccdbbcbcdacadccbcbccdcabddcdaacdbdbdaccbdcaddaccdcdcbddccbccdbbababddaaadcabbcabcbdaccdaaccadaadcbadccdacadddccbcadcadbaccbaabbddacddadcbdaaaddbdbacaabbadcaacdadbbbddbcaccbbcdaddaabccaaabbdbaacadbbacbbcaaaabcdbddaccbacbbdabbbacadcbabaadcbdaaddcadcccdcababccdcddddadacbacbdcccabdbcdbddcaabdadddadbddbadacbcddbbbabadaacccaccabbcacddddbaaadbdadadaaabaaaabcadabaabdacadbaacddcdddbbddbaacabaaaabdbadbbbacdbacdddcbdabbccdaabbbadbbdaaccbbabbdcabcabbdcaaadcccdadcdddbdbdddcabdacbbbbbdddbbdbbcababcdbbabacbaddbaadbaaddbdbbadcbdcaadabdbcccaadbdcbccbaaabbcacdcbcdcccaccdaadabdacddaaacabaddbaaaddcccbdbdbdbbacaaabbadcbcaadccadcaacacdacdaaaaadcadaaacbaadbaadcbcdaccbbbaabdcbacdcacbbdaaabbccbcddacacdadccbbbadadcadbaaaacadbcaaacdccdbcbbdcadaaddbdaacbccaddbddacbdcaaabcbddaacbbadbbbaabbbaaccdcadddadbcddaacacbcbcacdbbaabccaacbcaddbdddabdbbddcadcdbbaabaccdbbccddddcabcdabcdddaaabbcbbbcbacabbddcdacbacbdcbccabaccbcaadccacdcbbbbadcccddccbbbbdaaadbcddadddbdacdbabcadcdcdbdacacdadddcaacaccbabdcaaadbbcabadbcbdbdddcddcdabdddaabdabcdbdcbdbbbdccdbcacccdbbdadbbdadabbccacdbccbdcccadcdccbdcccbadccdbdacddbbabababbbbcacddbbbcadbdadaddbccdbccaaaabcdddddcbbbcbdaadaccaacdccdbaacdadabbbcdcaaaabbccccbaaccababdbdddcbaadacdccabacbbbbbdbaadcaccaadcdbdbcacaaddbcabdcadcbaabbdccbcbddabdacbdbbcbbcbcaaaabacacdaabbcaccbacacbccccdbbaabbccbabdcdabaaaaadddbdbacbadaaddbadacdabdbbabbadcbadcdacdddcbcbbaccbccdccdccccbddbaccbbaddbcabdacabdddaaddbddddabbaadbbddbbdbbdcdcbccdcbaabcacbaadccdbbcbbcadbdaadddbbacdbaddabaddbaaabaacbddaadacdaaaccacaaadaadbabbcddcaaabbccacaabbcddcccddaaabadaabbdbbacbccaccbcdbbdbaacddccbcdbbdbdbbabacacbcacdaacbbcbbcbbbcbdcaccadccbcbdbaaacddcbbbcbddccacbbbbdddcccdcabdbcbbdbcbdcdadbcaaadcddbcaadccbbcddbcaacbdcadcdabdcbdcbbaaaaaddaccbbacbbaaccaacccaacbccbadcababbacbbcbccadcbbcbbbddccbccbcccdddabaabbbbabdbabdadccdaaabbababbcbbdabacbbbdacacdacdbaacaaddbababbbacdbbbcbadbcacaccdaabdccdddcabcaabbabcbabccbbaccccdccbcacabadcacbdcbadcabbdccadbdabbacddbdaaadbdbabdcbbcaaaacaddccdcabdabcaadaaadbdaccacdbdcadacbbaddcbdbcbccdcbbdcbbcddccdcdcbbbadbcdcbadbcbccadbcaddbadbadadcabccaacdddadcbccbbcdadbaadabdbcadcccbcdccbabadcbbcbbccaddcdccbadbcbdcdccadbaabaaccacbbcccabacabcadcaccabbdcbddaddcbaaadaaccdbbbddabcbccaaaaabcbdcbddadccdcdcbcaadddadbabaacdcbddabdabbdddbdadbbdbccbcbcdbbabadcdbdcdcbcacdbcdbdcadbcbcaccacaabcdaaaccdcabbcccbbcdbcbacaabadbbdbaadcdaccbacabaabddabacccbcdcdccddacbcbadbbdaccbddcbdabbcbcddcadbbcdddbbbbdacbdacccacbadcaaddacaddbbdbadbbdddabaccadcbaaaabcadbacdbaaccdcdabadbdbcabcadcdcdbdbaabbddccbabbcdabcbbdacbdbcddacbcbdbadbbdabdcadaccabcbdbcddbdccaccddacacacacbcccdccabdaccabdaabadbabcddccbcdabcabbdadbabbcbadcdacdbcddccaaccbadbdbbbbabcbbacddcccccdbabbaaacdddabacdcdbbcacabbcdacddddbbbdadcbdccbbbcbdbabacdcdbdcdabbdabbadbddbcdacabaddbbbadadcabaadabcbcdaabbcdcaacbbaccbdbaccdbabcbcdbccbbcdbdadaadadccbadcddbabddacbacbcdcddcaaddbaadccdbcbacbdcddbdacbbdbcbddddbbdacdbbccdabcccbcdbbbabddbbadadbcdcdcabbbaaaabdcccaabdcbbbcdbaccabdbdbdcbaddacdddbabcbbbdcbcbcbccdcacbbdcdcddbccbdbcdddaabaabbcbdadcdadcccbcdbdcbcdaadddccadcdadcbbacacccddbbddcababddabccadadacdaaabdbccaadddbcbabdabdacadbbcacccbbdddcaddcdaccdcbbdaabacdbccbacbddaccdabdccaaabddaddcdbbbbdaddccbcabcbaddacabbddbbabbddccdbcacacbcbbabdccaccdbdaccdddccdccaaababbbbadacbdbbabbacccadddcadaddaaccaacbaaaabdbbddbdccccdbcccdcabdabdcadbdadbbdbdbaddbcbcbaabcdbacdbaddacdcdddcaaacbabddcbcadcdadacadabbcdbcccbbabdabcbcbdcbdcdbdcbaadaddaaaacccbbbcacddccbdabbbadcbdbabbcacdbbcdbadcdaddcdabdbadbbccbccbacadcddbaabcacbcaaddcddbdadccdcaadbdbdabdcbdccbadbcbacbababbdaddcbddacddbadaaddcbbbbdbddcbbbadbabdcbdaadcdadabbadcaddbbdadcccdabdbbbadaaabbccadcaccaaadddbdaddbdabbcaacacccccacabbabcddbaccccddabbbccacccdbbabcdcdabaccaddcaabbbcdbdbddbbaaddcbccddcbddbbddbaccbdcddbdaacdcaaaaadddacbbacddddddadbadbcaadcddbbcbcbabbdcabddaabbbdddcbaddbbbddcbbcbaaccdaacbaabbdcadbaccddabddbdaccaaccddadaaaaddaacabbadbbaccdabbbaadccddbcdcccccbcbcdccdcddcbccacdaaddbdbbdbccdbccbacaccdaddbbccbacbdbbcccdbbcccddbdddddcdaccdddbcdbdccacdcabcbbdacccadbddadababbaccdacbdaabcddddcbdbcbbbcacaadbddaddaabbdcdddbbaabdaaabdbbcbbbdaddcdccdcbdbdccdbcadbccbabaadddcabdadabcabaddddcbbdccdaacdccaadddbbcdaddaadacdbbbbadadbdbaaddaadbcaaddbabbbdcdcadbdcdcbadddccdbcaddddccdcbbcabbbddaadabbcdaaabaccbadccddabbabcabbaabbdcdbbabddcbabdcbdbbdcabdbabbabcbabaaadcdcbcdbaaddcbcdbadbddcddacadabbaabacacadaacaddcbdcccdaccbadabcdbccddcdcacccdcccaadbbabacabcbbbcdabbaacdccadcaddaaaccdacaaccacbdccbcccbabbbdcdbadbccdcdcdbbbddbccbcacbddacacadddabccaaacbbccccaaaaccdcdddabbdbbaadaaaccdcdcabaacdbdadbdcdbadccbdaaccddbdbacacbaacbacabccbddcacabdaacacbabbccddcdcacaabdccabddacbdcbcdbcbbaabaabadbabcdaabcbbcaacababdcadababdbbbcabadacaccbcdbaadbadabbcbcbccdbbccbddbabdabaccbaccdcccdcdbcbadbaacdcddcbdbacbdbddcdbbbbaddcdbddbdadbdadcdbccadbccabcddaaddbacaaacabbcbbacabbbbddaabadadcdcbacadabbacdbacbadcccdccdaaacbcdcbaaaabaacaadcbcadacccbabaccdcadcbbcbbbdabdaaadccadcaaadddacdbdcabdabdbdaccdaccadacdbcaadcbbaccccacaccdbacadbcaabcdddccababbaccbcbabcdbdbcccdbcabaabaddbcacbdccdbaccdcddbdcdbabbaacccaddaddbbbdaabcdcccccdcdbcbcdbddaddbdcbbcaabbbadcdbcbdabbdbdaabbbaacaaddaabddddcbbcbcdddcaccbaadccbdccdcbbcddababbdbbdaddcdabbbdaddbdabdcbcbabaacabdaccbccdbcacbacbaddabadacccaaadabccababdccabccbbcbcaabdabcaadadaadddccdcbcbaddadaadbaccdbdbcbbaababbccbddbdccbaccadcbcbcabadbcbdbacdacbcdcdaacaaacadbcbbabbbcdbddccbcdcbacdadcccdbcccaddccbbdbbbddacdabacaccccabaacaacdccdccbbbbdaacdbaddaabbccccaaaaacdbacddadcabdcdbdaaabdbadbaadaddbbddcdcbbdcaadaaccadacbadcccadbbacacabdadcdbdababbcbdbddcbdcdadcbbbabbbddbdacdddccadbacdacdbadbdcddccaadddacdbcbabcbadaddaaccddacadcaddbcbabbdabcddcdcaaaccbdaccaabcbdcbcbcbbdabbbacaabdddababbcbdadcbaddccbdddcdaddcaabcdcbdcbdcccacbbabadbaaddcbcddbccbdaacbdbbbdadbdcbabbdcaabaccadcbabacbbadcadbaaababdcbcbdcbcdccdbadcdcbbadbadcacadddddcacabbacaabbddadaabaddbaaacaddbcdddabdbcacccabcbbbbcccbacaaabdcbaaccbabdbcaaacdbbddccbbccbcbcbaabbcddabdcaccaabdbcbddbccaadaddccaacccbacbbbcdccacaaaddaadcabcacddaacbdcbbdbbdbbbdbaccbbddbabaaaccabdacbabcbbadabbabcbbdbcaabdbcbadbdaddaccdcadcddadaacbbabdaaaaaaaacbadcdaacacbcddadcccdcaaababaaabbdacbccccadddcddcddbdabdabdcbaacaaddcbccdaaacbaacaddccbaaadaaabbdcaccbdadcbbccabaccdccbabbadbccbcbbdbbddbcaadbabaccababadcdacddbcdbabaaccccdccdaaadccccaabcdacdbccacabcaaccccdacdabbcdcaabccbddacacddbbdcbaccdbbadbcddcbcadcbacdabcaadccabcdbddbbcdddcbcadccadaadbbdaacdddcbadbaaddcdbccacbddddcccbbaacdaacdccbdbdabcacbcdadcabdbabaadccbaddadbbddcdbdccaadbdcbccabbdcbacdabccdbbbacbdaddababdbcabaacddbabcbbdbbacaadbcaaaabbcdcbdbcddddadcacbddbcdbdbcbcbcbdaccbdadcadccbaccbbdacaddccbcccdcdbadabdcccdbacabacababdbccdbcadbcdbbdcaccdcabdababbcacbacbcaacabdcaacabddbbcbddcbbccaacbcacdbdcccabacaddabcaaaabbccbccccaddadcadcdcabaadbcadbaddcddbddbaacaabdaddcdaaabaabaadcdbaabadabdaacacbbccabcddaaddddcabacadddbdbabcacadcacbcddabcadcdbccadaaccdcdbabcbacacdadbccdcbabbdcbaabacbddbdddbdcdabbcddccdbbadaaddcadbcaaccdbcaabaccbcbbdddbabdccdabbddcacccbabbdbcbdacdcabcaddcdcabbbbabcdcbccbbccdacdbcccbbbcaccaddaaadbbbbaadacaaabccddcbbbacaaadcdcdaaccbcacdddbcbbcaadacccbccaaccaaacbadbbacabadadcccacccbbaaabcabbcaacbcdaabaadacbdbacdbdccdcbdaddadbbddabbaccdadabbdbcddcbdbbaddddbabcaacdbdccccdadddabacccdacbbaadacdbdbabcccdacdddccabbcacdcabacccdabcbadbaabdbddcaadbbaccbbbdabbacadcbacccbbccdacdacddbadbabccaacdbcadbbbbbbddadcacabcdbbcbdcdcbaddcacadaccbacdcabbcacacacadbabcbbababdabacbdcaddbbacccaabacddbadbddbcbbccdbcadcacacddbadcdababaddcbacdbdbadbbcbdbdddcadcdbabbccbaaacadccaaacbbcababcbbadddcdcdabcacbadbbdbccbbcadbacaccddbbaabacdcbdadacadcddabbcbccdbdbcdcaaabbbaacacaadadcbcaadaccbdcbaaacdddbdadddcddbaadadbbdabddbacdccbbcaacaaaacacdcbbbdcbbaccbbcaaacddcdaaaadcddcdaadbdbcccbbdacadccabbdbbababcbbddaccdaacbbbaaddbbdbbcbcbacbccaadbbbbabcbdcdcbbcbddcaabcabdbbdddddbcdaadabbcbcccdabaccabccbcdbabdbadccadbadcbccacadbdcdadacacbbdcaabddbacdbbaaaacdbcacacabccbdcbddbdacbcddcddbaabcaadcccbabcabbadddbabbadbcdccabaacabbccabaababcabdbbaabaadcadcaabdcdbabdcbcabaaccdabbccaacdaaddadaacacccccbbbbddcaabacbcadccababaddcdadcddcaaccacddadbcdbcadbaaccdaabaccdddcacadabbaccdbbddadabbadadbbaacabcddaaddaccbddabbbcdcaaacabcbaccabcdbacabbabccbdccdbcbcdbbbbdabbadddbbbbdbdabbaadbbdadcdcadbacabbcadaacaddbabcbbbadccdddbbcabdbbdbdcbdbaddabbbaaaabcddbcadddcdbacadbbcdabdcadcdbbcaacbadbdcccdbddbadddaadaadcbabdcabbdcacddbdadbbcddbcccdcccabbdccacdbbaaacbadcacbcdabcddcaabbddbbccdaddacdbacbcbbcadddbaaabccbcdbbabcbaadabdcdabbcdbbcbcddadacdbcbbcdbacbbbdbabcdbacadcaaaccccdbdadbdaaddccacdbddacdadddadaddadcbacbdccbcdccddacaddbbcaddcbaabcabbbddccddbabddddcddcacddcbbbcbaaccbdacdabaabbbadbbcdccdbaaaadbadcacbadacadccdaddbaddbabbcbdbdcaaaadbdccaaddadccaddcdddbddbcbbcdcadbcbadbacabcdcbccabdbaaadcdbacdabbbcaaabdadddacdacadabacbdacbdddbdcbbccdcbbacabcbcbadbaaacbbcaaaaadbcdbbabacddcacdccbbabcbaacdbdccbdabdcabbcdaccbddabacdcbadbdbbadbbcacdcdaaabbacdaaccbbadcabcbdccbdddaaaabacacaacbcadbbcadadccacddddacccbbdadbaddaddbacdadcabdbabcaabcddbdabbcdbccdabdbadadbcccabbccdcdabbbdabbabbcbacacaabaccacbbddbdbbcbddddabbddbdcddddabbabcdcbbbbddccabbbabcddaacdcadabdcabbbdadadcbcdbbacdacabdbccddccbcacdbdaabdadcdabdbdcdaacababbdbcbaaacacdacacccacccacbaadbdabdcddbdbadcdcdbcaddbdadacddcaccaadbcbcdbbbcdbdcbaadaadaacaadbcadbbdcccabcbabbbcaabcadacbdccbbacbbccadcdbabbcdaaaacdaabacaaadcbaaacaabbdcadbbcdcdaaaccabbbbbcabcbacccdadabadabcccbacbdcbacaadbcbbcdcadcbbadcadcaadbdbdddacadcddbdbdadcbdcdaadcbbcaadbddcdbdaaabbacbcbababcdbcdccbdacabddddadbacdbaabdaacadaccbcaddbcabdcbbdccddaddabcddcddcabbbcccdadbbddccdcdadadabababacbdcdabacbdcbcbadadaddabcbdadadcbcccacabccddbbccabbdbcdcdbcdcccbcbcaacddcacadabbadddacabaabbdaadaaaacdbcbbdabdabbdbbcbdbbbcbacacadcadddbbccdaccbdddddcdbabdccbadccddcbacbadadbbdcadcccccdbaacbbdcbbdadbdadaaacbbccbaabbdbcbcdacaddccbdcdbaddaadacbcdbbbdccccabacbabdccbdbdddaaacadacdacabbbbbdbcabdcbbbbdaddbbcdccddaaacdaacbaccddaaccdabaaddbcadadaddabbccbbaccdcacacbcacbaddcbcbbcaddacbdbdacaccccbddcbaacddccbacbdcdcbbadccdbbcacdaaabddbcabcacacabbbaadcadddcdcaccaddcadadcddcdbcaadaccdabbadaddacaaaacdccdbbabcaabbcaadbdbbdccdccddcdcdbcaaaddcdbcacacccdcbcccbbcadddaaaaaabcababbcdbaadbbcddcccdcacaccddacabbacadaacabbbaadbcaddcdbbddaaaaccbbaadbcdacacadacbddabccccddbacacdcaddbcdaabcacabbdadbcdbaabdcbabacabcaaabbdbacccddadbdadabbdcaaabdbccaabbbaacbdabaaadabbabdbabdcaacccdccbacdaacaaaacbddcbcdcadccbacacccadbdaacabccacdcbbaccccacaaaaacbddccacacddddcccaaaccacbbdacbabddbbadbcdabadaacbcdcaabbcbdbdcbcacbbbdaccccadbaaabdaabdbdcabdbcbddbcbccdcdacccadcdcbadcbcaaccbcbcddccdbadaccacacdbbbcbbdcbbaabbdcccbddccacaadaaabbccdcbbacdbaacbbbdddbadbdbdaacabadadcacbbadabdcdbcaaaabcadaadaabdaaaadcaadbbccbaacdcdcabbbabddacabddbbbacccdadadabadbbaddaaacbdccddcbadbbaacbdabbacdabcbadbbcdbadacacbdccdabbbdbdcaacaaadaccdcaabcdabdddcdababbadadddcbbddbdccdbaaacddbcabbdcbcabdcddbccddacadaddbbccbbdcbdcdabaacabccbccdaccaddddcdbaacdacdccbaabbcbcdccccacbdaadaabccaabcbbabbcdbbddaccacbcbdbbcdbdcbdadccbbcccbdbaaddcbabbbdaaadcccbcadddcdacadaccbddcabdabdcdbdcddbcacacdddbabddadddacdddcbcccabbaccaacabdbbcdbdcabdbcdbddcbadadabbcdbcddacdacadbcabdbbcdbbdbdcbaccbbacdcacbbcdddbccdbaddaaaababbcdddadaccccbcdbbccbdddbbcbdbcdcdbdabcacdddabcdabbcadaadaaabacabccdacaddcadbdbdcddaaaaadabaabcccbbabbbbaaabdcaaabddbbdbaaddabadabbccbbbdbaaaddbdaaacdaccdcbaaddaaacadbbabdacccdadcdcbcaaabdaccbacabadbcabdbddbbcdadabbbdccbbdcbcdacdbcabaaadabdabbcccadaadbdcbdcbbabdadcbbcabcbdccaccbabcbdcbabadcaababbbbccbdcddbbbbaacababcccdcbadcbcccdbacccdcbacdcadcdadddbddcdaddbcacdcaabcdcaaacbdbcbaaddbcaabbdaaaacdcdbcdaacbcabccacbbdbacbcbccddddaaaabcabdddcaadcbddcabadbbabdcbdadaaddcdddbdcadbabdbaadcdcbdaacddbdccccacbadbcacdbcbdcbacabcbdadadddcdbdbddddacbcdcbacadbabbddbdcdacdbabbcabdabaccbacaddbbaaacbbcbbcadabcccccbbbabbacbbbaacaacbbbcbaaadacabdabcacccacccccbdddddcbdadbbbdbabbbacbdcccbbcadbbdbcabbadddbaacacadbccdcabcdbbcaaddbaacbbcbabadbacdadbcabbcccbcbadadbbaabbbcbdbdbcbdaddcbcddbccaaaadabdbadabbccbddbdcdbabcdcaabcbaadbabdbbadcbacdcccdadaddddcdacdbdcaddaccadcdcbabbcbddbcabdbdbdddaaabdcbbdacbabbccdbcabaabdbadbcdcbcdbcdbdcddbddadcbaddadbdddbaaacbbdcdcabcaabbccbdaadabbbbcaccccbdbbaddcacbbdbddabdddbabacdbcabaadaddccdacabcbcddccdbccadbddaddddbdadcbaaaccaabaccaddbbabaddacbbcccbcbaccaaabbbcadddbdadcbdcdcbbdacbabbccbacbdbadccbdcadacadcaaacccacabbbacbcdcaddacdbcdcaababdbcabcabcbdcbaaabdacadddbdbbdbddddbaacdbdcadcbbbddabbacdcdacdcddbbaadbaaabdcadabddcaabcabddbabbdadadccabcbcbdcdcdcddcadddddbcbdaadbcaddaccaabadbabcddddbacdbabbaaccdcbbbbcbdbabbabdcbadaddacbaadbcabddbdcbcccdddbcbbddbcbbdccaabbcaaacbcadbcdddbaccdccadadbcdbbcaccbbcbbbcdccbccdbbabacbacaccdcadccabadaadbcaadcdbaaabbdacdaadcbacccdacdacacbbcdbddaaddccdbcddbccadbddacbcdcadacdddabacdacdabcadbdbbbabbdccaccdabbbabddabacadbddadbcdabcdbbcaadabcacdbccaadbdaddabccdbaaabaddbbdcbdbdddbacdcaaccccaddcabbbddbbabadcabaabbacdcdcddbbcacaadabacabbdcbcccdcbbdadccccdcccbdcdacccdbbadaadacccbcdcbdbdabaacdadbddaddcddcccadcadcdbacdabbbabcadddddaabbccbadbacbbcbaaaccddcccabaadabbabaaadabaddbbdacbcbadbbbdbbaacdabbccabcbbdbbbbbbacaddddbcbcdcbdbcdcadcdabbcabacadcccccaddcbbbbcbadaaddcdddbcadbdddadbadbacacaaadccadacbbabbbbcdcadcbcbbcbaaaddbaaacbbddbbdacdccaccdbacadbbcddddccaddbbbacdbadcacbbbbcdbddaadcccbccabbbdabacaccbabbccacccaddaadcdadabdacabdaababbcbbccbbdaaaaadaddbabacdcddccdaddcaaaabbcbaaccddabbdbcbbbaddccaccdaacdddcdaabdcbdcddcdddcccacdbabdccddaaddcabddbbcbadddcdcdddabcbbadabaddcdaaadaabdabaccbabacdcdacddcabbadbcbdadbbdcdacccddccbabbbdcdaaacdbddacabadddcddcdaacaadabcdadaaccadaaabcdbacdadbcdaabadcbbaadccbcaaabbdbcddaddccbabdaabcbdabddcadbcbdaadaabbdbcdbbadadcdbcabbcbabccabddaacdbbbbcaddaddddaadccddbcbdadadadbcdaabcbbaaadcdacacbdcaabddabaabdaababbcdcbcbcbcddbaadcbbacbbaabcacccaacbddcbcbaccccadcbacbaabddcaadbadbbdddcbacdccbdbadcabdddbbaacbddcacddcadddadadcbabcababacbdadbccccabccbbbcddcbdccdcbadbaabcacabdaddcabdbcdbdccbcadddaaddccdcadcaacdcdabcccdbbabaabaadaaddabddaddcddaddbaccadcbbdabdbbddcccccdaccbaaabaaccbccdbacabdcabdcccddcdabccaaccabbbcacbdbcbaddabddabacadcadbdaabdbcaadaccdabcaaccaabbcccbcabccccbcaddccadcbdadbdbcbbadcbdbccabaaccdbdbcaddbbdcaddbcdddbbabbdabcdcbdbaadcaadabacdabdaaddccadcbbdcaccbbbdbdbcaaccbadcccbdabdcbababadddddacaddbbaababbdbcbcbcaabcaababbcdabcbbdaaccbdacbacabcbcbdcacccadcabbdaaccdcdbacdbdbccdaaabdcdacacbcbadabadaaddcdacbbdaaadcbdabdcccacabbccabbdbbabdbaacaddcbdcbddbaadddbaaccbcdddbdadcdddddbacbdaddacddddcbadbbcacacadccbddadcdacdccbacdbadabdcbdbabcabdadbaaacadddccadacbbbabaabcdccdaaddddbcdbaaabbbbbddcdbbacdbcdbcbddcadaccbbbbdaaadbadddcabbdbaabdacccdbbccbadccdcdcdadcabacccdcbadbccacdbcbccdacabdadbabbbadccbacbbcaccbdbaddaadaaaccbdddcdadddaadcaaabaddaabacadadddaaaaabaabbacbdcbdbbdadcdccdccbcacabddcacaacbccdabccbaccccbacbcddbcabcabbdccdcdddcbdddcdaaddcddbbcaacdabcbdcbbabaadadcacbcbbbaccbaacdbbabcacbabddcdddaaddabccbaccadbcdadcddcddaabdddcdabccbbdabbcdbabacbddbbdbcbcbadbccdcdddababdcadadcaabddbbcbbcddbababadadaaccbcbccadddaacdbabddcdbbcddbdadaadcbdaaddacbcbcdcbcdcbadcaadbcbdcabcdbcadccadcdccaabcdadaddbcacddbcccdabadacbcaccdbdabbbbbcdbbadacadbccaabdbbcddbbcdcacabccdccdccaacadcdcccccbcbccababdaadabbababaabbbddadaaacddbcddaabaabddbbbdbdabacccbbbacdbcdcdbaacbdaabbbdcdacabbaabcbbcabdcdaacdbacabadbcaadddaaddbaacdbdddbdcbbcabaaaaddcccdccadaadccacdadabccdabdbaaadcababaaccddbcccdbadbcadccdcaabcccaddddaababacddbcabadaccdcadabbabddadccbddcbadaccaadadabacaabcccccddddbaabcabbdbbacbbabcbdacaddacdaddbdccadccacdbbcdbababacddbcdbbbdbaccadacbacccadcacbaaaaaccbdcaccdaaabbadbabdaacbcdabadccdababbbbcdabbaadcabcdaabcbcadccdbbaccddaaddcbcabbbbdaacabccbdbaaaaabcabdbdddcdbdbcdbabbadacccbabbbbbcdacbabcadcbccadbddcdcbcddbacdacdbaacdbbdcadadddcdacbbcaabaabbbdadacdcdacccbcbcabcacaacadbcdaacadcadbdddddaddacacdcbbcadbcacadaaaddcaddcacaadbcbabcdccbcacaadaabdbcdccbabddacccdabadadddbddadccddabcccadaadddccbcaaacddccdbbabadcccbbdbacaaddcccddaaccacadbaaddbbcbbcdcaddaccbdddbccabdaacdbacbdabcbcadcbcbcbbbcdccdcabcbddbaaaccbaaddacdadbdaddcbcbabdaadcbaabddcbbdadaddccbcabcccbbdbddbccdaacdabcbbcddcdcabadddabacdabadbcbcccdbdabaacbacbdabcbdabacabdbbacabddaacbccacdcccadcbaacdbaaaacabaabcadcccadccccabbddcbdbaabcbbbabdcbddcaaadbddbbdcbbdbcabbbbbadcaacbccaaaacdccbbcbdbcabdbbbcacccccadbcaddabacbdccdccbabacbddbaccadaabdaddabdbccdaaccbcddaabbccccbdddaaacccddabcacdccaabcbaaaabbadcddbbdbbdcadcbacabddabccdacbacccacacdaddbbbbcabcaadcaddbbcccbcdaddbdcbbdccadadadcddacadcaccdcbadbbaabbdcacbcddaaabbbccbabcdabbdbdcbcabcabcdddddadbaacaddddcbdabddcadbbccdacbbacdbbadbdccbdaaddbbabbabbdcadadcdadbcabaaaabcbabcdddbbacdadbbaaadcdcaddccaabddaccaadccbadbdbabbcabdbbbbaadaddcbbbacddbbdabcabdacdbbcdabdaabbbdbabdcabdabcdcbbadacbccdcadaacdccbcdccaaccbbcbacaabbcadccadcabddadddbdcdbadddccabaabcccddbbaddabcdcbbadaabadddcddddaaabcccddbdbbdccbccbddacdaddcdbccbacdbbbacbdacbadaadddbbdbcbdbdbcccbcabccaaadadccbbabccbddbdcdabbbdaabccadbcacabddcddccbaacdabbccaabcacacbdacbbcabaccdabdcaddbcdcbadabcbabdbcdbbdbbccbbaabbcadabbcbcbdabbbadddaddcdabcdbaddbcdddddbdaccdbdcddaaccdbabccdadadabbdaabbdabcbccccbcbcddccabcdbcdabdaccadabcadbbdacddcbbaddabbdaddadbbbbbdcacbaadccbbabaabbbdaaacccbdcadabacaacbdadbaabccbabcddacdbbbbabaabddacdbaacdccdaadcaaabcdcbdadbbccccaddaadcbacbdaabdbcbcacbdbbcaaacddbddddccabdaaddccabddbdaccaaadaaddabbddddacccccccbdacaabbdacadbabacddddcdbbaabdbaaabadbaccbdaaadcadbdccccbddbdcadbacccbcacdddadcabbbbaadbcdcdcbbcbcbbbdbabccbacdbdaccacbcdaacbaccadaddcbdccdbcbbaaacadddcbabbbcaacdbdaabbbadabcbdabdcaddbbdacccabbaadbacaaccddccababcdccbbcadadbddacddcbdaabababcddaabacbcbccdcddccacbbcbcaadacabaadcbdbbbaacbbdabdbbacacddabccdbbbcddbadaaaaaacacdbadcdbadcdbccdaddcacbdabdcadaadadbbaddbbddadddacbadbcadbbcbdcbddbcadacbbcdbcccbbbabccdccdaddaabcaabcadacaabdcbbbcdccdcbcbdcccbbcbacaddabaccacddbdadcbbacaabcdcdcdcaddaccccbdcddadddccdaabacdadaaaaddccaaaddbdcdacaadcdadaadbacaadaaadccdddacadbbadcacbdbbddcbbbdcabdddacbabadcabbcdaaaddcdacdccaadacbbbdbbbcaabcbcdabcdbdbbaadcbadbabbbdbadccdaaababbaaaccdcbacabcbcccdcabbbbbccbaabcaddcbcdbabaabbadcdbccdaacacacccccaabadcabacbabccacbdbbdbbcbddaccaaddccabbddcbdbbacddacbbbdabacbdbdcdcdaabccbdacdbccddabdaddccddabdaabbaccdcaabadbddbdcbabbaacbaccadcbcdacccaccddddaabddcbbadbcddbbddbbddbdabbdcadbddabdcdbaccaadbacdccaadadcaddbaccaadaabdbcbabbdbcaddccdbbdabbdbaacbdaddcdaccbbabcadbabcbdabcccbababdadcbccdbcdddcbdbbacbbbbcdbccddcadbaadcbbcbbadaddbbbabdccbbacabccaccccddbbddaccbbdbcbbcaabadacbaaaadbbbbbddaabcdaddbccdcdcacdaccacdaadbadabcbabcdbbbcaacdccaccbdbbdacbacdddccaccabddabccddacdbcbdccadadabaacbdbcdbbbcddcbdbcaaccdabdbddbbdabdbdcdaaccdcbccdacddcdcbdbbbcadadabcbabadddbdcdcbdcbdbadaaabadbdbcadbcabcdbaabddddcadcadbaaaddccbcbcccbbdbcbdaacaadbbaaaddcbcbdaaaaacccacaadbddbccdbabdcaababadccbacdcadcccbcdabcaadabbddbdadaaadacccadcddadcddbcbadaccccddadacabdbbaabcaabadabaaccbaabdcbbcadbdcacbcbbddbccababbaabdacabaaccddaacabdcdbbbcbcadbccbcaabcabbadcbdaccaadbaadcadcacbcacbcbdcdaaddaaabddbbbddacabdbbbbdcaaaccdbcdaabdacbabcdccbaddbddacdbadabacbbdbcacdbdadcaabcaaadaddcabaddaaddaccaccbcacccbdadaddbbbbabaccadbbadbaadabcdbbcbcadaadbabbdcdcbcbabadbdcdbdabdcbbdcccccaabbbacaccaaadacdaacbadacaaadbdbdabcabaadcabbaadbabbbcaccbacdbcbcaccdcabaddaaacabcabdadacaddaddcbdcdcbdccdbdbabdbcaabbbddcbcddddddccbcdbcacabdcdaabbbdaacbaacbbdacccccdbbadabacbaccbcaacadbcbadacacdadcadaccbbdcdccadcabacdcbcbacbcabadbbbadccacdcdcdbcbcbbbacadbcadabaadaaacbcaadbdabdbdcbbbccacabccdddccbcdaadadbddbaccadbaabdaacaadbbabcbadcaaddbdaadaadadbddaddaacccbddababdbcadcddcccacdaddcadbadcdadaacdbcbcdcaabacabbcadaddddcbbcdcbdbdddaacddaacaabcddcbbabdaabadbdccdbcbdddabdbabcbdabccadacbaaadcaccbadcbdbdccdbacdddcdaacdbddcdaaadaabbccdbdbdbcbabaccbbccccaaaddabdaacacbbddcaddaaaadbcabcabbaddbadbabcadbdbdddcdaabcaadbbadbaabddbccccacbbcadacdbbdcbdcdcbddccadccdcacbdadabdcbadccccaacdcbabbbddaadbaaacaaacbddcccadcdaacbdadbbacdaabdccbdddabdbaadaaccaabcccddabaabdaccaccdccaadaccdccdacdadbcadbbcbacdcddbadbadcdacbadcbdcccdacadcacbbcbdcabbcacadacdcbcbcacbcaabaabcbbccdacbcbdccabcdaaccadcdbdadbccdcacacbddcbabaacabbabbdbadcbbaaccbabbcacaacdacaabbcdaacdbabadbadaaadbcacaabddcddcdadbabdcddadacccabbbabdadcacbdcddbcabdbbcbbdabaabcaddaaccbddbcacbcbbdcbdababcddacabdcdbccdccabbdccccbdcbccacbdbdddbdbdbddacdbbabccbdabaaadccbdbddcdbbbabbabadabaadbcbcadccdabbdcddaabdadacadabcddbbabccadbadacbccbacaabcbabcaddcbccadbdcdadddabcabdacbdaddaaaaadbdccbabdacdcbcadcbdcdcaaacadaccbdcddbbdcabbcbbadabcdbdbabcbdcabcbaaadabbacbcaababacbbadaacadccbcddbbccdddadadaaacaabdbdbabcadbacababcddbdacdabaaddbbbdddadaacbaacbacdcddaacdbdddbbcbcdcbcbddbadcdaddbcbcbdccaabcdcbabcdddddadcdbbabbbcdaddbbdbcabbbbbcbbbdcaadaddaccbbadbbdbddbdaccacccaabcbddcbbabdcacdadacdaacaabdddabbdaccabddbdaacbcbabacabaacbcddbadbddcddbaabaabddabbdbbabdddaadcbabbddaccacbcbadccacacaacbbdabaccaddbdaabccdacaaadbbadaabbadabadadccbdcbdadbbbadacadadbccacaabaacccbcaccbccabbdccccccbabaccddbbdccabbddbaabdacdbacbbcaccacbbdadbcdbaadacdabddbddccddcdacbbdbbacddbccdccaacbccbdbcdbacdababccbabbcdcdcbcadacdcbbadbbbccccdbaabaabbaddddccbdaabaabbaccbdaadbbdccaccadddbbcdbddbabbadcbadcccaaaaccddbdcddbccacbcabcdbadcbdcbabdbcbababcaababacdcccaddbbdadcdddbbddaaacbbbaccddbcadacacbbaabacabbdcdacdbbdddadabaacccacccacdbabccdaabcacdcaccaabaddcdabccddbcddadccbadcdaddccbaaaaaaacccaaddccddcdacdbdddaccacddbabdbdddbccbddcbbbbdbadbbbaaddaaccaccaabbdacaaaccdbcbaaaddbdadbaccdaacadacaddabcbabdadbabaccccdcdbaaddaddcbaddddbbadbccddcddabadccbdcdcdddcddbcacccddcbdcbdddcbbdbcbdbbccccccdcaaadaadadcbbabcaddbdcaacbbdbabddadcdadabccccdbbaabaabaabddbbdaadbbcdbcbdcabdaadbbcdbdaacddddbbcadacccacdccddacacdcccadbadaabddbaaaabacccbbcaccabcbbbcdcaddbbadaaacdcaadaaaaacadaacaabdaadbcabddacbcaaacacbdccdbdcaacbdcbababbbaadaabdacadbacddaabdaacbcbcbccdaddabdbdbbdbabacaddadaddabcadaabacccbbaabcdaaaabdddacadbcbbbdaccdddcbcdbcdabbbaaadddbcdccbcdbadabccdaddabcdbdbaacbccacaabacdddbabccbadbaabaacbabdadcbacbbdccbccdbccbbcaccbbaddcadbcbabcbdcbbacaabbbcddcacaaddddcbbddbacbcbcbdcddbdaadddcdadacbacabdcbdaadacadadccbabcaddadadaaaacbdababcababcccbcabddbcbbdaaabcdddbacdaddddacbdcabdbacbcddcaaddadadaabadaaaacddbdadbddcddcbccbcabddbadabddaacaaacadcdcdddddcdbcccadabbccdbcbacdcdacdccccdacadbdbaacddaacccaacbddbadaddcacdcbcacdabddcbbbcdaccbbcabcbdccabdddacdabcacadcbdbbbaaaadcbcccadacddddcddbcbbbaaaacddcbadbcdbdadbaaccdaacdcddaccdcdbddcaccdcaadcdadcbbbcaddcccccdbbccdbccbaddbabdbccddcbacabbdcccacacdaaccdabacdbbbaaccbdccdcadaadcacabcbcdcacadabcdacdccaadbbdaaacdbadacadbdbaacaaabddbaccdadbcccdddbbbcbcacdabcbcccbdbbdbadccdacbbadbbbcbadaddcadabcbbacdcbcaaaabbccbaabbbadaadadbacdccabaabcabbdaabacdacabbcbbbdbdacbbdcbccacdcbdcbacaabacabbabdacdcbbdcbdaaabdbdcdccbdcdbdbdcddadaabbbcadbacaaaaaabcaabaaaabaddccacdaabbdadbcabdaaaaacbcbbcdcacdaddbddabadbcaaadcaddbaaddabdcbadccdbddadcbacbcdccccdbdbbacdbcbadbbacdccdadbdaddddbbbbbcdddadadbcadcaacbcadadbbabaacbbddabadcdbacbdbabcdbacddcadabacabdcaacaccdbacdbddacadcaccaadcdacbdddabcaacaccdacaadcbaaccbacaabcdddaacabcbddccbcccadacbaacbbbcccacdbbababcadacccbaddadadabdddccbadddabccdaaacabddadcdddcdbacddbcdabddddddcbdddabadbccddadcbaaaadbcbaaacdbbccdcaccbbcaadcddcbbcbbdbabdaaddcabbcaabadcbcdcccbbbddbccaaaddabacdacddcabdabcaacbdabdaadbdbccbccbcabaccdbbcdadcaddccbbdcbbccaacddddcdcadddccbaacbcbcbadccaacbbbcddadbaadccdcaaabdbbdcbdbddddaccbdbccccddacdabdddbdcbbccdcdcacbcbcdbbadaabbdcbddabacdadcdaaacbdaddabccacdcccacdccaddcbaabcaadddccbaaaccbbaccadccdadcbbcbdabbacccddacdadadbdbacbaccacddcdbaddddcbddddaadacdbabadcaabcdcdccdcdbabbacbdbbbcccacbacdabcccbdbbddadcdcdbbdcbbaabadbdaaabbcadcbbdcdbbcacbabcadbbacbdadcdcbbddcadbddcaacccdbcdddadcaaadcdadbcacdbbcdcbcbcbbacacdddaaaacbcddcbcdacdbdcbcbbdbcaaabacbcaadbbdbdbacaaaabbdabcbbcdbacbdbbddabbdaccdaadbddadbcbbdcaacbdcbdcdaaaddadbdddcbbcdbdbbdbdbabcadccddacdddaccbcaacbbaabcddbdcbdcdbbcccaaccccadacbabcdcbddacbacbdaacacdbdcabddcdbacbaddddcabbbadacabcccccacddcbbdccbadaadabccbddbbadbacbadcbdaddadcdadcaabdcdaacacbddddacabbbbaddadbcaacbdbaaaacabdabbbbbcdaccaabccddbdaaccdaadbabbcdbbabcbbaacacaabbbcbcacaadcbabbacabbbbbaaddcbacccdbbcaadbdbcbaccbbdbdccdbdddbadabddbabdcbbdadabddcbbccdcdacadccdbbdcabaacbaadabdaaaacdbaccccbbcddbbbabdbccbbdcbbbbbddbcdbbddaabaadabbaadcbaddcdcbddabccdbddaaddababacdcdbdbdaaaadaacabacdddbaccaddcdbbabcabbacaaddcadccbdcbddacbdcdcbcddddcdcabcbdabaababdadddbccdaaaadcdbbbdcaddaaacdacdddddabacdbdccccaabdaacbadcccadccabbdbdaaacccbbaaddcdbabcadbadbcccbaccaabbdaadbdbadbdbcdbdbdbcbaacdbddaadbcaaaadccabaccaacaacdbcaddbbcdcadabbcdbaccbabaadacadddbddbdcbaaacbbcaccacbacdabdddabbcdadbabcbcbbcabdbadcbddacdbccbbcaaadcaacdbbbcdccdcaddcacaaabccdbacabbdbdcacbadcaccacababdccbcaaabbbadddaabcbabcddaadabccdcbdcbabbccaccbacdcabadccbadadaaadcdcbddabcdddadbcaadddabadabbacbbccababcbdcbdabccabdaacabbdcbdcbbaadbcbcdadbabbaabdcaacccccbdbaabcadcadbdaabccaacdddcbccadaaabcbbbaaaabcbcbcacaacabacbbdcbbdbcaaddbcaaabdcabadbbdddcabdcbabbacccbbdabaccabcdccccbbbdcbdbcbababbbddbadbaacaacaddaadcdabdbcdcaaaccaabbcbdbdaacbdaccdbcbccbbacdabddadbddadbcbdccacbadbddaadbcdaacabdbbbaabcdccacddbdaadbbcbcabdbcbcdcaaacbcabaabbacddbccacaddabddbacbbbdbaabaadbaaaddcaaadbccdbcbcacaabbdbccacacabdaabddcadbacdbbcbdbcbbacccabcbdbbcadcdaddcbaaaaaabbabbaababdbcbadddccddbdadbdadcacbcaaabdcccddabcdcbbabaccdbaddcdbaacdcdaacdbacbcbbabbcdaddbdcaadbdcccaacdacbbaacacdbbbbcacaacdbbbacadccbddbbbbbdbdadacbcbadcccddbcddbbdcadcaaccabcacadbacccbccaacccbacbbddbdcaddcddcadadaacdcaabbdddcdbbbdbcadcbcddcbbcadcbbbcadcdbbaacdabdacabbccddbddbdcabcadabadcdcbcddbbdaaaddcbdbddadbbbdddbacacccdabcbcadacadbdbcddaaadbdbabcccdcdcccbbcdbbadcdbdbaabcccadcdbbcdccbcbdbbcadbccdddcbbabdabbdabdcccdcbdadcaaabddbaacbdadaadbdbabcaabbcdadbbddbacadcaaaddddcaaabdaccaadcdcaabcadcccabdaabbbdcdaddddbbabadbbdaacbbadadddcacdacdaaaddabccbcdddbdbbbbdcbbaddacdcdbacabcaacdcccdadaacbbccaabcdacbdbcadcdadcbbaaaaaadbbdaaacdbbcaaacaddcdaacddbaddbcaababcaadacccbdbddbbdabbdddcdccacddccdbbababbbabdabcaadaabdaaabbbbcbcabddcddaccadbdcdbdaabcccadabaccaacababbbbbabacddddaababcbdcccacaddabbbcabdaaaaddaaddaaadbbcdccdddaddcabcccdccbcbaacdadddccbdccbacabbbccbbbcbcbbddcccadbccbacababdbdadabcdcaabdadabbcdacdbdadcbadaabcccddccadcdccbdabcdcbaabdcdbcccaababacbbdaddbcbbcbdabdadccdbcdbbdababbbdbdadaaaabadbadcadacaddbadbdacdbcaabdcbadbddbbccadbdcbbdadcbbbaabbcaacdacadcbdadddacabcadbabbaabaabacbbadbaabcddbddaaaabcabddcadbcdcbddcdddcbadcbbdbcaddcbcdbabaccbdcaadcabbbcaadabbbcbbccabbcacbdbddbdccbdcbbddcbdacbaaaaaacbccaadbdadcabcaabcacdabcadbaddddbbaddcabcddaacdbdabdbabbdbdbdcaabadcbbaadbdbacabdbbacddadaddcaaacbcacacdbaabacadbddacbdbdddbbaadccaacdacdaacbcabbcbdbbbdcdbbabdbadddaccaccddadbcaaaccccdddaaacbacbccaccbdacbbcadabbaaddcbbccacadaccaaacadbacaccdcdabbcbccbbacdcdddcddacbadcaabddcbdccacddcacaacdcccccbdbdacccabcaddcaccbbbdddbccdbbddcadcaacdbcbcccdbdcadbdddaccaccbcccabbdaaccbcbdccbcdcbabadadabbacaddabbddabcbcbbddbacbabdddbdaacddbbdaaddcbdbbdddcbdacacddabaddabcaccdbcbcdcaadabacadbdcaccdccdccdbbbdcbbbcacddddcccabdbbbadcccbddacacbadbaacdbdababdcbabbdaacaccdbddabdcbbdbbdddbccacbddbdbaccabacabaadbabddddbdbdbadccbadadacbbaddccbabdcacaddccaccbbccabbaadaaabbbbabddbcdabddaabdcdabddcbaacacdbcabaaadabcdbbabdbcbababdabcabcdcccbddcdbdadabdbcbbccaaadbbcbbcbadbaccccbadccdbabbcdbddabbcddaddddaccbbaabddbdbbacabcadaccadaaadbbbccbaacdaaadbabbbabbbdddbcccbcbacbabdaddcabcdabddbdbdacdcbcdbaababcccaacadcabbdabaddcbdacbbcdbaadbdcbbccaddbacbbcbabddabbddcacccaaaacbabdbddcdabacacdccddccbbcdcbccddbdacccbbbccddcbccccabbadcbacbcbcabcbdcbbbcdccbaabcacddddabccbcababaaaabadbbcddddddaddddcbbbbadcabbddddddbddbbcddbdadcdaadbcbdbccbdcbdacaabbdbddaaabbbabbdabaddccabcbcdddcbddddbbcaddabacbaddbabbbacabdddcbbbdabadccbdabbadabcbbbabccabdabdbbabdcadcaaddcbccabcbcacdadbdadcccbbbbadadbacddcdbdaccdcdcdabacdccdccbbbcbaaabcacbcbdacdaadadcddaccbacdadaaddaabacbaadbbbcddaacaaadaccbdaabcbadbdccdcacdcbdddccccdcbbbbabacaddcaddacddbdccaddbdcbbdbdbcbaaddbbdaadcbbddbcddbadacdcbbdabaacbaadbbbaaababcbadadcabbbdabbbccbdcadbcdabcbddababdbbcdcdacdcbdabbdcaaabcddcbaaaaddcacaabddddcaaacacdcadbbabbdddccccadabdaccbaccadaccbdddacdaaabaadabaacbadbdddbdbaaaadaaaaccaaddccdaabdccccbcbbdbbcdcdacdcccaddccbbbcccacdbaaccccbadacdadabbaacbdaddbdddcdbcabcbabbbcabdaabdcbcbaadddabbbccacabaddabcaccbdcbbcdddaccbcdcdaaabccbcacbabbababadddaabcbccbaacdacddcdcdbbaacabcaadddbbcaccbdabdacabbdbcccccaadbcadcaabcbbacdaccdccdbddcdbcdbbbdcbdbbbdddbcbdcaccdbdbddbaaababdaddbcddbdaabdccdbabaabaccdcacbdbcbcadadbbbbdcababcbadaaabccadcddcdabcbbbaccccdcadaaaccbccdcccdbadbcdbccccccaabacaccaaacbaccdcdbdcaaacdacbaabbdbabbaccdaadbccccbbacddcdbddbdaccbccaddbaaccadbcabaccddbdbbbbadccaabdaaadbbacacdddcacbddacccadcbcaadacbdbbcbddadacaccacbbcdaacdbbbcabdcacccbbadabddadabddcccacaaccbbcdabddcccbddbdbadabbadabbaddcacdddaacabbcbdbabbcbcaabacdbcbccbdadddbcdcaacbcdcddbbacacccbaadbaaaaccddcbcbadcbbdabadaabaabccdbcdcccacadbcadacabbdaacbcddbdbaccacaadbbbcbdacbadabcdacdacababdadbadccdcacdabddabaabdadddbbabbaadbaddaadaabbbdaacbcabcbbabaccabcddccbadbcdacdcbaaabdcbbacbccabcbaaddbbcaccdccaabdcbbcddddbcadcbdabbdbcbdbcacddcdbaaabbcacbaadbddcddccccdbcaadcbcbcadccbadadddcadbbacaadbbdacdddbacadaccdbabbdacdabbdccbbbadbbcaacbaaaacbbcbdddadbadaaadbadbdddbbcdacccbabdbcbcabcbdabbdbcbcbbaabdabdccacccbbadccdaddddaadadcaabcabbaddaabcbcbcdcacaccacddcbaaacdddbabbccdbbbbacdbdbcddadcbcbabcdacdbbabbdddadbcbbddabddaadbccdacadcdaaaaaadacddbbcccabdcacaabcddcdacabccaccaaccbdbcaacbdcdcbaddbccdcabbaddabbdcdcbdcccccbddbcdababdbbacaaabcabddbbddbadbcdddbdcdcdbcdddcddaacddcddbdcdacbdadbcddacbcadabacadbababcccdacbccbbcbbabbaddcadaadabcdadaddbbaaadcccccdbbdcdcacbcdcbaccbcacaaabddabddabbadccdbbcaccbcbcaacbbaabbbdaadcccbccbacdcbbacbbabdbcbdcaacddcdcacacacbddacabbcbdccabadadbdbcdbdcbcbcbacaabbdabcdcacaaadccdcccdbdcdacbdcccdadbdcaccbcdabbdccdcadcccddddaccddcddbdacdacaaabdccddbdacabbbacdbacbabddbcaacacbaabccbccbdbcbaadcadabdacaaabdadacbccbcbcdaabccbcddddabbbccdbdbbabaacbcccbdbabbccbbcddcabbaddccdddaacbbcdddcbbadbabbabababcadbcbdcbcbddddabcdbcababdababaddaabcadaaddaaddbdabdddaddcaccabcabcdadddccbdccbbabadcbbccdcdabaaaaddcddcbacacaabaabcbccdcdaddbdacacdbacbcabdcaccaadbaaccbbbabdbcacbbdadacaaabadbcaadbbabaadcbccbbdcbacdcdbbccabccaaccbccdadaaaabbabaccababbcdbcddacddccdbbabadacbadddbcaddbadbccbccacddbcbbbdddddccbbdbcdccdabbbdcabbaaababccbccbadbadbbacbdaadaabbdbcbbcccbacabdcdaadbdddbbdacdacbbbcaddbdaadbcadaccbddbbccdbabdcabadabaacaaaddbdcbacddcdbcdabdccaddaddacccbbccacdbdadddcccadadbdcdbcaadbadbdcbdccaaadbacdadcbdaccbbadabbdbcbbcbdbaccbabcbacbcddacaacddadadacdbdaddacdaccadcacaccabbbddcacdadbcccbacdcbabbcddadbdddbdacddaddbbdbcdaaadbbaddcbbaccacdcaabccccadbcbddbdddbccaaddcbdadaaddbccbaddccaacacabcbaaccbccabcbbbdcbaabcbacbbddbaccbdbacaaabaadaadcaabdbdbadbcbccbacbaddbbbbcbcbdbbcdddadcdbdbbadacbbbdddcaaabbcdcdbcbdcdbacccdcdaadcacbcdcabccbbdacccaaaaaacddaccbadccaccbaddaacdbdacddbbaaddabbabdadacdccddaadcadcaddbadacddccacdbadbbcbdbcbcdddddbbaadbcdbaddddaabbabbacaadabdaabaaccdaddccbacdcadcbbcddcccdacbadbbabacbcbacbdcaaacddccaacdcbddcbcbacddcbacaddadddadbadccbbddbddbaacaaaabcbadaabdccaabcddcbcdbacabccbcadbbbdabcbcbacdaccbabdcddbccadcbabccdcaabcbdbacabbbadddbcdabaadbbbbdbccdadbbdadadcdbbdacdacaaadbbbdbcadcacdbbdcbcdcccabcddbbbaadcdabdddabcabbcccbcadbbdbaaccacabbbbbabccbcadbabddbdabcdcdbdcbacbdbdcdbdabbbdcdcadcabcbadbccddaddddabdadbdaaacddbabbbabcbcbddbdbacadbabbcdadadbcdcdaabbdacadaccccbccaacbcdcdacaaaddddaacbbdbbdcaccdbccaaaacbdddcabbdbbbcaccadcbbdabddabaddaddbbdddbbcdcdccbdabbdbacacbabddcaddbadcccabcaaddccdaabbaacdaadacbbaacaabacddccaacddddaccbdcbbdddbacadaadbbadcaddccacadcdccadccdccbadccadcadcbbaaacaabddddcdaabbbacacdbaddcbbaadbacbbbddcaaccdbadaabddaadbdbddbdbbcaadcbcbcacbadbbbbbdbbccabcacbacacdddddcbdcccaddbbbadaacdaabccbbdbcabaadcdbabaadaddbbcbbdbaddbadadcdbaaacdbadbcadbcccacdbabbbbcacccdccbccddcadddcbcdcbaccdacacdbaadaaaddbbccacabbbbccadbabdbccaaccdbdbdbaadbbbacdcabbbcbccdcdaadaaaccadccacdbbaaacbacdbcccdcacccbccccbdbaaabdabddddbbbbcdacacbcbbdccdabbdaadbdbacaddccbadadbbddadcdbcdbcdacdbcadaccabbccddbdacdadddcdabacdbcbcbbadbbcabaacbbaccbddabdddcbcbdccbdaaaabacaaccdadadcaadcaccacccbcdaddcdcbbcadbabaadddabcccbbcadacbbcaddccaccbabdbbcbbdbdaccbcdacccccccbcacdacabadbdcaddbacbbdcbdadbdbcbcdcbdacaabbdacbdbcdcdabbbccdbdcbaabdcacdadcbadddccabdaccccbcabbacccbacddcaccdcbaaddbadcbbabdaddbcccdadcacdcbabdbdbcdadcbdcdbddbdccacccacdbbdbcbbbccdbabdbcdbaadddcdaabacabcabdccaddbddabdddbaccacdacddbcbdababaadcbaccdbdcbccacaaddbababbcaaabdbdccdaaabbacbadacccbdbcdbbdccaccadcbbbdcbabdbcddbddcaddadbddadacdabacdcacccabbdabbdcddaaaddbabdababcaaadcdcadcaadadadcbabaddcaddaaaabcbcdbaaacbdbbaddcacbcacaaccbdadcdcaabdbacaabddaddabcddcabdbcdbccaadbbaddccabdcadccbabaaabcbabdadbacadbccbbaabaabbcdccbcccbcbcddbbacbacdcadadadbababdccabacddccbbcbccbddddcadacdabcdccabcaddbdbcccbcaddcaadcdacadddabbdbddcbcdddccdbcccbdadbdbbcdbcdcbccbdccbcdbcbbaaacdbbbbcabacadcadacbdcadcdccdccbcbddaaababdadbdccddcdaacabdbcdacdabbbacddcddcaadcbaacaacbcacabacadacaaaddbccaddadddddbcbccbadcbddabbbbaadbdacdbdcdaadaaaccbdccdcaadbddccdcbccabaddccddbbaacabacdcdabacccbdcccccaadaacbbdacdddccddbccaaabdcbaccddccdbaabcdacdaaaddbcacbbccbdbbadacddacaccabccddacbdccdcbccbaabcdbaacabbdadbcccdadbdbbabbdbcddabbbcdccababadbdddccdbdccadcadbabbabbcdbadccbadbcaabdbadaabbaacabbbaaccabdcbacacdbcaccdbccdacadbdadaccbcacabddbccbcdccdbbdacbddbababdbcdbdbcdbbcdcabbdccaabdbddaccbccccacbcadadaaabbbdbcdcddbadabbadcacacbaaadcdddaadaccddcabdcaddcbbdacbbcabdccddddaabadacbbbabcdcdbbbccbdcbadababdbadcdbddabaaddadbdaaacaabccdacacabddddabbadbbbdcbcabdabaccabbbbbaaabccadbabbdccadccbadbaccbadcbdabbcaaddcdacdaabbbddcdabbbbdccacadadbbcaabbacccadcabccbaacccadbabbbcacaaacbadcaabcadbaaaabdcbcabaadcddbadcabbdacabdaabcddbbabbdabaacabaacccadcaabbccdbdcaadabdbaabddcdbdccbacababccbddacdbdabbaadbddacdbcadabcacddcbdbcabcdcbcddaacbcbccbadcddcabcabdacdcadccaccdcaabbdcbabbbaaadacabaddaaadbddddcbbadaadcacdcdbbadccdcdabbdbddaadadbdbcacadbdccdbcdcbdbcddbdabdbcabddabcaaaabdacdbdcababdddcdbccbdddcdacbadbbaacccddcabcaaadbbdaabaddabdddcaadcdbbcbcabcdccaabdabdccaabadcdbabdaaabdcbaaacdaddadbaaccbbabdcdaababbadbdcbadabbccbdcacbcdaabbacbdddddabdbdddacbdbdcdcddccbacbadadabccbacabdbbadbaabcbbcddcbbbabcbbaaabbabcaccabbbadacdabdcddbdbcbacadacccdcaccbdbdacaaaaaadaabcdbcdabcadcbdaadcaaddaabbdabbcaddccabadddccadaddabaccbcbcbcaddcaaacdacdbaabdccdccdcdcabddbbabacacacadbdcddbcdddaaaabcaadababdddbdbddbadbdbbaacbbdbabbbdacbaddcabdccabdaaddcbadcdcbcbbbbccdcadddbbdbbdccccbacadbabbbccbbcdbccbdcddcbdadcccdddcdbdbcdbcccaadaccdddacdadbdcccdcddcacabcbddaccadccbddbdaccbcbcdbdccdbbdbdcdcadddddcdccbdddcabbabacbcddacadcddadaadbbdabcacccadaadcbbdbbdbdbdaddbcacaabadbdddacddaaaaaadbbddaaaadaaccbbcdbcbaacbbcddbabccdacccdcbddacbdcacdbaabcdacbcccabbcadbbabaadcbbcabdcabdaddcbdccaccdbbacddbbbbdabddcadbdadaddddbaaadbcbaacabbccaadbacbdcdbcdadbdbbcbadbaaaabbacdcccdcbdabdddaacaadaabbacccddbbbdcbbbcadcdbababcadccbbdbcdaabadbbcadcacccbddadbbcbdddddbbcddcadddbbbbcabababacaddabcbacaacdbbacdadacdcddcdcacbcbcddadbcdcbbacdcdbcabbcdbbacbadbabbcdbddadaccaccacacadbcdddaccbbabacadbbcbaadcaddbbadaaabcddcabcabcbaabdbbdabdbbcadcacdacdadddcadaccaacccbddbcdbccacbddddcacdaaddcaabdbacbbdcdacdaadcacdabcadccbddbbdaacdaadcadddabcdacaaacaddaddaaaabbadcaddcdbcbcaabbccdcbbdddbdcaccaacdbdbbbccacaddbdcaaacacbdadccdbdbdbdadcccdddaaccabcdadccdadaaabcaaabbdbabbabcaacaaabbcdcddbdddcacaabbdadabadcaddbaaccabbdabddabbdbaccdcaddadbacddddccdadccacbbcbddccacccdccaaadadcacdbcacdccbddcbccadaacbbdcbacaaddaacaddddbdcaaaccdaadbcbcbcddddccaddcadbcbacabcbcaacdbbdcaccbbcdbdbabbdaaddbbaabcdbaabbccbacdcdbadddbbcdaacdcbdbdbccdcabddbccbdcacbbcbbcabcbbcccadbaaabddbbadbbdcacabacddacbacdcdcdacaddadddadababbadddaacbbdbbaadababaaccaaccdddccacdbbcaadddacdcbbcbbadcccbdaabccdabcdaacbddcbccacabaababdccbdddbddcabcbaaccbbcbdaaacdacddcbaacacaccccbdddddccddbcddaaadaaaabcabdacbbacbadcbdbcbccabbbdbbacdbcaddbcadddddcacbdbacbbccaddbadacaabcdccccbabddcbcdbccdabbdbcbaacaabdbcbddbacabdddbdaccbaccacddcdbdbbdbabacaaadddbaccbbcccbaccddddccbcdbbabbdaabdcbdbcadcccbddabdaadbabdcccaaddbdadddbccbbddaacaaadddaabbdabbbaddddbdbbbcbbadccabcbcbcbdacadcddcbdcbddacbddcdcbbaccacbdbdbdbaaaabdbddabbaadadbdabdcddddcbdbaaaaabbbbdbabbacbdcdacbbbdbccccacdaccbbaadaaabaabbcddacdadbdcbccaadaddaadcaddbbcddcaabacccccbdbddcaccabaaabaddacbddddacdaccabaadcbbccdcbdaaabcdcaccbbcddaadaddbaabddbdbabdddcbccaabdcaadaccdcabaabacbabcaccbbbcbddcddbcbcacabaacddbcabdaddbaccadbabacddacdddcbbadbadccbadccdcdbbaaddccbabccdcadcdcccbdcadcadaaadcbccbabbcabdcdddacbabcbbbaaaabacbaadccccbccaddcbdabdacdbcdbccdddcadadccaacacbacdbacaaaccccddbdbdcdaacbbdbababddcdbbcdcbcbddbbdcdaaccbbddabcadabccccbcaaaadadbcbcbaccddadbdaaacbcbcbaabcbacadbabcddbdcbaccabcabadabbccacdadcbbdaaddcabbaccbcccabacdaaadcbabcadacadbcccdbdaacdbdabdbadbccdadcdbbbaadcbbdcbdabadacbadacbaccbbbaddcdbbdcdaddbbabacccdbbdcddcdbdddaacaadcbadaddcaaaacbbbdccccadbccacdcabdcadbccaaadbaddadccdadbddaacdccabbbbbdbcaccddcadcaabbbbccccbabdbcbcccccddbdadcbdabbbddbadaccdcbdbbcadbbdcaacabdcdccabcacbdabcaddcaadcbdacccbdddcacacbbaaaaccabccdcaacacccdacddbdbcdddcbbcbabaabdbacabdcadbbdbdabbbbdddcbdbbacbdacdcdabaadbbbbcbadaaaaaaaccaacaaaddadbbbcbcaaddbdddbcbdbaddabcccbcbbbbcaadbadcbcbacccdbcabcdbbbbbbbbaacbcadcccdcaaadbdbbaddccdacaaabbcccaaccbcadbbdcbcadbabdcbcbddbdadbdbcbcadacaddacdccdacdbbaadbbbdadabbccdbbabdbccccccabaddadddbcbabaadbadbbbadbadbdcccababdcbcbcbbdaaacdbadbabbccdbbabbadcbadbcdcadccddcaddbbadbbadabaaaaacdaaabccaabbadaadbbdabdabdadcdccbbaababaccaacaddccadcbccacaccabdadbccaccbbccaddcbcdbbbaddcaacaddddccbcbdbddaadbdabcdcbdaaaabdabdddabcacdacddaaadcdadabadbcacbbabcdbbadcdabddbbadaaabdacccdbaabbccdbbbbddcacdaacabcdcdbabadaacbacadaadabbbcbbdaccddbcadadbcbbddcaaadabadacadcbbcbbcbbbcbaddacabbdbcacbbcbabbddbacdadaaccbbaabcbbcbacadcbbcbaccdbddddbbbcdabadaaabcdabccaacaddcbcbcdbabdbbacacbbddccabbdbaacbadbddddddcddbccbdddbdbbacabcddccddbcdadbbddcdccbbacadabbaadccddcabdacbabbaadbcdddcbaadcbadcbdcdbdcdcbbcacbadadaabbddaaabaaabadbbdbbbcddadbcabadccbbbaabadbbdbacbbdadcdddadccabbdbcdcccacadddddcadbbdbacbacbdbabdcaababbbabcabdabdcbbddcabcaacadcdcdbdadacaacbadcaabaccaacdaaacbdcbbccbcdccadbdccdbabacdddccbcbbcbadbbbaacabadcabaadcacbabcdababdbdcbcddbaccbbccccbdbddadbddccaddcccabbaacbddddcddbbbcddddbcbddcdbdbadcaaccddbcccbdbdccccdadccacbcbdcadcbbcccadbccaacaddabbadcaacbdcbbdccbdadaddcaccbbbacdbbbcabdccaabbbdaaaccaaaabbdabdcacaadcbcacbbaddddcbababadaabdbccbadddddacdddbbcdbccdadcadbcdaaddbbcaaddabadbddcdacdcbcccadabbbacdbbcbcacabbaacdbbdaccbdbccbdacbadcdbaccdddbdbcaaabacbcaacdcdaddcbdacabcdccbcbacccddaabbadcdccaaaccdddccbaacbbdabaacdddbcadacdaacacbabbcadbdaacbabbacaccdcaaddbccdabdacbbcdcbaadcdccdcdabadddadaddbbcaadaabcccbccaaaacababcbacbccccbacdcbdccddadabbcddbabccdddbdcaaccbccbdcaddcbbbbbabdcbcddacddcbccbbbbabccaacdcdcaacbddbadacbcdadaccdabadbaccdccdabcadbabccdcdabddaacbddcdabaaddcabbdaccbcaaaabcacbcbbccdccbdbcadcbbaccaadcacccabdbcdababadbbcaaaaddcacbcaabcdcadcbdbbddbbcacbadaadabdabbbddcbbdadaddbbbdcaadbadadabcbcdcbbcaacbdbbcbbddbccddcbbbabdddbdbdcdcbdcbaabbaadcbdccccbdbccdddaacbccbdbbbbcbbaabbabbdccbaadaddbacacadbadacccccdcddcddbddaaddacaddbdbdbabacbddddaabaababcbdbdacbbaddaabbccbacbcdccbacbabbcadadcdabcdcbcbdabbbbdaaabacacaabdbbaabddaddaddbcadacdacdacbbbccdddcdddcdaacdbadbacbbbabbbccbcaabbbbdbbbabdbcdccdabbccacdaacdbdcbddadcdbdbcbaadaccbcacdabbcdcbacacbcbcadcdbcaddbccdcadaadaddaddadcaacdbcddadcccbaccddcacbabaddaadadccaadbdacabcbaaabadcaacccdbbabccdabcccccddaaddadcabacbdadddbacdaaadababaddddabaaddbcbabdaacbabdaabdacacabadbbaccdbcdcdcaacadcaaccdcbcdcdddbabcaacbbccbbbdcbcdbabadbcdcdbddbbdbaaabdaaacaccccbddbacccabadacddacdcacdcbadbaaadddddcbbaacacdaabcabaccbdcbcacbdabbcbbdbaabcaabcbbadacadbdabddabddcdddbadcaacbaadcdbbdbcbbdaabbbbdabccacdbdcaccdcbbacabddcaddaabbcaaadddcdacdcabbaddcaaccddacbdadbdbaacadddaaddaaabbadaccbcabcddcccdcababbbddbcabdccbabaacddacbaddbdcddbabababacdbbacbdbdabaaaabbccbadbbdabddaadcacdacabcdcaabdabccbdacbabcddccdddaddddbacabcdddacadbbdcdddbcdacadbbabdadadbbbababccdadcbbdcacbacdaaacbbdbacbadabacbccabbbbdcadabcbbbcbaabccdcddccdcbdbaaacbcaccbbdccbacddaddcaabdcccbbbacdcbabbcddcaddabbdcadadbbacbccaaccaabcabbdcbdabadbbcbaaccdabbdcbbdadbababbdcadaccdcdaccdbbcdbbcbbadacaabdcaabdbdbbbbcacabaadacaaaaddcbdccccdabbcadabadaaddcaabbbbacaddddaaacdddddababdabacacdbcdbcdccbbbabaacbdaacabacccadccccdadcbbdddcbacadcdadcdccdabcbcbbcbbdcbbbbddcadadbdadbbabadddcdbdbbabacbadbcdcddcbcadbdbdcaaddbbbddbcdcbaddaaacbbcadcbdacddbdbadaacaacdbbbbdcaadcddbbddcccbcaabcaaccacdddcdbcdbbbbdbaacccbdaadbacacdadcabbbdcbcddcbbacadacabddcdbdacbdcddaaaddbcbbabbddabaabcadaaaadadbcdbddbabdbaccddcaddcbcbabbddccabbcdccddbcbbadaabbbdacbcadadcacacabdaaddaccccaddaabddbdddcadababadacaaacaacaacaacbbddbbcadbbccbaccacacbdbbbbdbbacabcaddbbadcaaccddccdcdcaacbbddddbcbacccdabababdcbabbbcbabbbaabaaddddcbdddbbbbacadbbccbaadadcabacadaaadacbccdabdcdbbabbbdabbbcbabcbcddcbcaaadcbccdaaaaabdadbacbcddaadddadcdcdddcaacdcdccacdcdbaadbccabbdaaadbbbbcacddbcddbbcaacddababcbcbcbbadbaddcdcadcddcdbabcadabaccddcbcaccaddadbabdddacacdbddbadcbdacabbcdcbdcabdbcbaadddadcddcbdcaadcddbaccdacacbdcddabbdacadcbdbbabdbcdcadaccddcdacbdcddcccddbbaabbcaabdbabdacbabbaaabccccacbccdddaacabacbbadbcacbacbbaacbbadabadacdbcaccbacbcadadcadddbcccbdaadaccdddcdccabbbbbabbdcdcbaaabccdcbdccaacccaccaddcadddbdbbcccbdaaaabcabaaaadaaaabcdcacbbaadbadaabdbcbadbdbdbadacabaadbaccadabdccdbbbccacacbcabbacbcadcdbbdacabdcbddbcbbccdbdabdddbdcddbacacccccbacccabdacdacdacadbaddaaddaacadbdbdacbdbdacbccccabbaabbdcbaabddaccbdcddbababcababacdbcbadabbacaabbadcbdbccdcddcccaaacbdaabdbbabdaadbadbdbabdabbcaacaaccbcdadadcaaaddbdaacbadbcccdadabbbdcbbcacacdaacbbcbbadacacbdccddabdccaacdcdcbaaddcdabddbcbbbdaccddacccddcddadbadbcabccbbcdbadcacaccdbbddcbdbdbaacbababcdbbdcabdcadbaaddddadacdacdbabddbdcdbbccaadcabdadabbddbdbcdcdacaddaddbbadabbcbbddaadabcdadbcbdabddcbaaddcdbaabacbcaddcabcddddddccbddcbabaddacaadacbbccaacabaabccbcddcdabbbbadccacbcadbacdbdaacbdabbbddddbccabbbcbcbdbbccbbcdbcacbbcdcdcaaabcbdadaccccbbcccbadccbbbbadbcaddbdddaaccdbcddbabcddbbdcbcdddcbbccddcbdaaddcaddcbcadaddbddacabcdbdadcddbddaadaaacdccccabccbbaacbcacaaadadbaabacdacacabbdaabbbccbcbcbdccdcacbdacaddcbccdcccdcccbbccbbdcabddabccdcaccababcabddcbbbbaadcbdabaadacdabcabcbbccdaccacadaaacccacaacbcabbbbbdccaaacdbbdbdaacadaaababadcddbdddabdacddbadccbcdbcacdbcddbacdbccdabdcbdadcddbdaaddcddbdbaccbcdcdbadaabbdbbbddccdccbcaaaccbcbdcbbcccdbddcccdbdcbdaabaabdbbbabaaaddcbbdaacccdabbbabbacdbcaadaacccaadddcdaaddddbadadbdaccabccdcbbadddbbabdbdcdabbbaaaacbccacabacdbaacbbbdcdacdaadbddabdcbbccaddcbccbabbaacadbbcdabbacbdbcbaabbcbaabbadbadbacbabaaadbbacbccdadadcadcbdbbcddbdacabaadaadaadcacbbbacdbdcccbbccdbccbcadcdaabbbcbccbcbabcbbccbaababaddbcbadbbcacaddbcdabdcdbddcdcbbcdddccddcbcbcabdbbbdccdaabacabbbbadaaacbcbcbbadcababbcdddabccdbdbbcadbabcbcdddcadaccddbbdcbcdbdacccbccadbdcacaccdddaccddabadbcbcadaadaccdcbbaddcbbdccdacaddacacddabccbcacbadadabdcccdacadcccbcdadcdaccccabccbdacbabbddadccabbccabbbbcdccbbcccbcddbdacabaaaacdbcbbadbbddddcdbadaadcbadbbccdddaabacabaccdbdaaaacbcbabbdbddaccabdcdbcbababcdcdacabddcdabcdabdbcaddabaabbcddaadadabcdaababccbdcbcacccbcaaccaacdbabcbbaadddbbacbcdbcabcabcbaacaabddaabacdbbdaaddacdbdcbcbadabadcbacaddbcbbabaacbbacbdcdaacbdadcdaacadbbabdbcccbdbadacbbccddcadacabdbcdbdacdbcdbdbdcbdbcdbabaaacbcdcabaccccaaadcabdcbccbcabccabcbbddccbdccbdbcbbdbbbcaaaaddcadcccaaabbbaddddaaaddaadcbaabdcdbccadbccdaadadaacbbdcabcdcbabdbaccaaccbcbadacbccabaacbccadbacdacdbabddcdbcddcadbbaccaaabccdbbdddbabcdabdccdbddacadbccbabbabacdcbcbbccacddcacdbdbcbadbddaababacabaadaddcddcccaabbacacabddaacdddaaaddcbabdabbadbcbcddcbcddabbaccccbbcbbbcaadcabccdbdcbbaabbdbabccabadddadcdcaabbbacabaddcbbabdddbcdabbdbaddcdabbdcbccbcaacdcdaaddadbabacdadcbbcbaaaddcabacbbaabddaacbdabaddcabcacdcaaadcdacadbaccbbaadaddddbbbdddbdcbddcccaacaaddcdbdccbdcbaccaccddcdadccddddbacdbdaacbccdcccadccccbbdbadaacdccdbbcbccbcdadcdbbabdbaccbaababcdacabdbadccbcbbcbcbdcdabbdccacdcacbabcbcbcdddbcaacbbdbbbaacbcccaddcbabccbabdbadddddbaadcadabdaadbcddccdccaaaccbdaacbabcdcbbaabbbccbaabddccbacabacaacdcacbbdbaacbbdddcadbdbaabcdccadaadcaddbadbcababcdcdccbcbdbbcaddcbacadadddaacadcdadddbbcacaaadcbaacbabcabcaccddcdbcdabddcdbcacbdddacbcdadbdbbaccbddddbbdadddbabbbbddcabadccbbdccbbcdcaabadaddccdabdadadbbcdbabcabbadbddddddcdabadbbcdaadaadaacbdaabcaabbcdbadcbccdacdcadcadcbacabacbccdbabcccadaadaccdbddbabdcbcaaacaaabbbbdbbadcbccdabdcbdabdcbdabcbbcccbcddcdbcbcaaacaabbbdcbbdbcdbddbdccaddccbdadaccdabccadcbbcbbdbdbabddcadbccdcbddddbaabccbddbbcbddddccaadaacbaabcdcadadcbddbaabbbbbcbddddcadbdaadbdbaacaabdbbbcbddbaabdbbbdbddabddabacccdccbacacadabdabaccdbabbaabacbdbbccbaccababdbaaabadaabbcdbbdbadbbddbacdabcaacdbbcdcbcddadccbdabccccbbdbabcccbcdcbddcbbdbcdbbaadbcbccbcdbbbcbaabdcbaadbacdbadccaaadabdbcbaabdbabbbabdcdddcdcdcbbdaabbdcccbaaadcbaadcdbbbbadbaddcbbdddbcbbccbabdaacbddadbdcbdddccabadcbabddcdabccccddcabcbabdcacdabadacdcabdbbcdcabaaacbdbdcabdaadcdcacdbdbbcddabddcdcdbcaaaacaabddcccaddabadcdbbbcbdbacacdbaaccbbddadccdbdcbbadabacaccdcccacadbadccbdcdaaaadbacdbcddcaacdcbbaaddcdddbacbccdbbcdbbabdcababaacddaaddcbdaddabddaccbabdacadaacbdbbadddaadbbbccdaabacaaccacbbbbdcbdaaadacbbacdbdcbbccdbdbabddaabacdbdbcbbccaabcbdcbddbaccccdacabcdccbccbbabddaaabbaaadabdaddcbaadbbbbdcaddaadccccababadabcacabadcaddbbcbadddccabacbcabddbcdcbbcbabdabccabcdacbbbccdcaaadccccaadcdbadadddccbaabcdcddbbdcaabbbbbcbcdacbbdacbadabbbacaabdbcaaabaaccbbdccbbcddbccbbadadcadddacbdcbcacaabdcacbabbccdcddbbdbbababdbabdbdcccadddaccbdcdacaabdddabbdbbadadcccadbbdadcacdcbabdbdbdaabccadcdcaddcdaddbddbadcbdacdddaacbaacccddabddabdcccbdddacacddbaddcabccabdacbdaaaacbcaabcbcacadaccabdbbcbbadaaabccabbbdddccccadadccbbdbdcddaddbbcaadbbcacccacccdacacbdbdcaaccdbcbccdaddbacbbacaacdbdccacddbbaadaaccbdddaabbbccddbacdbbacbccdacabcbabadabdccbbbddacabccacdcddbdcbccccccdcabadacddbababcdaadcdbcdddaaadccbaabcdccdbbddbcdaaadbbbdbadaacbaabdcabbabdbbddccaaccaabddddcabcdadcaddcbccaaccadcddadaaccacdbbdbbacadbbdcbcbcddcbcaadaaabdbcabcdcbdacadcbacabacaaabdbbdbdadbaccdbbbbaabcccdbddacbbcbbadaddaacadaaddbcbbdacbbaabaabbcdbadbadcacbacaddbadbaabdddaacacacaaabbbbaaccdcbcccabcdaabdabbdbddbbbaddccdbbdcbdbacbbaacbddcbbbabcadabccddbcdcccbabadbbbdbcddaadcdadbdadbccddbdadaabaddadaabbdabcbdcabddbcabadbbcccbaacddcabdbcadaccbadaadbcbbaacbaacddacbcbcddacdbadacddaddbcbcbddcaadcadabcdcddadacadbcadcddcdcbdcbbbadaaaaacdcacbbbabaabacdddccbbbbadbbdbadbdbacaaacdcbbdccccdaaacdaddcaccaacbaaadbcbaddaddacccbabcddaddaccaaabdabbcbbbababdabaaddacaacdbddadaddabdcbabaddaccccbbbdddbdbbbdcdbdbcbcdcaaabadabaaaadadbbdaaadaadbbbdcacbbbdcdbcbaaabdcdbbdaadacaddcadadddabccbbbabcddcbcdcdacadccdddcbbacdabcacbdcbbcdbdddbdacacaacbabacadabccccdcaccdccacadadcbdcbbdcddcbaacadaacccdccdacbadcadccbcdababbccbadbaadabbbdbcbddcdcccaddadcbdababbaacddbdbcbbaddcbbccdabaaabcaaabcaabadbaccdcaadcdabdcdddcaadbcdacbdabccdcaabcaaaccacbbdaabacbddbbcccbdbdcabbcabcddcadcacbcbcbddbcccbcdadbdadbcdccbbcbaaadbaaacdaccdbbdddabacdadacbdbabdcacabccacaababaaddabdbddcbcaccbaacbdcbdbacbbdcbdcbbaaabcacaacdcaadaddcbbcacabcaddacadddddcbdccaababbcadacdbcbdbdccccaacadbabbbcbccabadcaadbdacbcbbabaaccbcbccabdbddbbadcaacdbacdbdbaddbbbbbdcadbdaabbddaabadcccbadcbbcbadbccadcdbddccabaadaddaadacccaaccbdbdbbbbbacbdaaaaaacbcccbdcbbdcbbcdacdadcbccbdbdacbddaccbdccdacaddadbabbadbacdaacaaacbaadbacaaccbcaaaccbdbbadcdbaacaabababcccbccbbcbcddcbccdabbaccbaccabbbddddbccaacccabaaaccabcbbabcbbcbbbadcdbbaacbbccdbbbdccddaababdacabbdccbaadbbdbdbbcdaddbacacaaddcadaaadadccbcdadaacdbdcdddbcccacbbcdbacdddbdbcbbdcacbcbcbbadccbccdaacbcdaccbaddabcbbbdbbaacdaaabaabddcadabbaabadadccadcaccdccadcddddddcdaacdbababadacdbbdcdabcbdacacaddabaabbbaacbbcccabbadcdddacbdbabbcacbabaadcbbabaabcadcbacbbccbbadaadcbabbcddbbadbcdddacbbadbdcbdadcdabddadbdabcccacadadababbbddcabcddcbbdaabcabccaabcbdbddabacbcdcccdcdbacdabcbaabbcbaddbabcccddabdbddbbabacddcdddacccdacbadcbccacbdaabcdbbabdabadcbabcddcddabddbccadcabbbcadabaaccaaadbcbaadcbccdddabaaacadbcdbbdbacddddaaaccddbaababdccdcbbcdcbacdbbcccbdcbbbaadababccacaaacaababbcddbacadcbaddabdbdcdabdadcacdcdbcaaabbbcbdbacbdbccccadadcdbccdaccdddadcdacabcabdaddcaaaaddcddbccdadcdbaddcbccdcbdcbcdcbcbbadcdabaddacdadacacbdccccaccbcddbdddaddccbcdddbdddaaabcdadaaacacdbcbaccbcdcabdcaaabaccadadacabdbccddaadddcbaadaddbccdadadcabcacddaaaabaacdcbaccbabaadbddbdddcaddbdadacbccdabadcddacdddabdbacbadacdbcdddcddacacbcbbabccbdcadadbbaccbdbbcbcbcdadbaddbbcdaaabaabdddccdbcccdcccaaacdaacdcbcdabadddcdacdaacaaadabcddaccacadacdbbcdbadbbdccabbcadbabcbccbdccbbbaabacdbbbbcbaabcdcccbadabbbaccccbcbcbaacbdbccbcadadcdadbdabdabbaaddcdcaaacdcdbbadcaddacabbaabcaabdbbabacbbdaacbbbdcadccacbbcdbbaabbabdddabddbaaaadcbcdbcbbaddcbdcbdbdbcbbccdbbbbdbdbcabaadcddcbddbbabbabbbccbadbaaaaccddbaccbcdacacbdabacccccdcdacadaacbcaaddcabbbaccadbdacddcbdbbcdccdabbcdbbbbcacadabdbbbcdbbababaabbbcaadddddcccacbccbaabacaabbbabbdadaaaaddaccddcaabdadcdacccdddbbabadabcddacbddcdcdddddbbddbabdaacbddddbccccdcdadbabdcaccaadacbaacccbddcccbcdccbbdcddcdadaadcbaabbbbacccabcbdcbcddabddacdbddadbdddcaaadaaaddabaacdbcadadacbbdccddccbbbbddaaabcaabdbbbaddcccacddddbdddbbdaabdbcbbcbadccbcdccdbcdcdbbbdacdaccbccbddacbdabbcadadacaddaadcdccbaabaabccddacacdccdcbbbadbcaadcbcddcacbaabcabcdacddaacddadccccdbccdccacbcacddbcbaddcaabadadacbdcdabddabdbdbddcbddbacbabbcadbbadacbaccdaaabddaaacabbaabccbcabababbdabadccabcbacbddcbdacbaddcbabcacddadbdddbaabccbbcdbadcbcaddababdcdccaaaddcdddccbadbdbcdaababaadbcabaaadbdddbdbaadacbbdcbdbcccdcaccbccdcacbcdadbaacccccdaadbaaadcaddcbcaddbadbdcabcbbdcbcbbacbdbbbadbacbbdcdbdcaadccaadabdddcddabdcbccddcbdcaadababaaaaababaabbabbbcaadbddbddbbdadccacbacadbbbabbacccaaabdbdacbbababcddabdbcdadaacacaaaacadaaccdcccacbbbbbabbabddcaddccacbdcbcbdacdcbbacdaacaccabbcbcacaaabadadbddccdddbbbbaaacadbbaaacabccdbcabcbdabcbbcbabddaabbcdbdabadddbaaddaddbbdadbadbbaabbcbcabdbcccbacbdcacbabcbbcbdacdcdddabcadadaacbdcaaacaadbccacccdaadcacaaacadcbacadccaaaabbdaaddaabbcdddcbbcbccdcbaccbabdaaabbbcddabbdccdbadddbbdcccccbbbdcccabdbbbabcbbacacdddddaccadabaaccadccbbaadacdaabdcbbdbcbacccabaddaccaacaaddcddccadabcdccaddacbdcdbbbccbbcdbcaaacacbdcbddbdccaacbaabadcbbacbdbddbacbcdabbbddcabcdaabcccbbaacccacacadabcdccaaddddaddcaddbbaaabdcdbddabbacdcaccdadacddccbbaadbddaaabadbcaddddaadababddcccdbdcaaccccddacbdabcadcacdbbbdaddaabdadbadaaddbdddcdbdbdbadacabcddacbacddbacdbbaddccabadcaddaaaadcccbabaddbabbcbaddbbdbbcbbaabdaacdaadccaaabbdbdcbdabbdabcddcacbdacabccdbdcaccadbccaaacddbadaddacdacddbddbcaabbddbcaabadcabaaddcddaacbdadcddddadaabccbcacdbcbccddcdddadabadaddccbdaabbcacbcdaccaddcbdccbdddbdcacaaaaacccbaadcdabcbaddcddadadcdaabccbadaaccdddadbcdaaadbcbdcbcbddaaccbdccabbcddbdabcbdcbacabdddaabbbbaddbbdbdcabbcbccbdaccacccbaccdadcdcbcabbcabcddaacdacadcdcbbcdccbcbbbcaacddaacacccdbcacbbddbdabdacdcbbbbcddcaabbdbcbacbdcbadcbcbaadbcabbacdaadabccdccccbcccddccdddcbacdadcdaabdcabbbddcabadcdabacbbbacdddbbabbbabcdbdbbddcaadabddccabbddaccaaabbdaaccdddbbddadaaddadbbaabcccdbbdbbdcbddcbaddabaaababdbaabdbddabdacdabbadacbabcdbbdcdacbdbcbdcaabdbcdbcdbbcdbaccdbcadabababdcaaddbaddddcaaddbdcccdccdabddabcabdcbbacddbdcabdbbddcbcdabcddcddbcaaccbcbbadacbdabbaaaccdacbcbccbdbcaaddbaadcbaadadbbbcccdcdcddbaddaaacaaabcadaccddbcdbdaacaacacddcdcdbabdaaadaaaddbaaaadadbcbdcbdbbdcbbbbbcbbddbcccaacbddbaadcabbbcaacdabdbcdbcabbbbddbccbcbdddbcabbccacddbbbbbdbcaacbcbcaacbccacdcdcdbbbccaabadcaaaddbcaadbdcbaaacaadbbcbacacbaacaccbbccbcbadaabadacddcdabddabddcbbadbdcccbaadcdadcdaddcbaacabdbaddbcabcbbdaabcaaddddcdcabccabdacdcdbabbdcddbbcbabbdcccdadbbaaacabdaadcbcbabadaccdbddbcccadcbbccddbbccabbacaccdabdbcdaddabadcbcccdccbadbacdbddbadcbbcbdbcaaaccaadbdbbcbabbbdadbdaddccaaabadaaadababcaccbaccababdbdaccdaadbbbadccbcadabcacdddababbbdccbdccbaaacddadaacbdbddaccaccacdbaadbdadbbdbcbccadcbbbbbdbdacccacabacaacccdcddadcacddcccdcbcdababdadaddbccbbbcbdbacbcadbaccbbaccccadcaacdaabaaadcbadddddbcadcdabcbadcabbdddcbbcabdbadccdaaccddcbccddbdaccacabcddcabbacbbccbabcbdabcaabccaabbadaabdbaacdbbbcacadcaadbabdbbbbcabccadaabaadbcdcabcbbcccadddbcddbddbbadcccdbaadcbbacbbbaadbdabdcaaadbacbccdbbccbabdddcabdacbacccbacbcbbaacaccdddabdcbbbcdbcdbcccdcbbabcccdaccccaaaabbdaadddacbaaccbddccadaddcbbadacbbdaaccacabdabbadddbbcddabcbdbccbbdbbaddaacbdacdaacabddbbcddabbbdcdbdcbacadcdcddadddcbddabdcbcdbbacbbdcdcbdbbabcaddccaddcbdccccadadaccbadcdbddadcbbabdbbccaaaccddcbdbddbdbcbccbdddbdddcdacacbbdddadcaaabcbdabccccaadcbaaadacadaddbcbbdaccacdddccdaacdaacadbcbddbacdcaaaddcdcdadcaccdddddbddcadbcacaadbbadcbaccdccdacbabcbadcdaaacdcaababdcbbbaaabcccdbcddbdadadabdaaaccadbcacdadcdccabaccbbddadcaabcdccdcbcddadabdbcaddbbaaacbbdcdddabbaccbbabdcdbddbcbaababddbcbabbdbccbbbdcadabcdcaaabbacabccacbcbccdbbdccdbaddadbaddbadcddbadccbadabddddbcdcacccabdbdbdbbbcbcacdcccbaabaccdacbdbccabdbddaaabbabdddddccbaacaaaadaabacdbdbcdddcdababacdaababcbbbccdbaccadababbaddcccddbcabbbccddabacccadbbcbdaadcadbdbcadbcbcadbbbcdabbccaacaaacddbddacaccccbbadddbcbaccaabdacdabdbdabcabdccdbbadddadbccccacbbbaaaadddccadbabdaaddbcbacbcccaabcbcddcccbbcbdddddcbddcddbccdaacddacdabcadbdbcacdaccaabdacdadcacadbbdddbadbbbcbbdaccbdbbaaacacddaabbbbdcbbcdbdcadbabccacbbaddbadabbcdddccbdcaacddbcbabaddddbccdcbbdcadaacadcbbcbcaddbbbbcbdadcccbdbabcbacacbddaddcccdaccbccdadacccbadacabbbdbddcadbcccdbdccacddbabaabadcdaaddbcdbddddaaabbcdaddbbbdddadbcccdbbdbdadcabdccacccbcbcacbcbdbbacbdddaccacaaabababcdabadadcaabbaacbcdccabbaaacddacaabdbcdbbaccbcdbdaddabadabdaccccdcdbddbcdadcadcabcdabaabaccbaabbadacacaadadacbbaadcddcdbbcabccbcacbbcacccbccbcddbdcbdaadacacccbcabdcacaabcaadabbcdcabcddcccdacdabcacdbababaabcaddcddabbcaadbccdcccbbbcddcaadcbbbdabbbbdaacdbacdbcccdaaaddcbbbcbddcdcdcbcacadcdbadcaccbbaccbacaccdcdcdadbccbdcdacacdccbabccdacaccacbdacabadadbcacacabbadbcdcddcdbcbdccbdbadcbbcadcbbbcaabacabadddcaadcbccccbdcdacbbbaccbddcdaacbabbbbcacbdddacadabdaacadccccabdbcaabcdadbaacbaccabbcacabddcadbcccdcadbbaabdcdbadacccadcbdbccaaddaaacbbcaacbcbcdccdddcdbadbcbadbaaabdcacabbacadbcaaadbbdccccaadbaacacadadbbcdabacbcbdbcbdbadacdbacbbbbdacccaddabaddbdbddabcdbbdccddcdaadcccaaaaddadadacabbacbdbcbccacdbcdcacccadddcdaccaacbadbcadbcacaaaaaccaadccabddbcbcbaadcbaabbadbbaccddddccdbbbcacaaccddbbdbccddcadabddbdadddaacbdddaacabdcadbaaccaddbadcacbaccdcbadbabbbccdccadbcbdadbccdcaadcdcacbbccdacaadacadcccaddcddbcbbdadaaaadaddcbdbddacbcbbddadbbccaaccbcccbabdcbcbbbcbdabccccbbdcabbcccabcdbdadacdddaadcccbcdbabbdcbbddabdbddcbadabccacacccdaaabbdbdaadaaababbdadaacadcadaabbabababcabaaaccaccbccacbddccaaadadbdaddbbbdcccacccabbcabddcdcbcccabbcabbdccadcdaacddddaadbabdbaacaadbabcbbccccbbaababbbbddbccddbcbccbacabbabadacdcabbdddcdcbaabdddabddccdddacbadbcddddbcddbddbabcbbbdcacbbdaabdabaabbddacacaacabaadbacbbbdbcdacdbdbdccdcbadbaddbbabbbbaaccbcabddcbdbcaaabcaaabdddabcdbaddaabdddadbdbbdcbdddcaccccccaddaacaabbcbadccaabaddcbadbdcabccdbbabcdbadcbbaabcddacdccadbddcdbaadbbabaddcddbcadacdbcdcbbdadcacbabdbacacbbcbdbbccacbcaabdbcddcacdacbcacdbddbcdbcbbbbadacabdddbcabbbbabaccaaabdccbddccaccddcaaddaaaddacabddddbdccdaadaacbbcaaadcacbbccdbdcdaddcabdaabaacdbadaccbdaddcdcbabbcdccbcbccbdaacaccdabbaabbccadadccabddbbabaddcdbaacaacbcccdbcabbbcdccabbdbbaacccccbdddcbadacdbcaddadccbaacddacdbbaddddcbbacbdbccadadacbbabbdccdccbaacbcaccaadaacccbdbcababaabbadabbcabddbaaccaacacdcacbcbbcbadcbbcccadaacdcabbaadabababcdbbdccacbbdadcaabbccbbbbbadbbdaaabdcaadacbdbdbadccaddabbcabcbdcdcdabbdbadbbddbaabbbdccdabadbabcdcabdaaadbadacacdabdccbbccabdbdcbbcacacacabddccccccaccbdbacbcccdaacacacacddcdcbacbaccbabbdccbadcbdddadbcccdbbcadabbcbddadbcbcbcabddddabadadadbaccbaaddbcbddbadbbdcbbbddadcbabcabcbcabccbadcdbbbccdadbcaddbbcccddcacddbbaaaaccddbbdcddadcbdcbbaaddbcacccbaaabbcbcddbddacaaacbbcaacdbbbddadadbccabdacadabdcacddcbdadccdcbddbcabdcadcbdbcabbccacddabdbdacdbadcbbdcaddabaccdcacccddaccbacabdadaaccbaabaddacaacbabadcabbdddabbacbabcdcaaadcbddbacbbcdcdcbcbbabbbbccaabccccbbbcacabcdbdaaddbbadcbcbdcdbabbadabddddbdacdadbdadaabddbadddabbddbabccccccbdcdbcbcdaaaadcdcdbdbcccaccdbcababdabcccadababdcdbcbaacaddbacbbccbbabbbbbbcdaacacdabcbcddabddccacadbaaadccaccacabcadbbddcacdcbbbdacadddbadcabcaddbcdaababddbdbdabbadaabccdbbdcccbcbaccabadacabdcccbbbcbdbcaccddddaaaacbdcbdbaaaadaaaacdcdcdbdabdccbdcaacdbadbbaadddbdcddaadcacadadddbacaadcddbdbdabbbcbdcdccaadbabacbaacabadacbbcdbbaadacccaccdbacddabcaaadcbacbaabacdadaaacbcbbdadbdacacdbbabccdddddbbdbaadccdccbbbcababadbbbaadcddbccbcbbbddbcdcbaccaccbbdbdddccdccdddaacadcdbdbdccbbbddcbaaaababbbbaddbcdcddbabcbbdcadadcbccbacccababbbbbdaadadabdbaddabaddcbbaadacaadacdabddbbcdcbadbbdbccdcbbbabccccdabbbaaddcdbcadcaaaddaccaababdcbdcccaddadaccbbbdbbcaaaabccdcbdbcbdccdddbabbcadcccdaadbccdcacadbcabbddaacacacabcaddcbaaabcbdddcdcbbcddbdbacddddaadadcdbadbabdabaccdccbbbbcdbbcdaabcdcadcaabacbacbaaadcabddcbbcbabbbbaaabbcdcbaacbcaccbadaccddcdbddccbcacdcdcbadadbdabdcddaacdccabbaadcbacdbbdbdcdcbdbddbdccbdbadccdcacdaccabcabbccdadadbdddaaacdacadcbbcaaadccbcaaccbdcaaabccdbabccdaabacbdbcdbdcccaaddabbbaaaaddbdbbacdcdbcbbbbcbabaadacdddaadaddbddaaaccdbaabccadddbdadcdbcdaddcabdadbaacdbabadcbcadababacaccbcbdccbcbbdbdbabccadbaaccbabdaadcbbbaaabaaddccdddbdcddbbbacadbcbcbbaaccaadacbbbccbcddadadddccabdabbacadadcabcdcbbaadccbabbbdacbabbdbbacadcccdcabccacdababaccaabbcbbdaacbbbdaaabcbaaccbcbbcddcbbadadadaccccdaaadbccbabaaacccadabddaadadbdadcccbdbdcbabdcdabcbdbdabdaacccdbccbdbdcbaacdbbabddbdaabcbcbadccadbaaadcabbaddccaaccaaccbbccaabdbdcacbacbbbbdacddaccacbbcabbddbddddaadaabcadbcadbbaddcdccaabbaadbbabdcacdcdabbadbbbdbcadbbaabacdcbbdbcbbacbbbdcbbdbdbadcbabbcdcacdacaabaacadbddbaabaadcbdacddbbbabdcbadcdbddabbdacdbdbbacdabcbadcaccaaacccadabbbbbccdcbdddacdaaccbaccbacbdcddbbdbdbcaccdcbbaabddcbabdddbcabcacaababccdbdbabddbcdcccbbbcdcbabbbdaadcbddaaaccddddadaaacbcddbadbacbbccacdbccabdcadbaaccdbaccacdcabbdbddadccdddbaacddddaddaaaaadbadccaaaccdbbbadadaacabbbcdcccaacbcaaacddcacbdcbdcbdbbcbdccdbdaaaccbacbbbabbbdccacbcdbcaaadacbbdcabacabccacddcdbadcaabbdaccacadcbacddadbaaccadddadcbcbcbaacbababcabadbdaabaabcdbbaacccabbbccddccbcdaacdbddbddbbbbdcccdbcdbacdbdccabdbcdcabcaccdbdcaddcaadabadddcbdcdabdacbacabcacadcacbccbdaaacdbdddcadbbabbbbddacdddbdbbcddcdabbdadabcacbadcddabbadbbadaddddadcdbcdbdddbdcbcbbacdbdccaadcdaccdabcbbcbdcbbadddcccabcbcaccbcadcccdbaccaadabbbcbbccbdccbdbbdcccbcbaaddaddcbccadcddabacacbdbbadbdbdcadccccbbcbbdadabadbddabadbcacbbaaabbbbacaadbababccbabcbcddbcacdcdbbccdadbabbbbacaaacdddbbbcaadccabaddbccdcabccaadbcacdbcbbacdbabacbdacabbbdacaddccbaabcabdcccdcbccbccdbdbadbcaadacadcadbccaacbabcadadddadcbbbdbdadabaddcdbcadcadcdcadacbadbcdbbccdcccbccabcbbbacdbdbbdddcaabaddbbcbdaacdaacbdcabbcdabccababbdadbdcbcaabccbbbbbbacaaacdbdacababbcadcbdbccccabddaadcaddadcddbccbabcddbccdaaaadcaaccbbbcdacaadbccdcccacbdcbacdbbdcbddbbcbdcccbbacbadaccdacadccadddbaaccacdcaccdaddbbccbbbbadadbbdadaaddddccaababababacabaaddcdbccccccadabaaaddaaaaddbabcbcdbbdabbdddcddbccaaccadbaddccacacbbbbcdcdacaacaaccddccadddaaabdabcabbdabacdabcdadbbcdcbadcdccbadcdcbccddcbdbabbddbbdbddaabbaaabaaddbccbdbabcbdbbdabcabaacbcadaaabdbcbbaccacdcbbdcababbbcaacdbbdbdcbabbcddcadbcbbddbbbcddbdddacadacbcdcaabbacccbbbbacdbdddcbdacdbaaaccdcbdadbcccaabbdaadababbbddbdbbcabbacddcaacbcbabdaaabcdcdcccbccbbbabdcdbacadccabddcdddcbbdbcabadbcbccccdabadbadddaccbbdaabbcaaddcccbdadcbdddbbacadddaadbbadbacaccddcbdcbadbccaabcacdaddbccddcbbcadabaaabddcccdaccbaabbabdcaaddaadadbabbbadcdccbdcbdbbdcabdadddcaaccdcccccbaddadadbbdcadadaccdccadbabadbbdcbdbaccbcacdadcbcbddabacdccaccbdcacccadcbadbadcccaadacddbadcacadcacdbdccabbbbadbcabcddabbccccbadaadabbdaccdacbbcacbdcbcdccdbbaccbcbbdbcaddcaaabaaadabdbbccbaccbbddcabdddbbaaaddaadaaacacaccdccbbbcdcbabccbdbdbbdcbbbcadbaacdbbbddabacbdcddaacabcaacacbabbcddcccacbcaaddcbaabadbdaacddbaabbbccaacdacdbbadacdddaacaaaaaccbbbddadadbdbaacdbbbddbdabaccbcadddddbcccacbbcbacdcddbcacbdaabacaaabbaabbbcccaacccbbdcabaabbcacbdaabaadabdadabcaadcddacbbbcadcbadbadbcbaaaacdaaacadbccacdddcdabdcadbbdbddacbcaacbdbdccbcdcbdaadbadddbacbacaccddbbdccdacdacaabbacdcbbbcccaabdcddcdbcbbbdbadcddabdbacdbdcbbdccaabdcbbdbbbdabcdcdcbacadddaabdbddacacbcdacbddcbadcbdddcdacdbddacbabcaddadcbadbbadddcacacccbccdbbcbbddcbaacbabdbcbddbdcbbadcccbdacddcccabbbbbbdaadccdcacaaadcaaddaabbacadcacaadaabdbdacacddbacacbaacbbadccaddcdbabbdaabacdddccbabaadadccdbdacadddcbaadcbcabccaadccaaccddddacacdbdbcbdccaccacadadbaccabcdddadacbaababcdccbcdcdbdbaaaaddbdbcadbdbabdbaacdabdcccdbdaadacaaadcbbdcadadcddbdbaabccabddabaabdadbbbbddcbccadaddccaddadbbdcbcddadccababddaadbaddccdbbbbbdacbabdbdacaccdbabbbbdbdcaabbbdbbcacbbdcdbcbadacacbadadaccdbacdbbccadacdcccabbbccdbcbdbdbcabbabcadbaddccbcbabdbbdadccdbbcbccddbbcdacbcacdabbabccacbaadddbaacadcddadddbdcbbbdcbacbcbdddbccadbadbbacdbabbcddbbdbcddadcbcdcbbabbbacdcccadccbbdcabcbbadcdcdabdcbcababccbdcaaaabbadbbccdcacccacaabdcbdddccadbcbacbdcacbbacbcdaaacdacdcacbbddaadbdbacabbbbacbbcdcaabcabcdbddbabdaadcddccaaaabcdbddcabbcbdbbbdaacddbaaaabbddcaacccddbbcbccbacdcccccdaaabcccaddadccdbdaabacaccbbbcdcdacbabcbbdcacbcbcadcddaaddcbdaaacadbbbdbdacdccdddadbcaababbdbbadaadabcbcdcdcbdcdddaccdacabcbbdcdbaadbbcbbdabacdbbbbddcdcbbcdcabadbbaaadadadbccdcaababbdacadcdbcbacccbdbddbcccaaadcdddacdadacdbccaaacccdbcdadbababbccabbcbbbabaaaadaadbacabcbaacccbbcbcdaaadaadcbccddababbabdddaccbbaacdacbaccbbbaababcdbdabaaacacbbbadbadcbaaaadbcaccccabddbbadaddaacacbadabbaadccdddccacddcaaaabcdcbdbabaccdbcccbdcddcaabacdabbdbacacbcddbbcdadccdaacbcbaacadadbcacdacacacccddccccbcbcdacdbacbdbcacacdccccbcadbdadaadacdacaacccdddaadadaddadbdcbcbbddbdcbbbbaccbcdbaadbdcabdaddcabccabcbccbcbaababacddcdabcaddddcdbbbcccdcbdcabdabddcbbdabcaaaddadacaabbabaabbbbcbaadabaccbdbcdbdbdbbcbbcabacdaabdacadcccacddadcccaddccbbcabcabdddbdbcbdaadbaaaadbaababbcbbbbcddaacadbdaaaadaddcabcccaadbcccccdabccbdadbdcdcabcdddabcbbdbabdadbdcbdbdacacaadbadbaabacadaacdadccdbaadddbbcbaadbdaabcaccdcdbdbdbdddccbabdbcbbccaaddaadadacbbcbacbccdbdccbddddbacbcbaabdbcbcaaaabacabdbcabddcadccaabddcaadaabbbbacdabdcbaabcdaddbadbccddccabacadcbcadcaabcabdacbbccbbccdaddabadcbbdacbdaadbccdabddccbbbdacaddaccccbbadccabbaddacbccaccbbcbdcdacdadacddacabacbaaddccddbdcaddcdadbdcabcddcadcabacdcbbadcaabbbdbdbbcdbdabcdbcbbaabccadacaccdabddbaabbddbbacabbabbccaaacdddbacacdbbdcacbbddbcdcdcbdbadacdddadbcbddcdbbdccbbdadababbdbbacacabdbdadbaabbdcdccdbadcaacbdccadaaabbcdbbbcddbddcbdabadaaaddbcaabdbbdbbddaaabddacaddcaaddcdbddcadddcbadcdbbadbbdbbaccaabdddababccbbabcbdcdbabbdddaacaaadbcdbadcbbabbbcdcdbbddbbacddadaddcbddabbcdbadbbdbdcabccadadccabbccdadabdcdadbabdcbcccbdbcababdcbdbdcbacadbabdbddbccadbaabbdbabcacbbcababdababcdadaaddbbacdaddbdccadcbadacccdccddadbdcbbdddbaccccbabcdbcdcacabaababdcbbacbbccbcbcbcdbaadabbcacbdddaddcbadaadcaccaaaaaabcbacadbbdbdbaaaadcbcaccbbcbcbdbcddbcdadaababdaddcccaabbaabcaadbaacdbaccbdddaccdacbdbbabddddabddadacabcadcbbdadbcacccbcabaaadbacbbddcddcaabbaadaadabddacbdaaaadaacaaababacaaccccbdcdddaddaadbcddbcbbdaadcbabdbabcdbbbabcdcbdcbbacbcaddadcdcbadddacccabaadccbdaacaabcaacbdbccdbadccaaddcacaaddbcbddaccdcccaadbbadcaddcadbddabdccbbadacdccccdcdddbcddccadbbcdadabaadcdccdbdbacbdbabadcacbcabaaaabdadcdccdcbcbacabdcbacbabaaaacbbdbbdbbddadbdabadcdbdcaaabbdcdaacabcbcddddabaabdccdcdadabdbabaddbcdbbaabaccacaccbdccdcaaaaddddbbdbbdbbcdcaaadbaaddbdbbbacdcbbbabcdbcacbbddbccbdcbcccdbcadbcbbcbacbdbabbdccabdbbcdddbcdbcdadcddadcaddcdbdbcdccbaadaadcacaddcaacbbcdbcbacadaabbdadaacdbbdaddcbbddabbbbccbbcdabdabbcbaddcdcadacbadcacabdaaaaaaadbbbdcabdbabbbdbadccbaccbdccaacccccaacbdbddadcbbacccdacdcdaccddbbaccbdaaaabcdacdaadbccacdcdccbabadddbbaadbcbcbcacaadaacbdbaacbabcdbdbdaddcdadadcbbdcdcdabcbcadaddbcbadccbddbdcdabcbddbdbabdadaabbcdabcbbcaabdddcccdcadbcbadddadbababbbdaacddbcbcbcddadcddacdbaadcbdacbbabacaadbbcaabcacbaaccbcdbbccdbcdacdababcdcdccbbbddcdcbaacccabcacddbbdbadcacadbbddaabdbdbacabcbacdabbdcbacdbbdbbaccabccbccadabcadaaaacdcacbdddcdaddbdabadbbcbaaccacbbcadadbadaccabdaaccbdadaadccddadadaacbcbbbbcbabbddadbadbdbccadbbabcdcbdcdabcdbbabcdddbbacdaaabbababdaccabdadadadddcdcbaabadcdaaaacdbaadbcbaddbbbacbbbaaccbbbcabacaabadacddbbdcaddcdcbdddbbdabbcdbabbccbdadaadabddaadadabaaabddcbabccdcdaabaaabbddadddabadbadcdcbaabcabcccacbbdbadddbaaccccbcddbcdbddacaadabacabbcaccbcddccbaccabaacabadacbabdddbcdcdcbaddbddbdcdaacddcbaaadadcdaaaabcbddccdbadccdcbacdaaaabbddadbdbdaadbaaadcdddbddaadcdadbcbbdabcabdadddccdccbddacccdbaacccadccacddcdbcaaaabbcdcbcaacabcaacbabcacbdbdadcdcabbddbdacacccbbbadbdbcbbcccadadadcbaccbdbcbdbacccddddacccbbbcddbddbdbaaababcdccabcaabddadcabdcddbdaaaacaddcccaddbdbbdaccaabaaaaccdbacaacdcbaaaccdaddabaccaaadccabacbdadbccadbadcbdcdabacccdbabcdcbacdccdbabaaabdacbcbdaacadcdbdabdccddbcdbddabbbccbaccadabbadcbacadabdcaadcdcdbaccdaddddcbdacbbbbabcdacbaaccabadcdadcbcaaccacbdbddbadddcccdcdccbcdcadadadbbccdcabbddabcccaaaaddddcabdaccdaabddcacbbaccbbcaddcdcabacdadcddacaccbcdbcaabbadbdcacaabbdccaacabbaaddaaaaaabaacadcdaadababaaadaabcabcdadadccdbccdaaccbdcbbdacaabbbccbdccbcccbbcdbbdcbbddbcbaadcdadcbdccaccdbbabbbcacadabbdbbabccdabcccacbbcbdaacbbcabacdaadbaddcbcddbcadbcdccdbdaddccdcccbbaddbbabacadadbacdcccdbaadbbbbcddccacbcaaddcdabbdababdbbcbdcaddaadbaccbdbabdcadaacdacccdccdbbcbaacdddccdcccbbdcccdabcadbcadacbccadcacdcadddcaaaccbbdcadaadcadcaaccabaddacdccabccabcbbdabdbdccdccadccbddccbddbdbcbbcaccabadcababdcacacbcdaccdaddccbadbadaacdadcbacaabbbcbdacdabccdccbadabadddbcaccbdaaabacaacabcdabaabaddddccbdcdcabbdaaaaadaaacadadbadababcdcbdbbcbadbcaadcacabcbadcacdadbbaaaadbbcccdabcacabcdbdbadccabaacadbcdbaabbdddcbaacdacddaddacbbdcdbbacacdcacdcdccddacadbadacbcdabcabcbdaaacdbccddadadadcdaacacbccadbbaabbaacccaadadcccbcadaaacbbdddabcbbdcddbcdbdcbdbabcdaddcdbaadabcbcadcabbbdccaadbacccbdbacccdcbcaaddaaccbbaadacbacdbddbdadcacbdaaabcaadadcddaccabdcaabbdabcdbbdbaaddaddcaaaddcbcbcddbbdbabddccbdbddbcddaabdbbaaaccdbdbdbabacccbadddbacbbabccccaacaaddbaddbdcdacddbcbadbbacabdaaccaccbaabcdabbcbbabacbcddcbcbbacdacddbaabbcbcacdacddabccdcdbbbbdbbbdbbdddbcaccaaacbabacdbdcaabbbcdcddbcbdcaabccabdcdcbcdbdadacaabdcadcaccbbaadbccacdcbcadadababcadcdbcddbbbdbdcacaddbadacbbccbbcbcdbdadbcbcddbdcccdccabbdabbbbabadbaacccadcdaadbcddcbbaabcbbcbdcbddbcacbadddacacbabccacbbbbdcaabaccabccccbadabddcbacdcabbadcdcabdaddaacbbcbcdddbabaacddbabdcabbdcdacbaccdddadbddaddacaaccbacbadabdcbdbbbdbacbdabbcdcaddbaabdbaacaadcadcababadbacadacbaddadadbabcadbacbbccdcdbbcdddcdcbaddbcadddbdbbacdcaadcdddbcbccdbccbdabcdcdbbdddbcaacadcbbbcdcbdaaaacdaabcddacacdadaabbbdbcabcddcaacdbaaccbbaddbadaacbabadccdcbbabadadcacbcbcaabacabbccdbcaabcddadaaddcbdcbcdcabbbadcdaadcbcbcaaadcacaadcddbadbcaacdabacabdcabadbdbddabdcdcccadbbcadddcacbcdcdaacbabbdadacadbbabdbdcbbdadbbadcdaacbdcbccbabdbdabccbcdcdacbcccdbccbaaabcdbcdaadabaddcaccccbbdaacabcccadccabcdcbdcdcbabcbcacacaadcbbadbddcabaaaccdbdbabdbdbddbbdbaccaacbababdaaadcddcabdaaabddbdcbdcbcbbaccccabbacaabaaadbadccdddbccbddacbcdccbaacdbdcddcdddaadcdbddbbdcaabcacdbbadbadadabacbbcbacbdcbdacbbdabddccdccadbccbbbdcacbcbabdaccdadacbddcabbccaaacaabdcdcbbaddacbbacbbaaaacbbbacccaccaacbcacbdbbcccccbddcdbabcddddadacbdbcbadcbdabdcbacdbdacacacdadbddaccaaccbcabacbdbbcaaaaaccaacdddbbcadbacddaabbdcbcbddaacbcabadcbadbabaaaacdbddddacaddacdcdaaabaabacaaddabdcaadabdcabdbcdcabacaacadcdbccbdaaccabdccadbbaccacbcbcaadcbbcacacbdcbaacdacaadbccbaabbadccdadbcacddbcdccdaadbddbacbdbdccbacadddadabccbbdbcadbbbdadbadbdbdacdaccaaadaccaadaccbbddbccdbcdcddaacbcdcdbbbdaacbadabcbadbcddacabcadbddabdddaaaccdbbbabadaccdbabbbbdbbdbcaaabccabaabcddacccadcacaccdacaddbacbabdcbabdabdbabccacaaabacadabcbadbbbbbbadbabbddbdadabcdacbaddcaadacdaabbadabbacacaaabcbdaddadaccbbacbcdbdbdcddcaaadaaaacccabdcdadcdbbdbabbcaacdcbdcdacccbccddcbbadccdaabcddbadababdcaccccaaababaabdaabddaabdbdcaccabbadcdcaabdacacadcddacacdcaccddbacddabdcaabadcdadbbdbcbcdcdbadcdababbbdacccdccccdaabacabbaaabaacddcddaabbdbbacdddccacabdaacaccbccdbccddbbbadcdaccdcabbbacbcaabccdbbdabcdbaaadcadabcdcbdadddacbaacbacccdabcbaddbabcabcddadadaaaabdaadcddbbdcacdaddcbddaacbabdabbbacacddcadcacbacabbbadbbddacacadaadcbcdadbcdcbbcdbbaccbdccdbbcabaacccabaadccadcdbbbbcdabccbdaabbdaabcaacbabcaaaabccdcbaacaacdaabcaaccabcaaccadcababcbaaacbdcdcdcbccbaacdcdaadacbcbcdbdbcdababbccbccccdabbaaadbadcdbbbbcdcdcadbabdabadbbdbaddcbdababdcadbaaddbcdababcccdcdadcddadcabccbabbccccacbbdaabbddcbddadbabbcaccabcbaacdbdcdcdcdbdcbabbbacbdabcdcbcdadcdbddccaabbbbbbbbdccddbdbccadabbdcdbabbaacdaddcaaaadcddaadbcdabbaaaaabcacdbabacdbbdbbdbbbabacbacbcbaaabddaabdddaccaabaababbdaaccdddbacabdbccaaabddbabbddaaacddbabadabbcbdbcbacababdbdabbcdcdddacabdacaabdbcbbbdcbaacaadacdbbcbdcccaadcabddbcacdddbbbbaacaaaaabcdabdbdcacddadcddcdbcadcbdbbbdbaadcadacbbdaaacdbcadcbdadcdacdddcbadabdacbbbdccdadcabbcdbdccccaaaaacbccccbcddbcbbdcddbacddacadcbaaacbdadbaddbdabcaddbcaadbdbbbbbaabdbdbadbacdacaddcdcccdabccbccbcabcaddaabbccabdddaabbbabbadbabbbcbabcccabadcccdbdddccdbcaadcbbdacbbcadacccbccaacddbcdcccadddcccabcaacadadddbaadbcbbbdcbdcdbcdadcdccbaaddbdbacadabccacadcccdaaacabacccadabdcbbadddcabaccdabbcbcbadbdadcbadbdabbbbcdaaaaadbacdacdababdabbadbaadbaaacaadcbbcccdbcbbcdbbadbcabbdadbcbabbccddbdcaabcbcadacbdacccdacacbaacacccbcbbbbcdcbcdbacbbbccbdbccddbbbaacdccbdddaabaabaccddbccaabaabddbacabaddcbdcdcacdaccdcacdcdabacbbdacbbbabddbcccaddaaacbadbdcadabcbbacabdbbdcabddbcbdbdabadcccdbcabccbadcccbdbbcdcbddcaababbccbcdbccadadbcbdbabdccdaccdabacccaddbcbacdacccddcadcbdcaabdbabcbdadadcccdabccaabcccddcdacaccdbdbcccccbabccdacdcdbbcdddabcbdadccbaabbaaddccddbdbabdaacdcdcbdcbcdbbccadddbababacbbadccccacdbcdccbddbdccdcdcbdbbbabcaccacaaabbaacdcdcaacadcacdacbadcdcacadbbcdbbdbbdbcdddccdbcbcadbbbdbbaaabcddddccaabdaaacaacbbbdcdaddaddbccdadcbddbcacbccaddcdcbacaccabdcaadcdabbcbbdacdcbaddccdaabcacddccbccaadabdbdcdabaccbdbdbcbabdaadacaaaddcbabadbbcaccaadaacbbbbaabdddcbbabdacbaabcbbdadbcbaabbddadcbaaaacdcadadccaadaddacbdcabccddcbbabddbcdddccddbddcdccaabbccacabacabcabccbacbadcaabadddcdbadbcdccadbaaabdccbcacadadacaadcdbccbdacddbdcabccddbaadbcbadcbbbddbdccaaddadcbdaadcabaaabbdcabbadddbcbadaaacbacddabadbaccbdcbdcdbdcabbabcaacbbdcdbbcacddaddadcbabbccbaadddbacccdcbbaccbbadbbdcbdbcacaddbbaadcbadaddabbabacaabbdabcdadcbcadcbabdbdbacbbccacadadbbcbaacaacbcbddcbadcdbdaacbcdcaaabadccadcabcdbbbdabccbdabdadbdcacacaccdabbccccbbcabcadccbccddabbaddbddbbdcacdbbccdcddaadbacabaabdbdcbcccbaaabcdccbcddcabaaabcdcccbbbdddadddaaccbacaabdacaadabcddbabcbcadacdabacccadcdbcdabccddcdbddbaaaaaabaddddccbcdacbdddabadbcdabbbabaaaacaddcddacbcdbabcdcbdcabdbdbaccacbcbbcadadbabbaadabddccdbddbdbbadadcdbcbcdbcbadcbcaadbacabcbcbbadcdabcddbbbbacbccdabbbbcadcadaddabbcadadcbcbcdaabcdbababdcbaccbccabcbbdaaabccbcdcccadbbacbbacdbbadbcbabcadcbaddbbaadddacacbaabbcbbdcdbbacdbadacdbddcddcbdcddbcbdbdcabdbdbbbcacabcdcabddbbcaaabacacadacbaaabacbbcbacccdcbadbbccdccacccdaadaabdbcbdaaddcbbccbabcdddabbbacdaadbddbcccadaacaddbdadcbcbcbcdbaabaaabcaadadcbdbabadcddadababdbccacdcbbaccdaaacddbbacbddbaaacacdbaddcdabbcaadcabbdadabbcacbdaabbcccbbdcacaacaabbaccabcdadbddbabdddaadcaccacdbccadddcdcaacddcdbccaccdcbcccbbbdcccbccdbdaaacdbbdccdcbabddaabcbccbbabacccccbcdcdcadabadcacadbdbbcbaaccdbccabbdbdbcdcccabcddbdbccdcdaddbabaccdaacdbbaaaaaacbdbbcaaddbcccaababdadbbabbbadcddabddabdbcddbcdabbadadbabbbadabadddcdcbbbdacdbdaddadbdaaacdbbcccbdbccbbaaccadabaccdacaddcaabdcabbbbaccccaaadacaacccbdcddacadabdcbabdbddcdaabccacdccbcdbbcaabcbdcccddbcddacaadcdcdaddbcccbbbcabddabdbcddbbdbbdbdccabcdbbccdcacdbabbbcabaabbaabadcbcdddaadcddbcaaadddbbddcaacbadbbbbccbbadacbdbadbcdbccdcddabcdcacdcacdaddaadbdacdbcdbdddadbaadbbdbbcaadacccbcbcbbcabbabdcbcaccddbadaabbdacbdcbccdccccbbdbcdacbadaaaaaacddbaabaddaaddbdcacbdcbdbcbdacabdddcbccabbbdbbdddbcadadcabbcacacaacdabaadcaadadbbbabdcaacbbcabddaddbdbbdaabcaccbcddabadddbaabbbdcdbaddbcaddbaacdacbdbcacbccbbcbabbbbaaccacbacaadbcbddcbcadcccbbacdcadcbdcbbcbabdadadadbbdacaddabcdccabbdbbdcbcaaadacabcbbadbbccadccbddcddcaddaccdadacaddabcdcaacbcabcbaaadccadacbdbdadcdaccdbbbccbcaabdacaddaddbabddaadcdcdcabddcbaadcdbccdbadabcdaccbbbcdcbddcaddbacccdddadccababaddbbcbacacabcabaddaaabaabbbdcbddaadadadcaddddaadbcdbaaacaadbcbdcdbbacaaccaabbbdcbcccbdddbcaacaddbdababcdcaddabcdabaabaaccacbacacbabaccdaaacbccabadaccdaabacbcdccdadcdbcdbadaddaabaccddcbdbbcaabadbbdaddabadcadaadcbcadcbadabcabbabbbbcdacdccaaccabbaaddcbbbdddcbbcdabcaacbdcabcccbdddbdccdcbaccacdccacabccbbacdaccbadddbbadabbccabadbacbadcbacdddccccccbcddaddbddaccbaaccacdacaaaaaaadbcdddacbaabcacddbbadadcacddaaaacaacccdcaaccaddbaabcabbaadaddbbdaacccdadadcbdcbdbbccdccbbbadbadaccdccbdbcdcdaaccadbdbcadddbddcccccadaadbddccddbadbcddcbbcadbbcdcbaddbcabddbbcbcabdadcddcbdcdabaadacacabdcadacbbdbbaddbcdbdbbadbdbbbbbdbdcbbadcbdcbcadabccdabdabccbaddbdaadddadbbaadddacdbcbabccdabbaccccbcdddbabadabcdadbcbadacababbccbdbdbdbbcadabdbcbbdcacdbccbacabccbcbcabcdbdacdaacdcbbabccbdcdbcbdcbccaccdcccaababcacaaacbbbdbbcdccccabcdcbaacdadccbddbacdbbbbcdaabadcabacbaabdccbadddacbabcccababaaacbbabbddbbbddccabccbccbadcacaaabdcbaadbbccadcddbdbbbaddbccdcacacbbdccabdddaaddbcddaababbdcdcbddadcbcacacadaaccccdcccbdcbbbcbccddaccbbcbcbadccadaccdbddcbccbacccddabaadbaacbccdababbcbcaacbcdbdcccbcbddddccaddddbbdbccacacbddbaabadbaadbccadddccccddaacbacbcabaabbacabdacdccbddbbadbbcdcccdcaddabbdcbdcacadddbbbcdcbacdadbacabaaccdaddacbdcbbbbdbdcdbdbabbcdcaabadaacacbadcabccaaddcbcdbdbdbbddcbacddaabcbbcdcaadddbbcdacadbbbccacbdacacbcbcdccadabcccbbcbddddbdbdaadcbdaadaadadbcacbaabaaabcddbbdddcacccbaaadaddaadbcdcbbacadaddabccddaaccaddccdbbadaddcdcbdabcaadabdaddbdbdabbbcdcbdabcccccbbbdaacbaadaacbdcdbadcadcaabcdcbaabadabdbdbbdbdbdbabdaccbcaababdaaabddddadaccacdaddadbacbabaaddaabaacdbadabcbdcadccababddcdddbaccbdcdccbaaccadccccacbbaccccbbcbdbbcabbccababdabcabadccbbccddcaddcccdadbabdddccacaadcacdbaadccddaaaacaabbcddadbddbbbbdabbcabadbcdaaaabdcdabbcbcbbaabaabbadbccaaabadacbdacdcbccdadcdbbcdcbdcdaaabbbdaddccabbaaabcaabacacbbabbcacabbbababccbbdbcdcccbbabdcbcdaccbcdbccbbacddabdaaadabbbadcccbadaadccdacacbccccddabdbacabcaabadddccbbcdaccaaabbabcabcaadcbddddccbdddddbdabcabdbddaabbcbaaaacbdcabdcacdcabbbccbdddbbdddcdbdddbbaccdaadaabccdbddbbdacaadaaadddddacbadbcaaacbdcbaabbcbdbbcacdabbbddaaaabdbacbbdbbbaccacbdacacdccbadbacbccaccdcbabcdaccdccdbcdcbdcccccabdcacbdacbaabacadabaccddbbabdcbcdbddbcbcbccccdddbdcacddccaabadccaabdbbdbbcdaaaccdccaccaabccbdcdbdcdabbaadcbdaabddbabddddbbcbbacbaadabaddaaccdabccccbacaadcacdbaadbcccdcccdddabddadaabdcbaaabaacddbaadccdadbdabadccbabcbcdabcbdccdaabadaaccbbbabadbcdacdbaddacacdbbaaadaaddbdcbdadccbabdbbaabbadabddbccbccbcbddacaccabbbddadaabbbabaddcbdbccabcacbccbbbcdcbadadcadadccdabbdbdbddcacdcdabcbaccddbbdbcaabaacaddacbbcdacbbdddbcdcadcadaccbabbcaabcaccabcabcdcbcacccaaaabbddacbdcbbdabbbabcdcaccdbdaacbddadcbdaacbbdadadbbaacdbbdbccdadbdbcddbdbdabaddcaacddabbddddabdaabaabcbbabdcdaabdbbaacddaaccbccdbabdabbaaadcabcaadccbacbccdadacdbddcbccaabcacdbdddabbabcddbccaaccccdadadcabcadabbcdcddbcdddaaadbbdbdbdabdcbcdddaccccadabbbdabcbdccaaaccabcbdcdccacccbdcbabbccddbdccbdadcbcdccbbddabadadcbaacdabadacbbccbadccdcdddbccbabdcdabdaacddacdcbbcdcacbbcdacdadcbccbabdbdddbdbcaadbcaabcabccdaccbcaaccdbcabdacbacbabdabccdbccaddcbacbadddccaaccacdbcacbbbcaaaadddccbbdacaddcdadbaababdbbdabcbbdadcbcbdcddbaddddacdacdacadcbbbdddccdcbbbcbbdcdbdabaaacadaabadababddddabbacddbdbbdbabbdbaabacadddbbcabcdcccdadcbcaacbdcabdacbdddbbcbcadbbabbdabaaddbcabbbbdadacbbdbbcddbddcabbdcacacaabbccbcdbbaacbadaabdacbacbbcdbccdaaddaaddbbaadabbadaacbdbaacbaaadcaaccdcccdcabadbabdcbbaabcdbcadbabddaccbdcaccbcbdbdaaabcbabdbdbcdaddbcddcbcbabbcddbbcabdcdabaccbdadbaaaadbddbbdccddcdbbcacacdcbcdabbacadbabbaddcccdcdcaacbddccbdbcccddcccbabbdcccdbdadbcdcadcbcddcdadcddddcdbadddbaadcdbabadcaadcbaabadddabadbacbdbcbcbacdcbddaaddbdcccdddaaccacbcaccbccddaadadcbadbbaadadcbdaddbbccdbdddcdacdbddcddbacadbcddddcdccbbaadbdadccaaccdcabddadcacdaddbcbbdcbcaaccbbcbccabbabcabdcddccbcdbaddddcddadccabbbcdabcbdadbadaccbbcdcdbdcaadbddddbaaabbbcdcdbaccdbacdacddabaccdcabcbdaaadccccdadbbcabdccccdccabbbcaacddaababbbadcadcdbacaddccddcdcadbaddadcbaccbcbddacddbcbbadcdbdadbbcbccddccdcbbacdcbbbdcdbdcabacbacdaccbaadbdbaaababcccdadbabadaacbddaaadaddddbccaadccadadbbbdbadabdcbddbbacabcbcbdaacadcbaabdbaaaabdabacbcbbbdbbbcdcccaacaaaaddcadabcbdbdcccbbadccbbabdaaaabcbaabdbccabadccdcbdcabdbdcbcaabcacdcaccccdbcdbacaadcccdabdbcdccdcacacabbddcbacbabcbcaacddbaabdaabbcdddaaacbdbbdadcdbcccaddaacacdcdaabcbcccaccaabbbdbcbddaccdabadcabbbddacaccadaccbbdadcadcbbddacbcdaaddbabcdddacddcabddbcddccadbcbbccbccaaadbbccbdbdbbdcbdbaabcdcadcacdcdaacbabbbabadcbcdbbdbbacaacddacdbaccabcdbbcbcbbdccacbbccccbbbdadcbbdbbbaccddccdcdbdccdbaabadbabccbccbaadddbbddddcdccccdabcadadccaddbdaadcccadadaddadbdccaadcaacdcadcdacddbbcaccbdadabcabaadabdadbcabcbdacbccdaabdbcdcaaabcccadcccadbdcdabddbbaaccabdadabdaddbcccdbdbccdacacadcdcacbdaaaaacbbccacccadcadcabcbaccbbbcdacdabcabdaddabadaaddbcababddbadcbcaadabcdddaadbccbbabcddcbbcdaccccddaccbdddbbbbbccbcbdacdcdccbaacbbcabbbadaaaadaabbaabbbbcdccbcdccacbbaabcbdcdbccbcbabdbabdacdbcdbbbcbcbcaababcaabcbcccdcdcccabdaacacdccbdaaacabacadcdabcccaaccabbdbccbbcdbcbabadccacdcccacddcddaccdbccaacabacdcacadbdcbbadccacaaacccaddcacabdbcbadaccdcbdabcccddadacabaadababcaaabcadcdbdcbadccdacbbcddbdabaadccababddbaccddacdaaadcbcbabdacdcdbdcadbcaccbbbadadccaddbaaacaadbaaacdcbdabaaccdcccacbdddabddacabccbadccdaabacdbcadbaccbdddccbacbcadcbcdcdcadadbdcdccabbbdccbdaacbccacadcbaadbadbbbcdcdbdabddccacdddddabdcacbccccaabbdcdbdcddaacdbdbddbdddbabbbacacabacbdacdddcacbacbdbaaaaaacbcaddcdadacbbbbcacbcbbbcdabccccacbbadbcaabccdbdccbacdaccdbadcbbadccdadccadcbcdaaddaaadadddbcaacdbbbdbcddcaaadbcbbccadccdacbcbdcbccadbbbbabdbcbdaaccccdaaaadcbadcbbcacbaacbbddcbaadcbdbcaaaaccabcabaadcbacddaaabddadaccddacabddcdabbdcaacdabddcdcdadabbcaddbbaaccaadacaabacabbcdcccbcbadcabcbddcacbcbadcbcaacbcdadcabccbdbaabcbdbcdadbcabaacdccbaabdbcacccdbcabacbccbabcdbdabadcbbdaabddabaddbabccaaaabdbacbcabdabaccbcddccdbdbbabbdbbaacdbbabbdbcccdbdccaacbdcaccccbacbdabdbddbcacbdbacddbccdbabbacdacdcbccbcbcddbdddbdadcdaabbddaadaadaddddccccbdddcacbacacabadbcbcddbbbbdbdbdabdbddccaaaadabbaacdbcbdbacdbbcaaacdabadaccbabdcadccccdcbbcbdcdbbcddbccdcdabacabaadddadbabbdcacdaaabdcbbbdaccaddaaaaccbacccacabbbbbbbdbcbccdabacbdcbabcddaaaddacbdcdbbaacbdabdbbdcbdcdaaccccacbcbcccabbcbdbbbdbdadbabaabcacddcbcbcdcccdbbaaaaaaaaadbbbcbabcbbdbaccddbdbcdbcaccbaccccbbaddcabaabdcbcdcdcabbdcbbdbdbacddddbabadbdacadaabbaddccbbbccabcadcabcaadbbdaddbbddbbbacbccdaccacdabdcdacdacdddddbbccbbddbcdabdbdcacbbbabbdbdaacccbcaadcddcbabdadadddcccdbbcbddbcccaabbcbbaddcdaaaddcddaacdccbccbbbbaddbddcdcbbdcccddcabacbbcaabbacdaadacdacadaacadcabbbdbabdbaaaaacbaabcdbaadaddddddabddcadbdbaddcacbdcdbaacbabcabbabbccbbadcadcaabcbcabcabadccbccabbcaadbcdcdcbcacdbbaaaddaaaadcadaddadadbccadadcddccdbccbbadadbadbdaadcbaaccaccacbbcdbbcbdbbbdbcbcdbdbbcabdbcadabcddbcacbddbdbbbadacbbaaaadcacbabcdbacabddbadacdabddcdbabcddcbaccdccdaaddbbcaccdacddbdabacaaccdadacaadddabdbdcdbcddcbabdcbcaabdabbbbdddbcbbbcbdcdcacdcccaabdaabccddaabcdcccdddacdcabcbaddcacccbcdbabbacbbdabdadbccabccdddadbcdbbbdbaaabdbaaaaadcbadcdcbbccdbbdbdcdadddbcddccbbcadbcadbacbabdbbaabababadbcaabbddddcbddcbddbadbbcddbaababbbcccdaccbbaadcacacacaaacabddbabbcdbaabbcddbdaacdcdccbbdbbcadbdccbcbcbbbccbadbccbccdbddcadabdbacaadaacdccdaaccdccccccddcaddbabdcbbadaaabdcdbbbcdcaabbacdbbadaacaadcddddacacaddbadabbdbabbbdddaaddadcbacacbacccaccdbdbadcbbdaadcbdcccdaccdccddcccabbabbccccbadbcbcabddadbcdcddbbabdadccacdbaccbadbccdddbadbcbcdcbadaabdaadbabbdbadbdabbdddbdbdbcddcacddadcbcdddaaddaacaacacbacbbbaaaabcadbbadcdcbabdcccbcabbdcdbcbcadcbddbccbdabbddcababccbccbaacdabccadddbdbadddcadbdadbddddacccbcddaaddcadaaadbaaaabcddcdcdbadaddcdbddbbacbbdaddcbbaacabdbacbdcbcbdccbcccdaddcaaaacdbdbbaccbbabbbadabaddbabddcacadaddcadabbdadcdacbccaaadbccbbadaddbaddaabbbaadcbadbddcbbdacbdabaddbdccacaddcccbbcbddbdcabbcbdcacacadaccaadbdbadccaccadadbdabbcdbdcdbdccabbcddaacabbaaaccacbbadbccbcbcbdaabdcbbbcabbaabdabdacdccbbaaabccabbaabbdcabdaaddabcadcdbbdcdbaadddaddacccbdbbcadcbacbdbabbacddadadcdacbbcaddbbbcdbbabaadaaaadababdcccdddccabadccddbbbbdcbbddbaaabdcaababaaaccdbbabdabcdcddccaccabbbaaadadacdacccabdbdacabdbabbaddbdaccacddbacbccaddccacbcbaacbadadabddccccbccdaadacbcabcdbddcacdabaabdcbcadaccdacaabcdbbaabacddccaabdcbdbbddabcadbbbbcddadcadcadacccbaabbcccdbcacbbbacabbbdbadbbddaaadcacbcdacdadcbbdcbbcbdaadbadaaadcccbadcabdbbcbdcbcdbaacbbcaddadcbacaadcccacbdaccacdbccdddcdbcbccccdababcabacdddcbdbdcdbabcddadbbcbbcdbbacbddbbadaaccbcbdaddddbadbcdcddcbccbdcbbbaabdcaababbaaadbddcadbadaddcacbddabacbdcabbcdccdadabdcacacdccdbdbcacaaadabaccadabbdbabccbacabdbdbadcbbadcbdadbcbdaabbaadcdbaacdccbddacbcddccdadcbbcdaccccddacbcccbcdbbbdbbabcabdbbcdbcbabddaccdaabcadabddaddcdcbdbdcbcdbcbcbbdabdaabbbbbdcacccdaddababdabccccacbdbcacbbbcdbbbdaabacaccbabbcaadacbbdcaaaadcaacccbbcaaddbbcbbcbbdbbdabcbcaadbddccbdcddaacabcbbaddabaddadacdcbabbbbdccaabcbabaaddadacbbddbababbcdaabbbbddabcbbcdcacdbabbbdddccdabbcacadbdaddbbbcddbbdbadaadcaacdadaacbbccddddbdbbacddcbccdaddddddaaabcadaacccacbbdbcaabdcccaddabddcaabdddaacadabdbaadcbbacdcdcbdbdcbcdbaadaccdacadaccadcabbaaabdabadaaccabdbbbadbbdacdcaacacaccdcbbdddadccbcccdcbbcabccbdccdbcacdbbbaccdbabaaababcdadccbbdbcbaadacbdddddaccbbcccdccbbddcdacabcbbbdcbcdcdbbdccabaccdadddcdabcdbadabbcaacabdccdbcbabdaabcbcddcddadabbabadbcaaabbbbdbdcbaddddaabdbbacdacbddbcbcccdcddbdddcdaddcddbbbcdbcdbacabcbabacadbcabbbdcdbdaadacdacccdbcddccccccbcbbbcacbbbcacbbddddadaaacbdadcadcabcaccdcdbbdbaaacdcbccddbabcdcabdadbcabbcbdcdaacabdcdcdddcadcaccdaddbdbbdbdacdaabadbddcaccdcacbdbddbdabdacddccadadabddabdcccdddabacbbadddcdddaccadadbdbccadabdacddabadacccbcddaaacdabbdadcdbbdacabbdbdbdabaaddccacaadadcbcdcbdcdbbcbcbcccdbdbdbbabcccadcbcbababdcadddbddadcabaaccaccccaccdcccabcbaaabdadcddbababcccadcdcccdadcdcaddbcadbdbbaaddadabdaadbdacdbacabbabbbbadcdcbcacabbaddbdbddcdabaddadcadababbcaccbddbaaacddcdcadddadbaadabadababbbabbbbabbdaaadadbaabacaabdcdccdabbbdbaacabbcdcbbaaadaddddbbdbbdcadacbacbbcbdaabbbcaccadbdaddcccaccaccbbcaadccababaadacabacadbbbddbacababdddbaaacaacbacaacaacababacbcacbbbbbdabccdadabacbaaaddbddaaccddddcbcbababdddcbdabcbdcaaadbdbcbcadbbddbcbcaaddabadcaacbdcbdccaaddcaacbadadbbddbbadbabacccbacdbcbbccbcdcdcbcabbacabaccddcddccbcaadbcabbbddabcbdcddaacbcaddcaddccaddadbcabdccabaddbbadbdddabcbdcdcaadbbddabbaadbcdbdcdadacbbdbbbbbacdcbcaccdcacdcccbaababbbbcdddbbadcbcabdcdcbddacdacddcbddaaaacbbbdabadbacadbadcbdadcdcbbdbbbabbbabbdbdaabadccacdbaddaacaddccccadcabcdcbaabaadadcbdbdbacdcdddabaaadbacaabbaddcdcbadcbaabbbcdccadcdbbddcaddadcdbddbabdccaabdccddbbbadacdbbdcdccbcdcaacacdbcbababbdbcbcacddabcbadccbdaadaacaccbbadcbcbadcacdcbcccddcababacbaddbabccbbdacaabadbaacddddddccbdaadbdddddaddccccbabdaddbcaaadcdbdcccaddbcdacbdcbbbadbddcaccbdcccdccacaddcdcdbdcbbbbdadccacbabcbcabadcbacbbbbdcaaaacdabbddcaddbadcdcdbcbbbadbaadabbabaddcacbcdbbadacaaabacacdcaccdbbabaddbbcabacaabdbcdbdacccbcbcdcdddadcbdbadaacadbadcadacacbdbadbaabacdcabcbcababaadcbbcddbccabadbbbccabdabbacbcccacbdbcdccbacaccaabccbdcabbbbdbdabcbbdcabaaccddcabcbdcacddcadccdcddcadddcaacbbccddddcabcaaabbbbcbacabdbcbbaadbcdccbdcbcadadcbacddbcdcdbbacbadbaacdddbcaababdcdbdcdbabbdcbacacdbbccbdbcbcadcbdbdaadbdcaddcdbcdabbabcababdacacdabcabcbcabaccbaabdbbccdccacbacdbdaadddcddadaadbdacaddccbabadbddbcdbdcaadbabdbcdccadaabcacbdbbddccaadcabdccccdacabaddcbbbcdabdddbdcbbcaacdaaccccbbccdadbbbabaddbadadbdbaaacaddbbddcacdcbcddabcdadadcdbdbdcaccabddbabbcabaababacddcdabdddbcbcaccbbbacacdaddacadbacbacdcdcbabbbddbcbadddccadacbcdbdabdbadabbdbdadcccddaacdcbdabddacddabbbdaabdccdbabaccbbabacadbbcadccdaabbdcdcccbbdbdbddcbcccacadcdacbbacbabcabdddaddcabbabdbbddccdaabdcbccdcdaadddbccccdcaabaddbcacbbbbbabbccdbddbacdaacdbcbcacacbcaaacddaaaccbadcbacbddadaacdaddbaaabaaadccdcdcaacdadcdcaabbbbdbdababdbdbbcdcbbaddccbdccbbccbbcacdbbbbdacabbcdbbccadabbbddbdbcdadaccacacbdbcabbddccbcacaddabcccdbdbacdaddcacdaadddadcdabbcdcccdbcbbbbbddabcdaacbdcacccbbccbdbbacadbdbacbdccdcadcacaaabbcacbcbdbabdbaacaddddaabdcdcdcbdaddaccabbacdbbadadddcdcbababcbcbddacdccbdaadaabcacdabaaccbcdadababcdabbccbbcddaadadaaadacacadadccbcaacbbcccbddacacadddabacabaacdcbbdbdcddbaaaadccbbcdabacacbbcacaabcbaaaaabbdccbaabcacaaacadabadcbdbbccdaadcbaadbacccacbdcdbdaccbaddabbbdbcaaacbbcaadbaacbbcdcdaabacdcccbbacacccdbbccbcdbdabddacdbdbdddacabcddaccddcabadcbddaaddbabcccbadaaadabacdaddccadcddaaabaadbbddcaaadcbbbcddbdccadacadbccadbbbaddbdcccabbabbdbbcdabcdccdbcdcdcbdacbaccbacbcbccdaabdbabcdddbbbacdcbddacddbcddcabcdbcbababbccbdbcdbbadabccadbdbbcccccdcadbbccbadabdaabdaddddaabddbdcaccdcdbcddbdcabccbacdabacbcabbcbbaadbccbcdbbadbbbbcddcadbcbbbbaacdbbacbacddcbcbdaabdabcbddcdcbcabdcddadcdcdccdcdaadbcaaaaadbddcabbdaacdaadacdcbdbbaccccdddaacccacccddacdccadadcdccdbcddcdcaabdababaddcbdacddabacbdaaadaddbbaacbdabbddcbdbcbcbbdaaddbcbccaccaacbccadaaaadccaccbcadbdbcabcadbdadccabdcacbdbcbcbbdaadbdcdabcabbdbddaabbcbacdbbbccbccadaccabbbdaabccddaaaccbacacadbccbcaaabcdccbbddadccbabaddaabdadbaaccaddbdbcbcaccbabcacbddcdbaddcdadbaaacbdbcbdccdaccdadcdbcdcadbaaccdacdbccdbbbcddcbbadcbbabbbdaacdacbdacbccabbadcbaabadbcdbbcdbbcadadbdaabddcadacabacbbcabadbbdddabbadaccbcabbbaabbaadcbacaccabccdadbdaccccdadbcdabdaaacbcadbcadbadbacbaaaddccccdacabdaaadcbbbcabbdbabcbdaaaccdbacabdcdbbbaacbbdabcaddbccaaadabbaabdcadaccaccccaddcabbcaaabaadbadadcdccbcbcdccccacccaccaaadbadccdbabcacbaccbbcccbdbaabaddccadbccbbabadddbdbdbdccbcaaaaabbabccbabdabdcdcdcaddbdabbabdadaacaccdddaaaabacbddcaddddcaadbabbccabbddadbdabddacaabdcdaadaddcaabbccadacbddcdaccccbdacabbccdbbacabcddbddaaddabdbbacbccaabccbcbacbdacbcadcdbbddaccdcccddaddbbabdabbbabddadbbcdacaacddcdddacdabacbddcdcddcacddcabdbcdcdddbababaccdcbddddddddbccaccadacdbddccaacacaaddbbdacddcbabaabcbdddcddbabdcbdddabbacdabcdcaccababcabdddacbbbccaccdcddddbaaadccaabbbdbcabcacddddaabbbddacaabbccbadabaabbbbabcacccbaacadabbcdbccbbdbdadbdcaacaddaabbdbbabaccbdbdbacccbacbdcdcddcaccccdaabbaacaddaaccdabbbdbaadaabcbdcdcaaacacdbcabaaadbccabdcdbccbdbbadccdbddcdbdadadcbbdbdcacadcaadbbadacdbccdacbbbdcdcdbdbccbbcddcbdcaadabcbdccabbbdacccaccaaadccbbaaadbcadccbcdacbbbbdcabccacaacdaaadddbddbddcbbdddadbadaacadbcbbbcaadcddaaadaccdccadcbbaacbacccdcbadabcbcdcadddccbdcdcadabcbdbccabccadbabacbbabbbddbbbbadcdadcbcbadbddccabdacacbacbcdbaabccccdcbbdbcdcbacbdcbaabdaccbdaaaaaddcdccbddbdabdcdaacabdacdccbadddbabadadbbadcdbaabacabdbccadccbcbdbcadabccddcdabddbacbbaacbadabdbadbbcaabdbcbcbdbadbcbacaaccdccaaddbcdbbbbadaabccbbcdaccccccbacacaddcabaddccaabcdbdbddacadbacbccabbaacddacadbccdbbbabbbadddbadcacadbbcabacaadcdbbccaacbacabcacbcdbdcadaccccdbcdbcbdddbbbdabcdadccaccabbbacacdcacbcaacddddabddbbcbaddabbdddaadbcddcaaddbddbadcbcdaccaacaddaabbaadbdaccbbbacbaabdbabdbccccbbcacbbdabbaabaddacdbccbbcacdabdbbbbdcdcddacddcabdcbbaaadabaacadbdabbbcdabbbbcdcadcbcabdccdbbcdcadacccccbcdadaabcbbcbcbccdbcdcddaacccddcbabcbbbcacbcbdadadccddbbbcacabdccdabaaddadacdcadbabbbcdbadacbddcccccbdadccaacdbdcaccacdbcdccddddcbbbdadbabaacdbbbdaabcacbdbcdcabcbbcadbabaababdaacdbaaabcbdddabbcaddbcdaadcdabccdcdabacbddbdbccbddaadccdbdbcbbaddbdbdaadddacdababcdaccbddcdbdcdbacccdbcbabdccbcadcbbdcbccdcabdbddaaadddabcccdbbbabadbdbaaccbcdbdbcccbaddbaaccbadbbdbcbddbcaaddadcdbddbbcdaddacadacabbbdddcdddababddacbcddbabcdbadcbbcbcddddbaadbbabdcbcacbccabaabccdabadcdaabacbddabccbdcddbadbbaaabdbdbbbababddbddddabcaadddcbdcccbbbcddbdaacdbadccbbabbdcdcacbabbbbaacbaddbbbadbcbabacacccadaaadcbadaddddaccaaaddbbcacdcdbcbddabdbcbcacddbdbcddcadccadbccdbadbcddaacacdcdaabacadbbacabacbaddbbdbdbccdbbbccbcadccdababdaacbddbdbbbbbbadadaddccadbbdabaaaaacdcccbaacbdadbdcabdaaacdbabababbdcccbdabbaadcaddcabdabddbdbbbababbaadccdbcbdbbdcadbaabdadaccadaabadcccaaabcdcababccaaaaaabcabbadbcaccbcdbbcddaadcabcadbdbcddcacbabdcaabcaddbbccaacdbcbcdbaaccacbadaddcdaccbdbdaaadacdbcccabcdacdccaccabbabdaacabdbccacbdabcbbdbadbabaccdddadddacabbdccdcbdacddcbadadbcccccaadccbcdddcbddacabddabccbcabacbabbadbcbbabcacdaacbcdcbddbddbabaaaacbddcddbdaadbbabdcbdabdbbdacbcbbcdccbadddcbbbcdccaadcbdcabbaabdadaacabbdcbdaadcbbacddbcacccacdaddcdccddbcabbcacddccbcdcdbbdabadddbbdbbbcddcdcadccbbaabcbccdcddadbabadcddabcddccabddbbdccdcccdcccdbddaababcddbdcdcbaccbdccbdabacdcadddaadbdabddbababadcbbacdccbadaddbdbbbabacdbacdddcbabcbabaccdbbccacdbbadddcaaddbbbdbdcabbddabbccdcddccabbccbadbddaabdbdaccdaaadabcbdbcbcaadcaabcbdbcdbcccbccbaabbaadabbdbcbdaddabadbabccccbaadbbbabdbdbcdaddadaccbcdcabaabacaadacacbabaccbdccadacdacccdbddadcacaacbddbaccddabcdbbdcaabbcbbdacbcbdbdadbddaccdbabdacdadbdadbadbbadddbdccbbaacbcabdabcabbadcdcbabdcbbcccabaacccdadbbbddddbddcdcbbaccddcaabcddacbbacbcbbdddababaddcdbabccbbdcbcabbaadaaacacacdcdaccbcdcabdcbddaabcdcdbcbdcadaabdbaccadaaddcbdabaaaabcaccdcbcccabadaccbaccacdbacabdadcacdbbbccbbcaabcacbcbbaddcdcdcddcddaccadadbcaabcadcdcbdcbaccccaaaabacdcdacbacacdbdbcdcbccbcbbddbcdccacbbcdcbdacccddcbbbadcdcabdabdbaaddaacaaaddcdabbbbcadddbcdadbbdbabaccadcdcccbbacbbdbbccacbdaabdccacdadaccddccdbbcbcdadddbdacccaaadacdcbccdacacadbbbcbbddccddabcddbdcdcbcbcaadccdbcbdacabddabdcaadcaabaaabcddbbdcbdbdbbbbacadbdbdbbccbdacbbadbdadacaaddbadcbbcdcdacbacdaadcbcdbcbaaccbbdbaaaccacccccbadcccdcabaacbbbdccacddcdaabdbcbddbbccadbcdacbbcabcaaaddadddabbbabbaccadaadcdcbcdadddacbacdabaaacbcbaddaadadadaddabcbcbdccdcacdcadccbababbabddabbaabdddcdbdcbbcdbdbababbcbdcdacacbccbcbbbbcbdbabababadccabbacbcbdbabadddaacdacdbcdacdbcbadddaaaaddaadddaccaddbdddcbbcbddacdaabdbcacadbacbbaddaacadacbcbbcaaddbcbdbacaadadbabaddbacbaddccccaddcdddaacaacbbdcbaaadbdaaadaaaddcbbabddccddbdabbbdcdccabdadbbcbaaacaacccacbcbdcbddbcbbddbbcacdbadabccaaaddccccababdaccccdcdabcacbcdbccadabccbbcaddccdaddbcddadcbccadcaababbcabccbbadccdbaddbdcadcdadcdabbdcabddacadbaabbcccbbddbcaacbddbabbcdbdddcbaadacadbbaddbaaaddaddbaaadcbacbbacbdabbaaacbdddbbbdbbadcaaddcddacadbbcacdaaaddcadbcabbaacbcbdcabbcacbbdddddbccdababcadddddaccacdbbbababcddbabcaabdddbccbbadbabcadddcacbcbccbdbccccabaacaadcaacbbbcbaabdabbabdabbbdacacdaabcbddcdcccadadbdadbcbcbddcdccacabadabcabdddbcbdadcbcabbbadcaddacaadacbabcccccbddaddcbdbabdcacdbaaadbdadacbdabdcabbbaabdacbcddbbddbcddcaadbcccbaabcbadbcaadcbaaaadddabdbddbabbaaacdaaabcbbaddcabcdddaababaadccadccaadaaccdbcbdbdadddadcccbadcbabbcdcdbcddacbcabadddacaccabaabbbcbcdbdbbaddbdbdcacacdcbddbcadccaaaadadbbbacbabbcdcdbaaddadcadacddacdabbaadbdaaaacaadbbaacdbccaacdcbcbdbdadbabaddbbdabbccbcdabbbccbabdbccdacbbbbdadadabbbcbaaaccaabdabdaadabcccabcbdcacaadccacdadbcabdbdaccddbaabdbdcccabbababcabdbcababaacacddaccbbabadcbbaddaccabbaadbadbbabcaacaaaccccbacbbdaccbbcbcabdcbacbdbbaccbacabbbcbdcaacbdabbdbddacaabddcdbdaadbbccbbcbbdddccccbaaddcabcadddbcadbccdddbdaabbbacdbdacdaddadaacdadbdddcaddacaadcacdbcacbbccacaacdaabbddbabcddacddbcdbcdadbddaddbabdbaaddbdacabbdbdabbbbdbcbaacadcadbcbbbdaadcabbbcacacabbaadbaaacdaccdccccccdccabbbadcdadbbddacaadcddaaccbaccbddcacdccbdcaaadaaccabcdbccbacbadabbbabaadabdbbcbaadcacdddbabbcdbbabbcabdbbcbbadbadbcbcbaacdadccdcdaaddbabadaadbbcccdbcdacccabbbaaaaddaacdcdaccddbabddaabcbcaacbdccbddbabcaaaaaccdaddbaabaadcacbaaacddcbddbcadbddacabcdbdcaaadadcaaddcccdacabdbadbaddcbacddbcddbcdbadddbbddbdbddbabadacbdcadccdaccbdccaadacaacadbdcaddcdaccbcbbcabaddaaabdddcadadcbcaccddcdaccadcabbcbcbadacccdcdcadadbcccbbbaaccdcdbaaacbdcbabcadcddcddbcddbdcbddadadabaabbcbbddbdcbacccbbaddcaaaddcccacaadbaacccdcbdadadbaaaaadacbbacbadccbacdcadcadbccdcbbacadddacdbddababacddaddcacdcbdadcdcaacdbcbababbaaaaabcbddbcdbcabbcdcaaddcdbdcdbaddaadbbccbacdaaadbdcbcbadddcadbccccdcdbddcbcbdddadbbbabbbaccabdcaadcbadadacbabacbdddddbbccdcdddabcacbbbcccbbbdaadbbcacaabccaddcbcddcccaccddaccbabbacbabddcbcbdcabbbadbcbcdaabbbccbccdccbdacbbcddaaacbabbdbdadacbddcabdbbcacaccddbcbdadbddbcbdadadbaddadacdbcdccdadabcbbadabcaadcdbbbdcbcbabdbccccaaadbbccaccabbbbdaccabdbbabaaddbcdabcabbccacaaccabacabcaacadbccaddcacdbcacbcaacaabccddbbbdbabbaaddaaabbcabaccbbdccbbaadccababbccbaaabadcdbcabcaababbbaacddddcbbabdbcdadcbabbacaaaacccdabdbacdadbacccdbdadccdccadcccddcadccccadccabdbdbcdbaabcdcbdcacdcbbbcbbaccbbcbabadddaaacddcbabdbdccaabadcdbbdcdabcacbadaacacbdacbaacadccbbadcbdaaccbcbcabbbcdcabdbabdabdaaccbdbdcdabdddbdccbbbccbcbdbddcaadadababbbbdabcdaadcdcabcccccbbbccdbdadcbbcddcdaacdcacacddabdaabcdbcbbcddbcbaccabdcbccdbbdcdddbbddccadadcbcdcccbdadbdcabdddabddccddcbdcbdbbaccbbbddbdbaadadcbacbacdaaacadbcaddccaacbbdbddcbcdbcdcdcaaddadabbcadabbddccdbbbcbccbddbddacddddcdbcdcabaabcacdabcbddcdccbdaccccbbdcccdcbacabdcdddcbbbadabdbbddccdccdacdcaabcbdcbbbadbbacccadcdacbbdbdaabbabdccbbdcaddbbaddbdababbcaadacaccadacabaacdadcbcdcddbabbccdabdbacacdbbbdcbbbdbbdaccbdbbbcabcddaabaacdcabbddadabaaabddccbadcabdbcdacdbbbabadabddacbbcbaaaacabcddcbccdabccacacccddbbdcadbcbcadbdbbdcbcdaaaabbbbdadcbccdabbadabcbdacdbadcbdabdadbbdaaddbcadacbdadaacdcaccccabbaddaaddbadabdaabadbdcabdabaabcbdbbabccddbbcababdccdcbddacabddabdadbbcccaabcbcabcacaccaacabddacbdcdbbddbaccdbbdbaaaaabadbaabbdbcdadbcadaddbcacaadcbdccbaaadccdddddbaadbdbddaaacbcdabcbaacdccaadacbdcadccccabbdcaadabcaaadcbaaacdcbcaddadabadacdbdabdaabbaabbbddbaccccacaadddcabcdbbbadabcdcddbaccbbdbcacbcacadabadcbcabaababdcdadacabaabadcdbddaaaabddaaccadadcdbdccbdccbaaaddaacabcaccdcacdaccacdcccbddbcacacbcbdcdbadaacacbaabbdccdababaaaacabadccacccdabddaccbccdadaddbbbdcdbcdacddcaccdbccccacccdacacdbbabbaddadcbcdcbcbacbbbbabadacadaaadbababbdbcdadbaccbdcabcbcdccbcadabcdadbdababcdcbdaddbdcccbcacddbcbdacaccbdbdaccdbccbaabacddcdcdbaddcadcaccbcdcdabaacbdabbadbdbacdbcbaabdbdbbdbbdcdddadbdcbcaddcbabbdabadaaabcccaaacdccadccacabdacdcccdbaddcdccadabbadcdcaadbbdcbccbdccdddbbadcacdccbbddddbddcccaadbbdddaccabcdbcbabbdaabcdbdbbcbabbbabccbabdcdddbaaabaadababcacbaddaccbbbdacccbcacadcdaccadcdaacdccdbbccbbcbbdacaadcbaaddbabcdbcacadddccadddcdccbbaaadaabbaabcccbcdcbbbdacabbcdcaddabcaddacdcaabbbcaaaccdadbaccdcbaacaadcaacbdcadbbcdaadcccabbacbacaadcbdacadccadacabddaacccabadcbccaaacabcccbacdbaccddbcbaddddddacccbbccccacaddaadaabacddbadabbaadabbbabdcbbdcbbcdccbcdadabcbdabdabaaaaabcdcbbdccaacdcdbccddacaccbbdbcaddbddacdcdbbbddbbbccaaccaabbcdcbdcbaddccaccdbcbbcbaacadbaacdbcdacbcbadabbaababccddcaacbdcababbcbacadbbadabaabdbbdcabbadbbabcccccdcdcadcdabddabdadbabbcddaababdbdcdbccbdadaabccdbadbcdabbcbbdabcabddabbbdacbacbaccdabababdaaabbabcdadadccdabccbcadbaadcadaacabadbbacaadbcaddbcdccdacabacdbdababdbbddbbacdccbccbdcadcacaabdabcccadddcabdcdcaaccbccdbddaaabddcaacdccbdcbbdbabdacbabddbcdcaadcddcaabdcabcdaccadcdcdbcccbccaacaaaaabcbdaadadaccdaccaccbadcbccadbdbcacbabbccdcdddadbccdcccbcbdaddbacbbbddaacdcddbdcdcdbaadbbbbcccbdccccababadccadcccdaddabcacaacaadadccbddcbddababaddaaccaacaccccaacdcdadabadaccdbcaccdadbbbdcddacccababaacacadbdcdbdddacbddcccddaddddcdaabbbaacdbdabbcbcdaadbbbbcacdadcacbdbaddbabcdbaaccbddabacccbddbddbabcddbbdccadaabbdaacdaadacdabcbaabaabcbdbdaabddabdabdabadcddddaaacddccdccdbcbbbbcaaccacdaacdcdddddadcddccbaabddaabbadbddcdddacdbadcccccdbdbcdaabcdadbabaddabbbdcbdbcddcbcdbbcbdcbddbabcaacdacdbcacdccdacaadddaadaccbcaacdabbaadbcbbaccbacadadbabdbdbbbdacdabcacacabcbccacdadacadcbdacdacacbbbbcdccbcbdadaabaaaacccaddaccdadddaabdcadaccbadcccddbcbdaaaadbcccacdacbbabdcacdbdbdabccacaaacbddabcbcdcadadddbbbdcdbbaddbdddabbbaaacbccdaccbdccabcdbabccabababcccdadcbbdaaddbadbcbdcacadaaabcbbbcbddbacacbbbccabadcadcaadaaddbcdbdaaaddacccdabbaccdaddbbcccdaadbccabdddcddcacdccbacccbcadbaacacdcdabaaaadbbdcdbadcadddbcdaadbbbbcabcadcadabbbacddadbacbbcbcbacdaababaabbddbdaaadbbbdbabaacdbdbdbcadacaabbbadacdbabcdddcaadbacaccdccbcbbdcaccbdccdccbcacccdabacbbabdccbcbdbabbbddddbcbacdadbcdadbdddbdbcaaaacbdaabcbbaadabcabcaaabaccdddacbdbaabdbcabcdcddcbdbbadbabacbabddbdccdabbadcbddccdadadacdddcdabdcadbccbdabccadcaacbadcaaccdbdabbccacccadadcabacdaabadcbbabbccccacdaabddbacdbcbdaaddcaccdcaaaccacbacdbaaddcccbbbdbacdbbaccadcddbacdcbbdcbdabdbccdbbbcdadcdddcaaabbadccadcacbcbdcbbadbaaaacbaddbddcbcdabdbbcdcacabcbbaaaadcabbcddcabdbddbdcccbaddbdcbcadabcabbbcbbcbbcdcbbdadaacbabcaaadccadaccaacbbcbbbbaccbcbbcaaabccbcbcbdaacbcadacddbaaabdccbcccddbaddadaddccbabcaabdadaabbdbccacdaccaacdcaabbaabbcddbaabdbcbdacbbbbcbccccccbadbacbaaaacbcdcabdadcdbadbdacbadcdbabcdcaaddbcadccbcbadccdadccaacddbcacbbbacbabaaacdcdcccacaddbdacacaabcabbdaababcaabccdbdcabbdccbbcacddcddddaccadcadcdbbbbbbdacaadbbaacccadbdccdccbcdddbaddbacabccbdacabcbbcdcaddbcbcacbdbddcadbcdacdbaabcabaadadbadadcdbdacbbacabccadcbdabaacbcadadabadcbddddcbcdbbddbabbaacdccdddbdbaaccdcbcacaddcbccbacbbdacdadbdbbacaabaadabcdddbaccadaababdccbcbaddbdaabcccbdccddadcbcdaadbbadaacdcbdbbbccbaadabdaacbcabdbaccbcbbdddaddabcbbccddacccbadcdbbcdcbbcaadbabcbbdbdcadcdcccacacbddaadddbbdcdcccacdcaddaadbbadcacddbccbcdccacdacbdcdbbcacdabacacadbbbabdadbbdadbddadcaaadbacdbdadcbbaabadbdbddcaaabbacbdabdbdcbcadbacdaadadbacdcacabbacaabadcddcbbcadcabcdbbbcdbabdbdadbbdabbadddcbdddcbbaccdccadabdbcababdbbccbdbcadadddcacccaadcbaccabacbcbbcdaaddcaddcbaaccadddcadbdacacbbddddcbdbabacaaacddabdaaaddcbdbdbbdddbdcdddabbabddbcaabdbbdcaddbbdadcccbbbaacddbddbbbbdcaccdbdcadcaacbcabaadcbddadcbaadcbbcddcdcbbcddbcbabddbbdddbadbcbaaacdbdcacddbaccaaaaaaacabcabcdddbbdddcadbbacaacbcadabcdadbccadaabaabbddbcbcbcbdbcbbbadcdcadbcdacddccddccccabaacddcdabbbabdcaabdddbdadcbbbccaabaabdbcabbddccaacdbbbabbdbabdbbacacdcacbddcbbaddcccdddbcccddbdccbcbacccaadbdbcddacddbaacababdcbcbabbddccbddcaaabdcdbaaabbbcddcaaccbcccbaccaadbcbdccccdaddbddaddddbdcacddcadcbdbddbbacaaaaaaddccbddddacababbcdcbbbbbccdabdbccacbbcdabddaddccbcbaccdcadbcccbcadaaabbabccbbbabdadabdbadacaacadcdabdadbabdaadcacdcacabadbabdbcdadbccabbcbaccaccadacdcabcabcacbcdccbbcbdcbcbbcdbcbbcccdabdbaacdbbdabcddccdbaaadcdcacdcbddbcdcdaabbbabdabcbaadaaacccdaabbbdbcddaacdadbbcbdcaabacbaacdcccdcbdbbcbdccccbbdcbabdaacdcdabaacbdbcaccabdddccadcaaabcccdabbcacbcadbbbacacbbccbccddcabbbdaadddcbdcdccbaacdcbbacdbcbacabdacacbcdbddbbcbaabacdcabcbbbdcbcaccdaabcdabcabdbbbadbcdabcdbddcdaddbddccbaacbdcdbddcbbcbbbcdbcddcdcaaaaabbbccdaaadacadacaccdacadbaccbcdcdadbaaadddddccbbddaabaacddaddabbdcabdcadcbbcadadbcbddadadbacdadbbcabdbaaddbdbbdaacbdddaacbbbcbcabbcaccccaccaacbaabcbbaabcbddcbaaadcacadaaddacabbadcbdddbdcdabdbbbdabddaaddabdccdbbdccddbacacbdbaabcacbcbbdbbacbbbdabccbcaacccabddddcdacdadbbbcbaccbddccdbbbddbdcdbdaccddcbddbcaaadaadabbdaaadbbbabcaacbbbcbddcabbcddcdacbdbacaddadbddbcbcddabddcdccacbbdbddddcacacdabcacdaadadcdcaabdababdddddcacaddadcbadcdbadcdadccbbacbcdbbbbbaadcbacbaccbaaccadabbdaccbbcabcabcbbdadccaabcdaddadcccddacbdcbbdabacaddcdbbabcdbbcaddabdcabbddcbcddbbbdddadddcbcaacbacbbaccaacbbcaabbadcdbdaddccbccacdcabadbcdbddbbbbacbcdacbbdaddbaaccdabbacdddaabbddcccccbaccdddddcbcabaacdcdcccddbacddbbccbdcdcdbbacbacdcbbccbcdabcbbcdcaadbbaccdcbbcddaaaaaabdbcbcdccadbbabaddadcdaddbdcbaabdcbdbdddcddbdaddbbbbdacbcbabdcddaadddaccdbcbcabaddcbdabbbadbcdcbdbbdaddbdbacaabbcbdcdacaddccdbddcbcdadaddbdbaabdcdadcdabddcacccadaddadaaccbadcddaccdbccacbcdadbacddcdabdbdddbdbcbddaaddbbcbbcddacdbaccddcddbbcdabcbacaaacdbcdcdcdbcabbbaccccbddccaccdbabdcaaabdcdcaddbdaacacbbdacbbadbdadadbdcacaaabbdcaaacdadabacccabddbbdccdacaadccdcabbbbaaacadcaddabbbbdacccbcdbdcccacdcdaaaabdcdddaacaacaddbdbcadadbaaaddbbbdcaabddadcbaadaadddcaabcaddacdbaacabbcacaccbbbdabaacccabadbdcacddbddbaccaaabdbaccdcdbdadcaadbdbadddabadcbbdddabacbbacadcacacaaaabddabbaddaccdccbacbcbadccbabaacaccbacccdcbcdabbbbbbacadccbcaadbbcdbacacdbbaadccbbcbdabdbaaddacbddadcacabbbadaadbacabddcaadacaaaddcdbdcdbdaccacacddabcbcbbcaccaacabbccadabacddbbdbbaacabcbadacadacaabacacacdbaabcabcbaaaacabdaacdaaaccbaabbbacbbcdaccadcdcdbacbdbcbabdbdbbdaabccbbabcdbdcccdbacacdcdccaaddcaaaadcaddbddaacaddabcdabcaccbdacbcabcbadacddcdaabddcbacddadcdbccddddbbabadbdabbdaabdaacdbcbcadadbbdbbcababccbddaabbdcacadaabcddccabbbbdbbbaccacbabdbbcbcccabacacadbddbacbaddccdcacbbcddadccdbbbdbcbcbdcdcdcaadaddddcbdaadacbcdadbcbdcabdababcddadcdaadabbbdaccabcddbcbcacccadcadbcacaacbbacccbaccdbdddaabdbaadaadddddbccbddbbadccadaaaddbcbcbccddccbbcdbddadddacbaabdcacdbdaddcccdddcbccbdcabacddccccdcdcccdcacbacaddcbdadcbdabdbddccddbbbaadaaaaacaccacacaadddcdcabcbaaddacbbcaabbccddcdbbcbbacbdadbdcccbbaaadbbcababaacabbaacdbccadababadcbdbbdabcdcaadcbddbdaabcabdabdbcacdccabcbaacdcddddbaddcbcadacbacdacbbacbbdcbbdddcbbccbdddcbdaabcdccacddccbabbdcbbbbcdcbbdddbbcacbabcabdadabbcdadcddbcabdcdbcaabdcaddbdaccbdbcdadbcdadbdbaadaaabbdbaddaacaadabdaabbcddbcaaabaaabcadcbbcbbdabcaaacccbbdbdddccbdabdacbcbbadcabadbdcbdaacabdaddacaadacbddabcaadbdcdcabaacddbbbbadcdbdcdcdcaacccdbbdacbadbabdbbaacdcaddcddccbdacacdabbdbcacbdddddadaabaaaaaddaccaaddacdabbaacccbdbaabbddcbbddccbcaddababdbdadbbdbbcdccadcaccacdcdaaddabaadcdccbaddcaabbcabaccdcaadcdbacaddacabdacadddcaadbdcadcadcbcdadadaadacadbdddaaaabcdcdbabbaacdddaaddcbcbcadcbabdacbbabcdcbabbdcddaddddcabdadbbddccacddcdcdabcabbccbdabdbaaabddcabbdcbacbbcdacdbaadddbdabcbadcabacbaadbbbbaacbcbaaadddbcbdbaadbcadbadacccdbbacdcaadacdcbdddadcbadcabaddcbcaacadbdbacbdbcbccabcbbdbdacdbababbbbbaabdacadcaadaacaacdabbdaabaaccbdcdbbcbbadcaddacbbdddcbaacddaaacadaaaaabcacddbdbcddcbbabbcbabcddbabcbcabadcbabadacbbbdadcabdcccabccbdcbdccdaabaabcadcccbccccdbbddaabdcaacbbabaddabbcadddaaccbaadcdbcaabacbbbadaacbbacddbcbabbdaaabccabcadbcbdadcbbbddddcadbdbdadabcaccdddccabadbaacbacbaccbbccdbdbdabdbcadbdadbadddbcadddcacbcddbcbbabddbbcaaabdbbdcddbccdcbdbbbcbacdbabcbabcddcdcbabddbdabbcbcbcbaadbdddacdcacabccccaddcdabaddccdbaddbabcaacbcbbababdccbbcccacddcdabbdacdacccbdcabdccddacbccacccddcdccbcbadcaddbaccaaaaddbbabbcaacbcdabadccbbbabdbabbdcbcddbaaaadddacaabbbdddcaaadbdbadbbcacbcbcccdcadadbcaabbcaccadbacbbadcbddaadaccdbcaadabccbcadccdadabbcdaccbcadbcbcbcabdabbbccabbbdccbbbaadccdbdabbcacaabdcdbbacdbadddabbddbbdbcabcdbcadaaaabbdbcacabbcacddccccdbbbbdcdcbbcbcccddaccdadddabbacacbdcdccccccbbdabdcbcbbddaacdcacddcbbdabdbbbbbaabccbdcbbcababbdaaddbddcccdcaaaaccddaddcdbbabbcadccbacabdcdacbcadbbdddaaacdabdcbdadcdcacbbcacaddaaabadddbdaabdabbcccdbadaddadadcaccbddbbdcddabadaabaadbdbabdbdbcdbdccadbdccadaacdbbdddabccccdaccdcabbbddbbcdbdbbcbbbdbbddccccddcaabadcdcbabdccaacdbddaacbacdbbbbbcdacbabcacbbabbccccccbbbbdbaccbdaacdaacbcbaaccdadadbbccbabcdbccccbcbbabbdcdaacbaaabaaacdcacacdaacacaaacabaaaccadabbbdbbaacbbddcabdcbbdbbacbbaacaddaaccbabacbbdaadaaaabbdcddcacbaccbbdbbcdbddbadadcdcdccdcbbbcddaaccddbdaacbddbadabcaacacccabbdbcacdaadccdbaddddcacdadcccacbacaadbccdddaadaabacabbbdbbbbcdccdccbcabdacbadcbbbbbbadccdabaddddcbbbcbaabdddacbddadbccdadcdcbcdacbbdcdacaadbbacdbddcaaababaaacbaadcbbcaadbccdcdbadadbbbbddcabadbbbaadacccdbdbdccabdcacadadaddacdaaadaaadadbdcabcbdbadbcaabadddbcbcddddbabcaadbaacdabccdcaccabadbacdaaaabbcaddacdbaacacaccbaaccccadbadabdbcacccdaaabcbbbacbadbabcdbddcdabcaaabbcdbdccaadadcdbbabbadadadadbdadcabbccbdabdbdbdbccddababbacbaabbdcbcabadcaacdcbbbcdadbcadabbabdbcadabddcabcbbdbdbcdbdacbaaacdbbbbcbccabaddbacadbcbabbabcddadcccccbaddddcdbbaaacdbdbdacbdddbaccccaacdbcbdddccddccababddcbdbbaacaddabcabdcaddacddadccddcabbabaadacadacdcdddabcadcaadacdbbcccbccbbcbacabcbacddcbadbaadbbadbbbddcdccdccbbcdcdaabddcabcaacbdbccdbaaccbcbbdcbbbabaadbdcbbcaccadddbbdccddcdcdbadcbdcbbdbcbcaaaadbbccaacccbddbdddbcbaadcdabcaddbbbcadacbcddcbbbbdbcbdbacbadadabcacdccabacaabbbdbacacccbbbabbaddacbcdcddcaaabccacdaacabbdcabcbbcadcbdbcbddabcccbbdaabddbdbdbdbbaddcbcabccdacdcdddcdaddccbcdcbbcabccbcddabcdaacbdbdcccdcddcadbbdbadbbcbbdaaabadaacbbbddbadbddcadbddabdcdddddccdbccbbcacaccdddbbacaccabcbaadacbaabbbbbbdbdbaadbcbddacdabcdcdcdbdbabcdddcdcccbdabddaacaaacabadbccbabcbdbaabbbbbccccdacabbaccbccccbdababbddddbbabcdbdbcabbbdddacdcbaaddbddbdbcdccdabbddddbcabddbbaabbdcdccbdaacbadbaabddbbbaabbaccccacbbbbbadbbddcaddccbdccadbdadaabadcbcdbbccdadabcbaaddbaccddbaaacbbcdadddddaccbbbbdddaccaaadcaabddcacbadbbababcccbbbccccdbcbabcbbcdbaadaabaacddccbddccddbccbcabbbaacbaddcaacdacbbdbcdcacabbbaccdabdbbbbcbbbaaddcaabadaacbccadaacdccddcdcdcddabddbddccdaaacdadcbdaabbaaaddadabaadddaaabbcbcbdabdbacbcbbdddaaccbdaccbccccbaddbddddcdbbcdbbbdbdaddcbdacbdaabccaaadabaccbaacadacbbcdabaddacacdbbadcddaccadaccbdaadaaadbaccadababacaacbbbcddddadbcaddcbddddcdbbbaabcbbcaaacbcdddcbbaaacbccccaacdadbbcbcbabbbccabbcbaadaacadddcdcabcdcbabcbbcdcadcbbaadcbabdaccddcbdddadaabbabddabacdadaaaaadbdaababcaccbacbdcccdbdababcbaacccbdddcadddcdcccdacacacbaaaddbdababadcabaaddcbcddbdabcaabdbbcdbdbcbbcbacaccdaacddaccdacbbadbabbbdccdcddacaacccdcdadbbdbdbbadcadddcababdaadcacadccacaadacbdabcddadbaadbcbacbcccdbadabcbbdcbcdcbaccbdbabcbdabcdbdaacbbcbcdbcabdaacbdaaacbdccbacbdbbaccbbbbccdbbcbdcadaddacdacdbdaabbdbaccacacaaacbbacbbbdbaacbcdabbcabcadbabdbaadccddcbddbbbabdbbaadabbbaddcccadaabcbccbbbcbddabcdcaacbdbcabbdcccbbabdbcdbabacababcbababbabdbaaacbbdaaaddcbcdccabcbcbdcdcdaabbbcabddbcdccacdabcdcbbbddbcccacabaabdbcbbdbaaaddcbcabcbacbccdbbaaadcdbdbcdbabbbbbccaabdcdcbbbdaabaccccbcaabccadaaabaaaccbbacdacbdaadcbdbdbdaabaabccdbabbaabdcbbbccacdaddadbcabccbadbaacdddaddddbccbbabddccaaaddbbbdbccdddacdaadacbcadacbcccbaccccaccddcadababbcbbbacdbacccacadbadcccaaacbbcbacadbdccdaaabcbbbabbabaaadbabdabdcaabaccabdaddccddbabccbcbbddbabdddacddabddababccddcbcbbccbccbcbbccaabbdcacaabdcbdcbcaddbdabcdbbccbdaccbbabbadbbaccbadbdaccadbdcddabdcddbabbbadcaabbbcdcdbdbbbcdbbcadaaadbbbcdccadabaccadcdcbacdabcdbdacadcbbddcddbbbadacdaabddaaccbaccdababadacbcbbababcbacdbdcacdcbaccbdabbabdcddabbccbcdaddbbabbcacddacaabcbbddbbdaddbcabaacdcabcacabcaabbdcabacdcdadcbbaadacbdcdccadaccdcacdcabbddaddcbbaabbbaddddcaabcbbddcbadcdbadcaaaabbbadddabadbcdaccaabcccbbdbaccdcadbdaddbdccacbddbadccdcddcdadbdccddbcbcdaacccabccadcdcbdcbaacaabdbadcbdabdabbadacdcadbabddddaadababbcddccaadbcbaddacccbcaccdbbadacddacdcdacdccdbaddacaaacbbbdccddaacdaccabdcaaabbdabcaddbacdbbbbbbabddababbbabddcdcbccbacbbdaacacaaacbbcaabdbbbbdadbcadcacadbdbdccaaccbbbadbabdadbaaacdaddcccabaadbcadaaccddbbccdcaaddadacaabbdccacbcdddccbbadbbbdbbaccbdaaccadddddbcacbacbdadbcbcbbbbbaddddccdacdbaadbabadbbdcaadbdcaaccbaacdbbbbacbcdadabbddbbbddadcccaddbdddddbcabadcacddadcddaccdaacadacdabadcbbabbdaabcadcaccbadddaddbacdddcbdadccbdbcbddcabcaabdbcccababdaccbbbbbbbddbddcabcbdbacabdcdadaccdaaaaddbbbbdadbdddbcbdaaaadcdbbabcbbddacdcccaaaacccadadccdddbdaaabbdbbddacddcbabcabddbaaadbbcbacabdbcdacacdddcbbbdaddccbaaaccccbabbdcccbcabdbbcaddbbcdbdaccbdbbdaaaabaccababbddcabdaaacbaacbbcdbadaaabdcdccddcaaddccccdcaacbddadcadadbabcbbcddcacdcaacadabddabadabdacccdbdccccaabcadbbaabcacaabadbdadbccaaacaddcbbddddcaaadddadadadcbddaacbbadcddadabcdacaccdaccadbaaddabdadacbbdcdddbdbdacabdacadcbbdbdbbaaabccbaddaabaaddddcdabcacbcaddacadbaaaabcddccdcbbcbabbcdbbcccbccddbdbbdbbcacddacaddbcdcabdcababcdbaacabccccdccbbbaacabadabaacacdbaaacaaccbbcdabdcbabadcdaaabaabdbbabcacdbdbdddbcdcadabcbacabbbbadbbaadcadaccababcccaacbaaabaabcadcaaadacdbbdbbbcabbacdbdccaddbddabcbaacaccbaddaadbbdddabacddbdbcccadaaaccdabdbbdbcbbccbaccbbbdbbdbccbadcadcaaadbcdcaaccaaccdaddcaadcddcbcdbccabbbcaddbdaadcdbdddacbacdbbcdbbcbbcdabdddbdaabdaacdcabcdbdbabddbdacddbbcccbccdacbbdbdbadcccbcabdcacacdddcacbbcaacbbabdbcddcdaaaddcbcaacaabdcdddbdbbdccbbdbcdbcacdddddaacadcdabddddaacccacdabbdbbdbbcaacaabaadbcbabccabdaaabaaccadbcabcabacccdcadddbadbacdbcdddbbadacadadaacacaadddacbbdcddbadcaacdbdcddaddcabdcdadbcdbccaaadcacbddcbbbcdadcbccbdcabdbdcacdcbbdcaccdbbbcacdcbdddadbbbacacbdabcacddabdcbdccbcbdaacdaadaddbbcccbdbdcbddabdabcaacadbcdbcccaccdbbbabacbaadabcbdabaccbadcbacdcdcbcaadbdbdcddcbbccabcddcbaaaadccbaabacbbbacaccbbbbcbdaabdcccacbaccbcdbcbaacbbbdcacddcabdddadccddabcbbccbabdaababdaadacadbddbacbddbbddadcaaadddbcbdbaddabdcaddcbcabcbbdbcbdabbccbabaccabccdbabdbbddcaabcdacdabdddbdabbdcbcadabbdadadadcdbcccaacbdababdbbccbabccaddbbacbbbdbaabdbdaaabaddabdbdacbaadddaacdabcacabbbbdadacadbcaaccacdbdccbadaabcdabcbcbadcdacadbadacdabcccbcaadbaddddbccabdabbbbccddbadcaacacbdbbcaccbdbaddbcdcbccccacaacdcbbbdcdcabcaaacdbdcdbaacdbdcdbcdcbcaabcbbdcdabcdbdacdbdadcbdccaadcabbbbdcccbaaccbaddacdbdbdddcabdddcbbbaabaadddadbabcccbbccbaccabdcccdaaabdccabaaaacdacddcbbbddbccddcddcdbdbddcbcbbbdcadbabcbdcaabdcabdbdabbccaacdcdbacbbbbdbdbdacacbcbcddaaabacaaaadcbcacababbcacbdaabccdccbdbacdddbcaadabccaadacbbbabaccacbabddaadcccdacdbbccbaacbdcddbcbddabaaacaddacbdbcbabdccadacbccdcddbbdcbdccbcdaadbcccdbdbccaaadbacbbbcbddabcaaabbacbdbcbcdbadcdbaadbddbdacccdbaacbdaabbcbadccacccdabbccdaddcaabbccbddaddccddcdbacbabdddaabbdaadddaccbbbdbbcddbdbdcccddcddbababcddccbdaddacbbcdcdbdcbcabddbbdbccbcbccbddbdcdbcdcadddddaccbcbdbdbbbdbbbadabdacbccbddadadcbcddcdbbdabcacddababcadbdadabcdddbdaabaddccddbaacaaabdddabbdcbdcbadaabacbcbaaccccadacaaabdabcaaacbbaadaddacbcbdbacabcdababdabaccbaaacaaddabdbcbbbbccdbabdccbcbabccdadacbcdbbdbadaacccbcaabcccadddbdddddaadaddcbcdacccaaabddadbddcadccccbcbbdacdadcbddaadacabbbacbdcbbddbdbcbabcdacadaacbdcbccbbdbdcbccccdabbbacddbbaadbddabdccdcbaadcaaabcacabcdbadaaddcaadddbdadadbddaaacbdcdddbdddbbadbbccdacbdbdaddaaaddddcbcbbdbabbaadadcbbcaadbddcaaadbbaaadaababbbccacaaccdddddbababddbccaaabcddbbddddbcbdbbbcdbadddbddcbbdadbacabadaacccdcdbadcabaadcbdcbdcbbcaabbdddbdcdcbcdabdddbaababcdcdcbaaadcbbbadcdbcacadcdbcbbabadaaddddbbdddbabbacbdddbddcadaacdbdccbcbdbcbaccddabccbdbbdacccdacaaaacbabccbdcacacdccbdbdcbcdcddddbcbcaaabacdbaaacbbbbdccbccbcbbdbddabbdccdbadaacaccadabcadbaaabbccacddbcccabccbdbbccdbbaacaadacbaadcadddaaccbabdbcbcddababdbacbcddbadbcccbbcbbbdbdacbbcdccdbcdaccadcbbabcbacbcabbdcddabbddccbdacddccbaddbdabccabcaccdccdbbacdabaddcccdbabbaaccbdcbbdcadccbddcdbccbcadbcddcbadccdcbadddbcbdacbcdccdcdadbdcdccccdccbddababcbaabdacdadbaddadcdbabbbaaabbcdbbccdaaababcdcaddabcaacdcbbbcaadcbbddbcdacbbddbcdadcdcdcabdcbaddbbdcabbadbbacdaaadddcbadaabcdcadcdadbbbcdcddadcccacacccddbbdacacabdcadccbabdadadbbcdddabbddcdacdacabddbbaadccaadadccddcbcddcbcbdddbcbbcbbabcbbacabdbcbddbabbaacadaddbcdcbbcdbddcacccbabbbbabbccaaccdaabbddbaaacbabacadbdabcbdcabdddabbaddacbddabbbbcabcdccaabbbabcbdabdbbbabdcdcdcdccdcddbbcdbdbaadbbbcadbcddaaadbddbccdbdbcddabcdcaacbcdadaaabcaddcacdcdadbabcadcbddaabdcacbdaaadcbccbcaadbdabdacdadbdacaacbdddbdbcddaaaddcaddcbabbabbdaadaadcdbaccbadcbbcbbdddbaaacbdadddcbabbcbbaacccbcdbabacbddadbaaadbdbdcadccbbbccdcadabaabdcdccdcbbdabbcccaddaacaabbbdcddcaadaacbadcdccdbadbcbdadbaadccbbabcdbbbcaddcbcdadbaabccabddccbdbcbcdabcbbaaabaabcacbcdbbdacbddabbbbaadcbdbdddbdccdccbbbaddcbdbabacaadbbbbaaddcabddaacdcbbbcdddaacbdccabcddaaabbdddaccbbbaabbabdcacadcbaabbaddbccdcaabbbccacdcbadcadbacdbcddcddcaadaacbcabddbbcbbdccccdababaddcccbadabaadacddcdbdbabbbadcbcccdcdcdccbddddbdabccbdcdaabdccadcabccacdaacdcddaaaaaabaadaabdbdaacbcbcbaabacdcadcacdabbacbdaacccbaaccdbcbaddcbdadcccabadbdcdcdbbaacbaabbabdbabddbdaabbbbadacaccaabdbdcdadddcaccddaacadbbacdbcdabbbaddabdcaabcddcbadbdccdaadaadcbabcbaabbdddcacabbaddadcdbbdacbacbddabacdcdcdaaabcabddbaccbbccbdbcdbbbcaacbbccaaccbbbdccabcbdcacaabcbdaccababbdbcbcbdccbdcbaccbdbcdacbcdaddcddbbddabdabcaacdbbdcddcadddbdacadccccacaccbccaadadbdaccaadbbcaaabdcaaaadcdbccdadddbcbcbbadbbddbacbdadbbbddbbbdaddbaaabadcbadcdcccaaccbdadddbbadacbcbbbbdadbbbcacabacddababdddcaddacbaacccadaabcabcbbdaaacbbaaddbadabcadabcbbdccddabbcacbcddbddacddabdabddacbdadbbcbacadbcccbacdcaaaddcdbdbbcddcbadadaaaccbdbbbcdbddbacbcbcdabaacaaaaabacbdbdcabcaacabbcbcdcbbacdbbacbdccbabbabcddbcbcbddbbaccacaabbaaacaccacadcbbbababcabbacabbdddccdccdaadbddaacbbcbcacaaccdccbbdaacccdabbbbabacccbbbabbdbbabbdcadbdcaddbaaccbdaaadaacdbacadbdcbcbbdbaadcbdaabcacbcbdcbcbbdcdcbdddabdaddbcbdbdddcbdadddddacdddddcbcbadbcbbccdaddabaddadacdccaddabddabdbcbcaacddbbbccddbaaacbadcdcadbadabbbbaacaaabaadbdbdadddccdcbcbcddcbcbbadadacbbaadcbaacbbdaabaaadabdbbbcaaaaacbbbdbdbcdcdacbcabbadaaadaccabcddbdacddadadbaacbdcdbcdcbcbcbbdcadacadbababbdacabadcddddabdccbbccbaaaaacacaabdbaaabbdcbdadadbcccdbcdbdabcbadaaacaaaabbaaccddaddcccacabbdaaccdcabcacddabbbaddbbcbbbbaabdbccdbbaaabccbdcdbaabcadcbbbbdadaccbddcdbcadddcacbccdbcabdcabaadacabdadcdcdccdbdacbdaaccaaacccbccdaaacababdbcdbacabcdadbcbdcdcbaddabbdabdddbabacdbaabdcccbcbadddcbbdcdccccacdcdddabccacbbddddcdddbdbcdcdddcbdabcaccbadacbbaabdbbcddacddbbadddbdbadbcbcdbaaaabacacacadaadababdccaadcddadaaaacdacacdbddaaabacbaaabddcaacadcacdbdcddcacaaacdbccaaabdbdbcdadddccadcbaabdadbbdbcddbabbabaaacbcbbdabdcaaabccbbbbaabcbddaadbaaccababaacdddcadadbcaaaccdbcbddbbaadbbddcccaccadbbaacbbdbcccdbbdcadabbbdadbdbcdabdcaccdbcadcbdbaacdddcaccbcdbbbdbddbcddddbddcabbcbcbccacbaacbcadcbdddbbbabbbabdacbbdddaabbccdadaadddbcbbaabacdaddcababaddaabbcbcabdbabadabcdddadabbdabccabbbdbbbdaccbdcaaddccdbbcdcbcacbacdcadccddcadbcabbbdaaadbdbadcddaacdaadbcbaaddaabbbdbbdbbbcbbbcadaddbcaccccbbacaaadadbacdadddddbbdcadadbcbdcbacddcacaddcbdbdcddabdacdaadbcaaddbcccbcbccdbadabdaaabaddbdabacaacdcabbbbbbcabcacabbbbbbcddbdbadaacababaabcddbadadbadacbaabadbdbbbabacbcbbbadcdbdaddbacabcaadbccdcaaabdbcddbadbbbdaacbacadadbdacabdcbbccbbcaadaacacdcbcdbdccbcaabaabdacccaaacacababdccabccccabbbababcbabdaacabcbbababcdbcbcaadabbaabdadaddadcbbbdcdcbddaddcdaaabbcdcbccacadaababbdacbcbdcbdbadbbbcdccabcbcccacdbaaacbcacbabdbccccbbccbbdbbccccdcacddabacbdabdadbcdbadabdaacdcbdcddbdbacdbcabcaaabccdcabbacdbddbbcbccaadaabcadaaccbbbddcdbabccabadcbbcacddbbacccdcadcaacbdbbaadaddcabcaaddaddbacaccaaabbdbcccdaacddcaaadaacbcddacbcacbcbdbcacacddbcbcccbbcabbcddccbacaaccdaddbcadaabdadcdabcadddcadcdadbddbabdbcccbdbddadbbccaccbaabdbbddbbacdaaabaadacdaabdaccbdbbbdacccbadabacbabcddcbaaaaacbadbbcbadaabbcdcabbbccaabacbaabbcbacabbdaaaacbddbbabaaaacaacddbddabcaccbbcccadaabbadabcadbabbdcbbcbdaabdadddadccbaccdbcbdcabdcacaabbbdbabccdbcbabcdbdadcdcbcacdbdbaacbcdbbabdaaabcddbacaabbaabaabddaddccbcbabdacbcbaccdbaddcbddaaadcbcacbcabdbcccbdccbcaabacbadcaccddcbbbbcaccdcbddbbdbccbcdccabcccadbaadcacdcdcbdddbdadcababdcbccbdabacdbcddbdcdbcdacaccabbcabadabacadcdacdcadbcbbccadcadbabacdaaddbaadbddcdcbabccbbcbbccdcbdcbcaaadbdbacaadabcdcacbddcbcdbdaddcccbbabbbaaddcaddcbdcccdaddccdbacbdcacdadbaacddacdcababdbbccbaccbbdcbadcbdbaaaadadcadaacddadbcdaaabaabaadcbdbadbabcccbddcabbaddddacbbabacaccccddacadbdaabccdbacacdbbdddcacabbcbdabbdcaaabcacadbdaaacccbdbdcbbadbacdcddccbdbbadabdcacbacacaccdbadbbabdbcbdbcbddcabbbbbabbaacaddcddaaadccbbcbacbbadcccccccadaadcdcbdadadcacadbddacaabaaadbaadddaadacaaadaaaccababbbcaacdaaddcabcbdddbbddcddacdccaccdaacabcbdcddcabbadcaadabbcacccdbcddbbdaccaddcbcdcbddcdacbabddcacdcccbcdadbaaaaccdbbdcaadbaddcbcaddaddaabcbdabdcdadcbdcddabbdadbdccdbabbcadadbbdcdaccbbddaaadcaaccabccccabdbcaccacccaccdbbbccacbadccdbbaabbabdadacbacadcbbdabbcbacccbcbcabcbddbaacdbdbdaabbbabaadcddbaadacdaabdaaaccdaabdccddcbccbddccdbaccddcaabcddcdbadabcacbcbdcababbbaabcdbdcbabbbcaddcdaabbbacddbcbcdccdcbadcabbdabccbcdcbbdaaddbcbdcabcaccdcccbcdaccbaaccaabccaaabbcbbdcdbabcccdbccabdacaccbaacccbdbdcaabdbbabaababbadcccaccdbcbabcacccbbccdcacaddcaccccdacddcbccbbbcadcbbbbbdcbbabddccadadcaaaadddacaabdcbbbdbdbaaadbaadbcdaddaddaacadaaacaadcdbbadcdabcbdaabccbdddcdbdcbabdcbcddadcbcdaaaadcadabadbbbdbabcdcbdaadbdbdccaaccddbbcddabccdadbaacaccccddccadbddbdddaabcdacbcaddadbdcaadbcdccccbcdcbdcbbaccccacbaaaaaaccaabadcacabacdbcabcbbbaccbcbacbccadcddbbacacdadbcacddbadcbcaaacbdbadbacabbbadcdbbbcacbcdcbaacbadbdbbbbaddbcabbacccdbdddcbccddabadcababcdacdacbdbadcbacdcadddcdadddcbbdcbdbbcabaabadcdacbbaaddbadcddcbcaabbdcbaaacdcacbcaadccaacadddccadcccbdbcdbadabbbaccbaaddabbaadaccbcdaddbbbccaabcbcdcbbaadaacbccabcabadadcdcbdbcbcdcddccbdbabdbbbdcabadbbcadcadcacdcabcaabcbddbdccacddcabcbcbcbddcaaaaadcbbccbdabcdbcbdacadabccbababdcbddbccbddabcabdbdaabbacbcabcbcbbbcdcdacddcdbbdcbbddacbcaadcbbdbdcabdcdbddbdbbdbcdbbdaadbbccbcbbaadabaccaddacacbcccadacbbaaaabdbdcaabcdcdbdacddbbabcdacdbadaccddbaadadbbcadcddabadbdacdbddbabdadadadbcadaadadccaadabbccdbcaaaddbadddccccccabddbbbdcbabcdbdccdaddcabcbdababbacdccdddcaaddabcacdccaacadaacbbbdcbccccadaaabbddaccdbcbcdccdbbaaabacadadcdddbddadbbcbbbbbdabbcacdbaacbbbcdacbbddbdcdbcadcadbadbdbcaacabacdbbbbbcdbdbbacdcacbcadcaaaccbbbcdaaccaccdabaccbacabcccaabacdbacabacbbdaccdcacbacbacddacbbcacddbdbcdccbaadacddbbdbbaaaacacdcddccadcbdabdccacbddbdcccaddbadbcabaacabaaabdaddaddcbcdcdbbabbacbbccddcabdcdbddcbaccacdccaacbdbcadcccbbdbbcbbcdaaccbdbbcadbbbbcbabdaacbbcabadddddadabaacdbbacccccacaacaacbbdbaabbccbdddcabcbabbdaaabdbbdbcdbbcaabddabddadadcaddadadcbbadcdadbacbbdaacbadaabbadbccaddadbbcbadccadadadbdbacdcdbbaabdcbaaabacabaabbbcbdcccddadccddaaaabbaabcbbaddcacdaddccdacabcadddccdcaccccddadbdbabcabacacddabddbccaaabdcdabaabdcdcdcbadacbbacdbabbcbddbddccccbcabbaacbccdadaddcdcccdcddaadabdcadbcbaccaaacddbadcdddbdbbabdababdccbadccdccddcddcaacbccbbcacabddaabaccacdbdbcaabdcddccbadcbbccbdacaaabdbdaccacbbcdccbcbaccbcbadddbdcccddbcdaabdabcbabbabdabddbdddabbdcbdddabacaadcbdbccacdadcdbdadbabbaddcbacccbaddddcabcabdcddbddcaadddacacdaddcbdbccdddcbbccccddaccddaacbbbbbbdaadccddddbdcbbacbdccbbadcabbbbdaabdbcadbcbdbdcabcbcabbaaabbcbaadacbabdbcccbcadbaacadbbdbbbabdbbdacbbacccddddddddaaaacdbacabdadddbbdcaaaacdcdaaabcaccdabbabdddddbaaabcaabcdacdbbcbdabbababcaacaacabcccdaacbacbcdddacaaccddbbabcccacbdcaadccdbcbcadbacaaaabcbababccbcabbbadbabcdddcdabdcabccccbadacccdacccdbbccaaaaccdcdadbbcacdbdabbdabcbacadcdbdabcaabcdccbbcbdabbaccdaaacacaaddddbdcaccadcacdbbbdacbdcbddbacdcabaccbdcdbacabccbdacabbdaaadcbbbacabddabbabbcacbdccddcdaccdbccadadbcabccbcaddadaaabcabddcbdaccbacbacbcdcddbaccdaabaacccadbbbcccaccbaabcacbccbddacaccaddcdaaabbdbbdbddccbdbdddacdcdbaaadbaddbddccbdddcdccdbabacdddbccddcddbccddcaababdcdaabdaabdcacbcadbddabddcaabcaacaccaacaddccbbbdbacbdbabccbdcbacacbacbacdbdcabacbbbdcacaabdbbaabadccbdcdbaadbacdbbcbcddbdddbdbabdccacacadadaabcbddcbcbddccbdbadcddcbccbdbbdadcdcdbbcbaddacccbaddbcbdbaaabdadabaabbdaccbaadcadddadbcddbddbcdcdbbabbdadbaaadddcddbddaaccbcdccddbbacacccbdcdbdacdacadacbbddcadaccaaccddddcabdadccaddccacbacdbddadbadbbbcccabbcbcdabaabaadbdddbbaaabbacdcccbbdadcaccbdbdcbcbccdbccccbcddccdcbdbadbabccdaddcdbcaabcdbdddcdcbdacaccbccadccaddbbbabacabbddadbaaddccdbdcbcbadcabdcbbaabdcbddbbbdbacabaaacbdcbbddabbaaabbadbabdccbacacbbabbccaccddbcbbbdababbbcccabbbbddddcccdddddccbdccbdcdbaadabdbadadcccbabccaddbcaccaddbcddddddbdbaadacadcccaadccddcaadcdbdbdbbbbbbabbdbacdcbcbdbacddbcbddaccdcdbaddddcaadaadbaabdbcabbbbcdddbaaccbddcdaccbcacaddacdaacbbabbddccdacbbaaabacbcadbdaaabcbdbcaababbccabacbcaaacbabdbbbcbdabbddbbbbadbccbdbbbabbdbcababdaadbcdbdbacdbdacdcbabdaabaacdbcacacbbbabbcbdacaaccacbdaaaacaaddbcccbacbdaddaacdabbbdbdbacdccdbccdddbadbcdbadcbaaccdcbddbbabcccdabdcaadccbaaaccbdabdddccccdaadbcdcadddadacdacabdcbdcaaacddcbbacaaddddccdabdddbcddadaabdaacbcbcddcdbcdadadacdccddbdadccaddddabbcbdbabbdcdddccaddbbdcbccaddbdccbdbdbdcbbdcaccddcaaccbdbbbbbdacdddaabbcaaacbdccbccdcadadadcbccbaccbadcccababcdbdcabdddbcbacadbcbadcdbaacacbcadbccaddcabddcccbcabdcabdadaddbbaddbcabdcccaaddbdcdcdacabdcdcbdadcbcbccdcaccdddcacdbdcbcacbbaccbccbdabbdacaaddcacddccbbcbbcbccccccadbaaccbaabbabccaacaaddcbbccdbdbacdbdbdadbbdbcddcadcaaccabdbddcddccbdbbdbdddacbadabaabcacbcabaacbbbbabbbaabbbabcaddcdbacaddabbadbbbddcdbaaaddddbcadcbbcdabdadcacdbdddaddccbbbddbcadaabdbddaddbcbaabacbdadbcacbabbbcabbacdadaaccccdbdbdccdcacccdcbcccbabdcabbdcacdacbaddabcdbbadadddbccccaadbabbdadcbddddaddbdccbcbcbddcdbcbababcacabdbaacdcaadbdbdbbdacaabacaadcbbdcacbcaabaaabbabaacddbdbcdcbddaaddcdbcbcdccbbcabbacdcdbddbaaddbaacaaacaaccaddabcaacbbdcaacacbbbdabcbaacccbbdacaabdcddbaccbdcaaacdaadbabdacdbddbcbbadaaabddacacbaccabbbabadbcbcbbdcdcdaadbaabacdcdcbbbdacbcaacccacaaaccbadbacddcaddcacaadaddddabbccbaababdadaaaadccabaadbcbacdccdcacbabdbdacdbcccabbaabbdbdaaabcbcdddacadcdbbdbdcdcdbbdabccccddbbbaccddbacabbbbcdddcbcbdcabaaadacccabbadcaccccdddbdadabbbcbdabccdcddaccdabccacddcbcbbccdddcabadcdcdcbbdcaabcdabbaddbcddbdcbbcabdcacbcabdaacabaddbdacccbbdadaddcabaabadacdbdaadcbbdaaabacddcbaccdcbcabcabbbabbdabaacaddbccadbcababcaabccddaabaadcddacaabaccbdbbbcbbdadbbdbdcdabcabbcaddbbadbababbaddbdcdddacacbaacabdcbdcdaddabadacbdcbbaabcbcbccdbbdccbcbacdbbabdccdbbbccbdabcbbbbbdabadbacdcabbccadcccadaaadcbcccccdcdaadcacaacdbbcbcbabdaacaaadbbbadcadddbcbdcbbaabcbbbbacabcddbcdaaacadcdddaaaabdcdbbaaaddabcccccaabbadbbdadccbcbdddacbbccccbcbccbcdbaccaaccdbacbdddcdddccbcabccdcabddcabacbabdcdbabbbacccccbbcacccdabccdaadbaddbdcddcdbbcddccdabbcdadadddcdbabcdbdcdcddcdbccdacadadcbccdbddcadabbacaabccaabddadddbaccbdbaddbdbcbcaaaadacdbbcadbdddbbabcdaabddbadabddbcdaacdcaccbacdabccaccdaccacbdaccccaaccbcdddcdaaacdadcdbacbcdacacddcdadcaacdbaadcdcadbaccadbadaadcbbbbbaacdbacdbdbbdcadabbabdbddcabadcddbdddadbbcbbadbdacaccaadddaddcbccbbbaaacccccaaaaabbbbdccbacabddabbddcabacccaabbddcbbaababbdaddcaddbaacbdabadcacaabbcacdbaabbcccddbccbaaaadcdcccdbcccbcbbcbddbbdccbaabdaabdbbbbabdccdcddaddaadbccddcddbddaacadbadddcadacdcddbdcacbacbdccbdabccdbacbcadcddbdcbcacbadccdcaaccbcdacccadbcbcadbabcbaacccadbadaaccccadcdaddcbdbdadcdaacccaccdcbcbacddbcdacacdbdcdcbcacbcdbdbaacbabacdabcaaaacdaabcbabcddbdcbbcbdbacdcdcabaddadbbdaaabdcccdadbccddaaacaaaaacaadddcdabbddbbdabdbbcdabdcaadcdbbadcadddacbadaadcadcbbcbcbcaaaabaacaccaacdcbbbccbdddcbbaadadbbcddbddbcccaddbbbadbbdbcadcacbddbddadccaccbcacaaccdddaaacdbccccbddcbccdcadbcbbcbaaabdbdabddadbbbccbdcbbcacbdbdbabaadddbbcaabcbaadaaaabdddadcaacccbdbcadabacaadaddacbddbaddaccbbbaadcadbcbabbabbcdaacdbdccdaacbbcdadccbcadabcdccadbbadddcadccbabddcaacdcdacdaabbbabacdbabbdcbdaccbccadcacddbcadcdddbcdbbddaccdbdbcbdcbbabccbdccccbabbddcbabdadaadbccdcdaccacdbbcacbbaccdadccbbbcdccaabaaabbdbaabbaaddaaabcdddcaccaaadbbcbbadabaaadabdbaccdbbdcaddbdcabdbdcbdaaadaadaddaabcccdaacdacadddbadbdccdcbcdbadcbdddcdcbdcddcdabbcbbbdbcccacabcccabbbbccbcddcccbcddddadbdbaadbbaaaadddbbbaaaaabccdcbbdccdadbdcddddcccdbaddaaccdbaddadbddabdcdaddcabdccccbbbaacbacdcccdaddadcccbadbbacdadcbabdcbcdbbccbcacdcabcbcccbdccaddbabcaadbcddcdabddadbcbabbbbabbdaddddadbbdcdcabdcdcadaccbbdcaccadaddcbaddbadcccbdacdcabaaabdcbaacadabbcddbabbdaccdbdaabbdadbbccaadadacdcbcddcbbabcdcdcbbbcbdcdbcabaabdaddacbabddcdbbdbdacbcbcccccccdbaabdbcbcabaabbbbadcaacabdbdbaccddbacaaadddadddbccbbbbbaabadccaadaabccbdcdcbdbcadbcabadbadaadcacaacaabadcdcaacadcbadcacabbcdcbccaadbcbabbbbaabdadcabdcdcccadbadbadbadddbdcccbcbbaccabaaabcaabbdbbcaddbcdcdcbddadccadacaccdacbcacdbbbababaadacbbcbdddbbbccbaabbacbbcbaadbbaacbaadbbadbbbdcdcbcdcbcbcbdbcdbaddadccaabdaabdaccbabaddacdcbdaaabacabaacbdccdbaddbbddccccabbdccdbcbdddbbbddccdbabaccdaacbcbbcaaadcbccccdcacbabadaddbbacccadacacdbcbdbddadbdaadbadddcbcdbdabaadcbddbacdbdcbddbabaaaabcbabaccbdddbcdabbbaddbabbadbadccaccbbdbbdcacaabcababbcadaccadaadabdbbdcbcdbbbcdadccddbbdcccabbbbcaacccdadbcbbcbacccdaacabcdddbadbcdccababacbcacbabdccbbadbbaccddddacbacbadaabbababdacccbccaaacaaaacbddcdbcdabaacacadbbdbadaabdddabaaaddbdcbdbaccccbbbdacccacaddcabccdcdbcddacbcaadaacabddbaaadabdcabbadcabbbbcdccdbcabbbaddabbdcdddaddadbdabcaaaaacbabddcbacccbbbbcadccadcbccbdabcdcacbdbdbaaaaadcbdcbbdcaacdaadacdcdacdbcbcccaabdbabcdcbacdbabcddbcccacdcccaacaacbabcddbbbcccddaacadbadcdadbaccdaadcdbbbdddbadbbbbcacdacdbdaddaabcbacaabddaddabcbbdcbadbbaabdbbdaccddbacdaacddabcbaaacacabaabdcbbacaccbdacbccababacbcdadcaacddbadaddccbbdddbcdbdbdadbdbbcacdbcbccaadcbcdbcbbbdbdaadaacbabaddadadcbdadadbbbdbabcacacdbdcbbcadabccacddbddacacdbacdddaccbcabcacacadaabdddbcdabdcddbddcacccbadaaadcdcccabdbdcdcacdabdcbbdabcdcdbaccabdbccdaadbbdbddabbcbabdacdaadddbdbbdaccdbacabcbbddccbcddbccbcabcdcacacadbaaaaaabdbcdabccbbbbdbadcbdaaaaacdacdbdbccdbdbdabbacdaaddbcbcacbcbcbbbadcbdababadccbadcadcbacacbddccbbdaabddaabcababacacbaabdbbcbcccadcdbcbadaaabbcaddaacdbdaaabacbcdcdacadcddaabbacbadbcccbaaadabbbbbcadbaaccddbdadaaabaaaddccaccdcbadbbcadaabaaaadcbabcdbbabbcabbcddbbddcacadbbdbdbcddaabaccddaccbabbdaccbdabaaaabaaabdbbbdadbcccdcdbdabaccacbadddabbbbacccabbbcdcdddcadbbaabbddacdaabcdbcabddadccbbcaacabaacbcbbcaaddaaaacccbdbcdddbcdbaabbcbdddcdbacbdcaacccdabdbaddaaadddcbbadbacdbccaaacbaaddcadacabaabdaddbbddaaccadbdaabdcbbdaadacaccdbddacdabdcadcbaacbaacabdadddbacbbdabaadadaccbaddcdddddccadbdcbcbacddbddddaddaddcbdcdddaabcaadacddbcbcdcacaaaddccbbcbbdbbbdcaadddbbcacacbbabbbdadabdacabbbcdbbbbdccbaabbddabbbcdddcaddcbcbbbbcaccadcdcdacbbdccabdadbdabaabbbbccdbdadaccadcabdcacbadaacbadbdcdbbbddbcbccccccbcdbccccdbaaaabaccbaaadacdcccdcaccacdccbddbdbdadbcadbcbbccdacbcccbbddbddcdbabdabddccabcdbdcabcccbbcccaddbabbbacacabdacdbcbbbbacdcbadcdccacdbbaaadcacacdbdbcbccbdcccccdcdcabbcdbabacaadaccaccabbaccabdcccbabbabaadcaaabdbcdbcdadcdbaaacadbbccacdabdbaddcdccdadbaccdbabbacdbbcbacdcabdbacaddddcbbcdbbbadabdcdbdbaadddcdbdcadabbccbbcbadcacddcddacabbdbbbcccdcbdacdcccbbcccbabdabcccabbbcdaabbccbbbdbddaaabacadaccbcddabccaddddbcbdaccbcddddbdbbdbcbcbcabccaddccdaaabaadacabaacabddddaabcbddbdcbddabdaaaadcbbdddddaacbadccbaabbcbbbbcbcdbcaacaadaaaabcadcbdaaabdddbddbdbdbccacccadbaaddcbdbcdbcaadccbaccbacdbadddbdabdcbdaabcabdacaaaddabcdadcaaccdaababcdbcdacaadbbdcbbbdccbdbadcbbcdaccabdcaabcadbdbadcbaccbbddaacccaccdacdcbbbbbadbbbdddddbdbbbccbbcbbaddadccdbaddbdbcaccccbbcccdbcaddabcdcbbddbacacaaabbacaabaaadabddddbbadacbbccaacddccccbbdabdcdabddddabdadbccadabcddcdcbccdcccaccdcabbbabccbcaadcbbacaabcccadbdccddacbbbdaabddadcddcbdacaabddbdcdddbbaadaccabbdbdbbdbccbbabaddadcccacbcabbcaccadadaadaddbbaccdcbadbadabbcacbdbbacddcbbbcdbbaacabaadacababcbcaaccdcdddadcbacaacaabdcbcbbaddbdbabdcdacdcddcaddadccabcadcaaccbaddcdabcacccadcddacaddccdcbdbbdbadbccbbaacadddbdddacaaadacadbbddacacdabcacacadcadcccbcadddacaaacadcccabbccccbbdddadbdddccacbcbaccbcabcbaabaaadddbccdbcaaabadbdbdbcbcaccaadaccbdbcbabbdbccbdaccaddaccbadbcadcabbbbabadacbdadcababcabaaacdbcdcdbdcbadbcacabdbbbdbdabcbaaadaaabdbddcbdaadaaabbaddddbbddabdbacaccddadaacabcbacddabdbdbababccadaaacbcccabcbdbbadacbacccadbbdcadcbdabdcccdddaaddbacddbcbbbadbdcbaaddcabdcdbbcacaddbbadcbccdabaacdcbbacabbdddabdaaaaadbdabbcdddacdbdcbabadaccdccdbbaccddddddccaaadcabbbdcacbdcbcabbdcacabaacbaddddcbaaababbbbbcbacbcdbbdbdaaadbccdacadcdadbdacbdcccadbaacbdacddbcaaaabdcbddcdcbddcdbabdddaaccbbcdbdbcabacaaaccccbbbdbbaadaacddbccbbbabdbcabbacabdaddcbbbbdbdaadbbcccaadbaacdddbddbbcdddcbbcdacabccabdcdbbbbbbdbbaddacbcbcdadcbcacadacbcddccbcdabbccacbdcddaacadbacdbcaabdbbcdcababababdbaddadacadccaacbdcaccadadddadbabccbcdccdacccdaacbaadadababaccdcacddbaaaccbababcbabdccdabcbbdcabbacabadbcadbbbbadcccbacacacbadccbcddcdcbacbcacabcbaaccadbdaabcadbdbcbddccaabaddbbacbbbdcacbbadbaaacabdcaacddbaccaadddcbdddccabaccdbccdaacccbdcbbdabbbdbbbaaabcdccaccaddcadbddcbcbccdaddadacacaabccdbbcdbcbbabcdbdccadbbdbbcddbdcbacbbcadacbdaccdadaaabacbdbcbccbabdabcacccdccdcdbabdbacbdbcddbbcdacdbabbaccdcdabcddadcbbdbcaaaabbcdccdbbddabddabdabaadcbcaaadcbbdcbbcacacabcbacabbdbbdbdbdadabadcdbdadacbcacadcccbcabcdcbcbbdbccdbbabbbcbaabcaaccdcdcddccbdcadcbcaaaddabcbdcadbdabacadabccbaaabbdabddcbacdccbddabbcbadbbdaabcaabdbbababacabcdbdbdccadaccddbccacdcadadaaacccddcccdbbdacbdcacddcdcdbcbcbbdacabbbaddcacabcbaadcbdbdaacdcbababddacbaadbbcdbbbaadcbadcbdacabbbbcdacccdaddbabbbdcaaaabbdcdbcadbdaadabdaadbcdacdcddcbacccbdcaadbdddadcdaacdbcabccaabcbbcddbbcdacddccaccabaadcdbacdacbbcbbcdccbbddcadcababbdbaddbcdaaccdabcccbcbccaabdacbcadbaadababddadcccccbcaaccbddcbdbbcbadcdaddccaccbdddadadbbaacdcbdcbccbbadaadbacdddbacbadbabbaadaccdccdaabcbadcaabccaadbbadbcdabcbddbcdacbdcbadbbabaccbbaaacabddcbdbbbacaddcbcddcbcddbacbccadbbcbcaccabbabdcbbaddddbadddcbcdbaccdbcdadadbadcabcaccdbcbddddccccbcdcacbbcdcccaabcddccccbbbaccbcaacabddbbdaadacdbdccbcaaccdcbcdcbdcadcbcccdadaaadddacacaacbcbabaabbdcbccdbbdbabddddbcadacccdcbadaddbdabdbacdacdabddcbabdcddbbdabbacddddcbcbbbbacddbcabdcbacbdddcbbbcacdbcaddcbdbacddabbcbaaabdababbcaccddcbcdddcacdddcbbdcaccabcabccbddcccababbdcddbcbacddbadcddddacdabcacaacbcacccbaddacacccbccbaccddbbaacbdacbdccdcccadcbdcdbdcdbadddabddbcdacbadcdadcccccadcddacdadbbcddadbaabcccbddacdddccbcdbbbbacbdccaadcabbddbdcadccaabcdabadbaabbdbabdddbcddbdccdcddccbbcdcbcbddcdcadacdcbdbabcaacaccdacddabcbdbbbccbddacacdabbaadddccaadddbadcadcbbacdcbccdcbbdcdbcabddbdcbbabbbacddbabbadbaddabbaddbcbbcaddcbdcbbcccaacbcbcadaddcbbadbbadaddabddababbdbbbcdaabcddababcadbbacdabaaaccbbccdbddaabcbdacbcaaadbacccbccdddbcdcacaddacacaaaabccbcadbcdccdcdaadaddacdaccbddaaabbabdcabcdbcadadcdbbdcdddcadccdabacacbdacacdaaaabcddbcacdadbcbbcccdbcbbdddcdabccdbaaccccbbaddcddcbdcdaddaccdacaddcbacccabaacbdbdaccaaadcddadababdddacbbdbdddbabccaddacddcabbdcaacadabababaabacddddbcbbdabdaacddbdbccbbdcdbbbbabdbacbdaabaadbbadbccaadabbadbaddcbaccabacccbadbddcdaacbdbbbcdbbabddcdbbdaddabbcbddabdacbabcbdcbdaaabdadabddbbbacdddadcddddacdcbbcbdbdaabdabaccbcbbdaddcbcbbacbbbdcdacddccabdabbacdbddddbdccbaabaddacacaabbdcbbabddddccdcadbaabcddddbbcabbcbbcdcddcadbdcbdbababadddabdcabddddcacdcddcbabadaadabddbacbbcdacddccdcdaaddbbbacaadabcdabcdaccdbbabdbdcdacabdbbbdcaabddddbabdccaccdbaddcbadabaacdbdcdbbaaaacbcbcddbaacbdbbdabbbabaacdabbacadbdbbdcdaccbadbacadcbacdbddabdcabbaaadddaabbcccbbccddacbcadcbbddbcdcdcdaccbcdbcadbbcacadccaaadabddbaaddcaddcbbcabbcbadbbdcbdbbcbdbbabcbabcabcaccadadccbddddadcdabddbdddbcddcddbdcacbbdaddbcbaaacabbadcaddbbadcaadcaccbcabdcdabcdcacbbddccbcabaccbbdddacbccdcdcadbddccdcbadadbaccddcdcbdcadcdcaaddadbbbbccaaaccdadcacbcadaddcbdacbbacabbbcddbddbdccacaadadaaabaabbdbbdbccbacdbbccacddadabbdbadcabbcccdbadaccdcdcddbbbcbbccdbdcbbdabaadaccadbcbadabcbbbbacddbcbbbcabbcdcddcccdddccaaababacccaaddaadbaacabcbaadbbbcbcbbdcdbddaddddaacdadcabcbbbbdbcabaabbaccbbdbddabccabadaadadcdcddbacddcdacbdcacdbabbbaccdbbbdaccabddccbabbbbddcbbaadabadadcadcbbdcbbcbcbbadbdcdddbdaacdabdcdbabbbbdacbcacabcacdacbabdbadacdddadcbbcaaabcbbcabbabcaacdddaccaababcbadbadabcaabcccddabbbccbcddbabcccddccdbdbaaadcaacdbbdabdaacbabbbccccbbcabddaaccabdacadabacabaacdbbbbcdbdabaaabdbacaadbcdbccccbdcaaabdcbcbcaccdccddcaaabdbcccddbabadabccbcbccaaaccbaabbdcaabbcadcdabbbddacdbbaadabdddcbccadacabaaaddcbbbcbcbbdcbabdcbbadbcacddddbdaccdbaadbdaacabaadbabcbcbbccbcbadbbbacababdcdbdacddbbcaccbbbcdcbabcbbdadcdcaacbadacabaabcdccbcdbddddabdcddbbbabcbaadbcabdabcbdaccbddacbdbcdcbdbabbcdcdbcaabcdbcbbddddbbbdcacddcbbbadbdcbcababacbdaaaccddbdcbddbbdbaadadddcadccabcbcdaddcbdbdddcccacbaacddcddcccacbdbdcacddbccbddcbbdcadccbcaccbcddccbcddcadabaccdddcadacbccbbccdcbabadbcbbccbabddacdbddbddbaacdcccabbbadbadbadbccbcdbbbcabdaaccbbbdbabdacbaddcacbacbdbccdaabccddadcccbbbaadaaddadbbbabbccdadabcdabccdcdbccbbccbcddcbcbdbbbabdccacbdbcbadabbcbbbcabaddddbadddcddccbccdccaacdccbbacbcccdbcccdbaddaccacbddcbbbbaccaaabdaccbdcdcbacdcddaddacbabccbdddcbabdbdbcbbbddcabaaccbbbccdcdddacbdccabacdbddbdacdcddacddaaddcabcbddbdbabadacaacaccbbbdacdadbccdcadbbabbbbabdbaabccbcaabdbddbdddabdabbdcaaccbddcaabcdbbbccddcababdacaddccaadbacabddbaabdbaccadaccacddcdddadcbdbadabbadccbbcdaccaaddcccdaacaabdccdcaaaddbbabcdabdbdacdcccbaaaabbcacbaaadccadaadcbabcbdcacaadcbcaadcbdcaadcdbdbbbbacdcdbbabdcbbcacadcbdcdbcdbdbdadacdcaccadacaddcbddcdacadcadaadcdcabbbcbbdcaddbcbacbddbbbdcacbccdbdaabbacacccdccdccdbdadaccddbcdaaabaaadabbacadcbbbaabbaccabaaabacbdbccadbbbdbbbbcbdcadcbcdacbbadcdadcadcccbcdccadbbbcbcccdabcccbdcdccbdcaaaacbaababcccdaadcacdbdccbbdbccbbaaabdddddadbaadbadaadbcdddbbbddcdabbabcadccccbccdbdaabbaadbbadccadadcadbbaabdbcabcbbbdccbdbbddaaaaabaadbcbcababaadaabdcddcaaaaaaacabdbbaddccdbccaadccdcaaacbacdbcdbcacddaaaadabaccddbcbcccdabccdabbdcdbccdbcddbdddbaacddaddcbcbccdacbdabbdddcdacbcbcddbaccdbcbcdbabadcacbcdcadadcabcbcddcbbdaccddabcbabcdbacdabbbaaadbaddbcdaacddaacddbdbbccbccccbcdbdddbcdabdcbadcdccddcbccdaaddcbbbdbbdcbdbbbccabcdccacdcbadccaadcbababcdaadccdddbcbcbcbcababacabdcbabccbaabcdcaccdddbbddccbbbcbdbbdcdddbbdbbaabdbcbcbcddadcccdbadabaaabdabcbcbbbabadcdbccadcbaaaaababbabbbadbdaccdcdaabcabccccdbddaabacccbbbacdbabadcaabaaaaadcbdaccccabbbabdccbcbdaacbcdbadcbacbadbbbddccccadcdbcdcacadbcdddadcabbaaabadbbcdacaccbbacabcdbddbbabdaadacddaacbadccbcbcccadabbcbdbaacbcdabadabcdaacdabdbcaddaaaabaacddccdaadcdccbdbaaaccaaacabdacaaacaaddddadbadccbbbbccdcbbabbdadcabbbbcbaddbbabababaddcddbaadbcabdccdaacaccdddbcaabaadbbadaccabaddbadcdccacbbaababdadadaaadccbbabdcddccbbccdddacbdbbccdbacdddaaaadbbccbbdadcbbadaccbddbddbbdabcbbddacbbaddaadddbcdbbdcdddaaccbabadddadbccbcdadbbdcbadaddababdcabccadbddbbacdccbadaaaddccdcaaaadcccbaaabaccbbdbcaadaaadddbbcbabbcdbbcdcbbbbbaabdcbacbbbdcbdbabacaaccaabddcadbbcdccaacdcbdccaddaaccdacdacbaabbddaacbdacacdbcbbbcccdadddcddccdcaacdcbcbbaaacbbbacccbbdccaccdcbccccdadbdacaddcacbdacccdadaabbbaadbaddadacccbcdddcbabccbbcdadbcdcacdcacbdacacadcababaaacaaccbbccacddcddccbdcaabdccbbcacadaccddddbbbbcdcbdaaddadddcabcadaacbcacdbbbbcdbdadcdcdcbccccddccbaccbdddbccdaacddcaacdacaaacbbcdbdddabccdbbaaccccbacabdaddcacdbabdbcbdbdadbaacdbadacbcaddcacadbdacabcaccdababddcacdadadbcdcdbdaaacddddccdadabddbbcbbababaadcbdadcbbacbbabccdbaaadddcbccddabbddbbabbdcbbddddcadcabdcccbbdaabbaaadcabacdaccdcdbbdbbbdcccdddbcbbbdcadcbadbcabacadddbccddacaadaddaadcbcdbdacddbbbaaddcdcdddbbbacabcbcacabcccdcbaaaaccaaacbbbadbdadddbbbdccbdcdabccbcaacdaccaddcbdbcadbbdcccdbccabcddccadadbaddccccbaaadccccdadbaddaaaacabbccdcdbcdcdcacabcacbbbaddcbcbaacadabbbcdbcbcccdabacadacaabdcbddbadbaadbadcaccadcaaadaadcbdaacacddddacabadbbcbaddaaddcdbccacacbcdccdabaaacdbcbbcdbcaccdccabdcdabadcdccaacdacdcddcaacddcaaddacccdcaacdaaadbbbbbadcdaadcabacbccbcbcbaacaabadcdcbbcabcdaaccacbbbbcaadacbadbcbccbbcbbcddbbcaccbbcccadcdadaddcccbacadaaabccbababbddbddcdcdcadddcddabccccdabbcbbbbbbacccdcadbcaadbbccaaaaddcacbbbcaccaababdadbbdcdbbbacdadcdbdabdddadbbcabdbdaccdcaddbdadbadbabcacbbdadaddbacadccaddcbdbacacdbaaabddaddbcabccababcdbbdddccbadabbbbcabcdabacddbcdcdbcabadadcacacbcdcacbdacabbabbabcbdbcacbcbcccdccaccbcaaaaacdbbbadddababbaabcadddddacbabdacacaccccdaacabcacaaccdcaddadcbbccacadaaabdcdcdccdddaabccbbaaabcabddbaccbdcddcbacbdadbbaddcbbbbdcdddacdbbcabdbcdcabacbacbddbcacdbdcbabaaddccadbddddbddcddcaacbdccdbbbabbcaabbbcacadababdcbdcacaabbaaacbdbacdcdbbaccacadbabcaaabbbbdabbcbbdaadbbbaaaabccbdadbaaaadacdccbdcabbcacbddadabdbcadccaacddaddbcdadadbdddbacdbbdbcbaaadcbccaaaababaacdadccddbbbddbdcaaaabbbbbcacdcbcaabdbcbdbacdbabdbaccccdcadbcdbcaccacbdbcccabacaacccdbbcacdcdbaadacccdbccbaacaababbdaabbdcbabcdaacacababaabddddabbbbdcccbaddabbddaaaabcbcaacdcabdcdacccddbacadaccdbdabcaadcbbdbdcbcabadabbaddddadbbcbaccbbcddabbbbbadaaccaaaddbddbcdaaddaaddcabddbababbcdaadaabcabbcadcdbcaacaabcdbcbabddbbdadcabcbbaaabdadccaadbdacbcddbaccdabbadccaacaaccbadbcbbbaccdcccaabbbcabddddccddccbcbdadccdcddbccbbaaccbcabbcbcacccabbcbcdddabbccdcbccbabaaddcbabbdcaadccddccbdbcddcccbadbdbdadddbdbadcbaaabbdadccdcaadbabcaddbcbddccacabdcadcdbddbdbccdcddaaddcbcaaddcbadaccdccdbbddcdaabcdaadddcacabdbadbcbccaacaddaaadbdbacaadbaacacabbcdaabbabcadddadacacccbcacbbbbacacaaabbddcdadcdbcbacddbadbabdacabdadbdacbadcadccdccbbbdccddccccddbccbddcaacdccaabccabbdbabbdbdbcbdaccdcbaadccadcbbbdcdaadddbbaadaddabbbaccddaacbbdaacbbabcbcdaccadaadbbbaaddbccdacddbdbaaddaacccbbbcabcdbbacdcadccddbcadbadaaacbadaaadadbabcacbdcadcaadaabcdccbbabcbaddbdbbadaacccbbdaaababccdacdbddccdbacbddacbadbbbdbbbbabcabcddaaadccbadacbbcacdcabbcdbcddababaacddddddcbabcbaabbadcccdbdadacddbaabbddcdbcaabbabcabaccbbddadbbaaccadcaccadadadbdbaaabbacbbdacaaccbaaddcdccaaabcacdaacaddadcbcddacdbbcabcddbdbcbdacacdccdabbbbbaadadbadddddbbcbdddaaabddadadadbdcbbccacbdbdbdacbbcbcddbcccbabacdaccbddbcadbaabcbdaddacddbdcaadabcbdbbadabbbbbadadcdbbdddabcdcbabadbddcbdbacbabdbdaadddddabbbddcdcbdabdabcbaccdddaabadaaccdddadbaacdacbaddbbbbdbaddcbcbdbaadabbadccccccdbddbccaaaddabbdcabbdbcaaccdcdbcdadaddabadacadabcccbbadadacbccbabaccdcabcdcdcbaccccdddacbdbddacdbaaccbabdadbadacbbbcbcaadcabcccbaabcacbabbbbaababcdcbacbcccadabbbbbbccbdacdddaddcdbaabbcbdbbdcbbdcabacdacccaccacdaccbbcddbcaabbbdacaaccbbdacaddadcabccccdbcbddadbacbdaabcbbdbaabbbcabcabddacbacddbcbaacbbbcbadddcddcabccabcccbabaccddabbccddbdcbbbbaadbacadccaabcbcbdabacddaddadadbcddaddaddcaaaddccdaccabadcbcdccbdbdacabddcbddbcdcabbaccacabcbccccacabaccbcabccbcccccbddbdaabbcbddcacbbcaccbcadcbcbdcbcbdbdadccacdbddccdaccdabadcddbdacaccadcdabddccdbdcdbdabcbacbddabbbcdaacdccdbbcbbaaaabbdbbccaabbdcbadabcdbacaabaacabdadabdaddacacabddacbcbabdabdbabbcbdbcbcdabccbacabaaaaadcddbaadddcbabcbdddbacbddcabdadacddddacbbccaddcbcbbbadcccdcccabaadcbbbbcbadbdadcbabacddbbbacdccbaabddbdacbcdadcdcdaabdcabbbadaccddcbacacbbcccdcadaadbcbacbbcbdcddcdbcdacccbdcacdabdbdaacbdcbadadbdbdbddccccacacdddbaacbcaadacdccadddcaadaccbdcbdbbdcabbddadbbacdadcdbbbbdbbbbcadbcbbaabadbaccdadadbdbcccdcccbbcdbcdddcaabdabcbcaaabdbbbccbbacddcadcbcbdbaacbbadcddbcdddaaabaaccbcadbcaabbbccbbdabddbdcabaddabdccdddbccbcbbbbdddbcbbccdaccadbbdcaddcbbcabccbcdcdbdddccdbaabadcbbddbcabccacccbaaaddbbbaabdbdbbcbdbdbcacaabdbcacaccbaaaccaabcbaddddcdcabbabcdbdcbbdcbbdccdccdcbbddababcabbaabbcbcdbabdabbadbbcddbccdabdcaddbdbcacabcadbacbbdcaadcbacbdaaaacabdcaaacddcdacacadadddacbccdbcdbbbacbdaddcdcdbbacdaababddddcccbcddadddddccbadbababdacbacbcbbccaaccbdbaddadcccadcaaaddccadddaaaaccbbddcaaadbbbaaccbadabcadbabdaabcccbbdcdcaddacddabccbbccbcdcddddbbadcbbcadbdaddadcbcbbdadaadbdcaaaaddbdcdccdbbddbaacdbbcdcacddcdcdcddccbccacaacccdccacdccdddbccccbbdbaccdaadbdbcdbbcccdddbbddaadadcddbbbdbccbbabdbddcbabaaabcaabccaacbabaadaacbadcbdcccccbbbdacacbccddccadddccbbdccdcaabdcacdbdddcbcbabdbbadcccdbbddbcadddddbabbcaaacadbddcaddadbccaaacabdabacdbddccbbadabadabbaabcbdbdbddabcbcddcacadcdaaacbcdccaacdbacdacbcbdbbacabaaccbcacabcadcacdabcacdacbccaabcbdcacabdadccabcdcccabcbaccbadcccaabaddcabbbbaccdaddccabbcdadcdddcdcdadcabdcdabdacadabdadbcbadcbdddaadcaaaddcddbabcdabcdaabbddcdbdbabcaaccdbdaddbabcbdaabbabcdbbbdcdcddabdadaaabadccbcdbdadbcdbcbdccbaacccddccdabbcdbdbbbabcacabaccbbacbdcadabbabcdacbaadcdccdbbabadbbdbadaadcccbdcbdcdbbbbcaccccdaaccaaaabbaaddcdadbcbbadaacabccbdcdbdccdcdbbdaaacbacbbddcacacccbbbbaacbdcadcdabcadadcbbbdbdcbddbaaddbcbabbbcbabaadbcddadadadbccacabcbdbccddcccbccdcadacdabddaadcbcbcdabdddcbbcdabcbadbdccacdcddabdcdabdabcadcadaccbacbbdcdbdadbcdacbddcccbaaaaaddcdbccbccadacbdcdacbbbdcbdcacbadbbcaabcbdcddcbddcdcaadbdacbdbdbcbaddadbddacdaddbbbcadcdcaddcbadbadacddcadcddaaccddbddaacdbabcbbbbbdaacbaacbbcaadacbbbdaddcaacaacbabbadcaaabbbbabbacccaaababdddbaccccbabbcadcbdbcbdbddbcbccdadccaaaadacacabdcdccbddbacbdcabbaacdcabaacdbabdcacddcbdcbdcaaacdaacccaacdcbccaccbbbadcbbbcacccaaadaaaaddddaddbabdaaddbcccbbdcbbdbacabccaddcdacdadcabdcbacbcbddaabdbbdcacdbbddbbcadaaccadbdaaccbdbddadacabaacddbcbbcdddcbacbcdabaacddacabbadabbdbbcbdbacdcbddcccbacdcdaaabdaccbadcbdcccccccdbbdacdaaacaacbbbcacbbbadabddabdccabbdaadabdacbbcbdbaabcdcdaacbabbcdbdbabbadccdaaacddaddcdacadbdbbcabaaabdadbdadcdaddaacccbdadcacbbdbcadbabcabcbbcbbcccaccbccdaaaaaaaddcbbdcdcaabbaccbabbbbbcaadcaabbcbbdbdbabacccaaacadabdccddccccbbacabcdbaaabcdadcbaabdcabbdacdadcbbacdabdaacdcbbcdbbdabdcddccacbbbbdcdddbbcdaabacbdcbddabbabccabbddbdabbbbabaddbaacabaabdabcaccbbbaadabdddbdccdcadccbccbdbaabcaaadabacbcdadaccaaddcbbcbacbacbdddbdabaabddccbcdbcccdbdcbbabbcccdcaadbcbcabcdcbccabdcbaababcabaabcadabccabcbadabcccabcbadbabbbdbdcdcbbabcbacaadaacbacbadcbdcbcddccabbcdccdbdadadaaaacbacbcbdaaccadbabaaabdbbaaaaddcbcbcbabbaddbacdbcbaabacdadbcaccddaacaccbbbdbaccadaaddbdddcdbadbbcaabdaccdbcccadabcdcbbbcdadcddacadabcadbadccdcdcacccbdcddadcdaddcdcadaaacdacacdcaacdbbccdabbddaaaabbbdacbdbaacbadacdcccbcdbbddcbdcaccbcabbbacbcccabaadbcacacabaaabaddabcdbbbbcacbcdddccbbbcbdacbbabaabbcccacccdccababbbddbbcddcbcbbcadcddbabccddadaccbabbdaabbdadadbcdabdbcacbbabbbdbcbccbcbbdbacdcdaabbcdcdcabbcdbcbdaaabcdcabdbbccbaddcbbbccacdcbccdabdbabcbaacabddccdbbbbbcababccaaccaccbcabbddaaddacadbbbddcadbdaccdcacbccaadbbcadcdbadbabaabdacaccddaaccdbabaabccccccdacbadbcddaabcccbddbbdaadcccbaadccddcbcddbccaddadccdccacdbacbdcabaaacacbcccdcaddacadaaccdcddbddacbababacccaaabdcabacdaadbcdababcdacabccabbbccbdcdcbbdccdddacbaaccdcaddaddccdbabdabacdbaababadddddcbaddbbabbdbbbcbdbadacaaaaabddbdcbcbcadcdbaddaaadbbabbabddbcbabddacbbbbbdcaabadabbdbdbbcddacdcbcacdbacbcadcbbdddacababbcdcdadddcdabcbbaaacbadcbcddcbaadcbaccddbaabdbdbcccccdcccadadcbbbbdbbaddbcabcccbcbbdbbcccddcabaabbadbabbcdbcacbdcacaadabddbabbdcdcdaddaaaccdcadddbcbdbdaaccbdadadccdbbcbcbaacbcdbcaadddbdcabcbcaccccdcacbbbadabbaabbccddbadadbcaaaabaacccdcdaaabdcaccbabbbabdcddcbddbcbddbcddbbaddabaaabcbbaabcbacacdbabbdddcbaddbbccdadbdaaabcaabcdddbcdccbaddaddabbaaacbabbcddaadbcbdadadadabbbcdababdacabbccdbdcdaacacbacccaaacdcbdcdbcadadaabaaacaaabaabddaacaddbbabdcbdaabddcddbaccccccaaadbdaadcaaaaaaadbbbaabaadbbabacbcabcaabdcbbcbddbcdcaacacbacbccbcdbdaacacbdacdcddcadcdcadbadbadcabaabbabccaadcbdbbbcdcccacddaacaddddacadcbdbdcccdddadccdbccacbbaaabcabaacdccdaccdcccddcbcbddcbdacbabccbcdbadcaabaddbdbadbbbcdadabbaaccabcdaabbcdbbabcbadacbcababacadcdddbaccdbacbdbdadcbcdcbacdaaabaabcbadcadbaaddaabadcaaccbcbdbbaabaccbaaddbcadbcacddcbbbccddadaadcddaaabbabdaacdabbdaccaadabdbadbdcdcdbacbcbcccbabdcdabbaccbaacccadbbbcacdbcaddddcaccacbccbcdbadcaccaccbcbbbdcbcadabbccdcdbbcadbcaddabdbdcccbdcdaaaadcdcaddcbdaccddabcdddbdbcccdacdbbdbccdcbcddddbbbabdadbaddbabcdbcaabcdcdcdacdacddadabaccadabbacdaccdbbccaccdbdbaabdddbccadaacabbcaadddcdbddaaababbadcbbcadabaabbadaabaddccbdaabcdcddadaabbbbcccadddbcccbcabdbdabbcaabcaacadbccabacccbbcbdaaddbcacdaacdbbcbcabccdcabcaabddababadadbcbbccbaacdbaaaccadcbbcbdadbbaddacadbdbcbdbcdcbadccdbcddaaddbcacacacccacbbddadcaabbacbbaadcbabdabbcbcdaaccbbdcabbcbcabdcddccacddbcacdacbdbdcbcadaadacbabaaddcbaddcdaabcabdbacdbadddbbddbadccadaaaddbccacdbcbdaacbbcadbacddcdcdddaddbdbddabdbcdadccdbdcccbcbadcdbcbbcdbabadbccbacbdbccabdddabbcbcacdaccacbbacdabaaddbbaaadabdabcdbacdadcbabaabcdddddddbbbbdcacadddadbaccbdbdbbbcdbbbdcabcbcdcaaacccbcbddddabdcddcbbdaaacdacacbcdbbabbdacacddcbdccbdbacbdabcaacbbacbbbbccdbbabddbcdcdaadaddacbbcabcadbddccccbdbccdbaacbabbbdbdbcaccdaadcbbabdbcbcdddbcbbdcdbabdcadccbbacacddbbbbaabaadaddbbcdcdccdbcadbdcbadbbbcdcccabaadcdabaaadcdcaaddddcaaaccbdcccaadaaacabccdcbcbdccbdcdbbddacbcbcdadcdcdcbbbaadbbadacadbcdbdbaabcccbcadacacdbcaccabadbcaacbbcaaddacdabdccccbadccbaddbdabadcdcbcbbbadbbabcdcdcababadacbcbacdccdacdbcabbcabcdbbabaaabacbccdcdcbbabdaadbccdadabccdadcdbbadcdaadbcdaaccdcaabcbbcaaccddcdadbdcbbbacaadadbdadcaadbadccbdcacaddbdaccdadbdbdadbaadbabddbccdaadccadccdbbbcbacdbbbacbcccbaabdbcdcdcbdcaaaaabccadbbbabdccacbbbdbaabaadcdabadadbdabacccbbaaadaacacacacbdaacacbbcddbabcaabdbdaacadcbaacacbcbbcdccdcaabcbcbcabacbcdcddbbaabbdbcbaadaccbccacdcbbaacbddadbbaabcadaabaacbbdcbaddcccccbadcacdccbdddbcbcadadcbddbaddadcbaddbccaacbdaccddbdcaaccaaadaabcdbbdadadabadcccbddcbccadcaaabdcaabaabdaabcbdbcacdddcdccdcaddddabcabdcbacddccdbccaadcdcadbcadcdabbacabcddcbadaadddaaacaadcadbccaccacddcbbacccddcbadbbdddabaadddbabbdccdcbaacacbadcaddbcbbcbaadbcbdbcdbbccccacadcaadcaabcdbdcaccbccabadcacdbdbccbddddacbbbcbdcbabcaccaccbcbdcaccdcccbbbbcadcabdaddaddcdbcdbddcadaadbcbdbcaddbcadbbacddbdcdcbcbcddccabbadbabacddcacabbbbcddbcdaadddcccbcdabcbabaaaaaadcdddbbadbcccccbbaabcdddbcbacddabbcaaabdccccdbcdbaaaabccadbaabbdcbaaadcbbbddcabdaaadadaccdccddcdabddccdbabbababdbcdccbcbbdcabbbcbacaadaabccbccddcadbcabbcccdcbdacbdbccbddadccbacaaccbcaccdacacbdbaccbadbbddabbaabdacdbcbbacadbbcadbaabaddabacbbbdaaccbbbacaddbdcbcaabbcacabcccbdacbccbdcdccbcbbcadbbcccddbdcdddcadbbaddccbbcdbbabdcccabadbbaadbcdbbaacaddccabdbccbbdbaacaaddabddabccccdadbbddbbdbbbbbdcbabcddacbbaacddddaaacddcdcabdcdcadabcbbdadddbdaaccbadbbcdccbacaabbbdcbbcdbbdadaabcbabbacaddbcabdadbdcccbbbbabdcddabadbbbbabbbdccacacbaccdcacccbbbddbaccdcaaddcbbdbdacbbabbabaaacbcccaadbbdbdbcabdbbbbcadcbbaddabcdbabdbaccdaadcddaabbabbaadbcbdadabcdcbccdbadcccbbccbcbcbdcababbdbdaacbccadcdcccacbcbdbadabdbcbbbaccabcdcaabacdaccdaacccdaddbadbbbaaadadabaaadcbabbadbbcabdbcbdadcbbcabbbdcbbcbbcbccbdccddcdcdaddadabbcbddcabbbadacbddcdaddbccccbbabaadacaadbaabbccccadcdcccbbdaadcdddabcabcdddbdaadccbacdbbdacbbcbbcddbccdaaadddacddadddcbbcaadacabcbdcdbccacccacddddccacdbaaddadbacbbcdbbbccabbdbacbbacbabbacbbacbbdaccacabaacccabdbbbccbcbacbbdccbaddccbaddcddadacadddbadbabcbccbdddbbdcbddcaaacbdddabdcbadadbbbddbbdcaacbcdcccbbcadbbdccbddbcabcabdbddcabcabdadcbdbacdcacccbcbbdcabdaadcdcbccbbbcbbdbbbdbdccabdbcddbadcbbaccdbdacbbcdbaaabcaacbadbabaabdbbbdccccbcdbdcdbacbbababcadaaaaddabddbadcbbdcacbdbababbaadcbbcaaadddacccabbabbddbbdcbacddcadccbddbaadadccbdddbdddbabbcbccacbdbacdbcbbacdcddacbdbdbbdabcabdabdabbbadcaccdadbadddbacddcddcdaabccbcddaaadcdacdddaddcbdddbccdbbcddbcabbacbcdcabddbdcadcabcdbbdadccbdbdacdaadabbaabacdaadcdbcdadcadcbdbcbadadabdabddcbabbcddaddbcbdabbbdcabaabcabdccdcbcdaddaddaaadabbaabdbbcbcbddadccdbbacbbcadcbadabdccddccdcaccaacccbbbcddbbcbacdcbbccbacacbaababbcaacaaaadcdcdccbabaddaccddbbdbccdbbdcaadacbccbdbdadcbdddaaaccaaabbbadbadcdaadabaadcdcdababcbbdcdcdccabcdbadddcddbddbdbcdacddacdcbaabdadcaacdcdbbddcacddabcadbadbdbcbdbdcdcaabccadcaacbdbacbbcdbccadccadbcdbaaddcbdacbddadccacdccddcbbbbccaaacbbaacaabccabaddcbbddabacadbbcbcbcadaabcdcbbadbaddcdccbcdcccadaadcbadaaabbccabddadaddbabbdddbbbbdbbccacacdcccdbdaadcbddaaadadbddadcbcabaccabbbdcbdcacbadcbbaaccccabdbbbaddddbbccbccaddaddaaadbbdabddcadbdaccbbbabdaaabcbaaadabdcdcccadccddcdccadddcdcbaaabbdcdaacbbbacaabadabbdddadcbadddbbcabacccdacabccaddddaadccadcdacdcccccbdaabddaacabcbacbabacabcdadcaccbdabbaabbcacadcaddbddbbdcdadddccababaccabccabbcabddacbabccbcabcaccaacccbadbaabdbcacaadadcddcbaacbbcccababcadbdcbddabdddbaadddcacacddaacbcaacbdcbadbadabbbddcbcbccdbcdbdccabaccabaaabdbcbddbccabcbdadacbcccbabaaddaddbadbbabdacdcdbccadcdcaadbbbcadddaaccdbbcbcadacacacbbbdbbaddcbdabdbdddbacbcbdacbadcbacddbdbdacdacddbbaddbbbadbdacacbcbacadcccbdccbaaddaddbabaadbaccdcbdbcabbbdbbddddbdacdaaccbcaaccaccaddadccdbccdcdccddcccbcbcddcacacadaaddabadcaacdaabaddbccddcbcaccbbdadbcdbbbdbadcabaccdacadcbbbddabcbccbcdacccbcaccaacdbbbcdbbaadbbaddbdddaacbbabcbadcdadabbcdbaaaaaacccadcaabdbcaadccccacadabdcaccabdcadaadcddccdcccddabbbdbbcbdbdaacaddccbaaccadabdcbbdbcccddbccbcbbddadacdcdbaccacabdbbcddccdbdbadcaacdcdcbadaadccacdcdcbbccdbadaccabdbdbbcabaaddddcddbaadcbcdcacaabdccbdadbacababdbdddbdcdacabccdabbaccddcbcdabbdddadaaabdcacadabcbcdadcbabcdacbdccdbaaadcddbdbadcccbdcacdabacddddbcbcbbabbadbddcbaddaccacbaaadaaaaaabbcbddcbbadbaccddadbcdbcaddcddaaabbdaddbbbbbccdbaaacbbcddadcacabadbcbbacadacccccaccabbbcadcccacddbdadbbcbccdbdbaacccccccaddababdaabcbdbadcadbbadabddccddcadcbcbddcbdddccabacdabadbacdadddadbcddddccbcbdbaccdcdbbccadbcdacdbabbbdbcdbddbabbaabddbaabbacadddacccbcabcdcbdadbbbcdbdbccadccbccaaadccdcabdcccbdaacaaccdacbbcbbbbbdbddabcadcccbcaaacbbacdbbdacaaaccaaabbdccdcabcacdbadddbccacabbaccdaacbdccdaadbdccddabdbaccdddacaccaddddcbaddcadbbccdbaaddbdabbadddcadababbadcbdadcdcabacbbbaadcbdbabbccdacabcbbcccabdcdbbacbcacdacccacbcbbcddbbcddbbcbdbccdbabcacdbcbdaccbacabdabaaaacabdcabdaacdcbcdaccdcbcaadcbadaaccdbbdabacdbaaabacccbbbdbbcdacacdddadabccacdbbddbddbcaadaadbcaddbacbccdcdcdbadccccdaccdcdccbadcacddcacdddadbaccabccddaaddcbdcbcacbabcccdcdbbadbacdbccababbddbdbacbdcbdacbacdaaacabcabaabdccdbacadabaacbbdbbabbcddcccdbbcbdddabbdbcabcdcbbcddabdcdccababaaabccbacdbbadbadacddadccccbbccccbaadcbbbdcbdbcbacdddbdaabaadabccdbaaccdabcbabacdbdabdbdbcddacbbddddabadcddcbbdadbdcbdcdababbaabdccaccabcaadababcbabaccccdbddbdabbdabdbdcddbabcacccbbccbdaabaadabdccdbcbbdaccadaccbbcbbbacdbccdacabbccacdbdcbcacdcdbcbbadbbddbddbbcddcdcdaadaaabcddacababadaabccaacdbdccdbddcabbaacadcadbbdbccadabcabadbdbcbcbbbadaaadacdcdcdbdadaddddaadbabdbdababdbcccdbaabbdcacdbacbdccddcbddbbddbbcbadacdcdcdcaddaddcbcabbdbdcddbacddccdbbccadcdddabbbcdabcdcbccadbcdddcdbbaacbadaddcabccbbdccdbbbcbadcbbdddcbdcbbdacccbcbcdbddbccbaabbbaccbcddadbcdadadcabaccccbabadddacadbbbdadbdcaddccaaddddddacacaddcdaccabdcbdbddddbbbbddabdaabcbbbbcabdaacbdbccbabcacbccdbaaddbababdcdcdacacacdbdccdbdddccddddcdaabddbddbbcdababcbdddbdcdccbcbadbbacacaaadadcadbabccddbcadbaaddccabdacdcbaabdcccdcdbabcadcadddaabcdacacadcccbaabbadababbdbbdacbacbaddadabddbbdbcdadcabdbabddbaaaadacdcccaccababcbcbcbaddbbaddccdbaacddbacdbaaddacbdcbcacdbacccdbabadaabbdadbddccadbccdbcdbdddadabbcadbbbaacdbccbbadaacaadbdccdaccdbcddbbcdcdcaadabacddbaacbccbbcdbbbbadcaacbccdbcabbcaaadbcaadaabbdaaddbaaadbdbacbaddcacdccbbdbaadabcbbdacdcbabccbddbccbbdcbbadbdaacaabadbaacdaaacaccaacdbacadcdbddadcdbaccbdbacaabddbbdadbdccbbdbbbdccdbdbaaddbbbcddddbccdcdcacabbbcbdbbaaabaccabbbddadacbcacacbdbcddcacadaddaabdbddbdcdabddaaabcbdcddabdbcbdaabccbbbdcdacdbdacbbbaccdadddcbabdbcbaddabbaadaddbcbbcacbdacaccacaadabbacbdacbadabdcabacdccabccdcaadabbcccbbdbdbbdbaadccddaadbbbababcdabddbcacabdacddcacaddcdbcdaabbbcabacdaabdccdaacdadddadcbbcabbbaadbaacbaaaaabadacbbbdcddbbcddcdbabccabcbbdbccacabcdbbcbacbdaddabbdcdabbcdccacadbdcaddcdaccdadacadcdbdcdbbbacbccddacbcbcaadbaaadbacacdddcbcdadbbabdcdbacbcbdbddcbacaacbadadabacdbbabdccdababdbadacdaacbcacababaacaaaaccbaadccbbbacdcccabdcbbdbcbccdbbaccaabccaacababaaabbbdbdabdccccabdddabdddaacabcbdaddccbabdbdbabacddbcdcdddcdbcbdabadccbbbdddbdbcbacdbacbaaacdcdbcdcbcdaadadcabbcdaacdadacbdddbcadcdadbcadaddaabaabdaaaaccccabcacadcddaabdcbbdbabdadbbaccabacbddadcabaddcbdbbdcdccabccdbcaccdbdcaaabaccdbaddcdcacdddcdcbbcabbdcaccdabdcaddddbccdaababcadcbbdbbbadbcadccdbccaadbabbaccdbaabadcbcbdabdadacdbcdcacbdbdcddcbaddabcbccbacddabcaababbbbaaadcadaddcbacdcdaccaaaaabadcbbdaaaabbbcbdaabaaaddaadadbbcacadccddacbabbaadbadbcdcabcddaaddcbdacabaadcbabdbbdbbaacadcdababbbdcdabdacadadcabacdcaddddabacbbcdcbdbdcaccadccadcdadabbdbdbdcbbcbaddbacdbabbbadbadaaadcbabdcabcbcabaaaaadcbbbadabbccbaddddbbcdcadababddddbdbdcccdcabddbbacdccdbcaddbbbddaabcbadccaadbaabaddacaabbcbccacbadcadbccacccbddcdcccaddaabbcbbcadaccaddcaabddddcabaddbdabbdddcbdbcbbabdbabcbdabdbcdacccdbadbbdcccabaaabbbbaabbbcaabcdbbbabbbadccdabdbbcbddbbbabbabdddcbcbcdbbbddbdcbcadadbadbcabaacacbcbadbdcadcabddcaccadccdcbbdbdbdacdbdbdbabccaacccddaacbcdcdbacdccababaccbdbdabbdaaaccdbdddabdbddbdddcacadcddbbbcaddaabcadccabdddbaccdbbcccdcaadcdbdddcbbccbbaacabbcaaadadadbadbdbddcdbaacbacadcbcababbcdacbcbccbdaaccddccaaaadacbcacbbbdabaaacdabbcdbadbacdbdacabcccbabcacbddcdacdcaddbabbaccbabcdabcacaabdcababcdcbccdbaddabccadbbdaabcbadcbbbbbdddbcbcccdabadadbdccddbcbabdccbaaadbbaacaaadcbcaabcacadbadacbcbabcaccadbcadcddbccabbdcadcbccddbacdbcbdbcbbdabadcdbaccbbccccdcccccddaccdbbcdbddcddacdcbcccadcbcdcddbcacaadaddbaacbaaacbbaccbdcbccddcaddadbdbcdcabbdcdbdbdccbdacbacacbbaddbcddbcdaddaaccadaaaabbbacbdcdcbbcbbadcbccdbbddddbdcdabacabbdcbcbcbbdbcabdaddabadaabcacdcabbadcccccabccdcdcadadcbcbcddbbbdbbcccabcbacbabddddcbcdcaccacdbacbccdbdcdcabdbabbabcbdbdbbcdacdaadcabbdadcbbbdaabdabccadcddcaaddadcaccacbbbdbcbbaaddadabdcadcbbdcdddcabcdcabaddbddbccccbbcddbcabdadabcbdcaacbaacccbdaadcdbdaaabaccdcbdcdbdcacaddcacbcadcbcadbbaadbbabbcadbcdcabbcdabdddaaddddbcadbaddcadccadabbccddacababbbcddccdbbaabbbbdabadbacbbccabdccbabaccbcdcaacdbadcdbaaddbcadcbabcadbcaaddddaddcabdcbaabccacdbcdbdcadcacadaacadabaadddaadadbdbcabbcbdbbaabcbacbaabdddbbaacbdadaaaabaaddaacaaadbbcdacdddcabbbdaadaadbcbbddbcddbbdbaaadddaaaacbcabdaabddcdddabdcbabddbacbdaadaddbabcabdcbbadaacccdcccabcaddbbdaddccbbcaadabdcabcbaccddbddbabaacdbcdbdadaddbccbcccdabdcbcbbcccdcabcdbccadbaccccaaccabdcbcdddacddbdacbccdcbaadbadccbbadcbadadddbbbbbbbabdcccabdcdabcdccacdaaacdcadbbbbddadcacdaadadbabdcddbdbaddbaadcdbadcbaabdaabdaccbdddbcaacbbdcabdbcadaabbcabbddbcabacaddbbadbabbbbcdbacaaddabcddaabdaddccdcdaaaddacbacbacaddccabcabbdcddddbadbdddacdcccabbcbdcabcdabadbaabcdaabbdaabcaacddabdddbcdacdcaabadcadccccadbddbabcbcbdcabcacacaabdbcdccadcbbbcdacdcbcbbaadaaddccadccccbddbdbcddddbabdabbabbbccdaccbdbabbcccaacccdaabacbabaadddbcddcdbbcbddbccacaaaaccbabccdbabddaadacadccbcbcadaadacbddddbbadaaabbcbdabbddbbbcaddbbbcacbaabadcadccdccabcdbdadccdaddcadacaadaaccacccddddbbddbbdbdbdcbccbcadbdaddcabbabccdbccbaadaaaabdbddccccccdccbbbbcbcdaabdcbbbcddabdcbbbacbcccacccbacddbbcdcaadcbbcabddddcbddbacacccacabcaaacdcdbbcddcdbccbabbbcddbbdbdbbbbbccbbcdcdcdabbbabcddbbcdaccbbbcbdcaddccddadddaccacccdaabddadadbdacdcbdbdacaabdbccbccbcdcccbcdcdcabacbbdbabddbbbacdcabcccbcbbdcbddaaacdcbddadaadadaadaabcdacbdcdbccbcdbacdadbcabddbdadcbabcdcbdcbcbddccaddccacaacddcccdaccbdbbcbdabbbdcbadbdadcbccbaccddcdbcbccbdbabbcaccccbddcadadcdbbabcabccbbdcbbcdbbcbcbcbbcbababccdadccbccdcdbdcdbaabcadbabdaaaaadaddccabdaabdbacbbdbacdbaacadbabdbbbadbabacddbcbcbdccbcbdadbcabcbcaadddadbacddbdaacbbaddadcdabcdcddbaadbcaabacdbdcdcdabbabbbaccbabddccbadcdcadaaadbbadaacaaaabdcacdcbabcdabaccbccdcdacdabcabadadbaddadacbdbadccbabbccbccadacbddcaabcccbccddaccddbdcdbbabdacccddddcdcbddabccbdccbbcacbadaaadbcbaacdbadcdaacaadaabdabdbadadccccddcbcddaaccadbbadcacbccccccdabddabbdddacdaccdabadcbbcdababacbdbcdbdcdcbadcdadddbdbcbbadcaabddcdacaccdbbdcddbcaaccacacabddccbdcccaadbacbbcbcadddddcbdcbdbbbdbbbcbacbabccdcaddacadaddcabbdbcdbcbdbcabdcaabaadccccddacdcbacdcbddccdcdadbcbcbaadccaccbbcdbcaaacbcddcdccddcdcdbcdddadcabcbbcccddbcccbdabccbaacadadcadabcaaacdbbbbaaddbbbabbcbdacdbaabbaadabcdddadccadbcaccadabcbbbabdadcccaaadcabbcbbacdcccaadcbacddabdcbbbbbabdcbaadbcddcdcacddaadcabdbadbacbabbbabbacaddbabcaacbaacdcdbdcabadcbcabadddacbddadacddbababccdacccdbddabdaadcadbcdbdabdbaaacbcaabbacbcadacbbcacbabcaacbabbcdadbbcbcabcdccdbdcdbcdacadbcdadaaccdbabdaabaadababbcaaadadcabababdabbbbdbaddaddcccbccdacbdcabbaacdbbcbcdcbdcddaccbcbdcbbbcddbacbdabcbbbbcdcbabaadcbacbaaadacdbbaacdcaaaddbdaaddcdbcacdbdcacbaacbaabbcdddccbddabbaacbcbdbacacbccdbcbdcbbcdbcccddcbcbdccbaabbbcccbadbccddbcccdbdaddccddbbdbadbacddbaddcabdcbbabdccdbddbbdaddbbdbdbbcdbcdbbbcaddabccabbcddaddadbbbadddcbdccdbacbbacddccabaaaabcabcabbdcdbabcddbbbdadbcbdaaadbadddddbaadcbbadbbaaaadaacdbbdaacbcdccabbbaabbbaaaacdcbbbbdaabbabdcdcccacdccabaadaccaaaccdaacbdacbcbdcadcccccddaaddccbaaadbdadcdabacabcdbdcdddbbabcbcddcaacabdabccdccdadadaaaaccbadbcbbbabccbaaaaadddabdbadbacbdaabacbbaccbaacdbdabcdbccbdaadccdcacacbcbddddcaaabcdccbdabbaaaadbddadbcccaaccacbcdccbcdadddaaaabdbcabbcbcbdbdbadddcddadccccabddcdccdcbacaaabcbbbcdcdcacdacbbabaaddcbbbdccbbbabaadbadaddccabcadccbcccbcaaccadaaccadcccadddccababacdabddcddaacbcccdaaadbbdbcadcbdacccdcbcabbdcabdcbddaadabbccbcacdbcbabbcbdbacdaaddcdababcbbdabcbccacbadcbbbcabdcbbdabbbbaaaccddbadacadabcccbdbbbdbaaddacbaaaabdacddcacbcabcdccaaaadbbaaccbbcaabbacbbadcadacbbdadaabcdabdcbcdcacdcdcabbbcaadcddbabbbbdbcbdcdcbccabddcacdaaacabcacccabbcdcbdcddcdaccbaadaaacddadcbcacacbaaccdcddadddaadbcbbbaacbcdbdddacccdbbdcbdbbdadcaadbcacddcdcbacdcacddacaaacbabbbddddcdccabdddaccccdbdbaacbaccdadadbcdabbaddccacddccbcbcbaddcccaadcacabacddcacbaddccddccadaabcabdbbcdcacdacddddcbbdcccccaccadacadaccbdcbcaccacbcaddcbbcbdbccdbddcdddcbdcabcdccacbdacdbcddddacbccddbbcbddbdccaacbccacdcdbcaababadabbdbbacdcbcabcababaccacabdcdadbabdaacbdbbabccdbcdacbcbabbababdcbdbdcbcdbdcdcacdbabcabddccbaacbbbcccbddacbbadbabddadccacddcabcbcaccbbcdaadacdddbdabcdacabdbbdbcbcbabcbdbbaccbdcbcacaaabbbdccaccaabdaccccbddbcbdbccbcdbddadddcabcadacddaaadcbbbddabdddddaadcbcbcdcbdbcdabdcdbbbbddcbbadaddacbcddcccacdbdacbcdcddcccccacacacdcdcadcbbaabbaaccadadcdcdcbdcbddcaabbccddadcabcbcbbacbbbbadccbbcaadaabdbdcdcccacbdbccacbdddcaacacdacaccddbbaaaaacdbcddadadbdaadbadccccddccbcbcccdbbbaccbdbbbccccbdcbbbcbcacbdbcbadaacabcdccccddabdcbaddacbabdbadcbccbdcacdaadcacddcbbdbdadbccccdabbacdabadabcccccbadccbbccbdacabcacddacabbaabcbbdbbcdabbdcaccbddadbccddbaabcdcaacadabbbbabbbdaccacadbbbacbabdccbdaadcacacbccbcdccddbdcdcdbbdddcbccbcccdbbcdddcdaddbdbacbccaaccdacbbccdaddbbddbddaddbbbadddabacbbbdaaacbdabadacbadddcaadbcbddbdaaccdabcdabadbacabbbdcdaccbddadcbdccbacdbcacadbcdbbcdddccadabbadadbddbdcabaaadaaaaddbbdbbbcaacdadddcccdddabbddddbdcadaacdcddcbbbbbcaccbccdddcbaabaaaaddadbcccabdaabcdadbccbcabcabacbacbcaccaddbccdcbcbabcdabccbcbddcbbdcccdcaccdcbabacdddbdcddcacdccacccdcdbccaadcdaacdcdcaaacbadcadbbcbaacbbcdcbddadcccadbcbadbdbadaadcaabbcbdcdcadbcdacbadabbcbbabbcacdaaadccddacdcddacacdabcabbbcaddddadabdbacabbadcccdbcaaccbccabdbcddaddbbbccacbacdcdccaadcddbbdadbdadadbccaabdacabbdbdcccacdcbcdaacacbbcacbcdccabbbcbcdbadbabcccbbaaddabcbbcdadadabccabcacadbbcdcbabdbddaaacccbbbddbaddcacdbadcdabbadccabbabbbadbdddcadabddcdaddbccbbdbddaacdbddbaabbcccbbbccaabaddaabbdcbcbabbabbbddbccddcbaddbcdadadaaaadbcdcbcdbdacdddacbaaadcbdcddaadbdabcaaddbcacbdcbbcabcdbdabacccabadbdcbcdcacbaacdcbbbbbcdbcccbadadaadacabcdbacdaddaaccbddccbdbadaddccacbcbabbcdaccbbbabdabaabbdcbbbcdabcccccadbbcdccdadbdbdadacbcddcbaadcbdabbbddbdbccbadcabdabbabdbdabdbabbbbdcdcbdcbdabcacbcaacdcddbaaacaccbcccddcadcbcbdbbbdbaaddcbbdbbcdabcaadcacbaadcbbcacdaaabbbdbcbcabbacdcaddcbbaaccbbaabcadaaddacdabadbcadcddcdacbcccaacadacdbbabaddbccccdcdbdacabcbcdddbbadabddabbbbccddbbccbaabababbdbdababbaabdacbcbadcabdbadbaababaabddccaaabaddcaddbcddcbbbbaaddbdcbccabbbcacbacbcdacaabddbacdbdcbcccdbbacdbbcbccbcbbccdcccbdbabcbddaccdaaadcdbdccbacddbcbdbbdbcbccccddacaaccbdbabdaaacbcbcabccdccadcccdcdbaaabcbcccabadcccdbdcdbbaadccdbcadacbbddbddbaddcacbbaaccbaaacbacaaaabcbddbbdabbabbaddccdaadacbddaadccadcaccddacaddaabdbbbdadbbbcdbaccaadcdcdbbdccbccacaccabcacbddaabaacaddaaaddadbbbdcbbcdabbbbcdddccaadbbabbadabcbbbbdccdcddcbccabadbdddabdbbccbdcaaaaaddaacccbaaaaccdaddacdadbdabcbbdcdbbadbbdbbcbccccddaabdacabcaddabbcdbdacadbdaddddabcbdaaddccdccdcaddbbbddccdbcabcacaacdcaaacaaddcadbdabdaacbbdcbbaccdbdbbbdcaaadadabbaadacabccaddaaaccdbcbcabcdcdddcacddaccadcacccbddaddddaaaaadbcdbcdaaadaccdbddaaabaaaacbdcaacddccbcdbacddbbccbadbcbbbcdabcadbdcbcddbbddccbbbabacaadbbbcbddbadaccdacdbbadacbdcacdaadabacaabdacadbcbbddcddadddbcdcbcddccacdbccbccbcdadcbdcdddbddbdbbadcccacbacbdbdabdddddabbaadaabacdbaadbaddddbacdbcbabcdbddddabacbabdccdcabbaadbddcacddbbadacccabddddbbababbcccbdddabdaccdaadaacbdaabaaacbbdbdbabddaadddabcdacaadadbcddbccdbbbccbbdabcabddabbbbadadbdbcdcbadbacbabdabdcddcbababdddabbcacddbdcaccddabacdadcabcbcbbccddbbaccdbdaacbdbbbdacddcbccdcccbacaacacbaababaababaabbaddddacacbbbccaaaddbcadcdcdadcdcaabdacadddabdddabdbbabccadddbaabcddbacabbdddaaabdddbcbdcdababcdbbaadcaabcdccadbaaaccbadacadbcccbdbdddaabaccbcadadabcaacccbadccbbccdbddaaabbdcdbddadcddbacbacaddadbcddccccadbcdddbdbdaaddcdccdcbbdababcbaddccdabbadbcabdadbcdbccaddabbaadccdadddcbbdbdcabdbacdbcdcdcddbdcaadbacacabaadbbcaadcaabccddacbcbdbbcbdaddcdcbaadbcdcbdcaaccdbbdbdbcdbbdabddaabaccadcddacabcccbcdddcddadbaddabcaccdbccdcaabbdbdbaccabbacdccadaddbdabddddabbbaacacaaadbddcacddcbaabcabdcacdbaaccaadccadcbbccdcbacdadbcddbabcbdcaccabbcaacabbcdcdcbbadccaaaabbccddaabddcddcccdcdcdabccaacddbbabcdbcaccdbbbdcabbababadadbcdcccbbccacbddaccacbadaaaaaccabadabaabcaadbaddcddadbcbcadbaacbddddbacacddcabbdabdaaadaccacbdcdadaccadcabbbacaddabaacddcbbccbcacaacdbdbacabddddcabbadbcbdbccdcccdabbbbbaccbacaccdccbbdbddbbadadcadbadabcbddacbaacacdaccdcddddcaccccbabccccbdbdcacacbccdbcbabcccadaaabacdaadccbdacadbabbdcaacbbaaadaadabcbadbdbcdabacdabbcbcdcbabadbadcbdcadabbcaccdabdcdddacdabbdbcbccdbabcddabcdbadaabadcacdbbddbbcaabdbbadddaabddcbaaaccccaabbadbcdbbbaacdbbdadacaabbabbbdcbbbbababbcadacbcddddacabdddadadddddbaadacadbcbccaabacdaccbcbaddbdababbbddaaadcbaddbbddbabacadadbbaddcbacbcdadbcbbbbcddcaadbdbbdbdaaacbabababadbddaadbaadcbbdbaccbbbdcdcbdcbacccbabaaaadccbaccdbdacbddacbddccaacbcddabbdcdbbcbacdbdbaddabaadbbdcacacaccabcbdcaabdcddbdadaccbadcacbabacdbaacabddbcbaadaaaccadbbddbcaddbdaaddcabcdabcccbaccaaabcaccabacaadcbdbcdbadcbaacccdbccabdcdbddcbbaacabaddcdcdbbbbbcbaabddabcaddbdaaabdbbdbdbbbddbacdbcccadbdcbbbbadaddbabdcabcbaabdcabcaccadbdbdccabddddbaaccdcbadbdaddcddbadacddbbdbbdccdcbaaadabcbacbabcaadbbdccdacbabcddadcaaaddadacbbaccadddcdadbabdbdcadcaaaacddacadcaaccbcabdaaccbaddcdddbdbbccadaabdbdacaadccadccbbaacacbaacbcdbbcbdabaabdcadccccbcdbbbadacdbbcddabdcbccccdabcbbbcbdcdbdcbdabbacaccccbbddccddaaaddaadccbccabaddadcacbbaccccdbaabdbcbdccbddadbbdcdcabcacbdccbddbcabaccbcadcdacbbcccdcdbdacccaabbadcccdddddccdbcdbadddcdabaaacdcddccdadabdcccaadcdcbabadbcccbaaccabcbdddcbbacaababbbcdbdcdbcdcabbddbcbdbdaaadcaacdddcbaaaadccacbbbadaabcaddbbaababdbaaccbcdacaacbbddaccdbbcddcadbbcadaaaabbaaccacdccddbbbabddbaabdbaddabdbccddccdbaabcddacdabbbcdcddcbadbbbcabbcbbaadabcbcacadadadbaccbdadcbabcaddadaccbabbaacddbacaddcddcbdaadbbbcddddadaaddcbbbbdccadacaacbbddbabcbabadaccbaacaddbdbddbcdddcdbdaadbacddaccbadbdcbcbaccadcdcbbbdaaddacabdbabdadbacaccaddadddcabbadcdbccbaadbbbbaaddabaabcdabccdbcbbaacacaacbdaddddbcbdabcdbccadcdbddbbcddddbbadabdbcbccbbcbcddbaadcbcadbabcbccbbcdccddbcccacdbaddddacbbaadcbaadbcccddcdcdaadcbaddaaddacdacabaddadcdbbdacbdcbbdaaddcdbbabddabbbcabcaacabccbadcdcbabbbaacacddaaaaddccacbaddadacbbcbaabddadbbdadcbcadbdbcbbdddcdcabadbcbaabddcbdbdacbabbbdabdbbcbdcaaadbbdabbdccbadbdddddbaabadbcdcadccbdbbcccdbcbdbdbcbabdcacabadbcbddcdbddbdaaadabaabbaabababcbdaaabbcdbdccadacccabdaadabaaabcbcddcdbacaccdadaadbddaaddcaccddcdbbbdbadcbbabccbbdcccabacbaabbaccabbbdcdddcdbaacdcddacdcbaccacabcacaabcbcdbdcdaadbaccddaacaddcdcacddacdbbbadbacccccacdbadcdbccacbcbadadabaaaaaabdcaaacdbacaddcbbbccaaaaabdaccddaaabdcdbddbcaacbbaccacaaccdbbdacbcbbdabbdabdddbdadabbcadabbacbdadaabbbcaacdcbaadacaccdcdcaccbbbdacacbbcbcdbdadccdcdcaaccddcabaaaccbabdabaddbabbdccbacbaacaccccaacbcdddddcbdcdaabbbcdabdbabadbcccbdbadabadcbcbbabcdbabacdbcbbbbbbcccacdbbbbcdcbddcdcdbcddbaacbbbcadadcbbcbbabcbadcadacbadcbaacdbcddbddbabbcdccbbdabdadbcbccaadaadbcadcbbbbabbbcaacaddbccbdddddbcbaacddabbaadcacadbabcacbddbdadcdbcadcaacddbaabacbacacdabcdcacddcacacbcbddccdacccddbbdcadcaabbabccabaddbccccbabbcadbcadcacddbabccdccbcbdccdccbbdcdbabddbadddaadcddcddbbcbacdbccacadaaabacbdcdcccadddcbbdcbbdbacdadcbadbbddbaadacccbbcbadadddcdddaccdacbcbcbdbcbabdcdbadccdabacbaabdacbaddddcaabadadabccbcbbcbabcabcccdbdbddddadcdcddadbabdcbabdbbcacaaddbabdcbcaabcbadaddbdcdbddcdbdacbcdcacaccacbddccbaacbaabcabbbddddbbdbdbdaadbcaaadacdccccacbcccbcaccbbabdadccbaabbdcbabaccbbababdcabdcaccdcabdcbbdbbbcabddbbcccdbdbcaccbaabadcdcadaabbdccddabdcababbdaaddbabddcacbdcbcbbdacbdcdcdbcbdbdaddbddcabcaddaabbbcdcdaabbccbccdcadbcdadcababdccccdbbbdbbcaaaacdcadcabcbdddaaaadaaadacdaadabcbbcacabdbccaccadacaabddadadbcbdccbdcbabcabdcbdbbacdbcdacbcbdababccaaaacdcabaccaccbcbcbbcabdccccaccabaababbbdaadaabcbbbcbbbbaddacacccadcdaccbdaaadacbbbcadbcbddbadbadadcdabcaccbccabdbdbadcbaacccacacbbdbbdacbbbcacdacadccdddbdbbdbcdbbccaacddaccaaabcbdbacdbabbbaaccbcdaaabccbcbddaccbdbdbbbbccbddbdbadcddcdaadcddabbabbcdddbcddbbccbccdbcdccdcdcbbbdbdaaaadbbcbddccddbdbdcbcdccabbbbdacdbbaaabccadaaacdacbdcbccddadcdbdcdadaacddccbdcdddacdcddcaabacbbadbabdcbbbdbdadccddabadccddcadcdbbaaacacaddcdcbbddcccaccbdccddbbbbabdaadccaadbcbdcccccbabcbadacdcbaacaddbbcbdbdabbbdbcbddddbbadaadcdabcabcdbdbabcdaacccacaabccdcbbabddbcacaacbdcdbbcddcdaaccdcbbcabdaccbddbbaadcddccbbdaaddcbadadcbcabbbcbcadddcaabcddcdacdaaacdcbadacdbbbaabcaccaadbadcbdabaabbdcbacbbddcabbaabacadcacdabaccdaabccaaccaaaaadabdcdcbbbbcbbbddbcdcccacccdbdbcadbabdbbabaddcbaddddccaacdddbcdabbbbacdbbdcbddcabaabddbaadbabbdaabbdcbccbbcadbaabdddbcccdaabcdbbadaadaacadbcbabbbdabadcccccbacdaccdbdcdbccaabddabbaaaadcdccccbcddcdabdababbabacabaddaadabccddaaaaddbbdcccbcaaaabbcbcccdbbbdaadaddcadbcadbddacaaaadadbdcaadcccdbbdbbbcccdcabaccbcdadabdddacdcdbbccadabbdbddcbbdccbbacaacbddbcababcbdabbdccdcbcabdcddbcddcaaababaabdabbcdacabccdcaabddcaacddccdcaaaccdcddaacdbccaddcbdcdabbbcddddabcbbcbababcbccdcadacdbddbadcdabdbbbbcddcacbbcdbbabbdbccaacaccccbacaaccabbcccddcaddbabcdbcbcdcbdaabacddaccbdacbaabadbadcbaadbabcdaaaacababbabadcdaadacdaadbbbccadaaabbabbaabcccbccbacdaacdbdcbcdbaadbbcdbbbbddacbabacadcadbddbccababcbbcbbcdadccdcabbbbbbccabbadcadddcccddcadbccbdbcaabbcbccaacacbcccabccbbabcabadbabacaabddaddbbddccaacadbbbcabdbbbbbcdacbacbacdcdaabcbbcdcdbddacccddaabcadcdcbddddcddbbbddaaaadcabacddbcbbdaccdaabaccabdaaadcdaabdcbbcbddcbcbcdcdcadcbacabcbccddaacbbcbdbadcccccdccdacaccabddcbddcaaddadcdacbbbcccddbaccdccaabadccdccbbcabddbbadabbcccbaaddbbddcdabcbabdabaadccddcbbbdabaacacdabababbddbdbbdcaccccbadddcdabbdaddbaaddddcadabaabccdcdcbbdaddccabcbaabbacdcabaccdaacaaaddcbacddadbaaadadcbcacaaccdacbcdcccabdcdcdbcbcddcbccccccabbabdbbadbabdddcaadccccccdccddaddbccbcbccdadadbbadbbbcbcccbbadbcbbbcbdbbdbbdadacabbabaaabbbcbddbdaaaacdabdcbbcaacdddcdbbddcbbbdaadcababbaaaabaaadbdaabcdbcbbadaccbaddadbaddcddacbccccbddccdcbadbadacbcbbbcaaaacbdbdbbbbcadabdbccbcdbcadbadccbbabccadacdabcdcbdccadcdaadaccbdcdccabdabdaaaaddbcacbddbbadaacdacddcdcccabccdabbcddaadbbabdddaaaabcabdbdddbdaddcacacaabbcabaddccdabbbddaddabddbdbdbdccbcadbaaaaabcadcaacbaaabacbdcacddbabaacdaadacaadcbddccdddcdadbacdabcdaaacdabdccbabcdcbbacabddbcdcbdbbaacbbcacbcbccdddcaacdaaacabbaaccdbcaaadbaaccadbdaaaacbbcdacacdcaaacaaaabcdadaaadbcdcbacbbaadcbccaabbccbbadbcbbacdccbbdaddccaacbbccdcbbcbdcdaaadbadcbccccbbdaadadcaabccbbacbbaadbbddcdbcababcacdddbdadaadcacccbabdaabcdbcaadabcacbbbdbaadcbadcdcdadbbdbabdcbaadcbcbdbadaadcbaaabdaddacadcdbcbcaddacbacbcdabcbcdbbaaccabcaddaabcbcadcdaccddabbbbaccddbbbbbaaadcdaacbddacacdacdaccbabacccbbcabcbcaaabbaabaaccdcddabbcadbaddbcdddacbbdbddbddcdbcbcadbcadddabcbbddcbbadbbcdddbdbccbacbbccbcbdbccacbddbdcdccabcbaacbabaadcbabccdacbaabbbccacaaabbddcdbbbcbcbaacacbbbcdbccdcacbbabdbaacbdbccabccddacddabdbbdcbdcbbdbbbdccaadbcdbaabdacdbddaccdcbcaacdbabbdbcdbdcabababacaadcddcdacabdadbbabcbdcbcdbaacdaacbcaaacadaaaadcbadccacabbabbcdadabddcbdadbbcdaaccdbdbcaadaabcbaaaddcadaadcbbbdbdcccbcbcdaccbbbaabaadcbaaabcbbddabbdcccbadbbdbaaaaabacaccccdcbacdabaaccbdbbbbdcadbabdcdadbdaadcddbdccabcbbcbccdbadcdadcdacaacbccbbddbadabdbbddabbbdccbcdbadabbdccbbaddddcbcdacaccccbdacccbdcabddcddbcdbcbacccbdbdaadcacbdccdabdacbdcdccbaccbaccbdcacccdaaabbacdaddbbabcddbdbdaddbaaccadcaacddcacdcaadcddddcbbbccdaadaabbbbdadadbcdbdddacbcadaaacacabddbbddbcababbacabcbbaaaacdadabbddcbacbdaaacdbcadabcdcbdabbdadadbbdaabccccbcbacaabdbadbabbdcbacbaadbaacbaccbcdbbddbaacccbbdbddccbdcbadaabbdccdadbbdabdaabbbdccaddacdcbbadaabddcbbbcbbbbdbddaaaacbdcabbcaadccbbaabaabaabcbacaaabcadbdbbacabdacaacaadddcadadbdcbbaaabdadcddbcabddcbdbdccbacdacbddccbdbadacbdacaabbbbacbdadbababadadccdcdbbdcbccacadaabccccdbdcbadddddabaccdabddaddddddbdcdcbcdbdaabddbacdacbbccacabcacbcdbbaccbacbbbaacaaddddcadbaddbbaaadcbccbddcacadbbabdadbabcaabadbbccbcadddbcdcdcbdbdcdbdaacbdcadacdbabcddbbcabaddcacdbdbdccddacbdcacccdaaaddcdbdabaabbcbdcabdcccbdabaabdabcccbacdaccccaadbcabddbadadbadbdaabbdabbabaabdbaaaadbdcbbcdbaddabccabcdddcdacabbbaaabadacdcdabdabdabcddcbdddbdccbcbbdacabcbccddcbaabdbbbccdadacadddcbbbdbbdbdccdbadcadbdbacdacabbdcaacacdadcacccacddbabcdddcdddccacbdcbadbaadbcddcbbcacabdcbdcbbddadcbdbadbabdccaaabcdadbbbddabdaaaacaddadadddbdcdabcdbcabccadbddbddddbcbadbbcddbbccbdbbdcbcabcbadccbddddddbbbddcddbcbdaccadadadbbbbbcdabacacacbbdadcbcddacacddbdbccbddcacadbcdcabcadbbbabdcccdbdbadbdbdacccbaccdccdadbcddbddaadadabacabccdddacdccabaddbbdccccbabbcbcabaabdaacbcbaacbbccbbaabdccdadabacabddcbccabbcabdbbaabcacbcdaaddadadbbadbbddcddacaccdacdaadacdabbabbcacaaddbcbccbbaddbbbdbbbccaddbdaacdaaadbacaadcaacbcbdcdbccbdcdaabadaabbbbaccabcbcadddbdabcbaccbcbbccdbbacbdabaaabcbbcadadddddbdbabcdbcbcddabaccacbbdcabcaacaadbacddaacbcabbaadccbcbcdbbbdccadcbbdbdcbdbcbdaddadcccacdaadaaaadcdddbbabdcdcbdbddbcbbbdacbcdccbadacaddacccbaabcbacbbacaddbdaacdcccbbcadcaddaacabdbabbadadadcbdcdccacbdddbdbaccbaabbbbbbacadbbcadcaabdbbcbdccdaadbacbcddccbababbbaacdbaadbcbadacddbdacaddbbddbbbdbddabccbccabcddbbcabbbdaccaddbdabaabdddcaacbacbddabacacbabccacbddcbbaaabbddbadacdbbadbbbbabdacbbdbbbbdcbadcdbcdcdcddbccadcdcabbcbaadcccbccdabdabacacaaaccadabdcaabaacaabbabddcbcbbadccacdbbcdabbaccabcbccbccbdaaacdbaccbabccadbcabacadbbbbaaaacccabbaddcbddccccabadddcbaadbcbaacbcdadddddbabadcdccddbabdcbdabaadbbbacddddbabbccccdbaaaaabbbabaabaddddbadabcdadbbdbadbbabdcdbbcaabdbdabcdccbccdabbcbadcabdcaabaaddcbacacaddddbaadadaccddbdbdbcccddabadaaddbabdadbaacddcaadcdabcdadcdbdabbddabbabddbacbcabdccddccdaadcddacddbdacdbdcbadccbbbbacaadabadaccadbbdadaadbaabbcddbdcdbabcbbbcaabccbdbdadbddaaaabacabdcacbbcdabbdcbadabcacbacddabccdacdbaabdcadcadaaabdacabcbdbabccddccbbaddabbcaabaababdbaddddccacaccbbabbbbcadadcbdcaabbdabcbdbaddaadcbbdbacadadcabdbcadbdabacababccdbabbdadcabaadccddddddcabadbcddbacaccacbbaacddabadacbbaacabadadaaaaabdbdddbbdbdcaadccbacbddcaacdcdadbccbbadccbbbdbbbdcaccacaaacaddcaddccddadbbcaacdacacddccacaacddbabdbbaabddacbcbdacddddbadaaacaacbaddddbbdccccdcdcccaaadbbdcaabacadbcbcbbaccbdaddbbbdbdbaaadbbcbdcddcddadbbcbadaabaabadccacacdcddddbacbbadbdccabddcbddacbbcaccdcabbddaaacbaabdbcccccacbadbccaadcadbcccbbdadabdcaaacadddabdcabaccadcdbacccadabbdbccbcbbbdbdcadaddddcdabadbdcadbbbdadbabdddadaabcabbcaccdcbccdcdbcaacaaacccccadabbcacdcbdbbcacddadccbacdcccbdabbdacdcadadadbbdbcdccbcdabdddadcbcbdbcbacbadddbcbbbcacbdadcdaacbbcccbcbdcacdbaaacabccbcbaabdaaadccaccddcbcddbaccdbbabbacbacccddbdbaadddccacbcddcccdbdcdacaddccabacacbbadadddabcbbabcaaabddcbdbaaaaabcdbbadbdccabcabaccbadbbbbdaabdddcadddbaadadaadbbbaadcccbadbdacccadbadbbabbdcaacaaaaabdccccdabbccbadaddbddbbabadddadbdadbccadbacaabaadacbdbcdccbacabcdbbcaabdbbbadcbacaccadcdcaccbacabddcccbabdccbdbdaaddcabacaadcdabaaddbcbcadaacadaabbbdccddabcdbaccaacdbcbacbddababadcaaabbcabaabadbbcbbddccbadabdaabcbdbbbcbbaddadacaadcbcabdcbbcaaabcbdaababdbccdbdcabbdababacabcaddcdbacdccdaccadaccadcdaddddcacabdabbdbbcacccaaddabcabbdcababcaadbdcadbdaadbdccddccabdcbbbcdbabdaaaadabdaccacddcdaadcdcaabbabcaaaddababbabbababdacbbbcabdaaaabdbcddaacadbbacbcacababacbbcbbdbccadabdadbbababdcbdcddccadcaccbcaadaaadababddadddddadbddbbacadccbdaaccdcdbaccabdaabcdccbaaacacdcbabbbdbcdbddcdbbccaaacddbcbddcddddcbbbcbbaabbaddccbadbddcaaaaadaccdcdccdbddccaaaacbccddbdaddbdccbcccacacacbbdabcccbdbddcdccbacdcbcddcdacaaaaddacacabdabaadcdabacabdccdaacacbccadcbdcbbcdadaddbdaabcbdccdbdcccadbdaabdaadabdccddaacbbdbcbbcdabccdaddababaabbbdabcabdadabaaaaaaaabaaadaccbbccbcbbdccaccaddbccdabbadbaaaccbbbcabdddccbbbcdadcccbbcddcbbaddddbaddbdbcacdabcdbabccbdaccdbbcbdaacddbcdbaccddcbbccdadcadbcccbbddddcadcdabaabccbdcdacbddbcabbdaadccdadddaacaabbdcbcbbdadbdacdabdaaaccdddacdcaddcdddbdbdccaaaacdaabbcdcbaabcacacdcbcacbdcabcacbcaabbbddbdcbccbbdacddacdccbacbdbbadacdcdddadadbabcaaabcabcbaacababdbcccdabbcacdabdbdaacacdcadbcbcadbcaaaacadaacaaccacbcdabadddacdacdddabaacadbbcadbbbaabdbbcdbacdcdcdbcbbadbbccddaccaaaadbbdcbbbbaabacddbaaaaaacdbdbabaadbcccbcddaddaacabbcdbccdbbbacdaabccadbbcacadcbbccaddaaaaaabbbcccabbbccdcaadcdaddddadbddcbbadbcdcdadaaacccbbcdacacbdabdcaccdaabdabddbcccaacbccdbcbabdbbdcadddbaaacabbbacaccbaacbabdadaabccaadbccddcacacacababbabdbdddccaadabddadccbaddaaadadbdcdbccdccbaccaaababcabcbcccadadacabacaccdbabddccbcbdadbbcacdbdcadccadaacacdcbddbcdbbdabbbdcbaabbcbbdcbcddadadacdacbbcbcaaacdddbdcccdcbdbdbdaadadcbccbbadababcadddbcbbbadbbcabacdaccbdccbdacabcbbccdcadbbdbcdabadaccbbcdcadacbaadadcabbcbdccadaadbacccbcacbadcacadacacdadcdabddaddddbdcbdadcbcdcaccbddbcbbdaccccaaadddcaaccbcdbbdcddacabdbbdcbdabaaccdcdccccbdabcacccbdcccdddddccdbcddbcdbdadadbcdacaaabccbbdcdbdcdbabbabcbcbbcabdacbabbadcccbaabbbaaaddbbacdcbdbbbddcabdbdcdcadcdccaabaccbddbcddaabcbdcdccbbdccccbcdcdcaaaadccbadbdcbdacbabccdcaaabbbcbcbcccabdacaabbaccadbbabdccacdaddcdcbccadcdcdccbdcdbcbcabdcaccabcddcacdcbccdacabccbcdcabdcdcddbcbbbbbacbbaddaddddacddacddbdabcbabdadbccccdcdabdbdaaacccdcbdbdbccbccddcdaabacabbdacbbcacadabdcbbbacbcbdbbccccbdddccbddcdbbccdcabcbaaddbdcddbcdcdcaccdaaabdbabaaacaddcccbacbbbcacbacccbcdbadaabddadccccdaabdbaaccaaaddbababccabcddaccadcaddaccdabcdacbccbcbcbbcdaacbcddcabdcccdaadcdbdacdabcaccdccbdbdccccdddaaaccdacaaaaddbddacaabacddaadbdadcdaddcabdcddcadaabacabbcdcdddaccaaacbaadcdcadbdcacccbdabdabddccddbcbcdabbaabdcccdcbbbdddbbdadcbccbbacaadcadcbadccdccaaaabacbaddddacbdbadbaacabcddabdddbcddcdabcabdaaddbdcccbccbaacabbddadaccaddcbcdbdaabbcabbdadddcccdabdcacacbbddddddcacabdcccaddaabbdaaacbacaccdbdbbacbccacbddaacccbccccbddddbdcaadbcdbccadadcabbcddbcdbabddadbaddbdddcacbdabaaadbcbaadcdaacddcccaccbbccdcccbbcabccaadcddbdbabbbcbacbbacaccdcdaddabadbadbcaaabbbddcccaabdbdaabbbdbdababbbabbbaaadccdcadcdcdadabcadadaaccdbbbdddaabbddbacbddcbbadaccdabacacccbddcbdbccbabbccaddbddacdbddcadcdacdbddbdcacbacaaddbcbadbaddbaaddaaccdabbdbdcdccaacccddddcaadadcdaddcaccbcdbcccdcdbbbcdbadcdbbdbaddaaaadcaccabbbdcbccddaddcabaddbcdbddabdaaababddddaddbabaacccbadbcdabdbcbbcdcdcbddcaaadccdbaadcacdaabadbabcdcbabcdacbadaddaaabcadcdccadbbbbbbdbbcaabbaccadacbaaabaabbbaccbbaacbadaaadadadcacdaadcaaabcccadacbcaabbaaddcdcbabbdbbdbcbcbbbaaabbaddaabadcbacdacdbbaaddbccccdadbbdddcadbcabcadaadadbcbbaabdaaadbdbcbabcdadaadbcdbacdadbcabbddaacadaccbadccccaaaacacdbcaddccdcadabcbbabaacbacddbddcadbdbadadaadacdadcbadddcdcabadccacabcbcbbbaaddbdcaadaaaaadadbddadaddbdaabacdccdacdcddcdbcddadcdddaaabbbddcaaddabdbdbdcbbabbadbaaddcacdcccbdbdbbbcddcaadcabbbcacdbcdbbdaadcdcaabbcdcdbcccccbabcdcbdbdaadababddadbbbaddadcddcacadbbcbadaadbdccdaacaacadaabccccbababbbaddccddcaccababcdabbcdbbdbcbccdcbaacdcbccbaccbdaadacdccbddddccaaadccdabccabddccdbbccbcbddbcadacdabbdbdccaabdbbccdbaaccbcbdccdbabdaccbabbbcacdbbbdcaccddbddacbacdcbcadbcaabdbbbcbdadbadbcacbbbbbddbbbbadbbdaddaabacadacacbbcabbcbcdaaadcacacadcabbbaadadcbbddbcaccdbcadbbbbacacacaddcdadabbdacbaacadcdbbdcaddbbdccdacbacccdacdadccabbcccaddcdcacaccbbcbabaccbbcaddaabacccbdcbcdcdccbbdcabacdacbcbbdbdddcaaabbbbdbabcbbbcccbdcddadbbbcbbccdabadabddbacabdcbbccbbcdcbddbcbbabdddcbaccddcadcdabccaddbccddcaacaadbbaacbbbcbdcdaacaaddddbbbbcbbbbdaddcaddcbaccbdbdbacbccadaacddbcdcacdcaacddbcddcbbbcaddabbcabdbacbcdcbbacabababcbabcdcbbcbcbcbaaddbabadcdbbcbccaddcbabdaacacddcadbbddbbcabbdcddacaaacaacddbacadadabaaccbcbacabccabacdadcddccbdcdcbdbdacaacccbaaacaacbbbabccdddbabbbdadbaadcbdccdaabbbcadccddcccaabbbbbadbdcadaadabbbcdcdbccadabcbdadaaaadbbdabddccddcaabaadcadcdcacdacabdbbbcaadcacaabbbabbbabaadcdcbbadcaabadbcddbdaccdabccddadabccacbdccabbcabcdbbacdaaccaaadaacdbacabacbbaababcbdaddcbbdbabcabbcdadcbdddbadcacdbbccbdddcbccbdddcdcdbcadccadadbbddaabacbccaadcbdcdbbaabcdcbaccbbbbcabccacaacbadccadbaadbddddbdadabcaaadcdaaaccbaaccdabcdcbcaaadaccabcabaaabdadbadaddaabbbbbbdcddabdcdacbdcabcccaacdaacddadcbaaadbabddbababbadddaadaddaddacacbdaabbdbbcaccbbdcdaddaadacdbdabbcaddacacbdaaabcabcdcccbcadbdcacabdcabccdcaaacbadaacbdadadacccbbcaadbbdabbdcdbccbbaccdcabcbddccddaadcbadccdbcbadccccbdbbccdbdaabacccbdabcbbdacaccaddcdddcdaddccdacabacdbbaaabccdcadabbacbdbabdcdbabdcdaadbadaabcbcbccddaabbbccdcaccdbbdacdacccaabccbbabbccacacaaadcbccdcbbcdcadbbacaadabddcdaaccabbbbbbdabdaabaabbccabddaccdaadbccdadabacaccaccdbcddcacdacddbadaabadcacbdbbdbdcdbddcbddbdcabcdccaaaabdcccdcddadbccaadadccbbdcbdaadcdabcdbbccdddabcccbdccabcaddbbaaccacbccbddbbcbdaadbbbccaaaccdcacbcbbbcbdacacbddcdcddabcbdddcbddcabcbdbdccbdbdbaccabaabcbaacddaabcabdbdccbccdcbbabadbdbaabcaabadbcdaddabcaddcdcccdbdaccabdbcdabadbdbcdaadbcddbbcbcaacaadddbccaacdbbabbbabbbcddcdcbdbaaabcdcaccdccccdbdbbadcddbcccdbbdacbbbcaaddaabcabbacbdbbccdbbaddbcbcbccdccadbdabaabbccdcabababbaddbabbdbdacabbdcababcdbdcdcacdabcbdbbadbabdaaabadaacddbaaaaaadbcbdbbccdcdbbabccbdcbcbdcccbbccbccaaacccddbbadbccaddabcbdddaacacbaadacadcdbabadacbbddbdadadcbbbbaccccdddadcabcabcdbacbaadcaccdbbcdaccccacbaadbdabdacdbccbacdcdbaccabcadcdacddbccccacaaabccdabddaabaabccccaacaddabcbcabacabacacccbccdacdacabadabccabbdcdaddaaacdbbacdabdcbcaababbccdbadbdbdaadadaaaaddcacbaaadccbdcabccddbdcbbadbccadcadddcaaddcdcbaabbdbcccabaddaddacbbaccbcbaaddbcbcdbacddabadcdbdacdadabdaadaddcabdaabbddcbbbaaddcbadbdbbbddccaadcdbddbdddcaaacbdcbadabbdbdacbcdbaaaaaabbbaadcaddabccababdcccbdadaddcdddbcdaaaaddadacdcccaaabbddaaadadbbbdcadaabbcbbabdabbdbaccaccdcddabdbbcadbbabdcaddbccadbaacbcabbbbccadaaacdcddddabbddaababdbccdadbaabbcbdbdcadbcbaaadabcabaabcbdcdabcddbdcbbcdcacacbbacdddbbacdbbbddadbaaadaccaaadaddbcdbdddacaabcbacbaabcdbcbcdcacccbccadbbbbcccacabdacacbcdcdbbadcbaacabaabaacccadccdbcbacaacccbcdcdababaccccdbcdaabdddbcbbdccaadcbcbacddddcbbcbadbbdcbddadacaacccacbbbcbbcdbbacbcdbcbdbacbaacbcabbabacaaabcdccdcadbcbadabbacdccacdabcbccaacccdcbbcddbacacdcdacbbdbbbaddaacbaabbbacdbcdadcbcaddbdddccbcdbbabccbdcdbdacddacdaacccccabacadcddddbcbadcabcdddccacccdacadcadabbaacccbabadddbdbbcbdcbcccaabcdbacbacccabdadbdbcbaaadadacdcdaaaacdcccaddbadcbddaabdadbaacdccbdbdccacdbdaacbabdcbbbdcdadcacadabdbccbabdcdacbbaaacacbbdbdddbabadacddadcdbbacdbbbaacbabadbddcacdddcdabcbdcdadbbabbacdcbadcbdbaccacdabadcdcbdbbadcabdccaccccdcacbdbdcdcdccadcdbaabbccdcddabbdbcbdbbdbadaabaabaddbaccacbbcbabbcdadabdcaacbaacdaccdaadabcccdbcabadcacbbcadcdbddcacccccccbacbaaccddcbcacddbbabbabdabbdaaabaccacadbccaabdbbbcbdccaaaaaddabccdcdabcbaabdcadcdaacacccbbbdbabccdbbbccbbddaccdaadbdacaabcdddcddbcadadadaacdbcbbccabdaccbbcdcacdbacbddddcaaaabbaacacaacaaabbdbbbaabddbcadcadbcccadcdbaddacadddbacdabacddbaacbbcdcabbbbbabacaccccdbccddddbcaadcdddadddccdbbcbdaddcdadddadccaadbbdcabbbbababcbbadcacadaccaabdaaaacacadddcbcddddbadbcdbbddaaaadabdbdcadbbccbbbdbbaacdbbdaaabcbabdbbbcbcdadcdcbcbdcbdbdbdcaaabcacddcbbadcdcddddbaddacaabbcdcaddbabbddcbbdababaadcacbadaaabccddbbdccbaabbddacdacddccbcbcddbcdbacccbaabdbaaacacbcdaabdabacadadaaacbdaddbddacabcbaadaabbaadccaddbabdddadcadbadddadadcadadbcadadcdacdabaaddbdbadadddacddbadddcbcbcaaaccbbadabbbcbdcbbadadadbabbabcbbbbddbcaaddccbdacbacbabcacaadcbdcadbbccbdbcdbaadaccbabacbdbbddcaaaabbcbdaaabbaadcddacccbdcdaaadbbddabddadbbcbcadabdccaabdbbacbbabbaaacbdbadbddaadbcdbbddbaaadbccddbaccbbdbcbaabdaacbadbbbcaccabcdcdaabbbdcaddadbcccdbcccabadcbbccdbdcaaccbdcbcaddddaaccdccdaaaacbcbaadbaacaccabcaaddbdadccdbbdbadbdadbdbcccadcabdcaddccdabddcaacaccdbbdcdaaaacbcdbccabaacaaddacaabccdbabcdcbccacbdacabdddbbbabdbbbaacbacdacacddaaccabbdbdacaaaaaabcabbadccbdabbdabdaddacabdcddbacaabcbbcaabaadbdcddcdcbaaacdaddadcbabbbaacccdacdacadddccadaddbbbbbbcbbacddbddbbbcdcbbcbbdcacdcacbadcccbbaacdbcababbbbccbacadbadddcccdabbbadaccaaabbbdaacccacaabdbaabccbacdcbdcaabbbabdbdaadcbdbcacddbbdbbccddaddcbcadcadacdacbbaaddccbabcadbdbadccbabaaddbbddadccbdcdbccdccabbbcacbdbadbcddcacaabcacaddabbbdabaddbaacdddcdaaaccacbaddcddacdccaaccccbdbabbccddbadbabbbbdbabadbcbbccbbbccdbccdcaaccbdcbcadcaaddabdcadddbbdadbbcddabcbbdbbcbdddaabacddcabaaadacbcccbccabccbaaaadbdcaabddabcbaaaaadadbccbcbdcbdbdacbacbbccdaacacdbbaadbcbacdcaadddddcbddccaaddbbcdaabcbbbccbacdcdaadaaadccaccdbcadbcbacdabbaacddbbcccdbdcbabacbcdcacbcccbbcccdddccadddccbbcababdddbcccdaaddcacacabacdbdddbbdcbccdaadbdbbcaddabaacdbabbadbdcdbdbbcdbdbddbabbdabdadbcdcdabcadccdcaaccabcdddddacacccdbacbadddabccccccdaacadccdbddcddbcdbdbabdbbdbddddbcccadaadbcabcbbabadcddadbddacdcdcacddcbcabbbacbcddadcdccdcbbbdccaadabdaaadbadcdbcdbbadcdadbbbcdaddbcaabcbdddcdaadabdccbaddaacdacabccadcccbaabbcbdcadddddcabcadbdbdaccccabcbddabbddccdbbadacbccabdaaacabaaadbbdbcbcbadadccdcbacabdbdbdbacbbadbabaabbcbbdbbadbbbdcbabaaccadbdccbabccadbadbccbabddcabdcadaccacdcadbbbcbddbcdaadcaacbcdbcabcdacdbbdaddaabaacbdbdbadcabdcdbbadbcadccdabbadaaabdcaadcdadcacdaadaaadbbdcabbbdabccdccdbadbbbbbdadabbccdccccdaddcbbdbaaadbbbaabcbccdacbbdbcbbaccdaddcabcacbabccdcabcbbbaabccdccbdbcacbbbadcddbaabcccbddbbdcaabaadcdcbdbdaabcddcabbbddaacdbcacbdcdbcdbdcddcaaabccdcdcdbcaabbaadcabccabcbbadaccacbcdddadccdacccddacdcddaccbabcdadccddcbaadbdcdcddcddbddaccbbcbdbaccbcdaadbcadddcbbdadbdbcadcabdbdbdcbbaacbdcdbbdbdbacaccbdcdbcacddbbbbdbdabbcbacbdadbbcaddaccadabbbbdbaabbcddbdccbbccabaaaaaadcdccabbacddaddcbcdabdabcabacdadddbdddcbdddddacdbbccbaabbbabadadaabcaccbdadadbcdddbbccdddddccccdbbbababdcdbccdbcbbbccabdaaaccdccabccaaadcacdcbdabdbabbccacccadbabccababcdabdbacbaadbdadbbacabadbbddbbccccacacccbcabaadccdbabcdbbddaccaaaadcacaaaadabccccbacaacdadabaccabcbbddbdddcdcddbdcdbddbdacaacacbdbabacadbddbaacbacbbabadccddabaaaaabdabaadbdbcbbddccdbdcacdddacbdbdabdaadbcbaabadcdacadcbaccccdbccaaccbbcadabcdddadacbdccdbbbacadbcadbbdddccacdaabddcadccadcddcbabdcbcbdddcbddcaaacadbbdcdbaabdcbacaaddbcacadbbdcabbaccbaddbdababcbadcbdcacbcbdadcbdbcacccccdacccadcbcadbabccbbaaddcdbccbdcbcdbdbdabcdbabadcbcabdaadcbabccabddacaaaaaaacccadbabdbdcabbacbddabddcbabcaaadcdcabacdadcbccdcabbaaadbaadddcdbdabcadccdabcccdabddbacdbdacbbbababbccbccccaaabcabaabbcdacadcdbababadacdbcbacabababdbdaaaaaddcabbacabaaadcabddcaccddccadccccadcadbbdbbcbbddcddddadcaacccbaddcaaaaacddbdcadbdbccbbbbaddbdaccaadbacccdbadaadbdcdcccbddaaacddcadddcadbbbcdabadacbddddabcacddacdabbdcddabbddbcdddcadcccaadadbdcdcbcbacbdcddabaaadbdbdbdacaccaccaddcccdcdbaaaadcadbcbccdddbaddacacbababdbbdbdabdbbadcbcbaddbbdbaccccbabcaaacddcaaccbbbcacbabddcbabcbccbddbddbbcaddaacdadcaacdbbcbcbcdaaabdaddccaacdabadaadbdadcdbacadbdccbbbcdddddddccccccabbdcdcddcaadbabdacacdbcdddabcbdaccdbbabddaabcaddacdadaddbbcdbdabdcdaddbdcddbaacadbaaccaacaacbacbcccbdbbcbacbababcaccccadabadcdcccdbcabacccdbdbdbdcbbdbdbdbdadabbcabdacbddbdabcdadcdcadcaccdcabdcdcbabdacddaddbccacaacdddbbbcccdabcdcdaccbdadcdcacacbaddbcbdcbbccbabcdcdbdbaddabdbdcdcdbbcababdbacacccdbacbbbcacabdabbcacdbbdbddabccbccbccddbbbaaacbcbcdaabbddbacddacbdbcddbaabbaccdcdcdcdccadddabababdacdcdaccbcbdbaadbbddabddcbdbacbadbbbabadaddbcbabccdcbbdbcbbddbbbdbadbdadabddcbbcacdbcbccadacbbadacccaddadcbddcbddddcdcbacdddbddcacdacdbaabbcbaacdcbabadbbcaadadacdcdaacbaddddbdbdbdcdacccadcbaaadccdaddcaadabcbddaaaddccadbcbbcadbbddaaacacdbcdddbdcbadcbcacaddcbbbacccbdbbabbcdadbcaddbcdadcbbbdcacbaacadbbaacabadabcdbadaacadcacccdacaadbaabcadcbccbabdbdddabaddbdcdaddcaadbcaacaaadbbbbaaadddbdbbadadbddbdadcdbadcbbbcbdbddbbbababcadadacdcbdbcabadbcbddcbcaacbbdbbccadcbbddacbcbdbccdcddbcbdcaacabdacdbbaccdaccddbabbcbadccdabdacaccbcabcdbdacbcacbccbbcdcacdaacaabdbcabcdbbbdaccdacdbcccccbaabdadbaddddbdbbaddbdbdcdbadcddccdccaaccbdddbcccbbdcabccbcdccbbddbbcacbbbaabdbacdbbbaadbaaccdabbbbbbadaaaccabadaadacdbaabcaddadadaaaaaaabcdcacdbcacbbbbdbaabdadaabaabdaabccbdaaaadcbcabdcbcdacaddbababbabbabaaabdbcbabaddacbbbcaddccbdccddbbbaadabacabdaccdcdcdabccccbaaacccccdccbdaadbacbdcddbbbabbbcddbbbaccaccbddbaacdacadaddaddcbaaaabadbadabadcbcdabbbabbcadbcdcddbbabcdbcacdddcccdbbabddcbaabbdacbddacbaacddbbaddbcdbcbaacdaccaaaaadaddbaddacabaddbcacdcdaddacbabdaccbacccadddddbdbcddddcabbcccbcbbcdacabadabccaaacbdddaaadaabbbcbcbdcdcbcbcdacbbaddcaddbbbbccabcbbcdbbbcdadddbcdbaabcccbdcacbabcdabdbacadbbbbbcbcdadaabababcacdcdbabbcaaddbbddcbcabaaacadabaadbdcaabdcccccaadacbdbccbbadddcbaacadbabaabaddaacddcdccbaacbcdbdcbdbbdabdaccbdcdadcdacbcaccbaaadbcccccddbdacccdcdddcbdcbadacbacbdcbdcbbacacdcdcaadcdccbadbcaacdcbbacabdaaaabdccbacdbddbdacdcddadcddaababbadcccdbabbcadbddddabbcbbddddacbcdbdcbbccadbacbaabaacacccbdaddcbdbddaddcaaabbacaadaaabdbbdcdaabadabcdacadacaadbdbdbccdbccddcbbadaadbbbddcaaabcaacdbdbaabbabddaddddbbbaadbdacdccadadcdadaacbabbbbcacbaacaabaabadddbacdcbaddabccdcdacaadaadbdaddadbaddbbdcaabbbacbbcdbbabcbadcbbdacbacbbddddcbccdbcbaadbadcbabdcaccbbbcaabbacabdabcbbcbcbbbddbbadcadddadacadacbbaadcdcadcbddaaaabdddcddaacdcddabcbbcbbdacdaacadbadbababcbcbbacacddcadbdaadcbabdbbbbcacacdddbcacdcdbaabadccccdacbccabcbcadacddcaadccdabccbabccaabaaccccbdcabdbcddadccddcbcbdcbbdcdbcdddbccccacbbdbdcccadaacaaabcadccdcacabcbdccdcbdbadcbbbabdabaaabccccacaacaccbcdaaddaadbdcdbcbddbddcbaaddddcbdaabcdbadbbddabbbdbddacdadbdcdabbcacdabdacabcdaaadcadaaadacbbbabbdbcaddbabddbbacabbabaccacdddadcdccbaccbaccdccaabddbbcccaadabadbadbbdccadadacbbccabcbdcabbdcddbcdbaabbccaddabaaadcbaabcaadbdccdcbccaabdbbddbabadaacdcadccbcdddbaaacbbddccbabadddbbbdcddbdcaddcdcdcbbabdabbababbcbdacadbdbbbbcaaaabccdacdbbacabbbaacccdabbabdddcdcadbdaacddbacddbaccbdaadbddbbddbabbaadadadccdcbdcdbbadbdbdcdddcacaccddbabbbadcabbbdbbdabdcaddaacddbccaaabaaddaacaabbcbdbadccbbbacaacdcacabdcadbcacbcdaabbcbdaaacbbabddccdaabcccbbabcdddcaaddcabcdaaabcddabcadcbdcacdcbbaadcaabdaabdcababaacccbbbbccbbdcaaccdabddccbbaacdbbabcdbbdcbabbaddbdabcdaacbbddaacacaabcdacccbaaacccccdcabacacbcdcadcbbcddcabcddbcaadacbddacadacdcabdabdcdcbacbbdddacbddacdbbabbbcbbbaccaabacdadadcacdcaaddbddcccabdcadbdadaccbadcbcdcabdaddadcdabadabcbaccacdcdcaabdcbcdadacaacbacdacddcdbbdaabdadbabdbbdbaaddadcdaabdcbaaabcccdbbbadaccaaccaababcdbbaccabdacabbdbacdadadcdccbdabadddadbdbdacbbbcddcdcaabaadbbdccadadacdbbaadccbadbcacbdbccdddcabdaaadacacdbcdadabbadddddbccbcbbacadbcbccbcbcbdaccacdbcacababbcacbcdbbbcaddadbaaaddddccdbdcabacbbbadccbacbabdddabdcbbabaaaaaaabcbaacacccacbacbcabbcdcdccadcabaacbaabbcdddbcddcbabbcbcdbcbccacdddcccaadcbabbdabbcdcddbabaddaccdcbaadabdccddddabbaccadbbbbdbacababbaaabacabbababdccdcbdcbbbbddbbdacbdcdbcbacddababadcacaabbcaccbbddcbddbcdadcbccbcabadbbabbdcadbadabcdbbcadbccaaabcdccbabbdbcacaadbcbdbaacdadcdabadaaddccabacbbcdcbbaabbbabccdabccdbadaacaaadbcbcbbbcdcbcbabadabddccabdbaddaaacddccddcdbbadabdbdaabbaaccdbcbdddacbbacdacbbcabddcacdadcacdcbacbdcdbaacbaabdbabddcadbcdcdccdbaacacbaddccbcbcbdcabadcbdbcadbbacdbcdcdbcacdabbccccaddddddcadddacdbadabccdbbdddbbbabcccccabdadbacbadcddbbaabadabdcaddabcbadbcabdacddcacaadbbddbccbdcbddbccbcdaabdcaaabcbdccdcbaaadddbdbdbdaabccbbcdccdcaccacacdcabcdcaabcbabbddccdacbbcaaadaaacabbaadadcacbadabdcbbbaabaacbddcdbdadacbdadbdadddcaaddadbdaabbaddaabbdcbadcdcbabbbdbdcdcabcabcaddcdacdbdacdcbbbccbdbdcddbbadaddbdbdcdbdbabadabdcbacddbaccdddadacbbadbaacdcdccdbcddbbabbcaacdbdaabbbccaadbadadaabccadcdbbdbacacbddadcadcaaadccddbbbbcdbdcabbccccbbdddaddcaadbbdbccadcdcbacbddccadadddddcdcccbdbbbacdbdcaabcdbabdcdbbcccabbbdaddcbbbdacdcdbbbccdcbdbadaddddbbcbdbdccaccddabddabbdcccacdbbcabcdadaaaabacbadcddddbbddbbcbddbbdbbdcdbaccdbaabbaaadcbcbaddabbabbcdbcbbcdbbadcdbddbdcaddcacdbacacbbbbcddccdbdacbcabacdbcbcdbbaabbaaddabbcaaadacddbdccbcbaaddaaccadbbcdacacbccbdacdddabcbcdabcaccddcbadabacbaaddacadacbbdadcbdabaaadadabaaaaaddcbdadaacbdddbacbbdbdacdbbbabaccbccabdcaabbcbccadcadabadadbaddadbcddacbdadadbbacaaacbcacddcbcdddbbdbbddabdddbddbcbdabbdcdcdcacadcabdcaaddabccacddabbbaaabcaaddbdcdacbdaadcccdcddcacadcbbcbbbbadaacbddccdcacacaccdacccbccacdddbcdcabcdaacbbddcacdadcdadbabcacdadaddabbbdddddbaccdcacbbcaccdbacabcccaadbddccadcbdcdcccaaabbaadaadcadcdccbadbbaddabdbaacdacddbadadadcacaadcdacbdadadbabbddccaddacdbdcbaadcbcddabbbbcbbbddacabddabdcddcaaabdbddcadaabdbdccbadabccaaaaddbbcbdaadddabacdcbacdbcddcddbcbccadcddacdcdabdbaddacadcdcdcccaaaadbddbadddbccaaddcbabcabdbcbdaadbadaccccdddcdadbcbbcbcadaabddbcacbcbcaacaccabccbaabdcdaaaadcbdddabbdadabcbdacdacbabbdadbcdbcddcbbdcddbacabcbcdbdcadccabbccddcbbcacbcbcaddddadddbddaadcbbadcdcabbbddbbcccddbcbacacacadadaddacdaacacbabaaacccabbaabaacbdccbbcdcbcdcddacdcdcddacdbdbabcddbbaabdadccdbddaddadbbcbbdbaabbcddcccacadddbacbdcbbaddbacddbcbaaccadaaabcdadadcbdcacadcbcbacacaddcadacbbccdcbcccaaacdcbdabcaadbccbaabaddddcbbabdaadcdabbcabcabadddbcaabddccccdaabaccdcbaadaccdcdbcdccbacddaccacdbdaacbbbaadbabbcbcccbbbabbaccdadcbadaaadaccaadcaabadcccbcbbcacaaccdacbbcdaabcdcdadbdadbdbbdcaccccaddbdddabaacbcaabcdaaaadddbddbbcdbabbabaddabacdbaddbbdabbddcaaacbbabddbbacdbaadccbadcccdcadacdddbbdddcaaccdbbddcbbddcabadcbbdbbcdcacbbbdccabddabdabadadaacbcddbbcbbdabdcdcbabbccdaaaabbacdbcdcdbaabdcdccaadbacddcbddbdccaccbcbbcdbbbdddbdbcbdbdbccacabcdddbaccdcddbddadbddaabcdadcdcdbdbcbadaacdccabcdaccaadbdddcadcabdababbdbcbbcbbdcbdbdabcdbdcaccbcdbacbcbbaddbddaaabbdacdbdcdccadbbcddaaccabddccdacbccdbdacdacbdcdccbbbbabacbcdabdcabdbcddaaccadadddbbbbdcdadccbcadabcdcbbadccbbcdcbdbdcddbbdbadbabddadbcadbcdbbcbbccabccbdadbcbadaccabdabcddbdcbcbaadbdcccadbccacbadabbabdbaaacdcccadbdadbddcaadbcaadbcbbcacacaddcbdbdabccbcdababbbddbabcbabccacadccbcdbdacddddbcaccadcacababbadbaacacdcabdbdaabbdaccadcbbacbbaadadbccbbbadacdacbacdbacacbaaabccdbdcadddbbbbdbddcaaaaddaacdaababdcbacdaaddcbcccabcbacacaaaabddbdcacacbbbccdcbdbcabbdbcbccdbabcddcdbaddbbadadbaabcabaabadccbbdbabbaaadddabdbbacddcbaabbcdbaacbdacddaccbacacdabdaabcabaaabbcabcddddbabccdbabaabdbcbaabaabacdbdcccaaabacbcabbaaccdacdbbadaacbbbcdddbbbbbbbbabaccacaddabcbcaccdabcbcccbcabcbabbcbdcbcbccbcbdbbccbdbadaacddabadcdadaadbddbadcbbabdcabdbbadbdaaadccbcabdccbddadaccccdaacaddddddcddbdcacbcabaddbbbababddbdcadbcacadbbccbaaaaccdbbbdadbaadbbbbddabaddbbbcabdbdbbadcbcabbcbbbaadbadadaaacaccacaacbdbabdcaacacccabdbbadaabdabadbdaaaadaacdbbcdbadababadcabaddbaaabcbdcadcbabbdddbbbccdcbbaadbbcddddadcacdacbacdbabdaaabacdabbccdcabaccbdbdbadbdddcdabacadcdbaccabdadddbbdadbabcccdacaadadbacbdbcbacdcdacddcdaadcbdabacbdbabccbacabaabccacccbbddbcccdacacdcdacdacbbdbcdaabbcdbbdadabdacadbddbbcdadcdabddabbabbddbbbdaadcacabcdaacbbaaddbbbbacaccbabdcaaccaddacdccbdbababadaabcdccddbccdbddcccdcbadbbaabcaabccbccacbacabcadcbdadbaadaadcbbbdaacdacadcaababdbdbbaddcaadcdabcadcaddbcdbdccbadbbddccdcaaadcbccbacdbbbbbacbabcccaaabacbcbaaaccdcbaddbabaaadbcbacddbdaaccccaabaadcacdbbaabcccbdbcaccaddcdabadaaccbbbabdaccdcaddadbcadbbddbddcddcadbdaabcdcabdabbaadcbacddccadcadccdcbccabddabbddbbdaacbdbbabcdacaabcbacdddaddbbdbacdcbccccdabdacacbcccddddcabcdbbaddcdddaddadadddccdcabbbdcaddabaccdbdaddaabcbbbbdbbcbdaddbbbadddcdabacbdbaaddaccabbaaadaaadcdcabcdbddaaaaddbddaacbbcdcbcbbbbcaacbaacabcccabdddacabaabbbacaccacbacbdddacaacdcabccacaacbaddacabcbdbaaaaadbaaacccbbdbccdcccbddadbcaabcbbdaccbdcdcaadaddbacabccbdbddcacabdbdaabdcbccdbbabddbdcbbccbdcacacbbbdabdcbbcbcddadccbcdbcccdbaddbbccaaabacccddaccbbcadbbadadacacddcaabdbbdabcabcbbccadaccddddbbbbbbdddbdbdbbcacbcabdbbdabbbdacdccdcbabadcabdaddbccccccbbbaccbdcaabbcddcadadccabcddcdcdbdaabaacbadcccaadaabbacbbdcbabbbcbcdbdbcdddccdbcbcabaadcccbcccbbaabaacddacadaadabccbbcdadcdcdcbaddbdaabdccdbaccdbaddcabddcbbbdacacacdcbacaadadbacabaacbbbaddaabdaadbdcdbcdbbccddadcbbbaddccdcbbbbbabbddbcdaabdbaadbcbccdbdcbadacbdcdcdbaacadadabcbaadcaabdaabadacaaddaaaabcdbdbbabcbadbcbdddacdaddacdbcdcdbcbaaabdadddddacbcadcddaaddccadbaadbbbadacbbbaacddacaacdccdbaabbbdabadddadccaabcccaaacabdbbdadcdaccbadaacdbcbcdbbccdbacbccbcccadccbdadccaddddaccbdcdcdaddddcdababcbadbdbbaccccbcacdcadabaaadadddabcccaddcdcccbaaddbcdcbdbadbdcbcabdabcbabbddacbccbdacadadabdcbacaacbabddbaccadbcaacacacabbcadcabacacaddbbddbcbacaaabcabdabcbbdcdaabdccaaacbbbcdaaddbddbaacbbdadbcbabcbaccbaaababdaaccabdadcccccbcbbcdabcdbabcddcaacbdbcbaacbdbddacaacacabbcadcadaaacdbdacbbaabbdbdbdcddadaaaaadbbbcadbabbacdcbbbdadbabcacadcbcbaccaadbacdaabbcdbcbbdbabcddbcbaaacabcdddabdbbacdcddcbcdaacaaacadbbabcdddbbbadccccaacbbabccbbdabbaacccdabdbccdbdaacdcaacadbadabcdbbcababddaadadabacaddbadcbccdccdcccccdcadcbddcddbdcbdbbdccccbabdbbcccadabddbaaacbbaabcadcbbddccbccadbdccbcaccbabbdabaddbacdadccbdacccbdbabddcacdcddddcaadaacddbccdcdbdbaabcdbdaddcacdaaaadcbacaadaddcadadbbbdbadcacbbcabbcbabccacccbcdccbdbbacbbaadabbcdccaccaccbdbddaadbdaccbadadcaacdacdcbcabdabdbacbbcbccdbcdabcacdbabbbbacaaabdbdbbdadbcdcdbdabdccbdaabcdaaddabcadabadbcbbdccabaaddcdaaaccacadcdaccbadcddcababdccdbacadacdbdcaccbcdcadaaadcdbccddadbbbaadccbbcdaacccabbacaacbbbdcdcbbbcbabcbadaacaabbbdbbacbadbbbbbacbcaadacbcbcddbbbcddbdbabcaaabadcacaabdbadabbdadabcbcdaaaaacddcbccadbacaacddcdcaddbdabcddcccadbbbccccccbcbddbbddccbbcacddcbcbabadcbddcbabdabcbddcbbbdbadbcadadcddabcaaadcadbdbddaddaadaacaccabdbddbacdbaadaaccdaaadbcdcdabbbcdaaadcdbdbaccaacdbcdcbbdcdababaddccddbcccbabbbaacaaddddaabcabcbcbdbbbdcddccccbbaabadadcbcdcaaadccaccbdcbccbcdcaadcaccbabdbdacaacdcbbddcbcdcaddabdbbccdbdaacbbbccabbaaaddadbbddadbccabcdaaadcdccddbdcdaabdbdcbaaaddaadaaabddccdbbcbcccababcadbbdabcacadbcdbbbcabdcbadaaddaaaaabbbbddddbdadaacadddccbcbddcabddaabbabdaadcbbbdbaccabbdbccdaacaddcadaacbadaaccdaadccdcccbabbddcbaddcbadadcdbaaaadacadcacabacacadcbbddcbbadcbaabaabdcaadaacdcbdbccbacadcaddadbdcdabcdcbdabacccccdcccbacacabcadaaddaadcbbddabdbccbaccabacadcbbbabbcdbbdbbacdaaaacdccdbcdcbddacdadcdacdaabcdbbdddaaaabddbddaadddccaabaddbbcdadadaacdbadabadbcaadbacdbcdaccdacdcdcacbcbbccbacbbdbdcbadaaddcadadabaaacbdddccdbdcbddbadcaabaabbdcadbdbcdaaccabcbcacbbddabcdaaddbbbcabdcdbbcdbdaacadbcabacadaabadaadcdcbbabbbaccbcbdacddcabdadcaadcaacbddccddddadbbbadcaacbabbaddcbdaccbaaabcadadaacbccbcddcadacbaaacabaddddcabdcacccbddbcdddbaccbdcbbccadcabcddbadabaabddcdbaccbddcbcaddcbbccaabdaccdccccdaacbaccabbcbdaaabcbccabbdadaacbdbabbbdabcabaddbadcdbadddcacdabaccdbcbccdddddabcdabdaacdbadabadbdabcddadbbbcdbcaccbbbcdbcbadcdcacadaacbdaccdccdcadbbddbddaaccdcbbccbacbcaacccdddbdadbdcbcddddabcbababacbcbcdcdcbdcbbccddccadbdaadbabbddcddadaddbadadccaaadacddaccdacdbbbbcaccbbcbdcaaaccabbdcddacccbabbdbdcbbadacaababcdcbcacaaabadbacbbcccabacccaaaccabbdbdaadbccddcbdadaabcddacbccbabbcaaddaadbaabcccddacabbcbabbbacadccdccdbcbabaccdccbcacadcaccabadcddabbbacadadccdbccdbbcdbdcadcbbdcaabbcaadbbbabaccabacbccadcccbbdacaadabdabbaaaadabdbaddccbacddcbbdbdaddbbcbaabbddbaaccaccdcabcbcdbbbaddaaaabcbacabaddcbdabcdbbaacdcdbaacbbaaaaddacbdccddbbcadbdcbbcaaaaadacdbdccddcaabcbacacdbaddcacbcddbbcbacdddbdcdbcdbaabdcbbbbdadaacadddcbabdcacbadccdcbbdcdbbacddacadcdbccdbabbccdbdacbcccbccbddcaddccbdcdcabbcacbacbcdbcaddbabdbdddbadbcbaadbbaaccabbdddccbaacbddabcaaadabbbcdccccddcbbdbddddcdaccdbdaaccbccbdbcabcccbbcaadbdddbacdbcaddddbbbcadcccdaccddcadccbcccdcccddccbbcccdabaabdcabdcaabbcbcadccccdcbbbbaadcbbcadaddddabdaabbaacbcbaaadbddcbcacbcdddbbbcdbadcddbccbdabdcabaaaccdddabccadccacadacabccaccdddcdcbdcaaadaaacaadbaabdbacbddcaccadaddbaabccaabadcbccdacdcbacddcbdbcbbabbaccacbacbddcacdbabadcabcbbaadabbcbdbccbbdadaabcddcdaabacbbbacbbbbdcdbbcbadddbadaadddbdcbabcdcdacdbbaddacadbdbcbacadacdcdcccacdcabbccbcabccddbdddbbddaadddacadbacadbbcbdcbccbdcbdccdbaabacaccabcbbaddcdcbaacbabcaaababcdbbacbcdbdcdadbbbbbbddbdbbacdacbbbbbcbdcdadbbccdcadddcadababcdaddbabdadabbdcaabcdaddbdcddabccaabdddaabdaaaadaddabcbdcccacdacdbadbbadaaacabcadddcdbbcabbcddbdbbcaababbdbddcdcadbdcbabcccaccabaaccbdaabcddddabbdddcbccacaabdbcbaabdbbaccdcacababccabbddcdbadbdaabbbdbbdbbadcddcababdcaabaabbbdabaabdadbdadccdacabacddacbdcddabbdcabcddcdcccbcaaaabdccdbadbdbbabdddaaddbadbcadaabababbcdaaccaacaadbbddaabdacabdcdcbdbdccacdcaacdddccddaaaddaddcbcbcdddabddbddcbdadaddabacaabddbcaccdcbcaacbaaabdcbaaaccbdcbadaaacccacdaabcdbacbacddddddcbcbdddaddcdaadabaccdbbacdaacbbddcbcabbcadccabaadcdccdacbcdacbbaaabbbadcaadcadaaacbdacbaabcbacccabadbdbabcaabdbdcddabcccbbdbbccbabbabdbbbbcddbccdbdaaddbdddcdcbccaadcbdaaddbbdbbdcdddabbbcddddbabdcabaccadaabadbaaaccaaadbcaadccadabddacacbdaabdbadbccdccbacacbdcdacbcdccddcaaabdaddbabaaccacbbabddacbcdbadbabddbddbbdcdbbccdbdbaababbdbacbcddbacdbadbbcccbbcbcbcaaacbcdbbcbccdaacbacacadadccdacacbcbcaabdcbbabadaaccdddadbabbcdaabccadcadabccbbcaadbacacaccdbadacaacbadcbcddbaccadddcadbadcdbbdcaabccdcbdbadbacccaabbaabcababddaadabdaddbbdaadddcdbcbdddccaccdbbaccbdbcccabccccabdcdbaaadbdbdcbdddcdabbaddabbbaccbdacaddddcaabdbcbccddcbaabdcdcdbcbcccadddccaabdbbcddcaaacbdabcdbbccccbcababdcbabdbdadcabbcbddddcdaabbcbadcadddacacbbaacdabaabadaababbbdaccaabaacbabdbaccdbbbababcabbdabcaacadcdcbddcbadbcdbacaaaadddcdaabcabbcdccbcbdbcbcbaacacdbbbddcbaaccbaccabcbaadabcdbacbdbdbdcabbbbdccccacacadccddacbdcddcddaccdbccaadbadcdccdabcdddaaccaadabdbbcdabbaabadddaabdaabdcaacaaadcadcbccbcaabccbbdbdbaadaabccabdcbbdcddaacdccbbacdcaaaadddcccdcdbdaadaddacbccabdbbbdaccdbcbbbbadcaaadddbadbaccacbdabbcddbbabaabccbcaccaabcbdddabadccbbbaaabdbcaccbcccbcdcbdcbaaadcabcacbbbbcbdcbadbcacaddbdadbbccbaabbaadabcaadbbcbabacccdcbdccbcbbabcaccdadbacaabdcdcaacaddaacbcababbaaaadcccaadaddccbbacbbcbdbbcdaadbccbddacbabcdabbabdbbbcadbbaadabcdbcaacabcdaaaabcbcbacbabaccbbbbabadbccbabccabbbdadabbccbadbddddcabaccdabaacdcabaccadcddacaabdacdbdbbcbbdaddaaaabddaccbdbcabdbcbbaabdbdbbddccadcbdaababcdcccabcbadbbadaaaabaacaaadcdbadbdccbbbbcbdbbcbcacddcdcdabcbacababcccdcaadddddcbacbdcbbadbcbdccacadcbadbcdbdbdccbddcaccaccbadcadabcaaaddbbcdcabcbbcdcbbdbbdabdbbddddabbbdcbdababddbdccadaccbbbaadbbcbbdbbcdabbdcbdabacdcbbaadddabadabdcbcacddcbdccdcbacabdccdbbaaaabdbdaadbdcabcdccabdbdcbbbbaaaadadcdddbbbbbccdbdbddbbbabcdcddbcbddabcdddbccbbdbcddcbadccdbcacadddbaddcddacbcbabbdddaadadbbacabbdaacacdacdcbddccacbcbaadbcddbccddbbcaaddbdbabddbadddbccabaddbdacaccdcbbadbdbcadacccacdbdacdaddbcadbbccbccacdbadbcabdbcbdcacbaababbbabaccdadbcbcaabcaddbabcddbdbbaddaacdbacdcdbdbbadccbbaddabbdbcdabbbdadddbcbbdcdacaacbcbdacccdcababbcdacdcdcabacbaacccdbdccaaacbbbcdccbccbbbcbabbcaaaadbadcdadbddabcbacbddbdabccdbcabbcddcbbcacbadacbddcdbcadbdcacbdccacbdcddabdcaccbadcabcdbccdcddcdcaddcaaacbadbcddadcddcadcbaddcbcddcddbabdadacdbabaadcabcaddaaadaaddaacdcbbddddbadddcdacadbaabcdaccbcadcdaabbddbdbcadcbcbababcdbdcbbbcdacacdabdbbcbddcbddadddabbdbdbcbaadcdcacdbcddbcccabbdccbdbabbbbadcccdaaabbdddcaccddcbabbbccddbccdacccabcadccdadbddcadcbdbbcbcabddbbcacbcabbbcaccaaabbdbbddadaaadcaaadbdadcacbaadccdddaaaabadabdaccdacddbaacddcbbacccdabababbbcdbbbbbdbbaddadbbabaadacbbdddaaddbbbbbaddbbcbdbadbcdacdbabbccdaccacddabddbbcbaabdcdcbbabdabcbabdcbdddbbdddbdbabbcdabddddcddbaddaabbdcaadabdadbacbacabcbcdcadbcacddacabcaacacdbaabcabdcbcdcaaacccacaaddcabcdbdcbbdbcdbaddacbdadbcddadacdbbaacbccdccaaccdbcaaadbbddbaacbcccaacdbdaacdbdcbacdddaaaccabbcddacccddcdaaaabbadaccdaabdbbbcdcbdbdcddabbdcadbcbddccdbaadcaaabdcdcdabcacdabcbccbdbaccddbbacddbdcbbacbabaaddcaccadbaccbbbcbcaaadabbadcdddccabbcadaacdcbdbdbabadbdabcdacbcdccbbadadbabdccbdddadccdbccabbbbadcdadbaabddbbacdbcdcccbdcddacbadaaccbbaaccbdabdcbbcddabbdbadcabaadbdbbbdadbcadccbcbddabbddcccacbcbabaccadabcbaabdccbcccbcadccacababbdaabcbcbaddbacdadddbcbaadddbbcccbcaabdabddccddbbcbbaacddbbddcaaddaacdabccdcbadcbbdaabbaaddcadddbcdbbcdaddbaadccccaababbcccddabcdcbcddcadbdabbdcdccdcbaaacbcdbcadadcccbaaccaadcadcccbdcbaabbbcbcacdaccbbabcaaadadcbaaaacdaccbbaaaaaaaabdbacbbdbabddcdacabddcadbbcbaccdaaadabbaacbacadacccdbcbcbacadbbcdcadddbacdcdcccccdbaaaabdcbcadbbdadbdcabcbacbdadcacacbbddaaacccdcbdacbbcccbadbcbcdaadbdddddadbcbdbaddacabccabbbddcbbdaabbacddbabbcbdadcbdbcbbccddbaadaddabcadbdbadcbdcabdacccdaaccaadaccaacacbbacdbbabcdbbdbbacadddccdbdbaadacbdcacbdcddbcbbbbbadcdcddbcdacbbabaddbbbcdcacacdcbbbcdbddababccccaaabbaaddaabcaaabddaaabbbcbddaadaacdcddabdabaccaddddddaccbdddddcdbbdcbbdbbcabaaacabaaabadbaabadbacccdcacacbddadbaccbbcadbddbcdbbccdaacaaacabaaadcccadadbacdabdbbdbbaabdcaabbdadcdbbdbdacdbaacccdabbdacabaddadadabababbddacabddcbcdcdcbddcdcdddbcdadbdcaacccccabbccbdbcbcbbaaddacbdabbbdcbadabdbcccdddbbccadcbdadadaacccaaaacacdabcdadcdadaacacdcbcdccacdbaaabcdbcbdbddbacabcacdbdddbcbacdccaaccbcaabdabcbabbdcbcbbdbbabacadaabcccacbddddadcbbbbaacaacdcdcbbdcbbdbdadccddabaaadbbcaddaddcadccbdbbbdcabcdcaadbcadbadbacbabaaccdcabdbabddadcdaabcabddcabcbcddbbaddbdbaabddbaddbbbcdcbddcdbaadabbcccbddddacacaabdbaddcbdabbbadacbbbdccbacddcbbcddcbadaaadcacdaaaabbcdcaadcdbdaabddbcbccbdaaadddabaccdccbaaabcbadbadbcbdcaaabacdcdbcdaaccbbccdcabadbabdacbbdcdbacdbcabbcddbaaacbabcbcdccccaddcbaddccdacbccbadadcccdccddccccdabbacabaadddacbbbcbdcabcdbdbbbcddcbddaaacdabdbaacccccacdacacabbbbbbcbddcabdccbbaadbccdcacbacccbcdddabaaabcccaaabcbdbabaccdabbabcabadbdccacbbddcabcccabccbbbdcacbabdcbbaacdaabaccadbccabccbcbabdacabbdcddacaccddbacacbdcccaaabacdabdbaacdadadbbabbbbbbddbddbaaabbcbcabbabcaaaaddcdadbdbaadaccbacddccbddccadacccabcadbbbacddcbcbaccadadcbadaabccdcadabbcaaadddbbadbbcbdccbddbcbdadaaadbbbacaccccddadbdbdaabadabdbdccbccadadcacaadabbacbadcdbabcbaddaaaccddcddacdccbabdbbbdbaabcadcbdcbbbbbaaccdaccbccccddabaadccaabdcbccbddbcbddadadaadcccaaddabbccdcbbbdddbadbcbcabacddacbcabcaacbbdbdbcadcabccdcccacdccaddddbdaabbbaadbadacdcaacbbbdbadaddbbcdbaabdcadadcbdadcddccdbbdbabdcbcbbdbaacdcccacdbbcaaacddddaaaddddccacadabaddbbdadacaddadcbcdaddcadcbdabbdaaabcabcbbabcdaadbbbaddcaaaddacdcaacaabddacdbbacbcdcbababdaddbbccbdbbaaabdcdaaccddaaaacdbdbdacbddddabaabbcaddadccdbccacbdadbacccaccbdddcdacadbccdddbbbdaccdbcababccbcbcaaacbdaacaabdbddbddcbbabbaacbdbcacbcccbcbdddddaaddabbddabdddcacccbadbdacbccdbddbcbdcbccdcabcbcbacdbabbddccdccacddcddbbadaabadbbadccbddaabcaadbbadaddaddbacbdddaccbabcbddacbbdbbcccaccaccddbcdbbaadcbdadabaabaababaccbbcdabacabaddbaddabaabdaddabadcadabbbcbdddddcaddadcdadbbbbbbbdbdbdcabadacdcbbdcbabdabdadadbaccbbaaaaacbcbaaccadbadadbdbaacbbbbdabcdaddcbcbbdbdbcacddaaaabccdddcccaabdccadbdbcacacbbdbabbbccadbbaaaabbbbdcadcdbadbbdddbbdcdcddbcabcccaabddacdadbabadbbbbdbdaaddbacdabadaacbddaccabadadbbbbbbcccdcdbddcbadbcacaccdcdcdcaacaddcaccdddaddaacaacdcbcabdcdddabbcacddacdaabadaddaacdccdadbacacbbddaddaaabbabbcbacbcaadabaaadcddaaaaccbabbbacdbdbadbaaaaababaadbbbddaaabaacddacddbdabcdacdaacbcdadadabcaabcbbcbbdbbcaaaadbcbbccdabaddbbccdddcbcbdbccaacccccddaddcbdcdadccbdabdbbbdbdacacabcbccbccdcbcddabbacdbddcdaaadcdcadccbbddcbcbbcacdacadddddcbdbcbcbdaddacacbdbabdbcdccaccacdcaccaddbadbacdbdddabccabbbbddbcdddcbaaddabddddbbaaababadbacacdacbcadccdcaaaacbabbabdcbbdaddbccbdbbcbdbccbddbccacdcabcabcdabcaadcacbabdbaddcaddbdbbccbbaaccaabdabdbccbacbbcbddacddcacccdcdcbcddbcbdcacbbacddaabbcdddddbccbbdcccabbabcacabddcccbacddadcbcababbcbdacbacadbacaacbadccdcbbdcddcaccddbcaaaabbdbcdddcabbbaaddddcbabbccacaaaddddcddbaabadaaaabdcaddbbaddacbdbdcbbadbbbdccbddbabaaddbabaddbdccbacddadaaccbdbacaacbbaadabcacdbbdbadcabbabcbdbacdcadbdaadcbdaccbabbbccaccacdbacbacbdabccbbdadbadcdbacccbabddcbbbbdddacbddccaddbadadbabccbaddbadbcddbdcaacbdbadabdbcbdddbcbdacbdcbbccadbaddbcbccdbbbbcbcddbddbdbccddbcadcbdddbcdcddddccbcadbbbdcabbabcdbaadcacbbdbddbdabbacbccdacdabcaccbcdcdaabbccacabbabdcdbacacbcadccdbcbbdbbbdadccdadbaccdbccdddacdaacbbbddbadaacdacbdbccdadbbbdbaacbaccaaacbabadbcacbcbbbbccbdbbadccdbccdbadbbabdcdcbabcdadabbaadbbcbacacdbaacbdacddadccdadbacdacabcbaaacddadbddbcacbacdadadaddcbbbbadabbacbbcacabadcdddadaacbbddbacbabadcaccdadaacabdcbbdcdcddbdcbcdccdcbcaddbacaadbccadddbbbbaccbdbdddbdacacbcaddddadabaddabcbadcbdcdadcabdbadcccbcdbaabaccabdccaabdbdbcddaaabcbcddbcbdabaaaabdcdbacbabdababacccacddaaacccccbacbddbbdaadddddbddbccbdbabccbbdbddacccbcdbdadbccddddadaccbbbadcccccccddaacdbaccbdacabcadddbdcdcbbbbbcaacaccacccabdbbccadcaccddadccbbabbaccdcbbaabcacddcccacdadbbddcbaaccdcdbadcdadacdccabdabdbacbacbddacdbaadbccbabbaaddabbdcaaacbdcacacacbbacdbaadadddccabdadddaddabdbcadbbbdbabadcbbcbcbdcacbbadacaddcbdcdbbadbcdbbacbddcbcbacbbaaabdddaabdddbccbabbaaaacacbbbbcadadbcacddacddccaabadbdccbbbcdcadbbaaadbaddcaccdcbdddccbdbadaaaccbbdbddccdabcdabdacdadbcaadabcdcdbabadbdaacadcadcaaddcadcacdcdadabacbabdaabbaabbacbdababbacbccacdadcbabccbbdbbdccccbdbcccddbdbddbcabbabcadabddaaccacbbddadbcbcacccbdabbdcbcabcaddcdccdaababaadcccbacddaabdbbaacbabcacbdcdbcbdcbcccbdbcabaaccbcccbacaabdddcabdcccdbbbdbdbdbcdcacddcddabcacddabbaddaccaabbcbbdadaddbbaacdaaabbaaadaacaadaadccacdaddacddbdcdcabdbbdcbaddcbcbdccbadbbdbcdcacccaabccddbaaaaabccabcdadcddbadaccadabbacabbdaccbdabbcddaaadcaabaacdcadcbdbbcbcddcbaabdbdbbcdcaccbcadcdbdbddcdabadcdadbbbcaaabccbbcaaaaabadabaaaadbbcaaaddbdaababacaccacbccbbabcaddcbbadddbdbcddcbaacdaddaaddcacaabaadaccacbbadabbbdabbabbccbacdbdbacbabdadcbbcccdbbaadddcabdabcbcaacbdcaabbcaaacbdcbacadccadcdcabcabcaddababcacbadaaddaacaddcadbcabbdaddbcbbcbaabcbdaccdbbbcddbcdabacdadacdaccabbbcdabbbcccccbcadbcddbbccbaaaacdccbabdacdcabadbcaabcdabadbbdccaabababbcbddabcadabdaccacbcdacddcbdadcccccaabdddcadddbabbdcdcabbabbacacadadabcbddbbadbabdabaacdaddadcabcbbabbbbbcdbdbbadacdccbcdcdabcababccdabadacaabcbdaaccddabdbbcacccdaccaaacccdadaddbacddaadbadcbaabbcabdaabadababbbbccbdbbbcdabacbbbbabbcbdcaccdddaaadcadcbadaccbdaddabcabaaddddbccbdcbdbccacdcdbaadacdbdbcacbcaacccbaaaaaacacabbcdcbaaacdccbbbdbcaccbbdbbaaddabaaccababdadcccbccbbdaacaddadbbddbbadacccbaddaaadbcacabccaccbdcadcdccaccbcabccabadccacadcbbcbdcbaabbbbbaccacdbacaddbccbcbcdbbcdcdcaccddbbccbadabacacadacbbbbbadadabdcabddababdacbbaacdabacbacbdcbcbccbbcadcabbcbbaadacdbbbacdabdccbcdbcadadacddbcadbbbbbabdbabaddabbcdacaadddbdbabbdaacabbbbbcbdbaacbabbcbaababcbbdcdcbdaddddccaddccbccacabccadacababbdcadbadabbbbaaabdadcadddccbcbabbbccaddccbbaccdbdbabbdccdbdbdccccbaaaabadcaddaadabcacadbbbacaddbdaadadaaaaadcdddbbddaabaadcaadabcaccadcbaaddbbdadbdcdcbdbcccadabdabdabacbdbbdcbadacdbcaccbabadbdbcaaddbadacabcbcabddabdbaaccbdacdccacbbacbaaadadacdccacaabbdabbbcdabdddbdcddacbaaacbbbadddaabcbdcdadbcabdcacbdbcabdcacdbdabddbbbaacbdbddcbddbadacbabaacbcadbabdcbdadacadcacdddbbbacbbccadbccddbdccacbbbcccadbcdcdcaacbaadababdbdbcbbacaacaaaababcbbaabdaaabcbcddbdddabadddddbabcdcddacaadcbacbbaabdbdacdbabcbcabbacbdbdabaabccdddbcdaaadbabbdddabacacaadcdcdacbadbbcccbdbabcbbabccaadacaacdbbddacadcbdaccbbbaabbaaadadabdacbbabadbbbababdabcbcaacbdcdcdcabaaaddbabcdcddbcbdcdddadcddddddddaadadacbcaabdabbcbaaaababcbccbaabaadddccadacaadaccdddcdaaacbbcbbccacbcbccbbcccbacdcdacdddbccbaccadbcacacabadaaccccddabddcddaacabccabacbaccadadbccbddcbcdabddbcccabcaabbcadbddbaaaccdcadacacadacdabdbadbbcdbcdcdcdcbbbbcdddbbaccbbcacbbaddccdbbacddcdbdabbccdcdcababdadbcbcbdbadabdaacaddbbcddccddbdbbdbbabbcabbbcdcdddbbddbdacbabdcccddbbbbbdadcaaaccdbadbadbbdaacdbdbaacdcdddcdbbbccdcadcdaadcacdddcdcabdbbdbacdcbcdddcccabadbdcccbdcaacacccdadcddbbbaacdcbaddacbcabbdbacacddbbcadabbacadbcdbbbaabcaabcdddaddbdacdddacdacbbdaacdbcbabacdddadbbbbbabcbcbcdaadacddbcdbdadbdcbadbaabcbcaadcbdaadcccacbddbaadbddddcccdaacccadbbcdbabbdbcbdcbbcccbcabcdbacdcacbaacbadbaadcdcdcdbaddcaccdcaadbdbdccacabbaacaaddbababdbcdacaacdbbddadddcaacaddcdbabdddacbcddaaddddacbcbadabdbcccabdaddccacbbadbdbbcbddbdbaadaccddcacaabbcbcbbaddbcdbbbddbaabdcabccdddbcdccaaacaccbcadabadaddcdcccadabdadbabbbadcaaddbcbdccdbcdccdccdcacbdbaccdbbbdaaaadaccbaaaabcbdbcbabcabccaccbcabcaacbdbbbddcccacaacabdcdcbbcddaccbbccdccdddbbbcbcbacbbdabcbbdbabaccbaddbacdbbddccddbdcdbdccbbaabcbdabdcbbbadabccabdaadbcdcbcbabaaddacabddabcdaaacbcddacacbcbdbccdccbacddcbddddccbabadbdddadbbcdbcdccbcbababaabbcbadbcdcaacddcabbdbcddaddacdadabaacdcbcbcdddcdabddbdcbbbdacbdcbacbadbbbcddabbddcdbacabdbccdcacadcbcbddcccabdcadacbcaabbdaddbbbdacadcdadcbcaddddadbcbbdbdaaaaadcdacaabaddbcadcccacbcdcdacadcabdbcadadddaacbadadbacadcbdcbddcdbbbacabcdbdddcdcaddbdbddabdcabdacddcaccabdacdcbbccadbdabdcbabaacccdadcbdcabccacabdaaacabdaaddacbccaacadddbdabdadbcbabbabdadbaccadbbcaabdbcbddbbbbbdccaaddbcdddcbbcadbcaddbdcccbdabadaaabadaaaaadaadcacdddbddaaacbadcadbdddbadcccbbcbaaaadcbabadadcbdbddbaccaacbbdcbabdbabcbcccaadccbabcaaddaaaadddbbcdaddbccadcbacbcdbbdaadcababbacbbcdcdcbdbcaadccbdbdaccadbdbdbbbdcaabaacaccaacbaccdbbbdaaaddcdbbabcaaadcccccdabbbbacdadcdddbaacbddddaacdddaabcaaacddddbdabdcabcbbadaccddadacbacddbadbbdbcdaadbccacbdcbcdbcddacbbacbbdcadadacbadbddbabcdccccbcdbdbbddcccbdabcbbaaacbaccdcaabbddbbbbcabcabbccababcaacadbcaacbcccabadcabbdacddcbcbaddbdccabacbdaccacabbcbacccaddadbbaabdabacdbdddccdabddadabcbbcdadbdacabbbbdbccaabcabbcbdacaacadccbabdaacdcbdddbaaabadbdccdadcdcdababaaccddbdbbdcaaacbbddddacbdcbcccdbbaaaabdaddbcacbdcadacbbcaccccccdbcbadcbdddcacddaadcccdcbdcabaadcabddabaddbdabcbcdccadccddbbbccabdcdacccbddbdabadcabbaabcbadaababdadcbbbbacaccdadcdcaaabdbacdbdaaddabdadcdaacccadccbdaabcaccaddbbdcbacaadaaadacccabcdbadccddbbdbaacccacdddddabcccaaddcdbcaabcbbcabdbdadcadbabbcabbdcbbccadadadcbbdbabbcbbdbcccacdddabcdabdcabadbccdadccadaaccadabbabaabaacbdbccbbcadbcbddbccadaddcbacdcccdbdcdbdddddbcacdccdacbccddacbbaadbbaacdadacddaaabdabdaccaddaaadcdcaabddabbdabacdbcadccbcddaacaacbccbaaaabbcbcccdbccdaadccccdcbcadadccabdcaaccbadbccdcdcbddbdbbcacbcdbcdcbddcdbadbbcadacdacccaadbcabdabcdbadcbbcbbdbdacbdbbbdbdadadccaadcdaaddbbbccbacdbcbdadbcbabcbbbbbddabcdccccdaabcacdbcbbddbdcacacbcaccbdbdddbadbcdaccaabdbcbdcaabbdcddbcababbccbccaacdcbbadcddabcbdcacadacabaaacadbabbbcabcbdbbbbcaddadacabddbacadcababcacdbddccbaacaabdbcbcbaccabbcdbbcbccaadbdaaadaaaaddcbacddcccdddcbcdddacaabbdcccdaacabbbdddbcbccdbcbbcddaaccadcccaccabdcaccbabaadbbdbbcdabcabaaddcbadacaddcbbabaacdbddccdbddcabbaaacabbadbddbbacbccbcbccccbadbbcbcbccdcddcaccacddaabaadbdddbcbccdabdcccddaaddabdbbbdabbabcacdcadddcaddadbdbdcabdaccdcdacacaaadcbdadbaaabccdbacacbdbccababccddbabdbccacaddacdbdaabdbaccdcbcacdcaccacaacdabbccdacbdbaadcbabddbbddbbcdccadbabbcdbccabadcadaacdabcadadaddddadcbbadcbdaacbaaddbdddcacaadadadaaccbdcccbcbdabbcddcabbbcabaacbdbaabbbcdaccdabbbabddaaadadbcdaccabcbdcacadaabddbcbddacddddbabbddabcabbdacbcbbccbcbadbccbacabbdcaabaddaadbaccddcbdbdabdbcbcabaaabacdadabbddcdccacacdbbcaddcabcbabdbbbcccacbabdcbddbcaabbcbacbbcabadbacabbaccddcdddcabbbbdbddcaacbbadbbcbadabcaadccbdabcbbaaacdabbbbbdbdbcbccdbacaccbcbddccddcbbaaacbbaadbaadcdacacacddbcccbdbaccdaaccccaccacaacdacddbbdaaccdbbabbdcbbcdcabbdaabcaabccddaccbbdacbbdadabbaabbbcbccadacadabccadbcddadaaaabbdcbaabccaaadabbbaadbadcbcaadbbbbdcbdcdcccbbacbbcbcaccdadabbbbbaccbdaadbcbbccabcabbddcdcddaaadcbbcbccbdcadbbcccbacddbdbbdabdabdbcbaddaacbcadccdbadcabbbcdbdcacdcdbadbaabcaabddcdcaaadcaacabcddbadabdabbcacbdacccdcbbcadbbababbacbbacacbdbdadbddccbcabddcddacaadbdadaabaabbcbccdacdcaadcdbdbabdcbcbddbdccddcaaaccdbcaabdacdbdbdadbbacacbaabddacaaddbbbdccdbbcdcbdccdaacbabbbcabdbcabaacbaccacbadaddbbbdacddbadacdabcdcacdbcacbabadbcdbccbcabdacccaabbcbcbdddabbdacabccdacbdcaabadbbbaacccdbabbdcdaccabcdaacadadccbbddcdacccbcbbbacaaccbbdadbdbbbcadaabccdbaccddbbdcbaddccaaddadbbaddaddaabaacbcdcddaaabcbdcadddaacacbbddcdccbcacacbdbdabcddcdacddcdcacdbbadbdbadbbabccdacbbcdaaadabdadccbbdbadbadacbcbdaddcabccbdbcbaadaaaacabcaabbdadaaaaacadbbabdaddcddbbccbadcdadbbcdbadccccaaadacbdaddaccaadcddaccbadaddbbccdacccbbabddbcdbaaddcdadcddddcaabbddacaddaaacdcccabbbbddcbbaacbbacaadabddabcddccbdcdaddbdacadcaacbddcacaaaaddacacdaccacdddbcbdabddacdcdcbabbcbddbacabadddbcaaaccabaaadddcabcccadbcdcbdaddcbbadcdaccbcddbdadcddccacdcbdaabcccbabdacacbadcbbadbdadaaacdbbbbaddbcaadbdbacbcbbcbbaacbaccbacadccaacdadadcbcbcbcccdccaabadbbdcadacaabbcccdabdcbcbaacaddddcaacbcccddccddcdadcadddaadcbabddbadbbdabbdadbabdbcadadaaccacbdacaabababdcbabdabadcbbadcbabcaadbcccaaaabdbdaccbdadbbabcdcdcccbddcddcaacdabdbcbcacadbdaaaddddccbbbbabacdbcacacbdbadccaabbbdbdddcaddcbddbbacaadaddbacdbdccbbaabdbabdaddcabdcbadddbdbacacdcddcdcaababcabbacabadaabbbdacbdccddacddcabacadadcbcbdcdabdbadbcdbdcadcddcbdddccbdbcabcaaabaadaabcbccdaccabdbbcdadaacabbdbacbbcdbabcacbabadbaaaabdaaaacbbaaaaccaaabddabddadcddbdcdcdaddcacdcccbadcadadbddcbdbcddbcdcbadbcdbbdbcbddbadbbaddadabbaadbbbabbaadcababcadadccadacacabadcdcdbdcbdbdcabccbdabadaddabdcbbaccaacacbbcdcbcdabaddbcdbdccbacadbdacacdaccabcaacbbabacdddaacadcbbdccaadababddddccbcacbbddbbccdccabaaaccbababbcbcadbcabcdcdacccdaaacdaadbcbbdbbaddacbbbbdddaaabddaaabaabbacbbdcddddcbadbbacdadabbacdbbbcaaccabdcabccccdbbbbdbaadbcadaadbbbbdaccccbdbbacbbabadadbaacabcccdcbcdadadaacaccccdbbbbcbbdaacaaabcaacacbbcadaabbaacbcadbdcdaaddcddccdcdababbdbaaaabbaadddbcdbbbbdacbddabbadacccadbbcbcabdbaabcdcacdbbdccadbddccddadddbacdacddcdbacacbabadccbdbabaccaccbbbdcbcbbbacbaacccbcbbbbcbcdcbabacabdcadadcbaddbcdbccddbcbadcdcadddadadadcaddbcdbcccdcbbcaaaddbdbadbacdccadbccadbbaddccaaadbacabbbdbdddcccaccbccdcdabccacbaddcdbcdbcaabdbcbabdcdaddbbcaababddadbaabcdacaddcaccadadbdaacbabadcddbbdbdddabcbabbbdcdbbcdacbcaddbccbdcaddcdddaadbadbddcdcdbcbcaddcbddbacaddbcbdadcdaadbddcaaaadcabcbabcbabdbcccbadccaabdbaccddcbaaaddddbaddbcbbbbdbabcbacadcadcdcabcdcbdcdabacadccacaacbdcddadcacacbdacabacadcdbbbbacbabdcbbcbbcdcaccbabdcdbcadddcaacdbabcabcbccacbacaacabdcdaccccaaaabdcdcdaabcbbccccacbadadcaadddbadadacababdbbdcccaaaaddbccbcbbbbbdabcbacbccdabdddbcadbdbddddbcbcacddcccacdbccdddcacdcbdabacdbacaabbacbdbcdaacaabbdcbaabcbabdbadaccabbdbacbccadbdbaacdbcbdcbaddabdddaadadacbbdbcaaacbcbddbadadbcaaadbddddabddbddadbcabdbbbabacbbbadddadaabcdbaccccababaddbccddbbaabbaaddcaabbccadccbcbabddadbdbcbbbdbadabbaaadcbaddbcdbbaabaadcbbbbdccdcdbbabaacadcbbddbaccdbbaabbaadbddddccdababbdddaacbbdaaddbabcccadaddcacbdcccbdcdccaadccdccdacdbccdcaccccdbbadbadaacaddbccdaddbabaacbdccabbbbbcabadcdbbbbcdabbdadbadbcdabbaacbdcacdccabdddabccdacbaddbbaacdcdbdbadadcccddabdccddacdadcbadccccdbbabdccaaacadbcabdbadbddcdddcaabdabbcadddadadcaaadaadaabcaaacabdcbacbbddaccbacaabaadaddcacacbbccccaadcddcaaabdccacadddbadabadaabbbbaadadadbcccabdddabcadcbacbdbbcbbbbaccbabbdbabadaddbcabbdacdacacccbdabbdbbdcdddddcdabdddbdbddcabacacacaacbadacadccbcababcdddcbacadabdcbcadbbdbddccdbbcbcbcabccbbdddcbdbaaabbccdabbddadbaadbcadadacdccaabcdcadbabaacbbaadacbcbaddbbbbdbbdccddcbcbadddaaaadbbdabbdadbcddcbbcdcdababcabdbcddbbcaaadcddcbaccabcabdabdaaddaacdaacdcbbccbcaddbccaabdccdaabcacaddcabbbcbabbdbaaacabaabcbcacacbababaadbbcddbbdddddcdddbadadaaaccbbccccccdddccabdbbdccdcdddcdbdccbaadbcbbddbadccbdbdcaccccbdbadadbadbdcdacabcdcbcaaccdbddbacdbdbadcbbacaddccbcdddabaabbdacbaadccdcabbcadbcdbcbddaacccdabdcaddcdccbcbcbaaadadaacbaaddadccbadabcdbbacdcbddcbadcdcdcbbadddbcdcbadddddbbdbdacadcdbbabddcbbaacadacbdacdcddddabddbbacdbbbdddbbbccdcdcbbcacacbbadbcbdadbcdaccbdccccccbbcadbddbdaabdacaadccbcccacacaccaaacdcbabdbbddaaabdaddabacbdabddcdabbdcacabadcdbaabaddacdbcbbabbdbdddccbaabddddacaaddabbbbccabdbdaddccbdbbcbbbdbcacdacbaccdaddaaadcaccbdbabddddbcaacbdcccddcbddbdbaaadbaaacababccdacbdbbdadccaadbbabbbdaacaacbabdaadcadcacbcbabbdbcddaacadddcaababbbcccbbdccdddbdbbcadbdabdcacbdcdabbacacaacdcdbbbbccccabbbdcbadadbabccbbdbcdbbbdccdbbdcdbcdbbbabdaacadcaaddabcccbbbccbabccdbcbbcdabddadcdadaaaccdcbcdddadabacacdccbdbdbdcdcbdbcccbadadbcacaaabababccacccdabbcaabcddddcabcbbdcdbccaabaabbabdacbdbdcbabdcbdbbcbccbadddcaaaadacbcabcbdcbcdddddbcaddcdbacaadddccdbcddabddcaddcdccbcadcddadbbccaabcccaaddbdabbbaaabbdabcaccbadbacbcbbacaabbbbdadabcbddabacaaaddbcadddbddaacacccbccccdabbdaadbabccabacbadaababcaabbcdddabacdccabcadbbadbdadcdabbdadacbdbacaaaacaadbdddbcacccacbdbbbdcbbbddcccbbadcbdbaacdbababbadacddbbcdbccbdbbddaaddbbbcadbabdacbcbbdbcaaabacdaadbddcadcaabacaabbbabadcadcbbaadcaaabbbbddbbdcccdbcadbaadcccdaddcbabdccbbdddbdbdcaadddacdccbaccadbaddcbabcbdbabbaacdddabcadbacdcbbcddaabdcabccddabdbbacdabbcbddcdcbddadcacaabbcdaaaadccbcdbbcadbaacddbdaacaaccbbccbccbdbddacddbccbbcabdbbdbddbcdcdcadcacbaaacddbccbabbcbbcbcbaabcbdcacadbbbbdcddddaabbbbbcadabaddccbcabadadbcbadbbddcdabdcbdbaacbcabacbadccadcaacdacbcbaddabcbacdbcbdbbcccaadaacacdcdddaaaadbcdbdddcbddbbabbcaadcbbadadcabbdcdddbdcdacdccbaaabcaaccccaabdbdccdadcadbadbcadddbddccddbdcbcacdbcbdcaddababaddadccacdacdbcbbabddadbcdaddabcdcaabdddacaaddcccddcbbacddcaabddbdbbbacacadbbcccadbdacccacdabddabacdadaaadbdaaacdbabcbdadcbbcddaddaadaaadadadaccbddbadbcadbddcbbdcbcbbaaacdddacbbbbcbccadcaaadcccaabdacbbccbbcccdddbcddddbcdbbbcccaabacdacddacabbcdcdcacbaacbdbbbadabcabdbabbcdbcabcdddabbcabdbcbbddadbbabbaacccbaddccbbccdbdcbccdbcababbdcdadaabbcddccdbcadccbcbadcdbbbddcdbcabdbcadacaddbababaadcbcadadabbbdaacbcdddaaacdbcdbadbadbddbcbdbdddcdaddbdabaccadddbdbaacbdcdddabbcbdcbcacbbcdbbacadbbbdbaabdcbdddccbaaaddabcabbaaacccbaacbcddccaaaccddacdddabacddbcbbbdbbddccbbdbdacdaddabacdcdbdaadbcaaabcdaabbadabcddbcaacddbabcabbbdbbcaacabcdbbcbdcdbccbcddabccdbbbaabaabcbcdbabbabcbdbdabcdbcdaababdddcacbcbdbbddcddccacdbbcbaadbbababddcbabdbadadbcdadcacdacdbbbacdbbaddaaaccbdcaacdddbabcacdcdbdcbddcacbaabdcdbbcbdbaacbccabccbbcdaadcddbdbbaadabbbddaccbcdccadbbadccacbccbbbbaaadaccacbdcdbdddadabaacaaccdcdddcaddaddddaccaccbdbacbcaddcdacbccbcdcdacccbdddbcbacbcbcaacadcdaaddcbcddccbacabcbbcbacababdacdcbadccdabccbdddddbbbbbdcacbdcbaccadacacacabbddbbdbbcadbdddddababdbdbabddcacbacccdbccddcacbcdbdacdaaabcbbacadabcddacbcbbcbaaccbdaddbdacaaadadaadbdaacdadcddcacaabdcaabaccbabddcdacaccccbabdbdcbcccbabaddcbdbaacdacbabbcbdbddcdabbaddacbcaddbbdbbadabcbcacbacdbabcbdcabacacbbabdadaddccadacbdcbbaaacbadddabaccbdacbdbadddcddaccaabaddadacdcdcbdaababcbaaaadccbccdcbadbdbabbacdbccdccdcaddcaddbcddadcdadbddadbbdbabbacdddbccdaabbaabcbcaccbaddbacadacccbcababdbbcdbccabdcbcdabdcbadbdbcdbbaacdbbabbcdddbcddaddccacbbcdaccbbdccbdaaadbccaaaadbdcdbcddcdcbbaadbdacbbbaadcdcbabbabaaaababdcdbcaccdacbdbcabaadacacddcdcbdcaabcbbbdacabacddadbaadadddaabddcbcaaaccbcadabcddaaddcadaabccdbbdbddabccdccdbabdcdbcabbbbaacdcaddcadcddaccdaccdbdaddbaabdabccabdddbadaaabadbcccdbbcaabdbbcccbdabcaadaabcbdbcbcbbccbdaadbbbdddbbaddbcbbaaabdaabaccdcaaacabadaddabaaddcbabbcdbbcaaaaaabbbccbabddccddbcdacbccaccabddabbaddcddbbacccadabdcdbcdcadaabbcbcccadcdadcbabbbdbcbcabdcdbdcbdadcaacadabddadbdadabdccadadacaabcdbbcddddaacdbdbcbdcaabaacdcdbbbcdcadbddaaaabadccaabdbbdbacbabbdabadadbddbbabddabbcccbcabbcbbdcbbddcdbcbadabdababcadaddaadcaaabcdbdacabcaddcccddabcddaacdaabdbdbbabdaabbddadbdcdadcabcbacacaaacbcdbbcddbdacdaadcbcbcadacccbaadadcdbcdccccbacbddbaabcdcdbcadddadcadcbbcdcdcdaaddaccadbaddbabcdbcdcdcaaaabbbbdadbbdaaacabaaacddbbabbbcdcdbbbcaabadaabcdabacadaccbaaaabcabcdcdcbbacaabccdcbadddadacbbbcdcabcddcdcccacbabaaddacbadcbbbcdaadddcababddcccbdddadaddcdbcdcbadbcccccddbddccdbcddcdbddacabbabcdcbcbbacbccadcaadcdcccaacdcabadacaadccdbdabaabcdcaccddaccbcbcdddadddabcababbcabaddbaaadbddbbbbcbadcddacacacddacbacdabacdabacdadbbdccdabbcbcddbbabadbcaabdcbdbddcdbdbccaacbcaddbbbbabdabdccdabcccccbccbbbbdbdacdcbaacbaadbbaacacacddbbbbdabcbaddabcadcbcdadabdcaadddbaddcabcabcaabccddbdcdacddbccbabadccccccbcccbadccdcdbddccccdcababbddadadaddcacddbaabcbddbcaaaddcbcdabaadaccdccbbdcccbbbdbbbacdddddddbdbaaabbcaadcaaacddcbdcbcdcdbbaaaabbdcacadbadadacaadadbdaadbdabcccdbabbdccadbcbcbbdaaaddaccbccabaabbdcdbbbddccaaadcdddacdbbdbcadbaadbbcaccaaadcbbaaacdcccadbcdcacdbbabacddbadaaccddccbddcabdadbabcaaacaabdcbcbbaaaaaccaacbdbdabdbcdbbdcdaccdddbbbbddacbcaddacbbcacaabbaddcadbddbdbbbdcdcbcbaaaabadbdbdaabcabbcadabcbcbaacadccdacdddcabccabcdccccadcbababcbdccbacdadbcadddddcadccabbcdcacacbddbdcbcddbbdbddabccdbcbddbccdcabbabdcdcbbdbadaadaacaaacdacadadaaccaabaaabbddadcababaacacacaadddbbdcbadaacadddbcaacbcbabbdcdcaacddbbcccdcbdadaadaccacaaacdacdcdacbcbddbcbaabccbcbcbdddbaaaddabacbaacaabcbaacccdbcadabcbaabaacdbbcabadaaaaadcdababcdbbaacbabbdacdbbdbdbdaccdcadcbbaaabdccacbaacbaadccdacadabdaddbbccbcbbcddddacccacbcdaabcdabdcbdccabdbccdbcbcddddaccbaadccacdccbaaddddbcaaccadbaddcaaabddaabaaddcbaabbcaddbbbbbdacccddbadbcbdcaccacbbddbcbadacddcaadacabdbabacdcbacdbdbbdbabccadddabbacbcbbabcbbdbbccdcabddaaddacdabaccdaaacdbcbadbcbdbbadddddbaddaabdcaacccaccdcabdcbbcdcbcdbdbcbabacadabbcbcaabdabbdbbbadddadbbacaababcacdadcdadadbbccdacacaccaacdbacccbddcaabbbdcaadbadcadcbcdddbdabbacbadaacbbcdbdcdbbabcbabbddbdddbcbcabcbacdaaaddbbbcbcabaaacbdaadabbaccabcbbcccbaabbdccdaaddbdccddaabdcddcbddbabdcdcdbadbdadbcbddbcabcbbdbbadbacddbbbddbcdccbdbcaaaaddcbddbcdbcacacdbccabdddcadaacdcadddaacabbbbdcdacaccddccdcabbdbbabbbdbaccbacbdbbdbcbcdbdcccdadcaabcbbcacccccacbcddbbdaddacadddabbddcbadbbdcacccdbaabcdbcabcbdadbcdbdbbdacbacacbabcddbdbaaabacbdcbdadbadaadccadbcbccabdbdabcbaddbcabbbcdddabbdddcdacdaaddacbbdddabbccccaabaabcccacaddcacaabdacddbbbbbaabccccbaaddccbacddcacbbbbcbbdcbbcdbcddcabddddbcdabccbacccccadcadccaadabacddaacdddddacacbddadcccbcbadbcdacbcddabbbcdcdcbbbbdddcccdccdabdbccdcabbabcdbdccbbdcdbabccadacbddaadcadcddadddaaadbccbbcaccdbbbdadccbbbaabcbbbcbaaabaddadbbddcbccccaabaacabccaadcadabbcbacdcddadbcdbadddbacdabdcacadbabacbadadccbbacabdcabdcdddddabaabaddbbdcacadddddaabbcbdbbdbbcabbccaacbccaadcdabdaccbdaaabddbbddccbbdbcdadccccbbccdadcbcbbcbccabbacbdcbaacadbbaababcbcdcdbaddcadbcdddacbaabcdbdccbdababbcaabdcabacdbddddaaadbabcbdcbaabbdcaaadbabbcacbdddbbdcbcdcdbcbccccdcadbadddbbabdbccbdcaabbccaaabdbcabaabbbacbbbdcaadcbcbdcdaadbdadbbbadcddbaccbbbcbdbdadcabbbcccdadbbcbadacaddbcddbcdbcdaadaacbbcababadcacbcccddcdbacadccbccbcdddaacaaddadcadccbcbaadcacbbddbaabcbabbccaccdcdcbadbbcaaadacddacbaccbddbcdbddaaccadcbdcdbadccdaaaddaaaadabbdbbccdadabadcdcddbdaabbbdbababcaacbdbbaddcddacbcdddcbadbcddcbbdcadaadcacdcbadabcbbcdacabaabdbdadaaaacddddaabddccaaddbabcabccbcccbadbcaaadaadadcadabbdadcdbdadddaadbadccacaaccacccaaadcadcdaadbdacabcaaddadaaabacaddaabbcaccbdadadabbbbdacbbcaacdabacadbdbdddabccdacabcaaccaaabdabbbbbdaccbdcaddadbdbadcbdcacdbcbcabaabacbbaddbccbdabaadabdabbbccbbbcdcdaabcbadadaabbbddcabcdcbabadadaabbbbccddaacbbcbccacbdddbccbdabbabdbababacdcacbdbbaaacaccacccaddccbacdaabddccbadcaccdccddacacdbaddbbbcbcbbbabbcdccadcbddbccdcaadcbbcdccbdaddbcdbbbcddcaccbdddbdabdaaadccaababbbbbccccbbbcdcddcabccbaabaacddcacbcdaddacacabadddabbdbbacdcacdbbcacabcdcdbdbbbcaccdcabcbdcaaadcabbbbadddccacbaaadbbacbbbacaaabdcbbddabdbdababadacacdbdbacadcdadbbadacacbbaaadcabdddbdabcadcdabccbabcdbccddadbbdaddaaadacbcadbdbccbbcddddacaadaccccddbccbbdcdccababacbdaaadacdcababdcdcaadabdbbccdabbcacbdccbbbcbdadddddaaacabbabdcbdddadcddccbddbddbddbdababccddbddbccbbaccadcbbcbcaacdbbdbdddcccacaabddccacbcbaaababbcbaddddcdccbdcaccbdacdddbdcbcbcdaacbacaccbaaaaabcbbdbadacaccaabdcbbbacaccaacbaabcbbcbdccbbaaccdcdcadbaccbbdccbbdbdbbdcacccccabcbdabccdacbbacbabdbaacadbaabcabdddbddaacccbbdabbcdddcbcacbabbbcbcadaaacdaddaabbdbadbbaadaaccdcbdbadddcbdbbbdadbcaaabbaaabbcccbcbbbbdadbcabcddacccdcdbaccbadcdccaacaccbadbbadddbbcbbbaacdaccbadabdaaddddaacddaddcddbbaadbdcdbdbbaaaddbaadbbbbccaaccdcabdbbacbcabcaadbdccabccdcacdbcacddcccabbbbacdabddcbacabacdadccdcddabcbbdaadaccccdacdccdbcabccddbcbdacbdadbdbdbbabdbdbabdaccacbbbcdabdcbcdacbbabdbadadacbaaacdbaadbccddccccccdcdcccbdababdddababacbbdccccbcbaccdcccbdcdcbbcbddabbbbbbcabccccbaddcaaaccadaabaaccbabdbcbdcbcdabbdaddacbdcdcaabdbabdbdababdadadccddbaaddaacdbddcbcdadadbcaccaaaabbdbbdccccbaabbccdcbbaccadbaccaabddcbabaabcbbdbabddccaddacbbbaadbdddaabbaddaadabadbbcadcaadbcdcbcbbcbccbccbabccbccdbbcddccaabadcaadcaadbadbaabbdadbccaadcbcbbccacbaccdcadccbdacbabbccadbcdcadcddccbacaddcacdcdcaaabbbcaadaabccddcbcadaabccaaaaccaabcdaaabbccdcbbbabacdcbcdabdcccdcbbdabcbccdcbbacdcadccaddccdcbdcabadcbbaaddabcbaaaaaabddcbacaacbdadddaaabcdacbdbaddbdaaacdcdababbdccbacdaccabddbadbddbbdbccbabbdcbbabcbcbdacadacbabbabdbcadbadaaabbacacdbcccdacdddcaaadbbcccccbbbacabcdbcbdddacbdccdcacadcabddbabdcdbcdccddbddbabaabdbdbbabaaabcdabbdcddbcdaabdadbddbccaabcabbcddcbbcbcdccdadccadbbccbaaccdbdcdbdcbccaaaddbdabbdcbacadbbadacccadbcacaaabcaddbdcdcdddbbcabbcabdbcccddababdcbcbbcdddaacccddabbbcbcabbacadcdbbdacacdadabcadddbabcdddbbbdbdddbabbacdccbbdcbdcddbccbbddbbbbaabababccdcbcdddbdcaacbcabadbbbbdadcbabcbcbddadcdadcaacacbbdcbbabbaaabbdaabcbcadbcaaaabdadbbcaacaabbcccdddaccdcdcdddddcabccddcdbdabbdbacadabbabdbcdacababbdabcbdbdbacddbbdadbbcccbdbbcbaaaccacaacabdcabcddbaadadccbcddcbbdbddbdcaacdccdaaddcbdacdbbbbabbbabbdacbaccccddcddccbdbbddbaaddacbbabcbccadacbddbbcdddadccacacbdacbbbacdaaaccdbbcaacdbddcbdadacadbcdcacdcaabaadcadacdcbadcbaddcdaccadbcadbabbabdaabaddcdabccccccbdbccacbaadcbddddccbcbcdcdcdbaddcadcaabcdcdbddcbdaccabcbcdcdbadbdbbdccdacaddbddcacddcccdbbdacdcbbbadcbabadccabadbcdbbbbdbcaabdacddcbacddccaccdddcabbacccdbcbbadccbcbdcbcbdcccacbacdabcddabdbbdbcccbdbadbddbadbcccabaacaccccbadabdacbbcdbcbddadcbdbabccbcabbacadcdcaaacccaaccacbacbacccdaaacacdbccaacadcadbcaddbaaacbdacbaddadcdadadacbcdabbadadcbbbbddbcdccaccabdcdcccadaacddabbccdaccbbdcaacbdadacdacaabdcbbdddbbacbcdaabbbbdbdbbaadcdcabcccbacccbdcbadadbabbbababdadbbccbbacccccacaacddcbcdacaaaaadadbbdbdaacadbbddccbcccbbdabcaacacdbbdbaddbddabbbabcdccddaaabdadcaccdbdabdabcdcbdbaacccbdaddbdadcdadddbdcdadccbdcbcbbcdbacbdddcccdccdaadccbcadabddbccdccbdbabccddadcbcbcabcaccdcadbabadbdbcbaaccdcdcabaaabaacbbadcbdcacaabcacccdcddacdddccbdcadcabbddcaadabbcabbaddbcaddbcbacaadabaddcabdbdabbdaacaddcabddccbcddbabcbadcaddacacccdcaacbabcbbdcbaacdcbbadbadaabdbdabbcdbbbbcbccaaabcbaccabbcbdcccdadcdccbccabacbdcbcdcbaaddcdcbabdaacaaadbccdcbcccabbbccdaaacdacaddababadcbbcdcbacbaddddddbcdbbaaadbdacdbddcaccdacdcabcccbadddcaddaddccbbcdaacaccbddddbdddcdcccbcacddcdbaabbcccdacadddccaaadbaadcbdcbbbbbbabdcbcbadabbccbcacdbdabdaacbdacaddadbddccabddbdddabacbcacbcacdddbddacddadabdcadbababbbaabcbdcdcbccdccccdcddcbcadaaddcbcabdabddcdbccbccbcaaaddbaaadacbcbadddbdacdacabdbcadbddbdacdbcddadbdadaacbccadccaaadbdddbaddbdadbbdcdcbcbddbbadaaaddcacdcdccbcdcdaaddadbadbcccdccbcdabcadcbcbdbdddbccbdacdabdababdbcdcbcdbcdadbdcdbaabcbbabdbdbaddbbccadaacaacbdcabbcbbbadbcabbcbaadbdbbcddddbcadcddaccdadaaddcdddbdcddbcccaddbbabcaadbcdaddcdbcacbbbcabcabaadacdbdbbcbbaddcbcaabacdcaadacdccbdbbdbcacacbabbcabcdcccdadaadbddacddbcaabadabdccdddcbcacccaccbcdabbcbdaadbcbadbbcbbcaddcdabadbbbcacccdbacbacadacacaacaaaacdcadcabcabddbdcdbbadabbbdcaccdccdcacccbadbcdabcdbadacbacbaadccbacaddcaddacdacbbbddacbbdabacdddcbbdaccccadccaaccacbadaabddacbcbbcaccaacbdddacbbbdccacccdcdbbbcbacbbbacccccacdccabababdcdddbadbbabdcbbcacacacbabbdbbdcbdaabbabdbcdbcabdbdaccdacbbcdabacccdcbbcbccddcaadbcaadabdbccbabdbbcacbbadcddbacacbaadacbbaabcdbbcbacaabcdabacdccaacccabcdbdcdbccbbbbbdcadcccdbadadcaacbaadddbdbaaccbcdcddcadcccccabdabcacdcacddbbbbdccdbcdddcbaadbbdcccaddcdcbbbadaadbcacadcbdbdadbbdacccdddbabcbdcbdbbbaadddcbddbdacaddadcbddcaabbacdbccdaddbdbcaddcaacdbbcbabacbbacbbabbbaaddbdbacbbdbabadbccbddcdddcbbaabaddbbcbabcbadbabadcadcddcacbbddbacbbbbacbccadbbdccdcbccbcccbddccdcddcabadbcabbabacacbbdccabdaabcbbcbadadccdbcaabcdaaccadddacddbccbdbdcbcaadabbdcccddbdacccadcabdcbccbabcacdbabddcdbabaddccdbdbbdabdcbabdaccbababdddbcdcbcbddaacbadbcdbadcbdaccbaacbdddbabbaaadcdcbbadcbabbddadcbaccaccdbbdbcbccabdbbbcbabbabadacaccdcddbccdacadccbbbbccadcccbadcaabbccabaaabddddcbccdcdadbadadbbbddbdcbabbddddbacbaccadadbbacbbbcaddccaabacdabcadcccbdacbdaaadcbadccbaaccdaacbddcbdbbdcdcbddbacccacabbaabaccccbdbdbdabcabdabbcddacabdadbbcdacaabdccccbacacacabbcacddbddbbccbdadacbadbcabcbdbcbbccabcbbdbcdcdaaccddddcccdccacaaadabadcdbacccbcdacaacaabcaaaccacdadbdcbdabcbdbccddbbddaacdadbcaaacbadbdbccdbbabdadaaddbacbaaadbacbbcadcdcacdcabcdbadcdbadbbdcdccabccbbaacdbcadcbdddbadcaddbbabcdaabdcbaacadabadabcbdaaddbddbbdacaaaabdbaacddcccabcbdcdcbaaacbdbbadaaabdadbcbcdbddbcbabdcdabdccdbdadcbbadbbcaaddbbbbdadbccdacbddcdcabbccacccacabcbabacbabbadacadaacddbabdbacbacbcabcdacbdacacccbcdbbbabbcccadabddcadbdbadacaaaccaaabbbacbdaaccbabbbdadcdccbcaddcccdaacdccbadddbcdbbcbccaadbaabbcbccccdcbabddbbbccdbcbdccddcbadaabdbaacbbcccaadccbadadbcacbcabcccadcbbcbadabcdaadbabdacadbacdbcdcaadabcbbbcacacbbccbdbaaccadcddccacddbcccbddcddcacdcbcbbccbbacdabcaaccdcdccaacabcdaaadbbcbcbddaadccaacaadbabdadccabdacbabbdbbbdacdabddadadbabaaaacacaabbcacdbcacacacbccddcbcdbdccccbabadbcbbbbabbaacdbdcbadbddddcadccdbbadccacdbadbadaacacaabcbbbabddbcaabbcaadadbbbbcddadacbbaaabdcaddabddcaccdcdcbababddcbddbdccbcbccccdbdabdddaddbbdbccacabaabcdbddaccabbbdbcdccaddcccadddcccaacdcbdcbdbcbbbabdccccdbbdbbbdaabdccccbdcbbbbcabbacaacdbccacabbcbcbaabccdadbccdbbbacabdcabcbabadabdcabbbbdadacbabddccdadbdbbbbabcbabbbbbcacaabdacabbcabcdccbabccdcdaaadacdaababbadaaaadacbcbabcaddcaabadbbdddbaadccdcbdabbddaddcadaabcbdcbabbadaadddadcaabadbcdcacabbbbcdcadbbbdddadbabbcaaadbaaabdbaccabcaaadbaccddaacddabbbdddbbccaadabbbcdbcabaabcaabdacbbdaddcdcacbbdbabaabbcbaacbdbbdbccdacbbaaddacddbccbacddbdbcddddacbaaabdabdccdbbaadbcbddadbbaabdcccabaabddcaddbdbbcccaaaaadcccbadaaddcdaccbdcaadbbbabcbbcdccbcaadbdbbcbcddcbcccaacaacdddcdccaadabcbcdcbadbdbdbcbcdaaddaaadcdbbaadaadccdacacaccdcaccdabddccadbbbbbccaaccadbcadcbabdaddccddaadacaddcddbdaabdbdadcabcdbaababbdbdadaddadbbcabbcccccbccdbddbabdcbcdbcbcabcbbcaaddacbcccddbbddabbaaadadbacccddaddacdbaaaaacaaddabbcbadccaabddaacaddadbdbcbddbdccbdbcdcaacbdbcbdddaddaccbadccacdbbcbdcadaddbbdabbbbcbdadbadddcaaadadbbbbcabadddcccbddcacaacbaddaabdcaddbcadddcbadbdbaabbbbdddaacdacadbddcbdbdcadcccbcbbcddcbbdadbcbdcdccdddcaabadcddcbdccdbabccccbbbbcbabbbbdccdcaaccdbabaadadddcdddcadcbacaabddcdbbccdadaaaaaabcdcaabbddacdadbbcccbbddaccbacddbbaaadadadccccbdbbbbdabbaabbaadbacadbdcdccbadaaccbcabcaabcbbbbdbacccacadbdddbbbacbacbdcddaddabddadcbbcbbbaaabaadabddaaaaddcccaddbabbabccbacbbadcacccbbaaabdaddaccbacbdbaadccdbcdaddbddbbdbacadbaadcbbdcddaaabbacdcadbdcddcaddddadbaadbcabadcbddbcdbbabbdbaadcdcabcccddaddbacbadbdbcdbdccadbdaacaadbcacbdbbcdcadabbabadcdcbdabbbbdacaabadbcdaadccdbadbccdcacbcbcbcadaacbbaaabacaacbdacaccadbadbbdacdbacccacbdbcbddbdddaadccbbcccacdbbaddbaddbdcaadbaaacdadacabadbadaaddbbccacabadcdcdababcbccacdddccdacabacbadccddbaadbcdadacbbcbadadbddbbbbccdbccaaadaacdcbbdcbdbbaadaccbddabcccdaabaaadacadcddbbbdddcbcadbccbabadbabcacbbcdcdaacbcddbaaccdcabcbcbbddabccccbdcbadbbadbcccdcabcadbbcbaccadadbdabbbcdbcadbdacbaddddbcdccdbababcbbccddadaccaacacbacdcbbbcacdbddadabccdcdcbddddbaccaabaddcbacbdacccaabbbcbcbcddabadccadadcbaadbdcbcdaacaddddbbadacaaacabbaccdbbbcdbabddddabccaaaabdddbbabcdacabbddaabbbdcadacadcccdcbbdbdbdbbdabbbcddbdacabcbcacdaabdaddccddcbbabcddaacaaabacbdcbccbddbadaacdaddbcbbadcbadcdcdaaabadcaabadbacaadabcdcaabbbbcaccccadbddaacabbdacbbbcadbaabdbcbdccbddddbabcdcddcbddcbcdccdcbcadadbbcbaccdcdabbbcccccdccabcdbdcdbaadcdbaaacabbbbabdaccbabccccdcdbbbcdaadaaaaadbaddaacccbbbcdaddbbabcdcadcdbbccadbadacacabaaacbdbcdcadbdddbbbabbdaaddbdbaabdacbcbabdbcbabbbcbdabdcaabddbbdcbabaddcaacacdcdcbdccacacddddcacccbcadacadaabccababbdbdbbacbdcbcdccbdbacadddbcccbbdcabdbdcccabadbaaccaadcdaddcbcbacacbbaaaddbcbccbdcdcccdabccbdacdbaabdbdcccbaaabbbdddcddcccdaadbcccabbaddbbaddadccdadcaadbcdbdddacbacdaddccaabddacbadaccddbaababaacddcdccaadaacaaacccdadacadacccdddcbdcadaadcdbbcccbaacbcabaadbacbdbabbbdbdbcbdcdbcccbdbbadbbaddabdbdbddadbbbbadbcccddcbdadbdcbcaaadcdccccdbaaddbbdbabcdaccbaabaddbdccddacdbddaaddbcabadbbdccabdcabaacadbbdaabcacaadcdbbcdddbcdddcbccbaaaddbdbbcddbdbcdccddbaccdcabaddbbdaccbcbdcacbcabbcbadcbcbaaabbaaacdadbcdccddddddbcdadcdacadcbaabdcbddcadbabbcddcbdcbbaddbadaacbcabcabddbacdcdabdbaadbbcdbbcbbcabddbbbddbadcaaaccbbddbbadcdabbdbbadabadabacacbcabdccbdaabdcabaacbaaddacbdcccbbabdadddcdbcdbddcacdabbaadbbbdcdabacbdaacaddccdcacbaccbdabcaddbcaddccacadcbbcdccdbcacddbdcadcbbdbaccdbdbcdaaaadbbcbacabcddaccabcbdbcbcbccdacbdbbbccccaddacdbdaccbabdbccdbbcbccbabccbcdccadaacdbbbcdbccabbaaabbabacbdccdaaacaacbbaddccddcbacabdbbdddadcdabcdbbbbddacbcdbabdbdcccdcacdcbcbcbcdaaadcbabcdbcacdcbdccabdaddbbadcbcaccdaacddccbdcbddccadddcddcccdccbbdbcdcadadbabbbaaadbcabcdadccaaadacdcdbcccdcbdbcbddcbddcdbaaddcdbdbbacdcbcdccdddadaabdaacdbcdbcabdddbdaccddcbbacabddcbcaacacacbdcacaacddbbbccbddabdacdccbaadbdbbdaccacacdadcdbacdcbcccadbcadcbbbddabadbaacbbddabccbdaccacccccbabddbcbcddadacacdacabbdbbbccbbbdbcadcbbadddacbccbaaaddbcdbcbccccccbabddcbcdabbbadbdbbccdddaabbccdcbcaabadbdadbaddabdadcbbddaddbddacbcacdcbddaabccdbaddbcadaadbdbabdabdcbaabcdcbdaaabbbcacdacbacdcbbdabbddbacbddadcbbccbadbdddacddcabacaabbacbcacdcaabbaacbdababccadcbababacdaabccbdbbabddcacdbcbbdbbddbdaaacacccdabaaddcdbdccddabcddbdcdbbbdadcaacbaaaabdabcbcdacbcbacaabcadbacbacdbacdcbaccdcdcbddbbcbdabcdaccadbddbcababbaabdbbcddacaacbabbddddcdcaabddacddabddccadbdbdaadbaaaabaadbbddccdadabcbcbaabbbcdbddaadadddbdcacbdccbcaaddadadddbdcdcddbadaaacacdddcdcabdccabcaddabacabdadacbabddbbdbcadcdacdbcbabbbbcbcddaabdaadadcbdacddccbcacdadccbccaadbbbccbcabccddddcbacaaccaacdccdcaccbcdbbbdbbadccdccdadcaaabdaccbdbbadccbbdcacdcacabcdbcbabbabccddbbdccbacaaccbcadddccbccbdabcbcbdbdddccaaaaacdaabdbacbbdbcaadccbbaccdabddbbdbcadbbdbcabcddcbcdaaabacddabcbddbaccdddaadbabacbaddbbbddbcbbcbcdccbcdbcdccccbacdbcaadbbdcaadcbddddacdccabdacabaaadcdcabbadbdbcbbacddcdabaacabbadddaacccddbdbdcddcbcccacbcddbdcdcaccbabbdddadabcaaacaccddddbcaabdccccdcaaabbcdadbdaabababbadbabaaaadcaaaacbbdbdbcccbdbcaabbcacbdcabaacaddcdabbacbdabbacbcddacaadcaccbabcabdcddaacdbcdbccbadcdbaddbccaacaabdbdbbbcbaacbbcccbacbadbaabccdadaccaadaaacdbddcbbbbbcabdbadbbcbcdcdcccbabbbbcacbdcddbdadaacccccacccbadaadacdcbbbacddcadcdccdbdcadadcacbbcaadcbdbdccabacaabadbdbdbdbbcaaddcbcbdbbcbaccacddadbcaaaccdadacadcaaadddabbddbaadaadaccaddcaacbddabbbcadbbdbcbcbcbababaababaacbccbcccaccdbaaabbbadbbbabadbaaabadadabcbabdccccacbcaacaabbaccabcbbacdddabbaabbbabbacabbdbbacaddaccbbccabbdcabcaccbcaddacaaccbccccdccddcdcbccacbbddccddcdbacacadbdddadcababacdcdabdabddadbcaccbdbdabbdaacdabbaadcdcccbacdcbdbadbdacdacdadcabdbaccccbbbcacbbcdccabbcacbdaddbbdbddacacadddbacdccabddabdbccdaaacbdcbcdaaacadcccbaccbdbccacdddccadabaaccddcdcccacacacadcbddddacdcccdbcacdbbacaacdbaccadcdddbcaabaadbdaccaccbcddcbadbdbbccaaaddabdbcdacacbdbcddbbadccbdccbbccbacdbabacacadbbaaabddcdbcbccddcacdbaaacdcbbabdadbacccaabcabccadcdababcdcadaddbcddcaccbbbdddcaaacbdcbaacdbbcbdcddcbbddcaddcacbccbdadabcdadccaacaaaaadcadabaabccaccaddacbbcccacaabaaadcddbddccbbdaaccdaccbacabbaaadabcddddbccdcddcccabbaadabccbcdccdbcacddcbbbcdccccabaaaacbbcbaabcaabacccbabadaaadabaadcccaabccabddaacccabbabbdabcdadaadabcacdbdaccbbbbdbbdcaaadddaaccdabdaadbcccddaabcdaddbbdddadbdabadabbcbbbacdccabaaddacbbaabadcabadbcbaabbdcbacaaddbabaaaaccbabbbdbccdbbabcaadabcddbbdcbbaadbabbcaccaccbbadbccddcbdbcdbdbddbbcccabaaabaddcddbadccbdadadcaaccdaaaadcdbddcacdcddadbcdcbadcdbcdddcbdddaacbcacbbabbbdaadacdbaaddaaacaccccdbacdadacabbacdbaccbcdddddaadbabdaaccddddcaadcdadbdbddcbbbadcdccacabbddacbdcdcdccddbababdabbddcbadcccaadddbdcaccddddcbbaacdcacacdbbdbdbaacadaddaadbddaacabbbcccdabdbcbadbdcdccaacbaabdadbaccdbdaadbdabdcbbacdbcdadbadabbdaaccababdcaacaddcccdabcddbbcaabbbacbbcdaccdcadccaadbcabdcdbdddaabacbcbdbcaadabcddcbdaaddacbdccccabbadacbcbbdbabcbcbadacbcbbadbcdcbabcabddccbaadabdabccaaaaabcccbcdbacccdabbaabdacbbbadaabcabcadcacaaabcdcbadacddccbddabdcdbbdacadadbdbbabcbcdbadaaabadaabcdadddbcdcbadacccdcbdadccadbabcdcdbcdbccbdabacdbadbbaadbcdacdacadaacbdbbdbcddcbcaabbdbddadadabcabcbdbdbaccbabdbbbcdaccccbbbdccacbabacdbaaddcaadcaddbcaabcdcbacadcaddccdaabccddcbdcababdadbdccbccbaaacdabdadbddbabcbcdaabbbddacbcabcccbcdadcdbdcccdbacdabbdccdcabbbabcadababbcbcdbaaddcbbbccbdbdbccdbaddcdbaddadaacbcdddddddbbdddcabadcaacabcaadcbcbdbbabcaccbccbdcdcdbddacdbababdbdcbadcbdaabcdcdacaadcbddcbbaaccbbcdbdbabccbcdbdaacdcdcabbdaabcbdcdbbcbaabbbdddbcdabadcadddccbdbddaccdabbcdcbbddcddcdcbccbcacaabbccbdcdadddcccaabbcbcbabdbccddcbbcbcddcbddabbadcdcacbbbcbabdcccadbcbdbbcabadadacddacadcadddcddabcbabbadbcbcddcdadaabcaccadbcdcbbaccaddbcbbdbddcacabccbadacbbdabdcdccccbcabdcbccccacadbaccdbccbdcdbdabccaccbbcbabcaacacaadcacaccdbcbdbbccbaaacadbaadbbbdaaccacbadbadcaaccaadbcddcbacadbcaddaadddabadcdadadadcaccabacabdcacccabdccdadadacbcacacbccbbdbadabccccacdbabbbadbcdcdcdadababadbcaadcbbbdbdbbdbbacddbbadbaccbcabbcdccddcddcbdadabbadaadddacdadbdbaccacddcdbdcbacaabcbaadbdcadcbbdbcbdbddbbdbcccadabaadbbabaddacabbdcccbcaddacdcccbdbbdaddcbbcdbdbdcbbabcdabcbccbbaabbdcbdbddbcbacdccaacdadadbacbbadddbdbaacdcbbddcddadbdabbadaabaaaccbcdbabcddddbcbbabdbbdbababdacdccddcdbabdcacbacacadbbabddacbdaaaccaadccdbdcdddacccbbabaadcccbadddbcddcabbddcddccccaccbabcbcddcacbdaddaccaaaccdbaadbccdbddacdcbbbabbaabaabdcadaaabbaabcdadccbaabbadbbbbcddaddabaddcabaccaaccdbacdddbbccdaabacdaabdbcdcaccdbbddcadbbcbabcdbcdbcdaccdabddcdddcdbaaabaddbdbdcabbabacdcbacdaccccccdccbbbbcadaaacddbadcccdcbbdabaadcbacbcdccbddbdabddabcdbcdcbbcdbdcaaacbbcaacadbaddabcdddbccccadcbcbaccbdbcdbcadbadabbdcabaaaadbabadcbdaaccaadccabbbcacdcaadabdcabcdadabccbdddcbdcbbddcdaacccbdcbabbcbbcdaacadcdcdacdbaabdaadcabddbaaabacbbdcbbccdbcaaddaaadcbbaadaadaaabbbbbacdddcdbcdabacdbbccdcbbdbcabddbbcacacadbacdccddacaadcabdbbbbbbcbabaadbaaadaadccabddbdaadcbacacdbcdbdcdbacddabbbabdbbddadaaddcbaabcbbdbbcbbabdbdcccdcaacbddbcbaaccdbaaccdcbccccadacbdbdbdbacbadbbbcdcbadcbbadcddcdbcadaadabaabdabdbccdcabbadaacdbbbdbbbbcdcadabababbbbdccddccabacabaadcdddbcdcaddccacdddcccdcbbdbcccbcdacbacbddbdbbcabbaacabaddcdccbcadbaaacddbaabbccbaadacdbcddbaaccaabcbccabdbcbbbdbdaadadaccadbbbddaadbddbabdbaddcabacacdabacbadcdbdccbcbbdcbbcbbadbaadccccbabbaaabddcbbddbcacacbbbddccccdaaaddbdcdcacacbbbadbbcbbacddadaaadadbbbdcaaadcdacdaaabccbdbcbaaccbbabaabbbaababaddacccdbabccdcbdcaabccdbacdcacdddcbbddbddccbcbdbdbbcdcddbbcbcaddaacccbacddcaddcccbdcabaabbcacccaadccacaacdadcdcadbbdccdcbddaaacbbcbcacbadddcdacdabbadbbbbdaabccdcadcacdcbabdcabbdcabdaaccccadaaccbbbcbdacddccddcdbdcabaabccdcaaabbbadbbbdabbaacaaccabcabdbabcacddabbbbdbaacbcdcbdbcdbdbcbbabdddbadacadbddcddcdaccdcbdcaaacadabdcdccbbdbaddccbaddcadacdddbdbacdccbdcccaabcdbbdabccaaaabacdbcabcadbacdabdccdbddbbcadbcabdbdbbbddbcabbccdcdadbccaccdcabcbabdccaabdbcddacdacdcdbadddbccdabdbababdcdddacbccbdadcadbcbcbcdbddcabacddacababbaccbbbccdbaccacabcacbbcaaabbbddccaaaabbaccbdddadcadddadddaabccacbadbccccdbddbcbcdbacacbbbaadabaacdccaaaadaadbabbbdbaadcbbabccaadaaacacdcacccdaaaaddaddbcabadacdbcdacabccbadcdaccdbcadadcccacdcbcbcbcaabbaccdaddbbabddddbbbcddccbcbacbbacdbcaddbdaddbdbcddacdabaabdbccabaaabbacabcabbacdddaabddbdadadabdbccdbccdbcdaabbcadabcadccbbabcdaddabaddcadacdcdbccbbdcddaabacaddbcadcbbbbdcaabbaddbacccaaabcbbbabcddcaabaadcbbdbdaaccbddacadbddbaccbbdddcdbababcddbdcddbdbccccadcbaaaabacadbccbddaaabbdbdcbcdadbddbbaabcddabccbadcddbacdbcdcccabcbacbaadabbcbdcbbdabdcacbdaacdcdcabdadbbbccbbbadcabdcbddcbabcabbdbdadabdbbbadcdbbddcbbdabbbdcabdccbbdabddddcdcaccaddabcacbdabaaddcbdadccdacbdbcccadacbdbbbbdbdaaacbbacdadadcbaabdaaacdbcadabaacccbabcccbcccbbdbbcdbbdbabccdccabcabadccbddbacbccddcbcdcadaddbdabcaaaabadabcaddadaadabccacbadcdcaaaaababddaacdbabacdcdababcbbaddbcbaaacadbadcabddaabacddcddbcbabccddabbbadcccddbaadddbdbacdcbacbccdcbbbaadcaaabcddcaacbbaadbdbcbbcdcccdbbbabaacbcbbdcadaadcacbcccbbcdadccbbbaadcddddacabadcdabaaddaaabadcacbadccdbbaccabcdaabccccbbbbbcadbddccaadbdbbcbacbadcbbacbdddbaaadbbdabbaaacddaccacddbcadbacbcbddbbbcbbdabadbbacddadabdbbcdbcbcbdadbbabbbbbbcbddabdaaaaddabbcbddccdcbaddbcaacbdcadcabcbcabbdabacadacdbcadccdaaaaccdbcaababacbcddcbaccabdbddcccabcabacdbcacbdbbdcdcbcaccacccbdbdcbcdabdaacdcbcbddadacbbaddbacdcdcadaacaadbbbcabbaabbbbacccacabbcacbdddcaaddddccbcbbbdbcccdcadcabdccabbbdaabbaccbccddaddbdbcbbbdadbdcbdcaabdccaddbacabaadcbbbadbbcabbccccdadbcabaddccdbdcadbddacddbcdcacccababcbcbbaccdcaaabddcbcaaccbaddabddbdccacaddcddcbbcbbdccaccdaddabbaadadddbcadabbbacccbcbbbdcabbbdcdcacdccbbcaabbdbdcdcdcdabcaacbcdadbbabbbcaaccddaaacadaddabccaacaccbbacddbcabbacabcabbadddaccdcbdbdcbacdbaaacbbddcdbaddabcbbddbcdabbabadbddcadcdccaacaddaccacacdaabcddddaaccaababacbdcdcaaabdabccdadbaadbaabdcbbbacababbbdbababcadbaadabdccbcbadddcababccaadbbacbdaaaddcbdadaccdddcccdbcbabadbaabadcdccbdbcbaadadcdddbdcacdabaabadddcaabccccdbcbaccdcbcccabcabbbdccbdddcccdccbdbcccaddbcdbacaddcaaddadbaccabbabdccababcbdadadcbadbcaddddbbdbdcbbbcbaadbcbcacbcaabbbcbbcdbdbbabbddabcaddcccdcacaaadcbdabbccadbbbacdcdccddcadacdcddddbcddccaaabdbcddccacdadddbdaddaaccabbcbddcadadabcbccbccccdcdacabdcbdcdcbcbcbcaaddacbdadbcdbcdbccbaacbabdacdbcbaddabadaabaddccabaaaccaacacacdacccabcbbdddcdadadcdddcacbacbcbdacbddccccaaddcaddabbddacdacaacdbbccbadadaacdccdaaaaaccacaadbaaddddabacaccbacbccdacadcabdcaacbbcbadbbcbccddbaadbbbbbdaabdcaadcadbdacbdabacbdcadacacaabcbdbdbaaddbccbbdcabdccbcddbaabcacbcbccddddcbaaaddbccdbcdcdcddaacccadbccdccaacdcddbbbdbcbaddcaccbdcbccdcaccabddbdbcdcabaaaacacacaabcbbbadbccaadaabababbcbcbdbadbdaddbbcccaadbabdccdacccadbdcccacabaddadddaabccacdddbbcadacbbcdbcdbdccbacccbbdcbcbadddcdbddbdbaccdccdddbddabdbcddbadaabaccddabdcabbdddbbdbadacbabbacbaadaadbcdcbbcccccdadcdacbdbcbdcddacbaddabadbaaacddccbbbcadcaaabbaacabcacdbccaabdbdabdbabdddccdaacbcadbaddcdbdbdcdcbdbabbababbddccbdadcdcaadbcbcbbdcbcddbcdddbddccbdddbabbcddadadcbcddcdadabbbbcbccadadddbcddacdbbdaadaddaadddacbbadccdcbdbbcabcddabdacacabccddcabdbbdbcdaadcccdacbccccddadcacaadccdcadddcdcbbacccddababaabbdacababdbcddaabdcbabbdddbbdbabaacadaddabdcbaccbacddccaccdbaddcddbdcbacccbdbbbcccdcdbcbadcbadddcaadcbcccbbdadbaacdcbdaabbbaccacaddaaddddacbdcaacbbcdababcaaabcdadadbcbabaddacdbadadddddcadcdadcaddcbddcacadcbacbcbddcbaadbbadbaaaabdacdadccdacbacacdbdacaacbbccadaabdcabaaadcaadbababddcbacbbdacaaaabaddddcbaabcacdcbdcacdaccddbcabdbabaadbcaaccbcbcbbdacbcaddaababcdbddadbadbabdadcdabcdbdaccddcccabbadbcdaaabcbcaddcbbcddddbbccccaaadacbadadadcdbdcadbbadbccdbabbacbdbacdcddadcadbaccabdaacddabdccaddbdaacbbdbcdbdbbcababbcccccdbbadcabdbadaadacaadbbdabcadaabcbbccbbcccccbdabcccaccbccddcdcbadaddabcadcbaacbaacbcdcdcccdaccacabcaabbdbdbccdbccdcbaddaaddbddbadbaacacbddcabbdcacbcaadccbbdbaaadbcaddbddaabdddcdcbacaababbcaccccdbacadcaabdadacabdacddacdbdddaacaaabcbcdbcabaddacddaccadcabadddbdadbbcbdddabaccabddbdcadbddccbcabacccacdbbcdcbcaaadaaacbaaadddabadabadcadbdccacbdacdddacbbddcbdbcdcaddadbccdaabcabcdadcccccacbabcbddcacabacdacbbababdbbabbdcdcdababbacddcbbbacddabbccbabdbcaaccdbbccadcabbcbbadcbadabcccddcdbdadacdacddbaaaddbddbbaabbddadbbbaccccdaacadcbabbaadbbcddabcddabaaadccabbdacabbcccbbdaaaccbbcccbadbadbacddcdbaaccbbcddccabcccccbacadcbdcbacabdcccabdcbbddacaaaaadccbadacbdcdcbbaccaadabcaaccdaddcaccbaaccddadcdccdbbbbacadbbcbbcaadbcbdbcadbcbbcaabcaddccadddadcbabdbaaaababaddcddcccdbaadadbcbcbabadcbbacabbcadbdcdadaaaadcacbacaaaacabdcbdbcacdccaaaadbacaabdcacccbcbdaadbbbacacaaddbdcbadacbddadcddcacbdbbbbdddcbdcdabbdcacdbdcdbbbbaaaaadddcaccdbcdbadacbcadabcaaaaaaaacbbdbabdcabaccdacdcaacddcbddaabbbdcabacbbaacacbbaacacdcbcadadbdabbbbcacbccadacccacbacbcacabdabdbbaabaadaccccbdacccadbbbacbbcaacddacccdabcabdaabacddacbdbddadccddbccdbababbacbdbddacbbdcdddbdbacddbbdacddbbadcadbddabbdccbadabbcddbbcccbabccbdcbcaaadaacdcacbdadccaddaadacbadcbabbddaddbaabdaccbbbdaaddbabccbcacdcbddadadabcaaabbccdacbacabbdbbcbaddbddccbabdbdabdabaaacddcacabaddbdaccdbcababbdaccbdbbbcacdbcdcacccbadcbccdbbacddccaddaccaddbacdabdcccaadbabccadbdaccbcbcaadadddcbdcabddaaabcccddaadcaacdddbdcdcbbbabadabbdbdbccbcbbdadbbdbdaabacdaabbddcddadbbcbbcbacbcbabccbccdcabacbdbcbacbbcdacdbcbcbdacdbbbbacbadaaacbadddccbcddaddbcdbddababbddcadacdbacbbccaaddbbdadddbbdaacbacabaccabcbbcabadacbcbaccbbdcdbdaabccabcbaabcaaaaddbaccccdcdcbccbdbacdadabdacbbccaccbdbcadbabacaadbdcddddaabaacabccdcaadbaaacdaadbaacadbdabbacdcacbcdadaabbabddbdcaacadaadcbdddacbddbacadbcdbbdddaabccbcdddadadddacdcabbdcaadacbcbdbacabdcaaadcbabbddddcaddcdbcbcdcbabdcdccadacbcadbcbccdabadaddabcdcabaabbdbcdcbdbbbccbbabdbddcabbbaadcbbadbbaabcbbdbcdadbcdadddddacbbdbbcddbdddbdbcbcabdbbddbadaacdbdaadcaadacadbbadccccbcacdbbabcccbcdbbcadcbadcbdabbddadaaccaabdcbdaccbdaadaccccbcadddbcaabbacbbcddabaabdbcbaadababbcadbbccbaadaabccdcdbcbdababadaaacabcccbcacabdaddcacadadcaaacddbbaabddaccccabaaabaaaabbbdaacbcbabcbbddbaccaadcdbbabaccdcacbddbdadbaabbdcabdadaccbdcbacbbaaabcbcacdbcdadbdabcdacdcbcddadcabcbdcbdcbacbacbbababbdccbabcaccbabacddbaccabcdcaccbaaccbdccdadbaccddbaaccbcbadaaabcabacbdcccadbbdbaddbddaadcbbbadcdaaaacdbbaccadbcdbdaaacacbcaabcaddcaadadcabcbaabdabcbddabccdcaaddacbcacacbdabaabccbacbbdbbdbbcbbddbadddadcdadaacddbddbdbadbaacbccbbaaddcbabbadccbbbcacbadcbccdabacacbbacddbccbdcddaddbcdccabdbaccccddacbccbcdbdbbcbdacdaadaddbcdbbaaacadaccacccccdbdaddbabbbacababbcabdccacaddaababacaababaadaaddbccbaaaaccbadbaacddbacbdcddcbdaaaddadaccbdcccbdbbcaddacdccbcdbbaaabcabbdbddbcbcbdddbacadbbbaacdcbaabbaccdccdabbcdcbabdaddbbcbcbbccdcdbdcacabcdcdcaddbdadbcccbabbbaddbbdabddbdccbcbbdddbdccbdbacadaddcabdabddaaadbdaadbaadbbdaaadddcdbbcbbbcdacdcbbacdacaabbbdcdbcbcbaddaccddcadadcdcbbbbcbaacbbdacbdcddabbcbadacaaddaabaccbdabdbdacbccccdaaadadabdccdbdcaadaccacdbcccadaadbbbdabbcdbccdbdbdbdabcccbcaccccbdaaddabbcaabdddbadabbdcacabbccdcdcdcdbcbadbdbdadacaadbaccabcaadadabdcacbbdbacabdcbaccbacddcdabbabddcacddacabbddccbbccccdaaddbcddbadcdaccbbbcbddaabcdbdcbddaaddcdcdccbbaddaaddaaaacdaaaccbaabacadcbbabcbddcbbbcaadcacdbabaabbcabccdaccbbbacddcbbdcdbdcdbbbacbdababacbbdcdacaababddcaccdadcdbacaccdcbaabaddbacccbabaadaadcbdbcdbaccbbdccaaacaccaadcbcacdaabdcdaabddadabcbaaaddbcacdadbcadcddcdbabbccddddbadbccbaacbcccbbcbabcacadbdacdcccbccdcbdbaababdddabbccddbddacbbbadbbdadcddacabbbdababcacacaacabadaaddcacbabaaabdcbcaadcbdaaddaddcbdccdcbabddbabcaacccdbcaacbcbabbdadddabdcdabcbadddbabadadbddbdcdacddbacccbdbacdbaadabdbbcdadcbdccbcdbdcabacbddddcbcdbcbcacaadbbbbdbdbccddccbcbcbdadbbdbaaabababaddacdccbbaacaaabadbcbdcbdcddabbbbbdadddaaddbaddacadaaabccdbccccabccdccadacabdaadabaddbbaacaadabcacbbcdbccdcabdabacacacdddbcbcdacabbccdccabcbdcdbcdababaaacbccbcdbbabbbbdbdcdaddcbdabbccccdcaaacbabcabadaddcaddcbacbcaaaddadaabadcabbacabbdcbcadccbaaccdbcadbcbbabdaccdcbadbaadcddbccaddaaadbbbadaadbbcccacccddbaabbcbdadbdccaccccbadddddaacadcaabacaaacadbbddccccbcabaccaccbdbbcdbabcdcdccdddaacdcdabccbdadaacacdcabadacacbdacbbdbabcdbdacdddcdbddcdbbbdbdcddbdcdbcbcbdbabadbcadddbccdbadcbddcccccaabdadddbdaaddbdadbbcdacbdcddcdcdbabcddbbdbabdabdabababbbabcabbdadadcccccadbcbacadcdcbadadabdbbcbaaccabacaacaacaabaaacdbdbcababbaaaadabaccbabcacaddabaddababaabdadabbaaaccdcccaaadbbacbdbddddddbdabccdcdbcdbababbcacddcbacaccbbaabcdcabddbccdabacaddadbaabdbddacdcabdddabdabcabcbcaaacbaaddccaccbbcdadbcbddacdabadaadaadccadbdcdcccabcccddadaaccbcbacabacdbccaabacaaadbababcdcbabbdacbdcacaccbccabbdbbaadadacadababdabadabddcdcbbaddcaacdcbddbbcaadabbbbdcaacaadacbaacbcddbaabcaccbaddbdbbcbaaacdbcbccbbadbdcdaaaccacabdacddbcbcacaddcacdccbcdcddadbccdcaaaccdacccbcaaddcaabacabaacdccbadcacadcabaadcdbdaddccdcbdbbdcbdaaacacdcbacccacccbdddbbbbaacbdbacabdbbaaacbbabcacabaaccddcdbacbdbdbaccdbcdcccdcbdcdabaadaaadcbbdbbcbcaaadcdddcaddaddbabdcddccbcdaaddabdabacbdcccbadcacbddbcdbbdcaaccaabcabbcdbcdccaddadacbcabccdcdabbdabbcaaaacddaadcbbcdcbcadccabbccccddccdbbcbdadacbbccaadcdacbcaaaacdacdaabaababcdbcccdddcdddbcbaadcbccaabbdcbcddacbbabcabbbabacdadddabacddcbcbcadccdbbbadacccacdccccccabdbdcbdaddccbbaaabbddacdbbaacdddddbdcadcabadcadaddaaacacbcdcdcdbbdcdddcdcdbcdbddbccddbaabdacccddbacbdbbdacdbabdbbadbacadccbdbdaaabcdabaddaabacdabddbbdaabcdbbaaacccbdbdacdabdcdcadbbdbabacadccdabcacccdbadcbacddbacccbbcabdbddcabaadcdbddbdbaccbcacdbddcbcbccdaaadddccdcddccbacbccbdbbcbcddcbdbbcbabdabadccdcadcbcdbdcababbacdccdadaddccccddbdacbcabdcbaadbcbabbaacaccccddbcbbdcdbdbdcaabdaabcccbddaddcacbbdbcccccdbdbcbabdccbdadcbbbddcaccddadcbbddcbcbddacdcaaabddddcaccaaaaadadbcdacccabdddabbcdccbaabbdddcaaaddcabaabadcbaddbdbddaacdadbccccbcabbbadcbcbdcbdcbddccabdbbbccbcaabcbcbacadddcadccbddcdbacbcaababadddcbabacdbddaddaaaacbcbccbdacccbabccacccdabdbbddadacccbddccacaaccbacbbbbcccbbccbaaadccccacccbadddacbcabbdcaacbcdcdbadcaaaaabdbdaadbbdddcabbbdaabbddabdbabbacabbcaccacdaaabbadddcabcdadacacbabaabcddbacabdabdbbdabddabbacaacbbadbabcbdcdcbdcddcabdcdcccdbdcbbddbccabcabdadbcbbaabddbdbbabadaaddbcdbccbdcddacbccbadadcbdddabccabbdcdbbaaddabddcacbdbadacbccbbbaabaaabbadddddcdcbdadabcdcbbdbcddabdaacdbddcccddbcdbddababbcbddddaddccbcbadcbbcadadaccbddddcaacdddbdadccbdbaabbcccbdcaacacdadaccaabcdacbdccbddbabbadadaaabddcacdccaacbdaaadcddbcacddabbdacddbcabccacbbcbddccadacdcdbcadcaabbdccadbbddccdbdbcacbccadcdbaadccbbabcbccbadccdabcccabbbcbcdacaccabdabbcbdbcaacacbbabaaadbbddbabcbbdaadaccdcccddbabcbaadaacadaabbcacabcdddabadbcabccbcdcdabddacabbdcbadabadddabaacaadbdcbaababcccacaadabababacdadbaaacddbdabcccbdcaddbaaabbdbcbddbaadabbdaabcdbdccabdbabbabbdccbbbcdcdccadbbdcaddbddaabbddacdcadadddccbcdadabaadacbcdcdbbbacdbbacdbadcbccbdabaaddccacdcdababbccbbcbdaddcdaddcabaddacdbddabdcadadbacaddcbbaddacdbcadddbbabaccdcbbdaccdddbadbaaabaaaabbcbbaabbccbacbdccddcbddbbabccbdcdddcaddccbdccdccccdbdbbadaacbccabcaaadaddaabcddbccaabaaabddccccddbdddabccbccabbbcbcaddcddcdbdbcccbcabbaaccacaddacbbaadacbaacacdbdaabcabbbdbdbbcabbbaabadbdabaabaabbabccacdccbdcadacdcadddcdbdaddaddbcddabdbcccdacbdbbcacbaccbdaabdcabadaabbbdbacbabddcccdcbbdaddabbbdcaadabcdcacbabdcbdcbbbbbdacccbdccaccddbbcdddaacacdccdaabcbbdaacdaabacbbdaabdcdaddbabaacadaccddacabdbcaddcbadbddbacaaadbdccbaadcbadbabbdddaddbccdbddcabdcbccdbadcdbaccdccacdcadbcadcaababbbbcddcdbadacaaabcabddcbadccdaaaaacabadddaadbaacaaabbacaaddacacadcaaaacccddabdbadcaddacacacccbddcbcdcaacbcbacdcdcaddbdaabaadccbabadbcbdbacccabbcdacccadbcbaaccaaddcdcbcbbbbdbadcabbdbcbddbdcaadcaabcabababddbdcdbdadadbacbcdadbbccdacdccbabbacbababdddacdbdcbdaaacbabbcbabbcabbdaabbacadcdadbbadcccbcdbacccdabbbbddbcaadacaccacdbcabadabbcbacabbccbcaabcdaccacaacdddbddcaadadaccabadcaadbbdcbacbbadccbdbabdbdcccbcbaaabcbacacabdddaacadbbbbdbbaabbbaaabcbadccbbbdbbdddaaadcaacadcbcccbadadcabdacdcccacabcdcbadcaddacabcabbdccabbdaabddaacacbccbcababcdaadaaabddbccdddaabaddadaaadadbcbdcaabccbcccbadbacacaaabacbdabcccbcccaaadabbcbddaddbaabdadcbbbacaccabccbadaaddaccacaaaacccbcaaadcdababbaaccdbaddaaaadabccaabbcacabcbaaabacadbadddbadcaadcddcbcabaadcaddbadbbacbacbbaadddadcdcddcdbccadbbccbdadcbbcddaabbddcbcaadbdbbbdbcbdbbcabbabbbddcbdcdaacdaaccdacdbbaccacbbbbabbcacbacbaccaaaadaacdbcccaaaddddddccaadacacbdddbddaddccaabcadbababcbcdbabbdbabbbadbdaadbcbabddadadacddaacabbadabcdadaaaaabadbdbcbdbdbacabdbccaabbdbbadcbcbddcadbcbbddacddadcbacadbaacbcddaaabcadbbccadcdbddddcbaaabbddadccbdcbabdbaadbdaddaadbcacdccbaccddaaaaacbbdbaabccbabdddbbaddbbcdacbbbcbcabcaccaababddbcbccdbaccbacdcbdcaccddabadbdcccaaccdacccdabdcbbdbcdbcddacddccdacbddbdbdcbdcababccdbcdacbadccadbabaadccacbbcddbadbccaadccdbcabdbbdbadddacbbccdbbbcdbddcbadbadccddcbbcdcbacdbbdbcaccdabababcdcabdabcabcbaadabccbaaaddbcbdaacacddddbabaaabbbdbdaaccbcbaababdaaabbadbbbcbcdabbbbadcbacaacaccbbcadbcbbaddbdbacddcdcdbdbcaddcaaaacbbccbaddabadbadddadcabbbcabdacdcaadaaaaaccbbbabdbcaddcacdbbdcaaccacddcbdcbdadbcdcdcbdcabcadbbdabaddcbdabdaccacddccadadcbddbbabdcbcdacbcbaacbaaccbddbaadccdacdaccdbbcababbbaccbabdabcbddaaccbcbccbbdcadcacdcbdbbcbbcccadcabbcbadbacadcdcaadcadcadabccadaaaadcbcbcbabdacaddcbacccadddbbdbccbbbacabcbacdddbdcadcbccabaaaabcdacdacdaddaabbcbbaaacabadcdadabdcddbbcdbcaaabaabccadbacbcadcbdddcaddbdacacdddaadbaaadcaddcdccdacbdcaaccbbcacbcccacaaddcdcddbdbbcabdddabcddaaabcccdabadabaacadaadbcdddcdcaacadcdcababaabdcadccabbdbadbaabcacbbcaadbccabdaabcccbabacdbcbbcbacbcccdccaabbdbcadabbddbcacabdcbdadcdaaadbdcacdbaabaaabdaccbdabcdbbaadaabbcaccbcdadddbdddadbdadcddcdccabddbcbabbbdcabacbabdaadaadabdcaaaccdcbbbdaddcdccbbdacddaadbadbcdbbcdbadddddbdacdaabbdbacdbdcbbabbdbbccdcdbcacacdddbabacdabcddaccbdbdaabdcdabaddbcbcabbabccbcbcbadbcacbabbdcdddcaccddbdcaccacbacbbaccdaccaddccabbdbddabcdbacbccccadaacdbacbdabccddbdaddadaadadccacbacdbcdbdbdbdcbccbdabbabdbdccbbaddadbcdbbbbadcaaacbccbcabcddcbdbacbdcbddcccabaaddbacdcbabcddaadccdcccaddcaccadacaadcbdddabdacddbcddaabbdbbbbcadbacbbcbddadbdcdbbdaacbdddbdbabaaccaabccadddbaddcadaaddbdabadcabccbdaabdbccdbddddaccdccbdaddbadadbbacbaaabbcacaabddaaadcabcbccaccacbdadddbbcdccbbccdaadabadaddadadcdbdcddbaccacbbacacbdcacccccdbddcbdbdababbdbaddbaacbdbcdaccaadddaabbccbdcbbabbbaacdcdacccaddbadaacacdddbbcacabcdaccddcddadadacacbcaabacadaaacaadbacadadadcdcbbabbbcbcaaabddbacdccddddcbdababbdacdddbbadcdbbdcbdbbccaaccbadcabadcbababbbabbcbcdadaadccdabcbbdbcbcabaddaabddcdabcccaaccbdaddbbddbabdddbcdcaacccbdaddcaaaacacdcaaccbbdabcbdaabacbbccbadaacabcadaaccdddbbcbdcbbcaacadacccddabacdbabbcaccaacabbdccbdccdacbdccbccdcdbdddaaacddcbdbbbcbccabcbbcdcddddbcbcabaadaddddddaddbcbbbadbaaacbcdaccacbcdbbcdaabaadadcccabddaababaccccaaadaccabcccaabacccdbdadadcddcdbacadacccaadaccddaadaabdaadcadccaabadcacdcbbabacababcdbdcaabacabbbdadaabadaacbdbaabadadcbcdccddbacaacaacbbccadbcaabbccccdadaaadaccdadcccbcccbabdcdcdbbcbcddccbdadbacccdccacccaadaccdacaccdacacaccccabbcccbbdbbaccbddabdabaaddacddddcbadbaacacbccdccdcacdaccbcddbbaadadabacdbdbabccbabbcddcddcbbdcacbdcdaabdaaddadaddddccdadcabcbdcdbadccbdcbbbbcbcadcacacacdbbbadcabcdccbbacddabdcdddbcdabdddcaadbabacddcddcbbbbdddacbcbabbabccbbabacdbbadcccbabdbdcabbabbcbcdbbbaaaadabcdbcbdbabbcbdadabdadabcdacdccdcddcddabcaccbbbdcdacbacdadabaadbcccabbdcdbdbbddbabcdbcbcaadcddbdddcdbdbcdcbcccbddcababadcaacdaddbccbccddbcdacbacbcddbdbbcadcdddbcddaaddabbbbadabaadacbababdadccdbdaccdaadaccdcdbdbcbcacdbbadcccadcccaadaabbabdcccddcdccacacdacdbbacabccbdcbbcabaabdddaadcbddaddacabdbbbdbcbaabbbdadadbadacdbdbcbdbbabdbcaadbadadcdacaaacabbccbcbbddaccdcbbbcbbcbbcddacaabcdbcaabcbcaddcddddbcbabaacdbadcbdcbbcacbaabdadcdccbdddcbbdbcdcaadcadbbadcbbcababddcbcdddadacdbbbabcbbdccbabcaadbdbabacabdccbabdcdbbdbcddcdabbbcdadbdbadabdbddcacabdcdcbbbcdacbbbadcdaccabbdcbdddccadcdddbdbbcdcbcdaccaccbcbdcbcdabaccdddabddaddbdbcbacddccccbbdcadabccacaddbcacddbabbbbdbdaabdbddcadbcdcaabccababcabcaddccacdbacdaadbcdbccabbccdddbcdccbdacaccdbbcbacadaccdcacacbbccadaadcdaaabacbbcbcabdbcddcddadacbccbacbbababcdaaadbcadaadcccbbbcdaaadccadaabdabaaddaacbaadbabbdbbdccbbbbcccacdaadbdddbcacaadcdddbadaddaaadbcbcdbbbaaaccabbbaadaccbdaccccaacdcababacbababbaddcaccdacdbbddbadcdcdacabdcdadcbaadbbddbcdbdbccbababbdccccdbcaabccbbacbaacbdaddcbccccbbdaaaddbbccdbdaabbacddbdaaabdaccdcbcccadbaabdabddccccabaadcabbababbcacbabbccbaddabacccdcacaacdcabdcbcadddcccbcccddaccbacbcbbabbaccbcbbaadaccbacaddcacccaaabccccacabababdcdbbaccdcbabbaccabdcdcadcdcabbbbddbacacbcdddcacbdbaabacaccbbbadbbbccacaccccbadccdbabaadbcbcdbbbbacaaacdbabbcdccddacbbbdbbcccadbaccbcccdadbcacdbcaaaabadadcdccbaaadddcabbbddcbbddcdacdbdbaddddcbccbbdadbdbbbcdcbcabcabddadcdbadadcbbbbdddcacbaaadbddaddbcddacbaaccdbaabcaccdcbabbcbcbaccdaadbbaabaabbacbdbcdbbbcdbddbaacbcbcaaddbcbbacbbcaadbadcddcabdcbacadacbbaadbcbdbacddbbccabacdbcbbdcacbcdcdcdbccbdadcdacbddaadccdbcbcccccccdaaaaaaabdcaccbdcadccccddddbbbccaaaabdcaabbcdbadbdadcaacaaabadacbcbaabacdcaaadcdaaaadbdddccacbdadcdcbdddddcccbcbdaabbadcbbadcdbbaabbcbbcdbcdaaabaaacaaccabcbcddbbcccbaccabbcadddddacbbcccaaddcbabccaddbdbddcbdddbacbccbaaacdcbccabccbcacdbcbacdddbaddbbadaddcaaabcbdbbcaacdbbacdcbdadbbcdcaabdabaccddddabaaacbbdbdaaacbdcbaadbabddddcdcaaabcddabadacbcdcadacbaadbbcadcdbdaabdaaaabbdabccaadcadaacbddcccccbbbdadbddcdddcdaaabacdddcdabdddcdbadcddbcccaaacbcdadbcbccaabdabdddacccdbdcacaacadbbcdcacaadcbdabbbcabaabdccbacbdccdacccaddabaabdcddabaccddbccdcbcdcdcccdadcbcbaaaaddbaacccdaadccadcccdcabdbdcddabcdbacbadcbdaddabaaaacdbacddaadaddbbbdcdcbaaaadacdcadbaaddcbaccbbadcccabadaacabadabbaaaadbabcdbaaddacdcccddacbcbdbababcaaddddbdaacbaaddabccbdcbccbaadbacccddddacdacbdbdbccabbaccbcbacdcbcbcaacbacdbcbabcadbdbbabdcdbabcdcbdddbcdddccadccdabddccaadacdbcbbcbdbbacacbcaaaddabcdadcbbcbcdcadbbababdcbdbdcccadbadbacbccdddbaadbbbaaadbddccabdaccccccbbdaadaadbdadbccdabaacdcacddcdadcbbbbcdbabdddbacdccadbbbdacbdbbacadaccccdcdbbadbdaddbdbbadbdbabdccacdbcbdbabcdddbabcddbacbadbbbcccacabdbcbadaaccdcdbccdabbbdcacccdcccaacaaabbbbbddcbcaabccbdaabbcbddcbdacbbccddbdccaacdbcbcbdadddcdcababbddbbbacbacaadbabdababccadbccaddddbdbbbadcabcbadbdcaddbbbdbcaccdcbadacaaacadbdcaadcccdbabdbccacbdbabadacccdbacdbbbcccbabbbccbddcaddcdbacdadaaccbccbbdbdabdacbbabdcacdaaddbaccaaddbdbdaaddcacdaccaacbadbdddcbaddbccbbdbdcaabcbdabadddcccbdbcabdddddccbaacacdccaadcbacbbcacbbaadbbabbbcbdacaccdbccaabbdcbbcccbaaacccbbacbbccdacacabbdacbcacdbdcccbdabccaddbadacdcddaaabadbbddbbdabdcacaaccbbbbbcbcdbacaabdacabcbadbdcbadbcbcdcabcaadadcadbcbccacdadbabadbbaddaaddabdcbcabbbabdabdcaabbcbbaddcabccacabccbcdacbcddbcbadbdbaccdcbbdaaccdcbdddabcccabbcadbcdaaadcbdcccddacbadbbddcdaddcacabdcdadadbdaaadcaddbbbbbcccbcdcdbadcdccbabbccaacbaacbbcdacaacaaabcaaacdcadaadbdbcccdbcdccabaddbdbdbdaddbdbadbdccacccdabcacdcdccbcbaadddcdacdaaaaccadcdccbddcbadbcdaddbadddccabddaabcaacdcddadbdccbacaabdbddcbddaccccbcbcacacbdddcdacccbbbcdcbabaccabbbcdaddddbbadbacbcdcdbcdbbdbadbabaabcaabcbdabbbdabcabcabacbcdadddbabcaababbbdaddcbdddcaacdddcbbdcacabdabddddadbdadacabdddccddcacbddcadcaaddcbcddbdbabcaccdcbbbcacddabacdacadaababacdcaccbccdcbddcbbaccbbaaabbbbbccadcbbdcadbbccbcbcbbaaaacadccbddabcddcaddbaacbbbacbbaacadcacdacbadabadacabbbabdbcdbbaabddabbcdddbdddccacbbabdabbcaadaaadbcabdbacbaadacaabaaadcadabaabcbacbaccabbdaaaadcbcbdcaccacbccdcbcbaddcaaadacbdddcdcdaddddcaaccbbbbaaccbdcacdcbdcbcbdddaabbbbabdbaabbaddadaadabdaabbbcbdbadacbdbbbbbddcbaccaabdbdbccdccbdbddccadababccddadcbdabaaaddadcccccddccaadabccccdcdadcbdddddbcaacddcadbacdddabbcbccbdcbaddcabbadcbcdaccaccbcbbdabbdbccddabbdaacdabbacabcbcbdbdacdabbabbadacdcbabdbabbcdbbabccdadabbbbcadacdccddcdbbbdcacbaaacbccbbacdbabbbacaccdaadbddcdaadbcadacddcaaadbbcdcdbdcbbddbabdcbcabcddcbdacacddcbcccaacacdabadcbcbccadcddcabadbaabaddbcdbabddbccbbdaadabddbcababbbbdbbadaacccdddbdabccdbdccdccbbabdbaddbbaccbcdbaadddacbbdbbbabccddcacbcadadbaddacabcbcccdcbbdbdcddccdacccacdcbaddadcabcaaccbbdbaacbdaadaaabdcacccaadcdacacdbaaaacabdbccadadababbcbdcbcbbcaccbdddaccababcdacdcdadabcacadadaadcbbaacdacbdccacdacabacdabddadbdabadacdbdccccddbccbddadaacddaabcbccdbdcbacacbabcbbdcbcdaabdbdacddbcbddaadbaacbaaacdddcbddaaadbdcabbacdaddcaaadaddcdbbcbcbbdcbcdaadddcaccabdcaddcbbbbddcdccdadaadaccdadaadaadaabccacdddcdcdbbcabccaddaaadbdcdbdcabbadaaacbcdddcdcdddcbdcddcabbadcaadcacdbbbbcbdbbacdbcccdbcdbdbdcabbacccaddadacaabbcaccabacddcdabbbaabbddadbbddccabddbdbddbccdcdcbccccabccddbcccbadbddadcaadbddbadbbdbcbbcddabcacaccbcdccddcbdddcbabcdbcddabcdcaccddbccdcadcdbdcddbaccdbabbcbcccbcbbbcbadcaddcaaabdccdbdadcdcadcbacbccaabbcdcdddbdaaadddcbaadbbdbcabaacdaabababaddabddaccdabdaacacdaabaccbdcbabdcdbbdcdaccbcaacdbdcbbcbcacbacbdbbcdbcbacabcaaacbdbdbbcacdcaabcdcbdcbddcddaccbcadccadaddbaddaabadadaccadbdadbccdddcdcabccacdcbbddcbbccabbddbdccddbddbbbbcddddaadddcbdaabbdbcccccababdcbbdcaddacddbdcbccadabddbacbbddbcccbdaccbaddbbddddcbdccadccdadbccdbdcadcabbccbdcccdadacbaccabbacdcbabddcdbaacdddbacaabbbdbdcdadcaadbdddddcacabdcaccabaabcbdadcbcbbcbcacdcdbddbaccbbbaaccabcccabbcdcaacddacdccbdbcbbcbaaccabddbccababccdacbaaaadbbddcaddcdbbadcccdbadcdbbabdddaadbdadbcbbcddcaabbddadcbbabdcacabcbcdbacbabccbbddcacbbcbbcbbdbbbcabcbddacbaadddbbabbadaccdadacbdcabbcddbdddbcbdbaaccbcaabbcccbacacbbdbbdbaacdadcbdcdccadcacacdbaddddaaadcdadddcbaaacbaabcddbabbdacddadbadbababcbdabdcddaacbaacaacdcbaabdcdaddadadbcccdacbacdcaaabacacccccbadabaaadcbbbbbddaaabbaaddadbcdcdddabccacbbdaabddcbabbabdbdccdcaacababccbcabdacbbcbdaaabbdbcbddcaadcdacbbdbdaaaddbacdbdcadcdbccabccdbbaaddabcadcadbdabbbbacbdacdcaacdabdabbcbaccadadddcbdbccacabcdcdbbbcdcccdddbccdbbaaddcaabbbcaaaccdbdddddcacccbcddbbbdbcaacabadcadccbbacbacadcbbcbadadbcccddabbdbbdcacdccbdcbcddbacbccdbbbcdacadabddabbadddabcdcbbaddbaabbabdadbaacdbaabaaccddbdbacdaaddcbcbbbdccabdcabcaaabddaaabdbadcccdaadcbbbacdcbdccaacdccacabddbabacccaadbdbdbcbbcccbaadcdcddbbbbabadcdddcddaddbdbacaaaabdaadbbbcbbaddcdadacdbcbbadbcdabdccdbbdcbdccbcdbdaabbbbcaddadcbdccbbaacdcbcaabbccbdcdccacdcbabdcdbbbbaaadccdbadacdabaaaccabadaacbdadddcdbadaabbacbdcaacdccaccdbdbddbdbcdcbddcdabbaccaaddaaaaabadccccbaccbbcccccdddabadbccdcbccbdbbdaabacbccdadabcacddccadbbadaaaddacccdaadcdbcabcaaccddadabbadcaaabbabdcccbaaabcaccdaabbabccabdaddaddadbacdabccddbdcdcddbcdcbababcdccdbdbdbababcbcdbcaaacbddddddabbacaccdaccccbcdccbdcbdbcddabacaddbbdaddcdbbddcaacdbbccdbcaababddcdaccacdddddadbdbcadcdaccbccbaabdcabbdddadadbdbddbcabbaddabaabbaaadcdcccabbccaaccaacaabdacdbbcbcabdcdddabcbdcaabcacabdbdbcabbabaddbbaacdbccdcbbabdacdbdbadbbadbbcadccadbcacadbbcddbabcaadaabcccbbccbdcccdabdddbbbaddacbcdadbbacdbddbaccaabddabaadadcadaacbbaaddbabcadaaacdcbcbdcdcbbabddcadbbcdddabccaccdaabbdccabdabdccbaaddccbdddaaddddcccbdbaccabbbcaabdbadadcbbabbbbbacbdbccdddcddabccbabbddacacacddaaddddbdaaddcbdaacbbcaaddacabdabadcccaacbdbdbadddabbcdcacbbbacadaadaccbabddbabbcbcbaaccbccbbdadcbcddbabcbbcdbdaaccdacbccadabdccdbccadccddcabccbbabcbacacdbbaacadabbbabaccdbaddcabcaacacbabbbdddadaaccbbcadccccdbddbcbcaaddadaadabcaddbccbbaddbacbbddabdacdabacbbaaabacbbccaacdcbdacdbbbcbcbcdacbaddcdadbacddbcacadabbcadcacbadbaaacaaacacdbdabacbdddccbaadbabcbcaccadacdaccabcdccaddbbdcbbaacaabaaccbdbacdcdaadaddaabdabddddcccbbcbabcddabdadbdbbabacdaacbdaacacadabdcdccdbbbcdbcdacdbbdbcdbcacddbdbcbbcbadacbddccbccdaccacdbbccaadbcbbdcdabaddcdccaacacdccbddbcbddcabacbdbbbccaacbdccaadcbcbdabadadbdaaabccdbaaccadbbcdaaacdbddccdddaaaaadadbdbbcdcbacbaccddbacddacccbbabcdcadabacadbdcaabbaabbcbcadacbddbabbcbdbccbaaacdddcddbdddcabaddadbbcacdbaccddbbadddcccbcbaaaacaadabbdaacddbcaadabccaddbcbcdacddcbaddddcbccaacbcddcacbabadadaaababcccbadcccbbacbcbcbdacdcadabcdbbcadbbdcccadccbcbcabacadacccdcbcdddadabbddcaaaaabaaadddddcbbdcdcddcccaddcbccaccbddbcdbbcdccaabababdbdabdabcccabdabbbdbadacdabdbaaaccbabadcadcdadddaadcbdbcaaddcbccbcdaaabdaaccbaabadccdbbbccabdbaaccacadacadadcdabbadacccbcbabbbbabdbdabdbdadaadddaccccdddadaaaddadccbcdcbbddcdbbdacccbdbbcbdabdccdbbbcddbccbbccadddcbbccccbabadbbbdaadaadacabddcbaaaccbabaccbdabccbcddaabddaabdcabaccddbccadddaaadadadbcacbcdadcadddbaadbbcccbbcdcbabbbbcddcccdcaaccbabdcdddcccccabcbbccdbacbdbccbcbdbcaabacbbcdbdddcabacdabbaccddbbbddaabaddddbbdbacccadaadabdaabccdbdabcddcdccabdbdbdacaadcbccddabcdcbaabcbdccddcadadbddccadbacdcabdcacadddcdbbabcbcddcadbadbcadbbbcdbdacaddcdcdaabcabacbaaacdbdaadccabdaccdddbaaaaccbbcaabaaaaadacabbccbbbcbcddaaadcddbbbdacbacddadbdabaccbcacadacccbaaddabbbddcdadcbabcccbcabcadadaddbbbabddaaabadbadbcdbaadaacdbddbbcbabdbbddbabcbdcacbcbdccbddcddadbcbbcddaabcdabbbbadabcaccdcaadbbbddcdcbcaabacdbdaaaddaabadcdadbdbcdcddbccacbcdacbcaddadabbdbbdccdbdbddabbdbababcbaadbcdcdbdccdccccbbaaabacaabbabaabcbaabbbbcbbbbccccabaaaddcbcddccdaabbdbdacddccbbbcbdadadcabaabcbaccdbabbddadcdbbcdcdcadbcdbdbaadcbbddaadbcdacbbcbadbbacadcbccdaaabadcbacadabcbcdadbcacdaadcbbbbcadbabbdadbabccdcacabcdddbdcadcbdacacdacdadbbbabcacdcabcccdccaacbdcdabaccdaddcabcaaaacccbcababacdbcbabaccbdddcccaaacaadcddadddcabbcaadbcaaabcabadbccddbbbdcabdacddbccdacbcaabbdaabbaadabbbacdcdbbaacbcddcdcbbaddccccacdcddabbaccdddddbbadddddcdadbbcbccddcaadbbdaccddbcbdbaabcdcdcddadcddaccacabbbbcadcdcbcdcbdbcdcacbabdbabcdaddacadccacacbdbbacadddcaccabdddcaccbbaaaadadcbdcbaaabbbbacabbaacabcdbcdaadbdbabbdcaadcbddbdbbbaadabcdcaccdabcaaddaadbbbddacbcbdbabccabdbcaadadcbcbacdbccaacaadabccbcabddbccacdbbddbbabbcdcdabcdcbdbcdcaddbcabaaacdbaacbacbddcdcabdbdbabcdbbabdcbabdababaacabdcbabbbacbdddcbbacabbdbbbbdcabcabbcdbbcaacbadcdabcbbdbdbbdcdbcbbbbcbdbabacabddaabaabddcadcccacccdbbadbccccbdbddbabcdbccacdaadbcbbcdddadbbaddcadccdcccccddbddbaadaddbaaccadcbccaabbcbcdaaaacbdcbdaadccdadcdbcabcbadabadcbdadddbabcacddabcbbdbbdddcbdcdadbbdacccaabbdccbcccadcdcaddbdbaacdcacdddbdcdadaccaddacbbbddacddccaaabadbabbaabddadadaabbbbacbdabcacabccabcabacdcadcacadddabbdbbcabbbaabbabddbbbdbcddbcaadadbadbcbbcadaaabaddabdbbbbacabacdcbddaddddadcbcadbabcabbaacabbbaddcbaaaccdbacabddcaccbadcccbacacabbdcdbcccbdcabbadabcdadbdbbcdbaddadcaccbdcadacdcbdbcdcdcabcdbddaabcbbababcadbdabddddabdbbbcabadbaddadccaaabcbaadaacdbcbdcdddddcacaddbbbbcacabacadacbaabdcaddabbbcdcadbcaddbcbccdcddacddcdcaadacdabdcdaacbbabbabadbbacdaacaccacdcbbccabcdbdcbdaacbccdddabdbababbcaacaccdaccdaaaadddccbbdabbacadaaadcdabdbbbaddcdcbdccbcdbadcdbcbdddcddcbbadcadcccbcbadcbccaadcdacdcacaabbcdaaaaddddadcdccbcbacddbbbcdbdbbdcbdccdadbcbaddadabcdcaddbdaadbbbaababcacbaadbcccbadbbdaacbbcbaabaabddadadbadbabacdbbbcbcbbcacbdbbbcddacbaabcbdacdacdccbcbaddabccaddabcbdddccdcaddcdbcacdbcaacaccbcbadbccabaddbdcaaadccbacbaaaacaaacabbbcaddabacdcdcdcacabbaacdbdbbdbacabadcdcddcdcbbdccbaaccadaacaabcaadabddcdadabbdbccbcccbcdbcacacbadbabdbdaabdbdbabcaccbdcdcbdbccbaaadabccdbabdcddacbdddbccbdbdadbdcbddcdccbdaccaadcaddbddbacadbddabababccdadccbddbdcbaddcccdddbddcbdbccdbdabcdaadcdbbacbbdcddccbabcabcacdbbbdcbcadaacdbcddadadcdadbdaddaaaddcacaddaadbbdcdacbabbbdaddadcbdaaddddccaadbdadadadbccbdacdbcacaccbadcabbaaacbccdcbccdccacabdcdbdbbdbababbacbbccbbadacccdabdbbcdbdabadbbdbabbbadbcaaabccacadcdbbcdadbadbddbdbdddddcbabcbdcacdcbccddddcbbbadccaaaaacdbccacdbabbdcdbdbdacaabcdbdbccbadddbdbacdccbbdbacdaadddbbddbcbcdddbaddabbbaccbbdabccadcbddadccdddadbcbcadcdacbbbbacabcddaccdbdbdcaddccbccaacaaaddccbcbccaccbcabcabdadbcbdaabcbbbbbcbabdabcacadcbccbbadcbaaccdcacadccabaabdcdaacaabbabacdccdcdcbaaddcacacbbcabdcdddadadaccbdadabdaccdcddbbadaabaccdcaadbdaacbdbcbcaabacadacabcdcbcadcaadcbbbabdcdadddcccccdccdbccacbabbcaabddcdbdcddddadbcbaccddaabbbdddbbcaaccdaacadbdacadbddcaabbdccbddcdcddbcbbbdbddacbdccdbaddbcdbacacdaacaadaaaabcaddbbaabacacdabdabddaaacdddabadbddbcaaddabbdbacaadbddcbaddcabcadbdaaccdabbabccacbddbbbcaddbcaaacbaadbcaadddbddaddccdbbbabdcbddcaadbcabcaaadaaaabcddbdbcbcbbaaacccaadbaadbcbaaccaadbbdcacadadcaadbaaaaccdbbadaadddadcacdcdbdadadcabdcccddcabdaacddcaddcaccaaabacaacdcadadcbdadadcbaccddcddcdbbbbdccdaddadbabcaaccabcaabaddcdcaaaddaacccabdcdbbbcdcabbdaacbbbdbbbacdcccdbacbddacdbdabcbcacdcabadabddbcccbcaabdbdddbcbdadbdcdbccaccadaccbbdbacdcacadcccbabcbcddaadbdacddabbdcbddacacdaacadccddcdbabaddcacbccbcdaddbaacdcdbbbdcbbabbcdbbabcadadababbdcbcaacbcccbddcaaccacacaacbcdcdccdcdbbcdadcbdccccaaabdadaccbbcabcbbbddadabddcaccaacaadaaddcdddbcdcdabdbbddcabdcabdbbdcbbbddbbbdabbddcbabddbcbddadddadaabaddccdccabacaddcbadaccdaadcaaacbccacccbbbdcabbdaddacbdbacabaacaabcddbbabcbbbababcddbdcabbaacbcbbcdcdadabcbdddcbcaaacdbabcdbbacdabddabbbaabcacaaccbaadbadabddbddbbbccdbadaccdddbcbcacbccbdaabbddacbaacbcdacdbdaccabbdcbbacaddbddbadbdbbbcdbaabccdbddccbccacadaacbbaccdbbabbbcdcdcdbdddaccdbabcdcccbbbbcaadccabccdcabadacabdbdcdaabdbbadbdaaaccccbbbdbcadaddadcdbbaaddbdacacaadccdbddbbdbbdcbaadddcccdcccdcbcadbaacbbbdcadcacbaadcaadbdabbdabdcccaddcaabbdbddbbabdbbdcbcccbacddbdccdbbaadbcbcddacdabaaaaababcdcadcbabdddddccabbccccdddacdbbabbddbbbaddcdcaddbadcddbbdadccaabddddcdbbdabbdbbaacbdcbdcadcccccdbdcdcdacbabcdbcddbbcbcabacabaacdccddbbaacbddcbabcacdcbcdccbabddddbcbbbcacacbdcacacbacabddcaddbbabacddbadddcadadcdbdaabdacddcddbbcbbcabaabcaadddddacccbabbdbacaddbbdaddacaabccaaddadbabbadaabdacbcbcdbbddaccdaccdbabcbddabccbaaaacbbaabbcdaccadcdccdaadbcbdddcabcdabddcdacdbbadadbbaadabacdbacbdccacdbaabcbbcdcdcbdcdabdbbdbaabaaacaacdaabacbcddadbbcdcdbabdbcbcccdcbacaaaabadbdabbbdbddbadcdbadcbabcbacaabddcccddaabdcddaadcaacdabddbbcccbdcaccddbacadddbbddbbbaaacccabcaacacbbacadbdacaccbacbdbcabacbdacddcbabacdbdbbacccbddbaddbccddabccbdadbcadacdddccdacbddbbcdccdcccacccdadbdbaaccadcabbabbbabdccddbdabbcadcbcddbabbdabccccdadbbcbbdddccccadcdbbbcaccaccadddcccdcaccaadccdbbacaabbabcdbdcbdcbdcccdddcccbcdaabbababdcaabcbaaabccadcacdcdaccbdbcbcbdcdbcdcdabdcaaaaabddaacadadaadaacbdbbdbbaddaddbbdabdacdaddccacacbcbaabbcdcdcbcadabddcacbbbabadacdacdaadbbbcbbdcaacdcbdcccccbccacbcdcccbbbbcadddcabbbadddcbccadbabddccacadccdadadaabcaadbddabcdaaacdacbdadacbdbabcddddcbdbaabbccacbacadaaacdabddaadaacdbbddbddbdbadcdcacacadaaacbaadddbddbbcdcbbcabccaaacdddcadcaddaccabddbbbabdcdbddccadbdbddccadaaabdadbddabbbacabaacaaadddaadacdaadcddaddbbbbbadcacdbdcccdbadacaddabbbbdddbadadcaccbaddbccdcbbcbbaabccabbcbacbcacdbcdddaacdcadabadcbddcabcbcccaddabbdccacbddbbadaacdcccdaddcbcadcadcdabcddbddabddddbaccdacccdccabdaabbdadadacdbadacdcacacdbccbdcddaadadbdbbadcbcbddcacacbdcdcbdccbaadcbdacaacabcdddbbaccdadacbaacdddadbbadbcabbbddbbadabdcaadbcdccbcaddbbcccaaacaabdcaccabccdaccddbbbcbdcdacbcaaddddbbadbdbcacbcbdbdadadbddacabcccacdbabcaaccccabcacdddadbcddadabbddaadbabdbadbcdccbcdadbbcabbabacdcddabccbcbabdadbaaadaadacdbddbbdbcacdbcdacdadabcbbabcabaaccadcddadccdcdadcddbbcabaacaadbbaadcbadbbdbaaaabdbbbddcdddcddbacddcdcdbbddbadcbcadaaccbbbabdadaaacddadaaabaacdcadddabdabaaaabdbcbcdbdcbabcdaccdaacbcbaabccacabbccccbdabadaaaccadbadbbdbdccdcddacddcdcbcbbdaccdbdaadacdbacbbddbadcacdabadbdabababbabcdbcbbbcccdbbcadcbdaadcbbadcabbccaacbbadcacddacabdacbbdcddaddcccbdbdbdcbcadacaddcbacabcdbabbdccadcbbbdcbdbbbccaabaabcdbabadcbabcadccdadaccabbddadbcacbcaacccadadcdbdaacbbacdbdccdbcdcdbaaabbabdddccbbcabbcdabcdcaaababcdbddccbdbbaddbbcabcbbdbddadbdadcbadcbddbbcbdadcbdcacdcabbcdaaacbadccddbbdccacdcaacbabcacabbcbaadcdcddaccbbddcbadaaabadbccadcaaaddbaddaddaabcccdacdcccccdacbbbcabaabaddacbcaaccabdbadccacdbbcadadcbcacbbdaabbcadbbadbdbdbdbdcbdcabddcbcabababcaacbddaaaabbcdddcbadadaddccadbdbaccbaacdddbbcccadbddbbacaaacbddbcdbabacaccdbaadadcbddadbadcdabcdabbacbbadaabdbddcbaccccbcbdddcccddabdbbcdbdccdccaccacdbbddcdcdacaacdbbadccbbacccdaccbbaaadaacabdaccdaddacadccbabdcdaabacadcaccdbbbcbaacbdcbddaddabdadaccbbddbbadbccbbbcbcdbdaccdcbacbadabddaadadbadacaaadcddabcaaaabdbdbdbaadcdabdbddadadccbabbbbddcaadcbbadbaaababbdcbacbbccbdcadadcabcbcccbcaadcdbdcdbcdacddcaabbdbabcbdcacbbaacacbddaddcdddbbccacdabdaabdcdcbdaacbcbccbdcdabccdababddadcdbdbaabcabaabdaabdbaadaddacbcadaadddddbcaadaadabdabddccbcabccbabcdaddbdacabbaacbaaaadaadbdcbbccbacabacdddbdbbbbccaccadbbadacbaadcaccaacccdadaadbacbdaabcaababccbbdabcdddacbadbdbddcdddaabacabcddbcacbddbaaadbdccacbdaaadaccdbaccdaccadddadddcbdbbdbcaaaaabdbcdacbdaacbbadbbacdcaaadddcbaaaccabdccbcbdcbdaddaddadacbbcacadccddcccddabbcbbccdbaabbddccaadadbabbdbababddccaacbaddaaabccadadabbabbdbbdddcacacdababcadcacbbdbabdbdacccbabcabdbcddcdacabaaaaabaabccbccaddabddcdacbadbcadcdadcacacddccaabddaddccbbdaccacdbabacaabddcdaccbadacbaacdcbcaddbacbbccbdbdcccbadbabddaacabddcdcdaacddbaaccbdbdcdbdbaabcddddbdddbabccbddcdbcbbbadbccaadcbadbcacabcaacabadaaddbddddcbdaccaaacbdbbcddadbdcaccdccaacdcbccbbdcbaddcdcdcabbcadbbcccddbdacaabbcbaadaabccbdcacddbcacbdacaaaccdaccdbddcbcabdcabcdbabdadbabcadddccdaabaabcbabbccdbbacabdabccccbaabbdaaabdaaddbabccbdcaadbcbabcbdaddadbdaccbcabbacbcacdcbbaaacacabbbbbdabdbdbbadacaacdabcbbbccdacdbbadbdacbdbcbbadcbaadccabdacadbdaadacadabbaccbbcbcbdbddbadccadacaccaaccabacbdbacbbabbcdbcdbbbadbadabbabdabbcdabcbddabcbcabacbbdcbcdacdbabadabdaadacdaabaaddacacbbcbcbcbacdcbdcbadaaccbbddcbbcacddcaccddaddadbbaccabadcbcdcdcdcacdddbdbbcdabcdaadcbdadcabaadaaaacbaccdddbdcdcaacdddcccdbcbcbbdabdbbccadcabbccaaaaabaadcacacadddcbcbbdadcbbbdcbbacacbabdcbdbbabddbdaaaadacabbbdcabdddaddadcdaaddbddddbcdbbbcdbbaaccdbcddddaccaacdadaddbacbdbcddaaddbcadaababaaadddcbcaabcdaabbdcdbbdbdbccbdbdabddabbaacbacacabdcddbaaadccbdcacbcbddddbbabbbbdcdcadccbbcbcdacdaaababbddddbbdadacbccdadcbdabbadccaadcacdcdbbaccddcabbdbbbcaddbcbadabaabcbdddbddbcddbcbbbabbdcdadbacdddcabbddcbacbdbcdaaddcdbcabdaaaddcbddccaaacaaabcbacbdbcabbadbacbddaaababcccabdddcadadbbadbadadcdabccdcadbacdaabdabcaaddbacdbcaadcdbabcbbbbdaacacbbdacbcccacdcaaacdbcbdadadcddabbcabdddbacacbaabcaccabdccdbcdbabcbdadbddaccdbcdbcacbaaabbcaccbbbbacdddcdccacbaabacbbdccdcdbbdccdbaaccaabcbddcbbadcddadcccbadaaddadabdadabdbccacbbccaddddcaabadaadddcdccbdcdcbbdcaccdabbccacbbbcbbdabdbaccbbccbbbcaaadbacbbdbccdacaddaaacaaadabbbabbbbdcaaacccaacbcdcacacbdaacacbbdadbddcacdacccaacdccaccadaababdbadbaacddbdbacadabbcbcdadbddbbbaaabcbcdbadccbcabacbdbadacaccbacccacccbbcabcbcbcddbdcdabcbdbcdbadcccacacabcbccddadadacaccabbdddcadaccbcbccbddbdaaadccaaacbacdacdccdcaaddbbccacadaacbdbdddbcadbdbbbdaaddadcaddabccdacadcbbadbcdcddcabcdbbdbdcdadbcadcdabcdaaababbbbccbcddbaddcaaaaccaaddbcabccaacbcbdbcbbdabbdcdcadccbabbcdcccccbbabaccbabacccdbaacdacdcaacadcbaadccaadcbccbdbccbbbbbacaacabdadcdbbdacddbccbddacdbdbbcdbdbbbabcabadcdacababdacdcaaabccbdcddbadbbdbccacdccdbadcabbdbdbcbbbdabbdbcadaabbabcbbaddbadccdbdccbcaccdbacacbbbbbdbacadbbddcdddcadabaaddacdbbabdcdbdcccbccabcddbdbcbdbcdabcaaaddabbdbcbcbbdadcadcdbbabadcccbbcbbbdabadbbcbddcbddbbabbccccdadaabdddbcddcdaaadaabdabbbdbadcaaababaaacccdccacdadabbdcbbbdbdcbbcccadabbadcbcddbdbadddabaddacbbadcacbabbbdcdddadadbcbcddabcbdbbddabdcbabddababddccdbcbcabdcbddaacddddcbabbaadcdcdaaddabdbdcbbccddbbcdbdddacdbdabbdddbbbdbcabddabdcdcccababbbaabadadaabacaadacabdbabdaaabcaaacdbcabbddcdcacaccdcadbbbcbcccbddbabdddbdcbadaccbddcdaccdcacaccdbaddbdbcbdddcabaadacaaadabdacddbacdabaadabbccaabdadddaabadbbbbdddcdaabccacaadabccaaabdcdcaccaaccdcbcbdabacaadaaacdbcbadcdbabbacbababdacdabdccabdccdaabcaccccdbddcbbababcccdddcbbbacdddbdcccbdbdcdadcdbacdbccddcccaaabbaddabacbbdaabddadadccbdcbabaaaacaadcabaccdbaadccaabccbcbaaaacaddcadbcacacdbaadcbddaccdbbadaaaaacdcbcbaccabdacdcaccdcbdcabbcdacaacbbbbddddaacadabbcbabcdccdaaccbaadaabdbccbdbaccabcddacbdadccadaaaccaddcabbbccacdbdabbcabaabaddcdbdbdbcbbcdbcdbbdcacdaacbdadaddcbaacccbdcabdbabacdddbbddbddaadadabddccadabccdabadabbbdbcdacabdcdcdaddcabbaccbacdccdaabbbdabdcacabbbacbbcabaaddbdbdabdbacbcdcbbacdaabcccacccbadadcbdbcbcbbddbacaacaacaaddcabcdcdabbbcddaabbddbcabbdbbacabdbcccbbaddccdacddbdbccbcabcdbccdbbacbdbdddbccadddaadcddbccdcbaaabcacabbadaaddbddbcddccccdbcbccaaabcbcbdcaaabbddbcbcaccbaddabdabbbbbddddbcacabdbbcbdbdcdadbdadcaaaddbadadadbbdabbbaaabbdbabbcccabbcbbdbdbdbdcdaabddcdcacdabdacbbddbcacbbaabccacbdbaacdbcadbddbbcabcbdacabdacdacdabadbbbbbababddbabacdabddcdbdbdcccdaacaaacaaddbbccaadddcaabddcbccccbcbdbbaadbdacaadcaccacababbddcbaabdbcdbbcaabdbbccabcbbbddddcdbbcaadbddacbbdadadbadbdbbabcbbbcbbdacdcdabaaabaaabdcddddabbdcbbacabacbbabbbaadddddaddccddcbcaadddbcaccaaadaabdbaddddcbccccdaacdbabdddacbaaabdcadacddaaaddabcccccaacdcaccddcadbdbcbcadddabddbbacaabcbbddccdaadcbddcabbaddccdcbccbcbbdadccadabbacbabbcbbcccaddbcbbadbaacbdccadadbbddcaadadcbcbabadddacbbdcbabdadbcdababcacbacddcbdaaddbcaacdcdbdcadbbababccbabababcbcbbbaabacdadccccccbbccddcdcccdbaabdcbdaabbaaccbdabddcbcacaaabbdbcdbdbdcadaaadccadadaabcdadcccdbaadbaabbadbacddacaaacbcabbbbcabdbaddaadcaaacadacaadcabccaccbadbadccaaabccbddcadbbddbaaaddbaddbadabdaacaabccdbbacbadbcaacbdadcdccdabdccbccdbddacadaacaabdcddcbbddcbcbababaacdbadcdacdbaccdbcadbbccadbcbddcdbbccdcdddaaaadcddccaabbcbdcccabbaaabbbdcdbbaacddabddacddabbbcbbdbbddcddcadcdacadadbcccdddacabddbcacbcbcdbbbaaabddddbacccaaccbabadcaaadcdcacbbbabbddcccbaabddcadccbacaadcabbccadcaabddbbbdcdbcddaacbaacaadcbbadbacabccacdbbccaddcbbbcbadbbdddacdabbbcdaaccbadcbbaadbcdddbabacddbabcdabbdbbddbdcadbcdcccbacdacacdacbddabcdbbcdbbcdaadadaccbbadbaacccbddadcaadbbbdadabdadcdaccacccacddbbccbdcccbadaaaabcacddcccccdacccddadbdcadcaccabaddacbbacddcbaabbcbdcccdbdcbbdacabcdbabcdcddcddbbcbcccccccadacbbbcacbbdacbadbaabdacbbdbcbaaacbbdabcaddbadddbccccabcdcbccbccadababbbccbdbccdabbdaadbaadabacbcdbaaddbbcbbdbcdcbccbdbdbddcabddcaadaabdbbddccdcdbcbcbcbbdbdbcadabcccbcccdbbcaadbaaccaadabdccdccbbacadddbbcdbcaababbcbbbbbcbdacccaaacdaadadbababbddcbdbacadbdddddcbbbcdcacbbacdadaccadcdcacabbdbdbbcdaacaaccdbccbdccaccdbccddabcdcddaaabadcdaccdbdbcadccdadbddbdcabaabcabadcdbddaaccddbdacccddccbbcbddcbbcabdabdcbdcbcdbddbdbdcdadbbaccabdddcbcabbaacaacacacaadbbaaabaacacabbcbdadacabadbccadbbdddbadaabdbbabacdddabdcbacadbbabbbacbababccdadacdbacbbaacdadbdbaaddddaadcbadbcbbaabbcabaaabdacbbaccabcbdcdadcbbbbbbcaacbcddbbaddacddbbdadadbadcdbbbbabcddbccbdadacbbcbbbcbddaddbadaddbdabdadbacbcdcadaaddbbddbbaccadabbaabbaaadbbbaacdcddbacdabbdaabbaddadccbabadacaadabcacbcbdbdbabdccdccccddaabbcadaaacdcacbdbbcaacddacaccbbdaaadbccdccccadcbdacccadcdccbbddccbbbdabcdadbcbadcdddbcdcdaabdcadaabdaaccccdacdbcbdabbbaabcccaddcdadbdcabbabadbccabddcacadaccacbbdcdcbcaadacbbdcbbacbdcdccbbadcccddaddcdcdcaaaacbacccabdaaadbbbdacacdaddbdbddbdcddcdcbcdcdcbcdaaabcbaccbcdcbdcaadaaacddcbbacbdacdcddcbacadbcccdacdcbabaaaabcdcaaadabbdbbdcbbadbaaababcbbbaabaccacadcbbaacadbcbabcacaadbdbaddbcdabadccbccabddbddcdccbacdabacdbbcccbacaabbadabdcdccbadbcdbaaaddbbbbcacbddacbdbbbdbdcbdacaaadbbbccbcdccabcabacddbccaccaadcdbddbcbacbbdccbcbcddbadaababbddbdbacdcaacaddbadccbdbbbcccbbbdbbcccaaacccddaacadcabdbadabddacbdcdbbdabbccdcbcdccccbacdadaaadcdaacdabbaabcddababdaadadddcacabdddddcbababbddddbbbacdadadacababbcbcacdaaccdbcbbadddbaacddcaddacadcaacaaccdacdacabddccabbaadcbbabbcddbabbbccccacaaddbabcabccdbbcbadcadacccddbbdcccbaacadbadcdadbcbccbabddbacddcdccadbddbcacdcccbcbbcabbcbdcabadadadcacaaccbcdcadaaacbbaadaaaaddbbddcabbbbdcbbddcddababacdcaacdabaadacabcccbdddbdccdaabaaacccdcdcbbbddcbbacababccaccbbaacbadbbbcbcbbaaccdcddabcddacdbbdbcbbdbbacdcdacbbdcbdbcbbadcaacbcddcbadccddccbbdbbbdbabcdadbccdadcbaadbbaabadccdbcacddacdbcbddbdadbdddaccbbcaaadadddaadcabdccddbadacbcabbccdacbbbcddccdccdcbadddbdbbabcadbddaaabbdcccbacdbcddddbdacbbaacbbcacdbdcbbbccdbacbbcaaacbbbbbaabbbabacdbbbacccabccdabdcacbaddadaabdcacabadabccddabacbacbdcdcdddadbcbdcbdccccacccbcbddacaaaaaddabadacaccdcccaacaabdaabddabadddcbaccdbddadbcdaadcdbbbdcadddaccdcadadcdcacdbccaddcbbbbddbbdcbaadcababdabacddcacbccbdbabacaaadababddaddaddacaabcccdaaaaddabcdabdddddcacdbdacaddaddbbddbbbdcbadaaaddacacbbbbddcadaaddccabccbccdbdcadcacabbaccbbadabdbadaaccbadadcadbaabdbcdcbcdbbbddbacaadbcddcdcbdbdbbadcacddbbbcddcbacbcdddbbdccdabdadacccccdabcbbbdadcccdcbbcdbabaacbdcbcabbdcdbacbcdcaababcbbbdabddddcdbbcaddcbcbbdaaddddcbaadcacadbcabbadcddaadabcbcdaacadcbabadaaacbdcbccadcacccbcbcaccdcdadbbbdcadbbababddddacbaccddcdbacdbccaaaccbababdabbcdddcacadcddaacbddcddaadcbcdaddbabdcabdbdbdbbdadacdcdbcabdcdcbbbadabbbccddcbdcddccccdddbdbbadddddaacabbddbdbaaacbacbdabcdcaccabacdcddbcaacaacbdcdacdddabadadbcccccbdbdcbbddbdabcdaaadbcbabacadbddcbabcacadbcadbbacabacadacacadcaacdcbbcbdddbbcbdddcdaccabdbdabcbcbabadacabaacbcdbcbcacdaacdabbdbdabbacccdbbaddaaaaaaaaacacdcdbabbbdcbdabdaaabdddbbaacdcbbadbccccacddbbadabdddbdabcbccaaddcdbdadbcbacdaadaadcabacbbddcbdacccdbcdddbbcbccdcccbaabdccdddcbcccdacacccdacacbcdaaabacdacadddbbcccbbcdbbdcacdcaaabaadbdbbdbddbdabadbbddbabadbbbdbabcaacdbabdddabccddbababdacbcaababccdbcdaaacbacadadbabdabcbcadbbcbacdbcaaccdbbadaacacccccabdadbcdbdaddbddabcdcbcccbcdcdccbcdadcdbddaadcbcbdabdabddddcabaddddcbabdcbddaaaccbadacacdcdaaaacbaddaabbdadabccdabbdbbbcdcadbabbccbdbdaddcabcdbcaabdabbcdbaccabbbbbbcbcdcbddbabcccacccadbaaccccabbbbbdccbcdbbdccaabcccacddabcbdbbcbccbaddcbadbcadcaddddbcbbddcaacadbcacbaccbaadbbbbdbadaabbcaacacbcbcbaddabdcbdbddacdaccccbaccbbaddababdbcaaadcdbbcdbdbccdccadabcdcacdbcdcccdbcdbacabcdcdcaabadacadddcbadadadcddcacaadabbdccdaaadcdbbcddbcbaabaccddacbaaccbacddcbdcbabbcaaddcadbbdacbcbabddddbcacdcdcbabbbcaacadacaccaabcabcbcdcbdbbcbadbbccaabbdbddacababadadbbccddbdbbdcbcddabccccaddbaacaddcbcaaddadadbdcacabddbcbddaadddaccacbddacddaddbadbaabcddbdaccbcaaaacbbdaadccbccadddccaaaababadbbcdbcbdbcbaccaddbbcbaadddcbaccccdabcacaaabccacbcabacdcadcccbbdcbbdbcbddabbaacaaccddbdacbbacbbdabbbdacadcdbdadcdbbbadabaabcddbacddcdcacbdadcddbcbadabdaadaadaaccdbaccdbbacdaaabdccbbcbabbdbabaadcdbdbaabcbbbccccbbcddcccbccabdbacabdcaacccbadacbdadadddcbbcbdbadbbccdadcbdaddcddbdcccbdbdbacdbdbbddaabadadaacbccdcbdccacccacdcbdbdaadcaaacdaccbdcaddbddbdcacccdbbaaccbbcbbadcccbddbbdcadddbddddbcaaddbdbaaccbdbdbddbbcbbdaadcbdbdcadbddcadacccacbacdbbcccdccbcdcacacabadcdadadcbccdabbbadbdcdbcbbcbbabbbbdcccbccacbcadbcbaccadbacbcadcdbabdddacacbabdcadacadcbdadbccbbcabcdabbcdcacdddcbabadbbdaccbdacddaabcaaabccbbabadddddabddabababcaaabbdcddbccabdbccccdcddbadbbdbaabbdddbcdcaabbadcccaddadddcaacabbcdacbccdaababbaabcdcacacaadababbccbcbbabdbcacabcbcacbdbcddacbacacbcaaadacaabccbbcbdcbabbacbbdccadadccadabdcdcaabcdcdcabbdaddadbcdacaccdbbcbbbddcadbbbbbbcdbdaadcaccdaddabbcbdbaacacabbabbabdcadddacacbcacdaacdddcaacbadcbddbdaaaabdccbcdbbaaacbdabbbdaadbdbcadcabadcbbddcaaaadaacabdcdabbcabddabacddaacdccdacacbdadcccaaccadadbbdcdbdaccbdbdbdabcabadadabbbdbcacadcbabccadcbcadcdbcadccacdbacaddcaabadbcbdacdcdcdcbccaadadadcadaddbbbdcccbbaccbcdcdcdbbaabacddabcbcabaaababddaacbcabdaabdaabbcbdcabbbcdadaaadabbaabaaabccbaccccdadadcbccdabcdbbccbbcaaadbdbbdacccccdadbcadbdcbaddbbdcdabbababdababddcdddbdcbccacdcccdbddabbddacadabbbdccbaccbbbdbbdaacbdbdabbadcbbcccdaaccdbdbadbdacdcabccccbcdcabcacbabcdddcdccdaccbcdacdacabdbcaabbdacababacbcbcbcdcccbcabcbabdabbacbcccccccbbcbcadcdcccbdcadbcdcbcbbadbadbddddbbabcdbaabdbcddcbdcccbbcdcddacbccbcaadcddaabbcbcbdccacccaabcacacbbddcbdadbddaddbdbbabdaadcadbcadadccbdbbbdbadcdabcccacacbadcdcdddacbbacbddabddcbcbabaccbccccdbccbcaaabbbbbaacbacbbacabcbbacbcdabaabacbdddbcddcaaccbbcadabadbbbdbdabcadaacacdcacbabbdbabdadbdddcacbadccaaddaaaabbdaaaaacddbdccbdacbbadbcddcdbcbcbddaacabbaacdabcbbdaaacabcccccabbacdacbadbcdbcadbcdbcbcccacbcbaddddabdabbdbbbabbaaababaabcdadbbcdcbbcdcbadbabdcdcbdcaaaddcddacbaabadbbbadcabaaabbbdabbcaacabdcdbbbdadbbdaabcbbadccbcaabdabaadabccaacbdcabbabadcaadbabdababdaadcbaaacdbdbddcdaadbbdbadaccaccbcbbcccccdcacccdccbcbdcbccbabaabaaaddadcabbdbcbddbccbbaadaaabdbaddbdcbbbcdcaabcaabbabbbabdccaacbbdbacbddddcabababdddabadcaabcbdadbccdabbbaaaabdcadaacabcaaddaaccaddcbcabaadbaaaabaaadbdbbbddddbbbbbccdaddcdcccbbbacabaababccbaabdddcdcbbbbdabddccdddcddcdcadaadacdadcbbcbccbdccabcbdddcccbaaccbdddbdcccdddcbbdadbaadcacbaabaddaadaddddbbcbbcbbbbdcccbdcdabaadbcdbdcdbdcbbddbcacbcdabcddddccdbcdcaddabcdbadaadbdbddbdddcbabaaabacdcdddcdcccadcbdcdbadbddbcddacccacadcbdbcabbcaaddbdddbacadbccaaaccddabdaadbaacacbbdcbcbcaadcacdbcddbababacbcbbbbcbacbbdcdddcddbcbdbccccadbccabbdcdaaddcbabaacdcdcdbbbdadcdacadcbaadbaabdbdabcddbadddbbaaccdcbbaddacaccbbddcacdcdbdddacabdaabbdccbbdddcbbddcbdaaadcdabaadccaadcbbbcbbddcabbabbbccadbdbdcbdcacdcadacbdabbcddaacdbaabbdbbacdcdcaadacdbbddabcbbbbcbaaabaacbddcbacbbbabbbdcdddaaabdbabadcbdaddacbcbbcaabbadbcaccbcbbdacccbaabaddbdcdbcadcdcddcbdbcdabaabbddcbabbcdddbbadcdbcabdcbabbccaaacacccdabccbbaaadcacbcddcbcabdcbccddabdddccaaacacddadcdbbccacabdabbabbcbcadaacabcdacacabdbcabcdbbdbddccbdbcdbbcbbbddcdbcbbdaacdbdddbbbdadbaadcccaacbdaddcaaababdadddbdcaabdbbabadcbdccaabbddddcaddaabadabbacbbdadbbddbddaabddddbbabddaddcbdddaaadbbbcdbaaccddcbacdbbcbdcacaaddbbbcaacddaabbbbbacadabcdbcbaccbdaccdaaadcdbbabbdaabcdbaacbcbcaabbdcdaabadcbcbbbcbdbddbcbaabcbcbaadcaddadadbccdbbddcddccdabaabdcccacbcaccbdadcbaaacdcdadaccbdbacbdacadddcddbabbcbbdbbdcbbabcaacdbdbdbaddbcccabbaccaaacaccbbdabcbadbacbacaaccabcccddddbdcababdbcbadaaccdbbdcdacdccabadcccbbccddadcbcbccadddadddbadddddbcdcdbcadbccdcccbadbacbadbabaadbbacacdacbadacbcdbcaacbcadcbaaccaabbddcbbadcbdacbcacabaaadabbdbcbacaaabddadabcdccbdbcdcccabdbaaaddbaaccadcbacacabcdcdaacaabaddddbccddbaababccabaaacbadbbabacdabaabbdcddacbcacbcddcbdcbccbbccddbbadcdabcadcbcbcccdccbbccbadbcbcccdabcdddcdadabdcbaccdbaadbacbbabbdbaaacdbcaacadbddaabadbddaccacddbddcdaacadcabbadbcbababadcbcbdcdccaaaabdbcdbdbdddbbcacabbdcccdaacdcbcdbacdbddcbccbbdbdabbaaadcbbcbdbdcaabbacacacbcaadcbaddddbdcaddbcbbdadcbcbdcadcbbabdddccaddbbcbdcdadadcdaabcdabcdcabcbdbcdabadcabcdbbdccbcccbdbcbcabcababdabdbaddaccbadbcabccccbbdaadccdbddbbadbbbccdabcdbaadbdbacbbcbbadadccdbddcdcbaddaaddccbcdcaacbccbdbbbbbcbbcbcdacdbabbbaadbaddadbadbbbabbadacdaccbccbddcddddcbabddccdbbcaddbbdbdadccaabacbabaabacaadcaaddbaaddcdbcbbbcccbaacbcadbccbbbabbaaacdadcdaabbdbbccbabbbbbcddcbbdaddacaddbaadddbdbdabcaddbbabdaacccccbdaccabcabbbbcbbddaddbadbdcaaabbbdcbcaabcaaaadbacbcccbbcacbbdddccdacbaacacacdbdccccddddbabccccacccbdaaabcadddababbdabdaccaddcdbcccdadbdaccbbbadddbdabcddbcbbdcbccdbacdccaadabddacabaaddcadbbdccbdbcaddaccbabcbbdadccddcdcabbbcbaccbbbcabcbaadccdddcabcdcccbcaaaacbdbacdcbddabddaaccbbcbacdcacbdbcccbdcaddaadadbbbddbbcbdcabdcacaabcdbddadccacbaaacaddcdabbdacaadbddcaaabccbaaddcbaddacddbcddbacabcbdbddbbdbdaccdacacdcddabbccdaacaccabcadbbbaababdbbbcabbdcbbaddbcbdaacdbdbbaccddbabacdcbabadbabbbbdaaddcbddaaadccbccdcccbbbbadbdcdcbdcbbaccdccccddaaacbcbdaabcdcddccbbcddadbccadaadcabdcbcbaccccaddbdccdccabbbbcbdbbaddcdccbbbbabbdacddbaaddabcbbdbccaabcaacbbddbcbdcbabddbcbbddbbdaadbbbaaabcbbabdbcddcababbacaaabacbadbcadcaccbbcadbcdcbddadccdbcdcabdacbdbabcddcadaccacbacbbddbdcdaabddcaabdccccabbdacacbacadbddcdbbbbdcbbdbddabdbaaaaabdbbdbbaaacadbcbcbbbdcaddbccddcbcaabddcadbdccddcbbbccdcdaaabdcbdcbabaabdadaabaadcccccbddacacdcabdcbaabbaccadddacababbdbaaabaadbccbbccbadabadcbbbcadbddacbaccbcbacdbcbbdbccdbccddbcaababddcbbdbddcaaccadacdadcbcabbdbaaaacabdddacbadacbbcdaccaabdccbbacdabbabcddcbcccadaddcaaacaaacbdddbdbdbddbcbacacadddbcacacacdbadbadcaaadcabcacbddcbaadbbacdbdbdadbaccabdbdcbbadcacbabcddcbbacdccacacaddbdaabdcddbacadabcacbdabcaaccbcbbadbbaabccbccbaccdaccbaabdacacdcacdcddabdabbdcccbddadacbbaacbbbddbacdbbdbbddcddabdaadbddbdccabdbcaabbdbdbdcaccddaabdadcdadaadccbadbbabbabcbbcadbbbdccadbcccccdccddcdbacbdabdadadcdadbcccdddcdddbbdabdcdbaddabddcbaccabccdbbadcbbadcbcdbddabccabdbcbdaccbbbcbdbaaacbbcbbaaadccabdbcdabdabbdcccdbbacbddadbbacdccabdadddabdadbcdddddcabbdaaabcbccdbcacbabacadbabcaddacbdbababcacadbabbbccadbadbcdabaabdcdcdabdadaddaabcbbdbacabdbabacbbbdcbcdaabdcaabadbcaadacaadbcaababbcddabdcbbbbaccabbacddabacdcdcdbcaaadbdaaddbdbadbdbdaddbcbbccdcacbadabccacaaaadbacbacdcaabacabdaaaabcbdadcabdccccabbbbcbdcbbaaabaaaccbbbaabaabcdbbadbaaccccacadaabacacbbbcdaccbbababaaccadbdbddacbabacddabacaaaadccacbcbccbcaabddccbccccabdccabadcbddbacacaaaadadaadbabcdccdddbacdaacbcdbbcbbdaabddaaddbdbacdaaddccdacbabacabdacdcbbbbbcdccbdddcbbbccaaadcbadddacaaabbbacbdcbadbbadcaaacdacadbbccdddccaacddbbdadabbbcddaacababcdbabcabcccbdbaaabadddadbccbaabbccccdabdabbddaadbcbaaabcbcadccadcccddcccbbdcdacbabbbbcddbcdbbcbaadbcccaddddbbdcbabbbdcbcddbcddcccbbbcbabcacabbaadccbcbbcadcbdbabacdbabbdbccdcccacbcbadbabbbdddcdacbbdadaaadbdaaddcddaadcabbacadababbcabadaaacbabaabdabadcbcadbbccddbadddbaabcdcbddbccdbdbddcbdaccdabaadddccdbbdbacbcadbdadbdadaacabadbdcaaabdaacbdcdcaabbccccbcacbddacaacaacdcdcbbaccdcbdaabbcccaadddbacbcdbcdacaacdbbcacddddaccabdbddabdcbccbdadbacabccbadcbddcccbcddccdbadabbddaddbdcddcdabcaaaacdcccacbdcbbdbdbcbbabacdcdadbbcbdcdbbacaccccacabbaddbcadaababcdbdadcdbdbabdacacbadbdbaddcbcbbdbccaacccaccdcdccdadcabadbadcacadbcaabcadcaacabcaacdaadbcaddcdcdcdbcddbccdaccaabcdbcdbdcbbcddaacdbdabaacbacadbabbbadccbcabdabcdcacbabaadaaacaadbddcccdbcabcdbabbdbcbbcbdacdadaddbacccaaacbdaacbabacddcddccdcccbcbbacddccaaccdadacdbbcccbdaaadcccbddcacbbbabacbbcccbaaabcbadcbacbbaaaaaaabaddcabdcdcaaadbcccaddcbaabccbacdaddcbddbdbabacabbacbaaddcaabbcaadbcaaaaadbddabaabacbabacdcddcacacaababbbddadbdccbbaaddbdbdaaddcddcddcdcbdcdbadcbcbdcdcccdbdcdcbccaabbabbbbcabaabbdbcbbcbdbbccbcdbacdddcbbdacbaadbbbccddbdddcdcbdadbadaabadbccdccccccacabbaadbcacdbccdcbbccabbbbbaabcabbcdbcbccaddccbcddcacbccabccbcdaccccabdbbcdaabbabbcaaababbabadadcacaccdcaaccbcaabbdccdadaddadcacbbadcaccdcdaabbdaabcdccdccdabdbacbbbabbaadabdabdabaddccdccdccbbdccccddbcaddbcccddddbbcddcdbaaaccabadbaabbdcddcacacdbccccdaabbcdacbccadcabbbbccdddacadadabcddaccbbacbaadaddbaabcdbacbcbadcdadbabcbababadbbbbaabdddcbcbaccaaacbacbddaddabdcacbcdcdcbddddbadccaaacbddccdaadbbdabdbbbadbabaaccbccbcbcacbbccabacdbabbcaabaddbabbbaadbaadabdadbcaabccaacdaccbcccabaaccdcbbdadbcacadcaaccbabbacaaadadaccbdacdcacabbcdcacbcbcdbddcacbabbbaabcbccadacddbcddababcddcdddacaddacbcadccaaddaababcdbbbbabcaacbabdaddddcacaacdddccdcbcbbccacabcccaacdbcabdabbcbcdabcbacddacdcdabdccaddbbdbaaaaadcddbbaabaccacbdcdbdccbaadaabbadddaaadcbddddddbcbabbadcddbcaddcbbdcdcdaccbdadaaabbbcadbacbaddbaaadbdbbdbadaaaddabddcdacbdaddbbcaabbacadbcaccaadbdaacdcccaccdadabdcadaacadbcdddddaadcddbdcaacdadadcacaacadddaabbdccdddaccaccadbbdddbcddcacbbacbcbcccbcabadcccbbdccdbcddbbcabbaaadacdbdddadcacbcacabdddbbbbbcdbccbcaabcdacbbbbbacdcadcadbabadbdaabacdbabbbbacddddcdcbdddcddbbcadaaadbdaddcdabbcabbadcbaacacabcadbbababacccdabdbaadadcadcabbdddcbcdcbbdbacabbdcbbdbcccccdacabcbadaaabdddccddadbbccbdddacbbcccdcaaabccadcbacbcddbcdbacbabcbacddcaccadbbabbccddabaaadadabbccbbdcaabbaaaccaaadaadcbbabaabdcaadcbadcdddcdacbdaddccbdadbbbbcadaaadababccbbdddadacdbbcbddbcbacacadadcdbbdccadbabbadadbdbadcdadddbbaacadcccaccccbdccaddddcbadcdcabbdddbadcbccadbbadbccacabdbbdacaabcdaddcbbdcbbdadaabbbaacabbdcdadbabdddbcbaaaacaccdddbcbccacbbbbbcaaccdcdddcabbcbdcbcdcbdcdbabdbbbdaacbbadababcabdacbaadaabcbddccdaaccccbcabaadbcacbccbcacbcddacdbabaadccdabbbcaccaadcadcdacccccadcbcdcdcdabcadccdddbabcbbbdacccdbdcbddacbdadcdcacaabbbdbdacaadbbcccccbaaaabbddcabdccddadbdacccbcccabbabcabbcbcdabdcacabdbdbcbbaacadbadbdcabadccbcddcccbbddbbccabacadcaddaccababdcaaadcddbacacbcaabaccabacddadcdcbccbddbbaadaddbbcccbcccabddcdaaaabcaaddbdadabccbdddcdddcccddaaddddcdabbdbaddbccabadccccbbbaabcdadacabcaacabcbbcdcacbbaadbadaddbcaaabacbcaddbdaadcdcbbbccaaadddadadcbaabcadacdadddaadabdbabacdaadccbaccbbacccdabdacadbaadabaaacdcddadccddababaabbcddadbcadaddbdbdcadbacaadddacbaddaadcbdbcacdbacaadadababbacdcbcbbdacdcdaaadbabcccbdbbcaccdbcaacdadcbaaccbcadacdbacaabcbaadabaddbabcacabacddabccbdaabdcbddccbbacdcdbcaccacacdbbbbabbcbabaabbcbabdabbbbabddccccbaaaaccdbaddbbadbbcacbccdbabdddaacbaccdccabdbccdcabcaadccddaadcaabcdcaddbbdacdbdabbbcbaaaabadcdcccaacbabaccdabbbccbacddccbaacabacbbdaadaadacccacbccaabaadacdbdcccdddbdbcbacbcbbadbdbbcadacdccbdcdaabbcdcbbbababaabdcbcddaddabbcddbdbddcabddccadcbcdccdaddabddbbacadbdcabaabdabbaaccdabdcdbcccbabadccabbbccdacddbccaacdaddadadcaaabdacbaacadbcbdcaddaacdddbcadcbacdbcdabdacdbdccdabacdabadaaccbdccdababbcdcabcdcdbddcdaadaabdbcaccbbbadbadbddbacccbdbdddcbadacbacaadbcbaccdcaadadbbacbdbdbdccdabaabdbdbcddbabdaadbbabdbabcccbccdcdbaadabdbabcdddcbcdbcbacadcccdbddbcbdacddbdcdbbaabaadcbcadaabbcbaaabaadbdaacbbcdacdbbccdbcdddcadbbcddcadbaacbcdbaaabadbddbabdcccddabbdaaddcddbdcdcddcbdbcaabcbbbacdbcaacbdccbdbcbddbacbbbabdbabdbbcdcdbbdabbdcaaddadbbcaddaababbccdadadabdcbdcbdacacdaddcdbaadaddbdbdcdccdbdcccadbdbddaaaccdbadbaaabdcddaabbbacabcdddacdcddccddadbdccaacadadabdcabcbccaaaccaabdcacdcddcdcbabadbdacbabdbbccccaadacbcadbbbaccabcdddcadadbbbcadbddadaabacbbbbdbcdaccccbcaccbbcdcbcaddbabcbdbcaacbbaddadacbabbaabcccadaaccbcdbcbbbcdadbbbddaacaddacdbcdaadabcbbccadccbccdcaddcabcdacacdccadadbdbaacacacbdcdcabbbaacdbbadaaacbdbabaacbddbcabdbaccccdcbbcacbbbdabbadabddddbbdbaddddacaaacccabaddddddcbcabaddcdacccdbabbbcabdbbabbcaadcddddbadcbbaadacdadddaacddacdaaadbbbdbdaccbccdcaaccccaadddcabacaabcdabcbddcbdcddbadbaaadabbdbcccacdaabacbbdaddadadddbaaadbabbdaacddbbddadcabcbdccbdbdaccbdcbdbdddaddbbbbbaaaddddaddabbddcbabbcdbbccdcacccbbaccaadcbaccabcbdaabccbcdbbcdddabbdbcbcbadcaccabdccbaabadcdaccccdbaaccaabcabcdbcbbbacbdbcbdcbdbdcabcaacdbddcccbbbccacaabbdcaaadddcddcbabacabccabbcbdcdcbcdabcdccaabaadaacdbcbcdacdcacabccdcbcddcacbcdcdddadcadbdbdbaaaabacbbdbdabbbadddccbcdbbcbbbbbbccadccaaccacdcaadbbcdabbbabcccdcddacacaabaadaabacbdbaaabdadbcbbbcbccccddcaacbdaaadabddcdcccadbdadadcacdacdccadaabcdadddcdabbabddabbdaabdcadbcbccbaacaccabadacdacdaabbcccdccabacbaccadbacbbbaddbcbbdabdcdbaddcdacdabdadcbdbbcaaccadbcbbabbcdddcabcccdaabccbdaccdcbdddaababbcbcadaaadcdbbdbdacdbbbbdabbccdaddbcbabcdccbacdadaaaaacaaacdbacdaaadaddbadaacbdccdaaaccdddabcbccbdbddadbbcadaacacabdcdddcbaadabadcadbbdaabccbbacacabdaccbdbdcbbccacbcaacdaaddcaaadcdbbabddbaaadbbbabccccdcdadabadbababbadacdabcacbccabcacbaaddbacdacbdbbdbdaddaccaddaaacbbbacbbccbbcbbccadddbcadbdbbcbcdaacbadabbddcddaacbbdbbdbabccbccbddddaababbcccddadccbdcdbcadcdbbbbcdbcbccdacacabcdccccabcacddacaaacdabdaaddcbbcbbdbdbabbcabbababddaacadacbadbdbbcadddacbdddbbbbcbcbbcccbbacbbcbbacbbbcdddaaccbaabadacbdcbacdcdaabccbabbccadaddcbbbdacaacdbbcdcaccdcbbccacddcddabaccbaaacbcbdcbacabcbcccccacadaddbabcdbbcdadcbadcdcdabdcccddbbdacdbddaddbdabcadabdbbbbbbbabcdcbadcaabbcacabbdbacbdddcbdacbdccaaaabaccaadddadbacadbccadbadaaacddcdbaacabcadadabdbcccadbbdcdadbdaddcaacdbcbbbbddddabdadcaddaccccabbcbdbbbdddbbabadabdbddcacccadbdacaadcbddabdaabcabdbcbdbcdbbaadcbacdbaddcbadcbbadbabdcccaacadcaccddcadcacbbcabcdcabacaacdcbdabcdddbdbcdddcdbbacdbaaababbcbbdbbbadcbcbbbbcbdbdddbccaddadddacdadcdaabadbcadcaddcbbbddcbabbbabadcbdbcaabaabbbabdcdbaccdccbaaccccdcaaacbbdbbdccabaddcbdadccaaaabbcbcababcacdbccbbbbdbaadbbabaabcdbacdbccbcdcdcaaccbcbcaadbbaadadccdacadbaddccbdacabdabcdacadccbccbadbccdabbbcaadadbdcbaccbcacbadbcdcdbacddbccdaabadbcddbabbadcbadccbdadcbccaaadddcbbadccdcacddabadabcabbbdcbdaddcdbcacacaaadcddabcbbadccddddcacaadccbcbddbccadbacccdadbcdbbadcbdcaabaadaaacaacaadbadacddbbaadcbabcaacdddcbaadbcbdbaaacddacdddbbcccccaaaacdabcddbdbcabcbbabbbbaabbdacabddcadbbcdddbbabcbbddaabbcbbbbbbabaabadbdbbbadcdabadaabcdbcccdccbddccbadaadcbadbcbbdcddbdbdcabbccbcaabadadbadccbcababdccdcdbadabdbbaabcabacdcacbdadcccadcdcabacbacdabacacdbadadcaaabcdadbdacdddccddaacbacdcacddcccccdbcacccacbadbddacadabdaccdbacbbaabbdccabbabddcaabaacbdabcbbacbddccadbbbbdbcadabbcdaacccaaaadadbcdbcaadcadbbddabdcbabbbcbabadadaaaaccaadbccbddbdcacdadaaacdccbbabcadcbaaabaadcbdabaaddbbabcbcaabcbdcaabaacbcbbddbababcdbbddcbcdcbbdccdddcbbabcbbbaccdabddbbadbbbbbabbbcacccbcdabadcabdbcddcabdbcbacaadcabbcdddacbdcdbcbccdabcacccbcdbcdbccdcbccdbadbbcccdbbccdbaddbdbcdbdccaabacccbbcabcabbabadadbdadacccbabdbcdcbbbbadbadacdcdcccccdbbcbdcdcbdbbdbdbdbdaacdbdcacdbabcaabcabbddccabdbcabbbdcdacccadccaacaacababdadbddcbccdcbdcccaaadccacbccdcccacbbccddcaaadbcdcbaaddbddbabdddcbcbabaabddbaacbbaabaacaacdbdcdcddccbadaddcbcacbcbbdddcdcadcacdacdbbadbddddbabbbbbdcdbdacbaccdacccbdccbccbddacabbcbbdcaadaccdcccbcaddaaadcaaadbccbdbccbaadbdadbacacccabbadbbcbbaddbcbbbcbdaacbcabcddcadaadbccccadacaabccabdcbaabcccdadddbaacdbabaddaccdadcdcabbcbaadbdabcddacdbbcddccacbcaccddbaaacabccbbbcbcacadbccacdcbbabdabccdabdabdbbdaabccdddadcadadabcdabbbaddcaddaddabbdadabdadcbabbdccbcccdcccaabbccadbcdabccdaddcdbbdccadcacdaddabbabccbdbaabbdbdacacaabaabcdbaccbdddabbbabaddbbadbbadadcadcddabcbccabaccadbbdbabaccbbcbcdadbbdacabdabcaabadcdcbbacbbabcbbbdcbdddacabddcaccaabbaababdadbccdbbdccbcacabbadbcdbbcddbbabdbccbcccccbacbcabaabbbadccbaaaddcddbcadbaddaaccdbbadcdcbadbbbbaabccbbadbbacdacdacdcdbdadaccbccabccbcbddaaadcbcbdcdbbcbbddcbcdbcacbadbdacbdabbcaaddbabdcbabdcabbaccbdbddcdcdaddddbccdbaccccadcddddcadbcdbdcbdbabdcdaaacabbbaabbcdbabbcabcbaddbcabadbcacacbaabacbdacbdacdbdbbcddcacaaddbbcbbabcdaccccbccbbcadcdacbbcbddbadbbcdacccccdbdaacabcaddcbbbccccacdbcbcccdbbbacbbbbdbcadbcdacadcbbdccdccdbcbccbcbdccadbccaddbaaadcdadaccaaaaccddacadbcccbadbdabdcdaadbaccbadcaadabaaabadbccaaccccdcaababddacabdbabbdbddbcabdccbcdcacddbccdcaadbbbacdbabbbadddbcaadccddadbbabccddbbacadbdbcabbdddddbcbdbdcdcdcacbbdbaaacaddcdabddadaacadcdaadcddaabadadadaccbadcaddadcccbbbbaddaabbbadaddcaacbcdcacacbadabcbcbbbadaddabdccbbccabcdcdcacddddbccabccbbdcdcddbbcaddbbbbdccbadcddadaadadbddbddaacdabacccbabacddadccdcbbbabdcdbcccdbbdcabcaccdcdaacabbaadbbadbbdabbcabbaaabdababbcabbddbdaaadbdcdcdacbddadbbbacbbddaacaccacacbadcadbdaacdcbcacccdbabbdabcdbccaacbabccdcdbcbbdccdccbbdcddbdabadabcacadadbadabcbdaddabcbcadbcbabbaddddbcbabdabccdcbbcdcaadcadcaddcacccbaacbbacadbbcbaadccdaadbbcddaacaaaddbbbdbacbadccdcbcbdcaabcdcdcccdaabbdddbababaaabddcdddccbbcdacaabdbbabcbaaacacbccbcacdbabbdcacaccadccdcccdddbdbabcabcbccbbdacddcacbaccdcbabbbbadacadcbabacacbccbcbdddaddcbdaaacdacdcdddadcbaabaccbabbbcbccaddbbcdcbcbbcbbbcccddabdcdcdbcccbadccaddbdbbdcdbabdbbccabcadcdabbcdcdbdbadbdacaaaabacbdacccbbbbdbdaacacdcccabbabbaabbaabcddbccbddccadbacbdcaddcaabcbcacadacaddccbdadabccaddadbdbbdccbdbcabadbbadaadbddcdcbcddaccccadbcbbabdcddcddccaadacbbdcabcbacbccacabbaccdaabbdaacdabcddacadaddadcccaacaabbcadabcaddabcaacbaccadbdcacbcbccdcaabddadbcbabdaaacbdbbcbdbaabbabaddbabbbcbdcbcbdaddccdabdbcdaaccdcaccaacbdbbdacacbccbcaaaadabacabbdbacbdcbbcbbadaabccabbdcdadcccdbbcbadbdcbaccaabdadabdaddacdabcbaddacacaaabdddbbbbbdccddabcdabbbadbdbcbacabdcdacbccadacbacbbabcbbadbacbcddaabaadbaacbadddbdbbcbcdbaacabdadbaaaadaabdabcacbadacaaaccdaddcdbabddaaabcbcaabbaaaabaaabcbcdabcaccbdcbbcdcbcdbdcbcacbbbdacccdbbaaabcadcdadacbbddbababccabdabddbdbcbbcdadbaaacabbdbabcbcaddccabcadaadcbccbcbacbccdddccbabccddcdcabaccaaabccddcddcaaabaaaccccacabacbddcaadaddcadacacccdcccabdaaabacccddcdadbdaacdaabbbcacaccbccaadcbddcccbbdcbacaccccabbdbcadaacbdcdcbbbdadaacbdabacdcbbcadbddccbacaccdabcacbbbacaaadcddbccbabccddbaacadbccdaacbdadcbabbccdcddaadcacbcdacbbddaabdcddabaabadccabdbbbbdbcdaaddbdbcadabccacabacabdadbdaadccacabdadbccbbacdabdadaabbabdaadacbaabcbdbdabaadbccacbaadbddddaacbddabdadcdbdaacadaccccdaddaabcbbcaaccadbaacabddcacbcabacccaadbacbdaacddabaadcaddbdacabdcadbcdadbcdabddddcbacdddaacddddbdccadbcdcacbcdbdabdaadddbdddacbbacccccdaabccacbccaaacabdddacdbabcbcbdabcdbcbadabdbbbdcbddcbccaabdcddcddcaaaccacbcbbadbbddaabcdaccbbbbdcdcbcbdcabcdaaabaddcacdcbabdbbddddddcdcaddbabadbdadbcbcccdddcbcadcdccbcacbdbcabacdcbacddcccaacbcbccbccbbdcddbdabdbcddcddcdaaabdcddacbaabacaaadcbcaaacdabbbbbababdabddcbddcbcdcbbdcaaadaddaadaabadaaacadbdadddbdddddcacdadddbabaaabbdbbdabbdbccbccdcacdacdbcaddddcddccabbbbccaadddcaccdbdcbcaadaacdcbaddbadbcbbbdaaadbdbaacbaadcadbadbcccbaaaabdcbabbbddddbaccccadaccabaacdadbbbaccdbaaabdbddcbdcddaadaaabaacbbbbdbdcbcdadacbaabbbbdbacddbcaabdbbcbdbdbaadcadcdaadaacbdcbabcadaddacaaddbdbbbdaddadaddcacddadabbbdbbacadcbbbcabbdddccbcdbabdacccacddacaadcaddbddcacababaddadbbdbcbbabbddccbdddaacdaadbacaaaddcaacbbdcacdbcbadbdaaacbaaacadcaacadddcbbddbbcadcbaadadccdbdbaaaddabdcdaadaadbcccdbabbdaddbacacccacabbadbcacaaabbabdadbbcaccddaabbdcdadadaadbbcddbabacbdcadccacabddbbddcbcaccaaabaaacadcccaccbaccccdcdbdabbdbacdcdbbaacccbddcacdaabcabacadbdcadacdacbdcdabdbdaacdcbdbbddbdcacdbbcaacabdacdbdadbcbcccbccdacccddccbcdbaccddabdbaaacbaadadcacabbdddcbdbdbddcadddcbabdcbdcddcbaaaaadbcaadbbdbdcddbbcbbbcdbaababcdcbccabcbabccbddaaccdacdbaddbdcdddaabbabaddbbbdccbaacdbcdcccbdcaaacabbccdcdcdbcadbdcdaaccbaabcddccbbddccddccbaabbccbaccadbddbcbabcaacdddadccddabbddbcbcacdadbccbdbdcbdcbaacdcdbaccbdaddabdcdbabbddcacbbacaabbdbcaacccccbdadcdccddadbdbabdaddabaabbaacabacccacaaababbddaadccbabcddcccdabaaaadbcccabcdcdcbacdacdbcbcdadbccababaadbaabaddcaaaacabbacdcaccddddaddbccbddcccdcbcddababdbcbbcbbccdcbdbababcbdcdccadacaabcdbdaddddacdccaaabdcdaabbddabcaacbacbacdddaadbdcabacadbcabdabddcadabbcdaacddbaadbdccbbacdaabdcacaadbcbcddadbcdddadacdacdccdbbabacbacdcdcadccbaadcbdbdcabbbcdbcdccccccccdbdaddabadccddbdaddbacacacadabadccdaadbcbdddcdddccaadbdbddbadadaacbcccacbbcabdaadbaccaadcabdcdbbcbcdcacacbacbbaccdabdddbcacccccadadbcdbadaabdccbccabdddcbacaaaabdadccdbdaddcbadccadaacaacdbcabbaddaaddbcccaadcabaddadbdadbbdaddccbbddadacacaabbdacccbaaaccbbadbddcbbdcccbbccbabcababbaadaababccdaaaabdabaccbcccabbccdddadadcaaadbdbddbdadbdcddccbdddacbbbdcdaccdbbbabadacddddaddccdddcabbccddbabbcccdcdcadadadbdabdcacdcddbcbdaadcbdbabbaacdaaacaaccbdcdcbbcacbdadabbccddbadcddbdcbccbbabadcabccadcccdddbabccbbcbcacbcddbdbbcbbdbdccacadbacdbcdadccbaaadbccdbcabdddaadbbcbbcccdcabdacddadabbbcaabdcbbbdbbcabcbcbcbabccdcbcdccdabddccbbcaadcccdadcaaddbcabdcadacabddbbdcddcddcaddcccacdcbbcaadacbcadddbcddccddcaccabcadcbccdbcdcbaabcdbdababdaaaccbcbabcabbdaabbbabcbdacccddacacabbdacddaaacacaabcabbacaabbcdbcadbabbbbdaddacccaadcaabcadcabccacbdcbccdbbdcddacadbadabcbbcddbcacbdccbabbdbbdaddbbccbddadcbbcadcbdcbcdcacddbcbbccccdccbaccadbbbbdadbabcdaadbacdabdadacbcaddaabbaaacccbbcbdabdcccdbabbcdddbadcdccccdadcbadacdcbdbaccbccbbcdbaccbabbadddabababddcdcccaccabdcabaabbdaacdbdbadbdcbbcbabaabcabacaaabdbdcbbdbbaabacabbabacdabacddadadcabcdadbddbcdaaaddbaddaacdaabacaabbdaadbccdbabbccabbacbdbbbcccadadccbacbaadabdabbbbcddabcacddcacaccdbaacdabdcdcadddccbdcdddbbcabdcbcacdadbdadaaccbbdddabdadcbdbacbcbcdaadaabbbdddaaadbcbbaddbacdcccdacbabdbaadcaadbdcbbcdbaadccddacbdaacdbaacdadcbbbcdddbaccadddbaddabbddccadadcbaaadcbabdaabcabbdbcdacbddadbcaadbcbcdbbddbdbcdaabdbdbaabaabbadcbbcccddacbcabdadbaabcaacbdbbbdccccdaacbabdbcdcbddbbdbcbbbbbdbdadcbcbabbcabcbdbcadcaacdcbdabdbdaaaaddcdacccbabdccabdddbcbbddabbbbabdcccbcbccabcddcbcbbabdbabbddcbdadabddddcabbddaddbcacddcdaaadaaadcdccaadadcbcccccdaaabbcaacdaccbdbbdadcbbadadcababbcdcdddcdbbacbbbcdccabcdccdddbaababacbdacbacdacdccdcbcddbaddaaccdcdcdadaadcccbbcbadcccbcdadbdbaabcacdadcbbababdcbcaabbbcdadbaddcdbdaaccbddbbbcbccbcddaabccddbaabcbdcadcccbddccdbbddccdddaadbcbdaabcbdccacdbccaadbccadabbdbdcadcbdabddaccbdcbdbabbbcdddcbcabcddcdbabdbdbcaddcbbbaaabdbcdcadbaccaacbcacbcadcccdbbbaabbcdaadbcbadcbacbaabbbcaddacccbddcabdddcccaaaacdaccdaabdbadcddadccccacbccbdbadccbbccbbddcddbcdabddabdabaaaabcaadacabbbacdbbdadbcaadccbbaadadbcdccbcbbaaacbaddbcccbadbcbcdabddaabcdcacddddcdaaadbabbdbbccdbcabdabdabacdacdadddcccbcabcbadbadccccbabdccacccaddbbbccaddccbbacdddbbdabacaccccaaddccadbaaaacacddadacabcbacbbccdbddcbacbbbdbbbdaacdbccddacdbdbcbaabddbbadbacdccdbbccacbbbddaadbcdbbcccccaccbaaaaabaacbcdcdcdacaadccbadcaccccbbcdaadabcdcaaadcdcdbdaacaaddbbcdbbcbbabcdbcbddcabcdbacbabcbaddacdbaabbddbacbdbdbaaddacabcbbaadacbcdddbddcdccbdadcdcacbdadadcdbdddcaddbcadacaccdbddadadacbcdaabbdabcccbccbaddddbcbdbaddcacacdddbddcdbcdddcbdaaddbbcabbcbdcadbabbaddcdaaadcbcbadcbadcbacbadbcbaaaacbdaadacbacdbbdaaadbdbabdadbbbbadccbbbadbacbbabbbadbacdcabbbcabaccbcbbdacccacacdcaaaccbccbbcdbdaabaaccbccccbccbbccdddadaaacbacbbdddaacdbbacccadbbddadbccdcbaabbaddadabaaacadddaaadaaacdbddcbdcbdccdbbadcdcdbdbbacaadcadacbcddcbcdcccccdaadcabcabdccaaccdabbcabbbcdcbbaabcacbddacaacccddbcadbbdaaabdccbabbcabdbbacadacddacabbdcababbacbbcccadbbcdccacaabcadaabdacaddaddcddccccacbddaababbabddabbdddcbcccdabccdccdcabbddbdbdbabcbbbdcccddbcabdcddbbabcdaccbbbacbccddacdacbbcadcacbccbddbcabdcbdbcaaccbbadbdacadbccdddcdbdcbbbabdddddbabadadbcaacdcbcacccdcdaddcacccbcdcddcccddaaabadbcbdcccdcdbcdaddcdbccdadcadaacababdbaddbadcaddaccdabcbbdacddbcbbadccdaabbcbdadccbbaccbbabdbbaacaddbbabddddadcacaddadacbbcbcaadbbdabccacabbdbcbbaddbaacbcbbadddaccacadbbadbbacadddbccdccddbcbcdbcddbcbcbbdddbabcdacbacaccbcccdcddaaccabcdbbdacdbbaaabdaababacdadcaaccabdddadbddaadbddbadabaccdddbdddbdcaabdddabbacbbbbabdabddbdcddacbadabdddddcbcdbbbdacccdabbdcbbcbcccddddbcacdadcacabdcdbbddaacaccdabbdabdabbddcbcdccdcadadcddcbacdcbbbbacbccdbaacbdcbdaacdbcbddcbdbcdaabccdcccbaacaddabccbddbccbcdddbdaacabadbbaadbdbabccccdcddbbbcbacadbaaaabbdcbcdddcadbccbacaadabbbabdbcdddacadbabbddabcabbaabababdcbaaadadbadccaabacdaccdbcabdbaccdbddaaabcbdcdcdcdaaabbdaaccaabcabbcbabdccbdcbbbcdacbdccbabccddccdcccdbaddcbdadccdddaabdaaacbbcabccdddbdddbdbbaccdbbdacaadbaaddbadddddbdcabacdccaccaaadcaaaaabaadcacccbcadbdabdaccccdbacbddbbdbaccbabccdcccbdabcdadcabdadbdcdcddabdaacaacdcbabcacdbcdaadddacdccacaddddbdcddcdddbccddcadcbbbaddbcbadcdbccdddcabdbbdccacadcaaccbbadbbbaabbbbcdcadabbabdbabcbdabdaddccdadbcbbcdccabaacdadbcdadddadbabbaacbbbbbaacbbaabacaadacccbadadbadaacaaaadbbbddbbcabbccbbcdcdccadcbaaaddcdcaabcacdcbdcaaadcaabbcdbddcbbbdcaddaddccccdcaaddabbdcaacdbbcdabbacbbbacbaccbcbddabacdabcacdbdddccbdbaadddbacdcbbacbbcdbbbbcabababacabbaabbdabcbdbcaaaaabbddbaaaddbdacacadaabcccbababbbddabbabacbadddbdbbbbdcaabddabcccbbaaccaadabbddcbcbdddadaddaabbbbacbacbcaabdcbabcbcabadbdcacdaacbbbadcbbcbccabdaabbcdadcabbaadbcdbbabdadaabadddadaaddcbaaadadbbacacddbcadbbadcdcbccbabaababdcdcbbcdadbbabaadcbdbcabaacadbbbddbddddacaccaadbcbccdbcccccccacbcdddadbcccadaddbbabcdbcaabaccaacadbccaddababbcccbccdabccdacdcdbdaabdddcddbddbbcdacdddbacbacabcacbabcbacabdbabbacdabbcaababacdaabaddcaccacaccbaababacdabaabccbaacdbbdccddaccdabccdbbbcabadaabccbacbcdcbccdadcabbbabdcabccbdcdccdbcacccccbcbcdbabbdcbacdbddabdaccdabcdaccddcbbadcbbabdabaccdcbcdcbccddacaababaaccbcdddbbbcacbacbdadcbdddbbcaaccdaadbcadadbcacbdcbadacccbcccaaddcbbabcabddbdcacccdddabbbbbdadcddacccadcddcbddcacdadbbcbbbaadbcdcbbcacccccabdbacbcbcbbdadadcadabbadddacdabcdcddcacdadacdcccabdadaddcaddbcdcadcdbdccaacaadbcdbabddddbaadddabcbcdbdcdcadccdbdcbdbabbbcadabbacbbbabcabbadabacaacbadcddbbccadcbcacdbbabadabbccacdddddbcaababcaaaddadbdcaabcdabcbaddaaaaaddaccdaaaacabddcaddbccabcbdcbddabccaadccaacdcaaaccacbabcdddcaaadaddbbdbdbabdadbaadcaadbbdadaaddcbccbcaccaaccadbacbbbccbccaaadacbadbaabbbbbbabaaadbbbdcccdbbcdabcccbabcdccccccdacdcacddddccddcaadbdbacaadbaccadbaacddbdcdbabcbabdaabadcaccabcdbacccabdbdcbadadbaadaddbbabccdadbdbddddbdabdacbdaddacccaabbcbaadcadadbcbccbbcccdabdccaddbbdbdbdbdcabbbcbdcdcdbacdccccbacbcdccacbdadbbaabdbdadabcdcccbdcadcbabcadcbacaacccddbdbabdaddcabdbdcabacdadbcbcbdaacbccbdaadabdbdbccdabccbaddacabaccdabbbabdbcbbabcacbbaacdabdbbaacacbdcddaacbbdccadcddbddccccdccbdadabdadaddbdbddbcadccbcdbabaadbabbdabbacabcbdaccabcbcbaacaadacddcaacbddddbbadcadadabdaddbbbcaacbabdcadaaaddbbabbdacadcaacbddcacaadddadcdbadbcbdccdababdcaddddaadccdccbdccacacdabcbbabdacbcabddbadaabcdbcbcdadadaabaacabbbdcdbdbbddddcadbbdcdabbbcdbdacbccdabdccaaabdcdcddadbddcbcaddbbddcbdcadbbbdddcbabcbbccdddcbbbaacaddddacaaadcdccbdaaaabdaacddaaddbddddccadbdbbbdbbbbccbaddbdcabdcccbccddcaaadacdaaabcaaadaacdadbbbcacbcdcdbddbacccabccaabcacabddddbdbcbbaadbcbddddbbcaadadaddbdcddbcbaddcadaccadcbaabccbcaadddaadccadaadccdcacdadadabbdddddccdbcabcbcddddbdbbaabbddabddaabcadbbdcaacbcccccdccbbbadcadbccadbabbddddaabdbcbadcaacccdbaabcdadabdabdabcbcaabababddbcdaaadcaaacaaabbdabacabdbbcbdbacbadbbbdbbababcacdabbbabadddadadcbbddcabbdaabaaaabbdadbdbdcacacaadddbaabcbadbccacbabbaccccccaacbdbccccddabcbbdddbdddcbcdbcdacbbcdaaaaccbdccaabbbaabdbdaacbabddcbaadddcaacacabdacccaabadadabccdacbbacbcdbbccdbcabbdbcaabcaabaaddcaddccdaadcdbabadbbdadbcabacbcdbdbdcdabadbdcadcacaabcabddbbdaaaacaccddccdcddcabcdbbacdacdabbabdadbbaccbcaabdaccbcddcdcddabdabbcaabacdcdcaaaabccbccbbaacaddaacabababcbdbbbdcccbdcdcabbddacccdbcacbcbcbcdbcccabdbabdbcdbccccaaaababddcbccaadabdbbacabbcabccbdcbacddadcaabdcdbdcadbddcddbcbcaabadccdcdcddbcaaccabaabbdacdcbddbbacbabcadbdcdbcdcccdabbbbccbcdcaadddbbbabcdbaabdcacaacccbabcddadbcdcdccddcdbcddccacdaaacdadcbabcccbacddccbccccbadccdbdbcbbbcacbddaccdaacaadcacbbcbdcdaadbddccadddccbdadbbaddbdbbadbabbabcbbbddcaddaabbdcdbdaadaaddbdbddcabacbcacdbcaabcababbdaaddbdaddbdcbbcdbdbadcaccdcbabcadbcbabbcbdccdbbcdbaddbbdbbbdcabbdadabcdddbbdbdbbacabadadddccacddddccbabaaadbadcbdbdddccdbbbdbadbcbcbbccaaadddacbcbcdbddddaadccbddacabcbadadbccdacababcdababaadbacadcdccbcabccbacbbcbbdcbdbcdbaccdacacddbbddbaabadbccccbaabbbccbcddcbdbcddaccdadcbbdddcbabbbaaaccaabbabcbdacdaaacabdcddcdcabdbcadabdcaaddcababcdbcbaccbdadaadcdbadbcdbbdabdacbbaddacbdccbaababddbbaabcaadacacaadbdcdbabbaacbcaaccdaccbbcbdcdcacdadacccabaaadbcdbaabcadccadbdabbcbbbcabacdccaabddbaacbcddcabbbaababadacbbacaaddabdcccddabdcabcbcbccddbbdcaaaccaddcddbcdbbdbdbbbbccdbdbdaabacacdbdbbbbbadabcdcdbdcddcadbbdcbadacaccaaddacaabcaabccdcdddcadbabaaadacaacbdbcccdbcddcccdccdabdcaabbdbdcdbbbccccbdbcaacdbabbabadabaaacbbcdadbbcadcddbcabccddccdbbdbddcaacdcbacadbccadddccabdbbbbbabaadcdccbcdbaadccdcddadbdaddadaadbcddbdcbabbbcccbcabcdcbacabcbabababcddcdbbadcbaddbaacbcdbaaadcaaabcabaaabadabbacbabbacaddaaabdacaabbdbacccdbacbccdbabddccdadbddbbaacbdcbdadbcdcaadcbdacacaccbacdbddbaaccacbbbbadaddabbabbaacbadddbbdbddbdddbbbcdbddbcaddaddddbaccbadacadaccbabbcadddadcccadcacbbcabadaaabdaddbaadccacadcbbdcdccccccbbabdaaabbbbcdcbcddbaacbbabcdbaacdabcaacbaadcdbabdccaabbcbaddaaabbbcdddadbcbadbdcabcbadcbabdabbbcbcdadacccbccdabbadccacadbbadbccbaabbcabcccccdacbdadabbdbcdcddaaccddcadbbbbddbbbbbdaddadabbdddbdabdddaadbbcbcbcdacadbaadaddbaabdadcbacdbaabccbcbdacbdbacbcabcdcdbaabcbdcaaddbbdacadabcdbdbbadaabcdabccacdaacabbbbaaccdbbbcdbddbdbddadadacdcdaacbaccacbdacbabbdcadbdcbddaadadcdcdcbaaabccdbbaadadcbdccdabbccbaaaddbdddaacadadbbdbaabaacddbcabaddcbdbbdabbdccbadcdaacddcaacbacdcaccaaddadbdaaabaccdaaccddddbcaddbabdadccccbdadacaddaccbbdaaaacaadcccdcccbccadccbbabdadcaabbdcdddbaadacdbdbdadbbcdaddaabbdddddbcddbcdabaaaccacaaccddcaaacdddacacdadcaddbbdbcbcabcabacdadbcddbbaadababdadaaadddbdacccdccdadccbdccdaacbbdacbadbcdabbccdbacadbcbdcbbdaadaaacadaabbbddacdbbaacbccbbdcaccdbaabbbadbdbaddacacbcdadacddabdcadacccbdccdadbbcccbdbbccdcdbccbccdccbdbdcbcccdabbadabdbbababcbbbcbcbddadabacdddacbabdccddddddcabbbbaabcbabaaacadccdbbbcbdbbcacbccaababdcabaaadbcdbdbbbdbaababaddddddaaddcacbbbcabdbccbcbcdaabccadbbadcabddcbbbcbadabbdcaacdcbbaddbbbcbacccbaabdbcabbaadddcbbabddcdcdcacbaddbbccddbdcadaabdcbccbadacacbdcaaabdbcdacccdcdadcadadcbdbabdcbccababddccbbdbadaaabddaacacdddbbbddaccabdcddbbacaadabacadccddcbacbbacbdcbccdcbcbcdddcadaacdbdbccbdcaaddbcaccbacdcdbdadabdccbcabcccdaaccadcddccacadddaabbaaddcbbdacbacbaaddcdbbccdddcaadcdcdbdcbbadcacdbdddbccdbbdcbdadcdbccbbadddcdaabbddaadadccdddababdddbccdccabbdbdddccdabbcdcaddcbaccdccadaabbbbaacdaaccbcccbacbadbdabdadaddcdabacdbababcddccbdbddabbbdbabaaddcccacddabcdcbaaaccaadbdbbcbadacbbcacbbddbbabcccadadaddddbdadcbbbbbbcdbbdbabbacdcbabdccbdbabccaacadddcbbabbacadcbcdacaadbdcadccabbcbbcdcdbacccaadacadabcababbacdadcbcbacbacabacdddabcbabcabdcbdccadadababbaabcccccdaadddbaadccdaabccddacdacbadbdcabaabdaaadcbbbcddacdaddbccadbaaabaaadbddadbcbbabbcbdcbaaaaccccdcbcdacddbaacbcaaccaabadbccddbdccbabcacdcbbdacbcaaacaabbcabbccbbdbdcbabcbdadaccdbdccaaccdcaadaacdcbacccaadadadcbcbcbbdbaccdccbdaccacdccacbcdbabdbcdacdccdcdbbcdddadbddbcdbbddbdaabaadacbaaccdadcdacacbbbdddbcbcacbabdcacbdccccbbacaadcbbdccabddccadaaaccdacdccdbbcbccbabdbaddbabdbaccdddcaadadbabdaaacacbadabccbccabaacabdcbbdbbdadadaddabaddddbbcbccbbacadabbbadccddabccaacbaacdbadadbcbcbbcaaddcbccabbbdccdbaabadcdacdbaddbdaddacdbadcaadbdadbdddbbbbcccdabccbdadbbcabdacdddbcacabcdcacdbcddaaadddcdacbccbaccbabcabcdadbdbbbbbcacddcdabcaddddbddbbbbbacabcccccdaadaabacbaddcaadbbbacaaccbaccdbddccdccaccdbccdcbdcbdcdbdcbbcaacdddbbbabdcbcbdccdcbdbcdbdcbbbccdbabbcacadbbbbbcbdbdadbddbacdbddbadabdbbccbadbaaccbadcbaadbacdcadbadcbcbbabacababdcdbabdaabcaaadcbadcacabaadccaccaddcdaaabaadbbcdbddabacbdcbbdcdcccacaaccacbddacdcadddaaadaaddbabadbdbabaaaddbabdcccbdddcadcbcccbccdabbcddadcdadbaddcccdbdbddddaaaabababbddbdabcaabdcbbddddbddadddbdaabbcbbacccdbbdbcbcdbcabcabccaadbacbddcddbadcbacbdaabdcbbcadabbdcdabdddddacadcdbacaadacbbadccccabaaaaddbdaaddabcbdccdadbbddbccbddbabdacbdaccccbadccccacacbaaccddbcbababcadadbabddcbabbadccaaaacbccdaaacbdbaadcbbcabcbcbddddcacdacadacbadaadbacadcaddcccababcdcbababcdbcbadcbaabcbdcdbddddbbcddaddbcccbcdbcdbddabdcabddcabcbaaaabbbcccabcbbcadccaadcdccbaaadbacabdacdbbadaadbcdcadaccccacbdbdbdcbadcacbbbbccddddbacbbdcbcccacaccddbdadddcbdcdbdaaacacdbddacaabcdbcbdccccdacacbcddbcbdccbabcdbacbbdcdcbbdbdadcbdaccccdbbccaaadcbaaabaabdbbdbcdabdcabcaadcdaccdbaaaaddabbbababdcdcbaabaddcdabadadddadaccabcddabbbbabbadababaccdcccadbaccdaaddcbadbaadbaacdabdddcdccadddddddcbadadadabacaddcdaddaacdccaaccbabbbdaacddcddbadaacabdbddcabdbbaaadcdbddcaaadbcacbaccaabdddadcdddddccabdbdacacddcbcbbccbdbbaacdadbdaddadcbbcabbdaccdaabacbcdbadccabddcbbdcaabbdcdadabdacaadcadcccacadbbabcaaaccddbabcaacccaabdcdabdbcbddcabcddacadaaabcddbcabcadabcbcccddcdadcddaddcbacbbbdbdacbddbbbbbdcbdcabbbbcddadaaaaaadaabddcaadcaaacaaadccacbdbdaddabaaaddbdabaabbbabcbaabbdcddddbadccacbabccbcbcdbddddacdcbadabdccaccbacbbabbbccdbdbacaacadbdbabddcabababbbadabdddabbdabaccbcaacabbcdabcdbbaacbabbaaaccacdddcbbccaacddcaabccbbcabcbddcadcdcaccddcadacaccdbbbbaabdccabdbbddcdddaaadcdcbaaddacdddccddcdabbcbddbdcbbadbabcbadbdbaccacdcdbddcbabacbdbdbbabacbbbaacbacbbbadbccaddccadccbaaaaadaccdabbaddacbcbbdcacbaabdcccbbdaccacbddbaaabdcdabdccadddbbacddaadadcbcddcccbdbcdbacdbddcccccabcddbbaccadddababcddbbdcbcaadbbccacdaaabcdbaabcbcbdcbddbdaabdcdbbacbcbaacacccaaaaddaacbbcdcbdddddbcccaaaccdbbaacbbdddcadcbcbabaadadcaaadcaccbbaacccccdbabbabbbcbabcbbcbbacddbbaaccddcdccbdddddacdbdbaaabddacabbbbbabbccbbbdcbacbccbbaabcbddcadbcabcbbddccadadcadcbadacddacaacdabbcdddcdacddaddababdbdbabbbdbdbacdbdabbbaddabcbdbaddcabcaacbddcacadbccbcccdcabcccaddaaccabbbdddbdddbcddbaadcddbdaaaabdabcdbdcdddcbacdbcdadccaacbdcbcacdacdabbccdbcadccbbdbaaaaaadacbaaddbaddbddcbacbddcaaccaabbcbcbcaacadccaaaabbdacbcacccadbbddbbaabaccdbcdbbbcbadabcabbbbaddcbdbbddaadadabbdcabadddadbbadacbbdbdaccccbdccaacdbbbbcaaaddaadbcbbdbaaccdabbbbbacbbdaacdbbcbadcaabcbaabddaaadbdbcaabbdaadadbbcbadccdbdbcdbaaccbabcbdbbaadaaabcababacadaacbbccadaadbbdcadbddddaddabbacbadbdaddabbbbadbbcbdbccbdcccbdcaaaadbdbbacbdaacdbdabccadcdaaaabcdcddcbacabacbbacbaadbbccbaaabddcaaccbdbbbadadbcbadbccbbdacccdaccaadccbaaabddaabadcacdcaccacabdddacbcdbbcdcbddbbdbbccdaacbacbbabbcbadbccaaddcbcbbabbcabcaacdabbaadcdcadbbbadddacbacbcaadccccbbbbdccccbdaacbbdcbdcacdcdbdcdccbccabacdddccaabcacdadbdbddababddabcaacbdbbccadaaccdcaddbcbbcbbdcabdccadcbdaabbdddacdacbddaadcccdcaaddaaaadcbcabcdaadabddbdaccbdaabccadcbdbdbdddcdcacddaacdbcdbcaaccdbcbbbadccbabaadbaadccaabcbccacbcdcbacbbbaccbcddaaacadaaddcacabbacadbdabbccacaccadbacbbdbdcabbbdcbcaacacaadcdadccdacbdcdbdbbddaadcbaddcdbaaaddadcacdbbabadcccbcabaacaaabaacacbaababddadaacbbcbbcbddbacbdadcbcbdddddaaacaddbdbabbcbcbbadcbbbabadacbdddbcdbbbadabbcbddaadbbcbabaaaabcbabcaccccabbcdbabccdddabdbdaddcbaabdbabadbbdcbcbbaddcaaddccccddaacbabdadddacdabdcaacbcddddacabadbbaabcabbdcdaddaabbcdacbcdbcddcbdccdbddcbdcbcbadcaaabbcaaddadaaddaadcdbbadbdcbbdcabcdbcdccbabccadbabdcadccabdcadbdacccbbabdcccbbdbbadaddcbbdcbababcbadddcadddacdabbbbddbbbdbaaccdadabbddbacdaaaaaaabccdcdaabdaccbcaaccccdbbaddbcdcaccddccaacbcdaadaaadcdbadcbaccabdcabaaadadbbcccacdbbaccabaaaabbaadbdcaabdabdadacbcdcababcddbddbbaccddabdacaacbbacddaaacbcdbacdaacbbcdccdacdabaddaaaccabacbcbbaddcbdbdbddddaadbaddacaabaaccaccdbdccadcbacdaadadabcdabdbbbbbaccbdabaaccdbacbabdaabcbbbbddbcadcbdbaabbbdbdadbbdaadccaabaccacbdcabcadbabddbdbbbddcaababdcdbcbacaddbaacacbdaabccdaccccbcbbdcaaaadbaacdcccbcddbcdbababcdcbdbddabdbbbcccacabcbdccacdacbdadcbbadbabababacbdbbcccacabddbccbbaacadadcbaabbcbcdcccdcbabddadccacccbbbbcdbabbdbcbddabbcccddaacbbccaccdbccaadbcaaccaaaccdbdcdaacaccaadadadbbdcabbdbccdacbaaacddbbddcacdbbdddbdccbdadadccbbcbcacdbcddcdbabbdbbcaccaccddadcaadacbbcabbcbacdbdbacdbdaccbdbaabaaadbbddbaabacbaaabdccacbcccdaadcadacaadbaadcdddadabcabdbccdbdcdacaaaabadababddbccdcdcccdbbbabaadbdcaccdadcaaacbbabbaadcbaaababbbdbcbdacdcdbaddbcaaacbcbabccdabccaaabdbbdabbddddbdbddbccadaccdbcdcbdaacdbcdbdcbdbbdadadbdcbaaabdddbbcdddcdbcadbbddcdaadcbaccdddbcbbbbcacbacbbbbacdacdbcdbbcbbbcadbdbcbcadbdbaaaaaadcaddcbbddbcabadadbdccadcbabcbcbbdbcdadcbccacaacbacbcbbccaddcdcacbccadbaacdaaccabbddadcabbaddcbddbdbacbdbcbcacaccaadaaddadabcaabbccadcccdcbddcdcacdcddabcbdbacbabdbacbaddcbcacaadbbcbcdcbaddacbcdcdadadbaaaccabdddbbabacdddaddcbbcdbaaabdabbcdaaadacbccbbddacccbacaaddcacadcdddcadddcbdacccdbbcadccaaaabadddddbcbacacbbcbaadcdbaccdabcdadcbdcaaacbaacaadabdbdcacdddbbdbadcdccacdbdabcdaaddcddabcbbbcdccccdadcadbbcdbcbbbdbddaabcbdabcadbbccacddbdcbcccdbdabdabcdbaacccccabcbcbcbcadccadadcdcdbbbddbcadbdddcdabbbcbbdbccadbdadbddbaadddbddadbcccbddababcbcddabdbbdbcacccababbabcadbdaacbacbdaccadabbdccbabadaaacbaddddbaacabadacbbcbbcbdbbdaadcbbcddcabaaabddbdadcdbbbbbadbbcbccacbcbdcdbaddccaccbacddcdcbdbddbbdcaddcddcdcaadcabbcddbbcbbdcadbcacbbbddacbaadaaadacabbabbdabcabaccabdddadadbacbcccbcdbaadccadcaacdcbaaacdabdcccbaabcbdbbbdabbbabcbbbdbbbbbbbcbabcdbaabcddbaccdbcacbddcdacdacbbbcbddbddcbcadbdcabcacbdbcadabadbdacccdacaacbbcbacdcddaacdadabcacbcbbbacabccdcaddddcbcbadadabcddbdbdbddccbaaacbddbcbccacdbccbbddaababddbdadccbdabcdcaadbccccbcbbcccddcbbccadacbaacbcaddbcdcabdaaccdbabadaadbacdbccbcaadbbddabaaabbdbbdbaacbdbdbaaabbbbcbddaddaadaccddadccbcdaabdbadcdbbbbdbddbdbacbdacdbcbaddaddbcacbacaadbdadbbbadacdbacabdcaacaaabbbdcabcdbcdddbaabddcbdbadbcdddabddbdbdcdccdaaadabdbcabbbaddddbddacbbaabbbaabdccdabdacabcadadaaabbdaddddabddbadabcddbdbccbbbaacdbdabcbbcbdddcdccacaacadacdbcaadcdadbbaabdddcbbdddbacaccbacacdbcbcaacaacbbddcdcdacabddccccdccadbbcacacddcbdbbabacbbdaadaadadabadadababbadaccdadacdcabcaacbcbddbcbdcadacbabbabcabcdcdbaacdddaaddbcadaabddbadabbdbdaacbdcacaaadcaaadaabdcadddababccccacaaaabbbadcabdcddaaadcdabbcdbcdadbdaaaddbbaabadadaadacbbaddcbacdcdadacaacacbbccaadadcbdbcbbddbddbdaacbcbbbdabacbaabdabdadbaadacacbadaccdabcdccddabdbcbadcacbacabbbdbcdbcddbcbdccbaaabccabcdacaacdbbdccddacacbbacaabdabdccadcaaacbadcbcdadaaabcbdddcabacbcadccddbbcbabddacbbcccbacbdadbadbcdcdbadcadbdcdccabdaabbdbbadcbbbbacdaadaaabcdaccddacacdbcddaacabcacaddbaaadbdccbcaccabdbaabdaabaddddccdcddccbcaccbccbcccdbddcdcdadcbacaddbdbddcbbdaabadcabacadcbbabbaccdbcadaccdcabddccddbdacbcbdcdcccacbddccbccbaabbccccdbdcddcbcabcbddbcadccabdaababcaddbaadddcabbcacdcbddbcacbdaaddabcddbcadcacaabbbadbccbcabcddcaadcdbddcbdcbdbdbcbadaadddadaccccacadcababbaacdcbdbdacbccbaaddcbbcdabbcbdbcccbdbacdccaacabdadbbbbbaababccbccabacccdcacdcbccadaababbbcdadddbadacdddbdbbacacacccdcaaccbadcdbbacaadddabbbddadbabccabaabdbccbcdacbbacbacbbbcdbbcadcdddbddabddcccacdabbdccdaaabcdbcaddbdcdcaacbaacaacddcdcbaccacdcddbdbbddcdbcbccbcddbbddcaaaabccbabbacbacbabdcdbbbdcdbaacdbbcabcadacccdadcbccddbcabadcdcbbdccdadabbadcdcadbdabdddbbddddbbcccccaacaaadbddabddabdaacaccabcbbcbadbacbcbaacabbbddcdcaadcddaadbbdbddabcdddddbadcdadcbccdccccbdbdbaacbdcdaacddcccabbdcdbaabaaddddcbaccadaddcaabaabccabacbbabcbadacbcdbddddddaabdcaaabbbadbabbbcbbadbbadadacbabbdabcdaddbbcacdccbabcbddbcbbdabcadabcbabbdcdcdccccacbadacaaadbabdadbabbcadabbcbdcababccbadcbcabaaaaccacbcabcbbdcacbbabbbcaccbbadccadddbbaddbcdbdabbddbbbbacdccadaaacdcbcbccdadbcbadabadbddcddcdabbdbbbcacdcdbcbddacaaccdacadbbddcacdaccadaccddacabcdadbbaacbcbbabdcdaabdabdbbbadcbadbaccabbcdbbdcaadbacddddbcbdcacdabddcccdabaacbadccdcdbbcddbbbdcaaccacbdcabaadccdbabcbcdabbadacadbcdadbddcbaadabbbcadbbaccacdbbdbbcdadabccbaadbaabababdddabcbcaadacadbcdacbbdccaacbcabdcbbdaddbcadaacddbdbcbbadcbdabdbcaadabcddcbdbacdbadcadcccccccaabacbacacbbcccbacddbdcaaaddbdcaccaadbddcaccadcddcaabdcadbddbdbdbacacdababcbdabcccddbdbdacaaadabcbdbcbcbaacaddccbdddcaaaabaabdcddcdcdcacddbbdcbaaaccbcbbadadbdddccadaabcddbcabaddcabdabcccddbcaacadacacabccacacbcadcaaccbddcabacbdcbcbbacccbabccdbadbbbbbcbcabccdacacbacbdabbadbcdddabcdcdcbbccdaaccaabaddbdbbbcbadbddbcbaadbbaabbbbacbadbbadbbdaacaccbdddabaddaccbbdbcdabacddcabbbcabbaddbbdcbdbbcbcddbdbdbdcaabaabacccbaacdacaaddcddddddbdcdbbbbccadbbcbcdcaacaadbacabcaaacdadddbbcaccbdbdbdcaadcaaddbcdabcdcacadaadbbbdddabcdbbccddcdaddbdacddcaaadabbdacccacadbcbcccaaccdcdaddccdcaaddcbdddabadbbddccadccddabdbbaddaddcdbaddbaaadcababcdcdbdbbbbdcddcabdadcabcabccbdbbcbdbaddcdadcbdbdadccbbdcbbabbcccccbbccababdbddaddabcbbddbaaabbadcdbdbcdcabcbccbadcadacbbabaaabbdbccabbdaacbcdccaaccbabaddbcbbbdbadacdcdcabdabdcbddcbcaccdcdbbaabacbcadacacaddbadaacaddcbadcddccbdcdacaaddbcbbdcdcabbadabcdaddacdbaadcccabcbbabcbbbacbcdbbcbdacdccaacbdbcadddabbabadcacaacbdaabadbcbccacabdaadcdacdcddccddbbbabaadbaccddcbcbcbdccabcbcdbcaadbaaacacdaccabdcdbcdadcdaaabbacacaacbbacccdacdadbdbbababbbbcaaaabaabcbbadcdbdbdbacdccddcbabadadcabacaacabbacbabbaccdcacaacddacadbccbbbadddcdabdcacdcaaaaddcccdcbadabacabbacdbacdabdbbadbdababdbaadcdbddcaadbddcbbbbcdbcdaacdcbcabcdabdbcaadabaacdddbcdbdcabbbacbcdcacddccddcdadcccbdcacadcbdacabacaddabdcdcbdcdcbbdccacdbaaddddaacaacdcabddabbdabcacacdcbcaddaabacbacdcadbbcbcdcbbaddabacdcaadabbbddcaddcabaabcbbbccacaacabbccacaaadbadaaddbddbbcbbaaaacddadddcdbadbabcacddbdcbaaaccbddbdbaddcbccacdbcbbbdbacccaacabccaabbbcaabccacdddadcdccdccdcdcdccadcdbdacadbdbcdbaaddcaaadcdaadddacaadbadbacbabbdbcdbaacaccccdcadbabadcaaaaaaaccadacccaadcccdbcaabaabaccbcddccaddcbdcddacbcdcccbccaabccbbbacaabbdccadadaacddbcdbddcabdaabdccadccbbcddcbdbadababbcbaaaabadcadbbddabaddbcdbaacbaaabcccbbcdbdbccbacbcddcbcccddbcbbabdcdacccdcaddcaadbcacbabbdccdacddaabddaabdcdcdbbdadbaddccbcdcbdaaccbddccacbdbdbaabdcbddacdaccabbabbaabacbcacadbdacccabdddbcaaaabdabaaaadaacbbacdacdccdcbcdbccccccbdcdcddbadddacccadcbcbcaabddcaddbdaaaadbddcbcdbcdddabbdbdbdddcadacabddcdadcaaabccccaabdbcdccdbaccdbaadccaadccbcccababbbcdadbabbacddacabdcbdccabccdaadbdbdbcbbbbcdbcbcdcacddacacdccdccbddacabacbcaddbdbbaaacccadbbbcadbdaabdcbdcddabbacdbabadabadbbddddababadaddbdaaabddcacababbddbbdaaacdaacdbacacdbaacccacadcaaabccacdabccdaacbbabccdbbcddbaacbabbbcdcdbdccdbbcbcddcbbbbcdaadcbcbdcaccbdaabdadadadabcdbdadddbabbcabcacddbbbaccbaabbadcccacaadabaabdadbbbbbdbcacccbcacdbabbdcbcbdadcaababbabdcadacadaacadcadccbbbbbcaaddddbacabdbabbdbdbbbdcdcacadcbaaaddaadcccdcaaadcbbcbcacdbbcbbcbbadbbcbdbadcbdbcbbdaaacdabadbbcacaadbddbacdcaddaaaabacbbcddbcababdbabcdabcdbabdbcacaddcbdbcbccaabaacbdbdbdcccbcabbbbbabbbabdccdabbcaacacacbbadbcbddbcdccababdbacbdcdddaaddbaadbdcdacbbcbbdbccacaadaadccbddccabcbaccacbdbbabacddbcbccdcddacdbababccaacbaabddbbdcdbbdabacbbdcaddacabdabdddacbcdbcdbbaacacaaaddbbadcdbaacbbcddcddabccdabbdbdcacdcacbcbcddbacaccbddaaddcdbabcabadcbacbabccaabbbadbdbcdcaadbdcddaaadbadcbadcdaadddbdcdacaabaddddddbdbcbbdabcabcacacccabcbacbcbcbadccdbaabddbccdcbacacbcdbcbcaadbcbadaccabcacdcaaaddacdbbdbbcdabcbbdcdcdccbdccbcdcbbdcdbcabcccabdbbddacccbbbbdcbbdadabbaacbcadccdcadccaddacccaacbbcdcbbbdadaaccbdbbabddadcddabaddbdbbaacbdddacaaadbadbbaaaadbbbbcbccbcdbbcdadbaabdddbadcadccacdabbacbdbbbbbddcbdadababababcbaacbaccabccdaddbdabdbabadcbbbcdccbdbccabccabbababccadccaabbbcdbaaccabbdbddcdacddaaaaadabdaddadbddaacbcccbacdcacdcbaadddbcaaaabbccacbddbbddbccbdbcdacdacdcaccaadbcbbdbdbddcbdabacbbbcdbcabaabdcdcdcabdaadcbbadbdbcacacabbdcddadddbddbdbadabccadddaadcdccccbbbacdbacbaabcababccabbcbccdbbdbcdadacdacdbbdbadbaddcbaccdaddbcbbabbaddcdcdcbbbbdcabadccbdaadcddbaccbdcbccddcdccccadbcaaccddabadcacadcabbddadcbddbbdbccbbadcaccbdaadbbbdcbbccacccdddcbccaccdddabdcbcdcdaddbcbacccadcdbbdcdbabddaacdabadddabcadcbcbcbbdaaaaaccadbdbdacbdacaccdcbadadaacdbdbbbbcdddccbdbbdaabbabcbaaddbddadccadddddcccabdaaabbacabadaaabdadaaabaadadbacbadcaccabbaccdbcbdaaddbbcdadbccbbcdcbdbaccccaababdcdcdabbcddbaaabdcccdcdbbbaddaccaabbcadaabcdbabcdaabbadbaacddaccdaabdcabbbaabddcdccbbbcdccdacbcabbbdbdddacaaaddbcbcaddaaacabbaaadcbccaadacddbcbacbdabbacbabaddbdabcdadcbacacdbaccadbabddcccadddcdabababcddaabcbcabccaacccaddaacabbddcdcbbbdbbdaccdbbcaabdbcbbabbcabbdbccaadbcacabbabcccbbcdcbabdabcddcdbaaacadbbbbcccbbabbcdbcdacbcbdacadcbbbbbcabdddcbbbbbaaabccdacbcaacbbbbcbbddccdddcaccddbbabaacbbadadbbabacbaaabccadcbabddcddbabcabdaaacabccaaaacbaccabaacdddbcbcaabbabbcacbdbcccadccdbccacacacbdadddbabdaccabcdddcabcbddbdadaaaacbbdbccbdbadaadbbbaabbacbabcdcbaacbcadbabccbaacacabddabbaabdbddadddaabbabbbdcadddabacdcdbccccadbbabcbaacbccdcabaaaddbddabdabcdadddaccadccbcacabdcddabcbadbddccbddaddcdddabacabcbbdaacbdbbbbcdcaddbbaadbddcaacbacacdbdccaddaabbcbdccacddaacddcadacacbadddcaacaabdaadcdddddbdbccbadbbcabaadbccaadcbdccdcddbdadcadbbcccadcbaacdccadababdbbabdddadbacdadaaddbadbccbacadbcbbdccacacbbdacadbcaddbaabdbaacdcadbadcbabbbcccdcddcbaadbbdcdcbabbdbaadabbadaababcddccbddcbabdbabbcccabcdaddbacbcbdabbabdcddcddbdcabdccbdcdbcadabbdabbacbdacababbcddbcdadbbcaadabbabcbbcbdddcaccabdcdadaaddcccbaabacccdbcabacdaadaacdcaacacbdccbbdbbadcbbdaaacccabcadbacabbacbbaabcacadddcccacacbbcbcbbacbddcbbaadacdbaabddaadaaaddabbaaacaaadadccabacabdbabdbcaadcaddddbdbadabcbcabcbbbcdadccdccbcdbbabacbddbbbbdddbacacdccdcdbddcaacddbddcadbccbbcadbabdacdacbbbacbdcdddbbadaacbdacabaddbacbabbbbabbcabbcaddacaacddccbabcabbaaccbadaabddcccbbbbdabaddbdadbdbaadcaaaadcdccaddcacdcbdbabdabccabbaabccbdacddacabdbaaddacacccdbdaacbdbabcadbabdcaacdbcabdbcbabcabccbacbbcaadbdaddbdadbabdddcbabbacdddabcdbbbddbacbcbccddbdbcdcbbdacacaacdabacddddabdabbdbbcbcbaaacaddaccaccadbdbaaaccbacdddaaccaaaddbbdabdcadbbdbdaddadbccaaaadabacbbbbacdcdcbcbbdcdacaccbdbdaaccadbdaaaaaddaacbdaadcacccdcbdcdcadadcaaaaccddbdaccdadcaaabbbadcacaccbbdcbdddadacbccdbbdcaccdccbbaadaabbdbdaddabddabdabccaacbcbbcbacbbadabbdcbbdcccaccdcdddcdbbaddcbadccbdcccbdadadcccadbbbcacacbcbcddabbddcacbacdbddbacacdccccbccadaabbbdabccdaaddbdabdcacbbdbbababbcddadbbdbddcccbcbdaadcbbdbacddccddbccbcabbdddddcabcdbacbbcdbddadbbbcadccabcbdabbdaababbacbcbbdaaacdbcbbbbabccaacbabddcabcbcbbcabdabbbdaabbaaddabcadccaacdcadadbddcabccdadcdcaaaddcdccbccaabaaacbddabababcaacddbcadaaadacadddddaadbadcadbbcbacbbddadbadcbcbbabcaccdacadbbbddcaddbcacbacaadacccbcbbaddbdddacdcbbddbbdacddbdbbbbccbacdbcccabbdbaddabbdacdacabbdaaddbdbbdacddbacdcdddddabaacbdcdcbaacacacbdabadbbbcbbccddbcdbdddbcbabbaacdbbcaccacbbcaaabadbbadcbdbbaaacbcbbcacbcbbdddbbcbdbcdcbbbccbbacbcacadddbbbabcbcaaaddadcbcdbacbcccccabcdcdacbaaccaccaabaacadbcdacbcacdcccaaacdcbbdddacccabdddcabbbacccbbbcabcbdcabcaacbbcbabbddadcdaccaaccbbacccacdcadbdcabbbaddcdbacdabcbbaabcdadababdbacdccaabdacaabcacccacdcaabadcbdacaddddacabdaadbddcaabcbbbdcdacadabcbaccaccccabcccdcaddbddbbdcbacdbabbcabcddddabdbcbbabbccaacacabddbccdacbaacaddbaacaadadbdabacdcbdbcacbcacabcccadcaddcbaddcbddbbcdcbbdccdbadaccacaadbbbddcddacdabbddcabbadbddacbdbbcaddcccbcacadbdcaadaccbdbaabaaadabbcbbbdcbacdbbdbcdacdadbcbbbbbbccaaabadabbcdcbbacbdbbcdcabdbbacabdccaabccbdddacadcccadcbababbbbacbbabdbcdababdcddacaccbacddcdabaadcbbbcdaaaddbcdcbbbcaccabcccdddcbaabdacaaacaddbbcbbdaadaddcccaccdadcacbbacdbbcaddaacddbdbcacdbbabcbbbbbadddbaccccbbabdcbbaddaccbbadbccbbbcabacdcabadccccbadaacbbadbcaabbcddadbbdadccacbbacbcbccaaaacddabacdadacbbbabbaacabadaaddccacdaddaaabcdbbbbadadabdaccacaacbcbbaccbbbccddddddbbddacaddbddbbcccdcacbcabdbdcddcacccabdaadbaaabccddddaaaaabdccaaacddaabcaadcbcbdcdaaadbbcdbadacdadbabcbcbdcdbcccdcdbdccccaacacbbccaacdbabbadaadcbbcabbdbcdccabcbadbbadabdaacaaababdcddcabdbbcbcdbabaddbabcbacdddcadcdcdacccabdbacdbcadcdbcbcbaccdddbdcbcccacdcadabbcadbdaddddbbbabdacdacdcabbadcbadabccbbcdabcbbcacbcaaddbaabdbddbbcbcbacaccdccdcddadcccbbacbaacbcabaacdabdacbccadbcddacaaacbcaaadcbbdccbbccdcdcbadabacacabccdbacdbbcaaaabbabcdbdaaacddbcbdcddacbcacddcbbaacaacacdacadbcccbcbabcadcbbabbaabdadbadbadbbaaababacacddadbcaacadbdccbbadaababbbbcabaccacaacddaccdbabccbdacdaabbaacaddbaaacccbcdbcdddcdcaabdbacabbccdadaacbdcccabcccbadbddbacddddddabdddaadbacbbaaddbcbbbbabcdacadcbaadcabbbaaaddbcccddaaddbabadaacdadaccadacdcbaddbbcadababbabdbaacaacdabddbccbdbdabcabcaddbdabddadbaadabdaabcadddbccdbaccbddddddcacdcabcbcdaddcaacacdadacbbbacddabdddddbddcaacdbcdaddcadabdcbccdaabdacacabbbccdddccbdacccddaaaaaccaabbcdbbabaacccabdbdbdcbccdcbdcbdabadbacabcbdcccbacaaabacdbbccdcdcdcbbbcbaccbcddbadbcbcdcdccdbdccbdaddaabdcbcbacbdcbabdabbbdcabdcdabcdbbbbaddacdadcdbabbadbbccadbccdbdaccbcdacdbbbbaabbbccccaddddaddcadaaadbddadabdabdcbccbbabcabbbbcdcdaddbaddabbbaadadcbccacdccaacaadbaabbdcddcccdaddbbaabaccdadadadadbadbdbdcdcccbdabacadbaccacdcbdacbdbdaaadbdcdbcdbaddcbaaacdddabbcbddbcdaccacddbbbbcdcccbcccddbabdbdccbacdabdccddcadcccadcadbcbcdaaddabaabdacadbdaacdcaaaabbcbaccdbbcdbcbccdbaddbcbdbdddaadcdccccdbaacdcdbddddacdbbbdccaabbbacdbcaaacbccdadcaccccccccdcacdbadddccabbcbdbadbcbdbacbbdacdaadaddcabcaabacaddadbbcabcdddaacdbccabddccaaadabaddadacadbdbbcdcddbdcbabcdbddcdbadcdaadcddabbbaddaddcdbbccbbddaabbddcddbbdabbcddbdbdadcbabbdddcdcdcdbadaacaaddaccabcdbcacddaaabbddbaccdbdccbcabcaaaaacbdcacddcbbabdadddaacacbbcbbbdaabcdabcbadcbdaadcbcccbdadacbdcaadcdccabddbabbccbdbadcddbddbcabbabbdcaacddbddadaaddbbabdabdcddbbbcdcbbcaabccaadcdbaadaabddbdccdcdbaacbdbcbcddbbbcbcaaaadcdcdbbdcddcadbadbdbcaccdddcbaacadcadaacabbccdacbbdaababcdbcabbaacbbdcdbbbdacacddbcdcaadcdaacaadccddaabacdadcbdbddaacbbbbbcddcbdcdaabbcccabcbdabcbbdbdabaaaddcbaadcbbdbadbcdbaacadabacabddaccddacbaccbbadcbdabaacbacadabdcbdaaacdabbabdbdcdbcabccaddadcdacbbbabbdddbbdaabbdaaddbadcbaabcbcbccccabdbbbacaddbcaabbdccdcbddcaaabbacccabbbcbbddcaadbaacababadbaccacbbbaaccabbcaabdbdcabdcaabadbbcbdcabbdaabbdabdcbabcacbddaadbbbadddadbdcabcaabdccdaabddbccddbacdabcacbcccbacabdddccdcddbaabcbbddacdcbadcadcbaddbcbdccaaddacbbcbbadcddcbadabdddadbdcababcbbdbaabdbadbcaababbcbdcbccbddddccadbaddbbbabbbdcaabbbdcccabccdbbaabbddbcbbaacdccbbaabcccbcadcacbdcaadabccddbabcbaddadbdbdbadaacabbdabbbcaadddbadaabdbabdcaabcacddddbbcaadaadabbbbbaacbcccabcabccdcddacddadbadbbdcaacbcccadbdbdabaabcdbaaddbbdaacdacabdcbacbadcabcddddacabdaccdcdbaadaaadcdbcdbdbacdcbdababdccdcaabbcbbabaabaddbaadcbcacbdbaddbccbbadbdbbccdbdabadbddbaaddbaaabbbbdcbadcdbbadcdccaddadbddccccabdbcbaadbaabbbdacaacdacabadcadddabaddbbcaaaacddbbdcbccbacddccadcabababaddcddbdbabaaacbdcaacdcadabbcadcbbadccdcabadbcadcbcbababccbdbadbaddbbaabddbbbdcdbdcaddabaccdacaccaabbccccadadcdaabaabdaabbacdcdbdbcdbaadaacdddcccacdaaabacbacdbadccacdbabddadbcbcccbbcbbcbaabcbaaadccdddbdbddcabdacabdbbadcbcbcaccaadccdbbbdcacbccdaaadadaddbdabadadccdcddbddcacbcadbdcabbcbbbadbbdcbcdcbdbdabddcbabaaacddbcdadccbddbcbabdcbbadbacdcccadacaadbdadddddbcaadabdbcdccdcaaddcadababdaaacabcadcbdadbdcdbadcbdacccdaddadbbddaaaddacbaaccabbacccaacbbbabaabdaddcbdcdacccbabdccdaccdcdcbbaaddccddaacdacbacadcbbbbddacbadcaadbcbacdcbbadadbddbbddbaddaaddddacccdccbbbadddabddacbccdabbcbabcbddacababdadcbcbabdbaacbbccdbdabcadcdabccdcdddaaabcacbdbadcbbbbacdbccccdcaaabbdbcdbaacdcbbdddabcaacdcaccccbcdddcacaddcbaabcbdacbbbdccbbcccbcacabbbcdadbcddbdcddccabdbabcdcbdbdcaaaaadbbaaddcaddcacaadacdacccaddcdcbcaabcaccbdbbaacdbddcddcaacbabbbbbcbdddacbcbbbabaabcbbcdaadbbdbaddabaadabdddccddabbbccddcadccbbacdbddacadaabcbcdbcabbcaabdbbbddddcbbabbadabbdcdbbbccdddabddddadcadcdbaaddccbcaabddbccccdcacdcaddabdbcdadacbcdddccabcbcababbadddaacdbbccaddbdbaacdbccdcdcccbadbdccdbbdcdbbbccabacbcbbdbdbcdbbdabbcabcbbccaddcadabbaacbdacaaccdbbcdcccdddaccddbdbbabadbadddcabdcaacbbcbcbddbbbcacccdacdcabadbdcbaddcdccdabbbdcbbcaadccdbcaadcbccabcbbdccbcdadbaadbdddadbacbdadbcdbdbddbdbccbbdddbadaddcddcabdbccbcabcadddadcbacdaccbcabddbddcddbbaababdbbacbbdabaddabcddabacccbbcadccbdabaabdcdadaaabbcaadcaabcabbcadacbcdddacbababadaaabaccddacabdabdacadbcbbbabdddcdcbcaadddabdddaacbcbdacbabdcbcadcdaabcadcaadcdddadddabdcacbbaacaddbabdbdbbddcdbbadcddbdaaadbbcbdbacaacbbdbdcbbbdbcbaadddccabbaccbddbdcdabbabddbcacdbadaddbccccbbbcabcbbdcdccdaacddcbabdacddbacbabccdbbdcaccbddbabcadacbcbadcaabcccaacccbbdccccaadcddcbbadbadadbdadccbacccacacbaadaccccababbaadaccdcbbbaadbdbaadcbcbbadcdbacccbbdacacacbabdbcdccdbdadaadbabdddaaabdcadabdbcccacdacacccbbddabdbbbbccdacbbaabbabcdcdbabdcddbddccbbcadabdcdabbdbbcbbdddddcaabcbccaadababbcbdcddcdaaabcdbabcbcccdadadadcaacbdccbcdccdcaadccbdccccccbabcdacbbddbdabadcabaacbcdddbbdddcbaabacbdcbaadcaabcbdbabbbdccddbbbdcadaddabdabbabbcaacdddccdacdddacacaddbcaddacddabaaccaabaacdbdbbabcccabbadbcaaaddcacadbcadbddadcdddcbcdaddbdacdccbcbcaddcbaaaadabbbbbbcaadddaaacaaccddababdabbaddacabcaadcabaabdcdbaddbcdaaccbcbdaabcbabbaadacaabbbbdcdabbcbadbdaddabbdacbdaabbbacaaabbcacdcdcaabbdcaadbcccdcbbacdadcddcdddbdcdbacbdccbaadbdcdbaddabaccbdcdaabbbdaadcdbcbdccaabbdccdddaaacacbbbbacccaddcadcdabbccdcdadcadddbabadcbdbaaccbdcadddabaaabdcbdbadaacdbcdcbabadbdbcbaaddcbadabddaabbccbcdcbbcaadaddcbcadadadaccacdddccaabaaaabdbacbbaacaabbcbddabaababbcbcaaaaadcdbdacdcacbdbdcbdcdbcbaabcbdadacbbbcadddbbcacdacadbbbdcdadadddaaabdbccbddcbbbbbddadaabcbabdacbdabacbbacaadbbaaadbcbdbddbcbcccddadabcdaabcaabdbcadcdadcdddadadbdcdbbddcbabaacccbbdadcbddbaccadadbacbccbacabdcbdcbdcbccaaaabbdddcbdaccdadddcaacbcbdbbbacacaadcbabadcddbcaaadadcdaabdcaadadcbdbbccadabaccdcbdbcbbcbaaabdcbaddcacbacccdccbddbbbdadbacbbdcdadcdabddadbccbbdcbbaabcdabddabacbdcbbcbbabbccbdabdccacbaacacbdbacccdcaadaaadccacbcabadcbdcccabbbbbabdbabacdcccbccaaddbbdaadcbcbdabdacbddcbbccdbbbdddcdacbccbdbdabbdaaccaadaaaabbababadcccaabdbbadbdcabbbdcbbdcaadcacabdabcdbcbadacbadacabacdadbdbbddbdaddcdcabbcacdaabdbcacaabbccdbaadddcacbddbbccadbdadcbddddbbcccddcacabbcbcddddbbbcbbabbdbbabdababdaacddbdaacdbdccccccdbdccadbabaaaabadcbdaacdadbbcaacdbabbdbbaabaddbdcddaaadcbcdcbdcbbdddadcadcbacbcdcdadbbcddccaadddbaaccdabaccacacacdbaaacacacaabbbcdaacccdadddbaadbccbbbdadadbcdbaddbdcdcccacbaddccabcccdabcdabcbbacbdaaacbbbdbcbdbabbaadbcbaddbbdbadaaadbbcddbaaacdcaacbdacbcabbaddaccbdbaabdbdcddacadcdabdaacddadaacbbaaadacabcbadccdcbcccbdddddbbcbacacadcddacbabdcbdbbbbbbdcddcdabdbbdbaadbbdcdbcabcadadbbaddaccccabcdbdacbababbbccadacaddabbcccabdadabdaabdcaacdbbadcbcadddccdaddbdccccdbcbdccbdabbbcbdaacaccbcbbdddaadbddadcbaacdbaaaaccddbababdaddcbaaccbdcbbbbbbbacaacbcccccabbccdbcabaddbabccbccbababcdddbbabdcbacaabbccaaccbbadaaabcbaacbcaacbccaadacaaddbccbcddaddcddddabaddbdcadcbccbaababacdaacadbbbacccabcaccbbccacddacdcaabcbdaaaaaaaddcdadadcbbbcaccdccacbdcdadcdccbccdccaddbdaaabdbaaabdbddccabdbbbdccdcadddcdaccccdccbcaadddccadbcdbabccccddabcacbdcbbddacacbccdbdcaccbcbddbadbdbdbbcbcccccaddbcbbdccdcaabcabddabcbbcbacccdcdbccdbaccbccababbdacaaccbbdcadbddcdaabbdabdcbdacadbddbddcbbccbbabdabbcdbccddabddbbdabaabccaabccdbabbababdadcbbccacbcdacbccbcadbbdaacccbccbdacccbdaacdbbbbcbcddaabbaadaccccadbabdccdbddaaaacbcaacbcccccbbdaaacbbdcccccbddcbbacdaaddcdcbcdabcadccdbccbadbabdccbccdcdddcabdbbabbdaabbbabaadbbbaccadbaacadaacbcdaabccaaadcabddaddddcdacaaccddccdddcaddaddcbdacacdcbcbdcdbbdbaddccbdbaaadddbbbccccaaddabbadbbccdbaaaabbbabcbaadbaabcaadcdcbacbdbababcbbdcccabbbdabbcbadbdbbcbbbbcadcdddacaacdaaccdaaaacdacdcaabababcadbcdbdbadcbdcdadacddddabbcdcaaacbbdbacdcaacabddbdaacbddbdcbadadbcdadcbaacadcccdaacdabacaaddcdaabbbdcbcbdcbdbbccaadcbcabacdabcbcdabcdcdbcddaacbcccddadbcbaddccdcbddabcdbadaaccdcbaccacabcbdbacaadadbdbdbdccdbabdbccdbcdccdacdadaacbdabbcdaaaccddbaadbcdbdaccabdddabddcaaadacabdabcacbbbaacbacacaccbbdcadddabbdccdbbbbbcdaacdabcbbdbaaabcbaccbaabcdbabaddcadbaadddababcbcacddddcacdcdcadcaadabcabddcbdaddbaaaddcabdabdddaaccbbcccdacbbcdbabddcccabaddcbcadadacabbbddaabcccababbdbbddddaaabccaddabbdacdcccdcdabccdbaabdbccdbacabbdcbcdcadcdcadadbbcbaadbbbbacbcbbbabadadaddcccabccdaddbdaaaaaddccdddcaccaddcadadbaadcaddbaadadcdaabbdbbbaacabaadadabcddababdbaadddacadcbdccdabcaabaccbaabbddbddbbbbddcbadbcddadbddcdaaadacbddddaabdcbcbcccadbabbdacbdbadcddcbbbacaddacdaddbbdabddbcbcaadbddaacdddccbcdbcbdbdbbbbdbaaababcbaacbbcaccccdcaacaddbbcbccdbddccaaadddbdccbccdcbabbaaadbdabccaacbabdcbaaabdcccbaddbdddcbbbddddadddbcaabccbbadabcacdbacdbccbdbdccadcdbcbdbcacdabbaaaddcddcbadbdbaddadccaabdcbaaccccbcdcadcdaadbccbdcdbaaaabacbbdbdddcbbdbbcbbbadaabbbaccddcaaccbdcbaabbbcbbcccbcabbdddbbacddccdacdddabbabbacccbbbddcacdbaaddccbddbcdbadcacbccbcdccaccbbdacabdbdcdadadbddbaabdbbcaaddaaaabbbbacddabbdacccbbaadcdacaabdcdabadcaaddcddadacaabddbcbbbabccdabcadacbcdaabdbdbddbbdabbacbbabccbacadabadbdcbdbbbbdbbcaaadbdddaabcdbcaaccaaccbababddbaddcdcddcdaacccbdbbcccccbdbdcacbabcbbbcbaccbacccadabbbbaccdbcdddccacbdaddbbbcabacabadcbabbbbcdcaccabadddddabadbacdcaaccccdadddcccaacacbacbdabbddadbbbbcbcabbabacdcbccccddbdcccbbdcacccbadbadadbbcdccaacdbddddaacbbbacbbbbbbbbdabdccbaccdaadccaaaabdabcbcabadccddaabdadbcaccdbdaccdcbacddccbbbabccddcddbbaaaacaadcaddabdcbccadcbacbbdddddbcdddcacaadbdcaccaaddcadabadbbdbcddaccccabcdbbcabdccdbbbcbdcdcbadaddacbbbdaabacabaabbbdcbcbdbcbdbbcbacadaabbbcbddaabdbaccacadbaadbacddcbcdabdbdcaacbbddadabbaabdbadcabadcacbacbdbbcaccccdbdcbbabcdcbacadcccdcbbcddbdacbbcccddcdccbadcddaddddabbcbbdbdbcdbaadcdbadccbbddcccadacadabcbdcadccdcbaabbadcabadcddccddcddddbbcadccbdddddddddaabbbccaabcacacdabccbadabddcbbaabdbaabbbdddddddcacabcdccacdaabbbdbdcdbbccaaadaddabbbbdcbbddcdabdbcdbdaaddbdadccaadcddaccccbcababcabdcaaccdbcbbdbbddaadcadbbcccdcdbcbdccbdabbacbaaddabdccacaddbddabaaddbcaccdbadbdcaacdccabdbccbabbdcacbbdbcdabdaabadbccccdcbbccbabcbbdabccacdccadbddcadadcadbdadcbabbcddcabacbaacacdabaaadbccccccabccbabbbaadcacdbadddadadcdbdbadbdcbddadabbddcdabbdbcabdcdbddbdbbbbcdacbbdadccbbdccbddcccacacbadddaaaddcdcddabccccddbcdcadbcbbdbabbdccabbdbddcaaaddcbadbccacabcaccbdddabdadccadbaaadbacddabdbbddbcdbccadcccaabdbcdbaccbbbaabcccadbccabdcdabbccbbbdddbadbaccaccbddbcbdabdacbbcdadbcbbcdcdbcdbbddaadadccddadabcccbdbdacbcddacbdadcaadacdcbcccbaaadbbcccdaaacdabdcddcdadbdaacddddddaabbdabbaaaacdbacbcbbcdddcdadcbadcabbabadbcbabacaacdabdabdadaadccbbabbabcddbcddadbddadcccdaddaaddbddacbdbbabadcccddddcaccbbcbdbdcbcabbbccadbaccabbcabbadcbbdbdccdaccbdadbccdaadcbcbaccabbbabcbabdaddbabdbbdccdaabddcccdaaacbbcaaabcaaccbcabcacdaadabcdcddbacdabddadbaacdabbdbcdaacdccccddbddabdcbaacbabccdbaabbbacdbcdddaaaddccddadabdbccbcccddadaabdbabcacbcbcaaaaaadbdaaacdacdcaabddcbbabbbdabacdcbbcbbbdbcdaadddcdcbadbababdcbbdbcdabbcaadcdbddccddcadbccabdaadccbdcbbdccbabdbabbbdddadddababdaadabddaaacbabbdaaaacccabdbcbccaadaabcdcbcaadacdaccdccaacccddcdcccccdaabbbdccdcbcdcacbdccdcbdbcdcdbaabbbdacbdbbcabdacddbabaccccbccaddcdadacbcdcaddbcbdbdcbaaadbcdcbaccdbbbabdbdaabdcacaabbddbbbcbdddcdddaccccbddbaddbacabcacaccbbbbbabddadaadbccaccbadbbadccaaabbaccdadacdbacbbdacddbdcdbbdacbbdcaabdadcdadcbbcbbccdcbacaddbbabddbbbdadbcdbaaaaddabbddabadcabdaacbadbacbaddadadaacddbdacaaabbdcaddbdddddaadcaddddccadcbcbadbaaadbcdacadcbcacddaccbdacdccadcbdaaacbdadbababaaaadadccbbcaabdbbbbaddaccbdbaadddabdadddacdadddddccadddbdccdadbdcacacdcdbbbbdcddacdbcabbbdbdcbccbccaddbaadbcaccddabcdcacbbbacabdbbdaacccdacbcaaabbaccbbddcdaacbcccabddadacddadcdcacadbbbbbacaabcacccddcacbcdbabadaacdcbbdcccbbdaadcabbaccdbbdbbabbbbabaaabccbbdaabbbcadaaddcddaaabbdaaabbaabcdddddcdacbccaddadacadadaacddcddbbadccdbdccbcbdcabbdddcaddcdbabbabcadcbcbccacbbaccddccddacadababbbcdbdcacbbdabbcbdacdcabccddccbcacbaadbbbdabcdbcacadcbdbdacbdacccdcadacddcadcaaabbbbadcbbdabadabbcabdaddcbcdcccbaccbdbcaacbdcacadbcdbddcdbdcabcbaaccaadaaadcddcbdaaaabaacdddacacdaddccbaaccdbcaccddcdacbabbbaddccaadaaadbdcaabbcddcbddadacbbdaccadbbdbabbbccdddaabdbabaccacdddbbaacbddbcaacbbdcaadabaacbadadbcaccbddadbcddabbaccdcddaaaabbbddbcbcbbdaadcdbccacbcaaacddbacdddccddcabaaadddcdacdccdbdaddccbdcbbabacbcdddacdddbdacaaabcbddabdbcababcccddbbbabddabacccdbdcdbddbdadacdcdbacccbbcbacbabababbdacddaccdbadbadcbcabaadadaadcdbcabddcbadadbccaadcadcbdacbccbcbadcbaacddabdddaacdcbbdbdddcbabdacdcccdbaccbccaacacbcdabacbdcabdaaadbbadbcaaadddccdcdccccbdddabdacccccaccccacdbbabacadcddbcbadddaddccabdbaaaabadbabbbbabdbacdbddbcdbccccadccbadddacaddacbccdbbbababdacdcacdbdacdbacbbcddabdaabaacbaccdbdccbcaddbcbbddcdacbccbcbcbaaccadadacadacadaacdabdadbabcdbbbbdbdcdbcdbcdddccbcbbadcccaaaacbcaadacaadaadcacaddcbacdaabbbdbcdadddcdcadbcddadaacdadcddcaccccbadaccbdbdabcdadadbdddbcccbdcacadbcbccacaadcaddaabaaabbacbcbcbbbcbddaabbdccbabbdddcdabcdbbdabaccccddddbdddccaaacccabdbbadadadbbbbcdcbcaacbdbaabbbbbbababdbddaddcabddddcbdabaacbcadbabbbbadcccababcaaaccdbbcbbccdcabdddcabccbaabccbacbbddcbbdcbbbaccaddccdccdadaabbbbbbabbdccbacbaacdcaadbdabaabccadcbdbcadcdcbdcbbdbacbdadbcdcacabcddacdcadadadacccdcdbdbddaccbbddadbbdcdcacbababcaadabdabaddbbababdbadbbcbcadcdccadabdcddbccbdacddbdcaabdadabddbbbdbbdadcbabcbdbabbcaddcdcbacbcadbbdacddcdcbcdaccbabdaabaaddbdaacdbaabbcdbacccbbbcaabdbccdbdcabbdcdaabddabbddbdbdccbdcddacbcdabdbdacabcdccddcabcaabcbbacbbbdbdaddacbadcbccddbcdcdcdbacccccabadbcadcdcccaababdbcbbabcbadcaaabccaddbcbdacbdbaaadddccabdbddadddcbaadaaacdbbaabadbcdcdaddbdadccccabccdbddccbcbbbcdcbadddacbdcdadacbccbcbcbdcddbacaacaacbbcdbccbabbcabacdddcbdaadbccabdabdaadadbacaabbaadabdadcabdabccabdbccacbccacabbacbadbdaccccaabddccabbbddcdcdcaddbbcbdbabacabdadcdadbccacddbcddbdacdabadcacccadabbcbdbbaaaabccddacbdacadaccbcbddccabcadbbabccabccbbcbaadadcdbaccabbdababadbaccbabbaaccdbddcdcaadbdabdbccddacccbdacdcddbbcddbdbdabaaabdcbdbdbaababdccbbdcdddabcbabcbddcbcdabcbdaacccacdcbabbdabcddbadadcbbdbcdcacdbcddcbdabacbcdccaddacddadcccdddacdcadccdbaacacdbdddbddaccbdaaacbacadcbaaacaabbcdcabcdabbacbabcaccbccbdadcbaacbbbbaddcabdcabcbaaddadadaadbbdbbadcbcddbcbcdabaadbcacddabdbdbdbdbbbabbdcccadcbcbaaddccdcaaaccaaaddbbddcccbdacdaadababdcbcbcbbacbcddbccabcdcbdaacaacdccccdcadccdcabaaaacadbadadbdbcbdacbaddbccdbaacdabbbbcbbabcbdcabcdbbcacbddabdacbbcccddbabbbaadadabddaddcccadacacdbcdbadbcccaadbdaabddadcbcabdcadabcbaabddbacdcacdbcadcbcabdbccadbaaaabddccbbbcdcaadaababbaacdbdbcadcbacddbdbbcbbcacaabdcacdcbdbadabcacadccabccbcccbbcaaaaddbbdccdccbcadcabcaabdcbadaacccdabdcdbacbcaccbdccdacccaadbbadbbdcbdacdccbbccabccdbcdaaabdcdcaadcaabdaccaacadcadcccdcdddaadcaaacadbcabacadaaadbcbadcccdcdbadaaadadaccbbdcdcbbacdabdbcccdaddabacacadacccacdbcdbbdbdabcaacbbaadddccdaaabcdbcdbbbabaccbdcbabcbdbdbccdacaccddabdbdaadadcdcdabaacdcabccadbdbdcacbddcdddbdcbadccbcaadabacaadacdccddacaabacbddacbcaaaaaddcacdddcdcbbadcadbcccaaddddaaaaddacadcdbbcccbdcaddadacccdcbcbcdbaadabcaabcddacacaaadcddbcccddcbbdadbaabbadddcdbcdaddaacdbacbddbdbcbabcabaaacccbadacaaaabddcbdaaadaacbabcccdbadcccabdacddbdacdacbdcddbbdccaacbaadbbbddddbacadcabdadabbabbcaccbbcbdcbcabddaddbadbadccddabdadacabaabaaadababddbbacaabbbccddcabadbcacbcacadbadacbccdcdbcabcdbaaddcdcbdcaddacadcaabbbdabdcdbadcaacbdacccbdcbbbdcbbadaabddcbdabcacacdabbabbbbbcbbcddaacaccccadaababcdbdcdaacbddbabcbadacabccadacddadcbbaddacbdbbcabcbbcaaadbdbbaaddabcdddcbcbbbadccbaaccabbaadbacdabcbadcdadabcdbcddddcbbbadbadbbcbdccdbdacbcadabcbdabbddbddabbadcdabddaddcdabcdcbdbbbacbcddabcabaabcbdbdcaadadddcbbdadcacabccddadadaadabbbdaabcbdcbacbcddddcccbbbcacbdbaddbddcdcbddbcaccbbdbdabdbbdcccabdbaabccbbddbaddabacaacabcdaaacddddbccbbaacadcdbacdccbcabacdcbaacdbbdaabbcdaadacaabbdcdadbdabdcbaaadcdacaddcbdacabdabcacbdaabcddadddbccccbacbdbbbcccaccbcacdadcadcbbdbcdcdabcadddbbdabcbdbcdbbaadbbcaaddaadadcadbacbddadddcccbccdcddabdaabcbcdadbccabdababbbaaacdccbbdcabccadbdbdbcbdccacbdccabbbbabdaadddabcdbccbccbababccbcaddaccbabdddbacaccabaaadbabaacabbdaccbcdabdacdbcbddadddddddadacacdbcabdbacdcdbababdcaabdddaddabaccbcddaaacabcbddcaccadcbddacccdccbabbddbadcdabdaccddbcdccbcddbcccabbaacacdcbbbabcadddbbdbcadcacdadaabcccbbacbcccbcdccdaddcbaddccdabcbacabadaccddcbacdaccbbbadcccbdaadacadaaaadbdccbacababaaccaacbbddadcdcdbcdccccabaaaddcddbcbcababdaabcccbbccdccadabbaacbccccdbcbccddddacdbdabdcbbcdbdcdabaaabcdbabaccbcddbadbcddcbbccabbcbabadcbcdcdbdcaaccbcadabbcaacccdbadaaddbaccbaadaaaccabaadabcbabbadcbbbbcdcbbddadaabcdacacbcccdcdcbddddbddaabcdbaadbcddacddadccabdcbcabaaccadcabbcbcbccbccbbbccacccbcccbaacccbccaccbccaccbdbdbbdccccadbcdccbacdcbcdccabaaaabadccaababbdcdcbaccbdbbdbacabaaaddbccbccdbbcdddaddabcdaaaaabacccdcbabbddacbcadaaaccadaacaddcccbacbdaadcccdbcdababbbacbbacbbabdcacdcbcabdcdcbaddbddccbdaacbddadccadbbbcdadbcbaddadadccbdcddbcaacccddaacababbcaadacbbabaabbadaddacabaababbcddcdbcaabbacbccbddabbbbdcabbcddbbabbcabdccbdccbacabbbbbddaadbbbbaabdacddbacacbccaccacacacbcdacbabbaabcaabbcdbcaddbbdbaabdadccbabadbdbcdcaabbddaccaaaaacbbdcbdacabacadbbbcbbcdcccdbadccdbcbddbbbcbddccaabcabdacccdaaaaaabdcbbcdaabbbdcccbccacabbbdbccccddccdbcaaccabddabcdcbdacababcddcadbcabbdcaaaadacbcccaaacbbbccdbdbdabadabcdbacbbacbdbdadbcabbdbbadbbadaaddadadccbacbcbacabbadbcabccccbcccacbababdaacacdadbdaaccdbbccdadabdbacccdaadcdcbdcadcdbdacacdbcddcacdbcbaddaccdaccddbabdddaddccacddbacbaccdccdabdddbddddcccdcdcadbcadbdbccabdbdbdbabcdbdcadbdcdabaabbbadaadaaccbbccbdcdcacdbdbcddaaddbddccbcdaddcbcadbcdbdcdacadabbabaccbddcdaaddcbaccacdaaaacdcabaaacacdccaacbddbddddcdabbbabbcdabddccaadcacdacbaabbcbcdcdabbbdadabbcbcbcadccddaaaadabddcaccaabdcdadbdccacabddddaddadaacbadccabcbcccccddacbbbbddddbaacbacccaacbacbaabdddbdbccadcbbbddaccbbbcbdccddcdcbdadbbdabbcbdabdcbbbaadbcdaaacdabcaacaaabcabcaddccaadccabababcacbabacacacdabcddccbbadcaacbaaddcaacaaddccbdadcbbaacdacdaaabbcbdcdbbcaabaccbbbdaadadcadbacddddbadbccabdbbdccdcadaaaddbcddcddbacbcbbacadcdddcdcbbabdccdbdddcdbdadddabdddbdbddcbadcdbbbdccdbcbccbcdbacbdbaabccabbcbccdcbaadccdbcdccabcabdbbacdacdcddbdcdadddaddaddcadcaabccbdacbabbbadbcacbbdbdcbdacaaadababbccdcbbbbccabcdacdddccaadccbbbbdaaadbabcbabdddbccdbcaddbdbbccbdcacbaabdcaadcdaddbbcaacdcdddbbcbcbccccdacbaabdaacdbbaaabadcbddacdbbcbbdacabbaaddccdabcadcbdabddcabdbdcadddbadccbbbdbcaabdacddaabbaacdddbcadcddadaaadcdbccbacdccdcdcdcacbdccaccacadacbcbccdcabdccddcbcbcabaabcabdaabbddcbaaadccdbcddccdbbcbdbadaabddbcadbcddcabaacbcccdcbabdcddaacabacadabcdbcdaabbccbdbaacbdccabbdccdaaddbdccdddcccaaaabaacbdcddbaacbaabcdadabddcdadddcddbdcadccbacbcaadbdddcbbddbdadccbbddcccbccdddccbdccbcddbaacbacbddddacabacbcbbacbcaacaccdccbcacacdbaaabddddbcccdbbcdbbdaacabdacdbddccacbaaadccabbbccbdacccbbbbddbcccdaadbacdbaadcbddbbcbdcbdbaccdabcbdcbabdcddcbdabaccbddaccdbbcaddbbcbacdaccdccddbcadbbdabdbdbdcddbcddaadabccaadabcdcaabcdddabddccddcacddacccadbacaadbaddaccbdadcbdbbcbcbbbbaacdccccabaadddbcbabbaccabccaddacdacdddbadccdcabaccbcbdcaaacaabaabadaaadabdacdaaccbdccdacbbabbbdcddccdcbcdbbaccbddacacabbadbababcdcdbccadbcddbbccdacbacdcaccdadaabdbdadaacbbcaccdbabdbabbacdaaabcdccdccdaddddcccadbadbcbdccddcbccbdbaddacabadcaabdacaccbbdbabbcbcacbbadcccdbdacbaababdcdbcaccbdddadaddbbdbdadbcbcdcdbbdbaadaccbcbabcbcabacadaaddcbcbabcddaaaaacaaaccdcdaaacdddcabcdcbdadcaddcdbbcbbdadacabddbcdddbbacbababdcabbbbdccabdabbdcadaddbcdcbacdddcbaabdaaddccdadadbaaadbabadcacaacdcbacddcbcaaacdaddaacccddcbabaadcabaacdbdbbddcbabdacdbdbadabddbccbbbcabccdbbcccacadbdadbcbccdadacdcacbbcccaabddcddcacacbabcaacbbdcdabdbdccbccdcdbdaabcaabddadcbbdcaabcaacddcdbabacdccdbadcbddbcdbaccdcbadcdbccaaacbcdbdabadbacaddddbabbccbcdbbdcccdabaccabccbbdbaadbaacabaddddacbdbbbcadbcabacddcaccddddbcbdcdbabdaaabbbbadabbadddabbaaccadcdcccccaccbbbbdddabbdcdbcdbabbbdcddaccaabddbaddcddabccbabbbcaccbabaccaccdbcbcdbdbddbbdcbbcaabdadbadbdacabcbcbcadbcbaacbcddbddabddcdcbdcdabdbbbcbbbbddccdbabdbacaaaabbdcabdcdcbbaacbcccddbbdababbdbdbaabdbcbdbdcaacbdabdcccdcabcdcbddcccbccbbaadcbdcddcdadacbdccbbbcdcaacdaddbdabdbacddbdbdcdaacbabdaacabdcbabbbbbcacabdacbbaaabdbcddbbabddccbcccbaadddabdbaddcabdcadbbbcccaabdbdbbcdccdccdbabdddbadbbcbbbabbcadadcabdabacbdcdbcccbaabccdbdacbaadaccccbcadbddbabbcdddbbadbcddabcacddbbcbadaacbaacabcccccdaadabcabbbaababcdacbddbbacbacabadbdabbdacbcddbabcdcddbbadaacacddbcbabcabcccacbbdacbcdbcdbcadbbbabcdaddabddbaabbdccddcacbdadcddddcacbcadcdbcbdbaacbbdadccaabbcaabddbadbdcbacbacadddcdbccccdadcaacdbbbccbcadbcdbccacacacadccdaababdcaadaacadacaaaabcdbadbbbddbdbccaddaadcadbcbbddacdadadccbccaabcbcadaaaadccdadaabcddccdabcbcbbaccddcbcaabddcbddddcbadabbdcbadaddabbacbddabbcbaadaaabbddbcadacbdacbcaaadbbdaddacaddcbaaccddccabdcdaddcdcacbadbaccbadcbdcdbcaddddaccdcbddbacddcaabbdddaadcddabdaccccccbababacbdccdaacacbdadbdadcccddbabdbbabbddbccdcbddbacdbbccaaacbcccacacbbcbdbddacccdaacbbbabdabdadbddcdabdadcdbddbccdadadddbdaccaccaababbbdabddcababdacaccaccdaabbbadbccabddbdaaaababbdcdbbaaaaacbaacdbdabbcbddabbbadaacdadaaaccccccdacabcacbbcbbadcbbdccbdccbbcabbbdaccdcaabdccacbcccaaadacbcaadadbccabbcbbbcbabadcdcdababbacbddbcaddcbaabcccdabbbbdabbbcbaaacbdacabacdcbbcdcbaaabbddacdcddcbbbbaddcaabcdacdbbacddabcdbddbacddccacbccdbdcdddbbbbbdddacdaccaccbcaabbbcbaacbabaadcdbbcbacacccddcbbbcaaaabdcbccbcdbcddccdcdabddcaccdccccccaadccbddddadacbcadcaddccdbcacaaaddcbadbdcbcddbcddcbbaabbadccdbabbaadbbcbacadabbccdddcabaaadbcdccabddcbdddabccccbacbbbcacddbccbadcdabccabcbdadcbbcacbcaaddbdabccbbdbcaabdcdbacdbbbaccacababccccddaaddcacdddcbbdaddbabadbdbdaccbaababccdbadcccaababcbdadddcdbbbbcccdacdbabbdccbbccababdcccbdcccbdaccdabbdcaccbbabcddbcddaadacbacdadacdddaabcbccadbadcabdbcbcdadcdcacbbcbddbcbbbcccbdbacdcdaaabddaadbadbcacdbbcbbbbdbdaaccdbdabdababbccbcbacabdabadaadbabdabdcaaddadaacddacdacaddacaabbcddaaaadbbadccabbddacbbacacaabddadaccdbdbbbcaabcadcbdbbaacaacddccdbccbbcadcbbcaaadacdbdabbacccdddaccbcbaacdcacdbacddbbbdcabbabbadabbcbdcdcaaddbbaaddbbdcdddbcdbdcccdadcacaccbaadbccacdbaabaccacbcccabcbbacaaccdacddcaacccbbccddbccdcbcdbbbbaaaaddddbaddbabddddccaaaaacbaabdacddbccacacbddbaaadadcdabcabcdadacbabcaacdcbbaabcdbbdbabdccccbddcbdcbaabcddadadbbcabddbabadddbdabadddcbdaccaacaadcaddbdbdabbacdabbaadbbcccaaababaddcbbdcadaaccaccdbcdcacaabaacbcabdabbaadaacbdbbcbccaddcbcddbabcabdbadbdddccbdbcddbdaadcbbccccdcdbdbbcaddccaccbabcacddccabcdcdadcbccbbacacacdaadcabaccddccadabaccdcbbdbadccabccdcdaaabdccdabacddaddbdbbddaaacbcbdcabbbabbaadbbbbaadddccacabcabadbbbbbcbcbcbbaacbabdcbbabcaddbabdccbdabdccdabaaddcdbabddddddaddbccacababcbaddabdacddbcbacddaacaddcbdcabbbbbcabcbdccaccaaabbddacaaaccdbaddadbabccaaccbcadcdbbddcacbacadbdcccbcabdabcaddaaabbabbbccbdbcadcaaccdbbdcaadacbdcacbdccdbcdbbdcaabcaabcccaccdaddabbcacccddacadddbbcabddadccdbbbbdddbdbcddabdcbddadbccdcbacadaccdbacccbabccdcbdbccdcdbdbbdbcbddaccadbbdbabbaabbbcadadcdcdccdbdabbcacbbabdaaadddabadbbbcbdaacaabdadabdbbdcbbcdcdddcccabccaacdccdbccbaaadddcdbdcdbdcabbdaadabacdbbccdbdbcacbcddbbadcabdbcbcabadaaadcdcbacabacdccdbdbabaaddcadaccdabbcacdacbdbacbaacadcdabcbdbaadcbadacdbddaaadabdbacaadbbadcdaacdbbcddacdbdabbaabadddbacbbbbbaaabcaadaddabacaaacdcbcccbcacacabbdcbcdccddbcbadabbaabcdccaadadccbadadacdbdabaacdadcccbadbcdcbdadccbccdcbaccbabbcdababbdbaccdbccbcbbcadbcbccadadaccccbdddaddbaacbddbdbbbbdaabbcababadadcbdbbddcccdbcabddadadcdddcdcabdbddcadcccbaddacbddcddaaacbccbcbadabdadabbdaacdaacaabbbdcdbbbdccbcdcdaddaaabcbbcbdacbbdaadbbdcdaacbcbcdaddaccacdccaddbccadcaadacccbdbaacdacdbbbaadccabacccbddbcabbbbcbdcaddadbdaacbddacbaadbdcccccbbdadbbaaacdacaabcacdacdaddbabbddbadcdbbcddbabdbdbbdbbccdcccacbdbbdbaccccbbccdadbbacbadbbadbccdddbbbacdcbabcbcbdcdaaabbcbacabdacbabadcabccbcbdcaaacbbbcbcdcbadcaadcacddadcacddadcaacbacdcacabadaaccabddadbabccaadccbbbadbcbcbaccbddaaadadcabdcddbccdbbacbaabbaabddabcdccdaaaacbaddaabddcdbbcbbbaccbcbacabccbdcddbcdbdbdcaaacadbaddbdbbaadbcbabccdcbccacacbbbbbddbbadadbbddcbdacbddbbbddaccdbdccabbababbcdcdbddaadacdbaccbcabbaacabdcbbaaccdbbcaadccdadbdaabbbdccaacadaadacdbaddccdabdcaccbdcbdabcabacdadddddbabcbdbdaaadbaacdbadbbdbddbbabdbdadadbaaddbacdcabbbbdcbcddbcdcccbdbddbbdbabadcbadddcccdabbcdcbcacdabbdbadacdabcdcbcdabcacbbdcdbabcbddaadacacdcdbbadbaddadddbaddbdcaacbcbccaddbabbcddcdccddbbbbcddbaaddcbdabddbaddcddadacaacdabdacabaaccdcddaaccadbbadcabcbbabdcbabbbbaccdcccaddbabdbdccbbbdaadbcdcadcbdcbdadcadddccdbbbdaddcaddcdcccdcbdbabcbaccbbbdbadbdcdbadbcbcabdbcacdcbcaacddcdacdbacbbcbdbdacacddbddddaababadcccacdabcccdbcbcacadbbaaabcdbdcaaddcccccddadbabbcccabbdadddabcdbcbcbaadccabcbbbbcacdbabcadddbdddacaadccabaddadcaccabdadaabbbcbcddaacadbbbbdddaaadaadcabdbdccdaaabbbcccbddcdddbdcccdabcbbdacbcbaaabdcccacdcacdbcadadddcbadaadbcddbddbbdaddcaabdcaadadbccabddcaccacddddaddaadbdabdabcabcbcacaacacdbdaababaccdcabacadccbcccacabcccbdcacabdaccdaacbbbaddbaaabcbbcadcddbacababdacbddbdacadabcccdaaadadcdcbdbabcaacdbbabccbabadadcabbdbbadccdaabddbcdacababcabaadddcdcbcddaabcddccdcccadacbadacdabadabcdccccabcacdacccdacddbcdaadbbccddddbcbdacddcaddaadcdcbadaadbacabdddcadadbcdbcacdcdcabddadccabbacbabcabcadbbdcddbdbabcdbdcabacaabacbbdcdbcdabbbacaccabbccaaabbdacadabbbacbbaadccdcacabaabbbccdcbaabdbabdcddabdcdcabaaccabcabcddccbbdbaddadadbcbdcacaaadabdabababdbbbbcaaddcdcdbadcabadaadaaacaccadcddacbddbbddabbabbbbacbbabbcdaddcbcacdbccacbdbddccdaddbacbadbdbcacbcbcadbcbdbdbbbdcdcaaddbdbacaaaacaacaccadaacccbacdacbdbacbccdbbdcbcdaabacbbaaddbbcdcddcbaadaddcacddccacbabbddddbdddcccdabaaddcdccdbdbcaddbdccbcddadacadcdbbadabbbccaccbabdabddddbdacbdcdbddadcbbdabdcdabcdbbdddccccbaaaccdddbdbacdbccbdcbcccddccacbcbddbcaadbddbbcccdbaddaccdcddabdbaccaadadccaabbcddbcbacbdabbdbcdabbaaaacbcabaccbbaddacaaaabcddbaacbaaccabbcbadddcadcaaadcdabdadbcbacbbcdaaacdacaddacdabaabccdcadabcadbdddddbdcccdcadccaabddcaabcbacbddcacacdcdaddabcbadbdabbcbbbbbcbbdaaadacdcaacdbbdaadcbdaadcdbdaadbaabbcbddaacdcbbcbcdabbacdcdcddbaaaccdbddcaacccbdabaccaadbbbabaddcacaabbdccbadbbabdcccbcaacacaccabcccdcdaadddaaabdaabdabdcddadbdaacdccadbbabbabaccbddabcbbabddcdddcccccadbacbaaadbbadadaddcccaadaaabacdccbdbbadaaaccdbdbdcddbdabbdccccabcdbbbdbccdbbbdacdcacdcaacdabbcbbaabccbbaaabaabcccdcbdcacbcaccbadadabdbddaaddbddddabcadcdcbcabadcddadbdcccaddccdbabdadbaaccccbaccdadaaccddadaacdcaacccabbcaddcddacbbcbbbbcabcddbbdccbbadbbcbcbdaaadcadcbbbcacbddccacabacacbcacaccdccddaacacdadcbbdcdbbddabacdcbbddadbbdcaabbcaadcddbbaabbaaaccadaabcacdbbbabcbcbccbdbacdaccacddadadcbacacbdaabcddcdabbcdcdbccabcccbcbbadbdbdaabdadcddbdbaabcadabddcdbaacbcbdccccddaddbadbbdaddcabdabababcacdbccbdadabccdaaacbaacddabdaaddaaaaccbbddacccadabdcdcccbdabccbaacccabcbbccdaaaccdadcdaabdadddbacaddabadbcdcbabbbabdbddcdacabcaccaadcaadaabcbdbdabaacccadbabaccadaccacbbdadddbcccdabbdcdabccbdaaabdcaddaaddabababdcdabbbdbddaddbbabbaadbdddcbcabadabacdbcacdcdccacdcaaadcadbddaccdbddbdccbdbdcbccbaaabddcbcccaadabbcdcbdacddbbadadabccacdcadbbbdbacdddddbdcaccacbaadbcaddaaaaaadcbadbbacbcdbdddbcbbabaddacbccdabaabddadcadbcdadcacccacadacdadbdddcccacbccbbdcacadacbdadbbddbccdbcaaabcdcbcdcadddddcaaacaabdadddaabddccadbaaaccbdaddddbcbdcbdccbdaaddaaaadbadbcccbabbcbadbccbcccacbdcdbbcdadaadbbccaabdbdbcbcbcbacdcabaaabdddbddbbdbcabbacabbbdddaccbbddadccdadbaacdbcbcaabcbcdbccdadcbdbccbbdadccbbbbdabbababdcaccabaadcacbabcdbcdaacccacaccdadbbacadcbaacbccadcbcbcacbcddcadabbadcddccaccbcdccdacbaacaccbcbddbbaddbdbbbabccddaabacadbcccacbbadbadbacbbcdbacaabbbbcbddbccaabcbdcbadbbddcdccdbddbcdbbcbacdbcacbdbdadabddcdacdccccddcbcadbdcbabddccdcbabcbcabbcbaccbabcaccddadcddabbadbdbddabadccabdbbaacdaadddbbacbcbbadaacaddacbadbddcbbadbccabbaaaadbaacaacaabddbcadadccbdccdbbdbbbcbabbbabbdaacdcddcbcaaaaadacbdaaabaadccbddbdababdcdbbccbdcbdabcaacddcaaabdaadcdcddcdccccbbcaaadcabccbbabbaacddadbbcbdcbcbbcdabaaddccdcdddddaacacdcbbbdacbbbbabacdbaabbdacaacaacaacdbcbcccaadcdbbdcadddbbcabcdcdcccbdddbdcbbdccdaaaaccacabbdbddadcbdbaaacaabbcadcabdacdcddbadadcbddbddcdcbacdbdbccdccdbabbccbcbcdadbccbcabacaaddddcacaccddddbcbcbbdbcacccadcccbcabadabcdcacabadcbabadcdabbaaaddaacaccdbbacdbdbbdddddbcccbbaacabcbbdbbacbcbbddadccbabcbdabdcbcdabaaddbdacaabdaddbbdbcbddbabbbdbdbdbacbddddbcccbbbbbddbabdabadccadccabdcddcbbabdcbbabadadbbdadbddbabbdbabdbdacbaabacbdbdadbbbbddcaacabcdcdabbbdbbdabbacccaabbbabcbccbdabdadaddacddbcbcaacbbbdbbabcdddddaadabacbbadaadcadccccadcbacdabbaaccadcbdcbdccccaddadbdccacbbdcccaabcabdbdbbbbbabdddadcaadcbadddbbdbdbbbbdaadcbaabdcbcbcaadbbbadccbbcbdbacabdacdcbdcddbbcbdbabdaccbdcabadacdacabadadacbabdbcadcbbabacbabbdcdcdbaabbacabcdbabdabdaaabdadaccdbcdbbbdcabaadccabcadadbbdcdbdddaabcccbcbcbbbcdccbbbdcbabdadbdcccccbacabcbababaababbccbcbacdbcbbccdbccabadcccbdcddbddddcddcbcbccdcdbccaaddbccccabcadababdccddcdbdccacbdcbabababaabbbccbabcbcabcddaddccbaacbdcaadbccdbcdcadccaababdbbddcccabbbaaaaabbcbcddababbbadcacbbaacadbbdadaabadadaaacadaddaadbddaccbaacdddadbabbbbdbbadcbdaaaaabdbbcaadbcdcbbcbdccaabacaaddbadcbbabdcbbcbaddcabdbcdcacbadcbbbdaabcccacbbbabdabaabccbcaadaccaccabdbcbcdabcdcccabbacaabcdabcbacddaadbbbcbdddbccdcbdacadcbcbbabdcdabbdbbddddddcbbdcabbdccdaddccbababbaadadddbdacdacdbaaadbdcbcccdddacbabddbaddadbccbdddddcdcbdabcdbdaddbcbdcaddbabcdcccbbcbabacccaadaddaacbdcdbadcdcdadddcccbacbcdccbdbbbbcdcbcaaadddaddaabdcacbcddabdbdcbabacbbababacdabccaacadcbdadaabaacbdbacacccddabbbdababbdadddaadacdbbbcbabdaabbbcbbbbbdcacdadbacabbbdcbcdaddcbbabacbabdccaaccbbbddadabcccbddacdbdcbdbaadcdbbbadbddbbbccdbababbdbddaabcacacadccaccbbcaacbdadbddaadbbccbccbdcdbbdbbbcabbddbbdcbcbabadcdbdacdbacabbcdcbbcdcadcabdcbccddbcbbacadddcbccdcdaacccdbcaaacdcbcbadcaccdbcadcdddbdabdbbaacdddaabdcbcdbabdaccdbbccbacaababacbccccdcbbcddcbadbadaababcabbcdaaadadcaacbcaddbcadbbbaaacdaddbdccabaccbcddccbdcbbdbbbbcbaacbcacbdccdadcacbcacbdadcddcbbdbadabaadcaddabbddcdcaaadbacbcbccacaabaccccdcadcccbbddbccdcbdadcadbdabccadbbabddcaddccccadbbccbbdadacdbcbacacdaacbddcacacbbdcabbbbcabdcccbdddcdbdccbacccbacbcdcdaddddddbbdadcddadccddcdbcbaddccbcbaadcdbbabaaccdcbacaadaabcdbcababcccdcaddcabcadcbcdabccbbbddbbdcadddbccbdddcbcaaddabbcbdabcdccccddaddbdabdbbdcacadcaabdcbbacabacadbcbbadabacbbddaadbaabccaccacdcdbbbbcbccccbdababcdddbccdababcbddcddcddbdabdbdacdcdcdcbcbdcaadcacadcddbbcbdcbcbaadbabddbddadcbacccbabbccddbbcaabcadccdcdbccdccacadcddcabcbcdccddbbbccbccadcaddccbbbcbbaaccbaddccddaadcdcdcbcbbbcdacbabbccbcabcbdbdaacbdbbaccabcadbaabccccddcddacacaacbcbbbbcaabbdcbbcaaaaadcbdcaacccdbbbbaadbcdcbbdaadadbcacbccdbabdbcbaccdcddbdaadacbabbddcaaaadddaabbbbdcadaadadadbdbaddcaccacbcbdbbcadbcddddcadcbcdccddbabbacdadababaacdbddcabddbdaadcbaaaaacdacbbacaccbabcaacaaabbbbbbbacccabbabbdcccbaaabdbbbaddacbdaccbbbccabaadadaccbbdcdcccabacbabcacdcaddcddbccbbddaddccdcbccdccadcacbbabcaabacadcacddadaabbbabccbbbadbadddcdadaddcddbbdabccbaacbddbcaaabbcbcbadbddcdaabcdcdccbcdccdcdacabaccccaabcabadcbbbcdaaabcdbcdcbcbabbbbdcabbbddcbdcddadcdcddacdcddbddbbaadcaabcdddadcacbdacabcabcabdcdacadabcdaabbbdaccccaccbcdbddacddbbdccacdbddbccdccdabcdcdbcbabcdcdabaddccdbccadcadaccccadcbaddbdcccdbcddddbbcdcdadccbaddcbbdadcbacacbbdcccbcacdaabbdcaddacccaabaaacdbacdbbdacaababdbbaadcdadccdddcaccdabdcacddbdbcaacbdbaadcacdddcbbacbdbaaccdddaaadcbababdabccaabdacadcbdcbdaabaccdbddcddbcdcdcdddbadbccbbadbaacadadcbaacdabdcbdbaaabbbbbcccdcaabadcbacbcbdddbdbcddcbcaaaccaddacbacbadbbcdaacdbdbaadbacdcbcbdaccbbddbccaddadcadabbadbcddabcacaccdcbbbabdcbcbcdadcdbddccddcbcadcbaadbaddabdcabdaaabaadaccdbaadcdabcbddaaaaaacdccaaacbadabbddcbadcddcbacccdcacacabbddaaaddbdddcddcddbcbdbddbdbbdbcdccabcaababbdcccdbcbabdcdbcaccbacdadcddacdbaabcccbdaddcdaaddcddbdbddadbadcccddbcacdccbcbccbaabaacbbbcacdadcbdcaccbdbcbbbadcddcbbadcddcaaaaadcccacbbacdaddbddacdaadbcbbcddcddcddddcaacdcabaddddcbaadbdbbbacddabaadccaccaddacadbaadbbbacdbadddcbbaaadbccabbadbdabcacadababbbacbdddbbbaccbbcdddbbabadbdbcbdabdcbccaacacbadbadaadccabcdaacbacdccddccadaadccbccaabaabbddbbcabbbadbcacdaabcbcadccbaadadcadddccdaccbdccdbbacaadabbcbcaccbabdbadbbaacaabdccbdbdbabdcbaabcacbbcbdaacaacbbcdacddcddacbddddccccbbcbbccacccadcbcaaaccaaadcbcbbaabdbbbcbdabaaaddddddbdadccbbccbbabaddbbaaabbdcbcabdbcdaabbaadacacdcdbbacbadcbddddbacdbccdacbccddbbdbdabadddadccbdabbdccbaacadbbbcadcdaacbdadbaddbbababaabadddabbdbabcaccdacacabadaaddccadddbabddabbcacccbbacdabdddacaadcbbbabdabaabbddacdbcacbddaabbddddbbbccaaadcddddadabdaacdcbbdacaaabbbcbbcddabdaccacaabbcbbdaddbcbdcbccbbabadbbdbacdbbdbbdaacaacccadaadbcbdabbcbcacbdaacaabacababdaaccaababaccaadcbbbcaadabdbcacabbabbabdaadbcabdbadbaccaaccdbdbabbdbacabbbcacaaadacbdbaccacbacbbdadcdcadabbbaadbbcdabcccaddddcccabdbdcaadcbcdacdbddcbddcdbabbccaadcacddaddbabcabadbadbddacacbcaabcdbabbbdccbcbdccbaddcbacabadddbddddccadccabaccbccdacdaacdbbbddcbbadacaaddbddbacbdcbcddcaacacbaadcddadacacdcbbaacdcdadbdbababbdcacacacabddddaccbabbadccadddbdbacbcaddadaaddbdcbacbcbaaaacddbdabacbabbbdddcccbbaaaaaadddaaddaccdaaadaadbdccdcdabdabdacdbcdbbadadcabbabadcbbccbbdcccbaaccbbddcdddaddddbdabadcddacbcadaadbbcdddaaaabcdbbdadadccdcaccbcadbbdcacbcdcbbdadcacaadcdaccadabbddcbcccbddaaabdcabbbaadaacbcaabbbdadaaccddaddcbbabccdaaccabbaccbcdaadcaadadbccbbcdcbabbdbdbdaadcbcddadabbbbbadacdacbbcdbbbcbbdbbaabdbbbabcbbbdcaabbbbcdcbcaabadcbdccbbaaacbadbcdaadccddcaabbbccadbdaddacaaabbadcacbbccabdcdaabcdbacaaabcdbbcaadbaccaaabaaddaadacabddabdabbdcabaadcbcdaabadabacbbcdcccbbabcaabcdbaacaacacdcbcdbcddacdababdcbbbcdbbaaccdbadadbcccdaadcbcccbbbabdcbdaadbdcaccbcccccdbbdccddacbabdcdbacdadddcadbbbacdbcabdacccbabcdbaabadabdaadadadcbbcbdccaddcabcbdabcddbbbdbbdbccbdaadadcbcbcdcdcdcddcadccbbccaddccbaadaaabcbdbccaaccbdbdabbbababdbdaadcaadbdbcacccaabadccbadaddaabdbcaabcddbdbcadddbbbbdacdcbdddddadcbdcababbcdccbdbbbbacdadcadcbccdadbbcdcbddbabbaaccabcaadadabddabddcaadbdabacdbbcdbdaaabbaacbddbddadbdbadcbbccadcdadbdcaacabbaaccbadacdacccdcccacbaaadbbcccabbcbdbaccdabccbdabcbddcdadbbcdaaccddabdbbcbbccdbaaaaddcbddadcbddbbadcbcbacbaaabcddaabbadaabaadddcaabbbcacdddaaccaacaccbabcdcbdcdbbacbbbccdaaaabbadccabbacdabbbabbcbddbddaacdcbcbcabbbccccbabdacbbcadaccddbccbbdcaabbbaabbabdababccdcdabdcabcaccdabcbaaddadadccdbadbdcbbbabadadddbbbbdcdccabbcacacdaddcbbcccbdabcbaadcabbacdccbcbbaadabbbddabacbadcbadaaddacccbabcbcbdcacdacbaabdaccacdaabdaababaacbcabacdccbdcbddbcbcbbbddbcdccdccdbbaaccbcccbcdaddbddbadaadcaaadbbcdaccbaadddbdadabdccdbbcadbcdcbccabdadbcbcacbbacdadccaadbbdbabcdddacbacbcccabbaccddcabbbddbcdccccdbbcababaadcadabddddadcdbdabdcdbdcaabbdbaadbcacbdbdacabbcadcbbcbbacbabcbcabdbdcbaabbacdbaacbabbdbbcdbcbcbaddcdddcbdaddccaaaaabdcbcbabccbddcddabbdccabbdbcccaabadabaccdddcccbccdcdcbadbaabacaaaaccbabbabdcbddccdaaacbadaccbabcabddccbdddcabbddbcbaaabdbcbddcddadcddcbdbddbabccbdacdacdacbcbcbcadccbaadbaaacdcdcbbbabbaccaddbdcaabbadaddaabbacacccddbadaddaddbccbdbacdbcdcacaabadcbcdacdcacdaacddcdabcabadccbaadbabbcdcaddcabdcacaaaabcdadcbdbdcccacdcbbbdcccabbbbdadbdaabcdaadcbabaadbccacaccaadaacaadacdbdbbbddaacbdddcbbcbcdccbdcdaabaaddaabaaabcadbddacaaccbabddbbbbdaabcbcbccdaacddaacabacdaadbcabbbccaaccaabbcbddcbccccdccddcabcabccbababdaaadbabbbaadbbaadadabdcdbacbddadbababcbdabcacdcadbcacaabdbaaccbbcddbdbbabddcbcadaccddcbcddcbaaddcbcbdacdacdbbbcbdacabacbdddbcbdbdbcdddcbdabddbbcabadabcaacbddcbbadccadbbdadbdbdcaaacbbcbaaccdbbacbcbcabbcdbcbdddccabddbacccbccadddadbdacbaddbadcbaabbabadcbbcbbcdbbdaadddabbdaccdcadaddbcbacbbcbbabdbabcaccbdddbbabcadabbbddaaccdbaadbdaddbacacbaddbabaddababdbcacddacddcdabcdacaacabaaccabdccabccdaccdbdcabcaababdbadcbdadbbdddacabcabdbcdcacbccbdadccdabbadbbdacdcaadbddcbdadbaacaacdbabbcbcddaccbbdaccacaacdbdadccdcdaaaabaaddbcacdddbbcdbbccbacacdcdddbbaccbbddbbadbbdcccaadddbcacdbabacbcaccbacabdaaabbabdacbbcdddbadccadbcbdcadcadabbddcbdddcbbdcccbadabadadbacddcbddababaaadabbacbcaaabcdbcbacabbddbdabbcbbacacbcaacaabccddaddcbacabaddcbddbddcdadddabdcaaccbbdacdbcbabbdabbccccbdddadcaaadccadaccbbacccdcaabbcadcaabdbbccccaddcdadbbacbcacdcdbdadabccdbaacbccccaccbbbbdbbbdaabbabcdbabaadacbcbddaabbdddcbcbacdaaacbadcdabaaadbbcbcdccbdcbcadbcaccddabdbabbdbacbbdddddcadbccddbbbcadddcdadbabaccdcdcabbadcdcababcdcbdaccbcdccbabbdddacbbacbdbcadaadacdcdbdaadddaaaadccddcbaabcacadbdcaabcbbbacabcbcdcdbcbbaddcadabcabdacadcccbccadabddccbbcacbdbcbbadbcbbbabdadacdbccbdaccbbbbdabbbdcaacacccdcdacbdabadbdcadacbadcbbbadcbbbbbbbbadbdaaccbcadaddcabcbadccbadcccdacdaddbaaadababbdddcdcdcbabcccdbbadbdcccaadcdadbacabcbacbcbadabacacadddadabbabaacadbdbadcbccccccbacdbdcabcaabbcdcdddbccdcddacadacbdddabddbbdcdcacdababbcbbdbaddbdccaaacbaabccaddcdcdcaaaadaacccbdbccdbaccaabadbdddaababbbaddbbbcdcaccbaaacaaacddaccdabaddcdbcdcdcbbaadcccabccccdbbadcbbaaabcacdcdaadccccdabbcbbacddbdbdbcabdadcdddccdaaddcccacbaabaccccaadbabccaabcadccabbacddcddbdbcbcdbdcbbcbcadacdccbbccbbdbcdcddcdcaadaacdcdcaddadbcdcbcccccdbcbccbacbaaaabbacbdcbaadbcadbbbaaaaccadcaadcaadadbabcdddacaddcbacbcaccbbbdbbaacadcaccacdaddbbadcdcccccdabdcddbabcdaadbcbddcaddcacbcbdcaccbdadcccbdddbbadaabbacdadbbbccdacbcdaabcdcbddaaadadbdcbaacbccdaccbdabcabcaddbddacdccbaaabdaddabaadaabdacadbbacbbccabbdcddcaacdbdbbcbabccdabacadccbccbdbbbaaababbdbbaccabbcbaccdacdabccdccdbcddcbcccabddcdabccabdbdbacadbadbbcbbcaccccbaacbdcabbaadbaabbdccbdabcdadbbabbdccaddadcacadbcddbdddbbdbdcadcbdcccdccacbbddadcdbdccccabdbcaddadcabbcaabdabbddccdbddbccddaaaccdddabdcacbbcacbcaadabbccaadbbddabaabccdadaaadacbcabdcacadacbcdaadbddabdcbbbbacadaaaddaacbaabddacdcaadddcbcaccdaaadabdbcabadbcbacdabdbbcddcdccdbdaccacadcaccaddabbaccbbadadbaacadababdbcbdccdbaccadbbbaacaadbdbcbbbaaccdcadddacccccbbdaabcbdcbcbccbbbcaadbaccaccbcdbcdbaddaccbdaccaacdbaaacaaabbabbbaddbdbbbddaadcadcdcacddcaabbbbbddbaaadcadbbbacbdcbbcbdbbbccdadaaccdcaadcdaabdddaabacdadaabddcbddcaaccaadaadaccbcacaadbabcddbdabccaabcabbdcddddacdadcddbcaaccaabadcdcdcbcccccddacadaaabaddddadcabaadcabaaadabdadcbabaadadbadacccacdadaadaaabbadcccddaccdbcbbccadbbbcabbabcddbdbcabbbbcdcbdbbbbdadbdacbccaddabddadbbadbdddccbacdbaaadcbaabdbbaccadacabaddaaaaadbcaaaddacabbbcbcaadcbcdcccbcbbcaddabaadcbcdddbdabaabddcdabdcdaabadabbccabcbdcadbbdbbccdcbbccabcccdaacbbddaabdddaabdbdadadccbaddaabdcadcaacccbdcadadbadccaaddcbdcabddadbdabcaabcacbcbdcbdabdddacbbbcdaaddbcddbdbcdbbcdcdddadddbaabbabdbbdadcddbcddbdbbdcbacacbbacdabdcabaaadacccabbccaddbbbabdabadcdcaaabbabbaccbbabbcddabbdbdabbbacbbadacdbbcbdddbdbbbaddbdcbcddabccadbdcaaaacaccbbccccbaddcbcacaabaadcbbdaddbcbccbbbcaaccaaaccabcccdbadadabdaaacdcaacdcccbbbcdcbbadcbcabbdacdacccddbdbbddbbccdbcbddcdcadbcadbdadddccdbbbbbbccbbdddcacabbadacbaaddbddcbadbdabbdadadbdadcaddcdcaacabbabadcaccddaaccabbbacdbcbdcdddbdbadcddaabcbbdabcddaadabbbcbcccdbbaadcdbadbaaddbaabcbbccacadbdddcbacacccbccacbdddaadbadaddcabbabdabbcadaadcaccdaaaaadddaaccabddaacccdbcababaadbbbcaaabaadadbcddbcabacdddbbddbbadddbabccbbaddadabaacbabdbaccacabdacaaadccaababbabbcdacbaabddbbaaddabbbdbdcbcdadcbbcccbbdaaaabbddcaaddbbbbdcdaacdaacacdbabbabbcddbddacdbdbbbcdbaccdccdaddccbbbadcccaccbcdbddaacdddbbabbdbacbdddccaabdbcaadcdcababcddcabbaccdbbcdadabdcccacdacbaaddcbbbabaaaacddaaabaccaaddcadcabacbaaaabaaadcdcddbbbbbbcadaabbdcaaccbdcdcddcdcbcdcbadabbadabbaaacadbaabdaaddccaacbbbaaddcabadbdbbcdbaacdddcbbccdabbbbbcbacbbbadabdbcdaddadcaadabcbdccabadcdcbcbcababbcccaddbbaccdadbdadbcccabbccbcaccbabbcaaacccbdcdadcbbdacadbbcaabcabcadcdabccdaacdbbddbdadcdcadcbabcbcddcbdbcbabcdccbdbdaaabcadbdaacbaacacdddcabccabdbcadbdacbaacbaadbdbdddcccaabbcaabcdaaacdddbcbccbcdaadabcbdcadbddbaabdabcadabdbdcbbdabccdaddcbbdbddcdabbdcbaacbbcdccaabbbbdaababdcaccbdbdadbadccbacdbddbbaccaadbcaaddcbccbccbbcccdcdcbbdcdabdcdadadcbbccdbdbdbadaacadddbcdddcaabdaacaaadcdbbccccabacdbcddbbaadbbaddbaaacccadbdaacbabacddabbdbbcbdadaadbabaaaddadbddacbdddcbcdadcadacacddaaddbaddcaddbaabbacbaacabbcaacdbbdbaadbccccdccacbbadcabcccbadbcbcbbabdbdbcbbadbbbccbccbabdabbbadbdadbacbacadabcadacdcaabdbbaacbcccbcaacaadcdbcdbdcbcddaadabbcbccdaabacdaccdbaacdadcddcdcabbccbadacccaabadbaaacbcbbbdabdadbacaacdadbaadccbbccbbbadbbcbaaacacdabdadadccccacccbadaaaaccddbccdccaccbbdaabbbaaccccaaacbadbbaaaabdbbabadbbccdbaacabcadbbdaacababcbbdcaadcbcddcdcaccdccccdcdddbdbdabcccdabcddacaddbcddddadcbcadbadaadacadaaadbbdbbaccdabaadababdbacacacaccaacccabaacccbccccdadbdccadcdddbabcabcdacadbcdddadbbddccadcdbdabbdbaabbccccddddbdcddddcbcddadccaacaccccbdadaacbaaadbdcbcdcacdaaaadbdaddacabcdccacccdbdccdbddbbcacddcadacbaccabaacbccbabddbcdacbdbddadcdacaddcbccadaabaddaabadcdcbbddbaaabdbbaaaacaddbbbdacbcaacbcadacdabaaddbddbbbbcbcadacacbcbcdbbddcadbdabcbcbdcdaadbcbdbaabbddbcabbcdbbabaadbddbadcaddcabbbccdbaabdadddbbdacddabbddadaacbdcbaccabcbbcbdaadddbadabaaccabaddcaacdaabcbddabdbcdabaadbacabdadddcdcbdbbbbaadcbddbabddccbababbdacabbdcadcadbdacaccdaaaadccbcaccaaddbaacaddcabcbcaabcadcdbbdabcacaccbadccadadacdaddcacdcaaacdbcbbacabaabaabaddabadcbbcabcbbcabaaaaaaaabddcaacbabdbbaabdbdbbdbbcaacaccaaccadddcdaabadcacdcacadbacbbbdadbbbcdbaadadbbdaabcbbaadddadacccdadabbdcdbbccabdcbbdcaacacaaaaccdddabcabbdddcaaabaddadccccddabcbcbcbcddaabbdbdddaaaadcdabdabdddaadcdbcaadcdcadcbdabdbdbcbcabbacbacaaccacddcbacadddddbbdaccaabddcddccaaacadabdacdcdadcaabcbabdccdadbcbdaaccdcccabcabaccbccddadcacbabcddaaacdaabbbcbaaddbdbbbbcbacabdccbbcaccbdcdabadacbcabcbadadbaabbcdbdccdadcdbbccabbbaacddbabdcacadbcdabaacbdcbdcbdbaabddcbccacacdcdccbbacbdaaccacdcaaacdbbcdccbcadabaababbdbcccbbcdacdccddccdacadcdaadbddcacdbaaaabbcdcbcbadcdbaadbcacddaacacbdaadabacbcacaaababaabbbdcdccdbadccbdbbdccbbcdbabdbddbdbdddacadbbccbbddcbdbbaabadcbcdcaaccdcdabbbdddaababcacbdaabbaadcadcaddcdcadccdaabbdaaadbacdaaabdbcbbbbbdbcdadabdbaddcbcdcbdbcaacbcaabacaaadddbcacacccabcabadaaadaddccccbabcbacdaadaddcdccbccdcadcdddcdccbcccdddccaddbcdcccdddccabbabcaaaacddccddacabcdadbabccdbbdbdcdbbacccdcbdcdcaccdcbbcdaccccdadbcdababdbaccbbbadddbbadccddaadbaaacbccacbcccbbbabdbadbbddaaaadadaabcbaccadabbacabccaadcadcacaacbdaaabbcadbddbaaaaaaccdbdcccbdcbdabcbcabccaacdccddcdaaabbddccbddbcdcdcacadcbabcdbcacbcbbacbcaacbbcaacacdaacbcabcabbdacadcaadcbcccbabbdddaddcdddadabddbdbadccabccccbbcabcddbabbdabcdaccbbdadbccdbbaacbddcbcbbcabaacdddcacaabdcababdbcbcabbccabaddcdddabacbcacddbbadacdaacaaaacccbaccdcdbabcdbccacbbbbaabddcbdddbdddcddcdbaacdadbccbdaccdabbadbabbabadbaccadbdddbcdccacbbbcddccbcabbdadbbbddcddbabbabdbbbadadbcdbaddcbcddbcaccdcccbdabccdcaaabbadcdbaaadcdbaacdddccabcdaadcabcbbdbcabcddcccdcccaaaacbcbdbaabcbdabdacbcdbabcadcbaccdbaccdcabddbadcaccbbdbddddadbabdccbdbacccbadacabcaacdbababbacbacdcdbcddddddabdbcccdbcadaaaddbdbcbbdcbbbcdcbdbbcdbcaaaddddbcdcbaaadddcbcbbdacdaadcddbaabaddababadcccccbcbbccaaaacbbccaadbcbdbdcbabcabbbacbacadcdacddbdabaccddddcacccddadbbbbacbacdcbaccacdabacbbdbaccaaadbdbbccdadbaacacdbabbdcbdadbbdaadbdccbdbdcddbcbbadaadbabdccccccbbcacbdaadacddddcbadbddbacddbaabbdbbaccbaddcbddcadaaddcbcddadbdbdbabcbdaccbdbbaddcdcbbdcaababddacbaaabbcabbbacccbdcccccabacaabdbabababacbdabaacddddcaadaababdcbdaaadbbcdccdcddbccdddaaaadbbddadaaccbdabadcbbabdbcdcaccadacbcdbdaaddaadacbadbddabcaaaccdbaabbadddaadadcbbcdcbadacbdccbcdbdbaaadcaccacdbbcbbaadbbccacabcaababacbccadabddcbdbcdbbdabbdddbaadbacdbbacaadbadbcaacdccddaacbaccddaacddabbdacbbbccabdaacacabadaddddadbddccadcbcdccbaaddccadbbcbacdbdcccdadbcccabadbcbdddcbddaadbcdabaaabcacbcdbdabcabcbcbbaaaabaccbaaccabdabddaacabdaccbabdbaabcbbdbadbaddbaadaddbdccabdbbdbbabbacdddccddbadcbcdddccdadbabbaadbddaddbbdbadabdacdbaaaabbdbacdcddcdddaaddbcbaabacdadbcbabcbacbcaabaccbaddaadcadbcddbabadbcdaaddbbcbcddbabacabaaabbddbccdbcdcbbdbcdabcbbadcaaaddbdaddaccbccbcbdabaadddaaccbcbbdddbbcabbbcbcaaaddbccdbbdaccdbbcdaccccbbbdbddbcbcbadbcbadddabaabaacdddabcddddbddababbadcbaccdbbddadcbabdbacacaabcbcabcacacccaaabcdcbdabbbdccaddccacadbacabcdcaccbcadcaddaccdaabcccbcaacabbcbcabbbbcaaddadcbdbaaabdbbabbadbdbcddbbcdcdbbcaccdbbaaacddadbbcabdadbdbaddbbcacabbadccbddaabaabdcabbddddcdaaacddacacaacbadaaacbddbbdbbbdcdbacdadcbbadaccbbabbcddabadcbaccaababbabdabadccacbddaabddccbdbbaccdbcddddbcdbbbbacdbcadabdbabcdcbcaccadbcccbbaddbdacbbcdbcdbbbaabbcbddcabdcdbacccaddddddbcabdcbaabbabacacbcacdbbdbdaddcbcbadcdbcccaaccccbdabcabaddaadacdbdccdbbadacbdddccbabbcbbacabaaaababcadbcdcdcdcdcbcdbbbbcbacaddcdacccdcdbbbddaccbbabdcabcdcaabcabdcadbcdacdaaacababbacccadccdccddcaddbaaadbbcbcbaadccbadddaaaacdacddcddadbcadaaccbdbbcaaccbabdbbcabbccacaadbdaabdbacdadcccdbdddcacbabcccbbababacbdacabdcabbccdacdacaabbbcbdccacbbbbddbdcbcbdcdadcdbaabdcbcaababddaddbbbdccaaaababccacdbdbaddbabcaccbbcdbdbdbaaaddcaabbaadadcbbbcbacdbacabdcbbdbcddcdcbdcdcbcacbbbdbbddabadbddccbcdcccdbccbabbbdbbbaaccabbaacabddaaacccbcdcaacaadccbcbcdbcdcbcccdddbbaabbbbcdbccbbbdddcbbaacadcadaccbbdbabbaacbaddbbcbbdaadddbcbcbacabdbcdcbcddccadaaaddacdccaddbbbdaaacacccdbadacdcadbcccbcbdacdabbacadababbbbacbcdbadbdadccbdcaabdccabbdcddcddcbbdabaccadbccdabacddcbbacbcdaccaacdacdcadaddabcdabcdacdbbaaacbaabcbaadadcdddaaaacbbcccdbcccacaadbddccbccabcbddccbdcdabdbaaaaaddbabccacaababddabdcbabbbbbaabdbbacdcdbbdcddbbbababcbbacdcbdabaddcdaacabacaabbabccdbbdcccbbbdbcbaabccabcaadabacacbcacdbacadacbccccccadaaadbddaacacdbbdaaadbbccdcaadbacbccbdbdcbbdaadbbacbaaadbacdddbadddcdcaaabbdcbbbcaddbacccdcbadaadbcddacdaddcdcbcccbdbbbdadcbbabbbbdabaabcbbbdddbcddccbccdababbbbdcaddadadaaccdabaaccddabddbdacaacaaddadcdbaaaadaccaacbbacbbdbbacbdbddcccdddcabdacdbdcaaccdccbcbdbbddcbbbbdbcbccacdadbbbcbdadbaddccaaaddaadbbbddacaacdcdccbcdcccddcbcbaabcdbdddddaabadcaadbabbaadcbdaabbdcbaaaacbadbccbddcaccacdcbbdcacabcddbbccbdccdbcacaccadcaddbabbccbbdbdcbadddbccacaccbbcdbbdbbdccccbdbbabddcabbdabdacdcddabbcdbbbbdbbaacaacbdadadbccdbaadbbbcbadcbccacbbaccccbdaaaaadaacdbdacbbbdadadacddbcccdbbdcbcdddddcbbbcbcadaaaabbdcdbcdadaacbdabcaacabbcabdbccddcacddbaadacaabacdcdccdccddaadbbabbabdbdadbdbcacdbdcbdcadabbdddcdcdbcdacdbacbacbbcddadcdcbabcacccbdbbcdddbaccdbbabdbadadbbabdbcdbdccbaccabcdacdabdcabacacdcdaddabbbdcddbabaccdbbaaddccaadddcacbbcbcdaccadbdcaacbbbcbdacbdaacddbcaababccddbdcbbbabadbadaaaabdabababccdddbbadbbdcbcbdddabbabbbabaabdbcbbaababcbabaaccdbddcacdcacabdddaacbbdaccbcddadadbdbdadacbaadcacccaddbdcababaadabcaabdcacadcaacdbdcaacadcacbadddccdaaadcabdddbdacbdcbcbbbadaacabadbcccbdbcabcaaaadcaaadadcdccaccddaaabcbadcccadbcdddbbadcadaacdaacabacddddabacbcabbadbcbbbcabbcbbcacdaaaacbcabddadbaaccabbbbcbadaadacaccdbbcdbdaccccabcdbdbabbbdccccdaaaddccabdccdbcbaaccbacccddbcdcdadbabdcaacbbbbacbababcaccbbcaabababcaccacbcbcdcabdcaabcbcdbaaacabdacbcbadccbcbdcbabaaccaabbcdbcadaaccbbbcbacbaaaaaacdcbaabacbcddbddcbaaabaabcbddbacabbbdcdbbccbaaaaaccdcacdabcbabcdbadbaaccabbbccbbbaabcddddbaadadcdccdbccbbaadbcbacaaadaadaadddbbabaddcdcaacddcdbccabcdbacbdbbcabdcaccbccaaadbbbdabbaccadacbbdadcbdcbbaaaadcacaaaacbcacbdadcbbcbbbaaacbcbaabdbccacdbdcdacabdaabcbadcabdbdbdbdbbacbcdadcbaadadcacacaccdbcaadcaddcbcacccdbaaddcccbadacdddddbadddccccbcabbdbdbabacdacdcdcdaadacaacdacbabccbcbadbccbbcddbaadabcdaabacbacadaabdcbbcdacadbbbbcdddbcabccbcbcddcbaadbdacdbbcbaacaccadbcaccbcabbccaddbaabaccbdacdcdbadbdaabadacadcbbddaabccbabbcbacbcabdaddaacccddaccabcccaaabdbcdbccbacbbdcbbdabbcccaabaabaaabacdbaabdbcaaacaaacdcdbccaadbcaddcbcdcdabbadbcaacdcbccdbbdbadbadbccbbdcbacdaabadbbbcaaabddaddadcbccdcdacbdcaccbbccaacbccccabaddacacbcccacbcadcacabcdcbcaacddcabcbadaadbcadcbccbbcacbbccaacdacdabcacbabcdbcbdddacbbbdddbbdbcaccbbbcccccbaaadacbabbcadbdddcbdcbddbdcadbaddbbcbbccbdabbcacbcdcaaaaaababbddccdabdbaccbcdbbadccbddddacdbbbbaaadccbcccdcdacccacabbcddbbaddbdccabccdbbbaaccccbadacbbcabddbccbcdbbacaabacdababdccacbacaccddbddbdbccdbbcabbadcbbddcbcababcadddaabdccdadadbcbaaaccadbcbbbcbdbacdccbadacadabbcbdccacbbbdbaaabddacbdbccdcdbaccaaadcbcabadcbcdcddbacbbccaabcccddaccadaaadcbabbacccccadcbbcccddbccdabdaccdcccbcaabbcdcccbbdcaadddabbaccaaddcbcdcbbbdddbbbabbcdacdadcaaaabdcacaabbccbbbcdddadbacaccacddcaadbddaacdbbcaadaccadcbddbcabccdaacbddbdbbadbabbcdddcadacbcacbdbdbddbdbadbaadabacdcddaaadaabaaabccbbabcddbbddcbdcadbcbabaccadabbaccddcbaacbcacaadbacbbbacbbbdcddaabaddabacdaabaaabbdbcbdbdacaaaaddbaadbccdbcddabbbbabaccbaadccdaadcaabdcadbccccdadbacbbcadadaddabbadcccabccaabacacccbaccbdadcbacbbbdadcadbdccbbcbdcacccabdbbcccbccadcaabcdaadcbbcbabcadaaaacabacbaadadbdbbbddcbcaccdaacdbcbcddddadbadcadcbacdddcdababdcdacbddbcbddaaccbddcccbadcbcbcdadbcdcaacbbabbacbcaadabacbaaaccbbccbbcbbadccaccccccdbcacbacdadaaadbacadbbadcdcbccddcbbbdadabaacaaccabbddabadcbaaabcabcbbcddacbbddabbcdbcaabdddcbadccaaacbbddabbbdaccabbbcacddcdccaccbdcaddadcbddddcaaacddbdacbdaabbcdaadcccbcdcadacaadbcdabbbabaddacadbccdbacbbacddcdadadbccbcbbbbdaadbcacaadacacdcaaadacaccaadaabcdbbdadbccdcbbbbbadaddcdcccbcdabbacdcbcadddabaabbcdbcdacdaccdacbaacadaaddbaaaccadbaddaaadbbadcdccdcabaabadddabbccbabbadbbaadbccdddabaacbdabdcbbccabcddbdcdbdbdcdadabdccdacdbaabccbcabbadcbbddaccbbdcaacbccddcbcdcdddaddaaaccacbcdccbbdcadacdddaacaaaabcacaacdddddcbabadbacbacbbccccacdbcbabcabddcadccdcadbbbcdacadbdbacbcadbaacbcbbddaacbcbbdddcdcbacdbbbadbdaadabcbddbccdcabcddabbbdacdbdacbcbcbadcbdcacdbcbdaddddabdadaaabdaacbdacbbdbbbddbcddbbcdddaaabcbddcccdbdaaaabcbbacbbdbbdddaaaacbbaaaaadddabbbbbcacdcdcdddbadbbccbcccacdbddcdddbcabadcaddccccadbdacabdcabccaabcddcaaabacdddbdcbccabbdcbdbdbbbaddddaaccbcdacdbbacdccbdabbbbccadaabbacdbdaabcbdaabcabbcbbacddccccacabadadddddbabbcacaddcbacbbbbccbcbcbcdcdcddcbcddaccbabbcbabadbcaabcdadccbdddbcabaccbdbcbcccadaadbbacdacaaadbdbabcbcddbbadddcaddcacacadabadccbdccdacdacaccbacbaabbccbbbbdaccacbddaaadaddcdbaacbbcddaccaadbdacbdbaaddbdcaaaddadbcbadddacabacabcccddaabaadadbcbbdcadaddbcabdbddddaadcddbbccbbbaccadaabdbccadbcabbcabdccabaccdbbdaadbddbacbabcddbdbcddadcccbdadcbbacdbdadccacbccadcddbbdbbdcbddadaaabbccaaacbcdbcacddaddccdbdbcdcbddccababcccbddabdddaddcdaaccaaadddacbdaaccdbacbaaaadccbdaadbacbddddcddbdccdbbccbbcacacdcabbaaccdcdaacacdccacccbcbbaccccabdaacaacacdcbbacaddadbcccbbccaccccabaaddaddccabcdacaadccbbcdbabbcaadbcabaccbacdbbbcdacaaacdbdbdacccdcbcbabcaddbacaccdccbbdbbcddcddaaabdbbbadcbddbdcddcdaccaadccbcbababbddbdaccbabbbbbacbabcbaccacbccadabdcacaabcbbaabbccbccbaadacdbcabbdbbbabbcdadbdbadcaccbacaddccbacdddccabcbdbcabccbaadbddcadcbbdccaadbadadcababaddbacdaddcadaacaddbdaabcbccaabcbcddcdbdbcddacbdbacacbcabddadccbbdbbcbcbbadcbddaccdabcabbcadbbdcbbaddbdddbcbbdcbbcddccacbcbcdccdaccdbacbabdcccaccabaaaadbacaabdaacbcadcbacaaababbbdddccbbcdbbcabdbdddaacccbabcabacbbacbdddddaaababbcaaabdadcbaadadaccbdcbdaabbbacabbcadbdcccdacbdbaccbcbaadaaacaaddacccacadcdcdabacabdddddadcabaddbccbdbadcdadbdaaaaadacabddabcbcbcbadabcaddababccdcbcbaaacbdcbcabbdbaadaddbabadbadabcabdddbdbdbadbbcabbabaabdddbbdbdaadcaadcbaacbcddbbbccccdccbbcbdbccbdaacccddcbacdcdbbbccbdabccdadaadbcdaaddbdccdbacccdddbcadacaccadcaddacccbdbaaddcbcbbabbacaccbcbabacdbbbddadddbdddadcaabcbcbbcdcacdcdabbddbdccbadbbcdbabccaddbcbbbddbbabacbbddddbabcbcdcdcbabcccdbdbbcdcaababadcdbadbadadabacbdaccccacdbadbaadacccabcabcbdcadaacacbaaacadbcbaccbbbbbdaaaabcdcadbcdaabbdcabcadbdbbccacccabdbbbdbdbabbcbcbabadbcadddbbabcdbbcdcadabdadcbdaccacadaddbabadbccbabcdcbaccccdddcddaadbdbacbdcadcddbcadcaddcdddcbdcdacbdacdcaabcbdcabccbbbbbaabadcdcacdbbbddbaacadaacdbaddcbdacacbcdccbbdccbadbccccddddbcabddaaaadbadaadbdbabcaacccbcbdccbaaccbcbbaabdcacdccbbddcabdbcdbaadcbcdacbbbdbadbbbccaaaddddbddabdbdaaddabddadbaaaddddacadcbddbcbdadcddccbddbadaddadddbbabccbdbbacddacbcabaabaadcbcccdadbbbadddbbccbabdacbdbdadaadbadaabbcdaaaabddcccbabbcbcdbabbcddcdcbddadaaadccccaabacddccbabdabbcdcbcbbddadbdaacabbbbacbcbdddaacabdddbbbbbadaccddacaadbaaccaddbabaabcccdacabbcdaadcbdbdbddcabbcddacddbdaadaddcccaadacbddbaccacacbcaabcbdbdcdaacbbcbbbaadababacbdbcadcccabcccadbbbbabccbbcaaadabdbbbdbbccabbdcbcdbaabccddcbabdcbbacdbddccbbaabbcabddcabbbcadccaddddddcbbcccaabcdbdacaaababacccadadaadddbdaacbbaccdcabbbcbbccdabaddcacdbbbbbcaaacbddcdbcdcbbbbdbccbdcddccaccccccbadcdadcdbcdccacabacabdcacbdbbbdadabadccabbadbdcccbacacabccbddbcbdcbcdddccacdaacbcccaabaabadacbbaddabdbcacdccbaacbabcdababddadabcbbbabcbcdcccabdcacabdacdbcbaacababbbdbbaacaababbaaccbbcbbcbcddabdbbdaadaabaabbdcdcadccaaddddcacbcddcdababacabadadbcadcadcbadbddccbdaddccabacbabbacdbabcbcdcdccbddbccbabaddbadcdccdadacaaddbabdabbbbddaccabaccbaacbcdddababcbdcddaccacbdcbddbadacaadadcccdcdabcddddbabdccbcbccddbccdbddbadbdbbdcccddadbbdcaacadbadaacdaadbdcdcccaccbdcbacadbaababaaddbdbbbbaadabcaabdacbdddcadcaddbaccddddbbbdaacaccbaaabdabbabdaccbbcbbaacbcbbadcaaddabbcbcbaccbadabbdbbcdbacddacbadcadcdbdaccdacccdabbbcdcaabcadcacadbcadadabbddadaadddbaadbacaddccadabcabbccddbbbaddabbcdaabacbccccdacdcadccddadccbaaaddcbbbddcbacbcacddaaacdbadaadccaaddddabdcbbcdbbaacbabadcdbbbccabbccdcccdaabcddababadcaccabccaabadccccddbccaccdbdacaccbdabaadbcaccdbdaabbbcdbdbdacbcbccbdcdddbcaaadabbbbbddcddcbccadaddcdbdddddadbabacbabcdcdddbcbdcbdcdcdacdabccdbbddacdabdaaabcdadccabadbbcdcdbdcacacabcbbbcbbadcbaadbdbcdadbdbcbacdbcdccbccaddbcdcbcbacbacdbdabbdcaadadcabbbbadabdaaacaabbbcbacdaccccabdbbdcccacccbdccddcacadaaadacaadadbcbdbbdbcaabbbcbcdbdddddbcdadccacbdabbcdababcddaddbadccccadbddcdaacccbcccdacbdacddddcadbbbcaddcbaddcadbaddaccccbcdbdcccdbcaccbddacbbcbbaacaddcbadbbacdbdbcbbdbcadccbaddcdcbdacdabdcddccdddcbcbdbdbddcababadacdbacadbdcccadbddbdcdacacbbaaabddbcadbbdcdcbdaacdabcbcdcaadaacccdcdcadabcbdaacbdacdcadcbccaccccbbddbbdccddccbabcbbcbbcabdcbbdddbddbbcdcaaabadadddccbddadadccaabdaaddcddbdddbcdbdcbdaddabcbcaaacdcdcddacbbaddccaacbcbcbdabccbcacbabbdadacdababbbbadbbcdaaddabcdddacbddcadbddbcaddbbbccbabccbddacbbcabcbddbdadbdaadadddcccbccdbdbacbcdabddcdbadaacdabccaddcbacbbabcccbaccadcabdcbcdccbababddbbcaadcccbcaccaadcbdabdaacccbdabacaadabcdbbccacadcdaacdabbcdcaddccbbbbabcdbdbbbdddcddbdbaabdbacadcdadcdbccaacdbccdcdabcdaaabdbacbdccdbdbbacbbbaadaacabdcdddcbdcdcaccdccdababdcdadbdcaabdacdacdcaddadbadbbdcaddabaaabdcddbbacdbcbdbbdbcbbbacbabdbadaddcdcbbbcbdbabdddccbdcdcddddbbcacaabbbbacdbacaabdccbbacdbadbcaabddaddbabddaabddbcbcdaaabbabcbbbadabdabacccbdcaccabccaadcdbbddabcbdbcaccdaadbddccacadddaaccbbdddbbdcbccbdadcbcaaddaddcbbbbccdbacdcccdaccdacdaccbdcdbaadbdacdcaaaddbabcdacdaccdcaaddcbcbbcaddadcaddbaabaabccbbcccdcdccaacccdbddbdaccbaddadadcdaadcdcabdddbdcccaabcbaaacadaddddabcbabccbabaabbdcccaddabcbdcabccabcadabacdcbadbbbccbddbbcadccccaccbcbbdccabdbcabadacbbbdccbbccdacaaaccddbaaadcababaccdcbdadccbccdaadddbbbbcadcbdacbcdadadabddcddbddbacddbbccaaaabccbbadadaacaabaaacdabbdaabadaacdbbabdddaadaabbdcaccbaacacddccbbcaaacbadaaaacdcbbabaacaacbaacdcdbbaacaccbbacdaaabcbccbadbaccccddbdcdaddbddadbbabaabacbbdaccabbdccdadadbaacbcabbaccdcbcacbdcbabadccdcacdadadbbacdabdbcbdbbaddaacbbaadaccbadaaddddabcddbaacddcbadbaabdccbabdababaaacdbcaacacabbcdbcdabbbcdabcddbbadadadbcccaadddddbbbbbabadbdaabdacbdbdadbcaabaadabccddbdbcdbdcaccbdbbdadcbbcaaacddcadadccbaaddbbbddcbdacbdbdbadadbbdccabacbbdccddcababdbddcdddbcbccdbccdadbcdaadaccadcdbdcbccaabdbdddcdabbdbcdaddbbbbcabcdcccdabbadbbacaaabbbcccadbabaadbbbcbddcbaaaccbdbabdadaaddddccaaadaabbabbcbbdacadadacccbaadcbdcabbbaccdadcbcdbcdcdddccabcbabbcaccddcbccabbcababbacdbcaabcbacddbbdbdcbabddccacdbabbcaadccddddbdcbacabbcbdcbbdaacccbbbbabbcaaddcaabbcdaacadacdbaadbbddadddbadcbbdccbbabaccabbcadcaccdbacccdcddaddbadbcbaacccdbcddbdccdccadbbbcadabddcacdaddabcdaccccbcbbdadbbcadddbbbcbacccdbcaaaabaddacdbdcaaccacaccabdcdbacadacddcaabacacacabbabbcaddbaccbbddbcbbbddabccbaaadcdadddddaaccbadbdadaaaadacbcccddbcdbdcccaddbacccccaaaabbadcdaaaabaaddddbbdacdcbddbddbacbdabcbcbadbbdcaccbcdccbcadaccabaccbcadaddccacdbacddcaccddacdcadadcaddbaacbcbaaabdcadcbcacacadccabdbdaaadddabcdacddaddcbcbcbdcbabdacbbcabbcdcadbabcdabbddddbbbcbdabdbbdabbcbcacdbcbabdbdabccccaababbbdbcbbdabbbbabdcabbcddbcdcbdbadcadcccdbabcdbaacbcbbaaccdbdccdbcdaadccbaccbccbdddccbdacccbaaadaccddbccbbacdaadababdabdbbbdccbbdccdbacdcdbacddabcccbbdbbbaadbabdcbbabadbcaaacdbdcadccadaabbbadbcabdbccaadbcddadcabacccaaddbdadbbccabdcdbddcadadcbbdacaabbacccdcccaccbdacacacccddbbbacacacddbdccdcbdabcaadbbbcaaadbaadbadabdbcaacaccdddbdcdddbbdbbaccccabbcadadcabcbdbddbacbaacbddccdaddabadabbdbadbcdbccdcaaacbaacaddbdacbddadaddabdddabcacbcdcdbabcdbccbbbbdcaabbbccdacbbbdaacaadcadaadcdcadbbbbacabdcaadbbaadaaabbbabcdadbabccaabdaadcadbdacbaccdbaaaddacbddcbdccdbbbbbdaadcdbbcbbaddbabadaaddbddabcadadadccacabdccdccdbccaadacaaaaaddadabadbdaabbcbacccabbacacbccacadcbdbbcadbadbbacddabbdbbcabdacacbaccbbdbbcabbcadcdccbdbdacbbbcacabcddcbcccdbbbbbbccaccccdadcabacbccdacaadcdbcdccddbaddadbdabbbbddbbbabcddbaaddaddcaddbadadcabcadacdabbbabdbccdcabcbdadbddabcaddcccacddcaaacdacbdcbdccdaaccdaaacccaabbaacdddbbdcdcbdcdadbadaddcdacaccbcccabbbddbdabdbadbdcbdcbcadabcdbbadbdcdacbccbcccadabaacddbdabbcbcadddbbbadcccbcbbddaddcbbaddaabdaaabaacdacbbaabbbccbccdbadaabacbcdbbcdbdabadbbcdbddaabaadadbbddcbbcddbbbcdccaacaccdbbcaacbabbadbbbbdbcccbcbcddaccdcdbdadbbddbcdbbbcbcbaadacbbdbbdbdacddbdbcdbacbcbbdddbbabbacaabbcdbaacdaaacdcadcbaabadcabbdccccccdcddbaadbdcbdcdadddbbdcbccabacacdbdbabaaabcccbcbabcdabbcdacdbddadccdcccccbbabbccadddbbabcdbdcbddaddbbabbaabadacbcdbbadcbbabdcdcdacadadddadaaacdbadbbcdcddccdbbcaacaddbdcdcdabbdabcaadbcaabcbdccccddaabaaabbdacababbabcdbdcbcabcccdddaccbdbbdcbdbdbaabcdaabddadabcbacddcaaaaacdddaacabaccdcabdcaddabdccacbbddcdcadadbcadcbcbbddddaddddbabadccddbbcadabadabbcbbbbcdbaddbccaaadddcdabcbadadcbdaaaabbbabdacaddbbbadcacacddcadddcbabaaccadcaaaccdababcbcdaaaddadabddadbaabaacdcadcdabdacbdbcbbcabbcbdacaaadcdcbcdacbbbcbdccaadcdaabdbdcccaccdbdabcababdcabdddbdddbacaabbcccaadddaadccbdcbdbaccdadabddacdaacdddbbdaadacdacbbbccabcdccccbadcaabccadbdcacbcddbccdbcaccbdddddcdbadccaadaacaddbdccdaadddabcaaacddcbbbadcaabdcbacccabdbaaaadccdcbdcddbbdcacaacbdaadcabdcaccbbadbdccbcdabbcdabcdccccdcdcbaaabdaadcbcaaabddaadabbbcccaadacdbdbcaccccabccaaaddadcdabcbcabaccadcabaccbcbcadbbbbdccbbdbdcdcdcaabbabdaadbccbdacbcabaadcccdcdbdbababcacbddccdbcabbdcabcbdaadbcdabdbaccbaababbbbaacabacdbcacddcbaabdcaddaabdbaacbdbdbddcbdcdbadabccbcabacbcbddddbbaddbaddababcaabdcddbacbdddaadbbcacdccbbcccababaaadacaabdabdcbdaaaccacdaadadaccacdcadaabcddabaccbbbcbbcadcacaaaddbbabadddbcbdcdddaaacabbdcbaadbccaacdaddbbcbbaacddaccbdacabcacbbbaaaabccaadaaccbcdacbdaadccaadccabbabcdbcabcaaccccddcbbbadcdccaaabadbbabccdbabdddccdcdbcabcbdbbbadccddacabdccdcabdbcbacabbbbaabbddcaaddbabaddcdcddbacccaabbcccccddcaacacadccacbdddcabbdaddcabdcbbdadacbdcccddcaddadaaabddcacbacbadbcdbdcbccbadbacaadcbccdcaadbddbacbbcaaabacbdcbabccbaaaddccbccbcdddcbcdadcbbacadcbadaacddbcaaadcbbcbbacadacdadaacaccbdabbcdadabbcddcaabbbdbdaaddabddbcdcbbbbbabcbcdcdadbaadddcaabccaddbcccdaadbabaadaaccbabdcbcdcdacaddccdbbccadcbbbdabdadcdcbbadbbdbdbaabdccdbbdadcaaaabddcdcbbbcbaddddddbddbdcbdcbaadaaabbdbcaacaddddbcdaacaaaddbbcbbdbacaabcbabaacdcddccbadcbcbabaaaddaaacdcaccccbdbbdaabddacdcdbddabaacaaabacdacbcdcbcaabcbddcbdbdbbacabcabacacbcbbccdacacacaabbdabbaacdcdabdaaaadccdcadabdcbcccacbbadbdbabbcdacdcbcbbcdcbbdadcbcddadbbcdbccbcccddadddcdcaabdbddacccbdcacbdabddcacadacacdddcdcabcbcadacdddddaacacabbdbcbcdbacccbdcacadcadaddabacabccbdacdbcbbddbbaddbcbaddacccdddaabddddcbbaacdccbdbcdadcdddacbbaaacdacddaddacccbdccbdabacccdccdbbabadbaccccddbcdabacdddbdcacbbbdaaadddbcacbbbacbdcaddabbcbdcabcbccddcaaaabcdbbbbdcdadcbbabcabdcabbaadbdcdddcbddcacdbbacacabcacabbdcdaacdbbdbcaadddbbaddbbaddcbccdacddcbcccbcadadcadbcdbdcbdbddbdaddbdabcadadddcbadadcdcddccccaaaadaaccacdaacbbdbcbdcddbbcbcadcbababdddccaacddacbabccbcbcaaaacbccbbdadccaabcccabbaccdaabadcabccccbddddadbdbdbbdcabaacabdddcadacdadcaaaaacbbcdaadabacbadabbddbdaabdaaddadcccdbdabccacbdcdddadabbbbddadbcbadbcdbdbcbcaaccbbdcaddacbabcbbadbacbaddcdadcdacaadcaadbbbcaabdcdcbbdbaacbcabdaacaadddcddbdcddccdbccadccdabbbddddcbdabdcbabcabbadbdcaabdccacdabcbdbdbbcaadaacbaacbbbdbcbcaddabbadbcaacdaabcbcbdcdcdcdbcbaacbdcadddddcbbcbadbabcabaccbdcacabdaaadcccbadcbcbcdbdacddddacababdbdcdacbdabddaaccdbacadddcaaaccdababdaddbaccbbaacadbcabccadcbbdbacbcadcdbcacdbbbdadccbdccadbdbbaccaabccbadadabbcbcbaaaccabcaabdcabbcbcdcbbdbadcddbbbbbccdaacbbdcdadbbbcbbbaccddacdcbbadbddaabbdbccaabbbcbcbbdcbcaabdddabcabcadcccadbacddbbbdadcadbaacaaaadbdcdcacbcadcadbbbcabcaccdcdadcbbabbddddbcdaadddaaaccdbcdcaaccccadddcababbabcaaddaaccaabddbbbacbdaaccdbdcdddccbdccadacdddabcaccacddcaaacddbdbbabacdbbddadcdbcadbacbabcbbcbabacbdacacadbcbacadcdabbcaaddaabcacbbadcdaddacdbdbaabdcbabadadcdcbdcbacaaddbcaadbacbadcacbbcbccaaabcaadcdbcadcdccacbacadcdbcbdbcdbcdddddccbdbddcdacbabbadabcbccdbabdddbdabcbbcbdcabcbdaadabbacbdddabccbbbaaabbabbbdcdaddacabcaacbdacaacbddbcadcbbbcdcbcdbadbbdcdabcaccbacbacabddbccbdcacdbbbbcbccdbdbcaaccbdccdacbbcabbbbcaabcccbdbbcdbaaaddbcabcaacabdabaddbcdaabddccdacdbabcddabbbdaddbacdccabbacbccaccadddbcbcccabccababdabbbbcbdbccbbabcabbcaaccaddcabcccdccddcaddbbacdcbdcaaaddccabbabbdddcaabcaacbcbababbaccccccdadbddbcdcbcbddabbccadcacdbcbbddaadbddcddbcacadadbadaabbbdaadacddbcdaabdbcdcdbbbacacaacbcacccbaabdbbddadddabdccbdbbacdcbadcccbddbbccbacacaadbdddcdadadcdaddababddcaaabdaadcdbbccabdddcdcdbdaabaddaadbcacdaacdaaccbdccacbbacdcacdaaaccbdabdddabcdccbbadbabccbdcdaabdddbcdccabbdcbbddddbdbbbbaadccaaadabdcaadcddddbdcccbcabbbacdbcbdbdadcdaadbbcdbadaabbdbcccabdcbbccbcdbcdddadcaacdcccccbaaadbdbbbacdccdbacadbbcbcccabbbdbabdacddbbdbaabacdcabbadcbbcadaaabcbcbdcabccbaabacbbabdcbdcabaccdddbadadbccdbcaaacabcddbcdcbddaccdabadaacaabdcbbccdbdbddadcdbabcbbdaaabddcadabababacccadbacddcdbcdadbbacdccbcbcdaaabdbbcbdacdbccccbcdbbcaabddaddabbcdddcbbcccaddcdbbdababdacccddbdbccdcddbdbcdaaabbbbbbbabdaadabcadabddbdccddcbbabcbdacbbcdcaaaccbadbcbabbbbabddadacdadcbcadbcddbccdcaacccbabccbbbcccadccadadcbdcddabcabaddbbcdddabcbdcabcaccbabcbbcbbabcbcbbccdcdbadcdbbbbddbadaddadcbbcbbaacccbdbaaddaacbcbcbccbbdacabbbcadddcddcdacddcbbdddddabbacdbdbcdadcaddadbcdcabcadccddabdcadadbbcabddbcdcdabaddccbbbbacbcbddaccadbcccbbbcbabcbbdabcddacdbaacbadbadbbddbbdcccaadcacdabbcbcbbbbccddcdbbbaaadcdbcdadbbccdbddbabccccabdbadbdcbbbdcccbaacdbddbbbaaccccbcadacacdabdcabcdcccadcadbaddcbbbbdcaaccadcbcbabbdddbddbadcbdaabcaaaaccaccaccbbdbcdbcdbacbabcaddadaaacbcdccbbcaadcdadcccdcddaccbbabadbbadbcdcadcacbdacccdddcaccadbccdacdddaacdbabdacccbcaccdbdddbdbcadcbdbcbdcbdacddbdabbbaacaccdaacbccbbadabccbdacbbdcbdadbaccccbdcbbacdadacdddabbdbadadadabcbddbdbbbacaacbdaacacbadbdacbcdacbddcbcbaaacdbddcbcdacbbcbacccdbcdcaaaddcdbadbcbaaaacdbabdbcbcbcaaabadddbcdadbcddabccddcdbbbcdbccbbdabbbcbcdbbdddacbacbcbbdccaadbdcbacaadbacbbaaabbaccdadaaddcaaaddcbdacbdcdabbadcbbbdbbbdcacdaadcbbbacbdbccabbabcbdbcadbcacacbdcddaabdcadbaccdcdbaabbbbbaccbacdcdbadbdddbaccacabcadabadcbaabccdcadcccdbbcccacccbaacdcdacbdadbabaadbcacaacbbcbaadaacabcbacadbdabddaddbbdbdcdbbdccaaaadacdcdbabcbdaaaacdcdddcaadaaadddcbaaddadcccbbcadaccdddcacdcbdaddbcacbaabcaacabbddaccaaaababdbbdabbcadcbcbbbcbcbacccacccabacbaadbbabbbcbcabacccdabcdccadacbacbcacdbbadbcabcdaacbcaccbbbbabbadcacaaadcbcccadacbddbddbccdaacbbaddddadaddbaccababacbcbddccdddccccccdaaddbddccabdbaadbcdadbbbabcbdadadddaaacabcacbcbccbbbcbabdbcbbbbbbbdcdaacbbcacddbcccabbcaddcccaadcccdddccaabbbdddccccddaabbaaabbacccbadbcaaabadadbbcabaacaabbcabaadaababadbcdcabdabacabcbccbadddccbccbaddddadacbcdccabcddbadaaacaccdcbbdcdccdaaaaccbadbbdabddbdacccbddddacadaabaaddbdcdbcaccdcbcaccaacddbdadababbabcbdbcdcdcacccdadcdaacdbdadcdbdacacbbbddabccaccdbbbcaacacccccdadcdcbbbcaabdaddadbbdbbbccbcabbdbbabacaabdabdadbabaddbdddaddbcacbdccacaccbcbddcaacdbbbabcdcacdcabacdbdbadcacbacdbcbdcdaabaddacddbdcbbbdabdcccacdbbacaaccbdcccdcbcabcacdcccdbcabdddcdaadbcacaabbdabbdadabbbaabbbaabbbcbcdcadbbdbccbdbabbcacccdcddadbdcbdcbcadddcdbdaacbcbbadcdabbadbcacabbbaaadadabdccbabbbaaccacabdbdbaadadbdaddcccbdadcbcbdddaddcbdcdddaaccadbbbaababcbbbdccabcabbccaadabaabcdaadcbdcacbcadbadcaddcbbaadbbcbadadbabbdbcbcbbadddcadbbcadcbcdbbdaaaacbdaacabbbddcbbcbbaccaccbbbbbdbdbcdbdbcaadcabcdabcadacdbbddcbbbdddcbabddabbbcbbabbaaccaddaacadcbccabdacbbcbcdabdddabaccdadaaaababdadaacadacbccaacbbcaccabbadbaadabccababbcbdbbadaaabcbdacacaddbcababdcbaddaaabdababbdaaccacacadcbdbacccbcadbbaabacdbddacbdbababdccacabdaddabdcababbcacbbbaaabbdccccbddbcbdcdbabcabbbbadccbdaddcccacbcadaabcadddabdbccccbacbccabdacadbcbccacbcbdbdbbbbbccbbababdbdcaacbcadaddadabaaccccaccbacbadcbadbdccacbddaddccadacccdcabcccbddaadadacbabbaadbdbaacabcdaacaadcdccdbbddcdddadcdbcabbbdcddbbabdccabddbddccaabcbbaacccbcacbdbacdbdaabcabbdabcddabddbbbabaadcadbcaaccddabbdcbadcababbbdabbccdcdbccbbaddcdbbbaacabdbdacdbdbcabcacbcdaabacddcaadcdcccbcaacdbbbbbbadcdddacdabdcbaacabcacdcbdabbabbddccbcabdcccbcdaccccdcaaaddcbbadbccddbcbcdaacdcbbaaccabbccabbabbaacbadbcbdbcabcbbadcdbaccaccbcacbdbddadddbddacbdcbdbcacdcaacdbabaddcccbdbddcdacbadadaadcdcbbcabbdaaaccbcdbcbccdcdbacdcaddabccabdadabcdddddcacbdcbcddacccaadadccbdabccbaabdadccacacccbaabdbcbbbbdaabcbddaccdadacccaadaabbaddbacdabbbcdbaabaddacbbbcdababcdbccadcbcdcbbbdcacdaaaaabaacbdbbbaabbacccdbcbadacaddbacccacdddabbcaacddabcccdccdbcddcbdababdccdaaddbccaabbdbddccbbacdccdbaaaabdaaadadbbddcbbddccacbbadcbdacacacdcdbaccbcbbcdccbaccdcdacbddaadbccabbbadcdbbbaabdcdbbabdbdaccaccacbbaabccabcbccdccdbbabababdacdbbcabbaddacaddbcdcbadaadbcbaccadcbadccbcccadaabaacdcbdbccaabcaaadbacacabababaabccabcdcdcacdbaddbdddcbddcdabdddadabccacaacaaabbcccdabddcabbbddbcbaacbdcbbdbddbdcaabbdcaaccadddadbddcabbcaabadaccbbdbcdcacdbabacbdacacaadabbbadbbbcbddbdccadddadddcaadbcadbbacbbcbaacdaabbaabbccdabbababdcbdbdbcddcbaacbcadbabcaddaacdcddddbdcdddbdbdaccddbdaabbaacbbaacbdbbddaabccbcdccdaabacddbbddccbacadccddbbbabababcbcaacabaaccdaaaacabcbadddbbbaaddaacaaaaacbacccaddaaacbadaadcddaaccaacadaabccddccbdacadcbabacabdbcdcbdadcddacdcadadadbcddbcdcdbadabcccbbbcbbcabdabdcdbcadbdcdaccbabaabaaacbadadddddcddaaadacbdccadaacabcdbddcbcdbcdccdcbdcbbbdcdcccabcadaacbccdcbbcaaabdccdbcddccdabcaaaadbbbaaddccdbcdbcaccbdabccdacdaccabdddcccdacabbddacdaaacaccddbadcbabccddbdaaacbacabadbaaacdcddaacbcadddbccdabcbcbddbdadbbbdbdaddbaaacbddbcbccabaccdcdbcaaacbacdbacaacaabcbddaaaacddddcbaabadaacbadabdddcdcbdddbcabbdbbcdabddacdbcabbabbbddcbbbdabccbbdddddaacdcaacbcdadddacaabcbccdbbaabbbbbccccabcbabbcacbaddbadccdbcbccaaddcabccbcdabddcddbbcaadbdbbdddacdacdbcbbbccaabbbbabdbbabbcbbbacadcddabccacddbbbbabbccdccaadddbbadaddbbaabacaabdcccbdccbcdadddadcaacdccdcabadacdcccaddcdcdadcbadcdacaadcadadcccadbcdcbadabbbcabbccbbbbbaaddbcdcbbdcdbcabdbbbacbaaabcbabdbadcaabdaaabaadadcbbacadbcaddddaddaaabddbabadbabaacbbccbcdbaaabdbacbddacabcbabaddccabdaddcdadbdcabcbadbbabbbcddcbdcbdcddadababcaabbaccddddadcadcbabbabccdcbcdcaabcdcabacbdaadddddadadaaabbdbcbaacdacdadacbadcdbbbdbadcbaaddddaadbdabbdabaccabbbcdadccaaabddcdcdbbabccadddcbaaaadaaaabbdbdabbbbdbbaacbaccbdacadbddaacabcccdcccbbbabcabcbdadaaddbabcdbccdacbcacabcabacdcbababcdcbbcdcccdadabcddcaadcbbcbcbacdbcdadbdaadbcacbcababcddadcaacdcdcddbadcadbabcbcbbcdadccbadbabbbadcccdcdabdbaabdbbdcbcadcdacabaaabccbbdbcdcbdbadbbacabacbbbcdbcbadacdbaddcddabcdabdabbbdddabddccdaabcddcbadaaaaabdddabcdcbabdbbcdbaabbbcddbccaccddaddadabdbcbbdbacbadadccbbdaacccbdcbdbbdddcdbbccaacacdcdcccbadbbccbdacdbccbacdacbdbcccbaddddccbbdbcbacbcbdccbcbbbaddbcabdbcbcdbdadabadcaccabddcccaaadcdcdcadbdbcabcdbbbbababbddbbdcdcdccaadbdddaddbbbdadabcbbbbdddacdbdbacaacbcadaccaacabadbbadcbcccdbcaababaabcbbdaccbbaadddaaacbaaadaddbdcccacddcadccbaadbdadbdcdcdcbdadcabdadbccbddcbdbbcbbbcadccbbabdcadaddccbcaadbbdabadbbdbccabddbdcdaadaccdcdaaaadbdcacbaacabbbccaadcacdaaacaccacdbccbdcacbdcaddbbdbaaddaccddcccaadaadacdbcbbdabccbdadcccadbdbacbbcbaddadbbbabddaadcbacbacbacdabadddaccbdbabcbaadcabdbcababdbdabdbbdbadbadcaccccccdaacbbadabdacadadacdcbacdcaaabaddddaabccaacdcccbdabdcacddbadbabbcccadcadaddaacabacaccaadbdaccbcaaaabbcbdabaacbcacddcadacdddbbacdbcbdabcbbdabacdbcbdaccaabbacdabaaadaadcbcacddaaabcdccbadbcabdabaabbbbabadccbdbcbbabcdbacbcbddcaddbacdcabccbabcaccdbbcdcddbbcdcaacbbaaadacbbbcccdacacdcbcdadcabccbcdaabbcacbbabccbacbbbcddacabaabcccaddcccdccacbdacbbcacabbbcaddbdbabdbbbbbbbbbbdcacdabcddbbcdcabacabdbbabadbcbdbccabcbdaacadddaaadcbbcbdbcbdcbacccbcabaacddbddcacdcbaadbacabccacadaadcbdbcbbabbdbaabaadacaccbaadcaadacdcaddbbbcbcadcbaabdbbccabadaadbabbccadcdabcdbcbdcdbdcaddddcbabacaaacabdabcdbccaadacdcccacdddcddbbbadbaaadddccacbbdcdaddcdaababbabdddcabccabbdccbdbacdbacbdcbbcbccaacabcadaacbcbabacadddbcbabddbddddabdcbdccabadbadbaccccdaadaaaacadabdacdbcbacbdcbbcccccccdcccabdbddcdbadacaabaddbcabdccdcdcbcbcccaddaddbcddbbaaddbcacacdbcbdadbaaacbddbbdadaddacbbcbcdaabccacdaabcadbdadaccdcaabdacacdddbddcadddcbbcdbbcbcbccdbdbdbacccadcdcababbcadbdcdbaddbcbabcbadbbacbbbbaadcabdbaddcbacdaccbdbaadccdcccbbaacbadddbcbdbdcccdbcbccbccbdbcaababdcdcabdadbcbdbbadbcabbadbddaaaddddbddabdadacadcabbaaddbddbaababdabcadccbacbcaddcbaacababbbabaacadacbbbaacacbacabcddaddacddccabbababbdddbdaadabdadbcbbadcddbdbcadcdcddabbbadadcbbdddadddbccbcccaddcaaccbadccbbbdbbcaacdddcacccacaabaccacaaabcdaadddccabcbbacabbdcbadabcadabacabddcabcdabcbcbccbabdbdcccdadadbbcaaaabcaccbadbcacddcabacbdacacadbbbdddbbccbadbdacdaabadaacdaaaadcccdbdaaacdadbbddbacabdbbcbcdabcccbabdbabcdbcddbabbdadbddbddcabbbcacdcbdbadcaaacddaacbbacbccdabdbccadbbcbaabacdccbccadbbaadacbadbdabcbdabcabadbdcbbaaddcbcbbaabcaaaaabdbcbaadbcadcaabcdccadbadbdabbadacbabcaacbacdcabadbaddaaaddadbabcbbdabccacdaadadbabddcdcabcacacccadbaddcccbcbcaaddaddbdccbababcbcabcabbcbcdbdccbcaadaaddddacbbcadcbcbdbbcaccbacbdbdbadcddbaabddcdccdacabbaabcbcacbaabbcbaaccacaddabdbdbcbdabdbdcaddaacccacccdbcababdcdaadadabcbdbdcaaabbbdbdaaaaacdaccbbbabcaaddccddbacadcbcdbdadcbccbcbcadabcacbcadabbcdbbcaacbacdacdccbbccdddabbbaacacbdbcbabcbdccadcbbcbdcdadbcdcdcaaddabcdccaacbddcadbaadacbdadcaccabdccdacadbbbbbacbabdcdbabbcdadcaabbddadadcdcbacaadccbcaccbdcbaccbabacadbacbbddcadcbcddbacbdadacbcddbbadacdccbaabadaaaadbbbacbcbcbdbacdccbcbcdcbccbaaadbccdadcbacdcbcbabaacccabcdcdcbbbbbacbdbdcbbddadbbddcdabddabbdaabbaddabbbbdddcdcabbacbaaddcadbadcbddcbaadcaaadcacaaddcbbbcdadaacadccddcaddbcadadbadbbddadcbacdddacaadccdcabaaacdabbadcaddcbbdcbacbbaaabaabccaabddadbabdbdbadbcddcacddadcccbcaabdcbdccbcddadcaacacaadcaddddadddbabcaabbcdbcbadbaddbcacbcbcccbababdaaaddadcddbbbacbaacdbdccddacadadccdddbadddabcbababcadddadcadadaabddbbbabdcccbbcbdcacddaccabccabaabdacacaccaacdabacddbaaddbcdabcabdbbacabccaddabccadaacdcdbbddaadbbabcdcbcadbcbaaadabbcabaddbdaabacccbbbdbabccdcdbdcbdbcacabbadbdbabbdcbaaaacbcdddcacacacbadcbbbccbdcdadabbdadadaacdbcbcabbaadccdcdcaacabcaccabcaccbdcdabdcadcbbccccacaabcadddccbacadabcccdcbaacdccabacaddcbaadccdcaddcadcccabcbadccbcacdcaadacdaaccdbcbccbdccdddabdcdacbccddbddbdaacadddcbbadbabbdaaacdbbcccccadcdcdababbbddcccdbcaadcdcbddccbbbdcdaccabbdbcaadbabbaddadaccddbaabcbbbcccadbbcaabcaccbbddbdbcddcacdadbcacabaaadcbbabddbbaccaaabcbbaddabbbadbcbcacaadaadbacccacaabacbcccaccccabdbdbadaaabaacadcdaabaddbcbbdcdcccdbaaccccbbbcaaacdadbbbaabbbdddcccadcabdcdabbaccbccdcaadbcccdabcbbaadddddcbddacbcbbaaccadbbabbccbcddbcdbcdcbccbcaaddcdcbcccbadaaaacdbcdbbadaccabcddabbdcdccaadbdabaababdcdbdbdaaadacaccddcdccaddcdcdcdddcbabbbacaaaadbabccdbbccaccacccbccdabbbcacbdddaabcbcbaddddcdaccabadcadbdacacdcdccdabddadbcdbacdcbcbcdbdabccdcccaaccddbacbbddbbbdcdcdbdccdadabcabdabadbacbaddbcaadbcacaaccbaddbdbdcbccbcdacbaabddddaddbabcbbdaadaabaadcddadbdcdccbcaddacddddadadcdbdbaaccbaaaccaacacddabbbcacabdaacbdcdaaddadcaaacbdcccacabaaadadcccaddbcbadbbcababbcadabaccbbbdbabaacbddacbdbbddbabadddcbbabbcccaddbadadaddaccdacbdccacacbabdddadcaacbbddbbdcbababcdcbdcdbccbbdcbdbccacbacbbcdcbddddcadbaabaabbbdddddcbccbddcdabcaccabaacacdddccabdcababdccabaabbcdbadcaadabcacbbdacbdddcdbbabcddacdbdabdbcbbbdacdabcabcbbcccbdbabbbccbbaccaacbcdcadddabddbbacbdaccddcbccddcaccabdabbadbcbbdacddbcbadbbacbccdbbbbcddabaacaddcdcdaacabadbaccaaabdcdbabdccdadacdcacbdcaacdbbaabdcaccdbbadcddcacdcabadacabaaccbccbbadaacdadcacbcadbaadcadbbaaaacabaaacdbdccabacadbabbaacaccddbaabcccbabacabbaadbaaaadccabaacadabcababdddadacdbddbddcdbbdaaacdadbdbdcddacadaccddbbbadcdaadbaaccdacbaacbdcdcbdcccdaccaadcaabbdbccadcbacabadddacddccddbddbcbcbaacdcdaddcbcbaaabadcadddcbabbaaccdbcbddacabaaaaccdabddcbaaddbcccbdabacddabdcbdadaadabdaaabbadddabcbbddbaddccacdacacdcbcdbdcccadacaaaaabbaaabaadadadbdcccddcbdabcbccacbbdddddabdcdbdcbaabacbacaadaccdaabcdbbbcbdbabbbcbbbbcdaaddcdcdaccddcbccddcdcadcdaaaacccdabacbdbbadadcccadbbadadbcbadaaccbbbdccdbcdabaadbaccabbcddcaabcbadcacdbbcaddaacdcdbcbddacccaaacacddababadacdbbbdcacaaccacddabbdaccddacbabcabbddbcddacdcdddbdbcdaaaddcddcbcaadbdbcadabadcbadaaddacbdcddabdcbdbbacacbdaadbbdbcddacacbdbaababbacbcbcabadbaccdcdaabdddacdaaaabddbdcdadddbddbccabdbaaccbdbadabaccbdbcbababbcacacbcbdbcdbcdccbddbdcacabbcaadcdbbbdbaadbcbccdccaadacadcadabacbbdcdbbdaddabcaadaccaadabddbadaaddcccbccdddbddccbbdaaccdbcdccdcbdbbbbbacddcbcccbbaacadadbddcadcbbdddbbbadbbbcbaacdaddbddbbccadabbbcddabddcbcbaaaaccaccdadddacadaacbcaabdbcbdccaaccababdaabaabdadbdddaccbdaadcadadbbddaaadacabdcbabdccaccbbdbdccadcddadadaddabdbccacaabdbbdbdcadabbbbadcdabbbbaacddbdddaabdabdaccbcadccdcbdabadccadcdddcadbcbaccdaacdadbacddcccbdbcdaaaaababdaccdaaaddaccccadabbdabbdaadadaaabbbaccbdacdcdaadaabadaaaaddccbacbdadbaadcbaccdbccacadddabcdccacbbccdccbacdcadddacbcdcdbdccaababbdacaddccacabadcababababbbcdabdcbdbcabadcbcaabcbbacbbcaabbbdddacaabdacbdadadbddcbbabdaacdbddbbbbcbccbbbbaaddadcccbccccddbcdadbccddcbcccdabdcbbcbcccccabacaaccdacdcccdcdbbcabbdacdbccabaacdccaacabccdaccccbdcdaaaccaabbdaabbdcbbbdacbbbcddccddacbabdadbdaabdcacaaabcbddabccababccbdbadababcbbdbddbbacdbcadadddbbdadadabbbddcbcbbdddcdbbbdcdcadcdadcabdbdaadaaaccabddadbdcbcdadbabbcbcadbacdbcbbabcdaaddbaacabcdadbddbccbccdbdbdbbdcdbadbcccdbcbbcdaccabdaadddbaadcdaadcadbcabaabadccbccacbcdaaadaacaddadadbaccabbcabdcbdbcbacaacbddcbbdcabdbbaabacdadbbbbddababaabcbcbcdccddbdadbabdccaaaccaaacdbabdadcccdccacdaabdbbdabdadddaacdaadbbadbdcaaccaabcabaddaaddadcaddaacccbbbdaaadaccdabcbbcdbbcbdaadddbaccdabcdcdbbdcbcacdabbaadcdaaaacbaccdddadcbbdcbabcbadbbbdbadbcabbabaddbdbccbbaaaddbbbcaabcabdccbbbbadacbbdabdadcbcbdcacaacbdbbdcacdbcacccdbabaccbcabaddbacddddacbdbbaccbcbdabbcaabcbbcacbdcacdcddcaabbacabaaddddacddccbccabccbacdccbabdcccbcdababcdcccbabcbadbacbadcaabcbbcbccacdccabaccccdadcbcadabdadddbdadcdbdbcacacbdbdabcdcadccabbcdcbdbcdbccaabbdaacbddcddcccdcdcbbddcbdcbdbddadacaadbaccbabcddbcdcdccacbaaabbbaddddacddddbcabccacdccbcabcadbacdccacadcbbadcaabaaacccbaacabaadddcabbbbbcaddcdabbcabccadcabdbaabddcabcdbdaacaccbadbbccbdcababccabbdddbccdddbbaddddddcdbacdccbabcdbbdcdbcdacdabdbacaadcbbcadabadabacaddcdbcbdcdaabdddccbdcdabbdaaabbccaacaadacddcdcdcdaaaddcdcdaaccddaacaddbbbdbbbaacbbdcabcdcbaadccdaaacaaadbacaccaccdddcbccbcdbdbddbdabdbdabbacbcdddacdddaacddabccbcdcaaccbcbbccaaacddcddcabcbcadacdccbacacdabadcddbaccacbdcdacdacaadabdcbbcbbdcdaabcccbdaadcbaaaaadabbcbdabbcdcaabbdbbdbbacbbdddacaaaacadcbbcdaaaaccccddabbaacbccccbcacdacbcdbbcddcdacdbabddddcbbccadddabacbabcbcababaabcbbaabcabbbddcbaacbbbdcdcacdbdbcbbcacdacdbadcabbbcbbcdbcbacdbaddaadadcddbcdbbbcbabccbabacbbcaadcddbddbcbcabbdbadbbddbaccacaddcbcdcdbaddacbcdbdbccbdabbdaaccaacbacbcbcbacbaccadbbccaaadcababbabdadabddaacbbacaddbaadbaabcccadbddcccaaadccdbcacdbcbccdcbdabacddbcabdbbdccbdabbcbabacaaabdaacdbbbddadaadbabcadccdadaacbacbcdbdcbaccabacddadbaababddaaadccbdcdbddbaddccabaccabcaaadcddcaccbcacaccccaaaacdddcabddabcddbabcbaabdddbcbcdbdccccaaddadabcabdccddbacdcdacadbcacdbbcabdabbdbadbdabbdcdbaccadaabdaddcdadbcaccdacdbddbcbbabbcacdcbdacaaacdcbdacbdadbaccbccdadbadadcddbbbcddaabccaaadccaccabaadbcbbbbdacacaaddaadbcbdaaccdddcbbabdbbdaabdbddacdadaddcdbbdcdbbbdacdbacdddadaccdcdbaadbdcdcdacdbadcbcbdddadadbbdccdbbdbbdabccbdaacbbdabaaccabadcdbccacbacddcbcddaccdcbbcdbbbadbdddcddabaaadcbddbddcdccaddbdbadddadabcdcbaacabbbacbbbadaacdbadbaacdcbcbdabaccbabbcdbbbbcbcbcbcbadaaccacaaddbcbaaaddadbcdbbddaaccbcbacdabdbcccccaaaccaacdbaccbaccdccbdbbdbccccdccdbabcdacdcddbdaacbbacbdacbddacdddcdcaddadcccabdbbabbcdbadcabadbccbbabacaaddddbccdccacadaadccbdbbbabdadbbacacabbcdbbacdbdccdaabbbaadcccccaccddcadddcabcabaacabacabbabbacbbbbccbcdacbadbbcbbddabacccdadcdaccabcdbcbdcdbcbcddbabcdcbdacbbaccbbbccbbcabdccbacbdabbcddbbbdacbdddcdbbacbdcacbccbdbacacbbcbacbbdbacdddbdccdacbdbacbdadbbdddddbbbcccaccbbdadbccacdaaddabcbacccadbcbcbccaaadadbbabaabdbbbacdabbbabdbbaacdaaaaccabbccaadddccccaadccbdcbbbaadaacacbcabaacacdcbabbabdcccadaaabcbcccbbbccdcccdbacdacbcaaddcdabbcbbabccdabdbdabadbddbbcbbbcabddacbaccbcaacbdccdccaacbdbcabbddbbbbbbbbcacaaabddbdddbdcbddddcbdbdbbcbcaabdbdbaaabccccdcaadaddababbaabbdbaaabdbdbbcbaccbbbabdcaaccdabaadabcbadaaadcadcacabaaadbdaabbdbaadaabccbaaccdadabaccddacddcadbbdabbccaabcdcaaddbcbbabdcdbaaacadbbcbdabdaaddbacbdbdcddccbbdccbcbcacabcacdcabbccdddcbacdcbcdddabbabbccaabcdabacbacccbbddbbaabbbabbacacbadbcaccccbbabadcdabbcbcdddbcdbabbaccabbaacbbdacbdbccaacbddcbcbabadbccbcaccbcacddcdbddcaabbbbabccbbdcacadabbbccabbaabdcbcbccddbbdbdaadacbddacddcabcdddadacbcacddbdcdabcdcdabababbdbcddbaacbabcadbaabcabacbcbcdacdaabcbccabbccbdaccdccacccbaadaabbdcbbcbdbcbcbacdacdcbcdbcacdacabcdcadbcabaacbadaaaaccbdcabdaabacbdadadabcbdadcdababbadcdaccbdbaccccddbacdacbabadccdacadbbabccadcacaddcdcdaacacbaacaaaabbcccbabbcccbcdcdadacbcaaacccbbdacdbddaabdaccbbdacdbdacadddcadddcabbaacdcbdbccccbdcabdbccdcbbaaacacaaddcbaccbccbdaabbcdbcacacabaccabbaaddbbcacaacbcbbdaaaaacdacdccbcbddbcccdcbdaaacdbabbcdddbaddbdcababdabdbdcaaddcacbaabcdaadcdaddbadaabcdababdbacbaabcbbacdbadbbcabcdbabacdcdabccadadccdbaabacddcdbdddadaddccadadbdaccdcdbcdbadababcacadddcbcacbcbcabbadddaaccdabdcccbcbbbbaccccdbccbacbdddcdacbbddadbdbabcdbcbcadcacbddbaddddaabdccaaddbbcdccaaacdcaccbcdccdacddbbcbddadbcbbabdbacbbdbadbbaccacccdbadadbaadadbbcbaabdcbddcbbadddcdcddbbbcdadcdcbcdadcbccabccdacccdaacbaccbacbcdccacbcddcbcbacaacdaadacaadcdbcaacbbabbbbdcbdbdcdcbddddddbcdccdbdbaaccbdbbcbcaacbabcbbdadcabbbcbcdddcbcdbbbdcadddbbdccadadcadbbccbbbcaaccbbabdbdbbddabdccdadcbabccccccaaaddbddcbbccdaabcddabbccbdcdbddcabcccadbaacdcbaaccbabcacacaddbbccacaaadadbbabaccbcdbddbcccdaaaabcccccdcaddbbadcdbbabcbbbcaadccdbaaacddabccacdaadabddcbcacaaaacbaddbbcbcddcccbdaabdbbbdbacdacccabcacdadbccccaacdcabddbdbadbcbcabadcdbcccdabcdbadcdaaababdacdcacbdbdcaacdbcdbabcddadaaabdbcbdbcdabadbadcadcaacbcbcdbcbadaccdbbcaccdbcdacbcbcccdcbbcccbdcdabaddddaabdbbbdaaabacacbadacdaadadcbcacccacdcccababbadccdaabaadccbbdacdadadbacbaaaaaacbcccbaadcdaddaadbbbddcaabcaaabbddbcddcacabcccdcadbabbabbccdddabbbaccbbbabbaddccabcdccbddcaadbdccbdbcababbcabccdbcbadacdcccbbddbabaccdbadbaababcabbdbbbdcbdbadabdbddabbcbacddcdbcacbbbadadbbbbdadacaaddaadaaccacabdadcaaacdabccbbcbdaaaabcbdcddcccddabbddbaccbaaabbacbbacadccbcaddbbcddbcadabadaacaabdcdaccbaddaadbcbdddabdbcbbddccccbdbbcccccaabaddddaabdbacacdabbcbadccadbaddadcadaacbacdabbbcacaabdcccacadaccaaaddabacaacdaacdbaddcdabbdcddcacadaccdabbadcbdaaabdabcaddcbabdbcbbcbbbbdbdaddcdbbaddddadccacadacdbccccdbbbdbabdcaddcaaababccabacddddcaaabbababcdbbbddbaacadccbabcdcbddcdbadacbbadcdddcdaccbabddccccdaaadbcdbcbcabdccadcabcccbadbadaaccdcabcdccdbbdbdaabababdbdcabbdbcaccbddbabbbbcccbcccdbbbcadadacbaabbcbadccdbcbdbcdbdacdadddaacacdaadabcaddabbabdabbdbbaadbaccdbcdcdbaaccdccdabbdcbbdccadacccddccddccacadbbcbcbccbcdcadcddbddbbcccbdbabdddadabcdbcadbbbabddbabbabcccdbcbbadaabddccccbbbaaddcccbbabbbbacdccddbcbabacbbaccbbacdbbadbadcbcdaaaaddcaacdbaaccbdcbcaacaddacccaabbdadaddccbdccccdbdaccabdacdaacaadbbccdabcdacaaaadaadaacdacbbdcdbbbcbbdabcbbdbbbbdbccabbdabdaccbcaaacaccbcadaabdddacbcccaaadcdaababcccbbbaaabaadbaaccadbbbddccccbaccbabaadcabaddbdaabcacccaddddbddabddcdcbcacdddcbccdabcddbcbadbbbabbcdddbdabcacddcbaccbbcbccdbacbacdbcbaadbaccdcaddcbbcdaccadadbdabdbcbaadcabbbcacdacacdcdabbabcdcadbbdabddbdddccababbcdaaddabccbbbdbdbcabbadabdabdddcbccddcbddbddbaacacdcdddabdbcacbaaadacdcbadcbdbacdbdbdabbbadacbbabaacacdccdaacbbacadcbdaacaddbbbbadadddaddbacbdbcacadcddadbcdbcbddaaacddcddacbcbaacaadbbaddbaccbdabbdbccbbcaadddcbdbaabcddbbdadcdbccaadbcdabdccadcabbdcaacaadbdbdcddcdcbdbbbcddaaababdabdcbccadcdadbbaabbadcbadcaaaabcccbdcbddbbdaccaddcadabcbaabccacbaccddbbbbdaadcdcbdabbdbaadbbacbdacbbdddadacbcacdcbdadccbaadabbdbbdcadaadacbbabacbcdcdacccbbdcaccbdadccdacacddbbbaaaddacabadbadbcabdabdcacbcabbbdcaddddbbddacaccbabcbdcccadbdadaddbaabcddbddcdcdcadbcbdcdaacdacccbdbacbdabbcbdcabcdbacdaccbccbbbaacbbbddaadcccdcbdccdbccaadabadccdcdddcbddddbdaabccddbddbbcdbbbadddccdacdcbaacbcbcbaabcbdbddbcddaaddbacbccbadcadacbcccaccbbbdcadbacdccdccdaacadacbdbabbaddbbcbccacdbdddbcdbcababcdbdbdabaaaccacadbccdcddcbbdcbdbccbdbbdabdbcbbbcabbdddcabcbacbadaddccabcdcbaababcacbccdbabdbbaaddcbaddbbadcaabbabcbbdcdbadccadcabcbdcacdbcbabaddcbacbadbbcbababcaadcbcbaccddbacabcbaacdcccbdbcabbaadabbbdbddcbbbadbdccbbaabbadbadabcacbdbaaddbbbcabcdabdaacbccbacbcbcdccbbbcaccacdcadcddbddabddadbabaacabcddadcdbadabbddbbbdcccbcccbbaacbaaacbabadaababbabccadbcddaddbbaababbbacddadabbdcabbcccbadbacbcbcbacbddddbcdaaaacacccadbcdbacadcabccbbadbdbdbcbaabcbabccdbdadbccaaadcacbbcaaacbbcddbdaacbadccdcbbbbddabccbabccacdcabbbbbadabcadbbcddcdccdddcccbcdcdcabcdbdabdcadbcbddcbcdaabcadddaacdabbcaccacddddcabbaddbbcddbccbdbddabbccdabbddaabbdadddcbaccacadadabadadbddbcaadabcadbcdddcdcbaabcdaabaccdadaacabcbccacbaddadccbcaabcdbccbcbabddbdbdacbcdabdcbbcabdadddbddadbabbbdbcdcbddcbdbdcdadccbbacccadaccbdcdcbccaaccacddccccdccdcdcbacbbacbdbdcddcdcadcbcabaddcccdabaaaabcacccbbbaddcdbdcbcddbcaabcbcabbabbbccabaababbdaddcdbacacdbabcddcbdacdbdccbccdadcbbcbcaccdadaddbbadbdbabcbcbdbadbbdbddcbbcdaadabdddacbbcbccbdbddadbaadbaacbbdbdacccccaccdcaabadcbdbcdbcdbabababcdbdacdaaadcccacbcbdcdcddcdddaddacbadcdbdccadbdadbccdddbdbadbdcadbadcacccacccdacbcdaccdbbbcabcbabdadbdcdabdabdacbdabdcdadabcbddcbbacacadccddaaddaabadcabcbbcbbdbcbdaacabdadbcdadccccbdcdccccccbcadadcbcdddbcacbddddbdabacacddcbddabdbcaddaacacbccaacadbabdccbccadcbcbdcdacbbaccdbbdbddacaddbbccacbdbacddccdddcaddcbbaccdbddcbbabdddbabccbaaacdaaaabcbbbccabcababacacddbacabbcdbcddcccdcdbdbabdccddcbcacadabcccddcacccaaacbbbacaabccdcbdbbadadccddaabdddbcaccdbdacabdcddbaccabdcaacbdddadbcbacacdcbcdccdbdcbbccbaddcdbbdddbcabccbbbacddcaacdbbdbabbddabdbaadaadbadaabcabcdcbcdbbdacdddccdcccadbbcaddbabdbababdddcbbdaabcccabbcaabbbdaddcdcdabbadaacdcbcdcbabcbacacaabdacbaccaaadadbdcbdcdacdabdbdcccdbbccbadcbabcaabcdcabacbddcdadadcbaabcacbccddcbbaacaaddbbddcbdcdcabdabbcaabacbcabdbacaadcbacdccdaabadadcabdcdddbcabadabaaacbcabcabacaaaabdddbdccddabadbaabaabababcbcaadcddaadcccccdacbdbababbadbbaaccacabccdbdbbaddbcabdaccddaadbccbccaaadcdcabddcacccbacadabbaabbaacccabcddbbcadcadccdaccaaabbacaabbbbdabdcdddbabcbcbcbdbddaccbbadaacdbbbcaddcacdbddabadbdbccaacadadbbdcccccbabadbaddacabcacbaccdbccbcccabaccccbabacadbdccdacbbaadcbbbdaabadaacbdabbcdaacacbddcbadbbbdddbaccdaabadacccdbcabbbbcbbcbbdddccbdddcaccabadbabbaacdabdbcbbcbdbccbbdcbaadccaacaadbdaacbdddbbccdacbadccddbdadddcddabdbbaaacababccacaaabbdbdbcdccdbbaacdccacddbbdcdbadbdcdbadccadbacbbbccbdaabbdddcdddbacabababaccdbaabdbdcddaadaabbdccaccddbbcadbdacbadcaaddcdacdcbaddbddcadbcbdcbabbbacbccbccaacdcaddabddaaacabadbaacdbabccdcadbaaacaadaabdbdcbaaccacadbbdbaadcddabcbddcbcbabcdacbaaacaacbccdabbaabcbdbccadbaacbcbdabbabcdcbddacdbcdddbdaddbacddcbcdabadddbddccbbadbddabacabdccdbdddcdacccabdccddadcbdcbcbddacccbaccaacdbbccbcabcabacbcaadacbabbbcdbdaaacaaddbaccaddbdbcdbdaccaabcaabcbcaaddccdcccbcbccdbbaaddbdbaaabbdbdddcdbabaccbccbddbcbcbdbacbccdabddcdaccbcaaaacdcdcdababaccdaadaaaadabcbdcaacadadaaabaabbbbaaaababddadbabbdabcdcbccaccdbaaabcddadcbbcccbdbcbdccdcaccbaabaadbbcbacbdacbbccadddadcacddbabbacddcccbbdabcacacadbcdcccbacbabdcbaaaadabaadabbcbbcabbddcdcdcaaaabbdcabcccdabcabaaadbdabdadcdabcbaccbcabaacdadacadbacabababbbdbadabbbaababdabdddadaaccbbddabccdbdabbcccacddcdbaadabbcacbbddcdccbabccbdaddbbcaddbddacbabcacddbccbdcbdccdaacdccbcbccbbaadcdaabacccbdbdccccaabaaaccdbddbddbccbdaccdcbbaadaaccddaddacdacadbddbdcbacdbababcbbacacaddcbcdaadbdacddacacacadcabccccaabacababacdccadddababacabaacaaccbacaaadcbcaddddcabddbccbbcbdaaccdccbdaabccccdaacaaabcbbdacbcabcbdcbbddddbaccadccbdccbaabccdcdcdbbdaaccbaabccccbdddbaccccdacadaadadadaddaadccabdabbdddbdabcccbcacdccdaacdbcaabcdbabaacbbdbaddbcdbddacaaaacbbaabbbbddcbdadaacabbcccbababcddbcdbcdbbdbbbbdccbacadcadadbbddacccaadbddcabbaccbcabddbcadaddcadcddbdaddbaccbdbdbbbbabadaadcdcdababcbbbdadadccaccdbbdcbddbcdbabadaaabcccbaaaaabcacdadccadbccbbccdcbdbccbbabcbcabccdccbabbdabacaacadddddcaccbdaaaacbbcdbbbcadbccbdcbdcdabadcdacdccbbcdccdadbccacdbccacdbabcddabacbdaadcadabddccadcaaaaacdbbdcaacaaabbbbaacbdacaacbcdbbbaddcbdbbbbdaaaccdacabcabcdbdddcdbccdbdacdbdaaabacdbbbacabccbdcbcadddcdcadbaacbacdbaabadaaabbdabbbdacdabadabdcbddcaddddaaccbaddacadaacdcdbdcbdabdbcadcdaaaabbbddccacabbabddbadccdbdcacccadaabbcdbddababadbdbabdbdacbbdbdcddbbabddbabacaacaacdcabbaaaddaabcadcdabcddbaccabbbdbcdddccaaddcddccaaabcdbaccbcacabcbaccaabcacaacccbcbdaabbcdddbaddabddbacbbaaaabddbdacadccdddcbddbdacbcccaabadcadccacbadbbabbbdccdadccbcdbbdccadcadbbbcadabdcdaaddbbdcbdabdadcaccaddddcaccbcadcbdddbdcbcadaaababbabbaabcadcaddaadbcadbcdbdcdcdccacccabdcbcdbcadabddccdbbcddbcccddbbdacabddcbdcadaabcbbadbbbdbbdacabcbccadabdcdbcdbaaabccbcbabacccccaaabcaacdaabdddaaabaadaabcaadacddbdbacbbdbdaacbbbaaacdccaccababdbdaabadcdaadbbcacadaacbccabaacbaabadccdbdbacabbccbbcbadbdcdbcddcdcbbbaabccdacaabcabdbadadbccdddbbbbcccddccbbbccdaadacababbaaaabbcbcbcadbcdbdcaacdccdabbbbcdabcdadbcdaccaadcadbddbdcbaddcdadacccbaccbabdddabbbbbdaadddaadddbbbaacdbaddbaaaddccbcadaddadbbbcdaacaabdaddcbabccbdcbaabdbbccabcadacbcaadaccbabbdddcdcaacabaccdacbacadabaabababadbabbaccaccbaaccbababcccacccbcacbacacabbbabdadaddadadbabbbcccbacddcdaabdbbacabacacdbadbacbccaacccccccdddcdbdccbcddbdccaadaacbddbbdaabdbcdabaaaccdbcbbdcdbcdbbbdcdbabdaacdcdaabcabcbaaccdaaaabcdcdbcbdabacbaccaabbcddcabadacbcadbabdbbacdabcbaddacabdbadbaaaaabccadcbddccaccccaddcbdbdbaadbaadbbabbdcdccdacbdccbcdadbddccabdcaddaacddabdbaaccbcadcbdccbbdacdbaccbdcbacbdcadcdadcbddcddbdabccacdbbbbabbdabdbddcaacbababcbacbadbddcbcccbabacaccbabdaaaabaccacabbadcdbcddbadaabcacddaacadccbbcabdbabccbccadccadaaabcdaadccbcbdcadbdddbcdcbcabbcacddabadadbdbddccacbabcbcacddddbdcddccbadadcdbdcadadbadadcdbbcbccdbbcabdadbdaaacbacdcdacdcabddbdccdcaadabcbcbcccbcbaabbdcaacbdadaacccdaadddbbadabbaccccbdacdbbbacbbbbacdbaabacbbdaadbcddadbdbcaacaacdbbbdcabbbacdbbbdbcdcdbbcdddbcabcddbdbaccccdbcbbaccbadaaabbbaddabccdabdcadcdaaaabacadbadcdabdcaadadbcbbacbadccdcacbbbccaccaccbcddcaaaaaabdccdaccbcdddbcbcbbcabacbdcabbcaaadbdcacdabbcbdabddcbabddacacaaddccacbbbdbacaabaadaadbdaddbbcbdbbbabadbbabccdcadaccaabccbcddaadbdcaabdcbbcabccacaddbddbddabcdddbdacdbdcadddbcdacdcbcccddaadccdbadbcacabadbadccdcaabbbcabddcccbbacbcadcdddaabccabddccbacadcddaacdddaacbacbaadccdbbabcacbbccbcbacdbabdccaacdabccdacdcacabbcdbbcabbacadcbadadbbaaabcccbaccdaccdcadbcbabcaaacbbdccabcbcadbbabcbabbadbbcdacccaadbdabadaacbadcaddccbdccdadcccbcdbcadabdacabdbdacdccbcccdaccbdadddbadaddaacbcbdcabaabccbcccbcabcbcbaaaaddbbabcabbacdadcabdabbabaadbdddcbbddaaaabaabcabdcccbcadbbdaadadacacabccadbcabccdbcbaccbdacdbaddacdaacbbccabcbddadccabbbccbcaccbacbcbbabbcbdcddcaaaccdbbdadddbacbcacaddbddabdddcddbaaabdcbdacbbabbccdbcbccbccbcacaacbdbcddbaccdcdaabaddadbdabccdbbbcdabbdcaaaaaadcbaaccadcacaababbcddccccdcabbbdacaddacccadbccccbadcdbaaddabcbbbddabbacddddcbbcccabbbcadbcbccdaadcbcdcdbbbbcccbcbabadccbcddcbadbbdcccadbabbcbccbdbcaadbbacdcbdcbdbcbccdbbdabbbadcbccbccbbccadcdbdaabccdbbbccaacabcdcadadacbabddcdbacdaccadabcacbaacabbaadccabcabbcccdadcadbdbbdbbabdcbddddbcbbddacdcbbcbdcabadbcadcbddacaabddbaacbddcdbabcaddbbdcdababaaaababbacaadaabdbbdbbcdcdacbabdccdcbadbaadacadddaaddbdcbbcbacdaaadccabdbbcacacbabaaacbdbdcabaaaaadaccadcbaaccddbcaaaccbcaddccadbddaadcadbcddbbcbacbcaacdbabcbcbcaabbcddabaaddbdcabddcbbccbdcabbacadcbcabbdbabababbadaccacbaddccbdbddbdbaddddcddcbbddacbddcdccddbadaaaaddadddaaccdbbddccaddddbcbadcacddcbcaabaaaccddcbbccadccccbaaddbccdabbdcabacbadcaabcdaadacdacccacacdddbdbcbaccbddbbdcbabbcdcbcddddccdabcacbdcbbcdaadcbdaadacdacdcbcbbaababcdbcadcdcabaddddbcdcbcccbcbaadbaabdddadbabcbacddcaaccbaadbadbccddbbdcbbaabcacbacbbbddbcbbdbbbcdddcbcacbaaabcbbdbababdbcabcabdbbcdcbaddcbaddddbacbdaadbdcbddccbbddbaccabcbdabdbccbcacbbaccbbbbabbddaaaabdaddbbbcdcabbabdadbddcbadbdbacaabbaaddadbaaababcbccacadabdccaacbccacdbddacdaaacdcadacbccbabadadcbbdbaccdadbbabdbdbdadbdddabdbdaadaabcdbacadddbcbadcbabadcbcccbacdcddbacdcabbcbaabddcaacbcbcdabbaabcddadaaacdabbaaccbbdaadcaaaabcccdacadccbdccbbaadcadaacaccaadadbadcdddaaaacbbdddbcccacabbacbbbcccadabcbbdcbcbdaadbbacabadabbbacacabcaacdabcbbcdbcdbbdabbdabcbcdcbdbdcaabcddadcaddddcabdaccabbacbccdacdbbaadddabbdcdabdddbabcccbbccbddbbbacbbdddccdbbcdbcabddcbbcddddbccdcdbabcdcdbdacacdbadcaabbbaadaadcabbbdcbaaacdcacbbdadbbcdcbaacacddcbbbddccdcabcbcbcccbcdbdcdcdabbcdabbabdcabcdbbadbdddddbbcddbadcbccbbcddcbddcbadcdcbcadcdbaccbccabdcadaacadbdccaacbadabbbabcdddcccaccaacdbbbadacaaccacaddabbabbbdbaacbcabadcddbbdddccdcaddcdbdadcbcadcdcadbdbaacccaaccaaaccbddbbbdadccabbcbbdddadcabdbcbcbcbbbdbaadacbbccabcdcadacabadbadcddcdccbbbdcaaadcddcadcbccbbabdcbbabccaadcbccdbbdcaabdcddaaababdbbcdcbdddadcdccddbadaaaabbabdbaaabdbaddddadcdcdaadcacbddabaacbdadaaadbaccbaaabccdacdcccacbdbbbddccbdccddacbbaaccbcdcbacccaddcbbabbaaddcbabcadabbbbcbabaacbcdaacaaacabadbabdbacabddccacacabdbcaabbcdbbaadaaacaacaacdccbcabdadbccaaccbdcbbdacbaccdacdbbadcadbadddbcdabbacbaacabdccbccadaabbddcadcbdabdaacaabbbdddbbbdbdaadabbaccacacbddbbcbcbcdbcbbaaadabdaabccdcbabbbdadbadcadcccdbddadcaaddadbdabaadabacaacbcdbbadcccaabdbaddacccdbacacdcdcbadcadcbcdaddbcbbbcaddacdcdbcaabdbaadbdbbbdcdcaccadbddbbabbcabaadcaaaaababaaaaddddcdbbadddbadaabbbadbddacaaacccbdccdabdcbdcdcccbbdbccdbbddcbdddabadccadbbcabdcbdacddadbcadabcbddbdbbdbbddbdbbdacaddaaaadbbdaaadcabdccbacbaaadbccdbbcdadddbdddaacbccbcacabcbabadddaacddabdccbcbacacbadaabbaadccacdaaacabcbadadaaaabacaddaaadabcdbabbbdcccaccbccdaacaacdcdadadacabcbadaabdbbaadcdccbbdaaaadcbbdddbddccbbadabccdabdddbcccdccbbbaaadcbdccdcbaddddcdbaacaaccbcbdacdbcadcddbdbbacdaddabcbdabcabaadcbcadabbdacbdcccdbaaabcddcaadbbcadabdbdbcaaddabcadbcaabbdcbaadacbdbbbaaaabbbcaacbadadacaacbbacbcdadbdadaccadaaaaddbabdcdbabcbddbadcabbcccadcddacbddcbaabbcdbbacaacbabacabccdcaadbaadcbababdcbacacbcbbcbdaddacbddcadcabaadabaaabadbdbbcdbaabbbadddddbacaaccaabadcaacbdaddccdccbdddcaaaaaacaaaadbbcbccbbaddaddbdaabbcbdacbdacdbcabddcabcbbbbdcbdbdccaacbdabaabbdbbddbbbbbbbadcbcbdcbacdacbcddadccaadabdccbabaddddddbddccbbaaccddaaadabcbcccbdcccbddbdaaadaaddcbadcdcdabbdbabcdabacddbbbddbacddccbbcdbacbacbadcacdabbacbadccbdacbdbbaabcbbdcaacaddcbbaacbccbadaadbaddbbcccadaaddbdabdabbdccacdccddacdcbcccccabbaabababbcbbbcbaadcdacbddbddcccbabdcbdbdcccaabbbaaacdbbdbcacdbdabbbddacaccacbcadddabcbddacaaaaadbbcaadacadbbdcaacddbabbbcacbdcbdcdbccabdccbadadcabcbcdcacabccbabbcdcbdadbddbbcbacaddcdadbdddcdaaccbaccabdbccaaacacdddadcdaadbdbbddaccaaadbdccddcccdbbddcadbbcbaccdadabaccaabaddbcddadbdbababbcacdcbdadbbdbccdacdadbbcdcdcaddabcabddabdbdbadccadbcddaddbddcdcdacaadbbcdaddcddccdabcadbdabdbabdccdbbaadabadbaaabbadddccbcbcbbabbaadccccdabdaadcadddcdbadddbbbdbaddaaaccbdacdbaabbbbccddbcbdcacbbcabcbbcbccaacdbbbadabaaaddabbdcbbdccaacacbbcdbcdccbbccbabdbbaaabbacdcbadbcddddabccbdbacbddaabbbdaabcbbadddadcbacadbdbaadcabaacccdacaaadbadcabddcaacadccbaddbbbcccdbadadbadaaddbbacaddcbcbcacadccbadbcddddddbbdcbbcbbddcdbcaabddadbadcddcacacdaddaccdacccbcdadacbddbcbdcaaababaccccaaddbbdadcbcacdcbabadaabbbbcacbbccdaddcbbcdaaaadbcbbddcccdddcbabaabbbaabadddabaddcaccaaadddaabbbbaadcdcadabbaddcddaacdbbacbccaabbdaadcdcacaaacdadcdaaaadcdcbbcbcdcccaabbcdbcbdabbacaadbcdcabdadddcabadcddabcbbdbcbbabdbcbbcadaccddbbaabacacadcddadadaddbbbddcdbacacabccdcbdcbbcbdaacbabbcddbddbbacacbddbbdbcdbcbbcaabaacbbddaaacbbdaacaadadddbbcbdbabdddaddddbdddaaccadbabbaddacdddddaddadcddabacbdbaaacdabcbccbdbbdcaacddabcaccbcbbbabaddacbbcabbbdaacbbaacdabcbbacbaddbbaadcabaabbbccdabbcdbbacacaababcbddacbdbdcccdcdabbcbcbaaadaacbddacabaacaacbcbaaadacdabcddbdccdcacdabcdcbcabbdcbbcdcdcbabccbdadadbacdcbaaaacbdadababcbdbacbdcdaaddabcdcdadbccabbdcbbacdbdaabcccddcaccbabbabcadbccccbbdbdbddaccacbddcdabbbadcabddccbbcabdddaababbcdbacacdacaadddadaddddbaacabdbdbdaddbcbbadcacacbcacccbcbcddcadbdbcadcdbccacddcddcacbcdcdcaaabacbaccbadcdcdadcbdcadabdaacccbbaadcdccddbdaddcbaacbabddbbaccbcababbaccaddbdcacccdbcbdbabdbccdbdccddcdbdcccbcbcddbadcdaddddbacdadbbdcdddbdbdddbbaadcadbdabbdacdcacaacbbaaddcddbdbdcbcdccaabdacbbabcdbacbbdcccaddabbbdccddcbcabdabadddadcccaadcbbccacbbadacbabdbabcdbbbadaadcdbccbdddbccccabbbbbaabcccccabccacaaccddbbbccdbbdddacaddbadddcbcdbddbbccccbdadbaccbbadadbbadbbcbadacaadbdddcacccdcadbbbbbdabadcbcadddbccbbbdacabaddacaabddddaaacbdddddacabcdbcdbdbaabaccadcabcdcdabbbbdbcbdcddddddaababaddaacdabdcbcbadacacbadcaccabdbdcbbdbadddccdacbabbdcbbbabcbaabdddadaddbbccdbdddcdabacdbcdcaddccadccaccdaddcbbbddcccabbbccdcddccabacdcdbcdabdccbcdaabbdcbcdddccbddbadaacaaaabbaaddabcaccdbccadbbaabccbdcccbdcdbcbccbcdccacbccdccdbdcadbcaaadbdacbacdcaabcbcccbccbdbbcbdbbdddacaddddcdbbbddcddcbbbbbadbaadaadadabbddaddccbddcabccadaddbcbabcdaacababdcaacdcbddcdbccacbbcbdcbcdbbaacacdbabcdbbcaabddcccbadcbbaabdcdadbddbbbcdacadbcaabcccbccdadadabbdaabdbbaadbabbddcbdbabdbdababcbaaaddbabccaadaabcabccddcdddaddacacdbccadcbdcaadcbacccddddbadcabadadccadabccdcacdbccabdacaadddacdcbdadbcdaacdbbaabacabbdabaabcabcdacdbadaabddbbcadcbcbddcdbaccdcdcdddbdaabddaaadbbaabdddabcdddaddccabccacdbadbbdcbcccadbcaaabababbbdadbdcdabacdbdddbaaabdbddbdbabcbcaaaccbcadcaaadaddcadbaaadabaabdbddbaddcaccddcbbddabdccdabdcabbbdcbdbcbbbbdcbccdcccddaccbdbbcddcbaccadccadacbcdcdcbacdbccddccbbbadbbcabcaccbdadacdcbdadcadbbbcaabdcadddddabdddaacdbadbcbabccdcbdddddcaccaddbbdabcaacddbbcdbadbdaaddddddcbcccdbcbaddccdcacbacbaadcdcdaadaddbadbccaabbdcbbccdddcccccbacacacdcdcdccdadbdddcbcccbadccbccddbadbcdccbadcaabcadbcbbddbaccdaaccdbbdbdadacbdadddbddcbbdaadcbbddbbdbbdaabbbdacdcbadcacdddbdbbddcccbbccbbdcbcacaabdbbbabdaccabaadacdabaabcabaadacadcdaddcabbcadccbaacbbbdcdbbbdbcbbcbaaccacabdbbdbabacbdddbaadbbabcadabbddcdccdacbcaaacacdbcaacdbdcadbbacaacdadbbacbcbdbabccdddcbbdbbaaabadbacbbacabbddbaadabccccaaacdbaacbbaddcdbacbdaccbaacbddcccbccacabbbcdcdccbcababdbcdbbccadadaadddcdcbdaacccaabcaddbddbacadbababbdbbcdaadcbbdacbbadaacaabacabdacaaadcadbbdabcaaacaaaddbacbcbdaadcabbbaadadcbababbbbdbaaabbaabdabadbbdbcdcccbdccaaaaadaacccbdbdbabcadbcbbbdabbcddcbcadbdccccaababccdbbbccbdccadcdabcbbbbddadabddbdbaadddabacbdbcacbbbcbbdbbddacccbabbabcdacbdabdcaccacbcabadaccbabdbadcbbdcbbbddbbaccbcddcddbcccbdcbdcbadbbabddcdbcbacbabbcdacdaddadbabccbbababcabbdacdccbcaadaabdccadcadbccadbddaacbbdcaabbbdddadabdaacddcdaacdaddadbaadbacadcccadcdbbadcbddbbcaddcbddcaddaacddabbdadcacacccdbbabdaaacbaacdabcdcccdadbcbbbccdcacbcabccbabdbcabcadcccdcdababadbcaaabcaadabadcbcccbbcbbbcabdbaaccbccbbdcbdabbadbbcbdcbddcbdaccacabbbcdadcdababbbcbabcccdadcabadbcbbcaadbbddabadbaabddacbbdcaccdbcbabbaacadacccadbacbdbdbaadbdacbacdbddbdbcdccbcdbabdbadbdbbdadddcabbcaaacadbdbbdcaabaabbbbbaaccdddaacbaccbcbcbbbbabdbccdacbbaadcdcadabbadcddcaaaddbbcaaadbccbbcbcadaadacddccadbbcbbbbadbdbcbacbacadcdcadadababcabaaaccabbbbbbcabcabcadacbaadabcadbcbbddadddccccdbdcadcddcbabccccbdabbaabcdcaabdcbddbbbbacaadbccccaacbabbaacbccadacacdcbdbcdbbccccbaadcdbddbadacaabaaababadabcccaddbbcacbdcddababacacddaddbdcbcccabdabdddcdbdbddbbbacababddbaaddabbddaabadaabbccddccdddcdcccbabbaabdbbbddcddcaadaabbaaadbcbcacdcacccddccdbdbcddcccbcbdcacccdbcacdcbaacbbbbdbabaccbbacbddcdbdbcdbcbdabcadcbcdddcacccdbbcadddbccbabdddbbddcbbcadcdcbccdbcccccbcdbddbdcddcbbacabacbccbcadaabccaadabbbdddbddabadcbccaddaaabdbdbddcdcdbdbbdbddaccdccaddbaccdabadbbbdbaabbabaabbddababbdabdcdcaabdccdbdccddcddabadcdcddcbcbcdddccccdacbaabdacdcbcbdbcbaccadaaabcbddcacbdbdbbbbaaccccccdbcbdbccdddbcadaabadbdbbacdbdabbbddaccccaacadddcdaabdadbbbadabacbbaddabbaddabdcbaabbabaacbadcdbcaacdbaaddaccaabddcabccdacadadadbabccacbcdbdbacdabdccbaddcacaadaaadabdbbdaccadadadabcaaccdbacdcbadabcaabababcbbccacbcabddcadbbdbbbcbdbbcbdaaacaaabcabaacaddadadbaaaaccbbabdaababbdbadacacbcbcaacaadaabdcababddabdcbcaaadccadccbbbdcaadacabdcddadadcbbaaccacacbdbdacbdbcaacbcabcccbadbdddaadcdbccaccacdddcbacaadcdabcdbdbdacaadbcbadcbbbbbccaabdabbdddcdaaabadddddbcbbdbaddccacdccbaabbcdadbbbccbaddacacccccaadbdcacddbbcdbbbcdcabbbddcabdcabaddcaadcdadcdacacbddbcbaccbacdbaaccdcbbdcccababbbdbbcdbabaccbabdbbadddddcbdacdccdadcbcbdabaddbdbbccabacbddaadababcdbcbacbbbbcabdcaddbbbbaaaacccacbbcaaacccacbcaacdccaaddaaacabbbccdbcdddbccaacccdbcdcbccbbacdaaccabcdddcdaabddbcacbcddbdbbdccdaccacdaaababaaaddaddbccaccadbbacbcdaadabbccdcbccbcdcdacbacccaadaacbadaabbabcabdaaddbadaddbccdbbbdaadcbcaaadaaccddbbbcacaddccbaadcabcacdbccdababcaacbabddbcbaccdaccaaaccbbcbdbcbaacdbcadadabadcacaddbdabdbddcdaddbbcaaaabadcabcdacdabdbccdaadaacbbdcabdadbaaddbbcdaaabbbdccbccabaaddcaddbadbddddbadadbddacababdcdcdaccabccbbbccdbdaaaacaccdbbbcbcdbaabbccacbcdaadcddadcccccbabddacaccdabaabacdcdaadccbaaaaaddacbcabccbaadaababdaddbdddcdabaadddabdbabdbdbcadcabcaabdcadcddcdddcdabdcdbadabbcdaaabdbbbdccbcbdcbbbbbbbcbcbbbdadccbdadddbcdbcdabaacbdacbaccdbdaaccbdaadcdcdcbcbbbddbaabbbcbddaadcbcbdbbadccacadbabaacccbbadcbccccccdbdbaaacdadcadabdaacddabdaabccacdcaaaabbabcbccacdaaddccccdbcdaccdcdacdccbbdbddadccbcbddcdcbcbccbdcadcacdbbcaabcbbbaddacdabdaabddbdaabbcbbbcbdddcbbddddbccdcdbbccbcdcbaddcacbcdcabdddaadbcdbaaddaacccaabbcdabaaacaabdabdcbaaacbcabdbddbcacabadadbaccadccdaadcccddcdadadcaaddcbccaacddcddddcbddaacdddcdbdabbcbbdbccaccaabdaaacbadccaadcadcddddcdcbbabbbdddcdaddadaccbbccacbacdbadddacabbabcdccdacdacbdabbabcadadbbbcacddbccabacdcdcaabdbadbbbcdbacadcbacdcbdddcdaabaccabccdadbdddbdabbadaaddbbacacacbbccdbbddaabaaaacdbdbbdbbbcabccacdddbcdaaccacdccbcddcdddbbdddbbaaaccaaccbddbbbdaddcbdbbbaccdaccdddcdcbabacccdcaabcadcbbdcaddcabcdadadabbcbacadbacdadcbababaaccaddbadbdcaacdabcbddadcdabddbabacdccddcadcccbdabbaabddbabbacddbdbdbacadaaaabacddacdabcadbddbaccabdacaadaaaadcbbaddaacdcbacadabdcaccbabadbdabaaccabdcbdbbbacacaabbdbcdacabbdcdbbbbbccabbcdbcbdaadbdcbddbdadacddccadbacabcacbadbddabdccbadcadbbcabcdbbdcbcddaababddcaccaabcbdadbdadbadaccbddaddcbadaaacdcdcabcabdcdadacdbbbcaacdbddabcbaddbcbadbcbcdcabdbbbcdcbadbaaadcddcacdbbbcaacbadcbadbadcaccbddcbddddbaccbbccdadacbabdcdbddadbdbdbbcdaddbbdbaadddcccaacbcbddabbcbbbdcadaadcacaadaddcbcdcacaacdacddcbdcdbadcdbbbcdcaacbcbdabccacabbdaabdaaddaccbbbbacbcaaaadbaabadaddccadbbaaadaadbbbabcbabaacddbbdcbdcadcccbcccbcdbaacadccacadabcddbdcdcdcdbcacccaacaaacbbbdcdbabdbbaccdbbaacdacccbbdbdbaadabdababcabbabaabdbbcaccdadbbccbddddbcdcbddadddadccccbadaacabadacbbcddbcbccddbabddacbbbcdabbaaacadcbadddacdbaabcdbbcdbbbcccbabdbdacaadcddddcddddcbcdbcdcdcccbdccdbabcdadccdbbadddbccdcdbcbadccaddabdbdabbcaaabdbacbccddaabbcacbcabcabdbbbdbdbbbbccccadddcdaaddbacbaacddaacdbcddcbaaabbccdadddbcabcabbbacccbdabdcbcaacbdcdcbcadcadcbbddadccbdbccacddcddacbabaddabaababadbcdbcccadaabcdbaadbcbaaccbcabcbaabdddbbbdbdaaaadbbbbdacababcdbcdbbdababcacdabcbabbddcccaaaaabbaabcaabdcbaddcdcbbadbdabbaadacbbddabbbcbdddbbacdaadbaddbcadbbdadccadbdacaadbcbcbdacbcababddbddaaadbdccccdabbcaddddcacaadcdbabbacccdbcaabcaadddbdcbdcadcccacbbacbdaddcbcadddadcaadcadbcdbaccacdcaadabdddbadbacddaaaabbdaabaacccbcadadacabdddbbdaadbadcdcbddbcabbddddbabacbccaadbaadabbbadccacbaaddbccbacbdaaccdadaabdadabadaaccabbddabababcbccaccadbdccacacddcdaddadddcdbcddcdadcdadacdcccbadbbbcbaccddcddaaabbbddabbacbdacbadbaccadbcbbbacddbcacbbadbcbdadbacaabdcbcddbcbcdddbacacadacabdcadddadccdcdaacbcccadabacdcacdbdcdbabdbbcbdacaabbadacaaabcbcbddcdcdbbaabadbdaccccdaaadcdcbcbaacccccddaadabcbcdacdddadbcccaaadacdbdbcddaddacaacdbccdbcdbadbdabbccabbabccdbddbabcadcadddddaabdbddacabcabdbcdaacddcdbdcbdbdcdacdaccdbcbdcacddccdbadcddbbadcbbdcccadbacbcacdccddaaabdcbccbdcbadacbdacabdddabaabcbbcddabdaadbbcccccbdacccdccbcacbaddccdbbdabcabdacbcbbcbadbaadcdcbddabccadcdbbdabdddbdcbaadcadccaacaddadadbccbddcbcbadabddcbbcdaccaacabbcbbacbcacbbacbdddcaaabbccaaddbbbccbddbdaacbacbcbbabcbaaaddcccababddcccdddcabdababbcbbbcaaabdacacbcbadbbcdcaddabcccddcdcbccbacacddbcbacbdbacccacdbddaaddddababbaacacbdabdcdadcaacddbcbaaabbdbadacbdbcdadcdbdccddabaabcabbbccacbbaddbbcabbccbbadcadcadbdddabcabcdbdbdbccabddddbaccbdadaabcdbddcaacadacbaadccdbabdcbbadcdddccdabcbccbbdbdaabbdbabdbcaacbbbdaccbbadbbbdcdddbcabacacacbddadacabdbccccabacadbbdcbbbddcbbbcaaaadbcbbdadcccadcbdaadccaaadacdcdadccbbdadccabdbcdabdddbaaacddcbdcdaccbaaaaaacdaabbababbdbcdaccadabbacabaaadddddbbbbbabdcacaaddcacbdabcbbdbdbdacdcdbbddcacdbbbccdacbccdaaadbcccbccdbccbdabcccaaacabbbbbdaaccdccaddbaacbadcadcccccbbbabcadbacaadadbdcddbbcdbcdbbddbdcadadbbccbbcbdcbdbadabbaacaaadcddcdaacbaaabbbccbcbbdcacbbdabbaaabdccacbcdbabdbaadabaadcababdccabbddbadcdcadcccdbdbacbabbbadbbbaacddaccbcccbcbcbdcabdaaadcdcaaddcaacbdcdaadcdddcbaaabcbacacabaadbbbccbbbdabbdcdacdbbadcdcbabcbdbdbccbcbcdbaddccbdadbbcbdcdddaaddcdabdbccbabcddcaadadaacadcccaacdbdadbdcbccaccccbaaadadddcbccbddaabaccbdccdbccbddccccdadddccabdddbbcabdbdbcbcbbaddbcadccaacddbcccabaabbccabdcdddccbddadcbaadcccbcdbcacaadaabcabccccbdaacbcccbbbccbcdaabbcdddcbdcbbacadddcacaababadbcbcbdbddcaadcbadbaaabacaadabdacadcbaaccdbcdbddbdadbdcddbacddddcbddcbcdddbbbccaabddadabbdcdcaaaddbddabcbbaaabccbddcaddcacacabdccaccaabcacdbbbccabbcbdcccbdbcabbddddacbbbcccaaaaccdadcdcdbaabbbaabddccadbadcacbbbadcaaacbadaacaaabcbcdbdbbcbadccbbdddcbabcdacaacbbdbbddbcbcdaddbdcccccacdddcccabcdabbaaaddaadacbdacadaabdcadcbdcdbdccdcbacdaddaababcabcdbcaddcbabbbaabcbababdbcccabdadbdbdcbcdbbcdababbccbadacbcbdcaaabbaabcbbcbcbabcbdabccddcbddcbbacdadcababccdaabbccdcbbdaabdabdacccabcddbddbabbbcbbbcdcbdcbbbcaccacbdacdaadabdbdbaababaaadcbcdbcccaddabbcbdabadcacbacbadbbcadaacccddbbbaccdaccabadbdcdaccdbadcaddbbdadcbaadabdbaadadacabacdaadbcdcdbdddacaacbdbdaadaccbacccbacbadbcccbdabdbabaaaabdcbcdacaccccbbcccaddbaacbddbdbcbacdcbcaddcacaaddabcdccccbddbadccdaddcbbdbdabacdccdcbacacddacacddaccbcadabbdaadaaaacbccbadcbcaccbdddbdcdbbcdbcbdbaabdcccbaccbdcabcabcaadaabaadcdadcdccccbbcdaaaadddccacbdaadbbdbdacaccbcccbccabdbdbddaccacddbdacddbabccdddbaacdaddbdbcbcabcdccccbddcbdaadddccccabccbcacadddaabbbcdadcdcbaccadabddddccccbdcdacaaccbabdbabcdadbbbadcbccccbdcacdbcdbaacdaaacdbbdcdacadbadabdbbcddbbddccaadcbcacdbabbcbabcbbacacadcdbbddccdbbdbbaadddcacadcdccccdaaddbaaaccbcabadccadddaadadcaadcddacacaaacadddcdabbdadccdadbdcbabadcccdabbaddcaaacdbbcdbaacdacacddaccaaccaccdaccaadacbbddbcbcdbcbbaacdabbbaaabcbbddccaacabbbdadadcdbbcbdabbccaabcabcdadbccabdcaccdcadcacbbabdcaaabcaccbcdabacabcccdddbcbcadadcabaabacabdbdacadccbbdbcdddcaaacdbdccbdbadaaabdccdaccbccbadcaaabcabbadcbaabbccdbaccdabbcbdbdbaabbddadddcdbabccadbbcbcbcdcaaadbbccdabcddcbadbbcdbdbabacadbddbcbdbcbabbabccbbdabaaccddbddbabcabcacbbbacadbbbbcbcccaaabaabcbccddccdccbbcbaccabadbadcacdccbdabcdbabbdccdaccaadccdabdbcbaadacbbadacbbdcaddaabbbdcdcabaddaacdbdcabdbaaaccacbbdbdcdcbbcadccaccacabcddabadbbdccdbdbaacdbaacdbcccdabaacacaacdcabccddadcabcbdbcdbdcbabbbbdbabdcaddbcdcdccbbdadbcbbcabcadacaaddbaabbcadadbcddddbbbccdbcdabcaaccbbabddbabcdabbabcbccabaadddbadbcdccadbaaacadabcdbdbdbaaadcacdacdcabdaabacbaddccbdadadababdcddabcdaacabacbbbaaccbcdadaabccddbccaadbaddbcbdcdacccdddcdcddcbccaddcbdbdbabacbcccbadaddbbddbdaacdbbddacccaabdadbccacdbcddddacccbdbabbbccccdadaaadbdcddccbccaaaacbcabddadbcdddcaccbdcadbabcaddbcbcdbcdacdabdbcacabbdbccabbddbabcaadcabbdbbadbdcacaadbcdcacbcbdcaadcdabdbbddcbcaadcccaddadcacdbbdaaccbdacccbdbbadcacbbabaabdadabaaccdadbabbabccbcbadabddbadaccaccbabbaddcdbaccadabbabbcbbdbdcbbaccbddcabcacdbccddabddcbddcdbbdabaaadccdbaadbabdcdabbdcaddcbbbbdcacdacdcbbaadaccabaadccacadcbcdbacbacadabcbdccbdbabcbddbdaacddbaabdacbdddbacccaadcdbdabbadbdadadbbcddbbddcacacabbbdbbdaddaababdcbabddcddbdddcbbdadcbcaaddaabbcaccddddbaaadddccadbbabaccbadbabbbbcbddbdadbcadcbccbcacbcdaddacdacbaabdbccdcdcbbcabccabcabbdcbadcddddabbdaaddcddadccdaaccdcdacbdadadcbabaaddbacccdccbaaabcbcbbbadaaddcadabdbdbdaddcdaddbcaaadbdbddadbcacdcaaccdbddadbcdcdadaaaabdaaabbdaadccaaabadababbccdcbababcccdbccaacadadbaabcbabdddcacaddcdbcccabbcabbadcddcdcbadddbaabcdadbdaabacbababccbbbcacdabbadcbacadcbdbcbbadabcaabbcddddcaabdccadabdacadccdcacdabaaabcbabbbbbddbccbbbbdabdbdbcadccbdcadbddaadcddbcadbdbdcbccabacccadbbaadcdcaababaadabdcaaabbbddaaabcddbcdaddccdbadbbbdccabbadabbccbabdbdcbdaaababcdbcabbbdcbcababbdbabbaddbbccddcbddddddbadbbaaaabbacaabdddbdbbcdabbbccbccdabddabacaddbddbdabccabcddaabbdacddacccdbadcdcaaabccbacaaacbbbcccccbcddbdaadcadbdaabcbdbbabbbdbdccdbbdddcacbaccbddbbadbdcccabcaabbcdcdbdbddbaddcabdadabacadcbddbaaaddabacdbccddccabbbbbbaccbbcdaaaccadadacbadbcdbacdddabbcadabddcbcddcddaabbcabadddbaccadadaabbdbccdbdabdcbabcadaccbdbacbadccbadccddccbcabbcdaadabcadddaadcacaddadcbbbbaddccdaccaccdcabbbcdbcdbcacbaadaabcdbbdcacacbccaddcaabbcbdddcadddbddaadbcaacbdacbbdabcadcccaaadbdbbbdaccaaddccdabbcddccabbbbcdcaaacbddcaddbadcddbcddbabbdbaadcdacdcddcdacbadadddbaddcdbddacdcdcabbddddaddbcacbccbdcbacaabbccacbdddcbccbaccababbadaacabdaacadbbbdaacabaddadcbdaccbbcbbbaddcaaccbbacbbdddddadcbcacdcdaacdabbbcbabacdaabcdbcdcbdccccacddaadcddbddbabdcddabbbccddbcdacccbdcaadbcadbadbcabaccaacabbbccadabbbdcdbcccbddbcdabaabdbbbdcdaaabcacdbcbabbbabdddccdabadbcdabacabbccdacbbadcbacbadadbcdbbadcbbbbcacabababdbcbacdcbbbbbcccaadabababbdbabadaaaaaddabccadbcaabadbdbdbcccacbaacbdbadbcdcbadddcadadcabdaddaccacdccdabcbdadacbbdcddacadaabcddbcacbdcbabaaabdcdacbdadabbcdbdcbacdabbcdbabdabbcbbddccddbdabdcdabbaccbaabbdaddbbbdadddccacbbdabadadacdadaaaaacbbbccbaaabcdbabadabbbdaabcaaaccaccdcbddcdddadaccacdddcbcbcaaacadabbaacbaadcbccccaabacacbcddabccbccbddaaacdcddcbbaaddbabacaabacbccaadcdbccdcdbcbdaaacbcadacdbcacccadcdaaaadbcbccadabcbaaaaadbddbbbdacabdbdadadbddcccdbcbacbcbdacbcacacaadbcacbcdcccaadbabacdddccdcdddcadccabcdbccddcaacbbabbbbcabcaaaaacbdbbbdcbcddaadcacdcdccaabbbdbdcaacaddacbdaabdcdacbabcbdbbcddbbadbcccabddbdbbbcddadaacbdcbddbbbccdbcbbbdbaccbdababcbbdaaacabcdababcdbaadbcccccbdddcbaaadbbbacbbbcdbcbcababcbbcaddaddcddbcdadcdadccdddaaabddacdaddaadcbdddcbbabaaadcdacdbaccabbddaabcaccbcacbbccbadabdbcccaabbbbdbababcacadcdccbbcdddaaddcbcdbdaddbbdabbdbdbbadbadcbddacbaacacdacaaccbbdcbabcadcbddcabacddddcdababdacdadccaccbdccdddadcdcbacbbadaddbbdbbcbbccacdcbbcabbabdcddddbbdbbdaaccbbddaaccbdddcbdcbabaabddddbbddaabccddccabccdacadccbdcdcddaaddacacbdabcbbaddabdbbbdcdbcdddbacbcdaddbacccdaccdaccbcacdaaaccbcbcdcdbbccdadabdbcdaaddccaccdbbdaabaacbcadabcbddabbcaacaadcbcbdacccdccddacbadcbccdbcdabbaddcccabacbbdabdabccdcbbabdbbbccacbacbdbacbdcadabdbabaabbbbbbaadbdbbacdabbadcdbdadbdabddbacccddccbacacddbbcbdcbcdbacddabcacbdaddcccaabdcccadddbacabbcdbaabcbdcadacdcddcaaabdaacbdabddbdbbdddabaaccddcdcbbbacccbabbcabacddccadbbddaddaaddabcbdbbbccbdcddcbaabababcacddbbacaaaadaabdddcacabaddaaaadadadabbacdbbacabaacaabbdddbaabadcbdcaabdaadacdcacabaaaacdbddbcbbbcaacdbabbdcaaddccbcacabcdacdacdbcbdcbbaaaaadccbbaddaadcbdacccacadccadbcaadbcbdaacdbddddadbccdacbccdcaabddcbbbbaaadaadaaaaaadabcbaaddaaacacacaddddaadaaadcdadabbbcbccababbaabaadcccddbbabbcbdcadcbdbbdaddbcabbdacccbdabccdadbabcdaabbbbccdadaaacbddbacadbdbddbaacbbccdbcbdaccbaaaabacdddbcdcdcacbdcbaadbdcccdcdcccabbdbacdccbcadaadbbaccacbbaccbabbcbaaabddbbdbbcdccabbdcdbadcbacacbcaadbadcbaccdddababaaaddbccdacaccbaadbccaaccaacdacbcdbcdbcbccdcaabadaabdaccbdcaacbbbbbcddadaaacbdbcbdabdddccddccbadaadddccdcdbbbbcacdccbdaacdaddbabcadbcdacdbacbcdaaabcaddbbbddbacddaabbacbdddacbdddbddcccdacbdbdcacccdddcbdacbabdacdabbddcadabbcbbbbcaadbdcbbcbdacdadccdcabcbacbddbbababbccbcbacacadcbdccaaccabbcdabcdacdbdbacdcbabdbcdccbbcccababcacbccabaacadaddbcccbddccdaabdbdababddaaccddddaabbdacbcbaabaaccbbadbdcdbcbcaabbaabbaaccacdbdaacbddddddddcccbbcdbdbcbbbbcddabdbdcaacccdccacadbdcdbcdbadadbbdcacbdacbaabcadaabccbbdacabddabdbbababddaabacbbbdbaaabdbdcdcccabcbacbcacaccdcadbbdababdddbcadbcabacbdbcdbddbdabbaabbabddcbddacbbaacddabdcdacaabcabcdcabdccdaadccbacddddbbcdaccdabdcabbbaacdcdcaaddaaadbabbbabddbcabacbbdbaadddbdcbcabbbcbdcaccdaacbcdbaccddbaddddbabbdabddabaaacddddccdcdabddcaaaacadbbaccbabcdbcaaadaaaacbbddcddcccbcadbdcbdccccddcdbdbbcabaadbbbcdcdabdabccbcbdbdbadbdcccdaccbadcbcabacbaabaabbdaaaacdbbbddaacbbdaacbccdadacacdcaddcdbcaccabcdbcdbadadddbbbaccdcddcabaccaadaaaadbcaadacbcccacbbbccdacaaaddacaabccaaddaacdbadccbdadadddccabbbccaaaaabdaabaadacadcbacabbdbdccddcadddbddbcbdbbacadadaccbddddcbdabaabbbbddabbbadadbcbdabddbaacacbbaaddddadacdbcbcadbdacabcbbbdbaaccdadbacacccdbdaadcddadbbdbadcbaabdadbcbdcbadcabaadcdacbbaabddbabccbabdccbccdaccdcbbacaccbbddcccbbacbbabcabcbdcacccaadcdabaddaaaabdbaabddbdbcaadacacabccdabbcbcbbddddaadabcdddadbdababcbccddcccdbbacacddbbadacdbababdbdaabbddaacccdddcdcdbdcdcccbbabbbcdbacdbbaaddacbcaabcaaadbaaddaacdddcccbddaddcabbacdabaaadaaabcddbadccaabcccbbdacabadddbaacabdccacadcaacaabcacaadaacadabaabbaabbcbacccdcdbbbaccabcbcdcdddbcacccaddbcaacccbbddaabcdcadadcadbbcbaaadcdccabcbaacbcddaabcdbacadadddddbbadccbcbdbcacdaacbdadaacdddbcbbbbddcaadabcbccbcdacacdcacdaaaddcdddccabcabcadcabbadaabccadcdbbdbbdadcddbdbadbcbacdbdaacdaccacdddddaaccccacdabbadaadbadacdddbbadbcababcbcbbbccbcabcbacbdbaddcaabbdcddbadcddadbaacbaaddbbbdabbbaaabcbbadddcabaababbdbccbadddbaacdbbababcdddcdbbdbcddbbcbcacabbacacabbabdaabdcdbdbcdbcbddccbbcddcbaddadbddaaaccabcadbadaacbdcacaabbdacbddadadddddacbcbaaccdcaddccdbbbbdadadaccdbdaaaabbbbbbadbaabdaababacbcdbccdaddbbaabbcadadcaddbacbdbcaaaabcbcbabdbcaadccbccacbbddaddcdcaaabaaaacabacbacdbbaccdcbcadbdbbcdaddacbcdbcddadddbbcbcadbbbddaabdaccdabdaabcddcaabccadbbcddcddddcdcacdabcaaacdbcaddaadabbaddaddbacadadcadbbbbdddbdbadaabdacdabbdddacdbaadccdbccdcbccaadcddcaadadddbadacbcbaacadaacbdaddbbddcadacbbbcabccababaaabcbcccdbbdccdbbdcbcaaaacdacabcababaacdbabccacddccdcadbadccaccdaabdbccddcdbacbdbbbcabadbadbbccbaabbcabddababcaddacabadcacddcaadddcabaabcadabcadccbccacddcddcadbbadacaccbcbbdbdbdcacddbbcbdcbcabdbcaaaccaaabbcbbbabdabbccacbdabbaddbdbcaaabddacabdcccbbadbcabaaaacaddbaaacdbacdcdcbaaadabaadddbbbbcaddbacbddbcbbbaaaadbddcdbbadbccadcaddcadcabacacdaabbbddacadaccdcababbbddadcbdcbabbbbbcdcbbdccadbbdccdabbaacbcccaccdcacdddabddcbacbbaddabdccccacbbbdadbacdcbbdcbbdcbdaccdaabbdacdbadaccccddcaaccdcaacdcdacbaacadccbbcccacdcccdcbdbabdcdbdabcacbdbdacccdaacbbdabccabdcbccdcaccdccbcaabccbcbccbdbdaaadcadddcbbbcbdabdcddbcabbccddcacddcddbddcdaddddaabadadbcadabcdcbcdabbadccadbcccccbbaadcdddbdcdadabccddcbbbcddacbbdcdcdaddcbabcddcbcabcbdadcbbdadbbbaacabcdcacabcddbdcbcaadbbbcbabbdbbdcccaabdcadbaacddacaabaccbdddbdbabdccabcbbadcdbbbaabdddaaadbdbbccabbdbcadadbacabccacabddadcddaabbbabaddadacdbbcaabdbcbdcacaabbbdccdacbbbbbddccbbdabacddabbdcbcbdccddbcacaccbddcadbabadcddbbdbbbbcadabbddadbbcbaaddbbadcbabcdadbcdbbcdadbaabbccccadcbbcdabcdabbbadbbdccdadbdabadacddacbcadbcbccbddabbadabbabccaddbbbccccbbddadcccbbbbadbcabbacbbbaaddccbaadddddbbbadccaacdcbaaaacdcadbdbbdbdacaddbcbbccdaccacbdcacadbcdcddbcbdaccaaccddacbdaaacaaadaaacabdcdcbcbbdbbccdabccdccacabcbcbbbacadcacddadaadcabdddadddbacdcbaadadcabbacaddcdabdacbadbaabbbdbbadacdcaaccabcbdcacdbacdddbcdddbddcbcdaabbcbbdcaccbdbcdbabadbabbaacbddacdbbddcabcdcdabdccccddccbcbadcbbabacccdcbaabbdcdbdcbcdabbbcddbcbdcdadbcbbcbbdadaabccaddcddbbbddaaaaccdcdacbadcdadcbcabcccababcabdbcbbcaccddaacbdcadaccdabbdadccacaabaadddbadbbdbddaccabbcccbdbdcbbaddddbddaccdadadcaaaaabacaadbcdccaddbcdcdcdbbbaaabbaadcbdbacbcbbadaadcdcabdaabbdbbdbabcdbbcbbdaabcdadcccaaacabdaabdcdcbbbbabcddcacbbddcdaccabadbacdbbddbbbdaccbdbbaacadabcacdabcbabbcdbbddbbacaabccbacbaabcbcbabaabbaadbdaabddaddddcaaaddbaabdcabcbcaaacaadadccbdbdcdddccbdbabcbdbbbccddcadcbabbdadddcbabcdddcabddbbddbcaacabaacbdccaaddbdcdadbbbadababbacdddbdbcccbcdcddaaabcdbabbdacbabacbdccdbaadcbaaadbaccccdacbbbbbaccabdbaabcacdcbadadaccbbdaddacadcdcccacadbdbabadacbdbdcdbdaabdaddbbcdaabbabcbabcbdadbdbdccacccbbcaaadcdcdabaccabccbdcdcbdaadbbccbadacaaaaddbadaccbbcdadacacdaabcdbcadcccabcccababcbdcbaadaccdaaddcdbdabbaccdcbadcbaccdddaadacadadbdcdacbdddaddcdabdcaddbcdbdbbccaacdbdaababdacddcddbdbadddcacbdabacbdaabdccbadadbccdabcdddadadbadaaaadcdbbddbbbccacbddacbcaabdabaabbbadacaaadcccadaadbcbdccbbacacadabddbcbdccdccbdddcccbcddbacbdcaaadcdddcadcdacadbcccdbddcbacbdcbabacaacdbdcbdbacbadcbbcacbdbadccaaaacbadabdbdcaadbdddbdaaaabccbbbdaddabccdbcabdaddccacacdcbddcdbbaddccacabcbdaaaabdbcadcdbdbcbbaadbcaabccbdccbabbdacbccbbadcdaabbcccbcadadbbbcdcacabadbcddcadbacdddabbdabacacbaaadbcbbdcbddcbcdadadbbbdbbaddcccbcacccbdabcddcccbdcbddbacbdbaabddabbbccbbcaadabcacaabcbabddbdadcbcdcabaacdcccddabaacacabaddbccbadddbcdbcbbddbddbacdcacdccddaaabaddadabaddcadddcbadbcbaacadddcdbbbdacbadaadbacdbdddbcabcccadacdddddcccdcdbdcdbaaccccbabbabccaddababaadbdcdbdbdcabadbdbcacacdbabdcaacbaabddabccaadbdbcbcdcbdcbdcddcbdbcdbdacbbbaabbcbcdbddacbdbcdcdabacdabadccccbadddcddabdacdcabcaccddbabbbadaadcbbcdabcbdcddbcacbdbbddbaacbcbdcbacbcdacdbabdadadabdbdccabbbcdcadaacbcaacabdadcbdadacccccaccdbaaacdadabbaaacacddabbbdbbbdddddbbddacbddaadcbbdbdddbdbdcbccbdcdbbdcabccbadcccdbaadadccdcabdaaadabbbcaccbacacbcdadbacbccbdacdbaccadacdbccabdcbaabdbaaccdcccdcabacaaabddaabcddaaabcdbbbcdddbccdacabacbcdabbabacdbabcbdabdccacaaadacbbaababacccaaaadadabbbdbadcdddbacbdbcccbbbbdcaacbccabcdababbacdbaaccdbdcdccbcbacddbccbbadacbcbbbccdbdbadbbadbbdbdbdbaacacadabadcdacbdddaabbabcbcdaaccbabcbcccbcabaaccdddcbcbdddacaaabbdbbcaabadcdcadadbdcbcdddacbabaddaddcbaabdccccdbbccaccbdabdcbcbdbbbdddacdddcdcbdacbbcbcddbacdacccaddbbaddcdccbbbbbddcdcaacbacbdbdadabadbbdbbadaadbbbacaccbdadcbdcddcbadbdbbcccadbdcbddccbacabbacdaaddacaabbcdbbadacbccdddbdbaabccaadcaacdbbbadabcaddbbbaaadddaacccaddccbbcbbdbbddaaaaccadcddcadbddddbacaadcaabbcbbccdcadbdbdaddcabaacdabbbdbddabdbcadabbbbdacdbabacddcdaaddacccbabaabccabaccccadcbccdbbcaacabaccbdcadbcacbbbabbdbddacbddaccdbbcdcdbdccccbbacdbcabcadabbcdaaaaaacacaaacddadbdcddabbabddbddcdcbdbcbababddaccddacbbccccaccacccddcbabacaaacacdaaabbdbbbcbbabaacadcacddbaadbcbcaaadcbddbacdbaabbacabcddbbccaacabcacdcddabccbdcdaaddddcbacaccddcdccbbddbabcbcbcbbadbbbccbbdbbdcaaddcdbadcdccbddbbcdacddbdbddddccaccdcabbdbdddaacdabadcbcddccabcddcbddaccdcbcadbccabdbdbdaddabbbaabcdccbbaaadadacdcaccaaacddbbdccddbdcdcabbcbdbccdddaabcdcbbdbbdadbdbabadcbbbabcbaaaaaadbcabcccacddabcabbdbddcaacbbabdcbbdadaddaabacabadccdcacbdbcdadddbcacddbdabccdcadabbbdbabbaacccbdbacccccddbbdddabdcaabbaabbcdadcabdadbabcdccabdcadbdaaadbbaaddadbbbdccbdbdbdbaddadbabddcdadbcdcccabbddcdbabbccbabdabcdbaadcaddbbcacdcaacdcaacddbaaadcccaddcccadccdbcddbabaddabbbaddbbcdddbcbdcbcaccdacbdabaddacddbdcdaabbaddacddacdbccaddcdcdbdaabaabbdaabdddbcbddacbbcdbbcccbcabdccbcbcabdaccaacadbcdcbdbcddcdadcbdddcbdaacabadaddaacbbaabbbabcbacbbbcadaccccbddcaaacbcbddccabaabdacbcddaaacbdddbadbbdccbaaddacaaaccbdbabdcbbadcaaccabdaacaccacddddadbdccacbabbdbcaacccbbaadbabaccbbcdbdddbcdbccabdbbcabdbacdcccbabcbccadccabbaaccadccdbcddbbbaadbaaabdbddcccdcabbdbaacdabccbadaddbcadcbcdadcadaabddbcbdbcabbdbbccaccdddabbccdabbbdbdbdcdabdcddcbccabbcddbccacdacadacddbacbdbbbddbcbaadaadbbcbaacacdbcaddbbddbdcabacdbbaacdcacacbbcbadacbcbaaddbaccbcdbdddccbabcacaaacaabdcacbcbddcddbcadadccccbbcadcdacdcbbbcddcbcdbabadbacacaddcccbcbabbcbcaacbcbdbbbccdbbbcaaaaddbbacdaadababdcbdcbdbaabcdcabdccdcbbbdaaccbccdacdbbaabcdacdbbcbdacabbbbabaabacccdadaccaddddcadbbcdddccbaccdaaaacbccbadcbdacbcdabcaacddcaadabccacdbcbbaadccdcddbdbaccbdcbdccbccbbcbcbdaabccbcbbcbcbddbcbacbadcabbdddbbcdcbabacabbcdabcbbabdcacbddbdadbbcbcdcbccbbacbaddabacbccbabaabacbacdcacdcdbbabddcabaadaaaccaabcbdccdbbbcdccaccaadadbacbbcacabcdbbbcbdcccadaaabddddccbabddbbcdabcbaadaaddabadcdbdbbadbdcaaaaaddcabababcdbadccdadbaaacbdadbcdcdddcaacbbacabababadadbdcdddcbcaacdaabdcaacaaacacdcbdbacaddccaaaadcdbcccccaabacbddbaddabbbcdabaccdbcdacacbabbaababacadcdcadabaadacdaaacdadccdccdadbaaddccaaabdadabdcaccbcaddbbdabcbaacdbcbcbadddacdabcbbabddcdacaaccadbadbccbbdbabdddacbbbdcaabdaccdacddcdcabbaadbcaddbbdbddadacdcabcdcddcddbdadcbdaddddcbddcabcdaaacadadcdcbacbcbcbdbaaacacdcbcbbbacabddccdbabccdbddbddacabdaadbcdddbadbabddaacacdddbccccbddacdabcdabbcdbcccacaadcabddccdadddcdadbbbbbacdacccaacbbcdacabcababbcabcdddaadcabdadbbbaaacbdcaacabbdacbaacdbbdbdcccbadbdbddabbdbdbdaabcdcabaddbabcdcbbaadadbcddbbabbdabdcddcbdcaacaccaccbccbadddacdcdcaacbcbaacacbdbdbdcdbbccccdbcbacdcbdacdccbdbcdcbccdcabccaaddccbaccddbbdbdbaccbdbdaaabccbbdaccdbbcbdccdadacadbcaccaabbadcdccacacacddcbddacdbddcbaddbbdbdcaacdbccbdbbcddbadcaccbbbbcaaddabaaaabcabaacbbcdccbadbacabbabcacddddadddabdbdaccccdcdaacdbdaaabddddcbadbaddabaaaadabbcdbaccbccbaadbdbdcaacababdcdabbdcccbbdcdabbacdadbbddbdcbaccacbadccdbcdccddcdbddaadbaacdcbbddacbaaddaabdaabccdaddaababcccbcddcccbcaaddbcaaaababbdcacdaadcbcccbbcadcdaabcaadbadddaaacbcbdbbbcadbacbcbbdabdbbdbabdadaabdaadacadacbcdddddaadcbbdaacdbadddaaaacdacbbccddcbbcbcddbddabcaddadabacddddcbbaacababdbdadabdccccdbdaaddccdbccbbbcbdbdaaaaaabadcddbbccadccbabaddcabdbccccdaddbadacdbaaccdaacaccbacacdcccdddccacccbcbdbdbdcdddcdaddbccddbaaabcaacbdcddacdcdbcdbaaacbbabbcdaacddaddbddcdacddcdbcdbcaabacbcbacbbddabbddacbbadabcdcbcddbdabbcddcdabbcccdadddacbcacabcdadbdbcaabababcdcdadcbddabcabcbadcbacbcbbabcaddadadacdbacaaadaddadcadbcaccccdabbaaaccbcdcdbabacbdbcbbbdcdaaaccabddbacabbbcccabbdabcabdcabaccdabddddbddddcddacdbddbbdbccdccbdcbbabbacdbcdadddaadbacadcabddbccdabadcabacaaaadcaccdddcddcccbaaabcddddcdaddabcddbacacdcabcaaabdaddbabcdaccbbadcbbadbccacaccbcadccaacbbddbabbaacdaaddadaccaacbadbcbdcbbcdcbcbdbaaadaaadcccdbcbdaddcdabbdaccddddbdbbbbbcbcbddacacbabbabbdacbbdbadcbcbbaaccdbaacbbcbbacbdacddcbbcabddaadbcdbcdddcdadccaddcbbadaaccdaccdddadcacbbadddbadadacacbdbabbadcbdcdaadcdcacdabbcddbaaccaadbbacccdcbabcaabbddbadaccaabaaccdcbbcbaadddacdcddacdcacbccccacabdadcbddcdacadaabaccbdcbddcaababccbccaacbcaccdcbbdadcabbbcccabbdcabdbbdddaabccabbddbacddcccdddcddcdcabdabadaabdbcddbcdcaadabbbdcddabdaadcadbddcadbbcdaddaabacadcdcdaaacdbadbababcbdadbabaaaccbacaacbbdcbbbadbcbcaabdbcaabcaaacdbabbcaaabbdbcdabcdaaaacadaccacacbadadadaadddbdaddabadaaddcbbaacbaccbcbcbcacbaddaaaaccbbcdcabcaaddaddadbaabadadddcbbbcdddddddddaabbbabbbaaadabdbcabdaabbddadddcdadccabadbbbacbcbadbccacdabdddcbbbccdbadcbacbdaccaadabccdcdbcbdbbdbbaddacbcadbccddbaccbcbbdbbbdaaabccaacabacccabaddbbcacbcbcbbbdcacccabaaabbbccdaaddaadadabbbcddddabaacbaacdcbabccbabccadcadacdcacbaccbccadddcadbbbddcabbcbaaaabcbddbbcdadcabbddddbabdddbadbadcbaaacacccadadabcdacaccccaabcbdabdbdacddadbcabcdadacdcababcabdcacbcadbdccdccadbbdacbcaabdcdbdcacbaddddbdbdbabcdcbbacbaacbbdaccddabaacccbdabdbaadbddcccbddaacdbdcbcadccbcaadcccbbcccbbabddbdabbdcdddacbbdbcacddbddcabddbbacbbacbbccccbdaddaaccddcdccddcdcccabaaccbbdcadcbdbbcacabcbccaddacbabdcccdcbdaaadbddbdcdadcaacdccaaacbbaaacaabaabccabcdbdbcbdcdbdbcdccabdbdbcdadacbbdccbbbdccdcdacabacdbcaccccbdcabcdddaacbbbddddaccbbbdccdabbbaababbabcdddadabdadddbabbacdbabbaadcbabddcbbcdbdaabacbbbdcacabbbddabddcbccbccabccccbdcabcccaaabbdaabdbdbbccbcdbbbcbdbdccdcccdbbbdbaabdcabdabcadcaabaccdbcadabcacbaaacbdcbddabadcdcabcabacddccbdddcdabbcbddabbcccbdccccabcdbcbdadadcdbcbccdddbadddbbaccadacbdbaadadbbacbaabcddccbcdbacdccddcbddccacaacacccadbdbddbacdadabdaaadcbbbacddcbbcbabbbbbadabbaadcddabadccdcdbcbabcacaddbadbdbddcdcccdbddccaadbbddbabbbcdbcbcacbbcaacabbaccdcabdddbacbccbbabdacacddaccaadcacddddbcbdaaaaacadacadbbaacabacbdddbacdcddabbbdbcddcaadcbcdbadadcbabbcbddbadaadcacbdbbaabbbccdbbcadcbacbbabbcdbcdbdddabdcbbababbccddaddabcdaadccdaccbdcdbdbbbcdcbbaccbbcdacacdbbabcccbcabdbdcabaaaadbbbbccbddcbddbcdcdaaabdaccadddbccdacccacabdadabdddddaadddaccbacbaaabbcbdcbbccdbcacbbaabdabdcbabdbcdcdacdacbbdabcadacbdaccdadbbcddbdcdbacddaccbcaccaaddaabacabdcdaaccdabcadadcbdcbcacaccadccddaddcbadbddccbccbadadbcbddcbbddcccbddbcccadbbdcddbbabddddadcbddbcadcaacdbacdcddccddbbcbadbdaccccadbcddddadbdccccdddaacbadaccacacdcbdddbaadacddabdbbabbcacbadaadbdaacbccdcdbaccaacbcdcbaacaacbdbddcbcbcbbbbaacbdcbbdcdbacdcbbbcacaabacdbccbbdbccccaacdabddcbdcaaacbbbdbadcbdacaaaddaccbbabbcacdccdccadbbdabbabdddccbcabcabdcadadbdccccbbdbdadbbbcaddcaccbabbbdccddbadcadabaacddcbbbddbcccbddadbcddcdacbadddbccbbdddbdadddcabdaabacbbddaddccacaacddabdbdaadadaadaaccbcdbcbdbaddbbccdbadaccaaabaadbadbbbdbadaaccabbccddabacddaacdddbddbbbdcbbcbabcabaadabaaaadbcddacbccdbbcbddbbccaacadbabbbcadccbadadadadcccaccbbadcabaddacbcbddbaaacbcccbcddddbbddcbdbbdbbbbbdcabcbbdcabdbbddacccddababbccbacdccbccbcddabbbaccababbacdacbbdadcbadbcdabdabddcdacdbbbadccaabbcccbbccdcdaccccaaacdcdccbaacdaddcbbacdbdaaadbbbacdadccabbaaddcbabcdbcbdcbaacadadacdccbbaacdccdcabdcbbabdddbcabbacabdcaababcdbcbababbdccdbddbcaacdcaaabbaddddabaaaaabdadcdababdbaaacbddbcdcdccdcccddbbdaadabddcadccadccadadccbabcbdbdcaabcddadcddcabdcdcbbbacccbacdaadcbcbcaaccbaabacacbdcbcbcbcdadcccababadcdcbadddcdbcacccababdcdccccdaacbdbddaccdddbaadcabbaacbbccbbcdbaddaacacdcacbccbdddbaadcabccccbbaabdcbadbddcdddcbabcbcabddddacddcbacbdccacbdbbcccbcaadbdadacacddabddccdcccaacabdbaabaccbddddabdadcabddbccdbbaccdacddbddcbdbbaacdbcaaadcdcaababccddaabcaadabdccbacbdbaaabcdcbcbcadbaaacacacabbcaccbadccaaaadbcbaccbcdadaddcddadbadcccdcbbcacaccaaaddabbcbabbadcaaadbdacdaabaacbacacdabbccabdacbbdbbcaaadbcbccbaaadcdbddcccdcbcadaddcabccaabcbbdddbcdacbbbabcadbdcaccabbdbcdaabaabbccaacddadcddbbaacdddcaadccbbbbbdabdacccbbbdaadbdcabadbadddabaabadcbacaddadbcaabcddaddcccabcadcdddddccdbdadcbadabaacdcdcaddbaacbbbaddaaaddcbdaaaabbcdabaddbddcccabccadabddadaacdbddacaaabbbdacbccdbddabcccdbbddcbdbabcddccddcbbccdcababcdaadbbbbdbccccccbacdddddaacdadbadadbcdcacbbbaccabaccbbacbaabacacdccbcbbbcdccbdcabddccdbccacddbabbcadbdbcbccdcdadacadaaddacaacdbbccabddadbdaabccacdabcbadbddddbdacbaaddddccdcadadbccadbadcdbdabbbddabadabdcdcaadcccbdbcacbaccabbbadadcbadbacdddabcaaccaccbdbbdbbddadacbbbdaadaddbccbcddbbccadcabcabdddbbbcbcbcccbbabddacacbaacdabbcacddbbbaddcacbdacaaccbbacadcdbbabbaccabcdccdcbddcccccaacaccbbadbddbdaabdcaccaacadbabacdddbcdadadcdcbcbbcbddacbdcbbacaabcdbdadcadbdaddccccabdddbdbdaabddcdabdababbdbbbcaadddcbddbadbbaacbbcbcabdbcddbbcccbdcadbabbccabccacdacbccabacababcbdbdbabbadcccbdcdbcccdcbaaacdbaddcbabadcbcbcadbbdadaddaccbbdacbadccccbbcdadbdaddaaadaaacbaadddaccddabcabbadbbdbababbcaccadbbcacbdcbabcacccdbadbcabdbdbbdcdcdcaadacdccbabcbbbcbbdaccabccbabaaabdcdcaacaabdccbacacacdbdccaabbbdaccbbadacadcabbdbadbcadbadccbbdbdabbddaacdbbcbbcbdbbcacdbcdcdcbcbcdccbbacadaddcbaacdcabbaaddbadcbcbdbddbbacbbdccaacdacbdddacbabacaaaacbbbcbbddbbdbdbabcdadababdaadabdcdbcdbccdbccaddccbdbcccbabccacccbcaccccbbabbbdcdacdbbabcdbaaabacdcddbdaccbcbdabddcbbcbbdccacbcacadbdddabbddbddcaaadbbddabbcccdabdbbbbabccddcaccdacdaacbcbbbaaddbbbcccbddcbccbdbbcabdbcdddbdcaabdadbdabdadabdaadbdacacbddbcdbcacbddcdcbadbcaabaacccdacbabaaabbcdabaddbbaaadcdcddddbbbbbabbdcccddbcaacadbabcbdaadbcddbccbaddaabacdccacbcbabddddccaddaaacdbcbcbadadbdadacbcbcbadbcbddbbcaaaaccbdbddaccdcbabbacbbdddacaadcdcdbadabcabdbdacdbaddacaacaccdccdbdbcbdddbbcddacbbaabccbacdddbdabaddaddabcbdaaabccbddbaaccccabcdbcaaacbbbbbabacacdddbadcaddabcacbacabdaaacbddaddbbaabaadcadbdabacadbbdaadddddbcbbaaabaaccbdcbaaaccabadccdcbddbbccddaddbccbdbacbdcabbcdcccbbbcaadcbcaccdccddbaaadadddbadcacdacccbccdbcdddccdbcddbabcadabaadacdcbdbabdbdccbbcbcbadcbcdabccaaadbdaadbaddaccdddbbdccabbadbcdabcdbcababddabccabcdadbabaaaacdbddcdbdddaaabdcabaabadacdacaabbabaacacdadbbdbccbacaadbcbbcaddddadbbdbacbdbdbacbdadccabbdcbbdbbcdaaccaccbcbcbaaadccacbccacbaacdababbcccbaababacdccddbdcaabbdbddbbbbaddaccbaaddbaacadbabcbbbaabcdbbabdbbaabcbabaabdadccbdcadcbdbddddcbdadacbdccccbbcdcbaaababcbaadcbcbdcbaddbbacbabcbddcbabbdaacdadcabaacddbcdcdcbdcacdbabcbdccddbbaadaadaaaabbaaaaaadbccaccadbcacdabcbcacdcadcbccccdcbbcacbdbdabdbadbcdccacbabdcddacbcdbdcadbdbdadacccbaadbaaacbabdcbdabdbaacddbbabacbccbcacacbcabcbbdadbcacdccdbdacabdabccdaacaadcbadaadabcadbdaadcbbcdbdbbdaabadcdbccbdaccacadbacabaacdcdabbbaddbcadaaaddcdcaabcbdddacacddbcdbdddbcbbbbdbbbdabbcbaabaadadcdddadbcbadacdbcccabbaacbdbccbbbcacbadaaacadbabbbbbdbaadaacdbbdbacbcaaccccdddcbdacbdcacccccdcdcadccbcdbabcbcbddcaabbddcbbddcabacbaaaababddcddccbadaaaaaccaacacdbccabbcddabbcaddbadadabcacdbdcdbdacbcbcabaddcbaaabbbccdcdadaacdbadbcdcdccdaacbcdaacaabacbbabdbdbccadbbbadaaaacbdcdcbbaadbdddbaccbadbacbacbbccbddcbcacaadadaddabbccbdcaacabddddccbbdabbaacdbcadccabababadacadaadddbcbccaaadaabbdbdcdddcabcadcbcaccacccabdcbdcbdadbbabdbdabadccdcbabcdcbdbdbbacacddaadaadacabbdbdadacddaadacbdacbcadaaaacaabbacabababaadaaaddaaccccadbacabddddcdbadadbbabcdcbdadacbcacbdabdddcbccdabddbcbadbbbcaadabbaaaaabbccdbccbccbadacabbdadbdaabdacbdcdaccacdaadddbcdcbcbabadabbaaddcaacbcacabdbbcdaaabbacbcddbcbabcdacacabaabbccdbcaabcbbdcbcbddbdbacccacbbdaaadbaddadcabcacabdbbcbcadddbcbbdcabacadaadbbbccabcadabbdbabdcdccddddacacadcdcbdbdadabdccbabcdcdccabbdcdcabddbdacccccdbcaccbcdbbdccabdcbddabaacdcbbcccccdadacbbbbbdcbacddcdacccaaddccbdcbbdabdbabddcbdccccddbbadddcccaacabdacdbbdcdbddbcdabbadcccccacbcacddcdcbcbaaaabcabcadabcbbdcabcccbbbbacdaadbdcbadabcdaddadcbaaaaababbbbbcdbddaadcbbcabbaddabcdcdaacbabbdbccbdbbadbcabbdadbbdadabccadaccbdabcacbdabbacccccccacacdccbccadcbaaaddadcddddcabbddacccdccaadccacacacadaccbacddddaacbbdcadcabaabaabbbddbaccbbccddbbdddacaaccacadcbbbbcdbccbdcaadcadadabcabbcaaacbcdacbbdabccbabdbdbdcbcbbbbcbcdbdadbaabdcccacbcddccddadcaadbdabcddbbdccbacdaaadbbaadaddaacdcaadbbaaadcabcccbdadaddaabbdbabcdaaacbddbbacdaadbcdcdabdcaaacddadcbbcbdbbaddacbdbddaacadbbdacacbdadcbccbcbacbcccbcabcdbacdcbcbaadbdbbbabcababbabbddcbcbbcabadadddddcaabdacacbcdcaacdcbcddbadaaabaaaddbbcadbadbccabbddcccabdbabadcccbaaabaabacadaaddaadcadcdabcaacacbcacaaccddcaddcccbdcddbacccabcdacdbddddaddccbbdbbaabcbbcbaaabbdaadbacbaabdcbcddcadcbdacabaccacdaccdcbaabdababbdccbbccbbaaabbbcbdbdcacccacddcdabcdaccbaacaaabcabbbccdbbcacbacbdcadaddadccccbbdbddbbaddadadbbabcddabbdbbbbbbccdcacbbbacbabbbdbbacdbcaccabbbbabcbabcbacdabcdbaaaabddcccabdccdacbcbbdbccdbbccacddccddbdcbcacaabddadbdbbadbdbaabaccacddccaabaaccbcddcacdaaddbddbdddbbcdddbbbbabccbbcbdbcccabddbbadbbaaccaaddcbdcdbaccbdbccbababbddbaaacadcbaddacbdbbadcccbacddbcbbacbabddaacddbdccaabadabadcdddbcddbddbbdbcccdbcdddcaabddababcdbcddbddacdbdbccddcabdbacbaacbdbdabacbdbabcbcbccdbccaabcabbabcdcbcbcbbdbdabccdccaadacbdababbdcbabcbaadacaababddaccbcabbdababcdadbdddbbcaaabaadadcdaccbadbbccaccabacbcdacccaadcbbccdacadadaacdcabbaacdbcabdbbddddcbbabcdbcbcdacbccdadcdbaaacdcbdbcdbabcbcdcadaacaadbacaaabbaacdaaacdbdabbadccdbdbadabbcbabcccadcddccadaaadaaccddccdcdacbaacdbbbbcaadabccdabbaabdbbaacaaaacdacddbddaaadcacbabbdacdabcbbddbbcacbaacddcbdccbcbcdbbbadabababddbcbddcacbdbccdaaadabbdabdababbccdddabcbbcbcaccbcddadabcabcadbabdccdabdabdabbbbaccdabdbacadbdbcdbccacbdddcbaccddbbdbcaadcccbacacbddcdbbaadbabcccdcbdbddaaabacbdaccaddccdbdaaddddcaacbdcbbdbbcbccbacdbacdadabacddbaaaacabbaacdddaddcabbacbcacddadbdcaadbbabbdacabadcdccddaadabbabddaacbcbcccbdbccdcabcbcdbbacccbdbbdddbbdbadcdcbcabadabdbbadbdaaccbccacddaadcadcaacabdddadbdbcacbdbddbcacccbdbdababdbabcdbccaaadbacddbcbadaadbccaddacddaddddabddadabbdaddcacbadabbabcbcbdbcdcbbcaabcbddbaabbdcbdacabcacaccbaaaddabbdddbcdcbcabcbcddacdcaaddbcbcdaccdcdcdacbaabbdbacdbaaacbaacabbcbaccaccdacaacadcdbcbdbdaacbdacdbdacddabcdabdcdbadbddbcbdddccddccadcdacacbbddacdcbcbdbbbcbacbcbdbcdcbaabdbdaaacdbabbcdadbbdcdcbddbbdbbbdbddddcddbddadacaccdabccbdcabaaaadcdccddababdbddbddccdcdadbcddcdcaddabbacbbbacbbdbddbddbbaddbbbadbccbdbdadcacadaabababaacbaaacbbbdaabaadbccdcdbcbcaadcacbbbdabccddadbcaccbdbdcadbacbbdcbccbcabbcbdbbcbdadacdaaaabaddbdccdbacdbbcaacdabbccbbcdbaaacdbcdabccbdaccacbbcddbbdaccdbcadccabddacbbbadcdbdbcdadddccdaddcbbdcaddcbcdddbdbdacddadadcacccacaccdcbdcccadbcacdbadacabdaaadcccbccdaccbdacaddaacdacabccbaaabbbbaabcbdababbbccbccbdacabdbbccdacaaaabcbabbdbccccbbdbbdaabacbccaddbdadcbcdabbaabcdcbbcbbacaabcbacaccbabdaaabcaacdaccdddbdddbcbdcaddbdccdbcdadbcdabadbaaaddbbbbcaccdddaabcbcdcdacdddacbbbabbadaabdddabcdaadcbcddabdaaabbcccdabdbcdadccdabcdcddddacddacbbaabccdaacdabbbbdaddabdaabcdcccacbdaabcdacdbcadcbadcdcaabdadaabacdbbababcbddacaaacaabbdacdbbcccbdbbcadbcdbbbcbdbcabcdadbbbccaabdbbabddddadacadadbbcbcbddbbacdabdbddcbaccbabdbccdbbadddaacdbacdbdbbbcaaaccbadbbddbdbdcbacbdbbbdcdddddccddaadaadababdbabdcddaaabcbbbcbcdacbbdcdddccacbcddbbbccabbbddababaccaadabdaadbcabbddababaabdbddccbbbdbabdcbdcccddddccbdaaadccbdbcbdacdacbdadaacdbaacababbccbbbcdacdccdaddabcbacbcdaaacabcbcdcacdcdbcadacabbacbabacabbbcadacdcadbabdacdbbbbdbdcccbbacdabdddcaaacbbdadbdcadadcbcdcdbbbcdddacddddbadadddabdacbbccabccdcddbcdddbbcacddbacddcacdbdcbccabcdcccbdaadbacadacabbaccdbccbdddccbbcacbcbacacdccaddabaccbbcbbcaccdabdaabdbddabbbabdbaddbccbabccbdacaaabcdddaacbdabadaddbbcddbdacbbdccbabdbbbbdbaadcacaaadbbcaacdddbcababdcbcdbccddbcbbbbdbacaccaadddacdbdddcadaacdccdbacdcdbaddbddcdaddbdddaaabbdbbabcadaccabbacaadaddddcbaaacbbbbddabbbcdddcaadddcdccbbbdcbadcabdbccabaccacddcbabacbacdcddbcadcbaddbabcbababdddbbacbbdadaacacababaaddcbccaccbadddadadcdcbcbbdaacddcccdbcbcbdbabdddcbcdccccabcadaabcbdabaaadaccbdccaaadacbdabaabcacbaabaaddcddbbabacabbabcadacaadccabbadabaaadcabdbbddbccabcbdcaccbabbacacbdabddaccbccadacabadbabaaabbbdcbabdaabccaaddcdcacdbbaaddcdacadbbbcdbadbcaacaaaabababdadbadabccaabbdcdadbdacddcbaaaabdcbbcdbdadbcadbaccccccdbddaaadcccbbaacaadddabbadbadcadddabcacdbcababccbccdadcacccacddaccdbcdcabcbbcbbccbbbadaaaacdabcadcaccdcbbcbdaddddabcadcdbcccadcbddacbadbacdccdbdcaaaccdbdddcadadabaacbdcccbbabcdcadadcabddccbcbcbabacaddaacbaaddaadacbacddcddddbbdddbdacbdadcababbacabacdccadddbcacbdbbabbcddbdadddaccabaddddccbbcacbcdabccdadcddcccbdbdaabdcdbcdddbcbaacdcadbcbabdaaacaccacaccabdbcbdabababaabbdacaabcdcdadadaaadabcccabbbbadcbcddacbbacddabdabccbbcdbddcadbbcaacadcdacadbbcddbcadcbbbabdcbaacccdacaccbdaccadddabcddaccabdcbcbbbbcadadcdacabdbdddccddcbbabdcadbaacaadbbdadabacdcbccddccddcbcdabcaccdbadadabadbacdcaabacdddddbaaabadcddddbddcdaadbcdacacbcbabdbddaacacccadabaccaaccddbbbdbadccabbbbccbaabacaabcdaddbaddbbdbaabbddcbcbddcdcdcbcccacdcbdcaccbcccbdddcadabdccaccddbbabbacdddbadbdcabadcbdcdbbdaabacadaabbaccbaccdddbacadbaaadcacbaabccbdbbbcbbddcabcdbccabaccdddcbcbcabbbadcddcaccdbbbcbdaccdcccdabacbcdadadaccbbcbbbbbaaacadcdadbbaddacaccabddcdacaabdaabbaccababdddcbbbcbbaabbbacabbacaacbabcdcadccdaadcbbcbcbacbdbcdbbacbcbbdaddbdcbabcdbaabaaddcddacbadbcddbcacccdbaababcabadcaaabacbdadbcaccbcacccdacabddabaaccbcdbcaadcbbbadbcbaabbdbccbcacbdcdcbcabdbcbcbadcacdcdbcdadaaddcbcaacacbdbbaccdbdbbcbdcdcdcdacddaacdbdaddbbcddadbadbabaaddcaddbdadbdaccdaabaccccabccaccaadcbdaabddcbbcacaccdcdbacbabdcbacbbcbcddccaccdaddcbbacdacdbbaadcddabcbbcddcddbddcaacccbbcadbddddaddbacaccacabcaadacccbaadccdabcbbcbabaacadadbaaaccdddbabcbaadadadadcdcccaababadbabdbbcbabcaabbdbcdcbaacbccabcadccdacbbdcbacbcbbbdccabcacdbbdadcdaccccbccddccdddabbccdcdcacdcbcbabbcdddaadbbdbbdbbdaaccbbccddbacbdccbcdbabdbabdaabacdaadaddacbccbadabaacadbbbbcaccadacadacabdabcacddaaabccbcddcbaadcaaacbbbdcdbcccdaccbcddacdbadaadabbdadccabdbadadcddcaddaaccccbacbdbcdccaacaccdacccdaadcaadcdcbaadbbaacddcdabdabdcbadaddbccbcbddbbccaccbcaaabbacbdaabdacadbbbccacddbcbccccacdcbbbbcbdaabdaacadbdcadcdddbdabacdcabcbbdbbdddcddbdaabdddbbddadabbbbcaabdcbcbccdcdddcacdccdbadbddccabcdccbddcaccabcacadbdaadaacddccbacccaabaaabacccacdabbcccddbbbaaccddddcddccdcdadbdbabcadcbabcaddcaadcabccaaabcbdbddbdaacdcbbbccbdcacddadccbcbdbaacccdbbcddbbabdaaacdbadabbacdbbbbadddababccdadaaadcdcaabcaacaddaaadddddccacbadccbdbbcbaacbdbdcacddbacccbadcdaddbdbbcbcbbcddcdcbddccbddddbcddbcacaacbadadccacbdcbccacbbacddcccbdbcadcbadcddbbbcbbcbdbaddacdbdcddddbaddadacbbcbdbbbcadbacadbcbdbcaacadcbacdadbddabdcdabccbaaabaddbbbdbcbcbdbddbdbdcddcdbcbbddabccbacbbcbbdcabcccdaadabcabbccdbddbbddbacadcbcadabdabdcbcbccadbabccaadddabdcaddbbadbbcbbbdacacaccddcdcbcbabcaabcbddbcaaaaccadbaddcabbbdcbbcaadabddccaddabbdcbcddadcdcdcadbdbadcdbbddadaacacdbdabcbabdbdacddcddcabdbaaddcbbacabcdabadcdbbbdbbbbdcadbddcbbdadadabbbbddacabaaabadddcadabbaabbdcdccadabcadaddbbadbdadddbcdbdaaacdacbbcdbaccbcaccadadcbcaadacccbddccdbaccbacadcaadbbddbcbbadccdddddaccaababdbbcbabbdbdadaaccaabbcbbdbdadacdbdbbaadbaacddbcaddbbdbcccabddabdbcbcacacdcdabbbcccacacccadabbbccdacccdadcbadbddcdcdabacbccddbddcdbcbbbacadbdbdababbdddbbcacdadddbbabacbccddbbadbadbacbcbbddaaacaababdaabaccdcbcbcdadacccdabbabdcbaadbbaccdacbccabcbbdddaaadaabccbddcbabbbccddacdabcacdcdbcbacbdaaabcaccbddacaaaacbbcdbccadddadbbaacdbcddbccddaadaaddcbbcabbcdbdbddbcdbbdcdbbbcabdabdbdbcbcbbaacbdbcbaadddcacddaddddccabbacdadacdabaaccadccdaadababaaddadbcbacddadbabbdaabbaadbcbbabadbabbabdbbbcaaddcbbacdadcabbcccacdabcbabccdcdadcaccacbbaddacddccdadccdaaacabbddacacaadcccddcbacdccdacbbbbcaacbadbbdddbdcccccbcbbcbaaabbbabdaaaaadbdacbddabbacbcddadcbdcccdadbdbdbdccbadbccbbaacdbabcbaccbbbacdbbcabccdbacacabadabcabccdcdbaadccbbbadcacccdacdabbcabdcbbccbadddcbcabdbcbcadabcbbccddccacbdddbcbcbbbadbacbdcbbbbccdcaacbdcbdadbadadcdcaccdcacacbcccabbdbabcbdcdcccaacbdadbdcdbbacbdadccadbaddccccbacdbbabaccccdccdcaddbbbacccaacacdbaabdcdcddacbddcacbadaaccaddcbaacbaaadacbbbccdabcabccabbbcbbbaaaabcdcbcdbdadbbbdcaadbabdcbcbccadaaaadbaccbdccbaccaadabdabddadbaccbbbbdbbcdcbccccbccbbcabcbbbadabdacbbcbabccbbdcdcaaadaddbcdbaadaabdabcdbaaccbdccaaaddabcbbbcaabbddadbddcdbaaabddbbdbaacbbadcadcaadcbddacccacdcdcdbcbdddcacaccdacacababdcbbbdcdabbdacbabaccdacacbccbacdcadbcabcddaddcdccbadacabadcdcadccaddadbaabaccbabdcbbdbadbbadacddcbcaacaabbddababdcacbccdaabadcddaacdbcbdccbadcbacbbdcacccadaabdcdbbccadacabdbbcbdcdaacadbaabdbdbbacbadcdacadbcabbdddbcccacbbbcbcaddcaababbccdaccdddbdcdcbcaadbdbdcdbdcdaddacdbbdaacbdbaccbbccbacaddadaccaabbbaaacbabbdbcacaabadcddadbadaabddabcdcdabdbadabbccbaacdacccdaabaaabbadbacdcaabbdcaccddbdabaccacdddadaabaaadbcbabaabddbcaabdaabdcdbacdcdbcbbadbaadababdacbbbcdbabbcaaadbdcbdaadbbabcacbccabdddaacdccaadadadcadadaccdccacacdcacddabbbcdbddcdbdcbaaabdacdcabdaabbcadcdcbadbbaaddbadcccccdbcadacabadddacacaddddcaaddaacbccbacbccbbadaccbaddbdddadbcadadaadbaddcddcdddbabaaabbbccabdbabccdbbbdcccbaacdbacdcabcbdbcdddbbbdcdbdbabacdddabccdbcbccadacbbdbbbaaddcbadaabcbbdccdaaaacdbbbdaaccbcabadbbababacadcaaacbdcabadabcccacaabadccbaabdadcaddadcddbcdcdbcbcbbcdbcdbabdcadcadccccbbbbbaccbaabadacadcdccbbbbcddcdbddabdddbdbcdcbabdbcbbddaccccdcabaacdcbbdddbbaaddcbadbdaadcbdbddbcbbcabcbbbdcdbadababbbbbdbbaacdbdcbdbccdaaddaddacbccddaabbacbddddaddabdaacaacdbcadcdbbdbbcbcadabbbbbaccbdcdccdcdcdbdadbaadcabcacbdbacbdbbbadabdddcadadbccdbacadaaadbdbabcbdacdcbbdcdaacaddbddcbabdacbaaaacbabbcbbbcdaababbbabbabcbcabcabcdccdbbdaacbacacbcacdcdcaddbdbbcbbacaddacaddaccbaacbabdcaaabdbddbdacdbcddbbbccaabcbaaacdcaddcabbabbdcacbcadabcdbcacdbbadcaddbcdcbbdcdabdccbaadcabacccddaccadbaaadddccabacdbbacccbadbddbaacdcdbacbddbbbaacabdddadbbdabddabbbccdbacabcacbadbcabdcbccbdbaabbdcdaacdcadbcdabddddbabaccdbabacccadabdbcccaacdbcaabdacddabccacddbdbaadbadcccbddbbccbdaaacadacaddadccaddcddadaabdbbccdcacdabbaacccadcbaacaddabaabcbcbcdbaadddbccdaccabddcdbddaaabbcddbdaddddbdbbbccbabdbdcdbdccccdbcabcccbcdcdcbbbcccacddbccccaddbcddddcaadccccdccadbabdacbaccacbabaccacccbddbadacbacdcdabbcdddacdcdaacacadbacbdbcbddcccabdcdabbbdaadcbcbdaaccaabcdcdacaaabababddaccbadbdacbacbcabddbdcdbacaabbddcabbacbacbbbdacabbaccbcbabbccccabbaddbadaadcbddbaddbbcbbaaaaaaaabdbddaaacdbbbaddbadcdaacaaaadaacbbaacbdadcddaccabdbcbcaccbbaabcadccdadbcaadaccddcdbdcddcbddbbbdabaacdaccdccbacadcaccdaadbbdacbbcccdbdddbddccaccacdcbabcdbddbbadbbcdbcbdacccdccabacdcbdddddddaababdbdaaabccdddcbaccdbcabacbcdcadaadbcddbdadadadddddbccaabbabccaaadddbdccdacaadaaadbdabaabcabdaccbcccdacdacdaccbadcdbccaccbddbcaabadacabcbccbdbbcabcabdcbbddccccdaadaadcadcacbcdabdddddcddddaacacbbbddbcdcdabdcbcdbbacbdadcbbdbbbabababdbccbcacbbcbbbaaaabadbaacdcaaddcabbcddacdcbaaddaabdcdbacacbdcaadccccdcbbbbaaccccabccdcaaacbaaabcbacabdbbccbaccaccdbcbdaabdbadbccdddbbbdadcbbacbbcadbddbbdccaacacaacdaaacaddbdbbbadcddbbbdadbbcccaccabbcacdcadcdadddbbbcddbabdabaabcbdadaadaacdcbbbacbadacdbbacdcccacabccaabdabcbcabcabadddcbaacabbdcbcabcddbccddbccdbaaabadaaddbdadadcabcacdcbabbaccdacbddcadbaaaaddcabbddcddddbdbbacbcdbdbdacccdbbbbbdddcabaabdabdcdddacadbccdabcacdacacbcacbcaaddacabaddcacadbcacadccabbdaabcacadaadbdbadabbdcadabbaadaabdccdadcdaaddcddccbbcacdacbbabcadccdadbcdbadcacdbdbbdcbabcaaabacbacaabbadccbdcbdddbabdccaccdcabadddcdbdaaacdcaadbaaadabaddccaaacadbcbacaabddcaabbcdadabaabcabbcdabcdbbcbbddbdcabacbdbaaaddacbccacccbaaabaccccabccddcadddcdbdadddacbacbabcdcdaacddbbabcdccdbdaacbbcacccdacabbddbaccddcbbccaabcccbbddcacababcbbdcddaababccccabccadaaadccaddbbdccdbcaaaccbbbdadddaaadbdcaababbabcddadbddbccdcadcccdcacbdbbdbcacadcabbbdddbddbdcdadbcbbdbcccbdbaabaacccabbbbcaccbccacdccdcaccdbddcdddcdcbbbcdcccbbdcaccdcbadaaabdbccbabccdacbbcccddbbddcaccddabdadcaddccdcddcbbaaaaddbdadabbababacdcccdbcdcaabcacaddadcbccdabaacadadbdbdbbdccddbaabdcbcaacdbccbcbddaccbbdbbaadcddcbdcadbabccccadddbaacccdbcbdadabbadbdbaadcdbcdadaababdbaabadcdbddcccbacdaccbdddcaacdddbbbbccdcadcbbdadddadbdcdadaacbabbbbadaabbbdbabbbdbbdabcdcabbcdbdbdcddacdaddccbcbbdabcdddabcaddccccddcdbbdcabbdcbdbcbacaaababbadcaddbcdabaaddbaabadaacdcdbaacaacadabacaacabcddccbccadddcdcaddabaabddabbbcdddbaaabacbdcbbcdbcdcbcbadaabbaaccbcacbabcbbddbabddbaccabcadbdacabdbabcaddbabaacdaadbbdcacbabcaabbcdcbcddcdcabbdbdbdcacdbaccbbdadbaadaaddbbddcdabdadbcaaaaaddbaddcabddadacbddaacccbdddbbabdcbdaacbacadccbcccddaacbcadcaacadcdcaddadcdaadbddaacbaaadccacbbbaccaddcbabdabdbbcdbabaccacbddbcdcadbdcddbcbbacaddcbdbcacbacacdadbaaabbaaadbaabcddcdbcdccbaadaccbcdcbcdbdbddcabcabdbabbaaacaaadcbddddcbbbdacacbdcadbbaccadbdacdbbdcccbcccdccbcdbddccdabacacbbccabcbbcadbddaacdbbabdbbdabbacabcbdaddcdcbabcdddaaddacaccbdaacabdadbdccbacaadcabccdbdcaabcaaadaadadcbccaadcacbcdcdcbcadbbdcaddbddcaacabcbacdcbcdabacabdadbaddcccdbccddbbbabacddabdacacababbbcdacdadcabbcaaaccdddbacaacadbbcddadddcbcaabcbadbccbacabdcaadbdacdcadabcbcadbcdaacacaccbadbacbddbdbcbdbcaabcdbbddbdbabaaaddbdccaabadcdacbbaabacadcbaabdcbdbddbdbcddbcdabbdadbccdacccccdacdbaccacabaacdaadcbbaacdaababaacbadcaddbdbcacababddaaaacccdddcbabbdccacdadbcddabbbacaabcdcabbabcddadccbbcddbdcbbcabbbadcdcbcadddaacabaccaabaabacaccacdbaacdadaacabdadabcdadacbdbadabaacddbdbcacddbcdaadcdaabbdddcdacabdbdbadacaddddcbbacdbcdaadbbbdccdadacaadcbacbbaccbcabcacbbacabcbdcaccbbbabbadaabdadcdacabdccdcbcdbaccbbacabadbcbaaccaaddadaadaacaccadcdbcacdabcdbbcbdacaccbdddadcdbcccabdcdbdbdcabdacbbdbaccabcdbabadabcdadaabdcbcdccacbdaaccccbdaabaacbabdabccddccdddbcdcadddccaddabbbabbaccdadadcabbcaaadbccacacababccadcdadddcaccccbddbcacccbdcadccccbbdcabaaaaadadcadbdbabcdcdaabdabbbbccacbbacbbdcabaaaabacbdaddbacdacabddabbcadbbdadadaacbcdadcaccbcbcccbdcaabdadacadadcccabdcbaccdbcabaacdbcdaacabdbcbcdadbdbcdcaabbcabcadcddcaacdacaaccccadaadbaababddbadbdcbcbbdbdacadcaccbcbaaccaaabbddcacbbaaaabbcdabcaaabbdcaadbcadccadadbaaccaccbdadccbcaccbaccbcaacdccbaddbcaaaabdccdbabdabcddacdbadbbcaadccabdabdcbddcbdbdadcadddbbdcbdcbcbcbdcbdcdbabdabdcadbcabcbaccbddcabccbdcddcaddbccdaadbddadbaabaacdaaaccdaabbacaccddbcaacccbadabbababbbbacadaaacaacabdcdbaccdcddabbdcaacadacaddbccacabcbacdccbcddcbcbabcdbdadcaaadcbaabaadbaacbabbadcdddabadbbbdbcacabdcdccdbbbcaddcddbacacddbbddccdadbdbddddcbacbcaabbaacdadcbadcbabcbbcbacaccddbbbbdcbadabacbbbdbdcdcbddbcbcaddbdcacacdaacdcdbbcccbcdaadcdcddbcbbaacbaccaabbcdbacccdcccbcccdcccdbbabcdbbdcbcbaabddbbacadadddaccdcbcbbaabacbdddbacdbbbadbdbbbbdadaccdaadcbdbabdcaccddcbdbcbbdabbdabddacadddaadbcaddcdcababaabccddddcacaddcdacddababbacbddadabaddbdcdbdabbbadbaaabcaacacadcdcaabcbabbcadabdccadbbdaabdcddabbdbdbcdcccbcacbbccbccabbcbbdabbbbbbadbbbacabcadcccbdcbbaaccdcdaabacbbdabaaabdaaaadbadbccdbdcbbcbdccdabdcacaaabacbcddbabcacabdcbacbcdadcdadbbbdbcabaabcacdaacadbddcdddbaadcbacbcbbadaccbaacdcddacacacaabcabdbbcbdcbddbbdbbccbaaadbbcbbaddaaaaacbcacbacaddacabccaccccacdabbcdaddcdbaddccdacdabaccabadccccbbdbaadcaabcbbbcccaadccbacbabbcbadcddbcdacabdabcddadaacabcdccdaccadcacdbbacccaaccbbcbbdbdccdccabbbdbcccddcddacbccaccddbccbbbcdbabadccbacdcbcbbacabdabbbbadbadcdcbaccdcdaaccbdbcbcccaaccaccbccdadacaabdccbdcbcadccadbdbcdbacbacbacdcbadbcdaabbacaadaababbdabdabdbbdbbddcbdcdcaabadbbdbcadccbaabbbaccaddacdababccbabdbaaccaaaadccdbdcabcbcbbddddcdbbbacacbbbabacbddbddadbacbccdbdbdaacdbbcbdbadbdcacbddcabbbaabacdccdcbcdaadbdccadadabdbcbcddcdcabadbdbabbbdabaabcdaaacdcccaabdaadddbbacacbccbbdcadbbadcacacbbacadcdcdbddddcdcadcccdadddaadbbadacdbaddbddbdaddadcabccdcccabdbddabdacdbacbabbadbbbcadbdbacdbcaddcddbadbccabadbcdabcbdcadcaaabccdcdaccabbdddbddaabbccddbdadaacacbdcaacaabaddbaabaaccbadcbbacccaddcdcbccadbadcdbcbbccacdbcababddcbbcbbabaddbdbccbacaadaadbaadadbcdbbacccdacbbdbabcdabddddacdabbbdcdacdaddcabcacdddcdbccbabaaaddaacdcbccabcccbabbdcdcdaabdccddbbadbdacddbdadabbbadaabadcbddcabcabcadacdbdaabdaaacccddbdacdcccadbbabcdcdcbcdbdbcacccbaaacdacaabcabdbacabcbaccbbdbdabcbabdbdcdaabbdcbccbbcdaadbaadcbdcadcacddadbaaccbdcabdaabbdbdadcbccbccddcbadbcdbbcabcabbcbdbadcddbaddbdaddadabdaababbcbdddcdbbdccbdabbbabaccbcadababbccdabdbbdacbddcbacbaabbccddbcdabccbccabcccadcddaacdccbbdddcdddcadacadbddbdcdbaadadabdaccadabdcdbcabcdbbacbbdbdbadbdabbdddddbdcabadddbcdbabacddccbcccadccbbcbdacdcdcacbbcaccdaccdcacdbadbdbdaacacbbdcbbacaccdbadabadbccbcccdaaadddbcabdcbacadccbdcddaacccbbddaacadccaacdabccbadccacacbcdddacdbbbdcabdcacbaccbadaccbbabdaccdabcdbdccdcddbcbccdacaaadcddbcbddddccaabdacbddcdcabccdbcbbdaaaabbcadbdbadcaadbcbdbddbdaacadabdacadcbccccdccdbdaacabadbaaaadaddccddaaccdbcddabdbbdcaacddbbcddcadadbdbcdbadadacccddddacaadadacdbcdbcabbbcdaddbccdcabacccacabdaabaccbaccccaabdaacabbccaacbaccdbbaaddcbaabddbdcdacbdcabcabbcdcbcdaccdaccbcaaababcdabcacaaaaabbddddbdacdadcaaccdbabbabbadccadbbcccdbbdbcbdcdddabbbdacacddbdcaadbcaadaddbcbabdcddaabaadcabcdbdccbaadcdccabcbdccabadadbcdaaacadccacaccdcbddacacdadbbadadbbadccdbdbadaababdbcaacadcbadaddbcaaccbcbddacbdadbdbacadababdbdaabcbbbbcdadcccdcdaccdccbbcbcaaddcbdcadbabcbdcdacddcbadbdcdddbabdaddcbcdcadcadaccccdabbdbbcbadbcacaaabbbcbaccadadbdbbacdcccaddddabbabbabbccadbacbabdddccbadadddaccabababcaaaccbabadbccddbcdcddccccacbdadbacabbcbbdbddcabdbdddcabcadcdcabdbdddcdabdbacbdabaacdaddbbacabdddbdcaacaadbcdbbbaabcbdbbbdccbccaabaaaaacdadbdcadadbdbdaaabdabcadadbaddaccbcabbbcddabccdcdbccccccbddcaabdccdccbddabcaddacadcabaaacbbaacbbdbabbcbddadbabccbccdbbdbaadcdbdaddcbaaabacabacdbdbaabacbdaccbbbaabbdccbacaacbcacdbbbdbbcaddcacadbdcdaabbcddcbddddcdcdddddddbaaddbbbcbdcbcdbdabdaaadcdbbacabcbbcbdcabdaddcadadcddadbadddcccbcdcbcdaadccbcbaabcdcabcadcddaaabddacdadcddcaacabbcdadcddbacaaaaccadbadbdcdcaaacdcbbacabcabcbcacbccadadaaabdbddbbbcacbdbcbbcbdbcccbbadbddaacbddabbdcadccdacabdabbcdccdcddcacacdbaadcdbabddabaaabddddbadcbdaaccdcacccbcadbcadccbcdaacdbbadcadababcbddddcdbbddccacbccdcaccabcddadaaaadddcbcccabbbdcabadbabbaadbadabbcbaadababacaddababbdaacbbcaaaacdcaabbddbcbdbdbacacaaabcabdcabdacadcacdccabadccadbcdadccaaadcacbdbbadcdcbdbdddbcbdbdaddabcdcdabcabddcbaacbcbddabbadaaddddbaaadbcdddbdadbcaabacbcacbcbcdaacccddcdddadcacbbbddcacabcccdaacacdbabccacbddcdbcccbaabdacaaabbabcbcdbadcdadbbdcadadcabadbacbdaddaaaabaccccbbabadadcbbdacdaabcadbdccccaaabcbbdcdbddbabbbccdadcacaabdcacbdbbbddcaacadcaaabdabcccacabadacddbdcaddcbdadddddacbabcbbcdacccacbbbabbbcacddcbdbdddddcbcdabbbacbbbbccddadaddbcbcaaccabcbcacdacdbabbacaabbccddbcdbbbdadabcbddadaacabcabaabdcdbcbabbbbbadabdcadbcbbdcbccdbbdadcbdadadadddcaadddadbdbbbbacabdacabccbabddbcbcdcccaaaaacdbacacbbbddcdbbcdccdacdaccaadccdcabdaadabccddadabaacadddbbccabaabcaabadacbacdbbbdbcdbbddbcadadbcdbbdaaaabdddddbdacccdcabcccdbdbabddbaccbcabdacdbdbbacbdadbadabbbdbcaabdddbdaadbabdadcccdcaadbdcaadabbbabbcdbcaddbbcabbbcbdaabcadcbcddbaccdbcadbbbcbdaabababcaacbcdbccbaaacbacbbbdcddabccccbcddcccdddabccdcaadcabdbbbbbbaaaabbabddbbabdccdadbccccaddabbbabcbabbacbadacadbbdcbbdbbcdbacabdacbcbdacaccddbbdacdcaacdbadddacdcaaaddbbccdcdcbbbdcdddcaadcadcdacdcbabdaaaccbcbadbcbdcacaadcadbbaadcddbccbaccaacaadbbcbacdadcacbccbbbdccabddaccbadaccaacdcbcbacadabcdbcbbdabaaccabbbcbbbaabcaacbbacdcdbdadbbcaadbdcbddbbcacbdbbdadbccdabacaacaddbaaacddddcaddadbbcccbddacacdaadbbcbabacaaacbddaaabccdbabdbcdacabddaadcdcbdadbcdcdcbccbcaaabdccaaaccbdadadbabacbdbaacadcdacaaddcacaddbcbbaabbbbcadddbbadcbcccbaaccdcbcaddaaaddddddaabaacadcaccbdcbbbbaacaccbcadcabbadcbabdcabbdbacccccdddcbaacdddaabdbabdbdcadbdbbcbbcdcdabdcabbaccccbcccbadcadacabbcabdadbdcaaadddadbacacacbdcccdaabacdddabccabaaddcbcdadadbbabccadcdbbcccaadcccccddbbcddccbcddabcbbabbadbcbbcabdcccdaddcddbdbddabacbcabbdcbdbdddabbcbccadbcabbbaaccbbdbbdcccacacbcacdaabdbdaadaacbbbccbbcdaacaadcdcbdcaaaadcabccdacacdaaacabcbcddbccaaddcbdcaadacdcddbbbdcabcdcbcaabacacbacadbdadcbbdcccccccdcbcbcbbaddcaabcdccdbddcdbabcdacccadcbcadabdaacadabaaaddddddbbbcabdcacdadbbacadcaaddadcbbccbcbbbccdacbaaccbdbccdddadaaaabaacbbbccccacbaaddabbbdbcddadacadbcadbdadacdbabadcbabdaacbabddcaabbbbdadabacdcccacaacbcdbaacaaccddaabccdccbccdbbbcdcdcaabdccaaabadcbcdcbacccbcddaadaaddddbcdddddadddcdcdcdccbdccdcbabbabdbcdacbaabbaabbcbddacbabccdbddbcbcaccaabbcdabcddbddabadcdacdddaacaddccddbdcbdaabbbbcdcabacaabcacabaabccaaccdbbcbbccdaacddaddabcbbdcddddbabbabbdabbacddacbbddbabaaaabbccdcbddaccaadaacdcadaaacddcbbacbddcbadcbcdbacacbbcccccabaaaaddadbcbdabdccbbdabdcdbdcccbcdcdbadcbaccccdacbacabcaccbabdcdbcbabddddacdbdbccabdbabdbbaaaabcdcabcabdcadccdcbcddcbcbdcaabadcbcacacabbadcdccdaabacaddaadcacdadaaaccadcbdaaadadcbbdcccacbacacacdddbcdcbcbcdcddabbdbbbbbddcdbcbadcadbddbcacabcbbabdccbacaccadbbbaccbdadabdbbddaabbaaaddabcdabcdbabbbaacdddcbbaaaddccacdaddacdbbdbccaabdcabcbdbddddddbcdabcadddbcaddadabdadccddadcacadcddccaabbabdadcbadabcbccbdddccdcabccbcbdabccbddbdaaacbcdcbdbddcabdcdacccbbbcdaacbacbccbaabbccaacdbdcccdbbdbababbdacdcadcddabcdddddabdcccdbcaadcdbbcacbacdcbadddcccadcaaacbdbbcdbbaacddaabcdbcddcbbbbcddccdbacbcbcabcccbabbcddccabbcbadcddcdddbbacddacbcbcdcabccdbcdbbadddcbaabbcadabadcdbabbcbbbabbdcbcbbdbbaccbbbbddddbbcccbdacacbbadcaabaddbadbbbdccaddaababddccbaacbcadbdcabcabbcdcabbbdcbcddccbdbacbdcddcacadcbaccddbcadcbaabdccbbdbaddaacdcdcddddabdddccaccaabccccadaadbddabbdddbaccabdaccbadbaadbdadcbacbcbcdcbccbbbcdcadbcdbcbaadbcbdadbadcdcccdcbddddddacdbdacadaaabbadcddcaabcadbabaccddcdcdbacddcbbaabdbddcbadddcdaabdddcbcaccdadcdddcdacbdcabcaacccabaacdbbdbadccbdbacacbabdabdbcbcabddddbadabdaccdbaaaabbbdabacaadabdbbddabdadcdddcaabaaccacdbdcacbbcccddccbabbaacccadcdcbdcbadcaccaacdcccbcadcdcabcbdcabbaacbdbcdabccdadcaadbdcaaabacbcaacbdcbccdddcacccccbbcdadbbcadcabcccadcccaabaccbcdadcadaabdccdbcdabddbccadddbccabdcacccdbbacadbcbdabcabbadbcdccbdcaabdadbbadcdcbcccaaadcdaccadddddabaaaadbcaaccbdbddbbcddaddbdaacbdbdabccabbdbbcbddcddbaacbdcdbbcabcbcadcaaaacbcacaacdbddacbdccdbdbcbaaccbaaabadbbcdbbbbbacadabbcdcddcdadbcbbbabbabdcaadbabacddbdabcbadbbddcaabccabdabadcddbcabdccabdcaadbbacdbcbcabaacbbdddbabcabbaadbcdcdcabdbbdaadcadaddcaccdcadbabbcdbacbcbadbadbcacbabdabababbbbadbdcdcadcadbbaccccdbdcdbbabacdddabaddccdbdacbcdbcadbcdccabdbbccdddcdccddcbddbbdbccbcbaadabcbcdbdbadcacdbddbdcddcacabbcdbabddadadadaacbbcbacbbaadacaccdccccccbadacabaabcadadacbacacaadbcdbcacdbabcbacbbaaddbccbddbddbbcbdadcdbbbbdbbadbbbbcbddbcaaabacabadcbdabdacbbbacbcadcbccabcddbbbcaccdbccbcddacdcaadbdababbbdcbddddcccbbbccbbcdccadbdaaacaaaacbdaaadbbcdbdbdabbbbbbbcdacaccabbaddbdbcabbbcaddcdddabacbbdbaaaaddbabcbdbddbbcddccadbadadddbacabbadadcbcccdcbabdbcbbaabbdabdcbbbcabccdabcbdaaaabcbacaadbadcdcdbbdbaccddbbddccccdcbaadbbadcddcdbaccaaddcdadadcdacbdabaaccbbddbccaaadbaaddddcbcdbbbdcdcddabbabcacbbabcddcbacdbaacaadcdacaadbacabdbcdadddaaaacccbdabbacaacbacccbcdbcccbbbdaddbbbbabdbcabddcaccdaacbdabbabacaadbccbabdabddbccdbaacbddcaccabcbbcacbdbcabcbdbbcddabdacdbdbdccadaacdcbbaabbccbacccabddbdabbbddbbaaabdbdbbdccdaacaadcabdbdcadcdcbcadacbcbaadcdabddbabbcabacdcbabcbabbdccdacbddcbbdcadccdbbccacdaacdaccbdbbbddcddadbddaadddacbbdbddbadcbabadcbbccbaacddcdbaabbdbdbcbdaabbcdabcdbccbaadcdbacabdbcdcccccabcccbabdcaddddcacdcaacddaabcbbdacbdbddbacccbaabbbcddbcabddddadaaddaccbddadddbaacadcdccadaadbabadbcabacdbacddcabacdbbacbdddbbbadbbacaabbdbbabbacccadcabdbddcbaccdacaadbcbcddccacbcbcacbcbdabcbdbcaacbabcadcacabacbccaabdacadddbbbbbbbdddcbaabdcbccbcbbbbbcbdadbdcdddccbaadadacbddadbbcddbbaaccbaddcdbbdccbdacddcbdbdaadbcbdbcabbadddcabacbdcbdacbabccddbaddcabdddcddbbdaadbddcbbbbaaaccdacacbaaadbabdacaddddcaaacdcdacaccdcbaccccabcaddabbddadbadcabcdacdbcdcaadaabacaacddcddbdbccacbadacaadcdcdcabaaaccccbcbcccabbcbabacbdadabcdcaaadcbbadbadacdcbabdaadbacbabbbabcbcbbcdacdcaacddcaacacdbbdaaabadaccddbadabbcddcadbcbdcabcdbbdcbdabcdcdacacaacddbbcababcbacaaaadadbabbcddccabadbdadccaccdcabacddabdcbcdadddbbacbcccddbdcdacabddbadcbdbccaadbbaaddabdabadbcdadabaccbbdddcadbdaabcdccbaabadbacacbaabddaccaddabaabcddccdaccdadacbdcbdadaaddbaccdabdaaccacaabadaadbbdaadbdbdcbbadaddacdbcabcbaacdadbaacbbdbabdbcddbbdabdddbdaddbabccdcdcdcabddaacbabddccbcbbcddddbbcdaacbccabdddcddaadbccabbddbccdcdcdbccdcabdbccaababbdaaabdcbabccaababbbdbccdcdcbccbcabdbdbddbdcaaccccdabbaabadabcdcdcaabacabbbbacbbbddddcdddcccbbdcaaabddadbbcbdaaaaabdbcaddadacaaddcdcaddcaacdcccbdcaaabccabbababbabbcbcbcbabbacacbcbbdabdadddbdbaadbcddaababcbcdabbdaadcbacabdbddacdbbaabbcbbcdcdcdcdabcdbabbbbbbbbbcdaaacddaaacabbbadcccabcadadcdaadacbbbbabcdbcdbdcdcdbcbadcabbcccdbacdcadaabbdcacdbbbcdbccadbcdabbaadcbddacbddbabdbdbdcaddabbbdbaabbacacadcdaacbbcbbaaadaadabddcbdabdbabbbddcacaccbbddbdacaddaabcbbbaabbcbabbdacacbbabacddcdabaadbcbcdbaaabdbabbcbbdcbcdacdadddaaddbaabdcdcbbaadccdbbaddcaddaddbdacdaaacabacabbbbbdbddbcbdacccdbdddcbcddaacbcadcccacaabcaababdbacadaaabaadccdaddacdbabdcdcbcabcaabddcbddacbbcabadbacadcdcabbccadbabcabcbdddccabacbcbbdabbdccbadadcbaaacbccdbabdabdccaccddbcddcdcacdcccbdddbcbcdaabccbdcdbcdadbdddbddbdabddbcaccbccbdbcdabbacabbbcdddbbddabbbcdbbbdaabcbaaddaabbcdcbaabacacbadcdddcbacdcacaacdbddbddacaccddbadbbbdbbcaabcaaabaaccacadcabaacaabbbadcaacbdbbdbdadcdcbbdabcabaadacbaaadcadcbcbbcdbbabcdacddadababcadabbcdcadcdbdbcbcdcbcdabbaddaaacddbbbdbcabddcdcbaacaaaddcaaccdaacbaadbababaaacbdddbbadbaacdbbbdddaddcaccbcacdacdaddcadadaabbcdcdadddddccdaaabaddbcacccbbdadaccddacadadcacdccdbbbcbbbadaddddccbcbdbaddcbdbabcabbcaddcdadacbdbdaacaabcadbbacbbcacdadcbcaacabddbdbdbaadbdcccabbaaddccbcbbbadcabcdcadddddbdbbaddbdbdcbdbccaacbdabccaddcadacccababadabcaaddddadadddbccdbbbbacaacdddcccacbdaadbdacbbdbadbdbddbcadbabccaaaabacbcabdcadddcbcbadaddbaabadacaabcddaabcbcbcdcdcddaaddabccaddbccaccacbcadbcbdcbbaccaabdbacacadbdccbbbaddaaaabbcbbaddadabdbcbaadbdbdacacccaaccacadcabcddcbbcaacbacabcacbddadaabcbddbcbdbcdddccddbbbdabcbccdcccbbcbaddcbbcddadcddaacdbdadcadabbdaddaadaacacdccacacbacabdccbaabaacdbbbabaabbcacddadcbbbbbdddaacbddacdaacdaadacdbcabdbdadbcddcbcbadadcbcbacaccabcbcdadbdacbbadddcbcbccabdacaabbcdaaacdcbdbacaabdaadacccbbdcdbcbbbcdbabdacadcadbdbadbbaacdbcbbbbbdcaabdcccbbdbbcaabadbacbcdcadccbabcaacacdadccccaabacaddddadbddadccdaaddccdbaccbbccdbbbdcabbabaadccccccadbddaccdccbbdbbbddaadacbcdacccdaacadbcbabddcdacbbbaacbcddadbdcdbbdcaabbbabcbadbcbcbddbccabbbadccdcddcaadcccbbcaccddaaaabdddcdcdbbaaddddbcbccbbabdcabdaadccaaddbcbadbdbdbdcddcaacadacbcacdddabbcbaccdccdaababccccacbdbbabdbbdabccddaabdbbbdcbbdaabbbbdacabcaccbadcabdacbdbadacdddbbdbccbacddaddbcdcacccbadcaabddaccdcddcabcddbabcddbcbcabaddccdadadbbbcadbabbbbaabaddcbaabcabbacbacbbcadcadbbdabadbaacbcaaddddcabdabacaccddbddccbbdbdbbabbcaccacccaacaaadccdcdadcbdbcdccbdadaaacbacbdbdacddddaadbaddbbcccaabcacddddadbcccccdbcaaadcdcbcabdacbaadbbcdbadcadcdcdadcbbccacbbddddbaccddddbabbbdbdabacacbbacbdadcdddcacacabbbacaacbaaacdabdcccccbabcdbaccbcadbadacdcccabdaacaddaacddbbcccbbabaccaacdcaadcaaacbdbbbddabbcacdccaaabdaabaacdcbdbcbbdcddacdabbacdddcbcccaabbacbcabdbadaacaacbdbbaabdcbdabbabdcbaaccdcbdbdbdbaddaccbdaadadbcdadcbbddcbcccddcdcccabacadbddadddbdbdaabcccbcbdbdcccadaddbbddbbdacdbbcabaccbccaaadcabbcddbcaaccdccdbdacbcacdabaabcbccbdaaadadbaadcdbdbbccbdbcccdbcbbabbaacbccddddcabdccaccdadccbbbdaabccacccbcbcaddadbccadcdcaacdbcdccbbdddbdbadcabbabcaccdbcbadcbbccbccbadcababdacdadbdaacdcbbbbabccbaddddaacccadddbdddcbadbdabacacdabaabdabcadbbadcacddbbccaccbbbddddbabdccbcadaadadddbacabcdddcaaaadbbccbdaaddaccacbcbcaddaadcadcccdbaddaadcdbadddacddbcdbbbbacdbbcadabadcbabdbadcabdaacccdadacacbdadbaaabdadbcbacddbcbdacdcdcbcbcbcbcbdcdbacbdbcbbbcaabbdbcdcadccdcdacaaababccdcbcbabadaddaacaccadadbcbccbadabcbabdaacabcaddbdccbbbcadaabbdadbaadbbcacabaabaabcdbbdacacbcadcaddbdaaddbdcabcbabcbdbdabbaacddacabbdacacdbacacbcdccdabbaabbcacabccbdddabbccdbccabdacbabddcadcacacabcaadcaaadbdcbacdcbdddbddcdacaadbbdccabcccbccbdbacdaccdaaacdabbacbdbbddcabacaaadbdbbcaacbbbbcbdaaadccbdacadbdadbdadcbabcdaaabacacbbaabdadcccccdadccabbbdcccaddadbbdcdbcabbbdabbccdbdcbdbdccbbcbccacbddcbcaaaccaacacbcbaadaacadabccbadbbcdbcddbbcdcabbcdcbdcbbacdaccbcbdcdbabdbcbccdccaaddcaacdbabdcaacbddbdacabacbbcdaabcdcdaaadcdacacdddbcdbdcabacdacabdadcaabaacacaddccbbbdabadbdbbddccacabbadbddadaccbbbbacbabdaddcccdcadadaacbdddbbccbacadbdacbacaababbcacddadccadbcbbaccdadabddbcadacdcbabadbacbdaddbddadcddababccbbccdcaacadabbaabdccabddddbadbcacccaadbcabdbddbcabcadabcbddaddbaacabbbaddaadabdcbacdacacabbaadcbaaacbddbabdaacdbccbcbcdbdabcadcdddaaacccddadacbbcddbaadadcbbaadaacadaabaadbcdcbccababccbbacacddbccabbcacddbaccadcdbdbbbaadcdcddbdddadaccdbcadabdccbdccdaaaaddbbdcdbdbcbbdbccdacbcdabaadbabbdbcdccdbbabcbddbcacdababacadaadaacacacaabcabcacdbbcbbbddabbbacccaaadcdbccabdbbabbcaacaadaacabdbbddcdcacbdbbdcbcbdaadaccccdbabbdcddbccdbbcbcbddaccccdcbbbaabbacccbbadddaaaaccccbbdcccaacbdcaadacbabdccbdbadcbbcbbbaccdbdbdaccddbaaadbabbaddcacadcdddbdcccadbcbaadbbdddcdaabbaadcbdccbbabcccbdccadbacdccaddaadccccdaadbabadaababaababbdcdbdcdbdbbcbdbdcbdbddcabbbabcacadaaacabbaaacbbaacacbaccdcbcbddcdcdcbaddbcdbdadbccdabbabcbabcbdcbcabadcbbddddadbcadadbdbdcccdbbcadbbcacbddccccbcaadbccabacaaccbbcabcbbacddabdcccdcdbdcddacaaaaabadabdaccdbacacbaadcccdcdccabbdbcbddbddbadbbbdbdcdcacdccddcabaabbbadbdadddababbadbdbadcaddcbddbcdacdbdadacabaddababaaabcbbdddccbdbbdddcaacacdccccbbdccbdabdcaacdbbbaaacadcbdbbcacbaadbdccdbccbdacbcdcdaddadabbdadbcdaabbacbdaaacabdcacdbadabdcdacbcadcbbcbadbbddbddbddacccacadcaaacaddaabaabacdaaaccaadbcdadaabadbbcabaddadcdbaababddcddaadabdacabcabcdadaabbbcccdbcabddaabcadacbabadcdcbcddcbdddacbdacbaddddcacabccacbdadcbaabbdabbbbaacabddcdacdbcaabddccddddbcdccddbdbdabdcabcdbbdadddbcdacbbbcaaacabdacabcadcccbacbbdacdbcdbababccddcabdcdbddcbbdacdbacddccaccdddccaccabbddaaaddcdbcbacaabccbdcbadcdcbcbaadacaaaaaadcaaddccaaabdcbabbccaacbdbccbabcabdadaadccccdcbbaabdbbccdcbbdbcaadbcbccbbadcabbaacbbbdbdcdabdbbbdabbbaaabbccdaaaccadbdaabddabbbddacabaddcadbbadaabbcdcabccabcadddddaddcdccbbbcabddaaabdcabdccdbacacbddcadbbdccbadbaacabdbbdcccdbdbcbccadadbcacccdbcbcadbaaacccddcdcbaaaaddaaddabcbabaacdbabdaccccbddbbcadaaabacaaddddddabababbdcccdaabccabacbcbccbdaaabbadddcbadbbdadaacadcdcacbadabbaaaadbadcadcabccacaccbbccdcaaaccddaacbabacbabdaacbbddbacdacabbcbdbbdacabccaacbcdcaadbcdbbddcdadbbbaddaacbbaabddbadaacdcaacbacacadabdadcbbabbdacddcbbccdbccabcbabdbbdaaccbbdccdbaaaacbcdbdcdcadcbaaaacdaadbbccbddbbbdaacbcddbaddbbbbbbacdaaccdcaadccabdcdaccaadbcbbabccaaccdddddabbadcbcacbbababdccaabadaabaadddbddacacbbdbddcdbbccbbcccbcdacadbcbdadccdbacdaacccbaadaaabdacabbbdbdbacbacbadbbcaacacabbbacdaaabbabbddcadbaabadccdbdddccccbddcdcbdcaabcbcaabacbdbddbbddacbdcbbbdcdcbadbbcddbdacbbbadbbcaabcdcccabacdbdbaabdacaddacbacbababaaacbcccacbddcdadcaadbbdddabaabdbcbcacdaabdcbbddcbcabcacbdcbcdbcbcbabcbbbaaadabdcdadcdaacacdcadacabbbadacbacacabbaabcaabbddbcdadcdbcdbccaccabcaddcbacccbacacabdbdbbccdcdabbabadcbcdacccccdbabbddbcaaddbcdadcaccdacacdcadbddcadbcbcbbbcbbcaadbdabbdcbcacdbbcbbcdccdcdbccabddbccaabbdcdcaccdcdaadabdcdcdacddddbcbadcdadcbbdbccdcdcbbbcccddbcdbabacbccbaadddadddddcdaccbcaccbbadbabccccdbdcbdcbbcaddcaaabaddbbdacdacccacdbdbabddaaacdccbdaabaadccabcccabbcadcbcddbccdcbdaabdacbbcaccdbabdbabdccaadabddbcbbcdadbcadadcabcddaaabaacbbbadbbbdadbabdddbbbcbbaadddcccbcabddadcaabdbbaacddccbbbbcdcbcccabbdcbcaddcdccbaccbbaabcbaaaccbccadccaddcbaabcaacbcdbdbcbacbddbcdbbdddcdddddabbcacdabccdcaddabadacadaaacdadacabdbbbdccaddbbcddacdcbddabcbcbbabbcacbaabbaaaabdabbaadcabaacbcaaadcdccaaadacdaaabbcbacdaadbdddcabadbabbdabacbbdacdcbacbddccbbdccddddcddccdadcbccbacddbdcdcacbadaacdcdddddabdddcaabbbdccadcaadadbbcacddccdaaacbbbaaabdaaadcccabccdccbdbcccbdcacadcacddbcabbdaddadcbbdacaabbbacdccbaaacdbadcbddbaaadaaddbbccaadaccadbbcbbdcabccbaaadadcababbdacadacccbddcddccbbacdccadbabababcbacacdbbdcccdbadacbdcdacddacdcabaaccadccaaadaddbdcdbacaabcbacdcddabababbdadacbbcdbbdccddbadbbbabcdcbadbcbabbbbdbcbadcddabbdbddbdabcbdccbbcacdabadddcaacabbcbcbbcdddababcdaacabdbacbdbadaddbbdcbbcadcadbacbaddacbcaacccccaccbcacdcddbaadbdbadbbaabbdabddadcbabcbaccdddcbbaaaacaabbcabcdacabaacacaabdadacdbcbbdbabcabcaaabbcccbdcadcdbadbccadddacdbbdcccbaddbbdbdcdddacaddcbccadaaccbcbbdcbbdcbbcdddcbddcacacaacbbcaacabacacdaaaddbbdbcdaddaccbaddddbbabaaacadadababcadabbaadbdbcbbaadcabdbabaabbdaacabdddbaddccbacbaaddadcccdaacabdaccbcccabcdcdaacdbbbaaddcbddcbccdacdaccbdadcdadddccacdaacdabcbcdcacaaabddaccbbbaadbdcbdbdadaddbccbadaabdcdadacadbbdcaacbcdacbbccbddaaaddaaaabdbbcabbdbdbadcaaaccccacccacbadadcdbbaacbaccbdaccdbabcbcbaddbabaabcbdbcbacbacccadbdcdadddcbacbddcccbbdcddaabbddcaabbadddbdcbabaddadccdcabdababccdacddddbcabbdabdccdbdccababdcbcdcbbdaddbddbcdcbabcabdacbbacabaacbdcbacaabcdddbbbcaadcbdbdabaacbaddbaddcddacddcdddadbbcaddadbbddaccacddcacbaaccabadcacdbadaccdddddbccbdbbbbdcdbcddcddaabbbcbcbdaccbcbccaddaaaccaddbbbbcdbbccaabacbddddcbcdbbddcbdbbbcccabadacadbddccddbdaadddccdddaaaaaccbdabbabcadcbaaccbccddaaaddcddcdbaccbddbcbdaaabdabcaacdcaacccadbdcabcbbcaacbdbddabdabbdbbacbbdbcaddbcdbbccbccdadbbcdcbdabcccbccbdbdadccdbabdccbabaccabccccbbabaabacabacbaaddacdaaabccaacdbbdbccacdaabaadbcacbabdbbdaccbbcdbadddadbcbcdbdacadcbadccaabdabaaacdbaabdadbcbadababbbbbaccbcadcdddcccdcddddccdacccaacdaaccccddaaddddacdacbbacbcbdbdbacbcaacbccbadbacadabddbbbdddcdacbadaccabdcddccacbcbabdabbacaaaddbbdcbdddcccbbbcdcbcaadaacababacbbdadbbaabdbddcaabcdbbcabacbddbdaddbbbddbbccbabcbddabbabcbdacacabdbcbdaaaadabbbaabbabaadcacbaaadaddddcdcbabbbdabadacaabdaabbdbbcacbcdccbcddcddccbdccdcdbacabdbbaaddccbbbdaabcbddccabcbbadddabcabadbddbcaaccdaabcaabbddcddcaaabcadbdbcadcacadbabcdddaddcddadbaccadcdbcccbacbbbaccbdadbdcdabcaaddadcdacdaabacdcbcdbbaccdbbdbcbddabdddccadcccbacddacbadbddcbdadcccccacaabccadddbacaaaccdabdcadbdbbdbcbadcbabadabdcddabacdabccacabcdbdcacaccbdcaaabbdddcddacdbabdabdccbdaadbdcdcdadbacbabdbabbdcccadcbcadbcccddaccadcbcdccaddadbaabaccdbabdadbcdbcddcccbadcbaabaacaabcadcbbcbbbdaacbabcdddcbcbccbbbddacbacabddcbbbcdcbcdbacdaacaacdcadabcabbbdaccbccbcadccdcbbacacbacadcdacccdbcbdccdbdcabbddadbbcbcbdaccccbadadaabbcddbbbdcdaabddaababcdbcbbdcddccbbdcacccbbadbcddcacdbbadaabdaddcbccbacddbacddbacbabccadcbbcadaccdbbcaaadacdcacaccdcdbdbacdccbabacdbacaddadaddbabddabdbcbdbcdccccadccdaaadccbadddcbbcacacdbaaabcbabccadaacccbdabbdbbbadbaacabadbabddaabbcbbacbabbdcdcdaacbaadbbbddbbacbbadbdcdabcbcdcdaacdaaabacdacabbdaaaaabccbcbccdaacbadbaaaabddaaccdcdadccbaaddcacdbccdbddbacdcdbbcbdbbacccdcacdbcacbcdbbbcdcbdcabbbddacbbbcddbcadbcabdcaccbbdbccdaabbdaddcabbabbcaabdbdcbccabbbbbacaccadadcbcbdcbacacddddacbcabcacbacdacdaabbbaabaccdbdcdcdcadcbacbdcbcbaccbaddbbbacacdcdccaacbcaaccbccdbaabaaadbbabdbdaccdcbbadcddcbcdbdbcabdbcacdcbdccdcbdbbddccabcdcbbbbcdcccdbdbbacbcaddddddbababaccabaccacabdaaaaaabbbbbbbabcddcaccabcbadadabadcadabcdaabdadbbbdcdcdcbcbdcbdcaaccbaddbdcacacdbaacbcccacbbaacccbccccaabbccdcdddadbbcddacccddcabbbdabddcabadcbbccbdccbaddabcaadababbabcabacacdcbdcdcccacabadacbacacdbdccdcbbacdcadaccbaabadbddddbdaccbacbdcaadabcabbadabbadbacbbbaacaadabadccccdaddabbacacdbacacabdcdbcbcadbcacacaadbbdccccaccacabdcdbcbdcdcbbbbcdadbcdaabbacbadddadcacccddadaccbdbbbbdbccabbaacccdbcbbbbcccaccbbccdcaaadbbbcdbacddccabacbcbbbccddccbcaaddbabbdccdaccbcdcdadaabbdabccdacdbdbdacdbbbddbccdabddabbdcccbababcdadbadbdbdbdcdddbabadadddddacdddbcabaccdcdbaddbdcbcbbdbbcccdbacdacadcbacddabbadbabcbddbcabadbbccdadcccdcdcbacccddaabcaaaabbddcbcbadbdcbdcbbabcdadccabccbacabcccbcaddacaccdccddcbdbdddadabccbbaacbddbbbcccaaacdcbcdaadcbbdcabbccabdbbdbdcdcbabbcbcdddbdaaaaddbddcbbccabcbcddbdcbcbdbacdadaddaaabdbcbcaddccadbaacbadccbcbdcbacdccbdaaacbcaadaacbcadcbcdadbadabbacbabbacbddbdddacbcddadcddabadaaacbddcbdcababdcaccacbcbdbcabbdadcadbdadcacbdbbacadcacaabacbdcadaaabbdacdccdbbadaaacddaaaabccddcbcbbadaaacdbacbdcdaddccbcccccbdaabbdaddadcabbdcadadabbbcaaabaccdcccabbcaacbadbdbbabcaadabdabcdbbdcacaacabadcdcacdababccadcbadbaadcaadcddacadcbbabcacabdbccbacbbcaabaaddacdcbdcaaacdaacabaacbdadcadcbcacdddaaccacabbbcacadbdbbcbbddddbccdbccbabbcabbcbcdaddbaaadbdcbbbdadabcdcbdbbdabcbaacbccbbbcacadaabbbcdaaaabddbdcabccbdbabdacdcadbaddbdadaacddaddbcbabdbddbabcbadcbadccabbabbadbddabdddcddbaadbabaacbcaaddabdacaddcdbcbbaccaacaccaddcabbdddcbbabcdadddadacccbaddcdbdcabbcbccbcbcabdbbdadcccbaccccabbdacbcacbdacadcdbbaaaccaccaacdcaaaadabdddcdcccbddbdadccbcbbacdbddadddaabddacabcbdbbdabbadcaadabbcadccabccbcabbbbddbdcabcddbaaadcbccbabadcabbcbabbdbddbbdaabacabaacaddbdcddbcbcdcaccabcaadaddbbbadcdaddbbcdaaacbdbacddbbcacaddacacccabbbccbdcbdbddaabbaabadcddcabcabccccaabcbcbaaabcccbbdbccacadadaabdbcdbaccbcbaaddcddcdbccbcaacbccacccdbcbbaabdbcddabdbadababbdadadadcccababcabccbcadccdccbddcabacdaabbabcccabcdbabbdcbbdaaccacdbbbcacddbbbbcbdddbbaddbbcccbacdbbbacddadcccdacababbccbbbbadbaadaadaaacadcabbcccbbdbbcaccabccbbcdbcdcdcbccccabacdbccdddbdbacdaaddbccdaddaccabaacabcccaddccdbaaccadccabcacabbbbbdabacbbbaddcdacaacdbadbaaaacacacbabbbccccadacdddadbbddcbcacbdbaacbbdbcdddbbdddaabaabddbcccbbdacaacacdbdccadbdacbdabbbddcccddcababddcdaddcdcddababcacacbdbacacbdabddabbccdbacccbddabdcaacadbbcbdcbbcabcccdddddaadcccbbdbcbbbdadbdcdaacbdcbaaacbdacddddadcbdbcdcddbdcabddbddadcbccdabbbcddcadddcbadccbcaaccdaacbbbddadadcabdadcbdcbabbdaddbcdacdaccaacbdadbccacdacbcabcaadcdccbbcbadbdabcadabdbacacbbadbddbccbbcaadbdacccabbcdcaacdcbbcbdbdbbcaacacbbbbcbcbcaadccdabcbacadddcabaccbaacdccbdbacbddbacbacadcbcbacbddabdabbdbbcddddcbaaabadacbcdaacdccdacbcaaabcbddcddcdcbbacbdbbcbdbcaccdaabaacdadbbbbcaddbaabbdcaddcbbbadbcdbdbabaddddaabaaccdcaccabcddcaddbdadbccbcbcaacbbbdbaadcddcabaabbcbdbdabaddcddcaaacdbabcbbcbcbdcdccbdddadcabdbdaccccbacadbbbbdcbcbabacbcaaabcccbcbacadbabcdcbdcbcdcadbacdacbbbbaccdccaabbabcadadadddbabdcaabcdadbbdbccbaabacaaadbccbaddccbcddcbdabbcabacdaaadcdbabbaaadbacddcaccaaccbdcdcdabbabacabddaaaacdddaabacabccddacbddaacdaccadbdddbcaacdacadbaddcbadadbabbbdcadccdbbaacadbccdccaadccbdcabbbbcbbbcbbbbdaacddbdaacdbcadbccbdcacaaaddcdadcaababadadbbacccbcdbbaadcdcdaacacbdbaabababdaaccbcddbdaacacccbabdcddbdaabdcbcaaccaaababbbbcbddbacbdaadabbacdbadddbbccabdabcdccddabddcdbdccdcaadcbbdaddccbcddcadbaaacdddadbdbdadccadabaccdcbacbabaacdcdbccbaccccddbbccbdbcabdbbadcabdabdbadcacbbccbdbadacadcdddcbccdbbcccbdadadaacdcaabcacbddacabdbccaaaacdcbdacacbddbbbdcbcbcbbaccddbaadccdaacbddbaaabbccbbcdbbdbdbccaabaddbbbbbdccadcddccbddcaddaabcdacbbccadcadaccadddccbdbcbccdcbcbdcdbababaddbaabcccaababbbcbaadaacdcbcbbbcabdbcaabdcabbadabcdabdccddddcaccdadddccadaacbbccbdadcdadccbccaddbdabdbdddbcbdababaadbcaaabbcabdaaccbabbacaaabcaacdaaabcabaadcbdbddabdbddabcbccaaacaaaaaccccdddcddbbcccbadadadbbcbbdaccbcaccaacdcdadababdcdbdbbcdabadcdbdcddaccbabcddcdbcacadddbccabdbacabdbaaaddbdcdacccdcdabaabcdabaaccddabbccbdcabcacabbbcbcbddbccaaaabcddaabcbaddbcdbaabbacbcbbcbdbbdbabdabdaadcaadaacbccadbdacbbdaaccabddbcadddcbcaaabacddbdbdbdababcdbcaadddbacddabacacadbdbbadacbdaaaabbaaadcabcdddacbdbcdbaccdabddadccaddadccddacbacdacccddcdcabadaccacacbdcbdddbbcbadbdcbabacbaabbddadddcddcddcdaabbdcabdadacadbcaacadcdddaaabcaaccbcbacddbaacdadcdaabaddacabdddaddddcaccdbcbbcdcabdadccbdcabbddadddcbbcdcadbbbbaadcbdbaddcdbcbabbbdcabdabdcaccbadaccbdccbdbadccddccbdbcddccaaccbdbbbdacdaaacccbbbaabdbcacadcdaaabaacccacabcdccbcabcabcbaabcaadcbcadbdbaabacbbbacabddcccbcdbbcccddacaabddddacdddbaabadcccababdcacaccacdacdbbddbabaddbdabcdabaacdbbcaaaaacbbbabaccbcaddcdbcaaaddccadbcadbdbdcdbbcadccdaaacaabbacbcccbcbcccabaadaccbaddcaabaababbcbacadcadbbacaacabcbbaacbcdbbadbdbcbbadbdaaadaaaccdabdadddccdccaacabadbcdddcabdcdabbccddcaabacdcbcbaacdbabbccaabadddddadcddddddbcbaaccddacccbabdcaacdbdbbabcdcadddbbbddcddbbdabacbddddaccaabaaaacccdbbdddaaadddaacddcdacacdcbcaacacdabaabdbbbbcbdabadcdcaadbababdcdaaabdbcdacbcdabbadbdccacdaacadcdccdddcdbdcbddcdbbabddbdddcdaddcdcbdbdaacbacdcbcadcdcdbbbccacbdccbcacacbddbbbcbcadbcacbabdaaacdbcaaccdddabcbdbbbccbabdabccbdabcacbbddcaddccbcbcdabcbabbbcadcadccacdccacbdbcbdadbddbcacdbadadbdacdaabbddbdbdbbbaccabdcaabaccdacacaaccbdbcaadbdaccdbcdcdddccaadbdcabcdbddddacbbabaaaabccbbdacbbbbacaabacdddbbccbdcbaaaddbbbbbcadddccccdccadddbcbbdbacdbdabadcdcacacbdcbbdcbcdbabcaddcbdaddcbccbcabdaddccdcbcbddddabdaadaadabacabcdacbdabddaadbdcabcacadcdcbbbbabbbadcabcddababdccccbdbadaabddddcdacddacaadadcabbcddccabbaabbbadbdbcbcdabcbcadbadcaddbacadcdddadddbddaabccaddcbadbcbdbdabbbcccbccddcddadbabadbacabcdadddcbabacbcdadababacdadcdaaabbbbdaddcddbbbdbbbaaaabababacabbdbdabdcdaaacddccccddaadaaccacdadddbadbabcaabcdbbbaadaadabadcacdddacaacabbcaddabbdaaddbbbdcdbabbaaadcdbdbcaacbcdbbdaaabbbabbcbbbbabbdddbacadbddaaccddbdccabbdcbabbcadbababadccdbabccbbdbaccacbdcdcabaccbcdacbcdccbcadbcadcaadcbdcbadcdddaacaabaccdbcbacbadbcdbbbbbcdbdddbcbdcaadbcdcacaacadbacdccdadabcaacbccdcaaacccaaadbadbcaaaabdcbabcbbaddbdbcccbacdaaacdadbddcbdbbacaaabbacdabbddbccaadbbcddcbdbddccaaddddbdabbcdcaccddddccabccaacabdadbacbbcacbabbcdbbacbdacbcbcaccdaabbcdbccacbadcadbadbcccdcabbdbcaabcdbbbaddddacadbdccddabbdbaabdaabddbadabdadadcbdabdadbbbcbdbbacacabbbbdcbccccacbaaddbbdbadccdbadccddcaddcabbbcdcabacaaacdabccdccbcbcdcaababbbcddcabadacabbbddbbbbacbacbabaacbbcbccbcdacabcadddbdaccccababcacdcabcbddaabababcddccbaccddcabcddcdbbaaabcacdadcaabcbaaabaaacabdbccbcabdcdacbaddddbbccddbabadadbdcccbdacbbddcccdddbdcbadaaadcbdabccadcbcaaadaacbdcccddbbcdccddabadcadbcacabdaadbcadaabdadaaabcacaadbaccddbcaddcbcdbddbcadbacbbaacadbabadadbdddbdaaccdbbddaddaacdcaadbbddbdccdccccbcdbcdbacbdcddbbadadbbddabcdaabadaacdbcccdddbddcbbbcbbaaaaddbbaabacbaabdbcbabadbbaaacbcbacbccbcbacdaacccdbdcacddcbabbdabbddbbaaccbbcccbcaacbbdcbbabbbbbccbddcdabacdbabdcbabbbddaaaadbbbabbcadcbdacaaaccbcbaccabbbdccbdabdcdcbcadbacbcacbacccaccddaacbcccdbaadcbdcbdacbccaccccaaaadbbadccaadcdccbabaaaccabbbaabadbdaaddcdbbdbdadddbdcbbbcadddcbaadcbcdccabbadccbcbddadacbbccacabaccdadbabcccadbcaddddabacadacddccbbbdccdaaddcdbbbdaababbccabbccabadadccdbdcdbcdbbaacaacccccccdbdbbcadbdaadbddaacccbddadbabccacdadadcabccbddaabdadddddaaabbbdcbaaddbadbbbbbbdaccccbbdcdabcbbdcaadccaadbadcdcdccdcadcbacdaadbaaabdccbcbacababcdadcbbccccacccddccbcacaddbdbbdddbaccccaacdcbaccbbbcccbadcbbbaccaacbaaccbcabbbaddcbacddacbacbbbdaaaccdddaacbcabccccaaabcbcaccbbcbcaacbcdaadaccdbbcbaaaaadaaadbcccabdaadbcdbdbbdabbacdcbabacbbcaccaaacdcdadaadbabbbbbaacbaaabaaddcbdbdcbcdbacccdcbdadccbcbdcbdbbdbdbdcabbdbaacabdaadbaccaabcbadbcbbaadcbcbdcddcbbdaacababccabaccddbbcbdaccccadaabbbdbdbbdccabadadacdbccbabcdbccaadcaadbdacbbcabdacbaacdabcaadcdabadaddcaadcccddbdcabccabdaadccccaaaacddbdcacabbcddcadbbaabcbcaaaccbddcaaaddcdcccdaccddabbadcaabcacadbbaaacdbacaadcacaddbbbcbdbcadccadcdadadcdbbadaaabaabccbbccaaccbccccadccabcacdddbdbbcbdccdbbdcacdbddcbacccbdbdabbcabadccccbcdddabbbdabcdcbccbcdbcbcabcababacbbcdccbddddbdcbcdcadaaaaaaccbaacdcdbabcaabdbbcaacdcbdadaaacacdbcdcabaabcdacccdddbdbdaadaaaddbcacaabccdaabccacbddbacbdcadddcaaccccdaadabcabccadabdacdbdccbbbacbcaaabdbdadcaaabaabccdbdbdcdbacbbaccdbccadbbabbdbdcdcbbacbdddbadbccaadadbdcdabccabddcbcdbaacdbbbbddcbdcdccadcbbadbcaabbbccccdddbadbbaacbddccaabacbcdaddcbbcbccccbccadabcacbdcbaacbdcacbbccbbbdddccbdbdcbdbbbcbbbccddbbbbabadddcdaccdcdcadabadbbdbcbddacccbdbdabbdababbcaaaacdbacaabbbbabbaaacdababaccaaabbdbcacbacbdcadbbcbdbdbbdddcbcabadcbbbbcdbddcddaaadabaadaaccbdaaddaaadbccbaddabcdcabacccadadbbaddccdcdbabaaaadbddaccaadaacdbbabddadbbbdacbbbdaadddcbddcdccdbbaddcbdddcbdcbdcbbacbdaabcadcbccbbcddacbcbcadababcbcacacaacbcaabdbbabcdbbdcbaababbdbdcbcbbcacaccdadccbdabbddabdadbaddacdbbcdbbadbabdccbdbbdccdaacccdcdddbbcdbbccdbdcdcbbbcbaccdcaaddaadcddcbcccdaccccabcddcaddcbaacbccdcbcbbacdccadcbbbbbbbbdaacdbbcbbdcdbbdcbaaaddbbbccdaacbbdddbdcdbadbacabcbabdcabadaaacdbdcaababbaaabbabccbabccbadcaccbcddcbdbdbbadcdcdbbdbacbdbcaccbbbcbdacddcaaddbaddcabbdcdabbaddbaacababbddababdbcabbabbdbdbcbaddbbcbcdaaacbddbabcbabdcbcbbccbbcbbbcbababacccadcbcbbdbbaabbbdbabccdcdadbcbabccacbadaddbbdcbcbaacbbabbbdcacbcacacabbaccbdabadccbaadabccdcddcabdaccbacdbacdbbadddcabbbbacbcdcdbccddccbbdddaadcddbadbbcccccdbacccdabadaaccaabcbacbcaacdbdbacbccddddbdbbbbabbdadddacbddbbbbbbbdbdbbddabdbcadcdaddbaabcaaadaccacbcabcdbdadbbbcbaadcdcdaddbdcdbcddcdddccdcccaccdaaacccacadcbccacabbdaacbdaaacdcccdbccddddaddadbcddccccddcdddbbdcdbdccabdcaacddccaccbbbddcaadbbabdacccdaacdadccbadccabaddacaababdbadcdadbbadcbabddbbcccddbaccabdbcbccdddbaaacccabaabaacabcaadacdcdcdcbddaacdaadbddbdbbbcabbbbbcadaadcaacacddbaccaddcbdccabbcabddddcaccaaabdccccbbbadccabddaaddbdbdbcabababaabddcddcbccbabddaabbacaccbadbcacbdcddbbbcddbdacdccadaadbbacdcaadbcaccdbadaaaadcdabbcddbacbcbdbacdddaaacdbcddddbdadacbbacdddaaccdccbdaabccacdacbccabccccbccdcbdbbabbbddbcadbadaadcaadabcbbaddbccbbdbcaabaaadddbdadcaacbcabcbdabbdabdbaaaacdddcbddcaaadbcbcaadbdadabbaaaaadbdadddcdbbabacbcbaaaccbbcbbbcdbacbbacababccdadbaaabcdcccdaaadcacabacbabcdbcbdbdcccccdcbdbdbcadcaaddabcdcbadbcdbcbcaacdbbbacbabccdabddabadababadcdbbcbddbdabcbbddabdddbbdbbcacdbaaccacabbcdbabdcdcdaccdcbbaabacbdabbacaaccbaacbadbdcddcdacbbcbccbacccddccddbcdabdadabadadcbccaacaadccbcbdbbbbadcbdaadaccccabcddcaacaabbbcbadccddababcadddcbcddcdbcdcaabbdadbcaadadbcdbcbdddbaaddcdacbbdacadbacaabcdcacdbcbbbdbcaddcdbccabbcdbaaddbdadabdaccdcaadaabdcdbbddcbdddcbcadcaddbccbaadccbbddadbdacdaabcdcdddaccbcdbddacadcdacadaacdaacbabdcaacaaacbccaabcdabcabbabcddcbaaddababdbadbdabbbccdbabddddcdcabbcccbabbccbcbabacbddcacddabdcadbcaadddbbbbdcbcdbccaccbccabbbabdccadcdcbdadddacaaccbcacbdbacabacdcdabdbccaccbdcaccacbcadbdbabbabbacbcbaccabbbacaabbdaabdacdabdcddaadddbcdbccdacdcbddbaaabbddadcdcbcacdbaabaacdbbadcaccbdadcdddccadbcbabaaddbadbddbcbaadabbbabcadccaaadabdaabaacdddcaadcaddddbcbccddbbbdbadccabbadaabbccdaadbcaaddccdccdccdddaacbdcabbbbbabaaadcabbdacaaabbbadbabccaadcaabbbbaabccdcdbcacccadbcdbcaacbcababddbdcddbbabcdaaccdbbcdcbdbdcdbadaabcbdbcaaacddcbbababdabdddadbddbcaabacbabbddbcccacbbccabbcbddaadacdcbdabbcadbadacaaacddcdaacacbbabccaadddccddccbbdbcabdcccdbbcaddcacddabdadbcbdbaccccdcddbbbcbbbbcbadccdaddcabbaaaddbaacdabdbaacccddbcccdbbdaacbaabbabaacdacddbcababbbbddbabaacddadcaabaadcddacdcdbbbdadadddacdcaaacddbdcddbcdbabaaababcabaaadccaaccccdcbbdbbdbadbcbddddaccbadbbcdacacbacbdcbbadbbcdcdbacacbbaaccbacadacacacddcccdddcbaddbbcaddbdcadcbdbabcddbdbabdcaadadaacbacdabcacaadbaaaacdababbbcdbcdbbbdacdabcacdcbdabddbbdaaacbadddaaacdddbaadccdcadaabccbcddbbcdcbadbccadddcdbcdccbcaabcabbddbdbcbcbdbcbccdbccadcaddbcccadbcabcabddaacdddbadddbdadbbadabaadacbcbcbbddacccbdaaccaadcbbabacdabacadddaacbbdcaadbdccabbbacddaaaddadccdcaacbbaddccacaccacacbcdaadddbbcadbdddcabacdcdadbcdcbbdaaaabdbcccabcdabddaddcabcaddbcbdaabaadcaddcbbcacbadadbaaadbdadcdabbdaabcadacbbccabcaddcbaabcaadaccdadddbcadccaaaadccaacbbccabcdbbcabcdaccaccadadcaccaabbacabababbddcadacdbbdacdbaadaaadcbaaadacbaabcddddabcbaddcacdddbdaabdabcddcdadcddadacdddaddbbcbdbacadcbbdccbcaadaddadadcdbbcddccdbbccabadbbdbdaaabadbcccbcbdcacadbbacdaabcabdddabcbddcbcaccbbbbbaacacdcdacbbcbbabccddaacabadbbddbbcbaaabdbdaddcdddcbcdbcddbdabccdcdadbabbccddddbadabadbaabccabbdadccdbbadbacbabbdabccbabdbdddabdcbbbdcababaadcbadaddddcdaaaabdaacacddaadbadaaacdbddbacbabacacbdbcbdadccddbabdcaaacaaddadbacccabaaddbbcbccbacdccbdabccdbdaccbcbbbabcbbadcdbdcdababbbdbccbcacccadcbbabdccdbdcdabddbcacddcdbbdbcdbddabbbcbbaaaaacbbdbddbacddcaaccbccadadcdbbdabccacbdabcbbcdbcbdcbcdcbabbbdcadcbbacbcbadabdbcccacccdcabcaadbcbdbdbabacdcbddbabccccbcdbbcbdacbaacdadbccacadbbdacaddcadaababdcbdcbadadbdbcdccddaccadcabddccddbcbbacbcaabacdbcabdadaccbdabcbddaaacdacbbcbdbbbbbdcadcacadddcacaabbbcbcdbbcccacbbdadbabdbbdbcdababadcdabbadbbadbbbbbdaaabbbcdacdbaabdbddaccacdbddbddccdcccdaaabcabacacbbdcabddbcccddaddbcdcdcdaaaabcaccaccbaccdcbaabacdabadccbabcbddbaabccdacccdaaabcaccdddbdaaadaaabcdccdbabbbdabbcdbdbadadcdadaccaaccaddbcbaaddcddaccbcababcbbbabbbdbadabdbccbbbaaddacddbaaadcbaccadccabcaaabbcdabbccabdcaadcacbbcbaaadadbcadcdcbdbacacadcaaddcccacbdaddcbdcbabdacbcaccdcadcacbbddbadcadbbacaabdcbcacbbcaddbadacabbdbcaccbbbaadcbdaabbdbccbccdadaacdbddacdcaabcbdcbabddcabbabcbcdcddbdacbbddddcbdbbdbaddbcbabbccbcddadddbcdacaadcbbcbcdcdbbbcccdabbbdcccddabbdbadbcaddcacddaadbcdddbddabcbbcdbcbddcdcbbcdccdbddacacbcbbcbdaacacbcbbbabcacddbdcbdbbbccddbbdaabaccadddadaaabdaaacdaaadcbdcdbadacacdabbadabbddcbdaabbadbdadbdbdaddabccddddbcdddacbcdbcaabbccbbbccacccbbcabaaacbaadabdacbccdcbacbbcdbdadacadabadbdddbacbbcaacabaadadabacbbdaabcacdaacaacbdacbabcdabadccaadcaaabbddbdcadddbddcbbbdbddbbdacdcdbcaacddadbaccaddcdbbbdddbddddbadbcacaddcabdbbcdacccacadcacbbaddcbccbdaacbccadaddcdadadaacbaacddaacacddababbacddbbaacadbcdcbbdaaccbcaabcbccbcbbcaddbcaccdccccdcbbcbdbdacdaacbbaaabcbcbcacaadacddcccdcdbdbacbbbadbadaccdccabccacabacadbcddddaadadbccadbdbcdbbbabcdcadaabdbbcbaaadcabadbbaaabbaacbbdadabcdbddbbddbbcbbddbdbcbcabdacbaaadbacdbbcacdbabbacacdbdbaddbbccacaabaccbacbbdccabacadacbbabcbdadbcaddddacadcdddbbbbbcdadbcbbaacbcdcccccaabccbccbaadbaaabaaddcabaddaaadadbadadbabbddaddbadbcdcdbcccabadcadbabbbadcaaaabdccdcbbcdadacdbbccdaadddaadcabdcbbbcbdcbdcbadcdbddacbbcaacbcbddbaaacdbbabdcadcdbcbbcddacbdbdbcddabacbbbdacbcbcacbbccccaadacdbdbbdbdbacbcaccabcbdbbabdadabbcbcadddabaddbdcbdacddbbbcddacdccacbadbdcccaaaaaadbaddadbbaadbdadbbcdddccbadbcdacdbccddbbddadaddacaccabcccbdbbccccacabddabbcdcdbcaaabdabdcabbcadadbbddbdbdcaadbcccddddbdaadbbccaddbaaabbacbdadcccaabcbdcdbadacdbbadddbdabaadbdbacbbcccabddaaabcdccdaacacacabaddacdacabccbacbdaccadacdccdcadbdcdcacadabdcbaacddacacbdddcdbaccbdabcbdcdabaacadadbdcbcbcdadddabdacccbcbaddadcababacaababbbbdacadcdcadbdcbaaabcaccaccdacacdacbaaaaabaccbcabbcbbbcbbcbdbdabdcdabaaaccaadddadbdadbdbbacdccddaaddbdbbdbdabcacbdbabdcdacddcaadadaaabdbcbbbabddbbbcadaabbdbcddcdabbcababaacddddbdacbbacdbdbccaaacddccdccdbadcbabcccccbbcabaccddacbdacdccdabbcaadcaaababddadbccbbbdbabdaaccdbabcdbbcdbdddcbaaacdadddbcdbddaadcbadaccbbabadacababadbbdbcdaabccdbbaadccdcdbdcdbaccadaababcdabaccadacbbcabbddadcbadabccbdabcbbabddcdcbdaabbcddbbbcbbacbbaccdcbababaaaabdbacabaaaadbcbadbbbbadadabcbcdcdcacbccbccccdddbdddaacdcdaccccabcbdbbbdddcaccabdbaccbdbccdccddcdcbbcdacabaabadcabdacccdadbabccdcccbaddcddccadbbaccdaaddcbbabcbddaddadabbacbbcabcdbadabaadadcdbacaaddddbacacacabbdaadbabbdbacdbcbccabdabddaabaabababcbddaababacaadcddbadcbacabdbdcbbcbaaabbbcddddbddddabbaccabbaccdaaadbabbabadabadabcaabcaaabdacaddaccbdadaaddbcadbbcddabbcacbdaacabcaaadbddcdabcadddcadcaddccadabdaabcadcbbbddbaabbdbcbdcdcdbabcadddbadbdbdccdcdaaabbdaadccadbadaccaccdbbcdcaaacabbbcadaabdabbaddcdccadaaaddbdaabcdaccbbbdbbbadcdaaadbdbadcdccaadaabdbdabdaaadcaaabadbbcdcccccaaddbccddccacbacadbccbbdcccbaacccbbbbcbabcdccaabbcaababbcbaacadaacbbdcbaabdbccbcaababbcccabdaabbcbbccbbbcdbadcbcbacaacdccbdbcaabbdbaaacdbbbdbcabbbcdcaacadcacadbabadbcdbcacbddcccccdadbbcbdaabadaddcadaabddbabbbccdbbadbdddacdbcbbcbabdadcbaaacbccdaccdaccbbddcadbcbadbbbcadcccdcdbdcabaaaaabaacbcaacacbddddabddcaddbbbabccaddcddcbaaccbddbdaabdabbbaaccdabdabbcddccadaaabacdbdcbbdabdabadbcbcdaaadbdabcccacbdcbbdcdbbadacbbddaaaccacbdbcaccbdbaadbbdbdbadbdcbbdbcccccabbcbcbadbbdbddcbbacdbdcadcaaacbbdacababbdadccbdbdbbcdbcaaccacadaaadcddbcabbaddcabcbdcacabaaddcdaacaaabbbaaaaaacaacddabbdccddcdacdabacddaddabcaabbcbaccdbdaaababbddcbbdaaacccabdcacdbcdcbbbccaaaaaaadbaacadaddccddadbaabdadaaabaccbbbaacdcccdbadbdadaddbbaccbbaacabbbdbdbdadabbdbadcbdcdbcbcdacaaacccccdccabdaaabbadcabbaaacddcaddbabacbbccbaddcacbcacaadcbddcadadddacdcacbdaaddbabdaabacadbaaacdaccabbbbbcabaccbbcaaabbaaaadcccddcccccbdbcbbdbdaabcbddacdbbabbdbcbbbaadbbcadbbbbdcdcabbccdcacddbadbaadbbbcdaabaabcabbaaacadcbabdbbbbdadcaadabadcbaaddcaabbdbbdacaababbcccbccbcdcdacabcbaabbaabddcddbaccbcccccdcaddcacbaccabbdadaacdcdacdbbabcdcaadaaabcbddbabcaabcddccbbadbbbaaabdbdbcaddddbbbdcbbcbcabddabcdcbdbabdbbdbcabbccaabdabcbdbcacadccbcaddccdccbcbaaaabbdddcdaacdbccbbadcadadacbadadadbdaabbddadacabbaaadacdbddbbcaaadabdbacdaadaabaaabaaaccbbbbcbaabadcdccbdbbcbbabacbbdbdcdbcadbacbaaccadabcdadacdccdcbdcdbcbcdbbcababdaacddbaccdcbbabacabbdbbabdacccdaaacddcbbcdbcdbddcbbdbadaadcdcbcdabddcacadbddcccbbddddcdbccdbcbdadaadcbcccdbddbaabbcbabadcaacacaaccdccbdbccbbbdbacdaddccdabdacdacdcacbbdbdaadabcabaacacbcdcaabdbbccaddcabccaccabdadccadbcdadbdabcdbbcadacacdbcbbcbabbdabacdcabbcbbdcdbddbacdbdbbcaaacbbcaccdcdbbcadbdcadcbbcbcdacabdabcbbabbacdddbadaaabdcacbadcaacbdcbbdbdcaababbdbabbdddbbadaddccbdbdacbadacaaadaacaaccadbacdcaadcbaadcdbcdabddacdbbbdacbbadbcbaccaddbcbaaabdaccccdadcbaddbaacbaaddbcbcbdddbdaabacdcdccdddddcadaaaabbabbaabaadabbbcbcbcbccaabdccbbbdccbdddcabcbdbbdabcdaccaaacadccccbbddcbaadbdbabbacacdacbcbccabbcdadabcaacbbdcdabccdbcaaacabcdcccbcaacbabcacdbddcacbcbddabdcaddcccaddaddddcdddcaccbdcddcbcaccdcacdbacacdbaabcabbdbccdacddadbbccaddabbacdacbacdaacbcaccdcdabcacbcdacadabccaddcdcdcccbcccbadcbdcbdbcddbbacdaacdcccaccbddcbbcddaaacdbacadaabacaaaacaabadbddccadbdcadacdbcccdaadbbddbbabbccdbbdbaddacabcdbcbdddbbddccbdbbdaddaadddcbacadcdcbcdcdbcacbbaacbacbabcaccbbbbadbcbbaacaacbcbbdbabbcdbccacaacdbdaacbacbcdddbdcbdacccbddbcabaddbbdaaccadbaacdbadddacacbcdbbcabaadbdbcdaadabbaddadcbcbbcdddcaabcccaccacadcddbdabdcdcdcacdbbdccdaacdadacdaacdcbacabccdcbbbbcaccabcdbddddccdcbbbdcbcdabbaadacccbdcddcbdbcbaddcadabdddcbcdbbbaddaacacbdcdacdcccadaddbcacbaddbcdacdadaccbcbbcbbdaacdaddabadbcbdadacdadcacbcdacadcccadabbddabbbcdcdbbbabcbcbbadabcddbdcddbbdcaadbaadbaacbdabbaccbcdcdadcbcdcbdcadcbcabcddcbdbbbdadcdbbcdcabaadadabdabdcccbdbbcdbbcddbbdadbccbcdddaacadcbadbaaabacaddbccbababadbcddccabccabbbccccbbdbdcccbdadbdbbcabcbcddacacaaacbcdccccabbadddbaddacbaabbdbaabbdbaaacccbacdcccccbccbaacaddbccbcbaadaddddbcaddaaabcabbddcbcdcccacadacadabdbdabdbcddbcaacdbadabaaddddcbbadbccadbccaaddddcaadbddbbdcdacbcccabbaadbdabbdabddcbabbcbbcdcadcccddbabaaaadcdacddddddbcbaacacaccbdababaacbcbbbbbcccbcaccadbbbcddccbcadbacababdcbacaaadcccbaadcadddccccbacbdadcbcabddaaccbbddccaaddabcbbaabcbcacabbbdddbdbdddaabbaddccabdbbbdddadbbbacbacbbabadcaaadbaaadcdcdbbaacabdbcdbbcdbddaccbbbbcdbcacbcbacdccdbbcadbdbbcbbccbccadaccbabacddbdadcaaccbcddbaaaabacdbcdcdabcdbddadaabbdbaadbabbbbbdadaadbcabbbbcdbdaabdcbbccbbcddcabdcbaddaccacaacaddbdbaacacdbbbabbacbdbabdcdabdaacdbcadbccbbadbccaaaaaabbcabcdbbdacdcaaabbddabccadbaacbcabbbcabddacabacbddabbbddccabacbbdcbdddabcaacdbaddbcbdccbbbadcccdacaadddadbaadbdaacbaacabccbbaaaadaccabdcdcaccabddcdabdcadacddadaccbddccbcaabcaaadadadaabdaabaabccbdccdcccababcacbbdaacacddcddddcdddcdbcdcacaabcbaadbbbacaadddabacbbbccddccacabcbbbccaaaccdaaabcacadccdacbacbdacddbbcaabdddbabadbbcddabcddbdccacbcdadbdbcbaaddcbcbbdabccccabbaadcbcbdcddccdabaadcbaadaabbacadcbddcdbdbbbabbadcacaddcbdcbbddbabbbcbadcabbdcaaccabcdabdadbcadbcaccbadabacccccccddbbabaaaacbddadababcccccddbccccacccbccdcccabccdaadadabaaaabaaaccabbdacdddacccbbaabcbbdccdcacabcbbddbcccbccbbcbbdddcdbbcabbdcddbabbcaccdbacabbaddadbcacaabbcbdcbbcddabaddaaabddadacaccdadbaaadacbbccccccdabbdabbddabbcbdabcbcbcbacdacdbbaccabcdbdbdaacdbaadcdabadabaaddbcbbaaadbbccdccaacdddddcdbccbcaccbcabbabcabbdddbdacaaaaadbcbbdacbdaadcabbadababacdcdaddcccbcdabcbaaddbbddccdaccdaddbcdbdcbaccdddbcbdaadabcdbabbbdbaabacdadabbbacbaaaadaabddbdddacadddaaadaaabdaacabadabbdacbddddbdbcdcdbcaccdcbbcddbcaccdadddccacdabdcbadababccccaddaddcbacaaadcbdaaacbdbcabdbabcacaaabddadacccaabccbcdbcaccbacdacabadcdbdbbdcadbaabacbdcbacdcadccabbbcbacdccdccdacddacabadcdddaabdcdcacacadbcabbbbdaadccbdaabcbaaaccabbcbdaccacaacdaadbaacccddbadadbdbadaccabbdacbbacadaacccccbaaaacbdabdadaccacdbcbcaaababccccbaacacccbbbccacccabbcbaabdddddbadccaadaadbdcbcacabccaabcbccbdcdcababdbbcbbbbdadcccadbbadcbcaacaaadbdcacacddbbaacdaaabaadddbacadcdcbdbabddcabbabbbcadacdbbbdbaaddbdabacabccdcabaaabbdcabbdddcddcdadddbaadbadcdbbbadcdbaccdcadddadacbbbcadacadbcbdcdcaacaaabcabdccbaabdcdddadbbabaabcaacdcdbcbcbcdbcaacdcbcbbdcababaadcadddaadbbaaddabddacdcabdbaaabbbbccabacdbdbccbdabbbdacdbcccbbcddaccacdbdcdacccddacabbbadcbadbcbddccaddbbbbbaababbddbddbdaadccccbdbbdadadcddbaadaccbaadcdadbaaacbbadacdbabbbdababddbccdcddbbacbbadaadddaacbcbbdcadbcabadcaabbbaaacdbabaaddabdbdaacadcacbbdddbabccadbbcacddcdaddbdcddabaaaacbadababdcacddcddabdbadacadabbbaccaaccbbcbadddbcddbcbdbbbbcaabbdaddbcdbbbcbadadcbbbcbdcdbddcbdcbdbbdcdddddccbdcbdaccacccbdddadccccdbccddcaddababdbcabccbcbacdbbcccdaabdadddacbaddcccbbdbadbdabbddcabbdabdbbaaccbcdbbdbacbbdcbacdbacccddacaaccdaaaddcdabcdaccccadccccccabaddcaabddacbaadabbabdbaaaccddbdbdbadddadcdbadbddaadbcbdadabaccbddbcbaccadcdabbccaaddaacadcbbbcadccabdbdadccccadbcdaadcadabbabaddbdbbadddccddccbaaacdcbcdcdcacacbbabdcdcdcabaccacbdbdbdbdbadbabdaabdcbdcdbdadcababcaaadcacacadbbdccacabccabbbddbccbaaaccadbaacdbbdbddddacdaaaccbdbdaacbcdbdabcbccabcbcabdcbabacabacaccdaaccddddbdacbbbcabccbcbddaacbcdaddbcacadcdddabcdcdbbccbbabacdbbcbbcccdaadcaabcbcccaddbaadabddbcdaacbabadbcacaaacbcbdbcbbbdbaabaaccaddcdabbdabaccadbbbdcbbcaaabdacadddadbdaabbcbbdbaddccdbadcdbbbdccbdabcabbdadbabcadbbcaaacdbbdbddcddccddddcadccbdcbbcddccddbdaaacccabdacccdadbbdbcabdaaabdcbadaddcbadaddbbdacccdbaccabdcdcdccdddbacdacdccabcdbddddcdcddcbaadbaddddbdbcdbcddbacbdcdcadddaabbcbcddaadcbccccbbccdcbdbbccbbacacccdadcccabaddcbbbabdbcdddaaacbddddabdadababaababababccbbbcbdbddbdacdaababacaccdcaccacdabbbcacabcabadabdcdadbbdddbbcdcbbacdddcbabcdabccbbaacbcabbdbcbabdcdcbddbdcbdbdbdbddbadbbbbcdcdccabcdaddaacbbcacacaacbbddabbcdadbbddadddccaacddbdbdaaddbbadbbbbbccbbccbdbbbdcdaaccabdbbbddadcdddddbcabdacdcdbdbabdbacbbabcdccadcbddcbcbdbdbbdbabbdbdcccdbcbaacdbcbabbaacbababbbaddbbcdabdccccddbccbcadcaabbabdaabbadbddbdadabcaabcbddbaccbadbbbdddacccddbcadcdcbbbbccbdacaaacdcdcabdacccaaccdddbdaccabdabbcdacaabbcdaddbdbdcacddddddbcaabbccbabdbdabdbddcacdcaabcdbbabcdadaadccddbdadcbdcaabcbccbcbacbcdccbdbdbdacadcdadbbbddbdccddacdbbbdbdacbcbddbddbaaccddaadbdaadaaaaaadbcaaadcabdacbabcddbdccbaddccadbadddcaacbcabccbadcbbddcaaacddaabdacbdcddddcbbacbacacbccacddbbadbdacbcbabcbbddcabddbaadabbddbccbcdbccaaabcccadadccadaccccabccacdcdbbadcddbcbadbbccdadacadacabcbccdcdcbdbaabcbacacbddddbcbcccbdddadddbbbccdcccbacddbdabdaabdaadbacbdccaccdabdacaabbcdabcabcbadbbcaabdbbdbddcaccdbaadcbcccaaaabbdaacddcddcabdabccbdaaaccbbaccbdbadacbdbbabadabadbabcccbdbcdabddcbcbdcbdbbbbdcbbbbcdaabcadbddbabdbabddacacbbaccbcadbbabddbccbaddccdbabaccaacaabcccdccbdbccabadbcbababdbaaabccdcdcbcbccbdabcabcacdacabbaddbacbdbabcdbaadbcaaaaabbdabbddbbdaaacbdbacacbadcdcaabbbcacabcabacabbbabccdcccccadabaacbcddbacaabcdcdaacabaddbacccadcdbdbcdccdacddadabdaccdbacbadaccbacaaadcaadddaadcdacbbcbabcdcadbbccaaaaacbbcbadcadbdcacabdadcdadabcdacdcdacaccacdcbaaabacbdbbaabbbbcadcbaabbbadbdaabaccbaddbbbbbcdbbbbddacdbcdabbbddcdbddbbcabdcdaabddcbcaacbcadaccbbdddbcdbdaccdbbbbdbdaaacdcbadcbcbddcdadcbadabccacacbabcabbcadbbbbabcbbddaddbacccdacdddccbabdbbdaaaabbdcddbbdcccacccbcbccdadccabdddcaddadcaadabdcbbababbccdccccbbcdcdcddacddadabababadbbdccabaadcabddbcadadbacccbcabbdcadaabaacbcabbdbdaddacdaadccaccbddddcabbcbabbaabbbabbcbbabaaccbdabcbbaadbdcbdabbbcadcdccaacaccdaacccaaacbccddbcbdcaaadbaccadcdcacadcabcadcbbddbccacdbccbadbabdabadcaccdbdddacadacadabcdcadbcbadaababaabacaacccdccaabaabcddbdbcccdaaacabdaaadacbaababdcabbccadcbddccddcddcaadababcdcbdbacbbbbbabcaddcbdcdbdabadcabbacbbdacccdbbadbaccdbddddcaadcbcbbabcdbcdaccbcdaacbcaabdbbaaaddccddcabccdaacbabcdbabbacdcacbbcbcabddccdaddabdaabcacdcdccdbbbabcbddaabbabaadbcdcddbaccdabadbbdbccbdbdaaaaccbdddacdccabcabacbbdccddcddcaabaacbabccdbbbbbdbaacdcaabaadccdcdaaabaabcdbaacbcccbcbdacccdcabbbaaadbdabadbadacaaabababddaaadcaadccdaabdcbdbaaaabaadcbcdcbcddaacdbacdcadaccccdddabbbdcaacddccbaabdbcdadcaadcdbcbabaabcacbcabbadbcdabbbddccbaacbadadaabdcadccbabaaabdbbabbbcbbdbabbcddcbabcadcccabbbdabcabbcbdccdbcbdabccdbbddbbcabcdddacadddacdaadccacaddcadcdcdccdbcccadadcbdddadaddbaababbcbccdacbdccdbbbbbbaacadcaaccccaccbbddbdbaadbdddaaaaabdbaadadbaacdccbbcacdcbbabcbbbdcbbadbadbcdbdacdbdccbcbdabaddadddbcdccabdaaaccccdaacdcddcaacdcacbdadaaabadcddabbaaaabbccabdabdccbbbbaadddbbdbcccabaabcabaabaabbdcacdadccdaadcababaabbacabacbabaaadbcabbdbcadddbabaabcabccdbdaadbcbdbddbcaaddaccaccbbdbabbcbddcaccdaccddddddadbbcccdddcabaabcbdcadcccabaccacbbcbbbccdbdacbbbccacdbdcdcdcdacabcdbddacdcbcbccbabbcdbbdaaabbdccdcbaaaccacdaadaacaccaabbbdddaabdcaaddcdaaadbdcdddadbbcbbbcadaabacaaddadbcabdddacddbbbcabbabadcdbacbdcacaaaddbabacacdacdccdcaaacbacdbbadadccbbdabdabdadccbabcccbdadccbddadccdddacbddcdcabdbcabdbdbcdbaaabdbadacaabacbdaacbcdabaacabcdbbccbaacbdbcabcbbadacdddcabaacabaccaacbdbcdddbaacaabbbddaaabbdcccbcdcbadbbaacdcabadbdccbdbccadaadddcbcdccbbabdccbcdcacbcccdabcabddcacdcbbdccdcaaacdbddabbbbacbccdbdbcacccabcaabcbdbbcacbbbddbacabccccdaccbbabdaccbaacbcccbbddddbacbddaddababaadbaacadbdcbadcddcbadaccbcbdcabddddcadcaadadbddddadccaadbcaabbaadbcccdbdbaccaabaaddcbdbbdccaabccadbacdddbababacdaabaacbaccdbadcbbbbdabdacadaabbcbbbbabbaaadadcddadacdddccbdbdbdbdcbcacbdabaacabdabadbacdcbcadacaaccdcbaabcadadccdbdbabcaddcbadaabaacbabdcababbcabbccaaccabdccccadbbdcaabcdddbabcdccdadcddbbcbcbadbabdcbdaddaaaacaabccbcdbbadbdddccdccdaacccbabacbbdddaddbaaaaacdaabdddbddabbbdbccbdbbcdbaddcddcddcabdccbcdcbabbbbadbbdacddddbbdababddaacbaccacaaccaabdbbddcacdbdbcdbacdadbcadbacdaaabbbacdcbdbdcabccabdbdbadbccdbdaaacdbbaabccdcbcabcdabdccdbcbaccaadacbbccdcbdadacabcaaaccdaddcbaddcdadababcbdbbcdddbdcdbaabdadcabaacaddbcbdbbacaabadbbacbbbddddddadadddbdacababdcabdbbcacabbadcdaababbdccacdbdadaacdbdcbddacdbddcbddabdbccaccadadcdaddabcbbdaaccbadabdccbcccabccdbabbaaabdddbacbadccacddcdbdddbaacdbccddacdaacadabbbddadcdcdcdacbcccdadadacacdaccbbcabbbddcccadbacbbcabdbdacbcbdcbadbdccaacabdabcccddbaabcacaacdddccddadbccbccabbdacbbbdbacdccaabcbccdbadaadbcddccbacbbabdbcddaadddcacadadcbbaabaabbcbacaaddabdddadcdccdbdbcdbaacaccdbbbdacbddaabacbdcabcadaabcabdaadaabdccaaaddbccbcacbbabddabadcabadaccdbcacdacbddddcacdaacccacdadbaadadcbdcabcddbcdcabbacabdbcbabdddbbcddacddccbdccdcaddbabdacbcdcabcdbaabcaadbbabccabddddccdccbdcdbcdababaaabadaaccccbcbaccdbaaadccdbabcccacabacbbacbdbadbbcccbabbdcbbbdadcbbcdcdcaacaccbadabbdcadcadbbaaadddddacabaaadbaaaabdaaddabaccbbddabaabcdcacaccbbbcdcdbbaaccabcddaaadddcddddaadaadabdccdbdbacabaccaddbaccacdccabcadcccbdcbacbcabadcaacacdddbcbabdcadbdacadabdddbccbcaabddbbbcdcdcddbbacbacdaaababbaaccbdabccbadddaccadacaabbdaadbccdcdcbdcbbcbdbbbacabcdbcdbadcacbcababbcdbdccbddaacdccdbadbabbaadbcaccadbdbbaaaadcabcadcdcccdabbbdcadcdaaccacbcadabcddcdbcdaacaddbdbcccdaadbdabdbddcccadabbacdcdacadbcaddbdbbbcccaadabbcbdddccabddadbdaadddbcdbcaddaaabcbbdbdbcddbbaaacddaccacdbdacdbccbdadbdbcdbdbabbaaadbdababddcbcbdabcbccdacddaaacbccddcdcbbbadaacbcbcacdccbabdbcdabbababacdbccaabacdadaddaccbaacaccbbbabbcadaaabccbadbcccdbbdddbdbbccdaccccbdbbbacbbcbacccbacaabcdccaadaccaabadacacdcbdadbbbddcadaddcbbcccdabbbddccbdaaadccdbacaabaacddcdcbdbcadaacbbaabcaaabdbbccdcbcddcddbcbbbaccddbbccdbababbcdaadcbbbabbbcacbaaabccadbbadbdbdddadbdcacccbdcbdbdddccadbaadacaddacaccaaaadadcdcaabdcdbcacbcbabdbbdabcbddbdcbadcacdacaddcbbdacbbcdbcacdabddcbdbdddaabcdabdccbbcadcbcadbdbacbbabdbddbdddbcabbbcacbdabbdbacdccbcdccadacbccccaccbbbadadbcdcbcbcddbadadcdccadbcddbdaddaadcdddcdcaaadbdcaaaccdbbdabbacacbdccacadbddbdaadccdacddcdddabacbbadbdbdbcddccccdcadaacdabdbdbcadddcaaddcdbcadccadcbadaacddbdaddadcbadacbacaddddcadcddaccbaaddbbddcbddbdbcbabdaddcbcbddcdcacdaacdbbdbdbdbddcacbbdbadbbdbbdaababcdcdccaadcacdbaaddabcbbcbdbdadaccadddabcaaabbddbbcdacabcabadbbdbddbbcdabdadbcbababbadcdabbcaaacaadcbdcbcbdbbdbcaabdbdbdddbbdbddcbbadddbcdcadbbaccadddbccccdbaacbaaacdcbabbadbaacccdcacbbcacaadcdbdadcbccddacbcacadbdbabddbcbddabaadbdaadbddbcbdcdbacbccacbaccabbcadadccccabdadaaaababbddbacddbcbabacdacacdbaabcbbbcccabadcaccbdadadaaadadddadbaabadcabbdbdaacbccbdbbbbaaadacdadddbadbcabdbdbdcbacdbabcdadbaccdddbbbaadcdadbdbccadcbabcdbadbacdaddabcdbaddcbcabdbbbacabbbdcacbcbcdaaddcdcbacaccccbcabcdbbddccdadcdcaadbcbbcdcabddddcdbcbbbcaaadcbccdcdddbdccaabbbbacabbcbdaabcbccbdbdbdcdbccbbdaabcacacadbdcbaabaadbdbcddcbcccbdadbaaacbaaaaccabadbbacacaaacbaabddcdaddacdccaccdddaaaaaccaadadbbcbbabdcddcbcdcbbbdaacccbdbbabbabdcddcacdacadbdacbbcbbaccbadcdbccacdbdcabdbdacabbddccabacdabccdacdaaacabbaccaacddcbacdbaacabcacdacddcbaadabbcbcaddaaacbdabcccbcabcadbbbbbbccbbaaaaaabddcdbcdcdbcdadabbdbbbbcdaccbcabadabacabbcbcdabddcbbbcadbdcbdabacaacbdacbbadbccbadaaccccbcddadccacbababbccadbcbcbbcddcdccadcdbccabdcbbabbcbdccacbddccddcaaddbaccdccdbbbddbbcacaaddbbcaccddcccdddabdcdbdaadcbdacbcbacabdadcbabcacccabccbdcdadcddcdacddbdbccddacbcabbbabdbbdbcaaccdacaadddbdadaccbdacddcadddcdbbcdaabbddaaacacbbadbdcbbccdbdddcccadddbcacdcbcccabdddbdbcaabcdcbcadcbabbaacdddcbdddbdbdbcdcbbabbadaacdabcacbbabdbdaabbadaacdbcddbcabacbbbbdbadcdcaddbdcddcabddbdacadabbaccbacaccdcdcdabdbdcbdddcdcacdbacccdbbcacddabcbdacabdcacbcbcaababbbbdccbccdcdaccccdabaddbabaabcabccdadabaddcddddbdcdbadbccdcbcbcacdddccdcbccaabbdabbacabaddbcdbcbddbbdbcbbcdadaabbaabcbbdbddaddbbaabcabaccdadadadbaabbaddcbaddddaddacbabdbbbdcdccdabdcdcdbabccaaaccccaccbdbddcbbcabccddacdcbadacadbaccbbcdabdacbdcadccbbaccbbdadabbbcdadccccccbdabdabdbbbbbadcccdadbbaaadaadbdbaaccbabcbbdcbbcbaacbbadacbacdbbdbaadcaacdcbadcabddbbdddaabdbcabccbcadadbcddaadbbcadddbdbaddbccadcdccbcbddddddcccddcdbdadcaabcccdbddbdcbcdadabaccabbbbcbcabdcdaaaabdcabcdddaacdcaacbdbbddbdbcccaaaccdacbddccaabdcbbbccdcbacdbadbbcdaaabbddccbadcbbaaadbbddbcabdbbbaaacbcabbbcaadcbaddcddadddcbbcbdbdadaabdcabbdabacbdabdacdcaccdcabdcaccdababcbacddabbbbddcbabacdbccccbadcbcadccbabababbaccddcdbdddbcabdcdcacabadacdbddcaabddbbdbcbddcdddccccbaabbbdadbaaacbbdaddcdcacddcbdbabddcadcddccddbcddbaddbaadbdaabdccdbdccddcdddacbcabadaacdddbaaadccbbccdadabdadbdbbbaccbabbccbbcdacddcaddbdbcadccddcbcdadbdabddcdbccaaabbccdcabdbabdbdbdddcddcbbcadcdaaabdacbadccbaadbbcddccbacabacbadabacdabacccabbacdcdbbabdadacccabcaaadadacddcbbbdcabccdabbcadcaaaccbdcdaaaabddbcddaaadadcccdcbaadbdabadccbdaabcccaaacabbacabdacccdacabbacaaddbddbbaccccbabbabbcaabbabdbbddaacabcbdadaddadcddadadbcaaaaccacabdbdbcaacaccdbacbdbbcbbbbbacaadcbaaadbccabacabcbcddbcbbbbbcacbdccabdbbbccadcbbdbddcccbabcddaaddccbbaabccdaacbdabbbbdccacdddbacabcabaddaacdcdccabaccbddadbcbadbaadadcdccdbaccdbbabcbadbbbddbcdcadbdbcdadbadacabcacdcddcbbcbcdaccabdaddaddbdbddbabbbddddcddcdcacbaacadcbdabbacdadbccdcbdcdddcacbdcbddccbabbbdccbaabacabaaaddddccdcbcccbdabbbdbcdcdddadcdcddbcbadbbcddaababdcdadadbcbabbcbdcbbbcdadbcdaccbcdccdbbdcadbaadaadbbacdacdabdadcdcdbdccaadcabacccddbadaccabdbbbccbacdbdabaabaddcddddcdcdddbbbccadacbbcbaaabacbbddaccdbcbccbaaaadccaabbacccdabbbcbbdcacccbcbcccddcacdddcaadbddbbaadbdbccadcababbbbcbdbcddddcadddbcbbabbbcacaabdcacbcdaaaabadbaadadccacaccabcabdaabacabaaccbcdbbbbbadcaaccdcabdbdacbbaadabcccbdbabcbcccdaaadcaacabcdabddaaadddadbbcbcacbbadadccacbadcbdaaddabdcadabcbabcabcdbcbcadaacdaccbadbddbadacabdbcadacabccdbadaabbbacadacddabababdcbcdbdbcabbdbbbdabdcaccbcdcbbacdcacabcaabadbcdccbdcabddbdabdbcddadcaaaddacdccddbbaaccadaddcdccbadbbababcaacdbbcdddabddcaaccdcbacbcbbcacbbadbdcddddddcacaadcacbbdbcdbbaccdbbcaadaadbcbacdadbaadcaaaadcadacccdabacbcbaddabacdaaadcdbbbccbaadadadacbcdacbdcdacabdadbbddadcaadcbabadbccbdcddcabbcccbaaabbccbbaacaacbbbbdaaacbdaadaacddbddacdbcadaaaacacacababadbbaacbaacaabaabbaccabdccbdadcabadbcbcaccddabaaacaddccdacdcabacdaaabddcadadabcadaaadbcababbdabaacbaddcabcbacdccaaccadacaddbcaddcddacababaadabbacbdcbbabcbaacbcaaadcabaaccbcbcbdaadacdadadbacbbaccbacaadcbabdcacadbdbdacacdaaadabadabbccbdbadcbbaacacdabacaabdccdabdacabbdcdabdcbaaaabcbcacadcddbcdacadcaddabbdbbabddadccbaddaccaaabacdaaacbaaaaacccacbbbdcadaddcdcdcadacdbadacddcbbdbdbcaddbcccadbcddbdcbcdaadcddbdacbbaddbbdaaddddcacacabccbcdbbacbdbdcbcdcbcccababbbcbbcbababdbbddbadcabcadbcaadadccbdcdbcbaaadbbcdcbdcddbabbaddbabbaabbcaddaabdbcbcadacbbdbbbabdaabaddabdcbbbaaacaabaccabaccaadcdcdcabacccbdcdddbdddcacbbcabaadbadabcdddccbbddcbddbbdaacdabaabbbbcdbbacdcbabbcbcddbdbbdbadbaabcbbdadcccbaddaabadbcacdababaccaccbacbbddaaddabccabdcdbcbabcdccccaadccdcccddbcdcdcccaddcdbdbaddbdccbddadcbbdddcccbdcbcbadaaaabdbdccbbdaabdbccbadbdbbabbacbbbcbbbadbacadcbccaabaaaacccacbcaaaabdccbcaddcccabdccbddbaabdcdbdbaaadabcabbabacddbddbcdddbdadadabbdddaccaacaaabacddcaccaccacdbcabddadaddadacbcbdcabbadcdcaccbbcaabdcdacaddaacbddbbbdabddbadadacddaaaccacbcaddcddbcdcbaabbcaccbbccddcaacdcccadbcdaccdbcacdabbcddbddabdcbaddbdcaadadbdcbcccabdbbcbddddddaadddddcbaadbbbdaccabcaddccabddacbadabbbabdabaaacbbabadbbbbccbdabcdddcaccadabadaabdadccbbcddddcadaaaaccabadbdbcdbacdbaacbdddbdabbdacacdbbaabdbbdcdacdbaacadcdcdabacaaaaacdacbcaadbaaaddbadbbcccbdaddabaabcbadacddaacababaaadadabbcabddacddcaccddcbccaccdabdcccddcaacbdadddbdaacdaadcdabadcdccbdbdaabaaacababcbbddcacabdbacbbdacccccdabbbadabbaaddbbbdcccbbabcdddbdcadbcbabbdbbbaabbbbacbdcaddaacdbadddabcddcdbdcdcbadacdbcdacbdbcbbadaaddcadbaabaddaacadccabbacbbcbcdcdaccccbbbbcabbbbadddbaabaaacbcbccbcadaabacdaacbdbcbcbaddbdcaadcccbabdbddcaaabbccdaabcddbcabaabbadbbbbcaacbdadbddbabccabcdddbccdcddabbbccdccdaadcbadbcbbddabacdcadddaccccccddbddacccbdcccbaadcababddadcbcbbadcadbbabaccadbdbddbbbdcddcddbacdddaacbcbccdbddcabadcbdbdcbcbadcdbbdcbcddbcbaadbaaacdbaadddaadddddcbbcacdcbbbcdcdcabcaacacbdadabbcabadbabdaaaadbccadbaadadddbaaaaacabbabcabbaabbdbcdbcadcdbccaaaabadcbdbabcbdccccdcacdbccadaacccbbacdbcdadcaccabadccbdbbadbabbdcdcdabcabdbbddaacddacbdddabdbdbacaaaadddccadaddadcbbacbdacccbadddaaacdabdcadbdcbcabbdddaccbcabaaaacddadbaadccbddabbcadccadabddabcbbdcbdddadccdcddcbccaddbddbdcadcaacaabbddaddcccdbdbcddcaadacdaabccaabbdcacabdaacbaaabcababdddbaccacccdbbccbaacadcdddccdabbccdbbcbbcdadcbccdadbbcdbcdcaaccddddadcbcdaabbabcaaaccaabcbdbdcddccccdbdddbaabbddcaaadcdddabddacdccdcbdbabdaccddcaadaccacddbbccddbbccdcbdcaaacbbcbabaacdbadaaaaacacbadbacdabacdbdcbcadbcabdcccdabdcdbdcaaadcdadcadcabcbbbdbacaaabdcacbbabcbcbadbbdcacdccbaadddcdadcbadacbcbabdddcdaaadbaababbaddbcbacdddcbccadcdddbcdbddbccbdabbdbbbbcdacbbdcdcacadbcdcbadbacaabdcdaacdcabddcacbacdbcbcbacdadbcbcbcadbcbbdcddcaaaaadabdbadccacccccdadcdcdbddcbabbaccdadbaaddbbdaccabbdbbccdccbbdbbdbcdacbdacdbcbcccbdabbbbbcbbcccbaaaddaadaaaddacbaabcccaccadbacdcbdbabbbbcacaaccaaaaabacbdacdbdccbacdbacdbdbdaaadcdaabcbabcabddbabddbddbadddcbbaacbcabadbaabbadbcbbacdccaacccbbdbcaaacacbdacadaadaacddaaaccbcacdaacaaacadbccbcccacdabbccbbdadddcabadcccdcbabbbacadadbcdadcdbbdbacbcdcbddccccbaccdbddbbbdcdcbacadaabacaadadcacbdccbdabbccdaccacbcbdaacbbbabaacacdccbacbaccbabaccbaaacadcabaaaaacbabbcbbacadcddaaddbcaaddcddadbccdcdcabbabdcbdadcaadbddcbbcabbabbdddbcbddddbddaddbbccaadbbccccddccaccdbbdabcaacdccdbddcbcaaacabbbcaaadbaaadacadaccddacbdbcbabacdbcabaacaabccadcbbcadacabcdaabdbabdbacdaacbaabbbcbddacdababdcaccabbdadcbacbadccbddaaccdabcdddbdccbccbcaccdcccadacaccaccdbccaabbccacbcddbcdcbddddcdddbdcdcbbaaabbdccdabcacbcdaccdcbadbdcbccdbabccbabdcbcbcccaddbaacbcddadccadddcccdbcdbbdbcdcadbbdbcdabacccdaacdaacdacadcadccbdbdbdccdacdccdaccbbbbbcbdcdbccddabdcbaccbcdaccaabcadabdcbdcbbcddbcddbaaccbdabccdabadcbdcaadcababbccaadadbcbbcadcaaaddddabcdacccaacbdadcbddcdbbbbbaacbdbbcbaacadcdbdcdbcdccaadacddbcadbccddcbdabdbdcddacdacbabbcdbdcddddddccdaaadbaaddcdbcdddbdcbcbcadcdaccbcdcbcadccdaccbaadcdcdbacabcaccaaddbbddcabdbbaaacaaabccabbbcccbdddbbabdcabddddaddaaccacdabbabcbbbcbcadbcdbbcccadcddbdaabbccbcbaddbdbbabacdcacddacbcccdbddaddddbdbdddacbcdddcdbbdcddbbbdadcddabadcbcdcacadbaadaacaacdcbddbbdddbbbdaaccddaccadacddcabdcbcdccabcabcdccccddbdcbbaaddaccadadadadabadcccccabcaacccbacacacccccccccbccdaaddacdbbaddabcabadddccbbabdaabcabdbccabbdadddbdcddbbdcdcabadcdbdbdaccaddaadbaadcdaaacadabdcdaddbcddcddacbcabcbdbacaccbaacbabbadbcddcdacbcdbadbaddaccbdbcdaaacabdccddacbbabadbcabaaccbadadccdcbcabcbcccccdbaccbcbcbcadbcbbbbacbabcbbdadccdacbcdaccbadbabbcbccdccabcdcdbbddcddcbbbbaabaaddadcdacdcadadbadbdabddacacdbdcbadbdccdabcbcddaabbcabbacdbcacdcaacdcdcddaddaaadadbadacadbbccbdbcbbbdabcbbcbdaaddbdccadddddbbbcccdbbddacbddacbabadcacbcbbbccbacddcdddabbbdcbcdbabcccbaabcbdabbddaaabdcdadabaddcabadcdcacabadabdddbbcbcdaadddbacabcaddabbcbcbbcaabcbacbccbbaccacbccdadabacaddddddcdadbbcaccbbbccaacccacbdcbcbbbdcdacbcdbddbbbababbabccbdbccdcbdcdddabbcbcdcddccbaaddcbcbbbccabdadacbbccbbddbcbcccddcdcdabdcdbbabaccdacbdcbbadbbaacbcdaccdabacbdacabbddbadcbacdbbabcbacbcccdacccbdbbbbddcdadaaaabaccbabcdbcbdcddddaddadbcddaababadcbababbcbddbbdbcdaaacddccbabdbbdbbddbcabacaadbdbccdaabcdbdcdcbcccadbbdabadbabdcdccdaacaddddaabdaadddacdbcdccaadaaaacdbdbbcabdacbabcbbbcabbddccadccbccdaddccbcdcdbccacadbadcccbcbdaadbbcadbacbbcbdaadbbdbbadcdabccadcddadacaddcdbcddacadaadaccadccabaccbbacbbcaaddcdbacbbbbaacdbadbadaabcacdbdaabcadccbadadbbcbccddabcadcbabbaabddbcddcdcddaccdccadbcbdbbbdbbadabcabbccbcacbcbcdbbaddbbdcaddcdacabbbacbdddddabdbcbcacaddaabcadddaabcadcccabcccbdbbcdcbdbabacaabbadadbccccaacccbaabdcacacbdcaadabcbcdcccacacadaaddcccacbabbbababcbbdbbddcababcbbbadcdcddccdcccbdcbdccbccddbdbabbdbbbabcdddabdcacabcaaabcaadbcaaddcdcdabacaaabdabacdcddaadadadacabbdbbddbdcdadaccdcabdccbaaabddbbbdbdadcbbdcabccdcccbdbbbcdabcccdcdabbddbbadbaadcccbbdaacbccbaadaaaccabaddbcadddbbcaabbcbbabadacbbbcaaaadddabadadabdadbdaaadcddbabacbaabbbabdabacbcdadadababcdcdbcbdbdacdbacdcbabdbbdbadcbbcdbababddaacbbdadacdadacdcdacdcdbcaacbabaddbcdddcccccdbccdbcbbbacaadcbbdabcbbbdbbacdbaadccacdcbabccaabddacdbacaaaabcabcbbaaababbcdaaaddacabdbdbbaadbcdcbaaccaccdbcaabadacdddbcadacbcbaccacbdbacaabaabcbabbdcdabdabbdbdbacaadbbcacdaababbabbcbbadcdbcaddcbababbaacaaaadcddadbcbdadcbcdbdcdddacaabaadadccbdddbcccdbcdbbcbacdbbdcaacbbbddabcbddbabcddcadbababdbaaaccdcdaccdadadcccadddbdacaaadadddddcbccdadcbacbbacbcaadabdaabdddbbbdacbbabdadabdadbadaaabdaaabbaacadacabadabdacddabddbdcacbababdbbadbbbcccccccdadcadabdddaabdddabbddddcdacbaabaadbcdcbdbbadcbadaccacabbbbbcdbaddbdbadaddacbdcdcbadabccccbcccadccdddcbbcaddaadbadcacacbaccabcbabcdacdcacdccddcadacaacbacaaddaacaadcddcbbcddccabbccbcbcabaccdbbdbbababcdddccbdacdbbbcdabbabdbdbdcbcbcacacbbdbbcadccdcabbdcaabcbdcdaadaccbdbaadaacabaacdbccbbbdabdbcdddbddaabbcbdbaddbcdcabbdbddabadcadccbbadacddadacccdabcaabbdddaddabadabdccdbccabcacbcdccbadccbabcbacbadabcadcaaacbbcacadacaacccbdadcddbbccdbabadacbabdddccbdbddbcdbcdbbdcaddcacccccdaaadaacabcbdbcccbadccbaddadacabbdccbbaacdabdadbcacabbaddcbabbdacacdbcbcddcacdbaabacdbbcddcdcbdadddcabbddcbdaababbdbcaaddaadbadbccccaddbacdccbdbaaaacdaaaababacabcbacacadbbbcdccaaaabcddbacaddbdccacccbcbacddacdcdabdcdabccdcabdbddcdcddccadbbcbdbcaccdbcbbbdaabbcbbcaacdcaaacadabacdaccbbcadcdcdbdbdaddbcbababcbaccaadccddbdddbdabdbddccccadbabddbbdcaccddccccadacbcacbcaacbcdbdcbcdcbbddbaaddbdadbbbddacaccdbadcbaaaabcbcdcdcbbacbdacacaddbdaaccbaccbaaddaddaabadbddaccddcacdabbabbcddbcaacacadacdcdccdcbbccabcacdccddccbdbbdacbbdbccbddcaccacaaddcbcdadabcbbccbacbbcaaaccccdbbabdcdcaaacbabbccdbaccaaadcbbccdbaaddacaadabaaaaddbcdcadabdcadcccbcdcdcadbdcbaabadbbabacadacdbbdbaadddaacacbcadccbadcadbdbbaacaccbdbbdddacdcacbddcdadddcbcacdbdbdddcdacaadadaabbbdbdcaddbbdbdbccdcddcbdadaabdaddcdbdbcddccdbddbbadddbccbdcdccdbcbacdddcacdbbacccddddacbbcacccadaccbcbabaabbdddaadbcdadcddaabbbadaacacdcaaadacbacdabadabcbabdadcdcddcccddcaccdddddbdabdcdbaddbdaadbadbddddbbadabcadcacdbacbcdccccbadbcddbbccaacaacdabbabcabbaacaacacbddccacaabadcddbcadbaaababcbcaacbadbcbbdabacabcdabccccdcdcaadcddbbdcdadbcddcccdccbcbdaaadcbbababbdccacddbdcdabacabaddcabcccddaabcbabdbadacccdccbdaaddadadddaaccaaccabaadcacaacdadcacdbabaccacbbcccbdcdbadacabaacabadbbdbbacaacbadaabbbadcccdbcbacbdaadcdcabbbcbdbaadccddbbbdcbbaadcaaadbaddbdddacbcddcdbccbacccaabbdaabdabdddaaadacccdcaadaabaacdbadacaccbdcbbbcdbccadcadacbcabdccbbcddaddcaabbbababbaaabddddabadbddcbddccaadccaaccbdccaabbadabcddbccdbbacbdcadccadbdbaacacaabbcbdcabddbdcaaabadacaccbbadcbababcabaaccbcdcbcaacdbdbcdbcdaaadbccdaccbbdbaaadbcdcbdabbbacddbabaabdaabcbdcbbabdadaacdcbdcdbdbdccdcadaacbdcccabacdbcababbbabdcababdaccdcddbddccdddddbcadcaddabaaddccdcdcabdacbddacccbdcadbdbbdcbdaccacdcdcdabcabbcbdaaccaabacadbcaddbadcdcddcabacbdacabcacbbbdcbdacdcabdacdbbdcaadccbcddcabbddaaaccaadbdaadadaadcdbdcddcabccaacbaaacbcacbddccaccabcdbdbbbcdcaaabcbacdbbddadcbaadcbdbdabccacacbadacdbbadcaaaddcccdddaaaaadcdcbcaabaabbddacbaabccddabdbcaaddbcbccaddbdbabccddcabaadccbbabdbadacadcadcaaddddcbcbcccbcdadacccbcbbdbcabcaabbdcbbddbddbacdadaaccabdbcabdaaccdbaaccdddaccbaddbabcaabcdbdaadcacbcddbbbbddbbbbdcddbdbccacabbadddcacbdccbadcaccadcbabaabbaacbdabdbbddcdbcdbbcbbbaacbabddaddbbadbaabcabadbdbbaabdddcacabdddbdcbcabadacbcdbdabbdacdaaddcccbdddbacdcccbabbcbaabddabaccacaacddcbddbaccbcadbcaaacdccbaabacdbdbbdabdccddbccacdaabbbadcddbdcaacbabcddadbaabbabbdbdaaaabccccacdcdadbbcccdacacaddaccbcbcaccdacaacddbbaabcbddcbbadadadddcbdbbadddcdcabcadcdbddbbabdbaaadcacbaabaabbcdcdacadcccbccabddbabcccbcddabcbbbaadccdacbdcdacdbcccdcdabdaacbddacacdbcdaccddabaccddabcaacbbbcdaadcdbbbcbadacbdbbabdddaadcccdcaabcaaaaccddadbddcdacdccdabacbddccdcaaacdabbbbdcadadcdaccadacbdacadcdcdbdacaabdcdbdddddabbcacddbcccdcaddcddddddcbabbbdadcacbbddbbdbdcdacbcacbcdcddbcbababbccdbdcadddadaaaccdbaabcbbddaddcdbdbddabaadaddbabccadacddaabbbcdbdadbcbdcabacddbdcbcaabdacbcdbbcbabccbaccdccbbcbacbbbddbacccbbcacabaccbbabcddbdcbbbdcaabcdacbabdbcacdabcacacbdabadaddbbadbcacabbdccdadbddacccdddaccccdbddaababdcacdbbcbaccadccdccddaabbbdaacacabdbddcbcbbdaaadcbccbdbacdbaccbbcbcdacccdbabcbacaddaddbcbdabcaacdabcaabdacdbabdbddccbdddcdcabbaabaadccdbcdaddccdcacdcdaadaddadbaabdbabaabcadbddcdadbdacacbadbcbbabadddbaccddaabddcdcccbdccbbabcdbbdbaabdaaaddbdadcdcbabdbbaabaabcbaacadbddacabbbdcaabaacabddbcdcacabbbcbdcdcccdcacaabbbabbaaacabcbadbbbbddcccdadcbbabcbabaabdbddccaaadaaadccadbcbbddcddcabcdaacababdbcadbbabdacdcdcdbdacdbdbadcbccabbbbcdabdadbacabaabccdacdccadbbdcadcbadbbdabdaadbacbbcaddddbadcddcbdacdccddcbcddccaacaaddddbcddbbacabdddbbbbacbbdcabbcabcccaddcaaddcdaccdbbdddbabdddccbacaccbaacaacabcbdcabaaaaadabbabcabbddcaabdcccdcddaccbadcaabdddadccdbccadbadcacaacdaccdbadcbdacaaabbabcccbbbdaabdcabdaccbbdcabbddcadadccabacdccccaabbadbbbddccddaddbababdacaaacdbbcaccabccabaaccdbbcddaaacdadddadbadbaacadabdcbdabdbccbcabbbbdaaccabcbacaaacacbaccbacaaaabbaccbbcddddbacbdbbbdcabbbaadcdacacdaadcccabbadacdcbcabdabaabdcdacbbcbbababdaaccbcaaddddbaabccaccbdcbababbcbbaccddccbbbcacaaabccdcabdcacaadcaaaaaabcadabaabaaaadddddcbbcabddcbbaaacbcbbcbabdaabcbabcddbaacbdabbbbddcaacacaaddbddcaaabcbbbaadccddcdaacbbdabbcdbcaaacadccbdacbacaaddcdccaccddcaadbdccaddcbbcbdbddcaacdaadaabdaabdabaabddcbabcacdcacdaaabaaabbacbbabccbdaccdbaacaacaabbdccaacaacbaadbdbdccaabdcbbbcccadcaacabdbcdacbccbbbdbbccacbabcdcbbacadbbbaacadbdbccbbabbacdcabccadbdbcdacddcbacbaacccadbbdadbbaabdbdadaaadaddbcdbbadcaaaddccbadddaababaaaaabbcacdaaaacdcccdabbcbaacddaabcbddcacdcccbdcbddccbacacdcbcbcbbddaddbcadcaabddbbbaccdaccccddbcddddcccadcadcdbaacdaabddadadabcabcbacacacdcacaaaaaabcadbcdadcbcbbacdbbdaaaadccbdabaabdadbdaaabbbabdcccaaddaddbcccaddacacbcabbcadcdaddbadaadacdacabbbdbddbcdddbddbdbdcccadddcadabdcaabadaaabaaababdabbbbaaadcbcbbcdddcbbddcdcddbbbcabdbdbabdbbdddabccbdacbaadadadcdbabbddcabbaccacdabbcbcbdddaacbbbdbabcaacbbcbaabccabbacddcaddaddccbaaaabdccdaddadbccbabdadabccbdcbcdbcadabcccddccccadccbdbdbddddaaddbdddbbcaaabbdddbadacbdddbaccbaaacbcccdcbccdbbcbbcdccababcacdbbcaacdadcbbbbcbabccacbcaaddbababbaddababaadddacabbaacbdcacaacccacbdbbdcbddadaaabbbdaaacbbdadccaadccdbbdabaccabdbddaabdcdbbcaaaddbddaabadcbdcadacddacdabbadbdadcdbdbaabaacaadbbdddbbbccbaaabddbbbdbaabddbccbbadbadbcdbaabababcbbadbacddaaadcdddcdbddcccabbbbcdabdccabccbccadcbccacdbbbdccaaacbdabcdbbbabdbdbdaccdcdabbdcddabdbbdbccbccccddbcdddbbadaccadabdcaadbadccccbbacbdcaaaadbddcaabdabcbdcdbbadcaaabaaddacbbabdabbcacbacbbbccdddaccbbddaacdbcbbabbabbbdcdacabbcdbbacbbbcbaadadcabbdacdaddcbcabaaddcacccccbdcbabdaabddccdaadcaccbacccbcaadaaabddabccdcabaabdbdddddaababbdcdbccbbadcdcdcaadbdadcaacdabdcadbbdddbacdbcadcdcbbdddcdbbabbcdbdbabccbabcccbdbcdadcbcdbbbdbcbcbbcddbbabcdabcbcaacdcdbbaccbadaadbabdabbdadcddacbacabddcbccbbacddabbabdbdbacbdccdcbdddcaaacbadacdddabcccbdbbcbbaadcacbbddcacddcaaadbcbabccdacbabbccbddbdbbdbbbabaabcacbcabdbdcaaaacddbabaaabaabdccbdabdbbaccdbbdabdbbbacbcbbdccbdddaadbbdcabcdbcdcdcbbbbaacbbabcdabcadbcdaccaadadddbbbccdcdcbbbacacdcbcbaadadbccddbcdbbccbdbccbbbbabbcadcbbdbcdbcabbbcabdabadbadaaadaaaaabddcdbbadcdbaccdbdcccbdccdbcaccadcabbadadddccacdcdcacbaabccbabdaaabcddcccccabdbaaacaaaabdbccccccbacdabcbaddccbbabcadbabdadcacaaabdbdddcbdcbdadcbddbacdacccdaadcdcdddcdddaacdacaabdbcadbaccabacbacabcbdcdcccaadcbcdcbdddabccbcbadabaabdbabaacbacbacadaadcabdcadccbcababbcbcdcabcdcbbddbcabaacaddaccdddcddacbbacbcddcbacaddaadcbadbadadddbdbdbccccabdbbacbdcbcbbccbdadbbdcbacabaabddbccdbbdadadaaaccddaaccabdcaacccacdccdbbcddbacabacdcccccbddbbdbdadbbdbaacaabbccdddabbbcddbcdabcdadcdbdabcccccadcaadbabcbdcbdbdabbbabbabacdadbbcbadacaaacbcbacbadcddadbbddccdabdbdddacadcbdddaaccbcaadbcbdabbcabbbbdbaacddcbadabcabbaccbcbabbdcadacdbcadbbabcddbcdacbabdbbababddbadacbaddbbdccaacadcbaababdccabbbabcddccbadbdddbdbbbabababccbbbbdbdcaabcbbadbdbdbcbccabcbddcbbdbdccccbcbcdabbdcddcbbadccccaaabdbaaabddcdbabaddcabacadcadbabdcbdbacbbacadcbcdbccabddabdddadcddabdddadbaadcbdbadbbcdabacdbbaccbdbdddccabdbcdabdbbaacbacacaacbcadbacccccbaaccbcbabdccdcaadcabacbdcacddbbabcccbdbacdcdbaccdbbaadaaaddcdccbabaacdabcccbcdbaacaababbabcccdacabacdcddccddcabbcbacacbcaacbcdaabccabdcbdaddadccadbbaccadccbaabdcbdccaacbbaaaddbddccbcdcdbaabababbbaaaddddbddcccbadcaaadbccacbbcbacbdcdbbcdcdcabacdcdcddadbcadbbdbadcacaddaddabadcbadaddcdbbbbdcbcdabcdcbcbdcacaaccadcadbbacabdbdddddadcccbccbdaaddaddbbcbcbabcdaacacddcacabbbcccadaaabbddcbcbbbbdabcbbdcaacbcadbcbcccacdacdbcadcddccacccdbaabbbccbccababdabbaacccdcddbdccddabbddabcdbcdcdadddbbcabddbcdcbcddbdcbbaacbcbbdabbaadbbccaaabcddbbdaddabdbcbadacccdaabcbdabdaccaaacddaaacabbdcdbcbcbbcddacbcaadccbcbdbdccddbcdccadbdaaabccbaabaacdbcccadcacddbbcabcacabdaadddbcbddccaccaaccdcbaaccbabdadbaaccaaccabbdccacbacbaaacccaacdbbddbadccbbbbddaccbcabdaabcbbdcbaabbccabbaadddddbaabacbcbdbbcccaadcbccdbcddccabdbbaddddaddbccacdcdcaaddadbcdbdadaabcadacbdaddcddddaaccbaaaacbaacddaabaaaccabcabdacbacbdddacdbdcbdaadbacbacdddbccccabbddddddccaccbdcddadadcbaaccbbaabcbadddddbcdbadcdccaaacbabbcaaabdbddbdbdabbcdcbddcabbadcaaadccacccadddabbbbcbdadadcbbdbcddaababbcadbbabdbaacdadcccadccaabaddcbbacbbbaccbadababccbbcacdbbbbdaddacccdbcbcacbccaccacbaddabacadabbcaccdcadcabdabbbbddacacabacbbabbbbacdcccadbbcddbcdbbbdabbcbcbcbadccdbccaddbadaadccdcdcabcbdddbcdaacbcddccacaaacccbccaddbccdabbaacdaaccbdbcdcbbdabcacaadacbdacaccddbcbbdaaddaaddcccbccbacbddcaccdbdbbddacddcaacbdacacbdcdccbacabaaabbcdaacadadcbbcaddbcacddddacbbbcaddbbcbadcdcdccccbbbbaaadacadcdddcaadbdcbaadbbdcadbdbbcbacbcbbccbdcacddcaaccdabbdbcaacbdababdbdabcdbdabcccbdcbcbcadabbabcbdddcacadbbabaaccdcbbbcdaaabbbacbabadabddbcbcbdbdaacbaccbdcaddabaddadbbcbccabacdbaabdbddaabbcdbabbdcddddddabbbaacbbdccdabcacbbddddcaaddaccdbabbcccdaaaacdcdbddcdaacbcdcbdbcdabadbdbcaaacbaddacaccbbdaccdbacdcabccdabadccbbbcdddbccacacbaaccddcabdadacdacdbcdbaaacadbdbbbdbdbbbaccbcbddccbcabcdbbcbbbdaadcdadadcabaacdcdaaacdcccdabbcbccdcdbcadccddaacdacabcbcdbadacbcbdbddddbaccdbaccbdcadcccaabbacdcdadadbdcaddbdcdabcbdadccdcbbbbacdcbadcbcacbdbcbcbcbcbbddccaddabcdbbddacbdcbaddcbaaabdccdaaaccacddbbcdbacbcacacaccaddddabdbbacddbbaacdcaddabbcccbadacdcadcddaacdacdcccddabaccadbdbacbcbababdbcabcbcbdbbdbaadbddcabbdacbbcabdbacaadccbadadbdcaadadacbacbdaaaadcaaaaadcbbabbbbddcbcdccadacbdbadbabadcdbcbcacabaadacadabdabcdcaadaccabadccaacacbabdaccabaaaadddabcaccabcddacaabdbabdbabbdbbcbadbddaddcbbabbaddadcdbccacacabbabbbaadcaabdcaadadbcbabcbbcdcbbbcaadbacbaccccccabadcddcdadaabcddbccabdddbabbcbdabcaacabbdcdbaccccbcccdcddcadabacadabcbacbacadadbbabcabcdbcbdcdbcbabbdcccaccdcddabbbdaababcddbbaccdbaaacbdaccbcabdbaacbaaabbabcbaddadbcbdbbadabbdbdadaccbaddcbdcacbbcbbddacabddbabacacabcccdccdcbccadcbcbbadccaddacddabbaacaaaacdddbccbbaabbbddadadacbadcdabdccddcdbacddbdcdaadacaacaabbbdbddbdaabcdaaaccacbaccadaddccbdbdccdbccdbcdbcdcddadcabbdacbdbbcbcbbaddccbabbcbcaccdcddaccccabcacdbdaabbabdcadcbdacacbabcaccbcabcccaaddaacbacdbbbddacdacbbccdbaaacdbcddbcbbbaacdddacbdbdbddcbacacbabddbcdbbaccadddabaddbdcacdbacbbacbdadadaccbbbdcaabaacdadddcbdaddbdcdccccdcdcccadacdacdaacddddbaacbdcccbaadcbdccbbabccccdddcddccaaadbdcbbbdbcbcdabacdccdbbbcbbdcabadbbacdddaccbcadbbbccccdadbbbcbacadbbcacbabbacdadccbccacacddabbbbabaccdccbcdadbcbcbdddadaaaccdbbdadabbbaddbccbbbaccdabbaaadcaaacbabcdcbaccccacaccdbbdadcdcbadabcdcdbabcaaacdcbbdbdabcbadbdbddacacdbbabbcaddcadbbacbcdaadadabbddbccddbadcadbdacdaacbccdcacdaddddcacddbdcbaabcbcdbacaadcbaabdacdcadcaddabaaaadaddaaadaadcbbdacbbdbbdcdaadbcccbdcbdbaccbbaadcaaccbcbbcccdadacbbccdadbdaddbaabaacbdbdbbacdcdadcbcddcaccdadacbbddadbacdcaabcbcdbdabdccaadbbadbabbbccbaddbbaddbbabdccaaaacbcbbaddcacabbcaaccdcbbcabadadddaaaadaabadaddcaccdcbdbaacbccaddcaadadaacdbbcadaacbcccdbcaadcadccaaccddcddadcdcbcadcdcccdbbadcdcbbaadcbadccadccbcaaadcbaccbcdbcdcdbaacbadcabcbccdbbdbccdabaaccdcdabdbcbacabaaadaddbaddcccabcbcddcccdbccbaacdaacbbdbaccabdcbcccccabdadbdabcabbbbcccdbdbdadaabdcabbddcdacbbddadabdaacaddbdbccccaacdcbdcdabbcdbbdbabbaadccbbdcdcdadabbbdcdbacdbaabddcacdbdbdadacacadbccdcaddcbdbdddaaadaddbdbadadccccbadbadadbcbcacabbbbdcaacbdbddcdccdbbabdcdbaddcdbdadaccdcadccadbbcacdbdbbcdcccaabcdbcdbbddbbddaacdbdddadcbccdaacdbaadbbcdabcaacaaaddaccbaadcdbdddadaaccaabbbccabdcddadccacbcccbcadbdacbbddddddbdcacbcbdbacdbcdddaadaacaabdacabcdcddbbcabcadbababacdbaddaadddbdddabdbcdcabbcdbcbbbbadadbadbababacbabacdcabccdcddadaccdcdabaaadcdccdbccbaaaaaabdccdbbcbaccbabacdcbdbadbaadbacacbacbbbddacdadcbbdabbbbdbccbabbdcabcbbcddacbdadbdadadabaadadabcabcabbdabcabdcddddcbaacddcbdaccddccacdcdadacbacbbcdccccbabacbacbacbdbdacccaaaaddbbbaabaadbdbcdaabdacabcbbccaabddbbddbbcbaaaabbbcaacaddbbdcacdaadabdabbdbbddbbbababbdabddbcddacccbcdcbdcdcdaaabcadbbadcadbdbadaaddbdbabdadaaadaadbdaacdaacbcdabcbbbacbadbdcbccaddcabbbbcdbacacaabcbdbabcaddaadbbadbbaabadbdbdbbcbdbcdacdcbbbcabacadabcccaacbcbdcdcdbbcbbadaddddaaadcbdcbdcbdbcadccbdccbabddcadbaaacabaaaaaadbcdcbaddacccbbddddddbadbbcbcbbccacdcbbdacbbabcdacdcbbaadcdaaaccdacababdddbcaaabddddddaaabadaacdcabdcaabcbaabcdbdaacddccdabcddadccbdccbbccdadccbaaaccccadcbdaabcaccccbddcccdddcdaadbcdbdddacdadaadadbabaddbacdbdcaabcbbcbbddabbdcdbbccbbbcddcbbbcadaddbacdddcaababaacbadbabbcbbbaabdbbcaaabadbbabdacddaabddaaccdbbacbdbabccbcdcbaabbdbbdcadbdaddbdacccdccddddadbbbccbddcdabdcacdacaacabcbbdcbadbdcbbabaacaddcdddbbcdcaadbdbbadaacbaccadbccbbbccdddcabacbbccdcddddadcbdbbbdbaccccdacbaaadbcabcbabddacbbdcddcaaaaccacbaabacbbcabcdaaaadcdcbcdcdcaadcdaabccbbdbddccbbbdcccccdadcbbccaaaaaaaadbacbcabdbdabbbadbdaacaddbddcabdaaaabcbaadaabdadbbcbaadbaddcacadbdcdcdaddaccbdbbdcadccccddbbcddccadbcbdbacdbadcbacdacaadddccdddcdadbababcbbcbcadaccacdaddcbccbbabcbcddbdcbbacbcddcdabdcdbcdbabdcdbcdbbccdcdcccdcbadcbbcaccbabbaccabdbdcbdcbbabdabcbccbadddadcacacdbdcadabcbbbbcabcdaaddbaabbddaddcdcbbbaadcbabdabaaddcdbbabaadbbdbacddaabbcbdccccbdbddbacbbdcbddccacdaccbbcdcdcbcbbdcbdbaadcbbabdcadccdbbbadbcadaacacbdcacaadaabdaaaaadbadbacdabbdadcbabdcaadcdcadaaacbbabbdadccbbcbdccabadbcdbdddbdbbdbabbbddadbbdbbddadaddddbcdabdddadabbcbbcaacbbddbdabcbcacaccabccabddccdccbaabacbbcadcabdbabadadabdbcabdbacbcdcabadbaabccccdacaabddadcacacbdbabbaddcbadaddadbacadbbbacaddacdbacbbdcacbdccabbcbbcbbdcbccdacdababbccaadcdcdbabbbbabdcbcbaabdcaaabadabccaaaaabdccaaaaccddcccddcbabccbbddaccabdbcddabdcbcdcdddcdccbccaccbdaadccbdcbdbcddbbcdcabcadbdaccdccbabdadccdacdadbcddacdaadddbdbcdbcaabbdcbaacbbbacdabccbbbdbcbdbcbbabbdcdaaddaddcdcbbccaacdadabdbccadbbabdcabdcaddcdabbdadbbdcbbdcdbbdcaabbcdddabdabdacaabcaccdbacbabdbdcbdbdbaabcbbcbbcbacdcbaaadadcdbbdbccdbabdcbcdcccdabcaaadaaddbdaabddbbddbadbacadbbcaccbddccabadabaadacadcacdabddbdddcdacbcdbcdbaacbadcadbacadcdccddadacdccbdabcacdbabddcabcaaabaacdbdcdccdddddcdaddbdbacdaddcddbadabddbaaaaabbddcadacbdcbdbadbdbcdbdcdadddadcacbcdddaadabdccddcdcbacacdaacbbdcddcbcddccdddcabccaadadabdcdbbddaaadcddbadadabcadbcbcbabcbcdbabddcdbcbcbaaadadcaabaacdbdadbccbacabddbdcbccccdcabadabbddbbacabdbaddacabcbcdccaabbcdcbccaddddbaaddbacbcacbaaabaabbdbcdbcccddadddaabbbcdaacbadcabdcdbbbdbcacdadacabacddacdaabdadaadcbabbacabdabdcaaaacdccbaccdcdbbddcbbdbcdcddbabaabcdbabacaaaacccccabbabadcbbacbddbbcacbacdccbcaccdbcbbdabcbabdacabbaadddbadacbaddabccdcbbcddadccadaacbdcccdbcabcbdcabbcadcaabaaacccabbbcbbadcbdcddabdbdddccbcbbabcccbbbbdcddacccacbbccccdbabdbaacddcdcbcaaadbbdadbacbbbdaddbbddadadbdabacbababacdadccaabccbccaadaabbdbaaaccbbcbcaaacaacbdbbbabbaddaababdabccbdaccdadabadbcaaddccabbcdcbbddbabdacbbbadaaaaadbcdbacbabbabaaabbadbabaadcdddabbbdbcbbaacbaddcddaaaaabcabbabdbacaaabaaadddbcdbadbbddacbddabcddaaddbccbbacdacaddaacbddcdcdcddcabdcbdaddbdadbccdadcdbdbddaddaddcdaaadbbadcbcdcbacaabbccabcdaadccaadabcdadcdacdbddcdacddbdadcdbbbabadadbcabcabbcaaadcadacadabdcccddbdddbccaacbaddadbabbaadcdcbdccaddaaacaabbcbdccadbcdaddddaaacdbcdabbcacabdabcdcbbadbabadbbdbdddabcbbbccdbddadccbdcaaccaaccbbcddcbcdccadbccbbdbdcddbbaaaabcbbccdbbbccbcdabbdabcddcacabadbbaadccbaccbdcddaadbbddccdbdbcacbdcabacacddccaaabadcbacabbbcbbacbdaabccaaccddadabdbacacbcdddacdcbccadbaaabaddacabdcbbdcccbcccbccdcbcdabcdbbacabdaacbbbddddddddcdaaadbcadbbabaaccdcdcccbbcabbbdbaadcdcdcbdbdbcddbababdcdacdbaabbcbaddbbacadcaabdddabcbdccabdcbbdcacbadcaadccbbadcadccbaddaacbdbaabaaddaaddadacbdddaaadbadcdcbccdcdabacaacaddccbdcacdacdbbddbacaadaaabdbaabcaaccccadacbabdddbdbdbcdcacbbccbbdcccacacbbdbbaccadcdadbdadddccbdcccabdbaacacbdacabdcdcaabcaaaaddbbabbdaddcbbcbbdcbcccdbdabdddbabcbcbdcdccdbdacabccacbacdaddcbdaacddaadaccdbddcbadcbbdcbdcdbcdcaacbbcabbadbdbdcbbdbddcadbabdbaadcaabbbdaaacdabcbcddddbdcdabddadabaadbccdbccdadabdaabbdaaccdbacbdaddccbbbdccbdccbaccddbcddbcdbcbadcbdddbaddaaacccdcadaabbadcdabcbabbddbbdacddcbbdbcabcadbbbdaabadbcdbbdcaaccbabcbcdcbcdbbcbccdbacdcaddbacbbbacacdacbcddbcddcddaabbbdbadaacbdbccbabccddabcabbadcbacbaaabdbdbcdaaddcabbccdcdccadbabacbbaacddacbcbcddabacbdabbccaccdbdbcdadaabddcacbbaacacaccdcdaccdadacaadccbdcbcaabaddcdaddabcbbcbacdaabadcbbbbbcaddabdbccdcdbcdbddbbccbbbbdbabdabbddaddadbdbdbaddcbbdcbdcdaddaddaacdbdddbcacbccddabbaadbcbdbbaaaccadbbbcdcabcbcdadcababbacbacbbbcabadddcdabbbadddbdbbaccddcccccddbdabccaccdcaddabcbdbdccacbcaddccccdbcbbbcbcbcacacbbdddbaccadcadbaddacaadababcdcccdabdddcbbbabccaaccbadabbdccdaacbcccccbbabcbdcadcbbbbbacddcccbdababbcaaadccdaacdaaabbbcbbdadcbabbcbaacbbbabadbbcdacbbacadadbdbdcccdaccadcadadbabccbcccbbadbddddcbcacddbddabbaacccaddaaabaddaacadccadcaaaccaaabbcaddccabdcacabddadadddcdbcbddcddadabcbcdbabdaacadccbdbcdbadddccbbabdbcbcbacddcdaddcaccabdaddaabbcccacadacbadddcddaabbbbdacbccabdaacdacbbaaacddccdddcbdbbbaabddbdadbcbbbcbcacbbaaddabddadacaadbabbaccbbcdadabcabcbcdbcabdbcdbabccdccadcccdabdcbaaabaabbdccdcbbcabacdcaabaddaacbcabbdadbddbadbdddbdcbbbadadbdcadabdbbcddbbdbacbccbaccaccbabdadbabaaacbbccdadbbdcbacaccaadacdcbbdbdcdcddacbcbdbbdadcbcccdbdbcabbacbcaddcadaacbccababdaddcaaadbcaaaabddddcdccdadbccadaaacbcdadbbdddcddcabddadbaadaaccbcccbdaccbbbccddccaddabbcdbbcbccbbbcddcabbcbcadcbbcabaadcccdcbbaddcacdbdcaaacabbcdadbcadadabcdadcaadacdcdcdcccccacacccaaccdbccabccbdbdcdbadccdbccdbbacbbabccaaadccacdaacdcdcbadbcdcaabddcbbbdadacaacdbabcacbaadaacdaacdddcbadcaaddaaaccdaadcaadbadccdbdcccddcaabcbaadabcbcacbbddacdbbdabadcccdadacdbcddbadccacaabcbddcbbbbcbcccbcbacdadbdcbbaaacdcabbdbdccbabcdbbddbaaadbabcdddbadbdcbaaacbaccadbddaacabbaaadcdccdaacbccbccdbcdcaabdccdacadddabababdccdabbaadabcadacddddcaaccbdaacdacdcabbdbdbbccbbacdbcdddbdccaadcbccbabdccabcdaccadbbbabcddbdcaccdabbdbacbaddabbadcacbabdcccabddabcbbdacdbabbdabcbddbcdbacddaccdcadbdaaabcaadcaababdbcbcacdabacdbbbccbcdcbcdccabcddacbbbcbaadcadbbaacccdaabbdbccbadacbcbcdbbbabdddbbbcdccadabaabddadcbcaaacabdbacddcdbbcbdbccaccdacbadcbdaadabccbaaacdcddabbacadcccbabcabdacccacabaddcccdabcdcdcbcdcdbacccdccddacdddccacdbabbcabbcccabdcbbadcbdbbdcacaabcbaadcbbccabdcdcbadcbdcbacdcddaccbbcacaaddddabbabababbbadbcbabbcdbdabdddcdadddddccaaabccdaacbaadacbcdbccdabcdbbbccadccabbbcadaddbbbdccadbdacbbdddacdbbdbbbdadacdcbbcdcacaaacbbabddabdacadcdadbaaccbbbacdabdbacbbaaabaacdccaaaabcbdadbbbadcabddadcbacaacdcabcdcbbbdbaaddcddccdbbbaacdabddabdbcdddbdcaaddbddcdabbbbbbdcdddbaaabbcbcdcbbbaadcbabcaccbaabdcadaacadcbbaaacccadcacabdddbdccddbbbbaddabccaacdbaabbbcbaaaddcbcadbaccbdacddddacbaadbadacabacdcdbcddabbbaaddbcdbdccbdaaaaaabcbabaaaaddbdacacbcbcccbadbcadabbaabdbacdbaddbccdbdccbddbabadcdccacbaadaccdbdcdddccbdadbabbadabdcdbaaababdccbcbcabaaccaccdaacccabbbdcbbacaaabdbdabcbacbabdcabaadddaccadbbcaadbcddacdddbabddbbbbaabacbcdabcddcaddddcccbccabbcbabbccabaabadaacddacbbbaacdaadaddbaddcadccdccdcdbacddacbcbabdacccbdcabcdbacadcbcbcccdbbabaaccdcbcbddbabcbdcadacdacbaadbaadcdcccbcdabbdabbcbcddadbcdcbbdddabbbcacdbbccccddccbbabccdacaaadcabaccacdccabcccabaadadccabddadbcdcabcbdababcbabadabcddcdcdbaccbaadccbddcbabdcacaccdbcbddbadcaaadcdaacddccbcccdbdddbdbccbcddbaaadcbabbaabbdddbddcdbbdcccbaccddacacacaaadcbabdcdaabcbdaacaabbdddacdaddabbcdddccdcccbbddaadacaaddcbddacdbabdddbcddbcdaaaccdcddbcccdacdbaccbccbdadacdcacaddcabbdcdddbbbccddadadbbbdadadbadaaaabdbbbcaccddadddcbddcdbbddcbbdadcdadacbddbdbcccbddabbbbbddbcccabcadbcdbdbcbbcaabdbaccbcccbadabbbaadabdaabdcdadbbcbacbadadcbccccaccbbaabdacbdabddccaabdababaacbbbbbbcaadbdddcabbacabcdcdccbabcdcacdbbcaccacbccdbabbbacccadddddccadaddbdcadddddabdcddaaaaaccdbcbdabdadbbdcacdcacdadbdacbdadcaaddbdbbbcabbadcbcbbcbcbdaadcbbbdaacdbacbadadadbcadabbcbcbacddccddcdabbcacbbcadaccacdcabddabddbdccccadaacdadddaccbdacbbbadacbcacbcccadccdccaadacdacdbcacbadcdbcdcaabbddcadbdbcabadbbcdbbdaabdabbbcbdddccdcddbdacdaddbabacbccbcadbcdbdddacdbcdaddbdbacaabcdababcddabdcacbabbacbbbdbccdadabdcadcdbcabdbccdcababdccaabcdbacbcddddbdaacbcdbcbbbbcbddaacdcaadcbdaadbdccbdabbcbbccaacdacdcccbbbbddccdbbbdbbdaadadadddddddcdbacbcccacbccccbbcbbdcccbbdcdbbcaccacccccaccbaddddcacadbbdccaccbcbacbcaacbbacdacabdbabdbdbbaacabcaccacbabbabaccdaabdcaadbbbbbccbadacadbccddaccccadbabcddbdacabacdbabbcacdbbcddaabdadcdabdddbdddcadcddbacbbdcacaddbbaddcdcdcbdacaacaadcbbcdacdaccbdddababadcaaaabaddbbcdbcdcbcaddbbddbdcdbbcdacbbccddbaaabacbaabccbddbddbcbbabaadbaaddbbcaadacdcddcbcbcbabcdaaaacbbcaaccdbcbcddcdcacbbaaacdbaadbccdaaabdbccbadddacadccabaaadacdbccdbbaadcaccbcbbcbbdcaddaaddbdcbccdabbbaabcbccadcdcbdddccbbcbaddaadaadbabbcdcddacbadbaacdcccdbdbcdaadcbaabdbdabccccacabbbddaabbdbdabbddbaaacbdaddcaccabaadababdcddababdddcdbbcbdcbddabaadbdcabdccdbcaccdaabcbbddacaccdbabddcadcbcdbccdaabddccdcdcabbdabdbdbacbcaabcdaccddcdbdabaadaddabbabbccaababbcdacabcbabccdddddadbacbdbbcbabaabaaacaaccabadadcbcadabcaabaddbdbdabdbccddbbbcccbbaadcbddbddbbbcacbccabccaccbdcbaddcaaacdabcbacaacabcbaccbbaddbbcccbccdbabbbddaacaacacdbdbadbdbdbcabdbacddcdcacbdbcdbccaaddcdcaacbdbaddccababccdcbccacaacbbcbcddaabbdbadaddcbaaabccbcddaddbbcbaadbccdadacabbaadbbbccccbcdbbdbabdddcbaddaabbbabbddbcbaddacbbaaadddddaacbcbadacdbbadcbbcddaadcbdabdacbcabbddccbaabcdaabcabaccbcabcacdaccdadbcddabbbcdabdbcdcddbbcbbbcbddbcdccadadbacdcaaabcdadbdcbadbbcbacbbaabcabcdbcdadadccbbabcbddccbddbabdbbcccddcdabbbcdddcbadddccbcdbdbbccbadadcdaababbbbaabbaaddbaabcccaccddcbdcbdbbabaaacccacbcbaadadbadcdacabbdbbcbdcabdbcbbcabcbabaabcdababadcbcaccbddadddcabbacadcaaaabbaacdbabddadcabdcbbaacbbddccdbbcbadbbcaacdaabdcbadcacbddabdaadddcbbbcaddbcdadaaddbabbbdbaadbbcdcaaacdaddabbbaabacbaadbababaababbdddbdabbcabcabacbdcbdaabdacacabdbccbabdcabbdbcbcabddacaaadcbcbddcbdabcdcdaabdbbbbcadaacdcbaabcdacdaccbcdaabcaccdccdcbccdbcdadccbaadaacdbdccabbabcaabbcbccbbbbbdcacabbbdabdacccabbbbadcbddacdcaaacbdbaaaaccddadbbacbcaddadcdcbcdaadbbdbbbcbbaccdacbadcadbcccbacabadaacaadacacdabddacdddbacbbcdcdbbcddcdbdcccadccdccbabcdbddaddabcadcddcaaadaabdadabbdcadddadaacdbbbdaabbdcdadbcbbcadaccbdbacaabdccdcdabcadbcbacbaaaccacdbacccaadddddbbddbbbbddddabcdbababcdabadddbaabdccdaaaabdbdcdcaaddcacbadadbbdbadcdbdaadccbcbccabdadbccabbddbddbdaadbaddadabbcdbcbcbaccbcbcbdddacacddcacbaabacbcbbdabcacacacccddacacdaabcacccacaddaaaabdcaddaabaccddbbdadaaccbdcddaacbcbdacdbdabacacdacdaabcacbddbabdbcbcabcacabdacdcbbabccaaacacdcbdadbbddddacacdaadaabdbdccaadcbcadbdbadacdacdccadbcbbacbbaadabbcbcadbdddadcdbadbbdcdcdbabdabbbadaddccbbccdbccaddbddddcdddaaddcacbabdcbbdcbcdbdbccccddcdccabcdadacaabacccbbdddddcbaddcdaadcbcbdabdbcbbdbbdbacdacacdabbcaddbbaadddaabbdbccbcbbbacabdcbcddabbdcadacdcddabccbaaabaadcbcacdbdacbcbbcbdbdbcbdcdccabccaacccbcdbdacacaddbdbaaaaaacddaaaccaccccdaccbdbdddcbcaddcddcbacccbccabdabaddadacdadadaddbbddbaadbabcbbdbabbcccdabbdbbddbacbdabcdadcbccccccdbacaabdddbbbbdddccadbcacbacdabdcdaaacdcaabdcbbbcbcbcaacdaabddcabaadbadabaacabddbddacdccdddcccccadcdbcadacacababbdcbddcdabcbdadcdbbabadabaabbaadadaabddadbbadcababbacaacadadabbbdbaabaaddcadddbaaabbdbaacddcbcdbccbddadaacdbacddcaacdcadbabacaacdbccadabaaacbdcaccadcbbdaccccabcdcaaacabccdcbdbdcddcdcbcbcccbbadbbcbdacaddaacccaadcaaaaadbdbcbbbcdccbbabcbdadabaccbccdbdbbadcaaabbaabddcacbdabcacccaacdddcccbbdccbcbbbcdabdadbbacdaaccdcdbbacdcddaabcabadbadbcbdcdadcbddcdabaabbddbabccccababadabaabdcaaacacdabbabccaabccbbbaadcbaaabdbdddbcacdcacaccbdcdcdcddccdcabddaccbbccabaddadccbcbcbadbcaddbbcacbacdcbddbcdbbadbadbcacbbabddbbdadabddcdacbbabdbcadcbddcbcdbccbabacdcacaccdbabbaddaddccbccaaaabdaacacdbaaabbcbadbbbaabbdbdadaccdcdaaaaaccdcdacabbcdddbcbaabccaddacdcbabcdaaabdaabadbbccabdcbaaaddbccdadaccaaccbbdbdcccbcccacbdcdddcacdddccdadcbcacbaccdaacdbadccabdbbaccbbadcadccdabbcaaabadbbbddadddcccdcadcbcacbaaccacdbcdbbbdadaaacbbdaabadacadbbcddcadbccbcbbbbaacccbadcaacccbcbbdacdcaccddcdacddcadddacbcbbdabaaaacabcbcbbacccadbbdbddbdccccbadcdbbcdacabbcaabacacaabadbdbaccbdcbbacdadacdaaaacddbbddcbabbdabdbdabcbbddbcbcabdbadddabdacdcbcdacadadadbdaddabcaacdbcbadadabcadacbaaabcdacaccbabccacabcbcadaddbadadaabbaaaabbabbcbccdaaaacaddaaccbcbabcdabbadaaacdaaaaabcdddabacdbacdbbbcdbbcadaabaabaadddcdaaadddbbccbabbcbcdaddcdaccbcbdcdacabcdcbaabaadaaaadaabcaccbacddbdcdbcdcaadcbbcbdbabadcaddcbabbdaddcbaabbdadacacccccbadaacbdbbbdadcbaccacbdbaddbdadbdaabdddadbcaadbdacbacbbacabacbbdadacbdbdbdadcdaacdbacaddbddacdcaacabdaccabbccacadbadcbaddadcacbbacddbbdccacaaacdcbaaadcbccccbacacacdbcdaabdcddcdabcbdbdbdabadddaccbcbabcaadcccdbbddbacaddccdadabcbdcccaaacbcbccbaabbdbbdcaaadbcdcbcddbdccbdaacdbcbdcdcaccaacccbdbadbcadcddadbdadbabadabcbccccacbaabacbbcbddcbcabdaadadbcabcccacacaabaadcddadccdcbabbbbccaadabdaabccddadcdbcdbcccaabccdcaccacccccdcddacdbcababcbdadbabdbcdcaabbaaccabdbdddacaaaccaddccbacbbcacaadcabbadadccaddbdcbcaadbccccdddcddbacababacacdbcccaddcbcddbcaadacdbcbacdbaadcddbacabadacbdccabdaacdadaccacadcddbddaadaaacacbdabbabcbdbcbdadbaaabcdbdbcdadadddbbacbcdabddbdabdcacdadadabbcdbcadaccccdacbccbcacdcdddcaadbabbabbdcbabbcbbcbdbdabddbcbdbadbdbbbcddbbabbdadccbaccdbbccdbaaaacdaabcaacdcdbcbacdbdadbddcabdcbddbcdabbcbaccdabbbdaaddabdccbcadcbbbdcbbdcbddccbccdcadbbdbccdcbccbcdabbcbbabdcadddadcddadddccaccbabddddabdbacbdacdbaccababcaccddbbabadadbabbcdcababcabdbbbcaabbddbbdccdbacdacadabbbadddadabaadadcdbadcababacabccaacbbbbdcacaadcdabccdbbdbbaadabacdcbabbbccbbbcbbdbdccddcccacdbdbdcddccbccbbdcabbbcaabdbddddccccaacadaaddabcabcdcbbbacbbbbcddddcaaadcdbaccdcbabaaabccddbbbadabadbbbaddbddbbabaccddbdbabcddcbbcdbabbbddbacbccbcabdccccabdaacdacabbcdcabdcaccddaaabddbcdcdbaacddadbcdcbdbccbbbbacddcdcadbbbbbaccbaaccbdddaccabbcaccaabdccbcabbdcdaadccbbabddbbccabcbddcadbdbcdbdadbbcdcdacbaadadbadccccdadcdddcdcbbcbdcdcdcbbaaadcacbacdadbaaccdabddbbabcadcadbdbbbcdadcddabdbadacdcbdbdcbadbdbdcadbacbacbaadbaccccaabadacbabddcbadddaaccbabbabbbddbcdccdaacdadcbddddadddaccddabbddabbadbaccdcaccbcddbbbcdcacddabbadbabbdcccbdddccbabccbdbdbdcbdaacabdddbcbdcadddacadabccdabadcccaacdbbcdabaabdcdcadbcbcdababbdbdacddcbbabdacacddabcaaaacdabbcbddaccdbbcbaadaccccdbadddddcbbdaaadbbbcdaadacdbaadaaabaddaddaacbbccdcdccdbaaaaaccbbdabbbcdaadaaabdbcadbaabccbdcbcaccbcbbabaadddcacbdcbabcccccdddaddccbdccddaaadacaacdaadbcbacdcdcbacadcdddbbbbcbcdaaabdbdabcabbbadcdcdabcadbbdcccbcacdcababdbaccdbddbaaddccdddcacdbbaaaadcddbdcbcabdcbcdbdacdccadcadbcbbdcbbdcaacbbdcbdabcdcaccdabcccadbccbccbbdcddbdcadbcbabccbdbdcacdbcdbaadbdaddcdbdaddbbdcdcdaccbbdccaacccabbabacdccaccbacbacaacdcbabcdbbabcdbabacdaabacddccabdabbbcaadcabadbdddadbcdccdcbbccdaaaadbddabddcdabdbadbbbcbbcabddcabddcdaacacaaacadbbbdaabccccbbdbccccacdcbbbcccaddcdbcdcccaaaabadbccddabaabddccbdbcdcbbcbbdacbaabddbcddacabaddbbadbcdbdcbbaccabdbacdddabadcaaccddacbdaacdcccadbbabcbbadacdbbabaabddbbdbdccdcacbbacbacdaacacbbcbadbccbbdccaababacbdaaacbddcccbdacaadcbcbddcdabccacadcbdaabccddaabcbcddbabcbaaccadcbddbdabcdabadcaaccbcccacdbbdddddadabacabdbbcdcbddbbcdaaabdbcbacbadcbaadabcaaddbaaddabacbbcbbdabbdccbccaaddbcdadadcaccdccbcabadaadadbabcdadaddbcacdabbcabbbcabbcdcbcdacbbcbbdaaacbdccbbcccaddbcbcdcaccdcdaadcdcddaaddbcbccabcdcbacabdbbaaadccabcadbdbcccccdabbaacccdbdacdcbdbddbdbabbdabbcdabbadbcbbddddbcbddbadaccbbcbacdbcdcbadadaddbaccadcbacbcccddaacbacaddbcdaabaccadadcaadaabcacdcabcccbabbdccaddaacabbcddcdcacaddcbddaccacaaacddabddcbabaaddabddaabbdcadabbcaccacbcdbdaacbababbbbbadbcdbcdcbcababaabdcbbbbdbcbaddcbccccbabdadbdbbdaacbbbbdbddbdbbaadbcccdcdababdacaababacbabccdcbacdccdacaabadcccddbaaddcbacadddcccccdaabbbcaacdcbbaccdccdddcbdbacddcaaacdbdbcbbdabdabdbbccbdbdbdcaaaadbcdabadadabbdbaaabbcbaacadddbddcbcbacdddcadbbbcacbdcaddcccdaccbaacdbacadcccbbaabcadbcbdcdbcdbadbaacadaabcdcabbcbbbabdadbcacdaadacadcbcbadbdbdaddbdcaaddabcbbcccddbdacabdddaabbbccbdbcdbdadddabaaaaadddabacddcdcccbbbcadaddcdcabdbcdbdbccbcdbadacaadccbbdcdaccabcdbbacccbbbccbcbdadcdddabacbdcbcdacabaadccabcadcadabaaaaddaabadbdddabaaacdbcbbdabccaccbdadbdcadbcadccaddadabadbbbcdddabbbdcddbabadcdaaccbaababbcdccabaccdddaddbbdcbddaddbcbdabbaadcadaabdddababdacacbbccccabcbccdbbcbabcaaacbaacdaacdadadccdcabddccbddbadacdabbdddabcdbcaccadacbcabbdcdbdaadadddabbdbbbdbadaacacccacdabcdadacbaccbccbcbbdccbabdbaddbbabaccdcdcbcdaadabbbdbdcccbcbbbabddaddddbdbbdabbabdaaccdcdccbddcbcdbaddbbacbdcddadcdcddccadbabdcdcddabbabdcadbdbdccdadcdddbabbcddcbdccbbdabadbbbddcbaadadaadaacdbacdcbdddbddbbdbcdacacbcacbddcabcabccdddbbacdbbbbdaaaabbcbbdbaadabbabbcabcdcdaaaddbcaadadaaadcacadddbacccabdbaaacccabbadddcdbdacaadbcdcadddaacbdabdcdadabdbcbaddccaaaabaacadcccadbbbacaabbddbcddaccccbbcddacdacaabcdbddcaadaccdcbdcadbcbabbcbcccdcbcbcddccabcbdacdbcaabdbadacdadadcbdcacacdcccdcacdddadaabadcdcdacacbaccaaadddadaaacccacabdcdbdabdabcddabbbcbaadaaacadaccbbcbccacbacbcccbabacaabaadcabdccdbbbdcbdacbcdccbaccacaadbcccaaccaaddacbabdcddcdacddaccdacdccacbcabbdbbbbaabddacaddbddccadabacbcbbabdddbcddbabadacdaccbdabddcddbacacdddaaccacdddcbdbbcccddcaabdaabcacdccdbdcccbdbacccdddddabcdcbcbbbdaaaadcdccdadddacdacaabcbaaccdcabcdddcacbabcacaacacacaddbaacabcadbdaaadbdaacadaacbbadbadadbbaddbacbdddcccbdbaadcadbaadddbbddbcaadcbbcccbacacbdabbdbdbccbadcbaccdbdcdbdcbaacadddcbaaaddddabcaacbddaaaabddbdbdaabaddcaabcbcabdcadbdabccbaacabbbaacaabbbdbacddbcbcccdacaddbbadbccdcaaaaacabbbbcdbcbdacddabccdadcccdbdbcdbabcddccddbacacbaabaccddbcacabaccbbaadbccdaccccdcbbddabacddaadccdbcdddbbddbbabaaccbcdbdaadabacdacadbcdccabdaacbbdccadbadbbbcddccaaddacaccadcdcbadcbdaaccddcabacbabcaabbcdbdcbbcabaacacbadacbddaabaacabbcadcdabcdbdadbddcccbaddaaddabbcbbbbaccdcaaacaacdddcaddcdadadacdbdacdbaadddadbcdcadbbaabdacabcbadcacdcccacddbaabbaccaaccdaaabadabbddadbcdbdcdddaccddbbccccdcdabcdbdcdadddaabbcddaabcdcdbcbacbbdcdbbbdcdbbababbcacdbbcbcddbbbbccaccaadaaabccadbdacbbbabcabccdbcadddbcdaaabacaaadccdbcccadadacacabdbabbcdaddacbabcabadacbacdbbbaadadcadbddaaccdcddcabaaddbacbccadbacadddcccbacccbadddaacbdcbdbddddbbbaccaadbacbcabccacabaacbcbaccccabaaddadcdbcacccbccdabbbbaacaabacdddbadbdddabddcdbcacccdaaccdbbcccaacdbbacddacacbdabdcbccadcccbccbbbcacdccadbcaccdaaaddbdddbacaabbccacdaaabaacdbadbbabcadcabbbaddacacbdbdbddaaaaddbdccbaadcbdaadaaadaadccccbcadaababbdbbdacbbbbdbccbddcdbbdcacaadcbddaabadadcacaabcddddddcacdbcbaabdadccbdcccaaabdcadbcdddcbccdacbaabbbbdcbcaddbabadabcaadbbdccbdccbabaadbbdcddcddaccdbcaccaacacaababaccbcdaacdbabbbcbadcdbdbcbadacaabcabdbcbcccaacbbbbabddddadabaccccbccaacbaaaadcacddbcbcabdbabaccddbddbbbabcaacaadcabddbcbacbccacbbaaabaccbabdcbbbcacdddddcbcaaccaddcdabadaadbacabdcadbbcaacbabdcbaccdcbcbadcadcabdaaaacbccdbcaaccabcdbabdbdbddaaadabccdbcccdaabcddaadacbddddaddccbaabcabcdcbbdcaacacdaccababaddbddbdcccdbbcabdadbccbcaccabcdbdbbadbdbcadcbccbdcccdcadbddabdbddcbbccccdabadcadbdbabbcaaadadcaccccadabacccbcacbcdbccdcbaaaacaabbbaabccbccbdbccbdabbbdbdaadadddbbbaccbabdcdacadbadbbacdcbbadadacbabcbadbdcbabaccbacadadbaaaddcbaaacabbbcbbdcbadabbbdcdddadaabbdaacaddcadcdcbdcbcababadcaacccddbaaadbadcdacdaddbdacaccdaddabddbbccccccbcadadddbaabaacacccdccdadcbcaddcdcadcbbacdbaaacdbbccddbabbadadcdbddcbcbddabcabdadadcbaacdaacccaacaabcdccaabdbcabadbadadbbddcaaadddbcdaaddbaddccdcdadbabdccccbbbacaccdbbddcdccaccaaaaccbaadbddbcdacdbbcbdbcbcadcbdccbcddaadbcdcddccccacadbcbcadcaadcadadcaacbabbdccadcbbaddccaccacdbddbdbbdcaaadacaacbdcaddaababdcaacdbbdcbdcbdaadbcbdaccddcdcacdcbadaaabdccabaabcaddcabbccabddcacdaccaccbadaabdbcdccdadabccabacacbdbdcccdacababacbddbbcccacddcdadbcdcaaaabaabddcccbacabcdcacbdccdddcddabbbacadddaccbbcaaddaccbbaaccaabcdddaaacacadcddbdcbbbcdcdcbbdcadbdbbdaadcbcddcddddbaccccccbdabdbdbacdbbcdacadcbaacadaacccbcadddaaaddaadaccccdbbcacbbcacdcadacddbbacaadbcbdcaabcdcdddbdbdacacddabcccbcbbbbdbaddaadcbdadadbcbbabccdcaddadccdbdcadbbacbdacbcccbbaabacbddcacbbacbbaabaddcbcabbdabbcbbdacaabccbaabdbcbbacdcccbcbabaacccbaaaabcadbcdabacbdbdbabdbdaaaccaadcccadccbcabdcdaabbaababbbdbcbbabdadcbdcdbbaacbaabbcbdcbabbddcabcacaabbcbdcbbbbbbbcaaddaccdbcdbdabadbbdbaacdbdcbadbbdcaaaababbabccdddcdaddcacdbacaaccaabbbcdbbcabbbdcabcaacacacbccbaabcabbdbacbdddbcddcabbbccbdcbbdbadaadcacbacbadbdccadbcbabbacbbadcbcdbdcbbaacbdaddbbcccddcadacbbbbaaaddccacadcbcbaabbbdbdbdabacdabddaabaabdcdcbadbdbcccddbbcbadbdaacbaabcbadbcbbbdcdabbcdbbaaddccdbdaabbaaacdbcccabcccbcbdbadaacccdbddcbdabddacbbaabadabddbdbaddbbcbdbcddacbdbbbbbdcadcabdcddaddbdacaabbcadbdbacdacccdcbdcbdccbdcbaacccaccacabcabacdacadcddcdcacadcccccaccabdcbcbcdacdbcabcacbadcbdbadaabbdccdbadcbdadadadddbdccbbbabadcccadaddddcbcddbadbbdddacaddbbdddbbbbaabbcdadadbddbdccdbacbbddbaacdccaabccccdaaadcddcbbdbcbccbbddabdcabcaccddcadacdbdcbcbdccbcaddcbcddabdcdaddbbcdcdddcccddcaacdbaadccddadbbbcdabbadcaabbbbcaccbacbbcbccbadcbadaadcabcdcccbdcbcacbdcacaccacbccabcdaabccacabaabccabbbaabaaadaabcccbaddabbdbbaadcaaacabccacabcbdbabadbbabadadcccbbdaaddbccbaadadaabacbaacdbcdadddcdacbdabacdacccdcbbcabccdaacadbbbccaddddaadcbdadacacbaddccddddbacaccabbdbddbccabcbaabbbddccddcbdcbbbadbacbacadbbcbbaaccbdcacdccbcdbcdbcccaaddaadabccabdddcbaccdccaabadabbddccdcdabaddabcadcbbabdacbcccddbdcdddcccdadbbabbababdddbaccbabbcabddcacbaacccbbbccddbdcabacacdaabcbcddbcddbccccbbabdbcadcdacbcadacddadaccaabddadbcadcbacbabbbbdccdcadcddbadaabbadccdbacacbdcddccabbdcbcdbcacdccdbaabadaacabcdbdddaccdbbadcdbabcacbaacabbcbdccddcbcabdaaabcadabdbbabccdbacccdadbcaccccabbdcaddcdcccbbdcbabbdcaacddcdbccdcdccadddadcbbabdddbcbcbacbdcbbbdccdbccdaddacbbdaabdcaacccbbbdccbdbabaddcccdaadcbcabacbdacbadabaaaadcaacbdbcddbcbaacaaadcddbcbdbcaabcaccdacdcaabbdaaaadbaaccdbabbcdcddadbbccadabcbccdabaadccabaddbacabcbbaacddcbbabbcddbccdbdadbbdddacdacbbddbababddcdccabbdaddabccdacabbdabbccabdabdadacbcabbdddbcbdddbcadbacccabcaadbdacbdaadbbaadbaaabacbbabccdadbcbbcdadacdcadbdcdacdbcccddbbaabdcbaddbbdadaadbdaccdacabaacacdabbdbbbbcbabcaaccdadcccbbabcadcbdaaccbcbacbbbddbcccbcddddbadaccbdadaaadadcabcbdcbdadcbdcbadcaaabbaacdaddbddbcbdcbcbccbbcccbbccaacaabdcbbbdcabadbcdddccbbccdbadabcbddbccaacdabaacdccadbbbcbcbcdadbdddabbbbbbcccdccbdbbdbddcaacabcccbccdabaccbbbabbababdadabbdbacbbbcabaaaadbbaaadcccdcaababdbcccdacabccdacdbdcbbadcddddcadabaaccacdcabbbdddadcbcbabddcdbddcbdbdbbadbbccccccbccccdbdbcbdcaabcddaacbaababbabbcababdabcaadbcdddadcabdcccbcbcccabbdbdaddcbaaccddaaabbdbbbaccbccbbababcdababadcdaccdbbaaaaccdbbcbadacadbaddcdcccabcacbbbccdddddbbbbdbbbcaddcaaccddcdadcacbdaadcdabbabbabbaddcbdaabddaaacbbbcdcdbaddacadacdbdbabacbdbdcddcaabdcacbbbcdccaaaaacdbcaaaaacdddaabdbcbddabcdaaabdaddbabdadccabdcacacacbbdbbdadadddccbcdcabacdbaddbdaabdcacbbacdcbcdbcbccacddcbdaaccdabddbbcbbcdbcbdcdddbbacaabcacadbdbaabbbccbdbaaadabdbadabcbdbaacbaabcadbcdcaccdbcdbabbbbbbaacdcacaaacdddabbaadcadcdacddcdabdccdbdbabbbbadabdcadddbbcaddddbcdaaaababccaccbbadbcbadbdaaaccacaaacbcababbcbcdaabbdacdadccabdcdadbbccadbbabcdccdacbdcccdbddcbbacbbcddcabbaaddcccabbabdbbcbcdbaacacbdddaaaabcdcabbacbcadcdcdabbdcbccabaadadcdbbabacccdadcbdcddadbbbacabaacdccbcadaabaabcbddaadddbcdbdbbbbbadaaabdccbcdadabbdddaaadaacddaddbdacddcdbbcdcbddcdcabbacddaddcaaddabbbdcbacbbacbcbcbddcdbaccdcddcdbdcbddaddcdbcdadddddabccbbcbaadcaacaacdcdaacbdbbbabaacddcaaabdbbacdbbacbcbddabadcdaabdccadacbabdadadacacbddbdcaabddddcddcaabdbbdaccdbacdadbcabcdaaccacbcaaabdbcaacdccbdcbacddabaaadbacdcdababadcddddddcabaaadbadcccccdbabcbbaabddbcbacdbcbcadbbdbbcacccdcaccbbcccabdbadbcbdbdaadbaadcaddbdadddcaabcdacabaabadcbaaccaddacaabaaadbcbabcbbccaadcadcabaacbbdaccacdcbcdcabdbbbcbbbcdddadacdbddbdcdcdccdabcdabdcdbcccbdddbcccabaacccadcbbdddbcbcdbabccdabadcbddddaccbbdaaccabbdbcdddbabacdbcadcbdabdcbbaaacdbbdcccccbdbcadadddaccaabddbdcadbabbcdcdabcdbdaacabdbbbdbbdbcaacbdcaddaadabbbbdccbaadbdbbbbbcaacbcacadaabdddbcbaaccbdababbabccaabdadcddbcabccddbcbacaaadcdaddbcdbbacacbdbbdacadbdabdcadacbbbcdacbddbcdaddccbbdbbbcbdcbbacadcdaccbccccadccbbaacbaccdcbcabddcbccbbdbdaacdcbaacacdabcdccabddabddccddcadbdbbcdaddddbdbcadcaaaddcdabaddbdacadaadaaacdcdcbdaabaddbcdadacadccbcbdaddadcbdcccaaabcdbdadacbdabadabbcdbdaddcdcbdcbadcbdcaabbdadadddbddbacbddcacdbbbddcddaacacccaadaabccabdbdcdbdadcdacdbbcccdcaadcdcbbdcbcacadbbadaccacbddbbacdadcaadbbcddcccbcddcddbcaaabbbbcdbacbddabdaadadbcaaacadabcbbdbbbababdadcadaaabdddccbccacccbcdbabadabbaadbaddbcccbabdadadcccbbadadcbdabcddbcabadaacaaadccadbccbdacadccdcdddbabbadbcaacaacdaabccbaabbddddacacdbdcddbbdcacadbbcadcbdddccdcccddddaabbaacdaccbddcbaddcacdbbccbcaddabaaccaacaaacadcaddaddddddddaadaccabaabcdbddbacccbcbcaddcddbbddcbcbbbdbdbbbadabcbcadcdacccaaacddcdcadcabbbadabadddbddadcdbbcdbaaddacabddabababbbadbdbdacabbcddddcaacbdadcadbacbcccadddadaacaccabdcbacdaaadbdbddadaabadddcdacbdbcbddbcbacccadcbbaacdbdbdaabbdbacaaaaaacbcbdacabbbacbadcabbabcbddddadbbabadbbbacaccbdcabacbccbbaacaabbcbccbbaccddcddadbaacdadcbaacbacbadbddaaadcdadcbacdccbacaabdddccbddcbbcddcadcbdadabdbdccadaadcbcbccadbacdcbbcabdddaabcdbcadcaadcbddcacbdccaddddbbcadbbdbbacccdcbdbddcddbcbdccbdccccdddbccdccccbccabbdadbabddcadcacccbbacdaacaadbabdcbcbdbbacacddbdadddaaccbbdbadabccbaaccbbbabbbbddcdcacbccddddbbbbabdabcbccaccaddacbdaccaddcbdcccdccbbccaacdbacdcdacbdadcaabcddbccccbabbaddabcdbbaaaabdddddabdddbcbddddbddddcdbbcacdabccaacddcbabbdbdcccaacccddbaddabccabadbacbadddbdbcbdbdacdcbbbdadabdccdadaacccaddaabcccabcbcadaababcbbdbdabcacdcbdcaaabcadccbcdbbaacabdcbacaddbcbddddccabbdcdddbcadcbddacbaccaacbdaaccdccabbcdacaadbcdbdbacddbacccbcdadbdcadbcccadccddbbaacacdaaacadcbccdddcdcbbcdcaccdacbcbabcabbbcccbcabbbbabaacacacaabddddcabccadbdaaabdaacbbbbcaddbcbacbcabccbcdbbdabbbcdcacdaccdcbcadcabcbabdccdcbcaccabbabcbbdddadddddacdbcbabcddcdaacdbaadddcdacbbadabbcaccbdabcdcddacbdbabbacccccccadabcacccdbaaaaacacaccddaacacaddbccabababcbdbddabdbacadcabadccabaadaaacdcbaccbbaadbdcbaabbccaabdbbdaaadaacadaacdaabdddaaddadcaadbadbbbdbcbbcddaccdccdaddcdcaccaaaaadccbbcadcbdcdabaabcabbdddddddaabbbdadbaddcdcbbcaadccadadaaddccaddbbbddccddadaddadabcbbaaacdabaaaabbaccdaccaccdabccaacacbbbcbabcdaabbdaaccdaaddbbaddccddbbcdcbdddadccbbcdbddabdabdcaacbccdbdabdcadcbbcaadbbbccbbddcddbbbacabdcbaaadcddbdacdbacdabddabdcddcbbababcaacbabdadcdddbdcdbdaccabdaacdcaabcdbaddcbaacaacadbccbcacbcdaabbddcdcaaddbdccdccbbdddccbccadaadaddbdbcabababbddadbdbaaccbdbbccbaadaaaaabbacddabcbccbacdbccbbdbaacccdcacbbdaddcbabaadbdbbaaaacdbcaaccbdacdbaddbbadcbbadcabbbcddbdbcbdadcdacdabddcbbadcdddcbcdaaddcbcdadababccacaaaabbcadbacdaabbaadcdccbdacdcdcaacabdbbdcccccacdbbabdcdbdbcbbbccbbdbbabdbddaaadbadcccacdacbddddadcdbcccdcddaabdbcabadbaaddcccddabddcaadbdccacbacbbcbcbddddbcaddcdddabaadbcdbcaabacbbcdcabdcdbabcbbcadcacababcacacaddcaaadcbcbcabdabbddcbabdaabcbddbbbaadbacbbbbcddaadcaabcabbadabbaabaaaccbbdcaabdbbabdddcbdbbccbbdbbacdbcddaadacbbaabdbaddcccabadbdbcbdbcababaddaabbccbbaccdaacbccaccbdcaabbdddbcabbccbbbabbbaacdbadbddabbacdaadddacacbbbbabdbbdaaddbbcaddbabcbbcbbcbbbaacbbbaabcdcdadcdcdbbdddbbdcccbaddbaadbadcabbbaacaaccbddadcabadddcadadcccacaddaddbddbddbbcbcbdbcadccbdbccacdcbbcaaadcaabdbadccbddacabaaadacdcacddbbbdacbbdabcbababacdccbdaacbdcbbabccccadacabccddabcccabcbdabaabdaaccdadbbadaddabcbccacbdccbbbbbddabdadcbcabbbdaadccacccccdcbabaaabbdbddbddaabcddbdbbddccadcbacadcbbabddbaacccbbbdadcabdcdbbdacdddcadbdddbcabcabddbcabbbdbccccaadaaadbcacdbcbccddcdddcbbacbbbcbdabbdcababadaccddaacadcdabdbadcbdabcdcbcbabccddcaabaccaadbdbcccdbddddddbbbabdccddbdcababaaddddbcccbdcaadbdbdddccbbaacbbbddcdcacdcccdbaacbbaaaaddabcaddbcbbcdcbcacdbbaacbdaabbcacdddabbdbcbcadbcbdbddacadcbbcabcacbbcaacadddcdaadabcbaacbcbbddaaaabaddcdadcbacacddbdacadabadaaaaabaacbccbbbddbdcdacbbaaaabccababaabacddbcadacdbdcbadadbbdcdacaccadcacaababcadbdabadcddccaaddbddbbaadccccdadabcbbcddbabcadabadbabcbbdacabacbcbdbdadddbdcddddcaaaadcdbbabbabbabddaaccbaadbabbccddcdbadbcacdbdabbdcdadabaddbabdcbabcdccbcdadbbcbddaddcdaabcbcaaccaccdcbbbabccaabacabacdadbababcabcbddbbcaddddcdbcbbbcbbacaaaccdddbddbacdaadcbcaaaddadcddcadcdcaaadabbbccbaccccddddcdcdccbbabdddabacdaadadacabdbadbdbcdbbbaaadcdbdbccdcbdccdabccaaababcadbbadbacadbcbadbabcaabacdbddddcbcadbbcddcabcbbccacccccdabacbbdcddababacccaabbacaaadacaabdabaabaacbcbdbbdcabbcbadaadaacbadbbcabbabbbcddbbacbadcdaddbdcbbccaaddddcbdadabacdbdddcccdbccacabccacabbacdccaacbdaddbbdabacbcdaddadcdbccdbbcbccabbadcdaddbcbdaabbdbdacacabddbcddccbdaacbddcdbddcdcbbbaadbbbccccadcddbaacacdbbbcadddbcbadbdddabcaaabdbbccddbcccbaaabcdabbaabdcbcdcbaacabcaaabbbcdcacdacbdcaabccaddcdbbddcbaacacdbbcaacbcadddadbbaaacbaaacdbdcdbbcccbccbddbcadccdbbacacabadacabdddddddcdcbccacdacabcbaaccbccacabadcdbccddccaaccddabaaddccacbbadbddbccdabdbcbabdbdbbddaadadacadbcaccacbdbdacdbabaddbbdacacbbacabbdaddbbbaacbbdcddababdaabdbdccdbacadacaddcdaabaadcbdacdbcbcdcdadcabbdbaaaabccdcaccddbdddbcdadaabbbccaccbbddcbdddbdadddadcdddadcbcbdbccdcdadbdddbcdaddbddbadaaacabdbbbacbccbddbcaacaacababccbbdabaabacdcacbacddaadaaccabbbbacbbddacbadcaaabacddaddcbcadaadddbcadcaddabbdbadadcdccdbbdccddaddbddcdaddadaddbcdbabbddbadbbaabdddcbaadcbbaadcdacdaabcbadcadddaccabcddbcdddcdabbcdccacccbddadccadcbdacbacdcdbcdacaaddbdddaaaababbdcdbbcaacdcadcddddaabbcdaadcacccabdcacaccabbabddcdbcadbcdbdbbbcababdbacbdbcbadbcdbabadcdacdcddddadcdbaddcbbbacabcaaabcdcdacadccadcbccccacadcddaadcdabcdcddacccccbadaaccabdbdadbbcbababaccdcbcbacccbdbbdbcaacbabbdddbbbccdccccdbcbbcbadaabdddbdbcdbdaaadbcdbdadcadbdabadbcacbbcbdaabccacdbdcdbdcabcdbacbaddddcddcaabcadaacaaabbcbcbababbcbcabacdcbcbbccdddcdacbbadabbbdbcbaabdcabbcbbaadbcbdccaacdabdacccbddaabbcddcdbbbcbdbbbcdadcbdabbccadabdbddadaddaddbabcbcbaaabaaaacccdbbbbbaccabbbbcccdbaaddaaacadcabcadabcccdadabadaddaaacccadababacdbbcbabdaaacbbaddccaabadabbbbccbdacbcbbbbbcddbabbcbadcadadbbbbaabdbcbdabbdacaadaaabbccdcacaabadaaadacdacccccdbcaaaabdbabdbaccbadaccdcbccccaacabbccbabcabddddcdacddccdacaabbbcadacabbccaaddbbacbadbcdbacdabbabcbcbaddabbdcbacadabacdcadaacbabbaadacbcaaadcddcdbbaaccbbdcdcdbcacbbcccadaacdaacbcacbacddccbddbbcccbdbdbbcdbccddcbacdbbadcabddddaccbcccacccacdbbdaabbcadddddbabdbcbbcccbadcadbdacbdaacadbcbadbdbdbcdaadbcaccdbdacabdbcaddadccaaabacadbadbbadcdabcadbacdccccddbcbacbbdddabcdcdbdcbdbbacaacbbcaddddcdcabddcdadadabcaccadababddabaaaaabcadbdcadcaddbbcbcdcabbdbaacbdbdbcbbcaccdbadcabbcdcbcbabdacaabcaccdddbdbbcdababdadcbbccdbaaadbcaaccaccabdabcdbbbccaaccaacdabdcccbcaccccadcbdcbacddaadaacccddadcdcbcacbdabbddcdddbcabcbcccdccbddcaddcccbcbbdbaadabccaadaddbcbadcaaaabbadaddcabddadbccadbcadcdcbdcdbbabdcdbbccaacbcbaaaacdbbbbababddcaabaaaacacddcabaadacbcdcddbbccabbabcdccdbdabcdabaccdadabacaacdcaaadbadaacaaaadaccddababadbbabbadadbdbabccdbddbccaaaddaccbacaababdcadccbbdcddaaadbcddbcacdbdaacbdbdcccdddbcacdcbdcbcdcccaadadcacbcdcbdadadbcddccadccbbcacbcadbcccdadaddaaacacdccdaaadddcaaacddddddbabcccdddacacdadddbaaddddabbdaaabbabcdccbbcabaaaacabcdbdbbaabbabcacacbbadccbdccacbaabcaadccbdccddaababacbdbccbdadabdccabdddcbcbacdcaccbbaaaacaadadabdaaaaabdbbbacaabdccadacadbaadddacdccccdabadddbabdcadabcdbcdcabacbdcaaacbcadccdaababdbbcbbaaabbdbcdaadaabcdacbaaabddaddcdbddcabcacaadabcaadacababacabaabcddcbdabcabacbbabcbbbddaabddacccbdabcccbcccabccbbdbdcdbdcbdbdddbadaddbbaaddabacbcbddccbbccdcddabbacdddcbabcdbdabcdadbdabddaadcbcbcaacbbdbadbdaaacbdcbbcbcbbdcadaadbbdbbabdaccdbccccbababcddbcbacddddbbbacabdbbdaacaadbbbacdbbddacadbaaaababbcadddbccbcccdaccbbadabcdbccdbadbaacbcdbacbccabbacbbdbcbcaccdbbadcabababbddadcbcdbdcccddaacdcddbaccaabcddcabaaddbbabaaccabddcbbdbdcbccbcddbcaaddcbbadaaabbddbcdaaccdbcbdcdcadddcddbabdabdbddababdbbbaaadcccadacbdddadacddbbaabadbcaccdcabbaaccdabcccbddabacddbddaaddaddaaaaabdacbddbccadaaabdcabbbcbdadbcaddccdcdccacdccaaacdbdacdddddacddaacdbcdbcdddbdcbcdadbbdacdcbddabcbacdaabadbbacbcbcaadaaccdbdcdddddddcbcbaadadaddddccabccbbccaaaddbacbddadbcaaacbdacddabaddadddddcadbddadaaddbcdcdbbdcdbbaaaaacbcdddabddcbadacddacddacccadcabdadaabdaabababdadabccbbbadbcdddcccdcaccbabddcddbdccbbabadcdddadccbcdcddbabcabbddaadbaabacbbbbcabdadbbbdddcdbccdaaaddabbddabadbadbbccdcbbcbbbcdbbdcbadddabbbaabaabcdbcadaaabbabbbccddbcddbcbccddacdddcddbdcdacbcccdabdcaacaccaddbacaabccbdbbcbccadaccbbcaaacdddacdcddcdccccaddbdaccdababbabbaaccdcddddbdbdcddbdbdbbbccccbccbbadddbdddcaccbcbbccdaaadddadbdbbbcadaadccabdabacadacacdaaabaadaccadaddaabdacbabcbbabbacdabdcacaccbccabdacadacaabbbcabccddcbacabacddabcabadadcdaddbcdcdccbcbbbbcdadbabaabbcdbdaaccacbbdbdaddddcbcabccaacbdadadabadbcabcaadaddabdaabddadcaacadaccacdcbddcabbadbaddababcaabcddcdcaaccccaacbcbabadbbccdbcbaddadaadaabdcabcadadaaabdcbcabbbbdaadadcacbadbcbdcbdccaaababbdccdbacdbcaacbbbdcacacbbacabdacbccdbbdbbbdbbdabadcbcabaaacbbbbdbbbcbdbacbbdbdbaddcabbaddbddaaabbabbcaacaaddccdbcddbcabccbaadcaccdbdbccacbbdbacdcbabcccabdbccccdbbbcaccbdccaadcadabaddaddbcdaaaaadcadccabaaadcdaacbbacdaadadbddbcabdacaabbbccbccdcbbbbddbbcdddbaadadbbcccacadadbaaddccbddabdcddcdcdcabbbacacccbcbabccddcaaaabcddaacabbcadcabcdaaccbbadbdcaacdbdcbadadcdddadadaacabddddbdcdcccadaabdabcaabcadccacadcacddadcccccbccaadbadaddddbcbdddaacbdbddbccdbccbcbcabddbcbcccadaccddbcbaddcaaaabbcdddbcaacabbbadbdacdbacabaaddbdccdabbabcacadbdddcdcddbbcccbcbbbabdbdddcbcaadaadabdbdabdbbdbcdacbaadbcddacbbbbbdabddaacccddadbcdbcadcaddabdcbccdcbbaadbabcddccacabcccddddaaadbaabdbcbcddcaaccccaaccdddbbccadcbbbddbcacadaabbcdabcacaaccbaabcbcbdbdaaccabbbbbacadaaccbbbccccdddbcdabbdddaddcdbbabcacbdaadbccdacadabcbcbaabadbdbcbbbdcbbddccdbadcccabcbdcddbaddcbddddabcddccabcddaabcadbcbcacabbcbbacccabbbddabdbacdbacdbaadbbcabbaadaaddcbddcdcabccbcabdbaacabdccdadcdddddbccddbcabaddaddbdaadcdbbbccddaaccdcbbccbbaaccabcdadbcbcbcccbcbaaababbbcddadbacbcbadcdacbaacddacbdcddadbadacacbdcaddccabbbacaacbaaddadccadbcddccadadccbaaaadcdcdcdaabcaaddacbaacbcdbbbdcadabdaaaaacadddcccdbbbbabbabcadbbadbdcdabbdccbcadbdaccbacadbdbbaacaacddaabcadddbdcabacddabbabbabddabbcdcddcbaacabdcbaadcbaddbabdcababcbdddaabcacdddbbdabdaccaccaadbacbbdddddddbdbccbbaddabaabdabddddaccdbaaabccdcbaccbccaccccbbdcaddcbbbcdbbcbbbddacaababadbddbddcadbdbadbaddcacccdbcaacadacabbadddcbdddaacabbdcabaacaaacddcdbdbadbbbacbddabaabadaacdabadcdbaabdadcaacdbdbdcdcbbdddbccbcdcababdbaacdaaacbdabdaacdbbcadaddcaccbdcdcdcbbbcabccbbbdbcbacddcacccddbadbcbcaaaabbabaccaaacdacbaccccccbadadbbabadacbdbaddbabbddabbcbdbcaacdaabcdcadbddbddbbabbbdabccacddaaadbddbaddacbabdccabcbcddabbcccdacdcbaaababbdcbcbaabbcbddbcccdbbcacbaadbbdcbaaacadbdcbcbdbbddbdadaacccbdccdaabdcbdcacadcadddbabbcbcdddddcbacdacadabdcdbbaadabcdacacdabdadcbdabaaaaddcaddaadaccbbddbcbcddbcaadccdacdacbbbdcdababdadbddcdadddbbdcdbcddbcaabccdcdaacccacddcbbddbdbbcdcbdbcdddbacaaddccabcbbaaacccbaccaacdaddcbccbdcdcbaabdcacaddcccdcaaadcbaacadcdbdcdccbdccccdbaaaabdddaaccdddccdbccddbabcccccddbdaccbbcdaabdbcdabcdbbcaabbbcdbacbbcdcddbabaccdcbabacbbccadabbbcbacdcbaaaabbddadccdcccdbdbdaadaaacccbcbcbbbdcadcdbdbcbbadabbdbbacabdbdcdbdbdacbdbbadccabccbbaadbcacdbaacdcaabdadccdbadcddaccdadcdadcacbaacbbdaabbbdbdcbdccbcdadbaabcaccccddadccbdbbdccbcdbdddccbddaccacbbcaadacaaaacacbcadbabddcabcddcbcdaddbbcaaadabddacdabdbadacdaddccababbdcbbcbaddbbbbbacbdcbacdbbaabcccccdbabcddaccadbdccadddbcabcadadccbdcdbdcaddbdadbcadbbdadddbddcabbbdbccabacabccddbcdaabbdbbcdbbcadadcababbdccacaddaccaadadcbddcaaccdcababddcbacbddadbddacdadcdbbccaccaddbdbdaddbdcccccadbdddabbcccbbcccabdbccaaadbabccacadcabbdcdacddcbccadbbdadddbabdabbdcdbaabdbdbabcacdaabbacbaadbdddcabbdcddbcbbadbdbacabadbbbbaaddbdcdbbcbdabcaabccbddbabaaccadbddbddcadbababbaaadbaddcdacabdddbcadbcbaccbbadddbcdbbcaadaaccabcbcaaadbaaccadbbcdbdcbacdabccadddacaacdbdbaddbaabadcadcbdbccaacbcbdaadcbdcdacbabbaadadbaabadadabacbbddcdbdbcdcabddcadbbbddbccdaabbcbbbdacddbadbaddbdcdddddaacaabaddbbabdbcaacacdcdcadbdcddacbbbacccccbbdabcaabcbaddbaaabcbaacccbcabcbddcccdcabcacdbbcabbdbcdcadbbbbacddabccbbacabadbcaabbcadabcddaabdbababccddbdacbbaadcbcdabdaaabbbacbdbcbabbdadadbbdaacadbabbdccdbccbacdccacdabbbccadcbdaaacddcadabcabcdccaccccaaaddcadcbadcadbbddbaabcdcacdbbdccbbdbdbcaacddabacbbabdaddaaacabcadabbccdcccaabaacddbcaacabcdaabdbdaadacdaabdcbcddadabbaccacccbbbddcbacdcdbccacdbabbbdcbbaddcbbcbddccbdbacacbcabaadadcacccacdabaaabcdcaacddbccbccbabaaaaadbddcccdcbccbaddcdbbadbcddddddcdcbcbdabcddccdbacaadadbbccdcaadbddbdadadcccaaaacaaaccdcbdabbdcddbcdcdcacbbbddddbdacbcbddcabadcddbacabdacdadcbdbcdccaabbdddcdacccdaaadbacbcdadcaadccbcbcddcbcaacbaaddcbabcadcdcbbccababbdabadcbbcccdbdacadcddbbcbcbabdbadadccbcdaaadaccdacadcabdcaddadabdccaddbcdcbaddbbbaacdbcabacaaaddbbdaadbdabbabccbbdbccbbbcdddcabdbcaaabaabdbababcababaabddbbbcadaacdbbacbcdaadcdcacbddbdcddccdcadabdcadcadbdbadcccdcbbcbdcabaddbcdbabccdacadbbbdbdaaaaaddbbadcdadbaacccdcacbdbbbacadbccccdaddcbaabbcbdaddcababaadcccbcadcbdccabcaaabbadadbbacdccccbacbdabaacddabbaddcccabbddbddcbccacdbbbbcbdbbabababcbbddabddcaadcdbbacbbbaccbbcbbaabdabaccadbaccddacadcaabbbbddddccccdccdcacbbdaaabbdccadddbddadaccbcaaccdbbdddcdaadccbccaabbdaabcbcdbcdaccaaadccbabbdadbdbacdacdaaacddbddbcbdaaaddddcdaabccddbcbdacddcadacbddcdabccbbacddcbaacdabbdcabcdaaadcacabaabbcbadbdababddddbacdddccddadcabcbddadcadbbaadacbdadaadccddbaccabdaaccbdccbddbbacaacccacbaddbaaaacadacadadabccaacaadaadaadcadaddadacdddcbdcadcbadcbcaabcbabcaacaaddbdbadaabacbadbabcbdacbdcaabdabdbcddcddacadadccadcddadcccbabdcccbbbaadadbcccadaadabcccdbacdadacbdcaacdcaadaadbcbcdbbdddaccccbaaadaddbccbbdbdadbddcccbaacacbdbbddcccdabababaccccddbcdaddcdcbbbdcbacabaacaabacdbbdbaaaacacbacbaaadacadbabdbaccdcbdbbcbcbcabdcadccdaacacaddbbdbdcbabbaabbdabaabbccababcdcbdccbbdacbacccacbabcccddadcacdbdcccbcbababdbcaaaabcbdbbdcdbcadbabcabacdadbadacaddbcabcdaacabaaabaccbabcddadbaccbbdabbabababdbadadcbddbbaccbabadbdddbbdacacdccbabccdbbdacbcbacacadcdcbccadccbdcadddaddaaaabaccadaaacbadaaaadcbbddbdacadddddbbaaccabbccddadddcdbcacabdbdbbbbaddacdacbdbabdcbdddbdddddcabdabbcabaacaadabdcddcbbabcacdcadcacaccdbacbabbdddcaaaaacdaaabbaccbdacdbbcacbadacadbbccbcdaaadbabdcdcaccbbabbcbacbbababcccabdbbbdacbdcbdbccabddaaadbdadaabbcaddcccaadddbadcbcbccaabaadbdddcdacdccacdbdccdbdcdbdcdbbbaadcccabaadcbbdcdccddbdbddbcddaccdbabaacabadcbdbdbcddbdbbbabaadaaddcdcbcabadadcabbcaccbbdacdcdcaddcadcbabccacdbdcbbbacbbabcaadadbbadcbdccdbdcccdbcbcddcdcdacbcddaaddcbdcbddcdddcbccbcbbcdddcdabbbbadbcbbcdaddbddaccdbaacaddaabaabcdbbcdaaccabbbcddccaabacadccdbccccdaddcdbdadcdaabdbacaadcbcadaabacdaadcaaabdbddcdaccaabcabacacbdcccdccbbdbaaabcccacddccbbacbdaccbbadbcbcaadbbaccbdbbaaddaabadbbccbbccbcdaccdcaddddbabbdbcbcccabbcbcbbcadbcbabaaddabbccbcbdcaabdbbccbbdadcddcadbbccbabdcdbbbadbaabadccacbbabababdccdababcaddcbcbcbdacbbaabdbaaaacbacacaccdbcbabbdabcaabdaacdcbddcacbabcdcabacdbbadddcddcbcabababcacbdaaaabbbdccadcdcdaadacdddbcdcabdbbbdddbacdddbbcbcccacdbcbcdcbadcaabddccbcbcabacabcadaabbbcbbacdccdcbbbcccdaccacdcddacadbcdccbcbdacddcdaaaaccdbbaabbbbdcbcbadabdbdbcdbbccdbbaddacddcdcbbcacddcbcbddbbccbbbcbbbacbcbcacaadbbbabcaacdbaacbdadbddaadaadbadcbdbcddcaaddabbcbcdbacbcadaccdddaacddddbbdbdcbdbaacadbbabcbbacdabdaacaacddbcdbcbdccabdbaaaddbdacaacbbdccddaddacddbdbadcaaacdbabbbdcdabbdbadddadbddcbcaddcabcbadabacbcbacbadbbadaddaaabaadcadddadacadcbdcddccbcaacbcaabdcacbdbdbabcbdcdacbdaddcdcccbdaaabddadddacccdbcddccabbacbdbcbcddadccbacdcbdddddadaadcabcdbdacccbdaddccbcaddcbbddabaccaadccadacacaaacdccccadcababbcbbdbddbccabdcabacdbbdcdcacdbdaaccaabdcaacdaccbcdbbbbdddcadaaadbaaaaabadddabbcdcdbaaaabdcacabcdaabcccbddcddabbaabaacccacaacbdbdabadbdbdddcabacccccbcbcbddadbbbbbacbbdddcdacabcbaadcbdcadaccbdadabcdcdaacbcadaacadbcabcacbbaabddadcdcbddcbabddddddbabdccaddabcdccaaaddbbddbbccbabcbbaccbddabccbaabbdaadcaaddaaabcacdacaadddbbcabadcbbdcbdbbdbdbbdaccacbcacdbdadbbadccbdbbabdacaabcdabddbacdccbddccccbdcbaaacabccbcaddbddcbaadcdbcbddbacdcbdcdbbbbcabacbdbcdadcdaaddccbadabadabadbbbccdcdadcbbcbddcbadacbbbbdababbbdbcaaccacbacbbddcbadabbadabbccdadadcdcaddabacbbaccadcbccadbcadcbaaacccbdaaabbddcdbabbcbddbabdbbacaddbccddcaccaddabccbadddacdcbacdcddcabcabacaccbadaadaabbabdaddbcbcdcbaabdbabaacdcdcbacbdbbabaabdbddbbbdaadddbbcdccdbccadbcdcaccbcccacddbaababcbccaadccccadbdcbdacddabdadccbdccddddbdaabcabddddaacadbcdbdacbbdaabaccaacabcadcbbccbccbabbbdaccdbadbcddadadacaadacbadccdbcabcbbacabdabbcdaccacbbddaddddddbdaacddccadbdabbbbcbaaabdcabddcbbddcdbcaccbaacbadccdabacdacacabacdcadaaadbbdccccbabccdcbbcacbbcaddcbccdadccacbbbcbabcaddbbcdabccbbcaacdcbacabcaabcabcadcabbcccccdaacabdabacbcbaaadbdabdcacbbaaaccabdbcaadaadadcdcdbdaacaacbbbcacddddbbbaadbcaadccdcccdbaddbcddcabcdccdcdbdaacddcacbbdbcabadbddbdbcabdbdbaaccdabdbdacadadbdbbcbddddbddbbbcbdbcddcdaddcdcbdadbadcdcccbcdcbaaddccdbbbadaddaadccdacdcbaacdaccdabdbcacdbadabcbdbdbdaccabcddcaccdcaaaacaacabaccbacbdcaddcdabbcdadbadbbddabdbddbccadabdccabbacbcdbbcadcdcdddacabbcaaadbaabbdbdddadcaccccbdcbdcaacabaaaabaadcdacddddbbcadabacabcacacdbbcbcdaababdaacabccdadacddcacaaabcdcbddaabbaaacdcbddddbdbdaabcadbabdacacbdccabcbbbadbadbbdcbdcdabdcbdadddccaabccdaaacaabcccaaabaabdbbccddcdacaabdaadacbddbddcbbbdcaddbcabdbabcdccbbddbbcdcccdbbdacbaaddabaacdbbcdaaacddbadddbdbdbbbbcbadcabacbbadcbdababbdbadadcacbcdacccbdcabaacabcbccdcbdccbacdacdabdcccdcdcdabadcaacbcbcdaaadabacdcbcddbdaddddbababacacabcdcdddaadbddadabaacbbbcdbcdcaddaccaabdcbacbbcdbacbadabaaadacccddddcdbabcdbbdcaddacacacabbbaddbbdbabbacaaaadcacacacbbbbaaabacbbaadbddadbdcbaacabadcdddbcdbcccccbaabcddbbbbdbabacbcdacaadbcdccdbbaccdccdbaaddcbcabbdcaddadbbcdabdbbabcacaabcaabdbaadbddbababbaadccbaaacdcbadbdcdbcaddddaddacbaadcaacbbcdcabddccbaaabdbbddadbbdcabbcbcacbcbcccccaadbddbdcdccdadbbcbcbaacadbbadacdcadaccdababcabccdadadbcdacccbbbbbcaadacddcabdccabddcbccabbacacaddbddbbdcadbaadacbddabcadaadcabdaaadbccaadcbbbddcbcdabbadaddcabdaadbbcddcaddccaccaaabaacbaccabdbddbaccbbaaaabbcbdbaabdddacacbbdadccdbcccbadaddacabccdaacbaabccbdbcacbbcdcbcacaaacbddbdcababddaddbdccadccaaaaddccabbcaaddccabcdcbabbcacaabadcababcadbdadbdbaababbadbcbaabcbaccbaadddaaabadbcbcabbcbdccdddadcbdacadbaddddcddccacbbdbacdaaaddddbdccbccaaabacadbaacbddaccacadabadbbbcbbabddddbadcccdccaadcabbcabdbddbbaddabcdabbcabbdbcccdccdccdbccdacdabadadbbcadbccbbbacddccaddabcdddcadabcdcdbdabbdaabbddaaadccbabaadaabbdbbbcbbcaabddbaaadddccbdccaabdcaaadcdcbdbbcbcdabbabccddaccacabdbcddddbcaaacaaabcddaadccbbdabddbcdbabcbabbdccdddbccabacdcabaaadddbdabcacaddbabcbdaacdccbacadcabbbcdddcddacbbbacdadbabaddcdaabbabdababcacdbadddbbcbcacdbdaaabbccbacdbbbdabdaaddcbdacccdbccadcdddaaabcdbadccccbddbacdcdbbacacdadacaddaabacdbcabaadddcabcaaacdadbbacddcbacdcbbbcdcddaddbbcabcbbdbdbbaabdcdaabacddccdbcbdcbaaacadbbdcbabaadabdaadbabaacdacbbcbabbbadcaabcaaabdcdcbdbbabcdccccadacdbddcdbccdbbbdbccababaabadacaadccccdbbcdacbacdbaacdbdabcdccaadcadbdabcdccbbabddacbdbaaaaabcdccbdaccabccabbdbccbacccccaababcadbdcbadbdaacabdcbadacadbbcaacbbaaacbcddbababbdcbbcdcdcbbcaaadcddabbcccbbbcdcdbacacaaacbcbaaccbadcadbddabdbaaaccbdbacabbaaddddbddcbccacbdcbcdaadddacbcaadbdabdbbaacdaabdcabccdbbbcbadddcbbadbccdacdadabbdcbddaadbbcadababcbadbacaaaabbacdaacdabdbacdddcdbbcadabdcbdcbddddaccbbabaabdcabcddbcdcbdbaaacbdacaaaadbdbaccacaabaaabdbabbaabaacddaaacbdcdcdbcdadbacdcbabcdbcbbcbadabccdbddadadabcddbddccbbcddbabcbdbadccabdbdacbadbabcabdaaccbabddcdabdabddccdccbbdcbccaacabacdcddadbcacdbaabccbbddcdbaabacbcdccbacdddacaababcbcaadaaccabcadddcbcbdccbaacbbbddabdaddbdabccddbacacacdcaccbbcbbbdddbcccaabbabdabdadacaacccbbdbadddccadadadbdabbcbbdddcadbcbdbbcbdadddcbacdaddaadaacaddcbcddcabadbcddadabdbdcbdddaacddbbcbabadadaacabcccbdcdcdaabdbbdadadbddadddcaccababbadbbadaacabacadddddbccabaddbabbacacabbabcbcdbacdbcacdbbbcabcadaabaadacaaadbbacbabcdbdccbdcaadbaacbadbcbdadadcadbaaadbaaccbaadbbbbadbaccccbddccdcabbbdaaccddcdcabbabdaacdaadcadabdcccdcbbbdaaacbcccaaaaacddacadcabccabdabdccdabbaabbcabdadbbaabbcaadbadcccccccccdbbcccbadccaabbabacdaaadcbadccccbbdcdaacccabdbabadccbbcbbbccadaabbdbabaabadbcbacdcdddbaddccdcdacdadbddbbabaacccddccbbaddcccccacdaabcdabdadbaccaadacccadccaccdbabadcadbcbbdcdaddaadaddddabdadcbcbbcdcaaaadddccddaadcbbbddabccccdbbbddadbdbdcacccdcadcbcdbcccbddccbcdbdddbadbccabdccddcbaccacdbacddbacbcbbbacbbdbdccadbcdbbbacbbbcbacdcbcbaadbcbadcdbcacadbacaccddcaddabdadadcbbdaccdcbacbaacabddbcbadcbccdabcdaabbcdadabbdcabbcdaadaadbdaabccddabcddabbbcbbbbaaaaadbdbbadbcdbacccbdbdbacdaacadadbadbcdaaddbcbbadbdadbcddabacbddbaadaddbdcacddabcccacdaccaccdcdbadadddbbabccdaacabbdbddbbdcbbdbccbbddbcbaddaddaccbcbadaacbdccacdccacdaaccdbadddaabaaaadaabacddbdadbcdcbbbaacadbdcdcbbccaabccbcdbcbaacaaadbcddabcdccdccdccddcddadaddddbbabbbabdcadbcbcadbaccccbdaabdcdcaaadbddacbddddcbdccadbbbdbcccadcccaccbccacddbadcbadbccadbacadbbadbcaadacacbbdbbacddbcbddddcdbbbccababadddcccbbcabdaaabcdacaaaabdbaccaabbbcabdbddbdccbccbdadcbcdbcaacdaccabbaaaccaabbbacdbdccacbdddbdddbcaaddcdcdcaddaabdbdbddadbaaddaabbbddbdabaacaabcabdbcdaabdcaabddaadabbbaabaadbbabccbcabbcbbdacbbbdcbdbabacbdddbbccbcdcbdbdbaddcdbcbcabbccaaaadcbbabbabaccacdacabbbcdccabdcddbcbbcabbaabbbdbdcadcaccddaadbadcabdacbdbdbacabdacbbaaaadbabdbaaacabdadbbabbcbbcdccbbdbbbbcddbabdaacaaabbddcccbaadaaaabaaabbbcaacbdccdacdcbcddccdcabcbbcdcacdcbcacadacbdbcddcbacddbbdcdacbccaaccdbbbacddcaccacdabdcbacacdaddaaabbdbbaddbddcabcbbdcaddbcaababddddbcccdadbcbcabdbcdaacaaaccbcadaacaddbcababcacbdcbcbdaabacbdadcdddcbabbaaccabbaaadbacadaacdcbadbbdbaaadbcbacabbacabbdcadbababdddcbdacdadabdbdaadcadbdabcadcdccbbaaaaabbccbdcbcdbdbdabdbbcadddcdcadcbabddbabbdbabbcbbbbaacacdcadadadbadbddddbaadadbaabcddaabddbbccdddbdccccdcadadbccbadcbababdabcabaaacdaaacabdabcbdbddbaccbbbadbcbbbabbdbddbaccdbbcacdcabdbbaccdcbcbbdaacdcbbdccbcbbadaaaabcadddcabacbbaccbcbacabbdaaddbcadbdccdadcbaaabdbcbdabcbbadadcabbccbdcadbabadbbabacdccadddaccccddacdcbbbabbbbadbbaaadcacdcacdaacadaccabddadbdcbcddabbdddccbadcccdbabaabacbcbbcbbcbabbddcabcdbcaccbccdccdddbccdacbbbaabbdabbcadaadcbadaccaadabaabbdaacadaabbcddababaccccdbbacdabbdaaccbccbbbaddcbddadbbaaccbdbaaabdbdbbcbbcbbccbbdcbbabcaccadbbccacaabacbdbaabccaacdbcdcbbdcbbcaccbaabbbcabdadcabbbccabcdcaabbccdcdbbbbdddaaaadbdaadabcccbaacdbddcabdddabcaabacdcabaacbcccbcbbadbcddabcbdaacdcbbbbdacdbadbababbdbddbccdacbacbdbcdbdcbdaabbabacddaaccbacdbdccadbbabababccbcacaddaccbdcbcdaddbbbdbccabcacdbccbddaddddbabaadaddacdacdddbdadaaadbadcdddaacdddbbbccdbccbdddaaacbaddacaadcdcdcacaabacbbdddbabccdaaacddacdbbbcbcdaaddacdccbbcadacaddbdacbdcbadcacaaacddabddddbdbdaaccdbdbcdddbacdabbbacaddcaacddadbaadcbcdaacbdaaaddabbaabcaddbbdbccbdbdbadbbdaabacdbcbcbdaabcddaabccccdccdaacaddddcdcabacbaaabbacaacadaadbabbcdbccdccbbadbbaccbbccddbcbbdbdccccabdcacbddcadcbaabaaabaadabddbbcbaabcabccbdcaccbdbdbdcabacdadbcaabccdaccaddbcdddaaddbdbbbbacaccdcaccdaadbccbddbcdccabaadbaabbadaadaadaacbcdacbcacacbdcacbdaddbadabdbdabbabcaadaccbddcdbbdbcbcdbcdbadbacadabbcdbdcccdcaccbdbddccccdbcddbbccbbbabbdabcdadbbcababadbdabdcaadadcbdbddbcdaacccbcbbdacddccddacabcdcbadadbdbcdccbbabcdcabacbccabdbddadacaacaaaacbddaccadcdacdbaacaababbbdaddddabbcdbaaadcccbdcbbdbcaccaccbcdabbcddcaacddacaadbddbdbcdabdadadabdcbcdaacadcadddcaacddbabbdbbdddbdddbbdcaaadbbabdacbbabaddaccddcaaaadbcdadaabbabdaacadaccaadabacbbabadabbaddcdcacbbacbadddbaaddcccddacdbbdbabdbccacdbcabdadcdbdcbbabaabbbccadccbdacaadbdbccdccdaaabadacabaaabdbccdadbdaabddbbdbcadcabbaaacbabdaaddacdcabadbaadabcdbddacdbcdaacacbdbcbcbccddbdbdabaaddcddacabcddbacdbdabcddadcabbadbcbdbbbadbcccdbdcdcbdcabddbbcaabcbbbbcbacdcccddccadaaadbacddbbbdcdabbdcabdbddacdcbdcdaaabbcaddabaddcbddcaddccbaadbcbbcabdcbaadbbabbbcadadbacbdbcbadcbdcabaabbaccaadaadadaddbccabbbdbbabaccbdacddbdaaacabaccaabcdcdbdcbbccaabdddcdaddddcdabbaccddaaddcabbcbcabbdbdcabacadccbccaaaaddaabcabcbcacdabacdbbbcddbcabdabbacdcbacbcdbbaaaaabbdadcdaacbaacaacddbccbdaccbcdabadbabcbccbacbbdacdbcdccbcddbacddababacadbacaabbabcbbbacabccacabbdbabdcbdbadcddbbdbadddbbabadbadaadbcbaababaddbdbabaaababcbaddcadcdbcccbbacbcadbacbcddbccabddbbcaadbcbabadadcababbabdddabaddcbbdaadddcdddbbcaacbaaaacacbacdaccdbdbdbacadaabcbbaadcabbacabcdadcadaddadcadbbaccdbbcdaacaccdbdacdcdbcccaabdcdcdaaabaadcdaadaadbdddddbcdbbcaccdcadadacdabcdccaabddbcdbcdcdaacdbabacbcadabaadbbcabbbdcdacabcbadabaacadbcbabbaabbbadddbabbbcccdcdbdddbcbacdccabaacdacddbcbbacabbcabccddcadcaadccdccbcabbbcdbadcbabcadabbcddcdacbaddacbdddbbbabbaaabdacacaccdabbbbccbcaaadadcbbccdbdbbabcdddabcbdcdddcdadadaabdadcccdaddaacaabbcbdbaaacdabbabbccaacadacbbdbbcddcdbacdddcacbcabdacabbdbbddcbbbacbdcbdcbbdaabbbdadbbadbcbdacadcabcccdbbaacbbaacabcabcadadcaacbdcabcbabbddababcbbcbcadaabcbcccbdddccaadbccadbcccdaccbdcbcccbcbcaabadccbbddacabddcbadbbddccdcdddcccbacabaaabddcdcddaadaaabaddbcadddbaabcdbcdbabaabacabbbacabbdadcdacaddabdddddbddabcdaaaacabbdcddcdbaabacbabcdcadddccaabbbcdbacbadcccbbdacabdbbddabbbaddbadacbbdacaacdccacddbbbdbbbabacdcdabaabdbacaaccadaadacdbccbcbaadcaabcddaaddbcbdbdaadcdcddadccabbbbdbddcbbddbbdddccccaadcdcdadbbacacaacdccabdacacaaaddaababacbacabccddacacaacbaccbaaaababcabdcadadbbcabacbbdddcbddaacdcdacaaabdaadbbcbbcdcddbcdaacabababddcbcdcbadbcaadcacabdcaaacbadbacdaddaddbbcdbccbaaccacacdbcdcabaddcddcadcaacbddabddababbcbdaabcbaddcbbcccacdaaabddbdccaddcabdddadacbdacaddcdbaddcdccbcaaacccaacbdbacccbbbcdbcabcdabcaccdbcbdccbdacdddbbdbbbccbabdcddbbdccacbabbcbcdaaccdacbadabbaaccbdbcbabcdabadbbaacbcdcaacabbbdbacabcccdbcbdddaadacdadbbbacaddbadbcacccbcdddbcccacaaaaabbbccdbcaccbabacddabababdaabbbdbaaaabacacbddacbcbbcccaacbbdbcdadbcdadaddcaaccdacabacddadcbacadbacdcdaabaacdccccaabcacccbccbcbbccdbadabadbbbdcacacbcccdabcbdabbadcbbdddcbacccdccabacbbddbaccdcccdbcadbddcdcbdacbcababcaabdadbadbdabdbbcacbaaaaadcdaadbaccdbbcbdbaacdaaabbddbbbadccdaacaabbbcbcbccacabaadbadcaacdaaaabdbbcaaaddcbbcdcbbdabbdabaacaacdbdbbabcbcbaddbcacbabbdadcaadcdcdccddaabbbcdaacbdabccabbdbdbacbbcccbcddcacacbabadaacccccdbdaadcdaabcaddbdbbdccddcabacbbdabbcccdbddaaaddaadaabbabbcdcbabbdaaadaadddabadcbdbacadcaaccdaabdcccccbadcacbaddddcbccbcdacbcadaddaadddbbcdbaadaabcddaacacbbadaaacabcacbacdabcbcbcbaddcccaccacdcacaabccbcbaddcdacccdaaaccabccbddcbcbdddaaddccadbbdcdaccadddadaddacacbaaddcccadcbabcdcccddcdddabdacadbcbcbaadabcbacdabbcddcdaaabadccdcaaacdcabcbaaacdcbacbbcbcaaaaadbadcaccacbbccddcbbbaaddadaabdacddddababbacddacbdddacaacacabbabaabcbcabbacaaabacddddaddcabbbcdacccabcaadbcbadabdbddbaccddacaabcbbbbcbddcdadbadbacccadcbaccdcbccbdaadbbaccadadaadbcccaaaccdaaaadcbcadbdcbbbbccbcbbaacbbdcabdcbccbaabcdacbbdcabdddcbabacdbdcaadcddbcdcaacdcacdccccdcacbcbddaddadbdddcacdaaacacdcdcabccabbcaadcdacbacccdcdddbadaaaccddccabdcdcdcbdbabdaddcaaccddccacdcdcddcacbbdbddcdbaadadcccddddbabbadcbaabbccbccbdcbdbcdcdbcbccdcabababaddcddcacddadaaadaddaabdcaaadcdabdcccbddadadbcccaacdcdacccbaacbdcdbcdddcdccddddbdcdddabbabdaddadccccbcdadcaddddbcddabdcccdcaabcdadaacddddcdbacbddcdcdaacbaccdbabdbddbbdaddbddbbcbbccbaababcdbadddbdcabbabdababcdbaddaabacadbdaccbdbabbdaaaccbddbddcbccdbbaacacbdbacadccccdbbdadabcbaddadcaacdbcbcccdddbcbcbbdcadbcdaacdddaddccadacbaaaadabdccbbbbddbaddcabdacdcbaabbbddcdcaaadabbadbbdcadcdabcadcabbdcbbaccaabbdaccbdbbcbbcbccdabbcacacacccdbabbacdbbcacacaabddaccbccbdccbbdbbdccdaccbddcbbccbdacdcacbacbcbadbdbbbaacbaddcdcdcadabbbacbcaaacdcbacbdbdbbddacccdddbdacbdaccaabbaaabaddcbdacbbaccbccadddbbdadbdaadcdacdcaaadccdddbddbcdadaacbcdaaabcaadabdbcccbccababbabbbabccbddacabdbbacaacbdbbcbaaadadddcddadabbabbbbcabddddcadaaadbabbadbccdddccdadacbacdaaccdcbdabbdddbdbcbcbaabdbaccdacaabcbdddcdbabbddddcacbbbadabcaaccbcbdbaadaacbdacbdcdccbcdadbcabcbbcabbadbddbcdbcbaccaaaacabbaddaccdbbccdcbaadbccacccdddcddadbbdbbadccbdbbbbbabccdbabadbbdcdddddaadbababdbdabaabddacbddcaadcbaddccbacbdcbaddaabaccdbdccdcabbababccadaddbdcdaadbcdacbacdaccccddbaaaabcbdcdbdacbcbcdbcaabbddddbadccbcbddcdddbacdacabbddaddabccbbabdbbcbccdcadbabbbddbadabbbccbdcabdccbacaaacaddacaaabaadcaadcbbcbabaacdbaacbcdbbbccacaabadcabcaacacdddaadcacccacadadbbabccabcaadacdaccdcdbacbcccbcbddaabcccabbbddaddbcbadbadbaccaaaddcadddadacdabddacdbcdccdccccddbcdbdbbdaccbddccaadabccacbacadadabbaaccababaadcabcbcabdaacaddaaccabdcbdabcdddacbbccccdbcdacdbadabcabdaddaadcbdcddadaddabcbbbcdbbbbccabbbddbdbccabbdaabdcccadabbaabdbdddbcaacccdbaabdaaacdaddddddabbdadadacddbabcbdcdddacdbadaadadcdaddbbdcdcbccbdcabcddcaabcdbbcdbaaabbccbdcdccaaacdabdabdabbbdbbbbbbcbacddbdacdabbccddadaacadaabddaddcbbabdcdddaabdcdcbadaacbbcadaccadbbbcadddabdbadabbdaaacccadbdadcaadbddbaabaddabcbcbbcadaacddaccbaadcdaccbbaadacabbbbcacadcddccddaccdadcbaabaacddcdaddacdcbdcadcdbcbadbdddaabcdcaadccaaddbbacddcdbddbadabcbaadadcadbaccbaacccbbaccacacbbccbddaaddcabbdadcbaacbcabbbbbbbdbabcdcbbcccadccbdabbcabbacdcabbddcaaabaaadddaacaaccadcddadabadbcaabcccbaddbabbcddcbddcbbccacacdcadcdaabccbbdccbbbabbcabdacbdddbccbabcbaabbcaccddddddaccdddddbabbbcdbbdbbccbccbdaccbddcddaabdbdbcbcaccbbcdcbcbaabbdbdabaacdaaddaccaacaccccdadaaaccbaaabadbcacdcaaadaabaadbacddaacbbdcaacdcbddbdacbaaccdacdcbdabbcabbcdccaddbbdbdcccdacabbdabdcaacddaccccacdccbbbcdabdabcbbdcdabbaabdcbbdaccbdbbdbadddbbddcdacbcbbddcadbdadabdbcbabcbbaabaccaaabcdacdcadaaccabcbdbccbdbabaddddabcdcabcccbaacbbbddacbbdbbbcdccadccbbabbdcccabacaadacdadacabdbcdcddbddbbcdbadcbcdaacddcabcbdcacbbabcbdbaadcdabbdabcababbaccaabbabadaaddddcaadbbbbbdcddcadaacadcaadaccbcacdadbabbcadbbdacadccabbbbaccbadddaaaadbdcbdcbbbaaddacccaabdbaddaabcbbccacdabbcbbaccaacbabdcbdaccbdcbdcdbdabbaabddbdaabbacacbabbbddcabcdbdbbcaddbbbddbbadcbcbdbdbacdcbddcbbbcaadabdaaddbadabbdccbabdbbbabcdbdbababbdbaddbbbddacaddcabcbcbadaadaacbcbacadacabbadcdccdcbabbdcdacbdadaadddcdcaadbadabcbdbccdbaddcbcaabbbbccbaabddabcddccdabbadadbbcdacdccaadbaaacbadadccbabacbacbcabcaaccddcaaadcccdbaaabdaaacdabddababdabdccdbbacaaddcbdbbdaaaddacbcbadadcbbabcbcbabbacbacaacabdccddcaabccbaaccabbdaaddbbcbdbabcbdacabadbcbbdcccdcbbacadacabdddcccbcdbaccbbcccacadbdaaccdaacdcbdcaddaaccaadadddbdcacbadddccbccbdacbcdaaccccaccbcacbddbcabbcbcbbaccaddccadbbccdcdbdbcaddcdbbdcbcdbaadbcaddacabbddbdaadbadbbdaacbadbabbbdddabdcdaadacacbacbdccbabcccabaaddabdbccaacdbabdaabbcdaadcbbdccbbcbddbbbacdaacdcabbcadacdbcbbcddcacbcabdcbddccbbbddbbbbabddbcdbbbaacccdddddaccdabbbcaacbddbbbbdaddacccdcadabaadcbbadbaabbbdbbbbdcdacdabdaddddabbddcccdaccbdbcbaadabdbcacabccdacbdaccbdaabbbbcadddccdcdbdbacdcdadaacbbccadbbbdbaccdaaabcbacdbbbccbcbbcadcaabdcbdbcbbdadacbcdcadcbbcdbddbdaaddccdaadbcddcbaaacbcbdccadabbddaadbdabdbbbdbcbdcabbabdadbcacddbcdbbdcbdcdbbddbcbacbddcbbabdadaaadbacacbaadbbdcbbcaaccacbcbaadddbcdcdadcddcbadacbcbbccbdddaccdbabcacdabbdbcdadcbdadbbababccdaacadcacbcdbbdccbcbbaddcddabbcbbabdacbcddbdabacaaccaddaadbabbaabbdacaadcadaaabababccbbdcbccdabacaacddbdcdcdbcbccbbdddbcbdaacbadddacdcadbbbdccbbaaddddcbbdadbacabcbcdacdadaadcddbbabdcdcabaaccccbadbcdaacbadbabccaccdbdcddbccdcdaadaadaaacbdbabbdcaddcbabbdaacbacacbdaddbbcacbdcdadbccacddcabacdcabddccdaddaadcacdbddcbdcbaccabbcaccbcbaadaaacdadbddaccdcabbbdcdbbcddadcdcadcdbbaaabcbccbacdacbcbbcadaaaacadccacdaccaadbdbaadbdadcdbdaaaccbdaaccbdbcbadbaccbabdcaadbcbbccccddbbcbddcdaadcadbdaddaabaaacdddcccbadcaabaaabccbadadacabadddbbddbbdadddddcadccbbbbcbbbacccdaaadaadbdddccbddbdaccbdccbddcbcaabdcbcaaaadccaabaabcbabcadaabdabacbacacbaddaacbadabccadbdaacbadcadcbdcccaddbbdcabdabcabbbcdcdaddbddccbcbaabadaabacaddbbbdabddcabdbcaadadcdbbababcaaddacaacbaaabdadbdcaadaabddbbddbbadaabbabcbbcaaccbdabddbddddacbbdbabdccacadadababbbbaadaadacdabaabcababbdaabdbbdaccaabcbbcbbbadcdbddbacbbadacbbcbbcadadcdadaacdcdaabbcacdbddacdbcadabbddaddabcddddccbdabaaacbbcbaababaacacddbaddbccbdbbcdcccbcacbdddaccdbcacabbacbbbbdacadbdddaadacbbbbbcbdaabbabdabcacacbabbdbbacbdccbdabbbbbadcccacdbdadcdbdbcbdabaadcdcdabadbbddbcccaddcbcdbdbbadadddaccccacabdcdacddabaadaabcccaacdbcccbdbddacddabcdbddccacaaaacdabaadbcdbbcabbcbacdadbbadbadadcbacdacbadcadbdccbbacccabbbaacbdddabadacddcdbcdaadbcbbabadabbbbcdbccaddddaadbcbcddcbdcbbabcccbcbccbdbcdabdadbacdadbdcbdcbdaaccaadcdadacbdcddbcdbaaccbcdbbbdaaadaaddccdcbbdacacbcadccbccbdbaabbaabcdadbdcdbdabdddbdcaddcabcbbdccdabdadbcbdabcdcdaabdcbabdccaccbcaccadacadaaadddaabccbbbccdcaaacacdabbacabaaacdbadbbabcdddcccbabdbcbacaadadbdcbbcbbdabbbcabbbacbcbdbacaadddcabdcacabdccabdbdadabdbaaababccbbbbacbdadccabbbccaddcbbacacadbadbddcbbdadddaadddcbcbbcbcabccddadcbbcaadbdbdcdcbaaaccbddaacbddbdacaaccadadbdcccbbcdbcacbabcbacdbbabdabdabaabaaacdaccbaabdcbbbdbbdccdbbcaccadbcacdbcdadbcdcbcaacacbbdaabccbdbaccdcbabbcdcbbdddccdddadadcababbacdaacbababcdbdbdcbbabbdacabcdbadbbabbaababddccacccbcdbcbdababdbbacdcbaaaccbaabadbdbbabbddbdbcddacbdcacdccbacccdcaddcbbacdacccdcaacaabcbbddddaaadbccccaaaaccadcbbcbcadcdbdbccaddddcabdadddbbdccdaabbacaadcdbbccddadbccaabbacdbbcccdcdcadabddbdabcadacbbccbdabdcdaddbcbacdcbccabbbccaadcddbdaaabbbbcbbbcdcbbbaaaabddbbbbdcdcbbaddcbbaabdcaddcbbaaacddabaadaddcdcdcdaacdddcdcacdacbcacdacbdcabdcbbdcdadcddddbbabcbdcddcbabccdccadccbaabccdaacccdaadbdddbcbdbbbacadccdccdbbbdbabaccbbbabcaacdcbaabaaadacacdddcdabbcbdcaccdababdbdcbdbabbacbbbaaaadacbcbbdadddbbdbbbbaabdacabcaadabcabbcdaddacbcbdaaabdccbbcdbbccaddaadbcaaccacbaaabcbbcbcdbabdaaccdbbbdadacaacdccbadcabdcaaadabdccdbbccbabcdcbddadacbbacbbcbaaaddbbbbcdcbbcdadcdaabdacbcccdcbcbdabbdbbcaccdddabbcdabbaacacdcaccdcbabccacadcbbaddddcbacdcaccddaccdddbbdbababddadccdbbdaaacbbcbbadcdbcacbaacccbddabababbdaddcacdbdcddbacdcabadadaacdbbaaaacdbdabccddbdacaccbccbdcbddaccbbaddbaddaddbadcbcdacaabcbccacbcdbbadabaaaaccdbbacdbbcccbbbbcddacaadcbdbacddcabcabcbcdabbcadbbacccbbdcaddcdcbdbbbdbabddadcabbbadbaaaddaddbcdbddbbbddbaccdccbccdbcdbbadbaaddabdaaadcbbdcaccddaacaaabbadccbdabaadabaaabacacddbdbababbbbddbbddccaaccbabaadcdadbbacdbbadbcbddbadbcbdbaadcddcddbdbcabdbcbdcbbdcdcadddabadabacdcbdcaadabcbbcdbacddbddbccccbcddcbbcdacabccbcaaabcbbcbdccacadddddddbbaabcbbbcdabaddaabdbcddadcddabbcddbaaddcacdbbdadacddcaccbbdddccabcdbaccdabdbbddddbdacabaadcadbcbdcccbbcbabbdbcbdcdcbcbcbbcbbdbbccaacaabaadabaddcdcbadaacacabdbbbbaaacddcdccdadcadcddcbabaaccbbbbadaaabcbdaaddabdcdaddddbcdcdaacabaaadaddbccbadcdbacddbacdcdcdadbcabbbddccbddbcbabdcdbbbbacabcbcdcbbdbbadddabaabcdccbddbdadbcaccabccbccacaabcbaaaabbccdbdcccdbccdaaccdaadccbcbcdabccbcbdbbcdcaddbdcbccaccbbdaaabadaacadbbabdccbcbaaaddadcbbbababdbadacdddbaddaabbbadbdccdccbadcababacbadbabbbacdacababaabcacccadacbdcbddddadbabaccbdcacddadadbbbabdbccdbdadcacccbbabbbccaaabbbddddaabcddbcdaadbbcdbadbbddacadcddbcacddcbcdbdcdbdabbadbbcadbdbdddcaacbabcdabdbcbabcdaccbdacacaaacbabadadaaddbbbaabdaadbdcbccdcaaaccdcaadcacccccdddbcbdadaaabbacdddaaaaabbbdacbbdbbdcbabcbcddcbccbbadccdadaddbccdabbcdccbadbbaddabbaddcddccdbdbbbcdacbdddbbddccaddccabbcbaaddccbcbacdcaaacacaabdadadbcbbcccdcacdbccbbccbcbcbcdacccddccddcabccdcbdbadcadbcbbcabdcbadcdaabbbcaccaacaadbaddbadcbcbbacabdacdcbaacdbacacddbcbbabdaabaadbcbcbacddcaaaccbbcbdaccbbaccaaaccacdbbacccadcbcabdaddbddaccdddcdcdcbbbbcdbdaabcbacdbdaabbaaccabacdccdadaccbadabacbaacbabdddbaacbddbdabaaabbcbabadbacacbdbbdbacaabbcdadacabaabdacbdcdbbdcbadcaccaccacdbdcacdaccddbcadcadbacbbbbbddccbdcdbdbbdbbdbccbccacadccbadadcddbabbbaaacaaaabcbbabcaaddbdddcaaccdcaccbbdcccaaaaccabadbbbbaddccababbbcbcbdcbaaddaadadcddacdddbbcbcddadccbaacccdbbcdbacabbadccaadbbbddbacbabaaadaabbbdbdbbddcdacbbdbddabacbbccbdbabdbabccabcdbdddadbbdaacddacbdbaacdbbbcacdabdddadaabaaccbcaddacdbabdabdcdcddbdaadbbaccccdcccddcccacddddbaabaaccddaccddbdaabbbbcbaacabbddcdcaddbddddbadabbcddacccbdabadaddbcbccacabbbccdccdcdbcadbbdabaacabbcdbdacbbbbdcbdbcddcacbdabcbaccbacdbccdbbbadaaccbddcccaaaadadcacdabcacbccdaabbdadcbcacdaddcdccdbbbdadacdbdccbddbaabcbacddacbdccbcbcaacdaccbcabcadcaabaabdabcadadaadcddbbddcacaaaacbcadbaacdccdcbaaaadcaabbaaccbdcaccabbaccbabbcccdbbacdabbdbbacdababbccabdbbdcaacbdbddabbabcdaaadbacadabcdbbadcadabccbdabbdbadaadcbdddabdccbdcabddcacdbaabcacdaaadaddcacdccbcbbbbccbbdababdccabbdcdaaccadcdccdbadddcabaabdaadbcbcdbbbbbdaaacadadcddbabcbccacbaabccbdcacbaacbcddbaaaadcdbcacabcacdabcbbdacdaabbaaaadddaaabbcddbddbdcbccdcdbadcadcdccdccadcaaccabccaadabccccdbcdccdcddcdcaabadcccdcadcbddaacbcbbbdabdabdcbabbcadddbbdbbbcaabcadcadbdcdddbabaaaccaadadcbbadaacbbcaabcaaadaccbbdbbdbcabcabcddcbdbbbdcdaccdddabbcddaadbddcbcdbddacccabdccaddbacabdabbdcacabddaccbabcaaddbdbdaabddddcbaccaacbbaaddaadacaccabdaadaaaaadbaccccddcbccbabaabcbbbcaadacacabccaaabcdabddbcbadadbabaabdbcacbbaddabadcdacbdbadaaacbcdbcdbbcddaccdbcadccdcabbdbcbcdccdddcddaabccddaaacdcbdcaaccadabbaaacabdbbdcdcddabdddadaddaacddcaacdaaccccdcbaddaabcbdacabccbddcacdbccddbdaddcaadcaaccdbbacbbbbbdcccdcccbbddccddcaabacbdbcaaabdacdbabbbdbabcdcaaaaddacbcaacacbcbcbacddbcbacbccccdbabbabdbbddabbbcdabccdbbddcabacadcbaaabbdbdcdacbadaaabacabdcabacacbddaacbaadabcccbdcadabdadabadbaabddabadbcadcaddbbaabacbacaabdbabcbaaabcbbadccdbddccbdbaaaabbcbccbdddbbacabbcddaaddaddccdddbbcdbdaaddcabacbbaaaccbcdddbacbcbaddcdcccbabcbdabbccbabdcdaadbdcbbdcbbaddbcdcababbbcbdbcbacbadaacbcacddadccbcdaacccddaadcdcabbcacbbcbdcbbcacdbadccaccabaacdabbdacbaccddddadccccbbdccddcbaaabcbccaddabadadddbcdaaacdcbcacacccdbbdccbccdabaccdbdbdcbaddcccccdbbcbdacbadddacdcdccccbbdaacbaaaacbdaabcabcaddbdabbbdccccdaacaacdaacdaacdccdbcbadcdbacbdbbccbddbacbadbddcbddbaadbbbbdadcbcabdabbbbbbaabbabbbbdcdcccdadabaadddbcbaddcabcdcaccdabbababbdaaaabacbccdccaabaaacabaaacacdcaabcdbddaacddbccdaccdbbdaacadaaadcbabadabdcccbbadcddbdaabbdcbcadcccbcaddcadadaddadbdcadbbcbbbbdcbbbdbdaaaabaabccacbbdbbcbcabcdcbccddadccabccdddadcdbcddbbadbdacacccabbdacdbadabaddacdbbbcdbbdacbabbdcdcbccbabdcadddbddacddbdbcababccddabbcacbbbaadbdbbdbdcacdccbdacadcaddaacdccbbabdbbcbbdcadcddbdadacbadddddbcddacbbacccabdbdcdabaacbbdbdcaadbddbcabadcacacdbbdcaddcabbbbcdacbcacabbaadcbcdaabacadbaacdcaaaabbbbbbcaacacdadcadcadccbbbbcdcdddaabdbaabbabbadcdaadaadddbacaacadabdbcabadcccddbdaccababacdccdccddcadbbabcccacdbcbdbbdcdaaacddacbcbbabadcdaacdacccccacadccdcabcacbbaadccbccdbacabacbdbccdbcbcbacbababcddddcbcdabddabbaccdadaaaccaabddddddadcacdbaddbcaddbadbbcbabadcabcdbdbbccdbaaabbdcdcdbaabccbaabdaaadaccadccccddcdadbcdbadbdbbdaaabbbcaaabddabbccabddcbdbbbbacbcacbadcdcbdbbcdbbdcbcbdbbcdbcbdcbbacabaadcbbaccdaabcbaabcccddddadaabadcbbacabaacaaaaadbcdcacbaccadbbaccbbcdbbbddcaddadabbccadcbdabdddbcadbbbcbadababccdaddacdcdcbcbcaccbdcbbbbbbbbcbcbcbdbbddcdbccbbaabdacdacdacbdbabaacbddccbbabccadcbcdcbbccbcccacddccdadabbcaacdbdbbbbbadaaaacbbabdcccabcabacddbaadadbbbaaaadabbbcaaddbcbccdbacaadcaaadaabbcdccbbcddbbbabacadcbcabdaacbcddbbdbadbbdadacaabccadcbaabdabcdcddbdcccdaabaaacdcccddcdddbdbdbdbcccadbadbcbcabbcddddcddbbdabbccdabbdabababbcdbccadbdabdbabcddcbadbcbccbabacabdbdddbbdcbddccdbdaccbccdabbacadbcbaaacaccdcccaadbaaabaacdbcadabaaccddbbadbccabadcddcadabadcddaadadccbbbadacaacbcaaaddcdcaaacacccbdbcdcbdaacbdadddabbddaccabcbbbabcbbabddcddbcbbaccccaabdcddaaabcbdccbbadbdbbacdbcdbcabdadbcbaacdaccabadbdbabbdccdcabdcbdbcbaccdcabdadadabbdadadaaacdddcbcbdcccabcdddacdcdadccdabaaaadddabdbaadcdcbccbdcbddcbaddbaccdddbdadbacbccadaaddbbcacbbbbbcabdbdbaacacddcccbbdcdadddcadbccbabcbaaadaacdbbdacddaadbdaddcddcbacabadccddcbcbbcdbcbadabdcccdbdcdaaaccdddcadbcbdbbabdabcbdccdadaabbadcaadbaabaaaddaaabbacaddacabccdbabacdbadaccaccaabdacdccbdbdacbbadcaabccddabcadbbdaabbcbbbababacdbccbbcbccbcdabcabcdabbcdcaabbaabbaddadadacadbbacdbccdddabdacdaadabbaddcdaadcabdbadcaccbaddadacaacaacaccdddccabadbdccacabbacacadbaaabdabbbbdcdacbbdbaaabbbddbcdbcdaadcccbbacbcbbbabbbdbcdadacbcaabdbbbccdddbacadcdcdbaaadcddcddbccddcddddadabddcbdbbbdbcaacbbaaacaacdabbbdcdcdcaccddbdbaddddccdbacacddccbdcdddabaadccbacacbbcdbbbbbbbadcabacbcdddaccadbababdadaaccacddbcddbddbcbcbcbccbccbacacdbabadbcacaacaacdbbacabbbcdddcacadbbbcadbdcaadbdcbcbbbacbdcdaccbacaaaacaacacbcdadacabccdbbabccabcbadbadccadccbccaddcccabccadaacbabccccdbbdbdddddbddbcacabdbdbbbdbacbaababcababccddcbcbaabdbcdacbcdddcacabdadcddccbdaaaccacbaccdbddbbccaddaadbbdacaacacccccbcbbbaadaacbbcdbbbdddccdcbabdccdbcababadabbdadacadadcccdcddddaccacbcacacdaacbcbbcdabababcaddacbdbddccababdbdabcbabccadddabadcdddbccdacaaadacbcbdcbaddaddbabcacbabcabcdadcdcbaabccadddbddbdacccadbcbdbbccccbcabbcacddbaddaaaaddcdadcdaccbbccabcdcacaaababcbaddadabaaaddccaabdcacccabcdbacddcbbbbcddcbadddbbabacbaacbacdcddddbbdbcbcbabccdbbcbbaadacacbcabbdbcdbddcbdcdaddabbcabaadbcbbcadaddbdabbdbccbacaaabacaabbbacccbbabaabdcaacbbbbbdcbcbadaadcddbdbbbbbbddcaaaadcabcdbddbcbbdccbabbbcdccbdbabbbcadaadacdcbdbbcaaccaccbccadbdbcadabdabbcadcabcaddacddcbdadccdacddcbbdbdbddbadbbabddcbbabacdcaddaaaacbbcacabdbddbadccdabcbdbbcacbdbbabbdbdcbaaddbccdcccdbbcdacbdcacdaadabbadcbaaacadacdadcdbdbabaccaabadcadcacaaacbcdaacbacccdbcbcbcbddcbbddabdbbbcaccbaccbdbaddcdbbaddddabbadbabbbaadbbdbccddacadabbcdcbbdbaabaadcaaaccbbbcddccacdaaabcbdbbbbadcacdccdacaaacbbacabccdadddacadaadcdbcccabdabccdacadbaddacddcbcadddcdbdccccdbbacadaacddbcddbcdabbbdadabddaddacddcacdbddbacbbbddcabddaabdabdccbccacdacbdcabbcadcdbcccabcbcbcdcbdbbdaadbbddacabcdabaddcbacaacbdcdccddcaaaaabddabccbbdbbbbbdaaddcdcadbabadcbbaabdbabcccdbbbcbabbbcadbcbbcacdbcadacbbacbbbaaaccabdabacdaacbcadcccddbabcacbbcbbbdbadcccabababbcabdadcaddacabccabababddcbacdbdbbdaddcaacabdabbdcbdbbcdbdababccadcbcdbbbcadbaacccdccaaadcdabccdbbcdbccbabadcaddadbaddabcabaacacbadaaccbcbbadcdbaadaacbadbabdcbcbbbbdbccababababcdcdbdcbcdbabccbcddaaadbaadabcabaaadcbdcbdbbddbdcbccacbcbacddcbadbbddabdbacbdaaabadadcccbcbadccaaabadbccaaabcbbbaacbccdadcbbbacbdcddcccccabbcadaddbaccbcabcadcccacadddaadabdbccabdbdabdaccccdbadcccadabcddddbccaabccdcdbbadbbbdbbdbdddddcbbcdacabcdccccdadcbaadbaccaaaaabbdaacaccacbbcdadcdaacddbcdbbdbcddbabdcabddcccbdaaacdccbdcbbdcabdcccbcccdcdabcacccdacdadccbcddcbbadbdcbcacbcabaccaddcaadbaccbdcadcabcdadbadbaaddabccdabbddababacbddaddcacbacddddcaacdadbacadcccbccaabdaaaabbadbacacbbcacbadacbcbaadddbadbcbcdabbacbaadccacbbcbadcaaaccbdbadaaaddbdaddcbcaaddaaadddaddbbddabdcccddaaccddcbcbadacbcacddababbdbcaabbccabdadaacbabbcbbcdbcbcdadbcbaaddcdccdbdbcbcabdbdaadbbacdacaacbacdbddcaaaaaadabcdabadbdadabcbbdccadcbdabdbaacaccdabaabbadaddccaddcddccdddcdcddccabcdcbdcdbbbbdbbcbbcacbdcacdddabbbddbaadadcddddbadbbddabcdccccbbaabbadcdaaadbdbdadcaadaaabdbaddaddcacbbaddadbadbaababbcacdcccddccaddcaaaabdccabacbdacbddcaabcbacbabaadacaccbbddadcacadcddabdbadcabdbaadbaacdcabcdaabdbcddbacdbcabcadaccacbaccaacdadcbaabbbdccbaddbaabdbaabdddcdaabcacadcaccaadbbabacacaddcbcbcbcdddabbdacdcccbbadddcbddacadcabbbddabdccaccdcadbbdcdcabbcabbdcbcbbbadaabbabbabaabaddddabbadbdbcdcadcabcabbbdcccaacacdabaacabaaadcdccadddccdadacaaaccabcbddbdaacddcaddbbdaaacaaadadcdcddddacbccbcbbbcddbabacbdaccaadcabdaadccddbbbacdadbdbcbcccccacaacccdabacaabbcabcccbbcccccbcccddbccbacdcbcdaddadddadbbbcacdbdccaaaccdadcbcbccadabaddccaadaacddacababdcbdddbdabbcacbacdabbbacbcbcadccddcdcacddcdbdcbaadbdaaddcbdbcbdacbbacdbdaccccbcabcaddadbaddababdddcbcdccbdbbacccbaccadbbdbbcaabadddccdaaccdddabbdabbbdccddadbbbacadbaddcbcdcaadccaddbbcabaaaaaddcddacddaccbcbddbdddaacdcbacdbabaddccdddadddabbbccddacaaababaddddacbcabddaacdacdbacbacdcacacbbacdbcbcadabdaaccabbccbabcdadabdcbaccbcacdacbccdbcbddccacdaddbdadddaadbcdcbccbcadbbdcabbcbadcacbaabcccdbbcbccacdbbcabdaaaadaacccddddbbbbbbaccadaadcdcdbdcabaacaadccdbabdbbcbbabcccdacdcbcbcccbbbbcdcbbadddbababbcddbdcdcccbaddacacddbcdcbcddcaababaccbdbdabaacdbbbccaaaadacaaccaddadaddcadcbccbddadcadbcbcccadcabcddbdcbbbaacbcaaddbdadbddacbddcdccaddddbccbbcdbbbbbbcdddcaaddabcdbdbaddbadacdabdcdddacdcaacdbaabcdbccbaacacabdcbdabddabbaacbcdcbbbdcbcccaadbaaaaacaddddbacadcadddccbdaadaaaddcccabbdcdcdcabdbaabcadbabbdacdbcbccbbccbdbaaddcbadaaacbacacabbbbdbcdaadbbadaddbcccadaabbdadadaacdcacbadcdbbbbcbbccccbcabbdbbbbacdbdaaccbabcaadcccbddddcdcdccddccbbdacaaabdadcabbdbadcdadabcbbabdbcabaccdcccdddbdcdbaddbcdccacaadcdcdaabbbcbcaacaacaadcadcbdddbccbcadacdaccbdbdddccaacdaacdcddbcaccddabdcacdcbccaaacbcbbbbbdbbcaadbacbbddabdabbadbcdbabbababbbccabbaaaddcdadcacbcababdbadbddacbdbdbcbadbbabdbddbacdccadbbcbdaadaadbaddbaccccddbcbcabbdcddcbacddaddcbbbabcbadddcaaadbbacacaaacadcddbdacddccbcdabbbddccbabcbbbdabadbbccccbdbcdccccdbdaacaccbabdcabbcbabddccdddaaaddbbbaddacccdcccbaccdcaddcaacabbbaddadcdbababbcdaddaddaaddabdbdbbbcccaaadadccacbdaacbdabcccaddcdbabcbdcabbdbabacdbaaaaadacaacabddbbddcdccbddabbbcbbccabacbddccbccaaabbdaadadbbbdcbacddbacdbcbacbbcbdcbacaacdcccdcdbccabbcdcddbaadbbdbbbddcdccddcdaddbadcbabadadcdbbadbbbdbbbddabadbdadbbbbdaabdbddcabcbaaacbcdbadbbbbcabbdbbdcadddacacabccdcbdddaccaaadddaacbddaddabbabcdabacddccaacdadcdbaaaadaacbcbdbdbabddcbacbaddacdbdddcdabcdbccacdbdbcdddacbdbaadbdacdccbcbbbccbdbbdcacdccadaaaccbbacbdacbadacdaccbbbabdadadbaaaddcdaccabcccbacacacacbacadcddcbdbcdcbbdbaaccbbbdcaadbcbbbdadcdaabaabaabdbcaacaaadaabdabadcccdcadbababbccdccbcbbabaadbdddaacdddbacdbbcabababbcaabdcdacdddaadbdbaacaacbcdbdcdbaadaaaddcabdaddacadabbcccbddbbdbaaabbcabccbcadababbbacbccabddabacbbbbaadbacdbdccdbbabadaccacbbdabccddabccabdaadbcbddccdcaabcbbbbccdbdcdbbaacbddacdbdaddcaabdcabddbbcadcbddbcdadcbbdaaccbabdabcabddaccdabbbbbbcbcdadabdbcbbbbaadcacbbdaaaccddabccabdadaddacadbbbdabdaabcadaacccdababcabccacccccdcdabdbbbcaaaacacababbcccccbbbaddaadcdcddaddadddcbacdabbcbacbcbdacccddadaddcbbabacabdbabdbabdbdbadbcccadcbccbdbabcccbaccadacdbdcdcbcdaaccacdcbddccacdddbcdcccbccaadabaacbbaacdcdddcaaabacbcdbaaadababccbdbbadabcbcbaddddbccacbcbdcdcaccccbaccadcdbddbacbddaccddcddccbabbdbcddaabbbcbcadbbbcadccadbbbdcbadadcdbabcddccaaccbacaddcbadcdcbcbacacdbaabdabacbabacadbbcccdcdcaaadbcdcdadccadbbabbbdbdbbbdaaabbdabddcbbcbcdccbaddcddbabdbcdaaababbaaccddacabcdacbbbcdddbacbbddcaacdccbadbaaacccaccbcaadcacdddcdabcdbdbacacadcadbaaabacdabcddcbcaaacacccbddcabadbbcaadaaacdbccdddbddabbccdccddccbcccdaadaddbbbacbadbdddabdbcddcabccabcdcaaddaaaadaaddcabccaabdccbbccbcbacddaadadcbdabcddbabccabcccdaacdaadcbaaacbbdbaaacddacdacaabbdcdbbbadbacccdbdcaabddbcabdcdddcbcbdcaaccabdcccacbdddbabccddcdcbdccdbaabbcbdacbbbccdacbddddaddbcbacadbacbcbbaabbaaaabaadcbdbcbdaccaccbbbbabdaccbaaccdcccadacdaabdbdabacadadbdbbcccbdaccabcaddaabcdbcbbadacbbbddacdcabbdcbcbabadbbbaaaccbcadcddccabcbacbdbdbcacdccbaddccacbbcacdcdabcaadcdcdabcbdbacdabcbcbdcbcadcbcdadadddacbbdcabcbcadbaccaaddcbaaccbcdbbcacaabccabdbdcacdbaccaaacaddbdcadcbabcdadddadcaacbdaadaacaacdbaddbcccccbcbdaddbcbcbdbdbbdbdbdacbaaacabbccbbbddbaccaddbcbddaadbbdcbdcbdbabcdbcbbccbdbdabdbadbcdabbabcacdaaadbcbabdcaacdcabdccbbaabbbcdbaaaccaddcbcdddacbadabcdccaaddcabbdcadddbbbbdcdabbcbbaccbbbcdcdabbdcabdcdabccbdadacbdadddadaacaabadcbacabdbdbdadadbacaccbbdcadcdcdccbddaabacbdacdabacbcabbcccacaacbcdbcdcaaaccadadadaccdbadcadcabbabdbcadbbbabdbcdccdbccbacbabdddadddcbabddabbbbcccaaaaccdbaacbbbbbbbcabdcaccaadadcdddcddacababcbdcbdcaacbdaaccbdcdbadcaccdacdadcccbddabccaaccbcddccbacbbabbcccbccddcdadddbcbbabbdcdbbabadcadbbcaababbcdcaabbcbddabbbbddbcadbdbcadacaaaaccbaabaaaabddabbadacaadbcaddccbacaaaabbcadccaacbbddcdabaaaacddadcddacbaccddadadacddcbcdbbbcbabbacbccacbddcaccdacbadaadcdaccbbdacacdbbbbdabbacdacdcdaddacbdbaabacaaaaaacbdbcbdbcabbaddcbaadbcaabcaabbbcbbbbdcdbdddaabbadcaaacbdbabbcbcbaadbaaaadabdadabdcdbcaccbdbcccabdddcbaddbbcbcacaccdcaccadddacadacbbacaaacccddbaabdcbaadccacaadcbcccbbdaacdcccabcbdbdbddbbcccadbbbbbabacdcdccdcadaccddbacabcdabbbbdbcbaaddacaddcddcddddbbadcaddbcdcacbabddcdbdaddaabcabbdbbbddbbbcbaaacacadddbdcddadddcadadbbabbdabdcddbcdbbbccbdcababccabbcccacdacaadbabbabbcdbbabdacccddbdcddbcbbbdcdbcdcbbaadcaabcbdcccbbaccabbdbcdabcdbdcbcaaadcdadcabddcabbbddccddabdabcdcadccdadcbcdcaddbbbbbdadcdaadadddcbabbaaaaabdbddcacdddbbaccdccacbbcbcdbbccbcbacccacddcbbdbdbccaacabaddbbcbcdaddddacddadddabbcaacacccbdcbcbdadcdbbbdadcdcddbcbacbbddbcdbdcaadadcabacababcdcadbbddaccacdbbabababcbcdcbadbbbdbabdabaabbdaabaddcacaabbcccbdaacdaabccacaddbacabcacbbbaabbbadababbadcadbadadbcaccdaaaacabacbccbccbabbaabdcccbaccdbbaaadbacbdadacbdcdabbbdaaaccacddabccaddabcbaababbddabbcbcaddcdbbddcabccaaadbbcabddcddccbcaacddbdacacbbdbccbddddddcdadcbdaccbccbccdacabbbbaadbdbdabddbacabbddabdcdcddcadabbddbcacaadbabccbccaabdbdaaaccdbdccbaaccbbaadddacababbdacbbcbdbcdadaaadabaaacbdbbcbbdcaaaadcdaccbadaacadbabbdbcacbdccbcbbdaadcacdadcdaaacbddabacddbbbaacccacaadbdcbddcdabdbdacdbddbbdcadcbaadcccddbbccbbaadbddadcbadbbabbddbbcbadcabbbdccccbbdcbabaadacbddadbbacccbcbbdaaabbdcdadcdbcdbcdabccdcbacbdbacdcabaadadbdaaccbdabcadcaabdcaadddcbcacbaabbabdaaccbdaddcdabcdbacccadbdacccdbbacdbcacccabbaccaccabbdabdbdcaabdabddcadacbdacaddbcdacbacaacaaddbbcaddcbadbadabcdbdaddcbccadabdcabdbccbabbccabcbdaaaaccbdddbacbcddcccddcddcbbacdbadbaaaabddabcadbcdcdddadbaccdbdccbdbcdaccbbdbcbaabbbcdaaddbbdbbdabadccabbbddabbcadabdaaaacabbdccdddaaadbaabdbcbdcaadbaddcdbdbbacdabaccaacadbcccabbacbcbdaadddaccddbaddbbaaadacbaddcbabdabcdccbaccddbdadcbbbdaacbbddbbddccabddaadaaadbddbcaddccadddcdaddbaaaaddabacabbacddcbcaadbcdcdbdcacbacadbcbdadacccdcdabdddaacaadbccddcabdadaaddccdabaaddcacdcbcbabbacbdbdbbadaaacccccdcdcbdaaaaabdaabbacdaaacbcadcdbdbccabdacdbacdcddacaccdaabbcbaabdddbaadcdbdacccddadbaaacabdacbacdbdcaaadabcdcadaaacaabacdaabcaddbcdcbaaabbdbddacaaddcddbcbccbdacadacacbbdabbbcadcdadaadaddcdbdabaacaacacdabacbbdbaacdabcaacaddbbababbdcbacbdbcdcbdadcadaddddcbaacbabcbddbcaaaaddaddbcccdbbdddaaaaababdcdccbbabaacaaddbdcdbcbbddcdccabbcdaadabdccdbccbddacdaacbbbbbaabddbdddabdcbbdacbddbbadaddbaccddccacabbbcabdbcaadcaaabcdcbbdaacabcadabbabacbadbddabbbbcacaadbcdcbbdaacbacbaccbacdbbcccbdbaaadacdbbccbadcdbdcbcdbcdbbdddcabcabdbdbcabbbacaabcadccbcccdccababcdaacababbcbcddbbcccdddcbbaacbaaabbaccaacdacddbbccccaddabcdbbbabbbdcadbcacdccbabaaaacccbcaadcacddccdabbbdabdccdaaadcbdcadaabaccccaaddcbdbcdccaabadadcbddbbbadacdcaccdcbcabacddbdccdabadbbdbdbbaacdbcbdaabdbacabbadbddadddbaadbabbababbdbdcbaabbabdbaadbaabdbccbcdacabddcabcacdcadaacabaabccbbcdbbbbdabacdababcbcddcbaccacabdababccbdcbdacbacdbddcdccabcbbaadbabccadaccaacbcaccdbbbddbdbcdcbbdcccddbdaccdcaccdadabdddcbdcbacbabcccabaccaabbcadabdaabdadddccbdddbdbcdadddccdbddccbbdcadbbcacbabacbaccbdcadbdadddbcadcaccbccadccacbcbabaabbbcacbadcdcdcddbcacdcdabccbcaddabbcdaccbcbdddddbadacdbdcdacbabddddbadacbbacbbdadcbbbadaddababadabacbabbdbbbddacddbacaccddaddcaacbabbaaccabaadadaccdbbdaacbcbdadaccaaabbdbcadbddbbcbddacddddcbcbabdabaaccdbbbbbcccadcdabcdbdbbdcddcbddadaddccaabdabddbcddbcdbddbabddcaabdaabbabcaaccabcabadbcbbaaacaaacadbcddadddbddddaaaaacbacbccbababdabdcdbdbccbccaaabaabcdcddabdddacbdbabcdacbdddbabdbabcbbbcdaadcacadcadabadddccaadabdadcccaacccdaabccbbbbcadaccddbdadbadadabbacccdbddcaaddcbbdcacdbcddbbcabababdccddccbbdcccdccdddabaabaddcdcbbdcdddaadbbadadcddaadbbccbccccbaabbacacbbaabaabbadaabbadccbbdadbbcdadabcaccccbacdbadbbddbdbbabbcabaddabaaaaabdacadaabaccbbdbcaabccbdcdcababbdcbcddbadaabbdcdcbdabdbabacdcdbbacadbbbdcbdcdcbbaaabdcbbddabcabddaacabdccdbabdbbdcaadddacaaabcdacacdaddacbaaccddbcbdbdbadcbddbbaaaadabccbacdabdbdbbadcccdddddddbcabadccadbdbbdbdcbbcaabcdbaabbcddabcddaddbcacddaccaccadcbbdacabccdccbacbbbaadbcbcddaacaababbbacabdadabacbbabbbbbdbbdcbcddcbbdadbaddacdbddbdbcbbcbadddddcdadbbabdcacdbbddbbddccadabbdacaccbaddbdddcdcbbccccaddcabcbcdbdcccbacdcaddbabbcdacdddccbdbdcabbdbccccbdcadaaccdcdcccdbbddbabbbbcdbcacbbababbabdbbbbdbaadadcabadabdbcbdcddabcadcddcbbaabcdbbccccbbcdcbcbdbadcddcdcaccdaadcddbcdbabcaacdbddaacdcdddcbbbaaabbccdbacdbdcdacdabbdcaccbcacdaacdbaadacddbabbaaccaababbdcbabbbbcbadacadacadccaadddadbcbbddbabadbacaabadbaaabdddddaddbdacacadcdacabdddcdabbddadccabbaddbdcddaacbbdbaabdadddbbcbdddcbabdaacbacccccdaabbabacabdaccbaddabbbcaddcbabcadacabddacbbcadaddbadbadcbabaabbacdabcbcadcbdddbccbacaddacbbcdabdacdabbdbcadbcadcbdaacbdabcaabdcbcaacacabccdbbdcabcbabbbcbdadbdcbacdbccbdccbbbacccaddaaaabdaabadcbcbcadbcdcbabcabbdcbcbadbdddbcccbdbcadbbbabdaaacbacbdbddbbcadcddbccabddddbaabdbaaaadabcadbbbbbccabbaabbadddacacdabdccccddbccdacacaaadacdbddbacaabcbdbccbbdaddbbbdaabadbaaccccaaddbccdcddacbdabcdcacabcccbcdabaacbddbddbdbbacaaaaaaaaadacdbadabbddbacbddcaaacdddaacddcaadbddadacdbbabbbcdadccbbdaaaddaccadbabcbbbcccdcdcbcddacabbddddddcabccabaadaaddbdadddaccdccdcbcdddcacbcbdccabddbbabbbddcabaaacccddcccacadddccccbcdcbdcacabaabbbcabccdacaaacbacbcadcbbcbababdbddabadbadbabbacadccdbbbaddbacdadcbaadababdddacaccbbaabaadaadbcdcdaccacdbabbdcadaacdcbcccaadcbbcbacbbdcdaaadaadabcacbcdcdacbddcbcbdababbbaaddccabdcacdbbbdbdabbbbabbdcbcdbaaacbcabcbaabbbaacdcddaabcdddcbbbacaccdddaaddbacacbbbcaaadbdcaabbbdbdddbaaacddbbcbcbbbadbddcbcddbcbacacdddcdbaabddcbbacbabacbabdbddbdbbbdcdaadbbccacdbcdaccbdbccdbbbccbdbbcaabcadcabdcdadabdacddcababbaadbaaaddbabaccbaabbcbdbcddcdcaaddccaadddacbaddddbddaddcbacdccddaccdbbaaaabbabbdabdccbccadddcbdbdccdcacccbdbcbdcddcdadacaddcadbbabcababccddacababccdbbbdbdadcbbccabdddccdcbaabacacdaacabbdacdcabdddabcbbcdacdadabcbbadbdbbaacadccabcbccccaaccbcadbbbbabdbacabdbadabbcadbbcddabbdbcccbdadacdcbbdccbbbdaddbbbbdaccbcccabbcbaaaddcdbacdaacaacbdddddcbaaacdddadddbdaacccadbcdcabbcacbacdccaabbdcbbbcccdbdababccabacddcdbbdbcdaabcccbbadccbcdbdbdbcabbdaadaacdbaaadccbbcaaaaaaadaaddcadddbaaadaacdcbbddcddccbcadcccbababadcbbaaaabbdacdaabbdaddcbcdaccabbbbbababdadddddbdabbcdabccbcababcabacdabcddacadbabdbbbbbdbacaabdabccabcaaabcdcccbcdbddadcdabbaabcdabdbaccdcbcaacaadbdbdacacabdadadaacacbacaadcccdaddddacdbdadbadaaccadacccbaabdbdbbaddddbdaacdbbaabbdbadaabadcdbaabdabccbdbcccdadcabcbdaaccdaaaabacccddaadccdcbbcccccbacbadacdababdabbdacddcbbcdbbbbcbaccbddaadcbabaddbcdcbcabccdbdbdcabdbcbddbdaadabcdbccbbacbaadbdabadbcbaccddaadadccbcdacdcbdcddcadaadcaadbbaadbbdadccbcccccbadacbdcbcaccbabacdcbabbbadacdccadacbbaabbadbbbbbcabacaabbbadbcdadaddbbddbdcabaccccabbdccbbcadbdccbbbbdbbccdbbdbdcdcdcbaadcacddcbddbbabbdcbaabbacdddbacdadbaaababacdacdbababcccaacbdbbddbccadccbbdcabaccaccacdabdababccadaddabacccddacaadcabcccbacbdcaccddbbaaaacbaabbaababddcbdccaaccbcaaabdadadadcbccdacaddaaaadcbdccaaaccbcccccdbadcbcdbdbbadbbaabdadadccbcccadacdcbaaddcbbadccdabbdbaaaacddbbaadbabdbcbabcbaadddbdbcdccaddcdacddbdbbbadbdbccddcddcbadbdcadabcbbaabddabaaaadcbccdbdadbccdcdcbbcaacccdbddcbdcdaaaaaabcaacccccbcddabacabccacccabddddbcccdddababdaabdbbdaccdcbdcbabcacaccabdcdcacaddaababbabddbdccbadabdcbabbdcbbcbddbdcaccdcbddacdccbabddcaddbcbcdbdacbdccdbabbacdbbadccbdaaacbccbadcabcaaaabbbcbabaaaaabbbabbddacbaabccbaccbdabacdbddadbbcabdddccdacaaddabdaabbdaddbcdccaadbbdccadcdbbcbdcdcbccbdbbabcaacdbccdbaabadcddccabddcbbcddbbdabcadabbcdaadadbbddddbddaacdbcbdbbccdddaaddbaaabdaacccbcccabccddbaacdabcccaaadddbabcadabccbacccbbbcaccdccdbcaaaccadacbcbdddadccbccdbdcbacbcbaabaaccbbcdaabccbdbcacadbbdabdddacbadbccdbadadbadcaabdbacaadddddcbccbacbbacdacccacddbdaaccbcdddcbaababbccccddcbdccbdcbbddbabbdcbddaccddbdcaaadccdcbbadadbcbacccdacbcbbabcbccdcabcdadccbcbccbccdcddbbaddacadddcbdabaddcacbccdbacdccacacdcabdccbbdcbdabdabbcccadcbcdabdabcbadaacdbaccaddccccbbcdabaddbbadadbdaaacccdcccccabacacbaabadbacdcbbddddcaacbbbbbcbddbaadbccbcdccbabadabadcdaacaaaaacccdcaaaadacbdacbaabcdadcadabaacccbabcdabbcabdbcdddddddaadbcccaacabddbcbdbbabbdbacbbcbdaddadddadcbbadcdabccccadaccadcccacdaabddcbdcdcddaabbcbcdcccccabcaddcbaccdcccadcccbbaabaacdcbddcbcabaaaddacbabdcbcacdcadcdabddbdaaabbbcabccaccacdbcaabbaaacaccaacbdbabdbbcdbcccdbdcababcdbaabcbdcbbbdddabbaccccbbbdabaacacbbacaacddcbdaccaccbaddadbaabcdcadddaccdcdbaaaccabdbdbacbdbbabbdcdcaddabcddbdbdbcdcdbbdadbbacbaaabbcdadbacbaabbbcacdacadcbaadacbabcbbdabbbbcddbcdcdbbdccbacdaddccdadddbaacabbbdabcbccdccccaaabcdbbdddaaabaadbdbcbabadcbcbabcdbabbbcdabcabbcbbbddccdaccbacaacbbbacccadabbdcdcaacabcbabdaccbbadbbcbcdaaaadabbcaccdaadacddabdabbcddcdcdcabbbacbbbcddababcccddccabaacdccdabdbaddbccbddddccbcdcadbbbbbbddccaabaddcaacdbababababbdddcadabcaddaddaacabdbccdbdddcbcbbddacccaabcccadabcabdaacacdccacdddddadabdabbcbcddabcbbbcdabcabcbddbcdcddbcbcccaadcbdccbcaaddddcbcccbbdcdcaaabdcdcbdbdabcacdbddbbabcbdbdccaacdacbbddccabacbdddbdbcddbdbdabdbacdaadddcbdddacbacabdabbccadbacabbbadcdddcddddbbabdadaaaacdccccbaacbacabbcdaadcddcdbdcbaddccbdabbdbbbdcbddbaccaabcabddbdddcdbcadbbcbddaacacdddccaadbabdabcaccddbcbaccbdbcabaabadbaabcbcbdddcbaaaacdadccdcbaddbaccabaaabcabcdbccaaadabbcabbbabcacdddcddbcbcdbaadadacbaaadabadbbcbaadbaacbbadccccbcddadcaaacbabbcbacbaabcadbccbaadddacadcbdcbcdacbaacbccacacdaadbbcabdbcaacccbddbabccacacdbaccadbdaccdddbbcddcddaabdabccdcaabbcadbbbdcccaccbbcabacbadbacbcdaacadcaddaddbbbadcddcdcbdbbaacbbccbdacbabdcdabbacdbdaabccbaabdbcdcdbcccaaadbacbabbabddcaadbccccdcdddbcdbdcdccbbaddcbacadcaccbabbbaadbdbcbdaaccaaacdddccbbacaaadabaaccbdabdcdcbaaddbdbddaabddabacbcbbccacadbcdddbddcbdacaabdcbaabdcbbcddbacbbdcbcabaddcabacdcaddcaaddcaddbabaacacbaaabdbbbcadabcbcdabcadababdaadadcdabddaddbccabdcdcdbbbddacdbbabaaacaaabaccacbdaaaaddbaddadabbbadcccaccdacddadabdcbbddddabdccdaabccbbccaccbddaadabddbbdadcbcccaacaabdccddadcdccadbcdadbadccccacadcdaccacdabdbabbcbdabcbbcccbcdaabbccccbcdaddbbdbcdbddabdcbbccccadababcaddbcacbdbbbbacbccccccbaaaabcabdcdcbdcacdbcccdcdbbddaccdbdcddabaddcbbaabcdaaddcbddadbaccabdaaaacbbbbcdcbccaddbcdabdabcbcccccdbcdbaddadcbdcdccaccccccbcbbababddbabdacdbddcbacbcbcadbbadabbbbbcbbbdcbddbccababccddaabadbabcabcaacacbbacddbcabbacdddcdcbdadcbbbdacbacdbcbbbadabccacdbcdacbcaaccbccbcdbdacbdbcdcacdddadcbdbccbacaaabcdbbcdabdbbbbcbabdbaddcdcbcadbdaadddcdcaccabcbbcbacbccbbbdbaabddcabdcaccdbadbcabdbaadadabcbabaabbabdbcddbccabbdcddcdcacacaddbccbaddbadbabcdbabaccdaacbbdbdbdbbacccbdbbcadbddcdcaacbacdacccdbbdbcabacdbadbabaabddccdadccbdcbdaabdaddbbdcdcbacbdbbbccdaccdbddccaabbcacadcbbdadbcdbdbcadddacdacaabdacdcadcaddbbbcdaabacacbbaadddabcadadbcaadacbddaccbdabbdccabaacdbbdbcbbbcbcccbdccaacaaacdacacdaacbaddcabcdbddcddabdadadacbadaadcaabcddbadaacdbdcbbdabacdacbabaaaadcdaddabaccddcbccdbdcdddbdbdcbcbaccccabccbdcddcdddccbacdaacccbbdbdddadbdabaadcdbddadbaacbacdabbdcdadbbcbabcbcdadccbdccaaadabddccaabdddbdcdbbacbdabccbcbdabcddbbcccddcbdcbcdaaccaaabaddaabdbaacacbbbaacbbaadabcaadccdaaadabcabdabbabbaacdadcbccdbabcbacabccdccccabacccddcbdbbdbccaccaadcaadbdacbcddcaddcdabaacbaadcacababacacbacccabacaaccdabcccdabcdddaadddabdcddbaddbbacdaddddcdbdccacbdccccabbbdaaccccbcbbaaaabbccdccccbbcbccacbadbbaabdbbbaabbdadbdadddabdbabbbaaccddbabcdadbcababdddbccbadaaaabdadacddbdaaddadccbdacbadacccccbccdddcadacbdccdbcadabbdaaacdbdadaccacaacbaccdabccaacbbcddcdabbcdabcbcadcbaabbbaccddabacaaaaaaddddbbbacbdbccaaacadcbdcbbbbdaccaaacdaccdbaccccbacdadccbcadacbbadbccadbcacbacabbabcbabacbdbbbcdbadaacdddbacdddddabbacddcdddaddbcabcbaaccdadbddadacbccbcbbacbcbbacadbcbdddcaaaddbdbadcddaabcddbbddcdcdbdadbcbbdccaaaaadddbadccabdbabadcbabdadccdccaacacdadadcaddabbddacdadadaacabbbacbacbbdacbdccdbbbaaacdbddacadcaacddbaccbadbacbdddacdaadbddabcbcdcdcaccbbbcdbadaddcddbdaddbdbaddcaacacbdddaccaccbddbdcadccdbbdcabdcdbcdcdacadbccccacbddcaabddabdccaaaccddacbdadbadacdbbddaadaaccbbbbdabdddcbddbbadccccdbbaddacacaadabaaacddbcbacdcbdbabddabcaaaccccdacdcddaaadcabbbccdaabdcddaabadcaaddbdbdccbabacbbcacaababbadbababcbdcacbabdbbbcacdcccddbbabaaddbcdcbdbbcddbaaadbdcbadbbdbcdbbcdaabacbbbdddaadcdddbbdddccabdbccdaddcaddddaabddadbbccbdabbbbaacabddbdbdcbdadddcddcdbbdaddbcbcabacdabcaddddcdabcaacbdadcdbccdbadbbbdacabbbcbacbaccbcaadcabacaadcdacdbdbcdbbdcbbababbcaddbabdcacdbcdbdacbdcadacbdabcaccdccbbbcdaabdadbbdaadbaaddbdabaaccbdbcdacbdcabdcccccdbcbdbbacbdcaccaacddbcaddadadaccaaabcabacbdbaadbccbcbbabbcccacdcadcdccbbaacadbcbcbacccdbcacdabbaaadabbaddcddcbdbdccdccbaacdbcdbacdbdacbcccdbcbabaadddbabbcdabbaadaaddbacbacaabaaaacabbccbabbdbcccddcadcccabbcbddcabddccbaccaccbbcaccbacdddbbccbbacbbcdbacacabacdcbabadbacdcddbbcdbacdbbbdcdcdccccbabcdcdcbccbddbdcdabbdccdddabbccbbbbdbdbbcbddcadcbbaacbadddacadabacbaaaacabbdacdcacddcaabccdcbdadaccdcccaddacbbdbcbcdbbaabcadacccabbbadaabdbdcdcabccaccbcdbdbbbdcaabaaddbabbbbacabcdbccbdaccbbbdbadcdbadabcdacccbbbcbddbdcbdccdccadbcaadcccbaccccdcbcbaabbacaabadadcadadccdbbdabcaaccdabbacdabaaccabaabdacbdbcdbbcdacbdcdacddcdcdacddbcacababcbdccdcdacbbdcdbcdbbacacdbbaaadbaaacaddddddaadcdccdacbbabbdcdadbcdddaaacdbdcbdcbddabcaaaacbcacacacdababbacdcdcbdbbdacbbabdaddcdaabdabbdadabddbcdbaadbcbddabdbccabcbbccddddddddbabcbcaccdaddacbbcddacabbccdbccaccbbcbcadbabbaddaaaddadccaaaccdbaddddcdcdbdcccccaadbabbaaabcbdcbdbbdbcccadbdacddcadcddacabacabdaacbdacddacdabcbadccdcdabbadbbbbbbcdaddacbcdddacddbadcbdcdacbbadacdcacdcdabddcaaccabccdbacadcbcadccccbdbdcbcadacbccddcbadaabdbbcccddabadbbbdcddddbbcdbadabbabdddcbcdbdacbccdddcbaacbccbbdbcdaaccabcdccdabddbdcbdaacbababcdcdabdbdccaddbdbcaddaccadacdcacacdaadcaaaddbdcabbddccaddaacdadddadacbddadacbbdbcddbaddacbdcacdaadcaccaddccabcbabbbccaadcaddcadabadcaadbbbbbcbacabdbabbcccacbacbaaaccddbbbaabdbadcdccbadaddbcdabccdadcdabbcbcdcdaddaccacacdbaddcacbdadcaabaabddcccaaccacdbbddddcbcbbdabcaaccbbdcabccccbddabacdbabcdacbcbcacdcdcbcbddccadabcccdccbbdcadabcabdaacbbdbccbaaadcaacbbcbdcaabccbcdbbcddbbaacccacddbcbdcdcddaddbbcaaababbbdadbdacbdbddaaccdabddbccbbcabdaddabdacaccccaacaabdacbcddcbaddcdcacbbbbacbadbdbccbbaaadacddbacbbcbccdcbbbbdaddccdbbbdbddcbcdacbdaabdbbbdabccbbdbdcaabdbcaaaccadbccaabaccbddbaddaadcbabbdcaadabbcdacacacdcbaddbdbcdbacbabaadbdaaddabcdcbdacdbacabdaadadbaabccdbccbadcdccddcadcacbbdadcbddcaabbcacbcabdadabcddacddbddcbdaacabbdbddcaacaccbabbdcaddcdbcdbbbdbbcddadcbbcbbdcadccccdaaacddcaabcaadadaadcaddbccddbcadabadbbdcacccdacacdbdbdbdabbabdcaaccbcdaaddcdcdababaaabdaddbccbdbdbcdccdcbbdbbdcdadccbbaabbbabcacadbddcbacbabddbcaccbdadccabbaadcaabbbacbcacdacbacabbcdadcbadcbcabacdbbadcacdbcddbdaabbddcabdcabdddccbaccaaadaadbcadacacdbbadddbababdaddbcabcdaabbccdacaabcbddcddbdccbadddbcddbaccaacaacbdbcccdbcbdbbbacdbcbadbbbbddabccddddbacdbcddaccbcadbbbdcbbbbcbdbdcddddabaddcbdbbbabcacddccbaaaaddbbbdbcbccbbddccccdbcdbdcccdcbddabadcbabbbdcdadddbaabbdabaccdabbaccdabccdcbddcdbccbaccdacccdbcdbbbbacbbbcccbbadadcabcaaaccdcbdbcabdcdbbcdcbdcdadcacbcddcbdbdbddddaddbdcabcaacbcdbaaadaacaabbbbdbbaccbadaacaddcaaadbcbbacaacdcddcbcbadacccdacaaccbbabcbadbbaababdcbaccadaadbaaabbadbbbbccbabccabcdcccabccbadbcaabccbbddaddccdddccadcaabdabddaabcaadddaacaabccddacabbbbadadadcddacbaadacdbcddbbbadbabcccbbdbaacadcccbdbacccbabcdbcaadbcdbbaaccadcbadadbabdcccbccddbdcbbbaacbdccccdadcdbcddddaddddaccdbacdbccddaacabadadabaadcdcacccddcadacabadcaaaacddabbccdaaaaabacccabcabacbbddcbcbccddbbacccaabdacacbaaccaacacbcbddcacddddbbdcbcbdbabbabdaaccbbaadcdcabaaaabaadbabccbdacbddbdbbaaadccabccacbbcddbcddbddbcbbcabcaccbaaccdaddcdaacdcbccaccaaccccbdaabdcdddabbdaadadbdaaddddbbdcaaacababcbabdbbdbacaacbdcbbadacacaabcbaccdccaacdadbaadbddccbababbadcacaacdbaccdbdcdddcbdbbaacbcdbacaddddacbcaabbcdabdbdbcdadddcbcccdbccdbbaabbdbcbdbbaacabcbcabaccaacdddbcbdcdacdbdbcaabdbadcacddbcddaadacddcccccabbcdcbdbdcdaacdccacdabbacadbaadaaadccddcbbcadbddbcbddccaccddabbddbbabdcbdcddabbcddaabbcdbcbdddadaaccdccdacdcddcacbddbadcabdcdaaccaadcbbcccadbaadbcbcbbabbadabadabcadcccadacdccbdbbdbbbccaccacbcbdbcbcccdcddabacbabccadbabbcdaccbcadaaccaaaacbcaaddbbdbdacadcabdaabbcbbbbcdababdbcabdbabcddaaddcaabacbddacdcdbbadddbcbdaabcabccbbdaacbbaaddcdbadacacacdadadbdddccdababddccdbbdcbdaccccccadbbaacddddcbcbdddacacabcdcbcdcdcbbaccabaaccbddacdbbdbbdcbbcadbccacdbcabdcacdbdabcbbcddbdbadcbbdcaddadbbbadcaabcdddcbbccccdabdaabdcdccbcbcabcccbcccbadcbbaacbccbcbbbccbbabbabbccacdadcbcdcabbbcacacbcaabcacdcccccbddadcdcdabacbbcbdadccbbabdadbcbbadaaabcbddaadbadcbccccaabbbaadbdbccaaaadbbadbcadacacdacccdddacddcccdccdaccdcdcbcbdaccddcbdccccaacaaacadadddaaacdbddccaaaaaaadbbbacbdcbdcdcbacacccbdcaabcdaaccccbbccdadaacddbbacbbcaadbbcdcdbbcaddbcdadcbdcccacadbcdbabbabbbcccdcabcbcbbdccddbbdddabbdbaadcadbddadbddcbbadadaacbccdcbcacaababbcdadbbcabbcacdbdadadddacddbbbadaabcacbacadbccccdaacbcadcdaaabaacbaadcadddcaadacddbbcbadcbdabdabcacbaddbdabaadbbadcbbdddccbcdddbdbccbbbbbaabbccbdcacacbbbdccbadcdddbbcdbcabdacdcccccadddddaadacacddaadcbabdcdcabcbaaadabccaabadccbdbbadadadddccaaccaddacbdcdbddccbcadddbdbaabaddccccabbcbaabcaadbddabacadacbadbbcbcccbbbaacacbadbdbdccdbabccbcabbdcbbacabbddaddacabcdbadacbddddcaaddcddcacacbbadcadabdddadabdcaaaabadbbddbcaaaabaadaaadcdcbadabcccbdbaaadcabdbadabbbccccdccacbabadbaadadbbbabaabcabcdddbabbccaadbbacaaaadacdabcdcddbcbacacacbbbcdbabaadadddcdddbcbbcabbbabbcbcabdabbddbaaadcdbacdcbdbbcaabadbbaccaadddcbadbacabbbcdadbadacaaaaaabaabadbbcdabddbdabbddddaadbaccadbcacbcbcabadddcaddcdcdcaacbdabdbcadadddaaabcdbaadbacbaacdbbcdbabccbcbcdcbcbddcbdaccbbbbddaabdaccbbccbbabacdabddcababbbbcabaaccadcbdaabbccddaadbcdbcbbbddbdbbacacddcbabbdbaccaddbcdbdcbaacccccccadbbacbcccdabcbbddadadcddbbdbbaddaaadacbccdbbcbccbbbdddbbbbacdcdccbbbabcaccdddcaaacbdacdcccbcaaacbbacbccdbdadaacaadbbabacacbdcaaabcaadddbcadcdcbadadcdddcabdacbbadccddacabaadcccddccdabccdbccbbdabadddccbacaccdbadcacdacbdaacbadbaccdaacdddabacadbaccccababaccdabcaccccbbdbccabadadcacbaadbbdaaaddcbdcadcabdcdddddbacaddaccbbcccbddbddaaaaccbaacccbaacbabbccacbaccbbcbbcccadddcbdbccadcadddccbcdabacbbcadaadcbccdbaadbcacbaaccdbaccdcbcdacbccabcdabbddccdbcddcaddaccbdcccbbacaccccacaaccbbddacddbcdcbbabcaccbcdbdcaddbbccacbcccaccabadbacacadcbadddcdabddbcddbdcadabbbbdbcbcdadbbbabcabddaacabbcbacdcdbdadbabcacaddbacbbdaddaadddacdabacbddcdcadacadbbcbbacbccaabdcccdcbcabddbccdbaadbdaddbbcadaaacbdacdaabbcacbadcacbbbabbccbadcacabbdbadadaccccbbbddabbaccaabadcaadcdaddddbdcbcdaddcbdccddaddbcadacdccddbaacadbcccccccbbaacccaadcadcacaddbdadadcadbcdbaccdaabddbdddadacdbdadbcdadddddbdcdddaaadabbcbaabaaaaacddddbccddbbdbdcbacdcbddcdaaaaccabcaddcbbcdddbabbacbabcddbccdddcdcddaaadccaabddbcacbaccbcdbdbadabcbaaabddddaddbadbcccaaadddcadaaaddbcdadadcccbbcbcdddbaadacadbaccadcbdadaabacddabbdacbcbdbbbcaccccdadcabcaaacddcacddbbcbacaadccdcabbcbacabcdbcadbbacbcaacaabbaaadbaccacabbcaabdacbcddbccbacbccadcaadbccaccbacaddbcddcdbcdaccabadccdcadcbdccbcabdaddacdabbdbacdbccbacddaabccabbbdabcdccdcdcabbbaabdcbdccacccdadbdbdcdbdbccbdbaaaaddddbcadddbcbadbabddbccaaddcabdcbcbbbbbabcaacccadbdcdcabaadbcdabcdaccaaabdaadaaddbcaddbbcaacdcddbdadadaddacdbacdaddaadcccbbccbacccaadbbacccdadbccabcbcdddcbbaabbacbddacaccdbdcaabcbdbdbaabbdcbadbbabcdbbbdbbcbbacadbdaabcacddcaadacccdbcccccbcdaadbcddacaddaacbdaaadacbababbdbacabcaacbdcbdcacaababbcddadbdbcbcadbddacbacacadbcacdbcaddcabadbcbccccacbbcabcbbbacaccdacbcadaacdbcbcacdbddddaabddadacdbcbaccaabcbaacadcccabddcdbcbdbccdabadababbcaacaccbacadacdccbcddaaadacdddbccdddddddcaadbcabccdcdbaccabbdacdccbcbccadccccdadbcabdcacdbdcbabbcbbdadbbbcdcacdaaadbdbdbadcccbbdbadbdcbadbcaadbdcdaccdababaababdcbccbaaddbbaadddcadcbdbbdcbdadddbdbcadcbdadbdadabccbbccadcbccbdddcaacbcbdaadbabdabcbacbbcabdddcacccbcbdcdbabaacacaaadcbbdbacacbcdbaccdadabbbddcadccaccadaaacdaacbbcdddcccbacabdcbcabaacdbacdcddadcabccbdcddccbddbaacdcbacbbddabccbdcdbddaaccbbbccddabcbcbadddbcdddcbdcaaaabdbcbacabdadacabbbcbcabcadcaacdabcdbaddadcbbbadbbcadbbadcadadccadbbaabbdcbbbadbaccbaacbaadbbdcdbbddcddcaabaacbcddcccaaddcddbaababdcbacdcabdbaccccccdcbaadbdcadcdadcbadccdcabbccaadccaadbbacadaddcdbcbdbbbdcadcdadcdcccbcacacdaacdbdabbcddadbbccbdadbabcacccccccadabddcaccddbacdbacbbdddadbcbdbababaadbdbdbcabcdcbbbbbcbddabdcbabccdabbbabbadddbacbdcdbcbbddabbacbcbaacddccacaddbbcababcdbcdaabaaaabbccadbbdddddbacbabcaabbacbcddbdabcaadabaacadccacbcbacbcbdacdbddbbdadcbaadbabacdcbaccaaddadbadddcbddbcdcbadbcbdbbbbcccdcbabacbdcdaddabcbcdcbdadcacaabdbccabbacaaacbcdabbdaacbbdcbaadadaadddcaabbbbbbadcadcdbccabbccccbcbddacbaabbcaadacdcaaabadbbabbcbadbcadbdabacacacdaadbadbbbaabccadcbdbacdbbdcabbadaadbacabbcaaaacaaccdbddbdbdbabadacdccdcddccabdabbbbddabacbccbdcabcbccacacbabcdcadcbcccadcdaaccdbddadcaacaacbcbacbddaaadaacababbbcdcbdccaabbbdcadbbdbdbcdbdcbaddcdbdcabbdadcddcacaaccdaabbacdcbabddbaadabaaddbaddcdbcacaacacbbccdacdbbccaaaabacadbddcbaabccdaccdbcaadcbdabcacdbadbddddbdbdcaccbdbbaabcabaacbcabbadacacbbccadcacbaaadbbdcbcdbbccccccaadbddaddbcacaababacbbabcdaabdcccccbdabcbbcccbbcbaaadcabbbbaccbcbbddcbcccababaadaadcbdcbdcabddabccdadcdccbbababbadccdbaddbcbabbcdaddbccbbbdcaacbaaddbadbadaddabbbbcdacbcdadbabdccdcdaaadbaddcccdbcccadaccdcaccadababbacabdddbaacbacacacdcaacaacbdcabccbaadaadbcdacdbccaadbadbcdbaacadbcbbdcabbcdccdbddaddbcadcdabccddbcadacccbcbcbbdabcdccacccbdcbddaccbdbbdcaadabbaabcbaabbcddbbbbdaaacadbaddbbcbaacdbbccacdbcaacbdbbbcdaacddbdcacbbcaaacccbadbacbddddbbcaaccdddccaadacdccdcbcdadaaabbdabaaadabbccbbbacbddddcdcbacddcdcadbcdaacbbdcdaababdddbcbbcddbdadacbcbdadbdcbacdccdcabccbdcbdcbdcbbcccccbcaabacccbcdbbbddddcadcbcabcbbaccabadaadcabdcbdadabcabdbdbdccbadbbdbcccaacaaababacdbaccccdccabdccdabacbddabcacaccadabdbbaddbdbaaabaabaaddccbbdcbabaacccdbdcbadacdadbcadaacaacacdaddbbdcdccaccaadbbbddbbaabcbaccbcdccddacabcbabacbdadddacdbbdcbadbdcbadaddaaaccaabbdcbdbcdaccaadadbdbcbdddccaadddcdacbddbabdaaaaadadbabbbcadacddbbabdaaaddabcbcbbbdcdacaacdacbabcdacbbccacbdacbbdbabbabaacbacadcbdbbdababccacadddbcaacbdaccdadaacbdccdadadadbdcdccaabccbcaaaaaccdaddbabcabdcbcbbccbacabdcbcabbbddbbbcaabcacdccaabcabbddccdacbbddbdbcbaccaaacccabbcacbbbacaddcddabaddabbdccadddbbdbaccaacbdbbdcdbcbbacabdbcabddcdcbbacdbdadbdccaccabadbacdabcdbabaaaabbdbacbddcadcbdababdcaabccdabdbdcabdcbdbccabacabbdcdcccbadcababccbdbbaaabacbacbbccdbdbcaaabdbbadaabbabcdcbcaaaabcbcccacbbbbdcbdbbaddcababbcaccadbbbabaaaacaabcaaddccbcadddddadccdbaaaaadbcadccaacabdbcdbccaddbbccbbbdadbbcbcbcadbddacabbcaccddcabcbbcdbcdbaaadabcdaabddacbaadbcaadcaddaaabacacabacdcddabccccdccacdbccacbcbccddcbdcbcdaacdccdbaaadcbbddaacbbadccaabdcddbddadbdcbddcaadcaddadcaadcbccbadbdddacadddcaddcdbcabdbdabdacdaddaaacadcabadbdcacdaadccdddcdcbadbccdccbcadaadcbcbacabbabdbaacbabddcbbcdaaadbbcbccadacbbadccdccbbacabbaccdadccaddbbaadcadaadbacadcaccdccddadabbacabdcdddbaddddadaacbbdbabadcbdabdcdababcbcabdccbcbdccccbaccaacadabdaddbdbdbacaaacbadbbdcabdbabcccadadabcaccbbabbbdaadbccdcacdaaacdaaaaddbddddbadbbbaaddaadbdcaccdcbaabcbcbcbbaccadbbacacabdcddcbaaabdddbdaccdcbaddcdcabdacbbbbcbdcaaacabcddbcddbbdaabbadabadbadaccbdababccdadccacbccadbabddcdabbdddcccdaacacaacccdbbaddcadbccddcdacbbbbacbcbacadaabcacdddcabcdacdbdccbbcbbddabadbbdcaacaacabbabbbbddbccdbacccbacacbadccddbdbacccdddddddacdccbbdaabacccccdaccbbaaacdaaadbdddddadcdcadadbadcdbddaabddacbccccabdbdbbcbbadcdccaddddbadabbbaacbcdbbbababbacccdadccacbcddcdadbbcaddcdbaaacabdccacacadddabcbddabdacaadaaccdbbdadcdaabcbbbdacccbdccbdadbaabbacdabbdcbbcabdaaabaccdcdaadaaddcbadbddabbadcdbdddacbaabcaabcddacaabacacaccacbcddaccdcacccacabdbcccabaddadcdadcabdcbacbadcccdbdcdbbcbddbadcccabbdaabcddcbddccbbdcdccadcbdacaddbbddabacddbcdddbccaaadcabadcbdaccdbabdbaccadbabdcccdcadadcdddcbdacccdaabaccbdadbdbcaabdbcddbcadbbabaacadcbdacbbdbcbdadacabbdcbabdaccdbabdaaaaabcabcaacaaabdcaaccdbdccaaaaadcaaddbcccccbbacacbcadddbdbabdbdbabdcbcdbaddddddabbabcdadaabacadbccbcbbcdacdbbbbdacddbabcbaaaddabbcccadcadccbacabadbaaadabcaccdbccbadbccabadcaabacdbcabbbdacabcacacdacbaabbcdbbddbbcbccadbbdcbdcdcbabbccdbccdadaddcadabadacacdaabaacbdabcddcaddcbbbccbdacccaaabbdbdaaccbbdcddcccdcacbcbacbaaabaadcdbcdcdcdcbccddccaddadaaccdaccccdaaacbbcacbbbdabbdabaccadaddacdddcbbccbcccbacacbdcaccddbadacacbccbadbbbcaababdadacacccadbddbdbadccddbacdcdcaccabccccddcbdabcddccaaddccacccaabdbdccbbbaadccdcacadbadcaacdadbccbbabcabddbcbddaadbdacdacbbbadacdbcbdacdaaaccbdaccababaadcccacbdacbdbbcddbdddddbbabbbdcbddbcbbdaaacacabcdbdaccbdbdacaacdaccccbabaddbbdaacdccaccbdaccaabaacabddcccbaabcdabacbbddcbbaaaaccdaddbdabddddcaadadbadcccbaabbdbbbcddaaacdcdadadcbabbdccdddbcbaddcbcacbacccccbbcbadcbcaacbddcacdbaadddcdbbbacbdccbdbddabddcadcabbdcdadcbcccbddaddbdccacdbdbbabbddbdcaddaaadbbabdddbaacacabccccddbbdbaacbbddbbaabbaacaccbdcabdbcddcbabacadbdcdbbddacbcaacadbddcaabaabcabbcaccbbabdcbbbbdaabbbabbddcbdadcababadbccacccabaabcddbcdcbbcdccabacadbcdddbcadbababcdaacbbdadcddaadbdbdacbcaaccadadacabddbdbdadccdccdbaababcccdbdabbbababbbabcbcacccbadadccccbdacbbdbaccbadcddadccbdaddaadbbabccbcaabcadcdabcbddadcbbaadacdcababdacacbadbddacabadddcaabddcdbbddbababdcccabcdbbcbccdabbcdddbaaccdbacadbbbacccdccacbaabaabdaacacdbcbaaadbbdbbddacbbacdbcdaabacbcaccacdabcdbadbcbabdaaabacddcdaaaabdbacccaabbbccdcdaaaabbbbbacaabdcbdcbdcdccbabdbacbaabddcdcdbacbcbcbbcbdbacbcccbcacdbabddbcdcbddcbacbabadcabacdbcadadbabcaccaacacbbaaabdaddaadcadbdcdbdcbadbadddcddcaabacdcabddaacacbdaddacccdcbabbdbdcdbbcddadabcccdcacaaabbaaadadbdcbacdbbaccccaaacdbbaccabdcbbcbbabbddbbaacacbccbdaddddaccaabdcabbdbccadcddbbbcbddcbdcdbacbdadbaddbbcaaccaccdabcddcbccabdbacbaadcdcbaddbadddaadaadcddddaacddbaadccaccdacbcabdadcaabbbaddbdccaccdcaadbacdcdcacdddbdaacabcddaaabbdbabccbabbbbcbaccdcdcbabcaadaaaddbaabdacdccbadcaabccdaadbbcdbcababadccbcbcadaabcbbabbacbaaaacdbccaddcadcccdbdccbdcdcbcaaddacdccdbadbbbaabbccbccbcddbdbdcaacccbbbaacdcaadcadccacbdcccabbdcdbbcbacbbdbaccbccbcdaddccbddcacaadddcbbbbdbdbdcabbabbddbbcaabbcadccbcccbcbbdcaaccbdcacdbbacbaacadcacdbabbcbdabababbaccaccccddbbbaaaaddaadbdabdbaccdcccdcdabddabbdcadddddabddadbbbbdbbdccacbaadbdadcdaddadccdadcacbdaddddacaadacdcbaddbcddaacbaabcccbacccacabcbabaaadabbbacacdddaddddbaababaabdbdabbccadadbacabdaccaadabbdddabccabdccccdbadbdcacabbcbbcdbdbbacacbdccdbaddcccccbbaccbdadbdbaabbaccddbdcbbdbbdaacbdaddaaadcccddcaccabdabaadcbbcbccabadbdbcdbdacdbabcabddddcabddcaccdaababadddbcbaabcddddbabddbcccacbdddcaccddaadcbbacbcacdaaccacccccccccbcdcdbbbbddccaacacdbbcccdbbdadcadccbccacbaadcbacacadaaabbabdbbdbaadddadabcdaccbcddaacdcbcccbdcccabccccbbdcdaaadababacabbcdaabddabdbcdcbaabdacccbbbbbabbbabdbcdaaabcaaacbdcddadbbdabaaaaaccdcdcabddcdaadbcacccacadabdccdcccbcacaadbaaabbddcbadadadcbddbabcdcbcabbacbdaadddcdaccbbcccdbbbbbccaddabddbbdacccbcdddaabbbbbbadaaabddabbdbcccbabcbcdcacccbcdbbbdacbbddadbbcbdccaddcccccababcacdadadabdbaabddbacdcdcbacbaccaacdbbcdacdbcbaacaccbacbadcacbbdcccdccadbbadbbdcccaacbccdcadbdbddcabbbbccaabadddacdcdcbaabbadddbcbcbbdaaadccaabcaacccbadabddbcbabbabdabcbcabbbdbcbbcdbadaccaacbcacbccaadabdccdbacbaadcbaddbbcaaaabdaabbacdacbbddbcbcbdddaddbadcaddbabaaacbbcabdaccbbccbaababbacdbcdbadcadaabdbdcaacbacabddbcadcaaabbcbcdbacadccaddbcbadddbcdcccadcaabaabdbaacddacabbadbdabcddaacdacbdaacbbabdcddbcadcbdbabbdabcbccbdbcbcbbbdcadcccadaabaacbcccdcacdabdaaaaacaccddbbdbdbabcadddabdcddadaccdccdbdaadcddaaabbbccadabacadbdcbbbccbacbbaacbdddaabaacaddbbaddabdcbdbcabacabcadbabdadadccaadccdcadccbadcababacccbbcdcccdbcadaccdcbabaacddcbddbbdbdacaccabddcabcbcacacadcccaababcddbdaacdacdacacadcdcabdabbcadbacbdbbbaaaddabbacccaddcbbdacadaddbaadbccaaccbabbcdbdaaddacbcaabbcabbccadbdcdcdbcbbddbdacaaadcdbdcbcaaddacddddaadbdbcddcdaddbcbaccabacbaacbbcbddddcacabddbabccbaabacacbacbacacbaabbabdccdbddbbbcddadbbbcbbbccbbbbbbacdcaccdaaaccdaadacbcabbbdbbbbccbdabadbdbbaddbabdbdbadbdcdbaacaacabcdabccbbdaaccdadacbaccdbbcddaacacaddbbcacbcdabccdbadddabbacaaabdadadcdaadccdacbcccccabcbcdcbadbbabbcabbcdbccbbddcbbbcdbdabacbbdddadcdcddabbbbbbabdbddcdcdcccdddaccadaddcbbcddbbcbccbccccbdcbbdddadaccdbdcadddddddbacbbdbdacbccbcaccbdbbacddacabbaacdabbccdacbdbddbcdcdbabccdbcbdbbaaddcbaddbadadaacccbbddbacdddabccdaabdcaaabcdbbaaddacbbccbbdaabcdcbcbbaaadabdcdbcaabbccdaabbcbaaddbccbddaddacaadabbabdbaddbababdccaaabbcdadabcddcacbbcbaddadaaadcabaaaccbdbccbdcabbbdddadbdbbabcadbbacbdddccadbcbbdcbaabadccbccbbabdccacaddaaacdbacbbdbbaabbdbabcdadaabbadbdbaddabdcdabacaadcdbababcdacdaaccdbdadcdaadccdbbaacbdccadacbdcacdccdbbddbbcddaacbdcadabcdadbdaaddaddbbdaabdcccdacdbbddbabdacdcbccdbdaadcccabdabacacadcbaacabaaaaabddacdbdcdcbbadcbcccaccccddccbbcbaccdcdddabaccacdcbbddacdaaabaacabcccbdaaccdcccccdccdcdacdcbccddacacaddcddcdcabadbdbdcdcddcaaddacbbbadadddccabaabdddbdabcccbddcddddcdabadadcbcaddcdbbdcdadbadbaaaacbababdaaabccaacabdddddbaaadcadcabaddcdbcadbdaddcdbbbdaddbabbcaccdbcadadaaacabaccaaabcdbacbbcabbaaacbcaacdbcacbbbbccadadabdcbcddadaabcbcccbaadddaacaaababbdabcdacbbacddbbbbbdcbbabaabdcbbbbbaccbddcbdaaaadbccddddbdccbabcbadaaadacbbbcacccdbaacbdcbcdcadcaabddaacacccbaacadadadbadadcccdadddbdcbcdcaddcbabadabdabbadadabdaaccdcbbdbddcacccaccbbadacdacacdcabaacdabbddcaabacdccbddbbbacddcbbbddbccdbddadaacbcbdbdbcdcbaaaaccababccaccdbccaabddcbcbcbdbdbdadaccabdcabaddccbadabadadabdcddcacbcaccbdbabddcddccaacdbcdcccdbdcdddbaaabbbadbabdccccacddadcbdcdcdcdadccbbdbbacdbddabcbcdcbaddcabdabbadacccbddbddddcdcbbcccddbcaabadcbdcabdcbaadbacaababacacdacdcbdcdbabccaaacbddacdcaadddadcbadcabdbabaabbdccccaaddcabaadcdddcddcddabcadacddaabdcacbaccdbdacbbcdabdcadddccacddadddcababbbcdddbacbaaccddcbadccbdcbddcabcdaddcaacdcbbdbcabbbbccbacbbdddbcbacddbadccabcbacdbcdcbbdcdadaaaaabcaaacadbbcdacddcccbbbdddccdcacaaadbcbdaccddbbcbdaaabbadcbbcabbccbcaadbcdcdaddbabdcaaacbabbdaacadbbcaabcabcdcdadabcddcccdacaaaadddbbbcacadcdbdcacacabdbbddbbadddaabacadddccabddcdbbaaccadaaaacacaaccacbdbacbdbcbaaadadaaabacbbbabbaadacbadccddcbaabdacbabdcddbbbcabcbdbcddadcbdbcdddcbbacdaacaacabccacbbcacaaaaabbbbbbadccdbabaacdaaaaddacccbacbddacbcacbaddabcbdddacabaacdcaaccdbaaadabbbdcbdbdcacddccaabdcdccbbcddcadcaccbcccddbdbadccddbddadcddbcadbaabacdadcaaadcaaacddbddccbaaadcacabbaacaaadbabcbabcabddabbdbccccdbababcadbbaddbbcbbcacbbbadcccdcddccddcabacbcbcbadcdcbbabbacbddbacddcbabdbbccaacadaacddcdcbbcbaccaaccadbbbabcbbcbaaabadaabcbbcaaaccabacabaddcdadadcbaabbabccadcdcbaccaabccababcacbbdcadcdbbbbaccabdddbdacbaddadabbbcbbdbbcbbdaddbabccccddccbabcacabdbddccabbdcccbbbdddabccdabdbacbbccbbdddaccdadbcadcdcddcddabdccddaaabadddbabccccbdbdaddaaadcdcdabbcdbadcddcccdaccbcdadbcdddcabdcddbcddbaabbddbadbdddacbcaaaabddccaccabcbcdbddadbbabcccbdcddbdabdbccadaabbabaabbbaaaccbcbcdacdcdbdccdcabbcbdbbdadddbadbdbadddccbddcdccdcdaacdcdadbcdabcaabcabaaaaccaccadadbccdbddddcbababcbbdbdcbadccbbdadaabdddbdbdabbbabcccabbbcbacbbdbbdbcdbbdddbbdbaccccbbcbbddaddcdbdaccadbcaacadcdbaacbbdbcbaccaabbcddbcccbcabcccaabcbbaddddbadaaddacddcadccdbbbbbadccacbbcddccadbdacacbcadcaddbcbacbdcadaaccdabcccdbcacdadbbdadccdaccccdbdbbbcaabcadcccddaadbdbaaabbdccdabbbdcabbcadcdbaaaccaacdaccbadaadabbcdacccaccdccbddbadbdbdaaabdadddddddcdddacaddaadbbccaacbaaaabbaabbdbbcabcbabddddbccbbabcccabcdadddcaaadcaaddbabdbbdaabccdaaddccdaccbbdbcccacdbaacdadddaccabcabddbaaccccddbcdbcdbdcdcaaabddaacddddbcbbdaabadababadaadcdcabcbacadddacbcbabddbdcbbdacabcabbdbdbadaccdbcbaacdcccaaaaddbaacdbcaaaaaaddbaacbccaacadaaabddccdbddcbdaadaaadcdddbcdccdbcabbadaadbdcccacacabbdaabbaddddbbcbbbcddbbddacdbccbdcccdabcdcacbdaaabcaabdaadabdabbdcdcdbaaddddabdcadbacacdacdcbbccacdaacccacdbbbdacdcdbbddcaababadabcadcacdadadcacccaacaddddbadadabdddbccdcaaddccadccdccbbdbcddbaccbcdbdddacbaababbcbacdbabdaabbadaaabbdabbddcacbdcbbaccdbbccdbbacddaaddbcaacabcaadadbbdbabaaddccbaaacbcbdbadcbcaddbadcabbcbddbcdcacbadbcaddcadabbbbdcaacdbbbdccccbdacccddababbdcabaacdaacbaddbadaaaaacbcacdbaacdaccbbcacddaaccdacdbbbadbbacbccccbccbbdabddacabaccdddacbcaaadcbbcddddddbdabccbbbbabcaadbbbbcdbcaaadadddcaccdbcbadaacdbcacbcccdbddbbbddcbaabdbaccdaaabdbcbacabddccbcbddbabbadbddacbcbbccadbacaabdcbccadcbbdbccabdbadbabdcadccaadddddbbaccaadcccadccacccaaaabbdbddadcbbbcaccacdcbccccbdaabdccdabcabbbaadbddcdddccbaaabcaacabddaaadabadcbddaabbbdaddcadbdacacacacccccdbccbdddadbcccdcbcbaabaaddbaacddabdcaaabadcaddccbdbcbbbbdaadbbdcbcdacccacadbdabadbdacbcaacbccbddababacadbbbddbacaaaabdccdddadbddbadbdbbbbdcdccaddcccbdabbdcbbabddbadddbabcccccdcdbabbdacadadbdcbdaccccbcaadccccadabaaabaacdcbcbbcaadbcaddababbaadbacbbbcdacbdbaabacaddabdcddcbccdbbbbddcbccdccbbbbbbbbccddbdbcddcdbbccababaaaacaccdcbaccdabcbcadcbcdbcdcbddacbdbdbcdaabbdbaddcdbdbbdcdbaccbbcacaabcdccbacbcddbcaadbbabcdadcddaabbbcdbcdabaccccbdddcacbdccaacbdbdcaccbabaddaddcdbbaadbbdabdadaddbcccdabdabbcadaabdcdabaccccddbcbaadaabdcbdaaccccaddacabaabacbcaabccddacdcdcadcbdbcaabcdcaaabddddbaaaabcddbcbbbbdcbdcccaacbbcbdacaaacaccccacadbaaacddbdbdcabcdccbcccbaacaadbaadcddbabdbadbbdababcdacbdbdaabcccbdddcbdccdccdddcccacbdddcabdddddcadbabbbbbdbdadcadcbababadcacadcababcdbaaddcbddaccdbbaaccadcdadadbddbbadcdcdbddccccbabddbbbbadadddadcdacbdbaaacaacaccbdbacacbcaabccabddbddcaccbdcddccabbdaddcdbdbdbbcdaabcabccadacccddcbaadbdbccacbbdadaadcaacbcccacbcbdbdbdacccbadbbbcbdbbbdcdaacbbaddaaccacbadcdadccdbcaaacdbcbacbdaaaabcbdbcdadbadaadbaaacbaadbcbbbcabbdaaacbcdbbdccbaabacdcddcbcdbcbcadddadcaacbadadddbcdbcdccadddccbbbbbcdbaacdacbdbaddadabaadcdaabcdcdbdadcabadcabacdcaabbaacdbbbbbdaacdabcccbaaadddcabdabbcdccbaacdccbacccabcadbdaacacbcccabccdddcaacabcbcdadadddaaddccdbaabccadabacaadacccdbdcdabdcbadcacacbcabdcbaaabcccddcdbcaabadcbacbbcaacabbaaaddabcbbbdbbcdabcddbdcacddcdcdabcdcbdcdccdaadcacdccabdaccccaabdbbdaabcbaaaaacbbccddbbacbcaacadbaaadbbabdbbdadcbbdbabdbadaaaadcccdaaaaddcabbdabcbdacaaccacdbbdccbbccbcadcacbcbbdccbddcddbbaccadbdaaddbaaaaccbbbcdcadaabcdabbaaddbacccccbcaabddacadddccddcaaabbbdabddcdcbaacbcdddcdddabdddbcbadadbbaaddbcbddbaaaadbdbcdbadcdaacbaaacbbbdcababbcbdcbcdcccbbbdcdcdccbcbdbdabacadadacbacacabbadbbacabbbdacaacbcddddbaaaaadbaaaadbdbccbdbbbbcbccabdbbbccadabaaaababaccdbbdcabccddadbbbaacbbccccdaacbdbaaddacbbaddabadcdabcbadcaaacbcbbadacacbbbadcabbabcaacbccdacabacacbcbdacbbaaaccacbcaabcadcddbbbcbacddaccdaaaaabbcddaaabdacaabcdcdcbcbbdbaccbadacdcccadbbdacdbabaacadbcadcbcbdbbbbbaabccbbddcccbbacbcacdbcaddadccabadcacbabcbdccbbdadaccdbbcbcdaabadcbdadccbcbcbbcdbbcaddadbbcddacadbdbdabcacbacacbbbdcddddbacdaaadaaccbbbdcdccbccbccaccccbabaababdbcdaddccbbdacacacdabacaabcaddbbdddcdaadaddbbccaaacbdcbdadccbcddddccabbccbbdcbdccaacdcaaacdbcbdbdbcbcacabcbdacbbcbcaabbbcdabaacacdbcbbaacbabbbacccbcdbcabcaacdbccbcacdcaababdadacadbddacbdbadaabccdacacdaaccdabccbabcbdbdbcdcbcacbaabddddcbaaccaabcadabdbbadbbbdcddadbcccbdabbbdbcdbdcdacccacdbabbcbddacadaddabcbdbabadcabaadaacdbabaddaccddbacbddccdcaccccbcadbdcadacccabcbcadaaabdccdcadadabdcdadabdbbcccccddccadbaccbddadbaadcbcdcadaabadbdabbbbcddcdacdccabbddaaaacaabbbccbbcdcacabaddcaccadbbadccdccaccddbbbbddcadacbccaaabaabcbdcaaadccdbadabccbaaabbabccaaacabdaadbdddacababadcbbaddaddddbabcaddaaadabdacbcdbacabcaacddacdaccdbbcdabddcbbbdccbbcdabaaaaabbcbcbddcdcaaaabbcbbaaaccbdaababbcbacbabdaaaacbdcbbcdaaacbabadacbbbddbcadcbdcbddbcccdaabcbccdcabddbdcdaaaddabbddbccaddabcdabacbdbcabcbdcabbcbadabdbaacdcdaacbcababdbdadddddbaddcdcdaddbbdaccdbdcaababadcddaddabbadcbbdbcaccaaaaadbabaaacabadbbdbabdcababdabcaadcbdacacabaaddcdbccacaaabbbadadbcadcbdadbaccbbadcbdddcabdaadcaaaaabacacacadcdcdccdacbbddcccbdbdadcbddadccaddaccadabbabbdcddcbccdbcbaccbaacbadaabdbdcbdbdaabccaccabddcbbabaaaaadbbacdcdccacddaddabaabbaaccbdaddaaacacbdcddaabdabacaccadccccbdbacdddacdabaacacdbcaadadbbaacbbbaacaabcccaaccccaabbaabacdbabacccdcaddbbababaacaacdbabcbccaacdcdcdccdcacabdcadadbbcbbbdbccbbdbddacddbcadadcdddbbbdbcccbbcdbbcbadbcaabcbaaccdcbdacaacadcccbddbbbaddcbacdddcaddcbdaaadcddbbcbdcbccbcccbcaccadbdbbcbddccbcdbcabbddabdbabbcabbacdcbddaaaadddbdabaadbdcdcddcdccbbbcdcbdbdbccbadcbbaccaabddbcbdbddbbabacbbdbcababbcadbbcdbbcaacbacbdddacbadaccbaddbdbbdaacaccdadbaacbdbcdccacdccbdcddadcdadbdcaabbdddcdccabbdcdbdddbdbbacbaaaaacabdcdcbaabcadccdddacabccbdbcdbaadacdadbddabddaaaacbababcbdbbbcbbdbcdddcbdcbbabbbddadcaaaacccababcddcdaadacaacdcbcdabbdadccaccdcaacabadbccacacccabbddadbaccbbadadbaacbadbacabddcddddabbcaaabcabdcdbacccccadacbbdccadcaccbbdbacdbbdbaacbaabddbabbdcabccdacdddccbbabdcdcdbaacadcaddcdabdbbdcbcdcdccadddbdbcbccdacbddabcbbdbbabdbcaccbdcdabcdcabddaaadcacabddccabdcdcdccdacaccbabadbbacdbdbdaadadadccacdbbcaccbdadddbadcccbaaddcbdbabdabaadbcbbabaacbabccbcbacbcdadbabdbdcbaaaabaddaadacdbaadcdabdcbdcbddadddabcaccddbbabaccbdcddbdbdaaddacdaacaadabddcbbaccccdddabcacdadcbcadccbaaabbadccabcbbddcdacbdccabddaabcabdbdabcccbbcdbbadcacbdaaddabdddbdddaadccabbcbbcdabbcdbcccbdcddaadabbccbcacbbaaacbcbbccadbbadbbdaadcdccacccacacccdbbdbdbdcbcbbbbacacdaacbcbaabcadaaddddcdabdcbbdcabdabadcbbdcdcdddacdcdadbccbbdaacbabdccddabbaadcdadddcddbdaadadcbbaddadaddbaabbdbddbdbabcccddadacaabcacbdadbbcddcabaabaaaabcaabccdddadbdacddacdcddcbcabcddcccadacadacaabbacbcdaabbadbbadbbccbacdabcaadcdaacddbbdcdddcdcdbcddadaadaabdccbcaaacdcbcddbaacdbabbbbaacbcccdbbbdacadbcaaccbbdcbbdcacaacdbcdadccbdcacadbaccadbbadddaccdbdbacdabcbcbbadaccdacbacbbbbaaabbacbdbcbdadbacccabccbddcddbccacddcdddbcbddabdcddcccdbbcccdccbaaddadaabcddddbbaaccdcbcacaacbaccdabcbbabaadcacdbaddaccbaabccaabccbadbaacddaacccbdcbdadbbcacddcbdadabdadacbdddcdadbaadabaaabbcadbdabcccdbbddbaacbddaaccbaacccdbaccababccacbadbcdcdacdaccddcacccddabbdddddbacabcbdcacabbbbbbdbabdbccdabcdcbcdcbbbdaacadddcaaabdabddcdccbaddcdabadcbacdbcddbbdcadcaacadddbdcbacbaadadacaadbdbddccdcbbaaadacaaadadbcadadacbbbaccbaacbaaaabccaaddbcddacaabdabdbcbbccaaadbddbdabdbcddbbbcdaaadcdbdcbccdadbbdaacdbabbdacdcbadcbadabadaabbdbadacdddbaacbdbcbbbbbddcdbccbdaaadacbbccadcccadaaaaacdccccabaadaccdcbdbccabddbbdbdacbcaccbccddaaddddabdbbddcaaccdcbdbacbaaabdcbcbaabbbdabbdddbcacabbabccabdcdcbccadbdddcaadccddcbcbccabaacabddabacddcbadddabbadbccdddaabcbbdabbdbdacbbacabccaddcabbdbcdbbcbbdccaddbdddbcaddcacabbbbbabaaaaddcdaddbbaaabbcacdccbabbacdcaccbdddccacdccddbadadcdaccbcacdcdcbadaabaacbdbcaccbaadaaadddacdbacdabdcaabdadcdbbdbdcadbdbadccdabaabcccdaacdbacbaadddabcadbacddadacaacdcbaaabbadaccccbbcbaccbbaabdadadbdadccccdaddaabbaadadadbadbbdaabaacbbbabcbccdbdccabcacadabbdbdcbbccbddbadcddbdccbdddbbdaaacadbaacdbccacdbdaaaabccddaabacabbbbabdabbadacbbcdcbcdcbcacbdacdcadaabdabaddbcdbbaccabcbbcabadcccacbaddbaddbddcddcadccaabcdcaddbcacbcccaccbccabdbbaabbdbdcadbbbaaadadccdccaaacadbaddcaabbdbbcbdcacdaddbcbddcadbcbdbdbacbbdcdcbcbcbccbcbbddcbddaadbabcccdcbadbdbbddaaabdcbacadbbabbacbaadbbaccbcbacdcbdabdbcddcabaccccdcbdccabaaccdbbbdacbdaaddadcadddbacbdcaacdaddbdcaabccdabaadaddadcdbbdbdbbcacabdddacaccdacdbdaabdccacddaccdabdcabddcbbaaaacacdacaccdddddddabcbdcdddcccccbdabbdcbabbaaaaccdbbbcdbbccbadcddbcbccbacdacbbdcdacbccdbdcadccdaaaaadabadcdbccacdcdbacabcdccadaccaacdbdcdccdacadcbcddbadcaadaccaddbbccaadcacdbaacbcdddbbdcdabacadcdccadbcbcacabcbabbccaddbcbaaabcccbdbbcacbbadabadbabbccbbbdabdcabbbdbacbddbabbdadbabbbdaadddcbccdcaabbcbbdbdaaacbcadabdcbadaccbbcbbddbabcddbdbcaacbcdadadccbbbdbbbcddbaacdbacbaabacabbacacbbabbcdacdaddcadacacdaddbddbdccdbbcbaabddaaaabdabbaddbaaacbcbbcaaacabadcadbbcdcddaabaaaadcaaccdcadbdadcddbcdacabcbdbcaadadadcbabdbbdadbccbbbcbddcacdacdcddbbaccaadabaacaadbdcabaabdcaacbccaccdababadccabcaaccbccbcdcaddabbacccccccddbcaddcbccbacbcadddcccbaaacabacccbbdddddcacdaddabdadbddbccbbcbdcaccadddbdbaabdaacbdbadaaaacacdacbcaddaaabdbadcbbdaaaddbddcaacacdbdcccacbcaabccacbbddccbdbcadcbdcbdadaaadabccdcbcdddcbbddcbccaddcaddbddacdcbdbcdcccaadadccdddaabcdabbaccdbbbcbddacabcdadadaadbadacbcbaadcaadabacacadbacccacdddcdacbdbddcdcdcacdddacbcdbacbdcdadacbaadcadddaddcbcbddddabbaabbddcbdbcaacaadbdabccabadbbdabdbabccdccdccdbdbdcbbcabdbaaabcdbabccbacddaacddbbcbabcbdccadadcccbcbaacbcaaccaaacbdadbbcccbbdcabbbabcabccbcdbcdacbdbdaccdacdabdbdacdabcaabdaccdcbbdabdbbdccadddbabbcaddacdadabaddbdabccdbbacccabdcbdcccdbcaacbbacdbbaaabcdcbacdaacddadbcbccbbdbcbaccbaaaaadbdbacdbddaaabdcbabbdcaaccccaacabccbaaadccddcbcacacdadabbabbbcabbcdcacbdcacdaddcdacbbcdcaddcbdbbcdccdbccccadaaadacbbddddbdbbcbadbbadccbabcbccdacdbdcccbacaadddcbaddadbdcaaaadadcaaababbacbcaabdabbadabdbaacbbdcaadbbbabddbccbdcaccdbbbbbbbdddacddddabbccabcbbaddbbccccbcaabbabaaacdabddbdcccbaabdbcbbbdbdbacdaddbbaddcaabaacdacacaadabcacacdccdddbbcbacddcddccdaacddbbadaccdadbbbcbbcadacdaaaddcccaacbbabbacbdadcbdcbdabbcacdbdcbdcbadcbccdbdadccbaabccacaabbbabacabaacbbacdbdcaacbdbabdcbbdbbcbcaddaaddbdabddbcccadbbaabacbdcbbbdcdaaaacbadbdaadadbbdbcacadaccddabddbabdcbbdccccdbcabaccadaccddccadbacdcddbbdacabddbdcdccdabccbbaababcacaaacdaadbbcbdcdbbacdbddbcaacacbbbcbbcdccacbabacbbbdddacababdccbabdcadbddcbdbbbbdacbaaccabcdaaacbdbaabacbadbcaabbddaacdacbbcbdadbabdcabbdcbaddcaddcccccbdddccccddacbcdbdababacacabcdaaddbcdbacdcabdbcddadccbbdbabdbcacbabdbcbbcbbdbcdccbdbadcdddbcccadbdabaccccdabdaadaabbdbadaaabdbcdcdcaccdbdccbbbcdcbdadbdacacdcccadbabdaabccbcdbaadccadadababcccaadababbcbdddababbabdcdacabdcdbcbdcdbdadddadaddaddcacbddbdddbaaabccaadddcaaacbbdbcccdccdcbacbbbcccdabcccaccdccbcdddbacbbddaacdbbabcadacccabdcddbbdcdbcbacccccdabbacbcadbdaabdccabdbabdacacbbaabcddcbbacdadcacbabbcbdcddaacadcbdbdacacdadccaacdcaaaabcadcaaccbbaddbabadddbcbcaabbaacbcadadccaccabaaaadddbcdbbbccbddcdbabcdbaaaccbbcabaabcbaaddddbddbcbdbcbccdbadaacbdbdcbdddaabbdacbbcaddaddbcbbcbadacbbacacbaaadabadcbbdacbdbcdbdabaaccccaccbcbcabdbacaabcaacbbabcbdcabdbdcddaaaadcdbaabdadbabcddbcccbccbacabcdbbcdcadcdccadadccbbcabbbbdbbccddcbdcabdddbabcabdcdcacbbbcddabbaddbcbadadbbddbbaaabacbabacaabcdbcdbbdabbaabcdcabbbcdacbdddaadbdddacabaabadddcabdccacadbcdddacbcdccccdaadbccbdbdcbabcdbbbbbcddbbdcbdbdadabcabaabcbddadacbdcddbbcdbdaadaabcbbdcdbacddcaccbcdcdadbbbacbdddadadddabaacadbacdaaadbdaddababccbdabccccccbdaaaccdddadcbabdbcccddcdbbbbdbccdddcbadadababdabbcdcaaacddbabcdcbbadacabdbabdaccbcddcddabacdbcbdacabcdcbcabdddcadaabbbbddbbadabdaabddbcabcadacbdacbadaabcabbbaabdbcdbdbdbbababdabcbccdcadbbbacbccddbcacabacaccbacdddabddbccbcaddadcbbbcbbadaacaddcdcbaadaacadbabbaccbcdbcdbdbdcbadbbdcccdbadcaabbadbcdbddccdbdcdbdcbddaadaddbddbaadcaddcdddbbdcaaccacbbdadbcaddcbbbccaacbcdcccddbdbcabcdcbdaaccdbddbcaccbaadbdbcdacbbdadaaddcbbbadddcdabcbcaabddbacadbccbacdaaabacacddabbbbbbaccccbabdbcdcabbdacbbcaddacbabadbbaabadccacbddcddabbacacbcbadbcdaacccdcbaccddddcddcbababcbaabddaddadabababdddacababdcccaadcbbdbabbdcdacbcdcaaacdacbacccdcabdbcadacaddcaaadacbccdbcbcaabbddcbbcccbcabacdddaadbccccdddbdcccbadccccbbcdcdbbdbadddcbdcdcbacabacdccbcdcdbcbddcdacccddbaacdbcbbbbcccdddadbcbbbdccaddabaaddddbcaadaacacdacbaacbaadcacdbcaadacdacabbdbabbbababdcdcaacacdccddaadabddbdadabcdbbcbcadabddbcbddbdaaabddbdddbbdbdcbabadbdbaaadcbaaaaabbbcdadcccdccccdacdcadadabdcabccaacccaaaaddbdddcdcdababdbcbadbbdabbbabcdabbcbbccdbccdddbdbabcdbacdadabbaddcddbaabdaaacdbaddaabadacdbaacddbddabacabcaddccaddddacbabcddacddaddacdbbbdbadccabbabcbcdcadbddabdbabcdcdcaaabbdbabcdbabbacccacdccdcbacccdbbaabbbbbbbbbddbabadddcadcdddcdbddcbabcccabbaabacdadaabadbbabbbbcdbdbcdbabacbdaccdbdbbcbdcdaccadccbbcabbccabaaacdabccbbcbacdcddccdbdbcdbdcddaaadaadddaacaabdaadbdadddadadacdcbcbcacacaaccacbbcacdbcbbaccabbacbcdbccadadaabbdccbadcbbaddbadabbcaadabddccacbdccaacbabbbbcaabacabdadadcbcbaccbadbcbdadabaacdcbcddcbadbacccbccaccdcddccdadadaccbbdcdcdbdbdabcabbcdbcdacccdbbdacacbdabbaabbdcadbdddadaabbdadaadabaaaaccdabadadbcacbbabccccdbbaaabbbbbadadcbdacbddcddacaccadbbdabacdbaadbbcdcddadaadbdbbcbbbbcdabbaabdabdbbaabccbbbddcddcdbddaacdbaadabacdbbbddaddbddbbbadbcbcababbdcdbcabcadaabcdbabaccdbcdbddabcbbdbabcbdddcddbcbcdcadccdcbcabbcbdccbbbcbabbcbbcaaaaddcbadcaddcbcbddcaccbddccbcdadddabadcbbaaabdacbbbdcaaccdcdbabbbcbcbbabcddbbcddbdabdbcdacacdccbdbabbdcdbcaacbbadcadbbccdcabbbcbcbbadbaddccccabbccacdbccbccadcbbcacabdbccdaddbababbcddbcdadbbbbdbdcddbacdbbbdcbaacabbdaaadacaaabdcbcbcbcbbabddcdcdbacdcdcacaccabdbdbcdcabbbbdcddacdcccbabbcbacabdbdcbcadbaacddcbcdbdbbbadbaadcdbdaabccbdabdccbddabbacdcaacddbbbdbdcdccabdcdbbbaacabcacbdadaaabddcabcdbddddaddccaddababadacbcdcbbbdccdcaddbbabdbcadbbadcdacddcacbcdbcacbbcdbacdbcbabdcbbabadbcdbaccdcdcabccdcabddadbbdbabaaaabdcdbdbdadcccdaabbbdaddbadcbddbacaddcdcacbcacbcbabdbabbbcdccdbccdddabcaddbcbccbcbbbcacdcdcaaabccdccdbaadccbdbbdbbbbbcdcaacdcacabcddabbccddbbbcbabcacccbdcdacbcddcadabdddddaddadbcaddddddcdaaccbddcccaaaacadaabbcadacdccbccaacdaabadaaaabbbdcababcabddbdccbdabbacdddabadcbcbbccdbdadbabdddaaaddcbcdbcdaabbdddddbdbdbdcabaabccdadbaabadbcabdcccdddddabbbddcbabddccdddbbcdbacbacabaaacaadccacdbcbddadadbdbaacdcbaccccdbdaccddaacbcaddadcbddaabbcaaacbcbbabdccabadbbbcbaddbbddddbddcacdbdaadcadcdabcbdbacbacbbabdcdaabcaaadccbbbbcdddaaadacadacbaabccdccaabcadaccabacdddcdabbbbbcaabacdaacadabcbacddbcaacdcbcadaabaaccbacbaacbdaabcbbcbadccbdbdacdcaadababcdcabdcbcbdaabcdddabaabbabddbadcdbaacdccbadcaabbcdaaddddbcacbbdddcbaaabacbcddcbcaadaabcaacdcccdccdcbdbaacadacadcbccddabdadbccccaabbbacaccddbacdacaacddabdbdcaadcccdcccaddabbcdbcdbbadbbcbcbcaddaddcbcacddcadcdbaccbcdbcaadcdddbdcbabdbbdddbddcdccdbcabcbccdaacabbbdbbccdabcadbccbdbbcbbccbcbccdabcaddccbcdcdccdaabdcddcbcaccbadabacdccbccdaaabdbccdddbbdbcaaadcadcaacaabadcbcbcccddbcaacbacbcaccdbbbbdcccdbadcccdcbbaababbcaaacabccdbaaaccadbdbcccacccabbbcbcabbbaccacbdbcbbcbabbdaaacddbacddcdcaddcaddadabaadaacbcbccbadccabbdcbcadbbbabdabacddbbcdbdbadbcdbccacaddcacbbabcabbbdcbcacabdbacdbcdaddccbddbaddaaabcbaababbdbacddbcdbddabddbddbdbabccbdbbbaabcdcbdcbaccdacbaaabccadddcacaaccddcaadbbbdaadaaccbbbddbcbdbacaadcddccbcdadccddbacbabbbdccccbabdcddcbcddbcbcbacbcbacdbdcbbddbacccaddabacabacdcabbaacccbaadccbccbabaaadaddaaccbbbaaacaddccdccaddacabaabcdbabbdbabbddbbbaacdcdcbabbabaabbdbcccabccdbdabdcaaccadcdbabcbbbccaabcbcdbcadacbbbcaacbcdaddabbcccbaabaaaacbacadabadcddbdccaccabdadcdddddddaddcccbcccaabcbdcbcacbaccabcbadbaacacdbddcdacdaddacbcbbcddacaacacbccbdacaadbaadcdcaaaabaddbaabaababbabcdaddcdbdcccabddaabcbabdccbcadbaaddadbcdadabddbabccdddbcdcccadcdcadddccbddabcdccdcabbbdbbbbdaccccdcaaadcddbadbdacddbacdccdcbadabcabcabbadbbcdbbcdcdababbaddcdaaacccaddbdacdddcdabddaacaddcbabdcdbcbacddddddbdbaadbacdccbcadccddaccdcaaaaaaaacadbdcccabaccbdacbbacbbdbcdacddabaaddadcbbcddddabcaabccdbbabcabacddcbccbbcabdbbccccadcccaddabdcdbcabbacaacaccdaccbcaaaccdaaacbbbccddcddddcddadaaddacadccbdcaccbdcbcacaddcaaacaaddbbabcaadaadaabdabcacccbccbadddcadcbaaaabccddcdacdadabdbabbbdbcdcbcccbddbdaaaaacbaabaddcdcdcbddcddaccacacdabbdbdadbddcccdacbbdcbcddddbcabcdbdccdaaabdaaacdaaddbcbacbcaabdbacdbbdcbadccbdadabbbbddcdbbdadccaabdadadbcdccddbcadbbddacacddbabcdbacaaaccdbacbdaddaabdaacddcdaabcaddccdbdbcddbcbdbbadbbbdbbbcbdcdaddabdbcadcbbcbaabcccccccacdcccbbcccaaacbcbcbbabcbdbcddacccddbaacbdcababaddccbdccadbdbdbbaaabddbaaabccdaadabdbadbcacdccabcdbdbccbdbccaadbcddcbcbbcccbdbbacdcdbacdabccaccaabcbbccddbddadbccccdadaabbbdcddababbcdacadcdcacbbccabbbbcaaabbcabdccbccccbcbcabbcdacddddddcaccbdbcbddbdabbcddaaabbcbdbcddaacdbbddccdabdcbaabcaccbddcdcbcdbadccccacbbcdcabaadbccaabadacbaaadbdbbbabcbbcadcdbbbcadcbaaaaaccadddacacdbcbcaadbcbaaadabbaabdabbabdccbaaadccadaaaaaabbcbbdabddbaddbadbcccaababbadcdaccbcddababaacacdacbdaacdddabaaaccbbabdbdbdabadaccccaacacbaacadcdbacbacbbdbbbdbccbcbdcbabbbacdacddcbbdabccababdccaaccaaadacacdbaacdadabaccbbcaaaddccddaacdccdcbbbcaaaababdabbddcdbbcaacbcdcacbacbdacdcbaadcacbbbdcbbccadadbadabdabbdbcccdbcacccbdbdcbabbdbadcaacacdbacccadccbdacabdcabacbaacbabdbcdbcdbcccdbcbcbdbcabaaddaadaddcabdcabdcbddacccadbcddbdccaabaacadcbbddaaddcacacdbcddcbaccddbbacbbcccbcacabcaddacdbabdccbbdcbadaaaabadbaaabccddadbccbcbcbbadcacddcdcdaacadcccbdadbcddabdaacdcacdcbdcdabacdacdcddbcbdcabcdaadccdbbadbbbccbccbcaaccbbddbddbdadadaabbcbccddacaaacddcddadbaabbbbcbbcdbdbcaacacbbcdddbcccbdbbbccbdaaaadbdaabdbbddacabdcccacdadaabaddcdaccbddccdccccaacabdcdcbacbbdcaabcccdbbbdadbdaddcaaaddbddddaadcbbbcdacccdccabbadddbcdbadbbbdcbbcbcbbcdcaaadaaaacccadabdbbbbdcaaddbbcbdccbbcdbbadacaccddccbccdadcadadabaadbcbbdacdbadbbdaccadcbddbdacaaadbbaccaabacddacbccdcdbbcbcaacaaccbcaabdaabbabddbccabbbbbadabdbaabccadcddaacdbdcaadbadaadadaababbadaacccabdcababdcdcacdaabaaababcadbdbccccdbcadbaadaddccaabbcaccbccdbacababdbdbcbdcdbbaadcbabccbaadadcbbacdabacddabcbcacdcccadacacdadabbdbacabbaddaaacddbaabaadcacbcabccbdbbdbabddabbddaddadbdcbaaaaacccbadbcacddddcaacacbbccbaacdcaabbcaaaccdddabaddcdabbbcabcdacdadabaaadbdabaccacdbdbacdcabcacccdbcdcdabaddaadabbadccbdccbccadbbbbaaacdacddaadcdadcdadabadadaabdcccacaadccbddddccdabbcbbcdccdbcbbaaabbaacccdadcbdcabbcbccacddbacbacbdcbbbabbcdaddcdabdadaaaaaaaddbccaaabcacdddbddbcdbccdbadbbddbcbadbabccacddbadaaaddbccbabddacabbadadbcaddbddcbdbabbbbacddccbaadaadbaaacabbcbaddcbadabdabacbcddaaccddcbcbabddbbcddcbcdacccdaaccccbccabbadacaababadcbbbabacbdcbccbdacadbaddadabdcbdcbaaccaddbcbcbcccacabaadabdadcbbccdbbabbbdbbacccbcbcddaabadbdbbcbadbaacacacbdbdbaadcbcbdcdbcbadadadbdcddcdaddbbbcabdcdabdbacabbdcaaacbddadcaddadabbddbabadbcddadaddcbacacaacaccccabbcaacaddbacdcdbdccacadaacbcdadccbdbdaccacdbcacabccadbccddcccbaccdadbaabdbcdacdccaaadbccaaadcabdddccdcbabbbaccbdacabaddbccadbcdbbadaacbdabaddddcdadcbbdddbaccaabbcabdadbcbdbadcbbdbabdbbdbdabdbacdbdddbcbbddcccacabbbbddadbdbcbcdddadbdabdccadddcacabccddcdbdacaddbbbdbcccdbccdabcddccdadacaddcabcabbacbabbcaadbcbdcdabdddddadbbbcdbcaccdbccbccbaadddddacadcbadaabdadaadbbadacbbadadadcabbcbacdbacdcdacbdddddcccccdaaaadcbabacddbabbcbdccabdcbabcbdbcdcbcdbbbabcbddadbcbbacbccbacabaacbdcaabbcaacbcaddccccbbdbccddbbcaacbddbaccabbbdadbdcdcaadddddcbbbabccabacddaccccadadaabdbdbbbdaabcdcbddcdacabcbbbadbcbdbdabccdccdabccaccbbdabcbacbaddacbababcddcbaaabcccaadabddccdbacbbaaabaaadadcaddcdbacbdbcccbccbdbaccbbcadccbaddcadcbcbccacdbdbbcdbabccaaabbaccddacadcacadcbcdbaaaccdcccdccbdcbcbbbabacabcdadcbccddcdcadbcbdddabccadbadcbdbbacbcdadabcdadadcbbabcacdaddabbaabdbdacbddabcaacdbabccaacdcadddabbbbdaadcbdcdadcabbadcaadbcdbbddabaccdcdbaadadcbbcdcdccacbdccbdddaacadcdcbdddcdbaaddbddcabcaccaadabcdaaccbbcabcbbabcbadacdabcbabbdaccbcbaccdbddabaddadaacacdddcdbabdbadbddddadccdbdadbbcdbdaadcbcccabdddbdaabacabcbacdaaaabcacbaaddccacbdcccdcabcaccbcbbcbddbdbadacaccaacbaabadddabddbbccadddaacbcdacaaccdaacbdcddadcddbdddbdadddbdddbacacbabddcacdddbcadcabbadbbbcdcdcadacbacbcbaddbbbcbdcdddcccdabaccaabccdcbdcaadbbacbddaadbdcbcdcbdbdcbaccbdacbabdbaaabbbabbaddbaccadbdbbcdcbcdcdabadcaacbdaacddaaadaaababacbadddabaabccabbabaaaaddddcaccbacadcbadcbccbcbacdbacabaadcdbdadadaabaaadbdcadbddbbcbbdcbddcbcdaddddadbdabcbcdcdddbbcdabbadbdddddadccdbadaccacbacaadbacbadcccabaccabdacabdcccddabcbabdaaaaaccdbbabbccdcacbaccbdbadbababbdcbbbabaddaaabbddcccbababaaaccacdccacdbbbbdcacdbcdbaacaacbbcdbcbbdbcabdcdaaccbcbbacdbbdcaccdccabcdcaddcdacdbcdacadaadbcbbabdaadaaaaadaddccabdabccdbcbaadbdcdcaaacadabcdcbabacaccdbadcdbdbbbabacbaabcacccdccccaccbaadbaaaabacadcbcbbbcabcddbccabdbabdcdadaabbdcbbcbccdbdaaadadbdaababccaaaccaacbbdbbbdcadcdabacaacddcdbdcadbbccbdddbacbabdbacbdddabcdbadbcddcddccccbdddcdcabccacdabaddbbddcccabbadddbcabdcbcdcbcbcadddbdacdadbdbdabcdabacaaacabdadacdcabdbcbdbbabccadbadcbbccaaddbabadbadaabaccdbcbbbdbbdadadabdcaacacbbdbabcdccabdcaccbdaabdadddbddbdcdadabdacdbdaabcbacbccdabcbcbbabdbcdbdcbbdccdddbdabdaacddcbdaccbdbcaabccdbcccdbdcdabdcdaccacacabdaaddabdbdcadddbdabacddcbccdcbddccbbdabcdbbdaadacbdaddcdbacacbbcaadddddbdbababbdcbdcaddaccdbcadabddadababdbccdddbabdaabcabbbaddcbccabbcdcaadaacdadacddcbbacacbbabbcdadbbdcbbdababacaabdcdbcccbcbdbdabcccaccdccbbadcdcaddbbadcaaabacbcbcdbcababbaadbbadadadadaadbbddccdaadbbadccdadcbaacddbdcbcddcbcadcccdadbcacdbaccbcddcbaabbdaddcaaadddadaaabbadaacdddadbbadbbcdbdddaddbdbdbbcadbddaddbccbabaaaaadcccdbdaadcacbccbbaadddadabccccbaaccdbbdcdbabddbdaacdacbbbcdabdddaabababdcbbacdbabbcabcbbdbacadadadabcabbddbddbdddaddcdaaddadddaadbdacbadadbbaacccdbccaabbdccadbbbdcdbacdaaaccbdacdbaccddabbcbaddddcdbdbccddbbbabcacadabccbdcdccdbcbabaaaaacdddaaaabadbccccbbdadccdbcacdacddbcadacccdddabdacbdddddbabaaaaadcaddaddbcacdabbdbdadbcbcdcacdbcbdbbcabdadcbcbdcbaadbddcdabcbdaaccbddbabdccaacddaabdccaacccacbdaccbbcdbccdcaaababcaacaaabdcdddddbdbacdaadaccdaaccacdcaaacdcddaacbabdabbbcdabdcbbbaddcbcaacbdcacdcdbbcbbbadcadbaddadbcdcdabcadabcadcdbcbaaddbdccabaaabdadbaccccddacdaddbcbadbabbbbbaddaccbadbbdbbcababcabcabbadcabddbdaaabacdcbccdddadcdbcbddbdbbcbcabcbcdcddbadbcacabdaccbadcabbdbdbaabbadabcbbcdddcdadbcdbbdddcacccdddbbddacaadacdadddaaadcadaabcbcdabcbcbccabbbbcbaadbbaaacbaabccabcaaaddaaccacaacaacabadbadaaccacdccccccdcddddccbcccaaabcaabbcccdbadabdbdcbaabddbddaccdbcacbcdabaabadcccdabcaddbcadadbaccccaccdddabababbadaadacaadacdaaacaccacdddaddcbbbcccbbacadbabbdadcccbdcbaabaddbcadddbbbbadcaddccabaaddacdaacbdbacbccdbdcaddacacbdbddbcdbdaacaacbdcaaadaababdcabaabbaccdaccbdabdbabddadacbcddcdbcdbccdaddbcddaaddbdddbcadbcddcbbbadbdcbcbaccdbdaabdcbaadcabdacdbbbdbbccbcacadcdbcabddccabaccdbadbcbdadbdacbacddaddbacbdbccabcdccaadbbadbadddcdcbbbaccbcbcacbbcddbaddbdcdadddcdcacdbbacdbdcbdccabadaacbacdaadaacadcadcdacaadcdbadabaddcabadacbcadbbbdadbcccbddbadbcabcbdbcbdbddacbaccacdcbdcaccdbdabaadadaadbcabacbacdbadcbddccacddcbcbdccdcddcaabcddccbbcbbbdbdcccaccdcbbacdbdaccbacaccbbadbabbdbaddbcdbaacacbdabaaadbabdbbbdcdcacdbbbcdccbbcdbbbcdabcadcddacdabaadbddccdcaddcddcdddaacbadcddaaabacdacadaadbcaacddcddaccabbacbbcbacabbbcbdbaadacdaabaccacdacaadbdacbdddaaadaabdbbcdbacbbadcccaddbddaddbdcbddbbaaabccabbcababdccabdcadccdadbaacaddbabdbbcbaaddddaacbdbacacccbbbadccdbaddbaddddacddabbbdbdcdbaaaddcacbadcaccabbdaabaaacaacddcacbdacbccaadbdaaadccacabccdbadbbcbacbcbddaddcbbbdddccdbaabcaabcddbaaacacadcbddccaacdaaccadcdcaacddbacaadcbbbddcbaadbdcddaccacaaccbcaabdbbcdccbdddcdaaaabdaddabdcaadcbcbdcabaccbbdcdbbccbcdcbacdaaddabcadacdbcdadcdccbcdbaaabdddddbccccadcbadddddbdaabbaabcabdbadababdcaabdbcadcbcdccdbadadbdbdbddabaaabdccbabbcadbdbcbbcaccdcaacacaddaabdbcbcccbcbdddbcbcdddcccdcdbbcbbdabdadcddcacdcaadcddbaccacbddcdcdcadaddbccabbbbddbbcbcdbdabaccbcdcbddbdaddadabdaacbbbbacdbadcbabbacddcdbdaadbbccdcbadadbdcddaddbcbdbacaacccbcbcdabadaaddabdccdddcdcdbdbdccaddababaacbdcbcbacacacbdbacbacbdadcaadddababbaabacdabddbcbabcbdabadcdcbbacaacbbabccaaabadbabcbacacccccccaaccdddcadbadaaabdcaabdcddacadbdaadcacdabcccdbacdadcdabacaaabbdbabdbbabbddbdabcddbbbbbcdaabbdaddcaabbbbbdabbadcaadbbdddabcdccbbbccdcdddbbacddbacdacbabbdbbbcaacdcaccbbcbbccbcbcdacacbdabadcaddabbbdbbbcbcacccaaacbbcbaaadaaaaccaccddabbdddccbcacbcdbbbaacbcdbcddaadbdbbcbdadccddcaccdbadbacdcbcdbadacacddbcbaabdcbcdcadcccdccbcdbccbcaddbcddcacdcdbbadcbdaadacddbccbcbbccdcbddcdcccddbbdcadaadaddaaaadbabadddcacdcbcbbacdbdaabbdccbcbbdcddcaccdcdcddaadbccbcaacbdbddcccbdbbdaadbddddbcabbdacabaacbacbaccccbcdcdadacdbcddaaccddbcdbaabcbcacdbbdadbadcdbaabaabcbaabcbbcbbcdbadacbbbbbbdbdddcddcabcdadddbcacaacacddddcccdabccadabcbbaddcbdbcbcbcbbbbaacddbbbabadddcccdbdabcbdbdbbaccaaadbacdcbcadccbcacbcdbbadccdcaacacdaccadbababdacaccbcbdaddbcddbccbaccdcadcbbbaadcaaadbcbdbccaabcaaccbbdbaaabaddbbcbbccbcbdaaddacaacdcbcbcbbdcddccdabaabcdbcaadcdcbcacaaaabcbdbdbdabbcbdccbbccbabbcdcdccdadacdcabdacbcacbdbccbaddbaacccdbbaaacdacadaabdccadabbadaabcddcdcacadcdacdabbbcaddacaabdaaddcadcbabbadbcbbcdcadcadccbadbcbabaddaddccddacbccdaddcacaddbbaacadccabbbbccadaaacacdabdccadacdbbabaadacadcdccbddaabdccdaddabcaababcdbbaabaccacaababcdbbbaadabbcabccdbbbaccbadabdcadcdaccccaccccbbabcabbbbcaabdaabbacccabcbaddcabaadaadbbbabaddcaddbbbacdaaddbabbaaacadddddabbaccacbacaadcdbdbbbbddcbddcdadbcdacdbdcdabdbdaacddadadcddaaddcbabaddadabdcaabbbdbcdcaabdddbaddccacbbaabcabddbdaddcbabacdcdccbabdddccaabbbdbabcbdcbdacaccabbabaabcabaacdaabcaacddbccabbdcaaabbbddcabcbaadddabcccbacbdbdbccddbaccadcdbbabbcdcdccaddcdcbdaddcdabdadbbdcddcdddbaabaadbababcbbddbabdbdcbccdadaaabaaadabdbabbbdabadcaaccdddcdccaacbbdabcccacbcbdcdcbccacbcbcbccddcdbbdbdcbdcdccacadcbccbacbbbdaabcaadabddccdbabcdabacabbccddcddbbacddadbcddadcdacbbcacbcdbdbadccccaabacbdcbadddcdbdcbcaccdbbbdacbbdabacdbadddaaacbadbdcbdbccbdacddcbabcdddaababcbabdcdcbbdaabdabdbbaddbbacdbcbddddadbbcbabbcdcdcadbcbbdabbabccdccbaaacbbdbbcaaaccccdacdcbbbbddadbbabcabbdadacadcbacbbbacbbcbaabbadbdcbcbbabdadbaaaacdbcabbacdcbbbcdcbcbccdcddabddbdbcdabbbcbbdcadbdabddddbdadcdbdcabadadbdddbaadbdadbdcdcbacdabcbbaababccdbdabbdcdddbccbbbadcbbcbbddaddcbcbdbaadbdbdbdadcdcbacadadadadbdbcddbcabcbbdacbccabccbaabaaabbcbdaaddbacdbababdacdbcaababbbcaadbcadcdccbbaadbbacbcaddbbdccddadddaacbcbaacddcdcaaaccacabdbdadadddbbdddbabcbabcdaddabbdcdddacbcddbdcaaddbdccbddbdadbbacadabbabbabadacbbdaacdcbaddcdcaacaddbbddacabbdaadbbbacdacaacdbcbdbacbdbdcbacdddbddcddccbdadbbddcddcdcddabdabdcbbadcacccabaabdddbaaacadbadcaabdbdadaccdabcaaaabdbddacaddcdcdaaaaaaaabdcdbcdacaabacbddcddabdddcbaaccdabdadaadcadbbdbdccbbdbaabcacaddbabdbcdbabbbcdacbabbdcbbabcbcadddbdcdddbdaadaccbacaddcccdbcaddbcacbaaacccbdabaabcddcccbbdbaabacaabbbdbbbdbdaaccacaacbccabcbbcacddacbacdcbdccbabbbadacbdbbdabbacaddaacaabcbaccbaccbdddbcdcacbddcdbddcaabcadacddcabbbdadaabccbdbabccddbbcdadbaadcbbbcaccdacaaaabbccaabccdcdcadccdcabbcabdbdcabaabbbbdbaccbadbaaadddccabbdadaadbdbdbcddadaccdaddcdabbbddbbbacaababcdcacadbdbbcbbdabcbcaddbddcbabcbcabbdcaddbabbaabddbadcccccdbbcaccdaaacaaccacaacbdabbccaabacbaddbbabccdcdadcccabddcdddcbccadbaababadcccabcbdbdadcdbdabadaadacdbacbabcbcacdacadaccaddacdcaccbbdacbaaacdaabcbabdbbdccdaddbaaaaacdcdaddcbdaaccaddbcdcaaacdadcdddabbdcacaaacabbbabcadbacbababbdabccbdcaadddbdabaaabcddaaaacbccdaacabadadbddadbbbbaabdaaddadcbdcaacdbacdcbbadbddadadbcccdcdcbcdbcadcdddcbbaacdbccccadaccddbbbbddcbbbbbbccdbbdcaccabcbdbbdabbdccddbbdcadcbbdabaccdacccbcacbdcdaaacbcbcddcdaacddbadcbaaabadddbcccadbaabcbcbdcdbbcaacccadccbbcdddbabaacbacadaaacddccbadabaddaccbdadbcccabbdddbdacacbabbbdcbddacccaadabbcdcddbddccccaccdadddaddbccbbccdcdaddccacdccbcbadcaadbbbababadcabbaaadcbbdccccdaaadccadbacdbbabcbdcbaababddcababcbbdddcddaccdccbcbdbdacdaccaababbbaddadddcbcbbabddbaaababcabddbcaaabacccabdabcbddbbdaadbacbddaccaaacddaaaccaaaadabbaccccaaddacccddaabbbccacbadcddbddbadadddacacdbcbacadbbcbdbccacabacbdabcacadadcaadbdabdcabdccbabbbbcadcdadaacbbccbabddddacbaaddcdadbbbccbbbdcbcdabadcdbcbadbbadbbaaaaddcbcaabbadccdddcdddccbbadccdabaacbacacabbcacadadbdddadccacdadadbddbcaaddcaadcadddbacbcbddcacdcbabdaacdddcaadbdbbbdadcadcbdbacbdabdbdccccccdbadbadcbbbabcdcdacaacacdabcbabdaaccabdcdabccbadbcbbccbbbacdcddaacdccccabdbaabacaabbbaacaadcdddbdaddccaaccdbaacbccccbabcaaabdbbbabbbdabdddddcaaaaababdbddbcdabbbaacaccdbbacacccccbccbccdaabadcccbbdbacbccdcacdaaddacccbbbacaadbadcddcdacadddcbabdabadacaddbbdaccbadccbdabaddbadbabdddabbbbacdbccdabaaadaadcadaacaddadcabbadbcdabbadacbcbdcacbcdabbadadcbacdaccbdbbbbcdcbbcbbcbbddcdaadcabcdddddaacccddcccabdbaadbcabcdaddbdccdbdcabdcbcabaccdbccbbcbdcbcbdccacccdbbdddbbdcadbadaacacbcaacddaadbbccacbbaddbbaccadaabccabadcbcadacadbadccbbbdaccaabacbaacddbdaababacccbdaaaacbddbacadbbcdbcbbabcbccdbdadbcacccbccbccacadddccccabaacbbcdcbbbdbbacbaddccaddcdccdcacdcdababbcbdabdabacbcccbadbcabaabcbadadabacacbdddaacdcadddabacbaabdcacaddddbbcbbbcbbccabcacadadcdcdccdadcddbbcbcabadabdbcaaadcdcbcbbbdadadaaaddbddcbadbaddcbbdaacacbababcaacbbddcacdcdcabbcbddbccbdbbccbacdaddabaccbcaacabcbabbbddcaacddbabaabcadbabcabbcdcddadccadcddbcbcbcddbdddacccdcaaacaaddddcacadcbbcabbbdaaccaaccaccbdbbbddaadacdaccdbdcdbabbaccddbdbbddddbdcadacdbbacdadadbaaddabcacadadbcbccccbbadaaaabdaddcaddddabcdaaaacadcacaaacbcddbaacdabbdcdcdbdadbabadddadddcdcddcbadcbcbcdcaaccdaccbbdcabadadccaababcacbdbccaacabddadddcbaaadcaadbabacacdbcbdcdabcdadddadacbabbacbccccabcdaabcacbaddcdddadddcbcabdcaccddcbdcdbdcbdabcdcabcdcadbbcaddadaaabdbbbabcadcabacaccbdccddaacbcbbacccabbdbbbacdbbadbccbcaccdabadbdabacbaddcadadddccacaacdbdbdacccadcdccaadccabbbcbbdddadbabaacbabbcdacdbdbabadadcccddbadbabacdacacaaacbbaddbddcadbdbbccdbdbbadddbcabccbabaadcbcaadddbddbcadabbdbcccacaaadcdcdabcccadaaadbdadabbbcdacdacbcdddcdcbadcabcbcdabbdbcacbbabbcabdcadbbccbbacacdbbcacbccccccbaacaaaddaabcbdadabdbbabbacbadbdbdcdaabcbabccdaacdadcdabaadacadbbbdbaabdbcabdbccdbabcdbdbbddaacacbbccdcddcdadbdcabbdabccaabddadabccddddcbabdbbaacddbccbdacadadaaadbddabdbadccbdddbaabcaaaababdccdcaadababdcbcccccdabacbccbcaacbbaaabbccbbdcadbabcaaadaddaadacdabccbdcddddbcddbbabdbdbbacbcbcddddcadcdacaccdcacbcdcccccabccdccaddaabbdadcdbdaddbdddbdabbaaccadddaddccabcdbbbbaabdabcccdacbcddadbbcccdcdacbbdddccbbbdcdcbddbdaacbacabacbcbcddabccbabdcdddacbdaddadacacdacaaabcaccbadddddccbddadacacbddcbdbbdddcbcaacabcdcadadaadbdbcdbacdaccadbcddcadbccbbdbcdcaccbcacabccdacaadbcabddccbbbaccbdbbbbbddcbabcbbbcaabddccddadaadddcaadddbccaabbadddddcddbbbbbaadbcbacaddbdabcdacddadaadaadbaccabdddcabdadcbacddcabbadcbdbbaababaaabbcbcabaadbacdaddacddcbdcbdabdadccabbccdaacbdacdbacaccdbcddbdddbdccccbabacacddbcacadcacddcccadaabaababdbdaabdaaacccabdacdcddbdbdbcbdacdbbbdcadbdacbbadcadbdaacbacdbabdcddaddcdcaabdcbdaabdccdddbaacadaabcdbcddaddbccdbdcbaadccccbdacabcbbdccbdaabacccdccdcccdbcdcdccdabcaacaadbbbcddddbbbbacacddccccdabbcacdbddcbcddbbdbdbdcaaaabdbdbbcccadacdadcdabcbdbdcacccbdbbbbbadddabbdaccdacbbcacaadbaaabbabdaaadcaaaacdbbbccaadccadbbdaabbcccadaaacbbcaacbadacaaabacddccabdccdcdcbcbbaacddbddcbcbccaacbabcddadbccbbcbbdcaccdbcacddabcdbdcbbcbdddbbbdaaddbabcdcaccadbdbbdadbbbbaaadaacaddbaaabcaaddcdcaddccdccccccbbaacdcdcbcadddababcddbbbcbadbcdcddcbbbaabbdabaacbdcbaadadcadcabddbcccabbcacaaacabdadccdccdacabacbcdadabbcbaddcababbbcdaadcbddbdcdbcbaaaabcbcabdbbddcbcbdacbacbdcdabccbcbddddcdacccdbbbdacbbbabadaccddbabcbbacdbbaadbbaddcddaaadbabbaaabcddcdbbcaaabccbacccbabccacdabcbaaacacadddacaddcbddcacdbbbdabbbcbbcbcacbcbbdbbbddddaddaaddabddcbcdddbdddabbcabaadcacaadccdbcadadadbbaddcaadcabaddccbadcacbbcadddabddacbcabccbbbbadbadaaccacabbbdddbbbcadacccbbddabacacbadcdbccaabacadbdcdbcccaccacdddacdcadbacbaccbbbbcbbcadbbcacbdddaabccdacdcabacadbcdbadccdddbabcdcbaabdadaadadbabbcdbcabadabdbdcdccabccddcdccbacccadaabdbbcbdcaadbcadcdaaadcacaccdabadcabdddbadabbacccbddcbababdadabbcaacdabdcacdbcacdaadbacbddbbdbaddabdddaccbacbdcbddcbcbacddbaadddbdddccbccdcddcbbdcdcdbcabdaaadbdabadcacbcabcabcdaabdccdcabcabcbdacddcdddcddcababdbbcbdcbacddadbdacabbcdccdadcdbbacbadacaaccccccacacaacbaadabbacbcabbcdbacaddcdcbdcddbcbddbbdbaabadbcbadbddbbdbaddbaddaaacbbccdddbcdbbdaabadababaacabdbcdcbdddcadabacabadcbccdadbbcadbadaadcccacaccbdbcdbcccaaaaadbcbdbbcddbdccdacddcdccababbadcadcddabcbddacbcbdccddadbcbccabaccabcacaabccdbbdaccaaadadcadbbaadccbbdcbdcdcadccdbdbcadaaddacbbcabccddadbcabbccdabcddababbcaabadddabadadaaabbcdacadadcccdcdcaaddbbcccdacacaccdbadbaadbcdbcadacccbacbcbdcccdcdcaabcaacbdcbbdacdcacbcacabddadccdcdaccbcbababdbccbcccaaddbdddbdbddbbdcbdbbdbcdaacaccdddabacbadcbdcaabcbbdddcbccabbddadccabaabcddaccdaccddabbbddbadadaabaacabacbbabbdbacbaddddddacdcbbbcddbbbcddadcbacdcbacbdcbddadccccabadaadbcadbdbaccddaaacbdbbaabcddbbabbcbbbdcbdcaccbaadaabbbbccdcbccacbcbbbcddcddbccbadbbcaaccacbcacbbbabcaaadbabcdcdcaabdbcbccabacdbacaacaccbbccacabddbdddccacbbbdacadabbbdcddadbbcdbcddbdbacadddbcadabaabcdbacdbbadabdbaccaabdcadcadddacdcadcadccacbabcddbaabdbcddbabacccbddacadbdadbbdcdcadbbcccbbdaabbabadcaaaddcdbddbabdadaddbcbbdcddcaddadbaaaaddbaaddddacdcdaadbaadcaaaaccadcbdcdcdabdcaabdcbdadbacadddaddadcabcbbddabaaacacdbadbcaaadbabdadacaaddddadacccddbdccccbbaaaccddcbcdcbbcbbabdaddcadcdadccbdbbcbdbabbcdadcabacabddcadbcaabadddabdddcdacdbdbcbacdccabdddbdcdacbbabbbbaababdacbcddbcaabddbccaaabadbabadbbaaaddcdbbbabccbaacdaabbcdbbadaabdcbbcddcacbdbdcadbcdcacbdddbcbbbbcbdcbdacbdcacdcbbbcdbcdabcacadaccbccdaabadbdcbcdbcbaadacddcccbabcbaabbaadbcacabcadccbbcddabbbaccdcdcabbdbbcbdcaabbccbbadabaddadcdbcbdabaaabbdbdadaaadbbddbadccabbbaccdbacccbbbccdaabbbbdcdabdbcdbcbddacdccbbabaccdcabddddaccaabcddbdaaaaccdabbcccaacaaddccadadcadddaacadbcacabbdacccaaaaababcaabbbaddcabbdbddccbbdaaddcbbbddbaadcaaadcdbadadcbbcdaacccbbcbbcbcdbadccccabdaadbbcbddcdcdaccadaddadadccdcdbbdbbccdbabbddacdccadcaabcbcbadaaccbdbaadccbdcabbbdabdabcdcdbccaaccdbddbacabbbbbdadbbdbcbbcabdbbacddcabacdaddbdcbdacaddabcbabdcbaaddbacadaddacbaaccdccbcdddadbbddcabcadbbdbccbbdbbcbaabddcbbdadcccdbdbddabcabbbaddaccddddddbbbdbccabcaabbcbcbccbdbdbdcadddaabbacbbbadcdddcacabdbdcdbaaddadcabbddcccdbbbbbccccbcccbdcacacacaddccbbbdcbcbccadaaddaaadbcdabdaacddbdbcdabdbccaadcbdadcaadcdaaaccddaaccaadabdbdaaabddcbcdcbdbdccbccdccccacabdbcdacadbabaccbbccbaabbbdaabaaacbabcdbddaacdcadadbabbdbadbbddcaabcbadcabaacaaaccbdabccabbbcbcdabbbbbcccbbdcadcaccabccaabdacdbdbabbbaaadadbcadddaabbaaabbddbbbaabbdbcdccabaabcaaddaaddbdccbbdccdcdccdacbdcbccaabdbabbdbccadabacddabbadacdaabccbbddabcbddddaccccbbbdcbaaccbdcabbbdcdcacbdadbbdccbbbcaccaccaacbbcdcdcdadaccababcabbbacabccabdabbdbdcbdddacbabccbbdadacbdaaccbcdcbadabcabbabcadbcdddaabadaacdbaaddaacbbdcdbbbbcdbbaaacdcbabbadacccbcbcaadaabccacacbbdadacaabddacdaccdddbcbbadacaabaacaccacbcabdccbacdbbbdaacbbdacaacbadddbcccdddddacddbbdcddadcaadabcbdccadcdccdddddbcbbadadbcbcdaabbaddbcbadabccdbcbbbacdaaddbdccdabbacdddbdbccbcbaacdcacaadcddcdaaccccaddcddcdccbaacddacadbdddbdcacbdbaccadcbcdcccdacbdcacadbadccbaddcdcadaccabcbabcbbbabadcccadaacddacdaddcdbcddcaccaabbddaddddbdcadbbaaababbdabbcdaabddbcddacbbacdcccccdbcbccacdcddbcdaabcddccbbcdbdcbabccbdadacabcdddbdddbddcacaacaccccbbbbbbbddcddcbdabbcbbcddaadbccdbbddcbbcdbbcaccdbdcbdabbbaddbaaccbcaaaacabcaddcdccdabdbcddcaabddbbdcabbbdcaacdacaacabcdadbbbaacacccdbdcbbdcbbcdcbbddcacacacbabcdcbbcbdcbabbcacddddccdccbcadcccdcdccacdababaadcdbacaccddddadacdacaaabcdbbddcdbbbddccdcdabdadabccabdddcbabcccccabddaddabadcadbadcabcbbddbacdaaadadbcadbcbbbbcdabddcccbaaaddbbbdccaccacdbbcddbdbacaabccccabcadcdbdcdbcdbacaaaabcbaacbcadcaacbadbcbbcbaacddbaacdacdcabaabbadcbcbaacbcbaddabccbdabdbbdbbadcdbdabacbbddaaadbccdbdbbcbacbbdbdabbadbbbcaadabbdddcdccdccccbadccadbaadbabaccdbcaacbbdddbdbddacbbddcdddbcbdbacabdabbddbbbcaadadcbccbdccbaababbaacccdbbccbcacbadaadcdddcaacadcaaaccadcdadbcaabaddcaaacddcbdabdcdaaadbbbdbdcccadaadacddcbbcacdaacbddbbdccbcabacbbbbbbcaadabcbaabaddabbbdddaccacdddbdbcbadbdcbcbdbcddadadcbbcaacabcbcccbbbdcbcdccabddadabcbbccaadbdccabccdccbcdbcdbbbdcaaaddcdcdaacabcaaabbdaacbadbabcadbcadacadddaabcbaadbcdbcacdcdadadabccabaaaaadcadcccbabdbbcbddabcabbbbbadadccccabbdbcbdbcbabcdbcccddddddbcaaadaabcabcbbcbadddaddddbccbdcccdabddacdcabcaccdccacdacbbbbdaababdbacbbaccdaccabcbdbcadabbbcbbcbcadcabbcbbdadbcaabcdbdcbbbddbababbdcddbccdbbabccdddbbadddddcdacbbcbbadbaaaadddcadaaccacabdadabcdcdaacbbabadcddbbadbaddcdcbabaadaccdbcbbbdbbcccbbdaddcadcbdaaaaaaabbdddadbcaabcddbddaadacccbaaccacadbabdbacbcbabadaccbdacbdcbadbcdddcbaddccaaabbbcbaaabbcdddacdcdbbbdacdcaadbdcbabcbbcabccbadcccbccdddacaaacabaddbaadabddbbdabbacdbdddcbabaacbadcbccdcdadacadbcbaaddbbbbcbbcccdddabcadcadaabddbcabacabcbbbcadadbabcabdddbbabdcbdbdcacbaaacbaccbaacdadcbdbcddbdbccabacdbbbbacbdccddaaaddbdbbaabdbabacddbaabbcdadcacabbaadbcdcbbcaaaadadcdaacbabadbbbaadaaccccaabbcdccacbcbdbbcaabcabbbdacbaadaadabbdccbbbddcabdccdbccbbbdaacbabacaaacaacadbaadabdccdacacadbdabbdddabdccddcacdbccdcadcacbadbaabccdddbbbaaabccbdaaaddccbdbabcbacaddcdababdbbaaaaabbabbadbbabbcacbcaaacbdddbcdaabaccadbbacdaabbaaccabcbcadddbabdbbdbcdccbabadbbcadbcadccdccaddbbbadadccddaacaaacddcadcddccacaaccadbbccddbccbbcccdbdbadcdaacdddccbddbdccccbbbccaaddaccbbcbabbccbadcbbacbbbcabadabadcddcdbcdccbbcbcabbdcababdbdbdbddcabdcdaacdcbaacaaadddadbaadadaadcabdbdbbabcccacaabdccacdcccbdaaaddbdaccbadbacadcadbbcdbaabcccdbdadddccadaadccbcbbaaccbdcaaaaabacdacbdcdddbdbccabcbbcadabbcaabcdccadcacddddacbdcbddabccdbaadaadbabccdbbdcbbdaacbbadaabdcddcaaabbacacccddabccbddddabcdabbbaaaacdacdacbbddacacadddcbacbaadcaabdacadaadadbbcabcddacbbbbaccdbccccabbcccabcbbaaadbddadadadadbbdbacdcdaccdaaabdbbacaddacdacbcaaabdbdaabaadbbdcccbadbacdbbbbdacacbcbdadbadccaccddababacbcaadaaccddccaccbacdacbcababbaddbabcabcbddabaddcdccbbcdcaacaccbabbddadbbddcbacdcacabbabcadbacbddcbdacacbbabddaabddbadcbbbaddccdadbbdccdccaddcdabdbcbbccadbadaadccddaaccbcbbbadbcbddbdbbddcadbdaabbbccbdbdccdabdcbccdbcbbdadbcabdbabbccadaddcbabcadbdcaacadbcbcaaababaabaabcdbadccdddcdaddbdacadcadcddbdbaddddbcdadbaabdacdcacabdbcdaacdbdcdddbabaabbbccaaadbcdcaadbddddadcbcadaaacbdadaabbcadcbbdcddbcabbcbcacacaccbbbccdbdacbdaaadbabbdcbbababdcaabcbbcccabababccadbbddbbbdadbaabaabaacbddbbcbdddbadabaaacaccdbaaadbcbbbdcdbdcbbcbaababcbbacbbccccccabacccbbcbcadbaabccbbcdbdabddbabcdcbcddaccabccdccbadcbcdacdcadcdcbdbcacbcbcdaaddccdaddbcbcbdadaabdddbdabadcddbbdaadbcbabbcadbdcdacbaacbcbdaaadacbccbdbbbcdbbbbccadcacbccaaccbadbaaaadcdbcadcbbaacbdbbadbbcdabaadcaccddcdacaabcdacdcbbbbbbababdbabcdbddaaddbbdbabdddbdacbaddadadaabbaddaacabdadaddbddaabccbdcadbaccbbbdacaaaabcaadbadbcdacdbcacdabcdbddddaadcaccdcdadbdcdbbcbbbacaccdbccbdacaaabdcccdadaacbdbdddbcddabddddbdbacbbcdbdbddccbdcabdbdbbccdbadaabbdaadbbdbcddddbaadbcccbabbaababbbbcabdbcdabbcbbabcdbbbdcaaddccdccccaddbbbbaacdbaaadadcdcddabbdddadcccdacbdddcadaccbdcbbabbdacbaacbdcaccaaabbcbcdddadaabcbacdaadbacbbbdbadbbbacdcbddaaacbdaccbdccabdcdddccbcaccabcbdbddabcbdaabbacacdcabbaababbbabddddaddbddddcccdaababddaccbbcccdadaaaabbcabdbacaccaaddcbccdadbddddbcdbbcadddbbadbbbdaddcbbcacdcabbcabbbacddbbaccaadcdbadadaadcddabddcbaacaddbddddbdcbbacdcbbdadcccbdbcbbadbabcbcbbdbcdadabaaadddacbbbcdccddbdcdddbacdcbcadccacbabddaaabdbdaacaacbadccdaccacaaabaaadaccdbcbabbbdcbcdcbabbddccbcbaabcaabddbabaabbaccabccccbcccbbbbddbaaaabbbbbcdabbaccbccbccccbaadcbcccaccaddaacaadddbccadbabbcdbcdadacbacacacdccdacddacbdabcaacbbccddadcbdddbcaaaaabaadbcaabdccdaabddbcbbcaccdcbadbacdadabcddbcbddddcadacbaadcdacababbbbdcadcbcacdaaadbdadabbcaaabbcacccaadabdccddddbccddcabbacbccccdccabcdcabdadbdaddadcdcadabccaadbcbdbbddbdbbcbcbbdaabbdaadacabcbcbcdbaccaabbdbdcdcadaaadccabbbadbbdcdaaccbddcdadbcbcbabcdcdbdadcbbbdcdcccccabdacacaabbacbdaacaadbcdacacbbdbcdccdbaabbdbababdcdcbaabcdcabdccbabbaddbbdddabcbdbdadbddacacdadcbcdcbcbaadcccbccdcaaabbcdcbdcccdbdabaaadbddaadacccdbcacbdcbbdbbadaccaabcabadcccccdccbdaabbaacadabcdcdddadbdcabacdadabcccadddbcabcdcdcdcaddacbdbdbdacdbbdbbbdcbdbcccaabbddacddccabdacbaadddabcaadaaaccdaababaadcabccdcdcddccaddccbccdcabdcbbbabcdaddcbcddaddcddbaaabacabdacddcccddaacabdadcbbdbdbacddbacccbaacbababbabcccaabbbabbccdcbddcbbccbddcadabdaabdbbddaddbbccabcdddacadbcabdccccddaabbbbdbbbbadacbddbabcadcdddaabaaddbacddaabdcabdcaaaddabcadadbdcccdbabcdbddacacdaaaabbababcdabcbdaaaddcadaccbccadbaadbbcbadddddaddabbbbaddabccacddaaccdacaccdddbdccbdbabacccdccbacbcabdcaacbcddcdbddacdcdcbbadddaccbbaacabddaaaabbcaaabdabdadabdcdadddadcabdadbbccaddacaabcadaabdccbbbbdddcaacabccacabdbbacbcaaaabccabccbbdbccabaaaabacbaaddddabdadbdcddbadadbbbdcaacacbabacbaadadcaccaabbccccdbaadacbaaacbaaaacccaccbbaabddacdcccdccbcacbcacadbcadcbcacbbddbdddbddddacdccabaacbcadbadaacccbdaaccdbbbbdabdccabacaabdbacaabdcbdbaccccaababaacaacbaccabbddcdccbbacdadcdddcbbcdaacdccbbdbadbdcbdadbaccaaccacacccbbdadacddddadddcbdbdbbcacccaadacabdcacaadacdccbdcaacddccdcdadacccaabcadaddbdccdbbdacbbbcadbaddaadcdacbaccdbdacdaababbaaaddaaaadaccbabdbbbbcbacdacabacacbcaabbddddbadccddcaccdbaaabaaacbbdcadccdacbbcdcbbccbccdbabdbcdadaacacdacacacaacccbbbbcdbcdcddcbadddbbaddaddadcbcdddcaadcdaacddbbdcbbcadadddacdcbcddacccdbcbcacaadacbadbcccdbaccbddbabbcaabdcbdcaadadabbcbbcababacbdccdabbadaaacdbdbbadcbbabbbddddbddccdcdddacbaccadcbbdbbdacdbdcddabdabcadcdacdadbbdabaacccdadbccbbaabcaccbcaddbabbaabdcabcdbbdbabbbddbdbabbddcccabdddaadcdabbcaabbdcdbcadbbddbaccdcbdaacdcbaddddabdabdcbdccabdcbaaacbbcbdcddbcbaacdcbbbabacdcacabbbbbcbbbabbbdacbddaacbdbdcaaabbccdbbbcbcacdaaacbabbdddcbacddbadbbdcbacddbdcdcbbcddcdbbccadaddabcbbabddddaadcbabdacaddcbaacabaacbcbddaabbabacabdaabddcdabddcdbadbbdddcdaabacbcbbaddbbadbdcdadabbaabdaadcbdaadcbaadbcbcadccbadacacaacabdbdccbcacdadbbbcdbadacadabdabdaaacdcdcbdaddadcbcbbbcacaabaddabcdbadcbbcdcccadcdccaaabcbabadccdaabbbababbdcacbbddaaaadbdcaacbdbbcbdbacbbcddabdbbccadbbbddcdabdbabbdbdcdacbccdacacbdcddabdaabcdcaddcdacbbadbddcaddcbbcaadbcbdaaddddadbcbbacbcadacbcbdacbbccacbbabdcccbbaabadccbbacbccccabbcabddacabcbcdcdaaadddabddbacabbdadadbdbcabbbdabbcdccbbbacdbccacabaadadaabdbabcaccbaababaabaabadcdcbadabdcbadadbcbbbddccbdccbdcabbdabcaadbbdcdcbcccbabbdcaaabadabccadacbcdadabbabdbdcccbddcddbadbdaabccbddbbdcbbadaadabacbdcdbbaabcdbbcdccccbaacbdcddbdbcddccbddbbdbddccdbbddbaaddcbcccbcabbdddbacccdabbaaabcadabcbadbdacddabcbcbdbdcdbacacdacdbbcdddacbcdadbdbdbadcbbbbcddacdcbbbcbddcbadcbcbaadcdbbbbbaadcdacbddadaaccadbdbbacbccbdadbababcddcdcdbddccbdabbddddccbaddbcababdaddcbbbdadbabbdabdaadbbbaaccdcdddaacaccadcbcbacbdbddcbaacddbdcabacbcaccdcdcaccdbaabbaddccddbbdababdaaabdcdadddbaaabbadabdcbaddbbabdbbbdcdbddcbbddcaccacbdaccacacaaaccccacdcccbadbbadacaddddacddcbdbbdcddbabbcdcacadadbcccdbbbaabccbddcdcbcbddbcabbaddbdddabbadcbbbdcbddcacdcadbbdccabcdcaacaabcaabcacabacdaabdccbdccbabacdddccacdcddadbbbbccccccdbabdaddcdcbbdbcbabbdbbbadaaabbcdddcbbbddbddddcabaadcdbadadacdcabaaccacdddadbbcbbdbdbcdbbdbadbcbcabacaacaadaaabddcdcddabbaaaacadcdccacbabdabdbdbbabadadbabcacbcdbbbccdcdcddabbcaacdacdddadbadbbbccbababbbcadbaadcacdabdbbaabdbbabbccccadbccdccaabcdddadbaccbaccadcdabbbbbbaaddbcccbabbcdbabcbcbcadcacadcacadbdacbcabacbacabaadbddabccaddaabacacaccaacbbcbbaaaddbabdddddabcdacbbbadbacdbcacbbdacdcdccaccdddaccadbaabdbdbddacddbdbdaaaaccdbdbcccbcabdbabcdbcabddabadbabdbdbcbcbbccadaadbacdbadcbcbdaccaadabcababcccdbdbdcaaddccbcdacbbdcbbadddccacbdbdcccdbcbbbbababcadcdabcdabdcadcddaddbaaadccbcbccbbdacbbdbbbabddabddcabdacdbbdacbdaaaabcdadadbbbbdcaccdabdddbcdbcacabaddbcdcbdbddbbbddcdaacbbabdadbdadbaccbbcdaadcdddbabbcabcddcccdcddccadadcdcccbddabddcaacbbdbcccccddbaaadaaaadddaabadccacaabbadcaaadcdddbbbdabacdaabcbcadbbabdcbdcadadcdbcbddbcbdccabcabbdacdacdcdabcacddcbdbacbcaadcbabacabcbaacacddababdbcbdadcbdcdbcbabdbbbccdabdcccdabdabaaacbbacadbbdcbdddacbbbabddddbcdcccdcaddcaadaacbbadaaadbcaacbccbdccbbcddaddacdbcccacacaacdbabaccddbabccababddbddaadcdbadacdacbdbabaadcbcadbdcbaaccddcacbddbcdbcdadbdacaabdbccaddbbaacdcabdaccbdadbcaaadcccdcbadbcccbdcbdccccdcabbadddaccbdcbcadadabdcdddccbdbdbbdbcacababadadccacbbadcbaacbcbbbcbdbabcaccaaccddcabdbcaadcbccbbddabbdcaababbccdccbdbdbadcaadcdbadbdcadaddbbdbbcadbccadadaacdcbbbccadcbcbbcacaccdbcaaabdcabcabacaaabacccbddaabbbabdaccdcbbaababbdcdbbbccbdcabaccdbabdbdacdbddbbdabdbcbbdaacbcbdbcabcabacaaccbbcccaadabadadcdaaabbdabbacaaabbbdbcabacdaaabcbdcacdadacbdddbcabdaccbdbbababaabdaabdaadcbcdcdacdababccadbbdaaabbccaaacdbcdcbccbccbdcbdcacbaadbdaabcdbacaccdacdacaccbcbaaabaaaddbbbddacdccadcdaaaccbbdcacbbbbbdcddcbcbbacacaccdcdaadaabaacdcaccdbbdddcccabddcdbdbcbddaabacbbacbaabdcaadcadcbcacababdcddbacccbdbacaddbaddcddabcdbbbccadddbacbbadddccbabadadcbcbaabcbbdbcabcdbbadababdbaddbbcddcdabacabcdcaabbabcacdbcbadbcdabcdcdcbcdbccddcdadabaaddaacdbcccbdddccddcbbabdcdcacacbadbdddcdabdaadddbbbbabacdacddadccdcbccbbbabababababcbcdabbaadabdddabbdbbbdcdbddbadacaadadcaacddaddaaaabaccaccbaaaaacabdccbbddadaddabdabdbcdddaacbababdddaaabdabacccdbcdcdcadbccacacbddbdadadcdbcabbddacbbdbbcaabcaaddcacdccbbcbaaaaacbcdabaaaddcbbadcccbdcddbabbbbacbbbbaaddbddaaadaccbcddbcbadddacabaabbbdcabdadbddcaccbbaaabaabacdcbbbaabdccabadaacabccdddcacadcccdcbacddbccadbbbbcbcaccadbccbabccdcbdadccbbcdcbaacbcdbdcbabdbddadaaccbabacdadcccccccbaccdbabadbbbbcadcddacaabcaabbaccdadddaccddbadabadaabdcccabdabbacdbcdcbaaadbcaddbcdbbbcdaddddbdadcdbdcacbadcdcbcdbcdbaaccbdadacbdbabaddcddacdcbdcadcbdabccccbacadabbdacdbaddbbcdaacdbabdbcaadbaccacddddbaacacaacbcccbdddcacacbbdccbdbcdaaccdbcaaddabccccdaabacdcdbcbabcdabbbddacbaaddddbabbacdbcddcccaacaccdaadddaaaddaaacccacbbaadcdcddddacdbaddaddcccbdbadcbcbbdcdcbdcddadaaddcbccccacdadcabcaacddbacdddacbbbdcdcdcdaaccdcdddaabbdbacbdaaaaabacabdadacacadbadbdbdabcbadaaadddcbcabdcccabadcddcacbadcbcbcabddbdcacbdcdbbbbbbbddccbbbcccaaccaabbadbdbddaccaaddabcaaababdccdccbddbbddccddbcdacddbdacdcbacccdcdbaccabacccbdacccdbdcdbbaabacbaccacbbcdbdabdcdcaaaaabcccdaccbdacaccdbddaaadcbacbaaccbcaaadadacbaddbaadabcdacddaaccbbccaccaaadcacadcdaaabdaacdbaccbadadbbdcabcdddadabbddcddbcddadddcddadbacbdcbcacdabacaacbacbacaabdbddacccadccaabbccabbdabbabcbaabacbddcabaabcbbcdcdcdcbcbcccdcdaadcbbcbcbcadaadabcacbaccbaacbddaaccaacbbaaacabbbdbadbccabdcddddaabcacbbacbacadbcbdcaccbbccddadbbbdcccbdacbabaacadaaadbaddddabdcccdbddcacaabdccdccbdaadadcdaacccadbbddcbaadaddadaadbacdcccadabbcadbdbabbdadbbdbcccacddbaacbcdbcabcaacbdbbacddccdabcccbcccabacdddbacddbaababddabbddbdddcaaaabcccbbcdaaaaabdbcdccddaabaaccaacbdbcccdaccabbcbcbacbbcadcdcadaccabcbaccbccacaacbdadabababbaacbdaadbdbdbcdbbaccdaccabadabaddcaccccaadacdcbacaccacaadbbaaadacdbdbdbdacacaacdcaccdcadbcdbcbbbcbddcdaaadcddbdbbcdababcbcbbadaacbdbdaadacdacbddbcbbadcccadcacbbdbbbbddbabddcaddcaaaadbbcddabcdccabadabbcaadcacbdbcccaddbcbcadacccdbccaabbdbcabcbbbdabbabadbabadddccbaccaddcddbbbcbbdcdbcdccdcdcaabcdabbbccadcbacabbabbabbabcabdbcdbacbdaaccdadbccbdcabcababbadaccadccabccacbdaadaddabbcacbbabbbaacbadbcbddbaccbdbbdcbaabdaacaacddbbadccaabcbbbbcbbcaabaccdbcbbaadbcbdcaaabdacdddcacabcddcccacbcdddabdaabbbcdbabdadacccbdccacbbcdccdcbacacdcadccbcbcabadbccdcacdccaccaccbcacaddbbbacbacdacbcbacdabccabcccbdabcadbcbbcccaadcdaaabdadbdbcbccdbdacaddcbabdaacadabddccbaccdababaabcdddabdabddcadddcdabbabbbccddbcbcacbabcbbadddbbaaacddbdbadacbabdaaaddacdadcbbcababcbbaddccabccbcbdaccbddaabbbcbbacaaddaabddbaadccccaaacdaddacbdccbcabdacdcdcbcdddbbdacdbadcacdbcbdbdcbaabdabadcabadbdacdbbcdcdbbbdccccdcadabbdcbbbdadbacbccaaacacaacdbbbbacdbbbdbaddacbabadddbbdbaacdcabcbacbcbdcccbccadacaadcacdadcabadcbcaadcdbddbddadddaaaacbdcdbdbcacbdbcbadaabcaacdccbacbcbbbddbabdcdaddbbbaacdababbcaadbbcaabbaaabbabbbacbbbbabdaacadbcddcadcdddacacbbcdddacbccacbabbbbabcddadaabdbaababcdaabcaaabddaaadcdacccdccadddcdaabadccbadbbacdbdcbbabccaccbabcacbbbbadcbcbdbbdcabdcdddddbbadbcdabdbadbbbdcccdcacaacbadacdadaabccbcdabdbcbdaadcdcddacdacdbabcacbbccabaaddbaaccbddbcacacbbabadbdcdabcdabadadcbaccadcbacaaaacdcacbddcddcadabccabcabbcddacadbccbcbddbdabbcbdccbbcbacacbcadcaacbcbccaacaadabdddacadcabcbadbdbccbcdbdcdbbbdccbcaddcdaabdbcbddbdcdddcbcdccdbcaaaaacadbdacabdbacccbcdaaadbdcabbacacbbaaccbddbdbaabcbbcddbbddccdddbdbdadbddcbbabcadaadacadaddcaabcccdabcddbaddbabbbcccbbbcdddcddaaabbabbbccccdbcaaddaaccbaccbcbbddddddbdddcdbabadbdcabdadbdddbddbabdadddbdabcddccaabcacbcbcdadabaccddbcacdabddcacbabcbccbcabcdcadabacdddaccdbddbcbaadbdddbabacccadaacabccbbcbbbcdaabbbaaccccbbdacbbbabbbcddadcaacabaacdaaaaaddababaacbbdabaacbacbbbbabcabbcadcadbbcdcbcadcadcbcddbacbcdaadadbbcddcdccddbbadacdccbbabcadcbccbaacbdccccdcaccaadbdcdcdadadaaddcaabcdbdbbaaabacbaabbaddcdccdcabbdbbaddbadcabdbdbcabbdadccaaadddacdaddcdbbbabbbbabaaaadbabbbdcbcbacdababbabdcaaaaaaaaaccbccacbccdcdbcabadabcdabcdcbcbcdaccbcacadadbadaacdaacdabdbdbccdcdbaacaadbbaaddbcaccabdccbcddadbdacdccbdacbbccbaccbadddaacabaadbbbcddaddadabacbcbabdbaababdbdccdbdbcddddcdccdbbddadcaaaabdacdcabcaabacbadbdbdaadbcccaacacadccadcbbccacabcaccbcdbadddccbabbbabcccaacbcacbdacdacacddcdaaababccddaccabdccdcdcdadddcdccccdcbcdbacbbdadbdbdabddcadbcbcbaacbbdabccbbadaaccdcdcddcbdddacdaaabcabbaaadbdadccaccccadadcdcbdcdbbaddabddabbacbdcdbdbacabcdbaccbadddbbacccccaaababcbdddcdacabbcaddcadaccaaddbbbddabddddcacdbccddcaaabaccccbcbbcbcadcbcdddcaccdcbaccaacbcbcbdaabcacddbbbdabaabbadccbcaabdcacacacdadadcacaccdcbccbdbbdcbcaaddcdbbbaaccdbcadcbcbadcdddadddcdcaabaccdbddddcccbbdbddcdcccccbbcbcabcbbbacdccccdcbcaacdaaabbbaaddccbcbaccacbdaccdcbbabbbddbbccdabaccabacacbccdcabdbdadccadccadcbaaaabccdcccbddbaacbcbdcbcbdbdadbcbcdacaccbaaadcabcbcdbcbadbbadacabddcccaadcbcbaaccdacdbddccaabccbbdbaadabacbdbdaddaccdbdccdbaaaabbccaccbcdadbccdcdbdacaddabdcbbababccacaaccdabbbbababdabccabdbaddcaabbcacbcccdddddcdddadaddabdacccadacaddcccbcccdadbbdbdddaddccddbcbcaabbaaccbcadacdbadcabdbdcacaccabbacddbaccbcbcbbdcddcdbbbbccbaacdccaaddccbdcabcaccdbdcdbbbdcccdcabbdabdddbcbaccdbadabbcbbcdbababadbbbdddbaddadbcacacbcdbdddbabadccadabacadabdcdaabddcdaaabbbddbccddcbcabacabbdcbccbbdaddbabdbcddacbbdcdbbbbacaaabacdadcbbbcdaacbcbcbabcbdbaadcbcbadcdcadbdcddbaaddadabbdbdacbdbcbbccdcdcbcaabcdcddadcaadbaabbaabacddccccbacaaacccdbbcadbacdbcbcabaddcaabbdbdbdcadddadcabcaacdddaabcbacbaddbbcaccbababbaaddcdcaadbcdababbaacbaccdadadcddacadbaaddcbbccabacaacaccacbdcdddbcadbdadacbaabcdadabbbdbcdacccdabccbddabcabacaaadbbacbdaadcddacbcacbacadabdbabdddddddacabddcbadccdbdddabdbbcdacbcdbdbaaaccbaaccccdbacaccabbccbaccabccbaadabcdbddcbcdcacabdaaabcbdaccdcabacbbcbdadbcaddbadddccdbdabbdcdbddaddbccdabcddcdaaacbacccdcbddacaddccbabccbadacabddbdddcaccbbbdcdcdccdbccdddcbaaddacbacbcbadadccdbbadbbcacaaadabadaddccbbbcdbabcabdcdbaaccaaacbcdabddbbcacbcdbccacddbcabcaaaddbcccddcbbbbbbadaacabbcdadcdacbdcadbdbdccbdbcdcdbadcbcccddddbaaddabcdabdcccbdaadddacbcaccdaabdddccabababdddcadcdddccdbcdadbaaccddacdcbacddadabacccbdabcbccbddbbcabadcaabcdccabcddadddacadcddacdaaabdcdababaabbdcabbaaadbdcaadcbacbacdccbcccbcadbaacadcddbcbbcdacadcbaddabbadccccdbaddadadbbbdaadcacbaddbbccddbcbdcdccdacbadbcdbbaccdbabbcabaababaacabacdbadcdbbddccdcbddbacaacccaacdaccdbadabcbaadbabcbbdcddbbddcbcaaacbcdaaabccbbadabaabdcbddcdbbabdcccaaabdccbddabbdaaaaccdcacdcdacabbbcdccddbaccbdddcaabdbacdaabbdacadcbcdbabccbaabdbddaaabbbacbcacaccacabcbbadcabcccdbdaabacbbbdadccbbcacacbdbbddabadbbcaaaacbdcbdadacabdcbddbdadbcaacbdcdadbcdabdbbbccaaddbbbbbdadbcdaaaaccdaccdbabbdacdcccccdbbdbdaaacacdcabddbbadadabcdbaabbcbcabccbdcbdbdccacbcdcccacabdcbacadddadcadadcccaddadabcddbaabccbddbdababcaaabdcbdcdcbacbbbdbadbdcccdaadcaddadddaaadaaaddbbbbcddadcaabcaacbcadaccdbbbacccabaabadbbdccdcbcdacabcdcabcdddaacbdabdcaabbbbabbbacbabbabbbcbdcbddadbaabcdbbbabcbacadddcccdcbddaadaccdcbacacbcbadccadadbbbdcbdbdcdddbcbdccddacacbabacdccccbaddcadbdabcadcabcccaaaaaabbddbdcdcbdbcccadcaacccdacccdccabbabbcdadddacbcbcdcddabddddacdaacccbabcbabacbcdabcbcbdccccdaacaaababdbddbbcacdaadbdadabacacaccadbbacdbbcadddcabdbdddddbbcbbacdabcaccadddaaaacddddddbbdaadbaccabcbddabbccdacacbacbaccdacacbaadcaddbbddacccccaaccddccdaabccdcabdcadccaadcdacacccddccbdaabccacbdbdaaccbbbcccbaaabcbcdcdacbcbabbbbcdbddbcaabbacdcabacdabdaccbbbcbadcababaaacbabdcbaddbaaadcdadcccabbbcccacdbdcacdaadbddcdabcbacacdcbabbbbbadbccacbccabacbcaaababbbcadbacdbbbdcdcbddbbcddcbbbacabcacbbcbabcbcdbbabaddadbdaabcddccbdadbdcabbcdabdcabbabdcdbcbdbddbbabbcbadcbcaaccbcdbdcccababcaccccdcacaddcbddcacbababcbcdbcbcdcabadcddcbbddbadbbdaabbcdacababdadadcdcdaabbbcbdcccdccadcbbbbbbacdbdbbbbacdcabbccaacccaaaabcdabdacaaccaacbadaccaabddadbdbaababbbadbaacbcbabddcbdbaadadcabadbbdbcdcabcdabcbcdbddddaacddccbcdabcadcbcaaccdacaacccddabbdccacacdbaccacbcddacadabcbabcabdadacccbccbdbbcabbdbcddbdbbcadacbbcccdbcbcabacbbbacacccacbacdaabcacacbadabadcdacaacacdbbdadcaacdacadcdccbabdbdabccabdbcaaadaacdbcddbcdddcbaddcabadcddcabbbdcbcdbbbbbbabacabadabbcabbdbadbcdaadbcaaadaaccaddbbbbdabcabdaddabddaabaadbaadadcbcbccacadaabcaacbabbdddccdaacdbbccdcddbbbcaccdaacdbbbacdbaacddcdcdddcbaaddbdcdcaaadcabdadbacdcbdccbbdbcdabddadadbcbccbadbdbcbdbdaaabdcddbbddcbbabaccccbcacccdadbcdbcdcdcaaababcbcadaaacdddcddccbbdcabdacbcabcabcdacccccbbdccdccaabbdddcbdaacdccdaccddacadacdcaadbdbbaabbdddcdcdbbadcdabcccabdbdacadccaabcdadbbbbabcdabcddbbbacbbbacbcccbabccccddcbdacadddcabbcddaaacacacdbbbcdbbabaaadaacbdaabcbbccadccaaaababdababbbdadbacddcddcabbabdbaabbcdaaccadccbdccdabcaccdcbbaaabcdacaccdbdabaaaacccbadacbabbabcdcadababbaadaabdcbcacabdbbcbdabcbbcacadabddbddcddabdcbbbadcdbabdbabccccbdbaacbbbcbbadcbadbdadbadcdbacbaabaabcaacdaacabddcbbbdacdcaabbbababaddbaddddbcdadbaabccabccccdcbbdbcbbdabbcacccbdaaacaccbdbdcddcddaadcbacdcbcaacbbbbcccddddbaccbabbcddcaaccaccbbaadbcddabcbbabccbddbabcaaddaabdbbaccbacbbdacaacaabccadbbddcccccadcccdcabbdaaabdaddddcddcacdabbbcccacabcdabcbaaddabacdcaaaaacabcddbacdddccadcacbccccaacbcbcacadbbbbaddabbbdbdbacababadbcddabdcbbdacaabbbbacacbbabcbcdcbddbaaddcdbababcddcccbcaaacaaacbbaabadddadacaacadabcccbcaadabcdcbbbbabccabaccaabbabdcdcacaaacadabcbcdbacbcbbcddcdabccbcbaccbcdcdadadbcbdadcaccacdbcdbddcddacabbdcccbabbaacabcadabdcbaadcbdcddabdbadaddaddacdbcbbaaadaabdabbbaaddcbdcadcdbcadcdaccdbdddcbdabdcbdbbaabdbbdbdccdabbaabccbcabbacabdddccbadbadababcbbddddbddadbcbdaccbdaadcadbaacdcadcbaacdcdbccbbccabadcccbcbcdabbdcbabccdbacabababaadbbcacdbbcbabccbbabcbaacbcadacddbaacadccaaadaadaddaccddaddaaabaacdabadbbbdaaadccbbabbccacabccdbcbdbaadcabcabbbadbcbdadadcbbbcdcaabdacdbbbbbbcacdbbbadcbdbbadaabcccdadbdcbaadbaabbcadccbbbcbdabccdaddaaaaabaabdddabbaadcddadcbcdabcbbccddbcdacdcbdaddacababaabacdbbcbbbbaababbbdbbdddddccbccaaacacbccaacccccdbcccabacbaacccdbccdcaddbcbbcbcddacddacdbbadbbaaadabccdcdcadcddbadbbbccbccddbcaaaabaaabcaaacdcbccabddddddabdcaacccdcbbabadcbccdccbbbdcaabdbabdadcdbdbcdaaacaddcccabbabddcdcbbbbddacbdcdbaacabbbcdcccdcdcdbaadbccbbbdbccdcbadabcdbccabcdccdbcabbbddcaacbbaaabbbcbcacbaacdaccbacdaddadcacccbdacbddbbabbbcddcbabaabcdccbacdcdaababbaabdccbadacabaadcacdaccacbaabadabdababbdbbdcbabbbbbbbbcbdacaddcdcbcccdadcbdcbcdaacccaadbcaacdbddcadcbbddcbddbdbcabdcabbdaccbabdaabbcabddcdbaaabacdadacdbbbcbabdddcdbdddacaabaccbcadbadabcbddccccdbccaddcdaaddbadccdbcbacccabbcabcaccacaddbdcdaaadcbddcbbddbdbbbccaaaacadaccaacbaadacdbcdbaabcdddbdadcbbdcddbaddbabadabcdcabcbadccbcdbcddabcdadadbaadcbcdbdaacccdcbbabbadcddadccaddadcbcaccbdaadadbaaabbadddcbacbabccbcdddaccaddcdaaabadbbbacddbbdaacbadaadabcdbabdbbbddcdbdbacdadcaccdacddababadaabbddbbbcadcaadcbcbabbdcddbabbbcdacaaadcccbcdbccbbaacdbcccdacddbcaddaccacabbbbcdaabbacbcaabadabaabaaccaaadccdaabcbaadbdaccaaadadccacaccababbdadbcdbcbdbbdacadccbbaabccbbabcbaacbcbdacbadbcadaccbabdbcddbacbdbbbcabadabcccbaccababccbbdcbddaaabcadddccdbdabbabacdaabbdabbdacadcbdaadadddcbbadaabdbdcaacaabbcdbccdccbacdcdcbdbcaabdcacabbaddacdcbadabbdaccabdbadcccdbbaadaaacaaaaadcbcdbdddabadccbbccaddcbaadadabddaccddccadbbdbabccddbddabcccdadcdbbcaacddbbddcaccbcabdbbcbcbccabaddbbcdbbcadbbdbadbddcddacacbbabddbbddbaabcbcaacbababacbaabbcdadccbcddbdbcccbcbccabdddccaabbccdbcdcdbadaadbdbaaadddcadddbdadabaabccaddaaaadaacdabbddbbcbbaaccbdadcaabbbccdbdbcadbccbaacdcbddaababbccddaddbaaddddddbbdadacadddcccccdbbacacdcdbcddadcbddcdaaaabccdabdcdccbcdaadbaccadbbbdabdcbdcdbbbbcaabbbdbcabccbbbbcdaacbbaaccdbbbaabcdacbdabbddcbdaababccddcacbdadaacbbccacbcbacccddcbabacdcaababbcacccacbcbbdbcacdbabdcdcbbccdaabcdccddabddbbabdcaaabbcaaabbcadabbddbddbbbcdbdcbbaacacbaccddcaadbdbccabcccdaadcbcccaabcaadbdadadccbdaabbbcabdbacbaddbdcddccdbbaaaccbcbbbadcacbcbddacabbbadadbcddacdddabdbacabadcccddcddcbcaddbadabcbbcbbabddaccadcddcbdcdcbacbcacdacdcbdadbaadddaabaacaabddccbbdbbdbadcadadbadcabacdddcdbcdddabbbdcaadccadbabaaabdacbbbdabbdbcdadaaccbaacabcbcdcabdcbbbbabdbdacaccacbaabcdadcddabdacddddaababdbababdbcbbdcabdcbbcaddcaaccddcbdacbaacabaabbdbbdadcbadabadbcdabcadcdadbccbdabdccdbdccaadcbbddcacbdbbbacdbdbdacbcbcbcdaccacadabadabbabddbaadcdcacddccccdcdbacdcbbaabbbdaaddccadcccdbaccddcdacdbddcaadbadbcadddcbabadcabdcdbaacdaaccdabacdcbcdbbbbcdbaacdddddcdddbacdddcddbadaaadbddcbdbbdcbcbddadbcbddbbbbbccddbcccadcbdbabbadbadbdaaaaadccabadbbbcbcdbabcdaccddcbddcdaacbccadcbdabddaaabdbddbcbcdbadacbaaadabadcbcaccdbbccadcacbbcbdbadcdcdbabbadbadbbbcdcbadbdaabdbcccbcdccddacbcbaccbaddaddacbddcbabadddbdadadabaaaddcbcbbabbcdbacbdccadccadaccdacbaadcbcdcbcccaabadbbcdadabbcdabaacbcaccbcccddaacabbdbbddaabddadbbbbbaadaddccacdaadbabbabbbcaccaccaacdacbdcccdddbdccabaaadaabdabaabcabccaccabbaaabddcdabdcbdadacabaadbbddadcddaaacbbaddaadcbabadbcdbbddadcacccdddbdccaacbccbbcadcadadcacadbadbadadcbcddbaccdddbdadcdbbccaadbccdcbcadaccadbcdcbcbdcadbaadccddbddacdcbbbaadcdcacdaabccdcbcaabcabcbbadbcabbcabacdbaabccabcdbcbcabbcdcababdbbcbccdaacdccccbbdbcbbdacdaacbddaaddcbdadddaaccdcbdaddaabdcbdbdcdadadadbdccbddbdbdbdcacabbcbadcddaaccaccaaaddcdcdaccdbbbcbcbcaddbcdbdbcccddccadddccadaabbdcdcccacdbcdddbcbbdcbcadaabddccbadccdccdbaaabcabcdbddbccccadbcabaaccbcabadddbbadacdbadcaddccbacdababaaacadbbabbbbcdcbdccbdaccacbdcadccacbaadcdcbbaabccdadccbdaacaccdccbddbaabbcabcdbbdddcbbddabcbabcadacbdabcccbdcacbbddcbabcbddaacbacbabbbacccbabdcaaaadbaddabdcbcaaccabcbaacbbadabddcddcdcddcbdaacbdddbaccaddcadbbdaabbadacdcabbabacbbbbccbadadbabcdcccdabbcabbcaddbacbbddaaabdbdbccbaccaaaadacbbdaabbccdddcabdbcdbbcacaacddcdddbbdcbddbbbbddacddbcabcaddcddcdaaabcdadbadbaaddcbdcbdbbabadddacdcddcadbcacbccbdcacbaaccaaadaabbdbaaabbbcdadcdccaaccaabbddabdcaddabbdaabdaccdbcbcdcaabbabcdaaabdcdacacbbcadabbbbbaccdbdabbdaacbdbacbcadcbcacbbbbddcbcdbaabaaccabdaabdbccbabcacdbdacbadcacbbcadccccbccdbacddddbabdddccbbdacccacdcbcccadababadccbabdccbddbacbddacbcdcbdbddcabcadcbcbccddcddcdabdbcbaccddbcaddbdbdbccaccdaaccacbccbcaddbccdacdadabababbbacccdccbbbaaacdbadadcaaabadbbcaadbcbaabdabddbdbbcbdbaccaadcaabbbbaadacccabbaaacaaaaddbdabdddaaddadbabbaabdcadccbacddccdbdadcccbcdddaacbacbbbdddbdcaaaaadcbbcaddcaadcddaaaacaaabdacbbcaadbccaabcaddcccddcadbdbdaddcccacdbaddbadaaacccbadbcbbcdddbbbadbacbdacaadbaaacaaaabadabbbbcdbdadaaaccdbbcaccbacccbdabcbbabcbaddcabbdbcddbadddbbadadadbaacaaccabccaddccbcbdcdbadcaaacbabbaabdacbabaacbdcdbbbdddccacbacccddbabcbbcdcabddccbbaaababddbabcddddbbcbcccdcbbcbbaacddaabcbcdbbccbabccacdcbdbdbdccddabbacaabaccdddbdbacaacabadabbabbadbaddbcbdddbdbcccccbbbdaadbbddaaaadcaadcbccacadcbbacdbbbdbacbbaaccdacdadacdaaddbdadbcdbacbcbbbccadcbabccbdaaadcbadddadbacbbacccddbadbabaaabdabdbbadddddbdbabbddbccbdbdbccdbdabdabcbbaaccdaccadbcacbdcabccdcaacaaacbddddbcbcadabccabbbacdcaacdaaccabadcccabdbdddbdbbacbcbdcdbcccdabacaabcdbdbaadabcdcbacbdbccaabdbdbdddbcccabdcdaabacdaadaabbcaaddaabdbccabbbadadabcbcbbbcdaaddccdabadccdacadacbaadddddbdbbcaccacadbcbacababddbcbcacdbddabadccbcccbdbbadadccbaaccbcdbcbccbcbabccadbadcacabcababbbcddcabcaaccdabdabababbaacadddbaaddbdccabbddbbabaaddccdddbacdcdcddddacbbddcdcdaccdcccadddcbbabdaacdccacddccadacbadcbddbbdbcbdccbdccdabddcbdbbbbdbcbaccaddddabccacddbcadcdbbbdcaacddadaacbccddabaccccccaaccacbbacddbabcdaccbcccaabcabadabcdcabdabcaccadbdbcbbabbaabacdcbcacaacacaddccbbabbaabbddccbcbcaddabcaadbadbcdbacdbacdaccaaaddbcaabdaaacbddcaabcdabdbddbaddabdbbcdacbbbacadaaabddbbddcbdcdbbababcacdcbcbdadadacbccbdacadaaccbdbcabababadcbabbbbbbbdcdbaccbabbdbddcddaaababcbdcbacbbdbcbdaaddabcbaaadaccbaadadbadbbaadbbbaadaccbccbcacabbdcbadbddbaadbddbccbbbbbaacdabaccdcabbcbcdadaacababbabcababcbbdbabddbdabbdbdbdcdcaccabbbcccaadbcdadddabbacbccddaacbcbddbbcabdcacaaabcaabddabcdcaaaccdabaadbddccbbabdddacccbdabbdabdbbdabbdcdddacdaaccaabdcaabcccbbdadcadcccbdbcdbbbdbabdacbccbcdcdacbdabcbabbddbdacbdbcbbdddccbacdaabdcbababadcbaaabbddbbcdddcaccbcaddbabcccabddcdddaaaddbadbccddcbaddcadabaadaacdbdbdddaaabaabacdacdbadadbcdcddabdcbcaaccccdbabacccbddabaccccdccdbddcdadabdadadaabaabdcddbabccadcdddddcbacdadaacaababdbbcddbddaaadccababbbaaddcbdbbacdccababbcbcbdbdbababdbcdcdbcccbdccaadcaacacaababacdddbbabbdaabdddadcdaacbbcbccccabbaaccbbdadddbdbadbdaaadaabcdaaadbabddcdbdacabbddaadccadabbcdbcacddcabbddabcccaacdbddbadcabbbbbcacccaccaacbcdaababdbadcccaddabbddadaccababbcbccdcbdcddaccccddaadddaacdcccddccbbdbaaccabddbdbdbccdddbdadbdcddddbdbaadcdababdacccbdbadbcdadbccddbbccddccdabcadbadbacbbadbbbcddabdcbcbbdabdbccaccdbaabadcccddacadcbbbddabdcdbabcadddacabbaccdcdadadcddbcdbbadcbdbabdcccdbdcaaacddaccbbbbabbbcbbaaddcddadadbbbddbdbdadbcdaabbdcccdcacbdcbdddccbaddcdbdbcbaaababdbcaacdabcbbdddabccbdbabbadbcabdddcadbccbdbacaadabcdadcbddaaadcccbabbcbcadbabaabbaaadbbabbbbdddbdacadbbabccbdacdadacadcaddcbacccdcabcbbabbcacbdacdbcbdccdddbcbbbbcbbcaadbcaccdaaacbabccaaadddccabcdacdcbaabdacbbdddbdaadbbbdbdddcaaaaddaadbdacdabbaabcbabbabbdcaacdddcaadacbbcbcccdbccaabbaddbacbababbabccdbaacdbdbdabadbaaccacbaaccacacccdbcdcbdcaddcdabcbacddcdacadcabcacdbdcbdbbbbddaabbccdaadbacdddcccabccdaadadcacdcbccccbbcdbdbbccbababababbcdcaabdadaabcdcbdcaccacbbdbcdaddbccaadbccddadccaaabccdbbddaabcbcbddcdcbadddaabaacbdbbdcacaadacdcccbbbcddbdbddbadcddacadabccacdbdaaabbccdbabbaadacdcbccdcaaadadacbccadaaccbacbbbcadabdbdbbadddccddabdddcadaabcbbbabbcdbcacdbddabcddadbdadacaccbaaacdbaadccdbacbbbaabdaaabcdccbdbacaddbbacccdacabcbacbcaadaadcaaccabcccabbddccadaadacdccdbcdaaccdcdddcdddcdcdddbdacaacddacccdcccbadbcbdbdaadcdbcbbdccccaabddbaccddcbbcaddbdbdaacabcaacbaccdbbdcbbabdcdbcadcabbbcbdcddbcdbdbcbbccdaaddabbbdcddbbddbaaacdaddaccaabaaacbdbccaddccddddbcbabacdbcddbbaccdcdbcdbcccddbcbcaccdcdddcdccddbbddddcadcdcabccaaccabcbcabccdaaabcddbcbaacbddaacccdcbbdddaadacabbdcbbcbcdbacadbdaddcbddbabdbdcaabbaabcabbbbcacbaadadacdddddcabddcbaaaadbababbcbbcadcdadbbabbacbdcdbdabbbaadacdabbbaabbdacacdddbaaddbabaabdabdbbccbadcbacbcdcdadacccdbbccbbddbbbccbccaadaaddcaacccdabcacbbddccdacbdaccbdddacbabcbbbdaaddacdccadababadbbaacacbbcaddaaabcbcdabdbccadbdcaabacaaaabcbabdcddabdaddabbcbcdbbcaacbccddbaabdacddbbbcacccbadcdcacacbbdadbdbcdbbbdbddbaabcddabddbcbaaddbababbdcccbdacdbdadcbaaadcacbabcbadbaacdcadacbcbdddacaadadacccbcddddcdcdcdbddadcadbbcddcdddbcbbaccadadaabbcdcbcadbdcaadcdcdccddcdaccbbacddcdbbaabbacdabdaccadcbcabcabadbdbbbccbcaacacbbdaacadcdbdaabdcacddabbbbabbccbcdbbdadadacbcdccabddcdcccbaddbcbcbbdcdccadbddabcddacdbcadbcdbdabbabddbdadbadaddbbdcadabdddddabadcadbadbabbdaabcaaaaaccaaccaccbdcabdbcdcddcabbccccddcddbdbdbaabbacccadaadacbacababcbcacbcabbddababdbadccdaacaadcaacaadbaccaabbbdadaaadbdcccccddbbdcbadaaaccbdbcccaddaaccdccdabccaaadbaaddddcbaaaaccdbbccdddbdbdbaadccdcddbaacaccdbbbaccadbbdadababdadaccdccbabdbaccbccdbacddcdcdccdacbabdacdaaccdbccbdbbdaccccbcbddcacddabdcdddcbdaddaaacbcbbcccabbacdbadaaaaddaacacacadcadcdadcbaaaccbdabbbbcaaaacbdcbcaaccbcccdadbabddbbaaddaaddbcacdabbaabdbdcadcdddbcccdbbaddcdcddbcdcbbbbcaddcbbcbdbdbdcaddbdddcadddaaccaddddaabbbddcdbdcaccacabbbbcbcacdacaabaddacbddcbbdcbabbacccacbcbbbaacccbdabbabccccbbacacaabaccaaadaadadadacabaccaccdddabaccdabcccabcdccccbddddbdabdbcdacbaccddcbaddadadcbcaadbdabddcabbbcdcaacccaabdadbabcbbdcdabbbaaddcabcdbcdabcadbabcdcbbddbadacdbdadabdacbcbadacadadbccccdacbbbdcacdbaadcaaaacadaddbcaabcacdcacbaacacaabababbbbdcadaacbccaaddbbccdbccccbbbadaaccccadcdbcaccccbbbbbbdbbbbbbccbbbabcaaccbcdaaaddcadaaadadbbdcaddbaaabddcadacacabdccadcbcddaaddabcccabccbbdddbbcbacadbdcdabbdacaadaabcbdccacbabdcbcdacdccbbadaadcbccabadbbcdbccdadbbacbddaaddddcdbdabadcdcbcabbddcbdacdcddcdcdabdccddcdaacbdabdcdadccdbbbcdacddddbabbcbddbddbccbacabdccbcbddcdacddcacccbcccaaddddadcaacccacdddddbcccbcaacccadbbdbabacdbdadcbabcbabaabbaaacaccbbddbcbabddadccdccdbdcbcbccbbdbcadbacaabdcdcbadaddcdddbccacbdddcacddcdaabdbadbacbcaadaadacbddbbccdcaadbcdbbcbdabdcdcabbcbabddcbacaadabacddaadcbbddcbdacbbcbbbaadbbcbddbdabbbcbadddacdcacadadcaaadbbdcadaaaadbcccbbddcbdcadabcbbaabddbacdcddaddaacdbcadaabccdcdcdaabdccaddccbbbcaacbdcbbbdcaabddcdcbcabaabbcdbdcccdabdbbbaabadbcaaccdccdaabaabcdccbbccdddaccabdcbcabccdadabdadcdacccacaccccabcbbdbcaddbcccbcbcbbadbdaccabdcaaddaadbabcbbcddcabaaddadcccadcbdbadabbbdabdadbdddaababbacaddccacbbbccacbccdaadabdbcddabcccdddccaddbabcadadbbabddabbcadaccabcdbccddbbadababdcbbaccbdbacabdcbcccdddaabcacabbbaabcaabddddabbacdaaacdaaadccbbdbbdbadddbbcdddabcdaddbbdadbdcddcbcacdabdbbbbccaabcdcddabbdaddcdaccccdbbdadbcddbbddbdaaacacdcaababadababbabccaaaabccaddbdabaadddadbdcccbacdcccbbadadadcbaaccadbcbdcacdccdccdaadccabaddcdcadcacbbbdcddddacdabaddcacaddadcbacbcbabcccabbababbacbbcaddacbdacdabbdddadbdcadacadddcdcdabbccdaaabdacbaabacaababbcadbdddcaabcdacbadbccacabdaadbbddbbddbdadcbbbcaaccaabddbdabdabcbdaacdbdaabcccddbacadbccdbccdadbdbddbddadacabcaaddcbccdcbdcaccbdcbbbddbbcdcbabcadbabbcbdaabdabccdddbaabccaadbbbcdccdcbbccdcccaaaadddcccdcdcdbcdbaaccbdaabcbcccbdbbbadddcdbbaddacacdbaadbcdcbcdabddaccaccddbbcbccacbddbacaabacbbabdacdbdadcaaaaaabaacbbbdbacbcdccacacbccbbbbbcbcdddabccbbacdacbacbcaccdbbabacbabaaccbccbbddbdbddacdcadabacddcbbadbadbacacbcbbddaaaaccbaaccbabaccdbaacbbcdaabbaacaababcccdadaccaacadbbbbdcabdcadcdcacbbdacdbddcddcbbcddccbaabbccbcbdcabbbcdaacbaccbbdaaabdadabbdacbcadddcacacdbbddccdbbccaccbdbcdacaadcbbbbbccdadbbadbbbcbcdbdccdaacbcacacacabcbdaabcccbddcaaccdcadccbcdbdbbcddcdaabdbdadacbbdbdddcdcdbcabaacdaabbdccbbdbcdbddddbbaddcaaaddacddcdaacdaaadaddbcaddbbdcaabdcdcccadadcaddcabdbdcdcdcadcdbbdadadcddacbbdbddabaadddbbadbbabcaacdbacabaaabcacacbadbabbbbddcbbdddbccaccacbcabccdcdbbbacbbacaacdacbdcbaabcbdcbaabcbacaadcdadcbbdccbdcaaaddbaccdacbdccbcdcbbbddbadbbbaadadadacaaaadabbbabdbccbcaaccbadbbaabdbdcdbadddbdbabccdcbaccbadccaadaddbdcdcbcdccbcdbcadbddccbbbdccabbccdcabacdbbabadbdaadaaccadcabadacadabccaabbcdcdbcccadbcdccbcdadaaaddbcdbcacbacbcbdadacddbbcaacbabdbbcddacbbbcbadaccaadabbbddaabccbaabdbdabadbdcabadaaaccaddbaacabdcbcaccabacbccdadbcbaacccadcddccbbaacbbbacccbbadcbccaccdacbabbdccacaaaaabbbcadcddcbbabcacabbdaccadadbaadcccdcdacccdbccbdaadbacddcbbcdbdaccabaaabbabadcdacbacdddbabbcaddbdbaaaacbaccdbacbabbaabbcdcdbcbbbdddbbbaccddcddbbcaabcddbbaddcccdaaaaacdaaccbbbabbdcacdbdbcddbcbcbabbdbcddacbcacdcdbbcaadbdbdbddccabbcdcadbccadcbcbacdbccbbcbbdcdddbcaabbcdccdadaabcdcbbcdadbacaddaadddbcabdabdcdadbabccabcddddabccdccdcbbbbdaabdcbaccaabcdcbaabcaadcaddaadcbccdcdbcddcaacadbbcbaaacacdabbdcdbcdccbcaaaababccaaaaaacacbcbdcbbcbabcacabdabcbbbcbabdcabdbdcccabccbcbccccbdcbdddbaabaabdaadabbacaaaaaadadbadcbcccdacbdaacbcbabaccaccbbbdbdabbdbbcdaddcbcabcadabaacddabbcbcbdadcddbddcddcaddcaccabdcddccadaabacbdabcaddaccbccbddaacccabcabbbaaadcbbccaaaccbaacddbcadabdbbaacbbaaddddbadacabddaaccdbccacaacddacdcccabccccabddaccdcbddcbadacdaccdbabdccdcbbddbaacccdaadbabbaabcccdcbcbabddabaaccadaadddccdcdbdbbdabdabdabcaaaaaacbacbddacbadaaabdddcabdcdcbcbaddddddcadbabbbddddccbccddccddccdbdaabdddbbbbdbadabdacdaaddcabccdcdaabaccbdadbaaadacdbbcdacdbcdcacbdcbcaccbcabbbcdcabaaccacdbcbcbbadcaaacadddbcdababccbcdcdacddadbaccdccadcdaccaccddbdabaaabbdacbbbdbbdcdcdcadadabccadcdcbcbddbdaadabccdcadbbadccddbabdabaaadaaadbddcbdccaabdcccdbacbdcdbcbddabdacaccbcdccdabccaccadaddddacdbddccbdcccbdacbcccadbbaabaadbacadcbbadccbaababcbbbddadbbcaaabbdddabdacaaadbaacbbdbdcbacdddbbadadddaaabacabbcacbdcdbacbbababdcdaacdbdabdccbccaccdcbdbbdcbabdadbaabccdcdbdabbbccabccbbdbcbacaaccccdadccbdcadbccdacbcbbbddabddddaddcddbbdbabbdbcbcbbcabbbdbdabddcaddbbbcbbacbcabcaabbaccacdadcaaacbdcdadccacdcabcbaabaabdcddddcacacaaaabddddcabdcbaddddbbcacdbbbadaccbddbddabacacababcabcbcaabcbaaacadbbadddcaddbacccadcabbdcddaaddcdcaaddbaaaadabccddcbbccdaaaaaddbdccbcdcddcdcccccbdbcdbbbddaadbbbddabcacaaacaabababbaabddacddbdacadbdacdabbbadbbdbbabcacccaaddddabdaddbdcdbdddacbdabaaaddbdacbbdcadabbbccdaadbcbabcdcbccaaadbcdadccbdbcdccbcaaccbcdcdbaccddcaddacacbddcacdbaddbbaccaaadcbbbdccbbbbbaddcbdbddaaccdbdabcadaaadcadccdaababcabcdddcbcacbacacbbaabdbddcbdddbdadcbdadbbadaabcabcdcbcdbbcbbbcccddcbaacacdabdacbacccbaccbaacabdcbdadcdbaaaabbdbcbbcbadbbbbbdbbabbdcdcdcadbccbacaddccddbacdbadadacaaacbbaacabacdbdbbdcbccbacaddcbdaddbdbbcbbcaabaddadcbcdaacadcacbbbbccddadabccbdaaabbcdadccddbcadccbdcdadabbcdbcadccdccbabcbdcbdccccabcccdcccaadaabcdcbbcbacabcbadbabaadcbbabbdbababcadcbcabdabddaddcbbddccdacacadadcaadccdccabcbdcdaacddbcbccacbdcdcbddabbdbcddaddcbddcabadbdacaccacbccbbccdbbbbdbbbbadcdbaaabacdccdcadabbacdbcdaadddcacadbdbcbacbdacabdbcddbccabbaadaacaabdcccddbbcdddccaadcbdddddabcabbcbcbccabacccbbcbccaaabaaccaaaabaacbabdabddcccbaabcadbbbacdadbacccacacacccbbbdbdacbccabdadadcabdbabadadddbbbcddaacbcaddbacbbddbaaadbddddbbacccbaddcdaaaddcabbccbccdaaaacddabdbccccdbccdacacabdbadbdadddaccccdbbdcadacccabcbaccbadcbdcddcaaddbcccabaadbccccadcbcdcdcdacbbcdaabdbcdccddcddcdbcacbbdabdbdaccbdbbadcdddbbcaccadacbaaaabbcbabcdaccdddcdcabcabbccdbabdaacaddccbabdcbcaaccdccdaabbccdcaadaacdbccbadabbadcbcadccaaabaccbbcdcbaabcdbddcddcdbcbcdbbbbbaccaaddabcbbbdacbccdaabbacddabacdccdacbaccbcccdaddabbaccaccbcaacbdcabadddbcacdcacaccaacbcddddacccdbbcdbbcbadaadbdbdcddcdcbdcccdcdddabbcccbbdadbcaaaaddabccbaaccddadadacbbabdaadabddbdacadacddcbbdaaacbbbcbcaabdbbbcabbbbcccbcbaadbcdcdabdbbabcadcdbbcddbbaacccbaccbbcccabbcccaaccdbbcdacbdccbdacdaddcddddbbdadbbaadacadddcddbddaddbdaddbccbbdcadbacbbdbcddcabcbaccdaabdbbdaadabaccddaabcbcacaaabdbddcdcbdbaabddddabcbddbcadcccbbcaddbbccbcacbcdadcbdccadcaabbcaadcddabaaadcbbcbdcdacacdbacbbacddcbdbcbadabddcbccdcabcaabaaddaaddacbcccbdbdacdacbdacbdacbbdbbcbdabbcccccdddaccbacaaacdcccbaaabbadddbcbdbcbccdacbbaccdbcdbbdabadddadbcdaddacaaddbccaccbbccaaacbddcdbaacddcbaabadbcbbcdabaccadbadaaaaabcacadbbbbdaadacdbdddaddcdddddbbdadccccdddacbdcbadabbdacbdcdbddadcddabadccbbbdddabdbcdcadaaaccbbbccdcbcbbcdbacbccaaaabdccbabbbbcdabbabaacccbdcddddbadddabcbabcdcccaccbcababadaacbcabaaaacabaaccdcddcbbcdabccadccbacdcccbdabccbbbacdddbaacccbbaaddabcdaacdabbaccbddaadcaaacaddabaabaacdddddbaaddacbddddacdccdaddcddadcbcdbddacbbbadabdcdbcbcbcccacbccadbcbbdbdcdccbaadcadaacbbabbbbdcaabcdccaccdbcdcbbdbdbaabdcdcddabdabbdcbadddacdcadaccaccbacdadbbbaaabcdabdcdaabbdcaddcdcdbdaabbbdbbaaacbbdbbabbabbadcabcabdbbddddaaaccccadbadaccccdccdabacbbaabaacaabbddbdbdbabdbbcdadaadddcabcccaddcccacbcbbadbcbdacbbcdacdbdadacccbddcabbdbadbaddbbaaddbccdcbaaaacacbbcbaddbcdcbcacadbdacdabddbdbbdbabbbcdddbabbdcaaaabccbaadbdabbabdbdcaaddcaabbdbdaaabdddbdbcaacdaabbcddaacbdababcadbcabccbbbccbdaaacdaadbdcddabbaabdbcbcdadcbbdacbdadbdcddcdaabbcacdbacbdbaabdcdcbaddaabaaabcdbbdbcddbacdaaadcbdaddcdccddcacbbcaddadbdadddcbadddcbbbcabbbbcccbccbbbdcdcbdacdcadbcbcdcaacbdddaadbcdcbbdacbcbdadadbabdaacccadaccdabdcbcdbbdcbbbbcbbdccdaccadaabbcbbddbdcdccbdadcdbccaabababdccacdacaaccacbacbdbaaddbbbbcdaccdabdbdcadbbcbdcabdddaccbcabdbaaacdabcdabdababdadbbcdbdcbdbddddcbabcbcbbbbbddabcbcadbaddacccdcdcdcbbabaaadaacacddacdbadaddcdcdcdabddcbadbdaddccbcdcacbbbbaacddcbbcddcaddcaccabccbbabbbabcdbbbdbaccbaaacadbcbbbadddabaccbcacbabdbccabdbdbbcaacacaaccacbccaddbadbaaacdcccbcbaacbcadaadaacabcdaacadcdbabaacabbccdaaaaadbdbddcdaaccbddbabaddccbbdacddaddbcadaacdabdbabbadbabdacbdcbccdaddcabdbbcdbbbabaccadcccbccbaabcdcdcacaaaaaaabddabbcccdbcabacdcabddccabdcdcbdacbaddadddbccdcbcddbaadadacbcbdaccadbccadbcccabaaddacbcbdababadbbabdbdbdcbdccbcadcbdbcbccdddcdcbddddcbaadcdaabdddbcaabbdddaccbdadddaccaaccababbccbaaaaddcbadaddddcadadbdbbcbbacddddadbbadabadbacbacdcdabdaaaadcbbadcdabcdaacbbbdddccbdadcdbdabddcabadbacddcabbabaadcadccbddbbadacadbcbcacacdbbdccdbbaacccddcbdddcdcdcdaddabadbdaacbcdccdcdcdddcbaadccbdbdcaacdccdaaabbbbacbbbbcbacacaaccbacddcbccbbcdabbdbadbddaaaadcbbbbaaadcdcadbccdcdbdbddbbcbabaddaacdaaddddbdaabdccbbacdabbccadaaacbdbadcaabdcbbcaadcbdbabbbcdbcabcacddbacadccbabcdcdabbdbabdadaaacdcadaacdccacccdddcdcdababbabaadcaaadbaccdabbdaaddccdabcdbccdcacabacaacaaadcaaacbbbcadbddadddbdacbbaaaacdbdadabbdcadbbbbcdcbaddbccbcacabcbdddcbbacbddbcbaabcabdcbbdbcdaaccdabdabccccdbccddcbcdbacdabaabbbaddadbbbbdcadaacddaacabadaddcbadaacbbccdcbbbddaccbcdccdaccacaccbdbaddbdbadacabaddcaddccadadcdbcbddbaadabbbdacbadccddcadbbcddcbdcadacbadccbcbdadcbbbbdacaabcdccbababdbdaddadccdbdacaaadcbccdccadbaadbcbadcdaccdcbaaadaaabbbcdbacbdbabaddccccbddadabbddabbddbbdadaccdaccddabaacbdcbccacddddaacaadabdccbdaaaaccbbddadcbccaabcacbdacaddbdaccdbabddadcacbddddaaadbbaddacbdcbbcbccdabadaddddcbbdaaadadaadabdadadcbbbadccdddbcdabacbddbccaacbadbdacdabcbbbbabcccbaabbdcdacacadbcadaaadacadaaaadbbddcbddbabccaaccdbcacaddbbabdaacccacacccdccbcbccaacdbacbcdddbcddcbdccdaacccaadddcdcdacdcbdbddbacacaadabccbaddbdcbbbbcbbdaaabbbaaaaadbbdddcadcbcbbcacdccbaadbbacbbbcaadbcabddcbbbdbbcabcbdaabddaacbbbbdddbaddcbacccdcaddbcccbcccbdabaadabcabacadaaabbdabbccdcbdcacbcabbbdacaadbcaadbddddddadbadcbcbbbbbaaaabbbbaacadaaaacdbbdabbbbcbbdacdcbcdacbbdcaaabddcacdddcbaacabbababbdbadccdccabdcacdacbbbbdcbdcdccbccabdbcccaccaccabcbdbacdaacaadacdbccdcadcdacbadccbbdbabbabdbdadbacaaaddbcbbccadadaabbabbadbdbcacacdbdbddabbdadaaadcbbdcadababbccccabdbacdddbdbacbaacbdbdcddcbdcdbbdbdccbaabbdcadbbdbdaabadbcbdcadbacaaaacdccdcdcaadcccdddcdcbbddbaddccbdaadbaabdadbcbccbadadaacadcdcacbddcbaaacdaacddcadccacbbdbcadaabadaabbcabcdbabaabbccaabbabbaaddadddabbbaacddbdddcbabcbcbaadabcbcdcddabbdabbcddabddadcdaddbbbddaddabcabcccbaddbcddccaabadadabdbabaabccdccddbaccacacdcbccbadaabcdacdbaadadabcdacaabbadabadddabbcbbccdcbcddbbddccddcbccccdadcbacbbadbadbddabaacdcdaadbbcbadccabccdcbdbadadbacdbccadcdabacdaaccabdbccbcbcdddcaabbdacccdbcdcacadbcabcaadbcaacadddcddcbcddcacbccdbcbabbddbbaacddbdacdaacacbaccdbccbabaadbcabddaccbcbaddabbbdbdbcdbdcdddabbacddbbcadcacadccacdcdacccaaddbbaadcacbbdabdbcdcaccccaccdbabcdaccabbbddbaabcbcbbbcbcccdbbcbbcdcabadacaabcdaaaccbcaaacadddcacbddadbaccdccbcacdbbacdcccacbdccadddbbadddcdbdbccdcddddbabbcdbccbadbdacdbbcabddcccaabccbbcdbccddbcccbdadbbdacbaddaccbcaacabdbddcccccdadddaccbdcaddadabddcbcaacacadbdbbbdbcbabbbdccacaaacdbbdcdbaddadcdaadbadabddddbcbcbccdbdbbdbbaccbcacdbddabadbbbccdcdacdbdabdbaadbccbcdaaccbacbadbbddabcdbbccdbababcdabcdcdbacbadcaadbdcccddbccbaadccdbcbdccabbcbcbabaaddbcadaaadbbbbcdcaaaacacabcdcadacadabbdacccabbadcdbdaaddadbadddcdcadccaccbdcaaaddcacdcbcccbadcccddddcdaccdacdcabdcacdcabdadcdacdabcadcbacccabdccaaddddcddcccdcdabcabbdccaabbacbbccbbbcabaaabbccbbbabdacacbcddaccadbbdbcbaacbdbabcbcbaabbcbadcbdddcdcbcddadabcdabcadddacbaabdbccbaddbcaadbabdaadbbbabadcbaacadccbababaadbdabdccdcbbdbbbdabbbbcaaaccccbdacbdaddddacacdbdacddbbbcdacbdbdadbdacaaccdbabdbdaaddbadcbadbacadabbbccbdbddacabcbbcaccbaddbddbaadbdaccbabadddccdcbbbcbbddcdadaddbdaddadadbcbabdcdcdbcacaabccdcacdcadabcdbabccbbcdcacacbccbbbaaccddbcaddabbdbbadbbabaaabcccbdbcbbbdbccdacacdbdcdaabacbdbdbbacbdcbaddabccbccbbcaaabccbacddddacbcdcdcbdbdadbdbabcdcacdccdbcbcaddabbcbadcbbcdbaaacccbdcdbbcbcbcabcdacacddcabdbacabdcababcccababbddddbcababcaadcbcdaabaaabdbbbcbccdaabddbbbabbddcdddbdddacbbbbadbdadbccbddccbccbbabcbdaacaccbabdcabdcabbacddbbababdabbdabdaccacbcdabadbaabdacabbbddabcadbdcbdbaddddcdccdbdabbdccbbdcbacbdadbbdaaadcccaacbdbccbbbbdcccdaaadbbdcbcddbccdbdccadadccaaaaacdccbabaabdaadacbcbcacadbddbbabbccbacccaabbbabacbabdcbbabbdaccbbddbbbdaccaacbbdcdaadbdccadccddabdbabaadbdbabbadcdaccdbabcbbaaaccbdccbcdaaccaddcadaaddcbaacbdbaacddcacddddbabbaadacabdabddcbcccccaadccdabaabacadcbdaddcbdbdabccacccabaaabddcccadcbbddcbbcbaaddabccacaabcacdadbabaadaacabaabdcbcdddbbcbccdccdbabcacacacaaacbdbadcbddddacacbdacadbdccbcabbabcdbcdbacccdaccbbcdcbdaabcacadbabbbadabdcacccbbaabaadcbbbcdbbaccadbddbdddbcbadbcccaccbbdcdcdbaddcdbcdbaaacababbabdddcacadbadcbcabcdbbabdbcaaddabbabddddabacdbbbadabbabbcbacaddddbacdbaabdaaaacdddcbddcbadcababdcbcdcacacbdbcbbbadccacdaabcccaabbdbbdadbdccdabbcababbacdadbcdaadbacbadcdbdcdcdadbadaacdcadddbbadbcbdabaadcdbbdddccdcdcbadbdbcccacbaaacddaabddbcccdccadbadacdccaaddddacbacbadaacbbdaadaddacdbbaccddbdbdabdaabccadaccdddcccaccbabddabcdcacadbbbdcbdcaabdbbacbcacbbccaaddacbdddacaadbcdaadbdacbdaacdbdbcddbbcdbbbabbdcdbdcddbdadacbaabababdaccadacbbabbdddaaddacdbabcddbbccabadcdbaaadaacbaccddbaccbabccacdcabbaabcbaddbdbcdccbadccadaaaddbcabcbacccabccaacbbabccdadacdbbccbcabdccdccbbbbaddbdabdaadabdcbcdbcbcdbcaadbdbacccbcdcadbbaccbcadacdaaaddcdcbcabdbddbcdaccbbdddacadcaadaabddbbbaadaabbbccbbdacdabbaabaabaddbcdabccdbdddbcdbadacbaddbadbbbcbbcccabadaddadbcbaabaadcbcbddcdcdbccdbcddbaadbaaabadcccacadccacddbabcdadcdbcdbdddcadbdbddbaccdacbbbabcdcdbdabaddbbdcbbacacbbdbbccbaadcbabdcbcddcaaddacdbcdaabbcadbcbbbcdacdccddabaddcabdaaacaacaaddaaccacccbdbdcaaaabdbabbacddacabbbccababadbcaadabdbbdcaccabcdccacbbccacdcccbbbbbabcbddaabcbbbbdddadaaaccdccdcdcdbdcacadabaaadbcaacbdacbaadbabbadcbbbbaabaabbaccdaccbcdbdaabbdaacdadcdbdcadcdcaabdbaacdbadccaabbabbcaccdbcbbaddcddabbbacbbdbcdbacaccbadcbdaaaabdcdabdacacadcadaabdcdddbcbaacdcaabddcccddaddadcaacacaadbdbabdacaacdccccddcdabcbdabcaddaccdaadadbcdcbcbcbdcaaccadaaaabddadcdbbbdbdabccaacaccbcaddbdcdaabbddcdaddadcbcaddacacbcdabadcabbdbaaabdaddacaaaadbcbaabbcbdcbccbcbbccbcdadccbaddcbddcbddaacbcbacaddbcdccdccdcbbaacabdbdbcdcdbbacabacaaaccabdadaacacbbbdcdcbbdbcababdddcdbacdbdabcddcabadbbcadadbdadadacadddbdcadcabbbaccddccbcdadbaabcaaacdcbdddcdcbcaccdcbddcbdcacddcdbaaacbbabccdcadbdbdcbdbbcbdacbadcdbdcbcdbcdbcbbacbdadbaaabccdbdabcbddbbbdcbdbddbbbcacadcbdccdbddbdaadcabbdbdbbbacaddcbdcbdadcaadbdcaadbdcabdbcddadacbbdbcbadbbbdbdbcdabaabbbabaddadaccbddcccdacddacbdadacadcaadccdbbccdcbaddcdaddbbdadadabaccacccadaadaababbdababbbcadbacdcbbdaacabdabaaabbccbcdcadcbadbaaccbbacacbbdbbdbccadabcdbacbbdbbabdbdccbbdacddcabbbaacccbacbccbaccdadbaadbcabbcadcdacbbcabdadaaabadbdcaabadaabcddbbbdddaccddcabdaccdbadabdbccbabdbcaccdadddcbdacbdbdadbccbdcdbdcbbbbdaadbadabcbbadcbbadabdadcdddacccccadababcabcccdcbdcbcdaaabadbbbbcaababdadddcbddacbaddcbbbcaabbaacbabcdcdccdabddadddadcacdcacdbacbaabdbbccbddcdccaadabbbdaccaaadacbdcdccaacaddbddcbdbbccdaacbdaadadadcbadaddabadbbcacadcdacdbbbccdaaacdabcadddabbbbddccadabadabcbcdaddacbbaacdcccadabcbaaacacbcccacdccbbcccdbbbdcddcdbcaccdcaaabbaababaaacacaaccbbbbbabdadbadbacddbbdcdaddcbaccdacdbaacbbccdaddddcadcaabbaadcdcbabcddcccacadadaccddcbdbdcddcbaccbcbdcdbbaccddbbbdadbabdcaddbbcbdadadcdbbacaadcacbbbcdaaabcdbbcadbbcabaabbbdaaccdabdbcdbdbcaabddbaabdbdcadbbadbcdccaacbbcbcddbbaaacaacadddcccbdcabbcaababcbdbbacdcaddccadabbcbbcabbdbaabcababbacdcdcdbbbacbcdaadaccccaacadbbbcadbacbcaadcabdcadddaaabbdabccdccbdcbdcbdbdcdbccbcbdbbdbacddbccbcddbdbacaadabdccabadbcbdbbbddddabaddabbcbbbbaddcbaddadbabcaaabacbacabbbadaabbbddacadcdddcbabdbabaccdacbbcbaaaababaddcbcdabadadbbcbadbccddabbcaccbaaccabacddacdbcccaaabaacccdbcbadbbdbadcaaadabdadcbcadaddddcbdaddbabacdadddccbcdbbabbcbdcbbaccbabdbbcbdaaadabddacbdbdbbdcacdcbccaabaddbabadadddccdcadccbcccbbadadbdabbdcbddbdbadbcacdabccbcdccdabcdbdcadbdcdbabddbbacdbcdbcdbdbccbdcbccdbadaacdddcbdadaadcadccbcadbadcbdbbdcabdbbbaddbddcdddcdcadabcabbdbacbdadaadbcabadabbcbcdabdcdcdcdaacaaabbccababddbdbaadbcabbabdbadbbadcadccdbaacbaabccdbcadacaaddcabaadbbdaacadbadadcbdbacbccadcdaccccabdcdbbcaccdcbcccbbcccaabbadccbacabcaccacabbdddbdaaadaaacdaabcddccdbdcdcaabdaabaccccddbcbbcbabcacdbdbcadacaccabdcacbabdbbddcbbadccbdcabddcaadacabdabdbcadadacbdccdcbddbcadcadacbbbccabbcbacacbdbacbbdcadabbbdbbbcabdaaaaaaabacadbddcbdcdcababadbbdbaacabdbddcdbcddaadccdddacabaddbcbaaccaacdaaadabccbadccddddabadcbddaacddacaacbbacacbcaadabcccaddaddcaaadcaccadcdacabbdbddaadccdbcbcaaaacdddcccadbbdcdcdadaacaccdcabcdcadcaddcaacdcadbbaabaadccaadddbaddbddaabbcaddacdbbabaaacdbabaabdcaaadddcabcabbdacbddccbcddadbcaddadcdabaabcbccdbbdaaddbcccdcacbbadcaaabaccaaabadbdadbcacadacabcddddccdbacbaacbacdbacbbbbdabcdcbcbcddacdacddccbcbbabcdccdacddadbaccaaacbbaabdddddcccbccdcbdbcacaccadbcdbcdadabdbadcdcccbccbaddccccddcadbbcabcccbdcbaadccdaaabcabccadcdadbacbbadaddbdadaddbdabccadbdcccdacbccacdcadadbdaddbbdabacdcdddcadcbbdabbcbbaadccddbdbaddcdccdaddabbbcbcabbbcddacaacdadabdcadcacbbdabaddcaaabadcbbccbbaadcbdadcdcabacdaacdbdacaadadddcacddaaabbacccbdaaabbaadddcbabcdddbacabbcacbbcaadcababbdabddbdbcacbdadccdbacacbdcacbccacdcacdcacbdbccbddaababdbccccaadddcabdaddcabbdcbaaaccdcbaccbbbaaaddbddbadcbbcabaaabbbdadccadbbbdbacccbdadcdabacdaadcadccdabdaabcadcbbcacccccbcdcbdbabdbccdadccbccaaaababcdaaabdbadaddcabbdddbbdbbcddadacbbcccdabcaacabdbddabcccbbaacbcbabccacdbdbbcdcbbbcdbbadddbabbcdddacaaddcaaaddbdbdadccacbbbbaaacbbdbbdbbbadabcaccdadccdccdbabccbbabadbcadadbbadbccbacabbbacaccddcaccacbaabccacdddadbdbabababcdddddcadabbccbbcaabdaadcacddddabcbccaccaadbabbacbcbbcdbbabddabaddbaddabbaaccaadbddbcacbadadccaacaddbbdaacddccaacbcbabdcbdcabdababadcddabbadaaabddbacaaccaabbacdccdccccddbadcbbbadacddccadbbdbddccbccbadbaccbabdcbbccbdbabbabdcacbbdcccdacacddcaaddbcbcbcadbdabbdaddccbbccbcabaddccbdaaccbddbaaadbcbacbdabdbaadcdcbabdaabcbdbdbdbbbadbdcdaaabaddacddbbccadaabaacaabdcdbbabbbbcbbcbdadadcacadcdbaccbdbdbacbcdccbacadabdcacdbcdcbbcccbadbbaabdbadccdabcddabcaaaaacccbcbadabbcaddbddbcdaacacbbaccdaadcccdacdbbbaabbddcdbaadbadcaaacbcbddccdbbbcdaabadbacacdbacabdccacadabdcbaadbdbcdbcccbbdabdcbdaccabbabaccaccddbdcdacacbddddadccbbcdaacbcdbbddddbdccbcabacabccddadbcbcaacdddbdacaaacdbcbbbbcccacabaaacdbaadbaadbbbabacbadaacddccdcbbadcddaccddbdbcaadcdaadcadbcddadbaaccbbdbddadcdaadbdbabccacabbdabcccccccdcaadddcbdadababddcdbbadaddaddacccbdadaddbddcdbbbdddcbddaccadadbaadaabcddcbbaacdcbbdccaccddbdbaabaadddacabbcabbcabddcaacadabdcbddcdacbdcccabacaacabbbbbbbabcdbbdbbbbaacbdcbcdddcbccddacacbcaaddcabababcddbbabbdbbcdcdaaccbdadddcccbaaccbbbadbbaccdabbcbacaddbbddcbadccbcbccdcdcddbbbbbbbbdbdabccdbabcdadcdadbadaaaddddadbacaddcacbcadaddcacbbaadcdabdbcabadbdaddcbcddbccbaddbcddcdbaddbcdbdbadbbabbdcddabbdaaccdaaadbbdbcabdcdadddbacadbddacaacdcbcdcbaddbbccabbabddbccababcdbacddbbacabdabdcbaaddaaacdbadcddcbdbcbdbdbacadbbdadaadaaccccbcbddcccdcaacbbcaaaabccdadddbdacaadcdabbbbdbadcddaadabcbbacaabaaabdbcddadacbdbcddbacdbddbbadaccadcbbbbddbbbcddbbbadddaadbbcdaaacbbbdccabdddbabcddbbdddcdcdaccaddddbaaccbbdddccdcdbdbcbbaabbababadbacdadcccbaddcddacdaacbddcddcaddddabccacdabccdadaddaabdacddcabacaacdddcddaaabbbadcddaccaccddadababdcbcbbbaaaddbbabaadacdaabcdbdbbcdccdabcbccdcaddcacabcaacbdaaabddbabcbbccddbdaabcdbcdbaaacacadcabdcccaadacacadabdaccdcbcabdddccbabbdbabcadacacabddbcbadacbdadbddaadbdbddacbccccddbdabcdaddbcadacaccdbaaadabccddcdbcbccddbdcbcdaabaabbdaabcbcdcadcadaacacbbdbcbbdbcbacbcdacdbdddbcaaadaddaabbbdbdcdacaacbbcdabaaccbbabbdadabbaccbdcabdabcbbcaaacbbcbdcbcbbdabaddbdbdcabacdcdccacbddbadcbaabadcaddcddcbbddcbcbcaadbdbaacaabdadcddaadcbdbcccbdadbadbcabcbacdabbbacabbabbcdcdcdacbaaabccabbcbacaacacbccadbbdcbddcbddcbdcacaacbbdadacdcbcdadadbadccdccddddcbcdbaccddccddddcbbbbcdbccddddaaaabdaccbabaaddbcadabccccacaadacdacbadccaddbbdaadcbbdcdacbaaccbaaadbacdbbabbacdbbaadcaaaaabdccdaaaddbbbbbddbbbadcabddcadcbbbccdcbcaacbdbbddccbdcabbccbcacdcadbabbcbbdcacdbacdaaadddbdbacdbdccaaddbdcbabdaacabddcdbdaaabbbccbbccddccabcbbcbbccddbcdcdadccddaddcaaddbccddcbbacbbddbccabdddbddddcccbaadaabccbaadbdccccaacadccbccccbcccdadcbbddbccdaccbdddadbadbabbcdccddbdcdadbbbbbbabdbdbdbcdbadcbcbcadbbaccaabaacaabadbabcabdacbbccbccdaacacbbadcdbacaaadaaddccdadbaacbcadabcbbbccdcdcddabcaddddaacbbdcbcbdbdccdcaacadbdcabbbccacababdbcdadcccbbddbdabbcccdcbaaabbcbdbbadaccddabcddddbabbdaddcbbdaccbdbcdabadcbcacadcccddcabacccdbacdabaccacdadcbbddaabaaabddaddadabdcddccadbcddbbdaaacbbdadcdcaddcaccadbddbacbacbbaddadabacadcaabcabacaccabaabdcacbbdbbabbcadddbbacdabbadbccdcdabcaaadadacabbcdcacbcdacaabcdbacdccdaacaadddaddacdbdbccbddddbaacabbaadccadcacbbbdbacccadadddbdccdbaabaadcbaaaacccbcccdcaccbdaabaaadbbdaddbacdaacdbbcababaadcacdbbacaaadacaccacaddacacbccdacbbaaaaacdbadadaddbbdacadaccbbcabcaadccdbdbdcdaaabbdccacadcdccbbbabbaacadcddcdcddcbccacccabcdacbaddcbdbdcababaddcadaccabbdabbbcadbbabdaabcaaaddabcaddddaacacaabbababbadaddabcccdccbbcaadcdbdacccddabdbbbdbcbabbbdcbabacdcabccdabcdddbddbbdddcbbdcacbabddddccacbccbcaaabdbdacbaccadaadcbcdbaabcdabddaabaaddabbdbbdaacacabddddbbdababdccdddcdaddacddddcadbaaadbbcbadddcdacbdcbaccbcccdacdbbcddcccdbbddaccdaddccbcaacdbdadcabdcadaabccccabcbbdbacdbaaccdbbbbacbdbdbccaabcccdadcdadbbbdbbddcdaaaccbdbbdaadaacbdacacddadcacdbbbacdccabbbbabcabcbabbcadacdabaabdbccdddcbdbaaaddaddcbdbdcdbbbadadbbbaadbaddbbbbabddbadbaacbcbacdabdbadaaabacbcaacaabacbaccccabbabbadcbcadcbcbabaccadddcdbdaaaabbccacababcbbbadccdcacacdadcdacdababdbdcaaabadcbccdbacaaaaaaaaadbbcadccbddbdbcbcaaadaacacdbbabbddacadcadbbadbcaddbcccadbbcadaccabdddccadcaccdacaabadadaaaaadbabbcbdbabadbaddabcacbdbcddcaaabcaccddacadcaaabacbaabcbdbaabdbdbadbdbdbbdbaacadaddddabadcccccaacbdcddbdbcccddbadbbcbdcdacdcdadbaabcdccbacdaaaacaabaadbcadccadaddbdacdddbdcdddcaadcdcdccdbacddddccbadcdbaadadabcbbccabbadabddccbcbcacbdccdddbdbadadccbabadcaaccbdddcbbdccacabadcbbbdbcbbcbbdacbbbdcbbdcddccdbadccbcddadacdbdaddbaddcabcdaccbdccdaaddabdacdbaaaaabccacdbdcdbbbcbaaabbbcaadcdacdaaaabcccacdcdaabdccbbddaddaaabbcacaadaacabcdbcdadadabbbbbcbacacdabddabbdaacddbdbdcadaddcacddaadbdcabdbddadccbcacbabdbccbbacccbbabcaadaaacaaccabaabacdacabdabdacabbccaaacadcadcacabdbcddcbcabdadcddadbddbbbacaddadddbdacbcaaacbacabbabcdcabdcdcbdbacbcbdcaaadcacabdcacaaadbacaddaadddabdbdaaacacdadccabddadabdbdccababbdcbdaabdcaaabddcacccbcdaaabbdccdaddddccacbaddbbbbdbadbaadbcddbbcaabbbaabdadcababbddbbddaabbaabdbcbbadcaacdcddacbbdcdaccbdadddacaacbddcddbdbcbcadaaabdbacadbcbbbdcdbabbdccaaaccbabbadbadbaccabdcdaaaddbaaabbddbcbbdbbabbdacbaadbaaacbcadcdbdadbddababddacaacdcbdccdccccbbdbacabcdbbdabbacbddacbdddccacbabacabadbbbacdadabadcccdaabdddacacbdcdababbdbbdbbbbaadaccbaabdcbcacbcacdccdbcddadbbbbcdbbbddaabaabccabdbaccccbacddcaddadcbaddcadcddccbcadadccdbacbccbbbcdbbacbcaddbabcaadccccddcbdbccbdaaacacbacaddbdacdbdccdcacacaabadbaaaadbcabcabbccbdcacbddddbbbdbbcddcccaadacacddbbabcdabcbbddcaacbddbdcadbbbbdbdccaccdcacdcabaaabdbccaddbdabdcacdaddcaaacdaaacacbbdcbccaacdbbabdddccbbdbdbdabdadacaababcabcdcdaaacddbdbccccabbcbbcabbacdcabdbabccacdbbacbccbdbdaaccabcbccdaacdcaaccbaabdcbcacbbddaacddcdbcacdaabcaddbcccbabcddccccaaaddabacaadbbbcbcbbbbbaacabdabcbbadddacacdbacdaaadcbdbdcbbcabadddbadcdbccadcacdddaaccbdadcdcbbbcbbdddaccdbddbbcbbaaabdddaacaccdcaacbabaabacdacabcbadacdcacbcabcaabcbdbddcbccbacabcadcbbadaabaacdddcddadabddadaccbaccdbabccdcddcdddabacadcdadcbbcdbacdabbaddcabdabdcbdbabdccbbddbacdddbaaaadbacbabcabcdacbaadcddccbcccdaddaccdababdcacccdaddbbcdccaabdcdcadcbaadaaaaaddaabadcacbcaadcdbcbadaccacabaaabaaaabcbaacbddbdbcddbbdaabaacbdddddbcacbbbabadcdbacabbabdbdabcddbbdbcbcbbddbadbdccdddbbaadabbabadabccacdcdccbcdabbdabdcbcdcaacbdbbabcccdabadccabacaaccdacacdccbdcbcbdccbacdbcdaaaccdbbccdacacacbbbaacaacbacbccbbbddbadcccdbadadcddcdadcbdccabddbdacabbbaddbdccadbbddbcaabacaadcbbbbbcbadcbbccbbacaaadbcbcaabccddddbabcaadcccbddbccaccdadbcbcddaabacacbadacdccacaaccdcbcadbaddbdccbcddaacdacdadccbddadcddacaabacbbdddcabbbabcdbacccddbcbcbddaacadbbccabadddccdccbcbbbdcabbdacdacadcdacacdccbcbacabdddbbabdcabacbbbcabbaccbdbcaababddcadcabdcdcaaabcbaacbccaaddadabbbbdabcbcbaccadccadcbacacbdadbaadababdabdaadabdcaadcdccddbabbadbaaacdcadbabcbccbbcaddcbaaabccaccccbdbcacdcdcabbcbcbabbadabaabccccadabdadcbbadbdbcbcbcbabdbdcbbcbdcbcdcddbabbddaaadacacbdbaccadcbcbacdcdcdabcddcccbcdaabdcaddcadcdadcdcbbbbadcaaddcdcacabddbbbbcabbdbbdabbddabcdaacbaaabbdcdddaacaabbacdcabaacccbdbacdbbdbdccddbbaabaaadcdaaaacccccdcadcbcacaccacddbbaaadaccbdccdddddbbcabadadddcbbdcbbbacddbdcaccbadcdbbdcbdcbcbdcaadcbabccadcbdbdcccdaacaaccaddbcadcaabbacbbddabdabdbacdacadbccdcccdddbcbdbcbdddbccbddbdababdccaccbcdddbddaccbdacdabadbccadaabcdcddacccdbabbbacdbdaacbcabbbcadbaaaaabcabbbbcccaadcaabbcacbbccdaabaadabbcdbbabaaabbbdbbcbabdcbcdadabddddcccbbdaabadccbababcbdadbddbbbccccbdadddacdcccbdbbacbcdacadadddadddcbbddccdaabbcababaddaccdacaadcaccddbacaccccaadcacacadcddadcbccbcdbdaaaabacdbddbabaaaddbacddbccbdddacadbbabccccaacabaabbbcbdadabbdbcbbcdcdabddddadacbaacccddccabaccaaabadcbbcbcacbcacacbdbadabbcdacbddbbabbdcccccabbdbdabbddacdaaddbacdadbcbbbbdcadddcdaabcacbdcbdbcdbabdccaacdbbddcdbcabcacdcbbdabbaaadbdccbbcdcdaabbbbbbdadccaccbcaccbbbcbbadacaddbdbdaadbcbdbcaddcbdbdcdcdcdcaabbcdadccbabccbbbbcacccdbabbaaadbcadbdaacacabcdcabccbcccdddcbaddaaabccccdacadddddabcadbdbbcaccbcdbcabcccbbaaddbaaabacdadcdabddbacaddadcabacdbaccdbbbbccaacacbdcccbdcbdabaacdbadcbadcdbcdbbdcbbdaaaadbbcabcddaabcacabaabdbdcddcdcbcaacbacdaddadddcadacabcbdaadaddcbcaabdcadcdbcbdbadaccabaabaddacbdabaaaddddaabbbcbabbbaccdbdacdcbdbdaccdabbdabdabdcbccbddcdabddabcccdcbdaacadacddddbbdcbccadbaccabbdbcdccacccccaacaacbaaaacdcaccaaaddabaadaadccdbbcdbacaaacdadcdaaababcdddaaaadddaddbabdadbdbdaabaddacaabaabcabbaccbbcbcbbcbabbbcaaddcdbbacbbababbadaddbcccbadbbbbcabcbbddaccdcabcccccdabdccacbadaaaadaadbcdbbcaacadcbcbacdadcddbccbabcaddccbbadbaabadbdbbacdbcacabdabcddddaaddccdbbdddddbcaccdcbddbbabbdbacdbdadacbdcdbbbcabdbbdabddaaabaabaddadcacccdbbabbbbbadbbddacbdbdadbddbadbdadcbdcbbdadccdaccaabcbcadcbabccabbbcddacbdbccbbbdddbadbdbaabdddacdcacddcacddbccbbddbdcabcbdbcbdaccaadddbbacdcbbbccbdaabbcacccbdcddbbcababdcdabdcadbccbccddabaddbdaadabbbacbbdbabdbdcdadbbbdbbadbdcdcadaccbababbabdbcabdbdadaaddcacbbccbdbbcccddbadbaddaccacdcacbbcbabdbcbccbdccaddabaadaccaababcddbabaaaaaddbbabbacacbdcbadcbbdaacbaddccddbcddcbcabcbdacbcbadbcbcbcbdacbbdaddccbcaacbcaaaaccabdadbbbcccbadbbcddacabcabbbcdbddbbbdacdcaabcddacbacdbcdabbbcdcdccdccbddabcddbdcaabcccdbcadcabadbdbdbcccaacbdbccddcabbddcbacabadbdabbaacbabdadcadbddbcadbcacbbdcdabcadadabcabbaaacdbdbaadcbbaaddbcacdabaaddcadcaddbbdabbabcabdbbaddcbdaaabbbbccccdacaddcbacaaddbabcbdbbccaccaaaaacdaddccbabdbbbbaadcccdcbcbdadcaabaaaaacbbbbaaddbcacaaaaccdcaaddcdaddbaaadacabaaaacccbcbaaccdbabddababcddcacaadcdabaacbcacacdadbdacdaddbaadacdcadaccadcabcdcdacdccccccdddbbcdaddcdbaccabccbbcaadaccaccadabbabdadbddbacacdaaddacdbabdddcadcbcbdbddcbdcbdddcdcbacadccdbababdadacccbbdddabbbcbccabadacbbdbacdcadbbcbddbdccdcdddaaaacdcddbbcaacdcbcccabcacddbacadcdbbdddcbbdcccddacbabacaaacddcbcbabccaaddbdabbaabdcdbdcbbcbbcdaabdbdcbddbdcbabdcdbdadcaabbabccccaddcbdacbdacbacaccdaaaddbbabcdccddbabcabbdadabddacdbaccadadacbaaadabcadaabcaaaddcaabcacbccbddbbbacddbcabccbdababcacddbabaccbcbbccacdcaabbbaabcadbaadbbbdabbbdddadbbcccaacacccbacddaccbbcdcbdadaacacbbabccbaddcbdbddacbdcdaaadddabddbdadabddddaabdaccbcaacbdcdacacdadccbbabddddbdbaabbabbdcdbbbdbdaadccdaaabcdccdaaabcdbbbdbdcccbbdaaddcdabcdcbadccbabdaadaaabdadacaabbdabababadccbbadcacaaadccdaccaacbadababadccbdacbdacdcabcdbbbabdcbdcacbbcddacaaacbcacbcccaaddcacbbbccaccccabbcaccdddcabadcabbbcaadacabcadaadbccdaababcdccdbbdaccbcaadbabdcbcbbcbabbaccbbabdddcacaabbaccadcadadaddbdbccdcacaacbcdddadbbcbccbbbbcdadcdaabadcabdccbbcabdbccddaadbababccbbbdcacdccbbcdacbcbccbdbbddddbbbccacdcbdccadbaacacdacaccbdaccbacbbcbcdddbadbcbaacacadbadacddcbdbcadbddcdcbcaabdacbdaaadbababdddadbcbbbdccbcabbbcdacdcdaddcbdcababccdcbadbdbdcaaacdaabacdacddadabcbbadcccaddbdaddddaddbbdddbcbabdbbdacdbdbdccddacdabcccddcddaadacddbbdaccdadbaadcabaddcdaabaddccdabdbdbcbcccbcabdacdcbbdbbdabdbdbccddcbcbadbcccdbcaabbcbbddbadbccdaaaaddccacdbbcdcbbadcacbdabcbdccccbdcabbbabcaaddabcabadbddbbdbcbdbbdadcdbbadabbbdddadcbbcadbabdcdadccadddbccadcdaadccadddbadacdddcbaaccbcbbdccdbcacbabccdcdadcaddaaccaccacaccdbbbbccaacbacdbdccadbcdacbabaddadaddddacbddabddabbacbbccdbabbdddbcadacdaabbddccaacbbbadababababbcabcbbbcdbcbbbbccbaabcdaaccbbcaaaabdcbbbdccbdbabaddbcbbbcbccdbddbcdddccabaacdaaadddacccdccdcbaacabacaddbdaacbbdbacaccaaacccddcdcbcdddaaaadcbaddbbadacadabddbaacbaacbbdbcacadcbadabbaaabcacdcdddcbaabdbadbddbaccaabbdadabdbdabcccddaacaacdabcbcaccddbcbabccbabadacccadadcabdadbabbdcddabdabbbcabdabcdaaccbcdabdcbabbaacbcbabdbbbbdacccacadbcabababbcdbccaacbddcaccbadacddadaddbcddcdbbddbcacadacccabadccdaaabacaabddcdcbbddabdbaaaabaabbdcbbabdbbbadcaccacacbbcbbddbcbcdcdbcddcdccbdaadbdbdbbacaddccccbddbbdbcdccdbadbdaadabcbaaabbcddcaddbcdbacdaaddccacacaddaaaddadcdbacaaaddcabdbcccacddaddbcbcdddadcdadccccddabdabbbdcaddcbbcbaacbaacbadcaadcdcaacbcddbccbacadcdbbacbcbabbdcaaacbdaaadabdddbdbbbdbaddccdccdcbcbabbdbbdccddccbcdcacdccadcaccacdcdbbcbdcacbabbcbbaddbabcdcadbbcddbbcbaadaacccdbccaaabccabadcbdacddccddcaaabbddcccaabddabdbdabadcadbcdbbadacbbcadbaccddcbcdbdccbbacdbaacbddaccddbdadbaacdcdaacacbdaccacdbabacdbabbacddddcaadcdcccbdaaadddbddcddacaadabcdbadbcadacabacbacabbbbddbbccbacabddccddcbcccbdbcacdabaaddadbccdabbbbcdbcdbabcbcadbccbcccadddbcaadadbaddadaaccbbacadadabbddccccabbdaabaccaabcdabdbcbcbbcabbaabbdbdcbabcdcbabbcdcccbbacaddcabaaabdaccccbccacaccdadadccdacacccabccdbaddbabacacabbacbdbbaacdbabbcbddcaaabbaccacacdaccccacccdcbadbacbcaccaadcacdbcbadabbdddcbbbccaacbddbbbbdddacabcbddbbcbcdaadccbdddddbaadaacaccbbbdbbcccbdbdcdcaddccaaccbaccddbabacdaddabdaacabcabcddcbcbcadadadcbcbccaaabdccbcabddcdcddbdadabbccdccadabdbdaadaaaaabadcadacccbacabdcbdbdbdbbdaabcdbaddbdcabdbcbabcccdbcacdacbbbbdbdaacbdccdbcccdbbdcacbcdcbcdcaabddccdbbaacdacadababcbabaacdadabbcbddacbbcbdcbcbdaadddcdcdbdacabcdacbabdbaacdaccdcbdccacbaaaddbddbdbcbbcdabaaaabbdbbddaaccbaadadacaabcddcdababcaabcabcdababcbbdcababbcbabdabaabbbdbccddbadabadbcbdbbddbcdcadabbaacdbadadabddccabdaadccaabcdbddcbacaaacabcbacbcbbcdcccababcddbcccadbabaadabdcdcccbabbbccccababdbacdddadcdcdbdcbdbbddcaccdadddaaaabbbcddddccdcaddabaccdbdcdbadbaccdbdacadcaaccddaddddbbbacaabdbbcaadacbbcdcdadbbdcbcccbbacddbadcabbcddcbaacdccbdadcabbadddbdbadccdcdbcbbbdcbabdabababcdbdcdbadddabbcddcdcabacdbabcddaaabdcccdccdbdbddcaddbcbcdacddacaaabbbbabdcdcaaadadcddcbaabbbcdacbaaacacdddadcbdbacbcdddabccdbcacdadcabacddbabbdaacdbaccababbacacaaccccabccbbcabccdcdcdacacbccbbadbacabaaaccadbabcdbccdddadcdbdccbcadbddbdacddacbddabdcadadbcccccdcdbdbadcddcddaaacddabbdacbdadcbdddbcbbabababbddadcbbbcdcbbaaddddcbbcbabddbbacbdcccddcdabaabbaaddcbabadbacbadcddbccccbaddccadaacbbdcddabbabbadadacdaaacadacadbbccadccdaaccbcddabbdadadbdbbbdabdacbadcbcddbbdaabddaacdabaccbadbbcdadbcbddcbbabbbdcbbacaacbdcbdacdcbacdcbbdbcadcdadacbccbdcbcbbaabcadccbabcababbbdcdbaabcddadddbbabbcbabacbdabcdabbbcbcbbbdadabcabcddcbcccaadccbaccacaaddadaacccdabbcadabcadabbbbdcbddcaddbdbddacdcccdbdababdcabccbccaaaddcabbbbdbcdcdddcbbcdabbacadcdadbaddacadccbaadadcbadabdcddbaadadabadcacbdcabcbbdcdadadccddacaacddcdbddaadccacaaaadcacbcbabbaabcdbabcabacbbbbbaaabbdcaadabadbdbdcdadbaddabdaaaddbaacdcdcbcaadddbdbccabcccbacccbcdbdcbbabaadddbdcdbccbbdcdabdccdccaddababbbdccdcbccbbdbcccbddcdcadacdaabaccabbdaadacadaaacdbaadbbaababbadbaacabaaaaaddadadbcddddabbcdbdbaadaccbdbdacbdabbbacdbddbbdbdadbaadccdcadbacdacaabcbcadacdcdccadaaaaaadadabbdcbcaadaaccbdbddabdaacbdcccbbdcbdadcbdbbddddbdccddbaadbcbadbdcbdccabbdbddaaaabcacabdbabcadaadbdbdaccdbbdccccdacbdbadcbdacbcbdacbcdcbbbbcaaaacbdcdbbbbddbcbcabaabcbbaaaacdcaabdcdbbabdacddacdaddbcbbccbcaccddaadcbcaacbabacdcbdcacbcbcdbdbdbbddbcccdddcbaabcdcbcdbdbaaccbacadacdbdaddaabcabdccacdaddbacbbdbcacaddbaccdabdccaaadcddacabddccaddbacdbdbdbdddbcdbdcbbdccdbccbddbbcdcdaccdcbdabcbdabcabaacdbbccdccdcdccaaabccdcbaddcacddadabdccadbddcbcdccaaadbbbcadccccbdcacdcabdcdccbddbbaccadbabdcbabbddbcbcbabcdddadcdcdbbcabbcddcbdaabdddadccadcadacacbbbdddbcdacddacacdcdabcbdadaaaacbddacddddbbadccaddddccbccdddcaabdcaacacdabccaddcabdbaaaaaaaaccbccbbaaabadacaabbcbacccddccabbdbbccbaddddccabccccbaadcdacbbdcadccbaacdbcddbacdadbdabdadabacadccccacdcbbcadcdcadabbdaabacabacababaabcdcdadcbcbabdcbaaccdcbacccdbdccdcccacbbcadaaadddacccaadbbdcaaaacccadccbcbbaabdcdddabbcddadaadcbbddabcaadcccacaddcbcbabbbacbccbaccdcbdcddcccacadcadacdabbadacaccbdabbbdcbcadabcddbcaacaddabcbcbdbabbacdcbbdabadabbbdcababbaaaadbbddbadabbdbdabcaddbadadaccacdbdcadbacacddbcbdabcbbaabadcaddaaccccbbbaacdbcabddbcdaccacabadcbcddadbcaddbcaabbaaccbccabbbdadbdcdccbaadabcccdbdaadcadaabaadcccbbbbdbdacddcbdbdccddbdbbbbadcaadcbbccadccdcdbbccaccabbaddabdccdcccaaadabbcbcbdbcbccbdaaacdbbbacdcdcbbcccaaddadabaccbcabaadaadadacdcdaaaacdccbbacbddccaadbaadbccadacaabbccbaacdaacadbbabbbcaccbdcbcdadadcacbadddcdcdbbbdadbddcdbbcaacabccabcbacadcccaaabcdaadddcaccbbaccbdbdcdacacbdbcdbdccbcddacaaaacbddaaabddcbdadabaacccaadadaccacbacacbcbadcacdcdcbddaccadacddccadabaadcbabbbccabcbccacdcdadccaadbdbcbbdcabcbbabaabaaacadadcccdaacccddddadcadacdcbcabbaabdadacddabdbbddbdcccddbdccbbaccbdcbaadddadccaacdaccdccbcbcabccdcbcacdbddccadacdacddccadccbcccaddbcabbdcdadcdbcacbdabcdaccbbdabbddbadcdaabbcdcdbacababaadcbacaadbbcbadccbadbbbddcbabbdbadbdcabdbbbaddcaacbdccbbcacacdcddaaaaaaccbadbdbbbbaddcbdaabadcbdbdbadacacbacdbddddbccdabcaccdccbcdaccddacdbddccdcacbdadaccadccabcbccbbbdbabdadbbadaaddadacccbdddabcadbbccacdcaaccbdbbbdbbbccbdccaacabccbccdacbddccdadaaaaddaaadccbccbdacbbaaadadcaabdabcbcaaddbcccbbdbaabaccacbaababcbdbcdbdacbdbabadbbbdadcdbdcbbcabcbcaaaaabbcdbcaaacaadbdcccbcabccabadddcacbacdadbbcbcbdccdbadaacddcdcadbadcdcdbcbadccccdacaddabdadccbdabdbcdaacdbabadbabdabcdbdabaddabcccbbdddbaddddabbccadaaadddcabddcbcaaabbbddadbadcacadbdbbdcdabccabaadbcddbabadcbbcadcdaadcdbcdaccbcddcdbcdcddadddacadcdcbddabcbbdadabbacdbcccdacadccdaadaabddbdbadaccccccbcbdabbacdbbaadcadbbaccccabdccabdbaddbacccdccabdcdccbcbacbbbbadadcabddcabbadabbbcccbcbcbdccaddbaaaaabaacdcaaadddccbddaddbbccddbacccbacadacaabbbabcabaabbcaaacadcbcbbbbcacbccdacdcdaaddcddbbbcdadaadddbacbdacbcaaacbbdbbbcbbacdbadbddaabcdbbaccdbbcbdadaabdcbbcbbcdbcabcacacacacbabccdaccbabbdcdacbbacbaadcdcabdcdbabbdbadcdcabcbaacaabacaccbbbadddccccdbcacaadbdddcdbaddcdbddcabdadadbaccdabcbaccaacbcbacccdddcbaccabcdabccdbdbdacbbddcbbdadbccbdcddccadbdbddccacabccbdbccbadbaadbabbcddbaccadcbdcccadbaaddadbadcdaacccdbbaadbacbaabccbbcddbcbcaadabdcbbbdbbcccbddcbddaadbbaacaddddabbbdcacccbbbdccaccacddabcaabcdbdbaaddabcbabbaccddbcabcbccabacdddccbacabbbcccbccdcbcbbccbadbcacbdbabaabaddcadacababacccadcbdcaddaccadcaddcddbbbddbcddaccadddacbcacbbcbaccdcacdccbcbaabacccccbbbcbdbbbbaabadaabcbacbbdbddccdabdadabdabcdbddbccbacccacadabaaacabccbdccaacdabcbdabaadbdbdadaaccdbbabcabdacdacbaaaadbbddaabccdbdacbbdddbdccaccccaabcbcbdadbcccdbbdcadcdbadabbadcabcabccbddcdabcacacacdccacabdbddccbbdcaddcbbcbbadcacddcccbcadbdcdabcdddbcbbcdadbbcdbacccbbdccbbcadacdcabdbaddbcbccbdbbdbbcdcdbbaabddbdccbcccabbcdbcdcbccbbadcbbbbbccaacbdbaabbddcbdcbabdaaccdccddcbabcdccdbcccccbddadddccacdcdcbcdbbbdabaacbcadcdccbcbbaacbdddbdaaababcaaadcabaaddabddbcbcbbcbdbabdddbaddcdaaacccaababddaddbcadbbcabacdcbcbcbcbcbbdacbdcdcbbbcbcbdcdcdadbbbaaddadaccacbbaaccdbbbcaaccbacdccdbabdadadddaabbdacacbaabbcdbbdbddbbbcccacdbcbbbbbcbadadadaaabddcabbcbbdbbdaacddbcbbccdacdddcbcaaadccbababdbddcccabcbcbaaaccdabbdcccccdddcadcbbabbbddbbadadadbaaaaaacacccdcbaaaabcbccdcdbdacbadadbbcddcdbcdddcacdabaabcaacddbcaccacbdadcbdaccbacaddbaaadbcbdbabdddbaabbbccaaacdbbddaddbadbdcdddbbcbbddbbdaabcbbadbbdcaacbaaccbbcbaabcccacbadbdddccdacaadbabadcacdaabdcabbbcbbcdcacccadcddadbccbaadbddddddcabcccbddcaacbdbaacdcaababadcadcddccaacacbadbcbaacbaccbaabcdcdbaddcbccdabbbabcbddaaaabacbbcdccdcdbddaacabddbcdbdaacdbacdcadbabadcacdacbcdbddacdabaaccbbcddbcdbdcbcadbdaacbbbabbbaaddbdabadbaccbdbcbdcdbcaabacdaddccddadcdadbcacbaddacdaaddddbcabcadcdccbbaabbabbcbcbcbcaaddccdbbddcdcabaccbcbcaaabcdcccadcdacbabdabadababddbaddbcacbcddbdbbbcbadcccddddbbccabcddaaacbccdcadcbaaaaabdadbaddcdaccbddccacdacccbcadabccaaaccdadcdcdcacddaacbdaacbbddbbbdbadbdabadbbaddacbbdcbdccbbbcdbcabadbbddbadabaccbcddbddbaadacadaaadcdcadbdcbbaccaccababcbbdacbcbabbbbadddccdabbdccccbdbbccabddbdcdccadccaaaadaaaccbcacdbadbbdbbadacbbaaccddcabcbcbacbdbdcaaabcbcbccadbcdaaacdbbdddaddbbcbabdddadddddbbdbbbadbcbdbbcaaccdbaccbaddbabdadacdccddcbcbbdadddcbddcdadbdbabbdaacbbbbbdbcdcbbdabbccbcaacccdadcbbccbadcacddbabbdcaccdbbbbbdadbccaddccbcddbdcadccbcdddbdcaadacdabbadbbbacbbaadddbcabcbacdcccbdcbabbdbbddcdcabdbdccbcbbadbdcbddaddbaaaccdaabccaaaabadabdbccbbcbbaabcdadacdddacddcbbacadcbadcdaaccbaaadcdccacccbbbbabdddcccbdbcbaaddadbabdbbcbdacccddbcbaddabdabccbbcdacdcdcdacaddbadcabdaddbbdbdaddcddadabbdcdbdbdbdaccadcabcbcaddbcbcdacbacadacabacbcabdbdaacdccddcdcbccaaabdbbcabbcabccbdddacaaaddbdccadabbabddcdcabaabccbbcaccdbdadbdcaaadbccabbababadadadbabccdaddccbbadbdcbdbadcdddbbdbdbadabbbabaddaabcacdcadbabbabcbcbadcbaacacdadcddaddbaddddaccadcbcaaacaadabaccccddbccddcaddbbabaacdaabcaddadaddaadaccccdcaaccacbcdabddccbbcacbdbcdcbbccbdadbbacddaaacbadcccaabbabcbdcdddacbcbdcbbdcabddaaabacabcbcadbdcadacacbdacbcdbdbadabbccbdccbcadababddcadbbcabacdacaccdabccadbbddabcaddacddbddaddddcdbddcbdcbcdacabbbacdddbcabdaadbccdbcbdacdadccabaabdabacbdadaabddcdadcdddddcdbcbdcbadddcccabccdbabbdccdbaadacdadbddaccbbbbcdcdbacdccdaadaabadbddcacdbadaadccacbbadbcccdbcadabbcdaaccadddcaacbaabaaaabaadadddcabcbbdcdacaadbbdcddccccdbbbddddcdbabcddddabacacdbcdbdadbddabdbcacdccddddcccddddcdbccabdbddbbacadbbaadcbddbacdcbbbaabcbdaacddcbcbddcddcbdaadcbaabcbaabdbcbbbdabbddcdddadcdabacccddabaddddbcadbbddcbacbbabcacbaadcaddcdcbcdabdcccbaaaabacadbccaabbddbbbabacdcddacbcbaddaadbcacdbddadcbabbadddbdcdbacdcccbadcdddbabbdcbbacbccccaaccabdcddcabdccddbaccdbbbcabcadcbdccbdbacdccabddddadcbcbddacbabbaaccbcdbbababccccdbcddddabbbbbdaaabdbbaacccbaaadbcbddccbbdbdadbddadbabccdcacabcdabcaaddbbcabddcabdabcaaccbacddadcbcbbbacababbdcadaadcddaddbabddcdcdcdaadadddcabacbacdcdcccbadadcbadaaabbccbdcdbbcdbdabdbddaccbadddaaccaaadbddcaacdddddacbadacaccaddddabbacbbacccbdbccbcabacddbdadbadabaabcadadbbbbdabaadcdabccacdabcdabadcbbcbcbdcadbcbdddaacdbcaabcddcadcbccdbdcccaddadaddadddbcccdaaccbddbcacddcbababcadbbadaabcdadddacbddbddadbcdcdcaaadcadbacbbaaaabdcdcddddcaddcbddabbbadadabdccacabddabcbcdddbbdcadbcdaccbbcaacbdacddaacbdadbdcdcbdbabcbaabbbcccbddbabaadbaaacddccdbdddddaddaddcdcabadcdadbbccabccbbadaaaacbccbbdcbadcabaadcdbacbbadaccaabbdccccadcddaaccbaadcdccccacddbddbccbcdabadcaaaccbbdabdcdbcbadababbbdbcccddbdcabcdbcacaccddacbddbcacdcbbaaaaabcdcdacbbabbcbadbdbdbacbcdbcaabcaabdcbabdacadddbcddadcacbddacbaddaaacbcacaddcbaabdbddbdccaacadaccbddbccdadcbdcaaacccbdadaabaadddbabcbcdddcdcaadadadbabdbdddcaaabcdcbdaabdcbdbabccccdaaaaddacdddbcabdddcacacdddcaadacaadabadabcccccbcadbaaadddbdaccdadbcdaaaaddccdacdcabcbdaacbaaadcabaaaddabaaacababdbcadddadccadacacbbaacbccbddcbabaccbadababadbcadabdadcddccdcddbcbddbcbccacdabacabdbbdcbcabcddcbbcbbbbdacdbaadbbacbaabadbacbcbdbcdddabdccaccadcccbdadddbbaacbdccdaaacacadadcddadbcabdbbccadcbbcdcbdadbabdabbccbdacacbcacccacbdcdbddddccddcabbaddbbdbcdbaababbdaabacbddcacbbdcadcdcaaaccbdadcaabcbdadaadbcadabaadddddddcdccbdbdddaaabdbddcccccdacbddabcdaddcabdaabadcbcababccacdcbbdabccdccdcbddabbadbaaadccbabcabbbcadbadadddabcbbbabacbcddcbcbdbddcbcababacbdabddcbdbddadaaabbcbdbddbababbddddcdcbccaaabcbbbaaaaadbdbbbbdddaccbdccbdcadcbbdbccaddbacccababaaabbaadbddddacdccabcbbdadbaddaddcdaacadddbccadbccdbadcdcabcabcabbdcacadaadbdcbabbabdaddbcbaccacaaabdabadbcccdbcbdabdadbcdbcbdbcbbccccdddbbabaddcacaacbdaccdcbbcadbadaaabcdabbdcdcdbbdcccadaccbdbdcacaacbbacacabbdcccbdcabdaadcaadbdbabcbcabbbdbaaccdaaaccbcdbcbdbbabdbdcdbcbbdbdcdcadccabcbaadcdcdbdcddbdcbbcdcddadcbddcdcbbbbadbdaabadddaccacadbbbcacbdbbadaaccacdbbcacbdbcbabdbdbbbbccbcddaadaabbccabdbdccdbdcccaccdcbdbbbddabdacdbbadbabbbcbbbbccaccddbabacdbbaababbddccabbaddcaaccbaccbccbcddaabdcaddaccaaabcdcddcbbcbacbcabcbdabbccacbaccadabadcdbdcdacdbadcdabdcbcbbbbdbbbaadddcdcadcbabcddadddbddcccbaadacaddbdddcaacabcdadcbbbaabccacaaaaccadddcabdbcabdcbddcbdbbbddaaaadddbbcadbccadddacbdabaadabadddbacadbadcabcababbdcddaaaabddaabbcbcbddadadbbadcdbddccbcaddbccaadadccaaddbbaacbbdabcdcddddadddcdacadddcacbcdbcdbadadcabbddccbdccccbadbccddbbcadaaaaccaddcacdabdbcddbabdbbcddadaccdbadbacacdcdabdacbdbbdcabcbcaaccbcdcdabcacdcadccbdcadcaadabbdcacabcabdadabaccacbdccbdbbaddccbbdccbbadaddaabdbdaaccacacadaddabcdbdaadbdcabdcbadddacbcbaaaabdddacccbadbdcbbaacdcacbabdcdbdcbbabbbaacbbdaaaddcbdbbcabbdddddbbadcbaacacccabbddbbaaaabbdddaddacbdacacdcdccbbaacaaacabdccabaacdbcdcdadbddddaabbcbcadadbabcddbbcdbddcbcbcabcdadabbbdbacbcccacadbddcdcaccacbddccccbdcdadabddddbbaddacdccacbcdaaddababbcbbcdbaabdbdbbdbbaddadddbbadcdddcbdddaacabdcdcdcbaaddacabaadabccdbcabaabcbaaaacacacdabbaaaddccacbbadadbdbcadcdccbbccbcabbaddbbaadcbcdbaddbabaccacddabdaacdcdbdccabcdddddaabcdaacabaadcbacbccbccccbbccbcaccccdbccabdbcddcdacabcddbdbdacadbcadaabaadadaabaacbabccddadcdbaacadbbcabdcdcbbdccbbadbdbaabdacbcabbdabbadabbdccbbacdacbbbabaccaddcacbaddcaddbcacddaacdbdbdbbdcdcabcbbbacdcaccaccadbababcddaddbcdadadccbdaabadcccaacddbbcccccddbdddbbdaaaadcbcdadbdbcdadacadddcabcbbaccdaabbddadbccacadbcabdbbdaabaadacdccacdcbcadcddcdbccdccadbcacadbcdcaddadcbbadcccaacbcddaabacdcbadcaacabdabbbabaaccdabbdddbcdbdcbbddaccddcbdcdabacdbbacadcacbbcabaccbbbacccbaaadcccccbcdddabaaaacdbbacacbdabacaadadbbcabadcddcdaacddbabdaddacbdcdcdaacbbcbccadabbdbcaabdbacdccbcabcddaacabbaadacadabcbbcdcdcadbdaabcbdbdcdccdddccddbdaaadabbaaacccaccaacaacdcbabcdddbcaaabbccaaaadddadbbdddbccacdacbcdbaacdddbdaacdbccbccdcbcacbdbdadbcbabacaacbbddbaacccbdbdacadcbbaddcacdccbdabcdbdacabbdbddbacbddddaaabdbccacdbacadcabbcdbdcbddcddacbbabcbcbaabaddcbbbbaaaabcbbadabbcdacbbcbccdbcaadbdbdbacdadcdacbcbbbbdbddcdddbdcdadacabccbdaadaaacbbacccabacaccbadcadbabdcaccdddacadbbcdcacbdddcbdaacbddcdcadcdabcddcccbbadddacadbcddcacdbabcdaccacdbabaabadbbbbabadaaadababccaadcbddbacdbcdcacbabcacaacabaabbcccbbaacbabbdbdcdbcdabbddcdadadacbbdbcaadaaacababbdabaacaddbddcbdbcbbcacdbbacdcbcbbddcdadcaadabdbabdccdbbdcdbcabdacbbcadcddbbddcacacbadaadadccdcbdadaacdcacdbbcbaaacdbaccbaddbcbdcbdaababaaaaddbabdaccdaabadaabdbbddbcadcbaaccccbaddbbababbcbccddcabdcbbdbdbcbbcbccddadbbaadbddddacdbcdabacdaaaaacbdabdabcddcbadadabbdcbbbdcccbdadacadbcdaaddabccbbdbcbbbaddcdabddbadddacbcdaadbdcabbdadbcccddacdcbbacccbbcadbbbdddabcbdabbbbcdccddddcdbdcabcadaadaaabacbbacabaaaddbbbadaabcdcbcabadbbddccbcadbdbdacbddddccbccccbcdbcdddccabadbbacabbcccdacbcdddddbdcbcbadbccabcaadddabcadcadadcacdbdacabbabbdccabccbbdbadbdbccbdddadabadabbcccacadbdcabdbadcdcbdaacacdcaadcdacbaadacdcbddcdccddbbdcaaabaccacadcdddaaadabccdabdcccabdcaabbadbdbcbaaddcddcdabcbcccacdddbbccdcddadbcdabcdabbbbddcbccbbdaddbcadcdbbbbabdcdbdbacbaddaaabdbadadcdaaccadbcbbdbcddaabbdbcabcddddbbaabadadddacbdbaacddcdcddcbdbcaaadbdbdcdabddbabacdccabdadbadcaccddcacdadccdaccbaadaccdbaccbcdcbdbcacbbbaababdcbdbdaddcddacdccbbaaababadbbbacbcaddcadacadbabdbcaabdbcaabacdabbdddddcadbcbcaddcadbaadbbddacccadbaaccbcdcdbadccbcadbdbadacadccabdddddacdcbdcacccdcbccbbdccdadaddbaaadbdccddcbaddcdbdcbbaabbadccdbbbcddbacdbabddccdaadbaabbabdcdcbccadbbbadabbbbcdabadcccdacdccacccbdacdabddbcabbcbadbcacddbadcacbcacbcacaabcdbcdbdbbbcbcdcdbcddadcdabaddbcbbbabdabbcaddbcccbadabbdaaccababdcababbdcbaaccadccdcbccbdcdbbcddcbbcdcbbddbdbaadbbbbdbabadacccaddcacaaccdcbbaccbcaaddbcaaccabcacaacbacacbdbcbaadaadcdaddacabaaabcdcacaccaabdadcdbbccabdbddbadbbbbabbbcdbdaadaadbccddccdddbbcdbbbacacdabdddcadabbaaadbccaaacdbddadbcbbadadcbddabdbadddbabbcddcbbdbdccaabdbadacdacaccadabcddcdacbcbcbbdaabbabbbbbaacacbdaaaaacbbcbdcdcbddaadbacbcbcbbddbcbbaddbacdcacdbacdcbdbaadacabdbdbadcadbacadacccacbbcdbbcbbbdbabbccbdbdddaabcdadcaadddbdbbabccccdcbdcaaaccaacdbbbbcccdccbccbdadadbbdbcbcdabcacdbdccdabdadcccbdcbcacaaaacbacaabcaacdcccaccbcccccccacdbaadadcbdcdddbdabdbcabbcaaccaaccdaddbcbbcdcdcaadbbabbdcdcdbadddbcabcadbddcdbadaacbccaddcdbaacbacccbaacbdbaabddacbdadccdcabbacbddcddacddcbbcbcdaccaaacdbabccbcdaaccbddadaadaadbdcdacccbacabbbbcccbcabbcbbabcbdddbbcabcacdddcdcabaabdadadcdcaabdbcaccddddbbbdadbdbadacdadbdadbdddabbbcdcbbcadbdcccdcaabaabbaaadabddbcccdbabcaacacaccdcaabdabbdadcacacabdddcdcabdcbbaaddbabbbcdcbaaaccbbaabcbddcaabaabaaddaaaddddabdcacbaccaabbbdbdcdcbcaddaadaabdabddbadbddcddcdbaaccdcdccaaaaddadbcbacbadbdaccdcbadcbacaabbdbadadabcacacbddbcdddbcaabcdbbabdbdcdbbdbabbdadcddbcddcabdbdcbddabcbadadcaabbabadaaadaacdabbbbacbabcdcbaaaabaacaccadcaacaabbadbacaacbabaadaccbbadbadbcbbcbaddbaabbbdccbccbbbbcaaabbababdadadcdbacdbcdbacdaabcabcadcadcdccbdddddcdcacbabdcaabdcdbabaddbddabdabcdaaddabacbdaabbccdaaadaaccdcdbadbcdddbabacbdaaaddbdbbcabbbddcdcdaccbadcadbdbdccabaaccdcbcdcabcdcbcdbcadacbbbcacdbadabdbcaaccbacbcacaabcbaccaddcdbbbbcaaacbcadcdaadabdadbaaaccbaaabadacdccccbdbdbbdcaaccccadbdabdbaadcddacbcdbcbccddcbccdcbbbdabddbdabaccbadddadcadadccbcbdabaaccdabaabcbcabccbbabbbababcdcbadaaccaddadbdacbaadaadcdbdbdbddbccbdacaccbbbcbcbadddbaccabdadaaaadaacbadabaddcabaacdadbbabdcacbbbbadadbcbcaddddcbdddacbacadddabddacdccabaadbacdddbaacadcdcbdbbddbdbbaddbaabbdcdaaadbbbacdbabcaabbdbbcaddacdaddadbcbdbcacbadbdddddabbddccdabbdddaaaddbdbdaaaccdabccdcddadacbabdbcacaadddddacdcddabdadbbbabccddcabbabacaacbabbbddcbcbcbcbdbbbcbcbaddcbcccbbaadaccacdaaacbcddabccaaccadbcbdbababacdbcccaaacaabcacdcaabadbdbcbdccabdcccdcdccabbdccaabbbccbbcabacbcbdadcdccabdacadcdaadcbccdcbdbdbdcbbbccbccdbbdddcbccbcaabcabdbccdccccbbcdacdaabcbacdcaadbbcbdbcddbbbabadbabbcddbaadbdbdabbbbbbaacbcdadabdaabdbcdbbccddbadacdadccadbbcbaabbaabcdccbbbadcbacdaaabbbaccccbdcbdcdcacaddcdabbbdcbaadcccddacaccdccbabbdadbabbcbdadcccdbbbddbaaddacdabbcadbbdbaddadbacaadcdcbdccabcccacccdcaacabbaababacaaadbbdbbbbbdccccacbbaaadbaadacddacbcdcabbabdcbcbddcbdbbdbacbdbbadaabbbabcdcdaddbaabbdddcaababdaaccabbaadcadccbbadadcacdbbcdaaccdaadbcccbacbddacccbacbbaddabdaacbadcbcdcbdbbcdccbadabadbacdbbbccddbcbdaadacbadcbcbdcabbbdbbcaadddcabccddbddbcdbdccdbdddbcdcdddcbbcaccdbadbbadcaaaabdacccdcbbdadbbacdaaddbdbadaddcbbcddaddccabdcadbddbbcdabbcaacdcbcabbaabddcaadccbccacdcabbbdcaacaacbaaaabbcdbcacabdcacdcdadbdabbdbbabbdddadabdbbcabcdabbdddcacddcaaadcbbadcabacbbcaaabacbcadadaacaacbacbdcbcaacddaacacbaadcdaadbaacdacbdccabcadbbccdcbabcdbadcbacaddcbbaaadcdcccbbcbddbdcabdcaaaccdabaaccbcbbcddbdbdaacbcddbbbdcaccabbabbcdddabcaccbcddacbbcbaabdbaaabacdacacdabaccacadcdbbccaccbbbcdcaaadcbcccabaabdacddbdcdddcabcaabdbddcbcaacdcbdadcdbccdbaaadbccdbdaddbbcccdabdadaccaadabdddacbcdadadcdccdbbcbdabdbbabadabdacaabdbbbbccaaadcbaddccaabdbdccccabbbabbcdbcadbdcacdbccdaccddbbcdccddbaaccdbacbdcbbbabbababccacdddcbadcadabcbbcdbbccacddaadbadaacabdbddacddcbabdacdcdcbaccdaddbcbdadacdcbbcccaccbcdccabadbbabcaaadcbccddbcaddaacbabdadcaaccacbadbaddcbcbcbabdcbbdadcaacbabdbadaaabadaadbbabdbadddcabbaadacacdcbdacbcaabbdadbdcabadbdbbcbbababccbabbdabbadcadbacbbaadaabddbcadccdbbbbbcbcddccccdabbdcccabdbbcaabcbadbabdbddbccdcbdbcdcbddbbaacdaddcdadddbbbdcdbdabccdddbbcbddacccadddbccdbabdaddaadabcaaddccaadcaadbdddadbcdbdbadcbdaccaacbbdabababaaacbbabccaccbabaabbddbddcacddadcbadabadacdbabcdcccbbcbdcccadbaaabbacbbbdadccacdddddbbdcdcdaabadcddddbccdaabdabdcdbdccadbcddddcbcbdbbbcdbadcdddcadbbaabdbdcbcdcadccbadcbcbccccbbadbcbdbdaaadaccdbadddbabbbddadcabcabdcbadbadcbdccccdacddbabbabcadbcaaacdbccddadaccccdccbddadbdccccabadabbbbbcbddbddadcdbdbccacbbbddccddcbbcdcacbdccabdccadcccbbdabcdddbbdabadcdbccbccdadcaabdabacadcbcabacbcdbcbdddddaaadabddbccdccbdabaddcaaccadbadaaabcbdabdcbcbdacacdbcacadbcabcbccaccdcbcddaadcdddcdccadababbdcddbbcccadbbaccbdcbcaaaadaccdddcdbacddabdbcdddddabacdaddccbddddddaabdcccbcddaabddbbaddccdaddccbaddcbcadabbddabbabadbaacdcdcbccddbbacdbdabadbcbbdbbaaadcbdcbdcbddbaaabacdaadccbabadddbbabdadaaadabcddbacdbcadccbbbadbabbabdaddbbccaccbdcbcbabdddccadcccbbabcccddbcbcbbacbbdddbbccdabbdcbaababbcdcbcbcdacbbabcdcccacdcdcddddbbaccdcccdcdaaadcbbbdcbabadcddaaaacbababcbbcabbacdacbbdbdadacccaaddcabddcbacbcaadaccacbbabbdcabdddabcdbdcacdaaacdadbacccdcccaaacbbddbcadbabddbdadcbbcaccaabdacddbdaabbaaaacddbbcaaacbdddbadcadaddbadccccbcaacbcddaaadcbaabdabdcdccbcdcccccacdabaccbaddcdddbdaddbbbbdaccacacdbaadbdaababcbbdbbccacaaccaaaadadcbbabacadbcbddbbbbdaaaadbbadadacabadbdbcbdbbdddababccacdccddbadacbdaaaacaccaaabaabadcddacdbdcbadccbbbbbdcbbcdbadadbdabdccccaadaddaabbcccdaadcbddbcadbbdcbaddcaaaaccdbdddbbddabacbccaccaaaaddaddbaabbbadbacbaddcabdbcadacbddcbadaccaacacccadabdcacbbadddbbdadddaabddbdabdddbcacdaddbdaabbcdabdbcaadacacbccacacddbdaaaddabddacaacaabcbbcadbcbbaaadbcdadbdadbcdaadbcccbcbacddacaaadbbbcadcdccaabccbacbccacccdbcabaccdaaaaabdddaaacaabbacbdbacbbcaddcdadbadbcdbccbcdaccabcabbbcbaadbbbaaacdaddbadcacbcacabcdddaddbdbacddadabaaacaccbbccdbbcdcbadaccaaabcdcbccadddddaadddcdccacbcaddddadcbddacacdbaacdaadbcbdabdabbcbccabdcdcacbddadcbdbbadcdabbaccacbbcaababacdcadcdcbdbadccdbcbcaadcddadddddaccbddacdbbacaccbcbcdbaccccbbbbbdccbccbdcadbdaccbdbdcbacabcdcbbdbcbacdacaacbcaacabbdaaccabaaacbadbabddabdcacbdcadaadadaababbcbacabbadcdcbcadbdbdbbaddbabaabbaddddcdadcaabcdccbcabdbcadbcbcdcdbddbddcadabdaabdbbdcdcdbdbbbdabdcbaccbdccaaacddcaadabcbccaabdbbdbbcaabcaaccccccbdccdccaccbbdbddcadababddbaadddcdaacbddbacbdbbabdcdcbadaaaadbdbbbdcccbbddadadacbabdddacccbcdadbddcccbbbddaadbabacaccdcbadbabdbcaadadbcbbbddaabbcdcababdbdaacbbadabacbbcbaaabcacbabdbddbcccbddaadddaaddcabadbbcdcbadabdadccdcbcabdbadccbccdccddcbdadbbbccdddaaaabdbcdadadbbabccbbacbaccccabacacdbaddbbadabdacaadadcaacbcbcddaccdbadcacddbbabbcadcaabbdbcbcdaaaacaaccbacddcdccbdbdcacacccadccccabdccdcdbcabcdcdaddcdbcbbccabbbaacdaddcdcddddabcbaccacbcdcbdadcdaaabaddcddaadbdbadbdbdabdbcdabcbccbcddccacdadaadabdbabdadabbdbdacccdabbabdaaaadcdbdddbddbbbdddbbddaccacddbbcaaaddacadddcddacddcbbdbdadddaccbccccaaadccaababbadabbacdddadabccddcddbbdbbbbbcdbcadacadbbadbcadbbcdbdcdbdbcabaaabbbdabcacbdabccbabadadbccabcddccdbbacbbbdabbaddcbaadaacbbbcaacdaaabcbcdaaccbaabcccabaddbdddacbcabadcdcddccabacacccacdaaccbbdabccacbacabacbdacbdbcdbdadcddacacbbbbabddcaccaadadcabccdadbaabbbdaadaabcccaadaaacccaadbbdacbacbadccbcabbaccdbbdddbbbbadbabbaabbbcdccbbdcaddcbbdcddbdababddbadcdbcabacbcdaaaabcbccbddabbadcbccddbbaaddaaabdddbdbdbbbdcdcbabaaabdcacbbcbacbbaddbddbbbcccaccdddccabbbdbaabcaacabbacadbcaccbbbadaadddbdbbcaacdbbccdcbdaadaabacaadbcadbbddbdabdaacccbccdbcdcbbbccdcbdabbbbbaddcacbbbaacdddcdcccdadbbabdccdaadcababbbaacddcdadadbaccbdbadcdbacaabccccddaddbaaaacdaabbbdbadadbdbadcbbbbcdbbdcaadababdbbbaccdabbbbbbbddacbdabccabbbacbadddbabbbaccbdbacacabcabccccddcbbbaaddaccabccbcdcbcacdccdadbcbbabaadcccaccbcaacbcbabbabadcddbbbcbaddcbacbbdadcbdcbcbdabcaaddcbdcadbcdadccbcddadbcddddababbaacdccbadabadadcaaaccaddcbcddbbdbdaaaccbaacdccbbdbbdddbdabdabababbcadaabbacbcdacbbbdccadaaadaddcadadacdcdaccbccdcccddcccbbabccadbdddcaaadcbdaacbddbbbaddcddccacddbbbacdabaaccdccbaadcbdacacadddbbddbbdbcccbaddaadacdbdcabaaabcccdcbdddaaacbaaabcddacdabacadadddabaccaaaacdcadcddcddabdcbbadccadddaaaccdbdbacadadaaccbdcdababdbdaacbaddddacbcaccadccddcccdbbbabbcaaaaabcccbaacddcbbccacabadbdabddcabcbdcacaddcaacadcadadabacacaaacdddaddccbbadbadadadadbacadcaadccdaacacdcadabdadbaadbdcaabdbbbdbccadccdabaaddcbddabcbcccadacdccacdccdbacdbbbaadbccaaabddabccaddbcaabdacdccdcbbacbbcbadbbaabccaaabacadcddbcbabababbabbaaabababaadadcadcccbdbaacbbabdabdbdddcaaccdccbabdbcaaaddcbcbbccbdbbaabdbcccbcaadacbdcbbdddaadcbacdcabccaccbabadddccacabbaaccdaaccadccaaacdcabcdabccdcbdcbcacaacbbcaaadbabcbbbaddbbcdbdbddbaacabbaabadaddcababccdbabdaaaaabcabbdcdabbbacaacdbccabddbaacbbbddcbcdccdbcdaddbbadbbaabbddaddcddbcdbbdaaccdbcdadaaaddbcaddabccadcdadcdadbadadbdacabaddcddccdcccbcbdabdbdbdcddabdccbdbabdaacbbbadbdcaacddbbccadaaacaaaacdbcdcdddbdabcacadacccdadadddbdadbdcbcbabbcbccdbddcccbbddbabddcabcdbcadbbcbdbcaaacaaaccaadbdaccacaccbcddbdbbaadddaababcccaddbcdacadddabbdaacacaacbacacacadbdaacbaccdbdacabdccccdcadcdadaabadadcccbcdacaaccccbddbcabbbdcaadaabdccbdbcccddddddbbbcdbdbabcdaddddacbdabbbaadbdddbcaaadacacaabaabadccdcdddadabbcacddcadabbabacadacabcacbddaaaadcbbdaacabccdbacbdabadbdacabddcadbccbcccacbbacddcccdbdbaccadbddacaddccbbaccbbbccbaabdcdaadbccbbbbbbbdadbaaddaacdaababcaddaddabadcdcbcbcbacddcdabdbccacbbcdbaaddccdddabadabadadacccacabdbdbacaaabacabbdcccdbbdcbcadbbdcccacbbdabcccaccaaadccbadddabdcbacbadaaccdabddddbbdadbddbdcdacbddcabbddbcaadcdbcdbadaddbbdbaccbadddcbcbcccccbdddcaadcbbdabbabbacbcdcaabaaadbbccacadaabadabdbbbdbdacccbdababddaacbcddadbdcdbbacaaacaadddcdcabdddbbcadbcbcccabbacaabbbadbbbabbdddbdcbdaccadbbaaccbcadbdcbacbdccababdcadbbcdbadbdaacbbcbaadaddbbacbcbaabdccaaddacdacacddbcbadaadbaaaacdcbabbdabddadcbdbaccdacacdaabacabbacaaabcbaddaabacdddacbaddcdbbdbdcabdbddcbacdbacdacbacbabcaaabbccbdcbdbbbbbdddcbaaaddabcadbbaaccacabdcdbcddbacdacccacadcabcaadbbbadcaaaccbadbdaabbbbccaadccdbccddaacababacccbcadbaccbaaaabaccbbddbdadcbbccbddbaccbababbccdddddcdcdcbbadcacdaabbcaaabcdbabcaccbbaabcdbbdcadcabadcbadbaabbaadcdacdbdbdccababcbcdbadcbaadaacdcbbddbaccdbcddcaaabadcdbcacccbbbcbdbdbcccbbbbaaccbcdddaddbbbdaaccbcdbcbdabaacbbbcccddccbaacaccaabacccdcbcbcaaaaacddbadcaabdadcbcdcaccaccaaccdbabdadadcbccaaddccabadcabdbaabcdbcbaabacbbbabcbcccbbcdbbacdccbbcdadcdabaabadccbdacccabdaabdcdaaaddbddccadbcabcbddbbbaddbadaacdacbaaacbabcdabadbcaaabccdaadacabadbaaddabbaadcdadddadbaaccbaccdbccaacdcdaabbdbaddcdacacbabdcbdbbacbdcdadabcabcbabaabadbcddbcdabddbdadcbabbcbabbdcdbcbcccdabbbcdacdaaaaadbbbbaadbbdaccdbabbdbbdccbddbdaabcadbabaaadbdcbcbaacddaacadbcbcdadcbacbccbbcbdbbdccadabbcdacaaabbabbbccbabdbabadcadccadadbcbabdaacaadbbcdcddbacabdccabadabadabdddccbdbbddadcaaabcadaaaabbddbbccacdadabbbccddbbcbadcdddaccddabbdbcacdbdcccbbbcbcadaaddaaacdbddcbdbbbbabcbbdcbcdccdcbbddacbddabaacdddadaaadbbbbdccbddabdcccbdcadbddaccbcbccadcadcbcccdcbbdacaacadbadabcccdbccadbdbaddcbdabbbcbcbdacdccdcdaddcdbabacdbcdbcabbdddccbbaaadabbddbccacadacadcdddcbadaddabacadbaaccccaccbcdacaacabcdcadcaddadddccabcbddccaddcacdaacccccdabbbdbbcbddcacadbaddbcddaccaadbbcadbcaccacbccdbcccbdadabadacbbdccdbcbccdcdacbcabacdbaaacbccaaacaaaccbbacaabdbccaaadbdccdababdadaddddcdabbddbddabbbadbdcadcbbaaddbdbbabdcccbccacbdcdabdcabbdccdcbdccbdadabcbcbdabccddaadbbdbacccbdbddddbdbabaadaaccdcabcbcabbdbbcadadacbcaddcbccbdaabaacacccabdbabcbddcbacccbaddccaabddcddbdcdbddabcacbbbaaacdcddcbcdacacbdcddbbccbccbbccbbcbbcabdadbdababdddcacdadcdcdbcdacacaabdabbaaabacbddbddcdbdbccdbddcbddbbdcdacdcabcabcdcdacbbdcdddaccdbaccbdbbbddcdadbaabcaaadcdccdcacacccccdcbcddadbaaabbbcddbdbdadddcacbdbbcddaddcaccddbbcbbcbadbbcdacaaaccaadaccdbdccbdccccdbbaababdaddbacbaacbbaddacabbadcdbcddacbcdbcbdcdaabccccbccabaadbdbdbccadddcadbdcddaaaccbbcdccacbddbaddccbdbbacbccabbbabacdbbaccdbacacddcaadbdbdaadadddaadbccbdaadcaacccbdabacdcbbcacbbbaabdcadbbdddbcaccdbacacddbadabccbdaacbabdabcabdbccdbdddddcbdabdcdbaaaacadaaaadadbbacbdcdbdabccdcbdcdacccbacbacbbcdbbdcadddbcadbbdabadacdaaccdcdbacbcaabdacaccacdccacddddadcbdbaadadaabbbdcbabbdcbdacacbdabaaddcacbadbccbdbcabcdcbddcadadbadacbcddbbaabacacdccadacddcaabcaabbdcdbacbcbdcaacdbbacadcacadcbbdddacbaabacccbdcbdcdaaddbcdbbddbaacbdacabdbaadabbcdcbabdabdcbdaddbdddbdccddabaaccddcdabddaccbdaadddccdcdcddcbcaacdbcacaabcdbbccbccdcaaddcaabaabdabdbaacdbdbacacbbdccccbdddaabcadabcddccabadadbaddabcaabcdbdabdaccdddddcbbdabadccacaadbdcadcabdbadcadbdacbbacaababdbadccddaddbbdbcbabddabadabbbcbcaaddbacaadbcbcddcbcdddcadacadcbccabaababccababcdbdcdacddcaaddcacadddadcabbdbadacadbcabbbddbbdacbcdddbbdddbabcccdabcdbddaaccdaabbabbcccabacbccbccacadcbcbbbabddacacbbcbaacbcadbddcbbccccbbdbabbdbcbdbdcaaabbdacacaadaabdcbbdabdcadabdbbdabddaccaacbacdaacbaabdddddbcbcbbbddabbadcbabbbbdddacdbcdbbdacbcdcbcadbcdbdcdbaadcddcdabacbcddcdbccacacdbdcdcabbadabbccaababccbbacbaabdbdcbbadacdabadabdccbbdacbbccaccccaabbcbcddcccbbdcdbabadbbccdcaabdcbcbcccddcacaacabdcbcdbbdbbcdccdcbddaaddcadbbbdaaccdacdddaacadcaacddcaabaabaaadddabdcacccacdbacdaaaaadacbadbccdcdcabcddcbadcdccabbccadacaacadcabcdbbaaabbadbacddcabbdbcbcbcadbbaaccacdbcabdaaaacadaabcccccadbdcbdabcabcaabcddccaaacabddbbcbaaaccdacadaddadabdbdcadcabcccbdddcdcdaabcccdbcadabcccaaaaadaadcbddbbdcddcddbdcddbbccadcdbdbacabcbcdcddadcacddbbdabbbcdbcbaadcdbddbcadacbcbdddddbcaadcbdbadabbbbdbcbdbbddaabbdcaddcddddaadbbaacdacadbbbcbdbbcabbcbbbdbddadaaadccbdcaaabaddcbbbbcaccacbcbbbdbaacaaaacccbcabbdacdddaaacabbacabababccadddccbcccbdbacabcdbbcdccdddbccbdabcdabbcbdaadcacccaddbbddadbddcadcdbbaabdaacbaadddccacbdcacaccacccacadabababacdbadbddccacbabdabdbdabaabcbaabcaaabdaaaadbdbacbbdacdbbabccbbdbbcbcadaabbbcbdcacacdabdbdcbacbcabcabbccaccaaaddccddaabbbdbdbdabcdcabaaadbaddcddcbcbbdbcdaddaddcdcbccbaabdaaabdbacbdbadaacaccddaddbabdddbcbdabdcddbcbcddaacbcccdcbabaddbbccaccadaccaabaaccbaadbcabcaddadadacbadbcddcbcdbdaaadbabacaddbaccbaaabcbaccdacccabbdcdcaaccacbdaabcbcadddabcacabacdccadbaddcbaccacccbcbdcabcadcabadcbbdacbaacadbdddcabcdcacdbdbcdcacbccdbccdbcababdcbbbadcdadcccdbacbcadccaccccaaccbcccaacaddddbdadbadccbcabcddacbaadabcaadbdbdcadacabdadcdadbbdbcdaadcaaadbbbdaacacbabbdcaaaadccacaadcbcabcbbacbcdbacdbccabdbdacaacbbcddabdaaadccaaacaaabbabbcdccccccdcccdddacccdbddcaabddbcbdadcbbcdcddcbcbbbbdbcccddbcaddabaacdcccdcabdcdbadabcbcbcddabcdaaccbbbccdbcddaddcbdddacbdcaccadcbabbccbbbbaccdcacbbdbcaddacaccabadcbabbcdaaaccacaaacdacbbdabcadcadcbbbacddcaccaaddbdacbcdbacdacabcaaaadaccbbabbdcadcbcddbccadababbcdbcdaaaabcbacbcdcabbacbadbbbdaadbaaccdabdddacccabdccaadaaabaccaabbbdadadcbaaabcdaacdcccbdaddababdcdabcddccbbbccdbdbdacddddacadccdcacccaabadabbacdabcaadbbacadcacbbbdaacadcdbbaaacaccccaaadabcbcbccbbdbbbbaabbdddaaabcabcdacdbdddddabacbbaaccbbcaadaabbbbdcadabbaaaccdbbcdbccbbdadddaccdbbacdababacacbadccccccaabcaddacadbccbdbcccbcdabbabadcaadddbadcdcabaaddddcbcdaadbccdcdbbcaabbdcbaaaacabbadabcaababddbdcabcabcbaababdcbdccdccdabdadbdcacdddcdadbdacbccdbbbbbbbddbbbaddccdbbddbaaddadaaccbaaacabbcbdbddabaadaadbdadcacbcddabbadbccabbcdbddcbbbdaacbdccabacadcccabaadcabaccacabbcccadaddbaadddccdbbdcbaaadcacbdbdbddabcccabdcaddcdbcbacbdadadbaacbcaacdcdbbdcabcccbbcdbdbbbaddcadcababcacbdcaccaaaccabbccaaaaacabacbdcccacbdbaddaacdcddcbcbacbdcccaaadacdcbccadbcccadaaacdddcdacccbdcbdccccddacdbdbbcabbcbccdcacbcbddbcccdbbcaaacaacddbbcbcddbbbdadcdbababbaabcaadabbccadcccddadbcbbdcbadacbbddbcdaddbcacdbcacabadbbcacdbccbdbcbbccddbadacddbcdcbdabcddbcbdaacbdbadcaddadcbbcbbbcdbdadbaaabbdccbdcbbcaadacbbabacabbbbaddbbcccabcdddddddcdadccacbadbddbccababbabdcdddbdddbbddcdcbdadacbddbccaaccaccdadacaaacddacbabaadbcbdbcbdbddcdaacccdadbccdccaacbadccaddbcabbddacbbcbdbcacddacabaabdaacdbdadcbabddcaddaddcdcaabdcbbadbbcbbbcabbbbcaacdadbdbadcbcdcbcbbaaddcbddbdacbcdcbccaacadbcbcbddbcaaadbdbadbacdbaddcdaccabadcbccdcdaabdccddccdbcdadbccadcbcbcccdcaddcbdbdcdadddacdaadddcccddbbdbbdaaabdcdbcdababdacdcbaabccbdadaabbbccdbacbcbbbccddbbdbaacdddbdcbbbbbbbdabaaddacbcabbabddabadaddcccbdcbaddddaabdadacbcdddaddaddcbbabccbcdcdcdabbbdcbabdaabcdbcdbdcbbdbabdadacdbcbcabcdabadabdabcadaaccbaaacdcdbadbbdcabcdbcddcbbdbdddadbddbabacdadadbbbabdbcbdcdcabbdabbbbaaddaddcbdcdabacacdddcaabbadbdbcbdbdaaccbaaadcadaabcbdccddcbdcddaaaaccaddbcacbdcabdbdcabaccddbdbdbcddcbadbabbbabdaacaaddaaaddbaccdabdbbcdbddcdabccacaaccddcccaccbcacbbcbdcadaccabaccdbdadcbdaaaadcbbcabdcaccbbcccccadaddaacdcaaaacacadbbaadbddbbccaccbdacaaadddddccaacbddacaadbbddbabcbdbcacdcdacabcabdbbcbacaacbcaaddbaccccbcabbbcbcbaddbbdbcaacaccbdadcddcaacabbdcdddcbbccaadbcccbdcbbccaaaaabcdddcddbdbadcdacdcccdadacbacdacaabdcdddabdacdcadcbcaabaaadcbbbdacdcdaabbaddaaccadccdacdaccacadaddaaacaadabcbabbbabdbbdcdbcdaaabcabcdadcbdbadbabacadbbdcdaaacbbdadadaccbcacdbaccdcdbccabbccaccdbbdaababbbcbdabdaabddbbdbabacbacbbcdacddaaadcddadabaaabcbdbacbbcabadcbdccdbbdbbddcccaccbddbccadcbcbadadbacadbdbccccbddaddacdaadcccccddbdbcaadddcbabbacdcbccbaabbaccbdbdcaadccccbbcaadabddbadcadcdbcbbcacbbbdacabbacdabacdadabdbbbdcaabccdddcabcdccbaaabbbdadaabcabdccbccabadbdddaccdbadccbdddbbdbaacdbccadaadcdccddcbabbdcdadadabababddbcdccdbddaabcccddbdbadccadadabcdabcbcddadadacddadccdbdddbbabbdaadabadacdadbbdbcddcacbbaacaccacccbcbcabcbdcbbbabbadacccacccbdcbbcdabbcdddbccadaccabaacacadcbabbbbbccacccacdccbdbcccacaaccbcaabcdbacbccddaabddacbabbdaaadcabddbacdbbcdccbbbddbbcabaadbdaacadcdbccccbabdbdaacdcabdcacccadbbbbccaabbbadcacdabdbdadddddccbacddbdaadbbabdbaaccbdcbbcadabbbbbcaddaaddaacadbaddacacaaddabacbbaacbbaabddbcadaacccccbaacbcdbdcbdddaabddaadddbbbacbdbdaaaddbbbbbaaacccddacdcdadddadcbcaddaddcbbcdbdcbaddccddddbcabbcbcdccbcadbbcbcbdbadcdddcacacddabbbbaabcddbdaaccbdabcdbddbadabbdbbcabdadcdccacadadbcabadcddcbbccbdcdcddcbacccdccdccbabcaabbabbadabcdabdccdcccadaccbacdcaaaacbdadddbbbaddadadcddcdadadaccdbacbbbbabcdcdaccbcadacacbdabbbbdcbcbdbccbcdcdabadadbdbabcadbaabdddcbccbacccddabbaaaadcadbaaddadabccbacdbabbcdcccdaddcdcdccaadacadaccdcdcdcbdddbcbcbbdadbdddaaacdbccbbccbbcbbbbadcacbdbadcbbbcdbdccbbdbabbaccacadadbcbdcbbcabdadccbbabadbbcdadbaadddaabbcdcccbacbcacadaaddbcabbaaadcbdcdbbdadacdbadcbccacdbbaadadaccdbbadabdadbbcadcbcdbbbaddddacaddbbacaaaadddbabaababccacaabbccdbdacbbaacccaccbbaccddddaabbccbabdcacabbdcdbcddbbabcbaccadaabcdaddccacacbbadaccccccabdbccadcdbabcbddaadcccaadbdaadcaacbbccdbaadcbdcdcccdbbcbbbbacaccbbacabcaadccdddcabdbbacbdaaadcbcabcbabcaadadddadbbbbcacddccadcdbcaadcadcbbdabcdadbdacadaaccdcbdbbadcbbdbdaabbcbcaaaadadbacdcdbdacdddcadddcadbadadabcdbdbbaaaddcdddddadadadccdddcadaacbcaaaabdddcddbadccaadbaddaaacdacbadadbacdbbaccdaccbbddcdccbacacddbbadcabccadcaccadcccdbcdaacdbddacccababcdcddcbacabcbbbccbcadaadcbabbcdbcbcaddabbadccddaaddccadbcdabddccddbacdabadcbccbcacbbaadacdccadabdccdbaccbdbccadcccbbdbaccaddbbdcccabcbdadabaabddbdcbcccbbccbcadcbbbbcccdbabacbdbcddbdcbadaacbaadbaaabcabddabcccaacaddcbbaccdcbdcabcdaadbbbbddbdbbcbcaaaaacabcdbdddddcbbccbbaddddcbaaaaadccacbacdacaacbbadcadadaacdcbbdacdadcacdddbdccbdccbaadbacbbbcbdaddcbbdbccacbaacbbdcddbbaabbbbdccdccbdbbdbcbcddaabbccddaabdcbbbbbccacccbcdbdbbdbccdaaaaaadcbdacacabbcbabbdaacbdbadbbddcccaabbdbdaadbbcbcaaadbbbadcdabbbcbcdcccbbaddbcabbbaaaddbbcccbbbcddcdaddadbaddadbbbcddabdccacdccbdabcbacabcbddbcadccaababcaaababbbacbbaccbdccaaccdadcbddbddbcbddccbddbabdddadabdcbccacdcddbcbcbcadadadddaacababddcdccabcaadcbcbbbdacbbbadaccacddaadcbcddbcdddabcacbcbddaacacddaadacaadabbdabdddcddacaddadcacbcccaabbbcdddbbbcbccbdaabdaddbbaababcadbbdccaadcacdbbdadadadadabccabbacbbbabbabbdccddbbdcdcbdbcaccddbadddadccddcbadbaadadacbbaccccbbccdbbbcaacbabdccaccdcabcbccdacbbcadaaccccdbcdcababcbcbddcaddadcccccddddbdcdddabacacdbddddccdbabdacdcbcbbcdbccdcbcbabddabcbadcddcdcbbdacdcaaabdadcbadccdbcaaabbaadbaadacdaacbddbdabccdcbcdabddacbaddbdcdccbbdbdccbcbbcabdabcdcddcacbdddcddcdcbadbdbbcbcabbbbbccacbcaaccadaaabadaacdbdcbdcbabdbacdcabacbcdbcadccbcabdbdabdacacaddcadcababdccbcacaacddcaddacdcbddacddbddadccbbbdcacdcacbacabccaabaacabbabdcabbbadaadcbcbabbdcaccbadbcbadcaacdabdaacccacdcdccbcadccccdabcbcaaccadcaccbacbcdabbccdbddcccbadbccbbbddddbdbdbacabddaaddacbcaccacbdabaccddbdadcdaacdccbdcacdcaaccabcccbdaaacdadabaddccccbbaaaaccdcbbdbbadcccbbcdadadabaccccaddcbcbaccabbdcacdcbabdadaabbccbbadccdcbddcbcaddcadadadacaccdaccdacdabcbbbdabdaddabcdcbbbabbaaaadadddadbabbbccabccdccbbdcdbcdcccdbdcdbaccdaadddcbcdbdbcadbddaddaaacadaabbacdccabaaaabaadbbcdbbdaabdcadccdaaabdaadcdcdadcacccdbabdbacccddcdabbaddcaabbdadcaacacabddcdaccaabcbacdacbdbadbbbdbdcbadbcadaabbabcdcdacdcaddcbabbbdaaaabdccbaddcddbdcdbacbaadbdcbaddbcbbabcabccbbddcaccacadbccdbcbdaddcdcbccbcddcdccdccdbdabacbadddccdddbccbbcccbadcdbddddadbccccabcbadadacccbadabcbbdacdbbacccbaaadbbbbbcbaacbacdadacabbdcaddabbdadabcbbaaaaabbdaaccccbccddddcdbdbbadddcddbbaacdcaaccdcccacbbaddbaacbdccccaaddcbdbdccaacacbdcbccbcddcdcccaddacdabacddcaccbdbbaaddcdcdcdabdbabdbdcdacddababacaadcbcdbabbbdddacdbdabcbaabcdabbabcadbdabdaaccacacabdbdccaddaaccdbdaabacabbccbacbdddbcbbaabbdabcbcabcdcbcbbbcbdacabcabcadddccccadabddacaccdcbbbaddaaabadaacaadbdaabbbdabaddbcdaaadabdaccdcddabcbcbbaddaaccdaadcdbdabdddcacdcccdbdbcadccabdddacdcbcbaacdcbdbcbdaabacbccbdddcabdadabcacddcbabdaabcbcbcdddcdaaddabacccabcdbdcbdaabaacdbacdcabdaadadabadbcbcabccdddbbcaabccbddadaabdaabccabccdccaabbccdcbadcaadaccddbabccdadabbbcabbaaacaccddcdcadbccbbabaccbabdcdacbcddbaddbbacabdccbadabddcccdacbadbaadbabbdccacdcacbcadbcccadcbaddaabddcadcabaaaacbadddbbdcaadbcacbcbcbabbaddbdaddcbdbdcdbadbcaddccaacabaadacbacdcdbdbacadcbdbcdbbcbccdcdcbcdddcdcbccbdacacabcccdabdaaccdadcacaaadbcbdadaabacdccabdcaccabacdacacaddabcaabddcadabcccdbaccbcbdcddacbaddbcdaccdccaaccddbbaacdacbbcdccabcbbcdcbcaddbbcadcdabadaabbacbdccddbadabcaddbbaccccccbdcdcbcaddbaccaccaddcadcbabddcacbdabdddbacbabddaaaadccbbcbbbbbdaccaababbccdabdcaacccaaacccbdbcdccdbbacdadaaaadabdcbbcddbcbdaaabcdbcbbbbcdacccacbabcddcddcddaaabaddbbaddcbbcccdcacabadcdabaabcbdbbbbaadaddacabbdabdbdaacaadbacdbdbacddadbbbdddbabbbdabdaabdcdcbbbbddbbdaddbaaabdcbbdaddbdacbcddbccdbdbdccdbccaaccacacbbaadbdaccbcaddacaddccbaadcaaaccbaaababdcacddcdcadddbbbddcbbacabadbbcacdbccadddddcbaaddcadccbdbcdabccadbcabdabbbaddbdcbabdccbdbdbdaaacdbdddcdbcbbadacdcadbbddcdacbdcbbcccbaacabacabddaddbadcadcadaabcddccabcaacbddadadadcacbbdbbbdabdacaddbbccacaddabcadbaccbaccabdbbaddbccbdcbbddcbaaacdbdbddcbdabddaabbcabacbcddcdcdabaabbabbccaaabcbabbbbdbcdacdbcbbabadacbbcabbaaaccdabadbaddcdbdbccbdbbabccccdcaaadaddddabcbdabbabbdbcacacddcddddabbcdabcabdcdbdddccbcddbccacccaccbcbdcbbaadacccccbdaccbcbbcccbdcaaddccdccdbabcdbdcbcdddbdabbadacdacadaabcdabdcabccadbdcaaaddaaaccbbaaaaaaddbadccbdcdbaaaaabbdddacadbddbddcbdbcbacdbbddcbdadccacdcaaacabcdcbaddcabaccaaacacbbdbcccbdabbdccbcbcccbdcbddbbccaaccdbbaaddacdbbacdbcdddadccdddbdcbcabaabbcdcdcbdcccddbbdccdcaabaddbabbccdbbcdbadcbbbbdcbaabdcaadcadddcadbdcddbccbaabdbadabdabbcbddabcbcdbddbdcdcbdacbcdbaadccccdbcbcddbacddacaacbbaadcccabdcacdcacdbccbabacdaddabcbbcabaabbabcdabcbcadcbcbaccacddddcbacabbdadacbaccbbcacbacccadaccccddadccdbdbbbcaacabdabbaaccbbdbdaababbdcdabddcbbbbbcddcddabcaacbaccddbacdcddaccbbbacdacddbdccbbbcdcdcbdbcadabcdbadacbdcacdbddbcdccacaadaaaccbdcbbbcbdcdabbacdabbaaaaabadaaddddaaabcddabdadbbcadadcccabbcdbbcdbbcbcbabddcbabcdababdbbadacbaadddbccdaaaddddbbdcdbdbcbccbabbbaadadcadccddcdbdcdcbbcdabcaabaabcbdbddadbbccadbcabbcbabddddaacddcdddcadcbdabdbbbaaabbccadbddcbcaadbdcdcdccccadbacdaadbccdacbabaddbcddddacdaacddbabdbcdadbccbccdbdabbbadbbcdabddacdacbaaccabdbbcddaacabbadcdbbababcbcbdcdcdacdabbbcbacbaddbbdaccabdbdacdcdddadccdccdcdacdbccbabcbcaadbabddadcddabbbddbbadcadacbabdddccdaccbbdadbcaaadadcbdaddcbcabadbadcddcabdbaaccdddcabddabbabdbbabcccdcdbadcbbbaacdaccadbadbbdcbdcabbadbcadcccacabdcdbcadddddabdcbbcadabdaaaddadcdbcabcbbadbbbddcdbcabcdaacdbcadccccdcabddabaadcdacdcdabcbadcdabaadcdbcbdaddaaadbaaabcabdccaddcdacbbdcbdbadacbdccddbcddbcbbacbbcbcdcccdbbdccdcbdcdabbcbadbbacdcbdbccdabbbdbdcaddadddabacdddcddcbcccdcbaddbddddcabddbdcbccaccbcbadabbbddbabbdaadbcdbcadbdcbbbccddcbcccabbdccddccaddcadcbcdaaddbccbbacdcdaaccadbcaadadddccabcaabcdaaabbdaccdabdbaaccbcbddcbbbdcdbbcaabdcadbcdabdadbadbaddbdbcaccabaabbababcbbadbacadadabaaabbdaabacaccacbacabcbdcaccbdbdccbcbadbadabddcabbdabcaaacaaacddcccabdbcccbaddccadbbabbbdababdddbddbacccabacaabbbccbbcdddcdcadbdabbbcacabdaabbdbacadaacbddddbcabbadddbcadcbdaccaabbadbabaadcbccbdccdbdbbcbbbdcabbaaaddabcdbcadddaddcaccbbdcbbaaccbaadbcaabbdcccdbaaacbdddddccdabcdbacabaabbcacbbbaabbbdacbaaacaadadbadbcdbcbcdcadaaccadbccabaacdbbbacadbdbadaabbcaccbbcccbccadbcbccbccaaabdaabcddabbcdbcccccbdcdcdbdcdcbdcddbddadbdddbccbadcacbddddcbcabdbbdaccaaadcaccbaabaddaaccbaddddbbbaddbaabdcccbcddcbbaabadbabadabccbbbddcabdbacdaaccabbabcdcabdbdbaaabacddcbcbaabcadccbbdbbabaabbcaadccabdcdcaabbdcadaccdacbaacccbabddaaadaadcadbcadbddccdbbcbbddadbcacbcaddcbccddccacbddcbcaddadaabbddbcadbddcbbdbaadcdcbdbcbcabaacbbddddaddabbacdddcdcacdcbddbcadccdbdccbccbadcaaabdcaddbbadcccbaabbcdcacdcabbcbabddaadcadcccbabcbdbaabcacabddbaccbbaadbcbabdcbdacacbdabbdcbdadacdcacacabacdbbbcdadcdcacbdbacdcdbcdbccdadbcabadbbccdbdbccbdaaccaabdacdbcdccaacccccaacccaabdaacdbaddbcabdccccbabbccbdcadadaababaabaabadadccdadabcbdbcaabcdcabbbdbdcddadccbdadadbaacbcbcbcbcccadcaccbabbacadddacdcadaaddaacabbddbbbdabbccdcbdbcddabacbbccccbdbbcdabdbccddbbddcbaccdddbbcbdcbbbadbabcdabdaabdcbbddaabacccabaaacdcabaabbdbcadccaddbcabdadbbbccdcbaabdaacdccadbccbacacadabdbbadaadcbacdbcdddcbbcbbddaccdcddcbadbbcadaadcaaaadcadabcdcddcbccbdbcbdabdbbddbaddcbddcbbbbcbdcaccaacdcdcabdbddcaadbbcaabdcdadbbabdbccbabdbabdbccdbadabaaadabaadacbcbbadcaadaddddbaddadcccbaadcababdadcdaadddbacacdbbccaadddddbbdadaddacdcdccdadadaacbaabcacddcacadacccabbcddcdddbcabddabbabcabdbddddbaadcbdcadadaacbdbcbcbccaaaaccbbbbbcbddbddabdbddbdabbddcaccdbdacddcddcccabaaaaddccdabddcaaadcdaaaacadbddabcaadadcbdcadddabacbdaadcbdadcacdbbddaaddabdaccacacaddcbabbcadcabacdabcdbdbaddbdacaaaabbdaaaadcdabbadcaaddddbcddbcbcadccbdcaabacaacacdbabacdbbaadcbdcbbcbaadcbdbaddacbbcdcabdcaadaaddacbdcbdcaacdccacdcbbdcbaababaadadbccdbcabcbacacdccdcbdddcdbadbdccdabacbacbbccabbbcadcacdcabadcdabbabdbcdbbbdcadacbaccadbadcadcdabddbaaabdabacaddbabbccbbdaccaaccadacacbccddbcbcccdbbabaccbdbabaacabdcaddbabcdacacbbbacdccbccacabccadddadacadbbdddaaadbabdddbddccdcdcdbbcbacbcbbbdbccddcddcdbcbbadbacacccdddcdddbbbbdadbaacabcdcdabcaacdadcbacddcacbabbadaadabcacbbdccadbacbdbccbbbadababdddbcacdaccbcdcbdbbcbbaabbccdcccacdddbaabdcdddcdcddcbbbdcaccabbdaadcccbbbcacdaadadbabcbdcbacdcdcdbabddaacabbabbdddcbcccbdddddcbcaabcdcbdaacadababcabcaaacdabadddcddbbcbdcaacaaacbbbadbabdcaccdcdadacbadbaccdabccdadbacbadccbcdddbbccbaadbacabcdaaabadcabdddabaddbaacbaaddacbcadbaddaacbccbbbadacbcbabcaccbcbadcadaacbacdcbbdbcbcbddcccdcdcabbccdacbadabbddddccccdddcadbbbdcaacdabdbcbcdaabccaacdcbcaaabcbddbabbacdabbdbdaddcdcbbccbcbbaaacbabaaabccdcbabcacaaddaaabdadbccbadaadcbadccdcbcdcccddcbcddacabaacabacbaacbbddabbbdddbbddacdacdabcdaccaacaacdddadadcdbcccdcaabbdbccbbccddbadbcdbbdbbaabbbcdccaabccbdcabdbbdcbdccdddccbbccacbdddacdbbabaacbdcabcaacccddbacadacdbadbdbdabddbadcacdacabaadadbbccddabcabdddbcdabbddacabbdbabdabddbcbbadbdbdbbcbdddbbaaddadbbccbaaddadcddcbbdcdbabcbababcacbbcddbbccbbcccbdcccbdbddbcbbaadaadbcdacadddbcddcdaaddaddbacdcdadaaaddddccdccadadaaacadbcccacbbdcabaaabbbbbaacccdaccbacdabbdccdbdcacaaabcadbbbbbcbbdbdcbabbabbdbbdacbdbaaabdcdaadcbcacbbbbdcadcdcdbadbaacdcacdbbddacbdccccbdcaacaccddbccddaccccdcbccdabdbbaadcdcbcbdadbddabdcbaaacddbbababdaadacddbddccadacddddcaacddacdaadbacaddacccaaaacbbbaddaacbcbaddbcccbbbdccddaabbccdadbcbcadbbcaacbaacdcacbbbababbbbcbacaaccdbbdadadccdbacbacddbbaacaaacdbbaadabaaddaddacbcccbbdcbccbaabacdbaccbbcccddcadcaaddacbabbbbbdcbcccabcbbbaacddcabcacabdbcdcacabcdbcbbaacbbaaadbbacaadcacccdaabbaabcccadddbbbabaabbcbbacdaabccbccbbbdabaabbcdbacbacbbbbdcacbdbadbaddcbcbdaadbddbadddabadababbacdbbaadacabcaadadaadcacddbbabadcadbbdbccbacabcdbbddaadadadcbdbdacbdbcbccdddcbccddcbccbcddbbbbabbadbbdbcacddbddbbcababdcaadacdaddddabbdaccacdbadabbaccdadaaacdbadcddcbbbdbcbbddabacacacdbbccdcaabcdbbccabdaadbcaaadbacbcdbcbbcdbadadcbddacdabbacbcbcbacabdddaaadddaacbbcacbdadbaadcbbcbaaaccbdccabadbacdbdbdbbcccbadaabbabbbacdcbcbbacadbdaadcbaccdcccbcbdcbdaadbdddddacddcadbabcccddbdadadabddbbcbbbcdcbbcccabaddcdaaadaacddcdccbabdddaadcddddbbaddbacacbdaacbbbdbcdabdbdbdabadbcbbbcacadcdcbbcaadcadabbadbbabdbccccbddbbadbdcaabbdcaacbabdcacddcacacbbaadbcacdabacbcbdcdcdbbcdacdcbbabbaabaaabdaaccccbbcbaacaadcaaadbcaadbccababdacdcadaacdbbcdcccbdabcddbddabcbcdcdccadbbbbdcddbdddcabbdaddaabaaddabccdbccbcdcbbbcadacdabdbbadaadccacccdbbcdbddbdbabddcdacacaacdcaaadbabcbcccadccdaadadddbcddaadcbadaaddddbcbcdacacdadcaccbbbbcccbaabaaabbdbccdcaaddbdbdcbcddcdcacdadabbcbcbadadccccbbadbccbbdccababbdcaabccacadabdcbacbaccdadadcbdbbcbbdccadbbadccdccdabbacdabdcdadcdadababbaccaddbbcbcaccaddccdacbdcaabacccbabcaabcdaabcbcdbbdadbdcadbddbdddcdcdddadbdbadacaddcdbccbcdabaccccbbadabaacdddcaaddddaccaddbcdacaadbdbbcccababdbbbbbccaaacbccccddddcccabacddabdbdacbcabdacddabdddabcccddcaacdcddbdacdbbcaaccaaadbddbaabbcbcabdcadbaccbbabdaccbcdbababcdcddabddaadcdcdcddabdaacbbcabcdcaaddabaaabdaadbadaacccdbbaddacacaccbdcadbdddbbacbacbdaddbdbdbdcdccbccaaacddaabdaaccdabdabbbbccccbdddbabbccadadabdcabdcbddbcccaaddddbcccdadadddddcbdbdcdcbcaaabddcaccbdbcbabdccaabdbabddccbaccddcbddbaaabcbaccbdaaddaabadcbbcddccdaadbccadcaaddddccdaddabcabdcbcdcddcddbcdbcdcdcaccbadbaabcbdacbbbcabcbbbcacdadbcacccadaaaadddbcdbddbbdaadcadababacbdacbaaabdabcdacdbbacbddcbdbdcaaaadacccddcbbddbdbbdcdccdbdaadaddcdbabbcbbbdcdbdcbabdaccbabacbccdbbacbcaaabcddacddaacababaddddcdbdbadbdcaddbdabbbaadbcdcdbdccabbddcdcbdacacbccaacdbdcddccbcddacdaaccadcccadbdcbcacdcacdacadbaccdadabbacbdacdacbbcbadaacaddadaacaaddccbdcbdcbabaabbcbdbcacaccaddcdbdccbdbadcdaabbdcdbbbddbbbcaaccdbbcddddddabbadcabcbddcccdddacadddbddbbadcaddabaadbbacbdacadabddadbaaabccaaacaacdddacdbdbdccdccccbccdbdbcaddbbbddbdcdbcbcacccccbaacddbcccaacacccadccbcdbcbcddcddcdaadcbbdbcdbccbaacadcacddcbbaaaabcccadbaadbadcbbcbcadbbbaacdbdbabccdacdacdddcaccbcbdddbdcbbddcdbccbbdbcaabaccaddbadcbbdadabdccdbbcbdccbbddbacccaacdaadaadadddcbbcdddddbabdbbabcbabcabccbccdbabbcdcbbddbbbbaacabcabdddabcddabdcdabcddbcccccacdbdabaaccbabaaccccadbcaccbacccdbddddcdcbdbdcbabbccbdaadcdddcdcaaaadccdaabdaadadadccbabddababadbdcdbdacabacbdabadacadabbcccabdaaabaaadadcdcacadddbcabddcbdcbbbabcabcdcbacacbadacdadbacdcbdaddaaacabdbacaabcadacccccbacddddccadacddddbcbaaadabdbaabbcaaaaabaadbbcbcacbcadcccbdbcbacaccbdcccddbddcdaabadacdadbdbacdacddaaaccabbbaaccbddcddbbbdbbdbabdbcbcbcacdbcabcaacbcbaadacdbdcbcacbcdacbccbcaaabdcadacdabcbcddbcddcacababcbabaccaaaccbddcdabccbaaddacaabdabadcacbdaccdbdddaacaaacbaacabbbbcbcdaddddcbdabdbaddcbacabddbbabaaddbbbbccaaabccdbdcabdccbadbacadcbcbabdaaaacbacaddbcdbdbadcccabaacadbaddccabddccadbbacabbdddbbcabadcccccadadaddbacbaddcdadccacdbadaacdbdccadabaddaddddcbabadbbcbcbbcdbdaabbbdcbacbccabbddcbdadcadcccdadbadcccbbaddaadaddbbbaacabadcccddbccaabcaadcbbacbbabbdaaacabdbbdabbdccbcdbabcabbacdbccaaccdccbdbcddccdddcaacbacbdaabbccaacbddddbbaaadcbcdddbadaccdadcbbbabcdcdaaadddbcddacddbbcddbcdcabacdacdaddabccddcabdcaadcbbbcdbdcaddbdccababacaadccadcbcdbbabcdaccccbaaddadbacbaddbdadddcdcaddbbacdabdbbaaabadddccbcbbddbdbbddddaaccabbaaabbbdacbccbabbcacbbdddaabdcabddbdbdbbbbcbcdcddbaaabbdadcdcacabacacadaabadcbaccabcbcccadcabbcbcddbbbaadabccbddaddaccbaaabadacdcbcbacbcaddbaabcacdbdddcbcbcddccacbbaddaadcbbdbcbbabccdcccddbccdccbaacccaadaaabdadbbcabbabddbabadccdadddddabaaadcabdbcbdccbabdacbcacccadbcbadcbbcdcadabbdaaadcabcdaaadacbaaabccccadabacacbcbddabdbcccddacddadccbdaaadcccbdcbcaacabddaabbadbadbbbcbdbacbbcbbabadadbcbbdbacabcbbbbcbcdcadabbbccaccdadddadbbcdbddababbdbbbcabccbbaaaaacccadccdadbddcccdbabddcbddbcdcadbaaccbbcbdacbbcddbbccbdcdcaabbcccddabbadabdbbdbadabdcacdccbcbbacaaacdccbabcaadddadbacdacabbbadcadbdbcabbdabcadbabdddacbabdacaacdaabbbabbbbaaacdacbbbddadbccccaacbcdbbaccdbcbbcdaabadaabccbaadcdcaadddcdcbbcacbbcddbacbdcdddaddadaccbabdcadbdbadabaaabbddddcdcbccdbbaccbbbbcacddcacbbaaabbcccacbbdaccabbadaabbaacdbbabbaabacbdbdaacdabbcbcbbcabddbacdbdabccbaccdadccccdacbdcababbcaadbdaadaaadaaddccdddbccccbabbbcbddcacbdaaccadbbbdbcdcaababddacbbdbdcccbccdcabbdcadabadbabdbadcccbbbbdaabcaaccccdbcbccbbacdddabccbdbacaccbbadcdabdbabdbdbdaaaabcbdcaddddaabcddddaadbaaddccbdcaacbdddaddabdcccacbbdaadcdbbdaacdbcddccddacccaaabaccabcdcabdbccacadacaddabcdcdbaaacabbcccdaabddcadcdcccadcdcdbdaccccdcdabababccadadbaadaccbbdbbadcbbcaaababcddcdcdcbccbbcbdbdcaacbabdbbcdcabacdadcdcdddaaaaacbdabcadbccdcaacdbcaabdaacccbcaacdbdabcbddaaabaaaacbcccacbdacbcddbcdcdcadbcdaaddcdabccadabacbabdaadcaaccaddbcbaaadaacaaadbdbbdcdddbddccadbcadbabbccdabaaacdadabdbbdbcbdcbcbdaabbbbcdabbcbcddacacaabaabcdccacbcdccaacbacaabdacdcaababbcadbdacbccdbaccbdaacbcdacbcdccbcdcccbbccddabdbcacaaaacbcbccaddaaadcaaabbcdadddadaabdcdbbcacccbcabbacdabacdbbaadaaaddccdbacabcdcccbccdaddacdaabddddbaccadbdcbdbcdcdbdbaaccadbdcbccadaaaddbbadbacbaacabdcbbcadbadbabbcdcbaabbadcbcbaaadcbccaaddabdbdabcbbcdbcadccddcdbdacccbacddaddddcdbccbbbcadbcacaacbccadbcdacccbdbabdcbdaadcadcadcadbcabbbbcbcbccbaaddcabccdbdcabbdaabbaabdacccacddbcbadbccbbacdcdbdbcccccabcbbbdbbdcabbdddbbddacaabadaddcaaaddcddbbbaacbbaacaaccbddacadbacabbcdabbacadbcaabacabacdcdbbacdddbdbcbbaabbbbcbcbbbdaacbddddbdcddabdcccbaaabdaaaaccbddaabbacaacadabdbbdbbbddaadbbbdccdaadbbdbadbabbbbcbcccbadcddbcccabdbadaabccbcbcbdccbddbccdbbdbbdaaadaabadaaddadcacbcacaabbbabdcbcbbdcccbaccbbbbcbbdcbccbddacbababbdadaddccbbdcdddbbcdbcdcbdbbcaaccdcaccbddcadabccbccdcabcccccbdcbdcbcbbbcccdbbcabcbacbbacadadaadcdaacdddbbcbbabbbddbcaabcdcabbcaaccdaaddabbbbbdbdcbdaaaddbaddddbddcdbaddbbbdbcadddbdbccacdaabbbaaabbdbdbcbbbbbbacbbbaacdadbbbccaddacaaacaabddbbdadbcacbabbdadcaddbbcddbaccdccdbbcbbabcbbcddabbdbccdbcdabbddaacbddadbcababddbaaabcbcacdcaadcbdcbadabdcbdcabbcccccdabddaacdcdccbdbdbaadcdcdbbdbadbdadabbbdcdbbccccdbdabccdacadbbacccabdbabdcaddbbbaaaabacdbcdcdbbbacbbcaccaabcdaadccbabdcaccddaadababacdcbdaacabacacdbcacbabcabcbdcddddddbbcaabadcadbcabccbaabbacdabbccaddaaccccbdbadbcdbdbbcbcaabaadaaacdbbcaccabdabcdbabbaddccadabdadadbcbacaaadacdcaddcddcacbccdcbaacdbdcbcbaddbabcabdcccdbaabdacaaaaadcdcacbbddaacbdacaabdaabbdbdadcbbadaabdddddccccbcbdcbacbcaabbdcccccdddaadbcbdacabbbcacbbbabccadcabcbccbaacacccaaaaacbcaadbcaacdccdcbacaabcdcbdbabcaddbaabdaaaaddcaaaccaadbacddabacccdcbbdbbdbcddbdadbbacdacbdbddbbdcbcbcabaabdbdbdcbbccbdcddcadaaaacadcccdcacacacabaadababcbddddcabbbcddcdcbdadabdabccdcaaddbbbcbdcccbdcabdcaabaddccdbbccacbacddddbcabaccaddadccaccbcbbbbbdabababcacdcbbdcadddbdbcdcbdbdbaabcdbccdcbcbdabccdbdbbcccccccadbaddcbdabacddddacbbbdcacbcdbbccabaacccdbacabddbcadadababdbcbccdacbcbdabadbbccbacbdadbabdaabbcccbadacbaaadadbaadcccacccbabcdbbbabbaddbbddcabddaaabdbcdcccbaadacccdadccdaddbbaacbcddadabbcaadcbabcccdadbbdddaacdbabbabdcdcabbabcdddbcdabbbabcabdaacbcbabdbdcbbdbacbbabcacbadcdbdaacdadcaaacdbcacaaddbabccbcbbbcabbdcdabaadbbdcbadcacddabdbbadccdadbbddbddbcdaabbadcabddccccbbdbbdacbbaacaddcdacbdcbadcbbdacdaddcbbabcdcbdaadccadadddaacbdbbbacaaddcaaadcdcccbdcddabbadabbaadcaabaaabaddcbcacbdbbbabadbcadcdaabaacdbcddadcbcaccccabbcadadaabccbcdcdcabdcdcddaacbbddadabdbadcccdbccbcaaabcccaaaaccdcaadcccbdcadacccddcbbbadadcdacbdaadccaccbdcaccdbbbbcaddadacadddaabbcaccbcdcbadabddadbacddbcbbaabccaaaccbaccbadcbcccbaddbbbadacdcddabdabaddaccbbdbdbaddbdaccaaaabddacadadcddaccadaccaddbbadaabdcbcabbdcaccbbcbcadabbdcaaabddbabccdbbbbdcaadbabcbbcbcdcbdabcccbbbcccccddccbbaaadbcbacadcabcdbbdddacdadcbaadddbcdcacdabbbcccdcadaacadabaccabcbcbcdddbbcdbccdbaabbddbadcdacabcbbaddabbddadcdbdadbbabdbbcbacbdbbdbacdbabdbadcbdaacbcdacaabcbbabdbabcbdabacaadbbbabcabbccdadabccccadbcdacbaddadbddbbbdbabacdcdadadadcaacdacababdacdaaadacaddddbbddbccbabcbcbbbaabcddddddcbccbcacbdbbdcaccccadcacbccdacbcbbbabbbbacacbdcdddadcacadcbadbdadaadcdbcccddccddcddcaadccdcdbacaaaaaacbabaccccdcacacdabcaddcbdcdaaccbcbdbdacaabddcbadbdccbdddbdacdbcddbacbbbdbbcabbdcdabadbadbcbccccacddabbabacdbbbbabcbbaadcabbbcaabbccdccdacbddacbccbccdbbdaacbbcdacbcdbdddaaacbabccbbdcabccbaabaaccadbadadbacbadccabbcbbadddacdabacacababadaabccadaababbddabacbcdbaabddbccacacdadbdbdabaccbbbbcdcccdabcaccacabbbaccdbcdabddacbddbcabadbbcccababbaaccbbbdcccaaabcdccdddacaadbadcdcaaadddcbcdccabaaccdbabdcdcbacacddbbbbaddcacbdddabccbdccbbcdcdcdddaddbbbccddcdcbddbbdbccdbabaccbcabcabdcddadbdaddbdcaddcccbaaccbbbaabadcdcccbdcbacacbddccdaddaddcbbababcddbbbbddaadcccaaabdacbdbddbacaddcaababcdbdcbdabbdccbdbdcbcdbaacabddabaaddadaacabdcdadbddaadbdadbcaaabadcbcdacdddaacabadbcdbbdabbcbacdcdaddabdaadcabbcccabbbbcbbcaccdacaacbdbcdcdaabcaadaadbcbccbaadddadcaacdcbaccdcddddababcabdbadbabbdbaaaaccbdaddaaadccccaccabaabaccbccddcdbccaacadbacadaacdadcbadaccabdddadbccabbadbcbadccdcddbdbaaabbcdcddcbcaaaaccdbdadcadbddcbddccbdcdccdcaadacbaddbccbaadbbacbcaccbcaccdabcbbbacdacbcdbacadbadcddcdacbbaacdaabddadbccacadbdaaccdbccbabadbbacacbbabccbbdadaabddaccacbaaccbcdcdbdacbdadbdcaddaddadccbccaadcbcdbbaccccbbcbcacbcbbaddbcddbdbdadcdddadcdddbddbdadccdddcbbcdddaaddbdddcdbbadabdddbccaacdabbacddddadbacdadabcbabddacadacababbbbbaaddadbccbbaaabccbdaadadbdbaaccabaaabbacbdcdcddcacbaaccbcbaadaddccccbccacbabcaddcbaaaccbaabdddacbdcdcabdbbbbaccdbabbaabdcdddbdaddabbcabcbbbaacdbdacdabbaaccacdbbbbacccddcccaddcdadabbadccababddbcccdbddadbdccbaacbdbabbbdacbdaddcbddbbaaddaacbccacbaaabadacdbdbcabcbaaccaabbadcddbbcbdbbdbcbbaaddbacbdbdbbbbcbaacccdabcacbdcdcbaaccdadcadccdddbaaabdacdddcddadcdddcabbaddbbbaabbcbdcbabdbcdbcbcbddacdabcbdcbbacbbbbcbacaabaddbababacabbcabaaadaddbcdccddbccddcaabbabadaadbaadbddaadabddbaaabbdbcccdacdaabdbbcbadadcdcdbddaaccccdcabbaadcadabcddccacbabbbbbdcbddacccccabbbaddbbdccabdcbcbdddcbbcaaabacdcbbdababcdccdcbbaadddbcadcdcadcdddcddacbdaaaacadccddcbddbdbdaccbadbacdaaddcabcbdbadbabddcccbdbccaaaddadddacbdbadbdddcddabcdcdddbababacbbccaacaaddcccbdcdcadacadadacccdccbabcbbbbcabcddcaadbadcaddbccaadbcdcbcbabacaddccbbdcbcccdaacadacbdbccbcdacccaccdaadbdacbbcbaccaccacaddcbdddcddcabbbbbccacbabdcdcdadaccadcaababcccabbdbadadbdabbabbbcaaadbadabcccababcdaacddccdcbdccdaccccbcdadddbcbacbbadabdddcbdacaacbaadccbcabaadbccddcabccdbdcccaadcbaacbbabbbabcbcaadabbaddccdbdaacabddcbabadcbbbdaaddadbdcbcbbccbdbdabadccdbddccaacbbadadaccbdaadadcdcabbccaaaabaabbdcbaabdbbdcabcdacdabdbabdadcdabaccbdddaabcabbaadacddbbccddcbaccbbbcabbbcdaccacdacdcddaacabcbcccbbbcbbdadcaacdbddbacaaddbdcccdabdadabbbacbaadabcdccaaacadcbdbaacaacbdaadddacacdccbadbcbadcababdacaadcabccddbacddadbddadcabddcdadbbcdddbdbadccbbcbbcbdbccdcaaaacdcbdbdcdddabbbcbdaddccbacdcdbccbcdbaaddbbdbdcdcbdcbcbcdbdbadbdabcbbcdcabbdbdddcccdbaddbccdbccbcdaddcddbcdaccbbbdbddacccaaadcddccacbbbcbddabcaccabdbcacdcdcbddbdaaabdabbddddacbacaddcdabcacbbddbccdcdacccaaaababcdcbbddabacbaccdacbbcccdaddbbacddaadbcddadbaddccabccbccdddbdaaccdbcdaccaaacbabcdcccbcabbdddaabadbdbaacbcbabaadcadcdddaabcdadddbcbdbbdccbbabdbcddbccadbaaacacbdbcaadacbbdacbcbbdcbbcdadcdbccacdcbddcbdabbadabdcaaddadcabcbbdbbabddcbcacbcadbcaaccabdabcbdbbdadbaacdaabaccacdabadbcbdbaaabdcdacddccddaabdcabcacadcdbacdcddcdcdabdabdabbcdabccacbbcdaabcbacbbaddbaadbccaddadddacbdaaabbdcaccdddabadadddaacbbbdddabcdcbadaacbdaabbacaacddcabcaacacccabadddbcadbaacccbbaccadabdcccbbdbbccbcdababbcddbadcabcbcccbadbaadbacaabaddcabadbbdbbacbcbdcbbcdadbdbacaadcaadacdbcaaaaccaddacbdbcbdaaacaaabacbdbcdcccacdacabdacaacdbdcadccdabbabdadaadcbbabdbaddbbcabcccbbcdabbddabaabdbadbbadadbcddcccbddcdbacdaaaddccadadcbbcaddbddaaadbdadbabccdcdddacdbaacaadcbcdbcaaddabadcdacbdcddbbbabadaabdbbddbdcabdbbdbdddcaabbbcdcadcbbbbdaaacccdbdaaabcddddcdcaccdccddccbdbcbbacbbccdabbddadcaacdbbcbcddddcdcadcccaabbbcabacdbcdacdaabdcbcbddbabbcdaadcaabbdabbacdbbcbcacabbdccbdabdcabbccdabccacddcacaadccaabdbddaacbbcccacdcdcdadcbdcdadbdbdcdbaddaabaaacadaaddcccbadbddcccdcaccaccbacacdacdabbccbacdbccbdcabcdbccbdaacadbadddabcdddccbaabcdaddccbcabbcacddbaddabbddcdbadcdcbacbabbbabacabaacaddcababcdbcababddbadcccacdddccbbdabccbaccbdbacccacaaaabcaccbdddcbaaaabcababbadcdddacadacccaccbbcbcdbcaaadccbadbbdadbdacddcbbbccdaaccabbbbbbacabdddabbccadbcbdadbcadadbbbdddabdbcdddbadabdacddbddababdbbcdcbbdaaddcbcaddabbcbcbcaaacaddcdcbbcbbaacbbcbcdabccbabbabcacdccbdcdbadababcadbabdadbdcddcbbaaaaadcaadadbabcdabcaacacdcadcdacacccacdadaabccbcddbdaabbcbbacccccccdabdcdcaaaddddbbbddbbaaddcabbbaacdbaddcadabcdacdccdcabccbacacbaacdcbabccbabdadacdacdcabdcacbaccddadadcbaaaacabacdcabcdbddaddcdabccdbccbcdcadabcbdbcdbbccddddaadcaadbcabbdbbaddbdabdbadcccacccbdcadacdbcadcabbadbccacbcdccbcacbaacbabbbabaadddbadcaaaadbadadaacbadabcccbbbacbbdbbbcdacabcbcdccbcdadbbbdbaddbcccbdcbcbbcacaacabbacdababcdcabbbbaabdddbbacdcbdcbdbbdadbabbbbbccbbcaaaaacbcadbdbdaacccbabcaccbddcadcddcbbcbccabccdddabcacdccabdccdcadacbaaddbddbbabaaacaaadabbcaadaaabadbacdacbabaddcddddcdabccadbadbcbbcabadadddcbcddbccaaaaddccadbdcccaabadadadbbcabaccbbdbbcccaabbcabdcdccdcddbcbbaccddddcdddbbcadcdcdbbababcadccbbadaaacaadcddbbdcdcbddcdbabbcadcdbbbaddbcbbccccaddbdabcdacaabccdaccbacddabdccdcabdaaabcadddaabcaccdbabdcabddbababdabcbdcdbcadaccbbcbcccadacdabbdabcbbcadcbbbdcbdaacdcdcbddbababdcabbbaadbadcbdccdcdddcbbbbdcdbcdbdabcbbdbabddadcdabbdadcdcbaadbcdcbbbbaabcbabddbbccabdbdaadabdddddadccccabdbcbbbbacbabdbccadabbdcacbbcaacdabdcddacbcaabbbccacbcbdabacaabaaccacababbdbddbadadbaaccdcacaddddbbbcadbcbabcdabcbbddccdabcbdadcacadbccbddcaacddacdcdcccacabdadbcbdabdccbcadcbbccccbaadadbdbccdccacddbbcaccbbdcbbbccacdccacacbacabdbbcbcdbdacdbdcacabadadacadbacdbccddaaaabbaddbcdabdaacabacdccbbbbbabaaaacacdabddbcdcbccccbbaccbababcbddadbcbdabcbacdcbbddcbccbbacacbdddcdbdcccbcaaaaaacdbcbccccdabccabadaabacbdadddabadbddbcbbbaccbadcbccbabdddddadabccaaacdaabddbbbacbcbdacacaaadbabccddcbacaaccacacadbdbbcdcadddddabcaddcaadadcbbbcaaccabcabcddbbaadcdcbbabddbadccddbabcaabdaacdaacbdaccdccdbcacadcabdbccacbbbdbcaacbcaaccaddccbcadcdaacccddacbdcdabbaadcdbdadbddabccddacdccdcbcabccbcaccbccdaabbaacbacbcdddbcccdadabdddadcabbaccdcabcbaacdaddcdddddcdbcccacdacdacabaaccadbbccbdbacbcadbbccdcaaabcacbcdababcbdacaacadbabbbcdbcbcaabbcdacdddbccbcaadbbacaddbdcbcdbdacaddadbbbcdcaabbddbccbbbbdcbbdbaddacccccbcabcaaadccdadacdabccdacdaacaddcccacdcacbdcabbccddbcacbbdbbaddcccdcddcddbbaaabccbadaadcccdbaacbbbacdaacaacbbacacddddcabccdcbbdbdabccccbacbadcddcbaadddbbbcccbcdddbacdabdcdbbdbcdbcababcbdacddbbcbbbbdcccdababbbcabbabaddbaadadcdbccbccdcdbabdbbadcbccdccbbaabaddddbcddbaccadccbaccbcbcadcdadaacabdcaadcbaacbaaadaaadbdcdbacbbdbbbdbcbbacababddbadbaaabddaaccababaaaaabbdcdacbccdaddabbbddaccdaacbacbdbddbadcdccdacaddbbcccccbcbbbdbcabcacdccdaabacbdccdbdccdaccabdabcadadcadcdbcdbdddabcadddbccacbccdbdccbdaddbdbacdacacaacccbbbaabbbdadaddcbdbabcdbdcdcdbaadccdbdbaabaabcacdbbabdcbcdccdddacdaddbbdbbdcbdbbdbcbbcacadbbdbcdcdbcdadadbcaddcdaddabbaccacbdbbbbdbbdccdcddddddcbaaabdabbbaabcdaadbbddccbccaaaabbdadcbbaadabcdbaccbbbabadccccbababdccddddcaaaccdbcabdbdbbacadbdbacbccdcbbaaccadbdbbdbbcaacdbacbcaaababcddaddadbacbaddacccabdbcbdbccbcaadacacccbcacbcabbaaadcaabcdccdadcdbacbaabddadaaacacbadacdbdddabdcbadcdcadaccabdacbbadabaccddaaccaadaabaccdacddbddccabdddacabaaadddccbacbabbaaacababbbaacdbdbcdcbacccbaaadabbdadcdadacdccbdaacbaadcaabdadacbabaadbdddaaabbcccccbabacadcabcdccababcaadbddcacdbdcaacbcdbbdbcabdcabbacacaacadabddccabbbbaabdacccbacccbcadbdacacbcacaaaaadcdacbccccdbdcaaadcccdcaabdcdddcabcdacbbbddacdbbaacbdbbcbbdaccabbdcccdaccaabbdcbcbdddbccbbcaacbbcacaababcdaaddbbdabacaacabddaccdabadbadbccabcadbddbccadcabbbbbacccadadbccdadacabbbcabacdddcbcbccbadcddababaacbacadaddbabddddbddadadbdabbbbbaaccbbdadbbbdbdcbbaabdabcbbcdcdccbdaabbcdbadcadbcddabbbaccbcdccbcbdbdbdacdcbdaacaacdbabbbdaacabdabcadddcacdbaaddbbcccaacadcacdbdaaddccacddcbbbbdbcacdcddadcbacdaccbdcdccddadbcdabbabbabbabddcdddbbddddabaadbdbbdaacccbddcdbdabbaddbdabbaaddcdcdcdddccbcbabcadbdbbabccacaabcdbacbddcbdabbdbdababaccdbbdcdcacdcdadadbacddbccddbdcbddacbcaabcaaacbdaadabbdaddacbbaacdbabaacdcdadcddbddcbdaacccccacccddbbdaacbabcbadaaadcddcaaadcacbdcbbaddcbdacbdbacddaaddbbddacbbcbdcdbdbddaaadbcddcccdcbcaddadcdcbcbdbacadabaaacbbbdadbcbccdabdccdbacadccccbbbdcaadadbcdccabacbbabadbcbcbcddbcabcbcbcdcbdcddbdcaddadcbdcccccdadaacbacdbdbbbbbadbdcbcadaadbdacbbbabccbcbdccdbadcbdbabacbcacbcbdbdadcdaacbcacbdccbadadcdacadcdacdbdadcbdddcacccaccbaacbbcdcdadbbbccbcabdbabaabaacacbddddbcdcbacacababcbcbacadadbcabcbadcdcdcddabdbabdbddaccacdcabdbdaccddbaacacdbbdccdabdcccbbbbbbacbccbcaccbaabdcadcbbdadccdbaadcabaacabdbbabacbabbaacbababbccaacbbbcadaccaddbdaccbadbccbddbdbdabaabbccbbadacbacdaaddcdabbacaddbdbbadcbcccaadbdbbcabcacadbababbabbbccacdaabddcccccbcacabdbbcccaccadbdadacbbddccbcadcdabcbdaadaddcdddcbcdcababaababdbccadcdadbdddccaaadadacadabbbcdcbdabddabdcbcabcadcbadcddbacdaccddbababddddacddbbcddcaddbaabadcdbaacdbabdddcabcaaacbabcdaaddccabcbddadaadbcddddadcbcaaddaddddddcccaddbadadcbbdaddbbbdbacdadaccddadbdaddcabccaadcaccddcadcdadbcddbaaaacbcbdaabcbcbacbcdbacccddadbdbaaaacdddcbccdcdaddccaddabccabbbbaaabbcccdcaccbcaccbdbcadbcdccbdcaaddbabaaadbadcdccadbbddbbcbbaddaacaacbababccabbdaadbbccdcdaacaacadccaccdbcbacadabdcaddbddaaaabbdadaacabbbbcbbbbcaaadabbbdacdbddacddbadabdbccccbcbcbaacacbbbcaacbdbdcacbdcbaabddbdcababdbabcaadcabbcbbcaacacacadbdbaabbddabcdbbbbadbabacabcdaadbbbbbbabdcbcdbdbabbdadcaddaadbbcbaaacacacacaadabddbbdbbdbcbdccdcbdcadbadbdadbdbbadbabdbddadcdbdbaacdbacdbdbadcbaccadccbdbcbdbadabddaadbbcdccacacbaadddabdadabbabcadbcbccabccbddcbaadddbbaaccdbdabbccbcdbbabdbacddbcaaccbbccacdbddcccdccbdbdcaadccabdbabcdbaaccddcaccddcddacdaacccbdcabcdbadadbdcddacdaadcbbbcabdbaacbddadacabdaaacbcaddbbabccdbbcacccdabbdaaaabcadaccccbadadadcbbbdccdcacdbdbdbaccacddbbaabddaddccddadcdaddabaaaabadacccbabaacdccacadbbacadabbdcdacbcabddbcbaaaddbaacbdabdbbdbabadabbdddbcadddabcbabbababdadcdcddacbcabdcbcdacbcdabdcbbcddbbadaacbaaaaabdbdbbacbddabddbddcccbdbccdcbcdcdbbcabdbbadaaaadbcadadbdbcdbdbbcdddaaaddbabbbbbcaacdbdcdacccbdbabcabaacddabcaddaaadddbabaacbabbddcacccaabddddcdcdbccccabbaaccbdddabbbcbcdddbaabcdaccdcaabcccbccaccdbdcdabaadbdaaaccadacacadcbccabaacdaccaadbdbcaadcabadabcaaacaaadcaddbaccadaddbbbccabbabdbaabcbababdbdcbababcaabbcbcdcccbacccccdbcdbbacaabaaabadbdadaccadbbbadbbcbcadbadbdabbbdadacddbddbbadcbdababbaaccbadddddbdbbdccadccaddccdaadcbdccdcdcddbcaabdbdcaacaabdbcaaadcabbdadabbaccbbaaadabcadaacdccddbcddcddccacbcabdbddbcacabddbaadabbdbbdaabbccaacbcdbccdaddcdacbaacabbacaaadbbdbaacbbabddcdbdabbcaacabcadbadcaddddbabbdcccacbddbcaaccddbdbdcdccdddbabcdaadcababdbddbddbddcdbbbddcaaacadcdcabcdcabddcacbabcabadcacbccbccdacdbbcdcdbaadaadbbcddabaccbbcadcdccabcabbbbcbdbdaaacacbbdadcdcdcbadbcbaaacdcbccadbdadaaacbdbacdddacbacbdbabbabddbdadbababcaddabccbcbbabbaaaabdcbacdcbccddbacccaabdcdbadddaddbdddddcbdaabccdadaaddaaadcdbdbdbdbdcacbcadcdcaadbdcaadaadaddaccbbbddbbdabddcdddcacccbccddccbacdbbcccacadcaddadacaadcdbccdddaddcbcbdabaabccabbacbaccdbbaaacbdcaccbbacdbbcdaadcdddccadcdadaddbcbdddbacbbccbcdccddadacdcdddbdddcbbbdbbdcdcacdaddddbdadbcccbcddcabbadbacbddbcccbddcabccacbabadaacdabbddccadbddbbcbdccbabacdbbcaaacaabbacaabcbcdaaabbddbcaacccddacbbaaaabbbcddbaadddcaadcabbbccddbbdaadccbcbcaccdbbcadadbbbddbdbbbbbdbdddacdccaadbbbcdaadcbdccadaaacccbdccaacdddbbcaaaccbabadddcdadcdccbcddbabdcbcadabdcadccbaccbacbbaccdccddbcdbdabaddcacbddbcccabbbcadbacdadcacccadcdcbbbababbdddddddbbdaabbcbcdadbacbdbbdacaccdcbaabbbbcbcadcacddcccbadbccccbbbbdaddbddbcbcdcbbddbcbdccbcaabddbaddaddbabdcdbcbaaddbadaaddadbbdcbaacbdacababbacdacadddcbdbacbdaccdbacbbacaadcaaadcccbdadcacddaadacaaabbddccadcadcbbccbbdccdccdbacdababcacbbadbdcdbacdadcddadaaddcddbbcddbccbaddaaaddbccbbabdadcbdcdbcbaadccbdaacdaadaddaacdaaababacccaacdcddbbacacbabdccaadadccaaccbaccaccccbaddcddbddbdcbaaacabcaacbadccacaddddadbdaccbbdbaababbcadcdbbdabbccadcddcdacccdbdddddccdadcbdcbbbcbadccddaabcadcadbabbdcccbbcdbabacbabadcadadcaaacbbbcabccadbabbadaacaaaacbcccbdadddbdaabcadabbbabbcdcccdddabdddbbbbccbdbcaacbdbdbbbdcbddacdbadbbabdbacaddbdbcbaabcdbcaacbbadbbccbcaacbaaabdbdcddbbacabcdaddadcdbddddcbdcabbcbcacdcabbcbbaabcbdbccdddadacbdadccddbadddbadccacadabbbbdcdbdbabcdddccabaddaccacbaabccacddbccbacbcaabdddaacccbccddcdaacbaadcbacccacaacbbaacadabddccadcaaccbbbabdbcdcddbccbcbbabacbcaabccbccdcddbdcabdabdbbabbadbbdcbdababbabbcadacacbbbacabaaabdaaddadabcdbcaddcabdcbbcbcbccbadbacaabbdadccabbcbbbdbaadbcacbacbdbabcccabadabbababcabdbccddcdaaabadbadbdbcbcbcaadacbccccbbcdcddcabacbbcbacdbddcbadddbdaaabdabbdbabddaabccabcacabcdcbdadcbcddbcdcaadccacabacabaadbcddbcaaaaddcaacdcadddadbcbccdcadbccaccacaabbbcbbdabdcabbdddaccbcbbcdabbabbbcdcbbcdbccbbddcdaacddcbcdadbbdaccbcacddaccdacccbddccdaabcbbdadadaadbcbdbcddbbaacbcdadaabdbbccbcddadcdbadbcdbbdbaabdaadccbadccddbbccdaddcdbaabadddabccccbabcabadbbcbcacdcdbcaadaccdbadcddbcabbcbcbaccaaadcacddbcadcabdcdcaacadaabaddcddbacddaccbadcbbbbdaadddbaddbaadcddbccadccdaabacbaabdbdddcddbadbdacaaccdbdaadddcaaacccbddccadacbdbdcaddcddcacaddcdcbbaccdccaacababdbcbaccabccabcdcadbcbcaaaabbbdddbdaaccaddbdcabcdbbadabdaabdaacbbabcbdccaacbadaabdbdcbdaadccacbbcacbadbaccdcbdacbcadaddacdadbcabacacadcaabcacdbcbaddadccdaabcbbcabddcdacbacbbddacdcdcbcdddadbbacbcdaacbbabbbcddbdbbdccabdbaccdcdddaddcadbbcddcbbbaaddbcaaaadcdaabbccbbcdcacdcbbbdaabbabcabcdddcadadcdaaccbdacccdbdbaaaabdaccbbabcccacccaaddabaccbbaaadbccabcdbcdccacbbcccbaadbdcbcdbdbaabaaabcbbbbbccabadbabbabdaabcdbbcbaacdcbbbabbbaacaaccdacadddbadabbcbdcccaddbadcbabccccdacbcadcccabdbbbbcaacdcacdddbacaaaaddabdacbddcbbcbbbddbbcadaccdbbdbbbbbdccaaaacabbdacdbbcbdddcddbccbccccbbabcdacdabaddbdcbccaddcdaccbacadcbaddacdbbdcacacdbcdadcdbdcacacbcaaddccbccbabdcdcdacddbcbbadbaaaacacbcdbdaabdadcaaabddbddacbbaabbcdcbcadadcccdccdddbaadcbccdbaadddbbacbbabadcaadbbadaddbcacadbdabccacdbbcddbccaccdbadadacddbacbaabcddadabcdbbabbdcbaacbddbabcbadaacbccdccbdabcdbbdcaccdcbaaaccbdbcabbcddcbcdbdaaacacbbabcddaaabdcbaabaaccddbbbbaaacbcadcdbcbcabcdbcaadbadbabbbcaddbaaaddbbcbcdcbbbbaaacbaddbdbbaccbaabbabcaabbcabbbacdddaacddbcddddbacaacbbdcadacabdabbcaddccdcdcddacacdbcabdddbcaacbbdabcccbbaacbadbbadcacdacbdddabddadddcdbdbbddacadacbcabdabaaaabadaabbbcbabbacdcdccaacbcabddabdbbcadcddddcabcdbcaaadbdbcdcccbaccaabdbacdabcdbdcdccbdadcccaabccdccddaccbaaadccacccbbbdadcadccdacdbbadbaaacaaaccacbcbaddcabdddcabcacaacdabcabbcadbbaaadccbcabaccbbacadcbbddacadadcbbdbaaccaacbadcaadbcdabbddcdcddadcacaaddcabcccacbcabbaddcdabccdaccbbbadcdbbbbdccdaccdccacabaaddccbddcccbdbddcdcaddbacddbddbadbccbdcddbdcbaccbdacbbddabcbadadbccdadaadabcdcbcbaaaabbbadbbbcabbdcdabdccbbccbbdbcbddccabbbbaddbcbbadaacbcddbcacdadbdcbdaaabacacdbcccbbadccbdaaabdbaddcdbdadabcaadcbcabdbbddddbddacdbdaddaaabcacdadbdcddddbabcdbbbcbadaaacdbcaaddcccdcadabbccccaacccacacdddbdbbadcbcbdccdcadccaabbdddbabbbdadcbadddaacdcaabadcdabaadaccccbdabccdaaddbdadbbddbdacddbdbccabdaabcacbcabbadcbccabdadaddcdaccabbccaaabacabcadcdadcaadabdcacdabbbddbcddcbdcccacdddcdaaabccaddccbddccccbbdbcbdcddbbdcdadbcccbbddddaddbcbbcaccbbacaabbadcabbcbcaaaccdacacacccbaacaaacbbaadacbaabcbbbdbaaaddbcbabdcadbabaddbaddaddbabddadbdccbadccbdbcabbbbbdadcbcbbbccddbdabddaaccbcdbcabdaadcabcddbbaabddcbdaddddcabbdadbdcaaccadaaddabaabdbbdddacbabbbdbdaacbabcdbabbdbdcccbbbdbcdacbccdbdbccbccdccaacbbbdbcbcdbacdbbddabadabbbabdbbbbadccbccbcbbbbaaabbdcdccadcccbddabcbdcacadbaababdaaccdcbaaacbdadcbbcbbaabdccddcdcbbdababacbcbadbacddbdaadccdcdbbbdadcbcbbbbbaabbddbdcbacbbdbaabbcdabcbcbcaabcbbbdccbccdcbdbaadbbdaaaddabbacccdbdaddcaadcbbddcccadbccadaccacddabcbcdcdcaadbdcabbaaabdaabacbabcadcbaabdccbddcacbbcaccdccdbbccbacdaadacbbdacbcdbcdddaddcddaaadbbacdbcddcbcddbdbddaadcbdcdaddbbbcabbdbbacbdcdddadcbacbbbcadbaaaadabcbbbdababcdddbdcadcddbcadacaaaadabcbcdbbadbcabdbbccccccbabddbbcaadcbbdccdcacdacbbabaaaacdaccadaacbddbaadadbbcbbaabcbbaddccdcdbaddbabaccacccadcaddaacadaccdcdaabaddddbcacaabbadaabbdaaaacbbaacdcccaacdaddddbbcbbcdbdbbddabdddcbbcdbcbddbdcccdacbbbcaaaadacabdabbbccdcddabddabdbbabbbbccdbdddddacdadccddcccaaabdddaadccdbaacabcbabadbbdacdacdcdcdcdbabadcacabbcbdbcbcaddaadabddaaccabcabaccadacbcaadbaabddddcccdcdcacbddbdabbbadcacdaccbcababadcbcabdcdbbcddabacddddbadcdbccbcddadaccaaacbcabadbddabddadadaaacaaabbdbacbdbadadbadaccabcdbbdcabaddbacbadcccddacaccdbbdbbadaddbdcbbdacbdcbccbabcbacacbbacaadadaabaaccbaabbddcccdcacabbacbaababacdacddcaddcbcdacadadbcbacbdcbabcddbbcdadcdccbcdbaddcbacbdbacdbdadabdaccdddcbbbdccacdadacaccbadcbdbbdbdabadcabcddabccbbccabdcaccdabccacabaccdbbdbabbdacbbcdaaaabaddcdaaaabbbcaccbcbcdccbadbcbaadcabcdbbaccbadddcaacbcbadaadabcbcddaccacacccdbdbbcacbadbcdcabaccccdcdcbbbccbabcacccdbcdbbdccdbaddddcccdcdccddbddbbcaacdbbcbccbcaababaddbbdaccdacacccdbbcababdbddacacbdbabcacdadccbaabaddbcdadbadbabdbdbcacbbccccbdbcbccbbbacbbccdbdaacacaabaabacbaadbdaaabcbbdcdaabbdcbcabcdcbaddcdadadcaabccacbcbbaaaccbbdcadbcbaaabaddcbcbabddbdaaccbbdaabaaccbcdacadbdddbbdadbcbbddccbcbdcccbaadcabacacccadbcbbaaacadabadbddccbcdcbcacbdcbdbadcabaddbdbcccccdacaaaddcdbbdcdbddacabbaadbbdcddaacaaadcdddbbaccadcbdbcddcadaccdbcdbcbddabbbcdaacccbbcbccadcdacadbaacbbdbabbbcdacbabccdacddadbccdadbcdaddcacccaacbccccdccacccbdccdaabccaccacddbddddcaddccdbbbbbccabdddddaaabbdadbacdabdcbbcaaabadbcabbaddcccacadbcaacdccccabadcddcbbaaadcadcadddadaabacaaabdbdacaccbddccbbaabacbcdbdcabbbddbbabcacdbcbccdaccdbabdddaadcbdccbcccadabbaaddcaaabbbdacaadacdbddacacccbadcabddcbcdacbbcdcdabbddbadbdcdbbcadddabcadcbabacdbddcbcacaadaaacdcdbccbadacdacbbaddbdbcbdacbdbdbdbcababbbcdddabcdbadaddacbcdaabacababcbacdccbaabcdabbcaabbadbdcdaadcabacbdcadabbbbbadaacacaaabccccadbbccbaaaddcdababaabbabcaabadcccacaaaabcbaacbbbccdbdccacbcbbbccccbdbcdbdadadddcbccddbcbabcbadcbddcabbdadabddcdcaacddbbccabcdcbcbbdbccbdbbadccacbbbdaadabcbddadaabaabcdcacacaaaacabaabcbbacbdaadddcacbbaacdddcbcdcdcaddadcadbccaabbcaccaaddddbcccbcbbddbdbbbcaabaaacccaddacdbdbbacacbdacbdbcbbbbcaaacbdbcccbdbcadcacacddbababacbddcbcddbbdcbacacdacdbdddadaadccdcccbcdddbaaabddbadbabbbdaccbbdbadaacccbdbccaabddbaccbabdcaacbdaacdabaabccbdbbddabbddabbdbbcbcaaabccabaadadabbbbdaacbbcbbdcdbcdabccbbadaddabadaccdcbcabcdadadbabccacaacbbdbdadcbbcabccaadcbbbcacaaddababcbdcccddbcbccccccbadcdaddbbcbabacdacddcccddaababccdcdcababdcdcdbcbaddbabcbaaaccacdbbadccccdacddcaabccacaccbccdcdcadccbbbcbcbacdbcabacaadcbcccadadabadabdaadddcdabddccbcacdccaabaddcbcadbbaaddabbaddbbcbdacbbabbbbdcaddbabddbaccbcbacaddbcadcbbaacbbcbddcbccadacdabcbbccaccadbdcdccdbbbcbddcddbadaddacbdbccbcbacccbdcddcadabacaacadacaadbabdabccdcbcbbbadaacbbcaccdccacccbadccbcdbaabbcbbbaabcbcbaccacbdacddaaaacbdccbaadbdbccaddaabadadccabdddaaaaaddccbbbddcdaccbbdbbdaaacddabbcaddddbbccdacaccdaaaadbbadacdccacdbbbaaaaacacbbaddbaabbddadaaaadcdbacdadbdcdbaddabbabbacddabcacbbbbbabdacbcbcccacdbbaccbcadbabbcbdaaadcaadacadcdadcdbacbabcdcbbabdcbdaaddbadcbddbabbcaadaacbdddddcabcddcdaccbbcdcdddacadcbdacbcabbabdcdbbddacacdbbccaaccaacbabacbadcacddabdccdcdbbbacbcddcadbddbbddcacccbaccbdacbdbdbaaadbaccdbbabccbcbcacacccdbbdbdacddccababdcaabbdcdaadabcddaabaddaaddabccbcdabbcdbaadcdaccbbcabbbbaadcdbbcdacadcccdccaacbdcbddaddbadabaabbcacbdbcbaadcbacacddaadccbabaadaddaabbadacdcdbbccbccbcddacdbccbacccbddbddaacadbdabbcbcbdccccadcbabbacbdccbabdaddcdbabccbabdcbaacaaabdddabdabacacaabdbabddbbaaaabcdabbabccabcaaadcadbcbddddaddcbcacddabdcbddabaccddddaacbadadcccbdbcdbcccdcdabdccaccddddcdddcdabaadbbcdccdbbbbacbdaddabbdddccdaadcdaabcaadaadcadbadcccdbabcaccdacdaddcadbaacbabaabacbbcdbacdcbdaacccbabbacdccbbacdcabaabcabccacabdaaacbccbdacbacabadbabbbbacdaaadadbbcdacddadbaaacbccdbbaabacdddaaddbadcddaccbddaabbbbddacabdbddccdbddbbcbabbadbbaaabccaddacabdbbddccbddadacdcdcdcbbdcdcbbdabcbbabcbddbbdbddcbacdcbcaddacdbbadbadccaddcbbadcbcacdcbaadbadddcbbacdccbbccbdcbdcadaacbdccdcbbadccdbabbcadabdccadbbdddccbcdbbcccabaabdaadaabaccdbcdcbddcbbddadbdccacabcddddcdbcababacaaadcaabcaccbdaabcddbbcbbacdddcbccdbddddacdbccbcdcabdcaacbbabcadcdacddbdcaddccacabdbabadccbdabbccddbdaabacadbaaacdcdddabdbabbabcadcddcbdcdbaaaabbdbcccdbdddbbacbbbddaaaccdbdabbbdccdaadcccbcbacccdaabcadaabacacadabcacacaccbdddcadaccbacabbbcdacacccbadabdbdadddaabcadbbdcabccbbaababcdbbbcdaabcbadcdccdddbcacbbacdcccacadcbddccabaacbbdccbbdbbcbaacbddccbcabadaaaaddcbdabdddddbabdcdacdbbddcdddbbbcdaaaabdddabacbacdbbbdcdbbbdcacdadbdbdacdcbcabcbcdcabaabdcccbdcacaccadcdddddbaaaaabcbdddcbbcbdaacdbaccdbbdccddccbdbaddadddcbbcabaadcddacbbcdcaacbcbddbbbacdcaddddddacacaccadbcdcacddcbccbcabadcdbcabadbdccbabadbbbdacbdbadcdaadaacadaacbbccccacbaacdaacaccbbdbbdbbbcabcbdcadbdcbaabdccddddcbdbdbcccdddcccdaddbdadbaacbcaabdbbdccdbbbdaabbcbabaabcdcdbdbcdacdbadddbddcaccbbaabaddadbabbddcaccbccbaddccadccdbaddbdbadabacacbbbbdbaaddbccacdbbcdabbdbdccbbbbaddccabbccbaadcdbcbddacabdbdccbbdbacadbadcdcbadaaadbbcdcbbabccabddaaccccddbbabdcaddbdcbddbacdcbadacdadddcbaabacabacbdbacdabcdcdcacbdacbcadddacdabadcbaaaddbdcccddbaacbbbddaabbacbadddbdaddaccdcdcbdaaaddaacddadcccadbdcddbbadcdadacbbdabdacbcabbcdcadbcbacbcadaccbccccbbdbdadbbdcabaadccdbcabcadadddbabccbbcabcdacdddabbabaadadbcaccbbddcbaabdcabbacabddcdccddbdaabbddddbbacddbccacacdbbdcdaacbdcddbabcbdbbdbcbadbcbbcacbcaaccdcaabaddcabdddbcbccabdcdcbcccacacadcadaccadccadabacddcabddbadacbdbdddbdaadbabcacaccadcccbbabaabdcadccbacaaaabdacbbbcdbcbcdcbddbdbcdcaadacabcccbdbddcddbcacdcababdaaaddcacacdcacdcbdcbdbbcddaaaacbccbbcacdbcdbbaddbabdccacbbcadcdcbbabcaaaabbdcabcacdcddcaddbcadbbcddcabaadbdbadcaabdcccaccacbacddbdbbcabcadcaadcaabababccbdaadbbdaaacacacbdaaabacabbdbdcaccddbdadbdabcacbacdbbbdbddccbaaabacbcbabccccbaabddcadcbcccbaccbdddddddbbabababdaadaddaaccccabcbddbabcdaccacabdacbcccbcaabcbbadccabbcbacdcdcdadbbbddbbdddcabdcccdaddbcbdcaabcdccbdadcbadacdaccdadccdbccdbabddbbdcabcbdabacabdcdcabcbbdbcbdcdaccbdcdacdddbcbabcbccaccbcaacdabdacaccbaddcababaabaacbadcbcbcacacdcaacbadcbdbadaaacaacdbbaaadadcdbadcbbabcdacadbddbdbbdadaddbdabcdaddabdbadcbaabbbcdabcddccdcdccbbaadaaaacdabcccaaccbbcbbbddabcabbcccbabaadaaaadbaadcddbccdddcccbadacabbddccdccbcccddbdacdbddcbddadabdbdbbbbdaacbdacaabcaabddaabcddacbadcacaacddbddcabbabcdbcccaaaaabbddccbaccddcbbcbcbaacbbdbcaabdaacaacaabbbbbaacbdaaaadabcaababdaddcbdcddaadbaaacdbbaccbbcdacdddddbababbbbdbbadadbcccdddddaaabbdbaadaabbdbcdcbbbbdbdccdaaacbbddbadcdaccabcbbdcaccdaadccabbbdabadcbdcbaadadccadaccdbabccdaccdbaabcbcbddbcabcaadcaadadaccbddabccbbcdbadabadabdacbddcbabcbdadbaadbbaabadccddaadbdbbababbdabdbcdbbaacdcbcccabdbcaacdadbdaadcabdbdabaabbdacacdbbbbbbbccaacbbdbcaacdabcccacabacdcbcdcbcdbaddcdcaaadbddaaaadadabcadacadbacaabadbcbcadccdacabdaddaacddaaccbcaaacabadbdccbcbdddcddabbadacabcbaddcdbbbcddadabaadbdaabdbbaaccccddacbcdacbdccaccddacdcdacdbdbbcddcadddccdbdaacadbadacbabaabbdccdbbcaaccdcacdbccccbdabbacbbbcadcccbbddbdcdadbadcdbabbcacbcbbadccabdddadadadccaddbccdbaccddbadbdccbdbdacbacbdacadbbacddcccaabccdbdcbcadcdddbdddacbdadccbabbcbadbadccccdbddbcaacbbddcbdaaaabdbaabbdbbddabdbbdbdbdcdbdbdcbabbbdbbadcccacddbcaddddcbadddbaaccdbbbdaccbadbaccddaacadbdcbbccadabbbaaadcbbdccaddcbdcbbbcabdcbbbcdacdcbdbadadbccbcccbbddacdbccbccabcdbbdccacacbdadbbacdcbdaddabbbddcadddccdbacdcabbaddacadccabaddbbcccddbacbaadbbcabdcadcbdccacccbababdcaaacdbcabcccdabcbcabacbabdbaddcdcacabbabddaaaddbbccdcbbccbdabadbdaddbbacacddaacdbccdaabccdccdabbdcbddbbcbbcdbdacdcbdacabddcbbcbbdcbaacabacbabdbccbcbdbdbacbbaaadadbcddcdbdaaababdccdddaabdcadbddbbccabcacbbabbbbcacbcdcadccaabcbdaabcacbaacbaccdbaaacdbdcdcaadccdbbbcbabbcaaaabccacbbacacddbcbbddcabdcbbacadbbabbcbbddccacabcbbbabddaddddbacbbbabdbacacaddaaddbacadcadcbabcadbaccdddabbcddadbbcacccdacbcbcabbbbcbcbbadccaadccabbadcbdabccdcdcdbbdccaccbbccbabcbcdaccacdbcbbbccabbbdcbacccabbccacadacbdacbcdadccdcbadadbacdddbcbdcaaaadccddcabcdbccdacadaadabbadbccabcdacbbdbcabdbabacdcbcaabcdbdacbabdcbbccaabaabcbaccacabcdbcdbaaadcbdcbdcadbddabbaddbbdcaaaaadcbbbcdabbbaaabcddbcacbadcdbaaadacadddaabaccddccaadaabccabdbbbbbdacabcabcdacbcdabbcbaadccababbacaccccccbdddcaaddadcbbbacbaaaacdcaccccbabadcaddbdcddbacbccbbcdabcbbbaacdbcbccdccbbdbabcdaddbcdcbdddccadbaddadacbcadabdcabbacabcadaaccbdbdcaddcccaaccdacbcdcdcdddbaaabdaacabdddcbbbcacdddaacabccdaadccabbbadacdcdccacabbddddbccbbddccabdbccacadddaddabbbacdddbdddabddbcdbadbcacddababcddbdacdaccccabadbdccbcdbdddbaabccbcacacccbbbadbcccbcacbddbbbbadcbaccbdccacccdcbbdaaacabcdbadcbbbccccabaaabcbbcbadbaacdbadbaacacbbdbcaadaabdbbbabbdddbdbdacdbadaacbadcaaaacbdbabbdaddaddcbbdabbdbcaccabbaacccbbbccccaaacaadacccaababcadbdadcabbcdcbdccaadbbdaacdbdcbccdcacdbaadababcadbccaadcaaabdcbddbcbaddbbccccdddaadadbbaadcbabcbaaaddcbdbaaccaddcdacbaacabcaadbcaabbddcdaacdbdabbbaabdddccabddbacadccbbcbdabddaadbdcbdbaaabddcacdcbcbbdcbabccbabbbcbddbdbacbddadbbdacbdcbadbbcbddbbcacdccbcddcacbaccddacacddababcdcdbccaacacdbdbcadabbcaacacbaaadbdbcdbccdbabdbdcabbaddcdddcdcbbdccdbcaaadbcaccdacdadcbcdcaaccccddbcdbbddabcabdadcaacccabcdcbacacbbcccacbcdbdaccabdcbdddddadabaadbdbabdbccadcccadcbbbbdbcbcdcbbcbbbcdacabddbabdacaadcadcabacadbdbbcbcbabddddcabbdcccbcbdcbccacccadcbbccbacbaadcdcbcbcdbdcdcbcdacbbaaacabcdcabcacabbbaaadcacdcbaccccabacaaccacbcacbdcdabaabadadbccacbdbddcbcbabcacacbdcddacaabadacbbbacaccabcdccddccaddbcacbacccbcdbdcdadcdbaddcbdbddbacdcadcdddcbbbccbbddaaababcbbdaabcbdadcbccbdcdbaadcdaccbdcbbdbaddbcccdcddbadccdbbcbadaadcbcabadabbcaadaaaabdcdbdcbddccdddccacdcdabdacadcccdbdacadcdccddbdaadabaddcababcbddacababdababbaddbababbadacbbaaccdbaaabdbcaaabbcdbacdbdddbddbdcddcbcbcaabddadbddcdbcddccbacacbccbaddcdbaabcaddbcabbaddacbcacdbdcbabdbccdabcbbdadcacacdbcbcbcbdbcaccbbbdddcbbbcccacdbdaccbcadaccbcacbdcccbcddbbbbcaccdcabdcbcaaacdadbcddbcbcaaccbdddbdaaccadadbcbcabcbaccbdbdddbcaaccbdbdbdadcbbaccbcbdcbaabcbaddacabdcbcbdbdabcdbbddacbcdbdcdacdbacddabdcddbcaaaaaadabbbcbccacdcbabcbaddbcdcdbaabcbbcbcaadcddcdbdaabdbaaacacbbabbabdccbadadbcaaccddbdacdddbaadaccddbcaccdbbddcccacbacddaaabacadcdbcbcdbccccbadcbbbbcdbabcddbcbacaccbdddacdcbbcbbcbbdbdaadccdabddaacadbdcacaddbbbcacddbbcbcacccbababdbacdbaaaabdccbcbcdcdacbdabdbbbabdaddcddbabdbaabbbacccabcccddbaacbdbcbcbbcbdcbcaaadcdabaababcbbabcabbaabaabdcabcadddadbbacbbcacbbbdacadbaaacbbcbaccdccbcbcaaccdddbaacabbccbcdacbacbccccdaaadaacdbdddcbaacacdbdbccbababcadacacccacbccaadadcbbdccbcadaaaabcdaadabbdacadccccdcccccbbaddcdacdbdaaadcbbbcaabddabadabababbbcdccabbdcacdacdccaaccaaaccacacadcdacdcddddcacddddaaaadababccbbdcaabdabdddaaacdadaaaaddcddddbcacccdaadbcacaabbdabdcacabadddbabadddbdccbacadaaabbcddbdbdabbdabcaabaccccdaccacbbcdbcbadbaddddbadacadabdddddbdaccbdbcbbbddbccabaddcdaccddbcdbbcdddaacdaaddaccdbaaabdbddaababdadbbadacadaabcabadddbabaccbaacadaccaabdaaabdbdcaccddddabcccdcbdcdccbbaaaadcdcdbbccaddbbdcdbacaabddbcbdbdbdccadcdacbddcbcdbabcdadadbaadabbdcbcccbadaccbcaadacabaadbcdaadbdbdcdbbcccbadadcbddbbbccdabdbdcabbabbcbacbbaadcdcadabbadcccdddbdbccdcbcdbcccccbaaacabcdccdcbdcddcadabdddcdcdbbdabbaacccadbaddccdacdbbacdbdaaacbbdaaaabbcdaddadcbcbcdcacabaacdbddbdbdbbbbbccbbbcbadcbacaccdcdbadbdcbccacbccccbdcdbdcbdddcbdcbbadbadbbcadcacdcabbbbdbdbbcbbcbbddaadadccabccacbcabcbddaaddbabbcbbbadabdcdbabbdbdbdacabdddcacadaadcbdbdcbddbbdddbcdadaacbccdcdadddabdbcdbcdabdccdddcccbdaabaaccabadadcdddadcdcdbdbcddccdbccacacdccccccccddddbbdabcdddaaabadbbcabbcdcadabbbcdcaacbcadbcbbadbbadcbccbaddaccbbccccabddbcabbbdbcdbaddcadadbdabcabdcbdbbdcddbcdadcabdadaabdccdadabcabdaadaddcdcaabccddaabaddbacddbdaaacdddcaaabbbbbdbbaccdaddcadabddcacaacccdaddaabacbdbadaaaabdbaababaaadacacdbabbaadaadbdbddccbaacdccbadbbcaabcadcdbadbdbdddbbbbbacdaadadacdbdbcabaabbdbddadabcddacddbcababbddbacccddacabbbbbbdccacadddaacbccddaaacbdcbadcadbbcddcacdadbacbaadcbacdcccabacdcbabdaccdaaadbbabbabccdbbcbcbbdacacaadccdcdbabaccaaacdacbaabaaaddcdcbcabbacbcbcabcabacdaadcddacadabbabdabaddabcaadabbbccaababccaacdacbdbcccdaabbcbdbcdbbaadcdcabbdcccbbccbbadbdcbccbcbbddabadddbbaddbababbbbccababdccaabaabdccddaacddcdcbcccaabdcbdccbdbcdcbadacadbddadadbcdcaabbccadcabddccaabcbbddcadbddccbaddddcbbbdbcaccabdabaaddaadbdbacdbcdcaaaaaabcbbcacadadacdbdaabbbcbabaabbbbdddcbbacbabdbacbabcadbbcccbcbadadacbcbbdcdcbbdbadcaccccbdadcacbbaabdaadaddccdadbdaaddabcaacccabbbbadbbddbdbdccaacddcadbdccadacaccbdabdcbbaccacabdbadcbddbbdcaabaaacbdaadbddbadddbaabcccabdaaccbbabdccdacaaaaccdabbdabddbbcbacaddaaacbdddbbbddcdabaccdcadabadcbaadcbacabccadcbccbcbadccaddabdccdcdadbdbddaadabdddadacacbdabcccabaddbdbcadadadbcbbcbabaaaaccacabdcbbcaadcbbbbaadccdccdbdcbcacdbaacaddddccacbccbbadcaabdbdadaddadbdacaaabbccbdcdaadbcbdccdaaadccadaabbddddcbdbaddbcaadbcdbdaddaabbaddbcddacbaabdcdbbabdcadddbacbacdadabbcbdadcbdbdbdcaaddadacdbaabdcbbdacaadbababcbdcdbdbcdcbdaabdaaaadcabdbacaddbdabcbcdddbdadbaadbdaacdcabdcbdcbbabcdbaddbbabccaabaabcccbadcdaaadbbaabcbbaaddcdbcacaabcadcadabbaabbaaaadaccccabadaadcdabdabbcaaaddccbbbcbbcbabbadcdabbbbacbcacddaabbcdaacbabdddcacabddccbdcbdcdddabcabddbaabdccadddacaaaadaadcaaacdbdbdddbcddbbcaacddabbbcaddabcdcdcdcdcccbbcdddaaacbdaddaddccbcdcdbddaaaadbccddbadbadbdadccbabddaabaacdbabccbacddcabacddacacdaadcdbcbdccccbcdcdcddcdabdadcdccaccdbccdaacaccbbaddbcbdacccdaacaccbaaadcbdcbbbccbddadaccabbaadbdaadcddadcabdbaacbbabdcaadddacdbbcbdcbadbabcaadcccaccacdbcacdaddbdaddbdddbaacbdcdbdadcbbcccddabddcacaadbacbabcadcdadabbccabaadabacccbbcabcacbcaacbdbaadaaadcccbabbdbbdcadbcdcdacdbaaddcbcaccddccaacdccdabaabacdcccadabddaddcdcacccabbacadaddccccaaadbcdacabcbabcddcaacbadddcdadbcabaccdbbdadadbcbaacbadcddbaaaaabdacbcbcaaccbacbdaccaaacbcddcababcbaabcacadccdaccdbcaccbaabbacccaccddbadbdcadccbcdccaabcaccbccbbddcaabbcadaaabcdadbbbdbbadbbddbccabcacbcacbbdacacaccdbabdccbbaaaccbbbbdaaaabbabddbabbdbbdbcbcddabdacbcccddbddcdccadbcadbbaacdaaacccdcabdccabdbcbccdbbbaaadbcdcdbbdadbcdbacacaddbcadcbcdcddbbabacdaabcdddadccababaaddaacaabcbdbadbdcdbaaabbdbcacdccabaccacadbaadcdddcbbbdccbcbacdddabaaacbccbadcddbbcbaddbacbbdacabcdbacdccabbddcdadccdcddabddddcbabcbcbdabcbdddccccbddddddbddccdbcbbadaddaabbaaddcccbccbbbababacdbccddcdcdbbccccabddccacaabbbaabbbbacbbaddbabcdbdbabdbaabacbaaaccacccbbabbdbdcadbdcabbcadbdbcbdcabbbacdbdddbaacccacddbcaacdcabbacaadbbbbaabbdbcbadcaaccbbbdacbabcdbbcadacbbdbccbbcbabcdddccccbdadbddcdcdbcbcabaaaacbddbdccadaaccdddabdaccadaaabdacacadbcabbabcbcdabbbcdbcdcacdcbbdccbbbddddcbaabbbbbacbbcabbbbbdcdcabbdaadaadbccbbcccbcdbabadcdcbbaaddbccccaccbbbcadbcdcabccacbcbcdcddbcbacabdacdbccbbadccbabdbbaabacbcbdbdabaaabaababacdbabcadbcbcdcadbbccbdddacaacbbbcacccdbaccbaacdaaddcdcccbbbcdbbbcbcbabdabddbdbcbdcaadbaacbbcbacbcbccbcbdaaaacddbcdccddbccbadbabccbababacaddacddbcadccbbccccddbbadcdcccabadaaabdaacbbabcbdbcbcdbddcadaccbadbbdadccacaabdbccccaabbddbcaabbbdbcddcaddaaccbbacbccadddcddbacdcdabdbccabaddbbdcadadbbaddabacdbaccdacccdcbcaababcbdaaddddcdaccbaccdbbabbdddddbddaacabbcccbcabbcdcdcbadacaaabbbcbcbdbadbdabbabcbdddadcbadadbbbccdadcccabadcdbadacbaaabddacdccbaabdcbdcaabddddadaadabbacddacacbcccaccbaabdddbdcaaccaadcbabdbdadcbbdabcdbcbcbddddbadcbbccdbbdbcbddbbbbadabcccabdccbbcdabddcadadddadbddbbdcbaaacccabbcbdbcdabccdccddcbdddccadcddcbdcaacbdadcaabdddbcccddacdcaabadddbdaaadbbbcdccabcbcbaacbcacaabbcbabadacbcdaaaccbbadabcadbacbdccbbccbcdbbcdacaabbabbaabcccdcdccacaddacdaccccbdaddbabadabdbcdddcdbaababdaabbbaddbcccadbcdaccddbcbcccdbdcadcbcbaaccdcdaccbbdddadddbcddbbbccbadabdcbcaacddadabbcbadbcccdacdbdbbcbbabdacdddaadbaddbddcdbdcbccbdccdadadcccbaaadbaaadacdbbadcddccbcdcaddabbdbbcadbbdaaadddcabdabbcbabcdcbbcdabbacbcbdbaabacdccbbbacbbcaccdbdbbdcabcbddbdcbccacdaaddcacbdddadbabdcdaadccbdddddddaabcbbccdabccbdaadaddccbadcabbaadbabcddaaadbddcddccbdcadcdccadbadbbadaccacccbcaacccdcddddaadcacdbbaabdabdadaccbdbcadcbbdcabbcdbaacaccddabcccbbbbcdbcddcacacabdcddddadacbbdbcdbbbcdacdcbdbcddbaadacaacaacccccacdccdbccbacbabbcbaacaaabccccdacbcabbbbbdccdaaddcbaaaccaabadbabbbcaaaddddccadaadbbaabdcbdaabcbadcabbbcbadddacdbdaabadaabacdbbdcbdccccbbdccbabbcacdacacddcbababaacacccaacdbacbbaadbbaabdccbadcbaccacdbbacdbddbdaacdbabbacdcacaabbddaacbdbacabcadbccbcbcabdddadddabbbcccadbcabbbbbcaaadacccbaabbbcadaadcaaabcaccacadadbabcbddbdcddcacaddbcccbadadabdbbcbaaddcabaadbccaacaabcbdcccbcadbaddadddbbbaadcbdaccaddcddaabcacdddaccbcdaccbdbacbcaccbcbacadbddcabbaaabccccaabcbdcabbdddcabaabbbbcdabbdbdcbcaddbabaaaaadaababbdbabddabdddaabddbbdacabbbcccacacbcccdbadadabaadbdccbdbadccacbbcabbaaddccbdbbadabcccddccadababdabdddcacaddbcbcdcccccdabdadddcadcdabbababaacacccbbbbaadbacbabdcbcbcdccbbdccabbcabcaaacdadaaadbaaabadacacbaaadababbdccaadccdbadccbdbacbcaabddaacccdcddacaaccdcaaccdcdacbadbbaccdbcccdcaccbdcbcbddbbbdaddcabdcdccccddbddbcabbaabdbbabcacaaaabdadaacdabbadbdbbcdbcbcbdabbdbbbbdabdccbddabcdaaadddddcaaccaccdaadbdacaacabadddabbdccaaadbabbcbacddaaccadccccdaddbcdcbdaadabbbdaddbddaaadccadbbbaaadbcabdadbbbccdadcddcdacbcbbccabdaadbbbaadbdcbbabddabbacbbbdabcbbcbacabbacdddccddaabcaabdbababcdbabbbcddbbdabacbcbcdddbccbbccccdbdababdabcbabcaabadbddadbdbbddacdbcdacacaaaadbcccacacadddadddbadddbdaacddcaaacaaaabaccdaabdbaccbcaaadacccdadabdddcadcbbabcdbddbaababdddbddbdcabcdbdcddbcbabbbbbbcbcdbaabdabcdbcbbcadddccdcccbcbccacbbbdadcbcbddaaaddacaadbabcccddaadbcbdcccdaababdbaabbbdcdbbdbcdbdddbcababbaaaabbdaadbbbddbccbdcaacacacaabdcbbddaccbbdcadbaddbdbadbbcaaddaaaabbdcbcdcbddddbdbdacccbaabbadbaacaddbdacaadbccbdadacddcbbbdcdccadbcdaaabacaadcccdababbcddcdbbaabcbaccdcacbababccdddddcbaccbadaccdbbcabbcadcbccbcdbaadadcdbaddbdaccbbadabddccbcbbdbbacabcacdcdbdabadcdbdccaadddcadcacaccbaccabbbcdcabbcabbcdddbadddcbacbbbbabadbdbbdacadccdbbacbbdcadadccdccacbcdccddaabcabcaacadcbddcdaaccdcaaabcbcdcdcbdadddbcababababbbdaabacdcdcbabcbadadbbaacadcccadabdddaabdccdcbddddbcadbcbdbcddaddabcdcbbbbbacbbcdccdadccbdbcdddcacacadccccdaaccaccccbacadbcaabcdbdddcdaddddcdbddbdbdcaadbbcbbdadbaabbdcabdbdaddcbacdbbcbbbbcaacadaccbacdbdabccbcdbaacbbadbaabcbdbdaddbaadbbdbbbddddaddbaadcbbddaabddddbcbdbbabbdcdbcdcccdcacdbdadbddabbadcbdaadbdaadadcbdcddddaacadccaacddddbbcbcdddbddbdaabcdcddddcaabdcdcdbabbbdcacbbbcdcdbcbabbddbaaacaddcbabdddbddbccbddbcdbbbbcacbaaadabaddbcbdaaabbccaddbbbdbcbbcdcdcaadacabbcaaaccdabdbdcdbcddacdaabcdbdddccbcbbdccdbabbdccaabddabcdaaaabadcabbaaabbbabbcabddcdbaabcbddbbbccadcbbcdddccccbbbcdaccabdadadadcdaddaccdaababbbaccbccacadacaadbddbaccaaaabdddbcbcbbbdcdacaccdcadbacdcbdbabbdadbdbaaaaabcbcabaddcababccaaacabbdacabdadbbdadaaccacdbddaadabbcdbbabdadbcbaabbbddbabdaaadababcbbbbdabdcdabdcddccbbdbadaccddaacbcdccbcbcbdacabbbdcabcbcdcdcbdddbddababdadcbcdbbcbdbcbacaccdcddaaabdddbbbddcbcacdaccdbddbbcbbadbbdcbabbdabddacdccccddaaadaaccabdbdddcaaacadcccdacbdaaccdbdcdddbcacbaccadabcccbdbddccbbcaacaadaddaadbdcabdbbcbbaadcaccdbbdbcdddaddcddbacaddcbbbdaddadaabaabdaabdbccdaacdadcccbacaabcbdbbaccaacdbddddaaabcaddcddbacbbabaacdbdadbbabbacbbbddaccdbcbacbbacdcdddabbdcadcccccabaacdccabccaacbadbaacbacbdcacaaabcbcaabbdbaccbdcccaddbcccccbbcccddcbcaacddbbaddcccdaaccbccdcbacabbadadaaaccdbdaacdaabdabbdcbccacbdadcdababadcdabcddbcaabbdadddbbdccbccabababaccbcadaacdaadcbccdddddcdadccdbccacabcbcaaccddbccdbadcddaccaddaacbdddcabacbabdddcbdbdccddbcdccbccdbcdabddcbcbbacaabdaacbdbcadcdddabbddabbbaabdcccaccdacbbdddacccdccbaabcdbbdbdadccdadabcbdacadadcdcdbdddababdbcdbdbcddccdaaccccddbcbdbddadccdadbddabcdbddbccbabbcacadcacaaadddbdbdcddcbcaadadacbbcabdcabcabbdcdbbaacaddbdaaadadbccdabdcbaacacbadcbabaaaabbabadacdbbccccdbddadcccadbababcabbabdbdacbbbccccacdadcacddbbdccbbaadcdaaadbccbbdaacbcbcddbdacbddacabcaadcddabbbdbcbbcbbcacbcadaabbbbbdacdcbcadbdaaaacaabbbccccccdaabccdbddabbdcbdbcdaaaccbacbaacadccdadbddaaddccbaadadddabadaddabcabcdabdcdcbbaadadbbdbcbadcbaaadbabaabcddbccdddaccddcdbabccacdadddcaccbbacbbaaaadbabdadcbbcadccdaadabbcaacdadcbcbcbccdbabdddbdbaabbdaaaaadabacdcabbacbdabcbdddbccabcacdddbcdcbcbabdddaccdbabbcabddcbcddddacbdadabcbcadbcccaadcadccaaacdddbcabcddbdacbcadccbaabddbbadddbbdcdacdcbabcacdbccacacacdcbcdaaabbccdddacadcbaddaaacadaadacadacdddbbdbdadbacdcadcaaaaccadcaadbcbcbbbacbddadbdacbbbdaabcdcdbbaaddbdbbabdcbccdaacccdcbbdcdcbbaddcccdbddbbddbbbcaadcbbdaaacdcdabdddaacbcbcabacbcbbcdaabbbbbabacadabdaadcaadaaddbcbdabdaacdcabbbdbdaccabddccabddbdaddbaacbddcccbdcadcaadcbdcaccddbddabadbbcdaabbbdacbbdbdabccbbcdccdcbbcbaacccaacbbbdbabdabacbdaccabacbdacdcabadbbcdaaabbbbcdbcbbdaaacccdcbdadbddaccacddddcbaddbbbdcddacacabbcbaacdccbbdbacaaccbddacbdccbbcdbdcbccaccaccdadcdccdadcddbcbadddddbcccbcbcdbcaabcaddaddabadaaaaaaaabbcddbadcddddbddbabacbbcbbcdcdcdacbddddaddccdccdabcaccbcdcddcaacccaaaaadcbbbccadcdaaaaccccadcdcdccccaadbcaaacbdacbabdcdcddbcaddabbabbabbabccdababbadbdcdcdcdbbbcdaccbcaaddadccdcbcbbbdcacdadadaabbbdccddaaabdababdbbcbaadbabbbcbcdaacbbdbcdaccdaccccccddbcbaabbbcbbcbcbbddaddbbbbcdbccadadcaddcaddbcddbccacbacbabacbbbabadcccdcaabbbaacbacdcabbabccbccdcbcbbdbcdbcdaabbacabaabbabcadcabdddbacadbabadcaabaddaccadacbbabcacadbbbbaddcbccdcdaccaccccaabddbdcccadabbcacbccacbdaccbacdcddcccacabbdbcbcccdadbaccbbacccaabbbaadbbdaaacdddbcabadacccdacdbaacdaddbadaaccddccbacabdbabbabcdbbcccdcaccadbacaaddcdaabaddddbdbbcabaabdccabdccaacbcaaacaccccdabcddaccdbbaccbabdbaaabacddcbbbbbcabbabdaaadbddbdbacadbdacddbccbdcdaacbdbddbcbdddbcabbcbddbddbddacadbabddcaccdaddadbaddbdadacbabbaaacababbccadcbdbdabaddbccbbbcddbacaddabbbcacbbbbcdcbabaacddbacabdccdaadcacccbbdcbdadaaaacaddacdcccdaaacaddcdaadbdcdbdddbcaccdaaabaddddcbcabbccdaadabaacaabdccddaccbbbdadcadbccdbccadbddcccbdcddddabacdbcbbbcaabbdbcadbddddcbccbdabadcdddabaddcbbadcddabacbadddaadccbdacdabdabcccadacbcabcdccbccddbcaacdccbbbcddbbadbbbcdbbdccabbcbacbabbabcbbdabccdbcbcdadaddddcaccccbacbdadddadddababddbcbcccdddaaabccbddbbddbcdbacaaabdcadcddbbabababbcbabcccabddabbaaaccbcacdbcbaaddcdcdccccdccacdcdcacbabcaccdbdbccbadbabbadcdabcdaddbbdbcbaaadacbddbaacbbdccdbabaaaabacaddbcdbddcacadcdcabcbabcadbacbddbaaaadbbacdcdcaddadcdacaacacaaddbcbacacdbdcbbccbabbcabdbbbabaacbadadaacccacabacbbacbcaacdcdddcdccbbcbaccdabdababbcaacbbcdacaabbdbbdbcbcdcdbcbbacddcabcbdbbcbcbcdadccadcabcccdbdaadcdcbadcacccdabacdacbddbadcccbddadbdddbbaddcdabdabbdddbccdcabbcaccaadaabdcdcbdddcadbddbcabcbbcdbcdccdbccbcaadcbdbcabaaddcbcaddcdbabcabcbddcbaddcabaacdcccbaadbcdbadcbdabcaabcacbcaccacdcbacddaaddbdabcdddbcaddcbdcabcbaabaabcadcdddcbbbdcdbcdcdcbcbaccddcbacbdbaddcbcdbdcdbadddddacdaacddccaababdcbbacdddbcbadcbddcbbbccbadaccbddcaccccddcbbdacdcbcbcacbdbacacbabaacadbcdcaaacacaccbccabdccdcadddacdaadaabaddbccaccdddcbadadaabdccaadcbacdddcdbbabcccadbaadbaccbddccdcdadaccaccbdbbdabaccdaccbcccdbddcbcbcadacadabbcdddcdccdccdccbacdaaabdbbdcadcdcbcdcabcacbdaccaadbaabbabcccdcbdabcabbcacbcabcdcabbdccdbaccdbcbdcccbcabaaacaddbadaddabdacacbaddadaadcbadacbdbdcbdaabaabdbabcbbcaabdbdddbbabbdaccbddacabbbbaacbbcbadbaccbccdddbccbbadadbadcbdbaddccdbbaadabcbddaabccbdaaccaaddbcacccdbdbccadcababbdbbddacdbdbcdadabcadccccdbabcdcddcadcacccdbbccdbbbacdcdacbadcaadcbcddabaaaaadadbcccdcadadddadbcbdaadcdbacddacdcbcddaaabcdcaadacbaaaacdddbadcddacaaaadaaadbbbadabbbabbcabdbbabdcbacbaccccccacbdcabdbabddbadadbbadddadbdbbdadddbdccbbdacbbbbbccdabadabadcdaabbdcdbddabaacaabaabbddabadaccbacadadcccbcbcbdddacbadbacdcadcdabcdbbcdccdbaaababddcbbbdcdabbacaadbdccddcacbdbdbabaabacdabcbacbbcdcdcddcdadcdbaacbcdcccadadabdbabddcbddacacdddbbcdbacddbccabccdcaadcadaaccabcbdabdccdbddcbcdbddcaacababbcacaadaddcdcdbaaaabdbaddbabacaadcaaadacabbcdddbbbcadbdabcdccdaccdcdcadbaabddbdbacccdbbabccdccbacbabddbdccddcaddcacbdabadbbcabbbcaadcdbadcabdbdbbabccadcdbccbddacacadbbcdcaacccccbdcdcdadddbadbcdddccbbabdbaaaacadddbcbcccbcbddaaccbacddbdbcddbbaaadcdcbccbbdccbddccaaadbddccdbddaacadbbaddcdabacbaadcbdababdccadcbdcccddaabdaddabcbcadccddaadbdaaabbacdcdbbbbcddddbadbccaadbacabcdaddadadbdcddccaacdcbabadbbdcddbddbbdaddccadcdadbacbdacbccacacadccabccdcdcacdcbacaaadaadbbbdcbcbdbcaabbacbbbabcbcdadcbadaddcaddccacbddbcccaaccaaddabbdcbbdcbaabadaddbcdbbcbddcabdaacbcdadbddaaddcbbabbddacdbccbbcbddbcdaaadabcccbdbbcdcccbbacddbacdadaaacacbacaccccccdbcbccdbcadaabbbdcdbbbbcdbdbccbbbbbcbadddbadddcdbadcaccbdbcbcadabaddcabbbcdcbdadadacdbaacddacbadcccbacaabdcacbaacbdcadbbbbddaaaddcdaabaddddaccdadaddacdacbababcddbbabacccacdbcadbccdbdcddbdcbcbaadcacdaaabdcaaabadbadccdadaadaadbddaacdaaacdaccdcbacabbadcabcdcabaababbcacddacdbbbcdbdcdcbabaabaadadaadddcddccdcabadaabbadcabaadcadcbabaabddaddbcdaaacabbdacbbadabccbaaddcadbabacbdcbabaabddaddadaabbddabdcbcddbbcabbdabdcbdaaaccaaccaccdbcbddadbaadddacacbdbdbcdadacdbdcdacdadaddbababdbddcdccabdddcbbabbcbbbbcacdbbcbdcdbcdabdccdbbbaddbbbdbbdccdacabbcbcacacddabbdcbabbcddcabccadcbacbdadbbbacabccaccbbddabdbdacabcbabcbbbbcdbcaaddbbaabcdbbcdaccbcaaacbadacbacccbaadaaddbbcdbbaccdaddbdcacbadaabcdadaddacbbbbcadbcbbacdddbbaccaabdcabadbacdbaccaabbdbaccddcaadcaadbdddbdcdadcbdbadddbddabcccdcadcdaaaadaadcacabcbbdbacdcaccccbcbabdcabdbcadbabdaddaddbdaabdabbcbadcdbcbbbcbcbbdbdadcdbccdddacbbdbcdbacddcaadcbacddddadbcadbacddddaabbdcccbcacacbacbbabacbbbdabacccacacbadcadddddacdbadaccccaaaadcabbdbdbdbdccbabbbaccacbaacacacbcabbbdaddbacbacccdccddaccacabcadcddabcadbbbacadacbccacbadbaabbcbdbaadcdbcbddcbbccbbacbdaadbaddacadacddabadabaddbacccabcababaddbbddcaaaacbcaccdbbaacdbcccdbbccddcddacbbdcbaddbadcbcdcbbcccbbbddcdbbdbbacbbadabaabadbaccdaddbccddcdacbdbcbdcabaacacccababddcbbacbddcacdcaabacdcabdabcababbcbdbabdbaaacddbcbadddbddbcaabbaccbcbdbccbabacddabdadbabacbabbcbdcddddbbacccabcbdbcaabdadcbccbcacaacbdcaadbacbaacbadbadcaabcddabddbbdbcabadbacaccabccddddbbddbabbaabaacdccabcdbdbcddbddbcacbdbbdcabbbadcabaccddbccdcabdcdbbbaaddbcdabcdaabaabdbdbbcdbccddcadddabadbabdabcbbcbdcccbccddbcccdbdccdacadddadbacdcbbddcbdbcbbcaccadcadcdabbbbcddcdddaacbccacccdacabdbbccabaabbcdaacbaccdcabbbbcabcccdaacbbbdacbbbadadbadbdcdbdcbccccbdcbdbacabdcccbbccdbdcdadcacccdaadddbdccddadabcdaacddcddbccccdabcddcbdccbdcdbbddaaccdcdadccdbbbdadbdccdaaddaadbdabddcccccabaaacaaddacabbbbcabcdcdbabbbcaccbbadabdddbccbbaacbbdacaabdbacaabacabbddadabcccccdaccababbcbcbbccbcdccacdcdcbbbdddcccbcbcbcabcbcdadcbbbcccdcbabcbdcdbbbbdbaadddddaaadacabdddcccadacbdadbdcbdacabcddbbcadbcdacdcccbdaadacccbabccbbbdbbdddddbbbbcdbdbcbcbaabbccccabcacdddacbcabaadcabdaccccacbaacddcbbdcbaabbbdbadccaddbdbdbbbdcbabcdddbdbbdbdcbdbccbbbaadbbcaaaadbccacbacbbccbabbdcbcbbcccbcadbdbabbcbdabcdcbbbcaacacdbbdcbbdcccbcbdbadccccbddbaaacbacbcdddabababcdddabdbdcbcaadccbdacbbabacbbbbcabbbcbdbbddccbddcbbbaadacaabacdddbcccccbccbddaccdcaaabdacaddadbbddabbccbccbcadbaddbdcadabdaadcbcbbcbdcbdbacaaaaabadbadbbcccdaadcbccddbdadbbbddacabbbaacdddcabbdacbccaaaadcabcadbacdbcacbccbdaacbcdabccabccddadabaabbcbddaacddbcdaacdbdcadccdaadadaaddacdbaacabababddcbdbccbacdbabdbdbbadacadccdbacdabbddddaddbbbbadabddcdbcddbddbcbbbabdbbaadadcdacadaaaaaddadaabddcccdbddbbcdcdcbaddcabbbabccdcacbccbddbdccdcdbdcdbbcdadccbdbaaaddbdbdaadcdbbbacacdcabbdcddabcdcbabdaaabcdbcbdbaddcadccaddbacdadcbbbabdcbdccccdacadaadcadadbbbdbdcadacdccdcadddcddadaadcccabdddabbbcddddbcaacabbdbcabacdabcbcdbbdcadcbbcdcdadabcbbaadbcccabdabcbacbbcdcacbcdadadbabdacdadcaaaaaaaddbcabdcaabbcacccdaacdacdbdcccababdccdbbadbadacabdccadacaaddacbdbacaaccbcbbaaaadbcdcddbbcdacacccdbdaacddcccdacdddbdadccccaabccdcddcbaabacddadcbdaadaadbdcddbcdcdbcccdcbbdbccabcabbabcbbabcabacdcdbdabcbddcddbdacbcddbaddaaacbbdbdaddcbbbadaaadcccccccacbbcdbdbcbcbbcaacdacabaaaabccdaabdacacbaccdddacdbbabdaadaadadbbbddacbbbbcdbcddaadadcddacbcbabdbcdbcdabcbaadabcbcaddbbdcdbbcaddcdcbacbbcbbdbadbcbdadbcadaaadabcaaadaabdcadbcbaabaddccbacbaabddcbababbdccbadcbcccadddcaaaabdacdcccdccdbbbcbcabdbadadabaaccdabdccdababbccddbddaabbacabddabbcdcdcadcaddcccbcdbcdaadbdababcdadcbbadaccbcbdbcbcbadcacaddabcddcadcacddcbbcdddddabbcbbdacdcacddcadabbcaaaddcacdadcaccbdadbbbbdbdcaabccaddcdabcbbcbcaabddcaccbaccbadadadabbdbccdaddbdabbacacccdabdcdbcbcbddabdbdcddbabcdcacdacacaacadaacbdcbcabcadbacbddbbbbdcbacddcbcbdacbadaabdddbbaacdcbaccacaacbcaddabbcacdacdccabadbaccccaababadcdcdcadcdababccbaacbcddadbabbbdaddacabcdbddbbdadbdaccacbadccdacbdcacadcdbcbccaadbddbaddbbdaccdbbbdabcabddacbddacbaadababcbddacddcbdabcbdababaacadcacbccaababbacabccddaddbcdcacdcbadcadcadddabcbdcacabcaddcbbdbdddabadcdcacdbdaaadbacaccdcabacabdaadabddcdadccbaabccddbdddbbabacaddddbcbcbbcacdbdaaddcdccabaaddbbdabdcdacaaddddcbacddbddabdcaaabdaaccabdbcaaaacabadbccbccccbbdadaddcbbdbbadadbababacbbaddbbcbcbcdacdcadbcbdbadbdbcabcabbccbbcaaddcbddadcdddacabcadcacccdddadabacaabcdcbacccadbcabcabcbcbdaabaacccccaabbdbccdbddbbdddadcadcbcdabddddadabaddbbdacbabbbdadcbdbadddddbacdbbdbabddcbcccddbdabaddcdbbbcdbcabdadadacccacdcccadaacddabcdbdcbdbbcbbcbdadbabcaadbbccabbabbacdcdbddccacbdaccccbbaddddddcdcabcbaaacdcdacdadbbaccbccbacbccacbaadbccddadddcdbcbbdccacbdddbbaacbbcdbbbbbdaaaaddbcbccdcdcddbbbcacbdbbbbddaabbcddabcbccabdabdcdcabccccdbadadbbdaadacaabadabaabdaadacccabbccdbaaacdacdacabcccbcccccddaccdadaccbbcbacdaddadbbcbcdcdbccbababadbdccdadbbdcbbcdcbddabbcddbbaabdbcaccdcdcaadbaaadcddbcddcdadadbcbdccccdbbdaabccadcbbadcaaaaddbdaaadcbacaaaadbdbdbdbaacddabcdcdcacbbbbcbdacccaddaacacbababbdbbbdccddddbbaadbacdbabbcbcbaaddaaccbbcbdcdddbcacdddbcdbaabbcbbaadaddddbcdddbcaaacccacdaadaaddadaadcbacbbabddbcbddbaaccddddabbdabbcbbdbddacaaaaaccdbdbadabbacaadadaaaacbcccdacdadccabcaddddcdbbabdbbcccdadccdcacaaaccdcacabbcbcddccabacbbbbcddbbcabbcbdbcabdccbababacabcbdbadabdbbcaccbbcdacbdaccbdbcaddcdaddccdcbabbabcbcbdcabacdbdccdbcbdccaccbadbcdbbdbcdbddcbacccdcbdcbbaacbcbaadbbabaaabcbbaccbdbadcaadbbbabcbddbaacbacdccccdcacaabdadbbcdbaaccdbdcccdddaadddcabbdbdbaaabdbddbabbcaacbddaddbabadcacdacabadbdbdbddbaadbdcacadbddcccdbdbbacdbadaacaadbbabdcadbcbbcbacabadaabacdbaabdaccdcaccbccbdaddabbbdcabbacbcaaacdbcdabcaadbcbdcaabbabbddddbdabdcadabcadcaccbcadddcaabbadcaaabbabbdccbabbcaaadcbaacabdcaacccbcacaabaddcabddacbcbadaddcbcadccdacadacdbdccaccbabdcbcaddcacbcbdddabddcccbbbbccdaddadaaabcaaccdacabcbdadbacacdcadcdcdddcdcadddcbdcbcbdcdacacdaccbaaaabbacbcdabadbcdadddaaadcbdcbdddddadddbaacbcbbdbccabaacdadccabaaaccdbababadbaadbddababaccbcbcbabdaaabbdcabdcdcbdcbabdcaadccbddadabddcbbacdcddacbdccbdcdccbcadcadcacbddabbaadcbdcdbadcccddcdacdbabdbbcabcdadabbdccbcccddddaaabbcdcacbaddaacaaaaaccdbadccaacdabbbcaababcbddbbcdcaaaccdbcabdbabdcacabdbdbdbcdccbcbddbacdbdbbdccbcbacdcacabcadddcbdbadadbaadddccbcbbaaaabccbbbadcaccbbaabbdddadaabaccaacacbdbaddbcacabccccbbbdbccacbccaacdbdcbbdcbaacbdcabcbdccbcaabdadccaadababababdbbcccddbddbabbaaddaabbbbdaddbdadbbaaccbaddccabdcabcdcbbcddbbdcaaaabbabbacbcbbccdbabbccadbddbcacdcacdbcaaccdacbbacbadcddbacbabddadbabcbcbaabbdaadaadcdcaabadbccccbaacbbdcbdadcaadcaaaddbabdaabacccbdcbcbbccdabdcadbacddbcdddbbbccdadacbbababaccacdbabbacacdabcddcaccababadbaabcbabacdcbcbbbaacacdacbcbdadcdbddabccdddbacddcabcbbdbaaacabdabaacdbdbbddaadddcdbacdbccbdcdbdabdbcadcadbaccaabacabdbabcdabbddcaaacadccdabdacdcbdcbbadcabaadbcddcaddddcadccadbdbbbdadbccbcadccdccbaadcccacabaccaadbabbcaacbdbcbbbbcdbadbccaabbdcacaddaaddcdddbdbbdcdabcbacdbaadccdddaabccadddbdacabbcdcdaacdaddaaabbcdcaaacaabdaabbbccbbdddbdcbdcbdbaddbbddcadbdcacaacadcdddcdbabadcacadbadbaddbcdaaacdcdadbcbcbbccdcbbccbdbaacbdbcbddcbcacbacbaaddbbdbcdcabdbaadccacaaadbdbbadaadbaabdddccdcbcaadadbabddacbbabadbdabacccdcaacdacaabbdbdcccddbdabcbdddcdbbbdaaacccbddcabbdabdaccaadcacbdddbbdcdababddadccadddabcacbbbabdcdcabadcbdacdbadddddacbbbcbdadcbddbcaaaacaacaabdcaddcbcbccbccbddbaddbabbaabbcbcabddbacbbdbacadcdbdaaaddbacdaddbbbbdaaacbbabcadbcbbcbdbbacabddaaabbcacacaacdbccdaabcbbabbddadddcbccadbadadadbaddabadbdcadaadbcaaacddbcaaddaacacdccadaabdcccbadabacadcdcdbddcccacabaccdadadcbbabaadbdacccddcdcccbdcdbcbcbabddcccadabcdcddbcbdbdabbcdbcbccdacccbadbdddcdbbcacbacbccbacacaacbcacacabddacddbacbcbdadcbcdbcbdaaccbbbbdddcacaaccadccabcbacdabcccbbcddbabdbbdbbbabadcddcbdaddabadabbccbabbbcdacababbbbabadcdddcddabcaccccadababacddacbdbaaadaddccbbaadbbccacbbdbdcdbcdddbbadbccdddacaddaddcaacadadbcbcacabbbcdbccaadcadcbbadaaadaadccdcbdaacadbdbdddaabdabacabcdcabcdacdccccdbccccbababddcdbccacaddddcccdcdcbbbcadaadccbbbddbcadabdbaaadaccdddcaabaacbbcbddbcacaddbabdbdadddddcbdcbbddcaaacddbbbcadccdbacbcbdabdadcdbdcbcdbbcdbdcbbdaaadbacddcdbddabcdddbccadbdcdbdddcdccdacabbdccdacaabdcbaaaaacdbdbdaadcdcbbadaaddcbcdbcccccbabcacbcdaddabbdccdcabcbcbcdbcbdaacccdbdbdcdacabcbbcdcaccddabdddbbdbbbccdabbacbbabcddadcadddbccaacabdacabaacbddccdaaabdaccbabdcdbdbacbbabcbaddaaacddacbcbbdbbbbddbabbccbadbacdbabbadbdbadddbbabbbbcdaabcddaadcbdcabbbdcacacaaaaaacacadcbadadbbdbbcbcadccdccbaabdaaaaaccaadbababcddabacbcaccbaddddabaaacddddcdcadccbccdbdacbddcbdcbdddbdabaaabdbdacbccbcbcdadbddcabcaabdcdadcdacacdbacdadadddacbcacbaabbbdacbcbaddcdaacdadadbccadcbcaccbbbabcdbadcaccccaabddbadccdbdccabcbdccaccbcadccabccbcbcababccbabcbdadcaddcabdbddaaccaddbabacaadcdbcbccaabbbabddbcdadadbddaddabbbadcdadcabadbbdaabbdbababcbaaadabcadcdbcdbbadabddadcdbccbddbcabbcddabbbdadbddddbbbddddbbcdbccddcdaabaabbbbbcbbadaaabdaabaababadacbacabdcabddacadcaaddccbbccbabcbdcabbaacabdcaddbbacdaadbcaaddbdddcbdaaaabcbacdaacddcabbabbbbbcaadadccacccabaadcccaacdacbabbbcadbbbaadccbcaacbacdbddcdabacdcbbdadbadbdcadacbaabaaccbabbddbdbbcadddbdcbacdaabcdcaaaacbbccadbcdddbaaacdbacabbabdbdccdcdcdcbcbaadaaabbbcdcaddacdaabbcacdbdcbccaddbdcaadadacdddcdcadadcabcddbacbcbacbbbaddbdcbddbacdccabaaccbbccdbbbbccbbdcbdbcbbabcddaadbddacccdbdaabccacdacccadcbadacbcaadaaddaddcabcbdcabdddbddacabcbcbababacdccbadcacdcddcdabacbbaacbcacddccddccbccadcddcdbbdcddcbabcbccacbbbcaadcddcabacabbcacaabcdbdcdaccadacbcaaaddbcabbcbdcacdacdabcacdcadddaacbbbacbdcabbccdcbacbcbdcdcbdcbcbaaadcbadaccabcabbdbbbdcacacbcbdacddaadadbcadadbbdadddaacbcacadbcadbcbbadabcbbaabcbcbbcacdaadcacabaacbacddcdbdabbcdbddbdbabdcaabacbdabaaabbcdcdddddbabbbacdcaaacdcdadaabadcabadbdddddccbbaccacaabcbccdbdbcaabcacdaaabaadabbdbbdbccddadcddcdcdabcccccadbbcccaaacddcdbdccacddbbaadacbbdcbaddaddccccdaddaadbcdbacbaddbccaacbbbbdabcdacbacaaadddbcabcdbdbaccadddababbbcbbdaabdadadcadbdddaabcbbdaaaacabadcddadbdcbcaacaddbdcbdcccbaccddcbcbcacbdaabddccbbaaabcadbcdaaacdbbabadbbbcddcacdaccbbbbababccccbbdddddbcbabcaadccbbdddbabaaadacacdbbdaabadccdbbabbacbdbdadbaddabbabdbaacccacddbadbcadbbcaabdbcaddbdccacdadacaacccadaaaabbccdabdaaabdbbdcbaaabaddddcbddadcdcbcadddcbbbacadbdbdcddcbdcbdbadadadbcbddbcbcdbbbcaccbbbbabbbcccbcaddabdcbcdabacaddddcdadbdcdacdaaadcabcccadcabdbdddcddaadcccdadcbadbcdcbcbbcaacbaaacbacbcbccaacadcdadacbddcbcdcdacbcdaacbcbcacabdbdccbdbabbaacacbdacbcbaddcdbdaacdcbdccbdbabbdcdaabbaaabccccbacaacbddbabacdbccbbcadbbddcacbbabccdadaabdcbdadbcbcaaabacbcbddacdcbdcabdaaaaadcadcbdccabaddbababcbcacaabcdbaabacdaccaadbdbbaaaabbabbbddbacbdcdcacbcabbdbaabcbccdabbcdccccdbabadaadacccaabdbbadcddabcdbaadddcdacaaabbaaadaaadbbadbdadbaaabccadabdbdbabdbacbccccaabccdcbdadcbdcbadcacddacdcbaacdcabdbabcdbacdadaddbdcababacdcdabaadadaaddadddbaddccddaabdcacdbdbcbbaaaddadbccdacdbdaabacdcccdacdacdbcdcaabbbadbaabacaacdabddbbabadbdacbabdcbcaadddcbbbbbccdcabaddacadadcaddcdccbcbddcaaacbadcaddcabbabadbcdcdcbaabdadbbdbdacacaaddbbccabccdaabcdcdbdabccccabbbdcacabcaccacdabccdadbcdbddcddccccadcbddbacdcbdabcbddaaaaadabbbabdbbcbbbddaccacbbacbaabbbddddcbdddcabcccdddadadddabcacbbdadcdcdcbcbdbbcbcbaacaabccdddbcbcabcbcdcbcaabbbdcdbabdcadcbdddabcccdacacadbbcabaddbdaaabdbbaccbdbddbbdbddddaccdcdbcbbadcdbcccccddddbbaabdcdcbbacadccbaabbaaddbcccbbdcbbbbcccdbaadabcdacddbdbbaacdacddaaabbddcbbaccaacbcacbdcdacdcbcacbdbbcdcadacacdcaabaabbaabaaaaaabccbbbdddcadcccdddacbbadcabdacbaaaaabddddacbcbdcabbdddadbabdacdbddcabbddaadaadadbddaaccaabcabcaabcbccacabbccaddddcbbbccacabddbadbddaaabbadcdcdccdbacdcdadbcabdbcaddccaabdcccccabddddcbaadabdaabbdbbcdacdbacbbdadccaccbcdaaaabaccbcbdabbcdbdcbaacbcbcdddbaaacccacbbdadbdabdadddbabaacbbdaabaaabbcabdccdaaccaabcbdcaccaaacdbbccabddcddabcbcadddabbdcbbbdbcadbacdcacabddabacbbddddbdddcddddadbaddabcbddbdabdacaccdadadbbbbadddcabaadcdabddcdbabadabaaddabbdbbcdcdcacbbbcababbdadbbbcdcbaccdabbddcdbccbbcddbcbbcadcdbdccbdccbaccaadbbaacaabcdbabdbddddbacddacbacaacdcdcacdbabdabdcbacbbcdabdcbbaddcadbdcdabacbcdbbacbdbbddcdcabdccabbacdacccbadaaaadcbdcdbddbdbbcbbdbaacaadbdbcadcacaabdbcaabbcbbaacdbaddbaddaababbcdccbdcdcdcabbdcaccccddacddbbcdaccaadcbdaadbcdbcdaabaacaabbcccccdcdccbacabbaabbadaacbabccbacacadbcbccabcddddddadadbbdbdaadcbcdcadadaaacdcdbcbcacbdbadcbaaddaacbaccbbccaaaaddadadbdbcdbacaddccddabbaaccdddbdabbddbbcbdcdcdbcdbbaacaaddcabbcaadacdaaccacbddcdcbbabcaccbadcbbcccabdcacbcdaabbadddbabacbbbdabaaadcbdddbccbccaadbcccaaccddbbaadbbcbcdcaddddbaabbdcdaabcbdabccbaddddcdcaadddddbdadacddccadbaddabbcbdacacabdbaabbcbbbcbcbcbbdcbadbbcbabbdaaccdcdcaddddcbaaabadcbababdbaaadadcbccadccbccccdbadadcbdaacaabadadbbccdbbccabcbbbacccddbacaccaaaabadcbaccacdcbdbbcbdcabdcacabaddbcdbcabdccaaccbbabdcdbbcaacbdabaaacaaddbcbdabdcccaadcccaacaaacccacdbaabcbcdaccdabaacaddccdbbbdadabadbabcbaaaadbbbccccddbccadcbcdaccaaddabcbbcbbaabdadbbbbadaccbcadddcbaccadbddbadbacdadccdbacdacadbadcaccccbdcacdbdacdcaccabdddbdcbbdaaabcaaccbaabbdaaaabdbabcbdcaddccdaadddcbacdccababcdcdddbacbbcbabbbaccacaadacbbbcddcacdbabcbadccdcdbdbcbbbcdabbbaaaccacddaadbcaabbcdabbadbbadbdabacabcacbcdbaadbcbccdddaacdcdddbbcdaadbcadbacddabcbcdbabbbcadcdaccbdbcabccbcdcddaabdcccdbdaddaabbcddddacdadcaccacddcbbbddaccacbdaaddbababccdaabcdccaaabdcbcccbcdabdccdcabcdddaacdbaaacacdbbacdcbbcdcbccbcbadabdaaadaccbdcadbbbdcccbbdbddcdabacdbdabcdabdbadbdaaddccadbbdaadcdaacdbacddabbadbacacdadddcbccdcdbaddcadbabcdcdcbddddddcdabbbbbacdababccccabbdbabcccaacaacccdacabbddcadacdaadddadaddcadacaaadcaababcbdaabcbcddcacadbabbddadadcadcddbbbcaadcabccddacdaababbdbbbbdcddbbbbaaaccdadbbbbbbbbcadaacdddbcbabacdabbadaccdaccdaaccddcccdbdacbaddadaadcbdacdbbdbbaaacaadaddbacbcbacadddbcaddcddccadcdbbcbaddddcacddbddcabbbcdbaccccbaaacaacabbbaacdaaacbdcbdaccabbdabbaddcaccdadbcabcbdcbabaccadbdabdcbadddacbbcdbdacdccabccadabdbddcdabbdabdaccbdbbdccbbdcadbcbabbdbcbadbbccdaadadbaccdbddabdbaadbbbccabdcbcbbdaddcccdbbbdbaabdbacbcbcccdbcacdadaabdadbbdabacdbbabcaacdadcabccdcdabaccdbaacaaaaabddcdcbabacbdaccbbacbbabdbccdadddddbbaccdbcccbcdaadaaaadaadcdbadddaadadbcababdcbaacccbccaabdbcbacbdbbbbbaaacdbdbacaacbabdddbbcdcacbabbcacbbcdabbdbcdcdbaaadabbcabcadbadcbcdccaaabaddddddddbcdddadadcaccddbaccdcabaddbcdbbccccccaddaacadcbdbcdacaabbdbccdbdabdacccdcadccdddbddadbbbbbaacdaccdcdccdddcaabcccbbbadacdaddcbbccddbdadacabcbcbcacbcdacccaaadbdbddcccccdaaacbcbccaadddcccccbadcdbdcbadcdcaaacccddcbddbcddccbbcaccddabbcacdaccaadcddaadbdbdcdddbcbadadbaacdccbdbabbbdaddabacabadbdcaabacbdbbccbbbacaccabcdadbaabddcccdccabdbabaccddddabddacaadababcacabddbcbcbbbdacdabbbbdccacaddbacdddadbcbcbdcacbadbdccacabccddbdabbcbcdcbabaabbccabadcccccbcaddbdbcdadcabdcdabbddddaabddaaaacbbddbbbacdddccaaaadbacdacdabadbdcbdcbcdadbcdddabbbcddaddabaadbcaadcdbabacdccacbcacabdddcbccabaadaacaccdaacadaacdaadabaadcdbccccbddcbcddcccddbccccabcabddccbbddadacbdcccbadaadbadbdcbbaaaacdddacbddbdbdcaabdbdbccadbdccaccaaabbaabbdbcddaaddaaaadcbdcdbaabbcbbdbcccbddbcadadaaaddbaadcbcacaccdcbabbdbcccaddaaccccaaaaadadcdabbaacbddcccaaaaaadabcbbaccbbbdcbbbbdaaabbabdbacabccabaadbddddbdaacdbcadbcdcbdacccbdacdabbdadbdbcddcdddbcdaacbddcbddbcbbbcdbdbddcdcdabdddcaaaddabbaaaabadaccbabcbcdabcbabcaacaabccdcadabcdbbddbaadaaaaaadcabbcdaaaccdcbacadddbaaddacdbddbbcaadbdcbdccbbbccdbaddcaadbccadabdbdccbdadbdcbadbddabadbdbabaaccacbbcbabbbbddddababdaacdbbcbccccdaadaccbbacccaadcabbdaddccbabddcccaadababddadadccbbadbdcaadaaddbbbcbccccccbcdabcabddaacccadcdcdccbcccaadaadcccaccabcddbbaadbbcbdcabbcaabbcacbdbadcaacdcbcbcccbdccdadbbbdcdcdcbbdcbaddacbbdcacccbbbdbdbbdbbaabbaacdccdbbccddaccacaabbaacbdccccdaddcccddaaabaacabbcabddacaccdabdbcbabddbbbabaabcabbbcdacddabcdddcadbaccabaabcaaaccbcaabccaabdcabaaadabaadbdacbdabaadcadccdbbabcbdbbddcbccbaacdccdddbdabdbccaddadadddcaddcbbaadaababadaaaccbccbcbacaaccacdbdaaaabcdbcbccbaaccbdbcccdaabdcadaaabbbabbdccdaaccabcdcaddbcaadadbacdcadadaadadabdddbaadddccbdbacbbcbdbcdaddccaaaacbdccccdabdbcacaccbbcdbabdcaddbcdddcdbadcabddabaacaabdcdbadbcabcbdcbdababbadcdbbbcddbcbcdbbccccdabdddaddddcbbdadcacdcadaaacabccdacbacdbbbaaadcbdadcdcbccdddaabbbbbdbbaacabdccbaacbcdccbbadcbadbdadbacdcaacddaddcbcabcacaababaadbdadbcbaabcbaaacccccbdddbcacbccaaccdbcbcccbddbadabaccdaaadcacccacaddcdaacbabddccdcaddbbacacaabdbddbdcaccdabbdadacbdbbdbaacbdbcddcbbbbbabadcaaccabcdbbbdacbabbcaddabbadadbcadbdaacadbdcdccacbdbddaabccdbcbabaabacacbaccdccacbabcbacaaadacadcacacdbbaaabcacacddbaabacadadabbcbcdbababdbcbbaddbdbdddcddbdccbaddccadbdbabddaddbddcbdcacacacdccdbcaadcadbcaddbcddaadccaccbccdcadddcdaddabbbaadccbbbddccaabcacdbbdbabacaaadaaccbbdcdaabcdcaadbdabbaabbcaccadbcdaccaabcbcacdabbcacccdbcbcdababdbaddadbdcddccbbcdccbbcbddbabdababbbdcddbaaddaaaccdacbcdaacadacbadccdacbdabbcadbcaccdcbaabdcabdbbacaaaabacbdaddacadaaabdbcdacdbacdddaabacdabaddbcdaabbbddacccddbabcaaabccbcaccbaaaccbbabbabdddacabbabbdcdadcbabcbcdaddbacbbbcaaccbbbcbcccadbaaadcdccdbbbdcbadcbbaddacdbcdbabccbcadacaabdccbababaadcacaadabadacdbcadbdcacccddadcdcaadcdadbadbbcabccbaabcdddcddcdbacddabadaccbdadbddccdbdcbabaccbbbccdabcdddcdabaccbadbaccaadbdabdabadbcaddacddbacbabbdcdbdbacdadccdbacdadbbaccbbaabbdddbbadabcabdbbbbacdbababaccacddaacbdaaaddbdadacbdaabbddccccaddbddcbdacbddbcbaabbbbcadbcdaadabdcbccbdcbcccaaaacdddaddbdcbdacbadbdabbbaccdcabadadbcbcabdabcdbadaccccadccdcdadcbdabccdbdcabbdcababcbccbdadcdbadaaaabddbdbbdaadadccadacddadaababccbbdbaddabdcdababdbbcdbdbdabcdaaadcbcacabddcbaaadddcbbbcabdcbcdbabdabdcbdaaaabdcaabdaaadddccaddcdadaacdbacbbcaccabdabddcadcdcaccacacbbacddacacdbbaadcacadaadcdcaacacaaaabbccdbdcacbddacbdcdacaacabadccaddccbcdbcacdadddadbdcbbcababbbaaddacdadccccbbcaabadcbdadadcbcbccdcadccbbdaaaddadbdbacabbccccdcdddadacddccddabdabcbbcdcddaddbdadddccdaadcadbbaabdcdcbbdcccbcbbdbcaddbbccbadccadabccbcddddcdaabbbbddbccbaddcddacbbdbdaaccadbaabbaadbbbdbaabdbcaddbdabadbdadbadabaacbacdbbddaadadaccddcaacdccadadacaabaabcbbcbabdbbccaadcacbccaccaaabcbaaaabbbcccabbcaadbbbbdbadaadcacdacdbccaddadbdddbadaadcbacdbddabdacdbaacbaccddcacacaddabdbccbdbcadcdcbcdcbdadaddcbacadccabaaaadbbcdcacacddddcdcbaaabaacdabcddbddbcbabbaadabbadcbdcbdaccaccdbaddbacccdaaaabcaddbbbbabddccddaccbddbbbcbabadccdaddadcccdaddcacadbabbbcbabbdbcbabadbbcaaddccbaaacbccabacdcadaacabdbbabadaddbbccdccdcaaadaacdbacbadacddcccdbdabbaacbadddcaacbabcddaaccaacdbadaadbbbcddccacdddddddcbadddcabbbbdcabaaccadccdcccdbaaddddddbacacabccadcddcdcccdcbacddbdbacdabadabadaacdcbacadbcddaadcbcadbcbdadadccaacbaaddadcadaacbcbacdabcdbccdcdcbcbcaddcbcbbaddbbdacbbaadbcdcddaddbcaabbccbcdabadacaddccbbccabaababcabcacabcaacdbacabcbcbddcadbabdbcccbdadddadcbbbcbaddabcccdaddabdabdbccbbcdddbacaabcddcbaadbddadccdcbaabadcbcadcbcaabcababcbccaddbbaadbbcdaaacdaadcddbacbbdacdabcbbbddcaadaccaaaaaacabccbabbcbddbdbdbcddcccaccdadcaddacaacadabcdbdabbcbcccbaaacdcdaccaaabdcabdbcbbcdadcaddddaadacdabcdbcdacdbcccdbaddcdcdababaacbbcdaacbbbcbbabcaacbcbbdaadcccdbcacadcccdababacbabccbacdcacabbdbaddbbdabadccaccddacdcdaccbdbdabaabcbcaacacdddabbdadbdcbbadbabadcbcdacddccacbcbcaccccccaaccdbdcdcabdcdacdcdbacdccdaaadbaadccbddbbdcdbdcdcdcccbbaabbbccbbdbacdbbcdcbdbdcbddbaadccabbabbcabcaddddaddddcbbdcbababdacccacbdddaaaaabccaacddccbdcdcdbbccbdaadddcaabacccccdacadcdcdadaddbbacccddabaccbdaaacddcbcccaabdabbddabccdadbabccccdcdcabbcabddaccbbdadadababddddddacacddbaabbddaabcbbdbcccbbcbbbadbccdaddbbadccadccbaacbbcbcbcbddcbdbccdbacaacbabaaacdddababadabcdcbbdcbdbcadadcdcccccdccabdabaaadcaabdadbabaadacbccaabbacbdddcdbddaadabcdbbbdbcadddbdcdaabccbcabccdabbabccadacdbcaddaddccadcaadcaabacacacdbdadabbabccacabdcaddacabbccacbbbdacaccbcccabbacbbdbdcbbbdbacbbdcddddaadacdcbbcabcbaaacaabbdacbabbdbccdcbccdbcdccddcdadbdabadaddbabacbcbbadadabcadbabddcacaadacbacbccaabbbddababaabacabbcadcbdbdabbcccbcbcdcbdabcacaccdccaddbdccaabbddcaacabcbbdabddacccbddddbbcbdcbdccacbaddbbbbabbdacdadbaacabadbcbadddcdddddcbdadcaddddbacdabdbaaaabdcbdbdbdccaaadaacbbcdcaaccddcbacdbadcdcbdadadbbadbaccbaccbabdbccccaadacbbdbbdcbacadbbbcbbaaabcddcbcccabcbcaacdbacbaadbabaccbcbdcbcddbdbdbdccaddcbcbbabbbcbababddaaabdcbabaabdabbdabbcbddcacabdbbdcdbbbdbdbacabccacbdddbbbdabcbcbaccacadbcaacbabbdaaccbbdcadbbbacbdbcaadbbabddadddadddacbbabdabcbdcabcdcccddcbabaabdcdbbbbbccaddbddcdcacdcdbacabcbdbbbbcdabdddbbccbdbbbdcbbdbbadcabdacbdddadddcaacdbaaaadbdbbcccdccdddacabdddadcdcbacdcddaadcdbdabdbbadbaabadabddaaacacddaacabbbcdaabdcbcbcadbbdacaccdbcabcbabdcbcddbdcbadccdaaadacdbcabdddbddbcadddcdbdbadddbcdacdbdddbcabdccbdccaadbcddbaabcdacdbabaaababacbdcdadbddbdbbaaccbadcdcbaccdadaacaadadbcdacacdcdbdacbdcbabaddadaaccdbbcddabbababdaacbcaabaaccbbbbddbdaddcbbaabdabccaaabbbcddacbcccddacbcaabcadbcbbddcbccccbdbbdcccdabdacdabadddbdbaacdcbccdadaabcbcdcbbdbdabcddcbbdbcbccbcacabbbbbbaacadbbcbbdbbccbaaacbcdbaccdcdcadcaabccbbdccaccbabacaacccadbabbdacaddbbcacdddcbbcdbbccdadbaaacbdbaaaaddbdaabcadacacbddaddddcdbddcacdcbccccbbcdaccccdabbdaaacaacccabcbbcdcbdbdadbcacdccbcbacdddcbbbadabcbbdbaacadaaaadabadbbabcddcdcacabddaddcdbabccbbdccdbbdbbaddcbcbcacbdacbaaaddaaddadbcdaddcaadbddbdcccbdabaddcdccccccddcbcacbbadcaabdbddbcccbcdcdabdaabcddbaadaccdccbbcbbdacbabddcdabccdaccbcbcacaabdbbddbacbabdbacdcdaccbaadbdbbdcbacabbbbababadabcbcccdabbcadaacdbccbdaabbabbcaddddddbddbdbbabadbadabaaacaaccacacccbddadadabdcddbcddabacbbbbdcbabbcdccdddcabdccddbbdbcadddcbcbadaabcacdbcbcdbcccdccbbdcdabbadcaabaadddcaadcacbdcbdaadbbdabdccbdabdacbdbadacbadbabccadacbadcdccbdabbbcbddddaccdacaccacdbabaadaddbbccdcdbdaabddcaaabcabcddaaaabbbaadacbcaacbddbadbccdabbdbdcbdbcadbbdcdbaccccacdbbcbadbaacdbabbbdbdabbbacccddbbdadaabdddadcbccbcaabbbbadbcddbbbadccbbacabbddccaccacbccdbddcdddacbabdcbbbdddcbdcaddcbcbbcbadbbdacbdcbaaadacdbabaaccbaddcaabadbadacbbddaacddcbdbcabdaabbddccdaddadcbbdbdbbddcadbcaccadcaabadacbcccaccaaaaadbabbbaaaccabcbbddaaaabaabacbcbcbadcacaadbccacaadbacbdccaddddbbdcadadcbbadbcbcdbdacaaabbdbaddbbcdcabdbdbdacbaabdbdbaadcabaabdabcdcddccdcdaaadbddbadadcddbbbabbabbddcdabcdddcbbdabaadabddacbdbababaccacaacaabdcdbddcddbddbdacddcbadccaadcaadbcaaabcacbbdcddddaccbcacdbaaaacaabcccbdcbacababddacbbbadccccacddaaddcabbbccdbbabbccbabdccddadacdbdcbacdbcdcdcdadaadbddabccdbcbaaddbaabcbdbabaaadadcdaaaaacbdcacdddbbcdcabcccddcdcbdbdcabcbcbbcbbadcdbbcaaacdadbdacdcdbbbadcddaddbcaababdbacdbaaacddbbabcacaacdabdacaabcbbbbbaaadaaaccdbbcdcacadbaccbdcaadcbcaddbaddaddcabbbccdacdbbbadbdabddcdccdccccabdbdadcaddadcbadbbbdacccbcabdbcbddbacacdcbdbabbddacbbcdadcbcabaccdabdcccacdbbbbaadacbdabbcddddbaacddadbdaabacadadacaacddbacdbcabbdbdbacbabcbbbacacacbdcbdcbddbbaadacdcdabacbbadaaabcaadabcbaddabdadcddacadcaadbabbdbddbbbbbdadcbbdbaadaacadcdcdbcbaaccdbcddacbdaabadcccbdcdbdabbbcccbcdadabbacacbabbdbadabcccaababaddcccacadcacadcaadcabddbadabadbdccdcddcbbbbccbcbddddcdcbdccbabdbdcddbdaaabcbdbcbdbaadbdcacbcddabdabbcacdcacacccabbddccdaacdddbdbbdbabadbccaaaddcdcadbddbcbabacccabddcbdcbadcbbdcbbaaabddaadabcaacadbdaacddcdbbadbbadcabcddabdadbcadccdcaadbdccbaddacbdbdcdbadbbddadbcdaccbabbbccbababacacbbbcdbbcbaadcbcadbcbccdcdcddadbbbadaabaacbcbddaacdbaaadcdaabbdbacdabcdcacdbdacacdbdcbbabbcadacbbddbcbdadaccadcccaacaacdbcccdccddabccdbbbbbdbcbabcadabaaccccbbdacbcdcadabdbacbadbdbaccdccadbdbdabbdcdbaaaadcbadddbabcdbacdaadbabbbacccadabdccabbdbccdaabdaccdcccdcbaddacdaabaaababcadbdbdaaccdcdddbbdcccddcdbdacddccdabccbbcabbcabcbcbacaadddbacbccdbddcaaacbaacbbacdddbabbadbdacaccadabbbaddbaccbdaddbdccabccccbaabcbdbacdadaaabdaabdddaddbaabaacbdcadbadabaacdcdacaabacadcbbccababcaabddcdbcdbbadcccdabdababccdddbbbdcddaddcdbddbcccacaabbbcaddbbdcdbbcdcbaadccadbcbddddaaaacdadacacbcdcbbdcbdcaabbcabcdaaaccabbccddcabcacadaccbcabcbaddbdcadcbacadbabbdacbdbabccdacdddbdcaccadaababccacaccadddcadabccbaadaabaadaadacccdbaacaaaddaadbaccdbdbbccaaadaccbcccdccdacbdcddddcdbcbbbdacddbdabdbaddbbbbdacdcbabdcddabddcdcbdcbbdbbbcdadbaddabcbdbccccabadabcabdbcbabaddbbdddbbddccaabdaabcdcbcaddddadbddcbdaacdaccabacccbddaacbdcbaacabadabbccaccbddaabcaaaddbdbabbababacdbcadddbdacabddddbbbaabadbadbdcaaadacdddabbcdaccdbdabcbccbddcbdaccababbdbaadbaacbaaddbdcdbdbcccdabaccddacdccccdbaddbcabdcbabcbdcdddadcabdccadaaaddabcaddbaddbdddabdccdbbbbacacabdabccacdabbacbaaccadcaadbabdabbdbbcccccabcacbdbbdcdaaacabcdadbaaccbbacadbbcccdaacccacddbabcabbaadcadbcaaaadbacacbacaacdaddcbdbcdabdcbbccacddacdabddbbbaadccbbbddacdbdbbbddabdddcacaaddabaabdbcbabaacdacaacabcaddddadbaddccccbaaacbbdabdcdcabaadbabdcaadcdabbcacbcabcbbcacbcabadababdaccdaaccabcdbbbddbdbccccddbcaccadcacdadcbddbabbcddcacdaddbcbdcadccbacddadbccccacdcabddccdaccbacbbcabcabacacadcccacbcbaddaaadcabdbdccbbcbcbcbddcbbbccaabdacadbaaaabcbbdccbbdddcacabbdcdacabbbbcacadbcacabaabbdbcaabccacbddbbbdcadaaacbcdcdcacacbcdcabbcadcacabdbabbadaabcadccdcaaadaccdcddcdbbcbadcbbacabbddbcadbbbcdbbaccabdaaddccbdababbbcbbdbdcbccaabadabbbbbbbcdcccdcaabddcdaacbcaaadbdbcadcbbbcdcadaddabacdbbacdccdbdcdababbbcbcbcddadbadbcaddddacbbbbcabaacaabbadbcbcdbbcdcbdbcdbdaabdccbcadbacabacccccdbabccaddcdbbbacdabaddddcaccadccdbaddbccdccbcbcabdaaccabacaaababdcbaccddcbbabacdcdcdcaddbbbbbacccbabacbbdaddcbadaaddabccbddcbdcbcbbbcaabaacaccddddccdbababcaaddbddbbcaacbaadaaccdaadacadadabcaabddadacdcbdcdaacaccbbabbbbcccdcbdbcaaadaabadbccdcbbddcbcbccdbdcbadcdcacdabdbacaaaabcabaccabbcabddbaadccdabddaabbddacaaadabdbdcdaacdabccabcabadabccdbddbcdbadaacbcbdcbbddaddacadcdbaacadbabcbbabababdbaccdddaccaabdbcbddcacbddbcacbdbdadcbccbdadaadadaadbdddcaddbbdaacdcddacbaabbbbddccdbbcaaaaacbaadcbbdcbbbabdacbdcabbcdbbdcaddadddabccbdaccbabccbacbdacabaccdcbbdacdabcbacacbbabbcabaabbaddcbdcaaadcbdabbddbbcdccdcdcadbccbabbccadbdcdccdddbdbbbcadcbccbdaccdcbbbcdabcccbdbbcaccacdadaadbdbaaacdacdaddcadacccbbabaadacbbbbacbbbacccbbdabdcddbabdbbddaaaddacbbaabdadcdddccacccdabbbdbcaddcddcbbdacbacacdcbabdacbbaacabbdabacabdbcbdaddaabbacacddbdbadbbdabbbdcdaaaccbcadbaaaadabddbdbbdbddbdbcbbcaacccbbbacaaabbdabcbcdbcbcaccacadbdcdadaabbbccddacdabccdaccddddadcdacadabdabbcdcbcabdaccbbadabcdcbccdadcaaacabbccddcaaddbcbcbacadddadcccbdabaacacbdcababcdbadbcbbccabadaaccbcaacdabcabaabaadbabdacbccbabdcbcaabaddbcacabaaaccacdbddacdbaabdacdadbccccbdbbdcabdacacdbdbbccdacdddbcbdcdcdbabdbdbbdbaddcbdadbbcdcbccbbdcbcaaacdbccccaadcddbcbadacbbadbdadabbdadadabdadaaadcbbbddbacbbddddcbcdbbabbaabdcbabbdabcdbbccbbccabbbcbdddaacacbcbcacddabbbccdcddbbaadbccaabbacdbadbbbdcbccccdbbbdbaacddbacdddbbccaccdbdbabcdbdddabddcdbdadaabbddabdcdaadabaaacdbbdbacbdcdbcadbaabababcbddcaccbcbdcddabdaacaaaccddcbbabaaadadbadccabdddcdacacabaaccacdacbadbbcbbacccbcdbbbbdbbcdbddbdcabcbabdadcacaccdaccbbbcacacdabdbbbbdbdbcabdaddbacbbadcabbbbcbbadbddbccaacdbdcdddaccdbdacabaadadadbadcacaaadddaacccccbabcbdabcbdbbbacaddbaadadddacbaddddddbcabcbccdbaadbabadcbcadadcacdacccddcbcadaccdcdaacdaaacadccdbbbcdabdabddcbaacdccdcaaadbdbccdbdccdcbdbcdcaaccababaadbbdbdcaccacbaadaaaabcbbbaacbcaabcabcdcabaccbbbbacdacaaddcbbccbacddacbcaddabbadaacbdbaaaccbddcabbbcdbddbcacbadabcddcdcababdbbdbdabcadcccbadaadaacdbabdbadcdaaddbdddbbbdadaacbddddcbaacbdbaabdbdadbdbcdadaababddabaacdcdccdbddaaaaadbcdbbdbcbcddbbabdabddaccabbdcbcbcdbcadababdacbdcaaabadadddbdcbdbadabadddaabaadacbbaacdddccdaaaaddbccbbccddadcaaadbdbddbcaadaadbacbbacdcadaabbdcbdbaacddaacaaaddaaaaabbabbabcbdcbcbacacbaaacabbdddaacbabbdcdaadabdacccdbdcaacbbccccacabbabacdbaadaacadddcaddbdcbddbdbabdcdbaaabdadbadddccaabdbacbcabcabcbdabcbabdacaabccabaddbccdbbcbbdbccadabcdaccadcbcbdccaabadaabccdaabbaabbaccbcdacbaddcaddacdaacbadadacddbbbcbcbacbbccbbadababcbdaaadaacccddacabdabcabdaaccaacdbbdaabddacbcbaddcdaacadbdcccbdcadbabbdccaacabcdbbdcbccdabdadabadadadaacbabdcdbbcbcacaacdaaddbaabccadddaaddbccbcddabbaddcdccacdccdacbaacabbddcaddcababadcdbddabcbdddcabacccbdcbbaddaddbbcabcddcaccaababddbcbdacccccddcbbbcbacaadacdaddbadadddccbbaabcbabdbabdcabbaddccbaaccbacccbcabbccbabcccdbdcbddcbdabdbadaabbadadcaccbddbcdcbdcccbbdbcdacdbbadccbaacddddaddababcbdbddaaabcdcaadddcbbbbaaaacacabadcaabcdddcabdddabdbbdccdbdbbcaddcbbcdbccdacaabbddaccccaaaccabddaacbbcdadcdaabbaadddccacacabbbacddbbaadccddbabbdccbacaabccbccbabcdccacaaaadbadaddaacdccbbcbdacbcadbccaabcdbccabccbdcaccabddcdcbbbdaccdacacdcdbaccdacdabbadaccadacdddadcabcbaddadadababdaddacbabacddbbdcbdddbabcdaadcbaadacbaaddaabbabbbcdccdccbbbccbabcbadcdbbddaadbacbadcbbabdabbbcddadaaaacbdcbcddddbbdddcdabaaccadcbbbccbbbcbdaccabcaadcabaaccdbcdabbdabdbdcaacaddaabdbddddcdbbdbabbdcbbcabdddbbacbcdadaaaddcbadbdcaaaadaadbdcadbddbbacaaacddadcabcadcddcacbbcbabaaacdabbccadbcaccddabadddadcddaabdbbcdaabbbbbcbbcdbddcdacddcdbbcdaddcbcdddacaaccdccaacacdbbbdbddcdbbaacddbdddadcdacddbddaaaabcadbdbacbcddabaabbdcababbbdcbcaabbdabbaaadacbdbccddabdacdaddabcacabaddcdacbccbaacddcdddbdbacdbadadbdcabdabccababababbaabadcccabaddbdccdabdccdbdccabdcddccdbdbdacadbccadaaadabccbddcccdddabbacbbcaaadbddbadcadbaacccdbdadabdccaabcbcdadddcbabbacdccdcdaaaddadccbaabbdacbbabcaaddbcaacdbaadcbdcabccbdbaddbdbaadcdbcaacababadccbababbcabdddadcccdcdcccbdacbcabcbadaddbdbdbbbbccaadccdcdaacccbbbcdaababaadbabcadddbdcbadcdcabaddcabdbbbcdabcbcbdddbdbccbaaddcdddabddaacbbdbccbcbcaaadbbbcdaaadacbcccdbcaaaaadacdabadbcbdbacbbdaabbadacbaaddddcaddcbbcabccbbdadbbabcdcadabcdccbdbdacaabaccacbadaabdacbdacbcabdcbabbbbdababbabbbbcacdcbbbcbbccadbbbbddcacbbdcdbdaacdabccaadddabcabaabbbdbacbcdbcacccdadaabbbdcababcdcbccadadacdccaacadbcadcdcbdcccadbcddccaddbadbbdaadbaadabccadacccacbcbabacbadabdbdbdacbcdcbcddbbacadddbbccccbbaddcacdbdabcdbacbccdadcdaccabcdcadacccccbdaaaccddabadabbbacddcadcacdacbacdadccbcdbbacadddddcdcccbdbcaadadcbdcacbccdcbbbaaabadbabccacbdddcabcacccaabddacbcaaacdaadacddcdcdadaccaacaaadccacaabadddababaccacdcbdbaccacdccdaccaaabbadabbddcbddadabbcaacbdabcbdaccaaacbdcdaacdacddbdaadadbdadddcbccbbaccbabccdbddcdabcbadadbccaddbaadacdcdcadbaccaccaccddcabdbcdddcdacdcaddbaacddabdacbddddccbdcbabdadbbaccdabdcaacacaccbdbdcacbdbcddadcabbcdaddbccdabbcadcabbccbbbbdbbdcbacdaadcabcaaabdcddccddbaddbbdbbdcadaaddcdcccdabdbcadabddcabdabcdcbbabbcbaddcbdddbacbaadaabcdddabcdbcadbcacbcccbdabacabbaabbaccbdaddbcdbcbcacdbbcbccadbbddccadcdadbbdbdabcadbbcadacacdcccbccbbbadcdaabadcaabccdbcadcddababbccbdddbddbcbacacbdaddccabadcddcaaddbabbbdadbdabcbaabcacdcdcacdcbaccaaddcccbabbdacdbbbbdaabcdadbdcccaadcacccddaddbadabdcacddadddbaaadaabaaacbbbbdccdccccaacbbbbababbbbbcccdaddbacbdaccdadacadacaaccdcbdbddcddbcddbabbcdcccbaabadcbdbbaacababcdccbdcbabccddbababdabbadcadadbaccbcdbcdbaabcbdadcbddbadbbcbcbadcddcabaabdbcacbbabbabdbdcbdaccbabdccbadadddacbddcbacddcbbbcddcabbbaabcadbcdccdcdccddcdadcabdbabdddbbbcbbdbbcadaccabcaddacbbababbbdbcaacbdadbabdcccbbabddaacdccadbccccbcdcbdaccaadacdbcbcbadcddaacaabababcbcdccdaabddabaddadbacdacdaaaaccacabcbcbbbdacbaabdaddabcaabcbaacdddadacbacdcbabbabaabdabcbcbcdcccddcbcaadabbcbcdcaddbabcdbcacbbacacbcdcdcccaaababbaddaccdabcdbdbcabacdaaccdddacccdaddbabcddbcdaaadcbdacddccaadbbabdcadbbbccbcdaaccdcddcdddbdaaaacccdbdabdcbdcbdbbbcbcdaabdaabdcddddcaadcdcdacaadccabaddacbbddaccacdadcbaccdabcacaaadacaccccdbcbbbcabbabbcabacdbdbdbddcdaddabcacacdbccadbcabccbcccddbcdbbaddbadbbbbdcbbbdbbcaaaacaaccabddddacddcdacadcacddadcadbbdcdcddacdddbcbddadcaddbdcdabddacbcccbadaabbadadacdcbbbbbbbccbdcbbbccddddbaaddbbababcdbdcaaaaabaaabbadaaddcaaadcacbbdbdaaaccbcdbbadacbcddcdbcbdbbabcacacdbddaaaccabaadbcaaddadbcdcdbadcaaccadcacccccdcbbcccbbcddacccdabbcbbacbddcbdbcddccbdcaaacbbccaadaabbcaaddcbbdbcabcbadadddbaaaacdbddaadadabbddabdaacadbdbcbacbdcacadcaacdbabcabbdccbbcbdcaadbdddbdaccaaccddabbacbddaabddacdaadbacddbacaaabcccabcbdcdbabdaddbaacdbdaadadaacabacbadadbdacbadaadbbcccbdbabbcdcacadadddaccdabbccacddbaaddcccdcbcbbdbdbbdccdbdbcadabcadbcddacaddbbdaacdbaadbbdddacccaacdddadcadaaccaddcbacbacbbcaabbabdbacabaaababbdbcbabdcadccbdcbbdadabcbcaadbdacdcdbcdcabaccccdbcdcdcccdadbaacaaacaadbccdcdcddacbbacaabcaaccbdcbccbabcbccdbbbcbabadaaddbacacaaccdbdcdcabdcccdccadcbcbbaddbcbbcbcbacdbcbbdacddabdcdbabbddddbdccdbabcdbacbbaddbdbcdadbbbbabdbacbadabcbdbbbccbcdccccaddbdaaddcddbbdacdbdcdbcbddcdcccdadacdddaaaacadccdbddcdbabadddcbabbdacbadaaaccbdccbaacbccbdbcbadcbdaabdadbcccacbacdcbbdaaddcdbbacdbbddcbbbcbabdbccdbdbaabbcdadcaacacabbdadabcdccbcddcddcadbdcdbbbdcadbcadcdbbaccaadcdddabdaaddaacaacacbcbbaddbdadacddbdbaabdbbcbacbbadaaddcccadacbccccabcacaccbcadabbdcdcdbacbacddaaacdbaccbadabadbbdcbcaccdadabdbbdbddcbcacbccbabddcdccbabaaaccaabddcbcdcdccabaacdabaccccaccdaaccabbaadbcccaadbbbdacbdbbccdcaabcbdacddaadcdbdcdcdcddcddaaaacbccabccdadcdbcaddbbcddbabacbbcbcdabcaadcbbcbbdcddccbcdabdccdbbaacdbcbbdbdbddcbcdcdbdacddccbcadaabbccacadaccaabacaadbdbdcbbcacccccaccadccddadabccbcccbbbcaccbcddaabdddabdadbdcccbdacccaabddacabaaddbdcccddadccaabdbbdcaddcacacabdabddddabababccdcacddadcbcdbabacdbbdccbbaabacdaddaabcadadacdabdcacdbbccddcccddbacbaabadcbacbdddbaccdaacccaadadabbbcbdbccddbccdcbaacbbabaccddbdcacdbdbddacddbacdcdadccdadbbcdbdadabaddadddbaddddbbdadddbdccdcdbacaddddaadddaccaaccbbccddbabdadbabbbbaddaddbbcbdadbacabaadcddbcbbaabbaccbdcababdaadcdaccbdcabbbabbcdcbbcccccabdabcbdcccbbdcacacbaabcbabdaaacdcdbddabdbbdbbbadabdbbaacabccbacdabcccdcdaabbcacbaccbbccacdcdaccdcbdbdbadbabcdaabcdcacdccddccdcdcdacadadbaaddbdadbbaabcbcdddcbacdccacacaacdabbacbcacbcaadaddaddabaccabaddbabaacddabbaacbaaccdcbbacadcddbccbdbccbbcccbdaadacabaccbcacaddbbbcbadcdadadacbacddacadabbabadcddbcaabcbacbbcddddaadaabddabacccdddcddbcaaaabaabacccdbddacdacbaddbbbccbaadcdbcabbaadcdadcddaccacccbccacbaacbaccbbdabbadaabdaaddbcbbdbcbccdcacbcdabaaadbcaaacbaddadacaddcdbdddcccdbaacbdccdcbabaaabcdbbdbbaacbaaaccbabcacacbdcdddccadddddddcddbaddbaacdcbbabaacdaddcaccbdaacddbaadadbaccddadcdcaacabbbdbbabaaaaabdbcbbaaddbdbbaabbdbdbbacdcadabbddadcabdbdddaabadbaadcaddcdbaadbbadabbabccbbbbdbbadbacbaaadabbacaaaccbaaccabbbabcddccddbbdadbdbbaaccbcdacabcdcbbccaacbbaabbcaaddbabdddccacddaccddcbcaccdaacadddababbcccaccacbbdccddaabaadccaacbbbdcdbdadddddcaabdddabacaabbacaabcabacccdbcdddacacbcaaacacbddcddadccddbbccbcbaadcbdbaabbaabdddcccbadcbadacabcddaabdcddccdcaadadbabaccabcdbddddbdbccddbcbaadcaadacaddabccaadcababaccdbadbbcbbadacacdadcbabddddacccbbabdcbcaddacbccbcdcbdbdacbbaddaacbcaccdabdaaccabbcdaddcdaadcacdbdaddabadbcdcbcdcdbaddbabbbbccbdddddcadbcbcdcbbadbbaaabbabcbaadbbaddcbcdcdadbcacbdaadbaacadbaddaddaaaddbbaabcdbaccbadcddcbbdccdabdddcdccacacbdaabaabcbcbcbcaacabccdacbacdcbbbabaacabcadddddbbccbddaaccddadcabcaabbcccdcbdaacdabcbddcdbbdcdcccbbcddddabcbcbabdbbdabdccaadcbbcddcaabdccacbacaabaddbcaadbccabccdbcaadabddcdccbdbccbddcadbdcbdcdbddbcaacbbbcdabbcccbabadbabbacbddbbbcdcbcbacdcaddcadbdbbacaaacababdddadbcabbabdacdcbdcbdabdcaadcbdbddaccdbcdcadccddadcccddccbaaaccdcadabcccaccddaadacabccbbdacadddabcccdaabaaaccbbcddbdcadcddcabdcdcbdbcbdabadadcdcadadbbcbdbdacbcaccddddbaddcbabdbaaccccdaddbbbcbabdcccbbbbacadccbcadbdabdcabdaacaadbcbbccdccdcbddaabbddbcbcdbccbdcddbcaabcaccddbcdcadadbaddddcbdbacbaabccaadacdcbdcabaddadbabbbdabbdccaccbbdabadbddbbbbcdbdaacccdadbadaacbacbccdbdddaabbcabcaccdcdacddddacdccccaabbdbbcdaddadaabaccacbddabdbdabddccddcabdaacbdadcdcdbabbdaaddabcacadbabbdadbcabdbccadabcabddcdddcdabccacbcddacbabddacbbdcbcdbbcddcdbdbaddccdccdbbbbcbdabbbccdddcacbbddccbacbabcabdddbaadbbaabdacdbcccdbdcadccabccbcddabddcacbacabacdabacaadadcbbbcdcabcdbbdacbacadabaccabccbadabccacbadccacdcdcdcbdddddcbdabdbbbbdddaacdccbbdadabbdaabdbdbcddccaadbcbaabdbdcadcdbcdaaaaacdbcadbacdaddaaccacddbbcdcadcbaadbdaccbbadcccbaabdbbbddbbbabbacccdbcdcabacdabdcabaacddbbddabaaadcbcbddcbdbddcbdccdaacaadbddddbabdacbaadbdadaadcdacbdddbccbcbdcadbaabcadaadcbddbbacdcbdbdcbcbddadaabdbbaabaabccabccadabbaadbadcbcbadddaacdabddbbbdccccaddacadadbccbdadbbadcabddacdcbacacdccddcbbbccabadccaacacdbbdbddbcaacddcbadaabcbbcadadbbcbadaabddcddddcadbcabcabacbbadadcddacdccbbbcbbbcccadaaacdbcbaaabdbccdbddaddbdbdccadacaddbbadccaaacbcacbdbcbccaaabccddabcaabbabacdcbdcdcbaacaabdbcaaaabcbabbbcdacacaacddddaaaaacbacbbbdaddcdbdddbbcbdaddddaabbcbbdadbadddcacadbaadcdaccdabcbdbcbdababbcbbbaccaacacbbcccdbcadcdbbcdabdacadbaacaccbcdbbdbcbbbdccabdabaccabddadcddbcdaabbdbcdbbdabcdcaccabdaacbbaaddbaaadadddddaaaaddacbddaaacdbdcbadbbbdaadaaaaaabcdadccbddaabbbcbadbdccbccccbacacccbdcdddcccdaddaaacccbccbbbbdaddbdcbcddbddbabcadaddcaddbaaccbbacbcbaccdbabbbcdbaabadabccacdbbcbaddacacddadddadaddbdddddddbbdbcbcabdbdbaadabdaabbadabcdcccddbdddabacbbadddbdbaaababdcabdadddcbdcccacacaabacaaddadcdddcdadadcbbcabaabdaccacaaacadddbdbabadbcbcabadcccbabbdccbcaadaccdcaabbddcdcbacbcaaddabccacddaadbadadcddacddcbcdaacbabbbdbbabaabaaabbbbadbadddabdaadbabdbdbbaaddbadbaddabdabdbaacbadcdcbdabcadccbbbdbbdddadadaabbbacbaccacabbdcdcbcdcdcdbccbadcbdcbcccbcbddaadbddbcccbccaabaadcddbbadbadcbcbacadbbdcdccbcdabdbbbdacddadbcccdadaadcdcaaddadbaaddbdbdbdacadabbaddcdadbaccaadbdcddcdaccbdddadbabbccaabaabbbaddadbcbcdbdbcddbccaaadcbbcbcacbcabdbcdcdcddccdaabcbbcccdacaaddbbccdaaacbdcadcacbbccbababcdcdbaaddbbaabacdcdaadadbbbdcbbcadacaadacadcbbbdcdddddddbbbccdcbdbaabaadabccaddbcabdbacbabaababaaaacbbdabcccbbadbaccbabcaabadcbaadcdcbaddbcaadddbdbacabdcbccbbbbadbdcdadaadccdadacddbdabdbbabadcdddbccabdabbbdcbababccaccccaadaaadcbaadcacadcbbadadacacdccacccbdaaddddacdbccdacccabbacdddcdbbaabdccdbaddadcbabcabcabbbcbadcbaddccabbddddcccbaadbcaccdabaaabdbadaccdaddbbbbcbbcacdcaadaccbaaaaabbcaacaadaccccaddbacbaccababbccbaababcbabcabacacdabbaddcbaadcbacabacbddcbdadbcdbbddbccbbbaadabccbabcdcacabcdcaaccbddacccddbdaabacdabbacbbadaddcabcdcabbbcdbaddabbbbdaaacddddcbbcdcccdbcabbbaabdbcdadcbabbcdaaaddcbdcabcdaddbccbbcbadaadbadadbcadaabcddbccbcbabdabccacbdbcddcdabadaacdcdcabcddacaabcddacbdcbaadbcccabcbbddbaccacaccbddddaddadaaadccdbdadbdddcdcaabbacbcbbbacadbdabcbcccabcababbbcdcdbccdbaaabccabaadcdddbabdbdbdcbcccbaabbddcaadcdcdabaccacccddcabbbbaaacbbcbcbbdbbbaccddaddbcdddbdcbdcaacdcccbcddcadabadbdbcdbbaccbabaccabcdcadccccbbcababcbbccacdbcaaddcaabdbabacdddbbcdbdddcdbcbbdccbdabcacdcbbcbbbcbacacdccddacbaccbbbaacbdabbaabbddcdbaabbdcbdaaccacaababacadcbcdacddbbadcaaabcacdccacbdcccbccdbdbdddbdaaaaccdbaccdbcbdbadccdccdbadbbdaacaadaabbbbacaccacbbbccccdccbccacbaaddddcabadacaabaaaabbcabbcaacddcdabaacbddcbcbddcddadcdcaccabcabadbcccabdddcdbbbacabadcbbaacdacaadccdbadbaaabdbbccbbdcacddddbbacbaaaabccbacaaaccbbdbdaacdaaadddbbbadbbdcbabbacbcbbddcbddacdddcddbacbdbcadabaddcabdbcaacccabcabaddbbcbabdaaddcbbcccabbddacabdaadbcadaadbccbbcbbcdcccddabbadcaadcccaddbbdbccadcdcabccbdcddcdbbcadbbdccbacbdaaccddcccaccccddccdddddbcbcccbbddcbadaadbcbcbdcaddbddacacccccccdbababbdbbbcbbdcababbdbaadccbdcccabacbababccdcacccabccbabdccacabbabadcadcbabdbaacaccaccdccdabbbdabaacbbcbbdbcdadbddabbcdcbabdcabcadddbbbcadbbcccdcadddddbbcddcaaadcdaddcdaacdcccccaddcabdadcdcacdcabadbccabbbdcccbacbcaadbabcbcabbbbaabcaddcddccabadbcbbcadbabdadcbcadcbcbdbccdbadcabcdaadcdaaadabbaaabcbbaadaabbbdcacdbbbabbbcccbbbbdacacbcaaadadcdacbadbdbcaabaabbaaacdddabbadacabdbdcbbbbbabbbbccaadddbadbcdbacdcbaacaabbdbabacbddaddbcaabbdccbbcaaccbcbabcaaddaddcabadbaccdabdbcbcdabcdabcbaadaabcbacbbbaabacabaccbdbadbdaaadacaccccdaaaddcbdcacdddcdbbcdbbdbbbddcbcadcddbbbcdadabdccdbadcbdbcaccbbaabbacaaaadbddcdaccdadcdcadaccbdacdadccdcdaabcbbcddaddbcadaabaccaabbdbbddcccdbdddbdccbadaddaaaaddaddcbddaacbddbcbcdcddaccbbdaabadabaabdadbadbbdababbbaaacaabccbcaccadaadcbaadddaacbcbabacbbadbacbcadcdabadddaabbdcbdaacdcabdcbbdcbbcabaddbdbdcacbdadbbabddbcacdacdbabbabbbacbbaccbaadcdddcdbdaabadbbadbcabbbddaadddadcbbdbcbbdbdbbdadccdddbdbbcbdadadaaadadbbadadabbbadcbddbbdaaabdcccabcddbcbbabbddbacabddcadddbdcbbbadaccaaaaadacabdcdbaccadddacdcddbdbbdddcadbdbcaaddccbdaddabccdddacdccaccbcadaadcbbbcddbcaaaabaccacaaadcbabcacdcbdadaccabcabacbcdcadcbadcbbbcdacabdadbadacbbdadbdcdcabdadcadbabcdacacbdddcadaaddcdcdcdadbacccaacacbabddccbaabdbddbccdcbcbccabbbcddcacdbaccacbcdddcddcacadbbaddabbbaccbccbabbacddbddcbdbccbdccddcaabdcbbdadddabbdaadaaaabcaaabbcabdabddabdaaaadadddbbbadadcacbcacdacdadbdcbaaaccabbdbaabcdabdbabacbddbcaaddacbbbbbbcbcadcaccdcdcadaccdcabadcaadccdabcbdbbcacbdbbdbccbaaacdacabcdcbdcbddabdbdbdcadbcabdcbddacbbbdbaccdaadcdcbbbdcdbcadacbcbddddbabbbdccdbddabbdccabbcccdadbbddcadcbdcbcddabddcdcdcbbabaabcccdbbcabacdadbcdcbdadcddbcdadccacdaddcbcabbbdcaabcaaaacccdddbdadcaaaabdcccabccddcbaccdcaccdcdcdbcadadbdbaacbcbbdacdbcdddcbddbcdabccbdcbcadaaadcdcbccaabcabbcadddbccddddbbddacbdabaacadaaaaacccacdbbbbaacdccccdbbbdacdcadabdcbbdcaddcadbacdabccbdbaadaddabdbacdacbbabadbacbdbbadcbcabcbabdcdbdccbdcbdbbacbaadccddbdcdadccccdcbbdcbaabccccbcbbacddbbbacddabadabdbcbbdbbcbdccabddddbbacbbdbbcbbbbdcbcaddaacacabdbbcbcbdbdadaddbcaddbddacddacdbbbbdbbdccadccdabdaadccdcdbdddabdabbbcaabcabadbaccbdacbdcdadcdcbdbaaddcbcccdaccbaabbcccbcdbccbacbbbabacaaaccddbdadbddadaccbaabdadccaaadbacbacdbbbdccbacdcdbdbbccdbabdacddaccaabcadaabbdcaadcdcbddcbcabcdaadbcbbdbdccaaabdabaddcabbabdccbbcaaaaabcdbadbaddbadddbdcadabbabaaaddddcbbabddcccbbdabbabcaccbbdbdabcdaccccdabdbbdbbaacdddcbbcddcbbdaacaddddabaddbaccaacbdadacaabccabdcbcdaabddaddcaabcdbccccbcbcccbacbbcccccbddccbdbacabdadbaccadaaaccdbddccacbacbbddcdbbcdacbdaadabdbddcbbccbadadacabacacaacdacbdcdcbdbccdbabcdbcdbbaacaaccbaddaadccabaadbaccdadaccadcaddbbdadabddabcdbbdacabbadccadbabbacbbbaabcdcabdcbbabdbdbcdbdacdbcccddbddacaadcbdbbbadcacaacbbdbdddcaddcaccdabdbcbcbdcbbccaacdbbababdcbdabcaaccccacdacdddbcddbcaaaacbadcddccddbcabcaadaaabcccbccdbdacbbdadddbcbabcdcadadababcacbadcabdabccbbcabddccbcbaccdacddccccadccaccbdddabbbccadacbabbccadcdaadddcdcdddcdbbbadaaddbbcaabbbcbdcccbbacabaabbdaaabacadccbaccacabacddcabcddaccddccaadbddbbdddbcacbdbcadbcacbbbdcbcadccaccaddbbcbadbccbaddaccadbddacdddbcbdddbaaadbcbdddabbcaadadababcbdccaaacbdbdabcbadadcadabdcdbbacdbcabdbdbcbccccbbdabdcabaadcadbabcbadcccbddddbbdcadbcaadabaccccbadccbcacdbbabacbadcdbdbbaabbccabdcbdcbbcbbabcbabdadcaadcbdacabbdcdddcdccbcdbdaadbabadbbaadbcdddaddacddadcaaacccacaacccccacdbddbccdcbbddbbcbbabdabacdcdcaccadcbdbcdddddddabdcdbbcdaaccbdbccdcdddbdbacdabcadaadcddbbbdcbdbdcdbdaccbddaaabcccccbcbacdabcaabccaadbbaddddabacccbabaccbcbbcdadaddcbbdaacaaadcabcbaddabdddabbcdddcaaabbbdadacadbdabdabdbdbbcabaacbaabaccccaccacadcbcacccadbdcabdababbcccadbccddbcbcdccbccbadcacbbdcbdadabddacacbbbcbddccdbcadcacabbbadbcdabbccdaaddabcdddaadbbdaadddcadcdabbdacdccccbbadccbdacbcbcbdcbdaaaaacabbdaacadcabcacaadbbbdaabddbddaddcbaadabaacccdaabccbaccadcdaabcbcbbdcaacbbcdcbdcddabacdcdbdcbcbacadcaabcdacccdbcaddabaadadbdbbababcdcdbaddbabdcbaacbdcdbcbbcbacaaadabcbdccadbbabdcbccdcaddaccdccccdcdbbccbcdbacbcdaaaaddccbdbacbcdddbbddabcadccddddddcdbaccabbcacddbdccccbbaabadddccdbaaabaccabdacabbcccaddcaaaababbddcaddcadadbcbddbdbcdabdcbdacadaddbbaccbccacdcccabababacbccabbcbcbaadbadcabcdcadbbacaabdbcadcbdcdbabccccadcaaadcdcdbcabbbacbbddbdcabbbcccccccddaabddbabacbdbcccadcbaacdabdcbbbcbaaccbcbadabdcaabcddcadaaccbccdaacdabadacddbabadaaabcadaadccddccbaddddcbabacaddbacaccbcabbcbabcdbcbacaaccdaadbdadbcdadacdcabadddcacdabccadaadcacbcaccacabaadcbccbcbdacbacaadaadcaadadaacbacbbcbcbdaacadaaabdcbaadabddabaaccbbdaccbbbacbcabddcbbbdcbbdacabaccdbbabcbdadacadaccaacaabdbabcccdcacddcdddcbbccccdadbadcbdacabdaaabbdcbabadbddbcbbabacacadadddbacaacadbcaadcacaccdbdcdbbdbbadcabcaacaabcdaccdcbbdadacacdcbcacbccddccdddbaadcdbcadabddcdaadccdbbdbbcaddbbbbbacaddcdccabacdadcacbcccbbaaaaaddcbabdcdddddcadaabccbbbccbccdbcbaacdadabaacdbdcababbbadcccdbccccabaaccaaccababbdccccccdddacdadcdccbbdbadcdbaccacaaccdbbcdacccbadaaacaddbcbadadbdbdbddacbbcbcbaacaddbdcdaababdacdbcccbaaddbacdcadadbcbbaddaacbabbdbdcdcacbbaaaddbacbaccdddbbaccdbbaddcbcbacadbbbbacabaddbadacdbaccbbdcacaabcdcddcadcbbcddababaddadbdbaabbbabcdbcbabccbacbcaccadbaabbcbbbdddacbcdacadccbdcadacbdcccbbccdbbaaabdabbabacacdcbddaaabaddcacbadcbcdcabccadcdbdcdaccdabcdadaadcacbdcabbdacccccaadccbbabbabcbccdbdccccbdbabbdcdadadaadbccaddabadcdbccbbbdacdbadbdbaaaadabcadcbbbdabcdbcaaadccaadcacccbbdaababaacdcacabdbabcbccaabdbdcaaddcbaaaacbdaddcbbddddccbdbaadbcccabccbdcdcaacbabcbacbdbcdccadaaaadaabdcdccdbdcbdababdabaddabcbbabdabcdaadaabbbbabcccabccabbbdcdcababaaaadabadcadbdcaacaccdaabaccdaadbabdbdddbbabbcccbbcbabccbbcdbdabcdddcbbbccbcadcabbaaccbabbdbcdabaddadacbbdcadbdbccabbaacbdabdbdbcbbadcbbbabddbacdccdabbcdadcbdcabcccbcdbcbadcdbbcddbcccddcdbabcaabcbcdbdcccdbbaacddaadbabdbcccacdcbbdbbdcccbacbbabdabbbdbdaddaadddbbaadddaddbadbabbdcbcbcddcadacbcbccbccdcccddacadacadbaadbcbbacbcacdabcabadccadddbaaabbccddaadbabbbdbabaabdbcbdddcababcbbacdcbdacbaddbabdccabbdacccbacccbcaaccbadcdcbcbbbdbcdbcbbcbcaabcdcdcbcbbdbcacdcaccabacaaabaaabbbadbabccbdcdcdbcbaabdbddacacaadcdccdcbbdcdacaabdcbdccddcbaccabccdbbbabdcaadacddacbbbccabbbddcdacdaddbcdbbabcaddacdcbaabdbabdbdacdcbbddabbcadcccddddbbbdbbdcddcbdccdddcbccbddacabdacbbcabcbbdbacabdadadacbcdadccbdcadbbbbcabbbcccccccadbddcccacbccabccdabaaabacadabdcdcdacccdbcaabbacabaaccabaaddbbaaccadabcbcbdacbaaaccdcbdaaddadddbaacbdbcbacdcbbcdbadcbdddbaaabdbbbdaccaccbabacbccbaddacbadbcdcddccbbcdbddbbacadcdacbbbcbbaccbbaadddccbbdacbbccccbdbdbaccbcddcadcbcdcdacdabcdcbaacccdbbddaccdbabbcdccdcdaaaccccaabbabdcdabdddbaddbddddbadcbcccdcdaddcccabaddcbccdcbdcdddbdddccbbadbcdbbcdddabacbdbdcbdaacaaabcdbcbddbddabddbbbaaabddbdccddabaddddbbacdacacabdbcaabbcaccbccabccbdcdbaacbdcddbcabccaaccdadbdadcbacbbabcbbaacdccaacaaadddbcabddbbcdcdcaadaabbbaabbbcbabdaccdbcacaccbddaaaabbcdcbdadcdcacbdcaccaccbccdabbccbcbccbbbbabdbbbcaccadcbcacdacdcbbaccdbbadacdcaabdabcacbaccadabbcbadbabcaaddbabbdadcacacbadbcadbbdadaddabdcbdbddbbaadccbcbcdabccdcddacabddabdcbdddddbdadcdcabbccccbccadddcdcccbccbcbddcdabdbdddbbaadacaccabddbabadbdacbddcbacabbdddacadbbacdbddcadbabddcccbdacbcaadbdbdbacbccaccbdddbcdabaddaddaaaabadadacbbaccdcbccbdbcbaabdadabccdcabdccbdabccdccdcdcdbadbbabbcccdacdbcadbaccaabdabacacbadbacababacadccdbcccbbaaccccdacbbacbcbdcbddbacccbdccbaadcccbcaabccabacaccbdddbdbbacbbccabacadccacbcbadccdddddaaadcbbcbdbadcbcadbbacbccadcdaddccccddabddbaddcaddaabaadbdaddddaccaadddbbbbaabcacbcdcccacabccbdaccbcbdacbaaccdddbacbcabbddcbacaacacaadbdcabdcaacabbdcadbbcdcadbacbcccbaacadbccadabbbdbdcdddadddaddbbdaacbdcbcabdacbdabddcbbbdaddabdadacbbbcccdbbdabdbacddbdccaaadbdbbddacaabcdbacbbbbbbcbcbabbacadabbdabcadddcccbcbbcdbdcbadcdbbbcdbbcdccdccccbbababdcababdcdaadccbddbaadcaaacdbdbaaaabcbdcdcbdcdcaabddbcdadaabbdbccadcbdadcbadaaababcaccaccbccadaabaacbcaabddccddbbbdbaacdbdbdbdcddacdcaccbdbbbacabddbadbacddbaddbbbcddaacbbcccdddcbdbdcdddcabcddcaddacbaaaddbaabbbccbbacdadbdbccccdccccbabbaacbbbbdabadcbadbdababcdbccadcbcbbbbaadbdcabaacdabbaacbdcdcaadbadaacdababdcbdbdccccbabaadcbdabbbdaccadabccbdcabbaacaacdabdadaadababdabacbabadbcbacdbdbcccbcbacddcccdcdbadccdbbbbadbcacababcbbdaaabbddcbccbcabbaaddcbbcddccbcabacccacbdcdcbcddbadacdbaccdadcbdbbdbccadcdadbcdcadabcbddcbaccabbbcbadbcbccdcabbdbbdcbbcaabaccddaccbabdacbcdddadabddccdbadcdadcdadddadbacbadadaadbdbcaadbccddcbaccbabddbccdbcaaccadbaabbdbbacddcaaaddaaacdcaaadddbdacbcacbacaadcddcbdaadbdcbbddbdcdcdaaabadaacbbaadbcaabcdbcabbaabbbcaacccdddabacddcdbcbbdcdcabbcbbdacbdaabadaaaababccdddccbcbcbdbbdbdbaaacbaadcdcddabbacddddcccacdacbbcabaadbcdaacacdcbdcaadabbddbbaddbabacccaacdaabbdcddbbdadaddbdcabcddbacbdbcbcacbdccbaadbccbcbbaddaabbdbbbacadccdacabdcdadcdadbcdbbcddddbdcbbdbaddbccbbacacaaccbbbcbbbbbcaaadacdcacacbaccaccbaaadccaaaaccdcbcababbababaaaacbcaadddcbaadbdaacbadadccabcdbdbcbbcdabcddbccdccbbacbddacbabccccabcbcdddaddbcadacbbbccbdbbbbcbbbacccacbcacdddbabcbbbcabbdcaaabbccbbdaddacccdaacacbadbdaabacdddddbbcbadcacaaddddcbacccbdcbcdcbdddcdbcdbbacddddbccbccdbadaacdbabbdcbadddbcaacabddcaadccdbcabacbbabdcdbdcbaccdbbadabddcbadbbdaddcddbcaccbdbabcbacbadcdcccaabcbcaaaabacbdbbbadbaaadccbbcdccccdbcbacddcbdbcddbaddababbcadbcabcaddbaccdaaacadaaccdcccaadaadacdabbdbbaadaacbdbddbaaddabddcbdbdcbbcabbddacdbdbccddccadbcddcdbcddbabbcdadbaccdbaabccdddcaabbadcbbddababacbdaddadbaabbdcddbdbdcbcdcbcdbabcabaacbddbcaabcbdabacbdaadbdbbbbccdccddbabbadaadcccababcbdcdabcbbdbdaccbcbbbadbbacaaadabbbcddcbdddbaabccabbccbddaccddabdaadacacbbadacbbdcbadddbdccbaacbbbacdcadaacacbcaabdabcbacabadaacbbaaaaccdabaccdcbddcabddcadbdadacdccadddaabdababdbbbdcdcdbccbbdcdbcccaacdabcdccacdddbadccddabbdcddacbaacbbbddaadbcccabbcaccdddcdbcbcbdccabcbdcadbcdbbccddbddccccbcdccbbadacccbcaaccabcbabbcdbadcdadadacbababbccaaabdabdbdddbbcddcbddddddabccdcacdadabadbcacaddcbcacbabadbddbabbdabcbbcddccacadaaddbaaaddcbdcbaaacaccadadaadacaabbbbbaaaccbbbcdbacadbbbbdadabadaabbdaacaaccccddcdabbccbbcbcaabbcbbbdabacddbacbcbddaaddbadadddcbdbabaadbaacabccbacaacccbacdddbdabddabacadcbccccbadaaccabdccdcbbbbccaccdacbaadbcdcdbadcddbaabbcbdcacdbcccbcbcbdcbacbdacaacbdbddcdbaaadbcabccabdddadcadccdaabdbbbbcbcabdcbcbccbbabaacadbacbdbdddcccaaaacdcccaaabccbdcbdcacacdcbbaaadcddbcdabccdaabbabbaacaabccabdaadabdbcbabbdbbccbacbbbcdadccadbadadaddacdbcdbbaaaddbdaddbbdaddcbabdbaddbdababbdbbbbbcdbccccdaaabcacaaabdacccaddbdcccddbacbccbbcbcacacbadaabcbacbcbcccdcccdbbaaaaddbcababccaadcacabddadbbdbbbcdabbbddbcacbbcdaaccaadabbbdadbcbacdbdbdcbbadaaadbbcdacccacaaaabaadcbcccbbabaadaacddcdddadcdbddaddaabcdcabdddbbcbaabbcccccaacadaabddadbdabbbabaddabadccdddcdbbbbcdccbaccdbbbdcabadacacbcbccbcbbbcdacbbabaabcadacbbdbdaadbcdadababbbcbcdddbddddabbcbdbdacacccdddaaddcbdcdadbaaacaabdababdaabbbcbadbbabdcbaccbcbcdbaadcdacbcdbdcdadbbbcddbccbcbcdaaadcbccabbccccccaccdaccdccccbaddbdbdccdadbacdaaaaadbdaabddadcdbabddaacadaddbbaaabbadbdaadacdddaabaaccbccdadabaabadbcdbbdaddaaacaaacabacbdddbbdbbbaabdbabdbabdababccdcbcdaacdbcdaaadadaadbdbdcdcccaaddcdacdbdcaacbdcacbddaaacacbcbcbbdccaaddccabdadbababcbaadabbbaacadbbaadaabcaababbddcbbadddccbbcabaacddcddbdababcdbbdcdcbcaacadcdbcacccbaaaccaabbabcadadaddcacbdbdbadcaaccdddacdabdddabaccbbbacaadaabdadcbdcabcdccabbbcadbabddcaabdddbcdcccbddbccdabcababccabbcbcdcbbcddbbaadcddbdbdbcbdccddacaabbbcbdcababcdddcaabdadbbcbaaacaabcaddaadadcdcccabdbbbcbbdbcddabbcaccaababddbcadabbccbccaddbdcdaccabccaddabaaddddaacacccbbdcbdbcdabbbcbaacadaaddcbbccccdbbacbccbcbcaacbddbdbdbbabaacbdadacccacbcdaccdccbdccadcdaacdbccbcababadacaaacccbcccdacadbcacbdaacbcaccabaacaddbdbaadcbddcbacbcbdcdacadbadbdadaabdbbaaacbabacdbacaacdabcbccacccddcadddbabcccaaaddccbdddbadddadabadcabbabbaccddbcbbadaaaccdcbddbaacadcbdaddacabdaabbabadbbdadcdcdabbadddbbbcbbdabaabcadcdcababbdccdbbdcadabdbccccbdacdcbcacccbccdbbbacdacacaccbcbcdbadabdccbadabacaacaabbabdcbdabcddbbbddddbadcccaabdcddaadadadddbaddaccddddcccbdbbbcaabcbdaccddbdbcbacccbcaddacacdcdcbaaccbbdbdbadcdabdbddddabbcdacdaaaacaadabbdcdacaadcbbbbabdaaddbabadcbdbbbccbccccddddadaccacdbdaacacadadacddaddbbbcbdccabacbdacdcadbabaaddccacbdbdabcddcaacbddacacbcadabddbddbaadaccbdacbbaddcaaadaaccccdabccbbcbbcdbaddcacbaccddcdcbbdbbbcddbacbaccdacabdacdaacddbdaabbcdabbaddacadbdacacaccbdbabbcadcacbaacdbcddcbcdaaabdbbdacddcdbdabbdbacaadcdcdaaccdaaadcabdcadcbdaccbbcbbcdcdabddacabccacabaccbdcdddadcdbabddadabbbddccaadabbacdbcccabdddabbdccdddbabcaabbacbaabadccacddddabcccdaaacadbdabdacabdabacddccacbadbcdbdcdbdbdabdaccdaacdbaddccacdbddabdbacdbbcdcabcdcbddbaddccdbcbdcdaadbaddddcabcaaaaaadccccdaaabdbabdabacdbcaaccbcbcabcaddddcaacbbcdbcadadcddaddaaccacbdabdbbbdbdacaddcbbdabcadacdabccaaddbdadcadbdbbcdcaadabacdcacdccdcadcbaadbadbddcbadccdcbcabcbacaadbccddbdcdddbbdbcabddcccbdbcbbadababdcbcdcddaabdadddbaaddbdccabbcdbcdbbadacabbbbdcbaabbdcaacaacbcdbcccdacadacdbcddddbcbcacddbbababbcdcbbaddcaccddbccabdbccabdcdabcbcddbbbdaabdcaaaaaddcbdbddaacdcaddaaadcabacbddddbcabcbacccddacdccaccdacacccdbbabcdaacbdccccbbcbdacaaacbcaabcadaccddcdcabdccccddcddcabdababcdddbdcdbabbbdbbcccdddbaacdadbdbcbbdcabcadddbcdbbdcacdbcbaabbabcbbddcccdcbadaaacacdbcacaaaadabcabddcaacaadbaccabccdaddabdaadcdcadabbadbacaabccdacdcbdaadaaacdbdcacccbcbcaadcccdbbdcdbadadaabcbdbddabccbbbbadbbbdaddabbdbaadabbaadaadadcccdcccbaacabccbcdbcbcadbabbdbcdbcbbcccadcbaabbdbabcbddbaddbcacdcdccdaabbdccabcbbcdccdbbaabdddcadadcaaddbdaacbbadcaccccabbbdbdaddaacadbdadabbacdcdbbbdbdccdaaadbdcddadaaccacbbcbcdbaacdcddacbbcdddbbaacdaacbaacbcdacbaabdcdcdddbabdbacdcbabdcdcbccbcaddbccbaabbabccccacaccdcdcbbcabadadbbccdaccdddcdcabbdaadcaadcacaddcbdccabdacaddcaadccddaaacdbcabbdcbdcbdbbadadaabcbbbadbacaacbddddcdcababdaaacaabbcbbccadabbbdacdbadacdbadacdacacbcbabcccbbbaddcdbbcabcbaacbadabadbbabcbddcabdcddcdcacaccbaababbccacddaacdcadddddacbdcadadabbcdabcdbcdccdcdaccdbdbcdddadaaadddcabddddabaadbcacdcdbcaabcbcaccbbacabbabbddbbddadbaaccccdddccadaabdddddadabdbaacddbcaadadbcaaacaaddbcdcdcbdddacdaadcbbaabdccadacccddadcdbbddbddadcdbdddddbbccdcbadaaccbbadcbbaacabbaccadbabccdaadcabacdaaddabacdadcbdbbcbdcabdbcbcabcabbbbdcadbcaccaadaadbdcdababacbbaaccddcdccbbbdbbbdccaccbbcabcdacabadcdacdbbbcaacacdbdccdcaddbdaadbcdaccbcdddaacacccbbddbcbbcdcbbbdbcbccaadbaadddcddcaddadabccccbadbddbdbdbadddbdbdcbccccabcccccccbddabcccaaacaadacdacabcadaadcbdaacccdcbabbbbccadcbcbbcabaacccaababacdbbbabddaacaaddcbcdaaddadbcdadbdcadbbdcdadbacadababbcbcbbcbbdadaacdbbaadaddcacacbdbbdacdbccdbdaacbbadcdadcadabdabccdaabbbadccdbacccbaaacdbdbbcbbbabddddbabaacbcbbbbabadabbdcddcdaaadddcbcaaddcaadbbbdbddcddcdcacddcbccbdbcdcccbbcacaddcdadcdbcadbbcaaccbcdaaaaadacaaadaddbcdbbbbddbddcabcadbbbccababbaabcddcabcbacdcbcdbcbdaaabaacbbdacbdcbdabbadbbabdaadcbbaddacabcbdbbabbbbaacaddbdaacbbcbbccabdbaddccdcdcdcbaccbabadbcabdcdacacbbbadbdaddbbccbdbbbdbadaaaddabbbccddaaabdbabdabaaddcbdddcadcaaddbbdcccdcdaaaaabddabbbbadcadbbbddbabbdbabdbbbbbdaaadbcadbadacabbdcdcbadcdcabdabacdddddacdbcbdddcccbcbcbaabbdaddcddbdddbbcadbadaaaaabbbbabbdbcacdabdbbbbbddcdacaccbdaabbccdbbaaddadaabbabbccabbadbbbabbaabadcbbccaabccadddbdbbdaccdbcbdaacbadccbcddabadcacacdcaddbbdddddbdcabbdaccbcccabadbdddcdababbbbdcbbadabcddacadaaadccabdbdaaadbcdcccdadcbcccccaabdcddacabcddbaddbcbaacbacbccadbacdbcccabddcccdbdbcbdcaabaabdcbbddbacbdaadcabbbadccbdaadaccdacbcbcbdcadadcaaacaadbbbcacbaacccbdddbcbddcccdbdcbbbdbacadcbaccbbcdbddaabdaadbccccbcadbcbbdbccbcccbacdabaaadcaacadcabccaddacdccdaddcabadbaabbabaaaacadbdacaddaacdccbabcadddddbbdcaaaaabddaccdbbbadacdcdabdcbaaacabdaabacbaddbacabbaaddaccccaacbdbaabaaabbddcabdddbdadccabacbadbcadcacadccaccbcadcbdadbbabbbbbcbdbddbdbbbccbbdabbbdaddbadbadbcccaaabccbcaacddccdcbcddcdabadcccabdbcacdaddcabaaaaaaacbdacdbabcaabacbbaadbacadacbcddbdaddcbdccabcaabadcccdcbacaaccbbdcdbbbcaaabbbaabcbabaabacdcbaababbbccbdbabbcdabcaccdacacacadbdbabbbccaddbabaaacdccbddbcdbcbbabdcdcaccccdcdcbcccacaddbcdaddcbbccbbbdaaddadcbacbdbbadababcbcabdcaaccbadcdacccaacabbcacaaadaccaabdcbdbdacaccacbaadabdbbcbaddbcbaaacacbbbcacaabaddaccbddbdddbbdcadbccbabbcbbacdaaccacaabaaacdbacddcaaabccbabbaddcdcbabddadabdcdbadcbababcbcdbccbbddaacccabbbddcbdbdcacbccddcacddbadbdcdadadddbacccdcdccbdcaaacdbdabdbcbbccdccddbaaccabcdcaddabdddcdbbcdaacbccbdbaacabddbadbabccbabadccabdabdbcbadacdadaddbdccbdcaddbdbaadaaacbbbbdddbcdadbdcbaadcddacabaddaacbabddbacaaaabccaadccdccaddaacadabdbdadbddddcccdacaddabbdddcbadcbcccddcbdcdacabdadccadbabcbccbbbcbdaacbaadaaabcaddaddddbccdddbddbcdccddcacddaabadbbdbbbdcbddddbacbadddccbadbadbdccbababcdbdcbbacdbdcdaadcbbaabdbbcacaadcaccbabaadbcaabbbcaadcdabacbabdacbbadababdddabccdbacadcbcbcddcddbbbabcddbabcbaddddbdcdcbcbaaabcccbcaabbcccdababbaacbddcbdccbcddbbdcccdcaddbbccaccbbcbbbdcaadddddabcdbadaabccacadabacddaddadbdbddcacdadabcddcdacdccbdaccccadaaabcccbaadadabdcacbdbbcdbadaabbbcacdaadcaaaaaacaccaddbadcaaacaddcccbbcacccbdbccbdcbbbcdbcabddccdddcdbddcbdbdcbdcbabdcaccabbdbdabdddcccdbcdcccadbdbabcbbcabaadbcccaccacbaccdcccbbdabccbbbccbbaaaabbbbacddaccdadbddacacaadadadbdcacaaaacdadcddbdbbaabbdddacaccbdbbcccadddcbdccaaaaaddcddaccddadbcbbbbaddbbcccbdbcabbdddccdacaacddddddbadbbabbbabadaccaabdbccdbdbdadcbdccbbbadadbacddbbbccdbdddabaddbbbaaabcbbabcacbdcaccacaabbcdddacccbcabcccaacacdbbbbadacdbacbbaabdacabdbdaaacaddadccbccbdbbaaacdcadacbbabbdaadaacbbbacdbbcdddbcdbaaabddaabccaaacbcaacaccadbacbabcacbdccbadbacdbbabacaadbdaaccccdadabdbddbacacdcbdabaddbdcbccbdbbbaaccacabcdbbdddacacbcacaaaabadbcabcabdcccacbcbbabcbbaadccadddcadbddbadacbcdaccdbdcdddcbbdcdbdabacdccbabdabddcbbbcadccddaaacbdbababdaacbcdabbdbabcacacdcabbabcbcbdbacbaabcdabcbaddddacbbacbddddddcbcbbccbaaaacbddbdcacccccabbcbbadddabbbcbcbbaacabbdddbbabaacaabcaccbbdccbacbbbcdcbddddbaadbcdbaccbacbadadddacccbaaadbdaccababbccbadcbcaacacacdadccbabdaabcdacdddaadacbbcdbddaabdcaacbcaadbbdcbabadabbdcbcdbbabdbddbdacdbcdcdbadcccdccdcddacccadbcadacdbbdabcabbddbaadacdddbaabbaaaccdacbdcdddcbdddaccccaabacccbdcddacbcddbddbbbdbddcadcbbcababbdababaccbcaabdcdacdaaddbacadacbcdacdcdcbdabcbabbcaccdccdaabdaadcddadacbabbadcdccadddbccaacabdabdaadddbcaadbbbacdcabbbcbbdccbccacaaaacbcbbbdabbcdaaccccdccbcabacacccdddddadbdcdaaabbdbddabbcabbcbbacdbdbadadaccaabcaddcdcccccbbacacbdccacbccadcbccddbdcbdababaddcabacbcbacbccddaabbadacddacacdcaacbaacdbabbdaddbaaddbbdcdccacabcabcbbccabacbcbaaccabddbcbbddbcdadccacacdaddcbadbbcaccdabcdbaaabdacdaabdcdaccbccbaddbaccbabbababdbdadbabbabbbcdcdcbdaabccbcdacdacdddadddcacdacbadbaadccbddbcbbbdbaacbdcccbbcbacccdcdbbddaacbdadbdacbabacddccbabcddadbccacddddacabbdccbaacadcabddbacadabddbbccdbacdcdbcbbdddbdabcdabdadbaccadccbcaacdbcadaacbcaacdabaaccdcbcccbcbbcddddbcaaddadcbbaabcdbccbddadbabadbdadabddbabaaadaabdaddbdccbddbbadaabdbcacdcbabbcaddabbdddaadcbdccbbaaccabcaadaaacacddacddacdcccabdbabbaaacdadacdcbbbcbddbdcaabaabcdcaaadaddcacbbbdcabcdbcbddadccdcbadbbdccabcaadababccdaadcacaadbcaaacdbacdabbddbdbabdaacdcdaccdbaccdcabacaacccbdcdbddbaaadcdbcddacacbcabccddbdadcbbdccaadccdccccbdcaacddccbccaccaddcacdddccdccacaadccdcadaddbdabccbdababdabdddddbaadbbacbccbbdadbdababbbdbdbdababbacccabbcadcbbdabcbdcdcadaddcbcdcbaabbbbcaddadaddacdbccaadbdabcacbcbacadbcbbcccdcdcadddccadbdbcccaabcaaddcccabdcacbaabcaccdcacdacddbdcbacbcdbbcaacddbdacadddabadabaacccadbacacaacbbabcbcbdcadbbdcaadcddcddbdcbbadbabaddbbabbdcccddbacbacbbbddddbaabccaddadbaddababaacbccdddabdbdcdcdbaccbdaadbdcdbddaacbdbdaacaccbcbabcadbbddcdaaacaddabdabbddcbbdbbdbdbaadaadaddddcadbbdbacccccaaadbaabbacbaddbdaacbbaaadabdbacddbcccddabcdbcdccacdaddcbaccadbacccbbbbcbbcdbccddcacbdbbbdbbdbddccccabdccccbbbbddcbacccccbbdcabbaaabcddccdbcaddccbdcbacddabbccbacbcdcaabbccbacbabbcadbddbbccaabdbadbdabbabadddbaacadbddbcbcadbbaabcacaadabaaaabccabacdacbacdcaaccbcdcadccbaabbaccbcbdaaadcaacddcdacbbcdbddaccbccaacbbdbdcbacabdcacbcbbdccadddaaadacdcaabcaaddcbbcdcadcbbccbccaacaabdcdbaddacaaadadbbbbcdbabdddcdabdcadadaabbdaabdcbbdccbcdbdcbbbbbdadddaaaaabadaabcdadcadbbdbdbadbababcddbcdccccbbabcbddcdbaaccdbcaccbdddcdbbadcbbdcabccabcdaacbbaaadaddcdbbcccabdcddbccdacdbabcbdccacdabbbbadbdbbaacdabdadaacdadacdcadbacaddcdbbbdcbcdbbdbaddcbadcbddcbbddadacbbbbdcdbbddcabaaabdbacacdbdddaabdbcbddabcbadccbddcbabacadbaabaddbbcbdaaddccccccbcdbcaadccbbbbdbabccabacbcbadaccbcdabbabbabcdaacbcabdcdadbdaabbbbbbaacdbbddbcaddaaaabbbccaabdcaccdcacbdaadabcdbcabadcbbbbbdcbdbccaacdaaadaabdccdcbbbcadbddccbbadaacbbbcabddadcaabccabbacdbbdddaabdcddacbbadcadaacdadbaabcaacddadcdbbdaaacddcadcbcccdaaadcdacdddbcdbaccacaadadcdccbacdccdbcbacbbcaacbacaaddabbadbcbcbddddadccddaabcaddacbcbacccadcbbbccdcdbcaacddadbbbbaadccadbbcaadbcdccdbbbdbdddbcaccacabccdabcbbdbdbccaadddbbbcbadbadcbbbbcaabcbbcbbdcbadbccadadbbdbadcdacdbbdcdaaddcabccdbbcccbbcdbaabababbaddadadbdacbadbdcdaddbbdbaddbcadbcabaadbbddbaccacbcccdadbbbcdcbbdaadccdbcdcdaacbaabddaccbacabbbcdbdccdadabccadcbbdcaddacadadbacbcdbcdbcbadcacbabbbadabbcabcbdabbbacdccaaabcdadacadcaaacadbaaddbcadacbbdbcdabddbbcbddcbbaacddbcbdadbbdadaacbbdadcbcdcbacadbcddcbbadcbbccbabaadccdbddcabdacaabacaaababcaaaacaddaddaaadabdbbabcdcddcdbbdabcdccbaacadcdccccbcaddbbbabdbbddcbbacbccbcdbbbbdaabccdcbcbbaadccccddcabacddccbaccaadadbcbacaacbacbbabaccadddcabcaacbcddadcadbaabcbbadadabcacccdbcdcdddcaabcdabbbccacadddaadadababbbdbabbcdadaddbdadcbdbdddccddbbbbddccaccdabaddcaccadaddbdaadddccbdbccdaddcbcdcaccbbbbbdcdaccacacbcadaabbccddadddbccbacdcccbabadcdbbcdcaabbdacadddbcacbaccdcbcaddaaadddbdcddadcdabbabdccccadbadcccbcaddcbadccbbacbddbaddbaaaadcdadddbcabccbccdddbadcaadccddaaaaadddbbddcadcacbabbbbccbbcabcbcaddcaacbcdcaccdaccacdcabbdbddadddbdcddbccccabdaaccdcdcabbabcdabdcdcaabcbbbcbbdbcadcbbcdbadaaabbbbddddacddddbaabbdaacbcbbdbdbbcaaabbbaaaadbccdaaabdcaaddbddcddaaccadddccdabcabdbbaadaadacaacdcdacccddaabacbbaaabaabcddbaabcdbbdbbbbbcaadddbbcabbdabdddaadcadbccbcadaccdbadbabbddccabddbccaacdddbbccbccbadbdabacddbbddadbbaacadabbddccacbdadbdbdbadabddccacdbccdacdbadcbaaccdcdadcbdadaaacdcacbcbcddcdabbbacbdabcdbabdbbccddcddddaacaddcddadabbcabbbabdcaadabdcddbdaaadbdcddbaadbbcdcdccdbbdccabbcacbbadbaccbccdabcaacddbccdacdccccaaaccadacccaabccdddaacdbcaaadbbddabacaccdbabbbcbdccacbabcbbccdccaddcbdacbcbcbacacdcdbcdcbbddcadbcbabbddccabdbcbbbabbdbabdbabacadaacccabbdabadbbabaddacbdbbdabcdacdcbbbcddbccddcbadadabdccbbdccbdcabbbaacadbdccacbbaccbdcabbbcbdcaadbdddcdbbcaccaaddcbbaacaaaadbccccaabbbabdacdbadbaaccdadddbabdcccabaaacbbcbacddabddccbddddbdcbbbacbcacccabcbddabdcccbaccddbbcccdbccaadcdadccdadccbaaaadbbdaadadbababdbcddbadcadaaacaabbcdcdccccacdcbadcccaaabccaaddaaaccbacdbbcccbbadddacabadacadcabacdcdadadcddabcbdbbbcacdabccbcbccbcdacacaacdbdabbcbacbbcbadbbcacbaaaabcdbaaccbadadbcaacddcbbcababbbccddcadccadcbcdbacdccddccbaaaaddbccdabcacdcdbcbcdcbadbbcbcacbdcaadbdcaccdcbdabbbbbadbdaddaddbaabaadbabbaadacbaadaaaccadabababcdcabdaadcbdbcacaacbbcabacaadbdcacdbadbdaaacccdacbbababdabcbaabdbcabcacbacabcbacacaccdacdaddccadbadbabdbcdbddbdaadaccabadcbcdbbcdbcbcddbacdacddcabcdcbaadacdabcdcacadbcdadaaddcbddadbbadddcccbbbcacbbcabbcccacacbdcababdcadbbadbdcbdabccdcaadbaaadcccadbadabdabccaadbbacacbaccadcaaccacdabbbcaaddbcdacadbbbcdaccaaddbccdddabdbddbccaddaccabacacbaabbbdcaacaccababddacdbbbdddcdbabddddbabacbbbddddcadbaddddccdacacbacccbccddbcbddcaabcccaccbbcccddddabcbabadddaadbadcdcdaaddaabaabbadbbabbdbadaabdcbdcbddcdbcaaacccbaddacddbcddbbaaadccaaddadcdcaadadddadcbbbbcbadccbacadcaacabdbcabacabddccaadddbbcaaacabcccbaabbbbabaabbbdaccbbddcbacdddcdcabcdabbddbcdadaadacacbacbbbdbccdacbaddcabccbddccddabdccdababccdbddbccbbbdacdbdabddaccadacbbaddacbddabddbcdcaccadcacbadadbbcdbaaabcbadaccdbbbbadbbaddcbcabbccddbdcdbddcabacddccccccaaaadcccbccbbadccddabdcddcbdbcdbcbdccdddabdabcdcadccbdcccdbcdddbccabdbcddacdbdcdcdaaddbaabddcbcbcabbdadadaddacaabcbcdbabcdbdadbabdbcddadcdbabbbdacadaabbbcbabbacaacbbbadcabbbcabccbddccccabbdcdcbbdabdabacbddacaccdcbcabccbbacbabaacbcbaaaabacddbcaadbbcaddcdaccccaadcdcabbcdabbbacadaadacccadabddadddddbdacdcabdbadacbdbcdbadbccdaddbadadbaaadcdacbbbccdbbbbbadadcbdacdaaccccdacddaccccbccbabcbdcccdacbdaabcaccdddacacccabaccbbcdbcbdacbbabddacadbcddbbdccabcccbabbaaacdcdabcabacbaacdcbccbacabcdcbaddacdcdabaccaaaccbcbddcaaccbcbdcabcdbadbdbdbcdbccbdbbcdbdadacbabbdcbababdaaccaaabaacdaadcaabbbdddcdddbbccbbbdbcbcbbadccacdcbdccabcbcbbadbabcdcdbbcadbdbdbcaadadaccacaddbbcabccadbddbdccbaaccbdabcadacdcbcbaccbdcbdaddcdacbbdbbdbaadcacacadbcbaccacdadbbbcdcadcabacbdcadaadaadccaababcddbccdaccaaddbbdaccadbbcddbbabacadacbbdccdddddbcadccbbbdcbdbbbdbbbbbbaaddaabcaaccabcdbcdcbbccaccccdcaccccacadaadbcaddbddbbbbaaddabadcbbadcddcbbbacaddcabbcbabccadaccabdcddacbbbadabacaddcbdddbaaccdcbbadcdbcaaabaddccbcdcbabddabbbcabbbadcadaabaaaacdbdbbbabccddbadbacbddacdbadccbbcbbbcbbaabadbabdcdbdabdbbadbcddaacbaacbdcdbbbccdccabbdbdcaadcaccccbdbbccdbcadbcaaadaaccddaccaddbaccdbbaadabccaddbbcadcddddabccbdcddaacacbadaacbbddaabbdcaddbdbaddcdaacdccddcabbdcacccaaccddddaabcaccdcccbbbcaacbcdbbddddbbbaaacddbccdbcdbcdbadbddadaadbbccadabbaaaabdddabaaccaaddcbcaddbcbccbbcadabbacaddbdbbbacacabbaccbddacabdcbbdcccdbdbdccbcaadddcdbbbddbaacaabbacbaadbcaddcdadbcaacaadbabaccacacdbacdbdbdacbdbabaadcdcdbcdaccdabcbadcbdaaccbaaaacbdcbcbbccdddcaccaaabbbacbcacbbcbcddbddccacadcdbabaacdadcbcbaccdbdbabaaadaadcdacabbdccdaaacaccacbbaccacacdaccbbaccaccadaccacddbabdabbabcddadcbbabaabadabababcdacccdabadabbdddcbcbcbadbddbcbcadcccabbaacbcbbbbdccdaacdadcbaaccabdaacdcadcaaddbcaaddbacbdcccddbdcbaaaacdbcdcdabcddaaabadacdaaabbcbaaddadbddadbdccbaacbbbcdaadbdccbbaacaaaaabdbbbdacadbdccccaabdbbbbbdbaddacdddbdbadbcaabbbdbddcbdbdadccdcdacaabbbcdaaabcaaaadaaddacddabbbdbdaaccccbabbbcddabcaccddadacbdbccabadabdabccacabdcdadbbabdbaccdabacbabbdabddcabcaccdadbcddaadccadaaaaccbadaabbcccabcbadcbcdacddcbddacaddabdcadbddbbcabbbadabbdcccbcabcdbdcaacbacdaddcdddbacaabbbbdadddbcabcbdbdddbddbcdaddbdabbaccdccaabacbddbaddacabdbacbaacbccdbdacabdadcadacabdaacadadbdbbdbbdadaddaaaddaccdacccbcabdcabdbacbddababddabaacddbacadacdddbadbaaddaaaccadbbcdabbbbbaccbccbbcacbbaccbabbdbccdcaddbcbbcdacddbdcbcdaaacdbdcbbabadbbcbadbdcaadbcbcbbdbcdcdbaabdacadaddaacadcccdbcadadaaaddcadabdddcccbdbcacaabaddddabcdabddbbaabaccddabcbdbdadabcaaabcdcadbcdbbcbbacabdcccddbdcdcdcdbcdacbadcbbdabbdbcaddacbdaaddadcccbabccdbcccaddacccbddccadcabacbaddabbbdbcdcdccadacbdbbbcbcbdbcbbdbbdcacdaaaaacacdbccdbdbacaaddbbcbdddbcabcbadacbcabbacbcacbdcddaddcbcabcabdcdaaacacabadaddcaccbccddadcdcdbadaaabadccdbabaccaabdcdabaaccdbddadabbbbccacdaccbabcaabacaaacbbddacbddbcaccbadacaacbadcabacccacaaccbacbdaaabacccdbadacabdadcddbabdacbcdbdcdabcccaabbabccbdaccaaadbbbdccccddcccdcdcacbdbbcdadccbacaadbabaabcabcaabdddbcbddaaadcaadaaccdcddabddacadaddadddbccddbdddcabcbadccbcbcbdadcdcdbaacdcdbddaadbcbcccabbbcdbcdcdadacdcbddbccddcadcabcabcdacbbaaaddbcbbcaadddaacdbdbaaacacaccabacdddcdacbdaaddbbacdcbbbdcddcbacddabdabcaddddbdbbbdabbadccdbbcadacbcbccdaccbdddcbdcdcccbcadabcabdabadacccbcbabdbccbbddcdddacaababbbccccacbcadcbdcadaccccdcccaddcccdcdbcbbbbbadbadabaabbabbbaacddabadbdacdcadbdcdcdaaddbcbacdcaaadbddaaaacdcbcaabaaadacdaadbdaadabccacbcdbbdadaabadadbdaddabdcbcabbcbcdaccadcacbccbabccbccadcccaabcdbacbbdadbcadcbddbbacddabcdaabacbcbdaabbbdacaaacdcbdcaccacbaaabbdcdcddadcacbcacdcbaabbdaccbdbccbcaadaacabbcabcadcadcddcaccbcdbaddadccdccbcdbbbcaccdbacddbbbbadccdbacadcabbbdcacbbabbcbabdabcbcdbdddacdbcbcddddcbacbbdbbcdcabbbbbadbbdcddacccccbabacadbbadaccbcdbcdcdccbdacaadadcdaaabdcaaaabbddbccdbaacabcbdcacdaccaddacacccababacaaacabbddcccadbbaaaabcbcbdcdbdcbbaddbacaddbccaabdbaaaacabcbccbbaccacbdcdaacacaacdccdccaaaadddccdaabaaabccacdccccaccbadabdcbaddaddcdbccddbdddddaccbdbbddbccaabcdabbacccbbadbccdaaacbbcdccdbddaaaabadacaacbbabcdabaddbbcbcbcbcadaabcccbadcdaddcdbbccabacccccbcadadacdbadcbcdcdbbdadccbabbaabcddacbbdbcbdbdbaaabccddcbbcdbcacbbaacbdbccbaadcadbdccbbdaabdaccbdcaadadbbcabaadbbdadbcdadabdddcbdabdbadbbdcbadadadadbbacdcadccbccccbbddbbcacccbbbadbcbccbccccaabbabbdbbaabadcbdabbaadaadbcbdadbabadabbabadcbabacbdaacdcbabddbdaadaabddaabccbaaabaabaccbddccbbccbacaacbdddcdaadacdbacabddcdadddcccaacccabbbbbacbcbadbcbbdcabaabdccabaababdcccbadbabaaadcdadcdbcbcbacdaadcdbabccacbdbbbbddadaaaaabdaaacaabbdcdbaadcbcacdcddbcdaaabaaccdccbbacbbaddddacdaabadacdaddbacbcdddabadbabdbcacdabadcbabcbadbdaddcdcacbdcaadbcdbadbcbadbddbcdcddbaaaaabcaccddbadaacbbcdcdaababbbcacbaaccacdbcdaabddcdcbdddcaaadaaabbaabcaacdabddaacaaacdccaccdcabdcccdcbabdbbdcdbacacddadbadaabacccabaabdcdcaaabbacbadacbdcddaaabcacbadbddabadadacbdabdabcaabcdadbbbcbcabacabdabbdaadcbcbcdabdabbcbbbdcacaacbdcddbbbbdadcaacaccaacddcdcbddbcbddaddbdccdaaddcddaddbbcbcdbdddacbbcbdcacacbcbacbaacbabaaacbcaadcdcaacbdaabcacaabddaccddabdbadcbbcdababccdbbaaacbaadcdcdbcdbbdccdcddbbcacaaadbbcbcdadabbbabccdbcdbcdbddbbacdbbdddbccacbcbcdbcddadbbbdcddddaaadbcbcdacaabcbdbdbccadddaccddadbcabdbaadbdccdcddcaacacacbbbacaacbbddccbaabdbdabccbbbadadbdbddcdbbbadbbdbdddbaccacbaaaddbbcdbbabcabbccaccacdacbbaabbadabdbadbddbbcbdbadabadcccdbacaaaabdabbacccdddabcdaaddddcccaadccaacdbbbdbacdaabbbccddaaabcbcacbdcddadccbacbcbccccbbaccadbabbabdadbdaacdacddcaccccdccdcaacddabcbbaadbaddcadbdadabcabbdcaddabdbcbbacddddabdcaddbbbbcaddcdabbbddacbacbddabadacccaddddacbccaddddbddacdbabbdadaacbbbaadbcbbaaaabaddaddcccabcaaddbbcdcbcddcadbbcbadccdcbabbbdadccadabaadcbabaddacccaadabcacadbaaccdaacbdddddbdbccdcbcbbccdaddadbdcabdddaadaabaaccadabbaacdcaabcccddaadadabcccaddbcbcccdbbaabadcdcccbaabadaadcacacacccadacdcaaacbdcbbacbcbdbbcccbbbcacbbbacacddbaddabddbabddcdddadccdbaddcaadacdbbaaaddcdaccbbabaacdddccaadaaaadbbcdddaacbdcbcbcbcadbbcbabbbaabccbdadacdddaccacadcbbaacbcbacdcdbadbbababbbbcabddbbbcbcddbacccbddbbadbccabbabbadabddaaaacddaccbabbdccadddcdbbaaadacddddbcbcdbadcbdccbaaaacddccbcbcdacccdcbaadbcadabbbddaaccdacdaaadaabbbbadbaaaabacaaddbaaaacbdcdbddccddcbadccdbcbccbdcbacbbdaaabcdbbaaaddbbadbdcbddcdbccdbcbdbdcabccaccddbcbdcdbacbdaadadcdbcdabbbbabdadbdcbdcaaccbbdadddcbcbbbabbbbdadccacccacbcdcdcaabacccdbbccaddccacddbbcacadacdadaacdabdabbdbaaacbcbddccdbccdcadcddbbbaaabdccccabbcccbbbdcbcbbdbbadcdcdbcdbddddcbdabddbadabbddcaaabcdcabbabbcdadcacbcddddbbcadaabcbabadbccabdcaacccabbbccacaddbcdbbabccadbddbbddddaacccbababadccddcdcbcbabaddbaabaabdccbadacbacdddcdbdcaacccddbabbccdbbccccdbbbcbaadbddbdbaddadbcabcabbbdaabbbdacccbdacdbaddaacbbaccadccdccdbaababacaaaaabbcbadcdbccccddccabcdcccaaccaacacdaccadabdadacccdbaccaacbbcddaaccccdbacccdcdbcddcbabcbbbbbbaddababbcaaadabdbbdcdadccdbbddacdcccdbbcbddcacbabcdcdbacbcdabcbcdbaadddbdbbdbabbaaaadcccbcdcbadadcaacacbdbdaadbadabaddadbdddcbaadbdbadcdcddbdaaaabddbbbcadbdadabbccccbbaacacdabbadddbcaabbdbdbadabcddbdcdcabcdbaddadbcdcdcacbccddbdddbbccbacaaacdbbccbacabacdbbdadbbaacaccbbccccaacacdbcadbadbbdcdbbdaacbdadabcbcbbdbabbcbabbbccaacdabaddbaabbdddbadbacdbcaacdbdddbbdcbabbbcacbbbbacbaaddcdbdbbbddbccbadcdcdcaacbccbabbcbbdcdbacccbaccabdcdabcbbaaababdcdccdbaacadaccdbbcabbbaadbdccbbbbbcbadcdadbaccbcbddacbdbbcabbbcdacbbabdcaddbdacabdcdaadcdcaccdbdadadaccadcdccabadbcacdaaabacbdaaadbbabddaccacabddadddbdaaaaaccddccddabdbdcdabcbdcabaddbccabcaaaaabcddccdddcdabdcbbcdcadacaaadbdbcbbadbcdababcbbccaaadaacacdabaccdbdbaabddbacaabbccdcdcbdcdbadbdacbaacdcbdbddadcbdabbbbabcbbabcaaacbabbbaadaccaddabacbbabbdddaabbabcbcdaacacabadaadbcabacbcdabdbddbddbacabbbcadbdcccdadabacdbcbdbacacbabdccbbdddbadabddcdbdabdadbdcdabcdaadcadaabacbdacacabbbdbcaacbccaacbbadbcdabddbadadddbcbadaaadcdbcbaddbabddbbcccddccbbdbbacdbdadacacbaabaaadddbddbcadcaddaadddddcabacdcdcabcccbcbdbccbdcacbbcbbdaaadcdabaacababdbacdaaaabaadcbdbcddbdaacccdcccabcddadacdaccbaaddddabcbddabcaadaabbdcdaddbbbaaaacaaaaddbdbcdbdcbbdcbccdaaabdcadccbbddccdaabcabadddbbbadcaaaaddcbcccbaadcadaabccbdcaaccccabcbdacdabadcababaaacddacbddcdbadaccacdabdaadcdcbdbcaadacacacddcbbabcddbcabbaddccaacabbcdbdbcbcbbbdaddaaddbabbadbbdaaaadbbbddabddcacbdbaddbdabacaccaadadcadcabdadbdcdccabbacaccbdaabccaccabbdccbcdcbcabbabbddcdabaddddacaabccdacaccbcaccbaaadabacbbcadaabdbadbaaccddacadcdabbdcaaacbbacadbcabbabddbbbbacdabaadcacaaabaccdacdbccdadaadaadbcbbbdcadabbbaacdccaacccabccbdcdccdadddbdbaccdbdbaaabbbbbaaaccadbdcaaabddcacddacddccbdbcbdadbdbaccbbadbccccccabbcacaccaccdbdbbddaabaddcbaadadacbbdddbcdaacdbbabbdbbcbbdacccadcddcbdbdcadcabddabbbddaddcacdbababbaccbadacadbccbacdacadcadaaabbdaccaabbbabcabdbcdaddcccdacacbdcbdbabdcabcdccbbabbbdbabcbbabbbccccacdcdbccaacbabdccbdabbdaddbbbadcddbbbcdbacbaacbadcbbcdcacdddaccccdddabacbdadadaaabdbabacdbddbddaccdccaccacaddcadacdcbbbbcdbdcbababdcdcaaccaccccbcdbabcddcddcdcddadacdccddcbaadcdadabaaaabdaabbadcacccdbcbbddcdbacbabdbacbddbaadcadaccacacccdccaaaaadcbbacdbdcbcdabaadcddacbcaccdbcbadabacccdcadabbaaddbccbcbbdaabdbddaaaadaddcbdcdbabbbbaacbcaacdcadaabccdcdcdbbabcadcaddaccbabcababbdadabdadccdddbbdccbcbdcdbcaddcbcabcccadbbabcdcccacdbbcdcdbabadcdcbdbcacddbbdaaccdcaadaacaabccbbdabcdbaadbbaddadaddacaddadbbccbcdbabcacbbccababbdbddddcbbddbacdbbdbdbababbadbcbbbddddccaadabadabcbdadbbdadbcdaddddcbcddaabcdcbddaccaaaadcbdbddcdccddddbacbccddbdabccaadddadbadadadccabaccaabdbbccadbdaaccdbbdcabcbbcaaccaacaaadadabdcacddadacbdbdabaabbdabdcbdacaccbcaaaadacddbabcbbcdcdbacdacabccbdbaddbbdbcadcbadccbdccbbaccbcdbcbcddcbccbcabcbadbddcccddaacccbcdddbbbbcabbacaadbcdbadacbbdddcbcbdcbadababcdadbbadacddbbcbaabcadccbdcddadabdcbddcccddccccddadacaddcbbbddadacccddacddccacabcbdbddccddabdadaabbadbbbaddcdbaadcadddacdbdcbcdccdbbdaabdcbacddbddbbaabadaddababadbdcddacdccbbcadbdadcaddcdbdcdadcaddcadbbccadabbbbccdaaccaccdccbacaabcddcabcdbacdabddaabddcdaaaadcdbcbbdcabbaaddbcccaccbddcaacaacdbbadbaaabccdabdaccaacdaadddccbbbdaadbabdbadbdaccacaababadddabdabcadaaaaaddcdbbaccadaccccddcbcadcbbbddcdcbcaaaadbccaacabdbdcbabdbbadbcacadbcabbcbbdbbacbbdbabcdacddadbcaadbdcaccacccdabdddacaaaabdddcadddaaacdacbacddadaaaababbbbbadbdbdcabdcdabacccdddbbdaddcdccabacccbccabbddcbbdadcbaabdadcdbcbbadaccabcbdbcccaaabcddcdbbccbbcaddacdbdacbddaccdbbdddadbcdcdabcaadaabbcbadbabcaaaadaadccbdccdcbcddabbdacdbcbaaddabdbdaadabbbcaddccbcddcbbdaaabcaadbcbaccbbaaadddddbcabacaccbdacbdddcadbcdddcdabbaadabacbaaaccaddcaacccbcdabccbacddaccdcbbddbdadbdbcaccacbddadbbadcddbdabbdabacaaadbdcabdbbdaabddbbcbcddbadddbdddbdaddccaaadccacddbabdbadcbdbdddccabadbcdcbcaddaddbbcaccaccbdbacabdabbabcccddbbcdcbacbcadacacbacacbdaccaddbcabdbbcadcbcdadbbacdcbbbdbcbbcbbbddbbbdcbbbccabccdcaacbcbcdddaccdbbadbdbddcdacadacacaccadaccdddccbdadadcadcacabdacbdbcdbcbddddabcaddcdcaaccbdacacdabbdacaccbdadcbcdcdabcbddbcacdadcacdaacdcbadccbbdbaadbaabbdadbcdaaaddabcaddbbcacddbcdbcadaaadbaadbdcdcddacbaccbcadbacbccccacbcddaacbdbbdaaababdccbdbbabbaabdbcbcdacaaaddddadcccddccdaaddaccdcddcbaaadaaaddccddccbbcadbadcccdaabacddcbadaaacbcbdbcacbdaaaabacbdbacbdbabbcbccccdabbbdddcdadadccbbacbdadbabdcbaddbaacdcccadcccacddbdcadddadadcbbbcaabcaacccabcdccbbbbadddbcaaadcdcdddabadbaadcddaacadddbdbddacacadccbccacabcbdbdcacdbbbbbbdbcdbdbbccdbddabcadbbaacdccaddcaddcdcccbcdacddbbbaaccdaabdabbdcbbdcbabccaaadcaabaaacdacccdadabcdcaacbccccdbadcddbabadbcddaccbbaaacaadcbabbadbcacbbadadbccadcdaaabaacbdbdcccabbdaaaacddddaaabcbbdcadbaaccdcbcdbabaadadbbcbdbdbbaabddbbdbacddcbccaacabdadbcdcbbacddcbaabddddadbcddbcddcbdbbbbabaacabddabbcacbbcdcbacabcbdddcbbaadbbacdddccdcaaadbddaccdbbcddbaadbadbdddacdacaadaccbbaaacadcaaaadcadbbadacbbaabcadbbbaccbcdbbdccabaddbcadcdcadcdcabcbdacdccbdcccaccccaccabdddcbbacbcbadccbdaabdbbdddcababcdbbabbdadbbcdbddbabcaaabcaaaadbdbbaaaacadbdccdcccddabcaaacacddbdddacbdbccbcacadcdcddddccbcdbacdbbdddabaaddacbcabbcabbdacdccdabddcbcaacdabdbbddcbbcbacbcdcdcbdbadbbaabddddbadbddadbcdbbbdadacbbcbccbcbddbcdcaccdbbacaabadbddbcbababbdcacddbbabddcbbcdaccacbaaaabbdbdaaddcdccacccbbbccaabcabadcbcbaacadbccbacbbcbbddbdaaccadabddddcbdcaabaaacbbbbbcdbadaabadcccdccadababdbbddadbbbccdddacacbdaacbbdacacbaabcabdbdadabdbdbaaabcadbaccbdcdcbbaaacaccacabddcaabbddcdbbcdaaaadbdacbdabbdbccdbacabdbbcdadbbbccaaaaacdacbdbccddacacaacdadaaddbbadbbdcbcbacbdabbccbaaabadccbdbdbadaccbbcaadddbcdaccddcbbdbbdadbbcaaabdcadabbacbbaabccabbdabbaaddaacdadadddcdabddaacddacdbdbbdccbbaadbacadbabdcddaccdbaddaddcbadbadaabccbdabcdbabbcbdbcbbaddbbdcaacaaddbbadacabaccbbdbbaaabbbdbcbcbcaabccdaddbdbabbcdabaababaddbcddcdadbbcbbabbbcddcccadadbdcdabadccddbdccaaddcaddaabdcdaaddbadbcdbcccaabdbccdacadcbccddbcbddcbaabbabcacacaaaacaddacdaaddbccdaccddcdaaddcdaddaacbdddacbbdbdbbcbdadccaaccddaadcdbacacabbadadbbcddccccbadbbbcdbbcdadaabdadcabaabbabcccbcbccbabbcbabbdcaddcdacaadaabddbadcbcbaccbccacddcaccabddcbcbccacdcbddbbabacdcbcadadadbadddbbbcadbcbbabccdadadbabbbaadbabdcbacbcdbcddcddbbbcdabddbccdbabcccabcbadcadcaacaaaabbcdcdcbbcacabbddabbaccdaabbabdddadcacddaaabbacdcbabbddcadbdccdcaabcacabbbaaaddcccbdbbdccdbacacbbdbbbbaacadabadcdbacaccaabcdadcdaacbacddbbababcbccaabcdabcdaabbbddaccacddbbdcdadddbcabbddccadbabcddadadabbbdacdbbacadbcdacdcbcacddcccabaccababbdadaaccadacdadbaaaccdbcbdcdddbadbbbaabbcdcdaaaabcdccabcbcbcaaacdacaddcbddaddcacdccadaccbdacdbcaccbdcdabcbbdcdbbaadadcddbaadcdccbdbcdcaddaaccdbdccdaaaadabcddccadabcaabaadbbdbdbbbbaddcdcadccacbdbcccdbcaaadaabcbadbcbacaddbbbbcbcdbdddaadbacacdbccdddbacccdcaddddabaaddcacdadacdccbdcbdabddcacaadabacabaabdccddcadcddacccbaadbdbddbddadadcdaacbbbcdcbdabbaccccaaadcabccbcbdddddcbbcbbcaadddccbaccdcaddccabccbdbdddadbddbabddcbddacaacccacbdccdaabdbdcaccdbddccbbaabdbdddbadddacacccdccdbddddacccdaaccbadccaadcbbdabcdcdbbbcaadadadcbccabaadbabdcbcaadaaadcdccdadddbacdbabadacacdddccbbbddaccacddadcaabcdbbaababddbcbccdbbdcdddbcdbbccbcbcaaccaadcbcdcaaacccccbdacbcaacacabdbbbdbdbbcbbaabdaaabdccabdbabdcaabcbccbccbdddabacbbadaabdabbadbaccdddbdcbbcadddcacabdbacccdadccaaaabcaddbacadbadabaddaccabbaccaabddcaaddacdbcbadcabadadcaccaaccbcddacdadaaccdcccabdabbacdbcdccaaccbccdcacbbcaabcabbdbcdccbbdddcadabdacbaacbcacbababacacaabdabdcadbcccccdadbcbcbcabbdabacbdcbadcaaadddcaadabdcacddcbcdcdcbbdbdadacbdacabcdddadcabcaaacdccdccbdabbaabaccaacbddbaabdcacbdcbaddcaaaadaabcbacbcbbbacbabccaacccdcddacccbacbccdaaaadbabdadacabacaababdbacdaacdbdcccabdccaaccdaddcbcbaacdbadbccacbdaccadadcdbddadbaadbcabbcadadadbddadbdddbabbbbdaaacabbcddcbdbbccccdddcbdbdcdaaaddddbdacbaccbccccdadcbadcdcaacacbbbcacddcababcccddbbaaaabbdabcababbdacacdaddbbcbbdcaabbbadadddaccbccdcbabacdcabccbcbcddccacbbbccdabadbabccaacbdacdaccdbadaaadadbaabcaaddbcbbbdabcbbdbbdaadcdcbbbdbaaaabbdabdbacbbddbaabbbdbddcdaaaababbddbcdcaabcbdbccdcbcbbabcccdbdabbcadcacdaccbaacbccadbadcdcadadabdacaabdcbbccdaaccbcdadbaccbaaaccaddddbcddadcbbcdbaabbacdcdaacdbdacaadbbaabbdbabdaababdbabdaabdbbaaadaabbbbcbdadacdbdccbbaacbdccdadbaabbbacdaacbadbbcbadabcacddbbacdbcabcaabacbddabcaddbdaadccbdcadadcbcadadcadcdbccabaaddbabbabaabcadbddcdbbbcbbcccdcddcbcacdbaacbbccbadbbccadabddbdbccababadddcadbcbcadadbdbadbdddcdddcbbdccdcabadcdaadcbdcaddcacaaabaacbccccbcacccbbcbbabcbacaadaddcccbabbcdbabbacdcddcbbcabbbbbbdabbcdbbddaaacbccbbbcdbcdabccbbdccbaccdccabddbbdbcccdcaddccdbdabaabcdcbbdcdadadddbbdbcccccaaddccbacdacdbcaaadaabdabccddabadbdaaadbbdddabbbbcadccdcabcbbcdadddcabcdcaaaadbcccddbbddaacabcbbbababdadababababdaddddccaccccacabbcacdbcabaccaabbbdcaddccaabdccadbaabbcbdbacdacaaccdacdbddcbbcaacdabaacddcdbaabbbbdacaddddddcbacaabdcbbbcbaabdaddaadbdbdbaccbbbbbdcbaccacaccdabadccabddbcdcacccabbcacbccddcbacbabcddaaddcbcccbbbadaacbabaadcaddadabcbdacdddcbcdbcdadbbbddbdcbbacbbcbcdcdcbbbcdbbbdbdaccddccdcccbcacbadbcdbacaacababdccdbabdacdacdabbbdcdacdbaadabcbcbbbbbdaadaadacddcacccaaacbcaccbbacccacbacddaadddabcabcbcddabcacbdcdcddcddbabdaabccddddbcabdbacbcdcbddacadccdbcbddbababccdbcbbadacdcaabacccbaccadcdccdddcacdbcccbbcaabcbacabcdccdcbdbdddccdaaacacaccdbbdbbddddaacbbdabdabcbbaccdacadbacdcdddacbcdbcdacbbcaaaabbaddcadbbcacbbdabcabcabdcabcccabadcbbabdcbcdcaccbdbbaaaccaddadaaaddbbaabdbadaacddaaabcdcadbccabbdcdddccdbdddbbcdadadadbcbbacddcdcbcaccbbcabbcdcdaccbccaddacbbdacbadbcdadcccdbbadaacbccbbbdddcaadbccadabbbccadabbbbddcaddbddbadccabcaaabdaacbddcacdbcddaacdabacacababccbacbcdbccccadccbdbcadbbbbddddbdbbdaddbdcbddaccdaabdacbbbcdbcabdaaaddccadccdccacacddaacbaaaccdacdcbcbbadaabbaddcccbabdbbbdcddabaadbdcdaccdbaacdbabddabaaacadbbbbadddbadddbdcdccbdcbadacabbcdadcaddbcabdcdbdccbaaccaddbadcbbdbadcdcaadddcdcdcdbbbdadadaddbabdaaaadcabbccddcaabcbdcdcbdcbbcbbcdbabaadcacdbccbbbbbdadbacdbdbcaddbccdccbaddabbddcaaaacbdccadacaadccbbbcaccabcbcdbababcbbaddddababadbcddcabdcbacdddccabbabdbadddbbbbbcbdbbcbcdacadbadacdbcbcbbcdcdcbdbcbacbdacdacdcbdbbcddccdabcbabbbcdaabaaaadadacaabbdacbbbbcbddbacdcdaadbadcdaabacaccbdadddcdadadbcbadcbadcacbbdbcbcadadcdaacaadcddddbccdcdaccabadadcbcdddccccbdbddbaddddcdbbaaadcbaaabbdcaaddadcabddaccbaacccbddbcaabdaddabbdacbcacaccbccbbcaabcbdabbdcabcaaabdadbcdcbbbdaacccdbadbcccbcbcbddabcadbdddcbdadccadcbcaddcbacbdccdbbcaacbdccdbbbddbbcaccbbbcdcbabcabdacdcaccaacabdabdcdddaaabdbbbdcaadcbccacbcbcbbcccccacbcbcaabababccacbadbdccababddcdadbddaddaacbbccabbcaccddbddbaacdbadbabcbdadacdbadbdccacbcadddaacdabaababcdacdbcdaaacaacbdadaccbcacaabbadbcaabdbacabbabcbabdadbaddcadcbaacbaaaacdbbdccabbbaaabaddddbcbbbcdcaddcbadbcabddcdabbdaacdcaaadddbaddcabbbbababdcbbdabbabbbaadadbabadaabbaaaadccbddccbbbbdcabcaaaddaccdbdbbbdbcaacbcdadcbdbbdaccbbaccccbbbdcbdacdccbcbcabbccbbbdabddaccdabccabdbdcdcbabbdadccddabdbcdadbccccddabbbdcccbbbacdbadadddacdcccbdacdadbbaccdbabbbaaabcdcbddadcacccaadddadacdddadaaaddcbbdadddddbdabaacdacabbdbccdaccaaaccbbacacabbcbccbcbcdadccbbcdcabbdcbddbbbbbbdbbbdaccaadddcdbcbdabcbbacdabcbcbbdcbadbadcddacadddcbcbdcbbccaaccbdbdcabdcccbaabbddabddabbcdcaaadddaaadabbadcaddbcdabcdacacbaadbbaccabadcdadcdababcaabcddaccbababcddcdcaadcaccccbdcbaabcbdbaacacdccbdcdbbdcdddaaaccaacbaaabdcabbdadcddcabbbcaacbabbcbccdcadcbdbccbbccacdaaadabadacddacdcbaadbcaaddaaadbacacbdaadcdbbbbbcccbaddbdcacbaccaadaabdcbddacddccbbcacbdcdbdcbaaaacdbacacabcdcbdccddcddddcacabbddaabdadcaabcdabcdbbbccaaabdbacabdcacddbcddbdddacdcbcdccdcccdccbdcbdddbdbacddbbdbcabdddbaabcddaadadbbcabcadbbacccbcbdadbcbddcbdcdcbcbadbcaacadaaadbdbaaaaccbcbcdadbcddbcadaddacdbccacdaaacdbccdccbacbddaacddddcabcbdabcdbbddddaabaacddacbadbdaadadabbaabddacbdbabccbdabbdbbbaccabccbcdbabbacdcbaaacbdaaabcacbdcddcadccaadccbcccbddaaabdddcadbdcbacadbaaadadcabbbbbcbadcadbacdcdbaacbbacddddcccadabbabacdaadbbdbbadcdbabcabadbdacccdddccacddabbdcdcbdcabbcbdabdabbcaddadbcbbcbcddcdbddcbaacbabbdccabdbcbdbbcbddbddbbcaadddcaadbdddbdcadacbbccbcbadbddcabdabaababbdcbcbbccdddcabadbdabcaacdadabccacdcdddcabcccdbbadabddcbaadacbdddbbdbcadbccadcababcdbdadbbddaddbdcabcacdabbbccdbabdcacbaabdacbbbcabaccabcbdacdabcdbababbccbddbbddacddaacbbcccddccbbdcaaddcadacdcbddcdbdddcccdacaaddddadacabdddddbacadacaddabdacdacdabccdcdddcccdcdccdddaabaadcabddabbcdcabcbdddcbdacbbbdaadddbbabadbcdabbbdcdbcdabaddcddbdabacbbcabddababccccdcacdddaaaddcdbcbdccbbadbdadbdcacaccdaddcabacccbdcdadccaaddccacbcdcbdcdaddababcdacdcaccabccdbdbacabbbbbababcaaadaabccdbbcdbacdbdacbaacddcaabcdbdadcdacdcbbdbbbcadbddcbabdaabbdcdcbdababcdbcdddcbbbbbabaccbdbddaaacbdcaacddbbbaddcdbdcddcbcdcbddacdcdccddbcbaddbcdcbccccdadccbaacdbbbabadbaadaccdcbcabacdadadadddaadcbdddddaccbddabcbaccdcaacbdbdbdbdccbcdcabaadbdddddabcbdbbdbadcabdaddcdaacdacccadcaadadbbacbacddabaabdcabccaaaccdcbbcbbbbaaccbaccdbccabbbbdbbbddaaaadabcabbaddddbadabaaadbccdbcbaacacdcdbbbcccccabdbcaadadadacadddabdbcadbddacacbdccabbaaddbaacadaacbcbaaabdcacdcadccbcadbdcbcacadcbaccaadbbabddcdbdbccdcbdbcacbdabddabdcababbddcabdbaacbddbadcaadabcbbbacddcddddbdccdbbddccddcdccdbcbdbcbbdcabaabbdbdadbaccdabababbacbdbacaacbbacaabaccababccddcabaaaccddcdcccbaaaaabcadcdcbbbcadaddcdaadccaaddbdaacabbdaabccddbbdbbcbbbdccdcdbacdabaccadbbabbcbbacabdcbcbbddacadabcadcdcacbaabcbcbaabbbbcdbcddaabaadadadbdbcababadacdbbcbaabdcccabadccbcaabccbcbdcaccaccbdbcdadabcaadacdabadcadcbabcdbaddadbccdbccababccbcbdbbbdcacccddcdacbbdcccbbabadcdcbdbbbabddaddcbadadbcbbabcacbddddbdddcbabbaaacacccddbaaddabacdacbdbbcbbdbacdaacbdddbcabcabdaacbaccbbccbbcaababbdaacddadcbbccdabbcddcccdbbacdacddaacdbdaacacbadccdddbdabaccaacabbdcaaadaaaabbaacabbbcdbcbadcdadbdccbdbdddbbaddbbcbdbcaadbcbcbdcdccbdcbbddadadcccadcaabbaadbababcadbcbabbbdacbbadbbdaadbdddcaadcccccbdcdbacacdbbdcbadbcbccabacabcbaccdaabcabddacdcdcdbbaccbbacbadbaadadcbaccacddddacabbbcbbcccbbaaabcdddbdcaddbaaadbdddaaddcddbbdbabdcabbacccddcbbadbadbbddcaabbbaadacabcaabcbacbbcaabbdbaadcddadbcacbcabbddaccacbcadadcacccdaadccbcadacbbaacdbabcbbbcabdcccddbddaacdaacbcadcabacdbdbadacaaacbcaadddbcadbcdcdbdaadadcaadccbaaadbcabbcbadbdccacbbccdbabaccaabdbcbddccdbdccacddaabcdaaacdccacddcacabdbaacbaadddabdbdbdcdcacadaccadabdbcddaacabaccccaaccbcabdddcadabcbacdaddaaaccabdadddaddccabddbabacbabaacaacccbdadbddbccccacbdcaacaaadcacdadcbddaadaadadcdbdabcbdbaccabddcdddcbbbacbbbbbcbccbbcdbbdcddaaadacacddadbcadbaaabaababcbadadaaaadbacdabaabbdcddcccbbbdacacabcdccaabbaaccbcdbbaaadbcccabaddcbacbdadbcacddbdadadcbbcdaaccddcbbaabcdcbddcaaddabacabdccadabcdbcabcccaadcbdabacbcbadcdbdcbbabbababbbdcbcdbacddddccdcbdbbdcccbcbabcddbdabdcacbbcddcbcdcbbcddcddcdaddbcdddaadddcadcabcbcdbcababbdabbccbabaacdcbdbabaabdddccabbbcdaccbccacccbcddbdaaddaacdadababcaaddbacdcccdbcbcadccdcdaacbcadbdbadcdddccbbabadacaacccacacddbacadbaabdbdadcddacbaddbdcaaabbbddaddbbccbbabdbaaaccdbadaddddbdcabbabddcbccadcbbdccaddcabcbaddcbdbdccdabdbaddcacddabdcccbdcddddabbdbacdddadbaddaaadddaabbbcdadbbaabcbcbdbbcacbcdbcbacbcbadacadccbdbadcabdbbdcccdaaaaabdadabcccbdabadbdcabbbccdbdaaddabbdcbaaabcbacdcaacaddabcabbbddbdcabacdcdcdabcbcadbcaacdaccadadddddcdcdbcdcbadabbbdcbabbbababcbaccadaaabadbacdbbbcabcacdcaadcadacdbaacbdbdcdcdbbbddcbbdacaabacbcdbdcacaaabcadabbbccacddaddbcbbdbdacbabbdbadacadbadbdbcaabbcbcbcbddddbddaadbdbddddccacccccccdcbabbccdbcbddcbdabbdbdaddddacdabdbabcaddcdbaabaaccdcacdbdddbdcccbbdadbbaadacbaadabdaabbcaadaddbaacdbdbccbcdacacccbdabacdbcacbaadbdadddccbababcccccbbbbbadcbddbcddacccacccdadbacaddcddbccdaaadcbabcbbcccaddaadcbadbcabbdbcbadddcdaabdddcbacaaddadabbbddabdbcbbcabcaabddcbbadbacbcababbabdacbcbbabaacbbaacbcacbdbccbdaccacdbabddaadcaacaadacaccaddcadbaaddcbbbcbabddaadcdddabccdacbbdcbddbabaaaadccaaabdbcdccabdcbcbbbcdbcdaaaadacacdabddbdacbbcdddacbcdbdbadadcabcdbadadccddcdcbbccacaacbddbbadcdacbbcddbdbbadbccbdcacdaabcdbddabdcdcabadadadabbcaaabbcbbcccaccaddbaaabbddbbaaaadacdabaaadbdccdcaabddbdcdbccdaacddcbcbcbcccbbbacbbabdaccacdbaadddaacadaacabbabadcbdddaaabbcdbccdcadbbdcbacaabcaadacddbbdabdabdcbabcbcdcbacbbdcaddbbaabdbaddbdacbbadaaacaaadaddddbaaccdbcddabdaadadbacbbadcccacbdacbacddcaaadcbbacddbdcbdadaacdabcdcaaccaadcdaacdbbcaccdcdddbababdbccabbdaccadbcccabbcbcccbbcababdaaacaaadcbcddabcbdbaccabadacdaaabdcbbddadbadccbdbcbcaaddcaadbaabdbdadccbaaaacabcdaaccdbccbdababbacaccacccbcdbabdbcbabdacaabcdaacbcbcddaaadaaabadcabccbaccbaccbbdcbaacccaacbadadbdcaaadacadbcacbcbabcdadcdccccccbaaacdbadddacbcadcaaaccacdabdbbddccbcbdddbabaacaaaaadaadababaaacbacbbdbbcddbbcbddcbabacdcdbdccaabdaaccaabaccacabaaadaddacdcabbbcdbbadcabbddabccbacdacbbdccbaaadbcccbcbddaccabdbbbadaaacdcdaadbcadcbaccbbccaaabaddcbbbacbcbaaccbccacabdcdbabbadcaddacbdabbbaabdbbddadacccaaacbdaabcdacaccaacbdcbdadaaccbddccddccabaaccbaadccbbadacdbacacacbbcacaaabddbbcbaaddabaabadcbaacccacdcddabbbababdbacbdbdbddaabbdaacaacadababacbdadcbdccabbabccabaababcacdbddadbbabadbadddbcababbbdadbbdcadccbcbccdaaaabadabccdabdbbcbccaddbdcbacaabbabaaadaabddcaabbabaddccccacddcadcbbbbadddcbcbdcbbacbcadaabbcbdcdcccdbabddababccabbcbadacadddcdbdadcaadadbabaccbdabcddbcabcdcaccddabbadcdbaaadbcaabaaddbdbaccbabcbdaddaddabbababccbcdbdabaddacdbaddadcaccbcacddcddddcdcaddbbdcdccaabacbabaddacaaaacababadbccccddbbaaabaaacbaacccdddbbaddcdcddbbcdddaaacacdbbacdacccddbdabcdcccbaddcbddabcdcbdccacacddaaacbdabcbaadcaaacddcbacbccaddaabdcddbdccbddcbbcaddcdabcbcbbcaddcabcdccccbcacdbaccdbadaacdbddddcddaadcdbdccbbbaddabbccdbdcabcbcaadbccbacdaacbcbbabaacdabdccdcbcbdcadaaabdcdadbbcdcdcaaccbacdbbddcadaaacbbbbcccdcdabbdbaacdcabcbccdcbadabddbcaaaabddbadcdcaccabdbaadcaadadaababbdbdaaadadcdcbcccbcbddcbbbbaacaddcdbbabdcbaabcdcbdaaacbbdbaacdccdbbabbbdaccbadadbdcdcacaadcaddcabaacaddbbbcdaababcaaddbdbdddbccbddccbabbddababaddbbdbabbcacadcdcdbaaccbcbabccbabbcbbbdbcbbbbbcccccccdabdcdadacccbadcccdabbbaddadbbdaabaadbddbbaaccddbbabdaabbdbccbcdddbaacbaababaaabcaabbbdacbdcaacacddabbdcbcccbbabbcdadbaaacdddddcdcadcdcbccdaadacdbcdadbddbabaadbbcccdaaccdbdcddadcdcbcbbdbcadacdccdbbdbccdcaaccdbccbbbdaaaccdabaaaddddcbcbadbcaacadcdbacbcbaacbdbbbbbdccbacdabadaaabdbacdcdcaabcdccdbcdcbcaaaadbaabaccacdaabdbdbabcddddddcdbaaacccacbccaabcdadbddcbbdcbdabbbcdadaacbbccbabbbcbbcadbaababddbcabacbcdcdbcbbbcabccbadbadccbdcbdacccbddabbcbcaadbdbaaaaaabbcbcdacddaddadbccbccdcadddcbdcbadbdaadbcabdaaccbdcabdacbbcbcbbabdbccbabdaddcccaabdaaadcdadbccbcdbdbccaadbbaccbdcbbadbabbdddbcbadcadacdbdbccaccacdabbaaaacddcdcabbdcacaacbacaabbdccdadbdbcbdbbcccdcbcbcabbdabbaabbbbaabcadbdabbadabdddddbdcaccaddcbcaccdacbcaaaacdcaabaabccbdbcdbbdbbdcadaadcacacddbbabdabadbcddcccdabadccbdbacbdbbcbcdcccaaccadbcacbcdacaccddbdaaadabdbdccacdccabadcbacaddbbddcdbdadbbcbdaddaababbcbdacccbdcabcddcbdbbadadbdbcbbdabaacbcdaadbbdabccaacdbcbacadcacabccddccbacaadcaabbbdcdcdcddcadcccbaccacdcaddbddbbddbadbcdacabbcdaabdcbaacccbacbcdbabdacaaadcbcdaddcaddabddbaddcdbaccbbdbdcaaccbccddbcdcdcdccbbcddcabccbdacaddaabadcaaaddaadcbdaddddbadacdccbbcddbbadccbcaaaddcadaadbcacbabacaacdcadddcbcababcdbddddccacbcbbbcdbcddacdbdcbdcacacabccddaacdbbbacabdadcbcabbbddbdaccdcadbdabacdcddaccaccdabcacdbbaddbbaadaaadbdddcbcbadabbdbdbcbaccdcbbccabbcdddbbbabdbcccabddaadaacaababaabbcbbcdbcbcdbccaddbcababdabdddaaaccdbadbababbdcdcbccacdcadaadcbbaaaaaadbdacabdacbbcbcaccadbdbdddadbdadbdaccdccccacdddabdbdccaadbcbdcaacbbbaababcacdbacadcbdbcacddcaacaaadadaccaadbbccccaccccbdcbccadaaddcbcdcbdcbbbcbbaacbdacccdaaadccadaaccaaacadbabbdcdcdadaccbbddcbcaaabaadbddaaddaabaadaaddcaccaadadabccaddcbaaaaaddcdddacacbdddcaaadbdbcbbbaaaaadbaadaddaaccbbbadadcdcaabbddcadcdacbddaaadadabddbabcdbdccaadcadadaacbcdaaababdddbbddccbdccdbacdbcbbdcccacadadcdaaddabbbbdaacadbdcccdcdbcbcaddcbddbdcdccdddddbcadcdcbbccbacabbaaadbbccdadcccccabdbabbbabacadadcaacadcddbdcaadcabcdccaaddcaaadaabbccdbdaaccdbcadcaaacdaadabccdccddbdbcadcbbabaaabaadbdcadccabcccdbbddadabcbdcdbbcbbbcaddcbbcadbddbdaddbaaaddccbadddccbcacbdaacbdcacababdbdbcbcddbbcdcaacabdcddbddbddbcbdcbbbbcacbbbbcabcccbaaddadbdcbcaddbbccabaaadddbdbaaaccbcdaacbacabbcdcdaadbcbaaabacaddbcaacdaabaabbdbbaccbcacdcdddbaacaabbbbadaacbccddbddbbcbbdbcccadcdbdbbadcadaccbdccabbdcdabbccbddbbbacdbddbcbacbdaadaadacbddddabadadcbcbaadbbdcaaabcddddddbbcbdbadbbabadccbddcbdbaccabcccadbccacaddbdbbddacdbacabdcccddaddbcbcabcdcaacbdccbbabbdddabcbdbcacbbdadbbbcdcdabbcccbdcdabcbcbcacdbdaadbbbdddcadbbcacadabdaddaabcccbddacbbbadaadabbcabcdbdbbbcaadbddcaccccaaaabacadbcdadacccdccabacccabdabcccdbabcbbbcbbabdcddcdbaadaabdccbcaacdbbacbdbdbccdadcddbcabbbdcdcdacdcdccadcbccabddcbaaccdccabacbbddbccacdccababcddbcddccaacdbbdaaddbabaccdaabcdcacdbcbccaabbaabacdcdabcccdabbaaddacaddbbcbdacbabccaacabccacacdccccacdbaacbdbccbcccbccbbbbdbbadbabddabdadcbcccbdadbcabcddadbcdbaddbcadbbbbdaddddbdadccdcaddaaaacbbdcacbcddacabacbaaabccccddabacadbdadbdabbdabbaddabcbbbaacaadddacaabacbcabadccdbbdcbcbcdbbdbadaaaddcddcccbdbbdbaacccdacbaaacabdbcdaabadadccdcbbabcbddccabcdaabaabdddadcacbaacbbcbdccabbcabcccbdaacdadccbacacdddcccccddcadbbbbcdcbababddabbbcdbbcbacbcbbacdbcbacbbccdcaddcdcbdabccbbaccbcbbbccabdccdbaddcadabaddbabcddbbcbabbbaabacbbcdcbaccddcdabbcaadcaadcacbcbdaddcbbbabcbcdbbcbadabaacaadbcccbbbbbaabbbbcbdddaddacaacadcdaacaaccccaddbbdbccbcbddaaccaaccdddaddcbdccbcbbccbabacbacadaabdccaabbdacbbbccdcacadacabddcbcdcdbaabbdbaccaababaabcacbdcabaaadacaaccbbacabbcdbbddcbacaacbcbabcaccdddaadccbbadddbabdabaadacccaccdbbbdbaabaabdbcaacabccdcbbacdbccacdabadaacbcbdcdddaadcbadddadbbccdcaaadaadabccadbbddcbadcdcbdacdaabdbcabcbccdbdccdbaabddaddbabaaaccddcddbabdaadbcccdcbbabcbdcacdcddbcdabdcdbbbbdbadddaaadbbaadcaddcbcbcdabaddacabbdabccacbdaccabbbddaccaddcabcabbbaaddabccaccbbbccabcddcdcbdccbcbbbcadccabbddaadcdccacddadccdbacdacdcbbccbacdcadaabcdbaabdcaacdacddabcbadbaddbddbdbdcacccbbcdddabadbbabdccdcbacacdbcadccbcccdcbcbdbaacddcbbcdbcdbcdbcdbcccbaaacbbacaabccbccccccbcdbcabcacacbaaaabcabacccbbbbcaadaccbdcccdbdccaacdacaabbdcdacdaaabbcbdbcaddcaacdcbaadbdcbbdaacdadddcadabbcdabadccbcabadabacadaacacbbbccadcbabacdcabcdbdddbabbbbbbbabdcbcbdadcacbbbabbdabdcbbcbbccabbdabcabcddbcddcaabadcbdcdbdbaccbabcacaabcaaadbdbaaacccdaccccdcdcdbcccbbcbddcdaccaccdddbadbacdccdadacbdadbbaaddbcdcaccdabccbcbcdaddbdbdaddcadcaccdaccddadbdacdcddcccbcdabcaddbccbdbadbbaaabbadbccabaacdbcdbddcbdbaadccaddbddcbbabbbdaccdacabdddcdacacbcaacacabbccabadacbddcbccddbbcdacbacdcadcbbdbbcbabdadbcabdbbdccbcbabbaddbbcdabbcccbacbdcacdabdabccdccaacddabdddaabbcccddcdcadaabaabbddbdadacdbbaacdaccadbdbbcdbbbcdbadaddcacbddcadddccbaacbbaaabdabbcaabdbcdcdbcbcbddddabcdaccacadddacddcbcbcbcbabcaddccbdbdacabdddcbddccadcbcaaadaddadddadaabdbadbccaacdccbcbcdaaaadaadcbcdbcccbcdcbcbcbcbcccbddbdddaadddbcadddbabccbcdaccbbbaacbabcabccbacabaaabccbaaabcbacabdbabbddbbdaaaadcbaaaabababdbdccdadcbbbcbdddaacbacbddbacdcdcaabddddadcccdddcacdadbcbbcadccababbabdddbdadbcbcaabdcbdcacaaddcadddddbbadacadccbcdbbdacddccaaacdccdccdbaaaccccdccacdaccadacbcabbbbcaabddbbccbcabadacdacdcccacdcbcbbadbbcdcdddccdaccccbadcacabcccbaddabdbbccddcdbdddaddccdacbcaabdbdbabbacbcbacbbbbcbdcccbcbcdccdcaccccddbbacacbcacbbbbcbdacacdddadccacaadaccbcaaacbdaccdbadaccaabaaccabbbbcdadabbddaabccbdbacdbacbdcaacbdccbdddacadacbadaacdcdbdbbadbddbdbcadbddccdcbdabcaadaacdaccbbdcabcbbcdaaccddadccdcaabdddbbcbabbdbbcacdcadcbabcabadbdbcaaccccadadccabacbacbaadaddabbccaccdadadabcadabbacbcbdcccaacdcbbcbbabdbcbdbddbbdabbdbaddcddcbcbbbcdcbbbacabbaccaaabbbaacccbdcdddaaaccdcadbbbbccdbdbbcbcdaddaacbcaddadddbbdaaccddaacacacbccbacbaddbbcccbdaadaabccaaaddcdcbcaddbdbabaaaccddadbdcaaaaadbbcabadbccabcabcbdbaabcaadbdccadababbabaddcdbaacdbdbdbdddbbbdcdccddddabacbdacbcddaddbbbdababbbbcdcbbcdaccdddbaabcdccbccacababdcbbbcdabddccaacdacbccbaddbabbabacdabbdcddbaaaaaccdbaaabbbbaacabaccccdbacabbcbdddacdacaccaccbcbadabdaadacddbbcdccbcdadaaacdcadccabdadcbcdbcdccababcddcbcdcdaaddbcadbdbbbbcddabbacddadacbcadbacdbddccbaaaaadbcababdbbccbbbdbaaabdddabcdccdcbdaadaaddcaabbdbbcdcdbccdcbddcdbaaacbcdbddaacbacacbaadadadabbcaabbccbcbbaccabdacdcacbbccaddbbcbdcacbbdbddaaccbaacddaccbccccabadbaaaabacadcabcdcdbcacbaaacbcadbadbbbaacccdabdbadcacaabdbcdbadcbcccbbdbdadbaaaadadcdbccbaaaabdbdababbbdddbabcabdacadbbcddbdcacbbcbbaddccabaacbdcdcdacdcdddcdabdddbbaddbcbdbdaabddabcdbaabdaadcdccaddddaaadbdbdbddcbdcadbaddcbcdabbaaaddcbccacbbcbabccbaaabdcddcdbccabadcaabdacccadbbacacdcdabaccbdcbadbacbddbdbbcbaabaddbaadcaadaccaadcacbbcdabdaacbcbaaddcdbabcbcdcdcdabaaabcadddbdabadbbbacaaacbcbcdcbbacdbcdaadabdccbbdbbbcabcdbbdbdcbbdbaaabdbbdbdcdddbdcccbcccbacbbbabaddcccdcbbaadcdaccbccacbdaaadcbdcdcabbbaccbbdaccdccdcabbcbdcabbabdcbbacccabdabcacbcabdaabbdabdcbbaacabbbcadadbaadbbcccdbdaccdabacabcacdbdabdacacbddabbbbccbaaddaabdbccbbbdbcaccabacabbdacdcbababacadcadbccbbcddaaabbcdccdcddcddcddcacabbbbdcdccbddacddaddabbacbaaadbabcaaaddaccdbcdacbabbcadaadbcccadabbdabcbadacabddcbbadddcadabccccbcabccbbddbdbbdabdacdacccdbcbbcddacdacacbabbbdbccbdccbacdcccadbdaabbabbbdddcaacdababadbccbcdcbbabbadadbaddbadbdabbabddbbdabdbaaadcadbdcbdbcbcaaabdbdaabdbabcabccdacbbcaaabdbcdacabbcbaacdbbdaadcaabbadcacdcacabdbabdbdacbdcccaddbbaadbbbdcbbabbcdbaacbcbacdabdaddaddabccacddcccbbaabcdaaabcababdabbaaabddcbbbcbbbcbdcaaaccddbdddbbbaccdcaccacdbcacdaacdadcabcbdbaaadbabbcadabacbaabbdbadcbacdacbacabbcdccddbacaddacdccccbadbbdccdbcdacbdcddbabbdbdcabdaadabddddacdcacbddcdcabddbbaacdbadcdbdddbacdabccdaacabddcdcbcbbbddcbcdababdbdcccccabaabcdcbcbaddcdbacbcbcdddbbacbbdbadbccccdadbdaacdbbddcbccbaddcbdccbddcbdcddacbaaccbacdbdbbbaddbdbddbdcbadbbddacbddcaacbaadddcbcddcdadbaddbcdbbccdbaadbbbabcdadcabbadbacbbabccabbabbbcacbbacdbbadbcaabddcdacdacacbcabacdabbdabccacddaadbcabdbcbcddbbbaabacaabccdbbaddcbabaabdabccccdcdddbbcdccdacaaddaaddcddcdadbddbcbbacdbacdabddcabacdbdadacbdbbdcbaddbdaadcbdcadddaaaadaccdcddbddadcbbbadadaadbcccabbbaddbbcadccbabbaaabcaaccdbbcaccbaacdcdabcadbaadbabdcdddccdbbdcdadcccbdcbababcdadababdcccbdadadbbcabcbccbdbcddcacdabdbbabdbbadabdcbdbbdaaabbdbddacdcbabbabdaccbacacdcdbbadccbacdcaddadbddbadbdbadbbadadbddbabacccbdcabbbbdddbacaccbdbaacdabdcaaabaadbbbddccabaaccccaaccdadabcbcabadacbbcdbcaddbdacadcdbabdcdccccdbaababadbacddcbcaccccacdbcdccabbccabdaaaabccbccbacdbcbdbdabacccdbcdcbcddbcbcbddcddcbddabacdacbbadacdcdcccdabdbdbacdcddddacbcbcbbbdbdcacdaaaacdcacdcbaddabdaacaccdbacacadcacaaaadabadcccbbcccccbbdbdadcbaadbccdcccdbaddbbaddbcddbabbabcbdccdcccbcbdbacabbbadbcdcdadcabaccccbdbbcdadabddacbaddadcddbdcbaccbddbbadbbdacddccbbccbcabcabcacdacbcccabaabbdacdddaaaaabbbbbdadbcdcaabbcacdbddaaaaccccbcadabdcbdabbdbdcabccadccccadbbbddddbaabbbbcbcddbbcbbbccbbbcdccdbdabdcbcbdbababbadbabcbcdabbdaccabcaadcadacdadddcdcadbaaababacacdaacdccacbaadcacdcdcadabbccccacadcbdaacbbcdcbcdcdddcccbbbbcabcbaccbbadaacccdbdbdadabddcacaabbdbdbdaaaddaadbbaccacbacbaacabaababdcaccbadcacccadddabdddbadbcbdabcbaadcadddadcadcbccccdabaaadcbcdbadbdabcacccaadabbdaddbccdcdbcdbdcdabddbbdcacbabbddbbaacbaccacddddcaabccbabacbacaaddbdbddbacaccaaadadcabcdddcbbaccdcbabcbcacccdaaabcbbccbcacdbbacddbbcaddccbaaaabdbdabcaadadabaddbdaddcacbbbdacacbcacbbdddbbcaaccadddcadaacbccdcbcbaacddbbdacbbabcabcbbcdcddacbcbbddaabdcccbcdbcadacaabcacdbdadbbcbbdcbbabdbcbbdcdddcbbbbbcabbcaaddcabacbddabccacaaaddaacdadbccdbccaabaaccaccadadadbcbaddaabbccdcdcbbbcdcdaacabaacbdacdbdcdbdbcddadcbadabbacbcdabdcaaaccbcdbddaaacbcddaaadacbcccddcdacdbcadddcbcacdbadbccabcbddaddaddbcbbdcaadddbdabacadbcdcabccdcbdddbccdcdccbddccacbcbacdddabbccabacbcbadabbdaabcadddddabbbdcdadcccdabbadadbabccacccbbdcbddcccdbdadbaacabdabadbdccbabccdcdbabaadddddbbbbacbdadcabddadbccbdbcdcacdbadabbbaaaaaccbccbbdddbabadcccbdbbcdacbdbccbdccbccdbadbcacdddcdbdcacbcccaabddccbacdbaaaababbcbbdadacccbbdbabdbbdcbadcadaadadbadabadbacdacbbcdaaadbbcccdadacddbccddacbdbdddcabaaabadbccccdacabcbadabbcddacbdcbddaacbccbbbaccdbdccdbbcbbacbbbddabdaccabbdacdcbdadddabcadcdacddbaacddddaccbbabccddabbacdbdbabbbcaadaaaaabdabcacabbacbadacddadabadddabdbacddabcbbbbaadcabbbdddddaccbaddcbcbaccddbbaadcdccbabccdbabbabbdddccddbcbcddcdaddcddcddddbbccdaabbcddcbbcbdbbaabbdcbccaddacdbcadbbccababaabbccabbabbbcbdabccddccddababcadcbcddcbbdbcdcccdacbcbbbdcdcabacbcbbadaddbacabcdcbababadadbccdddcbabdcabcaabdbabacddbaabddcbcccddbbdcddacdadadbaccbccadbcccacbdddabdaaddcdcbdbccaaaacabaccdcacaacdabbcdcbccabdcbdbcaccbacddcbddbcbacbdadacbcddabbbabcadccbdbadcdddbcabccbabbabbbcacccddddadccbdabddcccbdbaadddccccdaccccababccdbdadadaacdbacabddaacdbcabccadcdcbbbdabcbaaabcdcccacbacbaabbdcaacbdcdcbcccaddadaadbcdadcccdaaacdacaaddabcbddbbcaaadaaadcdadaaadcbacbbbddccabbdbddcaaccbbaccadbbccadbdcdcdacddcbddbdabbaadbbdabcbbcdcbdddacdcbadbbcadaddbddaacdcbacabbadcacabccbbbadcbcabdaacdccdbbbbcccdddcdadcbbbdccdabcbddcccdcccabbaaadddccdaacaddbdccaddcabcbbaaaddccbcdbadccbdbabdddbbccadcaabbbcbdbddaccabcbbcdccdadddcacaabdacbddbbbbabbcadabbbbbdccadbadacbcbaadcccccaaaccabcddcabbddddddddbccdaccccaabbbbbdddaacaddcddddabaccbacccdbdbbbadcdcbcccadbccdbabdacccdadadcbcdabaacaadcbcaccdcdddddbbababcaccbababcaabaaacbabccbabdddacaddacaabbddadcbdaaacbdabcddabcbcaddaadacddbcadaccbdcdcaacacddacaabddcbbcdcbbcddbcdccbbaadbbabccccccccadadccdbbcbcaddcadccbbdddddbdcacadadaaacdbccaabcacdadcaccdbcbdadcbbcdabdddbbbcadabdadbaacaaabcdbbbbbdaadddadbcabadccacccbbadccdcdbcddddcbbbbbcdcccabdcbabbbbadbcaddaabdbcdbcdbaababbdaddacaabacddbbdaaadcbbdcddaadddcaccaabdbdcbddbccbbacacdacadddabaaddcaddbcacddcaaacdccbadcbabbddbdcdaacdabbdcaaccababbbbcabbacdaaabbdddacdbbacdacbaabbabccaaccdcacdccdccbbdaaaabaabcabaadacadcbdaadcadbdbccabcbbbddccaacabcdcccaadbbddadccbccdcbbbcabbcccbcabadcdbacdcadbdcaaadaccdddbaabbdbadcdacacaabacbbccaddbbcabccbcaadcbbccadbdddcacbcbdacdcddbdabdabcdacdabdbbabbccabaacbabdabbaabccbaaaabdddadcdcaacabbbbbccacbacaddbdddbbbdadcacadaddcdaddabdacabbbbadbdbbdbcbbdabbbacbcdbadcdddbaddccbbddcbdcdbcbdaacbbcdbdccdbaaddabddabddbaddcbbcbbaddddddcababcbddbcadaddacbaabccaabbbdcdcdcadaadcadbcdbadcddcbbcacccacdacbbddcacbaacbbaacaaddaacbcbcbabdacbdddaacbdabcbcdbcdcbcdbabbdadbabcbccbacbdcaacacdccccaadbcbcbcbcacacdaccccccbccbccbaddcbaadbabbdacdadcacdcabcdadcabaaadbcddbbdcbcabccabacbdadbbdcbdccbcabcbddbbccdaabbbbbddacacbbdabbdaacdccdacacacaabaabbbacdddcabaadaabbcaccdbcccbadbcacdabcabcdbccaacaccddccbcddbbbbbaacbbcdcaddaabbdcbccdbaddbaadbabbdbadddcccacadaccbabbbddbbddbabbcadbabbbdcaaccbccccbcacadacccdcdbdbbcacddcbdbacbbacbdcccdbdaacadddbdacdccbbaacdcdaacbccbccbdbbdacdccbdbcbdcacdbccdbcabddacbcadaabcabaabbdbadbcbcabcaadcdcbdccacacdbcacccaacbcdacaadabddacdbcaaabadbdacbddbadabcbccacdbadbdbbaabbcdbadcadcabcbacddbdbcbabdddbbddbcaccbcdcdaacbaadbcadabcbccacccbbaabdaacaaadcdccbdadabdaababccbcacadacbdadcadaccdbaaadccaaacbcababdabbdcacbcdacadcaabbcdbcdbdacabccbabababbddddbddbbdcaabdcaabdabadacaabbccdbddaabbcdcacadaacdcccaadaacadbcdbcaccadcabaaddcdabbabcdacadbbcadddabaacbdcdcddddcbacbcabccdddacabcdbacddcccacddcbcacabadccddcbcdbdacaadadcbccbbabcbdbbbbbbccbaabdcadddcbdccbddbbdcadbacbdccdbbbdbdacaccacaacadadcdbdcbdacbcccbcdbacddddbccbdbddaabdaabcadcaaccaabbdbdbcddcdbabdaadababdabbbaabcdbcbbaaddbccdacdcbaadcadaacbddadddbbbdabdcaabcccbabcbbdbbbadacabadbbcbbbcbdaabbddadbcdbdccabddddddbddaaccbaddbbddacdacbbadbaaababcdccdaababdddadbbdbabbacabcabbadddadcabdadbbddacadabbdadcddbcdbdbdabdcabbaadbbcbbdcdbbbcbdbbbcbbcddcbcddaaadabaaddacbcbddbbbdbbcdbdbbbaaaacadcaabcbcbadadacdbaccbbdbbadbadccbcbbcbbddcabbdadbbcbcbbaaadbddabaaddcccdacbabdcabcbacaadddccdbabbdbccccdadccabbacabdaacbdacddccbacbdcddddcdabaaddabdaacdadabaccbddbbcacbccdbdaaaabdcdcbdddbdcadbdbbcbdabbdbabbbcadacccacccbbadadbcbddcdbdbbdccbcabbcdcbaadaaccdbbbadbdcbbbdcaaadddacabacddbdababdadbabdcbaddbdabccadaacbcbbdabccbadbbbcbccaadcbcbaccdadadabbcbbccabadaadacbadccdbddbaacdcccbdaabacccbdbbdaabaadabdbcbaaacadbbcdadbbcdabcacaaaadadadcadabbcbbdaabcccdbcbdddbaabbddaccddacaadbcbbddadaaadbbcabbaddaadabccaddabababbcbbcddbacbbcdbacccdbabddcbbddddcddcdccadbbacadacacbcbbadbbabcdacdacccacdbbacdddbbdcdddbdacbdacacddbacdaaaadbbcdbabacabbbadbabccadcbbddcdbcacbbabacaddaacdaaaaaacdbbabccabacddddbbdadadcccbdcdbacdadbbadccdccddaccbbcbcccbcacccbbacadccbaaccadbbbccddcbcadccdaddbbbdadacabacddbabcdcababadccabaadaaccadcdbcdbccbcbbbacdcbcbdacccbccbccabcbdbcadbcddcdacbacaaddbdbdccbcbcdbabcacdbbdacbbcddbbdbacadababdadcdacddcdcacdbdaacdabdaccaadabdaddaacabcbabadcddccddbdccacaddcccaabdbcdddbcdaaabddaabbabdccbaadaabcccacbaacdcbddccbcabbcaadabdcbcddbddbbabbdcccadbddcccbccdaabaaabaadabaaacadcabbabdbdaadddabaccabccdcbbccaaaacbadbbcdcbadbdcacaaadcabbbbcddcdaabcaacddabbacbaaadcaabcbccacdadacacbdccdbbcaccbcbdadabcacddccddddcbabcccacdcbbdccbacbbcacacbdbdbbcbdbacaddbabddabdddbacdcacddbdbdcbbccabbaacaaccbdcbabddccdbdbdacbbaabbcdddcabaaadcaabbaacaabbabdcdaaddaaaadaaacbdccbcddabbaadbbadbbddaabdbcbddaddbddbbaaccabccdaccacaaabdcbaaaabdaddadcaddaacabcabddbdbcdbbabdbdbaaabdbbbabbcbabcbbbbbcbbaabdabcaacbcdcdbaaaacbccadcabaacaabdddbcdcacbddabaddadaabdaadbaadbdbdccbaababaadddacacccbcbbbccaccdbdaccbadacbbabccabcbbbcaadcbaaaddcbbbdadaabccddaaabccdaadbdcbdbbddcacadaaaaddcbacddcdabbacdbdacdaabbcdddcbbdabadaabdbddbdaaacbaacdccbcacbcbccaadcccdcdbbddaadcbdbbdbbaccdccabccbacaadadadadaaaaabaacdbccdccbcacccabdddddbbbdbcabdbabcbddbdbaddacccbccadadadbacaccdcabdcadcccbcbdbcdbaadcbbcbdbdccddbbabacdaabcbcabacacadbabbabbddccbaadbcbdcdbbbcbdddddbabacdccccdcaaddabbbcdbbabcbdcbcacbcdbbabdccaaabddddabbbcddbacabcbbcabccbaaabcbbccdbbbccbbddadaacbbddababdbaabcacdcbabbababbdcabdbaadabcbbbdadddcacbbaabbbabbbcbdcacadabbbcdccbccdccbbaaccadcbcdabccbccbccdddaacaacaabaaddccbacdcddbcbaabacdcbbcadadccbdadcdddbbabdacaddcbabdacbbdcddcabadcbbacdaaaaaadbdbabbbcdacabbccddcdaccdbcacdbddddcdbbaaddccbdbcddbbabbadcaabdbbbdddbcadcbbcabadcbbcbbacaacbdccbcbdacbabbdcccaadbacadaaaaacdadcbbbabccdddddaadacddbdcadcbdacadacadcccdaddbabbacaaabbcdcdcbcbbcdbddbcbbbbdaacbddcacdbaddadadadcadaccbbcddabbabcbacdadadacbadacabbacbccabcadcdcccbbccdaadbaabbaccabbdabbaccadcaabcdbbddddbadccdbbadbacdccdacdcacaaacdadadbabbabcbddbbaccaccababbbdabaccbdabacbccdbcbcbadcacddccbaabddbacabdbadcdcbbbaddabbcddaaddaabcadcdaadcabdaabbcdaabccaaabcaddccaadcdbcadaaacdaabdbacbcdbaacddccbcbddcdacbddbddcddbbadadaccbcabdaabbaabbaddabbacacdbadddcbaddbaccbacadbdabdccaccdaacbcaabcbdacacdaabbacabbdbbbbdbdddcbabdcccbddcabbcdbcddabcaccccbbdcdbcbbccdabaddbcbabdcdcdabcdbbdbadccbacacdbabbcaabadaaccbcaadcbbabdbccdccaddcbdddccbbcdbddabaabcccbcbaabbbccdaccdbcddbcabdaaccaaddbacadbbabbddcdaccbddddccacdadbdbdacdbcbdbbaddadbcabdacdcbcabbbdadcacabdacacacccacacbbababacbabdbddcaadbbccabdddaadaddaadacbbabccabccbccdbaccacbbddcdbddbcaaacbbcdbdbbbabbaabccadbaacdaabdcacdddaccaccbaddababadacaaccadcdddaabbbcbabcdbadcaabdddbdcadcaabbaaadbbdbbcacdabccdbdacccbdadaddddccbbbcadbabacadbacdcdaabadbcbddaaddddcbbdbcdbcbaddabbbcbacccbcbdcbccaadcdddbababbccaacbbdcdaabcdacdbbddcdbccadcbdcdbdcabaacbaddbacdbabaabbbddbdcbadbdaccbbcaaaacaabbbdcaaabaaadcddaabddccadbbbccddccdcaccdbddaabacbdcabacddaabdbdabcaaaacabcadbbccaddabbcbbbdadabcaabacaabdadcabdadbabbccbbaaddadcccaccadccadddbaddcacbccaadacbdddabccbadccdaadbadbbacadddcbcdddbdbabbacbdbaadaadddbcacbbcaabcbcccccdaaacbbcdbadbcacaacabbbcacbadabaacdbbdbbaccdcbbcacdbcdcdbadbbdbabcabcadbbdcacdbdabdacddabbccbabadababbaaacabaaacccacbbbcbcabadabcbabcbbbabdbbbaabacdbbacbacdddcbaddbbbdccacdbddadcbabbcbcbdbabcdbcbcaababbaaaacadbababaddadadcaddaadbdcccdbddbbabddbbdbaabdcadabdddbaadcbaadbddcbcbdadddccaccaacaddaddcbaacbcccdcbdbbaaadbacdaadccbcaddddabddccacdaddcbadcbdabaabbbccbbbacbbccccdbdcdbddbadaaddcbabaadacddadcbaabbaaacbcbbdbabaabcdcbbccadcaacdcacabbdababbdaccdbbcccbdacbbbabccdbbcdbcbcaacdaaabddadcbcbdbccabcbacbcababdadababadcbadcbbabdddabaccacbbbabdcbcbcbdcaaaaaaccaacabdddbabdddcbabadccccaaadcdcaaaddcddabccadaacbcbcbbacabcabbccdcbcaacbbcaaacdcdbcacacddababbacbdcddcacbdcbcabaadbdbcaabcdcbacbbdbccdddacbcabbadaccabdcddadddbddaaadbdccabcbbcaaacacabadbdacccabddcadbdccbdacdcbacbabcbabdcbaccbdcdbacacbadcbcbaddbacccdadcbdbcaacdddaadbcaaaddbdbacbbbddddddddcdbbccacacbdbbddbdaadcbcdbdababacdcaddbbcdbdbbcbdaabbcacccadddccbcdccbdabaacacbbcbcacaaaadabadcccdaacdbadabdcacadddacdaabbcdcacbcdabcbddddbadcddccabbadabddcacbddacaabdcbccbaaccadbddcbbcadbadbaadcdacabdabbacadcbcdcbcacdaaacddababcbdbbaddaddadbadcbcbddbbddaaadcbbdbbdaccddaaccbabbcdcdbbdcdaadcdbcdbcdcacadccdcbabbbacadddcdbdccacabbbdbaabbcaacbcdaababdcbaccbdacbcbadcccaaccbaaabbcaacddbdaaacaabacdbccabcabcacacdacbbbcbbdbbbccabcdcdcbdcbbdcbdddcdcaacbccbcdbdbdaabaddbbadbaddcdccdccccdddabbabccbbbcdacdabcbbdbcccbdbccaaaccbcbdbccaddabacacdcbcbacddbdddacccabcaabdccacddbbadabcdcbbdbbaaacdababccdbddaaccdbbdabaadabcbdbaccbacccbdccdbacadccdcbdcaabcdcccaacabcbcdbacadcccbbbcacddbcbcabdbdabbbddcdbabbadccacbadadddddadadbaabbaacccdcbcdbdacdcccbdbddbcbcddcbbacabccdaaabccaadcaddbbcdbacbdbbabcbdadcaacaacdaabddcccbccdacbdaaacacbdacabbacabddbaabcadacdaaccdabddbbbabacdcdacbcdcadbbadcbddaacdbabadbdaadaccadccaadbddddaccadbbddaadacccbdbcbadcbbabadddcabbaaccbddbcacadcccaccabbdcabbabdabadccacbabcaaccdbdcddabbbcadacdbcdcddbccdbbbccbdbaadbabaccccbdcbbdbcddbbbdbbdcdacaacdbacabdbbdbbdacadcadddbdbbbdabadbbabaddaddbdcbcdacadabccbccdbbddbbdcdcabaddbdbbaaaaabddadcbdcaddcdbcabcbddbbcabdcbbdacaddacddcbbadbccbdaabadaabdccbbbdccdcaadacadcaddbddadcdcbbccabcdacabaaaaccbcddacddbaaabdcabbaadcaccddbcbbcbddaabcbddbadcacabcddbbabddaaaaabaaddadcddaacacbaddddbbcddaabbcacdcddccbababdcacdabcbcbcdabcbcaddcacddaaddcadcbcadcddcacccbcdbbbdbcbacbccbbbdbdddddbbdccdbdbcccdccbabaabcbadaccdcabbabcbcaaddccaccbddbcabdabacccbdbaaabdcbcdbaaaabbacccbdbaccdcacbdadbbcbcbbcdacadbdcacdabdddbbdcabbbdbadadbdabadbaccdccbaccacddaddbbcdadcdcbbccccaddccadbbacabbbdabbcdbaaddbadddbcdcddcbadcdbbabadccdbdbaadbdaccdcbcbaaabaaacaddaaadbdacdabcabdcdccdccdbbdcbbadbdabadccabbaccbbadbdbcbbadadaccbaaaddbbbcccbbcabcbdbdcdddadbacaddcdcddbcdacbbacbcbcacdaadbaccddabababbcccdabdacdabaacbabcdccbcdbbdbabbbccdadcbbdadbcacdabcabdcaacccabccaabbcadbbcacacccbabccbddccdccaccbbcdaccaabaaaadbabacdacdaadcdaaacbdcbacbcdddbaddcbbddccbdcadcccbadaaccdcddabdaaadbbccaddbccbdcbaaaccacccdcacacbdacdacdbaacccbadbabaccbcccabacadbcbabbcbdaccccdabdbaccddaaccadcbcccbaccabdbaaabcadbbbaacbbbdbcaacdbdbbccabbbdccbacaddbadccbcbcdcaabacbbddaadcaaacbabcbadabcadcdddbdadcdaadbbdabcbcdbcababadbbabdacbcbdadacccabdbcccdaaddbdcccbcddbdbdcaabaccdccbabcdbccdacbdbcbcdbbdaaadcddaadcdadddbdacdcbadcbdbadbbbbdacacdcdbabbddadcaacaacdabdaabacbbdbbcddadcbcbdacddcbcbbbabcccaacdcdcdcaaddbacabdcbaaaaaccddbaaddacdabbddabccdacdcdbcabbdccbcbacababcbbaabadabbaccdccbdadaccbacaccacdabdacadbbbccbbacdcccaacdcdccabbcdaaccdaddcdbcadcdacdbbdddddabcbddccacccaabbbbdaccdbcabcdbabbabadaabaaccdccadabdcccdbbacdcadaacdbcdcdbcddaccaaadbcacaacdacdcbdcbcdaababdcbdbbbadcddbcabadacabaacaadbbbcbccdbdadaddbbcabadcccbacbbcdcbdbdaacdbabdcbaadcbccbdcaccbcdabbcdbbcabdbdccbdadddaddabcbcabbacdadadcadabbaaabccbaccabdcbbadbdddbaacdcdcddbbbdbcacaabcbccabbdaccabdbddaddaaacadacdcbdabdcdabaabddbbabbcdabadccbcbdabbacccaccdbddbddcbdacdcacdccdccbcccabbdabacabcaadbddbdadddadbcdcddddababacdbbbbcdddbcccdccdcadcadaacccbabdbababcdcdbbdbddccbbdbdcbdcdbcbaaccddababcacdbcbbabbbaadadbaadbddccbdcbccbbaabcdbcdabdbababbacdadcdbdcdcbaaaddadaabdaabbccccccdbcbbacbddbbdacbcbdbacbabddccbdbdcabadbaddbcdbababcaccdddbaddbddabdabcbbbbbdaabbdbbdbdcabcbcbcdcadcdcccacaabbaccbaddcbbbacbaaddaacbabbdcdabcdbcbbacbcdddacaabdcddddbbcacadddcdbcaaabcdcdccadbadcacccdbbdcddabaddbcccacddbdbccaadaacdcaabbaaaaaaabdadcbcdcabdcdbabaadacdadadcaacbaadbcadddadbaddcddbdcdacdbacacacacbababaadbbabcbdbdaaabccdddcbacdbdcabbdadcbdddbbccaadacadddcdbbacadbacacbccbbababdabbbdaddcdaabbdcccdaaddddcacbbbbdabbcdbacdadbccacbcdbbccdacbcaaccbaddbdadabcbddaadcaadbcdcacbaddabddbbdbccadadabbadadbbcbbcbabdbdccccdbbccdddbccbddaacccaaccbbaadbcdacadbdbddbdacdacabcacccdabadadbaacbbbcacdbbdadbadaabcdbacbdabcbddabadaccddddbaacdacbaacbdcbaacbbdabdadccddcaaabdddbdcaadcabcddadccdbbcdcdbdcbacbbbbbbbbdcabbbaaadadcaccdcdbdbbbcaabdbbaaccdcaccdccdcccddacacbbbbbcdbdacaabbabbdddcadbcccadadaadcdacdaadabacdacbdadadaadbcacbadabcabdacdacdadbcdbccbaccabdcabbcbbdabdcbbadcbacdcacccaacccbdbdbaaaabdccacabdaccdcdbaabdddcbbdaabcacbcbabddbdabacadbdcdadbccacdacdadddbdcbadbbddcbdbacddcdcddbcabcbdababcbbdbabcabcacbcccdaddaddaccbcdccbdbdadddabcdbbbacdbcbbacbdadcbabaddabccdaabddbcccbcbdddaddbacdccdbcbdcddccaabddadadcbabbadababdaaccdcbcdabccbbddaacbdcabbabcbbdaaadaddadbbccbdbbcacddadddcbcccbadcccbddaabaabccbdaabdcddcdbdbdbbbcbbadbacdddcdaabbcccaddcaadbddbddcdbbacbcbdabdabdcacabaacadccaadacccbdddaaadadcbcdaddaccbaabcdadbbccbbcbbcccbdadddcdbcacacaacdccacddbbacdcbdaccdcdccbadabbdaaaccbcbcbdcdddabdcddabbadacbdbaacbbcccbbacdbdbddaadcbadbcccddbdacdacbcbacadbcdbacccdcdcabbdaccdadddbabbcabcdadcaacbcdacaccdabaabcbadccddabaabdadbadacbcbabaccccaadbcdbcbdcdbccbccdcadcbbacdbbdacabdcbdccdaadcadbbbbcdddaccacacbddadcdacdbcbaabadcccbacacabadbccaaccacdbdbabcdcdbaadbdaaabaacaddccddbdcddbacbcdaadbcdbaaadaacdcddbaadbdcdbaccdaaabaaadbdadaacccdcababbddbbdcddccccbdaccbccabdadaddabdbcadaabccdabbbabcdabaacccadbbdbbbcaadbccaadcbdabadcbcdaadbbacacccacdaadbdcacbdbcdadbaabaccbcadcababdacddbbccdcdacadbcdcccddbadbaabbbccdbbbadcaabddacccbabddadbadcdddcbcbbdcacdcaabdcaddcbdcddadaccabbdcdcabcaababdcdbcdbadbadbadbdacadcbadbdbabdcdaccdbcadbbdacddadbbdcbbdaaadadbbdbcbdbbbabcdcbccdacddaadcabbbdccdacadaacbddadbaccbcacbcaaaddbdcabbbcdacaadbaabdacadabbcbbabccdcdacdcdacbbcdcaccbabcabaddbcbbbbdaabcadaacaccabbbdcbbbbbabdbddcacdabbcbbabccddcabcbddabbbaadcccbcccdcababdcbcdbbbbacbaabdaabacaadbbdacdbabcaabdadbddadacbbcaaddadcadcbbacbcadcdcbdcbdaccddbbcdcadbbccdccbdbdccbdcccdadccccddaacdbddbaaadcbbacaadacbcbcdabdcadaddccdbbcdcdbbabdabcbadaaabcddbdadbabdcccaaacccadccbdaaaaccdcdacccabaccddcaaaabcadccadcadbbdaaddbadabbcccabddbcbbddcbdcadccbbbadbabaaaccddaccbbcaddcdbadcadbaddcdbaabdbbbbacccddbcccbacacdaddcbaabbbcabdbbddbdaabaccacbddccaabcabadcbcabbcbdcbddcbbdabaabcddcdccadddcccadbcccaccadaaacadbddbddddddddbadbbdcbdccacacdbcadbddcdccacabadbacdbbdaddabdcdbaaacbdaabbcdbddcaadcaabddbcdaddcccbaddcbddbaacccbbbddcaaccaadbcabbbdcaabadaccbacaaabbabdabbccabccddaccadcacbdddacdaadbcaaabbdccdbababbccadaacbbabbdacdcbcabbdddccdccadacdcdacacadbdccadccaadbcddacbdcdabacbdaaaaabaacdaddbdadbbdbdbabbcdadacaaaaaddcacdaccccdbccdddbddddbaacccccdcbbacbdabaababbcbdadddcacaaaaccaaddbdbdabaacbabbbbbddcdbadacacbdabadcbdaaadaabcaaadacbabddbcbddddccabdaababbcdccabcdadadabdcbdccbacbaabbbbabcabdcdbadbadccdaaabbbcaddbdcabcdccddddaadbdacbadcacadcdacdabdaadaddbcddaacdbabaaddcdacbabbbcdcacbddddaabccdaadbccbdaaaadadbcbddddccaacaccabdddccbdbbbcbdbdaaccbcaadaaccadcdcaaabdbdaccadbbadcbcdabaaadbbddbadccacaaaaaddabddccccdabbdaacdbdadcadbaddcacabbacdaaacdccdbaaacbabaaddbddbbbcbdcbcdcdcccdcbcabdacddbbacbddddcbdcadaacbbbddddccddaddbbddacdacccdaabbaabccbabcdcccbbbcccbbcadbdbcbbcbbacdddaaddddbdcabaacbacdbbbbcbbbbdbccbbcccbbcaadccdaddbdbcbabcccaacacdbbcadbcdaaccbaadcaccbbddacbcddcbbddcddbbddbbaccbbbbdbbabadcbbcdbaaacccacdbbcbbbcddcdbdbdccdbcdbbcdabcabcbaacababdbacbbbaacbbaaaacaaddbadccbaabcbadacdbbadacbdacabcbccccbabacacdacacccacadcdbdcadbdccbbcacbbababcccaabcadaabbacbbddddbddcabbcbdbddbacbcddcddddbcadaccbaaadcbddadcbacbcdbcbdacbdabdbaabdcbabbbccdbaaccbaadbbadbcccdccbcddcbcccdaacabdadbddaccaacdbdbbacdbcddcbbacbbaacddbdddcccbdbabaabbcbbbaacdcadccbbdbacbccccdadbbcbcdbccacdadbadbbcdbadaccbdacaacddbdcdbdcabbaadabddcbbcadcbadacdabdbbbbcadaabdddcbadaaaacabdbabdacbdabccccaadadcccbdaabdbabbccccbadadbaddddcccaccdccabbadacdaadddaaccbdccbabcdaaacabddabaaaddbccccbdcbbdbcbbdacddcabdcddabddbbabbdbccacbcbdaccbbdbcbacddacadabcdcbddcdddbdcdbbbacbbbaccabbaaaddddacbcdccabaabbbbddddadcbdbadbcdadcccabadcbcdbbbcadacbcbdcdcbacbbdddbdccbbadaccaabbcccbbcdbcdaabbaabbbadaddadbbcaaaadadabccaddcabdadcddadaaccacddcccaaddbccbdcbbabaddddbbacbaaccdbcbcddbaddaccdbcdddcbadbdddbaabcdcdddcabbdbbadcbddddcbdcbaaaacdbddcdaacababadcaadbbdbacbadcbbadccaabaaccacbcdcaccbcbdabddbbbaaaccccaabddabcbcddbaadbdabdaccdcaadccacbcdbcbcddbdbbcdccdacbcaabbbbdaaadacadcbbddbacddabbddadaadabbbcabbdcaddaccbbadbaccbdbabcdbcdadaccabdbccccdcdaddcabbcdbdcbdcdcbdcdacbcadcabdadccadaababdccdcbbcccccadcdcadacdbcddcadbdbadbdccbdddddaacbdcdbabbcdacbcacbbcbaddcbdabcdaccaacdbcabbacbddcdadcbbcbabbbcddcdbbadaaacddcabbadccacaacccdcdcdbdbbabdbbbcddddcbaaaaaabcaacadadccbbacdaacdacaaadcdcdbadcdbbdddbadabaacaacbbacbaaabbbddbbbbcdbddbddcbbcabbccaaabdacbcaccccabcdadcadacdbacbdbdaacbacccdcacddcddabbcdcdbcdddccdabbdbdacccbbccaadcbcdbdccdaabaabaccabacbbcbabdccabcacbbddcbbaaabccddbbacaddddabcbbbcdcdcdcabdbbcaccbbbbdcbbbbcbdadcddccadacaddcdbccbacaddacbcdcddadbcdcccdadcdadaaacaabccaaccacdbbbbababccadccdacababdbcaaadbacdaaccabcadcbaabccaacbbbacbcbbbbacdbdabbbddbdbddddaaadcbabdddcababbcdaccddddbabadababdbdbdadcbcbdcbbdbbddcdbacddcccabdbddbacdacaddcbacadbccdbaaabdadbccacaadbdddcacbbaaddbaabcdddcaabcadbacbddbbdabdbcddbdbbacbbdcdbcbdbbcabbdccaabdbadccddcabaddcdababcabaaadcdbcdcbbbdacbcbdbabacdbadbcddccacbcabacdaadacdaaccddcdbdcccdaddbbacddcadaabdbcadbcadcddcddacddddcbccddcbdbdbcddabcdacbdaaddcddabcabbbadcdbbbbbbdcddabaabadbcccccacdcacaddaaccadcadacbdcdabbdaddbabcdaaacdbddbcabcbadbcdcbacbcbdadaabcbdcdacdcbbbcadcbcadadaabaabaddbcdcdabcdbddabbcddbadccdbcdcccabbbbdddabbbdbdccdbccddbbcdcaccdcccbcadadcdaaabaabddcbcbadabccdcadbadcdcddacaddcdcdaabcdaabbcaaaaaabdbdccbbdadccbcbddbcddcabacaacccabddabbdbbdbddbddbcdacaaaaccdaccbacbdbcdcdcbbcbcccabdbbdacacbdcddccdcbcdcdcbdbdbbcdabcbdcacdcdcacbcccbddcdbbbddbcabcbbaccaadabdbadcaababbdbbbdbacbddcacccababbbbaacaaddcdbadbdcdaacbdcaadbbadacbcbcdadbbdcdccdcbacdaccaddcacbbdbaddbdbdddcabdbdbdbdbcaddaccdadbdadbcbacacdadaabdcdcbbacdacabdcddaacabaadbadabbabcddcbabacdccbadccbdadacbcabcbaaaababcdcdcdddaaddbdbbdddabdaaddccdaacabcbadbdbacacacbdadddcbccbbaccbdabdadabdacdbbbbbccaadddcbdbbacdcacabbccbbccbadbdcddbbabcbadaccbbdaacddcaccbdcbbcaabcaddddcdbcbcbadcdabcaadbacdbadabbaabdcbdabbbabdbbcadbcbadddabddbbbadcacdbbccddddbaddbcdbccaabbccccaadcacaccddabbccbdabbcabdcbcdbbdccdcdbcaaadbdcdacccadabdcaddadacaabcaddbbdadddaadaddcccccaccdcdcbbaddcdbaacabdaaccadbcdcdbdbdbcccbbdcbabbdddcdbbdbbadabbccccadacccacdacaadabcbcccacadddacddacdbdaddbadabcaabbcddbbcabbddaadcbacaabaaddcccbbbdaaadbbdcdbddacaddddbaccacccbbaabbcdaadbdbdacdbabcaabbdaabbdacbadcccdcdacbcdcaddcbadcabcacbadbadbabddbbcbdddabdacccdbaacabdbbddcaccdbdaaabacbbdbdddbabdbcdbdbcabdcccbaaabdbabdbbabcacbdabaaaadbbccbcabdabacbcacdddcbbcccdcbdccabbcbabbabbdccaaddcbcaabbcabacbaaadbcaabcabaaaabbddbdbdacddcbbdccbbadadccadddcbcaccaaabadadcadbbcddcbaacadbbdddbcaacdddcabccdcacbabaccbdbdbbbcbccadaaaccbcbababdcadcacaabbcbdcacbcddbcaddcdaddaadacacddbdcdcbbbbabbcdaccacaacaadaababbccadbdaabacbddbcbbaacbadabaadabacccbddbdaddccddaadaccbabbcadbadabdaabccdabccbcdbdcabcdddadcdccadabddddddaaacbcabccdadaacbaccbbdbbaddcbdcdadcaabaadadbddaadabaaccbdadaaabaacaaaacdbaabcacdacabaabcabacaacdbaccdccbbadaddadadcadddacaaaacacbdabbdcdbcbacbbdcbaadacccbdcdbddacdaacaaadbaacddcbcaccdcbdbacccddaccadaddcaacaccabbbadccbbbbbdcaaddccddddcdbaaadaacacccacbccbacacacbdccadbacacaabbcbdddddaddabcdbdcdacbaccbdbbbdccbbdaccacbcdadadbadadcdadcaddbdbdadbacbdcaaacbbddaaccbacddbccbcbacabaccaaccbdccbbcddbadbcbdacdaaabbcdcbcdbcbacbaabbadcdcadcbdcaaddbdbaaaaadbabbacadccddbcbbbcbbddaccabbdbaabbbcdcacaaccbaacbacbbdbadacacabdcbbacbaadbbcbaccaabcbacaabaabdbabcabdbaccabbcbbbcabdbbabbbabdabdacbbabcaaddbdadbbbbcbdbaaaadaacaabdddadccdcaacbabbdabaaccababbbcbccddacbadaddcccbddcbdadcabddaaabdbabadaccbdcdadabbdbacaccdaaccadbabbabaadbadcdddabdabdddaacdbcaaaadcaaaaabdcdabdddcdbcaadccccccbabbdabaaadbdbcaabaddadcdbddcbaaddabbdabaadcddccbdbbcadaaabbdccbddbbcbcbcdcddbddabcdabccbdbdbdcdcadccbbdabcdacdcacdadcdccaacacdcddcddbdcddbdbbaddccbdadccadcbccdcadcccddbcbaadccbabaaabcccbdaacabbccacbdbbcdbbdabccddbcdadbbdbdcacdccddbcadabaabcdddcddbcccbcacdbbbcddcaababcadcbdcbbacbcdccabdabddbacbdbddcddbbdddbdcbdabdacdcabcdcaabacbdcccacadadaaabbadbbdacdbdcabadcaaaccddabbbbcdddaadadcbcbdaccaaccdcdddccaddbabdddbbcacbdabdbcbcbccdbccbcaacadbbbbdaadbacddbbddbaadddbccacdccacdbbdbcbbbbbcaacdcacddcbcbcaacbbbdbbaacbaccdcbbbabaacabbbbabcaaadccdcdcabddccaaabbadbcdacdddcccbaccbdcbccacadbbccddacccbddcddbcccdaadaaccaabaacadbbaaddcacdccbacaddbaddcdcbdbbabbdbaddbdbbdbaadbcdcaadddcacdbcdabacdcddaabacdacdbaadbcbaccccbbbdbadacdbabbdddabcdbaabaabaaaddbabdbcccabbccdacddcddaadaaaabadcddbaccdddbcbcccadcadbaaabadcbbacccdbdcddcbcdcadcdacadbaaabaabddddadcbacbcdbbbccabdacdccccaadbacbaddabbbbbdcdaadbdccaddcbaaccccbdacccaddacbbcaacdadcbddcdadddbaccacabbabbbababcdcacbcdaccdcbbbaacadbbbcabcccccdbdbadcadcbbdcdddadcaccdbccbdcbbdbaadcccacdcdcabcddbddcaaccaaadbbbabcbbdcdddabccdadcbaccaabcbdcbdcbacacbacabdadadbbdabbcbdabbbccdbcddcabbdbbabbdcadcccbcdadbdabacbcddabdcddabddbccdbbcdbdbdcacbbbbaccbaccbaadbcdaacbbcbbdbabccbbcccaaddccdababbdcddddcabdcaabccaacdddcbbcdbcaddcdccbdcaacddcbcbdbbbcdabadacadaadabcdccccbbaaacabbdabaabdddcddaccabdbbacdabadbaaabaaaaaacacdbbcadbaddabbcdcaddcbacbcbababbbcdbccddbcbabaacadcaccbaabcddbbabadaddaabbacacbdddaccbacbadabaddddbcbabadbbcbbccdacdbbaaabadadcdbacacaabcccdbdbdcdcaacccdadcdbbacdcbccdabadbddadddcbbdcdbccdcccccbdddddabbdaadccadacaaaaccbcdadbcaddabdbccbbadbaaacdaadbabbdccaaaddaacacbbdccabccdddababaddddcdaabdaacdabcbdbbcddbdcccaaaacddcdadddaacdcdbdadddbdabbdddbbaaabbdcbdccadddacbbdbcbadbdbccdacccabcacadddbabdcccbbcadabcddcbbbcbbacacbdaddbaabcdbdbbbadcdcddbdddaccdbcbccaaddacacacdabaaacdcccabddbcdbccabadadccdcdbcbbdcccabcddcacccbddcadddbacdbbcbcbcdcddacccdddaaccaaabbccddccddcbbddbbcdbcadaacdbcadabbcdbbbccdaabbdacabdcccbadcabcbbadbcbddacaccbcdbddcbbaaadbcbdcddcaddcacacacdabaaddccaacbcabccdbcdbdbbbabbaaacdbdabdddcdcdcbcccbaaacbdaaabdbacbabbdccabbccbccbadadadbabbddcccbcccdaadcaabccbbcbbbdabdccddacdcabbbddabadaddbdcacaabcbabaacbbadadbbabdaabbcbcabdadabbdbabadabddddbcddbbbaaabcbabdbddbccbabaccccbaaabdbbacbbddccadbcadabcaababccbabaccccdbdbcacabbdcaccaaccacbdccccdcbbccdbcaadadabcccbcbdcbbbdabdadaacccaccdabccddbbbcaaabababcddccbbbaddcbbbbadcbbbddccbbbcadabdabadbcbbbbcaddbccddccddbcdcabdbbbbbcbccbcadbabbbcccccaacacbcadaccdabcbcabadacbbaccdacaacabdbbdbbcbdcadbbdbcabadddabbaadbccdabbaadbdccdbcdcbbbcababbacabcbddacabcabadabcbaabaccbadbacbaacbadbcccdabdbadbdbaadccdcadaacacdbaccaadbdbcabdccdaaadaacbccdcccdbcdbdaaaddadadacbbdcdcbbdaaabcbbcabcaaacdccadabbcbababdbabcccdbaabbadbbadcadcccdcbdcbccdcbabbcbcbabdccddbcccbabcbabacdccbddbabcccadbbaadcaabdcbccadcaddbdabbaaacdabbdacbabddabddbdcadbccaacaadddbcdbbbabbddabdddccabcadcaddddabdabaacacabbadcccbdbdacaabdbbcccacbacabdacabcdadcbbbaccdacdacababdbdbcdcaddcdcaadbcbbbdaaadcdaddbbbdacdabbcbccbddcbacccbcddcbabbdaccbddbcabacacdaacbddbbcbbcdcdccacaabcccdcccbbcbcddaddbcbddbbddccbdabbccaaacaaadccdccacdadacadbacddacdddbdddacaababdbdcbdccbbbacadbaadbbdbbaacaaabdcdadcbcbaddbdcdbbabbbdddacbbbadcdaccccabddaddddaccdcbacbccdaadbbdbaaadacbbdbadcabddadddccadbadaddaabdabadcbabdbaccdcdddadddccabaacdcdaacbcacccbccdbbcbaabacccbbccbdccddbbcababbcdbbabaadaadcbddabbbbbdbbabcaccabbdabcdbdcddbdbcaadcaaaccbaaabbbdbdbbdbaacadadbabddcccaadaabdadabaddbcacacabacaadabbddcdadbccbddbbaaaabddbadacdadcaaccdbdcdcbbcdbbcdbccbdddadcbddcacdcaadadcbcbaadaacadbdadddddccbccadddacaadacaccdcdadaaddbbdbaaaabaaaddcdbbccdbcabbaaabcdaacbdaddbadcbacacbddbaccacbabacacdbcabcdacbbcdadbcbbccdbabdcdacdabccdaadcccbcdbdaabadbdbcdccadcdcccdccbbccccacaaaadbcacbcacdbadbdddadabbbcadcdcabbbdaaccbcbcbdadddbadbadaacabccdabcbacddabdbabbdbddbcacabcbdcdbbbbdbacaadbdcbcddbacbbabcbdccbcbabcabbcbdbdbbbbaadcdcabbdbbcabdbcadbdaaccadcaaabbbdbbdcbcdcbadccbcbaddcacbcacdacbcdddbcbbaddadaacdddbcbaabbcacacadadaacdaacbaabcbccbdcaddcdcccdbcddbdddcdcadaabcaabddadbbabacbbbdbccbbdcbabddcdbbcbaacbacbddbbacccddddaacdcdcacbddddbcccbbcaadcaaaadcbbaadbcdcdcacbcbcdacdadacddbccdacbdaacccbccdcdcbabdcdcddaccbbbcbcdcdacbddacaadbbcdabdddcbcbcacbdcaccccdabdccbdbbbcaaabacbadbdcdcddabbbdbcbdccabaaaacacbdddcdcdbcdcbcddcbbbaabddddcacbbcbcaaccbbcddaccdcadbbccadacbabbdccaacaccadbccaabaabbabaddcbacaacabcccdccdcbaddbadadbddbaadccbddadcdaaaaaaccdcbcbcccadbcdbdcdaabaaadcdadaacabbdcccdcdbbcddbdddacadbcadbccacbbcdcdcbbcbadcdcddadcaaaadabdadbdbbbcdbcabdbadacbadbbcadccacdcccdcacaccccaaabdacbcdaaadddbdccadbadcbbaadcabcdaacbcadacccdadacbdabddacdddacdabbdadbbdcdbddaabbbacacdbaddcacbdaccdbbddabcccbbcbabbddacdbcccbacdbbbabcdabccbcdcccbabacdcaccdaccdbbccdbcdcacdadbabdbccdcdbddddbabaacaabdacaddcdbcaadbbabcdbcadbccaccdaadcbcdbccccbcddaacdbbabaaccdcbaaacbbcbddaaccbddbacdcdaaabbcbaddaabbaccadacaddadbdcaadcdcaddbdbbacddddaabcddcbaaddcacdcdadacdaaabdddcdacaccdbbbaadccbacddbadcdaacddbacbaadddbcabdbcaccddbababcaddabbbdabbcbbccdbaaddaaccdadbdcbdbbdaccabcbdbccacdbcabbbcbaaccbcdadddbbccbbbdccbabbabaacdaccabdbadbdaaddbadbaddbbabbbccadbacaaccbabaaacddbbbbacccbdcbcdcabbbdcdcacdcdbbadbcbbadcbdbccddbddaacacadddbaccbdcdccbaaddabdcbaabdcabdbabacdcdbaaddbbcccacbcbacbcacbccaccbcdaccadadcdddabdcdddbcddbadcbbcbcabbbabadabcbaababdbbabcbcdcbddbadddbddcadaddabcbaacbddbbddcbbababcdbcbbaccadabbabacddbadddbdabacbdcddbcccaabccbdbcbbababcdbcdadcabaaacdcacabbacddcacccccaacbcddacbdccdacbbacabcbddabbbaddcdcddbcbdbabaaddcbaabbaaabbbddacacdcadddbaacbcdacccabbacabcdbcadcadbacaaccbbacdccdccbcaddbdaabbbcbaadabaddccaacadacbcacbabadccdddbbbdbbaddcbaabdcddacbbabdbcdabacdcabdabadaddbdaacbbddbaddbcaacbcbdcabacccbacacccbcdbddcdcdcccbbbdaaaaacaadcacbdccadcdbaccbdadbccccaddbaaaacbadcadbddaadcbcadaadadcadcdbbbcddddbaadacdbddcdcbbcdbbbcbdbacdddcbcbbbccabaaabacbdbccababbadcdaccbbaaaaaaaccdaccbaaddddbcdbbbabbddbbcadcbdbbbbdaddacdcddacaabdacadbabbbbadccaccdbdabbcdcbabdabdcacbdccbcbbdacddccaabcdbabacbacabcaddbbdbbdadbddaddccaadccbdadbaabbccaacdccacdbaaadbaacdacddcdcbddcbdccadddbcabcabddabdddcacaacbbddbbbacdcdbbdbcaccbcbcacbcbaabbdaadabddccacbaccdcdadcbbcbdbabddbcdaabbacaccbbbbccdacbaabacaaabcccddbcbcdddaadcbbababbbdcddabacdcabbcbdadaddacbbcdadacbacbbabacacbdcbbdbcacaddbdcadddaaadccaabcbddccdcaaabcddccbaabdacddcccbdcdcadcccbdabdbacacdadccbcbadccacadacbaaacabaaaccbabbcddadbdcddcdcddcacbcbbccbbddaabbccdcacaacaadddacbbddabaddaabddbabdcaabddcaabaabdacdbbaaabcbbaabbdbdbdbbaaddccbdcdaddbcabbcddbccadcaaabaaadbddbdcbbbcbccddcbbcbdbdccbbbbdaabdddddbabcbbdadcbdccaddcdbbaadcadccbddcbbaddddccddbbaddcaddcdaabadccbdcdccbbcaaacddbaccccaaadacaadbdbcccdaddaccadadbdabaadbcabbabcaacdbbabaaabcdcbcabbbccccdbcadcbaaabaadacbdccbccbdbabbcdbdddbdacacbccaabacaddbbdbaabdbbbacddadababadabbabdacdadbcaccdbbdbcbaadadaadabcddbcddadacddbbcccdadbcbabdcadcadbaaadabdadcaacabbdbcabbcbbcbabadcdabaaddaccdcadabaabbddabadcacbddaccbadacdcdbcbbddccbcccbadbccacaddcbdbabaabcbabbacdadccadbdabbdabdbbabbdadcdbddddcbcddaaaacdbccacddccbbabcbddddbadabbddacacbadccaddcbdddcddcdbacbdbbabaaacacdccdddcaccaddbcadacbabdbadabccadbdbacbcaabacbdababbaabcdcdccdbdcdabaadccdbbacabdbddaadbbbbbbaddabcbcbbadbacaddbdcabdabcaaaabdbddcaaababdcddabdcdaccacbccadbabcbbaabdaccaddcddabddcddbcaccccabcbcaabddbbbbbddabadcadaddbacabbbcdcbdabdddcbcdadadcacabadcdadbcacbcdacdddddbbbaccccbbcdccdbbdddcacaacaadacdccddaccddbdbccdcbaddacccaabaadcdbccbbddbdbadbdcbbaadabdbcdbbbcbabdbdaadccdbccbbcdccaacaaadccacddaccdcdcadcbabacddcaabbbbbbabcbdbdbdbdabcdcbdaadaaadbbddcbbbabdbdbddddccaacbdbacbdcaddddcbccdbcabbabccacbbcdadbbbbaaabcdbcdcabcddaadacdbbccbbdaaddadcddcccdbccacacaabcbbdbbbbaaadddadbdbbddaaabdbbacabbdbbbdaabbddcccabaddaaadababddcccabccaddbdcaacdddddbcbcccbaccaaaacacbcabcbcbbdabdddcdabbbdbdcaccdabcaddcabadbdbcadbcadcbccbadabdbbbbcdddbddadaabcddcddcbddccdcbaccacacdcbabcabbbabddabdbbcbabdcbcdacbdbbbabbbddcacaddbbdadddcddadccabdbdcdcdbbbcdaddcdcacbccacaacccabdabbabdcdadaddbadbabaccbdbababccabddddadadbbbbcdaccaabdadbcbcdcdbcddbccbbcbadcacdacdbdcbaabbbddaacdaacabcddabbcdccdddbacbabcbadaadcacbccbbacddabddccbabbdadbdcbaabadbbbaabdddcbcdccdbccbcadbdbccacadbbbdaaccbbdbccbcdadcacdaadbdccddbdbddcaddcccbaaaadaacbdddddaaddbdadcabbcdcdcbcbbadcbaaccdcdcacbccabcbcddadbadcaaccabdddaddbdbddacdcadadcddadadddacdadbbbbbdbcabbdbabaaddacbabbcddbdbdadbccdbabcbcbdabacdddcbbccabacacdaacacbabdbbdddacabbaadabcbadcabdaabcabcdacdacadddddcbccbaadaccacccdbcabbacbaabbabcbcccbacababbaacdcdbbddcbdcdbdbcbcccbaccaabbaaaadadbaacbabbdbbdcbdadddacbaaabababadcccdccbcaccdbabadabbcbcaaaadabcaacbcaaccbbdbdcbaabcdaddcdcabccaaaaaccaaddcadcacaddabbdcbccaadbbbbdccbaaadddddacdcdbcbdacbabcadbcccacddbccdadbddcddbbbbabbbbabadccdbdbcaaadbbcbaabcdddacbdbdabdcbacbaaddbbccabcdadabadacacbddcbaabcdccbbadccaacbacdddaabacaadaddacdcccbdbdddcadccdaaadcadcabcaaabcabcdadbabdbdbccaaadabdacbcaaacdcdcbcbdcbcacccccccddaddacdaccacddacccdcccbaaacacbabcbdcdcaabaadcbccbcddbdbdbbbbacaadbdccabaabcccdccdabadbccacbbaccaddcddcabcddbbbcbaaccaaabacbbcadbdaacaaaaacaabaabdcacdccbaaadbcbdbdbccddcbccccddacccbaccadabcdbbdacaadbabcdbcadaccaaaaadabdddcdacdcbadccaaaabbbbbbddabadacbbdbbcdbacadbcbddabdccdaaaccdababacaaddddabacccccaaaabaabbbddbcaadddccccbddaacadabacaacaacccdadddcbaacbdacccbccdbddacbcbcabbaccdbccbdaadbcdabadbcdcababcadddbbdcbabcdacdadacccbabddbcdadaabbddcbabadbbdacaaaccccdaaacbccbcbcacdccbdccdabacdcbcaabbdbdacaddbdbaaabdadddddddccbbbacccccbbabcabbdacbdbcdbdbdbbdcbddccbabdbcbbbccaadbddcdbbacbdaadabddbdbdbdbccadbdaadcabaccbcabdbbcbdacdbccbacbbacacccdcbcccbdaabddbccadacaabdcdabcbbadbbcccbcaadcdbacabaabcdadddbccdadcbadcbcabadbdcaabcbbdbdabaddcabdacadcdddabdcadabdccbdabbddaccdbdcdcbddccadbcaadaacbabdcbabdbacaabababcdadccacadbbbccdcddaaabcbcbbbcadddcacacabccdcddddcbcdbbbdcccbcdaadbbbbdcbaaabbcaacdcbacbddaadaccccbaabcaaaccbbbbcbdabbabcabacdddccccddcadbcabdcadcadabcaddcbabdabbaaabdbbaddcbbbdbdcaaabcdacdddbdabcbbdddbdabbcaaacdbabbbabbcacababbbbbaabbabdccbdbadccdaaaacaacdcbcadacbdbcadcbcdabdbcdbacbbbdadaadcddadcadabdaadaccaacaabaaacddbbbccccadadadcccabbbccdadbbabcdddaabcdcccababbbcaddcdbbcbcbaaaccdcbbbdcbaddbcbadcddddcdaddaaddbcccbdcbabaabbcdababddacbdcccabbacaddaaabbbadbbabbaccdcaddaabaaabdbbdaccddbadcaacaccaadbcdbddbcbacddaaddcdddccabdbcaddacddbdccaacdddcdacaaacdcbbccbacbbcdacadbdaacbcacbbbbbabcabaaaccddcadbbcdabbbcbddbcacdbcccbdaccbdbdbabacdddcdccddbddcccccdcbdcddccbdabaccbddbdaabaccddbabcaddbbabadabdbdbaccabbdddcddbdcaadcacdbcdcdbbabbcdccdddaacbaacddbdbbdbabcaddbdbddcdbbabdcbbccbdcccbbcddabbddacbdaacaadabcaddcddcdbcaadacdbddcababcdcacbccccccacdcdddccacadcacddbccacdcddbacbaabdccdccbddcbdaadcdccabdccabdcdbdacacdaccacbadadacdcaabbaabaddbcdbcccbbbcbacabcdbccabacbacbbcbadcddccaabbdabdbcabdddbcadddcbdccbaddccaddababdbdcbcdccbdcdcaadcbabcdbaadaadbccdcaaadaddadccbddccdbadcccdbbcababcbacdbdcbdbdddccdcdbbdddbaacdbabbabbacdcabcabbbdbcbdcaaddcbbdcdbcbcdcaccacddbcdcadacadaadddbdccddbddcabaaacdcdcabcacabcccbabaaaaccdbabbddacbbcbdcbbbcaacadcadadbcabacccacabbaaaddbdbdddbdbcabbcbdddaaaaacddbabbadaaaabbcdacadaccacacbdcbcdccdccadcbacbbbbddccbcabbccccddcabdcbdaccaccccabbaadddbdaddccddacdacacabbcdcddadcddadbbccdccdcaddcabcbbdddabcbbbdaacdcbbbcccbdcbababdbcaacbddccbdbcabaaccbbacdcadbccadbadcbcdddaacbddbdabdcadccbbbcdcacdcccbbdbddaadcbbdbaabbdabdabcbadadccabaccacddaddcbdcaadcaccacabddcbdabcbabcbbadcbbbbaabcaccdddacbbdacaacbddbcaadbddcdadcddcdccbcbdbaadadcbdadacbdbdbbbadccddabdcbcaacaaaaadccdadaabccaddabdcddccdcadddbababaaacaaccabcdccbcbdbbddbaadbdbaabbaaabcaadcbbdddbcbbaccdcdadbacdbabadcdcaacdaccaabbcbccaadcadaadbdcbadbabacabaabcaccabbdadccbccbdcdcdadcdbdcbaaccadacdccaddcddcbddadabdaadcddcdcbbadacbaddaccbddddadacdbcdaacadaaabcccbabcbddabacdccaabcdcdadaacbddbdcdddadbdaadaccaaccbcaddcacbbccbacbbdcdacccbadcccbbdacbbdaddaabbcdaabddabdbbcbdacacddcabcbdbdaccbdcaddcdadcddbdacbabdcabbcbddbabadacaaaddcccdddbbbacdbaaacbcbaaaadbccbcdadbdbdacdadbaabddcabdccaaccddcdbddbacdbcdbaacadadbaaccbaddddaadadcdddcaabbcdacbabddddcddcdcdcabcbbcdbddaaabacabdbdcdbbabababccbdaaccdbaabcabbbdcaaaabaacdbcddbabbbbbbbabacdcadbcbbabcccaadaacccacacddcbbcabcbdcdbccddacdbaddccbddbbabcdbadccbadbaadccbadababaddccdcaddbcaabadabadcddcbdacabdbbccdcbaaaabcddccaaabacdcddcacbbbcdcacbaccadbbcdcbbbadaadadcadbddcccccacdabaaccdccbcbddcaadabcbacbdaddcbacbccdcabddcbccdddbcdddccbdbbbcbccadcbcbdbabdcdcdbbddbbcaadbbaccccbccdcbacbaddacbcdadabacdabcbbcaddcdadacbddccbdacadbcabcdcbddcaccaddccddcdcacbcbcbbcddabadbdbacccdabdabacdccdcccdacbccbacbbddddbbabdaadcbdcdbadabdbababaddcbcdcddcabaababcdcacaabdccbbcccdbdabbbbabaccbaabcaacddabacabcdccddccccbabbcaacbcbbdaadccbaabddadcacbdcdaaddccdbdabbdbdaddcdadaccdcbaddadacbadcddccccabcbbadcdaaacabdaadcbcdababaccdabdaacbacaadbdbdcdcbcbaadbdadbcbadbdaabccdcdbccadadbabdbdcbbdbcacdaaccbcccacbabbdbccadbbaaaababcdadadbdaaccbbbbccbadccdcccdbbbaadcdadcaccdbdcacacbaccdabbdabdaacbacbaaacdcdcddccdbaabbdccabbbacbddbbacdaddcdccbadbaddbabadcadadccdbcacbdacdbddaabbbacbbbacdaacbdccbdbdcccabcabbddadbbcaadaacbbdbadbabaabbcaddbabdaccccdbbbdabddadbaccdaacbadacbaaabbabddbdcdccdcbbddbaadaacccccbabbccabcaddabdbdaaaabaddabaabcdcbcccdccdaabcbdccddaccaccdcdabadccdcaabdadcdabbabdaddddbcbabccddacacdddbcacaddcbdcacdadcdadbdccbaacbacabaccadbacaabbcdbdaaaabdbdacdcccdbabdabdabdbbcadbdbbadabbbbcbbcacbbcbdcbcbbccbadcaccabdcdbadaaabbabbacaccdcddcbcadcddacacbacdccbdcbbadbddaabaadadddadccccadcbcbdcddbcbcacbcbccbdbbabdcdddbbacbabaddadccaacbbbbddaddcbddacbabacdbdbadccabcadddddbcadbdcacaabdbadbbbabcccbddcaacddcbccbdbbcdaadcccabaaddcacbdcccccbbdacbbccddababbdabdccababdbccabacbcabcccdcbccaaccdbcbdcbbddaaccbcaddcbdbdbdbaadbdcabccaabcccbaaaaadbcaccdcaccadbdacbcbddaaadabbcabaaacaabccaadcaacddbaaddccdbcbdcabcbddbacbbcbddbdcbbcbccbcbdaadcccdacbcbadcaacadcbdccbdadddcddbddcbcbcdddabcacdbabcbaaaccdabbbaddddcdcadacbacdbbadbcbaacacdcbddccbbdacaccabdbaabcddabaacdbccacddacadbaabdcbcadbccccbccaabcddbcdccaaaaaddaccacdaaddcdddbcddaaabadaabacaccccadbdacbccadbcdbcabdcdacdbcadabbbdcaaabdddabaddcdbdadbcbdddbbacaadcdaaaacbdccdcaaadacbddddaccacdcdbdbaadcbbabbdacbcccadddadcadaaadacaccdcaabdcabbacccdccbdcbbaacdccadbacbabdadddcdadbacdccdcbbcccababdcccabbbcccbbbbabaccacbabcaaabddaccbbaaccdabdddacbcccbdccadbaadcddbdaacabacdbcaccccdbcabbababcdadcaabbacdddbaaccaddcdcbbaddcbdadbcbdabdcaabaddcccbcdadaaabccdbbaacdbcabdabdcadbcbbdacadcccbabddacadcdaababbbcacaccdadadbdcbcaabbaaaadcdadccdbbcdddacaaaabbbcdabcacaccabcaabbcddbabcdacbbdabbbccdaadbabcadbacdbcdcdbabaacdccacababacaabbcccbccbadcbacbbbdcadbdbaacaddddccbccddbdaaccbcadbdccbbbdcdccbccdbdbbadabcddbdcbababdbadbcddddcdbaddcabbacdddbcbcbacbdcddbbbadddcdbcadccbdabbbccdadcdbccbdacdcabbadbbbacacadadadcaadccbccabcdaddccadababbdabdccdbaabbccacbdabcdaddccdacacadcabdbaadbaadcdbabaabcccddaadaacdbbcaddbbbccacbdcccbdccbcbdbddbaaadcaaadacabaccdccbbbaabcaacbddadabcacacdadabaabbdcbbadccabaadcbdccaabbdacdaccdbbdbcbbdbdccabcdddaaabdbcbddccacaaccdbdbcadccbddcccdbabbaabcacdbddbbbbababcdddacdbaccacbacaacbcabcaabaabdadabbcbacbdbcddbbdabaadadadcaadbdbadcabaaadcaacdcdcbcddcbbdccacdcbcacbadcaaabdbcbcdcbddccacadbddcabcddcddbddadbdcbaaadbdcdbaddbdcddacbbbcbccdddabcdabaddbcbdcbdbbacddbcabaabbaccaabbbcadaccbabdbcbbadbcdbccdcddccbaccddddbbddabdbadaaadcccdcdadabacbaadbadaaacacacdbccdbcdbcbbacdacbdddcdcaddcdbbccabdaababbbbacabacbbdcbbcccbddabddcbbbdccddcbcdadcdccbdabdbbbcbbabcbccbcdbaaaababaadaaabbcdadaacccaacaabdaddaacdccbbaccccaabbaadbacbddadbbcbcdaadbddcbaaabcacbcabbbcdbdbaccccacccccbbcdaadcdadacdadbdaadabacaddcddcccacabdbdabbcdcbdbaacdccbbbddcbddcdbabacabadcccbbcccabdbcaccbcaaabcbbcbdabbdbbaacacccbbbaacaddbadccdcbaaaddaaccdccccdbccbababbcaacabdbadaddacabcddabbabccdcdbadacbbaadccadbdcddacacdbabbacdadcdaabadacccaddbcaddbaabcdacacabaddbabddaddbdbbadacaaadccddacbcbddcbcbacadbdcabacaccacbadabbddbddcdbcbbabdbbccdbcaddccbadccdacdadbbcbaddadbddcddcadadbadddacdccdadacaabbcddabadddaddabddbbccbaddbddcdbacabbdadcccbddaadbaaaccdbdbabdcaadaabddcaddcbcdcbcccbbadbddcaacbbdcbadaaccadbcdddcababddcdadcdcbcdabaddaaabdddbcbaaaddbadcabdddcbabdcddadababddccbdbdcccaccbcabcaaacacaaaaadacaddbdbcaaacaaadccaaadbadddcababcccccaadabcadaabadcccdcbacdadcdddadbdaadccdabcbbdacddbaccadccdcdaccdaccbdacabacdbdddcdaadacccdcbabbcaccdcdbcdbcbdabcbdabcdacabbaaddddababcaaaacbacbaababcdccbbdcdadcbadaccdbbbdabbacabbbcbdbdccdcddaacbaccaacdbbbdbcaacbbbbdcadabacaddcdcccbcbbcccaaddaadbbabacbacbddcabcaabacdaabcddbadbbddddbcbaabbbbddbbaaabdabaaccbbbaadaccbcacdabaadcbbcbacbcabadccaabadcaddaadabdcacdbaddbcbcbcdbdbbccacabbbabaccaaccbcbbaddbcaccbccdcdddccaaabacaabdcdabcddcccbcdaddbbddccdadabcbccbdbbcbdddaacdbddadddaddbbaadccdccbcdddbdadbddaabcdcdcdadadcbcabddbdddaaaabdacdbcadccdacdbdbcdddbbddbbcdcdacbdbacabddbcbbcaccbcbbdabcbddbcbacbabcdacaabbccbddbcccccccbdacaaadbadaaaaddcacdbacdbcaccddabcbccbaaacaaacbbdcacbbdbaccdaaabcababdbddbdddaaccadadbdacddaaaabadbdaacaabbcbbddaccabbbbdacbdaaabdbbdccdbcacdcaabcbccaddccdbcbcbcbabbcacdccbbdccdcddadacdcadbbcdaadbdadbccabbdbbbaccbadaabadcbddbaaabadcbcbcccdbcdaaacacacbcbbcbdcbabbdccabdbdbaddadcbbbcacdcbbccdadadbcdaabbdadabbbbddbbcddbdaacabdccabadcdbdcbdadadaccbadabaacbcabdbaabcbbcdccbacbcbbdacccbbdcbbccacbdaabdcacbcbaccabadadaadcdcaaabcacdabbdbbacbcadacaabcaacdabbcbccbbbcabacbbcdbaadcdadccbaccbadcdcdcaacdcaacbbbaadccacaaddacdbdbadbbabbdddcdddccddccbbbbcbdaabdcbadccddaddcdacadbadabcdabcccdabddadddadadcbdcdaabadcdbcabcaacbbcdaddcdbccbdcdbbcaacdcdbbbaaccbdbbdbaadbdbddadaadbdacadddcabcccdbcbabadbacbaadacdbacacbbddbaabaddccbabbdcccccdbadcadccadbdcaacbabbdcabbddcddcbdaabddcbdcbdbbaaaddacccbcabbddaddadbdacdbcacdcabaabacdaacbdbaacacccadcbbbbdcddbdadbbcacbcaabdcacdcdbadacadcdcabddcaacadacdaaabdbbabdadbaaabadadbbabdcaccaaacbdabdbbabdcbdadcddaaaadbabccdcacdbcdbdcccccdcaadacacabbccddcabddcbbcbccaccdcdcccddabbbdbcaabbcadacaadcabbadbbaddcbcadaabbccabccdadcccadacbccbbddbbccbbdcccdcbbdacddcdcadcbcdccaaddcdabacdabcdbcbbcdcbadcaaddaddccaacdcddaddcbbccaadabdbdabddbcadbdcbbddcabccbaabcadcbcadabbbaaabcddcadccccabacdbcdddcccadbcadcbbdaccdbddbacbbbbddabdcbcacdaccdcdcaacccaddadbddabadbaaccaacdabbdbdbaccddbdaddcadddaddbabbbcabbccbddbdcabaadaddadbbdbacacccbcaaaabdadbcdbddbbbccbcddcccdbbcbbabaababbdbdadccabcaadccadabcdacbddabbddbccddacddddbcdaaacdacdbbaadaccacdcbbdbadbddcacccdacaaddbadabbbdbdabaabdadabccacaadaccdbacdcbdcadddcaccdddcaabaccccaaadbdddcdbacddddacddcabaadbbcabdbabcacbcabcdabacbabbbaadcccadadcaadbcddbbdccbcdbddddbdbcdcdabcaaddcbcbaddcbbadabdabcdacadbcbadcbaacadacbcacdbdabbaacddbcabbacdadcdcaccacabdadacadcbabbcdcabaaadabdbaaabbddcdbdbbbcaabcbbdcdcccdddaabbabbbdaacdcabcadcdcbdbbccaadbababddaaacbdcdbcbccaabaccdccaccdcdadaaadaadcdbdacacccdaacabbdacbcbdccdabccccaaadddcdacaabdcabaabcabddcacdbddcddbcacbabbbbcaddccddadaabababdbaaaabcdccddbddadcbcaaadbcbbcadadddccbaadcccabcdbccabbdbacbabbddaaccaaddbbdccbbdbaacaccbdcbabcccdaabccaccadbccdbadccddbcacbcccbbbcadddbddccbcbddabddbcdcdaaadccdbacbacdcbcbdbdbacbbaacaadbdbddacddcddbbaccacdccddbddaaabcaaacadcdacdccacacdbdbbaddaabcdbbcdddadbcbadaabaacdcaadacbdcacbdbabbbaaaccbaaacadaaddbabbbcbdddcccbdaaaadcbaadbbcadcbcbccbdadadadadaddabbbaabbaaabacccdbcbddbbcaaddcdcbacbdddcbccbaaddaacdcdabaacddccaaddbdaaddbdbbabbbbacccddcaacaabcdaaccadccddbacacaadbaddbdbccbadbccdbcdbcbbbacdbadaaaccbcccbbcaccdacdcabcddcbbccccaadabcdccaaadbcbcdccababcbbcdaabccadbbbdacbcbdabbcbcaacbcdbdbbababadccacdabcbbacaaabaccddbbdcaadbdabacabacdaacaacaddbcaaccdbbabadcbbdcdcbbcaabcadcbbdabdcdbdddacabdcddadcddcbacbdccddadbcabbcacddabcdbbbbabadcdbddbccadbbcdcbcbbbaccdbdbccdadadbcdcdacddbdaacbaabbccdcbccbdbbccadcaadbcabdcabdbdbbcbdbbbcccbcaabcdbcbdcbdbbbcccbaaddddddbadcbcccbacacbbdbdcabcdbcabcabdaaabcdccdbbcaadcbdbdbbbcadabdcbaaccaabadcdadacbabbcddbbddcbaabbbccaabacbdccacbcaadbcbbbacbcdacddbcdcbdcadababdabadbcbbbabddcaddccacabbcccbccaaadaddbdaadbbbcbbbccbadddbcddacdacccaadcbcbadddaddcddddabdbbacadccddacdcdcadbdcacaacccddddabdabbacbdabcaaddaacdbadbbdadbbaadacaccdcdccabccccbaaddadcbddbdacaaabccacdbcbbdababcddcbbbaaabbdccbbbdacaabdbdcacacbaccdccbddbcbcbaabcddbaccdcddddacbadccbcdcbdbcbdbacccbdccbddcdbdcaacbbbdccbcadbbabcbbbbbadcaacaadcabbdcbcaabbdddbabaacbaddabbdcdcdbaadabcbdbdbbaccadcdcbbcdabbccaabdbccaccdbadadbbcadcaabbacdbabbbdcadcbbbcbbdbddbacbcddaadbcccbcaabbbddcbadcbbbdbbbdcacbcdbbbbccccdcaddadddadcadacacdbbbddaaabdaacbaaccaacbbdaaddbddabbaabcddddaacaacabcbacbdcccdaadbbcdbdabccadabcbaaadaaabdbadaabccacbcabcdadaacbdbbaadcaddadbcbbbddbdaaababbddbdadadcdbbaacdcdacadadabbcbdabcacdaddccaacdbcbcadcabbbbcdbdcbaadccbbddbaddcadcbdacccbabadabbbcccabcdcdcaabbbcacbdaaddddbdcacbcaaddccdabaabaadcdacbcaadcbabbdabdcdaadabbcdabcabaacccbdcdddcaaabbcacdcbaaadddbaaadddcdbaacbdbbdbddadcbaaddadaccbbdbadcdcaaadddadbabdcbbaccadddbcccdcbbddbadaccdccdcbacddacdcacdacdbababaccddcbddddbccdacacabdddddddbbbbdcaccbcaaabbbccccacdcadbbabcaadaaaadbbaaacccdcbccbdcccadabdbabcacabdabdbadcacadcacdabcdcddbabcabcabdccdddccccacacbddadbbbdbadbccbaacaaddddbcbdbbdacbadbbcbbbcbcaadcacaccbcbccdddbbdcbbdbdddbdadcacdcbbccdbaabccdaccbccaacaabbadacdacdacccacdaacdabbdacadcdbcadbccbbbddcaabbcdcabbcbaadbbabdadbdabacdccdbdcdcbdcbcdadbdbddbccadaadcdbcccaddadaabdbcaddcacabdaccbbacccaadcdbcabdabddbccdcbabababccbdadaabbdbddcabbdcabddbaddddcdabbaadddddbcbdadcabcbcaddaacacbabbbbacdbcbabcdacaaaabcaabbacacbbdcbbacbbcabdcbdcdacdacabbabbddbcacabadacccbadabdadaddabbdabcbcbdacdcdbcccbcbacbbabbbabaccdacadadcdadbdacacbcbdcdcbccdbdbbababdbbdbbdcbadcaccccaacbdabacccaaadbdccdcbddcbaaaadbabbcddcddcccabbbccabbbcaaadbcadabdabdcabaaadbdcaccbdcaaccbacbbdbabacbbcabadbbcadcaacacacbddccaddccbbcbdadaaacaadabcabdacacbacbcdcacbbdcccbbccabcaaccddccdcacacadbbcbbaccaabbaddbaddbcdcbddddbadabccbddbdbacdccaadcbaccccbdcbbaccdbdcccbaaaaccbcdbacbaaabbaaaccadacabcabcdaccddccbdbbbccbdbbadcbadccdcccacdcabaccddabcbdcaacbbccadaccddccaabdcbadbcbaddaacddacbbaccddddddbcabccabcccdaddcbdaaadcabccccadadbadbbbbabccdacacdcbbdcbcacdbdadcddcabdcacbbdbcadcdbbababddddbbcdcadcabbbccbbbdcadaccdbaddbcbbdcaaacabdbabadbbaaaaccdddadbcacaabbaaccdbaacbbbcbaccdbccdbbdccddbcadabccccbbacaadcdddadddabdbabdddbabbbcdcbbbaacbdcbcbbbdbdcadacbdddddabcbcdbaadadacdaadbbacdadcabdbbdbddbdcacbbbabacbcdaddaadbbbdacadcccdbababbbcadaadacbdbdacacbaabbacbadacbbbbccccccbdaadcbbbcbcbabbadbcdaadccbaabaadacdccbcdbccbddcbdddccadbbdcddbbcdddccaabdaccbacbdcabccaaabccaaabdbbbacbbaadadcaadbdbcbbcbdadbcccaaddddbbbbcadcbbbdbbbcbabcccbdbdcadcadaaadbabaadaaacdabbaddcacaacddbcdaacbdbdadcbccaddaadccdadcbbdcdcdcccaacdccabdcaccdadddaddbbbabdbbdccaccacdcbdbbccacbaabcddacbaabacccccbdacbcdbadbadcccdddaaddadbcabccccadcacaaadcbdddbcbbcacabbdcbccaaadcbbdbadbddabbadbdddcdcdcccacdbdaabcbcbaaccdadcdbabadcdccdddcddabacbadccbaabbbcacaccacdcdccdbaabcadccbccdbcdacddacbcdaabbaacbcdcaaabddadcbbdcbbacbadbccdaccccbcaadacdabdaaacaaacaaabddbdaacbbcdccbbbcabccadabbccdccaaddadbcabdccaacdbabdcbdbabddacaabdcacdabcdcddcdcddbcbcaabdbabcaabdcbaabbcaccddcddcadcaaabacbcdbbbcabbdaabcbbcacdadaacbdbcddaacbcbbbabdbbadbaacbbadcadccbabcdcacadadaadccbdcccadcadaacdcbdbdcadcababdaacacdcbdabacddddadcdbbcdbcabcddddbdaadadbdabddbaadadbbbbccdaabacacdcccdabaddbdbcdbbaccbaadbbcbacdbdacaaddbcacbbcbcaaadaadcdcdaaaabbddddcbacaddbdbcddcdcabbdabcbdcaabddcbcabdabcacbadddcbdbacddccbbdddadbdadabaccaddabaabdaccabcdbbbcbbcaaadbaaccddbbaadadbbcccbcabdaadabcbdcaacccaabccddbbaacadabcbbdacdaaadcabbccacbbbdadbcababdccbdbbbcadbaabacdabbabaabacbbabababddaabccacbacdbbcbcbacdcabccddbbbdadddadccdacddacdbdaccbdaacdcdbdcbcaaaabcdadcaadcadbabbdacbbbaddcaabadccdcddbabccbddcdadacbcdcbcaccacbbcddbdbaaabadcbabbbddbabaadcacbababcacaacabcdbbcdbcdacddbdddbbcdbaadacaacaaadcdcbabaadcbdbdcddbbbacbbabbddacbbbacddabbdbcbccdbbccbdccdabacbcdaaabcbdbbccbaaddbaabcaabccadccddacbdccabddbccccbdcdacdbadcddcbddacccbcbdacdbdbbbacabaddddabcbcdddbbadcccbaaadacbabaddbdbdacccabaaccccdabcccddccdbbdcacbcdadcbdabbabaaabbbabcabacabbabbcdcdaacaccadabbadcacdddaacdbdbbbcbdcbdcccbabadabcacdacbdcbbadaadcabcdcabddcdbdbabacccddbabdccbdabbdbadbbcccbaaabdcaaaacbbcbdcbacacbaaaddacbdddbbabbcdaddbbbdacccadaccbbcbdcabdbbcccacbaaddaabdccaddcdadccaadaadabacabdbcbabcabadbccbcaababbaccddbcababadcaccabdbcacbcaccacbbadacdccbcaaaadcdbcadddadabcadacaccababcabbcadcbbbabdacdcdddcadcadbccdcbcbcdbdcdcbbdcdccddcdaccbbcdaaddcbabbcaababaccacddcbcccbacbcddaacbcadbacdcdbbaccdacddcadcaabbadbddbdccacbcdabdddcacddaabdabcbbcaabdbdadcbabdcadabcbbbbabcdddcadbcadddbdcbbcdacdddcddbdcdbdcdadbddddadaacbcccbbaaabcadabcbaabbabcbacbddcddaacdaddadccbcdbddbcbdddbbcaadbaccccddaadadcbabcbabddbbdbddddcadcbbbdcdbbcbcdcaabbdbdabdcdbdacabbccaabbabbccacdadacdbcbdacbcdbccbccdabcdcccdcbdbaddbabbaabddbadaabdcdabaddaabdcabaaadccccddbcdacabddabacadbaabacaaccdaacaadbacbddddabcbdcbdcdcdaccbbccadcccbadbaddadcaddcabcbbacdbbdaccaacddcdacacaadacbdcdccbcdcdbdabbbbdadbbbdacdaaaccccbcabdcdbdbaddbdaabcdddccccaccbbcccbddacbbdcdbddbbadbbbcabbbbbdbdcbbdcdacdcddadcaaacbdddddddcdcddbdcabadacdabbcdbbdbddccdadabbdadbcccbcacdcddcacdcbcabdabbaaabbcbdadacdbccbddcaccccbbabadadacdcacdbbccacdbbccbadabcdadccadcdbabcbcbbddaaadbdddaaddadcdacccbccbaabdddcbaaccbbcdcbcccbaddaaadccacacbaabcaddcabbdddbbcaccdbbcbaaaaaddcbdcbaaacbdbbaacbdaccabddbddbbcbcaadbcaacbabacdcacdcdbacacccaaaaacdbdaadabdbababacccddadadbccaabbccbbcccaabcdadbaabddcbdbabbacacacabbbbabdbddacadcdcadbbcdcbacbcddbcbddaadcbcbcdacdbabbacccdacdcabdcddadcbabcdbcbcbcaabcdcabccadbdcccaaccbcddbadbacbaadaacdabdaadacbcaddbcaadcdbadcbabcbdbcabcbcbcdbcbcdaddabdcdaddabaabdaabcbdccadaadbcbdbbcdcabbaccdbcadacbdbcddbbdccaccabcbacbbacdcdbdccbcbadcbcbccdacdadbcdadabacdddbcdbcdcddcbcccdcbaccbddbcabadcdbdcccbdabdadbadadaaddabcdcbdbbbdccaddaddcaaccdacbcacadcaabaaabacbcbbbcbbcbddddadbccadbddacdbddcaccabacadaccaaddccccdaaadcadbdbbaaaadbabacdcdbacbabbbbadcabbbbcdbdababccacdbdadbcbcacdacadbbaadbbdacbabdbbacaadcdabddaacddcabcdbacbdcaaccbccdcbaddccabadcbabcbadabbcddcbcbcacaaabbaaaccdcacacbbbddbabaddaaadacbacadddacdaccacacccaddbcdacbcbbadbdaadaabcbcdadcabcabbcaaaacaddcabadacaacbabadcacbbbdababcdbaccadadcbbcdcdacdcadddbdccabccdadaabdccaacadbccdbaadbcbbcbbdbbcbcbbadcbabcaddcadbccdbcdaaaddabaacdbcdcdddcbbbddadbcdbcbdcadaabdcaacdbbdcbcddbacbaacaabccbccbbacddcbcacabdcbaadcbddadaabaacbaacbcaacabaadaddbbddbbcacacadcbacbbabcddcabdbcabbcdcccaddaacbdbccacaddadbcdcbcabdbbcbcbdbbbbbbcadcdcdddaacbbabcaaabcadaacdbdddddbccdcbdddddaaccdbdbcabddbbcbdbcbacdcbdacbdbacbccacaddabbacbadabddcdcbcabdcbbcbdbaaaccddbbdcdcaddcadacdabacaabcdcdadabdbbaacbbccaaccddcddadbdaaaccbaabadadddabbcbdccacabaccbcbccadcccbccdbddaaadacadddaccdcbcabcabbdbaaaddacccaaaadbbcabbbddcbcddacccdddbcbbacddddababbaccccabcaadaabbbddcabddcaddbabdcbcdacbcbccbacbdbbacccdbbddccdacdbbbacbbdbbbacacccadabbbcdccdcccaccbbacadcbaabbcdcbacbbdbaddaacddcadaadbdaddbacbdaaddabdbcbdbcccccdadaddbdbabaddcbbadadadadbcdacbaabcdddcabadddcaacdbbcdcabbccabcdbabbcdbcacaacdacdccdbccbbbbacadbdabbcbcabbcdacbccdcbcaabacbbdadcadaadbdadccadbbdccdbcadcbbdbbdcaddbccbbccadaccddacacdaadcdabcacbabacadaadcadbadaababbbdabacbddcadcacddbdaccdbdaadadaccaaddaabaccadbccacacbdcbcdbaacdbacbcbdadaaddadabcdaddbbbabbbbccdbbbbdadcacbbbddcbcdaccbbbccbdbabcbdcdddacaabcdbababbbbbcbbcdabddadadaddbccdcdccbcdccbbdcadcdbbbcdcbacdbcdcccaddccdacdbaacbcacbbbbdbaccbdbdbbdabbdbcabcdcbacccbcaabdcccbccddcdacaaabdbcbabaababcbdccbccbadddcbcdbbacadadbcdcbdbbcdaacddaccacabcccadabcadadbccaccaccdcdbccadbcacdbdddadcbbddbbbbdbdcddccbdcaaccddbbbcbddcbcaabbacdabbaabbcabacdbacbccdbdbabcdbdabdbabdaccbdcaadaaaadabcccddbcaccdcaddbadcdbdcdcdcccacbdcbdaaccbacacdbabdacbcdcddcdccdcababcabbcdccdadcccdaabdadadbdddcdaacaaaacaaaaacdabbaaacaccddbbdcaaccdbbbaababaaadacbdbaacdabbadddcbbacdaabbbddbadbddbccbacbcbbdcbbbdcdbbaaadaaaaacdddaaddccbadcacddabdacdcadbbadaddabcaacbdcdcaacbccdacccccbbccbddcaaadaccacbbabcbaadbbcdabadbccaaacbaccbbbaccadabbbcdabdddcaccbbcbdaccbabbacddcabadddccdabcbbaabacadadbbdddaadcddbcdcccbdccaaccacddbbbcdccaaccbdabccadddccabdbcbadaaddbcbbdabbccbbabdccababdccdcaddbdcbdcaccccaaaaacccaddccdccccaabcbbdccacdacaacadcccacacccaddabbcaaabcbccbdcacbcdccccaabbcbddcdabaccadaacababaaadbaaddaaaaabaabddbbadddadddcbdbdadccdddbdddbdbcdaadbdabbddadbdbacccbaddabddadbaabcbaddcccdcddbbdbccaadcacabdddaaccbddddbadaddbaadaadbaadcaccbdbbbadccdcdcbbaabcdccacdbdaadbcbcabbdcadabdddbcaaddbdbdbbdbdacbcdababbcdaabaabdcdaadbdcdaacdbdbdcaabbcacbcdbcacdcbccccdbdbbaaadbcdbdcdcbbacccdbbbbacacaabdccaabadaaccdbcccacabaadbadbaacbbadadbccbbcaccdcdaabdacbdbacdaaacdadcbddddcaadcbdcadcacbcdbacdccdaadababcdbddabdabdadcbcbbbbddddadaaacdbadcbdacbcabbcdadbbbabcdcabdccbdcdccdaaadccaabaaabcababdddacddccaabaabcdcadbadbdccbabadabadabdacdcabadadcccbbbcbcbadadcbbbcbcacaacdccdadbbbcccbbaaadabcbbcccbbaaabccaabdabbcdccddddcabdacbdbbbacccdbcbdbdccdcabbbcdadbbdcdcddddbccdbdaddbccadadcacbddadaddbdaaaaccdaaddadbdccbdcadaadadbbcacbcaabcdbbbabaccdcdbbcaadbacdbcdaabdcbaccbabcadcabacdbccaccdadbcadcdcacadccdcbadcabbcaaadcabadbbcbcbbaaaadccccbbbdacdbcdadcbcdccadabccddcbaabcbdabcdbdbdabbaccdcbdbbabddcbbbcdbcddaaacacbaccbdcddaacbabccbccabaacbbbcdcdcbdbabcabadccadacadbadbcddbdadbdbddcccacbbdcacadbacdcacddacaadcdcaadbabdbdabdcabcdbdabbddbbacacbaaadcaddbdcaaacbcaddbcaadcccbacbaaacbbcbbabacdaadaabacbcabcccacabaaadabdacaddabbccadabaaacdddaacaabbddbbbdaacbbadabbddaaccdacbbcbbadabbdddcddcccdbcbaaacbacdabcccdbacdaddbdccabbaacdbbbdbcddaaaaddcbcabbbddcddaccddcccdaaaddbbcbbbaacacbcbbcaadaaaccacabbbddabdccbccbaaaaabacdaadcacadbdbbacbdbccdabaaccbccbababaabcdbbcbdddcaaddacdbbacbdddbdaaaddabbdbabdcdaadadbcdabbcabacccaddababcdbbcbcaabcdbabadbaabdbaabcbabcdcbacbaaccaaacaaaccbdaaccacbaabadbbdcddbabbdabaacbdcbbbaaaaacadbbadaacabddcbabbbbbbdddbababdcbcacaacdcacbcbcdadbbdcccbcdcadaaaacccbbbbdddcccacdcbdccbadccdccdbcdccbdbcccdbabddadbdcdbdcadcdbccdddaabbcacbbaddccbbdabdcbacacdbabbabccaabbbacccdcbadadadbccddcbaaccadbbcccdcbdcabbaacccbabbcabacbaadabdddbbbbdcabacccadbaccdbaabbcccaccbccbdddbaadacaaddcaabaaaaddbbddadbbacccbdbcdcdbabdddadcdccbcadabbacadcbdabaabbccbbaaabbbabcadadacdadbdbcabcdaddccabcdadcdccdcdacadbbadacadcbcbdadacbaaaddbbbbbcdaaadcabddbdadcdcaaacbbcacdbdabaaaaabccddbbdbddadaadacaccdadababababaccdadcadbcbdcdcbbcabbcabcdbcaddabbccbbcaccbababcbdacbabbdbccdaadcaaacbdaaadccdbdccdccbbabdadabdaabdddbdadddbbcdbabdcbbcbddbcaddabaaaadaacadbbbddcdbdbcdcdacaaabaaaabcccabacdddaaacadbbbbcdbbccbabcbdaccbcacbddcbadbbadbbbcbaaaddbbbaccabdccadcdcaadddddcbcbadbbdccaacacbabbdbacabababdadadddaaaaccdbbcbdadccaadcabbdbdcdcadaaacccdaadcddbaadbdcadcdadcdaababdcaabaaabadaabcbdcabbcbdbbcbbbabddcdcdaaabbbcaadabbdbccdbbabdbadabbddbccbabbccabcacccbacabaadacabbaaabdadbbdacbddacccdddabcbabcbaadbaacddbadabadccababcbaaccdaaacdbacaabbccdccbcadbbcdaddbcacddbabcbcabaabaabdcddcacaabaccacabcacabdcbdcccbbbcbabbdbcddbabbabaabddabcbaadbdbdabbbdbcaadacbdddbcadacaccbaabaddddbbcadaabdaccdbcbcdcaaacdcdddadddddacdcdcdcaaacdccbcdabbdaaacacccabdccbddbdcbdcbdcbcabdabcdacaabddabcadbbbbcbaabcabbcaaaccabcbbcacbdcddccdaddadcabbadadadaccdbbdcccbacdbcbbbddccaadacbdaddcddbbbbddbccabbddddacdbadbbacdbbbcaddbbabcddcdbbdcabaacacaababbbbdbdddabcaaadbbbdcacaabcbbbacdadbbaabbbadccdddbcbbddbdabbaabcbbdadccaabdbbcddacdcaddcacabcabcabbbcbdbcdbacdbbbaaddbccabdcabaaccbbbcacdabbbccdacbdbbcaccbcbbaabcaadddddbcddcdddabdbdadabadccadcbddabcacccabdabbdaadbdabaadccbcbacbabbdbaddcadddcdddaabdcabcacdcbbcccaadbbcbdbaadabdbbacbabcbddbdcbdcadccacabcbdacdbddbaccbacacabcccdcdbaadacddaaaaccbbcddabbaddcddcaaacbbdbcbdcdbbbbcbacaadcaaadaddacbbabccaabdbaddcacccbaaadcacbaacadbcdbdbcdadccddcdabaabaadcbdcabdbcbcddcdabaadabdcdcdbddbcdbccddaaddbbcbbbbccacddbdbcdacbacdccadacdccbccdcbbddadbdcaaabcabddbdcdcaccbaacbbdcaacaaacaadacbdaabcbbabadadacbbaaaacbbabbddaccabddaaaccbbadabbbcdddbadcccdadbabbdbbcabaacbcaaccccdadbccccbdbaaccbbaddadddaaddadcdbdddaccdbdbbcdcaabcdddbadaadbdcdadccabcddbaccdbaaddcaabbcccccccbacccaabbcaabacccdccdadddaadbcacdadbcababcadcdbababacdabcbcccbdbacadccdabadcbdaadaacdcdbdbdbbbabdccdcabacaddccdbcdcbaaaadddaadbdbccddbcdcadadbcacddddbabbbcabbdccbadbbdcabadccabdbcacddabbcccddbbadbbcbdabcccdddcdbdabbacbdbaccbaadbdbbabccabdbdccccbbcdbadaaadcbdbbabccdcdabbabbacddcbcbdbadcaccbcabcdccaacabadddbddadcddbbadbbabcbaaacbdbdaddbaacabdbbcbaabcbadbcdcddabbdcbbccdadadaaadcbbdadacccabdcdadbbdcbccaacdddbccabcadcacadadaabababcdddcabadcadcacabcbccdbcbbbcadccddacccdbaadcbdbdcbbcbccbcbbcadbbcdcbdacddcbddadacdbbdaacadabbdbdcbadaadddbaacbdcaabccaabdabdbacabdddbbdbdcbaaadccbbdcbdbdadbaababcbbbdbdccbbaccabbdcdddccaadddbdbabaaccaaabaccaaabdaaadbcabaacaaacccbdaadbaddbaddcaabbdaccacdaccbbbacbccabbbaadcbdcbdcabccbacddbdbbbbbddbbabaaddccabbbbbccbaaaacdabadbbbbdcadacbdccdabbcacadbbdbbbdbabcbbadabbadcddbdccabdaadcdcbabbbbacdbaccbaacddcdccdabbbaaabdbababbdcdaddbacdacaabddcbabbadcadcabbcacaabadbcaaabcaccbaadddabdbdcdbbbacdbadddccbddccdcdcabaaadcddccdaccbcbbcbbddadbcdbdbdcdacacdbdadadbabccbaccacddccdbcaddbcdbbcbbbacdcbddbbabacbcdcacccbcdbcdcabbbabbdddacbdbacccdacdcacacabcbcabbbdcbbbdbbccdbddbcccbcabcdadbaabaccbacdadbccdabcaacbaadadcadccddcdabdacddbbaabdabbdccdbcdaaddadbdbbdadbcdbcccddbaadccabcbaccbbcdabbcbbdbaccbddbcacdccadccadbbbbcbaaaacadabcbdcaccadbdcbddacadabdcdaabbbdaaacdbaadaabbdadcababbbdbdccbdcdddbabddccccbbadabcaccbadbbabcdddcaacbbdacccdaaaaccdacdaadbccdabdabacddbcaabacccdadbabdcaacddbbbdadacbcaccabbbcdcbdbcacdacdbacbdbdacccbdbabdbcabcbbccdcadbcdcdaadbaacbbddbabddccccbbcbdbcaaaacbbcaababdbbbcaabdcddbdbbbbacadaadaccccaaccbbadcabdddadbabcdbcabccbaaaadabbccacbcaabacbacacaccddbbcaccadbbacdcbdbccccaaddcbbdaccddaaaabdcbacdcaabcccabdacddbdacdcabbbcddaaaabcddbbcbaaacccbdaaddbadddccbcdcdccadcadbccabcabcacdbccbbcaadadcdbbadcbbbbdccadabbbdacbbdbcbababcccababdddbdbdbdbcbabbcaabcddcdbbdbdadbccbbaddadcaacdbbcaabdcaddaaacbbbaacbabdacadabdadabbcbabaddacbccaabcbadcdcbbbbbdbcdbaadcadcaadabcbdbbbbdcdbdbcadaaacaaaababddbcbcacbbcdcbbdcdcadcdacababdaabbdbdabddbdbbcbcabcaddbccbbaddaadabdbbacdbddadddbaccbbadccdacbadacccadcddcbbdcdcccdababbabadcdabaabbdbddcdcdbdcccbcdcddcbbbcbcbbcbdcbaacbaabbcccaacbadbbdcacbccaacbbbbdbbbbbcbdbbabdcaaccadadaddbbcdbccacbccbddbaccadcdcccadbaacdbbacccaccccccccaacdddbdbbadbbaadabddcdbbbbdcaabbdbcbdddbcbbcbbdaadcaccacdadbacdccdcdbbcabadccddcdbdddbabaabdddaabbacaaccdbadddadaacbcabcdbccdbbbcbdacabdbcadccbcbdbdbccbbcdabcbcdbbcabadabdcddabdbdcbcdddacbddcabacdadbdacbadbbddbbdccddacbadcbacbcbdccbcbcbcdadbaabdbbccabadabcbbccabcddcdcddbcbacbddbbdaababbdccaaabcdbbcddcdbbdadbacbaabcbbcdcaadbbddbaadbbcbcadbbadbbbbcdbbddabaadbaddcddbdaadaabdcbcdbdabdaddcdcdadadacdcbabbbddbdaacbcdaaacdbdddabdcbdccadbbdcaddcadcdadccdbaddbccbdbdcbbbcabbdcabbdccbcddcddcbbbacddcdcacdbcaacdaddacabdddbbddccaccabaaddbbcbbddcbcdcdabddccacadccbbddddbdcdaddbcdacbabacdadbdacbcccbbcbbdaacdbddadbcadaaabdbbacbbdcdadbadcbbbaaccdbcaadcadcbdaadddcbacdddbdbadbaabddbdccdbabbcdacdcdaccabdbdadcddcdacacdddbbbcdabcaddaccdbdbdcacacccadadcbccddbbabbbbbbdbccddadbabcbbaabdcccdcacdddabbccadcccabcbbdaccdbacbaabcacaddbcacabaacbababcbdcbababcbbaddbccdddccabdbaadcdacddcccadaadaabdaccbddabbdbbacacdccaaabdacbbaabcbcacaccdbdcdaddbbaddaaddbdbdcabccdccabadbbcaacbaccabddaddbcbdbaccccaccdacbddcbddcdcabdbdddcaabcdabaabadbdccabcbadaccccaaccdcaadabdbabaacbaddbadabbdddbcbbbddabbbabddccddcdbcdbdcbbadbddcbbcdcababaadbccdccccccccbccdcdadcccaccdbcdcdbcddadadbcddcdbbdabcbaaaabcbccbbababdcbbdcbdcddaaccabcdcbdacbccbbabbbccaddbbaddabaaddddcbcddabbdadbbadbcadbabcbbcacccadabaadcdcbabcccaabdbcacaaacddcdbdbcadabcabbdcbccaccbdbcbdbcadacbabdbaabddcacdabcbaaaaddaabdcddaadbaababdacdcaddcdbcdcdaaaaccbcaccacadabcdcbcabacbbcaaccbdadabcdcdbbbbccdbccdbabddddaacbdaddacbbadbdcabaccdacdcdccabbdbdabbbdbddddcacbbbdbdcaaadccaccdccabbadcdccacbabddbdacbdacabbdaccbadcdcbbacaaadacdbccbcdbadcdcacbcdbbdcbdbdbdaadaadcaaabcbcbcaadcddadcbdbbdcccbbbcbccdbbaaddbcadcadaabbacdbcccbdbddaccbdadcadbdaaaacbaabacabacbdadcdccbacccacbacdbbbcbccbcdbdabbdcddcaacadbcbaabbbaaabdcacbadbdcbcbcbabadcdabcabbbdccbacdadcacbcabcabbdddadddbdcdbcbbcbcdbcbcaccacadacdaadcdbbccbcdbaabddcdccbbbdcaaadcbbbcdcacdaadbadbcbbccbaacacdbcccbdcbdccbcbbdbddbaaaaddbabaaddadbdabdcaadddcabcbbdbdacabdabdbbcabbbbcbbcaabbcdcaddaadbbcaccbdaccdcabcbbddadbbabcaaccdbaabaaaababdaccbcddcbbabdacaaccbccdcadabbabccacdbadaabbbddbbbadabddccdcbbdccbaacdacacabcdcdbdcddcccbbcbabcadcabbadbdbabccdbadadabbcacdbcadabdccdddadacddacccbadcbabbdaaadcbababcadaacddbcbcdbddbbddccccddcbadcabbcbddbccaccaaccccdddbdbddcaadddabcabbbcccbbabaaccadbbbdbbddabcbacbbdbbccddcadcabcabdbddaabacdbbdbdcbbcacbbbcdaccbabcaddbbabdaabacabcdbaabdccddbbccdcadbddcbccdbdcadacdbaaabaabbadbcbbaddcaabbcdbdbadccccdddddabbbadccbcdbccbbbbbbdbbbacdacdbbdcaabbadadbccacddbaacdbcaddbdcdbcaadbccbacbababcbababaddaadbbadcddaddbcbbcdccdbcdabccddbcdcabcbcabaacdcbcbacbbadaacacacbacdabddabbcbcadcbddaadcbdcdaccacbcdddaadbbcddadddcdcdbdabcdcccadddacddacbaaccccadddccaacdbdaadbbbbdbbdbdddbbdddcbddbcdccddbacbbcabaadcbaaccbadbcaaaddbbccacccbbcddbacbdadddcccaaccadacbdacbdbcbccabbbbbbccabccadddadbbbccbcbcabcdadaabbcabdcddcdbcabaccacbccabaaccaadbdabbcbcbadbccdbabbabccaaccbadbcdcaaccdbbadccdabdbcadadcabaadddadcabddcbbcddadcbbabdcddbbaadaaddadaabbcdadbaaaccddcbacadabaabcbcaaddcababccbadcdbcdbbdcdcacbcdabcdadccbacddababcdabbdababbbaccdcabdccabdabdddbbcbddaddccdaccbdcbbbaccdbbdbacbbbcdbaddcdddacbdabaaadcccccbdabdabdadadcbcabcbaddbdcacbcacdcaababccaaadcbddbabbaddcdbaccccdcbbcdacbdacdacadcacaddcadbdaabdcccababddbbcccdbacadcbdccbaadcbccdddaadcaadbddbdadabbdabcbdcdcbdaadcdccabdabaaababaacbdbabdadacadbdabbcabccbbdbcadadbacdacdacddbbbdddcdbacdaabcdaadccacabcdccabdaacabbadacddddcbdbbcdaabddcaddacdabbbacbccdbadcdcabbaaccddbccbddcbbdccdbbaccacabcabaabbbcbaadaadbbadbacddbcbddaadabbdbbbbabcbbabbccddcaadabdccaacbaddadccbdddccabcaacccacdadacabcbdaadbddcabbccbdbcddcbdacabdacacbbddcaabbdcabddbddcbcbabcbdabbddcaabcbcbcacdaccccacdcacacccddbadadccdddcbacbdcbadcdaabdbdbbaabadcdbbcdcbaababcbdaddbabcacdbcdadccdbcaadaacbbdbbcbbdbcbacacbcdadacabcacbabdccabccddcbdbbbcaaddccdadaaadcdcbccaacdbcdcdcdbdbabdbbdbccddcbcbadbabcabdbadacbbcccdbadacddbaabddbcbcccdbdccabadaddcdbdcbacbadcbadbdddbaabbdbaaaadcabaabcdaabcabbbcbcabcaadbdddbaddabdbaccdbbdbccbdbdadaacbbbdcdbbbadacdcdbdbcdacaadacdbdaccbdddcbddcdcabcccabacaacdbcabbdddddbdabdccabdcbcabcdcdacdddbccbdbbcbbbdcbccddcccacabaabcdbadabddaabdabacbccddbcbacaabdbabacaadcacdccdccbddbdddbccbdbaacbcdbabcdabbcbddddcdbddaacadcccadcbabcbabaabbcdadaaacdbdabbbaccacacdcbcdaadcbabbaadbddcddcabbccddaabbbbbbbbccdcbabbcdcddccbaabdccbabcbacbcdccdbacaaacaccddabdaacdcaaacdbddbbbddbdbadabdbadbacbbcaacaacccabcadcdbcdbadcbbbadccbabdcaabcabcaccccccbcabadccdbdaddcdbcacbcdcaadcaccaaddbddadacbadcbacaddcdbaabcadbbadbdbdadbdbdbbdaaacbcadbcbdcbbabccbdaacadaaddbddacdabacbcacadddabbbbdabadaadabadccdaaaabbcbcbbdcdaadacdabdcacaabddccadddcccdcdaaadbddacdaacadcbdaaacddbccbaabdadcccbcbcbabacddbdcadbcdabdabddcaacbccdcdddbbbbcaacaacdcdcbcdbcaadabbacabdabcabbbdcbbbbddabbabaccbccabbccbbcddbcbddcaabdbbbddacdccaabbbdcabbdadbabbcddadabbbbabdacbcbdbdabaadcddacddcdddaaabbcabbbbacdddbcbdbdcadacdbdbbabcdbcaaaabcdbaadaaaacdddcbbabbcabcdaabcdbbdcbadcdbbbddacbcdcaaaabbbdbbccadcadcbbcdaadcddacdaabcbacddddaaccdbccaccdccbbcddadcbcbdcddbabbbdbbdaadbdaabcccaaabbbaadbdbcbabbaadcbbbbcdbdcaabadbdcdbcadcdaaababbcabccdbadbacccbbadcbaaaabbcacddaadbccdcdccdaccbaacbdddabcdadacbcccdbbcbadcbabcadbbbddbcaacdbabbcbdbaddacacaadcdcbbadabababadaaabbadabbdbaaaccacbaccccaccbdbbacadcdcbbacadadaabccbabaacdccbbbcbddcbbccdccbdcccddaaddacbabcbcbdddcddabdbdbdbcddcccdccacbbdbdbaadbbddccbbcabcabcacadbaadadabcdbcbacabdcdddabbacabbbbaaccabcbbcabbbdacccdccddccbabbbccbaaaaaabddacbbabcddddadcabcbabdadcdbdaadcbddabaaadaabccbaadcabddacddaacbabcdbdbdddcbcccccaacdcccbbdddacaabacdbbbbbabdadacdacdaabdbbbcbcbcaccdccbbdabbbcaaaadbcbacdbdcdabcacbccddddddbcaadcdadcbdccbdbddaaadadabaabcdcddabcbbbaddcddaadbacdbadbbbbbcdbbbdbbdadccadddababaadcdbdbacdcbcbccaadacbadbbdcaadccbccbdddadcbbbbbaddabcbbcacbcdbdcbabacaacbdacdacbbbaaadcccddaacbdabaacaacaddccbcccaacdabbcdadccccbcadbabbbbdddacdbbbaadbadabccddabbadadddcbadadcadcaabdaadddcdcdadacddbaaabdbdacdbaddddacdaacabaaddbadcbcacbbccbdcaacbadcdbdadacdbababadbbbbbdbabcdccacdcabbdaccbcdabdadcadccdcbbacbbaacdacbaccdbdaabaddbcccaabdcdacdcaccdcaaddcbcacbbcccccdbddcaabbcccbdbdaacabdcdddadcbcabbddcabccbacdccbddbadcaadcddadaabadbccbcbbcacbdacbcabdcccbabdbcbcadcccacaadddcacbdadbcbbbbcadadbccbabbbdddbcaabdddddcaabaabacdbabbccddbabcdcccdbacadbbccbbbaabddbccccbdcbaabbccabadababababadbadacacbaadbacdddcaadaaadbcddbddcbacdcbbdbcbccabcccdaabaddcbbcacdcbccdcbccabdbacbbcadddcdcdddacdbbabdcacdbdadabbccbdbdaaadcddbcaabaacbabdcbabbdaacabdcdabcaabbadadccaacbabdacbdbcadcaddbadcbdbaacdbcccacdccabdabbbddddddddcabbbdbcaabdaddaacbadcddcbbdaddaadcabaccddabdabdaabcabacbadadabdccccabcbaabbacabbdacbddcccdadcbdbbbdbbcccbabbbdcbdadddcacbcdaadaaadcbccabcdbbcdacacadabbcadacdbccdaaccbbaaccbdcadcabbbddcddacabdadbaccddbcaaccbbaaccddcaacddabaccbabadcbadbadcbcaaacbabcaccddcbbadbbdbaacbccdcccbbacbbbcdccccdaddccbccddccddccaaddddabddddbdbbbbabdcbadbcdbdcadbbcacabadbaadcccddbddccadaacbccdcccbcbaccbdcddbbacdabcadbcbabdabcccadccdcbccbabdbccdddacbdddacdaabbcaabadcdcacacaadbabcdccdddababadcdbccbccaabadabcddbbbbdadbcaccacadabccadbcacdcbcdcddcacbbcdbddbbacdbbbdbaacbbaadbcddbbabbbabbcaabdabddcdcaabdccbbdcdcbbadbcbccabbdbdadabaacbaddabacccaccddcdcbccccbbcccdbadddbabbdcbabacaadccadcccbdbbdcbcbcbaacdbcbacdacbdccccbaabbcabcaacccdaacbdbcbbbaadbdcadcbddabaccccdccbddbddccadabdaaadaabbdadccbadbbbbdcbcbbdbbdbbadabcdbbcaabaacadcadabbdaadbacdddddbcacdaabdbbabaabcacacbdddaaccdabdbcabcbadccddacdbaccbcbdacaabccababddaddabcaadbbdadcadbbdbbadbaabacaaaabdbbdadaaadadcccdbddaaaaaabccbaadaaabaacabccabbaaabcabccbbcaddadacbcaadadbdadacbabdabcbcbaabdbcabddbcbdccababbddbbaccaccdadcaccbbcbcccbbacbcabbccdbcdadcbddaadcacadbcbbdcbaadbcabddcbddcddcdabcbbbdbcddddcbcccccaddcbbbcbdcdacddcccbdacddaacdcbbcccabddbaadabcaaccdccaaabcaccddbabdbddddbacbdacbbdbabbdbdabcdaddbcbaccbdddababcdbddcccbadcdcaddabaacddabcccdacbcaddccdbbadcbdacddbaccdcbabdabccadadbaadacaacaadadcadcbcdbcdcdabdcaababcccbbdcccadaaabcaddadcaaadbaaaaacdbccbccbadbacdbbaccbdccaadddcacbcddbddcbbcaaccdddaacddaccbaacdcbccaabdcdacbdbcccbbdcbbbddddaccbbbcaabdcdabacbbdbaabddabadbbaccdacacbcaadbdadbbcbbabdcabbbaabdbdabdbdbaccbbbbabcacbdcaadbcccdbacdcbcbdbbaaddadbbabddddbddbdbabccabcadadbbacdbddddcdcdbadabcdcaaaaccdcdcacbdadcacddbaadacaddbdabcacabcbbdbbddcbbadadcbddbbbbccccbaadabadbbacbadbacdbddbccdccbcabaadddabdbacadcddbbbdddacabaddddbdadbbbdcddbdbdbadabcdbdcaccacbddabbcbcdbaacadaccdaacdccccacbdbaddabbcdaaaacbaccbbbdcdaaabadcaccabdcacaccabbdbcdbbadabdaadadcbdadabdaccabdbbcdbbacccaccbadbdbbccabcdbbcadcacdacdcbbdaacadccccdcddbdcacadccabdcabcadbdbcacbbacbdbdbbddbbcbdcaddbdadacdabbacbbdabadadcbcaaacbcbddaaccbdcbcdcbdabdabbbdabdaacaadadcbdaababcaddbbccbabcaacabbdbbdcbaabacabcdbbdbcbadadbbdaabadababdbbaddbbbdccdadbcccdcbdbbdabdaddcdddcbcbbcbdabdbbcadaaccdaacbddbddadabdacbdcddbccbcbcdccdbabbbcdaadcbbdacbddbdbdddccdbccbbadcccdaaaabbaacadbaacdbacdacdcdbdddccacbcdcdaaddadaabaddcbbdccbbcbacaacabbbbccacbbabcdaaadcbdcbdaaaadbcdadcdbbdbdbcdacbdccbdccacacbdcadbdacbdacccbacbcdcadaaaaddcbddcaacaaaaaadcadacbcaccaaaacabcadcdcddaabdabddbbcadcaaaaacadbbbbabbcbdcdaacccbbcccdbdccbdcdcabbaabbccbcddcdccbbcdbbaccccadbccbadbbababbcabcbbabbadcbcbbdcbdadbddbddbdccbaadcbbbadddccadcadbabacadccbbbdddcabccbbbdcdcaadbbddacadddadabadcdabadacdccbdbbcdccbadacbbadacabdababbdaddcccdbdbccadaaacdddbddaaddacbcbabadcddbbadcddbadaccbddacdccbacdcbabbdaadbbabccaaabdcdbbaacbcbabcdadccbdaaabcbadbbdabbdddbabdcdcaccacbadaadabaadbadaabbbaabcacdadaacdbdababaccaaabdcdcdaccddcbcbdcabcbaaddaaadaccacabccbbbdcdccacbbdabaadcabbacbacbcbbadbbccaaccadbccbbbdcbbcdddcddbdaccdbdbcddaacddadcdbadcbabbdbcabccacdadcdabcadaadaaaabdcbdacadbbaabdbacdbdadbbbcacaadccaadbdcccdddbdcabbccabbdaabbbdcdcdbdacccccbcbcaacdddcdaddacdcddbcbbbbbcbdbacbbacddccabdbdccccbdbdddcdcbbccaaadbdcbbcdcadacbbaddaabcaddaccabdaacbcabbcdcbbddbbcbdddcbbdaadbcbacadabcacdbaddaabdbabcacaabaabdddcdbacddcabbdbccababdcdcdbbacdbccccdbdbcabbdcdcbbcadcaaccbcabbabccccdcddbdbcbdccabbaaabbbbcaccbdacacdcaaaaccdcdabadbcbbcdcacddababacdcbcddabaccbadcaccdddcbdadbbbbbbacbdaddbcbbdccbabddbdccacbcadcdbacabcacabcddddcbdacdbbaadcabcadabccdbbcbdbaaaaccccacccbaaadbcbacadadbccdbbadacaabaaaabbbacadbabcdcdbdcccddcacbccaacadcdcdabcaddcdddbacababaccacbcbccbbddadcdbabdccbbcbbaabddcdcddbcdbcbccbcaacbacaabdddabdcbbcbdcdbbadabccdbacaadcbdbacabcbbcbcdadccbcbcbccadcbadaccbbbaadbadcadddadbdacaccccdcdacaacbcdbcadddbdbaddbccbdbdbdadaabacaabcbccbccacbcaccabbadcbbcaaabadaaabaaabddccdbbbacbabdbdcbbbaadadcbbdabadcbcddadaddaccabbadadbcaccddbcacdbbadcddacdcacbdbacddccbcdbbcadddbddcaadbcaaacbddaacaadccdbcbaacacccdbcdaacadcddcadadacadcdccbbbcdbbdbdadcddbccbaabcdbdbbddbdddcacddaccdddbabacbaabaabdbddcdabcddbbabacadbcbbddcdbcdbbcdacdaacdaabdbbccadaddcddbbabddbddaadcadbdadcbdbbcccccabaaccbbbbcbccccbbabdbbbacddbaccbbddcdddddcbdadbcbcacbaacbcdaaabcdbabbcacdccabacdacdcadcdbccbdadcacadacddacbacbaaabaccccadaaadadbcabdbdcdbdacbbaadcdcdacaaddbabddccdaaaaaabadabdadcbcabdbdadccbcbaadcaaaadddddcaccadbdacacdadaaccccbacdbabbabbddbccdbabbdddaddcccccdccbbacccabbacabbacbccccbacadaadbbcbdadabbbcdaadadacbbbbbccabacaacddbacccbdbdbccabbabcaccbaaacdccdaccdabdcadbdbbdbbcadddcbacbaaccbdcdaacbbbabbbbcadccdbbdacaadcdbbaabcdbaccabbbbdbcdbcacbbcddbbbabbdcacacdbaaccbbcbbdcdbacdcbccabbbbcaddbacadacdacdaabbcbbaddaccccacaadbadddbaddcdddcdbbaabdbccabbcbbdcdaccbdbdacdaabdadadacddaaccdbcbabdcabcccbdcdabdaddbddcbdadbdcdbababbdbcbcaaadabddabdddaaadddcabcdaaddaadddaabbadabdacbbbdccddbaabbbcdcadaccdabbbccccbddbdbdbdacbbbbddddcbacadaddaccabcaaaadbbbaabcacdccbdaadaacccbcadabcbdccbaddcdbddcaccbbdaacbdbcacdcbdbaabdbaddbcacbbbdacdacaaadccaaaacbabcdbacccbcdbcbadabaacdbbdbcabdcadddcdbbbdbcdccbcccbcabdcdbccacacaacbbbcdaaacabccabdacbdabcbabcdbbdabbbbbbadababbcdbdacdbcdcddddcccbddccdbadaddcdbdbddcbdaccbcddcbcdacadbaacddbabcabdbdadbaccdbdababaacaadaacbdaccdbbadbadddabaccadbdadbccacdbddddadbaabdbbcdabdcbbbbdaaddddddabbccbcccdbccccdcbdabdcbbdadbbbdaccabccbbcdbbbddacccdadcadabddbaabdcaaabcaddbaabbcaccbdbcababdbbdadddcddbbadccbcccaadbcddbdaabdbadbcbababaccbdbcaacaccbbcbdabaadbadddcbddaccdcbccaacaacaadaacdccabbdaddabbddbbbbcadcacbababadcdbccccdccbadbccbaddddbbaddccbdddabadadbbacbadbbdaaaacbdcdbbabacdbdbcbcccabddbcdcdbbadabdbacdadacddccdbabccbbcbdddacbabcbbcddbbadbdddabcacccbbababcdaacdbdadbcabdbdbbaaacdbbabaabacdbabcbdacdbcddabcababcddddacaacdabdaacbbcadabbbabccddacdcaabcccbacdbcdbbacbdcbaaccddadbadbbbaabcdcabdddbbcbddbaccaacbbaadbadbddadabcabacddaaddacbcbadccaadabddcabdbcabccaacccdbccccabbcdccbccbccbcabcbbaaaddccbdcbdbcacdaddaabdcadaacbadddbaddccbbbbbcaaacbacabaccdaaacacaaccaadbdccdbabcacbaabdabddbcaddddcbdabdcccdbacdbcddabcbddcdcacaadbcbccccbbcbcadaacaddbbbcddabdacaacabbcbcdabccabcbaadbdcaccbcdcdccabcacabdacaaccbddddbbbdabbbcaacadccadbbddcdccddbdbadbbddbdddabdaadddbccadbaacdbababacadbabbaddbbabbacdbcdcabdbdaddabbdbaabddbccadbbddadadcdaacdddccaadbdacbddbdbcabcacdcbccdbccadbbdcaaccbcabddddbaddadddcabbadadbbbcdadadbdbbaabbdbddcacaabcbbabbabadbacddbdaadaabcccbabdaddcacbadbbdddcdbababdbcdaaddcccaadaabbaaabbbdaabddadacdbabcbbdddbcccdcccbddcbcaccdbcabbadacbacacccbabbbbdccdbdbccaaaddadccbdddbdcabcddabdcdcbbcaacccdacccdaddacdbbcddabcbcacbcdccaabdaaabaccbccbacabddbdcdabcabacacdaadcacabababaabcdcccbcdadbadcacccaaacdabbadadcdbcdacabadadadbdbcbccbddbccaaadbddddbabdccbdadcdacacabcadbaccbccddabdaacbbdcacddbbadcccaadbbddbdbaacdbcbcacdcadaacbcabbabdbdaaccdcaadaacdcddbbaadcdbbbcdcccdcbbacbabaacbbcbbadcdaccccdabcbcccdcccbcbbabddbdaacadbbbadcddccddaccacdbbaaabbbdddcddddcacaabcddbdddbdadcbdbccabbcadababccbddaccbbabbddadacdddbcbabbdbccbddbccbbadddadbbdadadabcbcbcdbbcaddccdaddcadcbddddaaaabcbccabcbdcbccdabbbbbbcbdcadbdaabddddbdccbabbaadbbbcddcacdccbdabdcacbdbbacadddddddaddddbdbbaccdadbaddddbccdaadbcbcbabbbbcdbbbdbccbdbddbacabdbdddadbabaaddbcdcdddbbadcabdabbacbaadacabdbdcdaacaacacddcadaadcdcaaccacdbdbdcdcdcadacdbdcbbcabbcbbcbbbcadccabcbdaabdbadddacdccacdcdabdacccabbcdddcbccccccddbcacbcbbddbcdaaacddacdbddcaccbbccbadadaddbaaaacddbcbccaaadbdcbacccdabbcaacacdadddccbbcbdccbacddbacdbddacdcbcabbbbababbacbdbcadadadaabdbaabaccabaababddcaacbccaaaaadcadddabdadcaaccdacdadabbaadcbccadbaadcacdbbbaaacdacaaabdcbdcbabbabaacbbdaccaddbbbdcacbdbadddaacbdbdddbbaacccbbddaacaabbdcacbadaacdbdcbbaddddaacdbbacadddcdbdbdcaccacdbdaabdcacaddbbbbcdbdbddbbcbbcbcdcbbccacdabddbdbcdbaabaccadaccccaaccbacccdddcaacdbcddcbcadacccadcbacccccbcadbdbbbaaccdaaacddadaadaabcdaacbcadbddacabdddbdddcbcaadadcdadabccbdbbcccabbccbbbcadbbbcbcbdddbaacdaaddccdadcdbabbbaccdcddaacdaddbbbcccabcdbbccabbdccbadcaaabddbbbdaaddadccbacadadcbbdcddbbcdddcbbaabcbdccdddbbbcbdaadacbdbcdaddacadccbabcdddabcaabbacbcbdcacdcdcccdbccdddbaaadaadbbbacbaaabbaaaaacaddccccbdccccadbbacddbbccadadcaddabbbbccdcbcaacbddbcadaadccadaadacbcdadbdbcdabcbbdbddcbddabcccccabbcbcbcbcaacccdcbabcadcdbddcdddbccbdabaccbcaadacdcdaabbbddcbabadcdbbbbccbbbacdbdaacadbacaaddccbdbbbadbccccabdaddcbbabdcabdbacccccbacdbdbddacdabbbabcdacdbdaddbbdadbccbdbacaabbdbbccbbbdbcccaabbcdacabaddbddbdbcdbbacbdabacaaaabaadbddbccdbbccbcaaabbcccaadabddcbadcbcdddaddbbbcbcbbaaadbabddcdaaaaaababbaaccdacddbabcaadcabcdadcbaddbaccdcaabbabbadccbacdcdbdaddccdbdbbbcbaaddbdaaaaabdaacaabbdcbdcbdaddbabcccbbddbbcabaccaaddddcdbadababbaabcadbcacbdbdbdaaacdbbdabbcadbccbdacabdababababbcbcccccbbdacabdbbabddcddbbbbcaddbbbadcaaadcdacadbccbadcadabbaccccccbdbaddcdccbababbcbbcbacbabdaddbcbabcbcbbcdbadaadbbddbcdcbdcabbddbacbbbcbcbdcbcbbbabcdcdbadbcaaaacdcdcdccbdcccdbadcadbdccbbadcbaccccdcdaaccadaccabdcdbccacbaadbadacadaabacbdadbdbbbdacbaaddbaddcacbbccbabbbbcdddcbdbcaddcddacbcabbdcbdacdadcdaabcdcadbcdadacddbbacaacbbaccbdbacdcaddacdbdddcdcadbcdcddbaddddcddbacbdccdddbbbcdbdcdccacbdcccaaddacaddbbddddcdccdbbddddaaaddcacabdcdadbadbdaaacadbbadcbcbabaabddbcdaaaddcadbcabddbcdbddbcbabcbccbdbbddcbbcccdbcbabbabddbdcbdccbddaaabaadcbcadbdcdbdcacbaacbacaacdaddacbaacbdcdcbaddaabcadbbacadacbcaacdabcacabcbbdcdaccbdaaaccdbbdadbacdaccbcbbbdaddccdcbcbaadaddcaaccdccdadbacbbbcaacdbccdaccdccccdacdbaacaabadaabddcaabbdbaacccbdcbcddbddbcadadaabdbbbdaacdcacbabdadcabacbaddbbddccbcccaaaaaadadabbabbacbadbcababcdaacbbddabbdbddadcdddabacdacbadbbbdcadaaacbabccacdcdadcbbcdbdabddccacaddbcabbcacacdccdadccacbddccabdbcdbdaccabaddbabdddadccccbdaddaacdacdaabcabcaddbaaaadcabcdccdadcabbbadcbdbcdcadbddabdbadabdaddddbaddccaddcacbcabdbcdabdaaabddaddbabbcbbdddccadaccccbaddbbdddcabccdddabaabdccddaabaadcdcadabdddcdbcbadaacddacaccbadabcadddaabbbcccbaddbbcbaacaabbccbbaabdacbbbbcdcdaaacdcdbbdcdbaaaadddaccacdacdaccdacbdcbcddccaabccbbbbccadabbbacdbaccbcadcdabbcbbdacdcacacbcadadcacccaaabadbbaabcabdddabbacacbcccddbadcdcdccddcabdcbbbacbccddabccdcadadcddaadddaabcadcbacdccbcbccccdaddaadcdacbdddababdaacdbdbbdadadabaaacbddbbacbcccabcaccbaacddaadabcaabdccabbacbdadabaababbdacdbabdaacdddabbccaabdabaddccdccdabbbbaadcdcdcbbddadaaabdccadabaddcaacdacaabcbdddbbdaadadaadbdcbaaaaacdadbbcbaadacdcbbbadcdbbdbcbbdbaabcabdcdbbaadadaadbbbbadcccdbabdadbabacbbbadbcabccabccaccabbbadcadbacadbacadbcbdbaddcadbbcccbaabdccbadcccadbbaadaaaabcaaaaccdadcddadababbaaacdbddbdaacdcdddbbdbdbbdcaacbcaacddcdaabdccbbadddbaaacadcaadadbbcbbbcdddcbbcccadbaaddcbccbcaddccababdaccadbbbcdacabccccadbbdcbcbacdddcbdbbcabadcaacacabbbdddacabbcdabbabbddbabbdbddbcdabacddacaaabccabcabcabbaabacadcdcdacddccacbdccbcadcbbdddbdcacadadcdacaaabcadddcbbdbddbdacccddbdacacbdadbabdaadcabdcbabbacbaadbadbdacbacbbcddadaabdabcabcabdccababbbadadabbddbcabaabbcbdadbcbacdcbdaccdabaccbdadccaabdbddcaaaccbabbadbcbbdacbacdacdabcbcaadacdabdaacabddacabcbadbbcccabcdbdbbaabaabcacadabaccabcabcdaacddcdcbadabbaaaccdcaddcbdccccdadcccaaccaccacbcbdadbcbcabbbaabbcaacaacccccbdacabbcdaaabcaaabdaaacadacaacbcadcddcccaadbaabaddbddcadccbdcbbbcdacaababadabdccddbbccadcdddabcbcdbadbcdbcacdbaaabddbacdadbbcadcdbabadbbbcaabdbaaaccabdaaaddbcdcbdbabadccaddaacddbaacaccbbdcdcccacbcccaadbacacaaccbbcddcaaadababcdcbdaddbccabadccbdccbcdbbbaadccbcabadcbcccadabbccbcabbddaadbbbacacbbadbaacbcdcbbaaaaacbdddacccbcbdabbcabadcddbaacdbdcccbabccacaadaaadcbbcabddabbdbdbabcccdbccbbabdbcbbcdcacdbbcbabcabbcbcabcccdcabbcbcdbbbcccacbadcbaabbaaddbdadbaabcbadcdbacdbbdbbadbcbaacbbcaababacdaababdccbaacbaaddbbabdbdadaabccbcbaadcdccddabbcadabdccdcdcacddcbbcacbadacaacdcbccadcbdaccdaccdcccddadbdcacabcddcbdadddabcbbdddbcbbcadcadaacacbdadacbaddababbbadbcaabdbabdbdbaabacdbddcbabbbaabacbacbcbdadcacbabccaaccddcadadcbbbddddcdbdcbbcccbdbabdbccdbcddaacbbcdbdababdbadabdacaadbcabadabcbcacbabbcadaddddbdccdccbcbadabadcacdaabdbbbdbbaacddaabdccdcbacbaababbcdcdddaacaabdbbbbacccabbadbcddccbbccddaaaccdbdaccbcdccbaddbbacccacacaacbbaccaddddadccabddbbcbbddadbcaabadddcabbdbcaacadcacaaaddcbddccdcbcdbdbcdccacadbacaacdcbcdbdbbdbbabbaaccbbaddabdddabdcaabddcbdacdbadacacbcdaaddcddccbcdbdbadbaacbdabcbcbbdcaadcddcddadaacaddbdbaddcccbbcdaabbcddcdbdcdbdbdcababccaccbcbbdbcbacaddddcdbdbdbbcbbadadbadcdcccddcddcbdacadacacdcaccdacbaccbddddabbcadaddccdbabbaacbdaaadcaaccbccbbcccdddcbdbdaacbbdbcbabacccbbdcabbccbabbbcdcdcbcabbaddcbbcbabbabdcdcadadbdabbdbcdcadbdddddadbcbaabcaccdccbbdbdcdbcccbdabcaddcbcacbcccccdacacbdaacbcadcbacccbcbadbcbbbdddbdbbaddbaaabddddcbababcaabadadbcaadcbbccdccccbcdccaddcdbbbddaddbbddbabccaaabacdccdbdabcddbdadcccdcdadccbaabccccabaaaccbdbaadccdcccbbbbcaddbbacdbdbadcaddacccbbbcdbddbbacbdcdcbcdaabcbddccdcbdbdacaddcdbaaaddcbabadcddbbcacbdbdbababcacaadabcdaadcbccdbbdbacadcadccbcadcddaddbacdbdacabdabdbbdcbbdcdaccdbccccdccabbbbbcccbdaacbacdacbadaaccbaabcaacccbabccaaccdbcacaabcabddbcbbdccadcbaddcbdcaacbaaddcadadbdabdcadccdacbcbadbcdababadcabdcdaadcdadaaadcacdacdcadbdbdddaddadddcdbabbaacbdbbbcccdabdbdcbcbcaadbacbadacbdcddaaaddccbdabadddbdbaacbbabdbcdddcbbcbdddccbcadbdccdaddabaabacaddccbddcbbbcddabdaadbcacbbbbdadadccccaaddcbbcadaaddcbdcabbcabaccabbaddbabdccadbcbcdaaccacaccadaddaaaaabdadcabbddbbcddbdccbdbbdcdbbdcabbacabdddcbabbaccccdaddbbcdaacabadccdabcdddddbdbaabdaacbddaaaccdbccacaaadaccacaccbaddbdbadabdcadcccadabdcbdaaabaabbbcabdcaacbaccbdabcbdbdcaaabdbbbbddadbbaccacccdababcadcabaccdabdbbdacbababdcbcbccacbcabdacaaabcdabccbababcdbbbbaadbbaacdcbbcdaaddccccbcdddcdadcbdbcddcdaadaadcccccbaacdcccdaacbbdbaabbbcaaddddacbdcadacccbdacaddccadacbdcdabccdddcdcdcabbbbccaaccdcaadbbbcbbacdcadcbabbbcdddbacdbcccbdcaacadabdadaabacdbddbadcbcabaacccbcddbabcbccbbdaacabaadadbbccbddcbbcbcddbdaadaccadabbdcabcaabbcbababadcacddbbcadabadcbcddbdcbabddccdaababadaadadabbdbabbaadadcdaccbacdbbdbabbcadcabdcbadcaaadadabadbddcadcdbaabdcaabcdbbacdbbcabdbbbbdccbdaacaccbdcdcbccadbdbabdcdcccccabbcdadacabdbddccdaaaabdbdccdcbbccbaccbdabcddabddbbcabcdbcbadbbcaabadacdbddacbcbcdabdcddbdccabcddcdaaabcdcdbacbbccbcbdccbbbcacabcbaabadbcbbcabadbdbaaaadbbcbbacbcdaacdacccdcbbadddacbbdbccdccdbcdbcbacdcbaddcabadcabaccccbdbcadbcdadccaddabccadcaccdbdddcbbcdbbbaabcdbdcbbcccaaadacaabdabcaadcaaadbddbadcdbbcaddddccccdcaaacadcbcbccbaddbcabcbccbbabadbdbcaabddcdabaddcdacbaacdadddcddacddbaabaacabdcbaddadbacaadbccdbacbcdabcbdcabdbccdabdbdddaddabdcdbbccdbacbcdccdbdadbbccadbbdbcdaacdbcbaacaadccbdbcbbbcabdbbbcbaddcdbdcbcbcdddbccdaabddcdaddaccdabbbcbacccbadddcdcdababcabdbbdddcbbbbacacbdbdcaadbddddbcbcbdbadcabbbbdacbbdddacbcbcbaddbdccaddacbbcdbcbbbadadbaaacadddadadcaccdbbbbacbbbcbcdabbdaddaddddbaddcabdabccccacadbbdcccaabbbccbacaabbcddddddbcabbcddccbcadaaaacbccbdadccccadbdabdbdcadaaacaaaccbcbbccacbaabadadbdbcbbaabbbdbcdabccbccddbdbacbabdaddbddcabaabbcaaaddbbdccbbadbbaaabdddbbdddaacaababadbdbbbccaacbadbaabdbabdbdccbabadcabdbbdcbaadaaaaacbdbdccccccdcacbbdaaddaccaababbdbbcabcabbcabdbbdddcdabdabbadadcbdadaabdabacddadabcddaabaabcbadbdadbddbdbdadbdbabbdacdaacadbddccacacdcadbcacaacdbdbcdddabdbcdcadacabdccdcddcccbcdcacbabbaabdddbdaadddcdcccacdbbdacdbcababbaaabaddaccdccbbaaddddbbdccdcbdddaacdbcaacdbcdacbabaddaacadcdabdccbabdbdbadadcbbadacadddaccbbdacdadbbcdbbabacdabaaaaabddbdbddabadbcdaaacccdbddcdabbbbcabcbacddddddadddbcbacdbabbdcadcaaaabaabbccdbabccdccaccdddadcbabcdacdcbbacbabacabdabaaabdbadacdabddddbbaabddccddcdcadabcdaabccdbcbcbabdbdddbabdcddbacabcdabdbabddcbdbcdcaadbbbadcdabdcdbabdbdbbaacdcdddbcdbadbcacbdbdaccaaabccabdabadaccdacbcbcbbddaaaddaacbddcddbbadcadccdcaadcdaccbaccaaacaabbdcdbbaddabacdabaacddaadccaabdcadcacbadaabbaccaccddbddbcccbbcbdccccdbbbddbacccddccaabccdcdcbccbadcbcddaadcbdccdabbccddddcbbbbbcdaaabbdadadbddbccbabadddcbbacbdbbacbcacaccbabcabbbbacdbcdacbccbdbcaabaaadbcbbccdddcdaababddcccabdcccaddbdadccaacdbcddaaadcaddabdbcdcbcccacbdcacbadbadbdcdaaababbccddccadacdcbdaccadbbcbacaadababcaccdbacacabdddddcccccdbaaddadadaaaadaaddadbaaddabababbdbcaadbbadccdacdbbbcadccabcdbcccaaadabdbadcdcdbdcbbcbbdccdbcacaacbabcbdbbabdbdbdaccdcbddbcddccbdbabcdbacbcadbbcdbdbabcacacccaaddcaadcdbddcacbccbadbbbbbbaadacdcbadabaadddabacdabbcccdbadabbdbcdbbabdabdacaaaaccadcdbbbcbdddcccacbdcccaddaadbaadbbbdacabcacaaadaccbbcdcccbbbbcdcbcdabbbccdadbdbddabbacbcccacadbcdbbbcdbaaaddaaaddcccacacccbbcadbaaccbbcbdcccabbccadbcbdacbdaacdcadacdcbaddcadaacdabcabdbcccdcdbcbcbcacbbdcbccddadbaddcbbbbbcbacdabbbbacdaacbdbbcddcdbadadbcdbbdaaabadbcacccdaabcdcbadbabcdabcaddaabadcccddadaddabdbcacaadaacacddacacbaadddcdbddaaadbdccaccddbcdccacacdaaadcacacdbabcadcabccbababcbabaddacaabbdbcdbacabaabcacccbccccddcdcadaddbcddabdbbcccaaadcadcdcbbcbcaaccdaddccccccccacacabbbddcddbbcdaddaddbdcdcdcaaabcdabdbbdbdaadbacbccddacdddabcbadaddbbacdddbdacdacacdabaacdaadadbdaaacbabbdacacaaadaddcacdcbdacabcadbbbabcadaaddabdbcdbbcaabccbbcbbbabbbcacdbcdbcdaaaadadcadbdbadcbacccdaadaddcdaaadacbabdacabbdbabdcabcdaabcddadaadaaadddbdadadbbcbdbdabcdbdbcbbabccddccaabcdbaacdbaddcbbaadcddccbaccbaccacadbbddcbccabadcadddabbcdcbcdbabcacddbcabcbabababcdabbdabdbbbaacbbcbcbacdabadbacadddadadbaddacaabdbcbcbacbaddbbcbdbcdaacbdabcbdcddbddcbbcbacccbccacbdddccccdbcbcaaaadacbbcadcbdccadacdababdbaadccbbbaaccdcabcddbaaaadbddddadcccbbbdadabbabbddadbddbaabcdabdddaaacbabadbcaaaadacdbadabdaddbbdacaabdacddbcaadabbcaccdbccbbbbcdabbcdddaabacadcbaddddacbdbaccbbacacacaadacccaacdbadbddccabdccabddabbaacdacdcdcadbbbccbccbcbcacbbacccbdddbcbbbcabddbcaddbdcccddabcbbcdcaddabbbcbaaabcdcdcbadbcccaabcdddbbcabddcbdcabbdbcabddcddbbcbacbdbaaaacddcccabadacadaacaccddaacdaccbbabbabbabbdccbbaabdacaccaacbbacabdacacbbdcdbbccabdabdbdcababaddadacdbbbdbcddacddaacabbdadaabdabddabcbbdaccccdacacbadcbdabcbcbbcbccdaaaddcbbbdbcbcaabbcccaddbbcdbcbdbdcdbbcddadbbccbababddbbbcdbcaccacccbbbdacabdcaccacdaccdabbcbcdaabaadadbabbadbbddadcbbddbdbacadabcdbacbbdababacadccbadabccdaaacdbdbbadcdcadbbcbbbdbdbccacaaadcdcbadaaaddcabdcbaadddaacacaddbddcaaacbdadbdaacbcacacacccaababdcadbaacacaacabbdbacdcbbdcdacacdaabaadacddcbdddcbdbdbbabccbcaadaacbbcbcaabdbbddbbdaabbdaaccaaddcdadbbdbccdacbcddcaabdbbabbdcadcbcbcddbbccdbabcdacbdacacaaabbbdbdabbcbaacabdaccbabcbbbdccaadccdddadcacbdaacabaabbabdbbbccdbaaccddaccdddbbbdcbcaaaabbadbcdcccbdbddaaccbddcdacdcabbddbcabddbccbcccaddcbddacaacdbccbacdbadbdbddccbbcdcbacbcbbadabdacaacacacbacabcbcccdabcccccbcdbcccddddaddddbcdddbbbbcbadcddaccddcadbdbccbddbbaaacacadbbbbadcbbdddbdaacbadabbabcddcdcdccbbdaddbbbddbcacbccdbdbcddacddaabadbdddbdabcbdddbbbbaabadbdaadabbabdccbdbcadbcddcdadbaacddabbbdbccbbdadbdbccbddcadcabadcbacccbadcbddcbbdabbbabbbbdbdbadbbabacdabaaacbbaccabddbadbacadcaacbcddbdbcddccaddabbabacccbcaccdbcaaaccbcdcadcaccbaadabbcbadbbbcbbcbaccaccbaabdcabcbadcbbdcdaabcabbcdcbdcddaccbbacbcbccddbbdaabbabddddcddaadaddbbdddabcdcdadddcbdadaacccbaddbaccbbbbcdbbdbdabcdabcababddbbcdaabbdcabacadcdddaabdabbcdabdddacdabcacdbabaadbbdaadcddacccbbbdcacdbadaacbcacaddbccdbbaddcdddacdcbcdcdadadadababcdcddbacdbbdccdddccbbdcbbcbdddddcddabaaaddcbbddddccdcbbccdcacaacbcdabaaaacdbadbcddcdbcbcadccabacdbbadacdadddbbdaddbbdbbdbcacbbdabbbccbcacadcabbdcacddabcdccaccdadcccdcaddbbccdacdbccccddcdaacacbbdabdabddabbcdbcdcaddabccdbbacadcccbcbdbcabbadadbdcdaacbaabbcabababbbabbadaadbbbbbadacbdbbdacbcbacaacdcdcccccbcddcdcaabddcddcaaabbabacadbadacdcacddabdaaadddaccddcaabcbccacadcbbcaabcbdcdbccaabdcaadbaacabdbcacabcdcabbbcaddddaadaacdddddbbdccddcdcadadbabaadacaaaddadabccdbbccbbabacbbbbcaddbbaabddbbbccacccaccacdadadbaaddddbbccdbcdbaaccbbacaacabcadaacbdcabcccadbabcacbaaabacaabdaaaaabcddbcdbbcabbcdcbdcdaadbdcaabddcdabbcdbbddbdddacadabdaadaacdcdbccbcbccccdcadcdabddbaacbcbdbdcbdadcdaaacddbadbaaadaabaddbcbbadbdcccabccacdaccbbacccddbbbaadcbbdaddcabcdababdcbdcdccabababbbadcdcccbcccdaacadbbabbabadcdbbbdccaddadddacdcddbdaddabbdcbabccdbdabcdbccdddbcbbbbcbcccbccaadbbcbbdaddbdcdccaddaacccabbbbbadcabcddaaabbbaacadabcbacdaccddcdcbbdbbabdccdabbdbbabbacddabdacbcdbbaadccabadddbcdbddaabadbbccbbcbacabadabbadacaaabadcbadccccbdddcddacddbcdcdcadccdcbbdacacaaddccbdcdacdcdaabcacdbaacbdccbcbcadaadbadadcbcbabacbaaccacdbcbbdcadbccbbddcbabccdbdcbdaabdbcdaacbccddbbaaccbacadabddbdbcbddacdacabbabdbcdacdcadabbabdbbddddcbaddcbddcdaacbbadbaddadcdcacccadaacabdaaddbadaacaddcdddaabdaccdaacaaaddccadbbacbbbdaadcaaccdaabbccdcbcaabdbdbbadccadbaacadacdbacadcdcbaddadcaadcdbadbcababbadddaaabcdbbbcdbaabbddacacccbcccacdcddcbaabbddbbccabdbadbadbdddcbccbabcdcbcabaadccaccdabbccdbccaaccdbcabadaadbdcadadabdaacacdcdabbcdbbcccdabbdabdcbaccadbdcccabcddacbaaaccbddcbbdabbdbaaaaddcdbbdabbccabbaccbdadacdbbbbadddbadcbbdbcabcbbbdddadbbcdcbdcbababbcdaacbbccccdbcbbcadbdcbbdbbcbccccddddccdbcaabbdbabcccacbabbdacbaaadabcbcdaaacdcdcccbaccdccaaadbabbbbdbcaaddbdacdacdbbbddcacdbddcdabacccaccbbbcdcdbdabbbdcacbdbccbabddcacddbacaacdcdbdbdcbbcacdbbddccddcccacbcaabacaabcabadadbbbcbbaddcaaacdbdbccbbdcacddbdbcdacbcdbbddcbdaaddcdcdadabcaabbacdaacbbaadccbdcdbdbaaccdcbbcdaaabbdddabbcaaadbddadbbbcdacdbdbdacabacbbcbbbcaacdbaaabacaaacddaddaadddbadbaacacbbddbcbacdccccddcbdbdddcbcddcaadadccabdaddabdcddbddaaddcbdcbccbacbcbacbbdbdddaaacabbcbaddacbacadcddabbdabbdadcbbadbcabcbccccdbbdaddcababdacdaccbccbadacdddabccbbadccbcddaccbbadccadddabaaadcdbdaaaadcdbbdccbadabbcbaccdccdcbdddbddccbaddcaddbaddbaddcddddaaabaadbcadcbacbacbcaacdcbcbcaadcdabbbcadbabcababcbcaacadbacdbccbdbcdccacdbcdbddbadbdadcbdcdadbbddaaabddaddcbcbcdcadabcbdabadbbbaccaadadaacaccaccdabaacbadddcbbbbdabdaadbcbddadcabcdbbbcabadcbcbcacdbcbdabdbabacbcbabdcbdddaacdaddacbccbaccaaaadddcccccbdddcddaccdcdccadacdccadacdabacadcaabaaacccacdaabdccdcaadcbdcacbabbbdbdbbdcdaaabbcacdcdddacdddbaccddbabbcdcadacbdbacdacadbccdbabbdcdbacabcaabdacdacabcdaacdccacdcdddadbabcabcdbccbaacabdbcaacbbbaaabacdbacaadaccbabdabadbaabccdccacdacabcbcbdbbdbbddcdacbacbbbadacdadababbcdccacbcdcdbbdacbdadccdadaadcbcdbbbcbcaaddacbaccbaccdcdddbcadbadcdcbbbbdbddbddbaddaadaacbaaadbddabcbcadbbacddddcaccbadaabdacbcbcbabcaadabacbccdacdddacadacdcaabdacdbadbbdbabdbbaccdbaaabbaadddcdcdddadcdbacccaabacccdbdaabccaacaaadcdcadabddcbccbdddbdaccbaddddbaddbdcabaaaadcbaabbbabcdadacbbdacadbddbbaaacdcbcabaacaddddbabbaadabcbacdaadbcdcdcddacbadcddaaddabdaccdbcbddcaacbadadcbbcbbbddcbdddbbbbcacbbdcadbbaacbdcaabadbbcabdddbbadaaacbbabdddaacabccaadaadbbbdcdccbcdcbdddcacbbddcdbadadcbccacdccadaadacababbbbbcbacddccacdacdaacdabababbbadcdcaaccadcadcadccbbadbbdababbadbcccccbacacbbddccabcabcccbdadadddaadccadcbaaacbcdabbdadbaaccbdadbababccdccadbbaabaaaaaacddbcdbcadaacaadbdccbbbaaabadbcdacbaccadacdaacddddabcacddacaaddcdddcaccbddbcdbcacaddccbdaaaacddcbcabacbdbcbdddcabcbdcddcabacdbbadbdddbabbadaaacccadbdbcacbcbdbadccddbdcaddcdbbcaaacaccabcaddcdbcbcdcdbbdaabbabadddddadabddabdbccdcaaccbaadcabcacabdcddacbcbaadbaaabbddbcdcdcbdbbccdbdddcaaaabddbabadcdbbcbaaccaccaddcdadadddbdbbdadacadbbbabbdddaccabcccaabddcadababaaddaccaaacbdacacbbbabbcdbcbadbcdadbdbadcddadbbbcacabbaacbadadaadbcdccdacdbbbdaddcdddadcbdabdccaadbbadbdaadabadccdabdbadcaaabddaccdcdbacabddddbdaccdcabbacdacbdbacdbbcaabcabbababdccabaccdcbacabbcbdcbcdadbdbcaaaadbdaddaddaccddaacddcdcdccadcdabcaccabaccbaacaabdbddadbbdbacabbadcccdcdacbcbccabacbcbbdccccbbdacdcdbadccbacccddbabcddaadcccdabaabbdccdbaddbcaccdbdacadabbacdddbacdcdccdaabbabadbacacbdbbbbbabcccacabbdddcdaaacadccaabcbaccadcbbcbacdaddcbadaabdacbcdbddbcacdbaabbbdaddddccbbcccdaacccccabcaabdccdbcabbddccbdddacaddddabbbadbdbdbbdddcdcdaadabcabcdadbadddbdbbacccdacdcabccbbacdbdacabbbccbaccbbadadcddbaacccbccacdacacccacbcbbaddadbadbadbcbbbdbbbbbdcccadadacbcccacdadbbbcabdbbccabbbbadcbadaaaccbbbdccbbdccbbccdbbbdbdcaabbaaaabacbccacabbabbbabddcdaadabaadabdbcbcbacabcbacadbbddbcaaccabacdddbdaacddbbaaabacbcaaababadbcbccdababdbcadaabbdbdccdbdccdbaaabaccbcdbccaadcbbadcbddbcbacdaccdddaccccacbbdcbbacdbbcadddbdcacdddbbbddbbcbbadaaccaabcdbacabdbbcacaacddacacbbddbaccdddaadccdbdccddcdcccdbcbdacabdaadbaaacaacbbdbbbaacdcdcaadabcbcbdcdabcbcbbbadaaaacbcaaadcdbcbbacabcccabcaabaaaaabbaacadcbbcddbbdddbacaaccacaccdddadcdbcbbadabcdbccdcbbbdcbdbbcbdcaaabcdbcdadcaccbddbddaddaabacbcaabaabcaaadcbacdacbcabbadcdabbbabcbbaccbbcdbcbcbbdcaabdcdbcbabdbdabccbddaaccaabddabdacabcadbababdaaaaacababbcadcdcdaddbbacacacdbadaccbccddddcccccbabdadaabcdcaabdddcdaccdcacbabdacdcccdadbcdbbbcdbabbbabcadadddcbdcccddbbccdcbdcdacbcbcccaccddccbcdbccadbbbcdabbbcbacabcadcbccacbacaaababcacdaddaaccdcdbabdcbcbdacdcbbbdcacbbdbabccbcbacaccdbaaabbdddccdbcccbadcbddadababbbabddadabdbcbacbabcbbdacccbacdbaaadabacbaccbadbabccdacbbabdadaacbcbdadbdbdadcadccbaadaddabbdaabbaaccbdcbbabcccdbdcbdbdddbcbacdcccbcddbabdbaaddbbbbacaccadbacaabbacbbcdcccaaaadbcbbabdccaddbcdbbcdcdabdacbbadbdbaadcccbcbbcdbcbbbcbccdbbabdbacbbbcaabdadacdaaddadddcadacacdaacaaddacdcccbdbacdbaccaadbaadbdcddaccdbadbbaaddacaaaabdccadadadadbdcbadacacacdcdbcbdaaaadddbaccdcbbbbdadaaadaaddcccbbbcbaaadcaddbadcadccdaadbabccacdcaabddcadaaacaccbdaddcabbccbaaabdcaccadbcbdbcaaadabdbabcbabdadaacaddccadaadbcbdbdcbcadbbabbabbddcaaaacdddccadaabdbcbbdbabddaaacbccacabcddcbcbdbcacdabbbbdccaabddbaddaaccbcdaaabacddabbdacadbabbccddcdccccdacdbaddbacacaabcbddacacdbdaddabbcaabadaacdcbcaddcabaadbdbbcabdcbddcabcdcadadcddadaddcaabaccdcaabddcccdbcddccabbdbacdbdacdbadccaadbccdcdabdcbabbcadacbccbacccbaabbcddbccdcbadaabadbbdbaaadaaddcdddddadaacdcdddabcbcdabbbadbcdccbdccbcbbdcdcbcccabdaaacaccdbcaaacdadbabdbbcacacacccbbdcadcadbcdbdacbbbabdddcbccbbbadcaadddddaadadddaaccccdccbcbadddbabadcaaaaaaddbbccbabaaddccdcdbaadaadcbcccdaadddccbdbdcbcbbabadbbccabdcccbaccababbcbccadaacbbadcbaccdcaadacdabdddaabbdaabcacbbdaaabbbcbbadaabcbbccbabcbbadbadcababbaabbbcdadababcdbaacbbacacdacccdddacbdaacbdcdbccbdcadcddbabdaccccaaccbdbcdabbccabcadabbadbbaabaccbcdbcbdacbccdddcdadbcbabacaacdadaadbabccbbbcbdcadcdacddbcbcbbccaccbcccadcdbbdabdbbbadabaddcbabbbbddbabadcbbccbdbadbaccdaacaabdacbadcaacbaacbabdccaaacbdbdcabdcbbccbadbbadcdbcbaacbaccaaddabddcddacdcaabdaaacadddcddccdbbddbdaacdaadacbcaabaddcabdabdaaddcdbccbcaddbcccbadddacbbacbcbaddbbcdbcbddadbacccbdaadabadacacdbdccdbdcdddccaddbacdacabbbdbdcbbdcbaccadccbdacadcbbdbacadbcadbcddbdbbcdaaddcbaddaddaccaaacdcaabdabccdbcdbcabcaabcdcbcbcabcabcdddcddbcaddcddbacaabbccbadcccabbcaabcbdcccdadcdbbbaaadaaacccccaaddccbaacbbbccdcddddacabcbaddbcdbcbbadadcadacadaacdbaabbccbdbbdacbaddaadcacbaadcacadabddbdcaccbaadcbdcacbbbadcaadbcbccdadaaddcaaccdcbbbabbcdcadbaaabacbbabcacbcdaaddacbababbdddcdadbbdcdcdaccbcbcacaddbabdacddcaccbccbbccddaabdbadaadbccccacbccadaacbacbabdbabdcdadcbabcbdadacadcbbdbbadaaccdbdbdaabcdcddbcdaabbaadabbbcbadcdabaaddcaadabcbdccdbbacaddabcbcdbacacdaaadabdcadbccabccdbdbdcbbabbcdababdaaadaddcdabcabbaddbbcccbadcabdcbbadabccbbccbadcbbcddcbcccddddacccddbcacabaadbadabcaccbabdddabadccccddbddbcadddcdbabcddddadcaabdbcbdbbccddaaddcbabdbdcbcdbddbdbdacdaacbdaaccdcaddabdcbdbdcacccbbcacbbddbcabcdabadadbadbcbabddbbadddcbdadcdbcddbcdaccacaabaaadaccabbccccdddabcccdacbbdcdacdddddbbcacbdcbccbdbdcadabbdaabaabdcbaadadccacdccddcdddcccabcdcdabbcacdabbdbcbdadbcadabddbdababbabacabaddcbbdacacbdcabbdcddcdcbdbbdcaaabcbbdbddbaaacbadcdcbacacddbdcbccbabccabaaaadcadabbabcabbcdbdadabbbdacaacaabbddabadadccdabbbcdddabddadbbccbabdcdcdadbdbbbdacbacdbcdaacbdabddcadcbacabbbbccdaabcddcaabbadddaddcdcbabacdbcdccdbdbaabdbbdadcdbacacabdbdcadbbccadcbcbdcbdabbcaabbdbccbdcdccbbbbdbcbcdbbbbcdadacabaddcddcbaadbddbccbbacacdcbaabccccdadbaccbdaadccbaabbbcaacaccbcbaabdaadadcacdcdcbcbdacbacbbbcadbbbaabcccaadcccbcaaddbaccaccadcaccabbddaccdcbacabbacdbccdbcddbbbdcdaaaaabdadddcdcbcaddacabbbacbdddddcaabdbbccacabdbabbdbaaacbcddcbcddadbbaabddcbdcbdcdcaacdbacddadbaaacbbddaabbacdaabdbcbbdcbadadaccbbacbcacccbcddcdcbbcabdbaacbbabddcdbdacdbcabbbbabdbabccbdcadbddaaccbbbcadccdcbbddbbbdadabdbadddaaabbbbdaacaacdbabbdccccddcbbacacccbcadcbcddaacdddcbdccaacccaccbdccabaccdaaaababcacbaabbcacaadabadccddbcbaccadcbddcaaddddcbddcdcdabacdddddbdbdcdbcddabcbbadddcbabcaabdcbbbdcadbccccdcabaadcdbbdbadccdbbdccabaabadadabbdbbbdacdbcaaadaabadacbadbdaabccacbdadcacdcacdcbcdddaacabddddccdddbccdcdccdbaaccbaddacaadaacdabbccccaddbdddbdccccbbacbcabaddaadaacbddcacdacabbdbbadbabccbaaddacaaccbbccaccbbcdabdacbccdbaadddcdabdbbacbcdcadcaaacaaadacddaaabbdacdbbabcdabbcbbcdccbbddbabccacabdccbaaadbdddccbbbdcbddddaaacbacdabcccadacacddcaacbbdcdbdacbcdbbbbcabadcadbbbbdbcbddcababcbcabdadddbbbdcbadbcccdbdbddbaaabccaccdbbaaabadaabbcabbbaccadccadccadbcbaaadbddddadbcbdbbbdcbdacdcdaaddcdccbdcbbbbdbacaddadbddababbadddcdabbcabdabcabbcbccaacccbdaccbdacdbccdccccadbcbaadccdbddcdbdababcccbbcdabadaccaddbaadccbadccabdabcbdbcdaabdbdbbabbcdcbdbdbbacabbdadacacabbccabdbdcbbcababcbbbcdcabcdbddccaadacaccdbcccdacacaaadcdbcdcabaadbbadccbacdaaacdcccaacdbbcdaabcacdbaccdadaabbdcdacdbbbadaadaaabadbdcbdccaccbcdcdccbdbdadcdcccacbbcaabddadbccbdadcadcbadbdbacbddadbaccccaddcaaccbcacbbbaccadcddaaddbaabdccabcbadbbddbaabdbadbaaaddbadcacdabcaaaacacabadadacdabddcbabcdcaadacacaddbdbdccdddbadaccadbdbccdcbaacddbbadccbcbadaddccdcabbdaabcbdaadbdadccbdadbacbaddbcbcaddcbbbdaaccdababdcadddccdbdbdddcdaabcbcdabbbabbcbbdaaaabcdcacbdabaaddacadbdbcbbdcacadbccdcbdaabbbbdcbdcaccbcccdabcadaabbaaccbdcaaadbbccdddddbbadaddacddbcbbdbccaabddddaabaacdcababaacabccbdccccdbaddcccbdcaadbcdbcaabaababbadccccbbaaabddbacaacbbacdcbdcdcdcbcbcbdadacccacaddccbdcbdddddaccccdccdcbadbaaacbabccdcaadaadabccaaaaddaacdbcabbbdcbdcddcdbacbbccabbbbdadcbddbadacdbdccbbdbdbabbdccacdcddabacbdcbdddbcabbdcdacbdccacabadcadbbdabdcbcccacdacabccacaaaacddccbdccadddbcdbcdddaadcadbdbabcabbbdccaddccbaabddcadaddadbcacaadbbbcdccbbccbddbabdcbddbababdaaabdcdcadacbbcabcbabaadbcdcbacccccdcccddcdcdcbdabdbdacabbdbbcdccbcdaacaddddabdbababbaacdabdcbaddacbdaadddbcccbddcdccdcacdccddacdcbadcadcdccbddccacccbdcaddcacbbadddbbadddcdcabaadbdbaabcddacdbadcacadaccacadcdcddbbbcdaadcacdbccbbdbdbababcbdbdcbacdccddbaaccaadddababcdacbcbcdbbddabddadcdadbcddbdbdbdaddbbcbaddbdaadbddbbcadadbabbabacbcbccaaddaddaacaacdcbbadddbbdbbaccbdaddbcadbadaddbbacabbccddddcbaacbddddadbacacdacadabdcdbcdcbaacbadaababbbacaadabcddadaddbdcdabdadbaacbddcdbdbccccbbddcacacdcabbacccbcddbcadacaaddbcddbccbcbdcadaddcbaacaababbdbbaaacccbcaddbcadcbacbccabbcddcddaddccdddaabcbdbcdaccbaddabcbcaadaadbbcacbbcabbadcbadabadcacdcabcccacbbbaacdbdacabdcdabcbbbaaabcbcaabdabcbddadddbccbbcbcacdbbcdaaabaacaddddaaddabbaabbcddaaaddbcaaddcaccbdadbdccbccddcbbabdaadbdbbdacdcaacdcadccdabadcbbabbacaaddaacbabcbcabdabccdbabbdbbbdddcdcabccdacbdddaccdadcadcbbaabbacdcdccaccbabcabaaadccaaabadabdcdabcdcaaabbbdcaaccbdbcccccbaadccdccacacdbadbbbcbbdbdcadabacbaaadbbcbbdacbabdcadabcaababdccbbcadaaccddbcdddcdcddacaccbdbddcbbadadbdadabddbcdacdcabbadbcccddacdacbcadcbacabdbcabbbbaabcbccbcdcbadbcccbdcddcadcadabaccabddbadaaabdaaaaabbaaccabdccbdcdaaabadcaabcaccbaacbacbaccccbcbdacaaccbcabdddaddccacaadaabbcbcacbabccbcbcbbbbcccdaaabcbbcaadbcdbdcbaccabdccdcdddababaddbcbcadadcbacbcadaddcbdbabccdcbddbabaaadabdddbdadadcacdadbcbdabcdccacbdacccccadbbcaabcbbcbdcbbddccaccbbddcadcdbabdcdbccddcccddadadbaaaddabbadccaddabbccbaccccdbbcabbccabbcbddbcbadcbcccdadabbaaaccbadbdbdbcccbdacbdadcddaaabbaabbdbacbdabdddcdacbacdddbaaabcbbadabadabbcbcabddaacabbddbacbcbbadbcacababacaadcaaababccbadadcbcddaccadbdcbbabbbcbcbbbacbddcbccdbdbcbadddddabddcbddcbdcbbabdabcadddbaabdbcdccbaaccdbaacadbaddadaaaccbaadabdabccaaccbabcddaccabdcbabdcaabcacdddadccbbdcddcadcabdcdddaccaacdcccdadbadadadcbccacdabcadcabdbdadcbccbccadcbcbdbdaddbddccbbddcabccdaddccbdcabadbddccadbaaadacaccccccdbdcdaacdcdbabcabbcccccdbacbaccdbbbddbbbabdababcbccddabcbaddcdabbdbcddcdddbcacaddcbdccbcbadbdbabcdcadaadabddccdbaacacdacddbdbddcdcdbdddbdddbbcdccdddcdccbbcacddcacadcddbaccdadabacdcabadadbbabddbcdddcbbbabcaaadcbdbcadbbbcadabbadbbaaddaaddcbbcadcdaabcabddbbbdcbdbbbcbdcccbbcbccbbabbadbabcacacbccdcbcdbcccabbadddbdcbabcdabadbddcddcbcddbcdaccddadddbdbcbddbdacdbabacabbbbadccacdcccbcabbdbcbacbdbbdbacbcacdcbbbbbacacaacbadbcabdbccdddcbdccccacccaabccdddbadaacdacbcbdcbddaccabccbdcaddcabddccaaaaacdabacdaabbcdcadcdbdcddadcbdacaacdacbbbbccddcbbcbaabacccbbbacdbaccddadcdabadaacdbaaacddcaaacdbbcccccdbcdadbaacadbabccacdaddbaabbdbacbbdcaacbcdacdabcdadbbdbbcbbadcabdcabbcddcbdbadbcccdcacbabadbdaabdccccddcabdcdddcaccacdadbabcabdbcdabbcdccbdbbbacdaacdcbababbdbcbcadcbbabddbbbbbbdcbadbacdaadddccbacddcbbacaaaadccabcbcbddacbdbbcacabcacbdcbabacbcbadcadcacacbbcabddaacbcddbddbdbaaccdaaddcbbdcbadaadbacbddaacbcddccacbaacddccdcbdcdbbbcaaacbdbdddcdbccaccabdbdbdbdbcacabbdbdacabacccbbbdbdbbbaaddbcaabdadbabdddaccccdcacacabdbbcdcdcbbabbabcbbaacabcdcabaaddcbaccbbcbdababaadcdddacbbbababbacbdacdacdacadcdacacbbadbdcadcadbcbdcddaccabccddbaacddaacdaadbacaacbcbccdbbaabbbaccbbdbadcbbdcbddaadbccbccabcabcacaacbdcbaddddcdbcdcddbbadbcccdcdccaadcbcdbabddabacdbacadaacdcdabcdadbbcbacdbccbcbacccdccdbddbaadbcddbcbccbcdbdacdcaadcdabbbabacdcccdadcababdaacccdaaaaadbbbccdbbaddaccdbcdccaddacdbcacaadcddbacdcdaccdbdccdcdbcdbbbbcbdcabadbcaccdcbbbdbcbaabaabacdcdcbddbdbdbdccbcacbdbbadddaaadabbcbbacbbcacadbdcabcbbaabcbbcbbcddcbaabbabcadadbdcbccddbdbdbcaaaacaadadcaddacacdcbbddbdaaaccabbaabcaccdadcddccddcbabcacdccbaadbdcdddcdcbbbbcadcccbdbadbbdaaccbbaacbabdadcaaabdbbadccbbddcbadaaddcccbababdccdacdadcdaacabadaddcaaddbacbbdacdbacdbababbbcdaaddbcccccbbbdbccaabbbadbdabccccddabdaabccbabcdabcabaddbabcadbcbacdbbaddbdbdbdcbbadcaacbacbbdbaadcbbcdaadacdddddaccdcaaabbbabacbdcdbdabbccbdacbcbdcbbdacbcabbdbccabbbdbabddbddaababbabcbaaddabadcccddabbabdccdbadddcaddccbcddcdbbdcdabdbcaaaaacccdddccdccbdddcaaaacbdbddcdbabaacabbaaadaabccbbdaccdbaddcddcabdcadbbcccbdcadbcacdcbcadcbadcdbccbcddcaaabdcdaacdadbabaacdacbabbacccacbcdbcbabaabbaddabcdbaccaddbbaaddacbaddccdaddddcbdabdbacacdadadddaccbcaabacbdccbdbabbabaabcabdccbacbcdccdbdbcbbcdcccabcdcdbcdbadddcdbddaacdddcbcabddbbdaddabcdacbdbdacbadcadbcbbaaacbdccccccdcaaaabbdbcaacdbcbaabdcbabdcdcdddddbadbacbbababdcddcbcbcccbcabaddaadabbdaabcdbbdaccbabdbcdbdadaacacbdcabdcadbdbbcaccddcbdbbdbbaaabbaaacbadddaaaaddccaabacdacdbddbdccddbdcccddabdbbacddbcbdbbdccbbcdadcbccdabbdacadbbbcabdcaaaddadacdbddbbddbcabdadadcaacccabdcabdaaccadacadabaadcdcdacbcadabccbaabccdacababdabaccaaccbcbbacadacacabbaadcacddabaacaadddbcadbacacddbadabbdcdaccbbbcbcaacaddadbbcbdaaadbbdbcddcbddacabaacaccaadbdacaabbaddaacdbbabbabcddcddaabcabaaabddcbbdacdddacccbbcbdcaccbbabcddabddcddcbbadbbdbccdcaabbbcbadabbacaadbdcabdcddaddacbdbbbbcddaadadaacdbbcbbbababacdccabcbaacccccacabdddddbbbddacadcbadabddcbcbbcccdaddcaadccbdcdadbccbbdcdddccdabddbacdcbbcdcaadcbabcbaababcdaabcabcaadccbdbbdbdcddccdbdabbcabccdbdbacbbbdcdccccabbabcddacaccccdbacdaccbbaccbbbcbdaaabbdbabaaaacacccbaddcdddcddcdadadddbcdbcbabbbccbdbcdbdddadccccaadbdddcaabcccabacdaacabcdbaccdccdbccddbacdddcdcabbcbacdbcaddbdabcddbdbddcbbcbcdbcdbbaabdadddbccdcccddbbcddcdadabddccbbdcdaaabdcacddbdccbcadbbddacbadcbadddaadddbdddbddcbbdbaabacdbadacbddcccacdabbcadbddaaaabdcacadccccdcaabacdddcbacdbcaacdcccdcdddbbbcbdabbadcdbbdbcddcdcaaddaabacadbccdacdbdcddddacaddbadbbdcadbcadcacabbaacdacccddcabbaacbadbccdcadddcadababbacadcdaacaaaaacbcbbabaabacbcbcccdccdbdcbdcaaacbccabdddbabddbcaadcbabacbadbcaabddcaacddbbadbcabcdaacbbbdadabbcabdadbdcdaccdcbbcdcdcabbdbbcddbaccadcdabbddacacccbbdcdabbbddcbaacbcbcbcbdaaaadcbaddccbdddddbcbcccaddbddbdbbacdcdbaabcabdabdaacacbbcbbdabdbabdccdcbcccadcdcccbadbbbcbccbabccdacccabdbaadabccdcdcdadbbdabbdabcdadcbddbaadaaacccbbbdccaadabddbcddcdacadcdcbdbabdbbaddcabadcbbccdccdbbcdbcdaaabdacbcddcbcdaaabbacccccaaaccacbbadcbbcaccabcaaacaddcaddcbcadadbaddaadacbbdcccdddccdbdcbadccbacdaadaacddcbbdddadddbbdbdbbabbcadacaadbbadccacaadbacbbddbdbddddaccbacbaadcbbccacddccbabaadcdaaaabbdbcbbbadddbacaabdbbadaacbcbcabacabbbaccdbdabbbacbbbdaaadcdbcadabcdbbccabccbbaabdacbbadaccaddcaaabddaaccdcdcbbaccaaabdccbbcacacacaccdacdcabdabdcadadaccdcbdadbbddabcbcbccddcddcdaacabbccddcbcbaadcbcaacaadbdbadbbdaccadacadbddadadabcaccacddbbdddadadcaabbacaacabbcdccdbbadaadaadddcadadaaddaabcddadcaaddcdacdccdaaddbdccbacdaddabadcccccddcbadabacacdddbabdcdadcdddacbaadcccbababccdbbcbbabdcdaaaabadbcdbbaccdbbabcdaacccbccdbdcccbddbcaacbacbcaccdccbbbcdcbadccbdcbdbcdadacbacacbaaaccabdbccdaadbdcdbbdcabadaccaacaccbdbcdccbbcdbbbddccaadacadaccaabacbbbccbadbadcccbddabbcbabdccbbadcdccdbdbaccbdbcddcbdcddcdccbabaacdddacdadccccbbcadcbdddbbaccaacdbdddacbdbdabaaddbdbcdbacccdacbcdcabcbddcbbadccadddaaadacdbddbcdaaacbdbcbddcbbbacacdbbdbbadcbbaaccdbaabbcdadcacccbddcccababbccbaddbbabbbdadaacbdacdcacbddbddabcddaabdddabbdaabccdcbdadaccbdcaacdbcbdccdcddcadbacbcdbbcdcccbddbdacbacddabdbdacbdbabcdcaaabdcaacaaddbddabaaaaccbcccbaabdbdaddbaadaadaabccadbadddaaaccddbcbacacdccaccbacbabcbaaacaddcbdaaacdadcddcccadbcbcdcaddadcaaacbdcadddbbbbcdccbcbdbaccdcbcdaaacbdccdcbdcbccbdbbdaaadabadddbbabbbbdddbcbbcacbdcabbdcabdcbddccaddbcdcdabbcadaddabcdababddabcdaaccadbbaadabbbcbcbcdccbcdacbcdbcdbdccdcbcdddbcaaaddbbcbaabcbbaaaacadbdaddabcbbcaacdadaacbbbbabbcbbaaddbbaaadcccdbaadbaaccdcbbdabdbcaccaddadcbbdabaacabdcbdadbcbabaaacbacccaacbabcdcadbccdbaaacbadaccabaacdcdbdabddbabaadbdaaacbaaccbbaabaaaabddcbdcbddcdaabcbddbdbbbbdbccbccbbcaddcaaabdacbdcccaaccbacdbbadbcdaadbdacbcadabadddbbbcddabdcbdccdbddbbacaccdddaabcdbdccdabccaddcdabcaaaaddadabccaabcbdacccaccdaaabacacbccddbacabccbabbaddcbddcdcaccdbdacbaccbcaabcdcabccbdbaaddcdcbdccbcabcbbaadbbbdaaadccdbcaacbddbbdbbbdbdccdbdcdbcbaddddbaaacccabaabadbcbddcdacbcadaddcbadbdddabccbacbbdaccadadbbdbbaaccaddbdcbbcbdcacaddababdbdabccaadddbccbdbcacaddcbdbccdababbbbcbababbccddacadaccbaddabcabbaadacdcadacccacdacbddacdbaaddccdacbddccacbccbdaadcdcbcadbbdbdcbdddbdbccbcaaaacdaacccccdacdacabbabbccbbccbadddacabbadbcbbaaabaacabbcadbabddaaddaaccdbdacbaaacddbcccdbcabccbaacdbcddcaacbababcbbcbcbdbbdbbbbbcddbbbdaadcaacdddbcbaaccbbaadbcdbdaaabbaacbbbaababdaacbcacacaddadcdccdddaaddcbddbcccdaddcdbaabcbbcabbabbacdabbbadcbabbdabcacaabbbddbcccbccccbcbbcdbdcbacdbcbcbdacbcddaababdbcadcbabcbbccbcbdcbdaddaadbcbaacbadcabacdbbabcddccaadbabdbdbaadcacaaaccabdcbcbcdbdadabbadcdadbbbadcdbdcbbbbcddabacdbbbbbdbadabdddbbdbddcbabbbdcbdacdccabcbbadadbaddadcbadaabcaddcbabbbadbaaddaabcdddcddabcbbabbaaccbdabbbabccabcbbacbddddbbadbddadbddaaaacddadcbaccdcbacdaccdccbdaddcbcdbcddacbcdcadcaabdddaaacdbbcbccddacdcacbaaddbbdcbaccddddadcddabadddbccbbaddddaaddadaccbbcadccadaccbcccaababbdddabccddacbbdbaabcbddbbdabbbdcacaacacaabdbdaaadbbccddaddcddcbaacdddcaaddbcbccdbcdbadcdabcdbabbaacaccddccdbcbaaabbadcaacabaadabaaadccaabdaabcabadbdcccccacacdbabdcaacdacaadbddbbbbdbcddcbabbbaccbbbdbbbcdbcccbdbdddadcccdcbcacaadcbadacbcaabcbdbddccbddacacacdcacbbcacbdddcccdbcdaaccccbdacacaccadaadbccabbdcbbadadcadcaddddddbcdccadbdbddacbdabbdacdcccbacddaadcccbbbbdcdbbcacbabbddadadcdccaaacaddbbcdcdaaadbddddaccabadbcbdbdcbcbbcbaabdbdbcbcbaaccaadbcbaadcabcbccdbccdcdccccbdcbccddcdabddddcddadbbbcbcdcbbbcbdbcacaccbcccdcacdbbcbadaaacccaadaddbaabacbddbddabaabddadbcbbacdcbddbbacddbcbcbccbdddbddbaacbbccdacbdcccdbbbcbbdcdabacdcbadcbabbbccbcbdccaaccbbbbcbdcddcabcdbbdccbaaaccbbaabdcdccddadbccaaaabaddbccddbdbdaadbbdccbbccabaabacccbbbcababbadbddaacbcbccdddacbabacbbcdbaaaabcbcdaacaccbdbdbaabddabbccdaadbbdbdbcbcbdcbdbaaadbadddbbaacaacbaccaadccdbcbcabbbacabcabaadccdbccbabbbaadabdcacddacdabddcdbbaabddcdbdbdcaaaaacacaadccaacbabbbadddcddaccaadddbddbdcdbbdcadbaabbacbcacbbbcadbdbbaaccdbbcdcacabaabccdbacbadbcbdccbdabbcbacdaacdddcbcbdccadbdcbbdcabbddbaadcadaadddddbcaaddabaddddbbdddbcaaccbcdbdabddddadddaddbbacbbcbadacdaccacccababbbddbbdbcccadcabcbbdcdabbcbccaacbccdcacdadcdcddaaabbcbdaccbbbacaabacbbaabbdaabcabcacbbdccdddcaaacdbbacbabcdaccaabcaddcdcbcdcdbbbdddcccdcbdcaccadabaccaadcbdddadababaacbcacdabbaaadbbbdcddcbbabbccdbccabccddbaacaaacabaccdccbbabcdadbbbaaacacdcbbcdaadacbbccbddbcddbcdadbbacdbbacdabcadbbcabbdacabdbbbdbcaadaabdaabacbbbbaaacdbdbbaddbabacbdcbaccdbdcbccdaaacacbcacaacdccdbbdaaaabbadacdbabdacdcbabdcbcccaddadabbaccdcbcdadbacddbdacbcbbdbadcddadbddcdaaccdadadbabacdcdbcadccabcbbbdcdcddbdbaadddacaddbccbbadacabaaaccbbdddaddabadacbdcbbabaacbbbdcbddaababacdcdaabcadddaaacdcadadabcbaddabdababcccdbaaddbadcadcabbcccbadbacaadaaaacddbbdcdbddbccadcbdcbacdcdccdccbcadbcdababdcbaabaaabccdbbaadabaacdddcbdbcbccdacbdccbcdacbddcacbaddbddcdccbcdbcbbcbbbadbcacbbcddbdcbbdaadbdaadabbddabdcdbbcdbaccbcbcdbadacbacbbddcdccccbdaaabdbbacccabbbccaddabbabbdbbcdcadcbdbcddddbaacadbbdacdcdddbdcabcaddadbacabbbdabbbcdbaaabbbcccacdcdbabcabdacdccdacbaccddbdcccddcdcdadcbacccdadbccdbdddaddbabadcbbbcdabdababaadddcccbdbcdacbadcbdbbccbbdccabbadaaabcdabdbcbadcbcbbdbcbaaaccadbccbbadbdbbacdbaadacddcdcbdbcabdbcadbcbbabcddaacbdbadcddddbaacdddcbccaacadcdbbbbbacabaddbbaacaacddbdcdabddccaccbdbccdcddcccabccaacdcadbabcabccdaccacddbbdddadacadcdbbdcabcdcaccaadcadabbaccbaccccbdbabddbabbadcaccbabcaadbdbddcdacadbacdacadbbaabbaadcdbacbadabbddcabdcbaaccdddaabbcbacacdbbabcbccaadcabacbcacabacdbabcddbcadbcdcbacbadadbdcaddabcdcdacccacdbcdabccaabdddaaddbacbacdcaaaaacdbcccccdacdbbddaaacacbdbabbbacdabcaaddcbbccbbdadbbbabdaddcddccbcaccddccbddbabbabdaddaacadddaaaddbcacdbdabbabcaabbadabadadbbbbddbcdbccaacadcccdcdbbdccbbdcaddccbdaaabcddbccbdcaaccbbbcbcdcaddadddadcbacabcbdddcdddcccccdaaccbcdadbbabbdaaddbcdddababcdbacbbdbabcadabbdddacacabbabaabddbdbccdddcbacaacbccdabacbadbbddbcabbccccbadcdbcdcdddccadcbcaddcbadbcdbcbcbaadbcbdaadadcaddabcbdccbacbcaaccbcacbcababcddcdabccdbbddddadabbcababddbcbdbbccdddbbadcadacaddabcabbabcaabbddbcdcaccaaccbabbdacbcacadbabcadabbadbcbbbbcdddbdcdaddcdcbbdcbdbbccbaaccdcdbcdcccbabaddaaaacaabacddbadbdacbbbaabbadaccdddbcaabcdddcbbaccacbbdbbcdbccacaaabccabaadddacdabbabbdbaadbbdbcacbccdbddddcadacabdacbcdbcddadcaddababcccbddbddddbaabbbccdbbcbddbdacacbcbcbddddaccbbbbcccdcaabbaacacbacddcbabdcccbdbdaacbdcacccbdcbdabcbddaccabccbadaccddbabbccaaadaddabbaadacbdddacaccbaccabbbdacddccbdbdbdbddbdadabbbdabbaabdbbccdbbbbdbaccbbcbbaacaddadccdcbcbcbaadacdcdcdacadaccadbdbaccbaabacaaccbdabdcdcdcbbdbddadbbccbbcbccddccbadcdabaaaccaadccadabdcabddbaadbbcbccaabadcaaadbcaacbbddcbdabcddcbbabadacaddaccaccabcacaccbabadabbcdddabacbaaaacacdaccdacacacbccdbdbdcbaabaacddccbbacbbccdcaadaadddccdbadbacaaadbaadaaddbbddbccddbabbbaaabdabcabbbbbabdbabbccadbbdbdbdbcaddbbadaddcbdbbdaadbcacaacbacbdaadddbdcbdbcddbbccbcddacdcdaadbbdcabcadacbabaccabaadaacbcadadddaadbbdbabcdadbadbbddcbddcaaaccacabdbacdcddbdabdbcbbcacadcacadbcadacacdbadbbdaadbbccbaadadddbaacabdbadbadacdcbdbbdbdbddbdcacadbdbbcdadcbbcacbdcaddbcdababcdcbabbdbcdabaabdcdbadacbabbcaddabaabbaaccbbdcbaaccdbbbaaaddbaadccbabdccadadbdacdcacbcddadabdcaddcdddaaadcbdbccbacaddcdababbddbbbdacaacaddddcabaabcccadabdcbabadacddcbbabcaadaaabdabcabdcbdaadcdaadcbaddddcaccdacbdcaccbbcdbdadcabddbaababbadaacddabbacddbbaddaddbadcaccbdcabccabbdbadaaacaadabbbcdccaddadcaaadbacddcadddacdaabadcdacbadacdddabbbcbcbdddbcbbcdcaacccbdaccdbaabbdacccddcdbddabcdbabcabadaddaaaadabbdbbccbbcdcddacdbdcccdcdbaabaacacaabbdacccbacdacdbddccadbbbddcdcbadcdbacbadccdbccbbbbbdbddbdccabadcbcaddbaacbcdaccbaaabcddcbbbbadccdabdaaadbcdabcbcaddcaadacbbadcdbccabdccaabddcbcccbacbcdcdbcccadaaccbdacbdadbabcddbcdbbdddacbacdaaccacdcdcccbadadddacacdadcddacdbbdadbbcddcabbddbcdbdaccdccaadacbbaabcbbddcbcaabaacaaddcdcdddddbcbadabbbcacbdabcabacdadaccbacbcbbcccabcbbddcbcddcaabddacbcaaadbdadddadbaddbcbbdaddbacadcaabdabddcbacacdbdccaacacddacdbdabbdabcbdcabbccabacbbabdcbaccbadddacbbbadcabdaadcdaddccdcadcdadaaacbcddcdbccbdbcdcbaaacbcbcbacacaaaadcbddbdbbabcababacdbadcdbaccdcaadbcdadaaadacbbdacbaaaccbbbbabcbcacabcbbababdcdbcbbbabddcbdcbcdbdadcbaadcddddbacbbbabbbabdcbbccacbbabcabaaadbaacabaadbcaaddbaaabadcbdbdcccccddbdadcadbdbddbdaccbbacbddbdaccdddbcddbacbbcdccababdbbcdcdcbadbccbdaadacdcabdadabddccadbdabbbacdaaddaabbadcbcababcbddcaacdcadbdabdaadcdbcbbcdcdbcbccbdabbaddccccadddcaacbdcaccddbccddccbadbaabdcbacddbabdbccdcdaabbbacbcdabaccabdacccbddbbaacdbaaccaaacdbabbbbbdbdcadccbdccadccaabbbabcdbdbcabcdcabcdacaddcadabcbacdcacbbcabdabcdaabdaaddcbbababbcabcadddbdccbbcbbdcabcacbcaccaadbbbdbdcbaddcbdddcabaacccddcccddcdabdbccbdaabdcbbaddcddbacabcacaabcadaadcdbcaccdccddccbbdbbbbccadacbacbdabdddcbdbbccccdcbaacdbdbabdaaabcdbbabaabbccdbabcccdabbacbbacccbcccbccbddbcbbbaadcdbadbcbbaaadbbddcbadadaabaccbdddacbcddbdbdaadcabccbaddbbdccaddadddcdcbacbdddbacbdbcdadabddacadaadccaabcccaccbbbbbaabdcdabcdccbbabdbcbabdaabcdacccdccdadcbcccdacccddcadabdddbbcaabbdcddbdbaaddbdbbbdbbbcdcdadcccbbddbcadabadbbabdaacacdcbadbababcbcacddddcdbdabbcaabaaabdabadcdbbaabbbbacadbaacddcacaadbcccaccbdadadcdaabacacaaababdccabddbcbcdadaaccdabdaaadabacddcdbaccaddccbbdcacacdacdbdcabddaadcadaddccccadacdbdccdacddbcccdaadddbadbcbbcacaadbcaccbacdcbcbadaabbbcadcabbaccadabbaadacdacccccbbcdcdbcdcdddbbadcacddaddaadcdcbbdcbabbddbdddcbddbcbdddcbdcdcdbdccbbbadbccdaddcdccddaabdddacabcbcdbaccadbdcdcadadddacacaddcabcbcbcbbbdabadbbdabdcccadadcdddddacabccbcbcdccdbcbcbbddbcbbcbcaaddbbcababccdddbacdacbaaaacccdcbaddbdcbcdbcaddbbbdadcacbbbddacacddbcbaadcdacdabbbddbdcacbbaadaddddccaadadbbcbcabaaabdcaacaddbaaddacabdaacadbcdaabacbccdccacdcbcadacdbcbaadcdacbaaacbbbcacdbbacabbcbbcbbababcdbacacccabdcadbaddbddcdabaccbbbacbdaadcbbddadbadcbddabcccbabdbcaaaabacaacbbdcddbbdbddcaaccccbddbaccccabddbcadbbdddcaccaadcadbbddadccdcdddccdccdabdbaaaabccdbbaabcbacdbcadbdddabccdcdccbdbbcbcdbabdbadaadaccababddcbccbcdccccaaccaccdcabdcddbcdcbcdbadbbcabcadddcaacdaadcbacbadbadcbdbaacbabbabaddbcabbabcbacbbbacbccddaacbaadbcabcccdccaabcbbddabccbabadabbacabacadacabdbdadcbabbdccabcaabacadbaaddcbbaaabadddcccdccbaabdcbaccdbbdababcbcdcaabbdcccadcbddbcddbadbccccbdbdbbdcbbcdbbcaaaddacaaababcccddbdaddbaccaacdacabcadabcabcaacadcccccaaabaaddbbcbbcadaacacacacdbbddbccdddabcddabcacccdacddccabacbabcddacbcdacaaadccacdcccabbcdbacdcabcabbcbbddcccdbddddddddbacccdabdcbddaabccbdcbbbdbdcaabcdbcabcabdddbcabdabcadbaabbdddaccdbcdaacacaccabcabababdbcaadcbccbcdadbcadbabbdbabbdcdacaaaadcaaabcadcdadcacaccaacaccbddcacdadccbbccddadcaadbccdadadccadcdbbdbdccbdababaaabbdbcccbabdbbacddcaaddabcdcbaacdcbcadaacbcdddcdadaacbbadaacbcbdcababbabbbccabacdbcbbcbddcdcabbdababccccdadccccadcbbcddacdadbcbdcaccadacdbacbcaccbdacdabdaddbbcdcbccacadccdaabaddbcbabaddcbcbadacbbdcabadccbcaadabadbcddabddddcbdccbabdbbdbaadcbcbdcdbbcabbbbdccacbacadabdbacababadbadaaabbddcdddcbadadbabdbaccdbcbdccadabaddcdcdacdddadabcabbdccbdaaabaaadaddbaaccdaccaaccbcbdaacdcccabcacacdccddbccaacdcdddadadbdbadbcbdabcbbbaccdaabbbcbbdaaacacabaccaadadabadddadbaddbabbddcdbbccaaddcbaddadddbddccbdbcdddcdddaacaddcabaacabdbbbdaadadacdaadbddccddcdbcbababbcbddabdbbbcbadbdadbdaddcdacddbbdbbabdbbcddaacbcddddadaaacbdabbdbbddddbaacdbbadadbbcdadccbdacbcabbaacdcbbdbbdacabdcdddcaabbdcccbdadcadaddbcddadbadbaadadbbddcbcabcbcbcddcbaaddbaacbdadbacbcdadcdadaddcdcabddaacdcbbcabbadababdaaaadcbdbacaccdacdaadcababdbdadddcdcabdcabadabdcbabbdcbcbbbabbacbadcccacbbaddbbdaadcbbcaddbbcdadbcaadcddbbdabbcabadacccbbdbbadcbcdabbddabacbbcaadcddabaccacccadabbcabcbbabdbcabdbacddaaccdbcccdbbcdbbcdcbdbacbcbdbaddacabbadcdabcaaaccbbacdabbdbcaabcccbccabddabcabbcacacabdaccabdcbaaabccbcbbacdbdbccdbcdcacccbbbbadddbaaccccaababaaaacadddcdabddbacabbadccbccbdbacabcbcbbcdddbddbdabbdadabddddbaabbbbabcbdaccabddbdbbdddcadddcbdcacadcddaacddabbcdccbacbdddcdbdccaabbdaddbdaabcabadcacaaadacdbabbbdbaaadadcbbacacaadacdcccacdcdcdbddaddbcaccbccdcbbbbcdcbbddcccaddcbabdcbdbbaaacddabbaababcbcddbbabbdbaccbdbdcaccbaadddbcaabcbabcbcdadaabadacbbdabddcdaddccbbdcaaccbbccbdcddaacaddaacbcbcccdcbdabbdcbdaabdddbdddadaaadadacbdbcacabbabbddcaaacdabaccdcabcadaadbdacaadbccbcadbadcccaddcccbbcbcbbdcbdacbdacbdbcbcbcbdcdacaddbddadacdadcaddbaaacbcdcadcbdbacadcdccadccaadccaabccccaacabcaacccbbcaabacaadadccbacacaddddbbbaccabccdcabbcadacccbabacabaabdddbabaccabdddbcabcdccadbdbaaadcbddddaacdaccdbbadacbabaacbaaddbccaadaabcddadbaaadccadabbbcbddadbcbcccbdbdbcbcddabbaaabccaaccdadddaadadbbdcacabddadbccbbccaaadbacbccaaacccabbcbdbbadddddcaaadddbbbaaabccacbcdbbabcbccbabcadbbcdccbdddbbccacdbbbdbaacbdcbbbcacbbdbdbcdabdcacbadcbaccabdbacbbaabdcccaacaacbdacaaaccdbcbdcdadadbddaacdabdbadbdbdcbaaabbcdcacdcdbbcabdadaabbdadabbbcaacdccdcadbbdabcdbdcaccadacddbaaddcacbdcccbcadcdabcbcaacdbcdbcccdbcbaddcbbcabdbacbbbadbcaadbadcacdacadabccaddcbdcccbcaddaadbbcabccdaadaccdccdbcbcadbdddccacabbbdbabbabcbbadaccaddbdababcbcabbcabcbdbadaccdbdcaccdcbbbbbdbdcdccbaaccaaddabccddbbcaccbcbdddbbabbcdcddcbbacbcddcbabccbdcccbaadacabcbabcdbacdcaadbdcdadadcdddccdcdbadacdabcbddacbdcadadacabbadaccbcdadadaaaccccbadbccccccbcdadcbbdbabbadadbdabdbdccdcbbdbcdaddaccaacdddabbcbacbcbabddacadacddbcdabbdbbbaabddcabdcaaccacbabcddcccddbbaaadaaccbbdaddbabdacacadbbdbdccacccdbacbccbaadacabbaadcccbaaadcbbdbddadbbdacbbdadadabaccacddbbbbacbaaccdcdddccdaaaaadabbabbcdbabccdacbddddcacaaabdadabbabbaccbbaddbddadcdcddddddcdbbcadbccacbbaaddbbadbacdbdcbaaaadaccddaaabdaabbccacbbccbadabcaacddbddbaccbbdccdbdbdabadbdaabbadddcaddcbaccddbbdabddddbbbcddcaadbbccaddcbbacbdabccdcccbdbcdacbdbdadccbabaccbbbdbdcadbacbcadacddbddbaccdcbdddcadbdaacdcbbccccdaabddcbdcbbccdcbcadbbdcccacabcaacbbcabddddbbcdbabbdccdcbadadddbacbacaddacbcbcdadbddcdaababdabcccdcbabddacdcaaaabcbcbacbdadacbbcccacacccbadbcdbdbcdbabcccaccbbcbbddcbdbcbcccddabccddbabacbdacbabbcadbdabbdbddcbccddcdddaddabacbbdccaacdcccaabcbcdcddccbadcadccdddcbadadaadbcddcdbadcdbddbabccbabdbcaccddacdcadbdddadbaaddbacbcdccaacdcbcdabcbdadabcbbddadddabacdadbcddcabcacdacabadcbabdddbdadbabbccadddadacbdddcbabcdccddaaccccddcadcbcdabdccdadbbaadbaadaddaddadadcbabbbbaabcdadaddcdabccbdbcccdbcdaccdbbadabddaacbbacbcbbbccdbcabcdadddacbdbbdbdadcdccaddcdbaabddbbbbcadbcacddbddbbccbbadcadcdabccabcbddadcaadcddabbabccbddcbadcccdbaadbabbdcdaccdccaaadcacbbcdcacddadcaaadacbbaabddbcdabdbbddbcdaabbaadbabaabbabbcbbbadacccbaadddbcdddddbcbbcdabcdacdbabddbbbadbaddbaadcacbdddccaaacdadbbbcdadabcacacabbccadcadabdddddbabcdacccdbcdbcaccbcdaddadccabbbdcbbbacbdababbbcbdbdccbacdabbabddacbacaabaaadaccbaacdbbbcaaccadacbdaacccbccaddbdcadaadbcdbddcaadcdacdbdcacbdccbaddacddcccadccbbaddbccbcbddcacbbbcbccdddcaaabcbadabdbdddcbdcdcbacadbcbcaadaaaadccadacbbcabccabdddcbcbcbabbdbabaadbabcbbdcadaaaaaaabadbbacbacacaaadccaabcaadccbdaadbdcddbbbbaaccadbbabbacbabdbbaacbbdaccdddacdacdabdadbabcbbcdacdbbbdcccdbddcacabdabdaadacbacabacdcbacbdcbdaabcbdccdaddcbadcadcadbdbacbbbdbacbadcccadcadcccdcccabdbcdacbcacddacbccbcbcbccdacaaddbaddbcabdcbdccbbadadcacbaaddacdcdbaaddadcacbddcddbacdcababadcdbddacddbaadbdcdcdaaadbdadbbbbccbacdaddaddaccdcabddadddabbcdbbbbcdcbccdddadadcadadacbacbbabbaaddcdbdbddddcabcddadcbdbddbddddacabdabdbcaadbdbcbcddaabaaadacbbddbadacabddddcbdcdaaabddcabdccccccdcacccbcdbdabbabaaccbbdaaddacadabcdbadaaabbccdcadbcbdcacdaddadaaddcaabbddcaaccaacacccbdccccbcccddccdcabbcccddadbdbcdacabccbddaadbcadcbcccaacdbbdbdadcdbcabdaccacbdbcbbcaadbdacbaddddadcadbbbbdabdadbbdcbabddcbccbccbdaaabacddcaaadbaadcabbbdaaaddabcaabcdbdcdddbbabdcabbcabdacacbcabccdbbdaddacabbacbaadcccaddbaadaccccbbabccdccbbcccabddbdbdbbbcdabbdaddccbccbdddaabacccaacaccbdadddbbbdabadbddbdbdddcdaddbbadcbcdcdcbdcbbbacbacdbaabcaadbcdddbdacabbabcdbcbdacbcbaaddcbdacadcadcdadbdcadacacadbbdacddddacdadaccdccbadbacbacacdcdbccabdbbcbdcdbdadcbcdacbdaadaabbaadacdbbdcaabbddaaacabcdcbdaadacadadcabaabbabdadcbdccccbdacdbccaacaabbbcdbdadcbcbcadaabbabdabbacbbcbbaddcbacbdddcacdacbdbbaabccacbcaabbdcbdccacdbdcaabcccbbcbbbcdcdaadbbccadadaabaacbaccadddaaddcacbdbaccbcccdadbadbabaacccbbccbddcdbbcdbbaadaaacbaadabdbccdabcbbddcbaaccbbbaabaababbbcdbcadddbbaaacdbdcdccdbdadacaabdccddbaacdcaccbadacaccaccbaacdacbbcacadcaccddbadbdabbbadaccadccccdccdcadbdcacdbdccdddadbdcacacbacbdbbaabadcdddbddcbcdacaabaccadbcacbabcadabbcbbaaadcbabddbbdaccbbaccacdcbcbabdbbcdddabccbdddacdccccdbdbbdcaaadbcbdcdbadadbacbaacaadbdaadbbbacbcbcddabcadababdcbcdaaccabacaaabcdabbcabbabadbdbdbcabddcbabcadbbdcaadcacacbadcbccaacaaadbacddacddddcaccbdcddbcdcacabaadacdbadbacdbaccabcbbabcaaaadcddccbddddabcabddcbaadbdaccabdcbaccdabcabbcdacbbcddccbcbacaaaccdcadcabcbabcadacadabcabdcbbdaaaaddcabcaccccddacbdbbdaabdabddcaaaaddcabbbbdcadcaadbbcbcddaacbcabcaaccacddcdabaddddbabcbdcbccaacbcbdcabddaadcabacbaddabdaccdcdcabbcabdbcccabcbadbabddcbdcddddcaccbdbcdacacbaacabbdabbacccdcdcbaabdbdaddbcabcbddadbddcbbbcbcbccdaadbcdcdabcadadcbdadbddbabcdacbdacaabcdddbabccabddbcbcdddbcdaddddaccabccabcbcbaadcbbbcccdcbdcbddcdbdabaccbcdacaadaabdcbaadaccbbdacdacaccbdbcaadbcadcdaaabcccddadddabbbbbdcbccbadaaababbccdddaccdacacdabdabbccddcdcdbbabbbcbdbbdacbddbbacabdcdaadcadbddbdabccdbdcbccaaccbaabdcdbabbbbccbacbdbacdaabbcbbaaccacdbaadbbaaadaabcaccbacccdcbdbabacaaacdadaddbdbccbabbbaaaabdadbaadbdcaababcabcbcbacadddbbcacbcaabacdbdcadcdbdddbacbddcadbaaabbadcdabdaadbcadabcabbabdabbabaaaccabbabcbbdbadcaccbdbcbcdcbbbbdcdccdadcdabaccdddbbccaabdbdaadbdbcaacaddabccdbdccaacbddcdcbbabbabcdaacccaadccbcddadabcaccbbcddbacdcbcadcbacccacbddcbbccbccdccabdbcbaccdbcabdbdcacdccadbbdbcabdbbddadcccdbbbbddaacadcacaddbaddacabdaaadbcaacbacccaabcddcdbccacccaddbdbdaacdbbaddbabaabadbbddddaadcacabcaabcacccdbbdacaddabcbdbadcdadbacbabbadbbdddccdccaaaabaccbbaacddbbbbabdcddbaaabdbcdbdddabccccdbdcabbabacbdcabadcabccaaadbaccbbdabcbaabbaadbacdbdddbcabbacbbbacdaabdaababbbaccccccadbbadbdcdcdcdccacadddcadcbbbcccbabdcbcbaccaabddcdacdbbaaddcbbacbadccbdbccadbcbccddbaaddbbccbcbbaacacdcaabccbcdaabdcccaaadbbcabbbcadccdbbaccabaccdbdcacbbbaddccbbdbcdbdddcacccdbbaaadadacadbbaadaddcacbacbaddababacdccdaabcbbaaacbaccadadcaababccabcbaadcaccdabbaacabcdaacabaabaaacabcdabaddddbcbacddcddccacdbbbdcddddaaccdbabdadbdbacccbbcdaadbbaccbdbcabcaaadbababcbaadadcadbcbdccaadcbcdaacbbbadbdcbbacdcddcddbacbdaacddcbaaacbcbbaabdbbdacdcddbdabccdbaaacaccccddaaaaacbcdccccddcddcaacbbddabbbbbadcdacccaaacbcccdaabcadabcabbbbbaaaacadbacaabbabdbbadadcaababcdadccaccccdcabbcbbcaaccacbadddacabdccdccaddbbdcccababcdbbaccbabcadbacaaddcbdddababdddacbcdacccadccdabccadaccbabaacaabacacdddbbaadacdacadbdbcadcadcddaddbbbbbdacdbccbdcabcdacaaacbdbbbbbbcbcaabadaaaabddcacabaccadbabadbdaddbdbcaabcbbacbcccdcaccbcbbacdddddbddddbcaabdbbcdcacbabacacacacabdcdbadcddadbddcddccddbdcdaacdccdbdddbbdacaacbdbbadccddaabbddbddcbbbdbddcabcbbaccdbdaaacabcccdacbdaaacbbbddcadccdabbcdacabbddcbdabbccaadacacbacbadbadbaabbbaccdcabcbbbdbbccbabdbacdddcddaacacbbdddddbcdddaaaabccddacaaabcdcdbbbaadcbdbbaabbdcbadadcbbdbddbbaabcccbccaaaadbababbacbacabadccdabaabddbdaccccabcadcaaadaaccddababccdbcdaacdbdbbbcbcbaaddacdbbbdabbbacdadabbbabcbabddddcccbcddbaaaacacdcdbcdcaabcccbdcdcdcbadcddcccbadbbdcaaadbccdddcddcdbccacacdaadadbaadaaaadddbabadcbbdabdbdabcbbccadccdbcdacadbdadadcaabdaadddaacbccbbcaabbababacddaacdbbaacabacdbcdbccdcccaadddaccabdbcbdddddcbdadbabccdbabbadbbdbbdcdcabcbdbabacdbadbdadbbcbabbbbcbdcbbbdadccaadbcdadcdbccbdcccaaadcccacadadadacacccdddabddbacccabbdabdcbdacdddaccbccbdacadacabaadcaabacadbbbcaddccadabbadaadaacbbabbdddbaadacaabbbdbdababddcbcabccccbbddbddbaddcccabddcbaaabcadbbdacddaccabbbbddbcbcdadcdadbccccabcdcbdccdbdacdbbcdbccabadbacaacdcadddaacbcdadddbdababcccbdaabbabbbdbccddbbbcbabdbadbbacaacbbaddcabacacdbdddbbcdcbcadaddcaccacdacacddddacacdcccacdccbddbbdbabdbdcbdcaadcaaabacabcbdcdacccbdcacddbbcccdaadcbcaccddcaaccaabaaacddabccdabcadaaccadcaacbbabdbcbdbaabadccdadcccdaccbbcbdcbbcdbbbbaadabcbbddaacddcaaccabcccdadadaccdcdcbbbbadbaacdcaadcacabbaabaaccbdadbacaadbdcacccbadaccdbdbacccbdcbcdcdaadddbdddcaadacbbcaadcacacbcddbabccbacbbddcabbcddbaaaacbadccaaaaccaccdbcbacbbdcbccababcbaaccabdddccbdbdadcccbabacadabbadabdbaadbbbcabaaccaacabdbccbbbcdcbdaacabddbdabbabbbcabbccaccadcdbadcbaadcabcbdbabdcaabccbcddcaccdaaacdccdbabddacbdbacaabaaddbbcbabcadbabccdbabdddbdbadcbdcccababbdacddbbaaacdddaaababcabbabbacdbadaadddbbbaabddcdaaaadadcacbbdddacbbbcbbbdbbbdcdcbbbcabbcadadbabccadaccadddaacccadcaadcbdaacaccdddddcbdabbbddacbdadccdadadbbdccabaaabddbcaddcacdccbccaacaacdacbabcbcabbabcbccdcacbdcabdabccababaaccdbcbccbacabdccbdacabbaaacaadacacbababcbbcdadadbacadccccabcbbcacdbbcddcdacabcbdaaadbcddacdcdbaccdcddaaadadccdbabdbaacbacaadccbbccaabddbdccaddadabaadcddcaadbacaaacadccbccbdbcacdbbaccddbdbbbcdadbaabcadcddcaaccdddcdcbddabdbadccabbacbdcbcaabdccbcbcdcddcbacbccaacabbdabdddbcbddddbdbcdcaacdbbbcbdbbcbbccbcbcdddbaccccccddcaddaaaacccdbcddbcaddbaccadbbbddababaacccaaadabcbdccbdaadadabaadddddcbcdbcadcbacbbbdbddbabcdbadccdddcccacaabaddbcdaaabbbcbdcacbdccbcddbbaaccabccbbaddaaddbbacccddacbdbcbddddaabadcdbcdcddabccccbabbbabdacbbdbbaddccbdbcbcbabdaadacdbbccbaacaaaaaabdaaaacdcacbccddabacadadcbbdddbcbadacccabdcadbbbadbcddaacacbddaddcdaddbaaccbcbbaabbadcbbbccbccddcdadbdadccacdcaaaccaaaddaaccacbdcddaabaacdcbaabbcacdbbdcbadbdddbadcbcdaababaabcdaacbacbccbddbaaaccdbdbbaddccbadbdcabccdcacccdcadabddbaacabcddbacbddaabbdacacdbcdcadbbdbbddaccacdacbbaddcadcdcddbbdbddddaadabcbaadaaaadbcbccbbbaabdabbcbbadcabcdadcadbadaadbbbbabbdbdabdaccdcdcabacbcbacdaccdaddaccdbddcadbcdabcbbcbddddadaaddbbdcbabadcacbdcdcddcbdadccbcababadbbbdcacdbdcadbbbdacdbbddcadbcacbaabbbbbbcadcacdcdcdccbcbbdddccccbddcadbbadcddabdaaabbcbcdcabcbaacbadaddbbcbdabcbbbcbbcbcccabcabbdcdbadbccbcaaadbcdbdddababccbcbdcdaaacaccaddcdcdaddaaccacbbbbbcdcdccabacbddcaaddaccccbcaaddcbbcaacacccbdccabcbbbacaababddcbdcabdbcbacdbabacdcbabacaacaacaacdbdacdbcadcddaddbbbaddadaabacadccddbbdbacccbccacdaabcccccccdbcbaddababdcbcabacccadadbbccbcacbbcbcbddccdbdadcbacbabdcdbddaadcbcddcdaacabccbcccdcbccdbbaadbaadaacccbbbabaccabacddbaaaabddaddabcbaadcacbbbabbababcbcdabaccdacadccbcacaabaddaccacbbccddcaaaaccdccaaaddaddcacbbbbcabcaccacbdbcaaccddcacdcdbbddacacdadaadabdadccbbdadabcabacadacaaccccacbcbdadaadacdddbbdacacccbbbbdbcbcccbddbccddacadaabddccdcddcdabbacacbdacdbdacddadaccadadddabbabbdbdbacacccdbaabacaccdbddbcacacdbbcbdcdccbdbdbbacdadbdddbcbcbabbaabbacccdccddbdbdddbdcddcaabcbbadacbbcbbbadbccbbcbcdbccdbddcbcadbacabbdbddcadcaadbbdbdcacdabacccaaccbacccadccbacbbcdbccdbdcdadaabddbabaacbabcabacaaabdaabcccadcbbacbcabaabdccdacbbdbacabcdaccccdabcababaccdcacccbbcaaadcaacadadabaadddccaaccddadddbcdddbdbaccadaaccdaabcddddcdbcddabcbcdbddbbaddbdaaccdcabdadcaaaaddaabbddbccbcccabdddacabbadbcdacbabbbbaabccadcadbabcdbdbbdabdaabadcaaabcdbcacbabcbbbcadbadcdcdddbdddabcbcaabacccdcabbaacbacaccdccdabbbbaadcddabddbdccaddbaabaccaadaaadaacddddddcacdcabbaacabcaaacbccdacdbabccdcbcadddbbcadbdbddcabbacaabcaadaaccbddccddbbacadbddbdcbbadbcaddcaccdacccadbaddabaaacddcbbabbbaacadcccccbdcdbdaddabcaadadabbbcaaabbcacbcabaacacbdcbbcdacdcabbaccdbdadcdbcaddcacddcddaddbdcdaabcbddcadadacacddbdddbaddcddcdadacaccdadcddddaddbdcdcbaaaaacbbcbccddbdacabcbddddaadddbabcbdcaabadcadbcacdccadbdcbaccdcdccbcbdcdaaccccdbcadbddddaadcbdbddcaaddaaadcbacddadacddbbccaabcabbdbdcbcacbbbdababaadcdaddbdbabcdbbbddbdacdaddbdbcdabdcbccdabdacabaccdabddbbabbadbdbadaadbddcadaccbdacabadbbbdcdbabccabadbcaccccdaaccaababbabacbabcadbabdbcaabddadabbabbcacbaaaacbdddbdbbadadaabaacabbadccababaaadadacaddcacbbdcdcbcbddcdddcbadddbdbbcaaccbaacdaadaddaacbbadaaddbdbbadacbbddbaaddbcdbadaaabbbbbacacdbbccaacddbdcbacacccdadadbdbcbbdcbbcabbbbbcabcdcdacccbabadcacacccacccabdddbbcdabadbcbdccaacddbbabcacbddbbcbccdddcaccdbbacbcbddbbacadbbaaaacccbbbbadadabbdabcbbbaacddaccbbdaddbabbcacbbacddbbcccdaadacbdcdcccddcdccbcbbadddbbaaccadadcdababacbbacbdcadbcdabdadbacabbacddadddcaacbcaaadaaababaaaaaccdbdbadbacdbbdaaaccbccddcdbabaddaddabacacaadabdcdcbabddacacaacdcbdbbcccbbdccbbcbcdbdcacbbbdddccbcbbacadaadddaadccdbcadbdcbbaccbbbacdbcdaabacaccadbcdbabdbdbcacdadaddbacbbcccbacccabadbccbccabdaaccbcddcbcdbaddcbbbbcdaadcaadbdaabaaddbcbacbdcddbccbcdabbcbaddcbaababaacababdbbdccccbcbacdaccdbccbcabaadccacacdddbcdbbdabcddbcccdbbaababcbadbabbccbcbaccbccdabcccbbcaabcccbbdbdbbbdaabbacaaadcdddccddddcddabbcccaabcabdabdccddddacdadbbacbdddcadccacacabdcadbcddddabcadbcaddadcccbbbcdcddccccdcbbdddcddacaaadbccbadbadbcacbbbbdcddbaccbbcdbdddbcdabdaccdcabdddabdcbadcbabcdcddbaacdacdcabdddabbdcdbdabbcacadadacabbcbddaaaacbbddaaddcdbaacccbbcddcbbbabdcdadaacdcdbddaabadccdcbdbbdcccbcaddadaddadaababcbbacccddcbabaadcaacbdcdcabcaacbdbaddbabaaabcabbadbddbbbdcbcbcccaacabcdaadaaadcdccdbacabaacbaaccadbaaabcbacaaabdbcdbdccadbddcbcbdacacbcbabadaaadaabcbcbbdcaccbbcbaddabaabbaddccbadcbbadbcaccdbbdaacdcacdabbbaddacbcdddbcbbccdabaabddabbaadddcabcdbbcdadbaacdbccbabbcddbdacbcaaacacdbbbcbcdbaaaacdcabbbabaabbcbaddcbacdbdcacbaadaacbccbacccddaaadacdaaaacdbabdbcbcacddbbdaadababbabcddabbaadbcdcdacaadcacbaadabbbacddcdaacabbbaabdaacabaacbdacddbaaacaaddbaccabaaacabbbbaddbabbbdabcadccbbcacadaacacacbccaaabddbbaddacaadadbbbdcaabadccaccdddcdbacbaadbccdcbadbbacdaaababaacdabdcabddadacabaadcbdbadcbdbccabdabcddcabdabdadcbbbbbaccacccdadcbcbbbadccbabbbbcdbcbadbcdabadaacddcbdcabcbcdabccddcabcdadaddcbaaacbccbaacdacbbacabadddaaaaabcbbcaaddcbaacbbaababdaaccdcaaccacabcdbacadadbbaaccbcbbddcacaacddccbbbdbdcaacdccadaddbabaacbbabdcdbccaccccaddcaddcaddbcddaadaabdbcbbbbbbccdcaddcacbcbcddcaadcacdcaaabadbbcdbdaacddabbcbaccbdadcacabbacabddadaaadcbccbdadbccbcbaabdcdbbaabaabdacbdddaccbdcaabbdaaacabcdabadbccdabacbadcadbddccbddadddcbdbacbcdbdddbbdddccaabaaacdcacbbbdccadcaabdddadabadcadcdbabdcdaaabdaaaaaadaaacccababdaadadcdabbbdddbbbdbabbcdcdcbdccccbdadbadaaacbbcdaacccbddddcddbaccbaadbaadcbdcdcababaaccbbadccaadcdcdbcdadbccdcbbcdabdbdddabccdbacdaddbacbaaddcdcdacddabcabdadbbdcdadddcdcbcadddcaddbbabbccdcadbbcbdccdabbcdadaabaaddcbaabbacbcbbaadbcaccaacdbcaddbbabbbabdbadbcbbabdaddbbadaacddddbbdadddcdccbdaadacbdccdcacaadbdbaaacdaddcaacbcacdddaabcacababbbdadabbabbbdaabbbddbdbadbcaadccbdcbadcbcdacccdbdaacacbdaccdabcadcdccaddcccbcdadccbdbcdccbddaabccbddddadaadaaddcadcdbbcccaadadbdadcaadbabddcddcdcaabbabccbbddddacbadacacdcabbdcdddbcaaabaaadacccdaaccababacdcabcbcdcbdbbabcccacddbcccbabcbaacccabbbbacdbbabaaacaccadbbadbaaddcbdbddcbdccccddddbcadaaaaacabddbbabdcdbabddbcaabaaaccabaddbcbddcadbcddbcbcabcacacaadbdbdccadccabccbdcaadbccdaaaadddcbcacdcbdaddaccaadccabaaddddbaaacdbacabbbdcadbccabacbbbabacdbbcdaccddaabddbaadacdddcbbbadcaabddddddabdacbdabbbbddbbdaccddbacadbcbbbbbabdbdcbcdaccadcbaaaccbcddabdabcdbdcdacabccdddadccdddbcbdddaabbbcdbacaaccbbbcabccaadadbcbccbcdbbbbddadabdaddbdcbabccbbcbacdacbccbcaccbcaaabcbacdcbbdaadcbcdbdabacbcbbaabdbacaacadbbcccddadcbacbcbcacacdccbbdbdbcaadcccccdabadaaacaabddcdbcbadacdbbdbbdacadcdabbabbcddbddacbdccbdaddbadadcbaababbbaccaacdcddcdbbccabbadbbdbdcbdcbaadcddadbaddaddbdadcbdabcdadddccdaabdcdaaaddbadcbdcbbcaadabccdbccabdcdbaabcbabbcddaaccbdbacbcbbcdabdcaaaddcabcdcababdbbbddaddcababbcdbabbdcdcdbabbbcaddaacbadabadbbaacbcaabbacdaddadaccacddddcccacdbddacadbaaacdcaadddbdddacabddbdbbaddabbdabbcababaacbbdcdccbcdccacddbbddbcbdadcacacbdbaccccbddacbbcdaccddcadaccbdbbacdccadbcbcdbccacdaaddcbdacaddddbbddbabaddbbbaaaabdababbaabcdbdbabbdcbadacbdccccacaabdbaacbdcadabacdbccabababacbabcbcbddbdbcadabcbcdcdddcacadacbacccacbbdddbacddadcadbbbbcbaabacdacacccdccacaacbacccaabbdccbccbbadcbaaabdbcdacdbcdbacdbcaacabddaddcaadbbadaabbabdbdbdbccbbdcdadbadadabcbcdcccbcbabbdadcdddcbaaaabccbdbacbcdacdbdbadcacddbacacddcbdababbadddbacddbbbabaaabcbadccabadbadcccabddabccbcdabaddcdbbabcbdaddcabddbbccddcbadaaabaabddbbccabcdbcdcadbabdcaabbcaccbdddccbbddbdacbbbddcdbbbbdbdbdccdbabadadcbdbccadbbddcdbaccbcdcbcddbcdaddacccbbaaabddbbbadcdbabcccacadbbacdaaabbabbadadcddbcbdccbdbbadccbbcbbddacdbaadcccaabdcaacdaabcacadacbacdbcccbdcdddccaaddddddacacdddaddbdbadcacddadadbabdabdbbbddacabdbaaacccdaaccbdbbbababbacbabdbcaddadadabccaadcdabdaabcbdaaddddadabdddddabbdbdbdcacdadcbcdcddddccdbddbbdadddcabcacbabbccadaabbabdbcbddbbbbbbdbccdadbcbcbdaadbdbcaacdccbcccabdccdbbcdbcdadbdbbddbabaaacadcdbdcdaddaacdcdddbbbccddadbacddaadcadccbbdbacdcdaccdcdacaababbadbdaacbadbcbdbbcabbcacbadacbbcdcaaaaadcacbccdcabddccbadabbacdcccdaaccaadcbdbdcbcccdadbaaacdcadabbcdcaaaaddacdaadacabbbddabbdbbbacdbbaabadbaaaadaaadabcbdcdbaaaaacdbacbcdccdabaabcbcddcdadbdabdcdcccadcbcdadbcdbbddcabdaddadbccbdddcabdcdccbcbacaddbaaacdcbbbcabcabdcaccdcdaacbdababdcccbbdccbcaaacbacaabbdabbccddddacabbddbabcaabbbddaacbbbadadccbccabbbccddddaabbbacddbbacaacbcdbaaddadddcabcbdcbcdbbdadaacaddadbadbdaddbbaccdbbcbbaaabcdcacdbadaaddabacaccdccbccdadbbcdaabccdbbcbadaabccdcddcabddcbacbdccbadbbdacaabadbdaaaaddabbbbbabbcacadccdbbcddbcacdbcddcdddcdacdcddacdccbdacbdbaddacabdacccdbacddbbacddcdabbdccddbdcbbbdbacccbccadacadadcdacdacddacbddbcaadcdabbaadccbdaaacbdaddaaddacdbbccaddacadbbddbdadddabdccdadaddadadccccbbcacccbadaccdcbdcbccabadcaccabacabaaacabcbccdabccbdddadaabcacabaaaaaadddacdddcdabacaadbbdccaddcabcacdaccabbdcbcadcabbcaaabaabcacbaadbcbdbcbbcaadabddddbcbbbadaacbdbdacabbbdaddbacadbbacabaadbbaaacabbaadbdbaccbdddbcabadcbcbadaababbbabaacddbadadccddcddbcbbadabccdddabbccacccbccdbbacacabdddaccaddcacbbacdddaaddaaabdcdbacbddaaaadcaccadcdadadcdadbbaabbcabdbcbdcbcbbbdcbacbaadcdccbcaccddadcbdcdbbdcacacadccacdbcdbbbccdaadacabbaacaddcbbcbacacadabcabaccbddcdbbdaaccdabdccddabdaacddddadcaccdacbacdcabaaacdcdadabdcddaaacadabbbddbabaddcaabbabbcbcbdababcacadbcbcddccaccaddbdcaadbdcccabaaaadcdbabcbadcacdaabcdbdcaabccbddaabbbaccdbbbccdadcacdcaadabcdabcbadbdacddabbdddcccaaddaabccdcacdcacaddcbaabaaaababcbaadabdbababdcabccacdccdadbdadbccbabadbcbdccddbbcdddacddbcadbdcbcacdcbabcddbddadcdaaaaabbbbadacdccbacbaaabdcdadabaadaabacabdbbacaabbbadaaaaadddadddcabcbbccabdbbcdddcdbdddbcdbdbccdcabaddaabcdcbaddccabdbcbdabcaadadbcaaabaddcdbcdcbaababcaabbddbdaddbbdbcabdddaccdbabaabdcddbddcdaacbdacbcbbcdbbbbaccdcaabccadabcdddabbabdcddbbabdbdadcccacbbcbcdabbbddcaadabbcadabcbdaabbdccacddadadcadccdbbaaadcbdccdabcdddcabbcddabcbabbaabccadabdbcdddbdacadcddaccadadacdccabcacdabbacbdadcccdcccbaabdbcbcadccacdcbcbcaddadccabcdcdccacabbdacbccabddbdacdccbcabdabcdaacbbadabbbcacaacddabcabdacdcadcccbcbbcacdacadaadaadbaabbcdbbbcaddcdbdacbadbabababbaaacabbcadddadabccababacdcdcccaadbaaadacbcbbbdddcdaabcccdbddcaacccbbaacdccbbcbddacbcbcbdcbabccbbdbdddbbddcbdcdaaccaddbacaadcbcaaacaaacadbaacddddcddcbcccdbbabacddbccadcddccbbdadabdcaacddbdacdcbbbcdddcbbdaccdbbdcaaadccaacdacdbdaddacacdccbacbcdabbdaacabdacbadcacbcbacbbacdbaddccabdbbbdcadddbcbbcbabcbbacdccacaabdcdadbdacbcbdaaabcadaddbbccccabcbdcbacaaabccddaddbcbcdaacdbdacbcacbdddadcbddbbdccdcbbdbdbbdcddddddacddcccacdadadbacbbdcccabadbcaabbdccdccddaaccdbdadbabbdddbcdbcdabaddaccbcbbbdcbacdccabdaddccacddccdccbbadbaaadbaacdacddbacbddcabbccdadcdcacdbabdbdcdaddaacacabcdccdcddccabcacdcacddaacccbacacaabcbddabddaddacbbadcbbadbbdaabbcddbcbccbcabdbabadabadadacbdddbdaaacabbdbdaddcbabdacacbcdbbcdcaaddcbdcddddaccbbabdbdbabcabcdadccdbaaddbdadcbddcdacdbaddcccdacdbbbcbdaaddaaccdbdacdaccabbcabbbcaaacdaaccbabacccbbcabbabdcdddbaabacadcbabbbccdbcbababddadddbbcbbccabcbcdcbaaacccadccdcdbddaaccdabbcaacabdbabcbdddbabccdcabcadacdacaaacddddbaccbcadcdbbbdbdcadbcbcdaadcdaaaccabcacbabdbddbacabddacbdddaddcdcacacbcbcbcabdcbcdcddabcaabdaadbcbaccbbcbbbdbaaddaaacdabdabddcbadbbbbbbdbdbdddbaccbadadabddddacbbdacadadcbcddadbbccddaddcacbadbbcdcabddbabdaaddbacaadaabcccbdcbbdbbbcddbdaccbdddbaadccdcbacbdcbdccdaabcadccccdbaabddbbbdcdcaabcbddaadbbaaccdcdcaaaabcddaddacdccabaaabcccacdbabcccbadabababaaccacdcaaccccccdcdbdcccdddbbdbcdbaddcbcccadbbccadabbacbabaccbbadbcbaacbddacbbcccddccccabacdcbababaabdbaccabaabcdbadcccbabdccdddaddbbccbaaccadcddbcbdbcdcbbbdbccaadaddaddbadaabbccbdcbaaadcacbbbacdcbbbddbdacccbbdbccddcacdcabaacbbdabaacabbcadabdbcdcbbcadbdabadaddadccdaabcccacddabbaddaccdadaccddccdbaddaadadcacacbbcdbadcddbadcbabddbbbcbbdbdccacddbabcdbbdbcbcaddaacabcaaabbdbddcaccbddcdacccbdddccddadbbabbcdcaaccdbacadcbbaabddbbddadcabdcdaccdacadccdabccdacadcbbdcbcaabcbdbcbdcdabcacbbdccadddadcddbbdacddbdaacdabcadbbabcabcacbcdbbdcddbadcabbcddabadacbcddaabbadbbbdbabcdcdcaadbdabbacaaddcdcaacaabcddcdacdddbbccbcddddcccacabadbdabccccccaababcbccdccbbddabaaacddaacdbadbdabcaabbaccabbbaabdbdbdaacbabaaabcdadbacaccadccaacbcdadaccdcbbbaabcccadadccddaddcdabcaccdcabccbcabbbdbdbdbcadcacccacdcbbcdababadaacdaabadabacbdaddadadaabbdaadddacdabbaabccbcaaddccbababcbcdacaacdabbdbdadcabcaaabcacacdbcbcdbcbccadbdcdbbbabbdddcadadddbaccacaaddadaadbcccbcbbcadcddadddcccbcadadbccacbcccbbbaabadabadbcccdbadbbcaddabddcaacaabbbbcdcdacadacadddbadddcbaaccbbacacccacdacbaaaabdcdaabacdaaccdbcacabbcbbdcdadabadddbdacbcaccdcbbbcabbcbbccbaabdadacbdcbccacacaccddacccabbdbbbdabdcaadbcacddbbabddbcdabdddadbabaddcccdababbbbadcccbbbdbdbcccccbacdbbbccbcdacddadddddbddbdbbadcccadcbdcbaadaaadbcdcdaaccacdbccaccdbcabadacbddbabbbdcccadddcdbbaacddaadbcbccdbaddcbbbcdabaccbcbcdccadcbdcccddbaccbdaadcadabdcccccdccacabdabacaaccbbabaaddabaaabacacccbdbbddaddcccabbdcdddcaccdcccccdadadabbbabdadcbabbbcbbabcaaaddbbacaacaddaacbbdabcdbdcaccbbabaccdcaaccdcbbbaaccbccaadcdbbbdccabdbcccaabbacaacbdcabdbcddddabcaaaaddcdcaadacabcbaabadcbadabbdccbdadaccadbbbbcddadbdccabdaacddcacadbcdaacbbbddbacaccbdaaacddaacbabbadbcdbdbadaaadabbbbcbcbdaabddaddbcacdbacadbddccbddaccbbccabcbccbddddbcbbaddccbdbaccacbbadabcbadabadbcbadcddbbcdcdbdbdacbcdaabbaabccaacbacbcbbbaabaadcbbbacabdbcacdadcbbadddcbaaabddabddddbbccabacadabbbacaabbddacccaadbaabddabbcdcbaadccdbcccdbacbcbadbbdbcdaaabbcccaccbabddaddabccdabcddcbaccbcddbacabdcbdbddcbbdcaacccbbdcbcdacadddabdccbdccacccdacbbdcbdbcacccbbdbdbbbccabcdbbababdbacaaaacdbcdacbabbddcabbcbadbaccccbbccbdabbadddcaadabbacbcacacaabcadcccabbddbabdbbdacabacccbbbaddacdaacabdcdccbbbddadabccbbddbaacababdbcbdabbabddcbbaddabcdaaddbbdcdacdabbbdaaddcdadbdaaccbcbcccccbabaaccaaccdadadbddadabbdaacdbcdbdcabcbcbaaadacaccbacdbcbadadaaccbdbacdddbbddcdaccbcadbccccbbdbbadbcbcacccdacadbbcacbdaacdbccaaabdbbdaacbcbaacddcccbcabbaccbadccabbdbabadbabccdbaababddabcacbbabaddcaccbcbbbbddcbcaaccacabddabcbdcbadbbadddcddaacacbadbacddaaabbcbcbdcabaccccabcaaaabbbbcdddacbcabaaccbdcdabbacaabdacdbbdddccddacbddacccbdacdddaddddababbdbaadcbcbddcccbccdabdcbcaacbabbcbccacdcabcadacdabacabacdbdaaaaabadbbcddabacabdaccbadddcdbcadabddcbadcccdbaaaadadbcbdddcbadbaacababadddcbccaccabccdcdbbddcccbcdbddadaacdbdaacbdaabacdcbddcdddadddaaaabcdbcabadaddbabacdddacddbaaaabbbbbbddbbdadcadbcaaddbdaddbcacbbbbabbaaacaddabdcdcdabccbdbdaadcdbdbadababacaddbbbaccccadcbabdabcbbbaddacabbdadcbdcaaaddbbaabaccaadbcabbcccbcaaaddbcbadacdacabcbbbcdddbdcdccaccdbcadcbdbddddddddbccabaacaccacdbbcbaccabbaddabdcccaabbadbadcddddadcaaaacbbbcbacddbbdbbddcdcddccbdddcbacbddbcbdbccdaddcbbdacccccccadcdccdabbccbdbdbccabdacaaccbcdcaabdbbdaddacdbacaacddabdcacdbabbadacdbbcabcabccdbdcbbcdadaaacbddcadacbacababdadbacdadaaabdaabbcdcdcbdccdabccdccbcdcddbaccdbdbcdcdaccbaadaaaacddaadcdabbccbacdcbdddcdabacccaccdbadbbabdbcdadbdaccdcbbabdcadbaddaaccdcddadaadbacbdcbbadaadbdabbdabbcbabbbcbcbaacbcadbbcbbaabbdcacaddcccdacaccacdcdddbdbababbcbacbcdabbcdbccbaacbcbdadbbddddcccbddabccaaabbbaadadcdcdcadacddcbaacbbdbdadbcbdccadbdcdcccabcbbbaaccddacbbbabcabdbbcabcabbaddaadcaddbacbaabadcaadbbdcabcdadcdbddbcbdadbdbcaadbbbdabdddbbddaadbbacbcadbacdabbdbcabcbdcacccbbcbdddabcdcdadaddabdadaaacbaaddcbbdbdaadcbddcdbbacadcdcacdabbbbbaadbcdadbcdabccabbbcacacaddbdbcbdaadbbbcbadacccbcbbdcbccccabcbacbadcaabadcbcdbdcdbdccdbcbddcbaabbddcacaddccacbabcdbbbaabaaadacdbcacbbdcccbbabcbabdbccdabacaccabbcbaaabacaacddccaadcdcadadadddcdccdcccbadbbadbcccbddcbccbdbcadbbcddddbbdadcbcbbbcdbdbbdcbacacddadaaaacccaccdbbcbaadcbcddbbcacddacbcccdaddacadbddbbbcacacdddcbdccdacddbdcbbcbcacbadddacdabdcabddbadbbbcdadcabcadbbaaaccbdaaadcadadddaadcdbacabdadbdbcbacbabcbdcdbdadbccdcbbcddbbcddabcdaddbdadbababadccbdbcccdadaddadacbdaacacddbcabbddabcbbabaabcbaacbbbabbdcccbdabcabadabcbdccadcabcaaacbacdddacaacdaacacabaaadddabadbaaaaacdbabaccacadaacdccdbcddbdbcddbaaccacbddbccbbaabcbdabbcadcbdadcbdddaddddadbcbccccbbacdcbdbadabababcaacacbcbddcbdcdacbdbdacacbbaccdaddadccccbdbcabdacaddabcadaaacbacabccadbaaaacabcbcbbdaaaacddcdaaabcadccdbbacbdccdcccdbadacbbbdcdbbcddbcddcccdcaabbbaddddacdbdbbddcaabaabcdabdbbdbbdaabbccaccbdacbdcbbdcbadcbdbdabdcaadbbcdbcccadbacbdbcabbdbabdcdbadcbcbdcadcadbadaadbcabddbdaaabcaddccbbbaabdcdacabbdbcdddacccbcdcbbdacbbaccbdbddcdbcbcaadcdaccbcaddcadcdbbabcabcadbbbaaadaadabcbdcabcacccdcbcdbddbbabcdcacdccababbadbddacbbbdbdbaaabbbdcadbaacabaadbadabdddccaacaaccaadbbcbaccbddbcbccacbacaaadcabbcaabaacbddaaabcacdaaacabadabbdbdbccbbccccacbadacadadccccdaacbabcbdbcddaacccdccccabbbacbcdacaccdbdccaabddabababdcdaddcddbbbdbadadadbbcdccababbabdbbccbbccbbabbbcaddddcbcbbbbcbcabbdcdabccadddcdbbadcacbcddcadddacccbbcdbdbcacdbadcdcbbdadadbaadadbbcdacacbdddaabbabdbbaccdabaaccbcaabccddadadbcdabaccccabbabcadaaaabcddaaaabadbcabdcddadabcccabdaddddcdbccacdadbdadaabcaacbcdbacbcccdbcbcdadccabacdbaacabacdcabcddcbdcbadabddadcddcdaabbcaabdaddbddcdbbdbdadbdacdabcbdcbbdcdcdabbcddbabdaccadcbdbbcabdcdbdabbacabaaadbccaaddcabbbbaadcdcdcadbbdbdbcaddcadcdbcaccdbddddbacccddacabdcbcdcbcaaddadbbbcdbaaaaaabdcacaabdabbbbaacaccbdadbcccbbccbabdbbbabbbcbabdcbaacadbaacbbbccdbaaaadaccabddddbaabcdccdcacadacdccabaabdddccbcbbbdcdccdaaabdddbdbaabcbdabbaabbabcbdcbcbdbbdacadcdaaaddccdaddacaddbdccdcacabdcbdcbabdadcaadabbabaacaaaabdbccccdbbcccdbcaabbabaaacbabdaabbadccacddbcdacaadbcccbbbcdbddcccddbcdbaccaaaddcabdcadbabdabdbddadcbabaccbbaaddcdcadcccdcaabcbbbcdcdcacaaadaccabbbdcbddcdadababbadbddadaccddacccabccdcbaaddabbccdcdbbabacbbcbdbadbdaddddcabbccdadcacddddbccccbdccdaabcdcadaccbdddcbcbbadcccbabcccbbbcaccacdcabcacbabdaaccdacdcbcdbadaacbdbcdcdbadcaddaddbdadbdbbdabbddbabcdcddaddabaacadbcdbbbbdadbcdcacaaabbbccabbcacbbbccabcbcdcddbbaccbbcabdabddcbbbacbddbccbbdcbabbdaaaadbcccadbcaadadbbccbabaacacdbbacbcdbcdcddcdacaccdaddccadbdcdbdacdbccccbaadabdadcabbbdaaccbacbaccabbcbdbbbacacbcdbbaccbaaddcadbdacabadababaadddccbbaacccaccdbbbddcacadaddaaccbdbdddaddbcbddbdccdbaacacdbcaaddacacaccdcbcababcdbadacdcbbccccbccddadbadbccddabbdcabdbadbdcdcababbcdbbcaadacdacacdcacdbaaccbcabbabbaadbcccbbaacddababaccbcadbdbbdcccabdacbdccaccdacacaddddaacaacadbbaddbbdcccaddcccccdbdcaccccdbdccddcdabbbcaababbbaaaadaabbbaaacbbdbccbabcbdddaaacbdcbbbccadbadccababaadbadcccadcaadabcabcbbddacbcadbddbbdcbcaaddcbcdccbabbdacadacbbbabdcaaaaabbcdddcdbadbbacdbbbaddddbdadacccaddacbcbadccbccbadbccbbdddaddbbbdababacddbacdcadadabaaabbabcaaacccdbbabcbaccddccddbbbccaadadbcbbddaaabddccdccdbbbdcbadcadbdcbccbdcbccdcaaaaacacaaabbcabbabddbddaabbbcdcaddcddbcaccacbbaabaacbadbabaddcdadadaadccccdbdacdabdaacbbcabcdbcabcccbaccccdbdbbbbddcbacbbaccadbcdbcaacbaaacddabddcacaadacdacbaddadabacdcccddbccbcbaddaaadbaaaabcbbbacddcbcdcacdddcaddaaddaddabcacdcadabbbcaadadddacadddabccabdadbdacccdcbcabaadbacbbbddbacdcbdaaddccdcbcabcdbadbbcdcbadcdcbbdaaccabdacdadbcabbbdbcbcbdcbccacbccdaabdadcbccbbdbdacdacdaabadbabdabbacbdbbcdaddaaaccbcdcbddbcbcbbcbdcdabdbaadccdaddbdbcacbcaaaadcddccbbdbdbcbbbdbbdbcbbbccddaacdbcddbdcdcaccbcbbccdbcdccccaccbcacdcbbcabaddbadadcdbaaabaaadadaaaabcddaccdbcddddcaaacadcdadcddcacccacadbaccbacacbdccddcbadaadaabcadbbcaccacbcaabaddbdcaadbdcddaabcabccdadabaadcababdaacbbbccdcabbadccadaaacadacdcaccddcdcbabdbbcddbaaaaabcbdaccadabcbdbdabbcccbbdabaabdbddabccddabccdbcdddbddcacadcaaccadacabccbcabbabcbdbaadcdcddbcbdbdbbabbdbcdccaaabacddddbdbbbbdcacaccaacbadcaddadcbcdabdabddcccbbdbdcbbcbdadadaaacdadacacdcdcdaacdcaddabcdabaabaacdcbbdddccbaabcdbbadbcccccdcbcbcabaacdaccabacdcbadaaacaadcbccbaaabdbcdacbbcddcccddbddccbabbabbaddaddcbdddbbdddadaacabbcdabcbccdbbcadcacdbbbbccdaabcdbcabcdbcacbbdcdccccdccbbdbdbcbadaadbdcbaddcdbbdcdbdaccbdbcbdbadacdaddaadbcddcbacddabdccdcadcbaacbaabdcabaaccdcdbdccddcacdcbbdccbcdbabcbaacdcabbbddcbbdccdbccdadacdbdaabaabcddadbdbcbdbdbbadbacdabccbcabbddaaabaabcdcacbbbcacdddccccbbabcaacbbcddbacddaabcbcbdacccbbdbccadcbaddccbccaadbdbabcaadcbababddacdacdccbddadbdddbbbabbcccddbcabdcabbdcacadbcababbaabdbabbacaccccdaddbcbdddbabbcdbbbcbdbbddccbcabdbdbabdbbcdbcbcbdcddbdccccaaabbddbdaabaabbbacdbaaabbcabdaaccdddddcdaabadabaaddcaaabccaabbbdcddadaddbacbbbdaadadababcdabdbabcaccdaddbcdbcddacdaabaddbadaaabdaccdbabaaaabdaaccaaccbdbabccdaaababacbbacbabaacbaccbbabcdabcdacddbacacbdbacaadcacbcbdddddbcdadadcbbcacaacabcccbbccadaadabaddcabacddbccbccbbacaadccadcacccddbcacadcadcbcbbbddaabdababcabccaddabcbcadbaaabdabaaacccaabcabcdbbdacdbccccbdabbdaadcbbdaccbabbcabddaccbacbdcbaabbdccdddbbccdcdcbccdcccbabaacdcbacbcdadccaddbdacccdccbdcdbccdddcbddbdbaacbdcbdadaadaccacbddbabbabbddcaaabbbbcacaddcaddcacdcadacacbdbaaadbdcdddaddaaacccacbbacaaaddbbacaddadbadacbdadbbadabacabbdddcbdabcdabddbadcbdacdbbdbcddbbcdccccbbcbbdadcdaccadbcaaaadddbaadacdadddaadddcbbaabdbddcdccbbacaabdbcabbadcdaaddddcacaaadaccabbadabdcbccccabbcaaadaccdcabcbacddcabcdddaadddaabcbdccaaccdcacddbdbababcddacbbacdaaadbbacccadbbcabacbbcaadccccaccaddddbdabdcbccddddcadbaabdddadcccdcbaccbdadbbccccccabbcabbbcbbbaaaaadbcbbabcdaaccdbacabcbddaaadddddbaaadbaadbaadcaaadccdddcccadccadbbddddcdadbcabadabcababdbbacbddadcaaccbdabbacbacaabdccbdcaaddbbacaaaccdbbadbdcdbacbadadcddacaabcddccbbbbbcaabbdabcdaabacddbdadaaddabbaadbbddbcdbbcdbbddcbadcccddabdbacbcbbacdaacbdacdcdadbdacaccdbcdadabcdabbdddcccabaabaacbddcdbccdddabcdaabcabacbcbddbcbbdbadabaaacdcabdbdddabbdbccdbdddddddcbbccdababdcabddbbdadadbbddbbcdcabbadcbabaddbdbadadacbadcacdbdacbcacddacbaddddaccdaddaaaaccccccdabbbaadabdaaaaaacbadcabaadbaadbaccacdccdbdcbaaaabbaaadacbacbacbabbbbcadbdaacaddbbacddabbabbbdcdbbbcbbabccbccddbccbdccbcbddbbaddbccdccacacbbbcddaddbacccacdacdcaddbadbbddaadcccbbdbcacacabcbbccbacabbccbcabadbabcbcbcdabbcbbdccccaabbbcccbbbddaabbaabbbacabcdadcadcacccacbccdddbadaaabdbbbabbaacadcdbdadcccbababdbabdbbcaaacdadabaccabdadccdacbadccdccacadcbcbbdaaacdbcadcbcbaadbbdccbaadbbbbcbbacaaadacdbddbbaccabbdbcbcaddcaabccbbaaadcabadbdcbacbdbbcbcdcabcacccbaacbcabbdcdcaaadaaccbabcbccddabcbcccacabcabbcabcbdbbbabbabcccdcaabadcdddbcaaacdabbddbbbacbddaadabccadadabcccddbdcabbdabbdbbbccbdcdabddaaaccdcaccaacdbcaaabcbcbbaaaacaaabbabbcbcdaaccddcbbdcaaaaaaccbbbbbdbcacdbcdbddccdadbbdccbabdddccbdadbdcaacaaadccaddcdcbbdbbbbbbdbaaaabadbbcdbddcdccdcdbbbdaacdbadcaadcdaaadbcccdabbccbbacccccbadacdbddbdbcdcdcdcababbaabcdccdcdcdbccccdabbbdcdcbccabdcdcabcbccadccdddacaabdbcbbbabcdbdccdbaaadbdbacbbdabdadaadcbcacadbcccaddcadbbabddabcbbccadbbbdbcdcbcaadccdbcbadabbbdadcbbbbdbbcbdadaccaacdabcbbacddccdbccaadacacccdbbabccdbbccbcccbdddcbabbddcdddcdddacbdcbaabddcdcdadcaaacdbbacaddadbbdbdccddcbaabbbdadadacdcacbdbbdadaccbdcdddccabcbdcdbcbbcdcadcbbccacacadcbdaccadbbccbbabbbcdaaaddaabdbddcbbbcbabdadbbcacaaabbbccdbbcddadadcdcdbcdbdbbbbabcdbbdadbcddbdaaababccdccccabaabddbaabaabcdcccabccccabadcaabcdbbdabbadbbddcccdbaddbbdccadbbaddadddcaccaaacbaaddbbcaaccaaddabadadcaadbccddddcaabcddacdacbdaddbbcdacddccbbccdbaddccbddcbdcccbaadbbdbbaaacddcaddadddcaadbdcdaabbbddccddcdbdbbbcddcbdbdcdcdcbbdddddbaadbaaadababcadadbcbdcdbaaadbbdaabcaaddcdbcdacacbaaccdbadcbaddababaaabadcdcacdabbdaabbacabbcbaacdaddadabcabbdadaadbdaadabdcdcadccdcacbbbaadaaacdbadadbbbcbdddcddacdbcbbbbadcaccddbbcbacbdcbbbccbaddddddbacbbccbcacabbadbbbaddcbbdbdcabacdcbdddcccaaadabbbdcaadddbdbbdddddcccbdabdbbadacccdabdbabdcdcbcadccbaaaddabcadbccadccbdcdbbbdddcddbadcdddcdabbbabbcaadbaacccaaaddaccacdabdbdacacaacdaadcdbacdaaaccadaaddaaaaadbbccdbdbddcdbacbdaccadbaadddcadabababdcaabbadddbddbddadbdaddbaddabbbdadbabddacddacbbabbdcbbaaddbabdabaabcccbaadbacbaaadcdcaadbcddabddddaaaacacaaacbccaaccaaadabadddcbadadcbaabbcdadacaaccbbcbacdacdbbccdccacdabbbddcabacbaadacbbdcbbaabcadddbcdddddcbacaabcbbbbbdcdaabbacabadbdbaabcdaccaaadadcacdddccdcadcbbcccbabcbccbcaabbaaaaaadbabcccdcbdaadddbcbbdadbaabbccbdccdbddaaaddcdccbcbbbcccaadcadbadcacbccbccbcddcdbcbbdaddddaadadadbcbadbdccdbdbcaaacbcbdcdcadadccdccacbbbcabdaacadbddacbcdbdaacdcaddcbdadbcccabbcdadddcdddaccaabdacddbbadacaccadcbccbdcdcabcccddcbdddddacbabcadaadbcaabbcbabaaccccaabccabbbbabdaacbbdaacaddcacdbcccbcdadbdcccbdbbdcbbcadcdcdcdcacbadbbbacddbaccbcdabacbaaabcbababbcbbaabbabdbaabbabaadaababbdccbbcdccdccbdadbadddbcdcccbdbabdbacdcccbccbacdcdabdabdadddbaaabddacaabbccdccbcaabaddbbcdcabcccbcbcabadcccddbbbadbaddbdbacaaddbdaccabdddcbccdbbbbacdaddabcdccdaccaabdbdcdccaaccabbaacdabccaddcabbcdcacabdddacdcccadbbacbcbbaccdbababbaddaadbdaaddbaccaadaabadcccadbdbdabdacaddaadcadcddabdacabacaacadabbbabacbcccdadbadbabadbbcdbdccaabbaacaccddacdcccbcdabbbcbbcaabdacdaabddacddbabdabccbbbabaabbcadddadbaddbaaaaccdcccbdbbbaacdbcbdbddadddcdbcbaadbabcdadcdcddddbdcbdcdcadcadbcbbbaabdcacbaabbbcbacadaadabdbbbcacbcbcbcdbbcbbcaaacaaddddaaccdacacdcdddaccdaccdccbbadaadddddcbddaabbaabbcbcabddccdcbdbdcdbdbccccbdbddcabdabbcdcdaaaabaddbbdabcdadaadacaddabddadaddabcccdccbdbbdbadbdbdacdccbdbabddbcbbacbaddcccacccdaaccbaaaaabbbddaccdacbaccdbbcdbbdaddcacbdcdaddbbcdccbaddccabbadbdabcdbacabddcbdcbddadacaccccbddacccbaccdbcdbddaadcdbdcbadbbdaabbdbcaadbdadabadbbaccbcbadbddbbbbaddaadbbabaacacddbacaaadbcacddbddcbcdccbccbdbbbbbcacdbcadbdddaacbbcdcdbaacacbaddccaaccdcacadcbdcaaccbcdbddbaddcccdbbaaaddcbaddbdaddbdbddcccaabcaaaabdbadcbadbbbacaaababdcccdadddaacbcddddbbccacaccabbabdacbdddcbddababcddccbbcccbdbcccaddcbbdddccadccacaaccdddaadbcdbbddddbdbcbdababcdddaccbadabadbdadcabbababdadccbbdbcddbbcccbcabbcbabdbcbabbcbdacbcbcdcddcdbcdadaddbdccbaabdddbcbdaccacdccbaacddcbcbcadbabdcaabdaccbabbbbdbddcddcbbbcbdcbddacaadcdadabaacaddcddbcdccadabaddcbdddbcbabbcccadadcbcdcabccbcaccdcdcbddaaaacdacbcaadbadaccbadcccdbdccbaaadbabbdcaabbabbacccddcccbabacdaccdddbddcbdadaaddbdddaacabdadbabbbaccddcdacaaadcbccddacacbabcbddacadaccdcbbcabcadddaacadbbcbccccddaccbcdbddabbddcaccdcdaabbdabbdccbdcbadaadcccabddbabdcdbadddabddbcdaccdbdabcbaaaabcbdaaccdcadacacaabbdbaddcacccbdbbdbacbcbbdadccdcddbacbbaccbccadacaadbcabdcdbdbabbccbddadabaacaababbcdaccabbbaaaccddcbbaacbdbccdbccaaccbbaabadcccccdcdcbdacacbadccaccdbbabdcdcacddcadbcaadbcabcdcddddcabdcadddbbdbdbbaaacbccdacabacdaaccddbdacbdacdbbbababbbcdcaacbbdcadabddbaccaacbaabbbadbbbadcddadccabbcbccbbcbdcdabbcdcbdcaabdcbdbbcaddcbddbbaacbabbdcccaddbdabacdcbbdbdbbcdbddcdcacdcdbadcdabdccadbddccddcccacdcdbdacabdddadccdddccdbcdacdbdbaddcaaaaaaadadabccaadcbccbbabdcdaaabdcdccaabacaacabbbadddacaabcbaabacaabddabdaabcdaadabcdbbadcdabcdbbcbcbacabbcccbcaacbacdddbbcabccdccbadbdcddadcdacadcbdabbcbbcaadbadababdacdbdbcaadbcbdbbabbbbddbcccbbdbbcabbcdaadabaacaddabdcbaabddbbbabaddddabbadcadaaadcbddacabcccccbbadcdbbacbbacacaccbccbdbbdcbacccbdcabdacccaaacbbdbaddbcacdaddcdcdcabababdaacabbdccbdddcbbcdbdccabbcbababdaccbbdabaccaacbbbdcdbcdadcbbcbbbbbddaadccbcbdbdaabcdddbddaacdcdccdcadbcdbdaabcbccacbccdcdccabaaaaaacdbbadaaccdbacbbcdaaaccdcbcbacdddaabdcacbadabcbdcaddcbaadbbdbaadbdaaccddabaddabccacccdbccddabdbadbccaddcacabbabbacbaaddaddaadaccccabcbdadccddcdaadabcbbdadccbbddbadbacbacabdcbcdbcbbabbcbcdbaadcbbadbcbbcdcbcccdcdcdccbcdbaaaacdbccbabcaabddccacbbadcbacdbcbbbadabacbabaddddcdbcddbddcabcdccaaabaaaccdbbaddcccdbbababdcbcabbbbcbadcaacadccbaaccdbdbddbbaabddbdabbcbcccabacacbcbabaabbadcbabbddabdbdcdbdccadcdbcdaacaccbbdbccdacccbadddcbadccbaacaccababbcdcbcbdbaadacbbaadabacbcdccdcdadbadbbcadcbcdaacbaaccadabbdcbacdbcacabdbccbcccacaabacadddbaddbccababaadcdddddaabcaaddbcddcdacdaadadbbcccaabdabbaacbcddacbcddaabcadbaaaaacadbadcdbacdccbccadccbdaccabbcdcbdcaddcadaddccdcdcdccabcacaccaaddbddacdadadbdbacddabbbddcaacdcdbabbcbcbbbbcacbbdcdcbbcdddcabdabcacbcaacccdabaddabbabbbdccbbadbccaccbcdadcbbbcddadabaacadabddabbccadabdaadcaaaccadcdadadabbcaddbdccabcdddadcdadacbbcaababacdcbddbddbbcadabcdbbaddacdcdaccdddabaabdbccadbbdcadcbdaadcddbbadadbadddcacdbbaaabcaaabdabbdcccaaaadcccccabaaabbbbcccababddcbdcddbabbabccaaacaabdacdacdddaccdddaacbdbbbdccdabadddbdcbbaaacbccaddcddbaccdabcdbaacddabbbabbabbcaacbdddbcdadcccbcbdadccdcdbabcadbbbabacdacddcbcccaddabddaaccbbbcbadabadcdacbababcddbbdaddddabdccbacdbbcbdabcbacdbdbaadcccadbbbabcdbadcccbcddddbcacbbcbacdbaacbdadbacdaaadacbddccbbdacdacaacdabcdbdadaccbbbddababcbacdcaccdcacdadbdacdcbdddcbbcbcbbcaacaccbbcbdadbabbcbbcbcaadabdbdbcdaccccaccbcdcdadddbddcdbcacabbadcdbdaabbaddadcdcbccdcadccbadadbcaccaacaaacbdccdadbcadbaddddacddbcabbaddaabdcaaaddbcbddbbddaccbbcdabbccdacacbbaccaacccbddababaacadddbbdbdbbdcdcdbaabadbabadbcccddbdcdbabdacdaaacdcabdbccbcadaabbcacbdacbbdbdcbcabcbaddbccabcaddabdaccbdbbcacaddabbadbcacbcaabcadbadddcdbdbaabaaaaadcbcdcbdbdcdcaacabbacbacbbcddcbcbbdabbddabccbabacccacbcaaacdaabdcadbcbcbbbdcccbccaabacaddbddbdaddccadcacaadcccdddadcbdbbdaaacdbaaacbbbaabaccddcddaacdadbbddbbadbdbcbcbbdcacbcaaccbdabacabdbccaadacbcabddcddcacbbcbdccddaaaabcdcccaddabaddcdcadbacbdddbbbacbadbccbbdadbaccbaaddcdcbaaacadbddbbdbaccabbcbbcbbccdbcadcbcadccccdccaaabbcaddcababdccbbabacdddcbcbabdccddddabccdaaaddccbaddadaadcddbaddcabcbccbdadccabdbcabadacbdcdaaabbaabbbccaadbddbccaabbcdbcaaaabadadbdddddbbabaaabbdbcbbccccababdddbcacabacaaddabadadacbcadccbcbbacccacdcdcbdcddcccdcadabbdaacbccdcabaccddbddcbacdaacbacbcccbabcddbaabdbabacbbadbbaababacdddbcbcbdddacbcbcbabcadbddcbbdcdccddacddbcaaccabcccbcdcadbbcbbabbcdbbabadccbdbbdcdacdaabccaaadcbdcddacaabbdabcaadccdbcbccddcdbacddbbddaadccccccabacbabbbbcdccbabaddbacccbcddcadddcbdccdadbaccbabcacbcabbcabcbccacbcbdaacdbbacbaabdbaadbcaaabadacdcacddbcccaacddcabcbbadddbcccccbacbcddabadbcdcbbddbbcacadcbcbabdabdccdbbabccbccabacadabbabcadaacbccdbbdadcdaddbdbabbbccbbccddabccddcdaadcddcddcadbbaacdccaaaadaddcabbcbbdccdcacbbdaaacdbdabcdcadcbccdcbdddacdcbbcadacdcaaabddbbbacbababcdbdaaccaabcadadbadbbdcdcddccbababbacdacabdaabddaccacabbbbccdcacbdabdbdcadacbbcddaabdcacdcaabcdddcddddabdcadddcbaabcacdbdcdbdcdbabbcbbbdccaaddddabdbaaacacaaddacbbccaccddddbddbdbdbdbdcdcddacababbccaabbaacddaddbdadcabbaaadcacbcbbbdbdacbcadddbacddddbcdaaacbddbcdaaacdbcaddddacacaacbcdcbacacddcbaabdbbadbbbdbbdcacbbaadbaaaddbabccbdbbdbcbcdbbdabcabbbbddabcbbdddddcccbabdcbcaddcbacdcbbcdcaaaadcbddcbcacdacdaaabcdbbdbcbaaabcaaababbcacddddcddbdadacdbacbdcdbbaababdaadbddadcdcdddaacbbdccadbbaacabaccdbdbddcdbbcdadddcdccadabcdcadbdcbccbaacbacbaccccbaabbcdacaadbacbcbdccabbdccdcccbbbbbbabbbbddddddbbabbdbabbccdcdbacbdcbabcdacbcaabddabacdadacdbdbcaadddcaddbcaccaaacaacdcbaadcadaabadcccabcbcadabbbbdbdccadaccdaadabccaabaaaabdacdcbdbcbabcbbdbbbdbcdbcabcadbddbbcbdaadabacabcccdabcaccabddaaccdbadbbbbddcbaabdcaacdbdabdcbbaabddacadddadadaabaacababbcccadbcbcadbdbcdabcaacabbbcdacbcddbbccadaddbcdccabdbaacbcdccdcccaddcbdccacabaaddbadbccccdbacbaddbbaadbaddcdddaacbcdcadbccabcadcabcdaaddcabdbcbaaababbbdadbbbbcbccaabdbccdadcbdccaabdaabbaaccccbdcccbacbbcddbbdbcbbcccddbaaddcbaddbabcdbcbddcbbbaddbdbdabbadaaaaadadcaabbaadabbbcddbacbabddcbbcdbcbaabcddddacaddcabcabbacaabdbdbdabcddcbdabcbbacbabacdcbdadddccbbbaddddcdbbbdaccdcdaddbabcabcbbdbbdcdcacbcacbdabcdacdcdddacbbaacbaaadaadbaddccccbabbaabdacdddcacdbdcaddbdadcdddbbdcbbadcccbacadcaadadbbdddcdaaaaaacadcbcbababbabdbdaacacdacbccabdbadcdadacdbbadadbcddbabcdaaccaaacdbdacacdcbcdbcadaadccbacddabbabadadadbbaccdcbbbbccbbbadcaccaaadcdaadcdabdddbdbcadcaaabcaccbcddbdcdcccdacbacbaccbdcabccbcdbbbabdbbaabcaabaccbbddbcddabdcdbdddbddadaaacdbcbcdabacbabcbdcddbddcaddaadccbbacaddbccbaaadabbcadbaacacbaccabccacbcdbdacacbdacbcdacaddabbdddbcbccacdaddacadcabbcacaddbaabcaccddbaccccbbbddadabacdabaacddcdbddadcbaccccbbddaacbbcabbbacacdbdabbbacaccbcadbdadcabaabbddccbccbbcbbcccbbacaddcadbbcadaccdabcbdcddabababadbbbcaaacdbdbcbdbaddaaaabacdcccbcdbbccdaaddbdadaababccacbbaacabbdaaddbbbccabddabbbbcdccbaccddbdabbabdcbcccddbdcaadcaddbbccbbabdddccbdadcdadaaccbbbcdcbcbcccdbabbacaccabcccdadcccdbddddaabaabbabbacadbdbcbaacbbdaddaabbbadbdbaaaaababaddcaccababadcccbadccdccdabbbdcbddadddbcddcbbbaddcabcbadbdcddcaacdaacdacbdbcccbaabbabbadbadacbdbddaccdbddcaadbadcaabddbdcbacbbabdcaacabdbdcbbddddccbacdddbbbabcdddaddbcbbdbadddacbccddbbdaabcabbdaabdcacbbaccdcaabbacbaddbcbdcbcdaabcaddcdddaccdddddadccaaccaaadcddcbadcdaddabcaaccbcdddcaaddddadcdddbabaadcabdbbbbbacadbcccaddcbbdcaddadadadaaabbcbddccdcbbbabdabdabacadddbdbbbbcababccaaaaaccdcbaccdcacbcddbbbdbcbccaccccdbdcadaadacabdcdbbabbccaabacaadadbbbabbcbdccadbdacdbdadbccddadadaddacbaccdbdabaccdababdababbbbbaaababdacaadbcaddabbacdbaabdbacbcbcbbdcdcaaacaacabbacdcbbddcaababaaabacbabadccbacabcdcdaacdabcaccacacbacaacbdcbabcaabdddcdabdadbadcdbcccbacdddcddcacbdababdadadcacccbcddaccdbcdbddbddddbaacadbcbcccbbdaaaacdcaabddbbdddbbdcdcbbbdbdbdadaaadacdbdcbccbdbadababddcdabaadcddbabcdbacbaccadcbcbdccddaaacdaabdcddcdbcccaadcabdbdcdbacbabadabcdacbdddabbbbcbbdcdcbcccacbabbabbcccddbccddddcaacabbbcdbddaddcbbdcaccdabbdabcdbcddaadabbbbcbdcacbcdcdcacbdacbbdbcbbbbdcabbbdacaddacbcabcbacbcacbdbbacbbdccdabbaadcacadbdadaaaadcabaaaaaabcdcaabdbdabdccdbacdbdabccbcdbbdabbcbdbcdddabdabbcbbdddbddaccbaabdccdaaacdccdaacabdcdadcbbccbccbdbcabbbbacdadbabdaddcaabdadadddbbbbaddbdbdadbccaccbaabdbabbccdadbaaacadabbacbbbbadcdbccacbbabdbaaacdbaacddddabdadbbcbbacabcdcaabccadacdbaaaaccddbcdcdbbdcbaadddcddcdcbbccdbcdabdcbadbcbabdadcdaddcbadbaacdccacacaddadbdbcaaddabcabadcccaacacddcbbdadbdbdbbaaaadcdaaaccbdadacdacabbcddcadbabdcddcabbdbbcaacbcdbddbbcbbccddccaddacabdddbdababdcdadbdacdccdcdcbdadbddaccbcdccdcbdcbadddaacccdbccbbbbdabccabcddddabadccdacbdcdcbddccdbaccdbcbcadbababadaddddbccdddcadadcabbcaddbaddaaadabdacadaabdbcdccbcaadcabcddadbdcabdaadabdccadccabadddaabdcdcabbbabaacccdbcbadbabccacadacabbcacabaabadcabbacababbdcccacabcdabbabbbdbcaccacacaccbbbbdcabaaadcbcabdbadadccdaddcdddbbacbbdcaddaabcbabdddbabacadcadcbddbccaccadabaaacaacbabaacdccbcaadbccbbbddaaccbbbccccdddbbbabadaaddbbbdaccbadbaddadcbddaccddbacdccacbadacbcaccbdabadcbbdcbabaadabbbcbbacbdbccdcacddcdbacbdcdbdddcabccbaabddcddcabdbddccbcabacdabcbdccbccaadbdbdbdcdadadcddbadbdaacbdabbbbbbdcccccbdbabacbbacdaddbbbccabdcbcbacbbbcdbbcbbddbdbbdbddbaaaabaacabadaadacbadadaacdbadacbbdbabcadabcbaaadcdcbbbbcdabdcccacadaacccdbdcddcbcaabbdabacbbbdaccaddbaaabbddabbcdbbacbddbabbccadbaaccabbcddcbbabaccdcdabcdbdddacaddcbdccbdbddacaaaccccaaaccbdcdacacdcdcaccadbbacabcddabcdccadcddcddccbdccacadbcbdabdbaddbdbbbddcacacccdbaddadaaaacdcddcacdbddadbcadbbabcadcaccdccbbddcbdcdcccddabbaccabbcdaaddabbcdcadcacccdadbabacbbdbbbcddbdbdaabdbcdaddbaddcbcbbddbcdabacacccccbabbcaccacdacdbbcacbddaccadaaabdadcdacdcaadbbbdcbccdcdcabadcdccdccbdaababaccbcabbbacacabbccccdaadddacdcbcccadaacadbcaccdaddacccaaaacaacdabcadcaadcbcaaaaabcccdaccbdabcdabccaddbbddacacddadcaabbdcbaacbbdccaabdaacddbacdccadaddbbcccbdccbbcccdacadccabacaabcddadacdbdadacddaddbdcabccddbacccabaacaabccbcdcbcabcbdbcdddbdacddabdddabadbdcbaaadcddabcbacababcdabcdbdcccadacbbbaadbdaadcdacbbbdaababcbacdbaacccaabdcbdacdcdccadadabacdcdcaadcbdcdbbbdcdbbadcdccacaadccccacdcdbaaaaabdbcdbdddacaabccdcdabcbababdbdbcaabcaccbbdbabaacdcbdacbcbbccacbabdabccbcbabbcbacaaaaaaadbabbaadbbbabbbcbcdacbcacbcdbcbbabcbadbcacccddbaaccbcbaadbdaacbdbcbbabadadbccaddaaabaadbdbbbdabddccbbbdbdcbcdadcaabcbabaaadabcccbcbdaccbaaabaadadcddcdacdcbbacacbbbcbacddabcabdcbccadbcbadadbbaabdcbbbabdacabcadddaaddaccdaaccabadabbcbacccabadabdbcdbacdbcabcaabcdaabbaaacadddbcdadadadcbdbccdbcacdbabdacdcbbbdcddbdbbabacababdddbbaaccccacbaacdcabbadaaaababbcdcdacbaaccdbccbcbacbdcbcbaaadaddaaddbcddbccccaabbddabbddcbaacbbacbabbaddcbddddbcbdaadbdccbbaabaabaadcdcdccbabcacaacbaddadbbbddaacdcdcddabcbcaacdbddadcbdadcdcbabcbcacbccabacdcaabbcdbcdaadcaaadcddcacdbcaaacaadddcbabbdccadbddabbacacccdbccbcccbdaacbcabababdcccbcdcddddcbcabaabbdbddaacbccadabbdabbacbcadcdaadbbcddadbcbcdccdaacdcdcbbcabdabddaddadaaadaadcdcabcdbdabcaccadcddccccdacdbbdcbbabadcabdcdbddacacaacdcadcbbcddbcbcabbadaacaaaaabcdcdadccdaadbaccadaacaabbacbdcdddcdcccbabdaabbcbdbadbdcbdcbabbaadcddccaaadcacdaaaaccbaacaacabaadbacacdddbbbbbbaabcaddaddbcddcdcdddcabddddaacbaacbdbdbdbcdcbaabcddbcbbaaaadaddaaccadcdcdccdadaccccaaaccabccaddbdbdcbaabccdcdcdddbdcbddaddcdacacbbdcbcbdbaadbdbacdadcdcaacbccbbabaacdaadbaaccbadaababbaccbabcdbcddccbabcbcdabcccabbdbacadabcbadcbcbdccacddcdddaccaddbdddcaabbcbcaacbcdcacccbccbbddbbdcabccdcbaccbddcaabbcbcabbacdbadbcbadbcdcddaacbdbbdbbcdbcbccdbcadcabdababadbcdcabadbcbdbbdcaabdddbadbcacdcbcabdadacabaddaabcbccbadadbdcbcbbaaadbbbcdccaddaddccbcdcdccaacdabdbadbccdccacadbacdacabddbddaddbdabadccabbccbabcbccaaababcaacabcccadbacacadcaaabaacbccddacbdbaadbdbccaaaacdbbdadaaaaddccacdbbddcddabacdbbddbaacdcddbabcbaddcdbbddadcccdaddcddacdabdababdcbbcbbbadbdcdcaddbabbddbcdcaddbbddbcabcddcadcdcdcbbacdacbbacccbbdddcbcbcabadcadbdcbdcbdddccbccacccdadcbbbbddbcdcdacbbdbcacacabccacacbdaccdbcccbdcbdbbcbbbbdabacadcdccbbbcdadbcdcdcbaabaadabcbacbccbccabbabdbaabcadccabbbbdcddcbccdbababdcabadbdbccdbcacbdaaabcacdbbaacdabccaaaacbcddbababdcddcdbcbadbbccccdaaacbadddbdabcdccdbdcaadccabaaaabaddabdcdaabdadbbbcdcbcdbbcccbcabbbbcbcbbbcdaabcbaddcccbadacacabccadbdccaacbcccdbbadcaccbdaadddbacaabcdddbacaddcdcbcbcacdcbdaabaccadcacbdcbdcbcbbdcaadbcadaaaaddddbcdcabdcabbbdcaaacbbcaadddadcaabccdadbccabbadbabdbcdaaacdaaadacbbabbcaaddaabcdcabdbcacacabadbadacbcbcdbacbaaadddaccaaabdaaaaaaaabcadbcbbcdddaaabaadadcbadccbbacbbccdccbdbdddbcddddcccdaddadaaccadacddaccaadbddddbdbcbdcdabbababbabbbababcabccabbcdbbbcddaadcbcbbacabaadbaaccaddabaccbaddbcadcbaccabddcacbcbbbbababbbacddccdccddacbadadcdadcaddcccbbdaddaccadddabdbaccdcccdcbdcaabaabadbddaabaacdbccbabdabacacdbabbacdbdaadbbcadcaddbadbcabcabddbcbcdcdadccaadaadcbaacbbadccddddccbbbddcddcccdbddcdcbbdbaacbcaaaddcbabacacbbbadaaaacbdbcbcbcbaabcdaccbcbdaccbccbbccbcdaacdbabbcbdddabdbdbabddabccbbaddccaabbdcbabccdacabcdbacaccdcccbccbdccdadaccbdddbdbdddacccbadaccbadddbdcdacccdbdadddccbacabdacdcccbddcbbaccddabdaddaababbbdbbcdacbbddaccbadbacbacdadcdccccdbaadbdbdccbdcbbdcbbcbcacaaababcbcbdabbabcdaccdbabccabddcbccacbcddddcbacdbdacdbbdcaccccccabddccaadaacacdacdbbdcadabaaaacabcabbdaccbbbcbdcabcaccddbadcdaccbbbcaaddbbbdadcbbdcbdacbddbdaacbbbdccbabbaddabcadbddadbbadbcbbabbbddadccbbcbbabcdddddbccbdcacddbdcabbcacdccddbaacbbadadbabaaacabaccabbababbcbbddabdaacacdabbdacadaabddcccbabaabaaabaabdcdacdbccccaabcaccbadacbaacddcabaadcbbdbbcaacbacbbcdcccaacbacdbdaacddcbdbdbcdccccbbdcabbbbbaccbcdacbaddabdbaadbdbbbadddaadddadbbbcadaacddddccdddbaadbbbdadccbbacdcaddbadadcdbdacbabaabacaacccaadcdcbaccaabcdcdacabdaacaadacaddabcbbbbdddbbcbccaabdadaacaabdaaabcdadcbdaadabdbacdcadcacdcaabdbdbbcccaadabacdadcacdcadbccdabbdaadcbcaccadacbcbabddbbdacdcadabcdbccaacdcbabbcdaaacbacadccccadddbdcacdadcddabbcbcbccabaacdcddddbacccabdbcadacaaddcbccacabaccbdbcdadbdddbddbcbabdcdacccdcddacdcacbbdddbbcadabbdaabadbbadcaddcbcdacddacaccabdcacccacbdbbacbaabbcbbaddadcdbcbbbcdcdcdbadcacbacddbaaabadaadbcdaacaddbadcbacaaadbbbacccbcdddbddbadbbbbddbaaaaccadccadabbcbdbbaddacabcabbbbdaacdbcbdcbcbbdabbbcdadabccbaaacaaaacddcdccbdcddabbddbdbaadadbddcbcbdbcabdcddbdadabcdcbababbcbccababbbcddabbddacdbdabdcdbbacbccdbdbddbcdaccbcadabcacddaaadaddcbbdccbdccdcddccadaabcbdbabadaabbabcaaaacdbacccacdbdcdccaaabcdddcbcdaddddbcbdbbadabbbaadaadcabaccccaaddbadadadbcacbdccccacbadbcdbbabacaacabaaacdcdbdbccccacbaccbcdcdbccaabdaddcadabccdbbbcbbabacbccbdddcdcbdbccadaddaadbcdcbddcacbcaabddaddbacabcaddaaacaddcabdbcdaacccbadbbbddccbcbdbccdcdcddacbbaabddccaaabcabcbcdabaadaccaacbdbccccdcccbcadabcacadcadbddbddcdbccbadbbaccdcbbadddaddbdbddadbbcdbabdaacbbccdacdcbdbcdacdbcdaacbadcacdacbcbbbaacaccacddcbbdcaabcccccadcbadbdadaaaddcddbcdccdbdaaadbbaaaabaacbdbcbddbdacdcbbcacacbadabcbacabdacbddbbbaaacdabcbdccbcbdcadbbaccadbbddadaddcaabdbbdbabdadabddccccbddaaddbdbcaacabcaadaccaccddbdadbabdbdccacdaadbddaadaabaaacdbdcbaccddabbccabdbdabcbbddaaadaabbddabaddaacbbadaacdccabdcdbbaaddabadcadccbcaabddddbcbacccdddcdcdacbcacddccabaabacddccaccadaaaadcdadbacbbbdcbdadbaccdbbccdacddaabbccaaccbcabadbdcbbbbaaddbbdcdabddccbacccccbcbabdacdbabdccacccabbcbdbdcacadbadcddadcdcdcccdabcaaaabcbdbcbcbbbddaddbdbdaddbbcbbdddbdddccccbccbabcaaacdabbacdabdbaadacdabdccadadbcccdcaabbdbddadbcacbdccdbbdbcdbbcbdcaabbbbdbbaaaaacddcbcdabdbbcbaabdbddbaaacbbcbbdabccbbbcadabaacbbabaddbadcbccdccdcdcacbadbadbddcddacaabddddccadaacabbadcaabcbaadcbbbdbccddacbbccacbccabbccdcbbacacaadcbddcbbaabbcdabcadabadaacadcabbdbacabcaaacccbdcddbbacacbacccdaacbdabdadaabbbaddcabaddaacaddacbdabdbabcbbaabccddcacdabbdaccbaabdbadcaadbbdbcabcddacaddcbdbbcbdbccddbadaabccbadcbbddcdabddaacbaacacdabadabababbcbdadaadcbcdcdabbaddcdadaacaddbbbccbdddabbddddadaaddbaaacbacbdbacbcdbacdabacccdbbaababccaccddcdacabadabdabcacbbbaababddabaccbccbcbadbbdddcbcbbaddccbddadcaadbcabbccdbddabaabdccacdcbbcbdbbbbbcbaddbdaaddddccbbddcbddbddcddbbbdaaaaddbcabcbadadcabcbacaabcdacccdcbcbaccbcabbacddadadadabcacdcdbdcadcdcaaadcbaadcdadbbbbabacabababdabcabadabacccabcbdbdaccccabdbcbbccdcbcaaacbdcaabccadccadaabbbbdaadabaadaabbcabcaacabcccbcbaabdabddcdabdaddadbbcadaccadcdcdbaaacccbdcadddcaadaddaccabadcbadbdbbdabcbbcdadaddddbccdbcabcabdcbcacabcbacacdbacbaacadbdddcbadbaaaadddcdadbcdcacdabccdddbacbcacddaabcdbacbcbbcbbaaadadaaaaccdcabcadbccbcbabdaadbbaabbbcadbaaacddaaccbdaacbbadadadddccbdcbddbdacccbccdddbbabbbaadacbdbbcaadadcabcacaaaccbbbccbcddaacbdaccccdbdacdbabadabbadacbcdcbdcdacddcbdccbabbcabbdabcabdbadcbdcbbadbcdddcadadccdaaddcdbcabbcbbbbbdcbacdddddcacdaaadabaacdbacabcdddbcbdbddababbaccaddbdbbcddddabdcddbbbcacadbadbaaacdcabdbdabcdbabaacababbadbbbdaadacabbccccddcbcbadacbdcccadbbabaaaaacdcadcaacaaabdbbabcccbcacadbaadbbbbdaaddacacdbdbaaccacacaadddcbcdabddaacadaadbbddaabadcdddadccdddabbdbaadcdbcbbaadccacaadcbddccdaabaccdcbacdcadcbdddaabbbdaabbdaadbbdccdbbcdcaaaaccdbdabadabbabdabbcbdbddbdaabbbcddccbbcbcdcbcaabaaaccddcbbbdbcccacabcdadbabadcbaccddabbbcbcbabadcbacccdbdbddbabbddacdbcdaadbbcccbdbbdacdabdabdbbdadcccddcaddbacdaccdcbabddadbbbdbacaddcdaabaaccccbbdbadbccbcbcdbdbddcccdbcccddcbcbdadcabbaccadacabcbabbaacbadbdabccbaccacdababbcbccdabcabdbaacddbddbdcbacccbabccdadabaabadddbadcaacdaacaabbcaabcdbcbabcadddcdacacccddbccabcccdbacddadbaaccdcdbbdadacaadbcdcabbbbacbcbddaacdbdabbaaacbddcbddacccdaddcdaccbdddbbacaacbaccbbaccdaaddcbcaadaccadccbcbbaddcdbddbbdbccadacbacdcaaacdadcdadadcbbdcbcadbabcddaabddcaddcbacdaadbccbabcabddabadacabcdbddbacbbbdababaadaabdbddcacabddcaadccbadbadabccdbcbdaaacbabbcaddbbdcdcdababbbcbabdbcadcdcbcbcdcdccdabbabacdccbacaccaabcdcbddadaaabdccbaacbcbdabcbbadadbdbabaaaaabababccdbbdaacdcadabadbaabacdccdbcaccaabadaabaaddddacaaaddcccaadaaacadcbacbadddccabcabdbccbcbbaaadaabaddcdcbcacabacacbbaabaddcbdaaadbcdcadadcbccacbaabaadcdadcdbbdbabacabddcbaddbdccbadddadcddabdcdabcbcbbaddaddcccabacabadddcdcbccccacacbcdccdadababcbcbaddcaaddcdbbcbdccbabcbdadaacabbcbcbcddbccabcbdabaaacccdaccaaabdccdcaacbbacdcaabbbcdababdabacdcdadabdcbbacabbdbacaddadadbcccabbbaddacaacdcdcbccbdddbcdbbabccbaaccbcbdcdbadddbdcbcbaadccbcbabdabcdcabadbbdaaaaaacdbcacbaaaccaabadadccbccdadabadbaabbdbdcbadcdadbadbddbdaaabbaccdbbadbdadabacbddbacddaacdaadacadadddacacddddcdaaacdbbcbbbaabccddbbbddcdcdbacbcdbcadcdbaddbbdadabbbdbaaaccbdccbbddbcaddabcdbdbcadbbddbdcadadaabdbdcbbaacbdacddbcccdbbbcdcccaadbabbadddbbcabdddbdcabbabbcbabbdcdbbddbccdabdbdacdccbaaccdadbdcbcabdacddaccbcccccccddbbdddadbccddcdadababbadccdddbccbbdcdccbdadaacdaddbbacadddccbcdccbcbabddcdddddbabcbcdabbbabcbbbdcdbabdcbbbbbdbabcddbbdbcbcbaacddbbcaabdaccdbacbdbddbbcbdcabbabdaabacdbaaaddaacbddcddccbdcccbcddbccdacadbabaacadcdaaddccbacbabadcdadadacbacabdadacdccbacdaabdabcabaaadccacdcdbcbcdacabbbadbcbaaccaabccdbdbdbbcabadbaaacaaccddaabdddacaadcabccabadadacdadadbdcacddcdaddbdcadbcbbbbcaaddddbaabacadcabacbbcadccdbaddcdadabdbcabddaaddaddcabaabdbcaaccbccbbaaabaacaaadbaaccbacacccdcbbadabdcbcccbccbbdacbcdcbddcabdccadababaccbbcadabaacabdbdabbbbaddddbdbcdcadcabdbcdabbbbbbccbcaadcbaaccbbddcbdcaddddccdcdacddbaaaabbaccbdcbdbaacabbdccbbdabdbdccbbdcccabccbdabacbbaabccabddacbdbbaacdbbdaadcccbccaabdaddadadccdaaaacacaabbbdddbbcccacbbdabcbdddbcbbcabccacddbbbdddadbadbaabdaaababbdcaccbcacbaaabbbadcaacdaaaacabdcabaacaccbcbbddbacbdcbcaddbcdbcbabaadaaadcbbdccacacbccccdddabbadabbddcacacbbddadabbabddbcbccdccabbacbcabcccabdbaccadaadabadcdacbcaaddbbadcddcaaaacabdadbacddbdadacabcdbbdbcbbbccdbbdadabddcbdddbaaaccbaccbbdabdbabcddbbdddacdaaccaabdabcbabdcdbcaaadbcdbcadacaaaadddbaddabadccdcdcdbadadcddcacbacdadcaccacbadddbaacbabcbdbddaccccbcdadaabaadbcaabdbdadaaacaaccbddabcbcddadcacdcccdbdabadaacabaadbbdacbdaadabcadcadcaacbbaaaacabdbbaaaacbaddabbdccdbdadbdbdbdbdbdabdcbbadcbdbaaaababdabbbdbdaabdccddabbadcbbdcdbbbadccbdbcacbbbbbbadaabbdcccdbaaabadbadccbaababcaabdabbbdcadddadccbabacbdbadccabbdbcdcdacbaddaabcbcaadcacabcbbcdbdabccaccbacbccabcdbccbdabbaccdbaccdcbbabbbadcacbadbadcdbabcdbddbcbaabccadabcdcbdbccdacaababcbcdadabdcbdcabbddabdccbdaacdddbcddbbcabbcbbabdbbbcddcbbbaccbadbaabbdbbcdaabaaddabdcbdacadcddbacbcaddddbadcbcaddabddaabccbdaaddcaccbbcddbcdadbddabcbcbdaaadcaddabcbbcdadbbcbcbdcaadbadabdbbdcbaacdcbbcaabbcdacddcbcabdadcbadcccbaabcbbabbacbbaaccddbbabbabbbadabdcbcddbddbcdaddbbaaaaddbacabdbddaadddcdbadbcdbbcddaccabadbcaadaadcdcdcddbdddbdcdcacdbcccbdbdbdcabdbaaabbbdddbaaccbaaaaabbabcbccbaccdbddbddddabadbcadbbcaccabadddbaccbcdbccaaaccbbdaccabacbaabdbaccbdcdaaddcccabacbccbaccabdcacdbddaaadaabdddddcbccacadbadaaaccbdcbcacddbddaddbabadabbccabbcabdaadcbbddcadcbdacaaacbcddabcbdadcdbbcddabccbcddddaacabcabbacdaddcaddabacdcbcbaabbadcabbcdacdcdbaddbbcbacdbccabdabdcdacbbabbaadcddbcaddadadbaddabbdcbdbcbaddadcccaaacccccbcbbadccadaccacadabcdabacdbabdadabbcbbadcbbabdcacdbcbbadbbbbcaabbaccabccbcdccddadbcdbdcbdbacaadbdbaabadadbcadccbbdbbcbdcbdddcbabcabbcbbdcdadcdcaaadcccadddacdbabcaccbacdbcabdbbacbdcbcaacbdbccbdcabbdadaaccbbadabcaacdbcdabcccdabcdabccccaabcacbcdcacbbcabdcdbdbbaabcdadcdcdabcbdcbbcbbddcdcdbaddadaaccacccdaccdcabbdbaacdabdcdcccdccbcddbccaddbbbbbaaacaaaddbdadbdcdabccaddcdccddcdcabdbbccdacdbdccbbbbcdcacabadaaddbcbcadacaddccbcbbdaddcdcaddbadbcdcaddddddacaadbcadaaddddbdadbdccdbcdaaaacdbbcdddabbccdcaacdcaccdcbccbdddbcbdbbacbdbddaddaacdddadaaddbcdbbcadcaabcaaabccbdbddbddbcbdccbcbbbbbdbbadabdddbaaccbdaabbbabbacdcddcbddacadccdcdcbddddccddbcdaccbbdcaadccbabbcbdbbbcadabadacccddbabbaadaacabcbcbaacdaaaacacbccaddddaccbadcdacadbbcbcccacdcabadadaddbbcbbdcbbabbccbcabddbbbcaaaacdbbdaacbcbcdaadbdaccaddcdcdcdbadcbbadddcadaccdddbbcadabbdabdccbadaaddbacbdddcaacddddbabcaaabbaadaaccadacacaabcaadbcaddaadcbbccccabbdaccdddabbabbaacdadbbbabbcbadcdaabaddbaaaaadaabacbdddddcdcbacddabdcddcacbdbacddcbddaacdadaddbcdbccdababbacdcaaadcdaccdbbbbacdcdbdbdcbdccbdbbababbbdddacbcdbcbacbbcdcdacababdbdccabcdaababdaacccaacddacccadaaaabdaabddbbdddddccaabbbbddcaacbbbbccbbdcdbcbcbbccbcddabaadcdbdddcdcdccadbcabccbcbbaabbdaaadbdcccbbaadadabddaacacacbbbccdaaaacddadabaadbabacbbbbccbbdccabdddadaadbbdddbcaabbcbcaacddcacbbbbcabdbdacdccbdaddcadabaacbaaddaadacccdbdaaadddbccddccbaabddbdbcbabbaadbaccdaaaacbbababaddbdddccbdcccadddabdadadacaacddddddbcbbdbbcbabcdaacdccaadbcddaadbbddcdcaacaccbbbddabcdaccbdccdbabbadbaddbbccdbadbdbabaadccddbaacacdaaaaabdcacbbbaaaabacccbcadadabacdaaccbbcdcacababdcdbdadaadbacbacaacabbacbbbbbccabaadbdcdccbcaacdccabadbcaaaabaccadbbcbdcbabaddcbccadbbabdcdbdaaccddaaaaabcdddadbdcabcddbbccddcbaddccbaadcbabdbcdbccbdadabdbaaabcabbbadccdadabccdcdaddaabbadbbdcdcccbbcddddbdbaababcabbdabbdaadbddadaaddbcddbbbdbcaabacdadbaacdddbccdabcbdcacccbbdaddadbddbaaacdaaaccadbddcdcbcddacbbddbbccbdcaaaaddcbcccdccbbcabcbdccddbbadabbdbddddabcddaacabbbdabaadbccddcddcbdbdddbbacabdbbddccddbdadacdabaabdabbadacddcccdadddaabacaccdddacbccdbcacabdacbcccdacaadcddcbcccaddccdcdbbbaaacbabcbcaaaaaccbcaddcddbbcbdbddaddabacbababadacdddaccbabdadaddaaacabaadcbacccccabadbbacbdcbdddddaabaaadcbcddbdacaccacddcbacbcccaacadbdbbbcdabcaaabacaccccabcbccadaadacbbadbdbaccccacddcaaddbcbaccddababddaadcddbbcabbcbcccaacacdbcdaaabbddbbbdabcbcacbdbadaaacbaddbccaacddbcacbdbdbccaaccabddadcdbcaadbcacbdaaabbcaaabadcdadacbccbcddbddaccaccabdacdcdccdcadcdddacaadaaaadbddddcddcbbabcadabbacaabccaadaaabbbcabacddabdaaaabcaaadacdaadbaadddbbadbbcadadbabadddaabccddddaccbdbacddcddddccdaaaddddaaaaddabddabcbcbcdcccaddbbbaadadaccdacdaacdbcacccbbbaddbdcdbcbdacbaddcccbbcddbbbdacdaccdcdbdabccbbbcaddcabdbadcbbadbcbcbaabaaacdabccbcdcbdadacaaccaadcbcaadbddaacbabaddddbadbabdccaaaddcabaaaabbbaabbaabadccbaabcdaccadaccdbcbdabaadabcdcbcabbcddacbdddbdaabbccadbdadcdbbbabccbdacdbccaccddbdbbbbccdddcacabcbaacdddcbbabccaccabdaddbbddadadbcdccbbcbcaacaadaadbbcacaaccaabbababdabcbaabbabcbccaadcdbacdaddbcbccabdccbbcbdcbcaaadbbbbbdababdccbaadbdcbacddcbabcbbdbcaaabdabbbdaabddadaaddbadaddbccdbbbdbbdaabcabbabbdcbcbbbacabdbcdabbbabbdbbbaccdccdddaaabaacaabbbbcbdadaadabdcaabbbccdadcaaaddbddbbddcadbdbcdacbdbacdbddcddcdcbacaaacddabadbbabddcadcddacbcdbaddbabacabbccdabacaddcdcacacdcadccdddbadcdccdbbbbcaccadacbbaaadcddabacdbaacccaabcbacccccaadaadacccdaabacbdbabbbdcdcbddcddadbbcbddcdbdcaaaccaadbcabdddaadadbcaadabdabdbcdabacdadadaaddddaccaadccbcaacdbaddbdaadbadbabaacbdacbbaabdabcdcdddacdcddadaabdbdcdcbcbdaddbdbdcdabdddcdbabcabddcdadcaccdacbcdbbcadacababadcacbdbbdbbbbddabcbabbacadcbdcdbaaddbbbdacdddaaddaaddbbdacdcdadacdbcdbbddaadccacabbdcabbddabaddbdbaddabadbbdccbacacbccbdcccbbadccbbdaddaadabbcdbbbcdbabbaddcbcbbdcaabaaacacccccaabdcadcacbbbdacdbcadcbadabbdadaccdcddbbdddabbdcaaabbaaacccabddccbbdaaabbbadcdcbdcabaadbbaadbdbbdcbbcbdccbacdbacbbccbababaaadabdcacaccdaddccbcdbaccabcdcddacddbabcabdabbddbdbabcdbdaacaccddbcdcaabcdbbddbbccddcadaabacdadbabbbbbdbddddcbbaacbcbabbbddaaddcbbadababbbbcdbddaadabddbbbbbadcbaadbabcacdbcbbbbaabdddbbadccadbacbacdaaacdabadbdcdcdabbdbdabdbcbaabbbddabdadcdddaadbccbdadbdaacbdabbcccadacadaabcdcdadcdcbcaaababdbdabbddddaaacddbbddbbcdccabcaabdaacdddaccadadcabbcccddcbcaacccbdddddbcbbddddcdbcbddabaaccccdddccdcbaacccdcadacddacaadbbcadadbbbbdcbbabddddabbcbcbbcacbdadaccabddbbbbcbcbccababcddcabbaacbcdbabdaababcbdbabcadadcdabaadabbaaaacdadcababbacacdcdabadbbdcccaadbcddcbdbbcbdcccbccbccbcabbacaddccbcbbaccbbcabacaabbadbcbdbcddcbacbcbccdbcbddaaaacbbdcdaddaadacccbadbbbaccccddbdccacbddbbbbddddbcabcbdadaabbddddbbacbdcdcbdaaacbaacdaccadcacdacdaadaaacbbaabaaaacdabdbcababbabacdbcbaabbabdcbdadaaccdbbbccdcaacbadbaccbdbacccbadcbdddcacabbddcaabdabdbdcccabdabbbbddcbaacdcbaaccadcacadcacdadcdbadccdcbaddcaabccdcabdbccbcccbcdcdcababbbaccddacbadbdbadbaddddacdbcdacacbcbcdccdcdbbacddddaddccdbccbcdbacdcbbaacadaaaabbdccbbcbbabbdccbbdacabbadbccaccaabbccddaddaacabbdbccdbbbcabbdabcbdbdadbaccacbcadbbabcbccaacacdadccccabdadbbccbcdcccacaccdabadcdbdadcbbcdcdaabdbdaabbbbccaacbcbcbdcdddabaaaacaccbdcdddcbaaccdbcaabcaabadbbbabbcdcaccdaaabccaacabbdbccdbdccadbbccdbdddbcdccaddaaadabdbcaaaaadadcbddadbbdaccdabcdbbcbadcbbacaaaddaaaccdcdacbbcbbdccaddcbaccdabcbabaacbdaaddccdcbdcacbbdbcddaaadddddadddccccccdcabccdabcdbbcbcaabadbaaabbddbdddbcddbacabcddacbacabcabdbccdabaadadbcacabcbbbaccbbcdbbbacbcadcbdaabbddaccbacababdddbdacbadbdcbadaadaddbdadadcdadadaddbbaccdccdcbbcddbdbabbcdbdacabccaadabaccadbdcacbdbccaddcbbbbcdbabadbccbcddcabacabadbccdcdabdacbdbbdcdbbbadcbcddbacddccacccccbcbbcddcaabdcdcaabdcbabbccbdcbdaadbbabacdaabdbccddcaacdcbacdbcbdbdaacccaabbbdacddcdbdacadbadbbcbacbcbbbbdcbacbcbcadcdccbddbabdbdabdaaabbbdcacadddadaacdaacadbdacabdbbbcaccadbacaccacdbcacbccadcacdaccabbdccbcddbacdbdbcdccbcdcdcdabcacdacdbaadddbdbcbbacadbbdccbddbcbdbbabcabaabacbcdadaaccabddaddbacabbcdcdaddaabbcaaacadabdcbddcbaaddacbcdcbbbcbadccbabcabccbbcbcaccbcdabbbbbbdbcdadcacdbbabbbbbcdbccdacbadabacdaaacdbbaacacadbccdbabcdadbddbccbaabbacbaabaaacabbbbbbbcbaddbbbcdbbbbcbdcddcbdabaaddacccbbbddbbadbcdcdbbadbababadadbdcdcbcccdbaacdadaabccbccbcaadbcbbbcdbdcccbbcaddbcccaacadacbdaaccdbbaddddadacbaababdbbacaaabbaacbaaabadbcbdddbadabccddcbccdcabbcadcddcbcbabdadcadbbaaabadaababbcbcbdabddcbcbdcdbdaccadacdacdcbaddddadadacdbbdabaadddaaaccabadcbbdabdaabcdbbabaacbbcadababababbdddcdcabcbddadcdccbddbacbbbbabbacddbcdbdcdabaddacabbabcdbdddcaddcbbbdcaccbdbcababbddacbaadbccdbccddbdbaddbdccbccaddbbabcaaadabdcdbbbacdaddbaddcddcdbccadbacbabcbbccadbccbacbabdbdbabacbaddbabdbbdddccdbdadbcccbbdccddddbcacadddcaadbbdcbcadcbbddccdcdddabaccabaddaacaabcbbbbdcaddcbbabbbcabcdcaacadbaaaadaadbaccdaacaabbbbddabdacdbdaccbcbababaddcddcacacbacbcacdccbdbaabdcadcbcbadddacbaaacddcacadbaabbbccdbbddcacbbbcacaaadabdaccaccbdbcaddadbcddcbcdbcacdbbadcbbaacbbcdaaaabdacbcdbbcbbdadbdddcabdddbcbddbddaabbdbcdcabbaadbcbaadbccccaadadbdcbbdbacbdbdbcdcdaddcbbdacbaaaccddcabbbddadabdadcaccdcadddbbacbbccbabaababbbdaadacbdadbdbadccadadaabbcadbbdcaadbcadaccdccabbbacbcbbbcbcbaabacbcbdccddbbbbdbcaccadaaaaaacbdbdacabbccadcbbadbdbcabccbdaabadddbdaabddbccaabbbacaacbadbbaaadbadaadaddbddabacdcabbcbccabbbaacbdbadcbadbccaddbcbaabaadadcdcdcacbbdabaaadcdaadbadbcaaadbbdabdccbabaaadcccbbaaaccdaccabaadcbacdccacdcbadbdccabbdbcdbddbbbdddbabdabaacdbaddccabddcabdcbdcccdcdacbbcdbddcaaaaaddbadbacbcdacdddcbdccbaadaddbadbbdbcadadaccbbdaacaccbbddabdcadbabacddbabbdcddadbcbdabcdcbdbcddcababcccccbddbccbbabdabbcbaacadbbdbbddcaabccaacbbcadccbabaaccbadccaccbdddabadaddccddcabdbcbadaacdbbacadbbdaaadabbcabcaacdbaacbdabcbacaadabdbaddddadabbdbaadcdaaaddaccaacdcddabcdacdaacddbcdcbaddcabacbbaccbaccbbacbabdaddcadbaacbcbbabdcacddadccaaadbddddbdabdbcbcdbdbbbacacabadadcbbcacacdabbbcddaadaacaddabbcacbbcadacdbbcdbdcdcbdcaddddddadabdabcdbaadcabbbdbddcddccbcabdcaccdaabbcabcbddbaadacbcbbadbcccaaaabadbadcbccdaaaccccdbddabcbacdaddcdbcbadabbbdbcaadcdacbacdaadbdcaabcbcdddcadcaabddacacadbadcadddcbcdbbcbaacadcdadccdaddbaaddabcbdabccdbadcccbdddacbddbadcdbbabacbbbdbadacbabbdbaccadcacbccacbcbaadabadcbdabcdadbdddaddcbbccabbcbaabadcaddccdbdbcddcaadcaadbbadcacacbbabbdaaadbddadadbbaabbccdaadabdddcaaacaabaccdacbcaabbbdaadbbacddadabaaababaadccdabcdcadacabbcdbdccabbaaddcbabdabbabbbaccadabccadcbcaabdccddccddcacdcdcddabaacdbcbddbddadcbdabdacdcbbdcccacdababdabaaccbbaacccbaddccbbcacaacbcbccaabcbdabacbacdbabdcabacdabcacdcbbdcdbcdbcadcddabbddccabbadbcadabdbcdcacacbcbacdadccdbcdbbabbccbcddddadbcdbabdbdccbbacaddaaaaddccbcdacaadbaabbbaaababaacaaacaabbbdaacbcddbbbdbbdadccddcabdcacdbdbbaccdcdcaabcadbdcabbbbdacdbcbbadcdabdbdcbadadbdbabccaaccacbabbbdcbbbaaacacabdaacddabadbaadbccdcacdacdbbdabdbbbbdbbcbcaccbddcacabaadcdcacadaaacabbacbdaddbbccdacccdcddbbcdabbbbbccaacabcdbdabbdbadccdaddccdbdadcabbdcaddcbcacabbbbabbddaacbccbdcadabddadbbdbbabddaabbcdaddadbcbccbacbdddaccbbbddcaaaaacdaaaacadcbdcbbccaadbadbdbbbbdccdccbcdcadadbbabdabbaadcabdbbacddaacdcddccdbbaadbadbddcccdbaabcbcdbadadccdaabcdbccaadcdaabdbaabbcbbccddbcbdcaabccaddbccdbadacdaabccaabcbdabddacaadccdddcccbcadacbabccaddbdaaacccdaacabcdddabdacaddbcddddcbcbacbcaaababbababdbdbbdbcdcbdcccdacddbbbbaaabccddbbcbccacdcaddcccbbbaabccbdbabbcddadabdaadaaaabaddbacdabcbcdcdccacabcbabacbbdbbabccbaaaabdacbbcddddaccbcdddbdcacadbddbaadbadcdddadcaaabaabacccddcaacacddadadbddacaacbbbdcaadbcaabadcbaddaababcdddabbcdbcdcaadbcbbdbbcaaccabcddcabbbccdcbcdacabbbaaabdcbacaaacaadddbbaddaddbdcaccbcaaaccddbbccbcbdcdcaaadcdcaadcacaddbdabcaaccdbcaaabccbdcaaadadacbcdaadaadcbdddadcbcacbddaaacbcddccdcbbacadbcbabbacaabbdcacbaacdbbaacbcabbababbadbdbcddaccabcdaaaabccddddcdcaabdaddcacdccddbbaddcdacbaaadcadcdbdbdccddbdbbdddcabccaaacadbddbcaccabdcdddbadddacbadddcbbccadbcbcdabbbacadbdccbddacdcabddbbbbacdcdddccbbaadbdabccbdbbcbccdaaccbacddaaaadcbacbabaacbbcaaaacdbdbaacbabddaaabbabbccacdbcbddbbabcdbcccadadddccbcbdddddbbaabacdbaaddcaddcccadabadbddbacdbbaadcdbadadabccbcaabaaaabdddabacadcbbcababdcbdcabcabaabbaacbadbbacadaadcdcddadbacbbccadccccacdcacccacbdbcbbcacadbbdddcaccbababccdbabbdadadaacddbcddbaddbddbbaabccbdbadcabcadbcacccbddaabddacacbdcbdabcacadadabadabbbcaaacadcacddacaacabdddbbbadbbacdbcdcdcaadbbcaaccabbacabbdbaaacaaabbbbabbabaaabdaacaaadddbcbbabbcaaacabbcddbaaaacadbacbbaccdabaabcbcdcdcbdcbbbcdbaddcbaddcdbddbbcdbdbaacdcdaabaabaaddccadabbcbcdacbaccbdbcbbccaddbdbabbaacdbdbcbaabcdaaaaacadabdbacdccdcacdbaacbbbddaabbbdbccadccdcaaabadbcbbabddadcbaacbaaadaadabbabcddcabbddbdbadaccbddcadcbdbbacadcbbabbadadacacaaadabcccbadcaabbadadccbaaadbbdbcbababdbdacdbcbaddcddccccacdabdbbabcabcbcdbdcbaabdbbbccbdaadacdcacdcccaacbdcadabaccadbdbccadcccadbcbdbdccdbbdbbcaccddaddbbbbbbdbcadbdbcddcddbdaacaccccaccccabdcadaadcdddacdcdadbdddbaddcbddaaccadcccbdabadddbadcbdcadcdcabbabcbcadcccdddbbbcaaacabbccabbcdcbadbcaadbadbdddabbbcbacadadaaadcacaabccccaadcaadbdbabdacdbbbaccbadddadaddbdcbacbaabcabcaddcccaddbccdccbcbdcaadbbdacdcdacabbbccdaaabcddaaabdcadaaadbbcccbbbdccccbcdbbcbdabdbdddaaaddcbbdbbddaadaabadabddbdbcbbdaaababdcdabdcdbdcccbaadcbabbbdbaacdccddabcdbacdbdcaabcbdccaabbbbcdccabbbddaaacbdddbcdadbdcacdbbbadadcacccbbabaccdbbcacbdbddcbabccdacadcbbddaaacdaadabaaccbadabdccccbcaddcbbcbdccdadcdcdbbbacadbacaacaaadcbdaccbdcdbbacdbbcbddbdaccbdaabbdaddbaddbcdcbadaddccccaaadbdabccacddcdacdcdcacccabddacbaacacddabbadabddbcdadbaabaababbdcdaadacdbbbbdbadbcabacdcccbdddcdabbcbddacdcadcadccdccbcbdcabccbbbdbbabacdbdcbabbcbdaacaddcddbadadcdddbcbdbddcbbdacaddacaacbbcdddbcddcaaabdcaaccaacacdddaabcaadaaddbbbbddaabdadbdbcacbcdacaddaabaccadaadcdddbadddcadccbbadabbbabaabbbddcddccacddcbbdddcadccacccdcacaddabcbddbbcbabacdbbcbbdcbbdcdbdaaacbdbccabadcbcddccbdaabccddcdbdcbabbdbbbddbbdccacdbbaabbdcabcddccbbdaacbaccadcbddcdbbcbaccacbcbbbdbcaaabbdcdcbaccbcabdbdbadaccadadcaddacccabdadbbdbddbdcbcdcdacbdcbdcdabbcabdbdcbbddbbcdddaaaddaddbbaababdcaadcabbbddbabcdacacbadbdccabcaccaacbcaaaddbcdbadbccaaabbbaddbdccdddbbaabcdbdbcabdbbabbcbdbdcdcadcbacbaaaaaccbaaadddcccddadabdacabcaabcdbcddcaddbadaacbddddaabbcaccdacbcdbdcbbaabbacbabddcdadbcdcacddcaabbcbbcdbadaacaddbadacbcabdccdadacbbcbabdbcaaaacbccbdcdbdbdabcbadaaaaabcdcabcabdcdacababaabcaaadddcccbbbcbaacbdccbcbadbddababcaccabccaadabcbdaddadbdcdbaaaaaddbbdbcabdaabbcbbdbabdbcccdababdbcadcdbdacdbcacdadddabcbaccaddbaadadddabacadacabdbadbcbacbcbaabdaadcacabcbddacbbddccbcccbabbadaabcbaccdbbbdddcbbacccccbbbdbddddbbddaababdacdbbcadaccbbabdcdabdbccbaadddddbbccbadbdaaaccaadbaccaacbcdcdbcbcdacabaabcbcdaaccbaaacbcbbbcccbcbabbadccdcadcbdbcbbccccccabdbbdcadbbccdaddaaccdbdababdadddaadacdcbdbcacaddbdacdabdcbbdccbddacacccaaadcaabcacdddcadcdbcccabddabdabbaaddbcbaccdaccddddbaccddacbbcbbddaaadabbaaababddbcadccddabadbccbdbcadbdbbabaaaabcdbdbbdcdccadcbbabdbdaadbabcbadcaacbccbcbaadddadbdbacabdacbbbbdcabdcbccbbbbbcadabbcaabbacbcccbbdcbbddccddabbdbdbbcbcabdbbcdcdbbaacadbbadaabdccbdcbcbdaddadbbdddcbbcdbccdbccbccabddbacbabcbcdbadbacbcaadcdcbddaabbaddccdbcbcbbcbcbbbadbccaabadcccdbcdddcbddcbcabcbbabdcbcbbabccbddcbcbabadddbdbdabcaddcccdbccdbbdcccadacadbddcbddaddbaadbbacaadbcadacaacbbbadbcabcdddbabaaadcdccbddacddacaabccdbdaabcacdcbbccbdadabccbbddcdbacacabbccbcddcacdcbadabdcbbdaadbbcdcccadcdbadbbcbddadbdbdbadcbbdcccbcbabaadbdddacbbacabadaddbccccadbbbcdbdcacbbabcdbbbdccadaddbcaadbacddcacbbddbccbccdddaaaddbcacbdcdbadaccdbbcdadcdbbdcbddbadcdcdaaadacacdbabcbcdcacbbabbabaaaacccbddadbcadddacbcddabbbadbdabcccbaabcccadcdbcaaaaaabdadbacbdcabdcdccdcdaabdabddacbbbddababdddbcbdbbbabdacdabbaaddadabadbaabcabbbdaabbdcbccaacbbbdbacbbacbcdaadabbcbcbdddccccaaaaaccadadacaacccabdaddbabdcabcccccdbccacccbcccdabcaccdbbaabbbbcbdabdbbbccbaaccdbddcbddbaaacdddacbbbbcddbcdbdbaddcdcccdcbcdaadacadcacdbabbbacbbdbcadccdabdbcbaaccdabbdcbbddddcbccadcccbbbdcaccadcacacdaadcdcddadddcadcabcddaddbcabbdadabadcbbdbcabadddddaaadacdcaaabccacbdcdacaabadddbddcbacdddbcdcbbdacadbaddaaddccabaccbcbadabbdaadbdadabddbcbaccddbcdddbdddaaaacdcccddcdaccdacaabaaacbadbdcbdaaadaacccddbcabbcdbcbdcdbccdbdcdbcbbcbabdaccdacbcbdddaddaddaccbaadcbcaabcaddaddbcbaabbccddaaaacaddbcbdabdabdbaddbbaccccbcbaccaabadcbddaccccacccbbcaabbaddcbadabacabaccabdbadadbbcdcadaaadbcddcbbcaadaccbbcdacdcddabcaaaddbcacabacaccdabbaabcbcbababdbdbdddbcbdaddadadddbdddacbddbcbcddacdddacacaacbbbcadadccabdbdbbcdbcbbbcdcbcdbccdabcabdcdcaccbababcaddaabadddddcccdadbdacbdaadadabaaaccbcadadcdabaaccbaaabbdbababbccbdbaccacdcccdcababaaabadcdaadbdccbdcdbbacadccaddcccddddcacaccdaadabdbcccdadddccbbddcababaddbdcaaabbbbababdcbabcacaaaadcbcdbdacbcbcacbdddccccbccbcdbbbddbabbabdddccbccbcbbadbddbddadbacacaccbbdcbdabdcbdddabdddccbaddabdadcdbaadddadcddcabcbaaccadacddcbcdbbdaadadcdbabcbacbcabaaccadbacdcdddcbbadabacabbabbdcdbaaccdaccbabbcabacaacbabbbcdadbcdddbddbacdbcdddacdbddddcaabaadddaddbcccadbcddbbcbdcdccabbacbacdabacadbacccdddcacabcdccdaaddddbbaabdabdabcdcbadadadcbdaabbdbbddadacdbdbadadcdacbcdcdadbdddadcdcacccdbddcddcdbddacbbaddaaccdbdcacccddbdcdadcaacbcdadbaabbdcabbdcdcddacabadaadcccdbbcacbbbacadaabacababaacccdccadccadacdccbccacadbbbdabcaaabcbacdcdcacdbdbdcbbaadbdccaaddcabcbadaacccaccabdddbbadbaabacdbcdbccbdbbdaccdcadbccbbdcbbccddcdcddccbcdadbbadbcccaadaddababcdbadaaabadbdcdcccccbabdcbbdccdaaddccbccbddcabddcbbddbdaabccbdacdbcadacbbccabccddbdaaaaaccbbbdcadcadcdaccabcbaaacddcdbaaddbdcaddcdadccacdcddcacbcaaddcbbbacabdcadbabbbcacabbbcaaacadbadabccdcaccddbaccaddadcdbabaaaacdbacaddccdcddcccbbdbadadacdbbaaabaadbdbbccabccdcbcbdbabdadddddbdcddcaacdcccbaaabbbacabbdbddacddddabdbbdaacccddacbbbbcabcdcababbcadbdcdbcdaacdaaabbddddcbabcbacdbbaadacddabadcbacdacdbbaabcdbaabdbddadacdbddadacddabdcdacabbcdacddbaccaacdcbaddadcbdbcaaadddcadbadcdccabdaaccdbcbbbabdacacbaddcaacaccdadadcaabbcddcbdcaaaabcbbcdacdccdadcddccdccadabbdddadaacdddbddbabddcdbacbcaccacdddaacadcadbdaadddabaabbbacdcdcdcbabdcddbbabaadccadaddadcdcbcaddbdddaabbddbbcdddbcaadccddccaddddbacacbadacddddadccbbcbbaaaadbbccdabbaadbbdcccccbbcdccccadbddacacdbbaaabdabdaaaaabcdcbdbdbcabbddbacdadcaacdadacddabbcdccdccbbbdaabdbbbcababbcdcbaacacbaccdbbbbbccbddddcabcadcbcbddbcdcacdaddcabacdbdaddcadccdaabbbdcbadbcbcbcdadadcbdbacbcabacabdacbbcbddcdbcccbddbbcbacbdabdacabaadbdcaaaddcdacbcbaacadbbaacaacbbcbccbbdaabcddbcbbabbcbddadddababcdccbbcbacdaacbaabbbdabcbdcadacbcbdaccadbabbdcbccbadaadaaadbbcdcdaddbcdcdbcbcbaddbbdbabaaaacddccbacdabaabaaadcdcbabbcacadbbadabcbdaddbdbcdcbdacddcbdaccdaddcbcaacacdbcadbdbcacdcacabadbabccadbacbdddbadcbadcccdbaaaabcacbbbcddbdadcaacabbcbaacaadacbdbbcacdcbdabaacaaacdddccaccccccdbbaaadcaacdcacabccddacbbcbcdcaccbccbbcdcbdcccdadacccddadcacadbcacbcbdcdadcccadcdccbcbddaaaccddadabcdcbcaadcdcccdcbdbcbcdccacdcbcbbaaacbcbadddbcbadaaccdbadaabbdbaddaccbcddbaadcaadcccddbdabbdcccbcaacaddbaccaadcbbbcdaddcdbadbbaabaabbadbbcbcdbcacddbdbacddacacdbaaddcddcbaaaabcbddadbcacddabacdbacdbbaadcdcbbbddacdababacdcadbaadbadbddbdbddccbcabadcabbbbacbbabbdbaadbadbccaccadcbbddabcabaccbacacacbbbcadcdbbddcdbdcabadcaacdcccadbbbdcdbbdabbdadcacaccdbbdcbcbaadcdddddbdddaababdadbabacabaddccbacacdbdcabadadbcddbacaabcccdadbdbccbadacccbacbdcbdcdccdacdbbbdcbacabdacbadbbbadccaaccddcdbdabacccbabbdcbdddcaddbabbddddbcbaccdbcdaacacccbdbbbcdcdbcabaccdbcbaadacccbbccaaccdbcdccbaddddbdbacdbcdccbbbacccbcadddbbdbadddddadaabaabadcccabaccbadbcdcdbdcbdaacccbabbbcccccabcdddcdcdadbacbdbcccbcdabadcadcaacdbccdaacbacdccbadbccbbddadadabbbcddcdaddccbdbbbabbbabbadaacddbbcbabbaacddcaabccadaaacbaabcdcaadacbbcacadcddcacadcadcaccbbcabaaaabbbdddacdaddaabdcbdaaacdacddacccbbdabaadbbaaccadbccabaaadccbdddddcddbcaaccbababacbbcdabcaccbdaccbcbccbbcacbbdbcdbaaaaaddacbbbbabcddadddddbbbdacaabcaaabadddabbacddddcbbcabdadccacaacbcbbbdbbddcaaddadbccdddcdcdbcbddaabacddbbcbcacdadabcbbdcacadacdbadbdbbbddccdbbaccdabcdcbcbbddcadababacccbabcbbdbaadadacdcbcabcabaabdcddbcdaaabaaaaadbacdcbaadcbbdacabbcabaaddbcbbbaaddccbdddbdcdccbbbbbcaaaccbbccbadcaddcbaabddbbcbbabbadbcdadccbcaabaddabaadaaaabdcddcbaadacadbabbbbbbbdacdbdaddbddcaacbdbababccabdadcdbccacdacdacbddbaadbbbbdbbabbbdbbddacdadcbbbccdcccbcdddcbacbbaaabcbcdddccccbaacadccbaacdbdabddbbdbdbbcadaadbabbcabaabddabcbdbdaacaabbdccacacbccbccddaddbabccdabdbadbbbbabdabbabbcdbabbbcbacccabaaaabcccacbbddabddbcbbdcadccababbbccddbcacdaabdbbdbcacaadacdddcaccdcadacbaadaadadbacccbadbbcacacbdacabbdabbdacaaccdbdcddbbbdcabbdccaabcdddbddacadbcdbdbabcbbcdadabdbabcddadabdcbdaadddadadcdbdbadcccadcccccaaddcbdabdbcccbadabdadaadacdddbabbbadcadacbbbacdccacdddbbccbdcacddaacdbcacdcdcadabcddaadbbacbdbbbbcacacbbdabaadbbbaaccabbddcddacbcacbbdacdbcdcdbbcaababccbddbbddbdbcadabbcbacdbcbddcbdbcbacdabdabbddaadabaaccadabdaddddaddacddabdabcbccadcdbbacdbbcdadccddbddbddbbdaacdcadcdaadaddcddcabadcbcdaddacdacaacdcbbcbcdcbbccaaadbdacadbcdbcddccadabdaaddaabadcdccaccbdcacbdadbdddadddcbabbacccdbacbdacddbccccdcbacdcbcddbaacbdddcbcddcaaccabaadbaacbaaacdaadaadddaabddadabaadbdaccbccabddabaabcdddbcddadadcadcbacbcdbccdadccacdaaccbdacdcabbadbbaadcbbdbbdbacaadaaabbadabadbdcbdcbbaabbdacdbaccdadbbdcadabbcbccdabdddbcaddcbbdcbbabbdbdcadabdcbaaadcbaabdaacbabadcdbabccccabdcadacacbcdccbdddcbcdbdcbacdcbbbdddbabcaaabcdcaacdcbddbacabdabcdbbcbddacbaadcadcddadcaaabadacbbdadacbbbadadaacdcbbdcadcbcdcaaadcadccbbcabdbcadcdccbbadaadabdcacbdccbdabdbcaaacbbcbcadabbbbbcbccbcddadbcbddbccabdadcacdcccabbbcbdcbbcbcbaaddbdaacaabdbdbbacccdcdcdcbbdaccadbdcdbdbccbbcadccddcacddcbbbcabcccbccddcdbccdabcdabdccddacdaadbabbcbabdccdccaaccadaabcccdddbbcddbdabcddacacbcbcabcdbcacddabcacabbadcbabcdbcabdcdbbdccdbccccdcbdddabadcdbaccdcaccbacbadaccaacbcdbbccaacccbabdaacdbaababdbdddbacacbdcdacbabdcccbbbbabadaadcacbdcbcdddddadcdaacdaaaccddbcadaabbcbddccaccddcccdadacccaacddbabbadbcddcbdadbaaabaddadabaadcbadadaabaaaacadcbcbcabaaacdcbdacacabdaacacbacdacdbbdadbabaacaadbdbbbacaaadddacabdcbadacbbbdbadcdabbcdcdabdbbaaccccdbdcadcdaddbcdcdbdbcccaccaabccdbcdabbaddcccbaaaaccdadbaabccacddbaddbdbaababbbadadcaaaabcadbbcbbdbabbcbdadbcacdccccdaadcddcbdcaadacdcbccddbcbdbacbccbdbcccccaabacabcbabcbadcdcaccbacddbbdbdddccaaacbaccdcbbbabccaacdbcdabcaaacacccbadaddbdabcccddabbccbcbdbbdadaadadbacdbdcbbcdbbdbddcaddabcacacccbabbddbbaccacbadbacabbdbcacdbdbbabbacaaddadaaaccbcdabcbbdbbbbbdabcabcadbcabbdbabcbbcabccbccdcacccdbadbabcbdcaddabaaaccbddcddcdbcdcbdbcddadbdccbccccccbaabbdaacacdbacbddccabcaabbbdcddaacdcbdbcddcacddcdbbaaddacdcabdcacbdaaddcbbadbbcbabcaacdbdcadbacabcbcbcbadbbdadcdadbdaddbacdbaaabbdbdddaddacddcbaabaddbbbcbacdddbbbddcdcbddccbbabdaaabaadccddbaaadddcbccddcdbdbbacadadccaadacabbbaadcbcbcabcdbacabccadcaddabadabcacbadaddabadddabcdcbdccccdabdadcbbcdbabbdbdbacdaaccaacacaadabcdcbddcaddabbbdbaaadbbdadababbcaaccabcddbbdddccaadcdcdbaadadcacdacccdcddbaabcadbcbbbaabdabaadacdabdcdcdbbdbabcbacacdbcadababcdcbbaddadbbbbbbcabcbabbcdccbdbcdcadbdddcbccbabcaacacadddddbbcbadccbdcdbaccbadbaccbcddccadcddbbdbcdbcaccdacdcbaaadabcbcdacbcddddbbcdaaaaacabbdaadabccbbcadbcddbcddcbccaccdaaaaadaabcbabdadbbbaccddcadddcbccbbbcbaddccbdaccaaccbdacbaabbbdcabdbdddababacacbbdabaccdccddcddccbacbdddbcdaaaccaaaadcddccbabdbbbdcadbcaccddbcdcccbcdbdacdccadbcabbacccdaaacbcccdbadcaccbbcadbbdbaacbcacdbcbcbbcccddbdaaddacbaaabccacdccadccbcabaddbaccbdadcbbbbbadcaaadaabacccadabdbbcbcaacbbacbdcacbbbabaccccaddbdadabddacdcabcacbcaacbaddabbbddbdaccddcbcdccccacadcbcacdbaacdabcdaaadccbbaacadcadacadacdadbdddbddcbbcbaddabcabcbcbcbdddabadbaadcddcccabbbcacaaaccbcbaddcbabadcbddbdbdabcbbabccdbcbbccaadbdbbacddbdccabbabcaadadadcbbccaaadccdaacddbccabbaaaadbaaccddbaccccbdbccacdddaccccbcacdcaaaaccdbbddbdbbbddcbbdccaadaaacbbbacaacbdcacbdbdcddacaadaadcbaddbbaddabdadaadacaabaabddcbbcccadcdaaaacdbbcbbcabaddacaabbdadaabbbdbccdadbccbaaaaddabbadddcbacadbbbdcaabadcbccbadaacdddcccdddadcbbccccaabdcabccdadadcadcdacaccdccaaaaccdcbddaaccaccababbacaaabbdcdadabbcbadbadcddadbbdadcdbbccacbdacbddaaccbacddbccbcbaabccbcbdadacacadaadbbaddcbbabbdccabcdddcbddacdcbdaabbdddbabadbddbcdcddbaddcaccdcbaddbabbdcbbdbbadbddbbdbdccccbadacacdacabddacbcdbdbaadabdbbaccbdaaddcdaabcadcaccabcccadcdabcdabdbcaddbdcbabdbbdccdaaadddbdddcbbaadcacbbadccbccdcabbcdbdabaabacadcbaadbdaabcdabacbbbdaddccaccdbccbbcadadcbdcabdccabbdbabccdcaaaaadcadbbabbdcabcdbaaaaadcaaaabcbdaccbbaddcbacaababaadaaccbcaddbccbcbbddaadccdcabaacdaadcdddcaaabaddcbaabddbadabdbddabcdadaaadbcdccbccdbddbbabbcacabababccbdbddacccdcaacadabbbaababbcadddacddabadaadbacaaacbcdcaaababdbacbcacaddbdcccacdaaacccdacabdcabbcdbcadcacbbdbbbabbdacaccdccaccaddcdadbbddacdbdbccdbacdcdbbcabbbcdacbbcbcddababcbddcabdcdaccdcbccddcccacaadccdcabbccdbdbacbcbbabcaacdacacdccdcdabdcacaaddddbbddaccdcdacccdacbcaabbacbcbccabdadccadbababcadabaaaadcddbdcdbabbcdabbacbcdcaaadaddacbdacdacbabdabcbdaaacdabaacddbbdaacaadccdabbdaacccacdbdbcbbbbdcdcadbaabcadcbabdadcadaddcbcccacabcbcbbddddadaddcbbcbdcdddaababcccbdbdbdcadabbddacaddbdbdbcbaddabcacbbcbaaabbddaadcbdbcbdabcbbccbddbacadccdaacdacacbbccbdcadadbaadcdbdbbbdabacdbdcaccadbdabbbacabadababbbdadaccbcabcbcbcdbcddaacaacdbbdbaaaadbadbbbbdabbcbbcddbadadcacdaadadcddcabdaaacdacaabaadabcacacadcadbcaaacdbbcbcaabadaaaddcccdcbbbdababdcbcccbaabddbccbcdbdadcccdcdbbbbaaabbcbdabddcbddddddbabbbcccadabadcadabcddbddaccadadabccbbbcbadccdaaaadacabcacdabccdaddbcdadacaccabcdccbaadddbbcdbddbdabcbcdcaadcabcacbbabaabbbabbadbbdcbdddbcdbcadaabcbbcbdccabdacaacadbdbcdcccacbcbaaccababbcbcbadacbaddccbabacabdcbdbdbcaacacbbacdcacddddbbdbcabcabdbaaacababdbcdbbacacaddddacdcdbacabbcbddaaacdcddaccdcbbadadcccddccdcadcdbbacaacdbbcbdbbccabcdddddbababcaaddbcdababaacdbcdcdabdacdabccbcaabcaccacdcbbdbdaccdbbabaccacadbbcaaddcadacdababdaacbddcbccbccadddadddcbbdddcadcbabbdcadbabbdacaddbbaddacccdddddbdbcaccabdbdbbddcdcaabcacdaadadbdddbdcacddbcdbdbaacdbcddabddcacacacbacddabcbbbccadcbcaadbdcbccdbbbacbcadcbbcdcdcacaccbabbaaaddccaddadcdabbbbdacdaddcabaaacdadcaadacbacbbbbbaddaccbccdbbbcdabaddbacadcccadbadbbacdaabcdcccbcaddacbbbdbddbdcabbcdabaccdabddbdddacdbacdcadbadbcccdcdabbdbbdbbdacaccbaacaacadacbccdcaaacaaddabcaacbdbcdcacaddcabcabbbdccbaaadccbdbbcacadcaaccdddadbdbcbbbaabcdddaccdcacbdccccccdbcaccdaddcbbadcbdbcccbabdaabcbdcccbbcddddbbcaadcdacdcadaabdabdacababcccbcacacbabbcaacbbdcdcabdcacdbacccdbddccdaaccbddcadbadccaabacbbbcbacbcdbcdbacccdccddbdadadaabaaadacdacbccddbadaddcddabbcbbbcaadabdbaccddcccbdddddcdabdbcaddddcadaabbcacaaabddcbddbabdaddbaaabbaadbdccadddbbcbadbccddbabcaacacadabddaacaadbbdabcaddbcbadbdcacacddbaacdccddbdcadcdaaddcdbcbdaacbdddddabcccdacbdccadccadbdabcdddbadbdbabbadbbbdcbadccbcacdcdbaabdccdacdcbaddcaddababacbcddabbdaadbaddbcdcacaaaadddbbbaadcdcbdddcccccaadcaddcdbdbaaddaabaddbacdddcaabbacdccbbbbbdabdbcdddbdbcbcdcaacdbabcbcddbaadadbdbcaaacabdddbcacdbbadcdaadbdbbcdcaadccaddacadcdbddabacbabcaaababdccdbdddcbccbacadaaaabdbadbccbabddabddaacacdccdbbaacddabbdbdbaadadbdbdbacdacddbcbdbaacdbbdcaddbdbccbcabbcddbdbdcccdcbcddbbdbbbdbdcabbddaabdcbbccddcccaacccdaaacaadcabbcacddddacadbcccdadccaddcbadbccdcdacabbbcadbcaadddbcadcdbddccaaadadddccddcccdbbcabadbabdbbadbdacdbbcdbbbacadacdccacbaabdcbbddbcbccdcddcddaadbddbdccdbbaaadccabaaabcddbaccbddabdbadaaddbddaababbdbdcdacaaddccbdccacadbdaadbacdaadcddbdacdcccddbdabbaaccaaddadaddbcaadbdccddcaadddbaadcddcbadcddbacaadadccbbaacacdaaabdaadcbabdacbbbbbcaaccaaadddbdadbbddaadccbddbabbbcbbccacaabbbcdcccbcddbbbcbccaadacbcdcaadaacdcdcdbaabaaaabbdcbbdcccdbcadcccaaabdcabdddbbcbdbbcbbbcaaddabacdbbbbabacdcbcbabbcacdddddcacbabaddccdbacdbddbcbacccaacbdbcdabdcbcdbacbcbbbaabbacbbbbcabbcbdaadadcdcdcdddcabcacaacddcddacbbcbdabcaaaabccdcbbdcddbdbaadbbbdbcccabadcaddbabbdabaaadbdaaabbaacdbbdaddacbbcaabcbbadadbabbccadbabaadaddcdabdccbbdbabdacbcbcaabacabddababdbaddbabacbcddacadbaabdbaadbaacbdbcbcbbcbbadcbbddbaaccbddacbaaadacadcaadccdaabbcbabadddadaaddabcdccdacaddccdbadaadddadbbbbcaaaaaaacddbacaadbbdccaacadbcbadbcdddbcdbacbddbddbcbbbbbaccadbaabcabccdddcbaccccbabdbcaddcabbdacaaadaabbccdddabcdcdaabccbbaaadcbccdadddbdbaaaaddadbaabdbcbabbccbdbccdacbcabbddaaccbabaccccacdccdaaaddadcddcbbaccccddcdabaabdddbdbccaddcacbcbcbcccbbdabbacdcbcdbddbcccaabaadbcbbdadbbcabccccbabbddaaaaacadadddcdbacccadacaacadccaccddccdcddcbadcbdbacbdcabcbbbcddcbaaccbdadcabcaccbddadccdcaaaabadcbbbcacabcdadcdbccadcadcddbbcdcabcdaaddbdadadbdabdbdcbadcbdaaaaccbbcdacddcbbdbdacbcbcacddcadabaaccdccdabcdcdcabbdbdcacddcddadbdadaaaabdbacdbddbbdababcaabbdbdaacddccdcdababcabcbcdbbdbacabccdcccccddddbabcabbbdbcabaccdbdcabccbabdbbbbbbabcbadcdbbaddabbbcabdaaacbbbcaabadabdadbcbbbcbabbdadbabcaddbcabadbbdcdabccdcbcddbbbabbdcacddabdadbcccccaabbcdaabcbbababdacabdadccadcaccdadcadbdaccbcabbccbabcaabbbbcadaaaaacbabbdaacbdaccdcbbcbaacabcbdaddcccdcccdcccbabcdbcbcbdabcccacddcccdbccabccadacbdaabadbaaccbbaccdaddbbdcbcdbcbcbbbbcdcdcacabddbcabaaddbdaaccbdabccbddbccccccdaababbdcbcbcaaccdbbaacdabcdbabcbdbbacccbbbbdaabdbcadacacbcbdacccdbccbcabcadddcdcddadccbcbddacbddabddbcbcccbabdcdaaaddaaacaaadbcbcaccdadcdbdcdddbababacbcbabbcaccdddacadbaddababcbdaaaabacbabbcaddadacdcdbdcbcaacacdbbdbdbaacccbabccabccbbcdccbdabbbbcccacacbaadbadcdabcccaadcbbaacdcaacbaadcaabaadbabbbacabaddabcbacdcdbcdacdaccdacdbdddabdadccbadcbdadbabcaaabbacbbbbdddaadaddaddbbcdbabcdbbbdaaccadacbbdcdcabcabcddaccaacdcdcbacacccacbcbaaccacbadccbddddcbabaadbacdbdcabacacaadcabadcabbbddcdbadadcccccbddbaccbbbddcbcddabdadacaaabbdccdaadadacaddacccaccdbacacabacadcabccdcdaddcadabbbdccdccacaadabbbdbcbbbdbdcadadcccbdcbccccaabaadcbadcbbccdcbcccbacaaadbababbacddadcaaaabcbaccacadcacbccbdddbbdcbabbcdabaadaabaadacdcdbbacdcbbdccddbbdcdcdbaadbacabbcbadbdbabbcdaabdabddddbbbabaaacddaabdaabacbdcaccdbbcddccddadddcaaaccaadbcccadcbaddaadbdbcddbdbdddadbbdabdddabddddddacbcbcdbddbccadaddcdaabadcdccacdbacbaaccbadadbaddcccaaaadddcbadadbaaabdabdbdcdbccddbbbccdddbbabadadbdcdaddcbbccbadabdaccdcaabccacacbccdcbdbdabbdcabcabdacbaabbdadcdbcdcacbcbbbbacdccdcdbbdccddcbcaabdadddcdbdaadbdbcbcccaaaacaabccacbdbdbddadccaaaccabccbbcbdbdddddaabcbbadbccdbcdbbbbbadbcdbdbdabcaacabbbbcadacbaccddbbaabacccddcaaaadaadcddbdbcdbdbddddacdcbabdcdabccdccdcbcdddccaccbdbbaadacabaababaabcdabaddabcddcbcddabbbcadbbddbbcdadaadacbbdaadbaccbbbabdcaadbbdabbbbcadacdddaadbcbdccbccacccabcbcababdcadbdababdbdbbaadbdcddacdabbabbbccdddacdbddbaabdacabddcaabdbdcaccaadaadbdddcdbddcddcbcbabaddaaaadbdacdcbddbbdacdbdadaaabcbbcacadaccbdcddbddbcbdbadbcdcdacbdcdbbbdbdbcddcdcdcaddcabbcccadcbbbdadabcaababbacbdcbcbcbabcbddbdaccbcbbacdaccbbabcddcccccabbdcbdabddbcbadcdcaabccccdbbbabcdccbbdbabcccbcaabbddcbabbdabbdabdddcccabbbdbcbbdabbaabcbdddbbdccccdbdcaabbbacdacadcbadaaccbacacbbddcbddaaabbcabacdcaddabcadaacdaaadaccbbddaddacddccddcddadabbbdbaabccbacdadcdbabdbcacaadddaabcaaabcaaabcddabccdcbadbdbdbaccabdabacadbabcdbdbbdbcbcaaabbdcddbabacbbadccbcbacddbaabcdacabdcddbdaddbaacbbbcaccbdbccaadbddaacabadcdabdacbbbcbbaddabbdbcacbdacacacaabaddbadccacacbcbacdabddccbdadddcbcdbdbadacdcabdcdacbaadcbbaabdcaacccbcacabcadbdaadcdcdddbccbdbddabdbccbdcddacdcdaaadcabacdcabaccbcbbbccaaaddabcccdacbbdbdadcaddbabbbccbdbbaaddcadaaaabcadbabccbdaaccaabbbabdcbaababcbcdcbcbabaaadbaacccaadcddddbccacbdacacdabacdbbbabbbcabcacdddaccabcdabbdcabadabaaabcdddbaabbdcaaaaddaacaabdccacadbbabbdadbcacbaadacbbdccdabaaccbaddaacbdddcaadbcdcbbbbcdbccadaaaaacabcbbcdbcaddccaadddbaaccabaccbcadaacbaaddbaabaddaddccabbdcaccdacdbcdccdbbcacaccabcadcaacacbdbcbacbbabdabddbaaabdaccdabaabccacddcdacbdabaddcabbbbcdabcbdcddaaabdcdddadbabcddacadaacdabaccabccacabddcaadccadddccbacacabadcacabccdabcadcadbdcbdbdbbbadcccbdbccdccabcaadcccabcabdaccbacbaccacddbdbdadcdbdaabdcbbbaabcdbaabdbcbddcdddcdbabcacbcbcbbbbadddaadcbdcabdccabddddcaadcdadcbacbbdcdbdccbdcbddadaadbaabcadcbcabcbacadacaadbcddbcbcdbdcababbbccddbacdbdbbabbdcdccccccbdaadaabdcabbabdbdbdacccadbcacacbaccadbdbcbbbcdccdbcabccadcddbdbaaadbbacbdadadadbcdcacbdbacabadbddbdcddacdadbbbdbddacbbabcbaddcdcadaaabcdcdbabbbccabaaacadbacaddbabdcadaccaaddbbdabbabcbdcbaaaacdcbdcdcbdcbdcbacbbcacabbdccabbacabcabbccaddbddbdaacaadbadbbbbccabcbcbabaacddcbbddbdccbabcabdcbcdadddccaccdbdaddbddbdcbddbccdadbdccdddcbdbcbcccdddaaaccdabaacdcaaacdccdaddadcbaddccacdbbddcdbbbacdccdbdbcdcdabcabdabcbaddbbabdbdcbbadcdbbabddbdcbbbccdacdacdbbbcabbcbdaccbccacacdadcdbcbadcdbddacabaaadcbaabaccbccbaccbbddaaddadaacaddcdcabaabcdacbcaaabcaccdacdacddaccddbdbbcbcdbcddccbcbcbaacbbbdddaddabbddabbcabccccbaddccdbacbcddcdddbdbdbdabbccddcadabcdcaabbccbdbadbbaacdbabbdaccabacaaaacdadcbacdbdbbbaaaaaaaaabbdbcabbdcccbcabbbccdcbcccaabccddabadacdcadccbcdcbbaaacbbcdaddaaadadbadddcbabcbdadacccbabbabcdcbaabacbbddadcbccbcbadacdbbbbbddacbadcccbdabadadacdccdbdbbacdbcacbdcbbccadcaacabadddbaabacccdadcabdcbaabddbcdadbdbcbcaaaaddadbdbdababdcbcaccdaddbaaabacaadbcdbcccbdadddcaadcacbcdbcdcbcacbadcadddbddbacbcdacccaacaabdaaaabcddaabdcbbcadaccbcaadbcddbcbdabbdccddaacbdbbdbcddaccbcbacdaccaaadbacabcbbcabaccadabdddcbaddbbccabadaabcddcababaccadcacaaaabccdadbbabacdccdacbdccddcbdbcaabdadbcacccbbdcddcaabbbaabacadbdaaddcbccacadcacbdadacddbadcaaddcccabbaaccbaddbcbabbcbbcabdcbbaddddbccdabdcdaabbccdcddacbacbddacbabccccabbcdbdabadacabbcaacbbabbbcccbdcabdcdddbbddadcbbaccaaaabcacadcaaddccaacccabdbbaaaaadabcbadbbdacabbbbdadbaacdbdbccbaadaaaabbbdcabadcdddbadaacbabddddcbaddabacddcdbddcadcbbcbccadddaacdcaddddcbdcbbdbaaadadcaddbdcbdbdcabdadcbbbddbcccaaacacdccbcddcdabcddaadcadcbdaadcbbccdbccacaabadcddddabbcadcaababdaddcbdabdbabbcdbbcadccdbacbddbbacdddddaccbbddbaaabaadadccbcdbabbdddabbbcdabbbacccbacbadcdccbdabddaacccccddbcaccbdcccccaacddacdccccddddacddaccabbdddbdcaaddadcccccbbccacaadaddcbacadadddbdccccdbcabadcbacbbbdbbbcaddaccdccccccacacddcdbcadcccadabcdbbcababcbdccbcacbbabcbaabccbaacdcdbadcbbdadbdbbdcbaabccacdccbbbddbcacdaddcadbbcccdbcacadbadadccaddabcadbbbdaddbabccbaddccbbdccccbbabadabbbcbbbddbdabacdaacbcdddabddacccbcbabdbdababccbdaaabbcdabbdbcbdadcdacccbcbbcbbbdadbdddaabbadbbddabbacbcdaddadcabaadbbdabcccbbabacaaadadbdacabcbbddcbdaaccdcbbaccbddbcbdbdaabbdccadabdbdabdabddbdaddaabccbbcbcdadccbcccabdcabcbbccbbccacacaadbbbabaddccbbadabdcbcccddbcdabdabcbcaadbacdbaaccbcacbaacdadcddadcccacbcbdabdaaabdbabaccdbdcadabacdcdbbbcaacdcadbbdcdbcadbaaacdcaaddcabbcbbaaaccdadabddacaabdaddbdcacabcadbaddacacbbadaccbabcaabacdcaaccacdcdabbdddbcaacbaacaabddadbbaabaaabbddbadaabbcaabddbbcdcacbbdaaaacccadbbabdcaabccacdbccabcbcbdabbcdcccddccdadacdbcccbcacabcbbdcacadbcdcdccddabcbbbadbadbdadacccddabdaaddbbbacdaaabdccdcdabbaccbaccbaccadcccbdadababdbdabddddabbdbbadcccdadacbcdccdabdbacdcbbabdbabcacbadddcacccbdbaccbdcbddacbbcdbbbabdcdcaadcbcdadbbbcddcbcaadabcbcdbbddbccddbdcaabdccaadccdcccbcadcddcdddbddddbdcaaccbcbbabdaccdbddccccbabcbabbbddcabccaddbcbbdcdadbabcacccbdcadbabdacbcaabaabbbbbbbacddcdbabacccccadabdcaacdcacccddadbcaccacadbacddcbcbababbcadabcccdadcadadbacbaaddcddcbaaaddcdadadcdbadaacaaddcdadcacbacabdcbdcccbcbababcbadbcbcdcdcddbbdcdadbaadcaaddaadbbdcddcccadabacabbaddbbcbacdbdcaccdbabdbbcccbaaadaacdbdadaddddcadabbaaabdadddaacbdabcbbbaacbcbacbbadcbcbbaabcabcbaccacdccbcccbacaadbbdabdbdbbbbabcaadcbccabdaacbaacbacbacbaaaddddbacddabdcacbbbbacbbcbcbcbadadddddbcaccbbacbbccddcdbbbdbaccbddaaacddcbbccabacdccbabbdabbddbbdaaacbccbcabbcdacadcbacdabddbcabbcdaadabbbdbbdcdddddbdddbaacadbdcbcbdbdaaddbccaaccdbdacababdcbcbcabdbdacccbbcbdaadbddbaccbdcbddbabcabdcbacdadbdbacdaadadbaccadbcabaacaabccbddababacdbabccccddddbbccdcdacaccbddcdbdadccbaaadaaaaccbdcacbbacbbdbdddacdcaddaaabaddbaacaaacdccdaccdccdadadddcdadbcbbabdbadacbcbababaabccddccaabcacadbbdbadbbbaaadabbaccbcbdcaaaacdddbcddcdbdccdacdbdcdcadaabccddaadadbcbadddcdbcadacbdcaaacdccaadccbdabadcdaddaccbabaddbdcadcbbbabbbaadadddadbcbcaabbaabcddcddddccdddcdbdabbcabcdbcddcbaacabcdbdbdabdaaadadbaddabacbccdcacbaaadcbbcdbadcdcbbcaddaaacabdcabacbbccbaacbbcccacdaddadbcdaddaddbcbdabbdbbbabaccddaddddcacbcbaacdacaddbbbbdbcabbdcbdaccbdbadbbaadccacddacdadddacdacadbabaddabcccbbbccdcdabdcbbabcadbcbdbbdbacbdbcdbccddaabcacdcdcbabbcbacacdbabdcaacdacabcadacabcaaacdddaadbdabcbaddbbaccabddacbadbabccbacdabbabcaaaacdcdbbabdadcbbcdddcacaabcdcddaccbcabbdcaadbacccacccdccdccdcdbaccdaccaaacdabdbbcdaaabcbddcdcbdaacdcdbcdaddaadcabcacaaaacbccbdcdcbcdbbabbdabadbcddadbcabcdadbcdbbcddbccabbbcacbbadacbabcbcdbbabbddcddbcccbbadddcaddbbaabdbaaaddacddaadcddadcbccdabcacbbadaadbcbcbbcbbbcacbbdbcdaaadcbadbbabdcadadbbdaccacdcccbddadadaaadaadcdbcdcbadccabddccbdaddaddcbdaaddccbacaabdbbacbbbccdcdcabcbaabbccdcdbbaccabdbbbbcabbaadaaddaaaaddbbcbacdddadcacbacbbbdbacabaaadbaabbddcbdaacaacadddbaadcdbddcadbdcaacadaabacbcdacadbdcdbaabcccdcbcbabbcbcadaaccddddabdbcadacdcabcbacaabadaadaabacbbddabdbdaccdaaadcccbcacdacbdcabdbcbcadccccbcbabaaccbddbcacdccdadddcdbcbdddbbadbbbddbabadbdccdcdacbdcbcdbcbadcbbdbbcacbacacaaacbccddddccdcddddbcbbabcdadcdaaadabbabadbddaaddbcadbaabdbccbcaaddadaaaacdaaccdacacdbaddabdbaccbabdaacddbcaccdbcdaadbdccddcbcabacadcdaccdcadbddcadabdbddbbdddabaaabdbdacbcacdacbaacbabcadaadbdcddabcbcbbccdbdddbcdcbaabbdadccdadcabcbaacbcbdcbcbddddacccdbdabaccbabcdcbbacccdcddcddccbccddbccdcdbbcbbdcccdabdddcdddccdbdbccddccdcbcaccacbcdadabdbcbccaaaabdcbcbcadbccdbdcaadcdddcddcbabbcbbadcdaadacddbadbdbdaddacdcdcdbdbaadcdbcabbbccbddabaaabccbdbbadbcadcdcccddaccacadbbacdbdcdcaadabcdbaadbacbabcacabdbcbdddadaaddcccbbcacbaccbacdbaaddddcacddbbccdccdaddaccdacaccdaabcbcacccbbcdabbacbcccccbbbbcddcdbadaccdadbcaccacdbdabcddaddabcddcacabababaadabcadbbcccabcbaddadadcaadbccababddaacbcaacddbdccabdcdbdbcacaaabddbadbddcddddbacddaabbdacadcaaabdadcdbacdbdcbbbcddadcacdbbbbacdacdcbbdacdabcdaccdbbcdbababbcaaacacabaaadadcbddccacaddcaaadadcccaddcddaadbadcdabcbcccbcdbacdbaaccaddddadbbcdbbccacbbdccdcbcadbdabcdcdcaadcdaaabdcdbbcbdbdcaaadddccccdccddccabbbdbccabcdcaaaabbddcbbdaadcbccadddabbacbbdcbdaaadddbcdabdbadcddccbddcdbbddacdabcbdccadcdaddbbcbdabcbdaddcadaaddacaadccacdadcbacaadaadcbccbadaabcdacaaccdccbddacdbbdcdcbddccbcaaadbbabbcdcdbbadbbdbbdbcbdccbdcdabdbaacabccbbbcbcbccaccddcbcdbdaacdcadbcdaababcbdbcaadcadbadbaaadcbaadbdaddcbdbabacdaacdbdadccbabbabcbddcbdbddccdcbbaadaabbacbcdaaccacdcbcacdbcccbdccdbdbacaddddbcbdcadcaabadadcacdddadbbdaacddbbdbcbaabbabddbdbccdbbdaaabdbacdadaddaacddbccddaaabddcbbbdaddcbaaaccbccccdabddaacbbbabcbadadcaadbadcdcdcbdcadbcddcabcabaaabdaaaabcadadcbadccccbcdcdccdcacadccbcdabacbdbbadcaacbababadcbdbdbbdbcbccdddbaacaccbccaddccdccdadddcddddacbccbbddaccdbdbdcddccdddbcdbabaddbdcabdadbddccaccaddaadcdacacbaddbcbddaabccdddbabbbcdbaccaadbdbbbabacacbdabccacbacdacaddadbbcadcabaaacbcbdaaacbcccbacbdadcbacbdcabbbbdadcdabadcbbabdcbddabddacbcabcbdcdccadddaaccddaacbccdbbdbcbbaadcccdbaacbdddddbccabadadddcadcbadcbddbcddaacbcaccdcdcbdbbdacbdccbdcbdbbbaabcdbadadbdccbcdbaabdcdcccbbcdcdcacddcdbabcdddbbdabbbcdccaccddbcdaccbacdbcdbbbbbccdacdabbddcbaacdbccbacdabbbaaddddbbacadddcbbccaacabdbcbdbdcbddcdcdbcacabccdcbddbccccadbddbbaddddcccddbabcbaddbabccbbbcaadbbbcbadbabccbddbdbcaccccaadaacdbbcccdadbabcdbabccccaabddaacaccbbcbcabbaddbbcaabbdaabdbddbdadcccbdbcdddcaddbdabaccdddadabcbbaabdcccdbabcdddabcbbbbaaccabaacdadadcabbababddabbbcadbdabcbcdbcbbbcabdadccacdcabbbacaadadcabdcddabcdcbbccabaccbdcadbdbcbdadbaddcaacccbbbcbbdbacbdaadbcbcbaacaccdabbacaabbacdbbaadcadbaabcaabdabcbcbbaccdddadddadabbccdabcccbdabcabaddcdbdbaacdaccacbaaadccdcbbddcdcdbaaaaabcbcdabdadddcbabacbaaccdbacbabaadacabbadabdcadaddbadbccdaadbdacaacdcccaccadbdbcacbbddbaccaadabacbcaacdbbbdaddcbdaabcdbdcbbdbcdbbaddbdabcaacacbdaccdccddcddcccbbccbbbcccababaabbdcccdadbdddcaddadbbdabbaadadcdbaacbbdcbdbbdacaaabdbcccccabbcadaacbadaacaddcaaaccbcbbdbcabaddcbdddaadaacadccdabcdaddaacbbbabadaddacbbddcbdcbabcbdddbbddddbdcdabdcbbbdbcabaddacccbcbbdcdbcbdadacabdcdbaadbbcddacdbcdcbbcabddddbaadbdbaabddcadbbdcdaadcaabbcbbadbbdaacaaddabccabccadbcaccddbbacabaacabbdadbccabbabcabddccddaccdcabdcabbacacbaaacdbbadacdabcbbadcabbcdaccddccdbabddcdabbddddababdccbbbaddccaaabacdbcbcddbdaacadcabacddaadcadbbccbccbccbcdabadabaabacbbbacdaabbbddbdcbddcaadddccdbabbddcdcabbacccbdaddcdccbdbdaddbaddabcabbbdabddabcaabdbbaccbcaabddbdcbbbaadddbdbabdccdacdcccdbacbaadbbddcdbdcacbbdbbddbbdbabcacacaddaabadbdbacabacaadddcbabcacbaaaacbbdcbdbdbcccadccabcbbaabccadadaadcdcadbadbccdaddddabbcccdbcacaacabdcdabdbbdbcbacddbcacdcacccbcbadbdcbaacddbdcdacccaccdcbdbabbdadccabdbbacaabaadaaddcdddbbcaabadcbcdccdacacabdbcacddaadcacabcdbddbdadabbbdcccdbcaabbdadcaddcbadcaaaabacadbdbadddabbbbcdcdccbaddbdbacdadadcbcdcadbcabbbcaccaadbbdddbacddccddcccbaacaccbcabcdacbdddddddddadabcadabddcbadbacbcadbdcadadadaabbcabbccdbccddddbdcabddabdccbdabbbabbabaddbcdbddbbabbcccaacbcbbaadaadcccabbdbacdcdddbbaccdccabdadacacdccbdcabaaabddcdbbddcbaadacabaaabbaacbccddaadbbbcbbbcccddbdbdccccdcadacdacbcccabbccdddddacbbdbbaadccadbbbabdbbadaacdcbbcdbcddaccccddbbbadccaccdddcbbcbdccbbcbcddcadacdcdabcdaaaababaddbdcdcbcaccbccbdccdaccdbcdaaacaaddadaadbbdabcdabacacbcdadcbdadababadcadaddbacdccadccadbadbbbddbacbdcaababddcddbddbabbabadddadacacacbadcacadcbbabbbbdcbbababcacbaccadaaddcdacabccdcababacdbdcbdddabadcdabbdbcbbcdabcccddbcacbbaccbadcdbdcaababdadaaccddabacaddaaabbbcbccadcbaccbbdbbbbcdccdcbbcddacbbcdbcaabbccbacbcacdcdbdccaaddcccaddaddaaacbbdaacbbdbaadcbccdcbccaacbbabddaabacdddbacdcddccabdbbaddadaababaabccbacdaabdbbdadcccacacabdabbbbcacddaacadacccabcadababacabcadcdcccbdaabbcbddaadbdaabdadadbcbddbbbcbbcadbcbabccdcbccaccbcbbdcbccacdbbaacaabccaacbbdccbddabbbdadacdaacaacdaabadcddaaadadddbcaacddcacddbbacbccbbbbdadcdaccdabdcdcccdcdabbabadbbddacabcdaddbbabccbbcabcccbdddadbcdbddacccbdbabdbdccaabccdbbabbabbcbbbcbbcbadddbcbcbdabdacbadbdbabdcdcacbcaadbbcbadacbaccddcadabaacacaccccccbcdbbdddcaccdaddbbcbbddcdcbcbcdccdacbaadcbddbcbdaccbdcdbbadcdbbdcdbbcbababddccadccacaabcdbcdccadccadbccbdcbcacaacbaaabcabcabacbbdadbdbdddddacccbacbbccabbdcaccaddbcaddcdaadbdacbbababdbdacddcddbbcaaaabaacbcbcdabcdaccccabcbbbdccccccddbcadaddcabbbaadbdcacddcdbaaddbbbabccdabdbccbacbddbbabcbaccaabbdabbdabdbbddcbcdbbbdcccccdbdcdcdaaaabbacbaadcdbadadbddcadccbdacdadaadbdccccaaddabbcdbaaabcbccdcaadabcbabdbcaacddacbacdaccbbcbbbbbdababcdbabbdccdacbacbcbaacaaacccaadbbbdcabcdaccacdbcbabbbdacdcaadddddcbccdacbbcdccbcbdadbcbaadbaadccaddaaaabaaddaddbabbaaccbcbcdcdacbcadbbbcacddcdbdccbccddcbbcaaddaacbbacddabdbcbadcadbcdbaddddadbadbbdbbbabadabcddacdbaababbadcabcbacdbcaddaaccbabddccdccddcaacdbcbdbaacaadbdbdabdccacdbbbdcdcabbdadbacdbdbdcabaaaaacddbdccbbadddbaabbbdaabcbacaaaccbcacccbdaddcdbdadadcbadbbdcdcdcbadcacdcabaacdbdcccbdcadddcbbbbcbcbacdbdccadaddbdcadaadaacabcbacadddbadbdbccaadbaacacbdbdccaaddbbadddbbdbcccbcdaaaadabcbbcddbcbaadbccadbabadcddcdbacdcaaacaacabcddcdbccacabdaccdabdbacdcdbaaadbaaadbbacaadbcbadabdbcbbbacdbbdadacdcbbbacccadaabcabddddbadbbbdacdabcbaaabcddcbcdabaaccdcaaadaaaddcbcaacaddbbacdbcacdabddacbdcdbdbdbcdbddcdabcbccacaadbdacddbdbdccddddacaabbddaccbbccabddbcdccdadbccccaaacadabacdcddcdcacabaaddcbddcadcabbdaadabdddcabaacabcbccddaadaccddbdbcabddbbabbcbbaaddbadbcddadbdabbbddcacaddbdcdcaaadccaaaaccbbbbcaadddabdcdddbbbdacbaccaacadbbbbbadccddaadaddbaadbccadcbddadbdabbdccddcddbbcccbcdbaccdabcbbbbbacabcbcabcdaacbcdaabcbbccabaccaacbdcbbdacadaaaaaaaaaccdbbabadadaacbccbcdbdabadbcbacccbcabcddacaccdbdaddcabbbaadbacdabddcbababddaaccabdaaabcadaddbbbbdcacdcadbdabdddaabdabcdaddcbdbdbabcadbaadcbccabbbccbcacacbcbcabcdbdcbbcaccdadbabaaabbbaabadabbabbaabdbbddaabcacaccbbbdbbcadbccabbdaaadbccddaabbbdacbbddbaccaabdbacdadcdaaaddabcdddabdddbadbcbddababcbcdbccacacaaddacdabbbdabcaaccadaaabaabbbcbbbdcbcbacdcdccdaadddbdadcdcbdbaaacbcbcaaadadcbdbbdcaaadcccbbccaadbaaaaadacacbcddbababbaccbdcacaccbacbcacbccbbddbcacadabbdcadddbbabccdbcabaaaababbaccabadabcddccadabbaabddcaabadcbdddbccadbadcaabbdccabacaacdccbbdabddbcccbaccaacdaaaabbcddbbcdadddcddaddaacbbbdbadaccbccadcabdbbabadbbaacdcadaabdcdcbadddabbbdbdbdcaadbbabbdababddbcdcddcbcadbaadcbaabddbdcbcbaaabdcdcdadddaadcdccddcdaaabcbcdaaccdcbddacbccbadccdcbaadbdacaaddadbbcbdddbccdababbdbbbbbabaddaaabbdacdcdccadabbddadbcdcbacdbdddcccbbbaacdbdbbddddbbbcaaadbcccccddddbaaadccbdbbccdbbadcadbbabacadbaabdadcbadabbaabcaabbdddbbaaddbaabbadcacaadddbdacdbccadbcabdabdabcaddcccdaaddcacdaccccbadaaacccacabadddaadabdcccdcdaacbbcbdddcbdbcdcdddabbaadddbaacdbdbcdbaddbabcdbcbbadddaacbbbdbcaccadacababccaccbdcaabcddabcaadcacbcbbccaddbdaccbcdbdbbdbbaddcdbadbbcbcbbdbcaccddaccdcadddccdaaadbcbddcdacbbbacbddbcbcadbaacaabbbbadadadbacadababadbbcdaabcadaaababbcdaaadadddbcdbdbacbdaccdabdcabcadacadacddcdaabcdaabdbccaaadcaccccddbaccabbacacdabaaabcbdcbddcaabbbcaaccacacbddacbaadacbbadcbdbbcaaddcdbbadcdccaabdbbdbbcaabadbacbbabccddbcbccbbccbacbcdbaaacbcdbddabcbabacdbbaaacaccccacaaccabdbdabacbdabdcbabbaddddabbbbabadcdbaccbdbdcdcacabbdccbabcbdaacbacbdccddaabacababacdcbdbaccaadddbbbdccbabacbdbdaacbbdaabcabcdabdaadcacdaaccbadcaaccdaccdcabbcabbcadbaccbadaabbdcbabadcbadcabcbcccacdacdccccadcaadabcadadddbbaccddcbbcdacbdbadabcbcbacabcdaabaabaaadbcbbbbbbcadbbadbdbbdbcbdaabadccbaadccdbcadbccbbadbdcaacdcdcabdccbbacdbcabbcddcaacacbdcbbabadbdbdcbdccbcdaabcadddacabdaccbaacaddddadaacdbabaccccadaaacccdadbbbdcdaccaadcdacbbbcdcadbddaccbadaacbbddaabaacacaccbdbabbccbbdcddbaaabaccbcacdabacacdcdcccbcabaccddddbbabbabcbbcbdabaadccdaaabbdbbbccddbcbbabdbabdcadacddbbdabcdacdcacdbaacdcbbacbacadcbcbcdbacccdcdacccdddccbdcddaaadcabcccbdabdaaadaadccddddccbabbddaddacdbccdadcacbbcabdcddbdbacacbaaadadccadadbacdaadcddddacabdcdcdabcaadcbdbcabcbbdbadcccbaddbbaadbdddbccacdabbaaccdcccaddaaddcbadcabccdacdabccdccaabbdbabaabccdbcddaccaccacaabdbbcdcaccddbcbbaccacabdbabaddddccccdddbdbabbbdddccdcacabcbdcacdbcdacdadbacdcddacccdabdbbbaacabddcadccaabbdabccddadbcbcddbbcdbbddcaabdbdabcbbcbcddbdcdacdaccdccbdacbbcbadccddbbbddaddbdaabddadbbabcadcadcabaabdbacacabcbacdcdccdbccaabaacdddddcbbdbbbbdacabcdcdbccdbbdacbaadcabdcadcccccadbdbdccacccdaaabaabdbbdbcacddaddabdcdddacdccabbcdcbddcdcbbccbadddbbcabbabdaadbcbdabdddcacaaaccddadcbccdbbbacabddbdabbcaddaaddcaabbdcdcdbbdccdddbacaabcdaadabacccbcbdddcbdbcdbdaddcdbacbbdacdabaddabbcbabdcdacbcdbbbdbdcadbaaabbdacddbaadadbccaabdbddbdbdcbbbdbbdbaaccacadaabcdcdaadabbacdcacbacabbbcddcccacbabbcddddcabcabcbdacbacdbcbadbcadadadccbcbaadadcbcccbdbbdbaddbbbbbcdbcbcaddbddbaaddcbbdacccbbbdacadcacabdabcbdbcdcadaadaabbccdddccacdcabdadbdbcacdbbbababaddbdddbbdcccaccdcdcdacacdadbbaadbadcdcbaadcccbbbccabaddbdbcccbcaaadbdcbacdadccdbcaddbadbbccbdccdaabccacadbacdaabddcdadbdcdcccbadaaddccbacccbccdbbacacbcadddaaaadabddcbbaaaccaaadccddabdbbdcbdbdbaddabaaccdbccdaddcbcdcaadcaabcddbaaaaaacdddacdcddbdcbcddcbccddccbbbbadabcddbbabbbacccbaabccbadaccdbbdaabddbacabcaccddddcadcaddccbbdabdcbdabbbbbdddacdadaadadbacccbbaccbcbdabcbadcbbbccddcaacbbbabdadaaadbcbbcdbaacbabdbdbcbdbacbcdacbbdbbabaddcdccbdbcdccbddaadcabacbccdaddbbbcbadcbcdbbdbddcabadabcbadadacadbcdbdaacacbacdaccdacadcbcbcbbaacddbbcacdbccdddccbdbcbccdacdbdcdcddcbaacaaddccdbddaaacbdabdaddabbbaacbbbabadacccaaaaddadbbdcadcbcbaaabddddcbdabccccbcaabcaddccddcacccbaddbccddcaaddadddadaacacaccabbdccbdabbdaadddbabbdddcdadaacbcbbdcdcdacdcabddaacddabccbdcbdbacabcdbccaaacaabdacacbbcccbdcbdcbdcbacdcbbdbacdcabcbcadbdaccbcdaabbdadaabcaddbddddbccbcaadcaaacddbbdcdcaaabbbcbddcacdddbbaccbdadccdacbbdacdcdabdabcadaddabbdaacbdbbcdaaabdaadcadaacabcbbcbcbadaaacadaaaaddbaadbdcbdccbbbbccaaadaaacacdcdabbaacbdcbdbbbdcdaadcdbbabcdacdbaaabddcbccddddbbccbbccdacbaaaaabdcbbdbabbcabbbcbcdcbbcccacdcabaddbdcddabddbcdabdddcacbbbadadcaacdbbadcbabbdcdbcbdbcadbabdbadbadddcabddddcadcbacdccacadaabaadcbacbcdbbcbcbcadcccbbcdcdbcaabbcddaacddcdaccdadbbbccadcddbdcbbaccacaabbaaccdbaadbbbaccbbaaaadddadccbcacbabbddbaabcabbccacaacdabcdbbbcccbaacaaacbaadabdaabddcddaccddcddbcccbcdcaaaccddbccdcbccadbacddcadbbdccdabbacaaccbacbabdccdaadababbdbcdcdbadbddbacadbcdbcacdbabdcdccdcaabbbacababdaaddadddaccabdbacbcbdbcccaacbdbcddcdbadddccccbdcdcbdacaccccbacacdaccbbbbbbbacbcabbdaaacdaddbbccdddacccaacccbdbbdabacdabacdbadbdbaacaccbaabcbdaccdadccbabdcbddbaccacadaccdaddaadccaaddbdccbbbbccaabbcaacbccccbbbbdadbddccccbbbcbacbcaadacbbdcddbacaaddadbbdbbdbaadcdcdadababccbcdaadaacdbaadddadcadcddbccdadacbccacacccddbccbddcbaacddaabbbcadcdabbcaaacddcacbbcbbdaaacabcadbadddacbbbddbdcbdadaddcadcddaddddacccbdcbdcaddcdacbdcccdcdaabbacaadccbcdcdcdacacbbabdbddaacdcabcbaacabacdcccdcaccbdcbbadabacdaaabaaaccbbcddcddbcaccbcdacbcdbcddacdcabcaadcdddacdcbcbdbacddcadadbcbdbaddccdabbdbdadddaabcdcdbbbdadcaaadcacadbadbcdddcbdddabbcaadccbacbabbcacccbbdcabacdcabddcaadbbaacaabccaadbddacbbdaadbcbbcbdbbbbcadcdcaccdcdcbcbccbacbdcaaabdbcddcdaccacbbbddcccdadbdcbdaabbadbbdaddcaadaaabdcbbbcbbbaaaacaaabccaabdadbdbdcaacdbdbccbaddbcbcbadabdcadddcddaccdddabcbbdabaddcbdbaaddabdaaabaabcccbdaabdbbadacaaadbcdbaccbbcbadacbdaaaabbdcdbbbbcaccaaabcaabdaadbaddcaaababcadcaccdbaacbacaacadadbaccbcdacbcadaaadccaaddbcbbbababcccbcddbdbadbaabbdcdbcdbdabadacadccadcbdddcabbadcccabdcaabdabdddcdaaddbbcbbbddbdcccdddcabbdcdcaaaaacddcaaccabcaabddaccdcabccaddddcdbbddacadcdbdaacaabbcddbbdccadcdadbdbabacadbccbcdbaabbcaccacacabbccdbcbdbbaddbcdabcaddccacaabddabbccdbacacbdaddbaddcabbccccbddcacbabdcdddabacadbaabdccaadcadacbdccdadccbacadddacaddbbbbdbadccdcbacbbbccadcdccddbbcbcccdcdbcdbcaaabcbabddbdddcdbadbabdccacbbbcbdabaaaadbdabdcaaadadadabadbbcbabbadbbddbbdaabbbccddddabdcdbbccbcccaccdaddccaaaaadadabdcadccccacaabaccccabadbaccdcccbadcadcaacaadcdddababbacdaaacdcacacacdcaddbdddbbbdbbbaaabbbbbabadaddccbcdbbcddcbcbacbcdcacabddddcbcaadadaaaacddddbbaaabbddadadabbddcaadcddcadddcbcbbadcbdccbcdadcadccddbabccbbabddbbdacccaabcacdcbbcadadbdddcdddabdccbccdadacacdcbcbbbcaaabdccbbdcddbaaccdaddcdbdbaaaadddacddcbdadcaaaabadababcabcacbdadabbdadcacbccbcdaacdccddbbbdadcdbcbcbacaaabccddbdcccccdaaaacdaaddaabbccaabaabbbaccdaacbbdacbcabcdcacaadccdaddbcdccdbadddadaaaddacccddadddbdaccccaaddddacdacdabaadabbdcacbbcdaabaabaacbdbdbcddcababddadadcaabcdbcabcbbddacdddcbbacabcabdcdbaaabdcacddddbaabbdbbccbddabcacbbdcabdaacbdcdbcbdaadaccaacddbcbdbbbabccdbacadbcdadacddcabbdbcabcbcabbcccccacacacbcabcaccdabcddabbbdcbdbacdabdacbbbdaadcadddcacbbbdcaaacbdacccdadaaaaabaabbccdcadcdccdcdbadbcbbbdbdbadcdaaaacdbcdcdcbddaabdabadddddbcdaddbdabbbacdbcdababbcdbcbdabbbcaaacdcdacdcbdadadcbbdacbcaabcbaaddbcbdbbddadabcbbaccbbacabbbabbacadcbccdbdcccbadadaacccacdbaaddcadaaacaaadadbdcbdabdbadadbcbcabdacccadcdaddaaaacdacbabaaaaccaddcacbdaccdccdcacabbbdcacbcbaadacaddbcdcabdddaabccabdadddaacacddcaaabbccacccbdaccdaadbbccabcbdcdcbccdcadaacdadbbbcaddcacdbaaddddccabccddaaddabbcaccaabbdbccdcabadabdcdadacaddabdadbdcbdddadbcaabacddbdbbbbcbdaaadddaddcaaaaabbccccabccaddacaadddaabbbcaccaabdbbdbadbccddacacddddddaccaabbaddbdadacdadadbacacdbcbcbdbadddacdddbcadabbcadcdabbbcbbddcdacddadaaaccbbddcdaabacdbbaccbccabbcdcdadbddabddbdaddbbcacbdcabcadcacdbbbbddbbbbbddaccccaadaacbbbdcbabbbcbdadccbbcaddadadcadbaccbcccabbddbcdaacbcccdccdaabcacbcccdcbbcdcabaccddcacaacbdccccbbccbbbcbdcbabddbbbcdbbabaacdbbcaccbacbdccadccadcbbacbccdbdccabcdadcbdbcddabdddcdbdabbdbdbcacaddadbbcdcaacdcbcbdccbaccabaaabcbdcdacbbbcccbdcdcabddcaccccbdccdbcdcdbacbdcacacdddcadcbdbacbcbbadccacccadcbcdadadaadccdbcaadcdbaaaaccabccbaaabcbbbdcddbadaaadadacabadadbddcbcbddccacbaccdcadbaacdaacaccddabadabdccdaacdbccddcdcbddadbcddcdbaabdbbdbddbcdbddcdccccbbbdacbcadaaaaaccbbcbadabaabddbbbcbbcadaccdccdaccbaaacadcadacdcbdaaacbabccccbabadddbdbccbddddadbddabbabdaaaccbbcabababaaacbbbdbcbadabddaacacacdbaccbdcdadcbaadcadabcaadabbabcdccdddcbadddccdbacadcddbabdadddbddcddbdcbdbacdaaacdacddadccabdbbabdddadcccaaaadbcddccadccbadddbbcbdddcbddbddbbdccbbbdbdccbcacbdcabcdcdaacbbddbaacbbbaabdbccaadcbbdccccbccacbdacddacbcdbcacbdacbaaaaacababbacabcbbacddbdbabdabaaddddbbdaccdccaccbdccabbdadbbbddccdcddcccbdbaaaaabdcacbcbcddabcacdcbabbdbbcccbbccaddbdacdcabcdbcbacaacddabbdbdcccbcacdabbbaaccabadbdccbdaacabbbaddcacdcbbbcbdbbbcdbdcbdbdbdacdcdbcbaccabbdbcaacacbbaadacbaabacadccdbdbcbbbbaaddccabcaaabbdcddbcdabdbaaadcdcaabbdddbdccddbcbdddbcadbbbccdbbdabddbbabcaddbcddcacababdacdbddbdccdabdbdbbdbbdabccbdbabbddabcaabbdccaddcadbaddacbadaabbadbddabbabacabccdacbaadbdcdcdbaccddaaabdaabdbdbbabdbbcbddbdbaacbadabcdbcbdcddcaddcacbbccbcdccaaaddcaabaaabbbbabcadbbdbbabbbddbdbbbdaabccccbbbdaccdabcbcbdacccaabccddcacbcccdbddddacbbabbaadcddbddabacdaabdbbaaddacdaabdbabbadabaddaaddacbbacbbaaadbcbcadbddababcabcabaaaadcbbccabadaaaacbbdddbcbacbaaddcdddbccaccababcbacdcddabccdbddbddccdcdbccaadcabbbaaadbdcdccdddbbcdbdcdcbddccbdcdbdccabcbdddadbacddaaaabddbacadcadcadabbbbcbddcddbdaccbccccbcddbcdcbcacdaacbdadcbdbdccbcaabbccbdabadbcccbdbdbdcbaccddadbbdabbcddacdcadddbcacaccadcacadabacaccbddadbbdaacbadaccdccacbacabaccabddddcabbacdbcadbddbdbdbacddbbcddcadacdddbabcdacdcdadbacbdadddcbacbcacbcbcbaabbcadabbaacbdbbdacccaacbdccaacbbcdccbadcacdbcdadddccaccbddaacdcdcbdcbacdcdcacabbddacbaccbcacbbcabacbcbaacbabadddddcdaacdbcdcdbbccbcdcddcbdadbadddabaaccbaaaccbabddcabccddcaddacbdcadaacdddccacbdcddabbbaabbaaadaaaabbccbaaaabacdbcbdcabdabaaadaddabbddcdbdabbbbdcdcacaaaadcdbaaaabbbcaccbabaaccbddaaaabcbbcddbdcbcbddcdcababcabcdbaacbadddaaadcadcbbdacdcdcdbbdaabcbdadbbdaccadbaababcdadacacaaaadccbbdbabacdcbddcdacccbdcdcacadbdddcdddbcaacbbdacbabcbbbdcacadbbabdddacbbaaadabdadddcbbadaaacccdbadccdbacddcaacaadabdcbbcbbcccaccdabbbadaddbcabbcbbccabbbaccadddacbdcaaabaabcabbdbbadabacadaabaabadcddbcbbdabdddbbbdcabadacbcccbbbbacbdcbcabadcabaccabaabddbdccdbbdbabaccdbacacacaddbbcbdbbbabaadddabacdacbaddbccbbcbacdcaadbcddccbccaabbdddccbccbbbdcaadadccbbcbcdbabbaaababdbdaadacdcabdbdddbadcadaddccbbabddcbcddbddbacdadcaddcccbadbdabaabdcdccbccccaaddadbbabbbaccaaddcbbcbaabcbaadabcdbaaaacdddcbdbabbaccaaadccaccaacabdbcacbddcbbaaccdabdaadcbaabcbcadabdacbabcbcbcbccbacbbbccabaccadbcbcdaccddcdaccbcbcdacbcbcbbaddbcabdcacccabdbacdbbdcbcaaabcdccacdccaacdbbbcdccababaacdabcdaadbcdccadddcbdbccccbdccbaaddbadbaccabcbbdbacadaaccbbcdccabacbacccbdaacbcbcdcdabdcadddcbbdbddcbdddcbcbbbdcaccbbccbcdbbcbdaddaacdbdbadddaaccbabdcaaccaaabadbccdaacabbdabddbcdadddcdabaabcacacbaaacbdaacdbbbdbbccbdcbbdcdbbaddbdcbdaadcabbbdbdbcabdabaccdcccaabcabacddbbdddcddbadcadbacdcbcbccaaaacdadcbcacdbabaabbbdadabdbdcdcaddbcddcbabaabdcadccdbbbbabbdcaadcdcbbbbbbadabcbbcdabcacbadcbbbdadcadcabbcbdbdaadcbdcddaaddacbabacbbbbadaaaddddcbbabbadabcadbdbadcdbaababbddabbcbacaadbaddadbdcbcbddbdadadcaccdadbabcdbdccbbbccbadddcbcdacdddcabbcaaaacdacdcccbadbbbbadcddacbddbdbbbdaacaaadacacacabdbbddcccadabbbcbdaccccbabadabbcbdbccbaccaccddbabdbbdcaadbcaadcbdcadccadbadcccdbddbacabdabcbadccbcdaaacdadbaacdbadbcbbadbcddaccacccccbdaadccbcddcbbaaabaccbddccbddacddaddbcadbadacabdadcadddcaababdadcabbadcbbdaaaabdcddbadaacbacbbdbacdcbccbbdadaaabbbbacdcadbdbccbabcbdcaabbccbdabcccbcdadcbbcdacbaadaacccbaccaacdaccaaaccdabcdbdacdcbacabbaaddddbcacbabbcbacaadabcccdddadbbccaadbbdbdbbcdbcaabdaddcdadbaaaaadccacccbbacbcaccddbacacdacdbbcbbdcccaccacadbcdcbabddbcaadbdaadaaaabbdbcdacdccbccaadddbdccbddbdbabcbbcaaabcdccbabbbcaaacdcacddcaadddcaabbabacbbbdaabdcadbacbadcdcacdcbbdcaaacabdaddddbadbdbdaaabbaadddadbccddcddabbcbaccbddcabbbacddbbcabadaccbacabdadddadbbddbcbaadcbadcacddcbbabddddddddbbdacddcdcdbccabbaadadccabacdabddbcddababcbccbccddbbaacacbadccadacdcaadacbdbbcdcbadcdddabaadaddccddccbbadccbbbddacdbaadbbbdddabaacbbccccaabbaddcdcbddcbaaddaaabacdacbccdcddcdcddbcccbacdadcaaaaccacbcaccbcbaccbabdacbcbdcccbabadbcbcdabcdcadcabbbbcacbabbbdacdcabadbddacddbabccdcddbaccbdadcababcbaddcbcacdaddadbdccccccadcaaddbbabbddaadcbabbcccccaccaacabdbdbabacddcbcbdccaccdaddcbbcbbcdbdcdcacbddaadcbaacdccaaaadcdacbdadcaadadcbbddbcadbbdccacacdcbadabdbcccdbcdacdbcabbaddaabbddbbcccddbcbaacbccccccaccabbbdbdddbabdaccacbdccbdbaaaacaaaaaacbcdbbccacabddcbcbbdadbcddacbdccdddbcbddcaccbabaabbbcabbddaaabcadaabababbdaddacabdcbaaacacabaccdabaccbaacbccbcccbaccbcbadccccbbabbbbbbcabaacaabbddcbdbdcaabdbabdbcadddabcaacadccbccbdbcabddccbadcacbcacccbcabdbcbadbbddbbddcaabbdadacbacbaabcdabbdcdacdabcaacbdcbccdbacaddbcabacbacabacadccdcadddcbddabccdccacdadcbabaddabccabbbdbcaddbbbcccdaaccabbbdbbcaccbbadaacbdddcaaccadbacdcdcdaacaacbcabadccccbdbdcccdacbcddbbbcaaccbdbccddddcdccbadccccbaddcccaaacbddddacdcdccdbcaadbadcacabdadaabbcccdaaddabdadaaccbbdadaccbbddacdccabbbddddcbcdabcccaacaaababdccbcabdcadcdabdbcddccdcddaaabdaccbdcabbdbacddaacbddbdbbdaccddbbadaddcbdadcddbcacbccabbacbcadacdbbbbdabadabcbdaabcbcbdccdcccbddabddcabcacbdbbbadcbbacbabccdacbabbccdadaacdbdadcacbdcbabdcbbcabbbbbcdcddccaddbbdbcdadbcaadadbbdddcccdaddbbdbcbabacacdcbbbadaaccdcbadbbcadddbcdadccadbdbacdccdddbcbaddcbcdddcdabbcdddadccbaadbcdcccdccadadacbdbbabdbbaadadbadbaddbbbabaadcddbcddcabbdabcbdcbccbcdbdbdbdbccbdccbcbddcdacdcdcdcdacaabdbdcddcddbddadccbabaadbcbaacbbdbdaddbbbdbacaccacddbdcdadabdaccdccdbcbddaacbdabdabaacbabacbddcbcbbbcbaacdaaacbddbabcddccdbdcdabcbbcbdabaadbaccadccbcbdababdcbdbcbadacadddcdcccaadccbcaddddadbadddadcdbbbacadcdbadacdccaaadacabdacdcdabadbddacacbcaadabbbdbaacaaccbbdaccccbaababccbdcbcbabdaabadddbcbcbbbdbabbabadcdbdcbaacddcdbbdccccbcaacbbdadcaadbdabdaacadcdcccddacdcbbcaaddbbbccaaddcabccabcdaadacbddcaaccdbaaababcdaccababdadcaabcaabbdacaacdcbdaddbbabaadabaadabadbaabddcbbdbcdacddbdcbbdaddadbcacacccbdaccbdbbbcbdddaacbcbcaaacadaccacacabdbaaadadadccdccdddcbbdcbddcbccccddbabadaccaddcdaccdadbbacbaccdadccaacdbabdccdadcdbbcbcdcccbbdcbaacaabcccabbaabacdaabdaaaabbbdcdddccbaabcababadcdbddacbdbbbabaacbdbbcdcdcbabacbdbdadbdabdcddabaacacacbdcdcadbcdaabddaaaabbbacaddcbbaabdabdbbcdbbcbabacacccadacacacbadbaaaabbacdaabdbdcbaacbdcaabcbadbbcacaadcadaadbdcadbddbdaadcaaacbcdbdccbacdccdacbdbccbddbbbcbcababaccccacccdaabddabcdcbcacbdccbbdcbadbcbcdabcdcbbaacdbcdbbadaaccddaccbcadaaaabddcdbddcdadcbcabcdaaadbdbbdbdabbbaacbaacbbcaccdbdacbddddabaccbcdaddbabaddbdddccdbcccdbbadcacabacbadbacabdaddabacbdbdcdddbdcddcccbdbbdaadcdabadcadddaccccaabadbbdabaccddcdadccbbaabbbcbcbdcdacacdbbbccdcbabcbdbdacbaacdbbabbcabaaadbaaaacbcdbbbacaddaacadaaaddaabbcadabcbddadbbabbccbcbccdbcdaaaaadbbcaccccddabcdccccdbbabadcbabdaabbaaabbcabdbadbbdadcbccbbdddadabcbdacacbbbbaaabaaabcccacbbdbcabbdbdcdcbddddaccccdbdaabddcdabdaaabbacccbbcabacdddabacdcbaadacacabacdccccdcccccdabcabdbbdccadbdadacadcbddaccacdcdcbdbbddaadbdcacadadabcababaacdbacdbbbdbcdddcaabdaddcdacdbdcccccaaadcccaaaccccbbcdaaaacacacdadbbcccdbcdcdddcdcaabddddbdbdbacccadbcdbddacbddbbbbbccadbbbaadacdadbbbabbbbcdaccdaaddcaacbdcbacdabbadbadbbdcbccabbdcbadaddcbbabcabddacbdadccdaddacacbbcccabcdbccadcacdbdaddaadacddcbcaddbdaadcacdbdbcdabcacacccdacbbbcddccabcaadaadcbcaaabdcacbbaacbdbdacbdcbdccdbacbcaddddadbddbdcadacaabbbaccbddadcccbbddcbbdadabaddbccacabdcbdaddbcbccdaaaddbdbabbdbdbcadccacdbbbddbbccbdabcdbbccbccbcddacbdcacdcbabbaccddcadccdddbdccddaccbcabcdbccccabaccccadcbcabdcdbacccbadbaccdbcadbadbbdbacaabbddbccbdaccdbdbcccccabcbcaabadbdabaacaabbbdaaaccdcacbcdbabdcbccdabcacdadaacdcaacabccbcabbbdacadadabddadcccbcaddaccdababddadcbcdcabbadcdacbddcbbacbbdcbaaabcbaaacabaaaddbcabaaaaadaccbaccdbabdcdccaaddccccbcacabdccabdcccdbcbcdaababddbdaaddbddccabdcbcbdcbacbcbbccadbadccdcadadbcaddbcadbcbacdacbdadcbbbcbbabdccbbbaccdbdbdbacdbbbccdbcaabaadddabaabbcbccbaaacbbdcdcabbdcacbacbcdcaabacbccddbbbddabdbcbbbaccbbbcbcbbadcbacacadcbcdbababddcdcdbdcbacaaccbabddacdcacaddbdcaccdbbbbadacdabbddccbbabcbbcccccbbbbdbaaaccadbabdabbcaccbadacdaddbddcdababdaabcabacbbbaccbdcbcbcdacccbddbcbbccbaadaaaacccbcbdadcbaaccddbaacdccadadccadbccbdcacbaccbabcdccdcacdcbabbdcbcabcbcacdcaacdaaddabaccbcadbbabbcacddbbbbcdcaaaaabbddacbddaadabbacdabdabddcdadadddbcdcdddadacbbdcaadcacbbaadccdbdbabddddabccbadbbbbdccbdaccdcacaadacccdcdaabbaacdaababbacccbbdcbdbbcbcabccdbcabdcdabcdaaddbcbbabdbccbdaaabcacdaccacbbdaddadcabbbbabbbcdcadbacadaaccbacabcadbbbccbccbacdbddadbddcacccddacccbdadcdbcbaddcbacbccbacdccacbcbcbaddcadcdcbbdbcccadccbdaadabbacdbbddccdcbcdabbbcbbddcadacccadcabacdbaadcbdcbaadcabcdbcdacdcbbaaaddccdacdccbbcdccdaadbbbcaddacbdddddcbdbcddcccbccdabbcbaabbccadcbaddccacbdcbdbdaaacbcddaccdcacaccdadadddbdcddccaccccdddaabcbcdcbbcdbacbacbdddbcdbbdbbabddbdcabaacdcbcbbaaadcbdadcdaddaababdabcbbacdaaaacaccaaadcaabdddbdbcccccbbcdaaabbcacaadbdadaccdcdbdddbcdaababdadbdbabacadcdaadabbaabcabbacbacdbddabaadacccabbcdccabcacacadbdbabbcaadaddcdaacdddcbcabaabbcbdcdcbcdabaaccadabdbccddccbabcdcdaddbdbdaadbddcaddccbdcabddccdbcddaabcdadabcabcbaaccadccbacccacdbbbcbcccacbddddcccadcdbdbbbbddbcbbbdbadaddcabcddccbaabbcdbbcadbbccbcaaddaccaddddcbacccddcaacaaacdbbccbabcaabcccbddbbcbddaacdcdbbaadcbdaccbcddcacabbcacaccbbbcccdaabcbcaaccacdbdadaaddcdcdcdcacdcaaabbdcdadbdddabbdccdbadaabbacbacaadbcddababcbdbdcdcdccabacbbabdddbaacaaabdaacbbadacadaaaacaacdddccadbccddaadbdbcadbcbdabaacdbbacbdbbbdadaddbaccdadcdcddcbdddbddabcdacddcdbddabcbcbcbbddcdbbbcbdcdbcbdcdccadcabadbbcdaccdbdbcbabbaaabdaacabddccdacbdbadcbabadcbacdbbcbbdabdcbbaaccaadadcacaddcbaadabaaacdadbcdaacacccbabadbaccacbccacbbbacbcbddccaabddbdaabdabdadacbcdcabbbacbbddabadaaacdadbcacadcadcdbcaddabbccabdbacdcdcdbdadbcadaddabdbdcbbcbacabcddcacccbbaddcdadccabcbdccacccbabadbbdcadcddabdcadccdbcbbbbbdcddcbbadbddbdccbbdacdabadcdacaaacaacbdadbbcaacdbbacabdcccabbcdacbacbdadadcaccddbccacbbbbaadcbcbadacdbddababaabbbdddcbbccdddccacbcddbbaadddabadcadccbddbaadaadddcaddbdcccabdcabbbbdabadccddcdcadddcaacadadcbcacbbbbdbabbcabcabbaadccaacbcdabbddccdbbabcdbbbbdcdabcbddadbccddcdcbdcabdcbdccacbccdcbabaaaacccadbbcddbdcaacdcadadadddbbcacbbcabcdcaccdbdbcabddbbabbabbdbccacbaddcdcaacaabbcbddabdbadddaabadacaaabccbcdbaccadaacdbccccadccabacddabbcbabbabddbbdbbcadcbdbdbbdcdadabacbbcdcddddbbcacbddbaadcdccbbccbabccbaaddcbadacadcbacabbbabaccabcabdadbbabddabccdbbadabadbdacbbdbdbabcdbddcabcadbbdaadacbaddbaaccaddbbaddbaacdaaaccdabcdbdbcaddbabbdddbacdacccdddaabbcadabacddaadaabadddacdbcaabcadadcbdcbbdbcabbbcdbccbbadbaddaccbcdbbcadccdabccdbdabadccbdacccacacdcaddbbaacbcbacdacacaccbbbdabdbbbcadbdbdcdabdcaccbcccaabacdadbdcaddabcbcbcbdcdcaaccacadcdccabcdadbdaadccabbabcddbcccdacdccaddcdbacaaadcdbcccabdccaddcabddbccccbbbadabaababbbcabddaddbbbaccccababdacbdacabbddaaadadcdcbcabadbbcaaddcacddcbbacdacdddcbcbbdaabcdaacbbabdcadbaadadbaaabddadaadbabccddbcababcaaadbcbdacaddababaabcbaabbbbabbdadacadbbbaccadcbddcddaadaccdacaadddabcdbaaaddaacdadbdcddaacacdaabddbbbbdaddaabbbcbdbadaccbbaacacbddacbcbcbdddbddcabbcdbbbcaaaabcaadadcdaabddacadaaddabbbccdbbbcdadaaddaddaaadabdaaddadcccbdbbaaabbcdbbdddcaaadcbbdbacaccadacaaccccacacaacdadbbabaabdddcdacbbcbdbaacdaacadbdabbadbccbdbdbdccbcbbbcbdbdcabbdbcddbbdccabdbaadaadbbacdbcddcdcbbdbcadacbbccacabccbbbcccbbaaacabbdacaaccccdcadabddcacaacacabdaaddacadbaaadaaabdabdbdaaddbacbdaabddacaadddcdbdaaadcbbdcaabdcccadbbabcdcabaccbcdccddadaccacdcabcbddcbdbcbcaaaaccdbabcccbdddbbadadbadcdcbbccdbbbaaddccbacbdabdcaaabddacbcdaacdcbaaadbdccccaaadbbdacccbbcdcdcbddbcccdcdaabcabdaacbcdcbcdccddbdbabddcabbdcbbccddcabcacadadababbddbadaccaaabdbdabbcdbaccaccacdbdaccbcccadaaddbbbabacbdbdbcbcadaabcdbdbdbadcabadbcbbbacbcaaccbaadcdcdbadaccbcabcbcacbadadabbcccaacdbcbcaaddbddcddbbdbbbbbbcdddcaccabaadccbcbdaccccabdadbdbaadaaaddddadabadcadccdacdaacbdaabcabbbddcaccbcdbbbbabbaadaaacbcbddcbdcbaacddbdadcccdacadcdbcdacbbbbbcdcaccdbadbaacddadccbdddbcbbdddadcadadcbbbcacdaaaccbbcabaaaccdddadadccbbcddaddbbcdaadbdcaadabcddcbbabcbbcadcbddadbcbccaadccbcadbbdbbcabcaddbabdbccbcdbcdbcbdcdbadbacaabcbadcdcadcabddbcddbdcabdcdddadadabcbdbbcbdbcbdcbdabbbbabccbcbbdbdbbbcadbdbbbcdddcabcccadabbbbcbcbbabcabbaacbdddabdbccbbcadcacadcabcbcbbabbbcdaddbdcacaccccccdaadcaccbcbcdbddacbacadcacddbadabbabccdacdbcbcabcdadaaccccddcbdabbbcbcdddabbadabaccccbbcdcacadcdccabdccadccdcbcaaabdadacaaabcabadacdbdcbdcabdcccdbacdbddadbddcddaacccbcbabdbdcacdbaacdacadcaccacbbbccadbcaccdacbbbacadbbdacdbcadaacbcabdbaddbccbbbcbacaaaabbcdbdbdbdddbcabadbdabdacaaabaddbbaccbdddaccbdddcbbcbcbaaaadaacdadcdbbbbcbbacbacaabddbadadbbbacbadcbcaccadaddbdaaaaacbbddbbdadcbcaacacacabcbdddabcdbdcdaaabaccddabbabdaadcacabbcaccaacccaccbcababbccbabaabcbdbcadcbdbbdddbdcbcccddcaddadaaddcdabdcccdbbdbabddabbadcaaccabadcbaadddcdcdcacdcdbccacdaacdaaabbabddaadcccaadbaccdcbdcbcbabdcbcbbabadaccccdcdaadcaaadcdddccbdcacaabdbcdbacabdaacaacadabadddbbbabcbacdbaaacddbacddbccdbcaddcdbcbdcbaaacbaaadbdbbbdabadacddababdbaacaaacdbadbbccacbdbadacdbdaacbdccdacbddbbdaccbbddccbcbaaadddbadddbbcbadbacdaaddadcdbdbcdddadcddaabadccdddabbdaadbcbbcbddcadaabdbaadddcbcdbdaabdbdbbddbbbadacbdccacbdabdddcbabbddacaababbbcdbaacacacacacabbcbccabcacbcdbccdccbccddbadbbbccaccbbcdcdddcbabcbbcdbccbdaabaadcdbbcdcaccabbbdabddabcdbcacbacdbdddbacdcadbdaddcabcbcaaadcdccaccddaddbdcacbabcacbbdbbbbcdbabcbcbcdbddaccdcdbddbbbbbdbcbbccdaacababaccbbcdbadabdaaaabacbaacabcbabbbadaaaabbccabccbccdcbacccdabcddabbbccdabdddacadaacaacaaacdccacdddacdcacddcaddaaacabbbcddacbbdddaaaadadcbdccddbdbdbadcccbddaaddcccdbccdbbdbdbcaacacbbcacbcbadccbcbcaaaabcaadabbabaaadcbabccacdbdabcbdbcdcbccbbbbcdaaaadacdbdddcbddcbddbbcdbabbbaccdbabaacdcbcabcacacadbdbababdbbaabaadbccbcccbdbcccddbabadbbaaccbcababbabdabbdbaacabddcbdccddadbdbadddacabddbdaaccbbcaddaadbbbbddbadbabbbbccdbbccacaabdaadddabcdaaabbdbacdbaaaddaabbcccdaacdbaccbdddcacdccabbdaadbdcadacccbddacaabddddcdcadadcdbacbaaccaabbdbabdacdaaacaccbcaddccadaddaadacadddbadcbcbcdddacbaababadbcbbbbaaddbccabbddaaaacadbcccabcdbbdcbabccaabddbbdbdccdddbbcbbaddccddcbbabbddaaacacdbcacdabccddcbdddcbddcbcccbcacacaacbbddddbaabdbcadabdbdcccbcbbabadcbabcddcacbcbbacbaacbacaaccccccdbbdabbaccdadddbdacbcccddabbaaaabbbadcddcabcbbacccbddccbbacabadddaccdadacbccddacdadbbdcddbcddcddcdaacddaadcbcacbcadbbddaacdbaccbbcccabccabdcbdddcabdbcbdbdaadaadacddbabdabacababbccdbabbcbcaabcacbcbaadcbacaccacdabbddbadbccbdcbbbaacdabdbacbadddaaacccbddacbcddcdabbbdcddaabcbaadcdbbcbcbccdbbbcdcadcbddccbbddcbbbabcdcbbbbaddbdbbddcbaaadccaabccbccbdcddccbccdbdbbdacdbdbaaaddbadbdddbadcddcdcacbbaabccaaacdbbcbcbaacabdaabcbddacdabdaddcccbbcdabcdcacbdabbdaccdadccccaddccabcbcddccddbabbddadaddbbabddcadbddacbbbbcccacdaacbbbddbacabbcdbacdbdbccadcbdbcddadddbbadaaccccbaccbdcbddddbcbbcbcccdbbbdabacabaadbdbbdcbbdbbdcdaddbacaddacccdadabdcadacbdcaccddddbcdccbacbcdabddbcaaddddcddaacababcdabcadbccbcdddadccbbbbcbcabdcbbddbcbdaaabddcdacccdadcaaccacbacabaacdccdcbabadcaaddbadcacddadcbcbddaccaacdbccaddacbababbccacbcdadcbdbdabbbcbbccbbddcdcaadcbacdbaacacdccddddcccbdbccacadbbadacaabaabadaaddcacadcddbbcbddacdadabcdbaccaacadacaacabbaccbaddcbdbdabbdddbdbcaddbaddcbaaaacccacaddbbcdcdaacbdccaaabcacdccacdcabdbaaaacbcacbdcacadabdaadbabaabcbbddcabcabddccbacadcabbdcccdbaadadbdadbccadacacccbdcbcabdaddacdcdacbaccdbcdcaddbbadccdddcdcbbaadbcccccdcaaadcabadbdacdaacdaddcdbdbaaccbdbdabcdaccdcbdacabbdbdadaccdbcacbccddacbdbbbccbbdbacdbdbbdbaccabdddadcabbcbbbaacbbcdddbbdbadcbdccaacbbbaccadcdcdcbaddbcccdbccbcdcabaccbacadcaabdabccdbbdbbcdaaddcbcbddaddbaadcdddbbdcaadcccdcadabdcdaadaadcdadbababacbcbddbcbdaacdbabdaabcaabaaacddbadbcbbcbbadccdcadcadbaddcaccccccacbccbaaccbabbadddcaaabdcbddcbddacbbcccddcdbadbaabadcdddbbabbcdabbadcbcbcdbaabdbdccccaaadcbcdcdaacddabbcdcdadcbdbbabadbbdccdadcdabdbacbabcadcdbbaccbdabacdbaaacadddcaabbabcbcdabdaddaaccbcbbcdabacbbabdadbcdcbdcbbacabacbcaabcdabdbdadcacdaabcbbdbbcbdddcbbcbbbddacbccbddbcdddbddbadbcabaddccaadcbbbdddbdbbbacdadacdcacadadddddddcdabddaadbcbdabccbddbaabbabdbcbaddbdbbcdbdbccbbbcaaacbddaddacdbcadcdbccadbddabccccdbcdaacdbcdbadacccdddcbbacbdadcacdaaccbdccddbbabbdbacdbacddcacdbbcccacdccacbcbbdabbaababcacbbadadcddabbdcdbaabdcddbddaccdcadcbcbadcdadadcadbaccbaacacdaddbabddbbadbadddbbccbdbcddbaabdbcbcdbacadbcddccbabacaddaaadcddcacbdcdcadccdbabdcbdbcaabbabdddcdcbbbabdcdaabaddcdbaaddcddaaababbcaaaccbdbcdadbdabdbacabbbddcbadccbddbaaddbcaadddbcdcdcabdaccbaccacacdbaddbcadaaacdccaddcddcbbacacadcbadccdacccababdadbbbacbabddcbadacdaadccdaadbadcaabdccbbccaccbabbaacbbdcabccabacdcdaadcbccadacacddbdbbbbdbacccadbdaabcaccaddaddadcdadacadbbdbcdbcaacacdabdccbcbddcccbacadadabacdbccacaaddcbbabdaaaaadcabadbcdadabbbccadacbddcadaddaaaabdbdcccabdbdccdaccdbabacbacbbaadbdcbbacdddcdaddcdaacdcadbcaaaabacddccaababbaacbbbdbcdaaaddacaaaacacadcabcdcddaddbccbbdacbdddadcdcbcbcdccdcccbccabcdcccdbdcaccadcacacdaddaadccdcaadbcdbcaddbcbdddabcddaaabcdccdbbbdbcbcbaccbcdccccbabcbdaabdddcccbcdbdbdddbaabcdbbcbdabcddcacdabdccdaabddabcbbddcdbacaabdabbccbabbcaadcdcdadccdabdbcbcddacddacbcbdcbcdddcdbcbcbbaccbbdadcacddacadcbaacdaabcdbdaaaccbcdbdcbacbaccddddaabadddaacbdaaababbabacdadbdccabbccadcbaccbaaddbabccaabbaabaacbbabdabcaabcabbddbbccdcabddccdcccdddbccacbdcccbbcababbbbbcaabcddbabdbbbbcccadccaabbdbaacabbdaadaabbacadcacbcbbdddddaddcbdbadcaacbbadcccdddcdaddbdbdcababdbbcdbcdbcbadbbbbdaadabcaadacdcdcdaabbbaaccdcbacbbdbcbadacacbbadabccacadaadaddbacadacadabbadbcdbdbccdbdbdbadbadddccbadaacbcadcaccccaaddabddbdaaadbdbdabcaabccbbcaabdaddcdabbaacdabdaaaaabdbdadbadccaddcacdcadacbddbcdacababcadabcaddbadbbbbbcbbdadadddbcadbbbbacadbbbcadcaaddbcdcdbaadcdbcdcabadaaabbddbabbacbaddcaacddaccdababcaadddbcadbadbdcaaababccbccbccccdcacddbcdddcbcddabbbbaacdccdcdacccbddbbbbbbdacbcacabccdcddbccbdaddccccdbaaaccabdbccabcdaccbcbcbdbbaabaaaaaaccbadcdddcddddadbdcddccacabdccdbaabbcacdcbcacccacdbcaacbccccdbadbdbbabbccbcbdccdadcaacabcbcdbacbadddbccbcaddcaadacdbbccccadcdaacacbbcacbdcdccadcdaaadadcbaadbdabacccdccdbadcbcdbacbbcdadccaacacabdabdddaaadadbdcdbcdcbabbdbabdcabbcbbdaddccdacbabacaadadbccbbacbcadbdaaabaabcdcdbaddbcabbbbabacaaadccaddaccadbbcbbdddaddaacdcbccddbcccaacbaccdacddadcdddcdcbadccaabbdababbcbcbdcaaabdbddddadbdbbadbbaabbdbdccadcacdcaacbcbbaccbacbbbbddccdbbcdbacaaaccddbbbdadcccaadcbcdcdaaaddadcaaabcbbcadabccbacacdacddbabbddacabcaccadadabbccaaadaacbcbbdcdaadaaddbdbbabdddcdbbcbbbcdbbcacaaaaaccabbddddadbdcccdcbccaddcbcddbabbdddccbdadacabaaaadcacacacbbcaaadccccdacbabdbdacbdddddbcacaadbdbddaccdcdacdabbbdcbdcccbadaddbcaabcaaadbacbdbbcddcbadbabdcdacbddacbabdcbcdbaddbbadddbdddbacaaacdadcaabadddadcdadadaabaaadddbbcccbbdbcbdbdbbdddcdddddbddbcacaadbbaaaccadbbccaacccdaacbdadacbccdbbcbddabaccddbddbdbbbccaabccdacadacbacbbbaadbbdcaadccbbcddbaaadbabccacbdacaaccacdbcabadaacddadbcabcccaaddcacdcabbdadbbabdcccccccbbbbbbabdcccccadccddbbdadbccbdbcaaacabbdbadcabaaccabbdbcdabcbdcccdacaacdddbbcdcbccadcbdacaadccdbddcabcccabcccaddadaadbaccdaccbcdaddbadddddccbbbcabbcccabbdcadaddadcdcdabdbaaacccacbcaddacdcbbdcbcdddccbaabacdabdcbcbddcdbabdaddccdcaaabdabdcccdbbacdbbcabaccaddacbdabcbbcabcabddbbddbdbddadbbaadbbacacbbacbbcbdbdcaabdddccadbbbaccbcdadbdbdbbdbcacdcdbbabcaabdbccccabadbdaccbcacadddbcbcdcacdbbbdccbbaadaaccacaabacbcacabddbabcadabdddabbaadbbadacbaaaabcbaaddaccbdcccdccdbadddddadaccdbdbdabccabbabbdcaabbdbbbaadacccbaabcdcacaaadaaccadadddadccdbbbdcabcaadadcabccbdacbcadaddbaabbbabdaacdbbbbcdddbcbcaddbbbbccbccdcaddadaddbcbadccabdbcdccddaabadbadabddccbababbdcadbdcbabaacdcbbdbcdaadddbabbadbdbaddcaaacabcdabddcddcbccccbddbacacabdbacdbdbcbacbbdbadbcdadccdddaccadbcccbadcddcbdadabadccdcbaabddcdbcabdbdcaaacdcadadadbbcdcdcdaddbcaddbbdbcabbcccbbbdbbcaaadcddbadadadcbcadccbdacadaddaaccbadaabdcbccbcbbacabacaadacccdbdaaccbacadcddbcacabbaccddaabdcdcbbaabbcacbadddcdcdaaabcacddadccaccabcaddaabddadddcbacccdcdddabcabbddbbbcabcddabcaacdbbdcddbbcbbabcdddacabaddddddbbcccabbbcdbbcaccbddbacbcdcccbabdbcddbdbacacababddadaacbacbbcdacddccaabadbdbddbdabcbdaaaababdcdbcbadbcadbdbbadcbdddccaacddaccdcbcbabdbabcbcdcbacbccaacacbaaddbbdaddbadbaabaacbcdcccccccacbddcbddddaccdcdccbbbabbaacaddcccacbbbdbbcbdbddbddabccdcbcbcbcdadbbbdadadbdcccbbbccbdddcadcbacbbcabbbcbaddbcdcacbcbacdcdaadddcccbbacdbdccdcabadcaacbcddaabcaabdacbdabddacdccaacabcdbbdabddcaabdabbcadcbbbabacdcbdaabbcbaabddbdbabcdaabacbddbcdacadcccaddcbcbbdbaddddbdbdaacbcadbcacccccadddaacabdcdcabacbcacacacadaadbabdbcbddaccbbbacdaadadadcdcadbbcadabbadaacaababbbdccaabacbbaabdccbcabbdaaaddbddbcaabdcabdbaddadacdbbabddaacdabccacbbacdacbcdacaaabccadbacaccaccdabcddbddcdbaadcaabbaadcdbabcbbaacdcacbbbcacdcabdbadaabadbdbaaadbcddccdbdcdabddcbcccbcababacbacbabacabaadadcdcbbdaabaabbbcaacdcddcaadbaddddaadcccdbdcccccabbcacdcdbbdbcbdbddaccbdbddbcaabddbbbdccdcacbbdcabddaaabdbbbcacbbccccdaaacdccccdbbaccdbccccccdaddcdcadacadbcbbbdcacacbdcacccccadddacacddabdadbddcacdaadaccacddcbdcabaaadcccababcbccdabacdbcbcdaabadddacbaacadcbcabadbccacdcbcbbbcccabcdcddbcadbcdacdbbbbacdcbaabaadcbacadabcbcadcacdcdaabadbddaacbcabdccbbbcccabdcdcaacacdddacbcadbbbdcbbbcbbbdacacdbdbdccbbbccaccdadaaacbccabcddcbbdddcbdddbcbaccbcdabdddabdbadbcdacdadbbbaacadcdaccbbbbaaabaabdddaddcccbdacadabdacbbaadcababdbdddbdbcbadbabbccadcdadbdcdcaaaaaccccbccccdabccccdbacdabdbcacbcbcaacdbddbcadcacdccdbcaacccbcbbcddcdaaacccadbbdaddccccadaacdcdddaadcaaacabcdddbbbacdcabccddadbcbdadbdcccdadcbcacdcddadcdbadcbdaababcaacdbcccdcccdccbdabbababcdbbabbaccdaaaddbdaacadadaabbcdaccddcdccaabadadabbdacddabbccaccabdadcadacaaababcadcdbbdccbdbddddbbbdbbcaccbcbbcdbbcddaccccdcbaaacdadaabcacdbaccaadbcbabbbccdacbacacacbdadccccadaacbaacbcaaadbabaaabddddbccabdddbbdbaccdbcbacbaccadddddcdbbdbbacabaabcbacbcddbabbadababbaaaabbcdaccbddaaccbbccdaaabcaacdbdcadbdcccbabaacbbcdddbaabccbbaadbccdaabaccdaacccaccacdbcddccabccddcadccbcbdbaacabcdccbdccbaaddccddcaabcdddcabbbacdbcdabadcacbbbadbbcccabbdccbccdcdbbabdcaabdacdadbdcacbcccbacdbcacaacdacdbccdcbdadcccadbcabbbdcadcbbbcbdbccaadbbacbdddcdbcabbbabbddabcadbcadcbbcddcbacbdbbacdbcacabddaababcdbdbbcccabddbdbaddcabcbddadcaddcdbabdadbddaabcddcbabddbabcbababcccdccbcacacabadaacaabbcbdddbdcdaabcadbddabdcaadcadcbbbbcdbdcbbacaabccdddbabdacdacbcdccccabdaadccadbccdaddbcdbdbdbcdddaaddacabbdacbdddcbaccaabddcbadabadccbdccddaacacaddbdbaaaddbacdbbacbcaadabdacbcabbdabbaaabcadcaaadcdaadcadcbdcbcdabdadadcdbbadcccdabadccdbaddabaccccbbacbdacadacdcbdadcbbdccddcbcdadacbbccbbbcdbbdaddcbdbaacdcdbaabdabccbdcabdddabdddcccbdbdcacddbaddabbcaabdcccacdccabaccacaaaaacacacdbbabacbbddadaccdbabcbbaaacbabdcabdbabbcdbbbcbadbcaacdddcdabbcbcddbbbbdadddbdbaddcbadbbbdaaababaacadadadddcaaacacaadcbbbcdaaccbaddddbadaabdbacbaacbdcddbabbcdbbbaacddacdcbacccdacadcbdcaaacdddabbbdabbbcbdccdbdadaacababcbaaccadbddbcaddbbbcccababbdccdbdaaccabadbdbdaabdddddadbabbbdcadababbabadccccdcdaddcaccdbddcaddabbbbcbcdcdabbadcdbbbdbdcdbdbbdaddaddbdbaadacddbbcccbcdcaddadcdcdccaacdbcccbcaacddaacddcdbbbabbabcacbbdaadbdadacadddabdaccdaacaaadaddcbbddccbaddbdadbdcbdcbbaaadcadbbccabcdabdbbcbdcaacacaddbccadcbbdcacccbbbddbaabaacadaacbddbbabddcabbdadbdadaadbcadbcddbccdacaccbadcaaabadcadbbaababcdbbbcdaaaadddaadcacdcdbcabddacddcbbaccbdbdddbcbddcbabbdcaddccbcacbdadbcdbdababadcadccddabdadabbbddabdabbdaabdbcacbbaadacbddbccbcbdbbcacbbccdacbbdcbcbbbccadbddbabbbcccdabcaaddbbccbbcbcdaccaabbccdabccccbdbbdbcbadcbcabddacbbdcbaadbcadbdcdcadcbcaaacbdbdcbbcbbacbcbbdcdcaadacbaadbbcddbaddbcacbacdabdadcccdbabbdbdadadbbcddddcdabdcabacdbbadadccbdcacabcdbbbbddddaddadbaadcaadbcbdadcaaabcdacaadbaabdccaaaddadacacbdcbbcbddbdadadbadaabaaddbbdbbdddbabaaccabddbacbcbdcbacddddddcabccbbdaccdcccdadaaddcaadaddcbdaaccddcacbcacadbdbccdddbaacadaacbabdbaaaabdcacacbcdbaabccbaaaacdadbbabadccdacbaadbbadcabbcabccabbbadaacadddbadddcdccbdabaabbdcdabcaaabbdddcbdbcccbcabcaabbbcccacbdbccbbbcbbcbdabbadabcbacadabcabbaadaccbabadccaabcbadcdabbbbbaaddbaadddadbaabdadddddadcacbdadbdabaaccacbdccbbdcbbddcadababccaddcdcbbcaaabbbcaadacadbbadbacddcadabbaddddbccbccacccccbcacdcdbcbcdcbbdabcbdbbccdbbdccdabbcddbcdacbccbdddbccbaacaaabadbaacddddbaacddaadabbbaccddbdcdabbbdacdacbadbbdbabaacdacbacdccaadbcbbdbbcddbaaadcbaadabcdaacbddcbbacccbacbacddaacbadbccabaaacacdaabacbcddbcbabbdcdbbaaababdbcabbacbaadccabcabcbccdbbdaacdddabaddcabccacddcbddbadadbdacbacbdbdbaabccaabbbbabbcbdcabddbaaaacacbcdbadcbdadcdbbdcdcdcbcddcbcaacbabaadcccdcbccbcdbaddbddccddddbadbaadcbcdcacdddaacbbaddcddabbddddbcbdcbccdbabddacbccbbcbaddcdcbdbdcccdbdcddccabbaacbcaaaaddddbcadcadbcaddcccdbcdbcddbdddcbaabcaacdacbbbdbaadabacccaccaaddbccbcddcbcbadddadddcccccbbadadbcdddabccdcbaacbcddbcbcabcccbbadcccadaacadaadcacdbcaacbbdbcbbaadcdcdbddbaabadbcaabaadbdbdadabadabdabcdacccccdbbaadbcbcbcaddacacdbbddbcbcaccbdbdcbacaddbcccbccbacbdcccbdcbdacbbdabacbacdbcccddddcccbadcadacdccadcdddccbccaadbbdcdccdaccaabbccddbbcddbdababdadbccbdcbdbcabaccbdcccaaadbbdbcbabbdbadcccacbbcdcdadbcbaabaddddccacadadbcbadcbdbddddbdaacadcbbdccadabbbdbcbadadccaddbdacababdbbadbabbdcbbcabbcccabbababcabcdccaddcaddcbadacbcddbbdcbbdbcbaaccabdbaaccdcbdaccdacbacacbaadabadacbcbabdbcaccadaadadacbbbcddbbcdaaaabbadabddbaaddbddcdaccbbacbbccddbbccbadaddabbbcbacdaaadcbdcaadcacacabacaabbbcacbdcacdddbcdcccbcaabbbdbacdcadacbddcdddbcddadbdaaadcccccabaccabcbaaaabadbdcabcabacaacacdcbbdbbbaabcdcbdccdadbdadcbbbabacbcbcccbbabdadddbdbbdbbcdacccbaacdbcacdabcbacbdcbdadbbbbaaabcbcbbbdcbcdaacbddddbbcdbddbdbcdddcacaddacbdaccdbcacadaababadbdbcdadcdbdabcbabadcaabbdaddddaaccdbcdcadabbccaccbadaccadbaacacbcbbacbabaaabdabbabddcaaccdddbadadbdbdbadcccbbbccccdacdababadcdcaacbbdbcdaddadcbabaaabcbaaaccccadbdabdccdcdbacddbbaaccdcacabcdcccddbacbbaacacadadbbcbddcabddddabbadcdaacacacddddbbcbcbcacdddbaabcacdbabbbcacaacdaccccaabdbabdddacbbadddacacbddaabdaacaddaaadabdcbabdaabacbacbabbaacddadabcbddbbdadbddcbdbddbaccdaddaadcacabdccdcabcadbbcbcbdbddccdddacccddacaccdadbdbccbcaaddcdbcaadbcccaacbbabababcbdaabcabbdcadbcdbdaabbaacbadcbaacdaadacccdcdbaddcdbdcabcddcdcacbbbdcbbddcdcdcbbabadcddbaddbcbbccbdcdabbadabaaccbabddbddbbcbdccccbbbcbacbcbacbbdcaaaaaacadbaabdcbbbbadcdbcddccbdacabbcdaaadaabcdaaaadabdadabcdabdbcbdbbbbcbcddabcbacbdcdaabdccbddbdbddcccdcdcddacadbbbddcbbdbdacbcccbaadacaddacbdbdabcdbbdddabbddbabcccadbaabbbbbccabddbddbcaacbaabbbcdacbadcadabcddadabdacadaabdabddabbcadccdcaacbdacadbcaacbbcbddabdddadddbbbcabbaccadcabddbacaabadabdbadcaccabcacacbadccdccdbabcbcaabadddcdaddacadadcbdbdccbcdabccddcacaadddacddccbacbacbcacccdbaaddcdbcbabcdccbddadcaaddbbabdbadacbacddbccadaadabdcdaccbcccdadcadbabccadaddbdccccbbdbacdacadabbbcbadaabbbbbcdcadaaaccabbddcacccadddcabacadbaacdbdcbcbcbdbdbcbcdddaababcacddadbbdacbddaddcbacadcacdbcbdaabbcabcbdbaacaaadadbdcbcbdcbccbadbbdbbcddcbdcaacabcdcbadbccabacaddaabcabcbdcacbdcacccaddbcbcadaacacadbdcccdbdcccddcbacdbcacabccbadbcbbdcddcbaccbcbaacbcdabdaacddabbbcbddcbbabababcacbcdacaabaddbacaacdcddabbdaaabcaabcbcacbdbcdaabbbcbdaaabbcacdcdbcdcdaadccbdcabbcbcacbbccaacadbaadbbaadaccdccbbbbabdadbddcbbaabacadbdbaaabaaddacaaacadcbbbacdbacadbdabbaaaadbbadacdddaacbcdbbacbcaddabbdcccacdcacabadcccbabcbddcacbdcacabdbdcbddbbabbadaacbaddbddacdcabddbdacadccddcacbabdbcdaaaaccbabcbbbdbdbcccbccdcdaaabaccacddbcbdddccdcdabcbccaabbbbaabdcbbaccbbbcaddddbbbadacbddbbddbbbacbbcbddbbacdddcdaababbdacacbcbdaadaaaaccabccacadaaaacaddaaddcabcabcbacbbcbbccbdadccdabaccacdabcdcabdaacabbbbbdcdcddcbbacabcacacabdccdddbcacbcbabbcbdcbdbddcccbacbdccbacddabccbcacbdcacdcaaadabbadddccdccdabbdcbaaaaabcdbbbbaddcbbddbdcbccdabdadcabaaadadbbddcabacabbccdcbdbcddaddddcccbbaccdcaddbbbbabcbcaadddccbacbdbaaccdbcbaddaabdabacddaaaadbbabbcdbdcbbaabcbdcadbcbabcbcdccddcbbacaddbbacddbcbadadadbaaabbdacdccddcdccaddbbdbbccdabddaaacddabadccbbdacadbdadbddbbdcaaaabcbddacadddcabcdbdccdadaabaadabacdccdcdabacbcbcbcccddddaddadbadacabdbdcbdbddacaadadadbdcaababaccdccbbaacdbcbdcdcdcbaadbbcabbddcabcabccbdaadaaabbbbbccbabcaaabaabcbddbddcddabdacbddcdaaabddcdadcaddcaacabcdabdddccadabbcccbcdddcddabdbaabbcbddcabbcdabdacdbaddbbbbbccbadaccdcbbdbcababbababababbccacaadbaabccbcbdbdacddaacbdbdacacdabdaacaaaacdababbcbbdcbaccaacdbbaacbbbbbdbcdbccdaccabddacbdaccdabcdacbbaadbcadadbbdbddadacbdcdcbdbcdbcbbdcbbbcdabdbcadbdccdadcdabdbdbcbcadcacaadcdbbacdddbbcdcbcdadcbbacccacacdcdaaadcbccaabbdabbbdacdccbacbcdcddaabdcbddbadddaaaacdccabcbcaccbdddbcdbabaddccccdadadddacdbccbddacbdacacacabcacdadbdaacadbddcabbabaacbabdcabbaddaacbabccbdabcaabccdabaccddacbcdbbcaabcbbacbbaacaadbacbaddcdabdcabcacaadcbaaabbcbaadabddacadbacdacabdadbccdcdacbbaddbaddccdaacdacbabdbaddcdcddcabacbccbacbcbcaabaabbadcdcdacacacdaddbdbcacbddcddbdababccaacabbcbcbaacdbbcacbcddacbabdaccadbaacbbbbbacdadaccdbbabbcdcadcacbaccacddcdabdddaabccadadcbbbbdcbadbadcdabbaaabbdcaddaacdabccadadbbccdcbacabdcccbbcbbaacbdbaccbdabdcabbdcabbcbadbcccabccbacbabdcacdcdbcdbcbdcbcabdcdbbcddcdccddcacbcbddcbbbabbcddcacbbaaabcdabcbbdcccababadbddacabaabbdcadbabbdccddcbcacbaadabcddaccacadcdaccdcdcbadbbcbbdcacabbadbcdddbccadadaaaaabcaaadcbbbccccccdddbbbbbdababcabdbccadcccccdaccbdcccdbdbdabcdbcbbccaadaaacbadccddaaddcbcacddacdaccdddababbccdbaabbcabddcdcdddccbadbddbbcdcdbddcdddccddcbaababbcdcbdbdaacbacaacacdcbbdddcdcaacbaccdcbcdcbbbdcbdbdbccbaacaaadccdbdcbcdccdbbacdacdcdcadaadabacabcdddccdcacdaccddaacacabbaabbacdbdddbdaddbadcdaacbabbcdcbbdbdaccdccddbcbcbacbaccbadccabccbadcabcbddabdcaabdbadcbbaddcbcbdddcdddbadbbdcdcbcaddbcbacaccccdcddbdbadcdccccbdcaadadbcdbbddcaabbbbbddacdbbaacadbbcbddcdacdbadcaadcdadcadcdbaadcbbdddbcbbdbcabcdabbabadbddcbaacacadddbbacbadcdabbddbbbacaadaaddabbccadccccabbdaadccbadddcdadcbdaccdaadbcdcdbdcccccacbadacacdabbcbccdccdcbcdcccbcdcabbdabacdbbcccaaccbccccdcdaccbaddccdddcdddbadcdadddbddccabcccbddaddcdabddabddbdcddaaacacdcacdbabdbbdbcacbcaabbdcbbccadbddcacbdbaccccabacdbdbbccaccaabbaadaddcaacdaddbbadabacadcdcbdcdcdcdbdaddaacbdaddbdcbbbdcdabbcbdacacdcdbccccaaacbbbbccabcdbbaaadbcccbdcdcbadbacdcccbadacdbabbbbbcbbcabbaccdcacabdddddccaabadbcdadbcbacdcddabbdaccaacadddabbbcdabcbbdbcbddbdcbccddcdacddadcdaddababcdcaababcccbddddcaaddabacbcdccdddcacdcaacccabbdcdddbcdbbbccdacaadabbdbaadddcbdabbcbbbbbdbabddadcbabdaaccbcdacccbbabcdadbabbcdcbbdadddaddbdadccaaaccdacadcaadaadddbcbdbbadcdcbaadadacacacacaaaabcccbbddcdbacacddaadabbcbacdaadbdbabaadcadbbbdcbcbccdcaaacdabccbbaaccaadcaddacabbcdacbcaabbadacbadaadcadabbcbacbbbbaabbaacbbbdcccabdaccccbaaccbaaaccaaabdaaaaacbaccdaabcdccccddbcdcbaddcccbbcbbdcbdddcacdcbcacbcbbcdacaabbacbdcbadacccdaadabdccacbaadcccbadbdcabaacdcacbddabaacadcdbcdabacbcbbbbaaccdcbcbacccccdadaaadcdbcddbcadcaccaadcacdbbdbabcdccbdccaabbdaaddbadbbcdcbbbbdbcaccdbdbbddcaacaacdcddccdabccdbcdaabdcdcbddddabbabdabcbcacddabbbcbcbacbaabbaadbbbcbdbaadacadbdbdbbcddbaabdaaaadaabbbaacddddabcbcbacbdabaaacbacdddadadbbbcdabdaddadbcbacababdddccbbcccbddcacbdbccccaacbdaddbbbbbdbbdbcacbadccbbdcaadcdccbaaccbbabaaacaaabcdacacabbccadccacdbacababdbbbdcdadbadcddadcddadcbcddbbcaabacdabbdcabadcbbbccdaaabbdcdbcbadabccdcbcdbbdabbdabbbdbbbbcabadbccdcbbccbaadabdaacbcbddbbdcddcbadddccadaacbadacaaaaacbcadcccabcdbacadaacbabdddbcabaddaabbcaddbbbbdadaccdbcbaaabcdbdbaaabcaadcbadcaccaadbcbcabbcbabbcddaccaadaaadacccbdcaaadbddabaadbabdcdbadacbbdbcdcdbdbabacccbcdcddbbacbcabccbbacaaadabcbabccdcccbcacadabaccacacaabbdccabddccdabaabddbdcbadbcdddabdabccddcdacbababdbccabcbccbcdbadcacddabbacdccccaacabdccdccaacadbddcdbbacdabdbaaaadbbdbacddcbcbdabdbcbbcbadbadbbcbddcaabbcadadddddbadadaaabbacbbbddabdcdbccdacadaaddcdacbbaacdddadababbbbcbdcdabdbbcadccbbbbdbbbadbcbbcdccccbbccdccdbdcaaccdbdcbaacacbacbaacbbdcabcdddcbddbaabcdaddacdcdcddcacbcaddcdbcdbabababcdcadcdbcaddaaddabaacabddacabccdcddddbcaddcccbdcaabbacacccacbbbbbbcaacbcbcbbcaddbbdccdacaaaabcdcbdcdddcdcbdcbacabbaddaacbabbdbaddbbcbbacddaadadddbdcadbdbacdaabcdacddbdcbddbbdaccdacdcdccdabddbdabccdcdcacacaabbcacabbccadcdbccbcbdbcaccaaddbdccaddbdbdabdcdbcbdbcdccbacddcaccbcbaaaadcaddbcdcadacdaaabdcbaaddaaabcdccacacbdaacbabadcbacbdbaadbcaccdbabdcbdadbabaaabccbddbaabddabcbcabaaabaadbcacdcabdabddddacbadbcabbcdbdbdadacdadacabaadadabbacdbabbbddccbcabaaabdbcdddadcdbdaaacbbdbcbdddabcabbddaabccabaabcabbbccbaaadccadbcadabdacddcdbadbaadcacbbccacdddaabdbdacbbacadbbddcbdcbdccccddddacadcdbdbcaaacbbabcadcaababbabdabccdaabbbbddbdcbdbcbbdadbbcabbbabaaccdcdbdbaadcddbbdcaababcdccabdcccdcccddaabcdacdbaccdbbdabbaacbbdaaccabcdaadcdaaabdbaaabbbaaddaccbdadadbcbdabdbdddcdbdccabcdbdbdacacdbbadccdccbcbabbadaaaaabcdbdcaaabcdacdcbbccccdcbccdaddccccadcbbdaccabcddcdacbdaccddacbbadadcadddcdaadbcddbbcdaadbbccccdddcdcbaaaddbdcddadddaadcccaaccacbbcacdbadccacdbccbacdcbabdcaaaacccadddcdbadaddcccbcbdaaadcaaabbbcadadcdbbdbaacdaacabbcdddcdadccadbdacbdacbdbdadacbabbdcdacbabaabdddccbcccaddaccacbdabbcddddccccdcdbcdbccdbbbdbdadbccaddccbacbabccadcacbcdcadacdcbadccdcaaacabdaabcabdddddddbdabcddacdacacdaacdcaaadbbbdbcabcddcddccddaccaadacabacdddaaaadaabaaddcdccbbaddcbaaabcdadbdcacbccddbdbaddcbcdbaaaabacccbcdcadcacacaadbdadabcbdbdbdcbcdccbdcadcbadacabdabadddacdaacabdaccababdcabacddbcabaddbbcacbdaababacdbaccbdacbcbcabbbabdbbadadbdabcdcccbbacdccddbcaadabcdcdddcbadadddbacaabcdbadcabdddbccabadccdcdcadbaddbddcdbbabbaaacadabdcdadbdcbdbddbdabbdddbccadccbdccbbdcbaddbdbddaaacbaddcacbadcdbbcdbacddabdbdcccacaabdaadcabbcabbacbacbbcadbbaadbaaabbacdcdddccacaadaddabcdbdbadccdcaabcaccabcddcaacbdbbbacdbcdaddbbaccbaacccdabadddcaaacbbacdddbacbdbabcabcdadccbadbcccdbbccbbcaabbdbbdcababdabcdccccadaccbccdbaddccdadbaabaaaadddcbadaadbabbbcdcacbbaaaadccacdaabcccbbbbbbdbcdccdccbdbacdcacbbadbbadcadacbbabdbcdbcdbddaacdbadbadbbdbbbbdbddadbddbdabaaddcdabbdbbdcccbdccabacdaaccdcdbdcbdbaaacdadbcbcdbaabacdddccbbdabbbdabdcdbbcccaaddcdbabccaccdabcbcadbadbdcaabcaccddddaacbabcbabdadbccaddbbabdababccacdabccbdbcacdcabbbdcbaaabdccdbddaaaadadadbbbcbcbbdcbacddbccbdcbbdcdcacdcaacabdcabbbdbcaaabcabdaacacdbcacdabaaabdcddadadbaacddcbadacabbbabadbdacaccdcabadbbcbccaaddbbaacbacdacabbcadddabcabaabdbcdbdcbbadbdaddabaadbdbddddadabddbdabdccdbaaabaaaccaaadddcbcacdacaaaacabbcccbbabcccdabdabbaccdcbcabcbabcdcbcddacbdbaaacccbabbcbcbacbdddabdcacaaccaacabaccdbddcbbdabdcacadabdbcddcbaddcaadbbbdccaddbddacbdcddacdadaaacdbadbdddacdabbabdbdbddcadbaccbadaccbddcbdcddcdbacbcdcdbaadbbbaadaabadbdbdcbcacacaadabddacbbccadccdddddbbdacacbaabddacccbcbccdaadbdbbaacadadacccbdacccdcdaacaaabbbbaadaacdabadabcacdbabdcdaddcddabcbacdcddbbcacdbddbbddbaaddcabddccdaddcadbacacdbddcddddccbcaaacaadadcccaadcacaacdccabaadddbccabcbcaaabddaaabbcadbcaacccbbcbabddbaacabcddcbdccbadcabadcbdbaadcbbaadcddcccddabacbaabdadbacbdcbcdbbbddabaddabcdbaabddacaadbcabcabddabbaabbbbcbaccbcddabbaccbcbccbccccdabbcdbcbcadddccdabbdadaabdbcabbbdcaddcdadadadcbdcbaaabdcbadcccbaacaabaadbbbbcbdddcbcdbadddababdcdbdaddbbabdbbabbadbdbccabbabddcccccabcdcdcbbabdbbdcbacdccddadcbdbaddbbaabcdacbdbbccccababcdbbdcacdbbbbcbccbdbbddabcdaadadcaadcdabbaacaadcbddabdaddcaccdaaacdbacdcdabcacadbadbdccbcbbdcdbdccddaabaccdbabbaddbbbcbbcddabdcdccdcbbddbaacdacdadbdbcacbacdcabcadcaadbcbddcbcbccbcabcaacdaaadbdbccdccbdbdadcdcaaacbacabcaabadacaaabacbabdccdccbcaadddcacbaadbdbbddcacbbbdbbbaababdaadaabacbcddbaacdcbcccbbdacbccdcbadbaabcccbbbddcdcacaddcabbcbcaacbbcbadadbcbbcaaaccbaabacbbccabcaaaaadabdabdccbcabbaccbbadbabdbabddbdcaaddccdaaabbdaadbabccbccacddcdbdcbbccbdbcdacaabbaccccdacbddbdddcdaacdadacbdaaccbcaccbdadbbdcabdacccbbbdbcbccddcdbdddbaacddabcbcbddaadccdcddddcdadbccccdaccabdcccdcdddbabbaddbabccadddbacaaccbabadccccbbacacadacdddabbaaacabddaadaaccdbadbbccbbccbcbaabcbdcdaaccccbbbccabdbadddbcadbbdddbdbdbbacbadcaddcacdbddbbbdbbaaabcabddaaddadaababbdabaacdabbbbadadcbacaddccdacbdbabcdabbbcdadcdadaddcbdcaabaabbdcaaccdcdbcdbbddaabdadccbbcbcbdcaacaaaadcbcdbaacbccbbddabbcbbacadcbbaaababdaaddbdaadcaddbcdbcadaabdaadabcbbcdddcabbddbddcddcdbbaadaacccdacaadcccbbcddbacdbcabaacbcacbcddddbdcbabdbbbccadbddbcccdaaccddaadbcdacbdbddbbcbdbaccbccadbdccccdcbbdabccdaaccbdaddabdcbccdbbcccabddcdacddaaaadbdbbcbaacbdccbbcdcbcdaabcddabaabcabadaccaabcdbccddcccdacadacbdbdbadbabaaddcdcaacadacdcbdbabadcdbcabacdbcbaddcccddbbbddbcabaacacbdbbcdaaacddacbcbcdbdacdaaccddcabbdacacbbbcdbbaccdbacabbdcdaaddbaacdccbcaddcdadcbcbbcadacbacbadcccacbabaabcbbbadaababbabbbdddddcacababdabaabbabacdcbdbadcaabbdcccadaababbcbbcdbcbbdddaacdcdcdcaaccaccdcddaadccaacbbccccbbdcbacbcabaaddbddbbcdbcddadabbacdadbdaabacaccbcdbadcccacbadcccbdacdaccbadabcbddbcaaccccaddcdbbcccababdacdbaacdccacbaabbbbddcbddccaacabdbcdadabcaadcdcddbaaaaacdbabdaacaddacdcbdbcccdbdddcdddcbdccadbcabcdbcbbccabcdbacbcddcbcdcabdaddbddcabdadadbadcaadcdaaaacddaaabbaaccbdccdabaacaddbcdaabadbadcccbbbbcdadadbbddcdbaadbabdabdcaadacddabaaccabcabdbbdbcbcbaacddadccbdacddccabaaaddaaabbdbbaacabdcbbbdccabbcdaadadbaacbbdacddaacdbbbbadadbddbdcaccadacbbcdaddbacaddcaabcdaccbbbacaccbabcaccdbacbaaadabddcabacaabdbdaabadbdcbcddcdddcaacadcbabdaddadcdccccbddcbcdbbbbbdaaacddccacadcbdbaadcdccacbbbddddccccacbdbbaccdbbcaacadcabdbdcdcbadcbddcadcaacdcacbdadbabaccbabcbacddbdbadcdbaadcbddbcdbdbaabccbdaacacdccbaadacbbdaddbcbdaadbcddbabbacdcdcaccaddcdbadbddacabcbbdacdbccdccbabbdacdbcddadaabdaabcdabdaabacabacdbacddabaddcabdacadcbabdcbbccabcaddacabbcbbaccbddaacbaddddbbadacadbaacaaddbdbbadddabbcbdbdbccacbdabbbadcacadbbddbdabcabcaabdabadcbabaccbcdcddabdabdcbcdddbbddabdccadabccccbdacbccacaacbcdbbbaaccddaacbabaacdbaddaacaabdcbaababddaaabbdcbcbbdbcbdbdbcdbaaadacacdbadabcababbccabcbdadbcabbdaadbacadadcdbbcdccdbddaadacabaadaaacacdabbcacadadabdcbabcdbcdbddddbddaccaabcadbdbbbccdcabbdadbabbbdaaabbcccbbcabddacadbabdcbcdacaacdddbaaaddbacaabbabdcdbacdaabcabadbbabcccbabddddbaddbbabacadbddbccbbacaccbcabddaabaacaaadccbddddacdcdaacbcacaadccdbdbcdbddcdcbcdbcdbbaccabdcbdccaabddccccbacbbdbacadadacbcabaaadbbddcadbbdacacacdadbccbbddaacccdabcababdcacabdbccacddabaaaaaaccdcccccadddbbabcdddabbdaddbabadacdccbcbbadddadbccacacbbbcbccddccabacbbbbbcdbcbdacddbddabdbabaaaacdbaabbdbbccacdcbcacbcbbcaadcbbccbdaadccbcadaabbabbcdaacbcbcbaacdadcbccaccbaabbacaddcdaddcaccacbbbbddccddcadaacdbbccbbdbcbdbdbcbabacbbcdcbbabaaddadcbbbbabdcbddbdbcdddcdbbbbdcddaddabcdbdbbbaabcddcbbbaccdababddbdbbbbccdbcbccbdaabbbddaddcddddaccccdcacbdbcacbdcdbbbddcbbaddabaddbbdbcdcbbdcbddbdacdaabacaddbcdcadcddcabbabaadbbdcccabbddcbdaadddaacdaacddcdbaaaaaccaccccdcddcaddbbaabcbcbbbbcababbadacccdcdaaadbacdabbcbaabbbbabaccacccbcbcccccdbccacdcaccbbbbdcadabaabcbcbddcdcbbdbcbbacddacaddabcccabbccbbbdbcababbbcbacbdbadcbcaaacbbdccbdaabddbdbbdadacadabacbccadaacadbbcbcbadbacbcabbadacabdabdbddbaccdcdbbadcbbbddaacaadaddbdcabdcddddcbdbcaababbabbbbdbcaacacddccabbddddbcdcbcbaccabadbcdacacccbcadaaadbbccdcbbcbcdcdcbcaddbbbdaacddaacdcdababdcdabaaadcaaabcbbbabdbbccdbcabaccbaabbadcbaabadbdbcaccaabddbdaaadabbbddccdbcbbddcadddccbaabdddcadaaabadddababbdddddbdbddaadacacadbabcdaacbcddacbcbddabbaccbaddbbdbdbcadcbaababddbdbaadadcdcaddccbcbdddabbcadcdacbdcbddbcdbabdacccdbabdccbbcdcccbdbdccaccaadbdbcbdcaacaadddbdcdcbcbaddddabaaacccdaadabadadcdadbabadcaccaaadcbdcabaadbbdbdbccdcabacbbacacdddddaccabbadcbadadabcddcaccbaadaadbaaddbbdbdcaddcbbcadabbbaababddabbccbbbcacdaaadabdcbaadccdbcadbcdbddaccccddaaaacdcbbccbddcbbccbdadaaaddbdcadbaccaadccabbbdbbaacdacdbcacababbdacdbbdbcabbdcdbbddbdccabcabbabdcdaaabaccbdacbcccacdbdccabbaabcaacbabddcdddbabcbadccccdadbadccddcdadcbbcdaadaccdbacdccdcbaaaaddbbadbddcabbdbadddbacadcdcaaabdadcbcbacaadddaacaccabdddbdadcdddaabcdbddddabdcdcabdddbdddbccbadcaccbacdcbdbdcdbabbbbbadadbabbcbcbcaadcdbcacccdadabcdbdadacadccbddddacbabadddabcdbadaadababbacaaccbabbcddaccdabbadcaacbcaccadbddcbabcaacbbddbaadacacacbdbcdaccbcbbadadcdddbdddbcaabacbdcccadbaabbbaabdbaaddddcbbcdcdccbcddabaccaccdbdbbbdaababbbcdabacccdcbaabdddddaaadacdcadcacdcbdbccdcabbcaddbaabbcabdbdaabdcdabbcabacbcaddadcddddccbaacdbcddbbacbbdabacbcdccbabbaacaacacbddbccaaddadbbbccbabdbcdcdddddccddbdbbdabdbcddbbcabddddccccbcccccbaddaccdabcbacadbacdcaaadcbadccaadcbabccdddaddcabcbdaddcdcdaddcaadabcdababbcdcbdabcbdcaaaddacdbabcbaaaccdabbdccbdcaadaaccdbdddddadadaaccdaabcdddccccdcdcbacccddabdbcacdaadadccdadccdbcbbdddacdbcaccabcbbcbddadabadbddbaddbcdbaabadaddddbccacdbddbcdacaaccbdbddabcacbbcddadbadcbbadccddacabcbcaccbcbbcbaabcbdaaadbcacacdbccbdaccaaacaadcaaabcbdbaacdcdabdadcbacbbbdbbadaaacbabadbdcdbbdababccbddccbddbcbdcabbabdcadaadcadabccbccbcdccbcddcbcddcabcbdabaadbdbacdbdddcacadccbabbccbaadbdccacaadbbaadcbadbaccdaaaaaddabbcadaccddcbbdbbabcaccbaddbcaadaddddacdcbaddbdbcdcbdaddcbdbbcabadaaabbbccacccccddccadddadbaddcbdcadcadaccbadcdaacbacdabcabaaccdcbaddbccccddbccbabadacbcdbaddbaaaaabccaddbbbbddbcccdcabdcadaacbbcabaddacaccdbbaaccbcdddcadddcbddcbcbbcbddddcaaaccbadcdccbddadbbbaaabccdcbabbcdcddbcbaaaccbcbcdbddddcdbbcccccacdbdccabaccddccbbddcdbaaaccabcaaadbdadddcbcbbabdbabaacabaccacbdcdbbacabdbbcabdbcabddcbaddadcdbaacaadacdacabbabdddacabbacbdbcccaccabbccdbbdcaccbcdabacccbbacbddcdaaabacbabdbcbbbabadabadddcbcdbdaaaddaddadbbccaabdbcacdbcabddbcbcadcdcacdcbdbaacbcbabadddaddcadabbbccbacaabadbcdabdabccadcadbccddcbdaacaacaabadddbdaddcdaadcbabacaaaddcbcbbbccbddcbdbabbbdcbcbacbbbdbdacabddbdccdacabddbcbcadbddaacabdcccdbcbbdadbbadaaaabdbbabcbcbddddcdbdbbdbcacccadbddbaabdacdacdcbbbcbbdcdcbcdadbbcbdaddaaddbdaabdaddbbdcaaddcbdccbbcddbdbccacdabdcaccabbabbcdbaaaaccdbdbcbaadcbdcdadaccaabcabcdbddbdcbdadbdccacaddacbcddcdadbdabcabcddccdbbccdcdaaaccccadbcdbbbadbacbacdcabbbbcbccdaddccbcbabbaaabcacccbadcabcabdaaababbdbdbcccbcacccdaacddabadbbbbddabadbddadcdcbcdcdbdbadcbaddabdaccbcacbadabbadddabacccbadadcbacbccbcaabddaacdcbaaaaacbbbccabaddabadbaaaccdcdbcbdbdccacdbcdaabcbbcaaadacabbdbaccdbbbabcbccdacbbdaacaaddddbdcabdddababdaddacbaddacadacbcdadadbccabbcbcbadadbbcbccbbccdbcacddbcabbddcbbddddbbabdaadccbaacbacacacbbdddadbbbcdababcaadcccaadadadabcbaccbddaaddbccdadcdcabcdabcbddbbacabddaabcbddbaacbbcccddcbcbbdddbdbabdccdadcadabcdaacabcadcbcabbccbdaabdbcccccabcacccbcaaddddddbbcbccdbcbbacbadbbbcccabcaaabdccbccbaddcadbddadccbbcaaccbaadaaabdacbbddbdaaccdcaddbbaddcbcaaabacbbbdbaadbdcababddbdbdabdcdbddbbacbcdaadbdadbbccdbbbddcaabcabdaadbbcacccbdddadcbaccbadabccdccabbacabdaabadcdbdacdaddbbdcaadcddcaccbccabdccadcbaaddadabcccdadbbaccacdabcbcbacadaddcdacbbacdddbabdcbbcbbbacdbbadddddbdcbdbccaccbabdbbabdaabdbacdcacabddcbbacabddddadbadaccddccbdcbbddabbaacdbccacdbdbdaadabccaadadbdbcbdddbcbbccacdaabdadcccccdbdbbdaacbcbbdbcccaccbcccdcaacbdbdcbdbacdcdcddabcddadbdaacdcadccbdbbdabdddddadabddddbccacdbbddbabcdbcdbdadabdadcaabacdbdbcbddbabbbccadbdcabbbcbcaabcbcbbbcccaabacaccbacbbaabaccdcdbabaccaccaddcadddbcbacbccbcdcbbaaacdaccbbbaaabdcdccbbddbcbcbdbbbccbccdccdbaacacbdaaddbdcddddabdcbcbdccdabcdcccdcabacdcbdacdadbbdcbaabbbacaaaaadaadcbaacbcbcadcbddcdddaddddbdabcbabaabddddbccbacbcbccddaabbcdddbdadbaaabcbcbbdbdaccdcbdaabbbaadcccadababbbcbddbbcccddbcccdaaaabaccbcadbddabcdacbcdabdbbbccddbadaaccdcaddddbbadbaaacabdcbdcbccbdbcdcabddacdbacccddccdcadaacaddbaadabaabddcadaaacddcabadbcdacbcdaaaabcadcbdddacaabcdbbadcbcdbacaddacbbaacdaadadcbcbddacadbabdbdcacbbbddcabadbacbcdcadbdbaabacbdcdbbaccadccbcaabcbaddbaacdaabcabdacbcdacaaacbdccbccacbdaddbdbbcacaddcaccbdbcaadcdccdabdaacccdbcacddcdbdcaaccddcdcacacddcacdbbaacdcdcdcbaacdbdabbaabdaccddadbaadbababbacdaddcbbbabadddbcdbdcaccacdcbdacaddbdbcadabbcbdcacabdadbaddcdabdadadaccabbcdbcadabddacdcdbadacbcaadabbdadacabcbcbcbadbdaccbbcbbbcabddcbabcbaadaccbcdbaabaabcacacabcbcdbaccacaababaccbaaccdbbcadcddaabadbcabdcdbdacabcacacbdabdadcbccdccbbadbdcddacbcccadcaacbaaaaabdddacaabaaaccccbcbbdbbaabcadccaaddbbdbccaabbadadcabcddabdaadbcbaadccacbabdbbbabdddccaacbbdbacccdbdaaaabcccabadaaacdbcddaccdaadbaacacabcdcdcaaadadcbbccdcdaddbadbdacaddacadaccdaabcddbdabacdcabccabdaccdbaccabddbbbabadabdcbcbdbbcdcbddaccdabadccdadccbdbdbcacabddcbdcdcbaaaaabdacaabcbdbdcbdcddadacbcccbbcbbcccabcdcddcbaaaabbacadcaabbaaaacccacbbdcdcdcdcadadcdcaadbddbbacdbddaddabcacbaaadbadcbbbaaaaadcdcddacccaccacbadbcbaabadadbbaccbdaccbddabbcdbbcbdaadbaabcdccbccabdddbcccaadccabcdaacbbcdabddaddabbaaaacbbcdaabdaabccdababdbabacccbaadcdcacaadbbcbadbcbbaababaddacbbbcddccacbabddcaabcbbbccdabdcbdddbcabacacacccabcbcddacbcccbdcdacacbabdcdaabbdbcaaabbdbbaadacaacdabdcddbadcbdaacbcdcbcacdbcaccdbdaacbcacdadbcdddaabbdbcbdabbbabdbcdcbbcddaaddbbccabbabccadaaadbdcabccadcbdcadabdcbbccacccadcccadddcdcdccbdbccbcbabcbddccbdaacbadbaccbcbccbcaccdbdacbdcbcddccadddbabdcccbdcadadbaacaaacbccddbccbaacabcbcbdabcbbddbcaaabcdddccddddbcccabbaaaadbcaaaccbbbbdabdccbcddbcaccbabbbdabbdadbddbcaddddabbbbdcdacccaabcabcbabaacabaacadcaddcddcdaabcddcbcdabccccbbdbbbbbdadbaabcdbacaccabccdbbbdbadbdcbdccaabacabbdadadcdcadddbbbabcadcbbbaacabbcdcbcdbddabcccccddddbbdabaccaacaabbacdbcbabacbcadcdaaabbbcbdcbddacbcdcabacdcdcaabcacbddbbacbdcbdcccbcaddbbbcdbcdbbdccdaddccccdbdcabacaaaddacbddcbcbaababaabbddaddbcdddddccdadccadddbdbdadddbcacbadababbccbdadabccbbcccaadacbddaddcbdcbacdadaabbdadcaddabdabcaddadccbcbcbcaadcbadddbadadaadadcddbbaaaabbcaaacabddbddbcbdddddabbdadcdcdccdaddccabbdddbcbbbbbdaaddaccabcbdbaddcdbddcadabcaabbabbddcddcbacbcbccbaadaccaaaddbbadbaacacaccacaabbabbcbdbdbddbbdabccadabdbddaddcaaabcbdcabadcdaadaacbadadabadbaacbcbdcbabcbdcadaddabbcbcabaadddcdcbdbbdddbadabbbdbbcbababadcccadbdacccabbcddaddcbacadabcadadcccbbcbbabaccdabcbbccdbbdcabcaadadcdcdaabbcdbabadbbddcbccddbcacaaddbdcdcbbbbccdddbaccbdbdaddbdabcabbccbdbdacbbababdcabbbaddacdcdabbcbacacbbaaaaadbaabdcbbcdacdcdddadadcbaddbdbdbdbbabbbbdddabbcbcdaaddbabcbbcccabbdddbcdcbcdabcdcaddcabbdaacbdaddcaadaddacdabbdaaaadadbcaadcddcddcdcdbacbccbdbabdaddaabcbcbabdacccbacbcacdbdbaaaddbcbacaaddcccdcdaadcaccdaddaabcbbdddaadddcdaaabbcbddcaddbaadcdbaacdbcaccdcccbccbadccbbcdccacddcdbadabbacacbdbccaaaacadacacbadacbdabacacddbababbcbacdddaaaaacbaaddccdaabbdbacdcdcdddcadddccbcacdbbbddbabaacacabcdcdadccccdaacdadaadaacdcdadabbddcbbadababbabccbdadcbabdcdacadbcadccbdbdcbbbbccdaabbdabcbcaddaabcbccadcbcaadbdcbabbbcaaddcbbcaaadcbbbcbaacdcadacabbabdccdbbcbbabddbbbacacabbacbaadbdcabcdcaddaccbdadcddbbdcaaccacbddbcbacdcbbacbabdcbdbacdcdaadbdcbccdaaadcdbcaddaddbcbadbadadbaadabaadbaaaabccbabbaabbabadcdcbbcddddcbabacccbbadcaadaadbbbcdacacdcaadabaddacadacbbadaaadbbdbcccbcbbaaddcdbacabdbbcabbcdbdccbdcadcacadbcdaddaabddcbbcaccdddbcbddcacdcaadbbdadadabbdcddabcbaabcbadcbcdaacacadbcbddadabcdabcdcbcbcddccccabcbdccdcddaddcbbddaaacbdcabbbbbbcccdcbacdababacadbdbcacaacbcbbccddadaaccadabaacadbcdadacbbdacdbdbaabbdcaddababbddacddcddddcdadccbcadacabdabdcddbdaaaaccaccbadaadcbadcbbacaadaaabdcdacddbbabcacccaabdcbddbdbabababacdbbdbcccaddcacdccbcaabdcdabaabcdbdbdddaaabcababbddaaabacadacdbbbcabcacacddcccdcbbcadcaabddadcccdbbcabddbdccbbacbddbadcabaabbcdbdcaaadacdabbddccdbacaccdcdabdcdbdbdaadbadbbbdbabcbbabbcccbabdcdcccabdccdbcaddabaabaddcdbacbacaabdabdbcbbccacbdddcbabbbcbdccadbbdbcddcbcacddabdcbcaababccabcbdcbdddbdabccbadcdcbbccdbdaacaccbaacabcdbccdbaddcbaaabcacddbcdccdabbcabccdabddcdacabbbcbabdbdaaaababaddcdabcbddcabbdddccabdadcbddbcdadacbcdccdacddbabbabddbcbcaacaaccccbaacadcababdabddaabaabccdbcabddbdcbbdcaaccadbbacdbcbabaabdcbbaacddccbacdadcbbadddcccbadcbbddaaabbaadddddbcdcadbcbaccdcdbddaacbacbadbacdaacaadaadaccbcdccacdabcaacaddabdbaacaaddccccdbdbbbcdadcdacccdacbadccacaddccdcbdcbbdbdbcbbdbbaccabbdcbbddaabdcbabbabaaadaabddcdabbaaaaaadadaababaaabccaccbaadbcbadbdcbbadaccaccabababbdaababdabbaccdbdddbbaddbcdabcdadabdadbaabbbcbdbcadcaadadabcddabbccadcccdcabcabaddabaddbaadddcbaabaacdbdabcbabcacbbdcccbbbddaadccbbabcadbbcdacbcbcdacddcacccbacbbccbcdcbbbbdccdcaaadbdacaaccdacaadcacaabddbcbcddabcadcdabcdccbacacdbcddacacdccaacadbbaaacaddcdbbcbcadabbbcdcbcdaccbdaadabdbcbbbdccdabcbdbabddabacbacacbadcdbabddbdadbccbdbccbbbbccaadbccabcdbdddbddadcdcbabaadacabdddcacddadcddaaadbbaaacdaddbacbdcbdcaaacaccacdabbcadcdaabacdcabadacddadddccabbcdcccdcabcdbbddbbbdacababbcdccaccaadddaccbddddaabccbbbccabcbcbcaaaabbbcdcccbbaacdbaacdbaaddadbabdbbbaddaaaccbdaccbcbbaaaabcbbbcbddacdccbbccccacadccdadcbddadccccddaadddbddbadcaaddbddaabacaadbabccaacdbdacdbdcdcdaaaddcdcaacabbddcbbdbcbaabbbbdaadcbacdcdbbcaacddcbacadcdbdbcbbddaababddccdaddaabaadbdbddcbbbcbaddddabcdbabbccdcdabcaaaacbdadbaadccbddadaaabaddbacdccbcadddacdbaabdccabdcbadbbddbbddadccccdaacabddbacbdadbcbaabcddcddcddbaaabbcdabdacccccaaaccaaaddcdbbccdacbcdcbbaabcdddbbccbbdabccadccbbdcdbcdbabdddabdcdcaddcbccbcacaaccacccbadabdcbdbcdcbcbdcddabdbdacdbdacabbcccbaabacccddcdbbcddaddabdbbbaabdcaabbaacadcabdbbcddabbaccacbddabdabccdddcddabcddaacbdbbaadbacddacbdddbcabbccbcacbbabcddbdcccadaddcaadbdaaddacaaacadadbdcadbadadcbdbbccaabbbbcbbacdadddbaadbcabdaabaadabacaadaaadbbdcbbacdcdcbbbdabcdaadbcadbccadcbaccdbadccaabaaaaadabdcbbadaaddbdabcbcdadbadbbbaddbabcbacdddcdbaaadbabcadabddacdbbaaccccabcbbccdbbbbbadcbdbacccdabdcbabbdacabbbaadbcbddcdbbadbdbadcccbdcacdddacbcccadacbacbbcabcdbbdcddbdbcbcadbabccbbcabadaaaaabababaaccaacdbdcbddbcdbadcdbdbbbcbcaabacdbbacaaacadccbdcdbdbccadacbaabbbcdaccccbcdbdcdbabcbccdccbaccdddbbabddcbddbbaccddabdcdccbcdbcdadbbacacccadddbdddccbbcabddbdcbcbccdbcdaaadadbbadadddbccadacdccdddbaabacdabcbcabacabdacacbaacacddcabaccadcccdabcdadbbcbbbdbbaaadbcbbcbacdddbcddcadacdacbddaddacdcbddabbdaadbccaddbbaabbbabaaaadbdcbdbabcdbcbadabbdcddbcabccbabdbbccbbdbcaacdcddadccddcaacbaaddddcbddcddbbabcadcdcccdabbcbcaacccaabdabccbaacabacadccdbdabbdbccaaabccbabacacacaacccdaadcccacaaddccccacbcccdbaddddaccacadaacdbdbbcccccbadcdacaddbbbabcdaddabbaaccbaabbcddabbcbbbbbbbccdcbaddbdaadcbacbdadcdcabddcddbbdcccbcdcddadacccdbabacdcbabdccddadddcbabaacdaadbdbcadacaacbaaadacddbdbccbdadccabdacaddbbdadaabaabdaaacbbbacbbcabdaaacdabbadccaacdbaabcdbbbbacbbdbccdcbaddbdccccbcabccbaddacbdbbbcbcdcadcabacddaadcdbcdddcdccbcdbdccaaaaadcbabcbddcdbcbcccadbcacaddcbdbcabdacdaccbcdabdcbaaabbcababababcdcbadaabcdccadddaabbbdbdaaccbbbbcbddddbcdcbcddbccbdcabbdadbadaddaaaaaddbbcddbbddaaaaccdbbcddccdaaaaaabcbbbcdddddbcccadbcccccddcacbddccdaccccacabdcaadddadadccaaaaabbddaabdbcabddddadcbadabdaacdaccbcbadbbdbcbcaddabdadcbbccbdadadaaabdaabcabcadcbadabbaddaddbadcccdccbadcdabdbcdccaadabadbcacbccdabccddadbbccccbdabdbdcdabdcbdaaadbdbccbbcaaacdabadacabdacbcbbadacbbbbbcbbcacbbaabaabacbadbcdabdcdadaabaaaccacbaddcaacbcbaacdaccbcdccdcddccbdadacdacabdbdcbcaadaaaadabdcdccbdcbddacacbacabcdacdbbbacbcdcababadabccadaacbbacaaddabdacbaabaaaaaaddbacbabddbbdaaacdabcacbacadbbacbacdbaaccbcabdaddddbbbccccbbbdbcdbcccbbacbacbbbbccbacbacbdacdaadaddbbbdcdcddcaddbcaaccbdbaaabdacdcbacccaababdbdbcbaaadcbcabbcbaddcdbdbdddadabcaaccdcbbabcbbbabbcabdabbcbaddbaadadcdaaaccdcbdcdaccccbbbcbbcccbbdadabdaadddcdbadcbcbaddadadbdaacbcabaacbdbcaddbcadcdcddddaaadbccbbabcdaaabcdaabaccbaccadbbabddcddccbcbdccdbcdbdcddaabdacdbdbaaddbacbbbcdddbddccbacadcbbacadbbcaaccddbaabbdccabaddddcddacacccdcaaabbcaccbdbddbbdbbbbaaddaddcdddcaddbacccacbacbaccdabcabacbbadbdcabcbdbddacacacbcbbacbcaccbdcabbcdccdaaddbddacbacbbbdbdcacacbcdbbaaadbadcddbbcbdaacacbdbbbadbacadaaadaddbddbdcdccbacaaabbdcdccaadcdbddbabcdaaddccdccabaaadcdcbccdbbabcadabaaadbacddacddbabababcdcdbcaabbbccdbddacccbbababcdddcdbbcbbacbbdddbacabbdacccbdbaaacabccdabbdcaadacccdddcdaabbdadbbbddbbcdcababdbadaaacdbbdbcadadbdccbcccbbddacccdbdcbbacddcacccbddddcccbddbdbbcbddbcacaaccdadcccaddcdcbabbbddccbdbbbbdabcdadbabbaacddccbbdccbcdbacbbbbbdbdbddccdcdbccbabccccbacbccabbdddcbddcccdadcbadccbabcdcbdcadacbccccadddcadadaaaccdbbbacdabdbbbaaadbadbdabbbdabbacaaccaacbcaaacaadaadcbdcbddadbcabdacbdacddaddadcbaddbbaadccccacdacbadddcaacbbbadaddaadddcadcdbdddcccacdcbbadbdabccbacaccadaccbcdddcddabbbddcabaaaccadddddbdbccabccbaaabdaacdcbaaddbcaabadbbabdbdaadabbabdbcacbcadcadaacbabbcdacaaacdacabbdddccdcbdacccadcbcdadccdccddabdcccabcabdbcddacbcaacbdccacbaaabbdcbddbdabadcdbacacbdccbdacdbadadbbdacccdaabdcadbacbccadccadccbdcddbaaabadbbbdcaadbdaacadccbddbacdddabcaaaadbdbadccbbaaabccaaacabcbdbacbbdabdcbcaccababaddddbcabdbabdaadcbbbbcddddacdcddadcbbcbcadcaaaaaabacdddadaacaaaadadcbdbaadcbddcbabdbbbaaaaabcadccdbabbabddddcbbbbcacaaabbaadccacdcdddbcdabbdbbabbadabaacbdaaabcddbcdcadbdbddbdcaabddaacbadcbcdadaccacaadaadccddbbdcacddbcbdddbaabcaadadacaacbbdadabcdcabacaccbbdacdddadaadcdbaddcbdcaddabbdacbdcbdacccaababdcbdbcaabbabdcccaaacdcbdccaccbdbdccdddbcdadaacdacbdacdbbcddbbbbdacddcbdcddccbccdbdabdbddadccbbcbaacdbbbcabccacbccdbbcdabbdccbbbbcdbcbcbbbbcddccdacddaabbbccadcadbbadbcabacabcdcbcbaaadcbbbcaccdbbdbbddabdddbcdbcdaabacaddcbbdaabacaabdadcbcbcdcaaacbcccbdcddbadcdbaabdcddcbaababacccacbbdbdbdacabddacabcccbacdddcadddbaaddddadccbddabcdddbdabcdbcabcabbacdacdbaadaaddaccabcccbacacbcbdbadcbccbacbadadbabddaccbcbdcbcbcccbaddcbdccbaddacadbcaacadcbdcbcadabbdadadacdacaabbabcbbcabbbdcddddcddcdbcdcccbbbccddcdbdaccbcdadbbabcababcddacdaddddaacdcdccbdbbdbdbbdabaadcacaddbadbdccdbbdcccddbdcbdbacbaddcdbbbbdbddadbbcadbbbcaabbbabbcbaacbabcdddaabaacabcbdccbaadabddbdbbbbdccdccdbcaacaacdcbcdcacbadcabbbdaabbbdaabcdbbbcccbbcaaddcadbbabcbccbbbdadbadbacabdcdbdaddcbbcaddbccbaaacdacaaaccabdaabbaddbcbddbabcdccbbabccdbadaccbbabccaddcbcacadabcaddccdbcacbbdbdbcabaddabdaaddcbadbbddaabbdcaaadaaccbdccaadbbbacdbabdcdacabacdccddacdddcddacccbcdaccacbdbdcbbbcccdbbcdcaacddcaaacdbbabdccdbacccdbadcaadabdbdabcbacadabdaaaabaaadcccccddbddcdaaccbacdaaabcbcdccdabadbcbacbdcacadbacbccadddcbdcaccbbbabdaadbcccdabccaccdaadacbddacdabcdcdaacabcbbbcbaddaadcaccddccbdbaacbcacabcadaadbaddccbaddbcccdbcbadadcaccccddcbbcbcdddaabdadcdbdddabbcaabcbddabdbbdddaddacddcdcbbdbcbaacddbddaddcdbdcbdaabccbccbbcdaacddadbbdbbcddbadadadabacacdbadcbbbbbbbbdcabbacbddabbdcdaaaabdcaddbbdbadababbdbbbbbbcdbdaddadadabbbccdbabbbbdcbdaadbbddcddccdcddbdcbaaddcacbbacaaabbdbbcaccbadacbcbcacdccdbcbacbdbabdaaaddbbaaabaadccdcdcacddcbcaddbcccacdbadcdadaddbccadacadcdbcbdbcadadabcbadcbbbcbbbcccadbadcbabbbabdcdcbacdbdbddddbccbaccbdddccbacabddcbcdcdbbaccbcbdbcadbccccddbaadaadcdcddcdbcadbbaccaccbbbabcaddcadbadbcbcbacbabdbacdbadbccccacbacdbabbdbdbddaaccdacddcabacbbbdabadbcabccddbdbddbbadcccddbabadabbcaabbbbcbdbdbbcdacadcaddadbabbdcddbcddccbaccabbbaadbadbabaddacbbbbcbadabccbcdcdacbbbbaabacacdbbbdadddcababbadcdbcdaaccaaacbcaacccdababccacabdacbacdbbabccdadcbbaacadbacccbddbbdaddcabccaccbdcdcdaacbacbbbaacddbbdbcdbacacbdbbabbccacbbddcbaadabdaaddcdbbabbdbbccabdccbddcaabbaccbbdbabadcaadcadcdddcdcabcaaaaaaaaddcccdbacabccacbadccbbdccdaaabbadbaaaadbdcddabdbabbccadcbccbbbbbbbdaabbcacdcdbcaaddcacbbcadcbccdaaacdbdaddcdbcbcdacbaacbbbacccdabddadcbaadddcbbdcdbdabbccbaaababaccdaacbbbbbcccaaaccaddaacccadddbdbabaacddccbaddcdcababbcccabdcbacabdbacccadddcbdadccdabcdadaccdddcbcbbcdcddccacbbcaaaabcccbabdcaadbcbcdbacbacabdadbbcabdabaaabcabdbdcdbbbdcdcdbdcabcadcacdbbcbcbcbabadddaccbbbdbccaaaabcccacccbddbadccdaccdacdacacbbbddcdbbdaaabcbcababaddaabcaddbcbaaacdbbdcadcdbacbccccadcaaacdaacdbccacccdddcbbbdbddddcaacbbdbcdddbaaabbacdaacdccaadccabcdacaadacbadabadddccacccdcbbbaaccabccdcbccccbbacbacaabbacdbbddaccacdcdcdadccccabddcabdadaaddcccdbdabbcbdcddbbdadbbbacaabadcbcadccbcabbdbaccbabadadbdabddabccbdbcccccdcbdcbdbcacccddadbcccbddbbdabbdacbccbddababaaddaaabddbdddadbaabbbbbaccaddbdbdcddbbcddbdccccccacdcbbbdcbdaaddcdcbdabdaccbbbdbadccbbddacbbdcabbdddabcdcdccabaaacbabdcadcbaddcddbdddccbccdcbddccdcbcbdcacacaddaccaaabacbaabcdcddccbcbababbbaacdcddcdbcbbcddbbbabaadbdaaaaaccddabcbdbbbdbbbbacddcaabbbdcdbdcdbcadacdcabbcacbdcbddcbbaddbdaacbcdcadcccbbddbbcccdddbdcdabcaabbdbbbabcccdabdcdddbbabbbdbcbabcbbbcbdcdadccbbbcddabbabdbbdddabdabdbdbbacabbaacaabbbcdcbcdaabbbadccdbdcabacaacbbaddbadbcbabdccdbbababbbdabadbbdaabaababaddabdcdadbdadcddddbddbbdbbbabdaaadaabdabdbabaccbadbcabaabcabdbcddadcdbaadcabdaddcaddacdcbaccaabddabacababcdabdbcbbccacbdadbbcaaccccacdbabdbdbdaabaddcadddcbaddbcdcaaaddbadbddcbbadadacabdbdddaddacabccbdcbdadcabbbccdbbcaadacbadcabcbbcbbbccbcbbdbadcbcbabcbcbdcabdccabcbaaaaaababacdbddcbddbdbdcabbbbccaaaabdbaabbcbdbbcbaadacccdccadddccaaddcabdcbcadbbdaccbbaaaacccbcdaaaddbaacbacbcbdabbaaabcadcbabddaacccdbddacccaccadbaadbcbaabaddbccadbdbacdadaaadcccbdccdbdaddbbcbcddbdbbdbcbbbdabcbdcdbbdcbacabdcdaadcbbcaddabadddcaabcddccdcdaadbbdaddaadcadddcdbacddddcaccdbaccacdcdddcccaabdaddbccacaaaadaabcbddacbbcaddccccbbdadabddbcabcaccacdcddbabdacccccbcdaabbbccddddaccdcbbcbcbdacbacbaaddbddddcdddcaadacbccdacaaaacbdaadbbcbaacabaaacbcbbbdaccacdaaddccacdddbcbbadcbddcbacacadbdcacabbdbdcacadbcdacabcbabdabdbbcccdbdbdbccdaaadbadbddddabcadacdbbbcacbbabbdbdcbcdbaacdaadbdcacdbcaccdcdccdcbbcaabacbddaacbcadadcbdcaddabaccabcdabcaddcbdabbdacabcddcdbaddadcdbbdcbaddcdacdcdbcbdcdacbdbbcbddbdaccabaadbdcaaadbabadcadccaaaadadacacbcbcddcbabbbcbadcdbabdcbdbbcdccacbdaabaadacabbddcacaadbaccbddbacababbacbdcabdddccdbbbdbbccdcdddcbbcabcaaaabcdaacbbddccdccdabdbaaadaabdcdadacdcdbaccdcccabccdabccbbdbcacdaabccacdcbdadbbddbbcccbdcdbbacaadabccabbbbcdcccccbdcbcbbabdcadbadcbdbbadbdcbdccabdbdcddbcbdadccdcbdcccbddaacddbcddccdcbcabdcdccadadadbcabdabacabcaccabaacccbdbacaacbbbadaacadacaaaadbbdcacabdabcdadcbddacbcbabbddddccbadbcbdbdadbcaccaacbbcccabdbaddacaacbbddbdcdaabccdbabdccccbaccbddcccccdbccdabcbcadabdbacdcabaabdaabbdcacdaddbbddbcbcddcaacbcbdcaddaabaaadaaddcacaacdbbaddbdcbbabddddbdbbcdadbbcadabbcaacccbcacdbdcadadbbbaabdbdaaaaccdaadadbdcbacbddaaccbcbdbbdddcdbdbabbabbcdbcbdbdcababadbadbbbbccdabddbbbdacabdaacdaaccbdbbbacabddababdbabcbdbaaddcbaaaddbcbccbcbbdbcaadaaadbacdcbcadbbadaaccddbbddbaddadaabdcddbaadbdcbdabccbcabdadbabcbcbaaadacccaadababdcadabdacbadadcadbcbccdbbadccbdaadbcccadabcddcdaabcbacbbcdcbbadacacadcddacdbaadbdcacbadddbcccdbbdcadabcdcacabcddaaaccccacbcbacabbcdbbadbdaacacaadacdddcdcddbddbdcdcacbacbddaddbdacdcddabcaadcddbcabdbbdddddaddbddccbcbcacddbbadcbbbcaaccdbdabcadbacbadcacbbdccacacbdbacbbabacbdbadbdbdcccdbadacbdbabcbacbddccbbcbbdacaaccccdbbccbddaaacadacacdbbcbcdbcbcabaddaabcbbcaacddabbbbbaabaadcbdaccbabdddccaddbaaddddcbcbbcbdcbccaabccacbdcacdadcdcbbbbcddcbbdbbaacabbcabbddbabcbaccbdbbabcdcbbbcdccccccadcbabdadccaadcaaaadabcdcbcbddcadbcdddccdbdcaabcbbbbbdcbaaccdaadadddcddbacbcbdbdadaccbdaabcdadccaaaccdcbcbcddabbadcdbbbbdcdacabaaacabdcdbccaccadbcbcdabdacbcdcacaaadddcccdadcdcddbbbadacdcadcdccccbcabcdcbcbcabacdcacaaaacdcabdbdcddbccbbbcdaaabaddbbcdcbaabcabacdddbccadbcbaaacbcaddbccbbbabababdccddcabdcdababbaccbdbabbdcacdaabadcdcdabdccbbaddccdcbcacbddbdaadcddcbcdcbdadbbbbcadcbbdbbadaccbbabcbabccdaaaaaccdbcabdcccacbacbaddbacbdbaabbbddbcabcdcddcccbbdabbccbccdbcbadacaccaabaaccbabcabcaabdcacaacadccadddadbaacbadabcbbcbbddcabacdbdcbbacdaabdcdbdcabbaacbadbccbcddddcbabbcbccabcdacbbcccbcdbabaccbcdaadacbdbbcacccaddddaabcbccccacbcabbaddcadcbdaabcacbaabadacbaabbccccaddaccdcdbaaaadacadbddccdcddabccbbbdbcabcdabdaccacbaacbdacdacbbcccdadddcbdccadabacdcacaccbdaacdcdbdacdcdbabbaddaabdbdcabbdcbaabdaaaacbcbddcbaaacdabbbcdabccaabccbcbdcaadadaacdaccadabbcbddbccdaadcabababddbaadaaaccbdcaacbababadadbaaaaadcdcccdaddccadbdcabadcbbdbdcababcabcbadddbaabdcbdabccdaabcaacbbcbadbbbddaccbcbcdbadccdaabbccbdadaabbcdabbabcbacdddabdaaaccacdccacddcbaccdbcaabdbcbadaacdbcabcdadadcdbbbbddacddacabdddaacbabdbacbdaaacdcbccbddccdbbdbdbaaadbdadcbdaccbcbdaabacabbdcbbcbcdbbdcbdadcdbaabcdadabdcdbdacbdbcaaddaaabdddcccdddbdbcaadcbddaadaabdcdbbbabdddadbddddddcbdadaacbadabbcbadbabbdcaabccdcdcbaabcdcdbdabaaaaddbddabcccbdcadaacccacbadcaabdbdcddacacaabaabddbaadcaaacdbdbdbadbdbcacdbbdcaadaccddacacccdbcaaacbcdacdabccddcdabdcbcccaaabddabdadbccdbdbcbdcaddacaccacabacddddbaddcdccddcbbadcdabaaacbbbacdcadcccaabadadadbdcbabbacbcacacbaacbcabbbbbccbcabaccccddccaacadcadbbadbbcadcabcccabadbcaabdabcccbbbaaddbabcdcabbcaaadcacddcbbccbbabaaacdddcacbdddabcabdbdacaacbbdcdbdbdaacccbbddcababbaadbbaadaccdbbccaabdbadbaabbbaaaabbcbbcbacabddacddbdbbdbbaccbddcbdcdddbabdbbcadddbcabbaaccbbdddcabacadcadbdcccabdadaacadbdbacdadaccbdccadadaccadbccbcdaabbdcbbcadabaccacababdbbcdbaabdddcbdcaaddcaadddbbabcdbdacdabbbcdddaabbbacaaadcdcddadaaaacdaddcddbaacaababbabbaacccaacdbacdccabdaaaacadaaabbcadbdddcacadbbacdbaaabcbbbdcabdccdabcdcadadcddcbaadabbbbbcbcbadacababbabbccbcadabdbbcccbbdbadccbabbcbadacbdcacadcaddcdcdacccdadbddcdcdbcdbdccbdabcbddababbbdcbabdacdbcadbdccacaaabbdcadaccdabaaaaadbdaddcdcdcdcddbcbbdbcdacaadbcddadacabdaacdcddacadbdbdaaccdbbcababbcaaacdddcdddbcdcabbabdccbcdbabcaccbdaaacbbcddcaccdaaacaadbadbaddcdccabdaadbdaabbdacdcbcdcbddacbaabbbdbbabddadcadcbcacddadaabcdadcdaabbdccbaadabcdabcdbccacbcdbccdddcabbdabbdbbbcdabdbabdbabdabddcabaadcdaadddaddaacadaccddcaacdaddbddcaabccaccbcabcacdbddababbaccabbadcbaaacabdbccbbacdadbdbccdddcaabadabdddcdacaabcbdbabacdcccacaabdbbcabdbbadabdbccdaabbabbccdabadccddadbabacdccacbabcdccabbbdaadccbcbdddacdacbcccadcabacbdbadcddbaabdbbdddddbbacdaabcdbdcddaabbcdddbbccacbcbdbabcbbdbdbabadabbbaaabcaabacccabaddaadaacabcddbcbaacdcacdbacacdbadaccabdbdaccdcbbbdacddaaacdbadcbbaabccbcdabadaadbbdccccbcdaccdddbacdbbcbddbbdbbaabdcdbabdbcddcdccaaacdbaccdbdbdcaabddbdcbbdbaacbbcbcdacdbdbdaddadcbddccaababcbcbdcadddadcccbcdcbbbacbddcdcccccbabbacababacbdabcdadabaaabbcaabcdadcacadcdabddbdcacdcccbbbaaadbcccadccdcdabbdbaaabcabadbdacbccbcdcaabadddacbbcdbcacddbddabcccbdcddbbbdbaabdccbbaccddabacbdccddcdbacaddcddcbabacdbcdaadbdcaabbabbcbcdaddcbbcadacbbdbbabaabadbbaaaacdcabcdcdadbcdddbcbbcbabbccbcaccbbaaadbadacbdbaaadcddcccdddcbbcbccbccbddacdddadcadddcaaabdacbadccdcdacdbdaccbdaccccabbbabbbbdcacbdaacabcaccaabbaabdddcbadacdadccaaababcbcaaadcdacadcadabdacacbabacdaabccdaaaaacadbaabdcbbabadabddddadbbacdcbcbccdcbdddcaccccbbddaccbccbbbacddcaacbddaacbcdcddcdcabaddcadccdcaabcdcbdbdbbadcaaddacbbbcdcaccbdccddacddadbadccaaddcdaaacdabdabbcbbcbbaccbddabcbddbabccdbcbcdcaadadbbcddcadbcabbdbbacbbccbccbbccbcacdbcdddcaaadabddcbddaddadddadcbbadcbccbbbcbaaddbabcdcbdddcbccbbbdcbaddcdadcdcdbcdcdbbcbccbdabbdcaddbadcbccddbbbcdcccadcdbddbacdbadddaaddddbdbabdddcdaaadacdacaadddbcabdcabbbdbbacbbcadcdadbdacacadcadaaaaaacadccadcbadcaaccdabbaadccdaadaaddcaababdbcadcbcbbbbbcccaacdddcbabcdcdccbdddcdbbabcbbcaccadbdcbacacdbdcadaaccadbbbabcddbcaaadcbcadabccaadcdbbccaccdaaddccaacddaaacbbcaaccbbdcdbdcadaddcbbaacdbbaaadbbbddbdaadbaaadacaabdbdabbbcbbdbdbbdaadcbbbbcadcbacdbddabdbddaadacbddbadadddaabacabaacddaddbccdbdbabbaaabccaccddbdddbdddcbbdcbcaacbbccccccbccdacdbddbbcadbdcdbbabccddabbbccdacdababdccdabbbbbbcdcbcccabbdcdcdccdcdabdbdddcdabdccccbbdabbdcbcccaccdcadcbaaaaadcbdddcdbdbadbbdadcacbaadadcdcbcaadccacaacdbccdcccccdccdadddacbbcccdddcccccccbdbaacacbdacdbccabddcddddbcacdcbabbcbdbddacdbacadddcdcadccdcdbadccaddcccbbdaacabcabcababccabcbbcbddacdbaabdabccddadcbdcbddaabcdbbadabbacdacdcbcdddbcdadccaabbadaadcbcadadaaacacacaaccacadbdcdddcaadaaaadbacbdccdbdbdbdcbdaacdbcdbaaaadccbddbdcbcbacabbacbaadaaacabbdcbadcbbacdaddadacdbaadbbdacdaabacdccadcccdcabccbccadababaaabcbaaabadcddbdadabbddbcadacddbddaddbdcbccbbdbbdaacaacdbcdcddcabaabaddcbbbdbdcacabdcbcccccabdabcabdbaacbcccbadbacabcbadddcbdcbacbdaddcddcdacaccaaddabadddaacddbcaadddbddbbcdbcdddadbbccaadbdccadbaddadcabbaacaadacbdcaccdaacdaaadbbdacbbadbbaddadbcdbbcbdacbbadbdabcaddbcabcccababbbcacbbdacbcbbcbaabaaccbbaaddcabbcabadacaaaacbbabbddcbbbccdcbabcdadbbcbacdcbcaaaccaaddacbddabaaadabccbaaaacbbcdbbdbcaccccbabdabddaadabccdbaacbabdcdcadccadccdddabbddbaababddcadaddbcadcbddbadbdadaaaadcbabccbcaaabadbdaddcdddadcacacdcbbdabddcbcbcabbacaadaaaabccaccddadacbbadabbadababbdcdccbabcddabcaaabcaaccdacdbbdcdcbcbacbdaacdaddbbdaccbdbcaabcccaacdbbabdaaddbbcddcdcacdaaabaaabbdcadbbccbbaaadcacbdadadbddcaddabcbbbddbacadbccbbccbcccabddcdacccaaabaddbbdbdcabdadbbccccdbaaadadccbbbaaaaccccabbbcaaaabcdcbbabddbdadccdccdadcabbbcdcccdcacddcadbbbbccadbddaddbbadcaaaacbdaadcbadbbadbbdcbadccabdbbababcbbbdcacbcaaacdbbaaabdaddcdabddbaccaacaccdbbdcabdabcaadbcccaacbddadbdabcdaddcccabcabbbbbcacaaabddaaddcccbaaddbbcccccdcdddabcddabcabdaccbaaabdddabdadacbacccbbdcddbcaadcbbadbdbadcccccdbdcbbabbaabdbcdbdbdcacdcccbabccbddbcbadaddcdddccbdcdaabccdcaadbaacacdcccdcdccbddbbabcabbdadbcbcbcbbbbcaadcbbcadcccdaabddacbaadcbdddcddabcddbdcaabbdadcaabbcdbadaaddbcddaacaacbcadabddbbadcbcddbbcdabbaddaadbabbdddcbabbdaadbaabacdabccaaacbcaaaaadbadbbbbaaddcadabdacacdaddadcaccdbdabccbbadbdbbbbdcdbdbaaccbaadddbdddbdbdcdbcbaddcabcddccaadabacacadddacbbcaddbaccdcbccbbcaadcccadaaacadbbaccccccaabadacbabbadcddbdcacdbdcddabbdacbcaadaaccddaadacbadcbadabbbbabaaadaaacdddcaaddcbddccaaacacadcdcbabdacaadbdacdbabcccacdddacbbcacbcbaaabaadcbbbacdcaabbabaacdaaabbacaadccacabbddcddabcbcdcaaccdbabadddaaabbbdbdacdabcbcdacbacbaddcdddcbbdddbabbbaacaadbcaabacbcdbbbdbbddacbaadacabaccdcdbabacacdccdbdabddabcaadabcadccdbdcdbbddbcdcdacaacbadcdbdacbdbabbadddccabdadcabadcbaddccdbdbbacddcdbcddabacdbdbdacddabbcacdccbbbdbababdacdbadbadbddaaacbcabdbdcbbcadaabcbaddbaccdcbaaacaccbcbbcbadcbbdbcbbabcdbcccbcbbddabddbbdddadacdbccbaddccbbdddcddbdccaccccacabdbdcdbaaabbcaaaadbbcdbbcabdaccdabcabcbbcbccccbcdaabcddadcbadccccbabddbbcdccaacbbdddadaabcadacaabdacbbdcaacacbbddbbdbbdaddabdaaabbdbdcaabdbaaaccbddbaabbdcbbdbcdbbcdbccddddaaddcadcbdacdcdddadbdcdbbabdabccbcccccbccacbbcababcdaabddcacbcaabccbbbccbadccaadbdabaddcdbabccdcbccddbdbcdcdabccdddcbcdcadbcaababbabbbcddbccdbddcabdcacccaabcccacdbcaadcaabaddadadcadcbdbccdddcddaacdabccdbaaaadacbadccacbdcbbbccddbcdaaaabddababacddbbdbaacccadabbdaddcaccadacbabcbacbacacbbaacccdcbcaddbcbcabcacbbdabccbdbaaacdabadadaabbbdbddddadaacddbbbcccbaaccdcaabaaddbcaabbccbbddbcadbddccbdccdaddbadadccdcdcdcaabdcabdcbccbcdadcbdbcdccbbddbacbdadbababadacbbbdadddcabccdcbaacddaddabdcbaabdcbadbdccdaddcccccaadaabdbcdbbcddbccaaaaccdbddadaabbdccbbdccbdacddbbcabdadaabccadddcccabbdbbadabddabdcbbbacbccbcdbcaacbcbdcaddbdbbbdbdacddaddbcaacbdbcbaacdbcdacababababbcadbacbadcbaaadddddcbabbcaadddbcbdacdddbbaccbdbcacdcdaddbcbaddcbcdcbcdbbcbcababadcadaacaaadbabdbbcacbddcdbdbdbbaaadabcdbdabcddccddbcdbcacabbbbdcddaaaadccbcddabcdcccbdddbbddaaaabdabbaabaadcdbddacbdcdddcbaddcdcbacbdbbbacdbddbabccccacabdcdbbadadddccdbcadddabcbacadcdacbdddcbdcdadbbcaacabdaacadacdcbdabaabdbacaccacabadbbaadbcdabbbacbcaaaadcdabacaaaaddbacaacabbcbccdccacacbdddaadaadacacdacabadcddadcdacaaacdaabadbcdadbaabddcddabcdaacddccddbdcaddcacabcaacddbbcbababdbbcbcbdabacabccbabdcaddccdabddaaddcadcccdcdabdbdbbcacdbdbccccdcbddbddabacabdcdbabaadbadbabaabcbadaadcbaabacabdbccabcadcbbbcbadcdadabcacadbbcbcbcbadabadabdaccbadaccadbccccbcdbadcbdbddbdacaacbacdaaabacabdacbcdcdbcddcbddbadcbbadddccbadbbbbcdcadddaacbbcdbcbabbcddacbbbadabcbdcdbbdcbccbacbcaadbddbabadbcadcaccdcbcaacdabdddaddcbdaccadcdacaadbbbcccdcdcddbddacadbadacacccbccbcdcbadcabddaacaaaadbadccccabbacdaaaddddbdddcaadcaacaddadabbdbddadacdbdcacdbabddbdccadaacadcbacbddddbaccbbbcdbddbccbcaabdabbcadabcbbdcccbadccccdbcaabbdbacabdbcadddbdacaddacbcddbbadccdaaabddaddcdbabbcdbbbcbbdbcbacddddaabdcbcbcacdabbbaccbdbddcccccaaabcdabdaabddcdacdccadbdbacabbacaabbcadaaaaacaacbcaabddbbdccdccccbbbddbaacdacdbaacdabcccadbcdaabcccdbbcbabdcacddcdbabaadbccdadcaaddddccccdbcbbddabbaddcbdabbbdadaccaddcbdadbaabcbbbbcbcbbabcdcbccdcaccbcbccdddbcdcbddcdbdabbadcbaabcdbbccbadcddacddbaaadccbcbbcaabdbccbbabbccaaaacbddbbbccbcdacbaadadabdacaccbaadccbadaaddaccbbbabddaddabadcbccbddbddbcbcaadbaacddacabbdcacbdcaabbdddcdadaddbabcabdadadbadcdbdaddcabddcacdcdcbdadaaabadcadabbabbcdaabbcbdccabcddabdadadcaabbcbabcaabbcbdbbdadbaddcadbadadcdbdbbcdbddccaddacdbbccbdcabcbbabbbdddcdbbccadaddabbcaabdacbbdaabccacdacdcbbaaabbdcbaadbacdcaadadcaabcabdbccdbccbbbaababdbcbabcdbbaadacdacbabbbdcaccdaacbacbbdcaccddcbcdadcaacbbacddbbcacdaddbdbccbbbaacdaaaaddcaabcbdbddaaabbaacbddbaddcbdaaddbbaabadbbbacdaccbdabcdaddacbbcdcadcbddbbcdbdbddddaccccbadbbcaddbdcbbadcdabddbbbcbbdbbdccbcabbdcadcddcadbccabbbcdadabaabcdabaaaacccaabdcaaacbbcaaacaccddadbccdcbdcccdddcbcccdcdaabbbdcdabcabacbbccbcdabdbcacccaddcbadbaaddccdcdaadbadbbcacadbadcccabcdcaddabcdcbbcacaddcacbbdaaaaacbaabccacabbccadddbddcabbdabababcdcdadcbabbbabbbbadbbbaddcacadbcdcaacababacaacbaadabaabcbbaaddadccccbcabcdbdbdbbcdbabdcdbdbcadcacbbcddccaccbadcaacbaabbacbbcdbcaadacbcdcbabbabdbcbadcbdccdbdadadbaadbbccbdacadbbabdbdcddabbcbcabcdbcdababdaabdaaadabdcdbdddcddcbcbdbcabcadacbdbcadbabbcbddbdbbbcccacbddcbabadcabdbbbabbacddacaababdccbbabaabbdcaddbbaaacacaacacbbabccabaccacadbbbcabdacbbbdbbaacaddbbdaaabbcddcacbababbcdbaadbdcabdbcccdcadaadacdadbddaadabbadbcbdcbbaadbadddcadbabcddabddddbcaccaabbbabbcdbcbddabadcabdabbbcbdddcbaacbcbdbbbdbcabbdbcccacdccbcababdddcaabacbdbcabbcdbbbdcbcdccdacbddcdcdbabaadbcaddaccadaaabccbcbacccaadadbdaabddbadbdaababddcbabccdcadaddddcabacdacdcabdbdcaddabbcbdaabadbdddbdbbaadadbdcdadbddbdcbadbabdcdadbcabbdbacdccbdcbaaddbbcdddabdaccccdbcaabccaabaaadaababdcbcabbacaadabcdadbbabbdcbaaabbbcabaabacabcacabddcccabbbbcbccdadaaadcabaadcccacdddbbdcdacadcdcccccccdaddcaadabaaddcdababdcbdbaacccdbcddcdbdcddcbbddcacbaabdadabddbbbdddcabdadcadadbacdcadadbccbbdcabbdbccdbaddbacdcacddddccaabdddacdadacbabbcbbacdbdbcdcacaabacdbaacddacbabbbbaddbabbdabcaccbdbdbabcaaaccddcddcddabbdacbddacacccaacddaadbcacadcbbbcacdcddcabbadcbbbbdbcdabadaabdbdccabacbdaacdcdbcdccccaacbcaadacdcbabbcaacaaaadadcddcdcaaabdcadcacdacccbbadccaacbaaccadabbdbabaddcdcaaadbdccddccddcccddbbacaacbdbcdccdbcbddaabaacadabbdaccbdcbcccdcaaccdbdabaaddacaddbdbcdcaccbbadbbddaadccaccbcbabbbaaabbbacbdbddaccdddcacbdbcdddaaabcabdcbcbacdbabdcadcbbaabcbaaadcacaaadddabadbccacacdadbbbbdddcbbcddddcdabacdaccaaaaddabbabadbdbcaadbcbbdddbcbccccdbbcdbbdabbaacabcbadacadabacaccaaddabadaddcacacaaabacddbbcbdbcdabdddddaaddccccbcaabbddddaddbaadadcdbcbcdabadccbbaacabcbcbdadccbcddbcccdcbdaaccdcdcddaacadcdcdccddcdcaddbdccdddaddbdbbdabdaaacdbcabcccbbcddbabcccbdcaacadacdaadabbccccaddbdddabddabdbdbcbdccbbbcdabaccdabcddccdcadcdaabcacbacacdbbdaccdacbbbdabbaacadcaccccbcbbddbdbcbbdadabaddbdccdaacabaccdcdaadcbaaaacbaccbcaabadddcbcacccaaccacadabdacaabbccaacdbbabbbaccadcdabbacacddbccadddbadaccaccdbacadaadaddcbcbdccdcacaddbdcaacdcdddadbdadadcdacaabcddacacaccbcccddbacaabbcddbcdddaadabaddbabcdaaddcabcddddbabababadbdcabdbdccdabdbbbcccbbbcadacaaccdbbbbbaacbbaadbbddaabadacdaabacaaacbbacbaccbccbdaacdaacbdaddddbbbcdcdccadddcbdacdddaccdaccacccdadddbbbabcdbbbabcaaccdadbdcddcdcccadbdbcccabdabccbcabbdbccddbbdccacaccccbcbcccacabacacdbbaaadacdbbdccbcccbbdbbdabcddcdcccadcacaadcbcaabdcdcdbbccdcbbabacbddbcabacaccdcbbcacbbaadabddccbdbcccaabacadccbbadaacbbbacdddccdabccadcdbbcadcbcdcdbcdbaccdbbddbbaabccdbdbbaaaaadcadcbacbccdbabaccbddcaacabadbacdaacdbaddcabdadbaccbdadabddcabbbabddacaacccaadcbacabbcadbdabcdbaaabdddbdaacbacabbbcaccdcaadccdbcbbbabacbacabadcbacdacdddacbccbaabbdabddbdcdbabcbcdcddacdabcbbcdddabacbcabcdddbcbcaaaaadbbaddcdcbbbbdaccbbbdbbadccbdaaadcdcadbbcddacabbcdcbcddaadbdaabdbabbcbbacbacbaadaaacddacdccbbbdbaacadaadddbcbbbacdaadbcdacbbcdcabcadbaddabbbcbbbdacaccdabdacccdddccbcbddbaadbacdbbaabbbdccbcadaaacdcdbbcccbdbcbbadbddbadbbdcadabbccbcdbbbbadabcbabbdcbbcbccdaabcddddccdbaabbacdbbccdbbaacdbccaddbdddbbdabddaddaadbcabddcacddbcadbbacbcbacdcabbddbabdbacaadbcbccabaaccbdadbcdcaaadcdcbddaddcdaccdadddadbdaddcdbdbdaadabbabcbbbcbdcbaaddccacaabbdadabaadcbccdcdaadcdaadadadbadcacdccddaadaddbddddccdcadbdbbbcdcdbadaccaabdacdcadcdcadbbcdadcdcdaaabbcddcdddbbaddcbddddbbdbdabddabcdaaabcbacadbadbabcadcbccbdbcbadcddccadbbcaacaccdaabddcbdacbdbcbdbccccdddcbddabbcdcbbbdbcacacacbabbacdbcbdbaabaadbbaccbdbdddcddbaddbdaddbbacacddddbcacccacccdcccbbbcaccabbdcadcbadcbbdcbacaabbccbaaaabbdacddccdbbcadacadcabdacabaadccdadbccabbddcdbabcacadbaccdddadbbcbcbcacaddbccacdbbbbacccdaabcabdacdcddaacccbdabdbacbcccbdacccdabadbdacaadbdcbcbcbccccccdabacbabccbcadddbbdabdababadbcacdbaddbcabcccbcadaddababdacddbdbcdccddcacdcddcddddacdbbcaddbadcdcaacababdbadcddaadccaddbbacaacaadabdcddabccacccaacdacbadcddacbcbdcaccaddaadcdbbaddadcbccbcadbabadbacdccbdaabadddabccbaadcaadcdccbdaaabbacabccdcacacaccdadbdaacdaaaacdcbcacadacaacacbccbdaabdaacbaccbaddabaccbabdccbbabbdbaaacdcbdcacdcaaaadaddcbabddbdbcdabbcbcadbbabacbccbdcadacdcccacdbbaddcdcdcdddccbaacdcdbbbabdabadacbccdbcddadbaacabadaaaabddbacaaadacbabdcbacadcacdccadacbcbabbdadacbadbbacbbdddcbbbbaccdccbabcacdcbcaabaccaaccabdabcabcdaddaaaddcadbbaacbdaaabbdacdabbccbddddbadaaabbcdaaadbaabbacacacdbdccbddaabdbbaaaaadccccbdbddaaacacbbbcbddabbadababbacbccbcaadacbcbdaabcdadcdadabcdbcbacacdbbccbbdbcbacddbbbcbdddcaacdabcdadcaaaddcbcbdcabcbdccdbadddcadaccbbadaaaaabbdbcdabbcddabdabbaddbccbacbbcbbddbbdbccbdcdbcbdccbcaddbcccadbabdddcccabcadcaadcdabdaabdddaacbddadccdcdaddddbbbbdcaacacbbbaccabbdacacbabccbcbaddaaddcbccdcacdbaaadddccabccbdacccccccbddbaadbaddcddcacdabadddbccacdacacdcabccdacbadacbaddddcddbcdbbcabbbcbdaccbdadbbbbaddadddaabbcaababdabadaacddbccbcbaadbbaabadbadacbcacbdccbbabcdadbcabcacdbadcbcbabcdbdbbbbcacabaacbabadbadcbbbaddadaababdabcdcccdcccdcaabddcadcbabdbacbdacbdabcdaadcdbcbbadaadcbdacbcabbcabbbabadabaacdbcdbcdcdcadaddcdcbbbdcacbcdcbaccdacbdddddbadbdbabdddbdcbdcdacbabbdbbbabcbdaddadacaddacbcabddabdabdcccdddbbccbaabdcaacaaabdbbbccadbbcbacadcaddbadcbbaadbbabddbbccaabbccabbadaddbbcaaaadbcdccababbcabddccbadcabbbabdddaabbccbbbaddcdadbcbbadaabcddacbaaacddccabdcabdadabcadacbbabbcbcdbabdacaaabadbaddbcbaabccccbccbcdcacdbabbcbdddddabaaaccbcbcbabcabacbadbdcabcdbbcbddcdccbabcaadbadbdcacabbaddbaaddaaaacbddacabbcccacbbbcddbcdcbddaddcbbcdbdbacdadcaacdaccbadbcabdddbdaccdadbdbbbbcadbaadbbdcbaccdbabcccbabdcbdaddbccccabdccddacabaddadbdbdcaaaadbcdabddcdacaaadcdbccbbacacddddcdabdbaacdcbabababccdabdbdadcbbaddbcccaccbdcbccdababccccbccdbadcdcbcacadaddcacddcadcacdcbddaacbdcdbdbddbabaccbcbaabcbbabdcddddcadbdccdcadadbddbdadbcddcadbdddbdbbcbabccdbaadcdcabdcbdbccbacadacdccabdccddcbacabacdddccaadaaacdbdbdccdadbbbbdbcddcdbcacdbbccacddaaadbdaaaacdacccbbdcbddcccbdaababddcddcbbcbdbadcdcaddcbbccadccbbaabcacbbaddcbacbbbcccdacdbabbccddaadbcaaabbbabcdaddcbbcdbbccaccddaddcabacabdbdadabddcbcbdaadbbaaccacacbbcacbddcadbaaccdcdadcddddcdbccccababdbbabcccccaacbcdcabdbaaacdcabccbddbddbcbaadabdddaddcbacccdbbadcdcdabababbdbaccccadcbdaabbaabcadacccacdbdcbbadccbdcdcadabcccabdcbabaaabbcdcbbddcbabacddaaacccadbbabcdaaacddbdbabddcbbdbcdbacadddbdaacabadbaadcccdddbbdabcdaddddcadbbcbadddddcdaaacbbacdddbdbbbdcdccbabbccaabcbcddbadccaacddacbacddbdcdddabaabddbadcacbdababadccbaaccdadddbddbccdbcccaccddbbbcaadabaabdadbbcaabcdccbbbabdbdadaabddbaddcabdbbbdaaccdbccacbdabcbabcabbbcbdccdbcacaaaaccbbdbbcadbabacdabcaccdcdabdbddaaaacdcaacbbbbbaccadacdbbcccbacccbbdbadabadddcdaaacaadaaadbdbabaccdacaddbdbcbbdcacbdacacccdcaaadbcbbdccbccabdddaccaacbccabbacadbabdcacccddddabdbccacddcdadcdadbabadadaccbdababaacccdadadabdcdabcdccbddbabcdcbdddcbbdcccaacbbdddbaabdcabdacabacdadabcdbccadccccbdadbaaddbdaddaabcaadccbdbadabdcddbdbdabcbbdaaaddbdaddbbcaccdaabcddcdcaddcbdddcbccbadaabcbbcbacaccdcdcabaadddddadbcbccaadabddabcadbccbdaaccabaccbdabdddbddacbbdbddcbdccbdddbadccadadbcbacaccabdabdbccdbdbbaabccadcbcdcdbacbdbbdcdbbbbaccaaadbdbaadccccadcaabdddadabadcbbdcbdcccaddaadcbcadcdaddcacddaaccddbcaccdcbbbacbadbabdcbcadcbcdacdbdcbbabdcbcdbcccccbdaaadccbdacdbbabbdbadcddadccbdaddbaaccabcabdbacadcddbacbbaabcbcaacabbdabbbdadcabdcbcdcccccdcbbacdbcbaaccdddacdcdbcbdacbcdbbccdcbbababdbadbcadcbaaaabaaacbbbaddabcbcdbbbbcdddddaabadabcccddcdbbccadaacccccbcbacaddbdadddacadaacddcdbbacaacdcbdbcdccbcabbaccdbcbbccdbbcdcdbdbaaababccdddbcaddbcacbccdbdcaccbddbbccddcbddcabdabdcacbdddbbaaddadbaacbcbbadbbaabdcdbabccabbacabadbcbbbabacdbdbcdbdcbacabdadcdcabaaddbabbcbcbadddaadaaaccabadaaddabdabcbbcbbadacdcdbaccdbbdccaaaaccbbacdadaaadabbadbdddbacbccdcacaaddbbdcbbbcbbbddcbbddaacacbdbbdaccbdbbadcdaaabacbccabdccbcbbbaadcbaddbbabdccbabcababcacccdcccabccabacdcbdcadadbdbccaddbadaddbabadddabddddbbcbdabaaccdcbdaddcddcacbbabdbcbdaadccadbbddaaabdbbaadbbccbcbdaaaadbccacbcdbdcadcbaaacbbbbdcbdbbcabaadddabdbbcbcdcdbccaabdcbccdcacaccbaabbdcccddccbaacabcabdddacbccabcaaaadacbaadaddacacacdabbabdbccdcacdbdcacccacdcadddcdbabdbacbcabcabbdbacabbabdddaababcbacbcdaccbbbcbabdddcdcdbaaabcacdabbbcacbdccbbcdcbdccbcddaaaacadddbcadbcbbdbcddbcbcbbdababbbbbccdcadacdabadbaccbddbdccbbbcabacbcdbcabaaccacbccddbccdababbbadccacdbbbaaccdddaadbddbabcacbcacddcaaaabbbccbbbbbccdabddbbabdccacdcdacdabacbcbdaddbbdbdabacdbabcabadcbcaccaacacabcaacbcdacdcbbcbccaccaddaadabcaccabdaabacabbcaaaacaabdbacdcddccbdbbaaddabccccacaabadaacbbcacbaaadbdaacdcccccdcbdbcccbabbdcadaadbbaabcdccdbcbacacacddbbcbddabbbcbbcddbdcababcaccdbdbbbdadccadbbabaddcadacccbdccddcdbcdddaadcddddacaccacbbcacddadaabbdaaaacdbbaaaddcddabcadbcabdcdcdaabbccacdabddbcccdccaccaacdaddddcbbbdcdcbbbbccddbdadabdcbaacbdcccabbadcacdbccacdcbddbacbcadabbbdabdacaadbcdabbdbddacdbbdbacadacabdcadddabddbbcbdadadcaabdcdbcbaabdbccbbaddbacadbbbbadddddcbadcbcabcbdadabaadabdcabbccdacdbdcacacbadbabddbbaaadaabdadaaababddccbacaaadbbdaacbdcbccdbcadaadbacaddcddbcaadcdbbddadbcccacddccdddcabbdabcaccddddbcbcddbaacacaabdcaaacacdbabdcabcbbabadacaddcddcdbbbdcddcbbccbccbabdccbcbbbdcbcbaaabbdaccaddaabdbbddaabcbdbbbaacbbcabdaaaccaabbdcccbdcddadacdddddbabddaabacbcabcdccbcddacbbcbbacbdaacbcbabaadcdbbacbbccbacacbaddacabbccaacaaccadccddbcabbaddacadddbadccdddbadccaabdacbdabbbabdacbaccdcccbdddcdadbabdbcaabdcddbdaaacdcddcccddcdcacddbabbbccddcadcbccbcbdbcdbcaccbdaddbdbbcbbaaabcbcdbadacdcdccabdccbdbdbabdaccccdcadaddbcdcadabbbdbacddaaabadbabcccdccccdddabaccbbccdddbaadaadcabadcadcdcdbcbcbabdcccbdddccbdcccdcaccbcaadbbcbdbbccbdcdddcdacccaabbaabbccccccabddcdbbcccadcacbaacbdacdbabacbcbbbdaabdccadbbbcbacbadcbbdcababcadabbccddbcbdbbabadcabcacacbcacaaadbdccbcaddcbacdabaabbcaacbadcdcaabaccabbbbaaaccbabacabddadbaadadcdccacccbdaabcaadbccadacbcdbdabccabdcabcddcbcaaababdbdacadcadacbdaacdcdadaaaaaaadacddacbabbcbaabccbaababcadaabdadcbcaabbabbcdddbcadddccbdddcaadcaccdbbaaccbddcdcdacbaccbbcddaccccdccddababdaadabacbabaaabaabcccdacdbccbbbdcacbbabdbdbdddabbacdabdaaabccbdabcacdacbaaabbbacbdabdacbdcbbacdbabcbacabbcabddcadcdbdcdaadaadbaccacaddbbcdadbddadcbcddddccabacddbbcaabaaadcdbabbccaacaacaabcaccaddbcdcddacbaaccbddbacddddbbacaadbacdcaabdccbdcbcbbabdadbcdccccacaddadaddbddcddbbdadaddbcabcdabcddbcccaadddaddbccabcbbdcdacdcbddbcabcbcddccdbbbaacdbdcdbabccccbbcadcbbadabddddbbdbcdddbbbabbcbbdadaadaaabccccdaabbcbccbbbcbcddaaaccbccdcdcacbdaacdcabcdcacbdacabbbcddacabcadcabcdcbcacaabadccbcbaababbcccaabccdbaadcabcbadbddcbddbdcbdcaddddcbcbcbdbdacccdddcbacdadbcdaddacbbaacdacbabcdacaccccdacadbddbaacbacbacbbcbdbbbccacabbbbdddbdbccccaddddacaadbcdcbcaddcbadddbaaddbbcbbccbcdddacdccdbcadababddabcabababaccddaddcaacbcbdcbacdcdcaaabbcacddccdcaabbacbbcacbdbbcbcadadcbdbbccbccbadabdbddcaabdddaccaaccbadcbdabccacdcdcbbabdacdcbcdaaabccddccbdacbbdccbbbdccdcbdccbdacadcacbabdcacbcdddbbbcdaacbbcbdabcdddabcbaddddadddbbdbaaaccbcdddbcdabcdcabdbbbbaabcadddbbcbdacadbaaddbbabacdabacabbccadcbcabbcadbbaccdccbdccdbbdcbdcbdbbbcababaababbdabdaccdbbcaacabdbddabcbddcbadbbcccaadabdccbabdaacadcdadacbdaabbcbabbaadbadbadbcacaaabcccacdcacacacacdaaaaaaadbdacdaabdbccdcdddcdacadccbaaabbbcadcbbbbabaacabdbbcddaaadcdcccdbdccaaacadcbdbbdabacacabbcabaaaccccaccdbdcdbbbdccbccacbbaadbddcacabccaaaaaabbacdbaaabaddbbdabbccacccbaaaaabbddcbbadccccdadacacdadaccddbbbcbdbcbccdcdbbcacccbcbdbdccabcdccccadaddacbacccdbaacdcddddddddcdcbaccacbcbccdbcaadbcbddccadbdabdaadddddacabdcbdcaaddcbdabddcadddcacddbdddcadcbbbcaabbbbccccdaaacccbbddcddcdccbddbabbbbcdabcccacdaacdacddaabddccddadcbcbddcababacbdabdabaacbaabcdacdbaddbadbbbbcddaabaacbaacdcbdacdcabcbbbacbadadacabbcacaacccabacccdabbabaaadcbbabdcadacacdabbcdcbdbbaacbaccacaacbacbaccdbcaccdbbbbabacabdbdadbaaddabdccdabdccbdddccabdaaaacdcdaabadbbcabaacaadaaabdddcabacbbcbacacbbabdcbacadbadadabdabaaccaabdddcccabbbcccdbcddbdadbbdcdccdaddbddbabbbabccabadacadbcbcacbcbacadcbabcbddabadddacaaabdaacbdcabbdabdbbddacabcccacdadcddbdbaaccddcbccacabcabccccbbdaadabdcdccbcbabdaacaacbcdacdabdabdbddaddcabdacccabcadddadccacccccbbabdbbdbbbbcbdbbdccabcbbcacbadabacbaacdddbaadbdacabcbacbcdbcbdbddcaaacdbadbccdbababbcdddaccdadcbabaacbabadbcacacdbdbadcdcbaddbbbbbaacdadcadbbacbcbbaccadcadddacbccbcabdddadcdcabbadbdcbcccdcbcaacdbbdacacccacbccddcdbccddaddbaacbaacdccbaacdadaaddcdcbcdaaddabbdabbacdbcadacbcaabacdbccccbdaabaadcccbcdaadacccdaacddddcbcdbabbbcdbadaaabaabccbaaaacccadbcbadadcbcabbcadbdbdcabbadbdbbabcbabbcdaaadccabbccaadcbacacaacaaabdaadbbbbcaddbaadbbaaadabcbbadbcbacbabccddabcabdcaaacaccacaaadcdbaddcdacdbcdbacdadaddaacbacdcbaabdcabbbabdcbccacabaccdccbdaadadcaacdadddabacccdababcbdadddabdabdcdcaddabbccbbbbccbbcccbdddcddcbdbbcdcbabbdbdbdcccabaacabacdbdadcaacababcdadbdbbadcabddbccdaaabddaccdaaacccbcbdabbdddcabbdcbbabbabcadcdcaddbcadbdbccacadacaaabccbaabcddcdcddbbacdadadbabbdcbabcbbcdbabacabacdbacbaabdbdacdaadaaacadcbcaadbcbbbbddcbaccdcbcacaccabbcbcdbbbbcbbdbdbddaabbddddddbbdcdbaadcdacbadcaccababcabbbbbbdbaddababacddbbdbdcbcdbccaaccadacdaaacbcbcdddbaaaabbddabaaacdaaabbcbadccadabddaacbbddacaacdabbbdddbacdadabdccaadbbcbbaccdbccdbcabaddddccdddccdbaabcdaabaabcbbbdacdbdcadadbcaababdbcddbbcbabcabcdcacaadddaabbddadcbddabddadcaccaadbcdaabaabdbbacdabbbddccacadbcbcbdbdcdccaaadabcacdccaabccabbadaddadaaacabcccbabccddacbdacaccabccbabdbbbcbcaddacdbccdbbcdacdcaddaadbcdabdacddcdcdbddddbcdcadbbbccbccdccbdcbbbacdacdcdcabcccdbccaabdbccbaacaccbbdcbcdacaaacadccabbcdccbccabbcbcbdcdbcaaacadcbdcccbbcaaabaacdaacdabccbbbabcababdbbbadbcaaccbaacbaabdcbcbaaabaaadddbacddabddcbcabbcbdccaacacdbcbdcdccbdbbdcdaaacabddaacdaabdcddabcabbbbcbbdccacccabbbbdcaccadcacadadcdcdbdcdcaadbdadccbbdaacddddcabbdddadcacbbabaaadcbbdbaccbdcadabbadaddaabbbcbdddccbcccccbcdacdcabddaddbdbacaaddabacabdbacdbcaccabdbabbbbddcaaacaabaaccbbcddbcabdaddcdaabcacdbabbcccbdcaadcadcacdabdccabacdcddddccbaccaaaccdbbbdbaaddbcccbcddaacdccbbadcbabcdcdaaadbaabcbbbaaadacadbbcbdbcadacbbadadcdcdcbddddcabbababbcdcdcddbcaaaacccccdddabbaddbccddddbabbabbabccadabcbadbcacbadcabadbcddddabbddbdbbdcabbdadaaccbdabdbaccdbbccdbbcabccbacdbdcddcacbdddaacbdbccabbdadbabadbdabbccdacaaaccdcbcccbbbcccccdbcabbdbdabacdacdabbbccbdbbcbcbcaabcadabdcdaccbbbdacbabcddcdadccbdacacdccbbddaadaddabcdcbadaabdabdccaacacbbdabcbbddcdcbabbbbbacbdaaaddccacdbabccababdacdbdbaadcdbddacdbcaadacddacacccdcbbcadbacdcdabacdcdccbbdadbcaccdacabddabcddbabcadaacccaabcadcbbbbaddaaadadacbadddbbcaaabbcdbcddccbdccbddbdddcdabccadcabbdcddcdcbacbbabcabadcacccccdabcccdbbbaabbdbaaadaabddadcdadaddbccbcddcbbaacaccbbbcbdcabdbbadaaaaccacdcacdabacbccddaaadaaddaababbbdadbcdabbdbdaadbacbaaadacacddcdbdbdbaacacbdbdccbddbbddcaabbabdcbaddbacadabcabaaacbabaaccdadaabdbaaaacaaaacbbbbdcacbcdbcabaabaddadcbacbabdaabdabcacbbaaacabdadbbdcddbbadadcdcdbcaddccbcacacdbbdbcbcbaccbbbdbcdbaddbabcaacabbacaabbaaaddddccdabbcadbcdcacaaacbabcabbdbabdbbacacaaadbdbccbdcbaacadccdddaabadcbabddbdabddcdababbbdabcacabdaacadcccabddcdbccdbdcdcdabbbcacaadcccadddccddaddacbbcdbcddbdbbdcdaabdacaddcccbdaadbabdbddbadaadaabbaadadcdcddccabaccbbcccabcbbbbdacdabdbcdbaaddadacdbdbbdbdddbdbddcbbbbcddaccbccbabdabcadbddbdacbcdbacbbcaacdaabadabcadaadcbbcdcdcabbbddbabcbcbcdacbbbbabbaadcbdbacdcabcbaddcabdddacabdbdbbcdbacabddcacacabcccbccddccdbdaacdcccccadbaccbaaadcabbccaacbddcdbdabbcaabbddabbdadcddccabbaccbadaabaaccddaabbccdcddbbbaaaaacbbdcacbbdcbbaddacaabdbccacacddbccbdddaccbdbdbaddcdadababbbcacbbdabbcdaccdadcdcbddaddaabccbabddbccabaabdccdbbdadccdcdcaaadbdcddcbcdacadbdaacacacaaddbdcdbbacbcddcbcbcdbadbacccbaacbccddbdcbadcbdccdbaaadbcadbbdbacddcddbbdabccdabbbdbbdcdadbddbbbdacaddcdcbdbccaccabbbdddccbccbaabcacbadcabcbaabccacccdbbdababaaddccdcdccbacaaccdabdaccdbbbccbdacbddcadddbccadcacbbcbbdaccdcdbcabcbcadccabdcadddaaaabaacbdbdccbccadbcadcdabadadcaadbbdbddbbadccdcbbbabaabbcadaacaabccbabdaddbabdcadbcbdcbadcbbacccbabbcacacabdbadbbbdbcbcddcbcbaabcbbcadaccbabacdbcbcbaabdcddbabbbcdcabaaccbbbdcbcbcaddbbdabaabdcdbbcbbbdbcdcdabbbccaaacbaabddabbbbacabbddcdbdcbabbaccbdbdacaadacabcabdccdadbdaddccabdcaacadccbdbdcbacdddabdbbdbdaabdcbcaaddacdccdbcbbddbcdbaddadaccdcbbabdccbbacaadacbadadbbacabadcabcbbaaccbdbbcdadbabacbdabdabdbcaadaddcaabbdaacdadcccaaacdddaabaaacabbabcbdbcaaabbacbdcacdbabbacbcbbbbbcddbabbaadccdbcaccbbcadbbdccdcbcdaaabdaaadaaacdbddbdcddcdccccaccbdcbcadbbacdadaaccdbdcaaaabacaabcbdbacbcdbdadbadcacddaccbcdccaabcccbdbdccddcbcdcddabdabcdaddcdcacbccbbbcbaddaadbaccabddaabacbbadbabbbcdbbadcdddaddcacaaadbbabaabbadaddddccaadbaddadadadddccbccccdadcbdbadbdbabbabdcaadaddddbabcabcaabcaaadddcdbcaddaddaabadccbcbbddadbdcdcbcddccdbadaaabadcccbcdabcadabaacbcbaacccacccbdaacccaabcbdacdaacabddaddacccddcdcadcccbbddabddcdaaadadbddaacdbadaaacbdbaaabaabbbbccdcdcacadbbbabaabacbbdbcbcbbadaadccbdbbdcdabcabddcdbadbadcabcaddabdccdcbcdbaabaabaacbbcddadbaddcaddaabadbaabbdbdcdaabacbdcdbccbccbbcbbbaabaacdccddaccbdcdbdaccbadccccbcccbbdbccbcdcbbbadabbdabaabadbbcbdaadbccabbaaacbcbbabdcadabdbdacaddacdcadcbdcccabcdcbbccabbacaaacddbabcbbbccbaaacabcdbbacbadbadaadcbcbbccaaccacdabbccbadaccabadbbbbabdbcbdbdbccdbcbbddabccdbabaaaacadcacbbbcdddbbbacaddccabcdccaacacccaaaacccdccddbadcdbbabacabdbbadadbaadaccabbbdbadcadcccccdcdaaacadcccbcdcadbadabdcaadbcbabcabbdddddcdbbaaaddbdaabcbdacbcaaaacaaccacaacbbdaaccaddcabaacccbaaaccacbacabbdadbadcaddbadcbdbccdccdccbbdbdcbcbddabacdbdcacacbddcaddbbccbabccddccacbabacbadddcabdcccbcbbdddcbddddbdbaddbacabbbacdcadbcdabddadacddabbdccddbadaadbdacaddcdacdaacdccddbacbdaababbddcdacaaccaccddbcbcdbcbdbcacdbbdabbccdcbaadaddacaacbbdabdcbaabacacdaacbddbbabdabdbbabcbbbbbdbbcacdbbcbbabcabdbcadbcdaddbbbaaccdcadccacbaaaddabddbbadabcddbcabcdaacbadabbdabadcdbdbbacadcacacbccaadaddcddaacdbaaaccacabcccbaaadadacaabbbcbccbdbddabccaddcaacbbbcbaacacbdbdaaccacdaccabdbaadcdbcdadcbaddbbbddaadbcbcbcaddcbaaaadcddabddccdcacbcdabdacddcbddcccddcbacdbbaabbcdbbcdccbdbacbccbbbdcacdcaacbcbaacacbcdcdbadbdbcaadabdddccbbbbabddbbbaabbddaaabddbdaadadbacaddabbcccdcbbdcbddbddbdbccbdaaaabaabcccbddbbddcadaaadcacbcdbadbbdabdbadcaacbaccdcbabaaabadaccbadaaadcbdccbaabdcabdccdbaabccbaabdaababdddcbabcbccddcaaaccacbadbdcaabddadcbbddcbbbccbabddccdabacabbaadddbaabaaaadbabbcaacaddaabcaccccbaabcdbabdbacadbdaaabbacbdbaacabcbbaccaaabbbadbadddaabccdcbaddcddaacacacabbccabcbadcdaaccdbdbabdbdbcadbaddacabdcdbdddaccdccbbaaadbbabdaddaadbccbacabccdbddabcbcbaacdadbcdcbddcacbaddbcaabdbddcabdabdcdaacabaaadcacabbaccbcadccadcacdcbbbdbacdccdbdadadbcccaabcbaccbdcaaccacddddbdacdaabaacdcbdccaddadbaccbdabbbddcabddbdabaccaddcdccacbbbcdccbcddacabdddddccbdbddbcdbabdbabacdbbddcbddcdbaaabdddabcdcabcadcaaaccbcbcbcddacdaddcaccdabcbdbbabddbbdbdacccaabbaccaddcaacdbbbaaadbdbcdcdbcccccccbbbcdaaaadcbbacaadcdaaacacbaabcbaacdaabdacbbdcacccbcbbaacbacaaadcaaabcdbbdcccdbbbdacaddbaaabdabdbddadbadcadcdaaadaaadccacbcadccdbbababdddcdadcbdcdcbdabdbcbcbbcadacdbbddcdbbbdcabbcaccabbadbdcabababbddabbddabcdcdaaacdbbbacbcabaacdacdbcadbadcbcbcbacdacaaabcabddaaddacdaacbcacbcbdbdbcbcacdbbccccadbbcddccaacdbdddbacaabbbccadbaabcdcbbdddaaaaddbbaddbbdadcaddcaabacdcaddadaccabcdacbbacccdcadaacabbaddccaccbcbacdacbbbbaabddabaabdabdddadddadccaccabccbcdabbabcdbcbadaacbbabbadbdccddcbaabccabbdaacaaabcdaddabbccbaadccadaacadacbcadabcdbcbaaababddcccaadcbbccbdbdaccdbccddbddcabbdbbbaccbdcadbacbbaacadcccbbcbdbbcbaacdcdddccacaabdccdbcbcbabbdbcaccaabadbcccccdcddadbdcccbaabcdbcdadbacadbdbaacacabcaabbccbabdcadbadbdaddcdcbcdabbacdcabbcabaacaaadbacccadddababccbbccccaccbdaabbaabaddccdaadcbbcabbbcccdcdbbcbddadaaabbbbabdccdcbaaccbbbbddbcdcaddbdaadbcbddbbdbbacacbdcbdcccbcccabdbacdadaaabbbcdbbabdadaaaccbccbbbbdcaddbcdabaacdcccaadbcacdcdbaadcaadcbbcdbadaabcdcdbadacdbadddabdaaadabccddaddacdbaaabbdccbddbcaddcacbdacdbbabadaadbabdadbabcbcbddbcdcdbcbdcdcdbddaacacbddbbcbcbdccccabcabcbccacadcddccddabbddcaaabadabdcccbadaacccbabdababacbbbcbacdbccdacaacadacdccabaaacdacaccbcaacdddcacadddcdbdbacccdaacaddbcacbaabaddbbcdadacbacdcaaacbadcdcbdcdbcbcdcdacbcbabdabaaadddacdadabdcdbbdcdaadadcabdadbccccacbadbcdddcadbccdabdbdbbcbdaddbcdbacdacddcacabccbaadbbbbbcbdcbbaabbcccdadaababdbbbaddcdaaddbdaddbbbaaddddbbabcabadacaadabcdbbcaccddcbbdddbdcaccadcbcbaccdcaadddaadadacdadcaacaddacbaddcdddaccbccbddddbbccbdaabacbdaaddabadacccbdadcaaacadbabcbdbaaddbcddabdacdbcbdaccbbacaadadccbcdccbbddaaadbddcdcacbcacbadddbdadbddbcccdcdccacdbadabbadcbdacdcaddcbbdcaabcacaccdadaddcacabbbbcbcbabdcacacabcbdcbdbcbcbcadcbdabadbcbdadcdadadcddaaddbccdacaacaddcbbdbaccabacaccdaabddbbacbcbaaadcaccccccabbcaaaddabbdacaacdadcbabbaaddcdcaacddbadcacadbdadbaacbddacaccdadabdaddddddbbbdbacdbdaaccadcdbcdbacbbbaaabbbaaacddcccbdcabddcabbbbaabdaccabdbbdabcadbdccadbccdbbaaaadaddabcbdcacbbdabcbaccacaababbcbaddcababbbbcccbcbddadddbcbcbdbdacbadbbbddacdcdabbcbababbbbadacacdabdabbcdabdaaaddbacbacaacdddccccacddaaccbbabcabccbacdbabadaccbdbbddcacadbaababaccdddacaadbbcdbcdbbccacaadbbaadacaacbdbbabcababbdadbcdbbacdaabdbbdadaaccdbddbdbddbdbabbdbacacaadaabbbccbdcdcbdddcaaabdcadccaccdbaacdaddadbadbddacbcbacacbcbbcbcdabdbccddabddbbbbbddcdcbbbbbccccbbadbdbbbbbadcdbbddabbddbbdaadcaabdcdbbbbabccaaaacbbabcbacaaacabcdbaaddacabbdadccbbdddabbcacdbbbdabadbabdadbabdcaadabbdccadbcabaaabaacddacbdcbadabadadacdddbdcaacaccacbcccbddaabddcdabcadaadcdabbbbdcdacdbdcadabdccbbabdcccbdcdcbbdbaadacdbacbcadcdadacbdacdaddadabcacddcccabacbdcdaacbddadccdbaadabcaabaadbabaaadaadadacadadcadcccddcdddcadacaadabcbadbdaabababddcababcdcbcabdbbbcdbadccdbbcdbbbbabbaacbbaadcabadbadbdcbbcdbbdccccbdaacacdcdaccbaaabbbbdbbbdabdababdacdcbbaacbbdbdcdaadbcaddacccadcdacaababccbabaaabcbcbcccbbaabcbbcacbababbdbdbadadccdbdbaddddaadcaabbcddccdbddbdbbaaddabbabddbdbbacdabcacdcbcdacdbdacbaabdaddcdbadcbbbababadabacaddbaabdcadaddcaadcdddbdbbddaadacdcdbbcbbcbcbdaccbadaaddacccbcbdddcdbddddadcaaadbdacdcdbaaacbaaaaaaabbadcbabaacbadbdbbdbcbbbbcdbcabbdadadbbbbcaccbacaabbacddddcdabdddabbbabbdbbccdbbdcdaddaacdcabcaaacbbbbadbadcbdcddbabcbadcbbccccdddbddbcbabcbbdbbccbcddbaaaaaadccbcaacbcaabadbbbcacccbacabacabadccacbbdbbddcbbcddadcacddbadddbaadcccabbddadbdaaacccdbbdaacccbdadcdbcaabbddcdddddbaacbdccdcddcccdddacbbcacbbadcacaabbdcaddaacaccddadbcddacdbaaddccdacacadbdadaddaadcdcbddcdacbcbdcbcacabacacdcbccbddaaaccadaaabaadbacccbcaaadaaddccbccacaaccbdcbdcbdbcbcccaacbdcddcbcdacddcabbcddaaabadddccddabcacadbdddddbcacabacabbcdbcabddcbcaaabbdcdaadccdccdbbdacabacdcabadcbddbdbbdbcbbabcdbcdabbacdabbaddbcabbdcccadcccdadcdbacbddcacddbdbacbcbcbdddbaabddccbddcadacacdbacccccdabcbdddbadaddaddcbbbcaabcbbcdabddaadaabacbdadbbcddadcacabdbcabcdddbabcacaaccadbbaccaccabccbbdaddcccdbdbacbddbbcbbbddcdbadbbbbaccabcddcacbcdaaadaaacaaccdbdccacbbcdaadaddacbdcdbdabcacadbdbbbbadabcbbdccccdabdaccbdcdddaadccbabcdabbdbdabdabddaddcccbacaaacabadadbdacbcbbaddddddaaddbbacdbaccdcbcadacaabcddacdcbcbdadbbbadcccdcdbabaaaddbaddbdaccdccabbacccbdbaacbadcdacaddaaccbbaabdababdacccdabcabbccabcdddaaaaccacccabdbbbcabaadababcdaabccdbcacdcccbbddddccaabcdbccdddccacdaaacbacdcadaabcadbccdacacdddbcbbbbbbbcdabdbbdbbbbdbabcacbbccdadcbdddcaddcdcbaaacaaccbdcaacbbddbdcbddcbbbdbcacbdaacaabbacbddcbdcacccacabdcdcabbabbbbddccaadddddadddbbadddacadddabcdcbbdaaaabbcddcdcabdaacabcdaabdaacacbcccddadcbcddaddabccaabcadbbdbbabbaaaadaaaabdcbddbdacbcbbacddcccdacadbdadcccccbadadaaaabacccaacdcadbcbcdbddabdbbcdbacbccbadcdabbcbabdadcbaacccbcddcaccadddcbcdaddabddddcbacdabbdddbddbbcddbdacccdbbdcacacabcddabacbacbabdcdcdbbdbddbacaaacccaddaacccadddcaddcbbcbdcbccbccdbadbadaddbdbaabcbabbdbdbaadcbbdcbbdaaabbadbcbaadccabbabbdbccbccbbcdbcbaabadbcadcbbbdcddcaaccbdbcdbddbdbcdadabdbcdabcbdcbacbaabdabcddcabacddddadcbbddbaabaddadcccccbaacbdbcacdbddcbbbddadbbbdcccddcdccabcababcaddccaabbcdccdaaccbaabcbacbabddcacbbbacacacdbdbabcdcbcbaadddadbdcbdbacabadababbabdabccacbbdccaaddabcadacbdcabaadbaaddcdcdbcadbbacacbbabbccbbacdbdbaadddbdacaaddbbaaadcdbccacbcaacdcabbdcddbccddcddbbcbdabbacbdbdccacacdcdbaaadadbbdbccdbcdadbbaaabccdddddcdaabbdccdaaaabadccbcdbadacabcddacaacbcbcabbdbddcabcaaccdbadccaaccddddabababdddaaabdbacdbbbcdacaccddbaaddcacdbaaacbabacacbaacbdacbddabaabdbccbbdcadbbbdacdbcaacbcdcbaaabdddaadaaaaabdcaccdcacaddacdaadbcaddabacdadccacbccacdaabacbccbcaaabcabadbccdbcbcbbddaacacdcbcaaadddacaccaaacbdaabaaaaacbbcdddbdbdbcacdbbabbaccdcdbaaacadcbbccbbdcdbbbacddabbcadcddbdaaaabbadaacaaccbbdbaddbddcdcbdaccbcbcdccabdcbaaaaacaadbadbbccbdaccdbadaabcdcacddcdbbbcbddcdccdabacaddcdaccbbbadbbcdcadddccaabdaccbbccacaccddbaadacbaaddbddcbcdaaccbabbbdaddbcbabdbdacbdbcdddbccdccbddbdabdaadcdbddabadbacadaabddaabccbabdcadcabcdcbbdbadccaaadaacdcbbddadcdbadbabddacdcdccdddaaddbbbbcbccabcdccdadbbaadcadaadcaccdcdddcddbbccbcbccdcaccdcbbcbccccbcacdbbbcaadacabcdbcdccbddbabaabbbaaabcabacdcdadbcadccadcbadcdaccdbaddbdcbccaadbcdcbcdabcdaaddacbdabbcbadaadcdcacbbacabccaadaaaaacabadcccbbbaabacadcddacbcddbaaabacadddacbcbacabcbcbdcadbdadddbadcabcbbacdccabddaadcdbdccdbdbdcbcbbdcababbdacadcbdaddbbadbabdaaabbcddbddcabbdaddacadabdcdbcccdbbbbddacabcdbdcbcdcdaabcaaaccbbbadabbdabaaabdabaaccddaabcaaadbcddbccdcdddacdcadcdaccadacdcccbdbcabdcbdaccbacdbaadbccccbcbdabbccabdbcbacdddaccddcbcdaacacbdbbbacddbcdbcabcdcabbabbabdbddbaacdccbabcbbadabbcacbddaccccccbacdcccacadbbdbcdcbdabbcbcbdddacdbcbddcdbbccaaddbdccdddcbdcaaadbcdadabbcdddcbbcacadadbccbdacddbabaccdaacbbdbbabccacdcccaacbbabaabccadaadbcdcbabccbadbbaacdadadbadaadbbccbdcdacdcaaaabccadcbacaabbacbbcbbaddcdbccabdcdbbbdccbaabdcaadcddccadaaaadbaccbcbaccccbcbbdaabcadbbaaabbaadddbcdacdbcddabacdcbbdbdbcadabbcbbadbdcddabcdbbcbbdbcddbdaaabcdbadddccdcaadcbcdababccdcddcdcbaddbdcddbcdabdaabaddaabcbdbcdadbbdcabaccdbbcdbaababbdbacddbbcdadabcbcbccdcdadabcabbcdcddaabaccccabadcbbcddaaaaabbbaacdcbbbcadccdcccababbcccbdbcccdbbbaadcacdaabcccbdcadaaabbdddcbbcacabaccaacbdbaaccbcdccdcddbabdacabdcacdddcbcbbcbddaddacacddaaabaaacccccacabbacdcddadaabcaddbabbccbcbaddabbbabbbccddbbabaabbcadcadbbdbcbbacbaacccddabcbcdbbdbadaccbdccabacddadbacddabccbaadccdaadabaabadbabbbbaaadadaaacabcbbdbadbdcabadbaaacdacadbbadadddccaddcbbadddbcaaddacabcdbdaddaaaabcbbacbcbdccbcacabcacccdddadaadacabcdcccdaabbcbbdadabcdabbdcdcbdbaddcabbdacadddabaaadaabaabdccdbbdacbababbacaabccbbddbcaabdcbdadcbababaddcdabcbdccccabbcacaddddaabacbbdcdbbcaababddcaccdacadcdcdbdcbbcbdadbddcdadbdbaadaaacabcbbddbcbddcdddadadcaadcaadacadbdcacdcacbccadccbaadbaddaccdcaacdbcdcdbcbdcbaabcdabddddbcabbdbaacdccccdacbddaabbdddaaabcbaabbdaabaacaccdbdcbdbbcdcddabccadaaaddabcddacbcdbdddacdbaddabbddcacaacbaadcbabcaddbdcabdabbabacaddabaaaaddabaddbbdbacddccabbaacbcbdcaaccadaddbbadcaaddcacbccadadbbaaccacdabadbddcdcdacdcdadbddaadbbcdcdcaacdcaaadabbcccbadbbaacbdadddbdbbacdbdccdbbddbbbcaccdabbddaacdcbbcbbabbaacbbbbaccbdaacacaadbaadaaaccccbbccdbbbbabbcaadcaccdcadaadcaacbbcccaaddbbccaccdacacbdbaabaccaaccdaaaccbddbcbcdcbdbddcabadacddaadacbdabcbdabdaccdbaabbbdcddbaadbcdadbbbbdacbcbdcbcdbcdcbdcacdaccbcbcbbabcadaacdddacdcdcacdcacddabcbdcbbddcbcdddddcddaadabaabadddbbdaabbdbdbbadcbdcacdabcbaccabcadbcbcbccddcadcbccbcbabcdbabdcbcbacdcddbaaacacbaaddddabcadddacbccdacdcbcbccaaccddbcbadaaabdcccbacdaaddbdbbdbddabdbacddddbddacdcbcdbaddbbbadaaaddcdbdbbcbddcaacddcadcbcbcdbbdcddddbbdaaaabacacabaccadbacdcbcabbbcbbbacadacaababadbcccdddbcaacacbadddcddccbdcbdbbbdbddbdbcaadccddaacddccccbacdaddcacacaaccdabdbdababaddcbccdaabddccbabbaaccbddccccbadbbacadccdadacddcdaaaacbcddccadddbcadccdaadbbbcbbaadbbbbcdbacdbbacddbbccddaadbccbdddababbcacacaccbbdddaaaacaabbdcacdbacacaacbdcabdabbadcdbccdcbbbbbcdbadcacdbdabbaacdaacababcbcaadcbcbcccdcbbbccacbdaabadadcacbadadccaacbbdaabaddbcdcbbadababaadbdaabbcdadbdbabaddaabcdcbddbbbdaccaaccacbbadcaadddacddaadcacdccaddadbcabbbdbdcddbccdacbaaabdbcbcbcbdcbccbbdabbcbbaadbcdbcddcaccaccaacddbcbdbbdacaacbddcdbbccaacddbbcaaccadaabadaddcbbcacaabcccaaccbdccaccacdacadadcbbcdbbcdcddabaaabcdccbcdddcccabbdbddbdccaadcbbdaddccabdcdadaaabbbaabdabadadccabadcbbdbdabdbcabbabdcdbbaccaabaccdcbaacaabdbbddccdacabcbbcdadbcbbaaaccacacadddbdcdadbbbdcbcbbdcdcababacbcbcdacddbdcbdbccccaadbdbdadbdcabccbcbdddcdaababbbccaaccdacadbdaacbdcbdcbcbdbbcdbbdccbcbaacabaddacbccdcdbabbbcbdcbdddcccadddbabaaaaadadaaddcdccabcbbccccbccadcadcccccabadbbabacdbdaacdaadaddcddcbcdccababcbbcbcbcabcabacbaddadcdbcabbbacadbcbccbcdcaddccbaccbbbaacdbaddbcadaababcddabdbbbdbbbcbcdbbdacabbaddbbadabddaadccdcaacaaaccbdddddcccddcdaddbaddbdbccdbcacacccbdbcbbbacdbcccbabdcbaaccdbcacabdbdbbcabdddbdcdacaaccddaaabdcbadacbcdcaaabbcdacdabccccddaddddbadddbcadcaadcbdcbbabbbdaabcccddddacadcbacaddaabbacbacccccdbdbcadaaadcacbdbaccdacbccdabccaacadcaaddcbccdcaabdddcddbddacaaadcbcccaabacbaaccaaacdcacddbbcbadacaadabcaddabacacdcadadcdadcaaadccbbaddcdaacccdcddacbbabcdbbacbbddabddcdddbccbbddcadbadbbaacbdbaccccbdbcdcdababdaadbdabbbddadadbacddbbabbccbccbccdbbbdacbcdbacbcaccabdcacbaaccdcdabcadcddcacdcbddabbddbcaccccccbdbbdabadcbadcabcddccdacadcdadccaacaadcdaadacbcbdcbbddbbadcbcdcaadaadcaabacdabaccdbcccaccaacdbacadccbaddcbdbdddadabcdcdbbcdddbdadcdaaccaabcabababaddcbbbddbdaacaddcdaacdbdbdabcabdbdadbaadaddddacdbbadcbbbbccbcacbcbccddabdcadaddccabcbbbaddabccdbcbdacbadbddabadcbcaabdbdbadddcababacccbdddadbbcadaadbcbbccddbacdadcdccdabdbabbdbcdbadcadcbbbbadaaadacdbcbaddadbdadbddadbbdcdccbcadbbdacbdcdbdaaadcccbaaaccdccbbbcccabccddacccadaaacabcbadaccbadcabbbaaabbaaccdccdccadbdbcbadbaaccbcdbcaabcadbabcdadbbaaaaccbdcbadbdccaabdaddcbabcaaccadcddddcdbbbddccccbdadacadaadbcbddbdbdacdbacabadbcadadbababdcdbbcdbbdacaaccdbddacbbcbdababacccdcddbcbddccabdacdaacaabdddacaccadcbaccbbdcbbacdbccadcadcccdaaddccdcbbaadbbbddbcdacddccbcaacacddbcddacdbcbdbdabcdcccbccacadbdabababaaacaabddabcbabbdddaacdbcbcbdadaccacbcbacbcbcbbccbbaadaccbbcdacbadbbddddcccbdbcdbbdbddccccadbbddbbcbadabdbbcbdddabdcadcbbddabddaaaabdacbabdcaaccdbcdbddcabdcdbbddcbdadabaacbadbbcaacccdccdddabadababdaccaaacbdabcacacbdabcaaacbabdaaaccbccdcabbbdcbbbbbcbcbddbdabcdabbdbcdccabbdcdabcccbabcbcbcbbcbdacadccdaadddcddddbcbddcddcadaaddbdddcbbbbbdcddcbbaccadbcbccbdcacadbadbbccdbcbddccddabdaaadcbdcbcbccbacccaaacacdbbbdcccbacbddddabadccaacbdaabcbaacadcabbbcdccddddcacdccbcabbacbbbaaaadbcdcacbdacacadbcadbdbabccbbabcacaddcbacbadbccbcccccacbcaccabdaacacdbacbcaaaabaccaacaaacdbabbdbbaabacccbccbbbbdabcdcbcddcbbabbdababaabdbddabcacaabcdacccdadcbccdbdbbcccadcbbcddbdaccddacbdddbbacccdacbbddbcdadcbbcaacadaacdccacdbcccdccdccbacbaddababdacabacbdbdaccadbadbbbddaacbbddcaadcaaababcacadaadbadaacdcdbcdddadccbcabdcccdacbacbacacbccabcccccaccdadbddcbbddcbaaadbbdcccaadbccadccaccabdcadbddbbacbbaddbdbbdcccabcddcdacdbaddbbdcdddadcbadadbcdbbaabaaddadabcadcdccbcabdaaacbdacdcbadddcababbbbccabcbbaaacadbbcbcdadaacddaaabbdbabbbabaddcccaabbaadbccdbaacbbaacbbdcbccbcbbddcbadddbcbbdaaabaccadbcababbcacbbcadaddababdacdcbbbdabdbcbdabbcdbdcddacbcdbccbbcdbdadaccbbddbddcddbbddaaddcbaddbabcbdbcbacbabcacdbbcccaacabcdbbbadadadaddccdccabbabcdddbbccdadaccbbcdcdcbbcccbdbddbcbcacaaddaabaacbcbadbacabcbdcbccadabbdbdbcabadadcdabdccdcbccadcacbcaaacdabdbaaacbbdcccdaacdddccddbacbbacadcccbaaaaabcdbadcabcdbdcbbadadaaacddabadccbaddacdadcbadcccabdcbdadcdcabbaaababcdaaadddadadcadbcacdbcbbdbbcbbbbcbddcbdacaaabbbddbaddbadcccbadacdabaaccbaccdcaccbcbdacabcdccbcacbbccdadabaabdcabaccbcdbbccabdbcccbadacabbcdaddcbcccdccdbdcacdcacaaddabbcddaddabdccadddaccbaacbbabcdbbaacacbddbddcaacdcacbdaadbdbdccbbcbabbdacbcaabdcdccbdbaacaacacddacaaacbcaaadbdabacdcdacdbacaadbdddbddcccbadcabababbcbbcabcbdaaaaddacdadbbaaaccbcbcabcddcdcdaccaddcadcdacdbacadaaaadaccaababbccdacdddbdddbcaabbcadcadcacdaacaadddabaadaabdabccdddcdbcaadbbcdddcbcccacdcdaabcccadbabbddcdbdbabadddbcdcaaabccbddcadccabcbcbcbaadccdbbacbdcaacadcabddadcadaaddddacdbcccbbcbcbcdcbdbdccdcaddcaacccacdaccbbbabbcdbdbacdcbbaadcdabddcddbacacbccadbcbcbbaccccbcababdbdbacbbdabdbbcdccaadadbaadccdcbdbbbadbbbcbcdccbddabbdcbaccacbcdcadccacccbdcdccbadbdbdddaaaaddbbaacdbbcaabdbcadabaaacdaaabaadbcdbaadcddbdabadcdadddcbbbaccbabdabacdddddbacbbdabdadaaaabbcccacdcbdabdddbdbaaaccddadcacbddbcdacabdccdcbbcbddbccbaddaabdddbccddaccccccbddabbcdbaaddcaadcbdbcaaadbadddadbddbaacccbaabaccacdddddabbdccbbcaaadabdacdcdbcbbbabcacbdcababbbcaacbacacdaaaccbbcadabdcbcbdbaacdddbaacbbbcabcdacbdccdcabacaadbadccbacdbcadabcccddbbcacbbacadbdcdddbabcaacdcbdadabbaadabcdabcabacdbcbcaabdacaacbcaccdcaacbdccbdcbdcccbccdbbbbccadaacbcabdddddbaccccbbabdcbdcbadbbcbdbbaddbdcacadaadbabadbaadbddbddbbcdabdddcdadabddcdcbaacbaaabdddadbaadddcdbdaadddbccbdddccddbdbcddcdbaaabbdcbabbbbdbbdcbcdaccabaaaabaaddccabcdcdcbacabbdbcbdcccaacbabcdacaddadaaddbbcddbaccacabcbacbcbbcbbcadcdcddcbaadddbccababbcbbbdbcbbbaabbdcddabddbbaaacdacdbccacbbdbbbbdbbdbbccdbadcdbdcdabbababbcaccbcaabcbbbdbacdacabddccdddbadddcbadbdadaaacdaccddcdacaddcdcaccdcaacdccbcbbdcdabaccbccdacdaaccdacddbcbadabdaadcddbccdcbdaddaddcbcaaddacbdbbaacddbdcadbcbcaadaacdcbabcabcaccadadcadacbbdbccbbaaacaabacdcdddabadaaadaabbbcdbdcddddcccbacdabbcdcbbcbddcacdddcbacbbdbcdbddbcacccdddaaccdabbaaaabcdbdadcbacacaababbadcbbaddbddbcbbddbadabcdadcdcdababadbdacbbcddbabcabbdcccbcdbdbbabcbdacccbccbccdcacbacdbdacdbacadbccadadddabcabcaddcacbabcbdcbabdbcddbdddacddcdacaaadadccddabacdccbacbbcbdbabadbbcadddbbbcaabddabacdcdaadaabbabcbccbcddbbbccbdaabdbcbcbcbbdcbcadcdcbacdacdaabbddadaadcbaaacdcdccdbaabbabcdaaddabddcdabbdddbdaccbcadcbcaaddddddddccbbcbcbddaaaabbadcadbbdcdbdacbbbbddbadbcdbacdbacadbdadaddcdddddccdbbaabdbdcdcdddabddcbacaacddaabccdaccdbddcadcbdaaaaacbbdbdaabddabddbccbadbdbdcbabdaaaaacddcbdbdadcddbaccdcddcdbcbddcbdbabccdcdcaabcdcdbbdaacabcddcadbccbcadabbddabbbacabbdccbcbdcaabaadcacbcaacabbbbbbdbbcabcdbcddcbacbbdabadadbbabcdbaaadcdacdbcaabbcdcdbbabaccbdddadcccdcdabdcbdbcddaaadddadadadabcbbaabddababaaadcbccaacbcdccadcccacabbddbdcbababcacbdcbbadbbcdacbdaacacabbbdcdacbcccdaadaaadcbdcacbdcdaadddbcacdcdadcccbbcabbdcaaccbdacadddbbaddccdbbacddadbcadaaabdbddbcbcbbbdcdbcdacbacabccacdbaadaadcacbddabbcadbbdabdcdadccccacddaacacdaacabbcdcccaadabcaccdaabcaabbacdbccdbbabadcddacaaabccdbadabddaddbdadbdbabdacbbacccddcdcdbacbdaccbadccadddacacaccaaddabbadddbbdbabcdbaadbbbcadcadccccbdbbbbaadcaccadcbcadbcbccbccbcdacdbccabddbcabbcdacdcccdadddaacacaabacbbccdacabcabdbadbabdbbcaaacaadcdbaadbbbaddaccbcbddcbbbbdadbdbcbdaadcabcbdacaabdadbacccbcbbacbacacbadacaccdcccbbaabcddbcbdbddbbbcaddcdbbddacdcdcbccbaddaaccbcacbdbccdcbadcadcbcbaaccccabbacbcadaddbbdbdcddaaadccbacbcbcbbcddcbcddadadabbadadadaabbdbaaabcbcddaddabacbccabacadacbccadaccdbdbdcbabababcdabdbdbbbcbacadbdadaddbbadcadbbdbaddccdcbdabdacaaacddaabcabbcddacccbcaccbadddbcabccdcbbcaaabdcaaaacddacadbababccabccbdcacccbcdabbaaacdcbccbdcadaaabaaacbbcbccbadbcccbbaddbdcddcccabbabccaddaccdcdaacdbbcbcccbaabccccbcccbdacacccbcddaaabbbdadccadbdbbabadadbbbcadbdadddabdaabacbadcacbcbbddbdcdddddadbcadabccdcabaabcdabdcabbbacdabbcdacbccdbcacdbbddadaacacccadbbadbbddabdaabaaabcccccaaaccabaadbcbaadcbbacdacabccbcccbdaaccbaabcdccbbadcdaabddbcbbdadcbababadbaadbdbbaabcddbdadcacabcdadddccaababcdcadbdbadaccdaaaacddcbadacaadcbccadcacbbadbcaddbdaabddbccbaddbcbbaadbccadaacbdbcccdbbcccdabcbcdcbbcabdbaadcdcdacbddaccbacdcbccaacbbdbbabdcbccdadabaccdbdbbbbaccbdbabdaabccdbdcaacdacabccdcdcdabcadbabcccaacbbcacddbcdbbdcaabccbcbdabaccbccabbcbcdadccbacbaaaabcdccdcdbdccdacadcbcddbbcdcccdabbbcbcbbcbdcdcacbadacaddbdccdadbbccadadaacbdaaccddbddcbbadabadaadabdccccabdaacabadacdbdacacbdbcddadbabdcabaccadbacdccabdadbddcbaacdaabdcaaccccbacacaaaaaddbdcdcacbbaccadbcdcadbbdbddccbbbccbdbbbccbaccdaabbdabdcabbabbdddcaaacbdcbbddcabbcbddcacdabbcbcdcdabacdbaccaaacddcabdbdaccaabaabdaaaccdaabadabacbbbdccdadbbadbbdbbbaddbaabdcccaddcdadddbababdbbacbbdacbcaccdabcdcacacabbbbdbacdbbdddcbbbcdccccaabccdadacdcbbbddaadbadcdaddadddccdcbbacdabdcababdacbccdacdbbcdcdddabddbacbcaabaddcdabdcabacabdbdaabdbdcbddbcdcccbbdbaddbbcbdadcdcaacbaadacadabcbccacdabaabacccdacbaaacaacbabbbadddccbbbcdbbaabccdbcdbbccdcadabddcaacdadccbadcbbcaacaccdbbdabdcbacacbaacbccacbcdcacddddbacbbdcbcbdbbdbcccdcdaaabdbbadacbcdbcdcaaabbadaddaddbcabdcdccacbbacbbabdcadaacdddbaddcdddbccbacdbdbddcbbadbaddaaddbdcaaacbaaadbbcccacdcacbdbdbaaabcdabdcddabbadccbadbccabcdbcadaccabddbdcabbcbacadcddbbcaabddbaacbcaabddbacbacbaaccbaccaabdacabbcaddccdbddbbcabdddadddbdadbbbbacddadacbccababbabaaadccacdcbcbcdaacdbbabccdaacdbaabbccbacaccbbbdcdcddbccbbbabacbcadaabdbdbcaacccdccbcdaaabdcadcaabccbdbabdddbbdcadcdcddbacbabdbdabbccbcababdcbccadacddbbcadaccababbdbcbcadbdcbacbaacbbdcaccccaacbddcaabdbdbbddcbabdbacbdacbddbbbdacccdcbbbdbddaccccdcaabdcaadcdacbcbbaabdcacddbbbbcaaacaaabdbcabacaccdbddcabdddddababbacadbccadacccacccabdcddcacbbcbabdaacddbbdcabadbcbccbbcbcdccddbcbadcbdcddcbcbdbbbbabcadbbbabdbcdacbcbbbdaabdbbaccdcbabadaccbcccdacaacbdcccabdbaabbcbacacadcbbddccbaaaadbbaaabdbdcacdcbbbbbaabadbbadccbbbdcccbbbaacbaddcbbdcacbacbadbbdbdbcdbcbcdadbdbdaccabbbdcbcabbcdcaddbdcabdaddcacdcbcbaddbacbddcddacaaddadaabcacddacdacdacbbacbadbaabcbadbccdadbdadbbaddbbbcbddacdbcabadadbaaacabacddadddcacdadabcdabccaccaabadaaacbcdcccadbbabbdcaadadcaadabbdddbdcadcbcabadacccdcbdbbccadcbdadbccddacaadabdbddddbbadcbabbdddbbacbdbdadccaddbddbabcccaddbcaabacdcbbabdbaadcadcdabbcdccababbbddbadcadcbacbcbbcacabacbdbdbcbdbdbcbddcadcbabdcdbcadbdcccaccbdabcacdcbcdcdbcabcbbdcbacdcddbdbadbaabbaadbacbbbadcacadbadcccbadddabadbcaacacddaaaaaadddcbbcdddacabdcdbdddbbaccdcbdbaaccdbbacbddbdbacddbdabaaddccabdccadccadbcbaaadbbcaacccabbcaabdcacdbccbdcbbdbbbaabcbacbacadacabdaccdddbabddbcabcdbcdddcdccabbddcdbbabaacdacbcccabdcccadaccaabdacddddbabbbcdaccabbbccabbccabcddbcddddadacbdcbbdddccbbddaddabdbccadaaddddbabaddbbabdcaaccbaacbdbcbdbdcdaacbbacdadadccdbaaaabcaadaacbdabadccbccbbcdabbccbbdbbadbdcaaadcccaacbadaaacaacbabbbbbdcaadbbbbccbadcbbbbbddbccdccabdcacbabcccbddccbdcadacbaaabbbbaaadadabcbbacaacdcabbbcacaccbbcbbaadcdbcbcbadcbdcabcadcccdabacddbaaddcdbaaadbacdbbbabcbaaddacccdcbbdcbadbdabdbabbccbcbcbccbabcbbadcdaaabadcccbacbcaabacdcdaccaccdddbadcbbcabaabccccddddddcddacabacdabbcadbccaabdbabacbdaababaaddcaabdbcbbbaaadacbbcdddddbadcbbdcaddbabbabbddcccccacddbdbdbdcccabcadcbcddbbbccbabbaccaaaacaddccbbcdcccdacccdcabbdaabccbdcdbdaaabcacbbccbadaaaaacdbcadbacdcbbbddabaabbdbaabdbbaadbcacabdddbaccbdbbddddccbccabbbdaddbbbbbaaddddacbbdbbdcaadaddbbbcdaccbdbadbabadbddabdabcbcaaadacdadbddabaddcbadcbcadacabaddccbcdbacdadacdcacbbdcbddcccadddcadbdbbdcdcadacdcdbdcdcbbddcbccbcaccdabaabddabaaacbcdcbbbcbbcddaddcddcbbcadcbabddcabbcdacdccdacadbbadaaaadcacadcbdaccddddabcabdbdbaabdbaadcbcbdbbacccdacbccdcadbdcdadcbbddcdcddbbbaadacccadabcdbbcadadbdddacadbbaacbcadcbdcccdaadacddbcadacbbcadacbbddbdcdddadbcabbcaacbaddbbbaadbcddddbccabdddabaccbccdbdcabcdbcdbbcbacbccabaacccadabbcdcddbdddacddbaadbadaabacdabddbadaddbbbdacabacababbadbdbdddbbddacdbdbacdbaddcdbaccdcacbcccbdbccababbbdcdcbaacbcdccbbbdacbbacbdabbddabbddadbccbaccddbddaaaacdbbbbabbcbbabcabdbccdcabcabccdabadabbdadcabaaccbbcacbdaacbdbddcddbddddbabbcbdbccddcaddaacbbccdbcbaccaccbacbbcabdacbdbcbacadabcabadcbdadbbbbbccddaccaadcabdbbbdbdbdababadaadadddccccaabcadbbccdcccaacbacbdcddbcddbbdadbcabbcdbdcabcbccadacadbcbdadbdccddaddadcdbbcaddbabcbbcddbadcaadcbbaaaabbddcddcbaabbbbadacaadbcdaabbbbcdcadbcbdaacbccacbdcaadcdabdaadbaadccbbcadabdacddacadacacdcbdadadaaddcaaadaaccccbbcdabdbccbcdcabcabcaadadacdabaccdaccccddcaddacdaaadbddcacacdaadbbcacacccaacdaadccbdbddbcdadbcaccbbacbddbcbddcbcbbaaabbcdbdbcdcbbbbcbabbbddaccbdddaabaccccccacddacbccbaacaddbdacbacdacbdadbbbcabccbdddaabadaaaddcdbdaddccdcdcacddddbddadcbccbcbacbacaaaacdccdbadabaadccdcdbdbddcccaacabbcdbaaabcccbdcaacbcaddcdbdddbdcbddaddddcaaabadcbcbcddbccaaaddcbdcdaddababcabddbddcbbaabaaccbddddcadccdaccbaacbdbcbdcadbcdabadcbdcaaabaaadcbabdbaabcccbcccccaaaccccacaacaaddbaccccbcbcaccbdadaddbcbcabbbcccbbababddacacbbadbbbddabddabccbaacbcbccdaacbcbacbdaacbabbcdddcabaabacadbdddaccacacbabcbdbaccaccabdbabaadbddaaaaaabbbabccadcdddbbacdccaaddcdbacabcddbbaddbbaaaaabcacacacbadcccdcddaadbaabcddcdbcdaabdaddbdabcdaacbcaaddbcbbbdbccabbdbccacbaddcbddbaaadbddccdcdcddcdddcaadacdadaabcdbbaaaacbabaaaaacbdabbaaccdcdabbacdbddaabcadcacaddccdbdcdacaddaadddcacdadcdadcbccbddadacbadcacbaaadcbbbddcacdaccadbcbbcabddabbabbaadbccdadcabbabcbcdaddddbabbbaabcbcbcdddddabccbdcabcadbbdbdbcacbbacdcdaddcadaacabcdaadaacddbdcbcadccdabcbabbaaaddddabbcbbcabaccccddcbbbccaacacbcbbbdddcdbabbacaabadbcaaabddbdbbdddbcacadcdddddccaaabdadbcacccdbadbbbbcdaabccaabacccbbcbbdbbbaccdcdbacdbdabbabcadcddaccbbbdcbbcddcbcbcdacdbbaadabbddcdbccbdbcdcbabdbcabcdcbacbccdcdcadcaddddcbbacabdbcdcbcadccdabaccbdabdbbbcbdabddccbcacbccaacbbbaddcbcdccadadbcaddbdcccbddccbddbbabadabbbbbcaacbcbdcabdcabadccbdddbaaddcbacdaabcdbbcbdadcbcbcddaabdbadcacbdccdbabdcbadacccdbdcbacdababdccbcccbccdbacccdbcbcbabbbbdcbddabbdacbaddccadbddcddabbacbbbacbcddcacdacbbaadddaabaacdabacbadacacdabacbcddbbccbbbbadbaaaaabdbccbaaaacdacaabdbbabdbbdcacbbabaddadacacaadadacacbbdadcadaaddcabaacadddcdaabccabbacbcccacccdadcbddbaabcacdddcadcbbddbccadacabadaaddacacbbaccbbbcddbcadacdbccdbcdbabddadabdbbccacdcbdddacddbaadcddbcdabbddcdabbdbdcacdcdacdcdcaaadcaacdbbbcddbaccabccdbaacdcdbdabaadcaacddbcbdcadcbdccdabdbcbdddcaaccccbddcabcabacdbcbacdcbcdaaaaaabddbaacbbdccdadcbdacabcdbcbacbbbcdbcdacbabdbddaddbbdcddbddcbcaccadbaccaddacacbbdcccddaaaacccbbbcdacadcdbbcbcadbddcaddddacddcbbbaaaacbdcbabbcdcbbbdbccdcbbababcaabddbabdccabadcbbcacbdccddcbddaabcbadcaabcadabcdbbbcabdaccbaaaccbbccaaabdabaaabdabbccaadaabacbaadbdaccbbcadddcabbbcbacbaddadbaaaaacaadbcdcbdacddcdababcadbcbaacbdbbcddbdcacdcdadaabbbddcdddaadacdcabccdbaacddaaaadbabcdaaacaababbbadbabddbdbdacdabcbaccdcdddccbcccdcadbadadbaccabacdacddacccabaabbbbbdcabcdcaabcccaccdcaddcbcdabbddbcabcbddbbdbddddabdbcdbcdaacadbbbdcbddbdcdcdbcdcddcddabbaacabaccdacaddbddabddaaaabccddacaaadcddcbccccdbbdddcbbcabadcbadbabdbacdbddccaaaabddadddbaddbaadbbdaabdacbbdddbdccdbccbcaccddadacaabcbaabaadcddadcbcbabaabbcdacdbadddbadaadbcddaaababcadccdadcadabcabdcbaccadcdccacbcdcaaacbdbddaccadccdadbcdcddcccbdabdbbccdbbdcbbacdccbcacabbbdccaacbccadcbdcdcabcddabdabbcdbcbdaabbdbbbabdcdddcdcacccbccccacccbbdbccbdbadcabccdaaddbacdccbdbaacddaadcddbcabcadccdbdbbccbbccccbadadbddbccdbcdacadbdbbadcdbacdcbacadddbaccababbcbbdccddacabbbaadbcadbbbbcdcbaaabdcdbdadaaaadbcacccdbcacacbaddacabcdcccccbbbbbbdcbabdbcbdccdbbbcacddbbdcccbabdadbbacbccbbcbdbcabadbcbadbddaaaaddadaaabababcbcacbaaadbdccabbcbbdcbacccbdbabcabcdcdbbcddbbcbcbcaacdccadccbdaaacbbcabcdaadacaacabcaccbdbbdcccbdadcaaddcccbabcabcdcbaaccaaabbddccadbaccdccbbcadcbccbccbdabdcbdcdbcbccabacbddcdddccdccaddacddabacbbaacdabaabcaabbbbdccbdcbbdadddacaacaccbbdcdbccdaabbcbcbdadcdbcaacbbddbdadadcadaacdcbbabaadaacadbbbccdbdaddcaddabbdcccdbbaabbcbabbcddbaacaadccdbbacadbbadbbcdcbcaacddbbbcbbcdbcbbcdcddbcdbccbadbcbadaabbdccdcdabdaabdcababbcbacaaccccdcccabdacbcabbcdbadabbcacdddadcccbaacaaddbabacdadcdbddbadaadabdbcccdccbcaadaabcdbbdcbbcccaabbdcaadbabccdacadababbaabddbddbababbcbcaaacddabbdbcbdadaabbcbcadcbdbdacaacadacbbbbddadcaacdabadcaddbbcbbdcbaccbdbcabbbbcdddbcbaaabdadcdbcddbbcdcabddcaadcddcaadacbdbbcdbcccbdacccacdbaaccdcaddbdccadaacbbadbdcaaaddcacdbccdcdabdccdcdbcbccdcdbcabadcddbdbdccbbcbdaadacaadacaaadbaccacdbcbabbadcdbdcbdacdacbdbbbaaccddcaddddbdbcddaaccdcdbddbbbccacadbbdcccbcadaadccbacbdbdaadccbaadacccbbcdbdddadaabbcadadccacbdcbcccdcddadaddcdcdadbbbdbbabcabcddaaaabdbaccbdcbbcadacadcabddbaaaaadbcaddcdcdddcdccadbcbacdcadbcadabaadbbaddcadbabadbccddadadddcadaaabbbdabbdccbaaaabcccbbabaaaddcdbadbccdddadbadabbddcaaaadbbaabcadbbababbdddcaccbaccbbadbaacdaabccbbacdacbbaddcbbdcccadbbadbaacdcdddcdcbcddccdbcacbcdcddacacaccbbbdadbabbdcaabddddbcbdcbbdcbbcccbbddcaddbbcddcadbddccabcadcdcaacbbdcbddabbbacdbcdcddcdbacccbabbbaaaacdbaabdccdbcdadabccadcbadbaabcdaabcdbbbaadccccdccbcdbbcaddaccddcbcdbaacbaccddcaacaddacbcddbbadcbaddbadddaaaaaadbacdabdcabcbdbacacdddcdbabdccddabbddcaabaddaabcdcbddcdaddbddabccdcdbcdddccabcccbacabcaaabaaabbbcdabcadbddcaacddbbacdbddabdcbddbacadbabbdbbdbdbcadaddddcdaddaccbbcdcacabdcacbadcdbbdcbccbabcbdbdcddbdcdcddadadbdddaacabacabcdcbddbcbccbdabdbcdbddcdabcabcbcdcbcbaddddbbddacaaddcaaacadbadacadbdbbbbcbbbbbbadacbaacbcccddaaddcbbabaadaaddcdbdbbadddcbccdcabdbdbdccadcabbbacadddccaababaacddbbabbdaadbbdbadbacbdbbcbdbdbbdcbcadbbabdcdbbabbaccccbcdccdcbcabdadcdbcacacacacbbdabbbabbbcddabdbdcaddddaaaccbadacacbcdcaaaddbaaadccdaadacaabadbadbdbccdadbbdddbbacaacbbacabaccbababaccdcdbcaddcdcdddddddcbdbdadacbdcbbbccabddcddcdbcddbccacbbccbbdcdcdadccbcacddabbaccdaccabbcbbccbadacbddbbdbcccdadbbaabbddcabdddcdacccbdaaabaaccbddbabcaccbddbabcabdbbaaccdaccbdbcbabbdbdccbadcaaabbcaabcbacabcdbbaccbbbdbdaddddbdccacddaadaccddbabcaaabccdbbbbccccaacbcabcdcdbabdbacaddaacbabcccbcddbdabbadadcddccdbdadddbadadadcdbdbaadabaaaabbaccbddccdbbcddcbbaccbbabcaacddcdcaabbbbabdaccdacddacaddccdbcdbabaaaddddcdaccabadcdbbcacbcaadbcdcababaccddacbdadbbaadaabddacdccbbaaacabbdbbddaddadbdbbabbccaddcdbcbccbaabbcdcacbbbccccddaabaccacdabdabccadcccdddcadbccbbdbbbadcddbcdaacbbdbccdbddcacabbdccacdcdacdccbbdbbacadabddcccaacadccdbcbbcdbadbabdcaaaabcdcdbcbdcabddbbcdccbcccadcccbaadcbcdacddbcabaaccadbbacbbacacaadabacddaccbdbaadbabcbaadbbdaacbcadabaaccbadbdddaaacadbcbddcacaccdbdbcbaabadbcbabbdacdadabbaddbcbdbdcdabbcacdadaaaccadcabaabadbcbabadbdcdddcabcabacaaaabaabcadacbdbccbaabbbddbacdbdaaaabdadadcbdbdaababbdabbdaaabdccdadacccaacccdbdcccddcddaccaccddccdcccddabcbdddaddcbbcdccaccdbbbaabcaddddcaadbdddadbbacacddcaadbacbbacdcbaccdbadcaacbddcbdcadadbadcddbcdacddaadabbbbdbabddddabadabbcacdbbbdaccbcdcadbbdabbcaaaaccaadaddabddddbcdccbbacbdcabcdadddcbcacaabdbaaadccbcddbacaacabbdbbbddabcdbaaaaacdaddddbdcaddaddbabaaabcacadabbdbdbbddcdbcbcbbabcdaaaaacaaddacabbdbdaccbcbdcbadccadcabdbddbdadacdadcbccacacdbccacccdabddbcdcdaaddaccacbdbadbcccddcdddcacccbdaddcbbdacddbbddbbcacdcddbcddbdaddccadbadccdcbdbccadbcacdcbbdbcacbacbcdaadcdcaadacdadabbabaddadaadababcdadbbcacbccbbdcdacddcccbabbcabcacccadcbaaccaacbabdbabdbbbbacacbadddabdaaaaabacaccacbccbcbcbddccdcaccdbdbbaccbbbcbcbddbbcdbacbcbcbacdbadbdbdddcddbdcbbabdacdbabbcdddbccddbbdcabbcdaabacaaacbbacddcbbcdbcbaccbbcbdddbbbabdcacbacaaddddbbdbdaadadaddadcadbbabbdabbcddabdcdbbabbadadbdbbbcbcacdbcadacdbdbdacbbccdadbccdaacbbbabcadddcccdbcaabacbadddbacdcdbcaccacabbcdccaaabdddaaaabccdbbddcccbdcbabcbabacdcdbbdccdbbcacbbbcbacbbbdccbaddcaaddbcdcddddbaabdbbddbdaacccadcaddbbcbdccacccaccddcdccaccabddaddbccbbadaddcbdbbcadbdabcaddadcbaacabcdadccabdabaddcdbbdcccccbccaaddcaadaccacdacadbdcdcccadbcaacdccdcbddadbcadbcabadcbaadbbacbbbdadddacaababccaccabbbaaacadbcadcdacadbbaccadcadccdcccdadadbcababacabbaabdbddcdcbdcadccdbcddcbbdacccbbcacaaacadcbdaaddabdacbabddbcbbdabcbdcabccddbabdadacdabdbbcbabcadbaaadcddcdcdbcdbacbccccbcbbabddcaccbbcccdacadcbcadbdcbcbdabaacdbbabdbbbcdcccbcacdbbacccccbbdbdcccdabaccdcdbbbdaccdcadabccdbadadbcdddcbcdaaabcaadcbabdddaccbdcabbaaababdcbcbdaccbadabcdabdaacbcccacabcddcbbadbadddddcdcdcdabaabcdabddbaaadbadbdcbddcadddbaaacadcadbbbcbabacadddbbcaacaddcacddcabccacdbaacdaabbbdbadbcdacbbbcbacbdcacccbabaccdbdcacabbaccdccacacbcdbccbaaccbcdbcaccbcacdbbcdbabdbdccbabcdadcbbcdbadbaddbabcacccbbaabaddadaadcddbadabbdccdbbabbccdabbbddcdbcdaabdcbccbacddbccadbddaabcaabbddbdcbddbabbbcccccdabddbacccbdbbbbacacdabaccbcbcdbddbddaddaddccabccdadbcccbaaccaaadbcaacacacccdadbdbccbcabcdbbacdbadbadbbadcdcdbadcbcbbddbabdbdacaddaaccbabccadccadacbcadccdacabdcbabcdaabaadcccabdcdadabbdccdbdbcacaaacdbcbdbbcddbabdbadbccddcbcdddbcbbccaccacdcababaccadddaaacadabacdcdaaddaddccccdbdddcbdbdacdbabaadbadadddaabbbccabaacdcaaabbbdccdcddabaadcdcbdddcabbcabbacdccbbadbaadccbbdbbbaadcabadbbcbddbacbbbbaabbabcdbbabdcaadbddddbacbacbbdcabdabbdcaacddccdadacaddacbbdbdcabbddbcbacaddadcdddabbdaacaabcbacaddbcabddcbdcbccdcdbcaadcbabdcbcdcabbcdabbadccaaccacabcdadbadbdacdaadbddddddccdbadabdaccdcbbbaaaccbccdadccccdbccaababbddaaaccdcdaccacabccdbbdadabacabddaabddabdaddaabbbdddbdcccddddbccbdccccdabddbbaadddcadbbadcdbadcdbcabbadbbbadaddadacadaaddaadbacadabbabbdacababbabdacaababcdaadbbcabdbcccbcaabbabbdaadaddaacbaadbddcaccbacacbcabdcacaccaccdbcaaddcdcaaabcadcbbaccdacbcabbbbccdddbbdcdddcbcdaadcccbcdddaabbacddcdbddadadddddbabbddbbdcccadacbdaaacbbddadaaaabbdddbbccdadcadccbcaabcbcaddabcdddadabcadbaccddabcdbcddabbdaabcdadcbacbcbcdbcacbbacbcdcbbcbdbbacadbdabcaacbbbccadabddbcbccbbcbacdbcdacacbcbddccdbaabbddbdddaddacbbdccccacccbbcddaacccdbccccbabbbcadbadacadbdbdaddcddcbddccccbcbbadbaabcbdccbdadcacdacbddcdbddbacdaabccaaddcdcbbdbcabcdabccbbcadccadbabadbcadcdccacbcdbacddacccdbaacbdaacbdadbbcdbdbcbabdcacdabacadaaddcacbcbadcdbcbbddabadabcccabaddaccdcdbbadbdcbcdcacbdacabdddbdcdacbbbcdcaaacbadbddcadcacbbdbdbbabdbdcddddbdbbbcbaccbadabbacbaabbcbbbddaddcdacbbcaaaddcccddadbcabcbbbcbbbbaaaadbbbcbcdcccaabacabadaddcaddaaabbdbacdccababbadbabbdcdbcbbbcbdbacaaaadbabbdddcbdddbbaabdacbbacccdbbbbcddadbcbbdcdbbdbbdbcdccbdbbdccbbbcccbcbccbdcddbbabaacddbcbdabdbdcdbaabddbbccdbbbcbdbbbdbccabdacbcddacddabdcbbabbccbccbbbdaabbcdccbadddaadbaabacaadacaabbacadbdaadcdadccbacbddabcadbdbacccacadaccaccddbddaacabcacccbddbaabdbbbbcbccdaaacabdaabbcbaddcbaaaccbdddbbcacbacadbbbaadaadccddbdacbabbcccbbadddbcababcdcabbcbdaacdcdacccdabadcaacabacddcadbabccadadbdadcbcbabaddbbcacdcdccddbdcbaadbccbbcbdaccadcccbddbadddccdddbcdccaaaaabbdbbaacaadabacaadaadadbacadaccbacbbdccabbddcbbcbbbddbdbbbddccdadcaaabcaccadadcdddbdabcdbcabbbabcaabacbcdabbddadcabdabdbaacddacadadcaaadaadaddbbdcbaccddaaabbddaabdadadcacbbacbcdbabbaacbaabaaabbbbcddccacddaaabbacccdbcdbdcbdccbbadbbbaaaabaaaadbdcdbbdccdadddbdbaccdddacababcdddaadcbcccbadbbccadadbacdbdbcaddaaccddacabacbcbaaadcaadddaddbdbddcaadcccdcdbbcdcbcabdcccbaddddbbdbcacccdadbabadccaaaabdadaddcbcdaddbadbbbbbbbaabdaabdcdbabbcdacccdcdccdcbaacdcabbbacabcbabdabaddccdcdcadacbccaaaadadaabdbdbaddccabcabbbcaaaaaadaabcadccbbcdbcddbdaabadcadbcdcdbccaddaddadccdaabcdadbcdcddaacadbacdcaddddaacbacbaaaadaacaabcabadccbdcbcbdcbdacaddbdcbaabcadadcabbcabcdbcbbdadddacdadacddcbdabdbdddbbbbdadddadadadcdadddabbdcabdcdaddabbcddacabcdbaacccdbddbcabccccbbacbacabbdbcbcbccbbcadabbbcdabaddcbabcacccaddbddccdadcbdadcdbdccccbcdbdddabdcabcabbddccadaaaabddcbdbabcacadbadbadddcadcccccdaabdbbaddbacdcddadadbbbcaadddbaccbbaababdabbcbdbddacbbdbaadbadacbccdbbdabdcbddbcddadadccaadaccbbaaddcbbbddccbbaddacadbbdbabaaabddcdcabcbcccdbdcdcbbbdacbadcabdaaadacddcddacccbadcbdbcdadcbbdbdaddacdbbbabbdbdcaddaddccabccdccacbdaacacccdbbaacabbdbdbacadbddaccddcabdbdcddcccccadbaddcbddbdaacdccbcbdabcabbcbcbbcbacbcccdccabcdaabddaddcdcbdbccacdacdaddcdbddcdacbcddcaabddbbbdbbaccbabdccccbcddbbbadacdccbbddabcdbddccddcbdcdddbbdbbdcccccdddbdcbbdabcddddbdbccbabcdcbcddcaadddcbbcdaaadcdbcbdbcabbbabbbcbdcaacababbaabbacaadbbcbdcdbdbcbbdccdcbaddadacdccdbbbbbcccbadcacbdcdccdadbbadaadcaccdcbbddaacbdcaabadcacbbbdbddabcdbbcdbcdbabdbbcbacccacddcdcacddbdababbdcdbcdcddbaaccbcbdcccbcadddbcdcdbaadbaaabdadbbcacdbbccaadccdbdbccbbadccdbabcbcadcacddbabcdacdbcaddadbcbbcdbcbcaaaababbcccadbcdbdadacdaaadaddccbacbbaabcdcaddccbadbbaadbcdabcccccacbdcdacbcacdcaaaabcbcaabbccbbcadadadbccddcdacbbcccbababcbadbcbbadadbcccbcbcababaacadbcdbacbdccdaabbcaccbcdbddbcbabdadacdcccadacadbdbcccccaddcbbabaabdababcaddadccabcbcabddaaddcababdbcdddcdaadacddaccadabcabbccbbaaccdbbcaadbcabbcccaadbadcdbbccacdadcbcdcbacbaacacdaadcddadabaccdbbbcdcabaadaddddadaaadabdbacbdddddbbcdcdbbbbadcbabbcadaacbbcddbbbbaacbdccccdadadabccdbcaaacbdcaabbcdcdaacccacccabccacdbbcbcbdbcaadaacabccdbbcacbcaabcdcbacdababaddcdaacbcaaadcbbdbcacbccabddcdadcacbacdbddddadacddbdaccbaccdabddbaaddbdabddcaaccaadbdcdaddbcabdabdbdcdbaadbbdcbbacdbbbacbddbadbdbbbdabcbcccaabdadddcacadaabbdcbcbbbabdcdacbcbbccacabacaaabadabcabadcccaacadaacacccadcdaacbcdaaddcbdbbcdbbdbcbbccccdddabdadcbbcaccddacbcbbbbddbcccdabdbbaddaacaadcacbdadccabcdadbadadabacabdaccdbcdbddcdaadbcdcacbdbcdbabadcdbbdbbdddadabaabcccbacabdbcdcbdcbaccccdbdabcbdcbdbacddbbccdacbcdabaadbaacbdabbcadbabccabcbdbcaadbccbdaccdadccadcdaddcccdacbbcdadabbcacbbcbacccbdbcbbcbaacabdbbbcdaaabadcbdccbcddbbdcabccbacddcbadaacbcaaaccaabcbdaabddcacccaabbdcdbdcdaabaadcbbbadcabbcdccdbbabddadadcbbcbdcccdabdadbadaacccadddcaaccbadddccabdccddaabdbbbacdbccbbbadacaacdabbaddaadcccbdcddaadcccbbcbbcdcdaabdcdaccaadcccbbdcaaccccadccaabbdaaabbaacbaacddadaacddaccbaadcbdcaabddcbabbcdaaaddaccbbdcadcdaccbaaaababbcabdadbcaabccdbcccbdacbcabbacdabcdaaaabacdaabaadabccdbadbacbbbbddccbbdcbaadaccdaaaccacbadbaaadbcccbbdbacbdcacacacadbdabbcacdcdcadbcbbadbbbbdccaccdcdcacccbadabcaacdccbbadbbdcdbdbcbabdbdcddbabdaaccaacaccccddbcbbbcadcbdcccacddddccbbaaabbdcbbacacacbbabacdbbaabcaccacadabcabdadcacdbddcabaaaaccbcddbaaaaacaabacbabcdadcbdbdadbabadcbcccbddbddddaaacbbaacccddccdbcdbbaccabcdbacadcacbcbbacdbbdbccdcbdcbdabdacccaadbcaacadbdaabdbbdbcabcaccdbddbdaddddbaccaddacacbbddbbbcaabdaddcaaabababcdccacacddababdadcabdaaabccaacbcdabdcbbdcdaaabbbdccddcbcdabbbcdcabddccacccdbacddccbbddbdbaaccbbdabdbbcccdbabcacbbbadaaadbdaaacbbdcdcddcaadddabbaaacaacccbbdbdacadbcbaacddccdddbcbcbcddbccdcadbbaddacbabdadaadbcccccbbadcbdabbbccdcbcbdcdccdaddbcbdaddababdadbdabbaddaddbbbaddbaadacadcabcbddbcaddbbdabbdcbdbcbbbbabacbbbccdacaabdbaccacbdcbddacdbaddcbcabcbdaddabaacdddabddcdadbddcadaacbddccbcadddbacddabddabcbcbdcbbbbbccbcaabbabbadbcacdbaaacadbdbcbaacdcdcddadcacbbbdbaacbbadbbdacdcbbbcbddccacaacdcbdadacaabaacbababbbdcccccbaabdaadbaadcabaabddbabcdbcbcdaddddbdacaacabcadccabaadccadddabbcbcadcacbcbadababbddbcdaaddadacdbdbddacbbdcccccacaacbcacabdcacccaccbccbbabaacddddadcadcbddbcabdddcacccccbbaacbaaaadcbddbbaadbbaadacddcabaddbdaccccccbcabddccbabadcbcddadddbddbaadaadccdadbcbccbacbbcbdccadacbacabadbcdbddcbdacbabbaabdbdbadbdcbaccbbcdbabadaaababdcadccdcccbabddcddccdbcabcabcabcccbcacddbaddcabbdbdacaddccaccbcbdadcaaaacbadcaaaddadddcddcbcdccadcbabadbccbaccdbbbcdcbabdadabdbdddcdcdcdacaddaacbbdcacbddacbcbaaccaccbbadadcccaccdcdbcadbbbbadbdbddcddbcadbccbcddbaadacccdabcadaddcadddcccadccbdcbbccaaddacbcaddbcddcdbabdcdccdbccbcababddccaadddbbccdaacbaadddbccdcadacadcccacbaaabdbdbcbabcdcaadbdabddcaabaaadbdcbddbabaadcbbcdcbdaddaaccccccbabadbdbdaacddbacacadcddadbdaddbcdaabddabdccbbaccdacadbbabbbaaaaaadbabbbdabaabccbacdaabbbaaddbacaddbddcdbbbdccadaadbdcccabdbdcabccdcdcabacacccbcdadaabbaaabacaddcaadbaddbbbadcddabdaccddaaaccbcdcaaaabddcaccacbaccdccbccdbcdcdcaaabdcccaabbbcacddcddbbaabdcdabdbabdddcaccbaaaacaaaadccdabdccbcdbbddcabdccbacadabbdccdacaccadabdbdaccdcabbadbdcbbaccccaacdbabbcaddcadddcbdabaddddcdbdacbcaccddaddcaaaadacabbadddccbcbdcdbcabbaddaacdacdccbaaadbbbdbdbcaabbddbdcaaacbbbdaadbaadaabcdbabccbabcbbccabbdbcaabbcddbccccabbddaccbdaacbdbbdcdacbbbabbbbcddbccaabccadbbddccccddbbbbaacddaabacabcbddadbdbabbbcaadcbdddcadbdbddabcddcaaddcabaaabdbadbcabbabcaabbbdbdcbcccabcabdcaddbbcaaaacacddcbdbcbddcdaddbbcbaddddbcadbcabccbddaadcacdbacaddcbbbddabacbdddbbdcdcacdcbdcbdcbbacccaadddbbbadabbccaabcdddbccdbdbcabacccacabcbcdacdabadaaadccbdabbbbabaaaccdaacdacabdcabdacdaadddaadaacccabaacbcadcdadbabbcdcdaccdabacbacabdbacbaddcbbcaadbacbaccbacbdaaddcaabbcbbcbadcbadcdcdbccbcddbcbadaaccabddaadacaabacababbcdbcbdaadbabdcddcabbbcdaaccdbbbadcccacddabccdcbabbccddddaccbbcaadccadddacbbcdddaacbcadaababcaaadcbadacbddbaaadbcabbbacccadaabbacdddccbddccccdcddabddbcbaaaababbcdabccbccaacabcabbadbdacbdbdbddcaabbcccdcacbdbddbadaacccacdbdabcabccdadcadcabddcbdcbbcdcbddccccbdccbbbdccccdddbbcaaddaddcbadbdacdddaddabdabbdbdaabdacbcddadabaabddacbdcddccbdbdbacdddbdcabacbddcadcbbaaaabbcdccadbadbddabaababbbbbbdacdbcbbcccaadbbdddccddcbbdccdddbcbaacbccdaaabbbbadaaccaddccdabcbabcbccaadaaacdaddbacddddaaaabacadcddcdacbcaccddacbbbbabcdaddbadaccabbabdacdcbbbbabdbbaaccdadcbaaadbacbcbbcdbdacbcddddcdbbcadaaabdcdabdbbbaccbbbaccbccbadbdcbdadccddcbbddccbcddccddaaccbbbdddadbdcbacccabdbdcbcdcbddccbbcccbcbcdcddcdacacccbccbdacdcacccbbadddcadadbbabbcccddddcadcbadcbaaddbdaadbaabddaccbcdccccbbcadabddbabddaccbdabcacbdacddcaddaccdddacdacabcbdbcdbbbdcacdbdcdabbddadddacdbdbaddddccccacaccdbcccdbcbbacabcdadccacaaacddadcdddcdaaccbcbdabaabdbdbdbacbabdbbbabbdddddcccaddbdadddaaadbcbaabbabdcdccabbcabcbddbcbdcababbdbaccadaabcddaccdbcdccbbcdcaddbcdabdccadcbabcdbbddbadbddadabbdcbaddcbdadabbabdaabdbacccbaaaabbacddaabbaabaabbddbbbacbbdabcdcacabcadbdbbadaaccbbabbbaacbcacbddcadcbcdbcccdbadcccdddcdadcbabccbcabddccccbbcdddbacbdabadcccaabacbcdabddcdbbbacbbdccabdccdcabacccdcacbcdcbabdcccadcccbbacdacaddaabddbcbcbdbcdbcbacdbddbaadcccbdcadbabdbacbcbbacdcbabaccdbdbddcabaadcbbbbbcacbadabcdbdbdadadbdcbdcaccdbddbbcddbbcacbdbcddcddbbccbdbadbbcadddacbabccbcbadcdacadadcbadcdaccbabddabdddadcabcbbbcbabddbacabaaddcaadbbbaccddbcbcabcbdabcdacdcddadcbcbccdbabddddcadbcadacabacaddccadabcbdbdcadbcbccccacdbaaacabdbccbccaababbdacaaaacaabcccdbccbcabbaacdcaaabccbdcadaaacdadcabbcbaacbccabbadcaabdddddacbaccbaaddaddbcabaddbbcbaadccbcddabacdadcadbccbbbddcddcccdcacaaadabcdcbacdabcccaadaacdcdbdbaccdaaaadacaacdcbcddbdbbaacadcbdbabcadbacbdbbddbacabccadccbabccaacdabbaabcbcdcabbcbbbadadbcbaaabdadbbcbacadbbddacadcbdcbcadddcadcdddcabdadacdbccbccddcdadcacbcbdbbbbbabdbadcdcbbdddbaacdcaaacbcaabbbccbdcaccbcbdcddbdbabadabaadbddbbdddbadbdbbbdadacaadacdbbbddccadbabacdbbcbdacaaabaadcababababdbbdcbcbccadbadcadadaaabdbcdabadadbaddccbbbbdacdcabaddbbcccdbbabaddacccadbacdadcccdcbcbdabaccadccbddbccddbabdbdbcaaddaaaadcadacddcabbcbcaaadcdacaaaacbdbaddaddaddaabcbcacabbdcdccdddbaaddabcababdbcadbbdaccdccacabacdccabddaabbdaadbdbbbbddbaadabbaacbacbacccbccdddcbbdcabadcddccabdcbcbddcdcbbcabaddccbdcbaabdbabbcdbacacabbccdcdcdababddbbccdbaabbdbbccbaadaddcddcdbaacaddadacdcadbadaacbacbbaabcdbbaddaabbadcbbbdbabcccacaccacdccaabdadcbdbaaadaddacacdbaddcddbbbdacdbbbdcdccacdccaacaacdcbbdccaabaccbcbcdbabdccccabcacaabbccdbacbddadabbdccdcdbdabadbcbaacbdacbdacbbbdaddbadacadbcaaaabcbdcaaabddcdadaadcdabdbacdabccdbcdbaccabaaadcbdccccbcabbbcabbaaabcbbadcdbabddaaabbcbaabcdbbbcdacdcbaccabbacbdbdaaacbabddbadbaadbccdadaacacdddacdbcdbdaadcdcbcdadbbacbacbbdbdadabacddadbbaabdbcdacccbbcbcdbcabadcccdbdadbaaaddcadacdbcdcdadbcbabccadbaaddbdabdcdaadbacabbccacccddccddadbbdbababdacaaaaadbdacbcbdcbdcdbbdddbdadaddababcadbbcbdbbccabadbabbdcdcdbaacaabbcdabcdadaadadabbbadbaadcabcabbdacacdcbdddadabacbdddaaabcccaadcdacababdcaacdabbbacccdbbddbcdccdbdcbbbcddbcacdadddccddbbddcddaadcbcbbcdcdabaaadbcaababbcaaadccdababdaccdbaacccadabccbabaaddbbbdbdddcdacdbdbdabdcabbdddadabcbdcacbcbbadcaaaadbababbddaacbaaadccaaadbcdccabdbbadacadbcbdcdbabcbbdcaaacaaddadcacadccbdbdcdbadbcbbadcabddaabbbbadacbdcaddabcadabcaaabbcccddbbbdaddbaaccddddabcddaadccdcdcadbdaaabbcbcbbacdaacadddbddbdadcbddabcdacbbaacbbabccadcccddaadddaacaaacaccaacbaddcabbbbccaddcbbadcdbdbddbbbbddaddabaacdbbcaadbaddadcaabdddadcacacdccbaaddbacbddcddcbacbccccacddcaccbadbcbbccaabbabaabddaadabddaabddacaadadabcadabadddadabcddccadabbcddaaaddddbdcadddcacacbddccacabbbdacdbbabcdcbabaaddcbbadccbaabacdcadddbbcabaabbcaddadbcdcadcadcbbabbbcdcacabbdbcaacddcdddbcaaaaddddcddcdacaaaadddbaadcbdadcbcdadcadddabddcbabdabdaccadbcbdababccccdbaccabadbcdcccbadbdcbbdddcbaddaadabcdbbbbdadaabdacccacadcacaadbabaacbccaaaccbdaaccabcbcdccabcbbcbabbcbbbcddbcbcccaabaabdbbbbcabcddabbbabacccbdacaaabdcbaadabbbdddcbddcddbbcaaccdbddaccacaaddccadbdaaddbdcbbbadcbdbbbbadcabddbdccccbcabbddddbacacdbadbbadacabbaabcbaddcacdbdbbdbbcbdcdcccadcababdcdadcaddbdbccbabcbabdaddbdaabaddcbcbddacbbbdcacbbbbdadbcdbddcbdaabbabdcddbbcbbbababaddbadccbadaaaccdccbbbdcbaccbacbcadacadcdcdacdaaabdcbcabbacdabaaaddbbabccabcccaabaddbacbabaabcbdbbbcdcbbbdabbacadcdcdbcbdaabcbcccdaaacdacdbcbcccdbcaacbbccdcbacabdacdbcadbbddcdbdaccbadcaabbccdbdadacbdddccbdbdccdbcdbbabaabdcddbbbcadadaccbaaadcabbbbabccdbbcadcbadbaabbccaaccbcbdddacacdabddbbdbdbbddcdbdaddbaabddbbabcabaaddacacdbbacccaaaaabdacadabcabbccadbbccdabadaccaaacdcabdbabdcbabcbaadcdadacaadaaadbbbdcbdccbadabbbaddadddbbbbdddbdacddbcbdccbdabdadacaadcbabaaaccdcaaabaadabababbdcbcadddabaacbadbdbbdcbaacdadddcbcdabccbbcaacaadbdbbdbccbbcbdbdacadccbdbcccbcbcaadaccadbbdacaddddababbcdbcdbdccccbbdcdbcadbcbdbdddaaddcdbccdbdabacbcaccbacccbddacdcacadacccacacacacbdbadcabcddaadbbaccadcadaabadbaaccdabababddddcbbbcbabdadbbabcdacddabcaaacaccadacdacccbbabcdcbadbdbbdaaacdcbdadcabadcbdbcddcddaadcaacacbcdcadcaaabbbadcadacbbbaababdbdababadbcdadaadadddcbdcaadbdbbddccccacacccdacdadbbcaccdbcaadbdbcaabdaabbcccdbddbddcadbadcabadbcbbbddabbaaaddcdbcdddbaadadcbabbdbacbbabaabbbdcdcacdaaabcbacbbddabcbadcaddcbdadadbdddabccadaabdacacdcdbddcdabbaabaaaaabaaabdadbdcacadcddcbcabdbaddcadbaaacbbcadcdcaabddbccbbcdadabaabbcacbccccaccabbbbbdbdbbdccacdcabcbbdbddcabbabcbddacbadbddbdaacbaddaacacacddadaadcdbbabdccbdabdaddcdcbaabdcabdadbdddddadbaacdbbcbcaaddbbdbdcdadccccacbacbbdccabbdcdddcbaabdbdbdbbdbcadbdcbbdacdaaadcbdcdabbdadabbbdcaabaccdbccdaddcadcdbadbaadabaabaadbbcbddbaccdbdacacccdcdaaadcdcbcbdadcaaccbaaacabdadcdcccabbbaadadcbdadaacadcbcaadacbcaddcdcacbcddcdcccdcacaaabcbacbcabcbcabdacacdbacccabdddabdcaaacdbaaddcbaadbcccbdcdacbaacbdbcbacccdabdaddddaabddcadddbbbddbaccabacdbdcabaabddadbdcbdbbbdbbbdabccaadbaddccccacdcddbbacadddbbcbadccdbbcaadbcddddbacdbbacacadadcbccabbadcabaadbcbacadcbdccacacaacddbddbbaabababbccbacbbcdaaccbbabbcaacdaccdbcddccacbbddaadaccaabbdcacdbdaddabccdcbccadcadbdcbbdabbbdacadccdbdcdddcdbccadcdadbcddccbbdbdaaadabcaddbbbcdbadaabbacbbcaddbcbbaacbcbcdacdcbbdabccddabdadcccdacacabacccaccdadcddbbcdccacabddcaacbbccabdddddbadddccddcbbbabdabbddccccbcdababccabcdbcbbddabdcbccaadcdbdbbdcdbcaccadadabcaddcadadbddcabdabaaccacaccbcbddbacbbcaaacdaccaccbbdaabdcdaccdddaaddcadcaabaadbaabacdaabcbddbdaadbbbdaaadaacccdadbacadcdacadbddadccdaddbcbcdbacbcddddcabccccdaaccdbacadbcbabcbcabdcbbddaccdaadbddcbddcdacadadbacccbdbcbbdcadccbdddacccdaacaaadbccdacaddcacabbcacbbcddcdcabcbbbadabbabbacbdcdabcbdbadacbcacdcbdbaddbaccbcbcbbcaacdbbdbbbbddbbbadcadddaadbabbaccddbdbaccbdddccbccccabdbbcdababcbccacbcdbdbcaadcbbdbbdadaabcabdccbbcdbabacdcbdaccabcbbcabcdabdddadabaccdbabbdbdaaaccdaaccdccbccdcbbabcdadabcdbaadaaabcbacdabdcbadaadcdddcdbacbaadddadcaabcadacbdbbcadbbaccabdbbaaaacaaacdbccbcbddbcdddbbdacadacadacaadabdbcdabbacaadddbbccbbacddadbbcacdddddabacadabcbcbaacbcbddccddcddcabccbaabcbdbccccdcdbcbcadabaccdbabbdcdabdbbadcaaacddcdbcbccbacdbdcbbabbddcbcadbbacbaaaabaabcdcaddaadcdaccddbcbbdacabdadcccddbabcbbdabdabccccddaddbdccdaddadbababbacbbaacbcdccaadbaddacaacabadaabcdaacbabccdbcddaacabdbadcccdbccacabbdcbabddcddabdcddabacbdcbbddadcbbaccdbdadaaaadddabaaddbbddcabacbbbacdaadbcdddaabcddddadbcbcccdcbccbdabadbccbbdadbbcbddbadaabdcdaccabddacdbbbcbabdbdbcadacbccbbcdbabccabadbcdbcddbcddcabbbcbcdcbacacacdbcdcacdddbaaccdcdbbcccdbccabbacbdbcbcbdabcbbdcaacdddabbcdcdbacdcaaddacaccadacaabcbdcdacacabbbcaacbddccbabdbcdacbdbbccdbcbcddbbaabacaadccdbdccacacaadcacbabdbbdddbdbddbaaabdcacabdbccdbccaccadbddababcddcbaabbdcbabdaabcadddcbacaacdcbdddabbdabcbcdbbababdcbadbdccadaccaaaabbbaaabaacabdbcaaabdbbabdaddacaddcdcbdbcacdbcbacbddabbdcdbdccdadddccbbbbbdabacbbccbddabbdcbacabaacbcdbcdcbdddcbbcddaddcbdaccacdbabdbcbbdcddddacaadcaaabdacbccadbbdbaddcdccaadbddccdbabbbccababaddaacbcdbaaacdddcdcdbcccaabcaddbdadaaabcbddbbdcabcbacadbbcaccbcbbdbdcddbbaacadacadccdddaadddddacbbacccaccddbaadbaddcbccaaaccbdadbcabbbdddacabdbddbbddbaabadcdcbadacdbaadbaddbcdbdbbbacdadabcbbacacabcbdcbacbbbacbdacaacdbbdadacdbbbcdcadacdbdcaabdacddcbabdccdbbaccaccaacadacdcbdcadcdbabdacdbcaacaaaddcdddaadbbbddcdddcddbcabcabcbabaabdbdcccaaadabaadadbadacdabbabaacddbccddadabcdbadcbccbbaddbdddacddcabbccbcdddbbdbddaddcadcccbcbdadcbbccdbbdcbcbdccacaddbccdbddcabcabccdbaaabdbaacacdddbcabaaaddabbdccadcdcdcbbdbadadabdadbccddacbbaacabdbacbdcbbdbaaacbdbadccdbbdccabbddcacdbbdcabcbbdaccccdacdbcdbbabddbaabbbcdbbdcbabadcbcbbbadcdacbaccdaabbbcacdacccdaccddcbbadbbaabccaacaacdcddbdddccabcdabcaabbababcacadcbbcbcccbcabcbaaacdbccdaacbccccccbdcacdbdcacdccaabdbddacbbabbabbaaabacbabddaabcbabbdbcdbcababacbdbdcccdccdbcabdbbaabbddccbacacbdaaacbddbbbbbddacdbaabcdabcdaddacacbbdbcabbabddcdccbbdcbacacaaadccccccddbadddadacbdddcdcccbbcaabdbbbbbcaabcdddababdaccaccdbdbdadbbdadbabcbaddcbbdbbbbdcdaabcbbabadddacabcabdccabdbacacbaabacaaddbbddcacbcdcbaaabccaaacacdabbacadbdbaadabaccdcacccadadcdbdaddadacacbbbdbdadcbdabdbaaadcbbbcdddbadabbcadadccdcbcbadbadaabbbbbbdcacccabbbcccacbbbabdbacddbbdaddbcbdbbdccdbcbabddacddccbcbcddddabaabdbabbdbccabddacbdbacbdddabbabbadaaacacdacdbcdaaaabdbcdbcbccdddbbdbbdcdcdddacaabbadacbcadaacbabbbdcdbdbbdddadddcabcdabdbdbbaddbccdccbaabbcddbacbddbabbdacaddbabbbdbbadbadcbaaddbcabadccaccadcdccacdbbabcbbbabdddbbbddcdcdbcdabddacbcdadddbaccdddccddabccdaaddcdacacbbccbaaaabcadacbdadbccaccdbbbccddbddabddbdbccbaddbddbdbddbacdacaabbdcabcaaabdcadacbacdcbbbcdababcbacbcdaacdbdcbbdadaacbdaacbcadccaddadcbcbdcadcbbaadddacbbaccaaddcdaabdadbdddddcacbbaccaaaccbddacdbacadddbaacaccddacddcdddcdaddddbbdbaddcdaaacacddcbdcbdabbbbddabadacbdbdbcdaaddbabacbdbadacadcbbcdbcdadcabdacadbaabcbdcccdbdddbdbadbddcadadcacbbcbcbdcabbbbbcdddccdbdabddadadccbdcbacbbcbabccdcbcbcdcdcacbabdacdcbdddddabcccdaabacdadaccaaaacccdaddadbababbbbacaadcbadcdcddcbdbbcbbabccdbaabbdbcdbddddabdcbbcacacdbdbcabaaaacdaadcabcddbdaccabcaccdcdbabcccdddcbcaaaacacbcaaabcbbbdbacccdaddaabdbdcbbdcadccddaadadbcbbaabbbbcdbaadaabcbbadbbbabcdccbcbacbbcbaacbadcccabbbdbadacabaccadacdabbbabaaccccbccbbbcbccbcdbadbddccdbaaadbcddbcbdccaccadcaaccbabdabcdcbbddaacbabaabcdacacbaaaabcdccaabdacbacdbaaaddccabcbaacabacdccaadcbcbbdabbbcdbcbbaabdadddbdbbdbaacddabdddcdaabaaabcccdadbacdabddaaacbdadddccdbacabcdcacacadcbabdccddcbbdcbdacbdadbdadabaddbddadddbbdbdddddccdbcdbcacbbadbbbcadbdbbbcaabbdbaadcadcacabbcabdacaaaadddabddcbdddbddacdbcbbddbacbdbacbbdacacaacacbdbccadaccdbcdaaadcccbcccdcabddaabbddbddcbcbcccccdcabacddaccccdbdcabbccbbdbddbcadcdacbcbbdccaccbcbdbdccdbaddcbaacacdcdddccbcacdadbcadcaadcddbbadddcadccbabcaddacbaadbaacdccbbbddbdbdccdbabcddcadabcbdbcbaacdacdcbbabdaccadbcbbbdbcbcacbcccccadccbabadcdadaacbbcbddbadaaaddaaacbcbdcccadddccdbacdbcbcbbdbabcdabadbcdbbbccbddbbdadcdaabdbccaccbbbaaccbddbccbadbcdbcbbbacaaccbccacacaaabadaadbcaccbaacccdacddccacddbbaacaadcccaccddadcdaadaddccdadddaaccdbacdccdbcababdcdccacaabbbcbdabbcbbdaccacddbaaccccddadcabdbacadccdbbacdbcbcdabccaaccadabdabddacacbabdbbbaddcaaabbcccbcdaaccdcdbcbcbcbcbacacbacdbbccaababcdaccbbbddccaccabbdccabacdbadbccdadcdbddcaadacaacddbcdbbaaacbcadcaddcbcbccdaccbcbacadccbbabbcadcdcdbcdaabcdcbcdbaadddbadccdcaccbdaccabbcaddccbbcbaccbbcbdbadcdbdacabbdccabdccbbcddcbdcccbbadcdcdbcbdbbcadaabaaccaabbacdcdcadccacbbadcaaadbbcccbccbaddddaacdbabcccabccaabcbcdabbbbbbbaaadcbacacdabcddcddcaddcacacdbddbddcccddadccdbabdbccbccacaddadbcadabdadcbdddbddaddddcbdadadddadbaaddcbbdcdbccbcabbbcaccccabbcbcdbcadbaadcbacaacbcdccabcaadbbbacbbadabcaddacbaaaabbbadbbabdcddbcbbbbdbaccadbacbcbcddaacddacacddcbcdcdababdbbcbbccdccbdcbbdadbcdbaadcdadabbbcbdddcbbabddddcdaaaabccacdbdcadcccdbaaacdbbabbacdbddbdddddcdaccacbcabbaddbdbabaadaddbcabbacdbbcbbbbaddacbdbaaadccbbddbbdbbdcabccaccbabdbadcdbacbadadccdcbbddcaccbbcaacdbadbdacaddcacccabdbadcdbdbcadadabcdadddddbabbcdbcaabaccbaccdcdabddaadaddccdcdbcbadacbacbddcccddaacdcbacabddcdabcacdadbbcacdbbddaccbbdabbbaaabaacaaabddbdacbdabbaabbccccbdaaaabddcaaacddddababacbbcdabbbbdacddbbdbbdcddaabcddcbaddddddcccbabaacbacdabacadccdacdadabcccccaacacbbcdadcdbdaabcbccdcabbbbcccccbabcababcadbbcdddccbdabdaaacbbbadddabddbbdaaaabccdbaddaacbcddbcabdbdaabcdbbbdabdaacbcadbddbbdacaabcdaddddbdadaddbbaddcdaadadaabbaacdddbddbccacddbabacadabacaadaccacacddacccddcbbbcddcabdbbbbdcddacbcabddddcbabcbabadcdddbbacdbbdddadccbcdabdccbbbacbbddbaadaaaacbadbaacdbcbaddbccabbaabcbccddabbaaadbcacaaccacacdbabcccbbbdaacbdbbbcdacadcaacbaddbbdcbddadadbbbbdbbbddbcbbdbdccdbcdcaabcaddcddcdcbdbdaaacdcabbaaadbaabbaaabbbcbcdaccbcdbccbdacddbbaabcbbacccdcdccccacddbcbbacdcdabbbddcaadbaacbacadcadbcabcddcdbcdacbbabdcbcaaaacbbbabdaacababbaaabbcabdacbddcdddbcdcacdccdacddcdaccbabcdddcadbcdbdbcddbdabbcbbcbcdbbcddbdcccbbbddaabbbababcbdccdbbbdbcacdbbadaabbcbadbdacabaadcdcdabdabadbdbadbbdadbdcbddcbdddbcddcdcdadbcbdcaabcaabbbbddbababbcbcdbdbaddbdaababccaaadcdbdddbadbcddbacbdbbacbabbbcdbbaacabcdcacadcbdcbcbcdbcacbbdbcbbabdaccaaaabcdabadcbdaccddadbacabddccbcbcbadddddddcbbcccdbbcbccaccdaddddcccaaadccbcdbbbcbaddcacdbaddcbaabbbabbcbbccabcdbcadbacaabbbbccbdddbddddcddddbbddcbabaaddbadbcbcbcbcacbdadcbaacdbcbabccbcabbdbadcacaaddbdbdcccadacdbbbcaaaddabdacadabcbdcbdadbacccbadcacaabdbbcddcbcadcabbccbabbcbbacaccaaddccbbaacbdcbdcacdddabbdaddcdccdbbccaadabbbacdbdbcdbbbababddccdcadadbccdcbbccbcaacbdddddcbbdddbacaccccdcaabaadcbaccbddaacdddbddaaaaacaacbcbcbaacbbcaaabbcbcbbacdaaabaddbdabbaadbdabacccbbbccbadbbacdaaaadadcacbcbbcabadcabaaaadaccaccbaccccaadcaddacbbdcaccbcbbbdbacdcabcbaabbbbdaadaabbbacbaadcdcabbbcbcbcbbababdddbabcbddbcddadbadcddadcaccbabbdbdcbacccdddadbbacacdcdbcbbbcbcdbacbaabaadccadccdadddccbaccbabccdddbbcbcbbbcddcdbdbdcbaabcababdadcbcdccaadbadabacaaacddbabcbdbdcddaacddbcddabdbddabbcaaddbaadcbbadbaaddcdaddbbccacbcabadcbcbbdcdcabbddabbbccbabaddcbcaabaaccccccdaabdcadbdaccaadbaacbbacaaadbdbcacbcdabccdcacbaadbdacbcbdbbbcbcbccaaacbdabdbdcccccdacdccdbdddcdddcdcaccbcabadbacbbddabdbaddbaabdacbaabdabdaabbbadbaccacbbbdcabacaadcabaddcddabbabaddabccccacaabbacbbcbbbabcdccabdadddbbcbbcabcddacbbdbadbdcbbbccdcbdcaaddbaacdacdbbbddcadbcdccaccdabcaacbbbabaacbcbdaadbcaddbbbbddaabddddbdcdbaabbbbabaabcadddbccdbbbababdacaaaadaccabdbbdcddaabbddbbadddbaacdcabbdcdbddbabdaabdbbdbbbadcaabaadcbcdddbddbbabcbaabddabaadaaddadcbcbbacbbcadadbadbadaadabaaacbacdcdbadacbabbabdcdababdbccbacacdcaacdccdbdcddcaccaccbbdcdbcdcaabcacadbdabccbabdaacbbadbacaddaaadbdccaacaddcccbcbcbddabcdbbabdcaacdadbbbbbcaaaccbaacddcbaaadcaccdbdbbdddccbdaccdabcbdabbcdbcdcbddbcdddabaccdabadacdabacbdbcababdbdbdbcbdabccdbadaacccdaaabddaaddbdddcddbcdbcdcccaacdbadaabbbdadcdbaaabdbddbcbdbaabdbacdddabdaaddbabdbdacaccdcdaacdcdbcdccabccddbdbabccaacbabadbadacdaccdaddacaabcdbbaabcaaabadbbaaadccbccdbccaadddcdcdbbcaddaadabdcabdcadbbdbcaabdacbabbdbaabacccaacbdcacacbcccbcddacdddadcaaccbbdcddcaacbcbcabcccaabccbdbbddbabbbdcccccbcbdadbcbdcabdaddbacadbbbacbacbdcddddbaccbdaaaadbababbddcdadbdbbdabbbcadaddbdcbaaccbbaadcddaaccabcdabcddcadbbadddcaababdbbbddbacaacacacbcaccdcbbdbdcdaccbadaddcbdbbaaacaacdbbbbbaccbacbcbdbadaacaaaabbcdcbcbcbabcadccbdabbcacccbcdabdadcdddabbcccbdcbcaddcdcbacbdddbdcacadcdbcdddbcdcccddcabddbdcabdbacadddacacacddaccbddcbcdcbbbdbdadbacdaaabbbabaacabcdcadcbbabdacbdddcaddcbdbbccddcacaddadcbccaaaccaccbcccaacccadadbdbaacdccbdaadaaddcbaaadbdabcaadcdddcccdbcbbabbdbdcdadbbcddbaaddccccabcacbbbcbcbdabdbcaacdacbdccadbabcacabdddacbacdbabacbadbbabcbcaddbcbccabcbbbddbdacdaddaaacbabcabdbdcabdddcbcbacdbaccdcddabccaaaccabbabdbdbdddcddbababdaabbbaaadddcadbacaacacbbddccdccdabcdaadcbaaacadbccaaadcdaccbdbdabddbcbbbbdbcabdacaacbcbdabdbbaadadadacbadccbcadcabbbbacabdbabaabadaddbcdcdbaccacabcbacdddcdbdbcbaccddadbcadccccbcbacabdacbaabbbbadbbbacdddddbddbcbbdcabaccdccddabdcbcccbcdaadbdacddbbdadabadadbbbddabacdadaaaaadbdbddbabdbbdbbacbaabbccbddddaadbdbccdbccbbbdbbbdddcdcadaccadddbadbabdccccdabacbcbcbcbdcbbbaabaabccdddbcaaccdbacdbbacbdcccabbcbcdabbdaadacdcddbdcbccbcccddcccdacdcbadcbbbdcdbdbbaacbbdbabbacbdaddccddbcbdcbcbbcbbbdcbabacccaaaaadcddaddcacccbdcadcaadaabcaccababbbbdcccaabdadabacaddabacbabdbcbcbbbbdaccaaccaccdcdbbaabddaaababcaaccbcdcadcacaddacddbabdbababbbadcadbcbbbcbbaabcbadddbcddcddabbddbdccbaabaababccabccadbdcacddbaabdbccbbddcdcacbdbbaacdbcbddcbbacbadaddcdaadcbcaacaabdcbcbdcbcdabddcaaaacbdacdaddbdaccabddcbdccacaabdabddccbcadbbacacaaaddacdcbbcccbbdadddcccabdcadaccabbabacbcbbbddbacadbdbcccccdcdbabbcbddbbdcacdbdbbcabbacacbcaacacaabbaddccdbbbbdbaababdcaaddbcaddadcdcddcdcdaacaccdddadccabbadccabcabccdbadabbdacabcbdccbabdbdcabccccdddcbcdcbaacaaacbccbbccbccddbbbacdbcdaddbcddabcaacdcbdabababbbdaabaccabcadacadccbbddcacdbcaaddcaccacadddbcbcdabbbcdccccaccabdcadbdcacbccabbaddbbaaaddaccbcadaadcabbaacadbaadadbcaccadbaabcdbacbdbdabbcaaaabbbbabddcccbcadbddcabacbadabdcaadbdcbdbcaaadbbaaacdbbdabbabdcabcadccaaaddabbbbabcacaacdadbdcddacbccdbbacbdccbbdaabdaaadcccdbccadddacccbbbdbdbaccdbcbcdadaadabcaddaccddaabadbbbbdacccabcbbcbbdcadcacaaadcdaaddadcaadbaabdcdbbabbababccbabcbdcacaabbdbbcdcbcabbddbdccdddddbcbadabdadbcbdcacabdbdbdbdaadabbbcbacaaaaadccdbdcdaaddaddcadaddbaadacabacdbdacdbccbbacbcbbacbbbdbcbbbadbddcaabacabacbbaaacdaabaddbadcacabaabcddbbdccbbbbbabababdbdccbcabbacbacadcdbdaaabadabddadddbabdacacabdaddcdabbdccbccdabddacbcdcbaaadcaaabddaabbcdbaadcdbdbabbdaaccabbdcbdaadabbbdbabbcbbacdbaddcbcdbacdbccccdbdbadcbacbcbbccbcdbbabaacdcaaaacbbaaddccccbdddbbccdacacdabdaaabcbadcaaadbbddaaadcbcbccabacbbaadbbdcdcddcabadacdbbaadbbacdddcddbaabaddbdbaacbabdddcdbbbdcbdcddbdcbbddccddbdbcbabccabcccabaddabaddadabbdccdaddccabbccbacbddcabdcbdddacdbbbcabdaacccaaababadbdddccbdbbbabcdcadddcadcdbdbabbbabbaacccdabadcabdaabacddcdbbcbdddacacbadbccbbcaccbadaaacbdbbaadadcdacdbabcbcdbbbcccdadcadcaabccdbbbccbadbcdbadabdabbdcdadadadcdadadcaccdbbcbdcdbaaddddccaacaabcdaadbabccbdcccdddbdbbadcabdadbcabbbdbaddaddddddcdcdbadcabcdcddccbaaabdcabcacbdcdcdadcbcddabbdccdabcdddaacccdaadaaadbaaadaacbbdccdcbabcbdcadbbdcbdacccaacdcdabaacacbabbabaaaacdabcaaddadbbcddcccdcaccbadddbbabadbdadaadcaadbdbbcacdadcdaaacacbbcaaacbcdbdccbdabbaaccdccdbbbdacbcbdbcdbbbdacbabdcdadbdbdcabddbadcbbdddbbcbdadbaabacdbdccdcbdcdaacdacdbdcaadcbcbbaddbabbadbcacdcabcbdddabbacdddacbcdbdbdbbdddccdaacabcbdaadcbcdbbddcbccdadccbcdbcdcdbaaaacdcccbbabaabadbdabbababbdbbbcbdbaccbccdcabadaacccbaaadcaddaaddabbcbaaaacabdbbccdacdcbddadaaacdddddadbacddbbbbaabcddbbbbbcdabdaaaacaaaaacbbbccdbadacbabadacbbddcbbbdcacaaababccddadaccabccbbdbbadcaadbabdbdcdabbbaabbdbbacabcbcacdbdcaaacabacccdbdcbbabcbcbcdbabcccbdcbdddbbbcdbcdadddabdccdbcdcbdaddaddccddbbddcdddbcbcbcdbaabdbccbdacddddccacbbdbcdccdbcbcabcbadcacbdcdacdbbacdcdbdbadcacddcddadbbcadccdcdbaaccaacbdbddbadbbbabdcbcccaabaaaaccdabaababbdbbcabcadbbdcabcddbdbdaaadccdcdbbbabbcabaaacacdadaadacbdaddcdddcdabdddbddcdcdcbbccdadbbcbdcacabacabdabcabbaddabadcacbbdcaaadbbcacabadcbdabddbcbadacbbcbbabdccbbcdadbcabdbdbccbadbddccdcbbabacbacbdbdddcadbbcbdcdccaabbadbcaadaaadcbadccaabaddcbcddacacacccbbadbabcddbdcabacbdddbdcbddbbccbbdcbdcbcadccbddabcbaccbbaccaacacbbaabcdcdcbaaaacbbcdcbabaaacadaabaddbdbbddacabccccacadbcdbcacababacbccbccacabdaabbcbcdcbacdbdbddcadcabdaaabadbcbadadabcabdcadababbdddcaadbbccdabddcdabcaacdaadacbcaabbbcacaacbbcabdbcbdccbbccdbdbcaabdaaacdddbddddcdccbdaaadccadacacabbdddcaaaccbddcdacdacadaaacabdbddccdccdaddcbbcabbbbcbddddcbcbacbdadabbcabbaccabcdaadddadccdacacbabbdadcdabbbadbcaacabaccacbbbcccaccacadcdbcdaccbcccccccbdabbacacdbaabbbccbddbabdccbcbaaadcaacbaaddccdbddccacbbcabadabbdcbaaadbababaaabbbbcbcaadbbbdcccddbbbbbbcdacbcaaacbbdbdadadcacdacabaabcddcbadccdcabdabcdbccbccdccddaccacdbcaabaccccacbaacdabbbdddaabbadbabcbadcbabacaacbbadaaaababdbdacaadadacacbccacdcadcdbbbabbacdbaababbbbaddbbdbdabbacbcdcdbcbbaadcaabadacccbbcbcbccbadcddccaddbcaaaacdacaabbbbbdcacccdcbcacdccbbcaccaccdbadcdadcdddbdbaccbbabbbbaaadbbbddabaabaabdabbabbadabdcdadcdbbdcdcbabdcbcdbaaaddcddadcccbdaddcaabbdbdabccadbbdaadadababcccddddbcbcdbaacdccdcbbbbabdbcbabcddaabcbbcbbddccbccdadcaddcdcacccaddabbadccadcacaccacabacadcabcbdacbbcbcdbbbbacdaaddddcbbdaadbccbadcdbcbaaabdaaaaddbacdcacddcbbaacbbaabadcbddacddcbdbcacbdcbcadaacbbbdabdbddaacacdadabccbbadadbcddbacbddbbacbcdcabcabdbcddbcabdbdadcccacccccacdbabcddcdaabaaabcabcccbadcaddcdacdacabaaacccaacbdbcabacbdcaaacadaaaacdddcbdbbcddadbdcdcbabdddbcaadadbadaabaaabcbbadaacdadaababcddbbcbcacddabbcdcdcbccbddadbacadcdbbcacdbdccadacbbcdbadbddbcbdabdbbdadbdccdabbccbcabcadacdcbbdaabdadbccbcaabaabbbdbaddaabbbaadbbcadcabccdaaadccdbcbabdacaadcaacbdaaaacacbacccdbbdcadbdccaabdddccdadbbbadcbbdcccddaaabbcdadbdaaabbdcdbccacbbabdcbdabbccdadcdbbcdaddbbaaabaacdddbdaadacdcccdbcabdbabbcaaddccdaabbbbbaacbcbdabbbbbcbdccccbdbbcbbaababacbaaacbcbcdaccdcbdcbabdcdbcbdcadaddcdbacdaadbadcbadababddbaaacadadacbdcaccddaddadadbbccdbcdaabcddbbbcdbbabddbcbbbcdcaacbdccbababbcbdabccccaddbadaccdbdccdbbbadcaacdcdbcdbbbbacbbccaaacbbadaaadbccadaaacdcccabdabdcbdabbadcbdbaddbaaacacacdcccaddbbbbcbabbabbcabbcbaacbabcccdbaddbdbccdcbcaadcbbabacaabbadabbbbbbaabccddddcaddbdbdcbaaaaddaadadbbdcbcbddbbacccdbbacbccabbbbbcddcdabadaddbaaaabdadacaaacabcbddabbbbddcccdddcaddadbadcabdbcabbaacdbdcbbaadaaabbddcbdccdaadbddcccadcdaacaacddddcbbcacdacabbaddbccdcbaadaabcdbaaabcbabdaadacacbbcdbcdadbdbdcddaaaccdbcbaacaddcadaddbddabbbcbcbddcddadcadddcddbddbaaabdcdaaacbadaddbadcbbddacacadcacdddcbccabacddbbdcbbccccdabbbdadbbcdbdcdcdccaaaabbddbadcddcabbdbabbaadbbcdcabddcbadcbaabdccccdbdcadbdbdbdbbbdddaabaabaccaacbcdbccbbbbccbdaaaaabdcadcddddbbababcddbbacbcadbdadaddbacaaddbaadbcbdacbbadabbbcbaabdccaddcadabccaaadbdaccdadbddbcaacadadbaabadddbdbdccbaccaaadcaacbdcaacaabbbabbaaabadcdcdaccbaacbbabdccadadcddccbbdbcdadaaababcdaacadbaadcddbbddbdcaaaaccdcbbcbabdbbdddcabdbbdadbadcbcddcbbacaaaaaadbcdacbddbddacdbcddcbcddaccdaccaadbbcbcccbbbbbdcadcadcbddabcbbadccadddbbadcdccdaabccdddbaabdabadbbabbbdbdcdacbaccbdcbbaaaaacadbaddccddaabbbadcaddcabaabababaddbcbbabaabcdbacdbccdbcaaacddccdaaddadddddbbccdcddbbaaaccbcacadbaccacdbbaaddcccbcbbababbddcdcbdcccdbaacbdaaabbddacdacbacacddbcccbadcbddadbacabccadcdabcbcdbbbdabadbbbddbcbdcccacdabdacdcdcabccdccbbbaccbdccaddababddcdacbbccdcdbdcbacbdbccdcdbadabaadcacacabbdabaccbdbaccacacadbbbcbacabbdbbaddaadacbcdaabcbadacbddcadddabcccdbcddbdcbbbaadbbabaaddcaaabdbddcdcbdbabcaaccadaacbdabdbbacdcdcccbcdbbcbcaacdcdcbbbbcbbddcabbdbcadbdbaccddbdaccbdcbacbabcabdaadbbdbdcbccacbabddcccbcabbcaadcadbcadbadcabdbdabddbbddbdbdcdcbbcbabbbbdcbdacbdcbbcaabdcacaaabbccbabaccddabbaccdbcbcabbdcddddddbbaccdcbcaacdbcbcabcabbadccccadabbdacdddccadbccbdcbdcadbbadbccdddbbdcddbbdcddbddbdbcbccddabbbacadacbcabcccddbbacdaddcccbddcdcdccccbaadaadbadbcbaaabbacbcbcaccbcccaddcddbccdbcdbdbdbbbdddbbcbacadbccbbcbcdcdabcadaccaacdabbdaddccacbaccdbaaacabcdabbdadbbadcdabaacdddbdbccccaadcbcbbaddcdbcccbadccbcdcdabbbbaacdadbccbbbdcabbcddaadaaacbababcaabdaddaaaacacdbbcbcdbaccbbabbbaaaaadadaccbbdabacbcbaaaacbdbdbacdabaacadddabaccddadbadbbacbbcabaddcdbacdcbdaaaabbbbddaaaadaacddadadadbbaabbdcbadbabcdbbcccacdccacbbacbdacbbbabcababcaadcbbbcabcbabacccdcbbdbacadddcaabaccdacaddbdbbaaababacaacbccbccbcdbdddbbcddbbadacaaacaadbbdcaabddadbdbcaddbccbdbaaabcdcbdbaaddcabdbdcacdaddabcaddbdbcccdbcbdbbacadaaaadcbdadccaadbbbabdaadbadbddabaddadaabccabacacbbdacccbbdcaabcabdbcccabcadbcbaddddbbcdcbbcbdcadaaabbcdcabddaaadcbdddcdccdbccccbcdabddaddbabcdcdacdaabccddcdcbdaccadbadcabbaaaacbdacadcdbcccbdaddcabbcddccacccbdbadbadcadbddbdbaabadabadabddbbdcaaaaababcaabbbbacadddddabdccaddadcddcacdabaccbcbdabbdcbcbabbababacabdaabdbdcabbcdcdcbdcbbbaccbdddccccbcbddbbacdcdcdbbadcdacadacdcdccdadccacdcdbbccaccdbdbdddcbdbbcadcabdbccbacbccbcabbcdbccdbacbddbbdaabbbbdcabcbcccbbbddbbcbbdacadcadbdddcddddbcadbacbbcdcbbadaddcdacadcbadbcbdbccccbccdcbcdaddcbbcadddcaacbaaabdabaadaaacccdbbaddbaccccdaaccacddccbdadbbbddadacdcdcccacdbbbccccbbcccbabbabcadbbadabcbacdbcdddaaccbbacdccabcdbcdbaaccdddddaddabcaddccbbdbcbdbadbdbdadacacddbdcacdaddbabccdbbcdcabbdcbcdcaddacaddbacdadbcccdcacccaaadcbccdaabaaabdcababccdbcbaadcbccababadbcbaccacaadaddcbdacdddbacdcdcabadddadbcccdbdbaabbaadbbacbbdcbadcdbcbacabdaadcacdbdccaadbbbcdacbbddccbddcddcadaacaadcddcbdccbcabccbdaadcddccadacadadbcdcabaadbacacbcbcdcbacdccdbcdacbbaccbbccbbadbababcabadddccccaadddbaddacbcdaaaddcdcbaabdbdabbcbadccaddddbacdbcccbddbdbbdadbbcbdbbaaabdacddadcdabdbddadbdbbdadcdabdccdccadcbbccdbbbadadabbccccdcadcdaccacdbdadddcdacbcddadcbdbdbdbcadaadacbbcbbadadcbcbbdbbbacbbcaaacbbccaaaaddcacbcaaaccbcdbdaaaddaadcbddddbadcdaddbcbddabbacaaaabcadcbdacdddcdaaaaaababdaacdbadbbacabdadabaacbccdcabadcddddabdddbbadabcdcbccbdabbbcabaabccaddadbdabcadcadbdcabcbaccdcddaadbbdddaddcabcadcbbbcddcacdddcdabcbbaaabdaabccbddababccbabbcdaacccdcbbabbdbddcbaadcdaadbadcbdadaacdbddcaddbcaccadadcdcccdaaddbcababadbbdaabcdbdcbdbcbaabccdacaabaddcdbbbbaccbbdacabddbbbbdcdcacacdacdaaacbcacdcabdcaadadcdadabcaacbbaacdabadabddcdabadbaadadbdbdadaccbaabbdaadbbabdacaccdbbaadbaabbaacbcabcaccbddbccdcaaadcadcaadbbccabdbadbdcdabcaacbbcabacbdbacaacaaddbcbaccabcdabbccadbddbddccdbdbbddddddabaacbdcdcadcaaccacdbdbadadccbdbccaabcbcdbccdbadcdbcaacccbadabbbabdcdaadbdaacddccbdbadcacbacbcdacccdacdaddabbadabadcbbbdabdabdcaaababaababcdccbddcbddbdcacdcadbbbdbbccbbdddbabdbaaabbabbcdcbaacdbdababcadbabbabbccdcadbdbacbaaddacddacbabcdaaadaacdcadbddabdcbaddbdababbbbacacdbdaacabcbddcddadcdabcccacdbcbcdccccbaddbcbaccbbdacbcdcdbacdbbdbadabaadbbdbdabdbcaccacbabbdaddadbabbbdaccbddaccbddbabaadccdccbcaacacacdacaabcbaadbacbaabccbbacdaaadaaaaccddcccbadbacbddaddcbaadbcabbdbdcccdbbabbcbbacbbbcdbccddcbbbdbdabbbcddaaacaabbdbbdbcaaccdabbbdbaddacbdacbbcbbaaaababcacdcbbcaddadaadaccabcdadcabddbcacadcdbacdcbdbccdbadccdbdabdcbbdcaadacabdbbbbcddcdccadbccdadabdbdddacdbbddcbddcbdddbdcdbdbddcbcaacbccbbbaacacaaccbdaccdddddabbddbccccddabbccaaacbdbbcddcacbabcbbdbadccccddadabbcdabdaccdcdcdbabcdabdddcaacbdcdbabbcbaabdacaabaddadadddcaacbbbdadbacbbcacadcadcbacabbbbdbabacdddaaaddbacbcddaccabaccbadcbaddbddbcbccabbbccaaccbcdadcacadaaaaaddcddaabccbccacbaadccbdaaccabbcadccbabcbabccdcdbbcdbdcadacbdbbbdbdadaabdacbbabbcddbaaabbacaacaabcadaabcdcabcbddccabccbdadcbddacbadadcbdbaacbbabaddbbbadbddabbcbcdbdcbdbaabdbbcdcaaccabadcddcacbbabdcbacaccbcbaaacdcbcbacccbadacabcbcadaadaccacacabcbbcbccdccdddacccdbabbccccdbbbaabbdacadbdccdcddaababcbdaaaacbaccddbaabbddcbbbcddccdccbabbddbcbddbaacbdcabadbcddcdbcbaabbcdbcdacdacbcacddaaabbdaadbadacdbbadaccdbabbcaabbbcbccaccabcdabcccdadacbaaadbdadcbcddcccbcdbcbadaaabadadccdcbaadccbdaccaccccbcddadbbdbdbbabcbacacbccbdcdaadcabdcdadbbacdabdbbcaccdccadadddbacdabcacaacadadcbddcacbababbacbdaadcdabcbcbaaabbbaccccaddbcccadababcccdaaababbdccdbbcdbdaaabcdcbaabdbaabbcbaccbadccacdabcacacddccbacaaaabaccbaacbdbaacdabbbbbddbaddacdaccbadadccbaddddbdabadabaabddadcccbacbaccdcadcaabbbcdaaaabcbcaabbbbcacdaabbddabcbdcababbdbacbbbcbcdcacaabccbcbdaccaddbcddddcddcdbaccccbbacddbbcccadbabbbabbdcbadcdcbdaabcaaabdbccdabbbabaabccccccbbcbcbbdcadadbbbbdabcdaacddcdccccddaaadaccbcaabdcacccdcbdcbbcdcabdadbbbbdaadddcddbccacbabadabcccabbbabadadddbbcacdbbcbcccdbaaccabccbabadadcbbcbdbaacbcaddcdadccdbacccadcacbcbcbdcbdbcbbccbcbbababdcabdcbbdcabbcacdbddacdcccacbbbbccbbadcaadadadaaadcbbdcbcbcdbabccaacacaabccbacdaaaddaabddccbdcbddddabaaabcabacaababaccaabdbdaccaabdadcbaabccbcadbcbbcaaccbbcacacabadabacbdccccdcacbbdccdacbccddacdcdcbacbbcaaaadcbdbccadadcbdbacbdadababaabaddddacbdacdabbcbcbacdacddacbacdbbbccbcaaadacaaddaddbbccbccacdbaaaadcacabdddcddbadcdccdadcdccabcaaaddbdcbadcdbdcbacaaaaddbadccabdbadbcdbdcddaaddbccdacacdccbcbacddaddddacaabaccbacddcbccddcbbcaaadbdbdcbcacacbccaabccdcbbcddbababbdabaacbdcdabacdbbdccbccaccadccdacbcbcbbdabdaddacacccdbcdbbcacbbddccababaabacdaadbbcacdcbacbcbbabcaabdbacdbadacdccbabddcdcbacdbcbbcdadcbadddcccccbbddccdcbbbddcaacbdadbadccdbddbccbcdadcdbdcbaaccaabdccbbcbcaaadbcaccbadaccbddccaaabcbdcaddacaacacabdaabdabccdbcdacbdcdacdcadddbaddaddbccbdcbdcbabadccdddcadbddbdbaabbadcdddbcbddabbcaacacacbcdbacccddcbcdbbadaadbccabddcaacbacdcccbbddcacdabcaaddcbaccbbcbbdadacbbacaaddcddabccdddbacccbcabaddbdbacadbaccacccddcabbbddaccacadaabbcacbdbaabbabababdcabdbbadbbdbdaaaddbcaaadbbabdaacabbabdbdbaaacbbbddbdbdacbccbcdcbcbbbdbdbbdaddbbabcdbccdddcadcbccbcbcbbadbcddcabaddcaaddadcbbadbdccbbbccdddbcaabddccaaadbbcacaababcddbcdaacaacadabdcccbabdcddccbcaabcdddcbdabcdabbcddbdbacddddcbccaaaaaccbbdcbbcbadacbbadcdcbcddacdbdbdacbacdcbbccdbaddbdaaabbbacddccbbbbcdacdcabdaccbdabaacadaddccdcbbdabacdbadaddbddaccdadcdaacccbdbddabbcbcabdbddbbdcccdcdadaaccacadbdaaddcdabbabbbdacabcdccccbddaadcabacbaadcabccdabadbddcdbdbacccadcacdacaaacbacddbdbcdaddcddcacbdbbbddbbbbddaccdabaaaccbbbadbcacaaabcdcbabdddbadcabcddbcbcbbcabbabacdcbcbadccccabcdbacdddcabddbaaaadcaadcdccacadddbadbbdcaaabcdcbaaabaabcaabacddbcdbddcdbdbdcddcbbbbdcdbbbabcdadbcadcababccaacbbbabacadcaabbddbdcabddbadcbadddbcdcdcbdcccdccbcdaddcadbddacddbdaccbccdaaabdabaaadccacccbdbbccabacabdaddaadacdcbdaadacdacdcadcabbbaddbdaddddbbbadbbdcabaacddaadaaaabdcbddbdcccadbbddbdacbcccaddbddaccabaccadddbcddccaaadcdadcadcddcddccdaddabcadbacabbadbadccbbdccadacddccbaccaddbcdcaaadccdcdcaacdacbacabacdbacadbadcbdcaccdbdbabaccbadcdbbcaaaabcbcaaaddbddcdcdacbbccbdbacbbadbbcadcddadccdadadbabcbdbbbabccbbbbbddacaadbcbdaadbdbccbcdbcdadbcdabdbbbdbbdcdcbdddcbbabbddbbbbdbbbccabcdaaabcaaccabbbbcabbdaabaaabcbcdcdbcbacbbadcbcabacaacbcbbcaabaccbcddaddaadbbdcbdabdadbdddabbaaabcccadabccaccadcababcaaabdccabbcdddaccdaddccabbbbbdacbcbccaddbcbababcddcadbcbbabaadddcbcdadadbbbbdcbcadccbbcccaaccddbcaacdbbabacccbcacdbcdbdddaadbbaadddccdabadcbccccacccaadbcdddbbbddbadddadaacdcdaadcaababcdaddbdccaddcacbbddcadaaccdabcdddaabbbdbbabbabacbcccabdcdbabbccbdadbaadbbabccddbaacdabddaacbcdbcbddbddcbbcadbcacbccdcdbdbacaabdadcbbadcdccbacdcbccbcbddaddccbcdbddcadaadbaacbabbbbbcbbdaddddcbadabcbaccdabcbbcadbabdaaddaadcdacbbdbbbaaacabdcbbaaaaadccddaadccdbcabbbacbbcddaadddacaddbbbcacaacbcdabbcdddcbdddadccdcbcaadbacddbcbccddaaabadadaaacacdcccacccaaadababbababdadaccabdcbabccccdcacccaaadacacddbdbcccbbcbbdcddaabdcababbbcacbacabcaaadcdbacadbbccacddaabccdcbbdaabddcbcbdcbbcbdbdcbcccbadcadcdcdbaabbcccabcaccbaaacbdbbabddcaaddddddbbabbddbbcbbbbddbcdbdbcccdcadcbbbbcacccbadccaabadddadaadcbaddccadbbcadccdbcbabbbccabbcadccbddbadcbacbbbbbbbdccbaaabdbbccbcaabbaddbacdccccccbbabddababaaababcacbcacbbdcaaabcdbbacbaccaabacaadadcbbaadacbacdddddabbdcababcbabcaadcddcaddaccdcdacacbacaabcbacccdaaaadccdbcdcaaabacaaddabbbdaabdaaaaddcdaabdddacacabdccaddaddddcccacbadbcdabcccabcdbcddbababbccbcccbdacddcabdbbbaadadacaaadcbdbbaabbadacadbbbddaabccdacbbcaababaaadccadccaaddadbcdbcbdaaadaaabacaadcaccdaacbbabddabadadabdabdbddcdbcbdcadaadbcbabcbcdcccdccbdaacccdbbbacadcaccbdbbababbdbcaabcabbbddadbaadaabbadadccdddbddadbbbbccabcbbccbcccadbaacdbacbaddbadccbcbbccaabaddcbaaddaabccbbbbaadcdcdbbabbaadbbbadbaacaaacabbcaccdcabbbcaaacdacccacdcadaddacaccabaacdcbcbcaabddadaccbdcddccbbbcbcabcdacabababddaacbacabadbddcdcccbaabbcbacbbadaaddadcdcabaabdccbbdbacacaacbccccdcbabbadccdcbcdbbbabcdaddbdaadadddcadcbaadaacbbcbcbadbadabcbcabbbbababddbbabcbdaacabbccbbdabaadabbbaacbbdcbbaaaabddcbbcaccaabacbbbdadaabbaddaccccadddbcbbbadbacbbdacbabbadcaaaddacccdcbabbccddbcbccbbbcbcbddacbbccaddbddacabdabbbdaccbbacaaadccacbdcabcabdcccbaaabdccacdaacddaadcadadbddbcacacdcdacbbdddbbbcabcbcbdcbdddabdacbcbaccbcaddcaaabdddbabdacacaaaddbbbbdccbcababbdbcdccdadaabdabacbaccbdbadacbbccddabaadaadbccddddabdadcadaabbbcdbcbaacbdcadaaaabdccbddbdccabbcacdaabbddcdaccbabbcaddbdaaddcacddbaadcccdaadadcddcddababacbadddcddbcbccddccdbaccddaabcbdcabdbdadccddaabdabccaccbacdababaaaacdccbacccdccdaddbcbdcacabccccdddcbdcaabdcddcbbcbadadcaaddccaadadbbdccdbdadbbabbdcdbadbbddbdbabccabbbdbbdcadddccccbddaabddabbcccaabcaadbadcbccdadddbaaadddccabacdcaacdbcbdbdbaabbdaacccbacbccbdbabcdbdcdddbaadabcdbdcbbbcdcbbabbdabcbaabddccaacccacbaadbbcaddddbdddabbbaddaadbdbabadaddbcbcdbbadadaaacdabddccaacdbadabdcbadcaccddbacdbadccccacccbadadbbcddcadccdcbaccacbbbaaacabccccabcacaadbcbdadabacbabbbdcbccbddbaaccbdaacbbaadaadadbbcddbabbadbdaddaddbbacdcbcdaccdddcbabdbdcadbcadccacaacdcdcdccabaacaacbdcbacbbbadbbbdaaddadaccaaccbdabadcbcdcdcaabcdababbccdbdddcbbdbaddadcbcddacbadbadccdcdacddddbcabddbcaddbbacacddcacbacacbdbabbdcabbbdcdabcbdaccddcbbdbcadcabbbaccadabaccbbcccacdaadbcadccdbbaacbbcbdbcbdadddcbbdcadabdbddcddaaaaadacdbadacbdbcaddbbdaadabcbaaadabacbcaabcadacbbadabcbbaaaaccdadbabdcaabddccbdaacabbadddaadbcbddadbbacbcbadcacbdcbbacaddcabccbdaaacbdbddcbbaaacacdddbdcccdcdbbdbadbaadddcbdacbcbccdbbddbbbdcacbbcdcbdabbcbbbacadaddcdcadabadaacbbaadaccadabadadbabccbdadbacbaabadcaacdcaaaaabccbadbbbdbbdbadadbccbadacadcbcbaaadbdabbcbdbabdbdccaadbddbdcabdbacdaabcbbccdcbacdbbadacdcabdabacabdbcabdbcddcbabdadadaadcbbcbadabdacbcddabbcbcccbcbdaabddabbcdcaaddabbacdabadaacdbadddcabacbbddcccadccddcdbddddcbdbabaacbbcbbcbaacaabbcdbdbabbcdbbbbcdcaaddcbdddaaabadcaadaccaadbcbcbbdcbdbabcaadbbdbbdbcccbbdbcbccbaadbddbbcdcaadcaabcdbbadcabcddcbddbbbabbabdbdbcaadccdacabcbadbabdbdcbabccdbdddccacbabcbcdabdcdbbacbdccdbdbdabcbaddcbbdcabacaabcaacbadcdbcdacaabccdbabbdaacadddcccdcdccadcbaddcbabbdcaacddadabadcdccbddddbbccccbcdddbdbbbcbdddaabbbbbacccaadaaaaabdbbbaabbdabccbaadbddadaaddadbddcdddaaabbcccbdddbcadbbbbcaabbcaacacdcdcdbbbdcaabbdddacabbcbcbdadcacccddccaabcbabbbbdadbbabaacbacddcdcbbdcbbdbbbaadbbccdbbccabaaacbabdbacacddaacbaabadbdcbbcdbaddbcbbdacadacdbbbacbcddaadbcbbabaccbccdabbadadcbdcdaaadccbbbaabbcaabdadaaddabbabddcacdbdbbcaabadcbbabadccbcbacccabcbbaaaddbcacabdabcdadadbbdabcaacacccababccabdbbdbbdbccbbabcdccdbdaadcdbbdacdcabbbaaccadbcadacbbadaabbaddbbcbabdacbaadacdbcbccdbdacddcdccdabdaadabdcbadddaadddbdcadcbbabbcccadbbaaabcaadbbdcaacacaccccdabaccbdabdccadbcaccbbbacaacadbbcdbccdcdbaddbcdcbdddaccdabccbdddbdaccbbcdddddbacdccdbdbbadaaddbacacdaacaddacdbacdabbadcabcdcaaddddbdccacdbdaaabadadbdccadabcaadbdacdbbadcddaacdcccacabacbbbccbbabbdaabdcaaabadbcdccaabadaaacabcadcbbcdbbabdcbbaccbacbbabbccdddbacbdddbabddadccbabdcaacbbcdddbabacbaddccaccdbaddbdccbbbbbcacacddbcbaadaaccacbabcdacdccaddddacabdbdbadaaadbaacadaddadddcddcbbabdbdcddaadacbdbacbdbdacddcbdbaabbadcbacdccbaaccadbbcaccdbddbcadcbbccbacbbcacbacaacaadbcbbaacbcabadbbdacabccbacdcddaddddacaacaaadbaccbbbcdbabcababababcdccbbaaabcabdcddddcddaaadabdbbabbcdbbbaaccdabdcbacdbaddcaadcdaadbccccbaddbadaabcabccaddcdacbbaaccadacdcdabcdacddbdbcbbcaaabddadbcbcbddbbbbdabadcddddabadccccbadaaaacaacacadbcbddccbdaacdbcaccaaaddcccccbdbadcbaaadbcdcccdcbcddabbbdaacbcddabcadcadccbbcccbdddddbabacadaabdabbdcacadcddccbabbabacaabbaadcbcdcccbabacddbbaabcabdbaccaabcccbccddabbccaaabdbdbacabdbdccdbdcddaacaabcbdddddccddcaabcbabdbbccddbdbccbbbdddbddaacbdaacbddbaadbdacabdabdbdcbabccdadaadaadadcaaabaacbaddaaaccddcbddcabcbcaccaccacbaabbbcbacccdbdcacdccabdbccbaadbacddacdddddcdcbbcccbadcccdcaabccdbdcbbdbcccdcacccdaaacbbbabcdbbdbdaacabdacdccbcbacddbdcbabbacdabadacaabdaabddbdccddcdabddaaaaccdbccdcdabbcadbcdacbdadccbdbddadccadabbddbbccaabbdbdacbbaaadbccbaadbccabcbaabbdabbbaacbaaaabaddacabadcddbadadadcdabbbccdcdbcbbbdaccbdabcbaaabdbabbdacbddcdbdaacddbabbcddabbbbdcacaddbabcbbcdbdcbdacdacddcbaadadaadbcdaddccbbbcdcccacdbcbaadbbdadbdbbbdcdcbcbbaaaadadddabcdcddbaddccbcabdccadbbccabbcbcbbcaaabbabaadcdbaccbdaacddcdcdaabbcbddbdcadcabcbaccacbacbbaaadababbbcbbaddcbddbababaddddcbadacbccddbabdcabccccbbadbcbacaabdabcccdcbdddbcaadbcdbcddccaddbbabaacbcaacdcacbacabbabcadaaccddbdbdacabdcbbcbbdddaacabccdacdadbaabcbdabacbcddbdacdbdbabccadacacbcbdbbaccbdccababadcbabbacddcdbbdbdadddbdddbdbcccbadcdddcccacdcdabdacdaabdbbdaacbbadbddcddcabaccdadadbbcaaddaadcacabbdbbdbaccddddcbbdcdcbcbbadccbbacdccbbccdbcdbdbaaacbdccbdcdacadcbdbddacbdbddcccdcbbdbbccadaacacbdbbbbdbdadacbccbccbdaddaccbdcacbbdcadbaadddcdcbdccaabaddcccacbabcbddbdcbdbccdbcbdbdddacaadbadabbadabbacaddbaacadaaaabccbadaccbbabbdbbdadbccccadddcaddcacbbabcbadcddbbaadbdacddbcacadaabaadbccbaaaabacdbccbbcdbaaddbcaabccabacbddcaaaadddbdbcbcadcbdaadccababcacdccdaccaabbbdcdabadabbdddcddccbdbccaabbcdccbbbbcdcdcdbdcbccdbabcbdadccaddcdadcbdbcccadcbdaabdbdaddbbacccacdcdacbdbcbddabdadcabcdbcadbabcbddaddbaddbbddaabaadcabddcbcababadbcacaddccbbdcccdcbaaaddcdddcbbddbdbbdaabbdadccbcbbdabaadaadddcdadbdaccdcabccbccbbbdbaaddbcbdcdbcadbaacdbbaadbbdcacbbaadabdddbabbcdccbcbdccaccbbbabddcbddaaabaaacbdaddbddbcdcabddbbddaacddddbddcabddbbbabaacabbcdccddadcbcbdbddbadacdadcbcddacdbbadacdacbadcdbbdbbbbbcbababbcadbabbdaabdcdcabaddaacbdccbbcdbdbdbcdcbbbcabdababcabbcbddcdbcaaaacbaadbdaaabdacdbdcabbbbbdbbbddaadccbacacdccccbdddabbdcbacaacacdcbaaaccdbaddcadadabccdbdccdbdcbcbddcddbdbcbabcdcacaabcdaaaddabdcdccbaaabbbaccbadadabdccacbbabcabbaddcaadbbdcdbcadabdbaadcbcdadccbbaccdcdaaabcdaacccaabacbcacddccadabbbcdcaadadbddaaddddbcdcdddbaacbcbcdabdbdbdcacdcaacbbcadabacacabcaabccdacbdbcdbaabadbcddbcddddcbcdbddddccaabdbcdcddcdddcbabbaddaaabdbcbcccdaaadacdcbaaadbcabcdcbdaacaccabbcccbcdbbdbcbdcbcbdabdacbdbadbcabcdabdbcabcabcdacbcbbbcccacccadaddbabdadbbadbcbccbacbdcbddbcabaabcababcdadddbadbcbcdcbddddccdccdbbacbaabbdcbaacabcbbbabcdacbddddacadadbdbdcacddbddddccaacacbdbabbabcdcaabcbaabbdcdbacbdcdcdaaaacdabacacdaaaabbabadabaaccdcdddaacdbbdabacdaccaaddbbbbbbbdaddcbabbcaddcdbacaabdbbdcdcbbdbbdbccbdcbcacdccaabccaabaabadacdbdcbadcbbbdbbbadddcdabacdadcaddaabcadcdaadbbadbbcbbcbcaacababccacaddccccdccdcaacaccbccdaacbcbcbbbdcbbdadddbaacbbddbcdccdbbdcaaadcccbcaaabddcdbcdadabdbdaccabddbcdcbbdacaddadbacabbcbcdaccbdbcbdcddddcbdcdbcabbbadbcacadaaaabadbacaddbbcdbcabcadcbaacbddcbccdbdddaaabddcdcaccdabcacabaddddbdbabdcddcdabdaadaacdabaabcddbacdcbbdaadcacddabaabacdbbccbaadbbddbcbdddbbadadbbbcadccbbcdbdcbabcdbaddddacbaacddbaadcacccaddcbdcaadaccadbccbaacacbccbbcdbacdccddcbbbaabcccdcaacdddbcadabdacaadaabdbdcdacdcdcdcdddaabcabbadcaabbadccacdbddbaaccddddaccbbdaabaabbcdbcccbbdbadabbababbbdcbadacddadbdaabcaacbdcdadbdbcaccbbbcdadbacaddadbdadcacdbdaddcbcacccaaabbabbacacbadbccbdcacadaacbbabcdadccbbbadabadccbbdcbbdbaccdabbdcbbbbbadbbbcabddcdbaccbcccdaadbadbadcdabbdadabcdddacadbacbbadbccaddcddcbdaccdbcabdadcaaaadbbacadccadcdacddbdcaabaaddbadbbbaccdddbbdcdbadddcccabadcaaaddccbddaadbabacbcacabadcadbcbcdcaaadadbbbbdbccddbbcbbcacaaddaacbdcaaaccccdcccbddabcbbddabccbdacbccdddaacccbaaadbddaadcbdcbbcadabaacabaaacabdadbcdaddadcaabbadbdcdcaadaadccacddabdbaddadbdbcadacddbdabbbadcbbcbdcdadaadcdcabbdbdcbdddbccbdbbbccaccacdadabbdabccaacbcbaabbacbdabcadadadccaddddcaccaabaddbdaadbaadaccbbaabcdccbaaacbaccddbcadcccbbabdbdaaaccddacbbcbdacccdccddbcacaadcccadacddcdacddabcbcbacdaacadcbbddcdcdbddacdccdbacbcccdcbdaacddabbdbdbbbabbbccbacaccdaaccdcdaabdaabdabccaaaccaaaadacacbccadcccccbacabdabdddaddddabcbabbccdbdacdcbdcbaaadcbacbcacadddbbabcadcdbdaddadabcdacabbccccbacaaccacabcaacddccabababdbacdbdbbaaddbdbdcacaaabadabdcaacdaacdbdbbcdacbaababaababadacdabcccaccacddacdbbbbadadabdbcabaccbcccbbacbabdbdadccaaacbdabdbaaddbbdcadcddadbaaabbaadbddccaadcbcbaccddaccbccbcabacddacbcbcccdacdcadbdadcdaabaccdbaababcbdddbdabbadbadbdbdadcadaacbbbbbdacbdaddacbaacbbbaabbccaccadddadcabbcbcdabbccaacbbbcababcddbccbddacaacbdbbcdadaabdccaadddcddacddcbabdddbdcdcdbbcdbbbdbcdbaabbcdcabcaadbaadcdaacbdbadadbbddccacadccbbcccdcddacabbbdbccacaabdcbdbadaccddadaabcdbbcdbbcadbdbbbaaacdacaaacccbabbbabcdcbdbbcaabdbcaaabcbdaaddacadbdcadaacdbabbdddcbbbdbccaadbbbacbbbcbcbdabcabbadbcdabdccadccaadddbcdabdbcbbdbdbababaaaabbbccaddbcabbbdcdbbdbbdabdbccbdccbaccdbdcbadccbcdcccadcbdcbcdaabdcbbbbaccacadabbbdaaabacbaccaaabccbbdadacbaccdadcbadcbaabbbbdbbcadccccccbdadccbccdbbacbaccdddccbabcbdccadcdcdaccabadacdbddaaadbaddbbbaabcdbabaccadddddcabccdcdcadaadcdcbdacdbcdaaacbbccdbdcaccaccbddababdacbddbcdddadbbbdcaacdbacbbdcddadcddabccbbbcabccbbbabadbbdaddabdcbbbdabdbacdadccbbbccaccaddadacbabcbabccacbbdadcdacdcdbdaaacbdcacabaaaaaabdbbdbacaddadcbcccccdabababdadcbaaddbbddadccacabdadabcbdbddcbaccaccabadcbddcaaaaacdcdbccdaadcdacaaadbaddbcdbaddadcbdbaccdcaadbdcacaaaddddccbaabcacdcbbcacdacddcbbcabacaccbaadaaabbbccbaccbbccddcdcdabcbbaacccdabcddadabbadcbbcdbddabcdcccabcbdabbdddbbabddaabccaddacbccbcbadddaababdbbacacaadacabdcdbdaccdbbcbababbbcbabdbdccaaddcaccadccbcddcdcbabdbdabacbacbaaabcbcacacdaacbacddbdcbabdbbbcbcbcbbaddcdabdabdddccadaadbacbcdbdbddcbbbddcddcdbbbddabbdcbddabaabbdcbabcadbacabcacabcddcccdbcaadddabdaccdbdbdaddddddbddcbdabdacdadbdcdadcadbacbcbdbbbdcdcacdccdabbdabcdcdbacacddbdbaaacbcccbbbdbdaadbcddacddadccabbbdccdcddbacbcbccddbdcbdbbdcdbdaaaccacabddacbddccadaacddaaacacbabacadcbdbdabcacdcbacbcdddcbbccccdbccdbaacdccbabdccccbddcbcbbadcdcbbcccddbdbbbadbddcaddbbdbbaaccccbccbacbcaaddaaabcaccdddcaadcbdcbadbcabcbaccbbcacbcacdcdcdaccabddbadbcadadcccaddbabcacdbaaccadadbabaddddadcadabbcbcbdbacddaddbcacadbabbbbbcabadbcdbbacbcbbabacdacacbcbadcbacccddabdccdbdabaccbaddacacbcbdcbdbcdcbaadbbbbcbadbaccbcdbbaacdabbcddaddccbabacbacaabdbdaccdcadbdcadabcadccbdccbbadcabcaddbcaabaaadbcacbbdccbbdaddabadaadcacddbadabbadbdadbaccadcaadbbcccbdcdbdbcdddaddbadbabbbdcadcddcbcddccabdadadcadcadaaadbabdbdcbcdbababcdbbabdddbdcabacddddadcdaccabcccdbdcabcdddddadacbccdcdcdbccaaccbaacdaadcabcdadbabcbdbdbdadabbabbccddcccdcddbdcabbdbbcbddaadbdabdbdaccdaddadbdcccdbabcabaaabbccdadddbccddbabaacacbcbccadcbadcadbcccbaccdadbbbacbbccdddabbbbccaccccccccbdadaddcbcddbcbddabbbbdcccacdbccaadcababbbadaaabacbbdabddcadbadbacdadacbdbdcbbbbabddbbcbacdcdcabddaccbbdbbccbcdcadaddacbababdcdaadaaaabaabacbaacbdcccbbaccaadbaacadbdaaaaabdcaaddbccdccbaaabdcbcabcdbbbabdaccbbdcaccdbbcaacccdbccbcadcbcacbddbaccbbacaddcabbbbbbcbacaadacabbbbbcbdacccacaabdbadbcacbcacaaaadcaabdcabcbcbaadcdaabaccbabdacccbbaacaccddabbbbadabddbbbadbabdbccbaddabadcacbaaddaacbcbcacbdcabdbbddcbabbbcabcbbaccdabaabdbbababdaddcdbdddbbbdbadddacccbbcaababcbddbbbccbaccabdbcaaaabadddaaabbabcbdacadaddadddcdbbbbcdbcbadccccabdcdcabcddbcddabcabbbbabaddcacaacdabdbdcdbbcbcaacbbbccbacbaadcccccbabbdcbabcacbbaddbcdbdbadaccacdadcabbadddbaabdddaddbacbbdacccabcaadabbcaabdbadbdbcdaccdddacddcdbaaaabacaccbccaacaddabddadabccdadddaaabbadbbcccddbddcdccbccdbcdaaaacdbbadcdabcdbbbcbcbcaddbcabdbacbabbaadbbacaaababdddabddcbaaadccbbbdadddabaaaadabdadacbdcbbcaadaaccacdcbdcdaddbcadabdbbcaaccddccddddcadcdcaabbcadacdcdacbacbddcdbdcbbccdcabcddaccddccbcddbdcbdbbbbaacdacbaadbdbcaaacccdbbcccbdaadbdbdabbcdccddbdadcbbcaadddbadbbbcdbbabbcbabddbdccaadbdcccddbaaacdddddabaababaccbbbcabddcdcaacdbbdadadaccddadaaacbbcdddcbdadbddbcdaabcdcaacdcdcddcdcbddbbadabbbcbddcdaadacdcdadbdcaccaacaddccbbcabcdbdbbcddbcaadbddbaabaccdbcabaadadcbdbacbaccdbdbcbacbddbdcaacabcbadbbdababbbabcccbcccdadcdadadbaabbbbcaaaccdddcabbcddcabdddaacdbdccaabddaccaabacacacbddbaadddacbdbddacbcddddcdcccbadadcbcddadddaadcbbacbccddabbbbdaaabdbabcdaaaabbcdddcbcbbbcabdbddabcaddbbacabddaadcdbbdacddbbbbcbbcdbaaccacdbdadcbddcaccabcaadacccdabdbcbbbbacbaabbdbbbcaabbddaaaaddcccdcbddbcbadbabadaacdcbbdacacddadcaacdaccdcddbdbdbabaadbbaaacdbabbbbbdadcbdccbcbddabbcacdaccacccbdcbcbcdbacdddaccbcdacddbaccbcbacadcddcababdcdadddcbddddddabcdcbbbddcaaccdddbbcbbddbacbadcbacaccdbaddbacbcbddcdaabcddcdcdaccabacaababbdcadbacbccdadacdccdaaacaaacbddbdcaaccddbacccdadaccacbdcdaaadcabaccabcdddcdaddcbcbcadcddccaaabcabbcdcabdacabcdcadcdaadcdccbadbccdbddddcbdaadbdbcccbbadacddccbaddbbaddadcbcddadbcbdbccccccdcababcdbcdbcbbdbaccccdacacadadacdcbcbbdbaccbdcabacbaddacddcdacdbdbcaabbaabadbabaccbabcbbabadbbcacdaacdbbbddacbddbcdcbdabcaccdbcbacbdbddaaadddabaabdabcbdbaccaccbcbcbbaadacdabddcdbbbbdddcabbddcccccadcbaabbaaacacbbcdacacacdbbdcdddcdddbcddcbaabcbbcdcbabbbadcaacaaaadcccaccdbacadbacdbdcadcbdaddaabdcacbbbbaaadddabaccbdadcabcdadbbddadcdabcacacbdaddbbdbbddcbbaddcbdaacacddadbdbdadbbcaacadaddaabddddacccdacdcbcbacbaaaaabbccadabcdcdcaaddbddcdaabdddacaabcddacbdabacaabccacbbbdddcddbdbdccaadbabcccdadcaaadcbcbbccbbccbcdbdddadabcbbdbcddddbbddbdddabcccabcdadddbbbbabaadbabbadadbbbcbbddcaddbbabddbacccadbdccabbbbccadddccaaddbdadbbddcbdccbddbbddacaccbaabcbdcaabccabacbdabbabacbbcacdaadbaccaacaabbdabcccadcbccacccbbaadbccdbadbdbbacbcdababacadcbdccacbccdadbdaababddbbcaddbadadcabaddbacdabadabdabdacbddccddcbcacdccabadbbcdbacdddcbdbdabcbbbaadabbdbdacbdcdcbcbdacbabccdbabdcddbbdddbdacdacbcdaabdcccadadbcbbcbcadbcacddcdcccabbcadaccabdbbdbbaaccbbccabcbaabdccaacdbbccabaddcaddccacdaccabdcbdbcaacccdcbbadbacdbacacbbdbcbbdddacdaadbcacbbbacabddcddbbcbddbddbdaadaabadaaccddddccababccbaaccbdbbdcbccbcaacbbcaabccccaabbdcbdcaaccdbbdaaccbaacdbaaaadcbaccbdaddccbbcddbbcbddadcdbbbccdbdcbadbdcbccdccabaaddbaaaabddcadddaacadccabbadabbdacacddbaadcbccaaadbadddaaddbacddbabdbdadbdbbccccdbbbdcbdaddaabddbbdacdccacdbdbbdaaaaadccabbdbaabbcbbbddcdcbcbacabbadacbcaadccdbbbbbdabaabdaaadcdddbadddabccdbadbdddbcddaacbbdaddddaaccdbcbbccddbdcadadcaaaccbabbcaadabcacdaccabbccabbbdbccccabcadddaaccccdadbcabccacbbcadaabdbccddddbdadaccccbbccadcabdcccdcacddcacdbbaadabacabacbbadabcbaaaadbcacbdaadcbccbddbddacabcdcdddcabdbaabdccadcccabcbabccaaaccdbccdabcbcbdbaadbabbdabcbcdbdadaaadaaccbaccddbbcbcbdbaaadacdaaccacccdbbbababcabaaaacadbcdccbabdaccbabaacddbdcbacaacdddabdacdbbcdcbdbdadbabdcbacdcbdacdaaadbaaaacadcbaababbbccccacdbbdcacdaacacddacaddabdddcbcdbaccbbabacdcccaadbacaadccacbcdbbcbddadcbdbadcddabacdaaaccaaadbaabcddaabddadcccdddccabbcadbbccbbccbacbcddcadacdabdcbbcccbddcaaadbbbcdcbbacbdcbbbbbababdcbdacbbbbcaaabcbdcadbcaabaaadadbcdbbbbbbdaaacbddbbcddbabdddabadccaadddccabdcdbbadcdbdbdaadadddaccacaacaddabaacbdbadabbcbadcaabcbdbdabccdddbbddbcdcacaabbabbcdcbaddbabbccaabddabaadcdbaabdbdbbdddcbcdbcbadcdabccdaaadcccaababbccaabcacbacbbcddbacdddcaadddaadddcdcacbabccadddacddcdddbcdcbcadbbaabbdcbccbcacccccbabccccddddcabccbabbcddabbabdbddaadbbdcbbdbadadcbdadbbdcbaabccbcbabbadbbddccabadccabcbabcabcccbcadadddccdacbadbbcaacbcaabcacdaccccbacaacadbabaddabddcdaabdbddaaacbbdcbbcddccddcaadbbccccbccddbabcaaadddbdcdbbbddddbcdbdacdacacabaacddaaccabbdcaaccdcdccdcbcdddadacaddccbcdacbaabdaaaabadbddaabbcbadadcbaabcdbddababdbdcccbccaaaaadcbdcbcabbadbcabbbbddbbabacdadaddaaaaccdccababddbaaccbacbacddbdcdbdcaadddbbbcbdaacabbbdbcbadbdacbbacacdcbdabdccdcdbdcddcbaacaacdabbaacdaadcbccacbbbbbacacccdbbdcbbabdddbdcdabcddddacbacbaaabbacccccbacbdbdcbdcaaccaaddbbcbddcddbddbcdddaaadadacacabacabdabbdddcabbacdaabdadaabaacccdcadbacbccacbabdbcddbcddcdcbcccadabacbabacaabbabdcdbababdcabaddcbddcccdccadbabadcadaccacabdbdcabddcbbaddbcadddddccdbcadacdababbbdaadabbbbbbacddcbcbcacdbbbcdcbaaabcddadcdbdadbcccadcdacbcdddbbacccbdaadbdcadcabcdabaadbbbbcbbcccccbcbcccddcbccbcdcabacbdccdcacbadbadbbdcacddacadcdcdbccbcdabdacddcaaacbadcddcdbcccbdccacdaacbcddacdacdbdbaaaddccbdbbabcdcbdbdbabcdccacdcdcccacddabbacaccddddaccbbcddbaabbaadacadaaabcacbabbccddaabcdaaacababdbdbcacabbbdabaddbddcddcaacabacbbacdbacacaabbdcddadcbdaaccdbadabaadcddacdcbaacaccdacdcaadddbbabdbbccbdbacaadbacbbabcddbdcccbdbbaacdcbbdcaacdcdabaacbdccdacadadcadcdadacacbdaabbbcccacadadbaaaccbabdcddcccbbddbabccbbbdbbdacdcbbabcbdcaaaacacbcdbaddcbcbacdadccbbddcadccabddccacbaddddbdddcbdcbdcbbbadaccdcabbbbadaddadbbcddbdcdbacbdcbbcddcacaaccbbddcaadbbbabadacdcccbbbbbbacdcdcbbdbadbcccadbddadcdcbabccadcdbbadddbadccaaadcacdbabadcdaccbdddaccacaccbcdbbabcdbbcadcbdaaabcabacdadbacabbcadcbcadbbbdacdbdcbcbbadbbdddddccbddbcbcacdcaccbbacdddacdbdbaabbadbcdcdcbabaacdcbbcabdaabbcccdbbaadabacbaddddabccccdcbaabcbacabbdbdbaaccbdddaacbaadddaaccabaccbaacaabdbadadccddabddbbabcbddbbbdbbacbacccbacababcddcbcbdbcadbdcdacaacdcabbaaabcadbcbbdbaaaabdaaabdbbaadacddbdcdaaacbadacdcaaabdccccaaadcadabacddbdadcdbbbcadccadccddcbacbdaadcabdcdcddcdcddccbbcdabbdaadcdbaabdcbacabbdbcbcacdbdddddabbaccabdabddacabcddacbdccbddcbacbbacabadaacbcbaaaabbabdbdddcabdaaadbdcaadadbcdbcaddcaaacbddaacccbbbcdabbdbcbaaababdcdddacaacdacbcbdcbcadadcadbdddcabbdbbdbcbbadbddcdacdcadbdccbbdabacbdabcbdadbaadcacbcbcddcbdcddbacadbdbbcabbbcbaaadcdcddaabdbadbccababbcadabaaadcdacaaaadddadcbcdcbaabcddddcaccdbabdbaadbaadaaccbdbbdbdaddcbbbdababdabddcabcddacbbccddcacdbdabbbabbacbdbcdcadabcddddacbdcabdcbddbbaabcdcbccdcadaaaccacadbdccadbcadabbcabbacccbbadddbddddaacadcbdbdacbbbdddcccdbcbcccdcabdddaacdccddabdcbadbddbcacdadaabbabbbadbbccaaaccadbdbdbababdbdbacacddbdabaddcdccddcccbaaccabbbbacadddcacccbdabadcacaaabadcccacddbabdaccdaddacbbccbddaabdaccabcbcdcccbdccccccdddabadccccbddcadacacbaaacccdcdbbbdcaacbbcbadccbacacbacaddadddddcddbbdaadacccdddabaccbbaddbdbccccdbbaaabbbdacdccabbbbbdddaadccdccdbdcadaadbabbaadddccabccacbaaaadaaadaaddddadcbacbaddabdbdcadaabccdbbdddbddcccacadcdbbdacbcadadcadbdcadaaabcadcacbaddadbdcbcccaabcdadbbcdcddabbbbbaabdacbabdccbdbabdcdbdbcbddddcaaabccccdacccbbbdbdabcdbbaababbbabdabdcabbcacbcabdbdbccdabaaaaacdbdabbbbccdbaabcbabddabcdabacaadcabcacbbdddadadccdbadabadbccbdbbabbcdcabacaddadabadbadadaddddbbbabddcbdcbdabacacbadabbadcaddcbcdbdbcabdaacbadcdcaaabddabbbabcddbabaaddabcdadabbcddcadbddcabcaacbaaacbddcdbbdadbacbbaadddddccaabcbcbcdbbcaabbadcbccbbbddcdbdaccacbdaabbaaddbcbacdddcccdbbbadcbccacbbacabbadbaacddacdbcbdbcdbcdabcbaadadddaacbbddccadccdbddcbcaddacccdbbdbaacdcddcbcbaabcabddddbadabcddbdbddccdacdddabacdbbdcdacbdbcaddaaddbdbcaabacdcacabcdaccadbbaaccabcaabbbdcddbbdadabbcdcdbdddbacdcbcdccacaaacabcbdddcdbddccddbcadacbbabbacdcacaabdcdcdbadbdcacbdbbcabdadaaaadabcaadcbbdcdcdcdbcdacbdddcbababaadddbbddabddcbcbcbcabbdcdaacdcdaacabdaabdaddacabccacbcddbaddbddaaaddbadcaacbaaccbcdccdccaaddbaabccddacdaccddbacdcbadaacdabbabbbbcaaabacbcdcbbbaaadaaccbbbadbdabdacbbbbaabccdaabcabbadaccccbbcdcdccadbcbdbbadcbcdabddcaabcaadbccbcbaddaadacddbbcbdbcadddcccbdabcaddccbcbdabbdbbbcabdbbcbccdcabaccbdaaaabdbaccccdbcbdbbcbccaddbdacbbbbadcbccbcdaccaaadbcccbcccacbcaaddbcadadabdccbabbbbbcabddcdcadbadbcaabddcbcbccbaccbdbddabadcdbdcbabcbbadbddcbbdcdaabcaaacbcccabbcddcaddbbaaaacaccacddbccbbbacccddacbdcccdbcbaccdbcbbabccbcccbacbcabdacbdbaabadabadcbaccabdabdbacddddccbddaadabcdcaddccaddbaabcbdcadaaabccdaacdadadcaabcdcbcbadbadaadacadbbadbbbdbaaacdaadcdcabcbccaabccddaaddddadcbaacdaaccbcbbcacccbdbacbbccacbabdbdcdbccdcdddccddddbdddcbbacacaaabcacdbdacccacaaabbccccabdcbaabdbabcabbdabbdaacbcaddbbcbbcbdbbababdbcccbcbacdbaccddbddcabcbbadbbbaaabdcabcbcdadbccdbcbbbcdbaadbabcdbdacdcadacbabbccabbcbbcaaaddabbaaadaccabacdbabcdbcbababbddcaacadbbadcddadaaabdddbadacadbcddcacaccbcadccaabcdacaabddabbdbacdabcddaccdbdabbdacaadbbdccadcacdaaacbdcdccacbbcaaababdcbddddbcdddacaacdabbddcaabbcbdcadaaadddcddacaccbdbcaadbdadbcbbaddbbdbdcccdbacbbadadabddaddaddcddabccbdbbccddbcdaaaadcbbacacbdacbcbdababdabaaabbcacdcbdbcccbdbdcacdacbbadcccbabcbdddcaaabbdbacbdddcdaabaacccaabcccdcdcdaababdbdbadbccdcabadaacacbbbcacbddadcabddaabcdddcddbbbbbbcbadcbabbbbdadcccbaadaabbdcbbdbbddadadcddccbcdbcacccabaabdddbbbbbbadcdbacabdbdadbcccaccdbacccddbdcbabbcdbdababacbcdbcbdabbdadcbcaaaddccadddaddcdcbbbbabadbbbabaadaacaabcddabccadcbcbbbbdddabacbccabaddbacaddccadadbdababccaabbcccbbadadbdadbcbbdbabacaabdadaddbaadaabddddabbbbcdcccabcbcaacadddbcbcbccbddbdabbbbddcbbcadadaadccbccdbbbccbacddadbbabdbbadccbdbdcdaaccdbbbadabaabbdbaaadccacabaacddccdcabdcbdddcbbbcdcbcbbaadbbaddaccabcbadaacdbaaabbbddaaacbbcacccacdccbbdddcccbccdabcaacbcbdcddbbcacbbccdcdbaddbadbadcdaadbdbcdadcabcdaaacbdccacababcddbdabdacbdacabbbdcdbdddacbdaacacdacaabbcdbcaabcabdbbacbabbcadadbcbbcbdbdccbbaaddddabdaaddbddbdcbabdaccdddcaabdadbbcdcdaabdccbaacdcacbaabdccccccbccccacbdabacddaadbccabbdcaddcdbcdcacccbccccacdcbadcadaabbcccdabbcbaabdadbabcbdbcbdcbaaadcdbbdaabdaacccbbadabdbabcaaccbdbddadddcdcbabccdbbcbbaabdacabcdbacbadaabdaaabcbddbabcdcdccccdddbcdbbdcbaacddaccacccbcbabdacdccaadcabababddadbabbcbbcdaacadcbdaabdbacaaaccbcacabcbdcabbccdbcbdddbbadcdcdacdddcbcdcbabacadbccadbaddabacbcbbabdadaabddddccdddddbbdbbacdabcccadbdbbbccacbadbdbbbaaababddbbbbdcaadcacdbbadcabdbbcabdbacadcaccdbcacbdcabccadcdcdaacadabbcccbcaadaddddcdcadacbcdabbcccaacbcdccdcdbaaccddacccabddbbbdbbdaaacdddbbccdabcdbaaabccabdcaddccabcbcbbbbcabdaddddcddaccaaabcbcdbdaaabdcdcdaadccddaacadcabbdcbddbbdaabbcddcbaddaccadaadddcbccaabacdccadcccdabccbdcadcbaababcbbbcbacbcccbaaddcbdcbcabcbdabccccdcdaaabcbddbbaabbcccbaddacbdbaacdbccdbdbdabdddcdcccccbcacaaaacdadadbdbdbbadacdaddadcdaccadabbaccbdbccdaccacdadbbacdbccabdcaacdbddacbdbdbdacdaddbbaabccbacbbadaccdbaabbbdaacababacdaddcadbccbcbddadbddddcbcbaccdacaacbbbbddccaaacccabdbaadcaadcdbbbacbdbbdbdcabddbcacccdcbbddadcdacdcbcdabcbbbdaaddcdbbcadcaccdabbbacdbbabadbbbaacbbabbcbccccdabacdcbdcbcbdbdadcdbdbbcdaaaadbacbdbccdbdcadcbadddabbcaacbdbcabcdddcbdbccbdbcdabacbabcacbdaabdcbabcaacddacbcdaadbdaaaaacccbdccbdcbbabdddcdcbccadcbbcbddadbabdbdadbbcddabbddbcadddddcdcdbbddddaaaacbdcdcddbdccabcbdcaaaaaadccdabdaadaaacccaccabcbbadcccdaabcacdabaddadcbdbaadacacbddabaadcbabdabcdbabaaabadaaacdbddbddcbcccddcbdcccbcadaaaddcbcaabddddddddadaddbbcbcadadddbbaddbdcbbacabbabbbddadadcabaaaacbcdbdbaacbdadddbbbccababaccdbccabbdadcbcbacddcbdddccadbbcdcbccabdbdccddadbcacdbacabccbddccbabcccbbbdbaaccbbbdcadaccccbddbbaacdcbacccdcbcdacdacbdbaacdbacacaaacccbadbcabcddbdcabacaabbaacdccdaaaacccdbdcdaccbbaadadbdcdbcdbadbdbbbdcbbccbccdcdbdaaacbaabbbdbcdcbbddddabdacddbdadcbbdcadbdbabbbaaddaaddbcbdbbdcacbaaaacbbbbacaaadacdbcdddcaccbaacddbadabdbbccabbaaabcaadaabadbaccabcdbaabcbbbddcbccdaabcbbbaabacbaaabbcabacdbdcdaccaabbbaaadbbabdbddaabcbdbabdddacbddbcdccbbbcaccdadbacacdbadbcaddcbcdacbbbdcaadaaacbcacdaabbcbcdcccacadadcadddbcccbadcdcadcbcbcdccbdbadddbaabbcddaccdcbcadcccaaacbdcaabadccaacddbdcaabdbacababacaaabcabadababcaddbcdaacacbbcccccbdaadccccbbdbadaacbdaaaddabaabadcadccadbdcaacaaaaaddbdbbacccdcbabbbaddbabdadbadadccdbddabacdccdbaaaaadbbaabaabdbbcbacbbdcdbbbcaabcacbbbbdabbaadacaadcccbdabbacbdcaccbcbddcdcbddcbddbacbcddabbddcbadcacddccbbdccbbddccabcacbdcbdabcabdbaccddbccaaaaaddbbcadddadcdbacaabcccacbabddcadabdcdacacccbcabacddbcbcccbdabbcadbcabcdbcabbcbcddcdccaaccdddddacadcdcdbbccbdabdacdbdccbdacdcaacbcbdbdddbdcbacadddcdcbdaddccdaccccccaaaccddbaccdacddaaccbccaabbdbbdacbdcbdddcacbddbdcbbbababbacbbdbbdabcbcbbaabdbdaaddacbcbcdcbadcaaadaaddcbabddcbcbbabccdbcddbbbdacababccbcbdcdadbdddabbabacccdbacbcccdcdccbdabbbbabdaabdbcdcccccacaddabcdcbbabbaaadadbdccbdbdbbadbdcdbbdaccabbdbbdddbcdcaaaaacaadcccabbdcbdbbadcdadcaddbadcdcdbadacbddabcdccaaaccdcdbbcbabccddcccaacacbbbbacbbbadadddaddabccaacbdaacbbabaddcbacbddcddcdcddacaccccddccdccaacacbdcdbbdbcbabbcbacdcbbbabaabcbbbddbabbdcadbddadcbbcaabdbccaddddcabcabacbcbcdbdddcadbdacadbbacbabcaccccdabbdcbabaaddadbcaaabdbaccdbcbcabbbbcdbdccaccaacababddabccdccbdcbbaddddaddcdbadacbddbdcbcddacabaddddcbcabbcdaabcabcbbabacbbcdcdaaccbbdbdbacadbcabcdaabcdbbcbddcbcdadbcacdcddabdbabaadcbbccbdbcaddcddddcdbdadbbaccdbdcadbaddbdcbcbbbaabbabccbcddaaaaadaccbacaaccabdcabbccbcabdbdabadbadcbccadadccbbbbaaadbccbcccaccacdabddabdcacbcbdaccaacbadcccacddcbbddaaaacacaccbdcbcaaddaddbbdcccabcbcbcabbbbcbadccbabaaabddbbaaabddbbadcdbcadadbbdabccaacbdcdabbcdddbabbbacdbcbbcbbaadbbaccdbbdacacbacdcaddabadcdabcbdcdbbcdcdddcbaaaccdbdcacddacadcabddadaddccaaaaabbcddababcbcacacaabdbdabbacdbabddbcdbacacacadddbcaddddbcaaadabcbdbcdbabbcadacdadcbacbaadbdadadbabcbabadddcaadacdddabbdadaacddacdbbdaaaacacbdbddabaaccaadcdbbccbbcadcaddbcbdcbddcaaaddbdbcdadadddbbaddccdddccbbadcdcaacdccadbcbccaddcbdbadacddaccabdbaabadbaccacbacacbbcbabacbccdbdadccdabccbccacbcdcdbcaabcadcdbacbacddabcbbcdcdcbddbcacbddbbcadbccacdbdcdacacdadcddcbcdcaccaadbbbadbacdccaddbacccbaaccbcdbdcccdcadacbbaadcacabdcbdddaacbddadbbdcbacadcaaacdcaccadcbdcdadaaccdacdcdadadacbdddcbbabcdbcaccbaccbdbccddcadbdccbccacdbdbdbadaababaccaddbdcacccbdbbabcbbccbcbddbdcbddbadbadcacdddbbcbbcdcaccdbdbdacdbcbabccccacaaddadbbbdaababdcdbbdbbddaddbbdacdcbdbdadbdbabdbbcddaabbadacdccddbaabbabdcdbbccccddddcaacacdabbcbabaddbcbaaadcabacddaacdadaccaccbdcbcadaacbaddbbbbbbcadbddabdcacdacbabdbbaadbdbdbbbbbbbacdaadbadddaabccbddddabaacdaadcbbcacbccaddbbddcddacdacbbadbbddcaabdccabcdcbddabdddacdbdbcdcbaacdcbcaaddbbbabcbdccbaaccaabccdddddadadbdadcccbbadcbcbbbcbcdbcdbdbadabddbacadcddcabbabddbdbcddadbaaccbacdbacadcddadbdbacdddaccddccccbbaadcdddabbbdcddbdaacaadcbbbdcdbbcdcbcbdcabdabcadddcbdcaaadbdbbadaabccadaddabbcdcccdaacbbaddbbacbbcdcddbaddcabbaadcaddaabccacdbcdccadcbdaccdcdbdbbbddcdbdbddacaabddbbccddbadaacdbabaadcbacbdbccacbacbdaaabadabdabbadddcbbdbccbbcbaaadccdacadbcaacbdaccbcccddddbbaccbacadacddcccddaccbdcaaccbbacdcbaadadbdcddddcdcaccdcdbdcdabdbcbbabccddbccddccdccababcbdacbddacbbbaaadbacdcbaadbadccddcaadccaacbbabbcbccdcadbcacbcddbbbddbacdcaccddcdcabadcbcdcdabbcdbddccadadbaacddbaaccacaaaddacbadadcabbddcdbdbcabccbaadcbaabbbddabbcdaacadddabbdddaabbddbbcbdacbccaadadabdbaacaaacabbcbdbdabacddadbbbbdcacabacbdcdcdcbcaccdabccaddcdbdbcbcccbcbacdaddddbaddbbacaaccddbccdaccadadcaabccccadcdbccbbacbbaacbdbdcbbcaadcaccbdaddcdbaaabbcbdcbdcacdcaacdcadacbdabacababadadaadadaaaacaaacdcdcacbdddaabaadcbddbadcacaabccaaccbbbdbcabcddadbbadabaccbbadcadddcdcbbbcadababbcbdaccccbaddcddaadddacbdabcabddaabdadabaadadcdccaaacdccdcaccbcaabbdcbbcdddadbdccdcdddcabbabbcbddbccdacccdacbacddbbccbbcaadacbbbcbdbdddacbbcbbdcbacbbadaadcdadaaadbabbabddcadccaabbacbbdbddabcaababbadcacdabcddaaadcbbccddddbbdaadcdccddbabbaaccbacdcdcacbcdcbcbadbccddabadcccdbdccabccccdaacbbaccbbabbadcadaddcbcdadcadaadcbcdccbccbdddbbabbcbdbcccaddacdcaaadacadabacacbccadcbcdacbbacaabcbaacdbbcccaaadddddbcbbaaadacabcdacdddbdaaacdbdabbabaccbacbdddadbacbdabdcdbccbdcdabdbdbaccbdaacdcdadbbabdcbbabbdacaabadcbdadcabcdacabcbaaabdcadacaadcabacadbcadbdabdbaacaabcaacdbdcbbbcacdbbdadcbacaaabaacbdabadcbbccacdbbcbcccaccbdbcdcdbbadcdabdacbcdddbbcdbcdcdadaacaabdbabcabbacaababdcbacbcacdcbccdacacbcaaaaccddcadcdbddadabdacbaadbcbacbbccabcbbbcbdacbacccdcbdcabcadabdddaabbbddaabdccdddccdbccaadddccadcbcccdccabdcbadabacaabdaadbdbdbdcaadccdcddcdddbcdbabdaabcdbadadbbbdaadaaaabaccadbdbbacdaddbacbacdbdddbdcbcccdddcddadcdadbbccdaabcbcaddbacacaadbbcbabacaacbaabbcbabddddaacdadaadcdcbaabacacbccdabccaadaacdbdddbacbbabcddaabacbbbaacaabbbabcccacdcabdddadcbdcabcbabcdbdcdbbccbccdddddabdadbdadddbccbadcdcccacccaabddbadaacddbcaccccbadcdadbbdcaccdcadcccdacdccdbccbaabdbbadbdddacddbbababbdacdbbbdaccadadbddaccdbbcacccddabaaabbcbaadbcccccbddacaaaaabcdbaabaacbcbbddbacdcaaacddbdbaaadaaacbbbaadcdabcccaddabaadaaacccabcccadddabbcdbcdacdaabdbbcacaacbbcdacdadabbdbdddaddbaadbcbcabcbdbdbacbdadcbdbdbbaadddcabdaabaccdbabbddccdcdcacbbcbcddaaaddccdbcdbaaabdcccddcacddddbadcbdbccaddbcbcdbcbccddbbccaadadbdcccbabdaddbdbbddbbadcbacdcbbcbbdaadabddbbccbaacccbcbdbdabdcaccaacbbdccdbcbdcaaaddadaccacababdbdbbbdcbbaadbbddacdadddabababcbbbbacadababbbdaaaaabaccddcabcadaababdbdacbaacaadbcadaaabcbaabccacdddcbbbdabaacabcbdbccddacadccddcaababacbcccccabdaacdcacadbcabbadbaddbbcddcacbcadbbcccacbdbbcddcacabccabcdbaddddaaadaccbacadbacccadbabaabccdabdcabadaccccdaabcccacacdcbcddccacccabbccbddaabdadacacbbdcbcbacdaccbacdabacadaddcbddcbbdcbaacddbbdcadcdacbaaccccbdcabdccbcbadcdcbaaadcdacbbccbcabbdddaabadaacddcbcddadaccccbaacccbcdddbddbcccadcaacdabbdbaacdbbcbaddadacdddcababdbcaddbddbbabcbcaadabcabcdbdacabbbaacaaccbdbcdccddbdbdbcabacadaccccbbbdddbddddcabdbdccdaccaddaaacbaabbbddacabcdbaddbacdabbaabaccbaddbababbbcaddcccbacbdbbdbbcdcbdaaacbbdaacacabdcdacababdccbcbddacdacbacdacddadbbdbaacccdabcadbdcabcbbccaaaabbabcbcddcddcddbaadadadbabbaaadbaaaaacccbbbcdacddbbdcbddbbdabdbbcddaacddbbdbddacadacadcbdaccabdccdbddcabaaddaccbcaadcaabdbdcdcbbdabcbbadaddcbdacdaabbcbcacaaaabbdbaacdadcbbdabcaabcdaddbabdbdbbaaaabbbbbdaddbcbcddcaccccdddcaddccdbadaabacbaaacabdacaccaabdaccaaccbbccccccbdaccdcdabdcaabdcdddcdccaacadbabccbcdbabdbbacaddcababbdcabcabcaadcbbccbcabaccabddddbdddddbaddcddcaadccabcdbccadacdcdbbcabbccbdbabaaccbdcdbcbccddbacbbccadbccdadcadcadddabbbbccbdbdcbbcdbcbcaadcbbdbbabbaccdbbbaabcccbdcbbbcdaabccddbbaadbcbdcccbdaddbbacaddbacdadbdbcaacbbbdadddcccbcbaaaddababdccdcadcddcdddcdcabadbccdbacccbddadbbbabbdacbbababcbbbcdcbdbcdcbbbbdbbdabdbddbadccdabcaacccaddacbdbaccbcdacbbcbadbddcdcaadbbcbdbdcdabaddaaabdcccbcbaccacbdcababaaadddbddbdbcdadabacbdaaacabdaccdccdacddddcbddaccddcbdacccccbcbbabcdababdbdacadbccbaaccdadbcccbaccacccdcbaddcbaacacdbccdbacdaabbbbbdcadabadbdcddabcaadddabccbbddbccababadbdccccdaaaababadacaaccbcbcbbccbddabcabddbaabdaddbacabcbcaadcabcbbabbcdcdccabacccdbbbabacbddbcdacadbcabcbbcabbaccccdcdacccabcbcabbddacdbbbbdccdbacbcdcddadcaacbdbbdcabbbddcdcdcbddcbbaadddddcabdbdacdccbaacccbccabbaadcdddabadbcdbacbaacdacddcdaaddbaccaaadddbadcdababaaabbdbdbaccdccbaadadaabcbccdacbabcaddacdcdccbaacaaccaacabddbbaabbdaaaccccaabdbababcbcbddaccbcaccdabbaabddbbddacccacdcaddcadcaacaaddacdcabaddcbddbdaddabaccacdbaddaacadcddabcdabdcaaadcaadccdbadcdacccbbccbcaababbbabdbdcbbadbcccbddcdaabdbaacccadadcbacadabddcbbdbacdaaadadcdbacaccbbbabdcdadcadadaddccccccbccaccadcaabadaadbaaacbcaaaaaaabaabcaaccdddbcbacbaacacddabcbdccacdaacccbdaabccdcdbcbbaddbbdbbbaabcaacbacddbdcbccdcdddcacdadcdbbddbbaddcdbbbdbcababcaaacdbcdccbbdddcdcaaabdcabbbdcaabdcdddddcaabbaddcdcaadadbddadbdccbbbcbbcddbbbbaddcdcacdbddaaccdcacbccacbcabbaddacccaaccaaccbcdababacbbabbddcadbbbddcaccabcbddcaacdbdabcccbbbddbddcaadccbdcbcdadbaabccdbaaaddbccdcaddacbbcbccaacadccbaacdddddaccbdbcaacabdcccdcbcbcabdaabdababbbdbbdabcbbbcdbaaccbdbbccacadbbdaabccbaacccbddddbacdccbcabdcdbaaaccbbadddcdbbdcabbccaacacdadacdbccdbcdcbccddadcaaadbcdcbbbbbbdbbaaddaabbbbbabcdcddcbbddddaaaacadbdbdddadaddacdbcddcacabdacbacbccaddacabaddaabbabdcddcaacadaddbdbbabdadbdadbcbcabadbdbbddadabbdabcdcbdadbbbbcadbcccbddabbbddccdabaaddbddbbcaacdbcaadacccaaadddbdbbddacbdddddaabcbabcbdddbcdcaccbabdbbaacbcbaadaacacacccdbdcabbdcbbdbdcbcccaaadbadddccabccdddddddacbccdcdbdcddbbdcbdddaabadddcacbaacdcbaccbddbadcabdbbdddabbbcccdbccdadbbaddacaddbdcbaabccbcbbcbdadbcdadbccdbadcaadddbacbbcbaabdddbdbcbcbbaabaddabddbaaabaacdaaacbbbbacdcbcccbbbabdadaddbcbbcbbbdacbbdbcdabdaadabaabacdcbcdbddbcbcbccdcbbddcdacaccccacdcbbabdabdbdabcdabcbaabadabdcccabadcdadccdbadcadccbddcabaccddabadcdccccdbaccacccdbcaccabaddbdcabbbbbbbabddcdabddacbddbdaacbcaadbbacaacabaaaabbdabbbcdacaaadddabbcccadddccccdabdabccaabdaaccbbacdddbbbcaabccbabbbacbabaacbbabcbcabaacdbbdbbacbccdddbaccdccaabcdabdbbcdaccccccdcdadaacaccaccbacacacccabaddadaccdbddbcccacbaddacabadadcbbdbbbdbaaacbbddccadddccbabdadacaaabaadccdcbababddacabcbbaadcbbbcadbccbcaacbbdcdcaddabdbcaccbdddabbacadcbcddcdccacbddbadaaaacdcbacbbdcabaabdcdadcbaadddbbabacbcbcbbcdabcabbddacadaadddaadcdcbcaacdbaacadddacaaadbbbabbcbdbdadbdcdabbcacdddacadaabdabcdcccacdabdcccdcadcdcacbadaccdbbbbbbdaacddddcdbdddbaaccbcbbabddbbdacddbadcddbdddcdaacdadcbacdbdbcabccacbcdbdabdacabdbbdbdcdcbdcbdbcaaabbbaccdcdccadbbcdbaabadccabaacdacbcccabddcddcbbabbcadcbadbaaacadcdaacbbbabbdcbdbcdbcccdcccacbaacacbbadaadbdabbbbbbcdabdaaaaaaaabdbbddddaddddbcaadccacdbbbcccbabbdbadbbbbcadbadbaadaaddbdbaaacccbacdccbdbcbdcbaddbddbbbaabcbdccdbbacaccccdbddaabcacbbdacddaccbdcddabbccadcdbadbbbddacccaaacbacabacdccdadbdacdadcadddabcbbaccdacdbaddbdbdcddbacabdbbabacabcbadabcdccadbccaabcacdbcbbaccaacdcdcdacdabaaacacdcdddabbdcabccabcacccbdcaccbdcbbddddcccabbccddcbbdbadacbaaaccabddacabcbddcbdccbdcbbaaccdabdbbcaabadacadcdcdccbabcbcbdabcaddcbcbadacccdacaabcdbcdaadaaddcbddcacccccabdcddcbbcdccabaacbbcaaaccdcaaccaadadcccdcacdbdbdaaacadbcbcbdacbbaadadbaaabacabbaadadcbdaacbcdadcaadcdadcadabacadaabbacdcbbdaddbcadadbbccccbaadcbcbdadccddcaddabcdbcbbadbbacdbbbabddbaabccbaabaacdcbddcbaabdbdaadabaacdcdabdccbbacddddcbbbbcbaabdcacadccbacadddaadcacaaaaadcbbbbbcaadbbccdbbbacabbabcbbdaaaddabbcbadaadcdcbccdcbcbbaaabcabdbdadaadddabdddbddabdcbbbaadacddcdbcdbdbbdddccdabdbbdddcdbdbbbbbdcdbcbaabdababacdcbbcbdabcabcabdacabdabdcddaccccdbaabbaaddcbdbdacbbabacabbcbddbcbaadabdbdbcbaccdbacbaabcbdabbaabccababadddbcaababadcabaddcdaadbccdbbadbccacacaadabbdbadadbccabbddcabacababbbadbdcdaabaaabbbacdbcbcbadcbabacccadbdbcdddcbddbdcadaccbcaadbcaccbbcadaadcdacccddccdcaaadcddbaacdcdabdccbdbdddbbddacadcbcabddaaabcdaddbbdacbbddbccccadbdcbaabacbdbdadbbadcdacdadbdbbbcaabcacccccccabbcbcccaaaaccbdcddacdacdaacccabacdbccbababdbbacbacaddaadaddaaabdbbbbdcbbaacccdadbbacbbccaddcaddbacccccccbaaacbdacbcbddcadddcdbabbdcaccccdbaaaddcdccbcbddcdacaddaadbdbdbdddabacdabadcabccdccdaccacadddaacacabbadbacdaacbdacbbbbcbaaddacccccdbcdadddadbdbdaabaaacbbbcadcbcabacdabcabbcbdacaddcdcabddabbaaaaaacdcddddcabbcdacaaaacbdddccdaddccaaacbcabcbcadbcbdaaabdcabbacdabbaaabcdccccacabdddcbdddaadadacabcbcabaaacabbacabdcaabcccadbcbdbcbabddddcdcbbacddaddcdbadbcbcbdccacadccccbadadcaccbdaacbdbbacdcabbdcbbdbdddddadbabbccabcdacdddddabccdbaabddbdccaabcdadddbddabddcacdcbabbcbdbaabbacbdbdaacbaddcdcdbbdcaccadbbacbbbdccaddbacaabdbdbddadcbcbabaaaaacccbbdbcbbdcbcadbaadbdabbdaadbcbbbaabaaaaddadcccaaacaaccaadcdbccbdbdcaddabdababdddccaacbbaacacdacdcacacbcdcbccccdcbdcbbdcddadccbabdbacbdaabcdabbcdaddbaabaacbbbccdddbabcdccccdbadaabdbddcdabbadbabbdcdaaabbacdbdbaabacadbbaadcaccdcdbabaabdabcbdcadddbbddbddadccccabdabbacaaacbbdbdcaccdcdcdbabbdbaccdcbbaaaccbccdcabcbbcccabadabcbbdcbaacddacbdcadddadcacdccbdcacadbaadcdcadcadcdddccdbcdccbcaacbbbbacacadbacdcbbcacdccddbdbcaddcbccdbddbbdcadbbdbbcbdacbdccabbcdbbcbbccabbdccbcabcbbcbcbddcbbcdaadccbbbcdcccddabaddbcbcbbcbaabdbddacdbadaaccbaadbbaaccbdddbdbdbcdacdacccbbcbbddbccdcbcccaaabcabaacadbdaaddbadbdccddddadbcbbadcbbdbabcddcddcacabaacdadaaadccdbaddacbcabcdcacbccbabbcbabdccdccaaabbbdcacddccccaadadbcadcbccaabcbdbcdcccaccaadbacccbdaacabbdadcdccbbbabadabdcaaadaabcdcadddacaaabdcbaaacdddabcdcbacbbdadacbabccabdcccbcdbcbabdbbabcadccbccbaacbcbdcacccbcdbddcbbababccccddbabbbabcbaaabbacdabdccadaaacbbdcaadbabccdaadddababbcdbcaaabdcaccaaddbdcbdbdcadadaacabaccccbbbcbdbaddadbccbdabcdbdadcbccbabacbbdcadcadddbccdcddcbbaacdbdbabadcccbbdcbaabcbbcbbdaacdbbaacacabcacdcdbdcbcdcacdcbbddacacbadcbcdaccccbbbacbbddbadabbaddcbbadbdddcbacdbcbbcdcadbbbcadadadacddadcdbcdbdbbaabdbacbccabdbbcdddcabddadddcacbcbabcbbdaacccabbbbbdccaadbcdabdddbbcccadccddbbadbcadcdbcbacbbbabcbaccbcdbdbcbcccbabbdbdbbbaacadacaddaadccbdbadcbbadbccdcddabcbcddbcbdbcdaabbbbbcddddabdadccadadabdcbbadddbababbcdbdccbdddbbcbdcdadbabdadacbbbdbdacbbdcdabdddbbacdbdcabcbbdabcaaadbcdccdbddcddbdcaccdbcbbacabaacdddcbbcbdbdabbdbbdbcbaddbdbcadabbdcdddbdbcbdcbdbadddcddbacccdacdaaddcdcaaccccbadbbcbadbdcadababdcdcbdbddbbaadcdaddccbbdbbdbbcabbabcadaacaabdcbdbcababcbddaaaddbaccdbdadbdbdcadcbbcbbadabddcbbaacaabbdaabbccbbdbbbcaabdbabbccbabbbacaadabdbbcacdcbabccdbdbbccadbbbcdcacddbbdababaabdacdcdaadcddbabddbdccaacaadcdbacdadbcdcbdcdddcbbcbccccdbdbbcbabcccbacbccdacbabacccddaabdbcdddcdbaadacabaaddbcadcccbcabcdcacaacddbaabdbcabcdbacbacddbbabdacbaabdbdbcbbcbcabdccdcadbdbccaacaddbbabaaadaddccacdadbbbdccbbcdabccbaddcdbddccaacbbbabbdadadcabcacdaaddbdbacdaaaaaccbdadcabbbbaaabbddadbcadcadbaabdacdaadcbbaaacaaacbbcadbcdbbccddbdabbbaacadbabdaccdaadbadcccdcbcdcabababbaaaadaadadccbbadbcabcbdcdcdcacadcdacabadbdaadddbdcbddadcccccadbabcadadbadbbaaaabbacbcdbddcadcddaabbddcaaacbbbdabcbddbbdcaccbbbbddddbbadddbcdddbbaccbaabdbadcbaccaaaccdbcadcbddbbcbabdabcacbcdbcddbdccbdcdddbccaacdaaaddccdbacdccbdadccdbdbcdcdacbdcdcccdcddadbbbaddadddbbcccbbdbaaccdabdddcadcdacacdccbdbccacdbaacbbbbababccbcacadadbacddcbbaddddcbbcdadbdcadbbbbdbbaddcddcbdbaccbadcabcaadbdbbbccabcddccbdadccdbbcbcacadaabdbbadcbaaabdcacbacddbabcadacdbcdbabdbdbccaabdccbacabdcaaaadcaacdabcbdbcccbaadddcabaaaabccbddaabababcddcdbabdbcaabbbbccaddadaddbbbccabcbcdadcabbacadacbacdbbbcbcdadccacaddbccbbdabccdccddddbcddabcadbddbddaacdaadddbcacaccbdbcccbbbadccaddccabdcdccccbdaaacdadacabcdcccbbdbbaaccdbaacbacadcabddcdaacbbdbbaadddcdabbddbaacadcddccadbaaabbaddbcdbaccacbcbbcbcaadbbdbdbbbccaadbdbabdcabcaabbdcadbbbcdddabdcdbdaaaccadcabaddcabdadacbddbcbacdadaddccbcadbabcadcdacccdbaaccaddddbadddcbbbcabddbacbccdbcbccddbbbcdcbccaaaaababababcbaccabbcabdbdabdcadacacbbbdcacdaabdbdbdbbdcbbbbadbdabaccaabbdddbaadbadcbccddcadcdadbbcadcacdacbdccadbbccadbaaddcbbbcaaaaddbbcbcdbabbdadbabcaccadbbadccacacacdcbbcbbccbdaccbadbdaadbdbdbddddddddcddaabaacabaddbdbdddaacccbbdcdaadadaccaabdaaddaacbccaadbadabdaacbbcabcbdabadbbccdabdabcdbccbaacbbdccbdabddcaabbcabcbcdbbcbbbcadacaadcadddbbadbdcbbcdaccdddccaadcabdcdaabcbddddadbccccbcddbcaaccbbbbcbaaadaacabbbabdbadacbaadcdadcadbaadbcccaabbaabcadcdddcabdaccbdabddcddbdaccbbdabdcddbcbabbccccbdccbcdbccdcbcccaaddadbbaccaaccdcbbadcaccaadacdadbcdbbdbdabdcaccccdbcabdbdcbcdbadcbbbcbadcccaacacabcbccdaabbbdadcadacccdcddbdaccdccddadcbccccaaabbdacccacabcddbcdcdddcdcaccddadcababcacadababdbacdbcbcaccbbdbcbddcdbadbadaaabdcbaddbcbccbcccddabdacddcdbaadcbaabbadccacccaaabbbbccadcabdcaaccdaccbaaadacdcbbdbbaccbcdbbdaabacddbcbbcddbcaaabcaabbabcdbcdadbaabcdaaaddacdbaddbdbdccadbcddcdccdbbbadbccababdaacbbbaaacdddbadaacdaacadaddcaabcbbdccddacaddbacababadcdbdbccacddcadbacccbbdbbdddacdccbabdcadadcbcdcdacdcadcbddbaddaaabbbcbbcbaccdaadacbbbabbbcaaabbaaddbbdcdddbcbdccacadacddcddaacadbcacdadbbdbcdbddadddababcdddaaaabbbdddbcbadbbaabbdddadbccbbdcbdbabadbbdcbdbdbddcbccdcdcbcccacdabdaadbdbddbbbbbbccbabadbccaccdaccbaabaccccbdaacdbacdaccaccbbaddbaccadbaddddaacdbddddcdabdbaccbacddabacccabbdddccdcbddbacadbdbaadccddcdcddddcbaddbdcaadccccaaddcadddccccdbbcbacdbdbaabdacdaabacdbcdacdbbbccbcbcaabbcdbbadcdcbbaaacbcbacadcbabacaaddabddcbaddddcdbcbdcdaacdccccaaaabccbbdacdabadacdcaabdbbcaccacddbbaacbbadbbbccdccaacbddbbdcacdaadbaccbdcacacaadbaacaabcbadbbadcdacccdcbccdcbcdaaccdbbbdbaacbabdbcaabcbaddbbadccccccbdbacdcbdddbadddcdbacbcbbcabbbdabbbddbaacabcabccdbcddaabddacbcacaccddcccccaccadabbcccabbcabbddaacbcccdcbbabbbadcdbdaaacdbbcbccacdaaacdaaddbbccbcacdbdaadcddbcadbdddabacbaccadaabadbacbcdbcaacbdcaddcacacccadcbddcddbdbacdadadcbdbcbabdcbddabbcbabbcdcbbabbdcaddcacddbacbabababaabdcdccbdadbcccabbcdaabcabcccddacadbccdcdbadbcadddcdaabdbddcbcadacbdbcbbaadcddaaacbdcbcabadaacdaccbcbdcdcbabaaadddcdadcabdaddcbdaddabaaaadabdabbdbacbaccaccababcacdbccdaacabbbbddddddcddadbbccabddcbcabaccbbcdabcbaaacdbabaabcacbadcdbccacbabcbadcabdbadbcbaacbcdcdaaaccbddabcbadcbaaccaabcbabddaaddbaaacabccaabcdddacdacdbccdccaadbbbabaccdabcacdbdbccadaacdbdabcaababdbbdbddccdaabdcbcadabbbbddaccbbbcbdaabaaacdcdacdaccdbbdacdbabcadabadbaadddddcdddabddbbaddbcaaaaaddcdcbccdadabadbcbabdaddbcccaadccbdadacddcbacaccccabaddbbdacbbbdbdbabbbdbbddbddacbaabddccbcdccabaaacababaabbadccdadadbdcadbbdddbdcbbacaababcbaaadacacadbbbddcdbdbcbdccddadbdbbdddbbddacabcabaccadacbcbaabbbbbbdcadacbadddcbbbbdcdcdbadbcaaadadccddcccbbaaaacbbacaaadadacdaaccdbdbabdccbdddcdddcbdadbbaccaadbacaacbbacbcadbdcbcccbcdcdddcbadddabcbaaabbaaadbcbdcddcbcdabdcacaccdaaadbabcbdcbcbaacadbabcbbbcbabddaadbcacaaddccbbbbdabdcbbccbcbccdcbbdaaccabdcbaaccdddccccbaaaabaabcabaddadbadcdcbccddccbccccccacacdbccdcccdcbcabaadaabbbdcaccadcdccccdbabcccbbabcdaadddcacabbbdadddbdcabbcbaaaccdbaadadcdcacbbddddadcccccbdacbccaddbbddaddcccbabcabacddcabdacdcdaaccbdabdadcaaaadbadbacabacddcdcaacaccdbbbabcaaabcbdcbcacccadcdcbdbbccdcdacdbdddcdbcbbcbcadabdcaaccdbbbdcadcbaababcccadcbbbcacccdadcbacbccdbdbacadcabbdacddbccadbbdbabbcdbdcbdccaabbaaadcdabcabccaabaadbcdcabddcdcaccabacbcddddbccdaaccdabdbdccaddbadabbcbdaadcdddbaaadacdbdcacaccbdcbadabbaadabbdcadbcaaabadcbacacccccdcbacbdadccaacdbadcadadbdbcbcacdadcbbaacbbcaccccccadcdaabbacccacdcdcdbcbbbbaacddcdaaababccbccbcbacbcbbcdbadbbacdccaddbadacdcaaccaaacbdcdcccdccadabdaaadabaabadacbaadbbdabdbbddababdbdaaddbdbabccdbdbdccbcdbbbbbcddacccdacacbcdbbbcccdbbccdbaabdabdcdaddbdcaddddccabbbddadbbabbccabccdcaabbbcbbbbcbacdcdbaabdccccaacaabdcacccadacbabbdabadaaadcaaabbabcbcabbbadacbacadbdcacdabcbbcabdcaabbbaddbadcbddccbadcccbcdaaccdaadaadaadbcbdcbabbddabccccdaddacacdbddcbabacdbdccccddbcacbacbabadcbaddbcbbabacbddbbdadbdcabcddbddbdccbdacbadcbaabbadccbbaadbacbddacdbdcccaaddbaaacabdbaabaabccbababbabbdccbbbacbacbacbdadadbdabdacdbbadccbbcdaadbcacccccdcaddacbbdccbdcdcdcdbbacaddadbdabcccbbcbadddcadbdbdadacccbaabddbccabdabdaaabbcdbbbacbabcdcccbddbcbaaaadbaabddbadabacbdacacdaccaddacccdacdbdbcccaaacbaaabccdacbdaadbacbdbdbbbbaddababdadcdacdddcbdabbdbbdcbaaabaadddabdbcdbdaabadcbcddddababbdddbadbabddababbcadaadabbaabbdcbaddabbadaccccbdcdacbcdabbcbacddaadbbabccacdbadaabbdcbcbadbacabbadcaddbdbddcdddddbdadbdadaabbccdbacbbdbacdaaaccabbbbadcbdcddcdbdbabbabacabcbbbcdcbddcadbbdddbacddabdabaccabcbdcadcbbddbcabbdddcbbbccadbcbaabcccccbaacdabccddadcccadabdcdbccbdcadddaaddccddcbdccacadbcbcdcdbcaacbdacbcbddcbcadcbdcbccdbcacadccaadbbddbcaddbadaacadcdbcdcbccdcdadaddcddbcbbddcbbcacbcaadaaccbcdbbbaddcaabcddaccdaacddbcddbacccccaaacdbdadcbadaaaddbdbbbdddadcaacacbdbabacbabbdbcdbbbccaacacdacbdacbbcaaaccdacdccdbcadddcdabcaadddcbaaacbbbadccccaabcabaadcddabbaaabbcaabcabaacddbacbdbabacdadbdbcaaccadccdaaadacbadbacdbbbbbdbaacbccdacddbacaacdcdabbcbbbdbdcaabbbadcaabbdaabccadcbbcddbabbdaccabdbadaacdaccbbaddadbdbcdbaaadcddcdcbcdcacaabbdacdacddacbbabaabdcccbabccdcacdaaacdacddcccbdacbccdcadbcddadadadcddacbcabdbaadbacacdddcabacbcbcbcbaabcadcbadbcbdaddcbdaabccacabdddccbdccdbbdbbbdbdbbcaacbbdaccdabbccdaccbccaadbdaddbbabdbcbdcabbddddacacddbdaddabdccdacccaabadbdbdbadbcdbaaaabbaaccaddacadbabdbacacabcbcbbbdbdbdadddaaabbbbbababdbaccabdacddcbaddacabcdbacacdbcbaddcdbcbdbadccbabcacdccdccdccacdbadccadbaddcddcbdbdbcdcdcbdcacddddaabbaddaabbbcabddbbbbbbabbdcababbdaadcdddbacbcacbaccdaaadccabbbbadccddaaccbcbbbacabbbaaacdbcbdabcabdccddbbdcabccaaaacbabcdbacdacaacabdadbcbbbabdcaaadcdddbcacbadcccbbcdbbbbdccddadadaadbdadabbccaaccdbdcbdabadabcccabaaaacdaaccdabbdabdbcabcdacbdcbabdaaacacabcbbcabddbddabdbaadaadaadcbdbabcdcadadacbcdaacbdcacccbdbdddddbcdbdaabdcbbbbaaadaaadddcadcdaadbabadbadcdacabaabdcbcacabbbcaabacabdddaacbbcaddadcbacbbadabdccccddcbdaacbdbccbcbcccbcabdcbaaadccdcababdabdbdacbbbcdbcccdcdadccabbddcbbaddacbccbabbacccddbbabccadcbbbbaacadcddccabcdddbacdcdbdcccbcacddbcbccbbbdddbbcccdbadbcabddccbaabccdcaadaabbbccbbcbcbccbcacaadcdaaccaacaabdccdbacadbcaddcbabbbdabddbaaccdbbdbbbbdbcbcbcdbaddabadccdbcbbbacdbcdcacabcabacdacadbacdbaaacdddddcdaadddcadbcacdacddcdacccbccddbadabcccdccbbcbcadcacdabacadacbdddbdaaaacbddabcbcbdccbacbadcbcccdbcdadaacbdaadbdaaabcabaacdccdccbacbbaacddddccbddccadcaabbbbabbccccdcacbaddaadcbabcbbadacdbdcbabdadaddcdbdbcbbbabcdccacdbbdbccdbdbabddbcadccaddbadbcdddaadbaadbccbccbbadaacdadcacbbccabdcbaccabdadbcdacdcacdccdabccdacbbababdbabadbbdbdbbadddccacaccabacdbbdbacbaaacbdabcccaadddaaacbabbcaccbddbbacdddbcbcbdcbcddbccdcddaaabcdddaaababdadabbddddadacbccbdaabbbccbbacdbbabbbcaadaadaddabddcaadbddaacdabbbdabaaccbabcadbbcaacbbdccadcabbcccacdcdacbccbdcbababbbabbcabdadbcbaddaabdcdbcdcbbcdaddadcddacdadcaddadbcbababadccaabdcbbcdadccdadddaacdcccaacbdbcbbdccabcbbaaaabcdcbcdbaabdddacccddcabcdabcddaaaacccbdaadcaabaaccbcdaacbbbccdcaacaddbddcbcdcbbadabbddddcbcbcaadddcaaabbcbcdadacbbbabaabddcdbccdbcacdadddabbdcbbacbabbcaaacdaabcdbcbabbabdbbbbabbdcdacbdabaaddabdcaddcbbbccdcbcadcdcbbcadccabdabdcaabdbbcdcabbbbadbddddbdddddcaadabaaadbcdddddccddbbbdbaddcddbdbddcccbbddbaaadccbcaabcdbcdcbadabbdcabacccbbbcddddcabdbdbbaaadcabbbbbaccdcadcbccdbbabbbcabdccbcbbbcdadacdaaaaddaddaccccabadcdddcbcbaababcaadbcbccdbaccbaadcdbbcbabcadadadbadcccbdcdcaccadcddbdbcdbaaaccdbabbcbbaaadcbdbccaccbaabcaccccbadcddcdcaaccbdbacbadadacbdddabbdcaddadbbddcdbacdcaacabdddcaacccbcaaccdbbcacdabcbacbddaddddadddbbbbbbabcaabaabbdcdbbabdbdddbdacbcbcbcddbbcbbabcddccdccaaacddbbdbcdddbcaaabbaaddcddabbccabacdbdbaddcdadccdccadcbabbacbaadbbacbcdcbbcbddbbcdacccaddccacdbaccdddddbdcdbbacdccdbdabdabbcbbbabcbacdcacadbaccdddbddaadbcdabaccbcbdaaddaadacabbcbabbcbabaddaabcaccabcbddcacbdcbdbbcccbdadcacaccdbbbacdcabbbaadcbdaaadbdcabcdccabcbdcdcadccbbbadccabcbcddbdaccaacdabaaadbabadaabdbbdcdabcacbbcdbaccdabbccaddaacbdccbbbcdddacacacdbbdbddabccadadcacbbdabcacaddadcdbacdbbcdabcddadccdcddcdbabbcccddbdddcbaacacbcbbacdbacbcbdccbbcaccdcabcbdadbbaaabdddaccabcddababcaabdaadcbbcaadccccccdacaddcdcadadcdcbcdccccbdddaabddbacbcababccbcabaccaddaccdcadccacccdbdadcabaddcdbbbbaccacbacbbbaaaadbdcbacbbcddbbcdcbddbbabaadadbacbaaaaccccbddbddabaaaccbbabbdddbbccaddcccbbbdccbdddbbaaabcddacddcdbabacddcdccbdaabbabacdcacdaacdabdbaaaaabadbbccbbbaacbbbacbbbdccbabbdcbdcdddddddccbdaaaccdabcdbdcbddbcaaccdacabbdbbcccabddbabdbbadbddbaabccbdcbaaaaabcaccbbcddaadcaacdbbacbcbddbccbddcadddbddbcbbacddcadbcddcdbdacdbbbdbaddbbdcdccbccbbddadabccbdcdbacdbcabbdbbcdcdbddacbdcdcabbbdbbaaaadaabcadcdbccbbbbbbadbdadddddddcbcaacaadddccabccdcdbabacdacccbacdccdabdadadcbaddbdcbbddcdbaabcadddbccddcccdcdaaaabdcbbdbaacbcdacadaddccacddbddbadacacabbcdcbaabaaabddcdddaddddabbcdcdabddccbdacddcdbaabbcabadadacbbbcbdbabdddaadaabacbccbbdbabcdcaacdaccccaaacbcabdaabacadcabddbbdbaacbadcbadcacbacddcdcacacaadcbaccbacaacbbbcaddbabbbbdccdbbccdabbdcdbbdbcbccaaacaabbbabcadcdcdabccbbcbabdaaddbbbbacabdcbbdaaaccbcdbadcbcdbdbdabdacabcacbadabcbbddbcddbdcdccbbcbaccaabacdbcccbbbbcdcdbbccaababdacdcbacccbadbdabcdabbbacaaccdbddccbbdabacdadaaabbbbdaaccddaaabaacddaddbbddadccbddabbcaabccdcacdbbbdaddcbccbccbcbbbdcbcdadabddaacbbaabadbbcabdacdcccacbabccaaacacdbdbbbcdacdccdbacabbabddaaaacadbbdadababbacbdadbacdbcbcccddacdccbcacaaaccdccdddbbdabacadbbcdcccbacacbacdcddddcdddbbabdbacacdabddaddbcabbddabdcccccbbcdcddcdacddcddcdadccdbbccbacaaadcabbcabbbaacbacbbababdbbcdccdbbbacacdcccbcbbabaabbbdddbaabdacdbdaaddacdbaacabaddcdbdcaccbcbacaabacddbcabbbcdbbbcababaacabacdcdabacccadbabaabbaadcbbacaadbbdbddcaddbabacadbcdbbbcbababbdbddcdccccbbcddbcabdbadcbcdbaccabbbccbbcabadaabadabddddccabbaaddcaadcbbacaacbdbbdcbcccbbdcadccabaabcaccbadcbdabdbdcaccadcabbbdbddbcaacccdadddaabbabacbbbddcaacdbcdbddadacadcdbababbdabcbcdcbbaabdcacaccbccdbbaaabbcbdcddddcdbadbcdccbdccbbadcbacaddbbaabacbababcadcaaccdacdabaadadadbaacbcbcbddcdbdaadcbddbaadbbbaaadaabacbcbbbcbdaabcdbdcadbcaadcbcbbaccbacacccacdaabadbbbadcbdbbabcacacbbbdbdbbadbcdbbcdcdadaabcdcddaccadaddddbabaaccccdadddaaacadbaacdaacbccabbcdddcddcaaccbbaacaacdddcccbcaaacabcddddcddcbabbabdbacccabadbdbdbdabddddcbcbaaccdcadcddbadbbadcdabcdcbabcbcbaddadbcbdcbdaaabcdacbaabaadbcdbcdbdbbccddadccbbbbabdbadacabadbacbddaadcadbdbcaabacbbaadccaccbccdccaacabdbddaadcdcaddbaddcbdbbadbacdbcacbcbbcaacccabbbacabccadacbcaabcbdacdaacacababadbdddbacdcdbaccbdbbadaacbaaabcddacbaaccdbaadcdbabdcaccccddcddccadbbdbcccbddddbabacacccbababddacbdbabaddcccccdababdacbddcddccddcabdbcdabbdbcacdccdacdbbbbcdccbaaaddccccbcbbccdcdbbddcbbccccbddbbbaccadcdddbaabbacbaddbabbbbbddadbdaabdccdadddbbbcacdcdbdcdbbddccaabdabcabcdcdacdbcdbbacccdccabaaddacccdbbdbaddbabaccadcbdadcdcdcacaaddbbabbbdcaadcbacbdcddcbadbacbadbdddbaddcacdcaacaadbbbdccdadbadcddadbbbbabcacbdbbbcdcdcddaabdbadbbcbacacdbbbaabcbacaabcaadadbdcbcbbbaccacabacaccdabcdbddcddbcbaccaadcdabaaaccaadccabcdbcacaabbacacdbadcacbaaccbaddacbaaadadcbbabaaaadcdbccddababccabdcabdadcadabacbadbbbcdabdcbcbacacadbbcaacccacaaaaadbdddadadaddbdaabaadaadbbbcabcbddcaabbcddbdcbacbacacbdcdbcadbaaddaaccdbcdcbdabbbcbdccbdccacacdddcaccbccaabaaaadbbbbbadcdcadbabcbacbcdbcbdacccdcacbdaddaabbdbccadbdadacddbbcaabcacccbcbaaccbadbacdadadbbbdacabccdacddbccaababbacacdcdabccbabccaaaccaadaddbabbbdcaacddbaddcdbdabdbdbcbddaaabacdcbdcccddcbcbdbccabadbbabacccabcbaaabacaaaaacdabbcbcdabcdabbdbcbcdcbbdcdbdbaabcbcdcbddccbaccbddbadcdcaddacbcabccdcbbdbcacbcbbdddaabcaacacdabdbbadbbdcacaacdcadbabbdbcddcacbdcbbccdacbdabdcabdbadaabaddcabbbdbdaaacdbdddabacacaabdcddcacaabdcaddbdcdacbcbdbbbcaadddcaaddbaadddcccaaaacbbddcabdacaccdcbdabbdcbcdcacbabbacbddbbbdccacaabbccddcbdddaaaababdaaacbcdddbcacbbbddadbaacbccdcddaacbaaddbbaababadaccaddbcabdadcdbdccabadabcbcbbaadbaccadcabaadaccdcbdaaccbabdabccbabcacabdaaabaddbdabdaacadccdbaaaccdbbbaacbadcddaccbbbcbdcaddaaabbbdbabbdbccbadabadbcccaabddcdabcaccbdcabcbdcddccdbdbcaacaaacccbccdabdcaddcccacbacddbdccddabcaddcbabdbdcdbacccbbbadcbdbbcdcbbabdacbdadaddbddcbcaaabcccaadbcbacbccdbccdaabacbacdcaaacdcbdaddbcabcbbbaadcbdacbdbcababbdcbabbaccdbaabcabccdbcdcdbaabadcbabdabcacdabcdbbcabbbdbdadaadcccdcbdaabbccabbdadaabdbcdabddcbacabbcdadbaaabdcdbbbddcacccccbadcacbbbacbbadcdbdbbdddbbbbdcadbadbbdcdcddabddbabcccadddccdbddcddadacbabdccbdcbbabadbbdccbababaccbdacbdaabdcbbcaacdccbcbbdcdbacacdadcdabcdacadabbcdaccddacdaacbabbbbdbbddbcabccdccddaacccdaacdabccdbdacbddcdcdacabbcbbdddcacacbbbbbaaaccdbaddcaabaadccdbbccbccbdbbdccdddcbdadbcaccbdbbcbcadddbcbbdccccacaadccaddadbabdbdacadccadddadbacdbcbcbdcccadcbbbddbacbddcbdccddadcacaccdbcdbbdabaaaddbccacdcdcdbbbcadbdccabbbdadccaddbcabbdccdddbddaacaacbabbdbadbdbbddadaacbddcbaaddcbbbdbbbcdcbcadbbacabcccccbbaccdaabcbacddbcdcdbabbcaddacaddbdacdbbcdaadbbacaaddacadaccbcaddbddbdaacadadcbbdadbdbadbddddccdabccaaacbcddcdcdbaacddbddacdcdcbcaddaaadbdbccaabdbaaccaabcbccaabbbcbdacddaaddabbccacdbddcbddaaaadccaacdcaaadcacbacdcabdbdabadbcbabbbbcdabcbbdddbdaabaadbcbbbbccbcaabdaabacacbbcaddaababdaadccbddbadccaaadbccdcbcaadcabcaddaccddbcbdcaaacccbddddbdbbcdbbabbcabdbcaacccbcdacdcacbcdcccabacbaddbddadadacdacdabdcaabaabcccacdadcbcbdabadcabaccddccaadccccaaadcdcbacaaabdbcbdbddbcabcbbbbbbccdbcdddcdbbaccaaacbaabbacdbaaacdadbcdcdcacaaccdcbdaddbacadacaddbadddacdaabaccbacabaadbbabbbdacaabcdbbbdaabcbbdccccbdacaabccaabadadcaabdcdcacbdcacaadcccadadbbcbdcabbccbabdaacacaacccaacdddbadaadcddbdadadbbadbaccccdbcdbaccacbacdbbaababdddcacacbccaddacdcdcbbaaaabbaddbcaadbbdcaacbdcababadccadcdcddcdacdacbdbdbdcacddcacbacdcaacbacddcddccdacbdddcaaacbbbcdcbbcadcbdbcdbadbcdbbdccaccdacdadaacacbddbacbdbdabdbbcbaccabcddbababbbdddbbcbbdaadcccabdcdbdccdbcadabacbcbbaaacbdaaccdccabcbaabddabbdababbcdbdbaacadcbcaaaccbaccabdccdcbabaacbadcbcadabaacbdcabccacbcdccccaaaccddabaababdcadcbaccbbccdbcdaadbcbbadadddbdadcddacbcdbdcadbbddbdbaacbadaabababccaabcadbaadcaddbabdbacccccbbdbdaddaccacdcddaccabaacbdcdcbbacbbcaaaccbaaabadccaabadbaacaddabbcdcbabacadcaaccbdacbabcabacdaabdccaaccdccbcbbacdbcbbddccaaacdcdddabadbbbdbcbacaadcdcddbdcccbbbadcabcbdcaacbbaddcbbcccaaaacdcbccabcbdcbdababcbccccdcdcdcbaadcdacbcacabbbdaaadbbabcdaacacabbcaccabbbddabccbabddcbbdddbcdccdadddbddacbccdbccdbadbdaccdadaccddbbadabbababdabaaaaaacabbdabdabdacbbaacaaadccddcabdacadadadbdbbaaabdacdddadbdcdbdcadddcadddccdaccdcbbabbbaadaccabddbbcbcacbcaacadbcddaacddcdccaabccdabdabddccccbdccdbdcdcdbbbbcacaccbdcaabbdabddddccccbdbddaaadbcdcaacddbdbabbcaaddadcacaacabbacbbabbddbbbbadbccbdbadcaddabacbdbbdcbdcabacbaadbbcacbacdbcbcbabbccabdcabcabacbbcbabcdbbddddbadaabbadccdcdbbabccdcdcdacdaadbaadccdbadccdabccaddbdacaddccaaadbcdaccbdaccadadbbbdabbadaccbabdcacdadccabcddadbadccbacbbcacaadbbdadbbdccaddbbcdacaddddcdbbdcdabdcbcddcaacacacdcddbbdddbbdcddbcbaabacdddbcaddcccdddaadbcbadcbcbdabdbbdbaccacabcdaacacacdccbcbdaddcbcdbcaccddccdbbcddaabddbadbdcbdaacabdbbcccbaccdaadcccbaaccbdddaabccdbdaaaabdbadddddcbbcadbddababcaadaadcbbbcaaaadabbbbadcadcddcbdaccdcbccdbddbccbddadddccbbdcccaabaadddcddadaadabdbbbadbcdcdacdbbdcdcddbcaaaadadcdbbaacacbdadcdcaaccacdaaaccabcabbacadbbaadbbdbdcbddaacaadbbdcbbdbbbbcccddbbacdccdcccbbcdbcdaaabaccdddaaaadbbcbdbababcdcbaadbbcdaccbbcacbcdabcaaccbaabcdaabbacadddbcbddbcdddaddccbccbdccddbcbbbaacbbbddddccdcacabdcdbddccddabdbcbccdddccdcddacadaddbcacccaaacaabaaadcccaaddbbdbccbcbcaabbaccbdcaadbdbbcbacbbcabddbdbccdcbcadcdbbaddccbbbaccadaabbcacaadccadbadcccdaabacbdcaaddacdacdbcadddbcbadcbcdbbdcdccbcccdadbabbdbbcdacddcbadcbddcaadcbddacdbadaadbbbabbbdacccaddccabbdbacaacbbcccabdcbbccabcbaccabcaacacdaddcdcaaababddbaaabdcddddabdbdbddccbbcdcbcdcacbdacdbacccbaaaaddcaccbcdcaccaacdcccddadadcabadccdcccbbdcadacaddbccbdbcaccadcbbadabdabcadaabdcacccbbaddbccbcaccccaacdbdddcbbdadcbdadcbddbcabdaabaaabccbcbdabdcaabbaaadcdadcdcdcbaccbaaadbbbaacbdabcaddcaccadbccdbadccdcbdbdccaadabaabadabccdbabdcaaddabbdddadbcaacabcbdcddbdaaccdbbbacabccaaaaddbaacbcdccbabdcbdcdccadcadbdbccbadcdcbccabbcbcccdadcdcabdbdbbbccbcbcabcbccaacbacdabbbaadccccaccadbacacacaaabcaadaadbbaaddbbbddaaddbcddcaaccbdbadbcbbabddadaaacccaddbbcacccbbdbcccbcddbcaacdbaaadabaddcaddcdadbdddaccdbbcdbbdbddccdbcbabddcbdcdbcddcccaadbcddbdabdadbbaccdddabcaccbabccbcdabacddccdcbcbadcbaddbcbdcbdbdadbaabdabbdacccabbbcccbdaaccccdabcdbbabcbcdcddcbddbbbababcdbbbabacddcdaabbdccccabdabdbbbdabcadbbddccccdabcccbdccdbcbbbddcccddaddbbaabdadcadaacbdacdccbccdabdcaddbbaabbbadcdcbbcabbaacaacdcaaccabccddddaaacaccabbddbaabbdbaacbbacbaacccacbbadbcaadbcdddccccbcdbbcbbadbcbdddacacabbbcbcddadaddccddbdaaaabdacbcabbaddccaccabbdbbcdaadccababaabdbbbadaaddcabbacaddbddccadbbccdcadcbacbaaaabaabccacbabacabcddddadbdadadacdabbacbdbaaaccabadacccdbbcdadbdabdbccacacaaacacbddcaccaabcdcdadbcccdcadbadaddaaabbadaadabacaabccccdabbbcaacbcadaabcbddbbbbadadabbbcadbadccdadcdcabbbcacbccbbddddabccddcaacabbbccdadcbcddbcbadddababaccbddbbacdddcbdccbdbcabacbaadcabcddcddcbacdbbabdcddabcbdadcaccdaacccdbbbbcabbbbcccccdbdcdbcccdaadaccddbbcbcdcdaaacbaddbaaadcaaabacbdcbacabadbbbabbcaadbabdaabcdaabdddcbaabccaddbadaaacdacccacccacbcbcaddbabcbabdbdadccbbabddcdacbcbcbbcbccabcbbdaccadbcdacddbbbccbcbbdbdbaabbcadbccacbbacbcbdbdbbddddcdcadaababadabadaccaacbabdbbacdbdbcddaababcdbcacbdcdddbbbcaddcbabacadccabadcdcddcddcabdddcbbcbdcaddcacadcdcaddbcbbbbdacbdbbcadbabcccdbbdcbcddbddddbbcbaaccdcbabdbdbbdcdbbacbdcaacdbdcdcbccddbababcddcdbdccbaaabdadbaaccdbddacdccbdbcdaccbdccdaabbcdbabaaaccdcabbadcdadbddabdabadacbcbdcddcaabadddabcdcccdadbccdacbcbdabdbaddadacccabcadaacbbbaabababcdbbddbaacababadaccacbabbbcaaaabcbbcddaccbabddbbdccccacadbcdcdbdbacbddaadbaacbaabccadbaacbccaabbcdcbcddbadccddacdddcaacbbdabdcbadbaaddadbbcdbbbbabcbdbbabaccccbdcababdaabcbcbbbadcaacddbbcbbaadcacadaadabcddbadbdaddacbbbabbdcacaccbdddccdcbcdaddbadabaacbcaaaccbbadcbddbbdddccdaadaddaaddddbbbadbadabddccbcccacabdbbbbdadcbabaabbcadddddbddadccbdddbbcabbabbbbacddcadcbbdbbcaddcadbdbbdbadcbadadcdadacdddcadcabcdbabbbadddbbcbdcccdccddcadcccdacbdadbcbcadbaaaabbaccbacccdbbdaaaaaddccddabaacdcdcbaccddcbdbccdbbbadbddbbdbbbdbdbacbcadbddcacabaaaabcbcaadacbbacbbabbbcbbaacbdaaaababaaadbcdcaccccbbddbdcbdcddcdaddccbabacbcacaddcdbadaccacddbcbcdacbcbaccadbcbabbdcadcadddbdccaadbbdccbaaaacdbbadabdcdabdabbbbacdcdcdcccabbaaabaaddccbbdaaaaabaabadddadcdadaccaaaabacbadbdadbadbacdddbbbcdddcdcaabaabcabbaadbcccdaccbcbccbdcccbcabcbbbabcbdacbccdbaabdbadcdaacbbbcbbcbdcbbadaccddcaabbbbccdcbcbababddddbcbacdddbdbbaadcacdbabbaabbbdadbabcdacdddccdbccadacddbbccddccacacdadaacbacdabaddcbdaddadbbcdcbacdadbdaadbcbddadabaaddbddadaabdbabaddcbdcddcadaaaccbbdbdcdadcbcbcbaaacbbbbbacbdcddbabccdbccdbaabadcaaaadaacadbdbcbdbccdcaadcdbaaddcabbaaabdbbbbbcacabcadaccbbdbabbdbddbabdcbabcdbccbbcdabbadaadcbcacabbdbadaddbdbadbcabbadbdbbcccabbcdbcadabbbcbddbccbcbbbcbbcccbbcbaddccbccacdbdcdadddcbbacdcabdcdacccbadccbacddaddcbcbdaaacbccbdccacdadbdbcbbdbdbabdbdbadaddcbcdacaabbbbbddcccbbbbcadaabdaddcddbdadacaccaddacddbdbbbcaddadbcbcdbabababbcbbdccaacbbddcbcdadccaadbcabadcccddacaaacaaddcdcdcbacbdcabababdbacdbbacadddcaccdacbdaaacddabddacbbacacbdbaaaccdacbcddacccabaaddabccaddccabdacaabdacbccdcbccbbddcccdabaadbcdbddadaccacdcdbbcaddcadaabadabbddacbaccddcbcdcccbbbacabdcbdadbcbbdbbbbbcbcdddadaddbadcaacdcacacbacdadbacbcbabbbcbdbadcaccbadaacbaddabcdcbdabdcbdbcdbabcaccadddbadbcbcdbadbacabcdbcaaccadbcccbdbbacadbcadbbbaaddabdbbbabdbcbbcbacccdbbbadbbaabbdbaabcdadccbcbaccadbaacaaadccdccaaabaabdccdcbddbbdbdbbbbccdadbdddaacbbbdccbcaccbdccaacbadbacbacdbadaadbbbdababcdcccdcabcbddcabccccbbdbcdcacacdddaccabdacaccbadaddabaaacbcaacbaddbcdaabacbbbcbcaadccdbadcadcbbabbcacdcdbaacadbccbdccccddaabdbbccabcbdabadcdbbabdaabcbcaadddccaacbdabbdcaadbdccaabbdcdcddccccdbccccbdddcbacdcbaaccbddbacdadacacdbdaaabbaacbbbcdcdccbbddabcdccbdbdccbcdaaabcddccdadcbdacbdaaabadbdcdddbdbcbdcaadcdbcbbadaaaaabbdacbddbddcbbacddddcdacdbddbbcdbcacddcdddabbcabdaaadaadccdadddbbacaccaccacadcbaaddcddcdadacdacbabaacacacbadcccbcdbcbaaaaaaadbadbddccbbbdcacaadcddcaaacbdcddaabdbadccbbacbccbdbdcbcbcdacabababadbcbbccdacddbadbbacbdddccccdaabcbaadbadcaabbabcdaaaabdaaaaccadddacdbbdbcbdddadaddcbcddabbcdccdabdcccdadbbbdccccbdbbccbccaaadbdabcbcabacdccccadabacacabbdbcdcbadbdcbcbddbacacbdaddcadcabcccddccabccbccdbadbbadcbcbacbbbadbdaabbacbacacadbcdacabadccadbcddcdcabbaabdcbcacbcaddcbbbbbcddabdbcacbaaccbdbabadccccbddbdcbcbcbbdcdcacdacaddacbbcccddbabddcacbbbccbdacadcbbcdaaccbdbddcbdcbcaabdddbbabbbcdcbddbddbbcdbccabbbbddaadacbadcbbccaababcabcbbbaacdabbbaacbcccdacdcdbacbcaadbaadaaacbbbcbabdbdbccbbcabbbcccccdccdcbccdbcadbdacbacbdadbdcccdddbcabcbcbcbdbabbbbadbcdaddbbcbddacaacbcaaccdaaaadaacdcbadcbbdbaabdcabdabaaccbabbadacabdccbbccaacddbbabaddacbbbacbbbbcaabdacbdbbbcadcadaabacabcbdacabaacbcbaaabcddbcddccddabacdcbdcabbcaadcdadaaacbbabcabbdbbcddddbbaadacaccbcaabadabdacbcdacadacccacadcacdbdcdabaaacbdbdacacccdddddcccbcbcdccbbaabaadaadbdcddababdcddabccdcbaddbbbbcdabdadadbabdbdabbbcdbbdbbddcbadbabcccddcddacacdadbbdbdadcdbbcdbcbaabccbcdadcbacbdadaacbdcbccbcbabcbbdccdbcbbddbadddbdddcaaaabdcdbabbaccabbbccbbddcddcabcccacccdbbdcccabcaabbdacbdcbddbaabbcdabdbbdcacddaabddbcdcbbacddbadcadaaadcccaacccbabaacbcbddcdbbaadbbcbddbccaabbdcddcdaaabbcdcbcdbcccbccadbabccaccadabddacbdbdbbcccbacbbadbaccbdcbaabaccacaaccaddbdaabbadbccbdaabaadacddcabacbbbabccbdabcaaaddbccdbacdddbbdbdbacbabacccccdcdccabbdcdaaaccbbbbbbaabdcadcaadbbdbdbbdadacbcdbbbcdadbaabadcacccdaddabbcaabadddadcccccbdddccdddbcccaacabaaccddbccacdccdabbaddbcdcabddaabcbbbbbdcdbbabacbdccacdbcbcacadaccaccbcadabdcbbaadbdbbbbcdabbbaadbaadcbcbbbcdabadaacbccbdbcadcddddbbaabbabbcbbccacbbbaadccbdaccdaabdbbbcabaadabdcbdabbbcaabbaccacbdabbadabbddcabcaadbcbabdaadccaccbdcdcdddbccbaadacbbbbabccacabdcccddcbcbbaaabcccabbdccccccddcdccaabcadcbaacbbabbdddcddcadbbbabbdbbdcbacbacbdddbadabbdccdbdbdcdcdbbacbaabcdcbdddbadabbbcaaccaaaabddddcadcdbabbcbbaadabcddcdadabbaabcacbdbdcbacdddddadccaadacadbacdbbdaabddabaaacbcbacdccadabaabdbdccaadbacbbbcdddbadccabaadbbcccabdadbababddcbcbcadbcdbcdbcbbadbddadaadbcabbbccbabbaadabdbcacdddbabcadbadacccbaddcbcacabacdabdcdcacdcddbcbcbdcadcdaabdbbdcbcdbadbddaacabdbbcdabadcdcbcadaddccababdccddbbbccabcddcbbdddbbddbacbdabacdbabcbddcdaacbbbbdaaacdcaabadacdbaacbcbbdadcdabdbacbaddcbaaccdbacdaadbddbbcbacadcaddcbacacbdddbbccbcddaadddaaacdcccdbaaabdbccddccdbdcddddcacacccdcccccbcaadbcbdbdbcbcbadbccbaddbabddadbdbbddacbddddbbcbbadbcdddcacdcbcccabbddccabababcadbdacaadbdbdacccaabaacdcdbbcddbccccadccbbcabcaaabbbbacaadaccbbcaccbacccabdcababddcaccaabbcbadadabadccadaccbabcbdadcabbcabccbccadbdcdbabcacaaaddcdaadbdcddacbdddaccccaddaaadadaacdaadcccabbbacccddbddddcabdddbbbcbccbaadcdabdbbcbdcbcbbaddbcbbdbdaacddcbdcbaccbbccdcdbcdbcddaccdbcabddabcbdaababbdbbdcbababbdabbddacacccbabddbaacabcaaabbbddcaccadbcabcdbbbbbbcbdaacadbbbbbdddcaddddbbacaabdbbadacdadbbaccacaccadbbbcdababcbbabccabcdaddaadbcbbddcdacccaaddbccadccdcccadaababbdbccaadaacacabbddcdabacbdbdbcdcbaddbababbddcbdbaacccadabcdcbaccadcddcabddbaabdcdabaabaaccdaaaadbccbcddababddaadadcdcdcbaacbbdacccddddccbcaadcddbbcddcabcadccccdaaabbdbcbadcddacbadcddccbcaaabdababdbdacdcababacabbabbccaccaacccccbddbbcdcbbddcbbcdcbbbdbbbaaabcadbcddccacccbdcabdbbbadccccadbdcabaadadbbcabadbaddaadbbaacddccbacacacbaacabdbaccdccbcbadccbcacdbccddbdbaccaadbacbcdddccdcaaaddcccabbcdcabddbbbbabbdaacddbccbdcacbdbdcbdabccbdcdccccacdadbccbaaaaccdcaddacadaddadbbddbcadbacdcddabdbdbaadabbaabbccbbcbacacaadabcabbadbcbbbcbdcadcbdbcdabccaddcababbbbdaddadaadaabbbdaabccbdabbadbcbddbcbbcdbadacbabdbbdddcdacdabcbdcbccdacdcdccbbdcacddaaaaaddacbacbbbbcabdbacbcbddbdddcdcdccddcdcbbccbaacaddcdbacacaadcdbdddbadcbbdadacddacaadccbbdbccabddbbcdcbdcbdaccaaadddbcadcbacabaddacdcbbbdabbdaddabaaabcbccbcccddbdacbdacdccbbdbaacddcaaacdabcaaacdbcaacbabacddabcdbadbaacaccdcbccbabababcbcdbdcacdaccddaacccacbabcdbbbaabdbddacbdbcdcbdcadcdacabdadccccddcabaaaabbbdaabbdaadbbacccdbabaaacddbdbdadbbdabbaacaccdcbabccbddcbaaddacbabcdadaaacddbadacdcbcaddbbbbcdcacabbcbdcbccccddbcccdccdbcdacabcdcbdacccbaabddbabcbcdbdcbdccccccabbcacdddaacdcccdabdabdaddcdadcdcddbdccadddabbababbdbaaabbaadbcbbaaccdccdbabbbbbccbdbcbbbdccbbdbbddbdbcabccddaaddcbccdbbdababcaaddddacbabaddaddcabcbacdababbbddcdccdacaaddccbbcabadabacacbabccbaadadaddbacacbdcddacacdbcaaddaadbacdabbcbddcbcbdcabbccdbbbbbcddddcdbdcacaadbdadaabccbabbabaaaacdbbcccdbddddabbababaaccabdddaaabdccbcbdcaccdacbdbdbbabddbaadaacbbbdabcdccbdccaaabddcbcbbdccccdcabbbcaabdaddadcbddbbddddacdcdbaacbaacddddaabdadaddbcddaaccaabbdbaaddabadcdaddbdbdbbbabbddbacbaabcdcbccaddcabbbbdabbdaddcccaadbddcdadadadcaaadcaddbdbbbaacbcbacdcdcdbccddcccccaddbccdcbdcbabdbbdacdabcdadabdcbabddacbbbbbadbcdadcadcbcddacdcadbbddbddbbabbaabcdadaccabaaacadcddcdcabdcccdddddbabaabbdabadbdaaabdbadccddccdabbcaccdaabdacdccdbdcbcbbadbcddbdbdcbbaccabdabcdcacdccbdbdbabddacbddcabbbadcbabcadabdababcbdcbddaaabadbbddababddbaabdbcddbabadddccbaddaaabbdcdcaccbacbbcdbabaadcdcbbdcbdbbdcccbcdabdbcbcbccadbcacadcdccacbadbdaddcbcaacaaabcaacbcdacbddadccbcaccddbdbddaccaaacbaddaccddbcacaaadacbdccbadadbccabcaaaaccbaadbcacacaabadcbccdbcaacddcdcdcdcacdddaadbabacbabccbdacccbbdacdcbdcadcdcdaacccccdabcdacccaadaddddadaccdcddccdcddbbacdabaadccaccaaabaabaacaccbabbaccbccbbbdaacaacabcbcdccbbdddaaacdbbbaacadabbcdbcdcddbcbbccdacbcacdcbbabcbaabcbbdcaddbdabdcbddaadadddddcacadaaacddadaabbdcbbadcddaadabacdcdddadccbabcdcaadcbadbabbbabaccabbccbccaaadbcbdbcbdddcbacbcbcaadcdadcbdbddbbdcbacdcddabadbabbddadccddabcadbcccdbabccadbdbccdcacdbbcadaadbbdadcbbbcabdbdaadccabbcabbbbcdbcaaddcdbdabdcbbccacacacccabbccdbbaccaaabccbdaaaaddbdacbcbbbdbbabbbdbadbbdadccccbadaaaaacdccaacdbddbccbdcbabadbaaaabcadcdbcdbaccacaaddbbbbcbdacdbdbacbcbabdbbbccbadddbaadadabbdcbbbabbddabddaaddddacddcbbadabaabdddbaadbacbacddacaadbaacbabccaddcbabbcabaaaaccbabbddaccacbccdbcccabaaccdaaacababbabdcacdbdabccbacbaddaabdadbabdbbcdbddcdbbddbacdabdcaccbbaddcddacaabdadddcbadbbcbdddabccbadbdcadbbbbdbacdbabdaacbacbcbccdbccdcdbcddcddaddccadbaabddaacbbddbabbdbabaccbcdccdcabadbaadcdbabddaacabbbdadabbadababbcccbdcbdbacaacacdcabccbaacbadcbbabbbaacbcacddabadbccadaaddbcadcccadbcacaccabbddddbaaadcaaadbcdbbbddcadcaacccadacadbdabdbbaabdacdddaddcabdcbcbadcaabbaccdbadddcbcdabbacadccbbacbdbdcccdbdaacdcdbdbcbcbddcdbbccccccacaccdacabdbcccbadbcbccdbcdabddbadadaccaaabdcaadacdbbdbaabbabbdccbabbdadccbbbccdbccabbdadadaddacbcabddbdaabbcabbbbcbdbbbacddccacbacdacddaadbdbccccbccdcccdbdbbacdcddaadcdbcadabdbcbaddcddacaddaddaaadddbdbcddabcaccacccbaacdcdbdaacdadacdccbccaacdcbbcdbddcadcbdccccdbbabcbdbbabaabdccacabbcbcbccbbcdccaddbbdadbdbbdccbcdaccabbadabdaabbccadadaadabbdbdbcdaaacdbddbdbccbcdddabbdaaccdddddbddcdbdddacacbdbbabbabcbbbddacdbdbbbbdaabddcabcadabccdcbcaddbdbaccbbcbddcbcdcddbcaacdaabacbccbbdbacabcbccdddbcbdddcdcdacacbadababbacabcacbbcbabdabcadbcbbdaacabacabdaacbcacbaacabccacdbbcadcdbaddbaccddadcabccbcbbdabdcdcbbcdbbabadcddcdaccdbcdbdadaacbcbbbdadccabcadacdccacdbbbdccdaaacadbdcdbabcabcdcaadadabbcdddaaabaabbdaadcdccbadbdccdbccabacddbaadbcdcddccbabbadacacadadcdcbcdabdadbaadccbdacacbbaacdaddbadaabcacbcadacacdddadcdbccdbbbdacbbacbcddddbdccdddcbaacabababdacdbcdabdcbcbdaccddcccddcdbacdaacbdbcdccadaddaabcdaddcbdddbdabaccabaaacaccdbbacabddddacbcbbabcdbdbbcdccdcdcdccaddabcdccddddddadcadaaccbccaabcbcbcadaddbcdaaccccddbdbdcbdbbbbbdbddddacddbbaddaccbaaddcdabdbddaabacbddaaddabdadcbbabdcbadaccbbbbbaaacabdbcccdbbcdcdcccabcdddcadbbddbdadcbacbddccddcbdacdccabbcdcccaacadcbbadbdcddadbbdddbdaabcacdddbdbbdbccdcdcbaaccdccdbbadadabdabcdbbcabaddabbabbccacadcacdccddcbbbdbcdcadcadcbdbbaabbcccadddcaaacbcddacbddcbabcaadadadbdacbdcacaaacdacacddcadababdbddcadcccdbbbccddaddaaadadacaadcabdcdacccddbddbdbdcaddcddcaabaaabcddbbbdccaadbaadbaaddcdbbadbbbacbacacbabbbaccaadbdcaccdddbcbdbdadaadddcdcbcdbabcacbbdbbcbdcaabccbdcabddddaaccdddddcacaaaccccccaccddbabaacaadbaaccacddcbadbdbabcacccaadbbbdcdbadcdcdbbddcdadcbbaabbddaccbbcbacbadcbaabdacbcdbbbdadbccddbacbdbcbdadbcadbcdadcbdbbbadbcbdbcddaadccdbdaaddcbaddabbaadcddbacaaabdaacaadccabdaddcdbabbaacdcaacadcbaaadcaadaacbadbbbccbddbddacbbccdabcddcaabdaaabbdcdbaccbbbbdbbdaddcbbbddddabcddbbdcdcadbddcaadbaaabbccaccbdcbcdacdddaadbcdacbdddacadbbbdbaabdcdcbcbddcbdccacdbbcbcbccdbaaaccbcccbadbabbaaddacbcdcadaacabadcdaaaabacddaaddcdbdddbaadbdaddabbcbacbacdaaacbadbaacbcadccdccabcadaaabcddbdcdcdaacdbdcabdccccbbacdcccbcadddbaddcdbbdacddbdddadbabdbcdccbacbdcaaabccccbcabdbabdabbcdccabbbcbdabaacddcbbcdcadddadccaaaabadcdadcbbbdbadcccdabbabacddadcbacccaadcdadbcadbaccabddccaccbdaacddacbacadcacdbcdddadacbcdabaadbaaabacacababbccddbbabacaccaddccbccbcccabcbcbddbdacddabadccbcddadddadabcaabddcdadbbadcbdcaccbcaacdaacabcacaadcbbadddcabdbbddbdddcccddccdabacccddaaabdccbddadcdbdbabdaaddbcdccddbacacacdbcaccacdadbbcbdbdabdcaccdaccbaccdccdccccaacbbddcbcdcabbbdbdcbcabdcaddcbcaccdcacdccdadaacaacdbbbcaacbcbcaddbdcbdcdadbdcaacdbabadadbddcabacbcacbcabccddaddaacdcdbdbacbcabaaabacbdaabcaadadbbcbbbadadbabacabadaaddccdcdbbcdccbdadabcaabaaabbbaaacbccaacabaccabacdaddaadabbaccacdbbbdabbaadcacdabccbdabbddbbaccaccccdadcbbdadcdccccbacabbdabaaabbcbaabcaaddaabaacdcaddcabddbdabaaccccddcddabaddbcaabddaacbdcdbbbcbddcddbbdbbccbaacdaccbcdbddadddacaabaddcdabadcbaccdaabdadcaaacbabbdaacddddabcbaaaccabacbacccbcbbbadadadcadccddbcdadaddddbacdbaadbdabccbdbbdbacdbbadddcdaddbddbcbdcdcadcbacddaaabcdbccdadbaaaccdbcbaccdcdcabbdabcabaababcbcddbacababccbcbdbadbaabdcdccbcbbacaabbcccaccbdbbbaabaaddddddbddbbcadbccbacbbcabcddbbbcabadcdaadcbddacccbcbdacddccaabaddadcbbbbdadccbaaaacabcaabaaabdabccdabacdbdcccccaadcdaacbbbaabdaacaadcaaccbcacccbddadbadcaaabbcdbddccdcbdbdbddcdccbccbadbbbcabcbbcddbadadaabbdadccaaaaaccacbbacdbcbdabdcaaaddbccabbaabaabdcddaabbdcccbbbaabaabdabbdadcacaaddacdbcbaaabaababbbdaddaaacdddccbdcdbacdadaabcacdcbcbdbcdccabdcdacdbcdddabdcdabdbbcdcabccabaacaabcbbbcdbdbdbcbadabbabcbdcbcbabccbbbbacbcbbcddbddaadbcdaadbdcdbbcbcdccddbaaccbdbcddbbbaaadbacbbbbcbdccbbbcbdadddbdbbcbdadcddbcdaddaddacdaccbaaccddbabbbdbccddbacdcdbbcbaddbdabcaacadcbabbaccbcdbaadbdcbbacdcdccdbddcbacdbbbcdbddcabcacacdacdbcbcbcadcdbdccdadaadcdddcddadaacbdcabdccccdabccaadabbbdbadddddadbbcdaabccbddcbaaabdddbccaacbbbacaddacdbccbcdcddcddabdbaacddcdadbdccaccddcbdccdbdadbacbbbbddbcbadbddaabccdacaaddcbcbbcbbdadacdcdbbacbcdacdbadcabaabbaabcadbdcaccdcaacdacbcaadbbcaccdadbcccaddbbdaacdcddabddcabbbdbcaddcbccacdaccdcdccddbcdcaddacddbcddbacddbdcbaaacdbaddbcdaccdaccbbbadcdddcadcbcdcbabcdcdacdbcbaabcabbbdacdcbadcbbcacaabcdddabbbabadccbdaaabdaaadcdbdccbaadbddddcaadbddbbcbbcdbdbdbadabcabdadaacbcdbaddbcbbacaabadbdcacbbbaaacddccacaaaacccbaaacddcadacdccdddddcacabcddbcaaacccdcbbbaabaadcabcbddbaabbaabcbaacccdbacddbddbbccbdbcccdaaabdbbcddbcbcacbdbbbcdbbbbcabaccccadddbacadbcdbbaabbaaccddccddcaaddabbcdbbdcbdabdadaabcaadacbabbcddabbbadbdadcbcadbdcbaadbaabdaabcaccaadbdcddacccbcbbcdddaddbadcacaabdaaccccacabaaacbabdacbdddacadbbcbddbcaaadddcaadaddabdddbabcadcddacacdaaccbbccbabbbaaddbbccdcacabacdbadaddcbbdbbdcdaaacadbaaddddbacacabbadcdbbddccdcbacdcbdccdabbbbbabaaadcccbdcdcdcdcdaaaacaccadadccbdadcdccacbccdddbaaddcdcbcacbbcacadcdaddcabacadcddcbdaddbcdaccbcdbccaaaabcaacbdabdccaccdacacbcbaacabbbcaaabccdbbacaadddcddcbcdaaacbcbdbddaadddadbcbdaacaabdddccbdbcabdbcbabbaacacadbdbbcddadcddbdccdcdbcbdddacbcccacaabddccbacaaacabcddaacdcbaddacaabbcadbccaabcadaddabbbcabcabddbaabbbbcbbdddbbbddacabcbbacabaccaaadcdabaacdacdbaacbabcdcbbadaddcbacbcbddbcbdcacaadabbacadbdadccdcbbaddbcdadbdbccdbadabdcaadcbcdabdaddbaabdbcbddbcddaabdbacaddabacbacbabdaaddcdadbbadbbcbdacbabadbcbbdabaabbbaadcbcaabdcbccbdbababcbaacbbbbdcccbaaacacbdacabdccdbdbdccaccadbcabcdcccbcdbdccaadacaabdcaaddacbaaabcdccdabbcadbaaacbbbababbbdbacaacbabbbcddaacbddcacdcadcdcbcbdbaccabbdabcaaaddadcadbcacdcbbabdaadabaccbdaadacbacdddbaccdaccbdcbabdccabcbadcbdacabdcddbdadabccdabacabdacccbadcbbddbadcdccacbabacdcbccddadaaacbbabbdbaadcdddbadabddbaddaadcdbacdadabbdbdcdaaadacdbadadbddabdcddcdcdbdddbbcccacccbddadbdaadabadadcdabcdbacbdadccddcdaaadbcdbdadbcdcdcccadabdcaccdacadaccaddcdaababdaabbcdddaaabccdcacbcacabdbdbdcdbbdcdcabacbdaccbcaaabdccddbdcccadbdbacbdccbbadbaaddababcbcdbcadcbabcadabbdcadaddacacabaadcbbcabacbdbcbdbcbaddbacccbdcdbbdbcacbccacabbdbcadccbcdacccdaababcbbdcdbdabcddbcdcdbbcadabbbabddbacabcdcbbacbccadbccbcdaccdccbdcabcabaabdaaabdbbccabdcdbdccabadadcbdbcdacaaaababaccadcbbdacbaadcdaccbaccabcbbbbcdbccadbacabdcabbcaadaabcbaccaacdbacdbbbabcacadbdbccbbdaaddddcbcbbcdddcbabcddbacbabbacdbdacaaadabadddadbaabadbdaadadaaacadbdccbbdbaadcdcacdcabdddacbdcdaacdaddabcdbacdbccbbacabdccdaadbacccacbdcadddcdadbababbaccdccaccbaddacdadcddaabccbcbadddbbbacbcaacbcccbacccdcbdcdaccabcddbabaabcbadcccaacbdbbbaabbcdbcbdaaacdbbdcadaccdaabdbaacdaddccddabdcbdbdcdaadbdddbdbcaacaccdbdadbcabbadccabddbcbdcdacbdbbdbaadcadaccdaccaadccaadccdcbcadddbccaddbddabccbadaabbdcccababadcdbdddccbbbdcdcacbbbaadddacdcabdbaccdcbdccbbcccbbaaacaadadccbdcacddaccdbbdbaccaabcbcbaabbbdccbacdccaadadbabcbcadaccbcbbaaacdbabaaddadadbccbaccbddacabddccccccaacddbbdbbbdbdbaadcabdbacbaacdaccbcbadcaddaaddadacccddcbddcdaaaabacbbdaacadcddccdaadcabcbbcddabacdcdabbdbaaaacbaadbbbddbbcbbbdbccabbbaccabddcabadaccdbbcbcbbdbabaaacaaccdcadcaaccccdbccbccbcbdbbbdcabbcdabdcadacadaadbdcacdbcccbdaddaddbdcccaccabbdbbbbbabaccaabacbbccaaccabcdccdabacddddaccacabbababaddbcbdbabbacaccacaccbdababaccdbbadcbccccbddacbcdacdcaddddcddbbbadccdbcbbadcbdabadacaacbdccacdddccbbdacdcdddcdbacacccabcdcdcacccdddcdcccccccaacccdabbaabacbdabcabbaaccadcccddaccdcacbcbddcacacdbcabdbcbadcdacdcbdccaaabbbdaddcdaadaccbbbaddbabdadacdcdddbadbcadccccacaaaabcdbdbdabbdcadbcdcbdbbbccdbbcdcadcdaacbdccdbaaaacabbcbaddddbdaaacbabddabbaccbccaddddccabbdacdccabcaadbbcbcdacbdddabcacaddbacdcaddcacbdadacadacdcadabdaaaaccbdbbdaaccabaacadcadababacdadaaddcabcbaadcaadabacbbbaabdddcabaddcaacccbdaddccddccdadaacbcddbdcdcbaadbabacbaabcddbabcdccbdbababbccadadcdbbccbddbcbdaabacababcbbacbaabaadcbbadabdaaadddbdacbdabbaccabbdddcccccbbbdbdbddbabcbabdabdacbdabbddbabdbadccacddddbaabbabadbcbadabccddabdbaadaacdadbabbdabcacbcddcbbccdabcdabbdadddcbcdbbccabdaccdbcbcdcddccadbacccbdaabdbaaabcbccdbbdcccbbcddbaaccdabdbaccaaaabaababacabbcbcbccbcdccdadcccdcdbcbddcabcabcbabdaababdccccbdccddcabdbdcdcaaabadccdabbaaabbdcbbaadbacdccacbdcdddbbcbabbdbacbadcabddcdacadccddaaacdbdbcdcccccbadbdbdbabcdcdccbbccbabbbabcbbcabacddadbbcbbbcacdcdaadbbbabddaaddddbbaadbdabdbacbcdbabdcdaacdacbdbadbbbccacdaacaabbbbdbdbddcaacbcaacbcccabaaadadddbaccaacbdadadabbabcdbccadcadddacdbddccdbbcabcabbacaaadacccdadbbcccabbacaaaadbacadddddacaaaabcabcdabbdbdcdddddbababccdcdbccbadadbdbcccccabdcaaccbdcdabcddbabcbdbbbaabbcdbabadbbbcdbbabaacbbbadbbabaaacdddbdabdcccdacadbdbbdcadabccacacdbbcaadaacbdacbbddddcbadbddcccdccbcadbabdaacdcaccbdbccadccddbcddbacaaabcbadacaccdaabbaabacccbdacbcbabaacdaaccbcdccbabddcaccaacbdbaadaccdccbcbdccccaabccdbdbdacadcacbacbddddbdacacdcadcbdadbbacbacdacacdaacbacabdabbcdcbcddaacacabccccaccdbbbbbcdbccdadcbbbcaaabcdcaacabacaccdadbbaacaddbacbaccccaaddcdccdacbccbdbbcabbdacaacddccbddacadbddbbadbbcbcdbbdaabccaccabddccdadabcadcabbdabdabdbdbbbdcaacddabcccddddbcbddaabbaddcbdccdadacaaddaadcddadcabaacbcacbababcdcaaabaaabaaabbbccbcbddcadbadcbbdbbbacadbbdacacabdbbacbbdbccbbabdcbddbddbdcddabddabccaaabcadbbabbbcbbbbbcacddbdccdaddcdbabdbbddbacddabdddccccbdadbdacdbdbbabcbdcadcabbdbdcbabcccdadccbabcccabbacacccbcadaacbaaddcaddaaaaccbbdbbccaacbbccdcbdaccbdabadccbcabcadcbdaaacbababdcbdccbdbdbbacbddbadccbcccacddadcadbcbdbcbaabbccbbadaddacbadcbcddbacaadcacdaaaadbdddbacccbbddbcbdbdaddacbddbabadcdcdaabbccbdadaacacacddabddbdaacdcbacbbcabcaadcabcadbcacbccbacbaabaccdbabcbdacdcddcaaadadbdcbdccdbdcbcbcadabbcddaadadcdaaadaddabddbbabddcbcbdadaaaadcadddacdaacdaaccbaaaccccccabcbbabacababcbacccaacddddcbbddbcbaccdcbacbdacbabcdabbbdacbaabcbbdcbcadccabcdbbbdaaacbbbcddaabbddadcaadcbddbccbbbcddaadaacbadbacacabacaadbdcdabacdcaccbdacdbdabdaccaaccdaacbacdccadcbbcbcdddaacccadbabcaaccdabbcdabbcddcbbdbcbccababbcadbbccaacddbdbbcabdcdcdcbcaddbcbdabbbcbdcdddaaabdcacaccadacadccdccbcaaccdacdbabacccbbbacccdaacbbcdabbbabbdaabbdcabcdcacdacbaaaaacbaddabdabacacbaaccdbcbbcacaaacaccdaaddbcbadadbccbdddcabcbdcbcacbcabddcddaaddcbadabccabacabdbcbccccdaabadbbabcaaddbbdaddccbdbadddddddbbcdaadddbdbdbdbdaddbbcdbccdcdbbacaccbbdaadbcbacababcdbabdbcdccccddabdcabddcacdbccbbcdbbddccabdadaaabbcadcdadbddccbbdabbcbcacabcdbdcdccdbaabcabcbadbdbbbabccdaadbccddaadcdcccaaacabaaccccaaddadbdadaaccdbacabdbbaddccacaddbabcadaabddbcbbaccbbadadbbdbdaaadbdcabdbacdabddababdacaaaacdacadcdabbcbbdccdcdcadcaaabaaacabdccbacabcbccbaacccbacaaaddbaacbddcbbaaacbddccabbdabddccadccadbcddbdcdbcabdbcbacadabcacadcadcdcbbcbaddbdbdadbabddcabcbcdcacbdddaddbdbaadadbdadbbbdbaaccdabdaabdcdcaaabcccccaccacaddabddbabaadcbadbcbdccdadaadaacbdacbdbaabddbddacadbbbdaccbdaadacbcbcababddcadcacaddadcacdddbabdbadbaaaadabddbdcbddbaacdbadcbadbcdbbdbbccaacccadabccdccddaaccdbcabcdbccaddbcdbbaacbbbcbbabccaaabaaccbddcccbbcddddbbadaddaccadcabaadddcbadbbbacabddddcaadcacccccaaaabaaaabcddacdcacaddcabaddcdbaadbcccaabcbdcacdcbccadbaabbddabddaaddcadaabbcadbdabbcaddacabbbcbaaaacdaccdbbcdbddddabbdaabaadacdacabacccabdcbacccdccbcdbabdaabdcdadbbbdaccdbdccdbddbadbbcadabbdcacaadcbbdcabdcddabccbcabccaaacabbcdadbcadaaabaccddcaabaccadcbbdddccbbccadcbaabdbbbacaccadaddcccaddccdbdbdaaaadbbacadbcdcacdbaabdcbbdbcddccdadcddcabdbcbbccdabbbcdbcdcacdabbaacdddbcadbbbccdcabdcddbcacbadcadacbbbacbacbccabcdadadccbadacbbccbbcbcdbcbcbccbdbbbdabcbdbcddcdcaddddcdabdbddacdccdbcbdcbdcadcaaccddccbabbacbdababacdcabccbddbcccbbddcbaacadcdbccaabcddbaabbabdabccdddbccaccccadbabdccdddbcccddaddcaacddccacadccdaccbcdbccbbbdcbcaabdcababbbdbbaddabddcbaccaabcddcddbccabbbdcccadddadcbbbdcacdcaabaaadcaadadbccaddccdabbdddaaaacdddbbcccdddabdaccdaddcadcadbbabdcbcdacadacbbcaccdbbdcdacacbccdddacbcaaccaadcddbadaddbdaadcbbdddbcadadcccdddaacbcdacaccbacabddadcaccbdcbdcdaccdcdbdbabcbbaaababbcaacccabdacddabcaccdcdaacacbcacbbabaccbccdbdacaddaaaadcdcccbadababaddaddbbbdcabdbcdcbdccaadbaccaabdaccbcacbaabdbdbbbbccbbaddaccbadacdbdcbbdbaacccddddcbcbbbcdacdbabdcbcdadcabaaacabdcaaacabaabbccbddbddcdccbaddacadadacbcdacccbcdacabbbdcdbacbdabdaccaaabbbcdbdaabcccbdcdadbcaddbdddbaddaccddcccadaabdcaadbadadccdccacccdcdbcadbdabcacaacbadabdbdabacdcaacacddaaddcbadddbcbccdbaccbabcabcbcdcbdbbdadadacbdbbcdcbcaaabcddbabbbbcccdddcbbaadadddccadbababdcacbbcaaababbadcbdbdbbbbbbbbbbcadbbbbcddcbbacbccbdcdddadcdcabcccbcdcddbacadaadbdbaabbcdacaddaaadcdaabbbaacdcaddcbbdbcccabbcacdaadaabbbcbdabbadcdbddcbbbdaccdcaabddacbcdacdccdaaadaccaabbccbadcabacdbcbdbbabdbdbdcbcdbddaddbcbabaaabaccbbbccdaaadcbccdcdaabcccdbcbccdadaacaadcdcbdbabddadaabdabcadbddbabcaddcbcddcbccaccbdacaddadaccbadcddaacbbabaabbbccabddbadabcbcabbbbbacbdcccbcadcccabadadbdaccbdaabccacbcaccbcccbabcddcbcacaaaaaddaacabcddbaabaddcdabbcbcbdbcbcdbcadcdcadcddaadccbbabcdbbdccbcccccdbaadcacacdadccbdbbdaccbaaabcccaaddbccabcadbcbabbbdcbddaabcddccacccbcbacdacbaccadddadccbdbaddacdcbadaadbbcadddccbdacbbbcdacdaccccdbcddacabddabccdddccadadbcdbbbdcacccdbbbcaddababccbbabbcbddcdbcdbdaaabdbcadbddccdadbbaaabcabdbdbdccadabbbbaacbbaccdabbcbbbddcbabcdbabadddcaabbdadbcacadaabdbaddadbcadadbbcbabdbbcbaabcabbacddbaaccabdbabbcdcababccccbabcacacdcdbddbdddaddbddddabdcadcababadaaddddbdabbbacdbbdadbdaacacaacdbbccbbbbddbcdbbbdadbacdbdcddbbbabbcaacbdabbaacaadbcbacdbcdccaaddddaadabdcddcdcbadcabcdcdbcdbbcaaaaabadbacddabacbdcccdacdaacbddbadaaaaacdbddccdddacdabdaddbdbdbcccadbccbaabdbccacaacccccdaccabacdabbccdcbbaacbadcbcbcbdcaaacdddccddcbbacbacbcbacbdbbcbacddcadadcbbadbaccadbddaacdadbbdcdabcbbbbaacdccadbbcacabbaadaccdbcddabbadcbccbadabaabacccaadadbcababcadbababacdaccbccccbcdcccdbbaadddccbbdddabdcddddcaabdcddacdacacdccaadbdcdabbbdccaadcdacdcaacbbccbaaaddbdabdbbbbadadbadcdbabbacabcdcabbbbccbcdbadcccdbbdaabbadbaaadbdccdddcccbcaabdaadddaaabdcccbbdccababcdadcdcabcddabbcccddbbadbdabcccabadbddbdaadbabdcccbaadbbdbbccdbbdcdcdabaccdbcdcbccdabdcbcaadbcadbaddbbcaaabdcdabaaabababdcccdcddddadcdcbacabaccddabaabbccdacdacacdcbbcbadbcbabcabdcbbadabbcbbdcaaadcdcbbcaddbcddaabcbbadddbdaacddddaddaaacdbcdbdbccaadcbbbbaadadcacacbbbdddbabdbabcbbcbccdabadbcbcddadcbbcbbbddcaabcbaabaaaacabacdbccbddbbaaddbaccdcacccdacdcdcddabdcddbdccbddbdcacdddadcdaadcbddbabacacadcdaccdcdbadcaccabacaccaacdccaacbbdccdadbbccdcacdbdbbacddccddbddabddcaaddbdbcbcdcccdaaadbccaacbabddacdcddabacabdcdadbaabbcccdbcdaccdbdbddbbcacccddccccddccbcadbabaacbcbdbabcddcddbabcacdbbbdbccccabadbcdcdbaddacdcaacadadbbbcbddddcbcdddbcacaaddaacccddaaabcaadcccccaddcbdadcccaabbddbddcbbcbaacccdcdddaaabbdbaabbdcdbbbdcbddabcbdccddadaccbdadbbabdbdccbbbdadacbcaabdaabdbdacbdcdbadbacabcaaaacdddddadabdddaaabbcbddbadadabbbddbabacabdadbcabccbbcdacddcabdadcccbcaccacbaadccadabbdaaddbbaddccccdccbabbbbacdcbdbcdaadadcbbabbdcddccacbbcbcddabdddcacabcddadbdbccbaddcdcdadddbdaabbdbcbcccaaaccbdcadbbccaabacadbabaabdddbdddbbadddcdcacbcbcdcbbaabadadddbcdabdddcbadddbaabdddcdacccbaacaabddacbccdadbdadddccacbaaabadacbabcccacdaacbcbcdbbacbdcaddacbccaacdacabcdaacdbaadcbdbddabbabdadcabbdcbcdddcbbabcbcaabbaabdccacaddcadacbdddaccdabbacbaacbdacdbddabcdddabdadccabdaabcdbdacdcdbdacbdaabcbbbdccbccbcacbccbabcabadbabbbdcbbbdddbdcccadbaaabbacbbdacdbbdcaaaacbdbaccdbbcabaddbddababcbbbbaaabdccbaaddcabbacabbcdbdabbadaacacccbabbcaacdbdbddbcdaccbbaccbdbbcdabcbcbddadcaabacbdddabbababcadbaddaadaabbadbccaddcaabadaccabddbbaaacbbabdcdddccbdbcdccacbbabccaabddadaabdadcccaccbaabaabdbaadbdcbdccccccdddabadbaaadcbcbcacbabbaaaacaddbdcccbbabddabddddcdcaadcbcccbcbdcbccccdaddbabdaadbabdbdabdabdaaccdcdbcdbbdbcdcacaccdbaaadcdbabccbcbddbbbcddabaacaabaddaacccbdbbdabdbabaaaacccdddaaabdbbcaacbddbacabcddabdbadcbabbabaadddccbccccbcbcbcdcbbdbcadaabbbcbaaaaabccdcdcaabaddcbdcdbbdcadddbdadbbbcccbbdcdacaabbcddcccbdccacabdadbaadadaabcdccbdcdcdadbabdacdcdcacbdacbaccaabcdbbcbbbddacabaadbacccdcbcbaacdadacdcacaabdcdcbcbbcdcaccdccaadabcdcdbadbadbadacbdbaaadddbdaacaacddbdccbcbdcaccadcaaabcddddcdaacddacbccbbcdcddcadbbdcdbcadcdaccdadddcbbdcbdadbadcbcdaadadbcdadabcbbabbdadadbcddcbccacbbdbddcbccacbdcabdcbbbcacdccacacbaadbccbdddcddbabdcdbbabcccccddbdccdcdaaadcbdbaabbadbbcddbadbcdccdcbacddbacdcabccbbdcaaddccadcbaddbcdccdbdcdbdcaccaabdbdbcdbbaadbabcbdcbacbbdcabaabcdddadabbbbdbaaddabbbacdadbaaccdacddaabcddcdbdcadddccbababcdccdacbccdccabdaccabdcbdbdddccdacdcddcaaadcaabdddcbdaacddaaabaccdacadcdcccbdcbabbddbcadcabdaacacbbdbdccaacaddaccdabadbacbaddcbabbaabdabacacacbbbbaababdabcbbcbaaddbbcbdbcadcabadcdcaabcbcadddbcdadbabcabacadadddaddccadabcbbcdadadbddadccbcaabcacccabccbacbcadabcaabddbcbdacdaadddaccccdccbcbbddbbcddccabdaacacdbdadbdadabcdcdaaddaccccaacdbdbbdadbbaaaaacacacdcaaccbabbbdabddabadabacbccabcbdbcaddbbddabcabbccdaababcdbacbcacaadcdbccbabbbbbdacdbaacadbbddbbcdcdadbacdcaadcaadadccddaddcddcaadbadaddcdabdababdbbddcbccdacadacbcccacbcaacadabccabdcdbcbdccaaaacbddcdbbdccbbddbabdbbbcababdbbcdcacbaddbccdcacbddaabddbcabbcdaabccdcbaadcdacccdcccacdcdbdabbdbadcaaaaaaacadbadbaaddabbdacbccacccaddacacaacabcdbccbcbdbadcdbcadcdacaacbdacbadbaccdbadcbcccbdabaaddccaacdadcbdddbbbacdbdcdaadadacabcbbadcdadaacdccdbbcabbccccaaddcccbbddaacccacbdcccbbcaaccccbbbaacddacabcacdbdaaaaccaddacabbcbcdacddbbdcdddcdbbcddbbbcaadcaaabbbaabcacbcdbdbcbdcaaccaddbbcdbcdbaacbcabdabdaacdcddbdbaccbcdaacbcddbbbadcdaabcacbdbaabadcccdccaabbbadabdabbdabbaadaaddcbbadcddcbbcddbadcbcacadabcdaaadbcacbbdadbbabdacbabcdcbaadcdabbbcdcabbabbbdbdbadcbaaadddadcacbdadacbdcbabacddccbaabccbaaaabdbdddbccaadbdcaabddddddbaabdabbaaddcabbdadabaaaabdbdcccbbacbbcaaabdddacdbabbcbddbadbabdabbdcababdaabbbbcbcbdddbdddcdacbacddadaabbcadaaadcddaadcdbaacbbdcbcbcbadaabbdacacbcbabbadbcbbdabddcdbbbcababcbddccabcccaabdacddccdddaaccabcdcdddadaadabccdbdcbaadbaccacbaababdcdbdbacbdabddacccbcbddabdabccdddccbcbacacdcbbbcbcadbdddbdabdacdabcdbbcdcabbabccdabcdbddcdbcaddaacbbbcbdaddcdcabdbdddbadcabdddcacbbabadccbcbacbddabddbbabdbdadbbdbabdcdbbdbdababcbcaabcddabdbbcaccdaddbcbacbacadccbdbbbcabcdabcacccccadcdbbddaccdbcdcdbcbadcdabdbcbcdacddbcaacccdacbcabdccbbbbdaabdcdccddbbaddbadabadbdbccaccbdcdaaacabdbbccadbcbcdbcbbaddadbacbbbbcbddcaaacbcccbcddbaccbbdacbdbcbcdabbddccccbabdddbcbbdbbbabdccbbbdcbcdcadabacddaaacabdabacababcdcbcdaaacbabccabbccccdbabdbbadaccdbdaacabddaabcdadacdaadbccbcdbdbdbbabdcdbbacacddcabcbdabadaabbddcbdcbadbaacaadaccbbabcaaabacccccdddacacdbbacdabbbacbacbbbccdacdaaaadcdacacbabbccbdbcaccbbcaababcababadbadbdaddcdcacacbccdcddddbdaababccdcbacaaacccccddacdbdbacbdcdaabcdbcadbbdaacdcaabdadacdabdddddbbcddbcadbabddbcbcbcbbbbbbddabbbdbabaddbbadaccdadbabbccbddbbabadbbbcbbdbccadabaddcdbacdbbbcbcbbcbbcdcaabdddacccddcbcbabaaaddbddbccbbcbbdadaaacdbabbbddbbdcddccabdcadadbdbbbbcaaddabcbacdcdcccbccabaaccbddaddacacddbadadbdbddabbbdbccadacbaddbcbbcbcaabcccdadadcdbdcbbacbcbccbbccabbbbadaacdaaadbcacdaadcbadbadcccabdabcbbccddbaccdcadcdaababcddcdadbdddcacbccbacaacdddadcaacbcdabcdbddcbbdaadbbbddcdddcdbbcabcccbcabababbdcadaacdbbacbbadcacddaddbbaacaddccacccbbdadbccbcbddabcadbbccdabaabcdadbbdcbcbaddcccbbcbdbcadccddbcbcacdaddbbbadbdccbacdcaabdbbadddcbadddddcbcdcbaacdcddccdbbcaabcadaadbcddbbdbdbadcadcabdccabbcabdaacbddddacddabbdcbdcdacccbdccaadbcddbbddacabacdbacadcbcccddaaaabccddadabddadbcaaadcdaabcabcbcadcdaaccbdcccabcabaaabddadabbdabcbcccddadccdcbbcbcbbcdaacdcccbabddccdcaabccabadaaddccbbbbcdbcadaccbcaacbbdadbddadbddadaabcbabbdcdaadadbcaadccdbbaabbacbbdbbdddbcbccdacaaacaacbbdbabdcccadcdbbaabcaccaadbbaadacdadadaaabbdbdadabbdacaddcddddcbbdbbdacabbddbbbbbcdaabdaabcacacacadbddbbdcbccbcadbdcbcabdddbcabcdadacbdadbaacdcbacabbdadabdbbadbddbbadabbddbddbbddddadababcdbabbccbacdaaadabaacabcddddcbadadabbdbdbbccbbdaccabcacbadbbabbbcdbdacccddcdabdcbdacbbbdcdcbcccadbbbcdccbdaadbbbddcdabadcbccbdcbabcbdcbabcdaaccacaacddabadadbbcadabbddcbddcdbbbcccabcaccdaccdccddbccbcadcbbabbbcbbdbabaccaddbbcdbdbacbbddbddcbbdcabadbccadadacbcabdddacadddaddbaababdcadabbbaadacadcacdbabcbcddbbcccccbbbdcaccbabbabcabdaccdaccabbbcbdddabaccccdcbcadbcabccdaccadbadcdacdadaacbdcdbccabcbbcdbbdcabcacbdabcdbaddbdadcbabacdadbdbacdcdadaadbcdcadaccadbcbddacabdddbabbaaaaadabbcbacbaadacacbddbbbcaccccbcdcbbbdcdabdabcbacadacdabbddadabcbdccddbaccddcbbadaabbccdbccbcdbccbadcdabbabdccaadbbaabcdcbbabdddcbcbacbdaabcccbdcdaadcadbcaaacdcaddccdbcbbcccdbbdbcbcbddaadcaaadbabcbdbadcdadcabcbdbaccacbaabcbbbbdbdddbbaaccbabcdcddcdcaabdcbcaaddacbaddcbaabcdcbbbddbbbcaaddbdccbdbddbcaaccacbabcdddcdbbddacaacccdadaddabcabbaccaccadcddaabcaabbdaddacddddadcbaaddaaabcbaaaddabcbbdddacaacccdaaddbabbdbdccddcabaacdddaadcaacdacbbbbcacccccccbcdcabdaabbddbabddcaddbbbacdbcaabbbbacdabdbbadacccaaabdbbcbcabaccaaccbdbbcabbbabcaadcddadabdbdbaacacdaaaabbbddbcccdcbaaaacaddbdbaacdbacdcbbbdabbaacacddcdaccadddcdddbbacbabcbcbaddacdaccaaabccdcbabbabbabcccabaaaabdcbabdadbdcaacdbadbcabccacabbbaaaacccacddcbabdccbbccbdaabcbcdbbddaacbcacbcbacaabbbbddcbdbbdcbbccdabbdabcabccdcccbacccdbdabaabbacbccbdacbdabdaaaadbcdcaaabdbcddabaabdbbacccccaadbcaccbcacbcdbacbcacdadbddacbbbacdcbbdcdccbbdcadcaaccabcbdbbcabbdcacdacadaabcdcbdddbdcccdbddabcccadbdcacbdabbcdbbcbadbadddadabcaadcbddbaabadddddcbcbbaddcdadbddcddcdabddabddaccadcdcaccdabcbdcaabddbcdbadbdcdbcdbddaadbcbcacccdbbadcababbadcdabcbabbbabccbdbadcddabbccccddacaadddbcbddbbdacaccaadbbacadabcbccdbbbcbddadbdbbbbddbbdbccaaabcadabddcacdddaaacddabadaacbdcccddacbccbdaadbcabdcababacdcacaacbabddbbbbdccddabccabbdaabdcdadbaadaddbacbcdddabbcaccacaabbdcabcbaddbacdcdcbbbbbcdcadbbdbdabdbbbabcbcbaddddddddccdacaaaabbcdcccabadaaacbddcdcacabbabcadddccacabacccbbabacddcbcdaaacacbaabddaaacbbbdaddcccabcbbdbbbbcaaddbaabcdbadbaacddbddabbbccacdabadbcbabdadcddaabdacdaacddcabadcacdabbdcdbdaaaaccacdbcdddbbbaabcddcdcdbabaabadbbabacdbccdaadadaabcdccbcdacbacbbbbdcbadcdaddacbdcdcdcbdaacaaabcccdcaddbacaccdbcadcbbbcdabbcbdcbddcadccdcadcddbadcacacdbdcbbcabdbcacaacccbddbddcdbbdbbdbacccacacbbbabbbaabbacddadccddbccdcaacaabcbbdadabbabacccaccbdbdbacddccdcbabaadcdaddababcdbbaaababccdcbabddacdbbaccacabacaadcabdadbbdbbabaaababbcccbddcdadbdabcdbbdcdbacadbdddbcbbbcbbabbcbbcbbaabdaacbdddbcccadbbdbbacdadcbdcbdddddddcbbbabccabacabacaabcabddddabdaaadbdbcdcdbdacdbdcdcbdbdccddcccdbdcdacdabddacdccdcabdbbadaadaddaadbbcdaabacbcbbcabacddbccabdaacbbaadaadbccbcabbdbadbdbcdcdcdabdcbcacaadcddbabdbdcbcbdbdccaddcdccaacacacccdbcacbbbaccabbbdcbcabdbaaddcbcdabccbabcdabdadadababcaadcdacccaadabaaddddacadbbacadddaaadcbbbabdddabcdcadaaabcaacaddccaacccaaccddabdacbcddbbbddadbccdbbcbbcbdcbbcaabbbcbaaddaccbabbdacacabadbabcbcabbcbcbdcdadbcddaddbdacbcdaaccbaacbbadcccddaadcddabbbdccdcdddabcdddcababddcbcbccadbbbbcddcbdbbccbbadcabcbddcacaababccababdaabdababcdccaacdcbbbcbaaaccccbcdacbdcccdaaabbddccdadadbdbadbdbbadbcdcadabddbaadbddabacbdbdcdbbbdaccabccadbdbcdaabcaacbbcaadaaaddbcccabaabcbddadabacaadcdbcccadbdbabcdaaacabcdcbcbbacbcbcbacccdacbbbdbcbbaacdcdaacadacddbddcbadaaaacccdaabcddbbbabdbcadaddbaaadaaccaacaaacadadcbadbabbbddbdcaacbbcabacaacbdabdabcdcbccbdbccaaacdcddddcdacccbdcbcacbcbacabcbddbaccbabacdcadabaaaaadccbacacddccccbcdcaabccbbbadcbdcdddacdbddabcdccbbbbbcbcaabcbdbdbababcbababbbcaadaadabdabacdbcacdbcddbdcaabcdadbaadcccaabcaddcabcbdbdadccbdbadcdbcaacddcbaddddccdcdbcabadabdcadbddbdbbadabbdbbcabbaacdadacccdacdaccddbbbadbddbbadbbabbccdbcbadabbdcdabaadbccdabccabcabdbaddddddcdadbdcbdbacdbadbaccdcccacdaadcaddadabbbdcacbcccdacdcadcddbdcdcbdcccbbabadbdcbbbdcbcbdacdcacaacddbbbacaacddaadaacbddbdbbacaddbabddaddaabdadbcbbdbbdbaabccdbdddacddddacbcdabccbdddaccacaccaacbabdcabbddadddccacababddbbbbccbabbbcbadaadccaddcccdbdaaaacdccbdcdcdaddabbcbcbcaddbaadbdabaaddcabdbbabcaddbdcdbadbcccacaacdbbddcadcbaabaacbaacadacabaaacdaddddadadadbaaacbbcabbdbdbacdbccdcbcdbbbadcdccccbdcacddbaacdcdaacccabbcbabdddbacaddabdadadcccdbbddbaccdcdccaadcbcaacdddcdddabcacbcbdbbaaccddbadbbdcdabdbdaaababacccbacddbdbbaccccdadbccadaddadcbaaacccbdbbbabcadcaccdbdccddcdaacbaaacddabcbdddbaacbdadabdbabbbdbbcdddcbdcbaabbccadcddddcacddbddbdabdacccbbbdaaaccdcdcbdcdcdbdababbbdabcccabacbdcdabbddddbabcbabdcdaaacadbdbaccaacdcaadbddddacaddbbcbabccaabdcdabaabcdaadabcdcacdccdccbabcdcddadcccdcbcbdbdbbbdcddbbdacaadbabcccdcdaabbccbbadcabbbaabbdcbbbcaabcacaaabccbacabbccacacddccbaadacdacbcdabadbcdabbcdbaadcdbabcbbdaaaadbacdbadcdadabacdadcccadbbdddacddddbacadccdcaadbdadabcdccbabcabbaabadbddaaacabdccccbabdadcdcacddbbacdbbcacdcbdbdbbdbdbbadcacbcccacbabadbaccddbbaadbcbaddacbddaadbddadcdbbcabdbbabcbcbaacabadcacacdbabacccbddbcaadcaddbcabadcbaddbadccbcadbcdddacdcbcacaacbcbdcaaabababcdccbaabbdccdcaddcdbdbdcabbbabdccbacbcaababbdaadbaabbabccaacdbcdccdacabddcccbdcccdcabdadcdcdcababdaaddbddacdccadcbcdccbcaacbbcdcddbcdccbdaacaaadcadadacaadcacccccacbaccabcccbcadbdadcdbadbdbadabcadaaaabbbbbbdaaccaabcccadbcdbdddacdbabadcacbaabaaaaddadbbaabcbacbadbccdaaacdcddcbcccadbabcdcacbcccacabadadddcbbdcadcacdaccbdbcbabdbcbadbcbcbdcccddcacaabacaaccbdcdbdcbabcdbbbadbaaddacdaadaccbbaabddddcabdbcdadccbddadababbdadbcccaaabbccdbddcbcbbccacdcacbdcbbacaaadacabccbcabddcaccadbbbcabacdbabcddabadabbdddaaabccadacabdbbdcdacacddcdbcdadbbacdacdbdccbbbbdbdbbacccbacabaadadcccdaabbccabdaaadacabbcbdabbdcdacdbabcdacddabbaadbaabbdbcacbdcabcacdddabdbcdddbacdbabbccbbabaccdbdbcadbcbaadbbcdbdcababacaddaddbccaadbbabbbacdcbccacccbdabccdcddcaabbbbcabbccadabbdbbadccdbacdbaddccacbbabddbcbdccbdadacadcbcdaddacdbbaadaaabdddaacaddcbbcdbadbcabdcdadbacdbcaadabddddcbcacdacbdbccdaaddbabcacbbbbdacaddbbbabadcbabbddcadcdbcdbddcdbdbdcdbdcdccbabcbcdcdcddcbaaddbabbbbbdaadccbdadcbbabaadbbcdcddcccaabcbdbdcbcddbcbcaabbdbccdabbcddccdddcbbcbbacbbbcdcbacacdbccdbbddcadddbcbcbaccabdcadbdaabacdaabdbbacccbcdbadcdcdbaccabddbaaabdddcabadaccdbcbdadabdcdcdbcaacbbcddbddbabdcdbadaccaaaaaabcaaacdbaabaadabdcdcbcddbabcabdabaacbaabaacbaabadddbdaddddadbcccccaabbdbbccaccabcbaccdadaddddbcccbdbadcbcdacdabcdbdcdddbbbbddaaaccabcabaddacabcdaccacdbaaabddaaccccbabbbaadabbcccddddcddcaaddbdbbddbbccacbabdcccacdabbbacaaccaacaabaadbcbdaabddadbbadcdcdabaddcabbadcdcaccbbdccbcccdabbbacbdcdaddbcbbabcdddcbddbbccdccadcadabcddaaccabbcbccadbaccaacbcaadbcbcdbbbbcdadbdcccaccddcdbbbccacbbcbccabdbcaabcdaaabbbcdadbbbbdaadbccaaadddbbbaadabcdddcbcdacbddadcbabdcccdbacdcbcccddacadcaddadbccabacaccacdbdaaaabdcaababacabdacdadcbcdbcaacbbdcbcbcbbbdaacababaacabddcaddcacdadddddabdbccbbaccbaaaadcdcaadbcaccaabbbbaabbddbddabccabbbbddccdccabaadcccaacabbcbaddccabcbdbbcacbadccdddbbacadcacbaabcadaacdbdcbbbdaccabdbdadcaadbbbbbdbacdadcacdbbdaacdabdbddaabaccdadcbaccdbcadbbdbccbdbccaaccaaabcdcbaaaddaabaacbcacdbcaaabbdaabaaaccbdcaccdabcbdadddbdabbddbbcdadccaaadacddccdbccddbabcadaaabadaadcbbccbabbaaccdaddcdbacaddabacaccadaacadbdccbacaddacddabccdaddaabaabadbdaadacbabcabccbcdcdbcbaddacddddbacbbbbdcbddcbbcdaaaadbccacaabdabcaabcacacddbcbcccccccabaddadddadbbcbcbadccdcbddabcadbacbbacacabadadddcdadacabacaadccddccbdcaaccddbbbcddddbcbbdccdabcabccdcaccbbabbaccaaccdcbdaddcbdbabbacbadbcadcbbbdabbaccbbcdbacaacabdbbabcccdabbbbdaacaadcaaabdacacbcaacaaaacddabaccaaabbaabadcdcaccbccacdcdccdcacacadccdbdcabbadcdadcadadbdbbadadcbcdbaabcdcdcccacadacdaccdabaddbbcbbcddacdadabdcbcbdcdbdcacdcbdbccbadadcaacbcddbaaaaddcbcbdbcbccccaddabcabbacbdabcbdbaddabdaaadddbcbbdbbdbabddcbbdccccbbbcdbadbdacadaacaabddcaddccccbabcbcdbccdccbddccdabbccacddbaacdccbcabdcadbabadbadcabdbbcdbddcbddbaacadcbbdadddbacddbbacaddcabdccdcdcbacacbbaacdbaaaacbabdbcbbccadaabbdbaccbcadabbdbdccdccabcccaddbcdcaabdbbdcdcdcdcbbbddddcccabbdddaaaacacdcabcdcccbbbbbaaccbadaaabcaacabcbdccbaaaababdbccbcdadcbcbabdabdddabdbdbddddcdcbbcbbdcaabaabbbddaadcabdcbcbdcdcdbdbcbdbbaddcbacdcbbbbccbabaadcadbaddbaccdbcbacddacaadcabadaaccdbcdacaaadaacddccacccbbbbcccbbcaaadbdaccbbdabddaabcbaaddbcabcdadbadcaababbdddcdadadcdaaaaaaabbdcacbbbdbabaddabaadcaadabdcdcccbacabbbbcdadaccdacbbcadbbcacdbabbcaacbaddadcacabcccbcdccadbaccccacaaabcabdcaaaabbbcddccaaaababbaccaabdabbbdaddcaadbbdaacbcbdddbaadcbdadabaabbbbacaacaddacbacdbcdcdbacadadcdddacaaababadbdccadbdccddcdcbdaaabcbbabbadbcabadcbcaddbbbaaadbbbbbdccbbbbcbdcccdccabcdbdbcbdccaadadbdbbacaccadbadaaabaacaacdadbadbdbcdcabcaaabcdcacbaaabddcdcddaddbddccddccbdabdaabdbcbdacdbacccdcdcbacdacbcccabddadbdcabcaccacbaaaccacbbcdbcadcdbcddacccdcbacccbabbbcbddbbdbadbdadcbdcdcdccccaccddaaacdadbdcbbbcdcccdbacdbbaccbbdbdcddcaaddddbbbcabdbbacaabaddbadbbbddbdabdcccadddbcbcaaacbbddbdbadcbcaaaaabbdabcdbcccacdbdabbbddbccbbbbdcaabbdacdbdcbcddbccacbbbadcccabdcccccddddddadddabacdccbadabdbbbcbcadccaacdbaacacbbacccbabdbcdcbadadaddaacdbdadabbcccbbccacbadabcbbcadbdcdcbbdbbdadadcbadaaadbcbdbabcbbccdcccbbabcdcdacababadbbbbcdcbddcadddcadcabdbddabadcadcbbbcdcabcaadcbbdbababadabbdcbabbababdbbbddacdbabbabcdaaddbbacccccabadaaadabbddccbbacbbddacbaaabddaaddcbdddaabcdcbdbcccacbdddacbbddcadaadadcabdbbbcdbdbcdcadabbccadcccccacdcdacbbdbccbadbacdabbddddddcdcbcbbadbcabcacacccdbbabcaddabaabcaacbcdcdddcdcdbacaaabdabaaaacacdaddabbcaaabcddcdccbbbddcbadbbbdadbddcaddddbadcdacccbdadabcacdccddcabcacaacaadddcddaabadabdadbbbcddacccdaabdcabaacdbaaddccbbbabcdbdddacaaadcadadbdccbccccbcadbbbbbbdbacaababcacdbacdacabbaabbadacaabdadbcaccbdbadbbacadaabccddcdbdbadbddadbcacdcbcadcbcabaadbdcbcaabbadccacaadadbacdabbbbcadbdcccbbcadabcdcccabccbcadbdcbbdabcbcabcaabcbbbdbaaacdcaaaccbadbdbbcabacbccddbcbabadbccbabaccbcadadccabcdddddaddddccdaccbcdacccddbaadbbbdabbcbbbcbdacaabcddbccacdcbcdccbacbcbdcbbdbcaacdcacaaccadbaaaaddbaaadaacacacbabccaadbdadcbdbbcabaaaabdcabdadccdcbcbcbcdbbddacaaddaccddccadccacabccbbcdacadccadcbbabbddcadccdcbababdccccdddcdaadcccbcbdbbbcdacbccaaaaddcccbddaacdbdadbaacdbbdcbcbabccdadbcaccaadaabcdccbdaabcbdbbaaddbcbbdbbddbddbdaabbaaadaaddaacbbacbbbabbdbbbdabdaccddccabacbbcbadaddbbddbdbbdbdabbbdccddccbbdddccaadcdacbbbdaaaaaccdbaabaccabbdacbaabcdcdddbcdcadbbacccddbcadadadadcdcdaaacbbdadaccddcbabbccdcdcadcddadccabddabcdacaaabdcaaccacadbaadbcbadcdaaddcaadbccaccbbaaaaabbbaadbdbdbbbaacccaabdcabdaacbaabbcdbabcaaccbbabbaadcabcadabbbadacaabddacdadabbaccbbcdcbbccabadbcaabacdbacadacadbdacdabccdbbddaddbabcddbcbaadabbcdcccdbacdddabbcabdaccabacacabbdcbcdaabddbbaddaaacdbbdcbdaddcadcabcbcadbcdbacdccddabcccbbcaccadadcdabbbacbccbabcbadbbabcbcbadbdbabbbaccacbcddcbbbdaabcadaadbabbdbdbdadadbccbccbcdabcbdcacaaccadacbbcccdbccccddcaddaccadbbacbbaddccbabcadccadddddddccabacbcacaadcadcacbcbabdbdbadbcbabdaaaddadcdaccaaabadaaddacabcbbdccbdadaaabbdabdccbccddcacddbddccacbbdbddcacacabdaaccdabbdcccbdbdacabbadcccbdccaccacccadbadbdadbdacacbddcabacadaddcaddcaadbcbadbcddcadbddaddcacbdbacbccaabaacddababaabaabcabcddcadacbbcabccacbdddbbcdaaadbbbcdacccbabaccbdaccdddbcbcabcdbcaccdaaaabcbcaccbadcddcabdbbadaadaccbadcdbbdcdacbcadcdbcabbacbbbbbbabbcbabddabbdddcbdaddcdaacdcaabdddbabccdcdcbbdaaccacdadadcdabbbcdcdaadcdccccbbcbacabdcdcdadcdcdbaaacbbdaaccbbbbccccdaddbddbdbcabbdaaddaddababbcaabcccacccbabbbadbbdcaddcbccbbaaabaabacdcbaacdadcccdcccaaabcdbaadacbcbacdcccaccacdacdadaddcacdcbaccdaddabbcaababaabbabadbccdcbaabdbcdbbcbccadbdccbcdabaaaaadbbbbaaabaddbadcaabddbdcdcbcbdcdbcadcccddbacbbbcbabadacbdbaabdbcbababddbabbaaacdacdabbbaadcbbbcbacccddacbddcaccdbabaddabcdbbbcbcdddcccbabcbddbcbcdcdbbccdcdddbaddcddcdababdaddcdbaaccdbbdcbacbbdddcddbbabaaabadcdabadcdcaccbabbcbabbdabbababbbaabbacdaadbacbcaaadcadbccdbbccdbcabababdccaccbdcdbbdcbaddcdbcdcbddbbabdaabbabcadbbdaabbdccacabcdcddbdabccdababacabdcbcbbdcdadaaacdcaacacbbcdcbabcadabaacdacdbadabbcaacbbcdcacddcaabcdcbddabccabdcaadddbabdbbbcaabbccddbaccbcdddbcbdbddbbbcddacaddacdbdbbacdaabdbdabdbaaccadccbadbdbcbcacbcdcbacdabaacbdbbcccabcdcbadbddcdbddccdaddbacdbbddbcaaadadabcacdbccdcbdbddddccddadbdcdcccadacccbcaabdcbcbbccabbbdcbdcacabcbcbcabdcadcbdbbdadbbcdadbddbcccddcaabadadcdacbcabadcbbacabdaaccbcaacdaacbbbbabcbaadaccbadbbadbcbadcbcbdbbadccdabdddcacdcdcbbcaacbabdbbaaccaccbaddcbbaaadcaabaaccdadbcdcdbddbabbcdbbacbcaaaaddbddaccddcdcddaabaaaadbccadbaccccdadbdccbbbdacccbbabacdbbcbaaabdaadadccabaccbbbcbbbcbaacbbadccacabaaccacbdacbbdcaadcadbdcddcbaacbbcababccbbcdcbbadabbcdcdadaccabdaabdbdbbaacbbdcdcbcbdcccbbbdaadbcbabaccbcdbacabbdddddacdccaadababccccdaacbacccbbdbbbabcacddadacbcadacddcdccdbcdcbcaaddbaddacabcaccbdccbcaaddbbcbbdbaaccbabadcdbacadbccdbbddabbadddbaccdddbbbbdcaacbacbcbddcccdbcaaaccaaaaabcdaaddacacccbbcdabccbdbcadbcdcbccbdabcbcaaacdcbacbccbaacddbddacbaaabaaabbcdbaacccacacbdbcbddddaaaabbcbdbdcdbadcdcaaaccdbaaababaacdbcbdcacdccacadcbbdaccacdbadddcbabbdabdbdacbcbcaccdacdaadcdabbcbbbbbdccbdbaacddccdcdcaaccdddcbcaccddcdadcddddddbcacaccbbdcacbdccbdaaddbbcabaccbcacccdcdddccabbabbdbdcadcbabbcaddaadaaccbcdcdaccacddcacdaaabadacddbbacbcacaabbdddaadacdddbaddcadabbaaccdbcbdcdadbadbdcbbdcbabcadacccbcbbbcbaadcabacdadcddccddacaacbdbdbbbcdbababcbcabdccacbcbabbccbcadbadbabcacbcccbbddbdccaabccbdaadcadbddcbadbbcccdccaadbbacbdbdbdbadcbaaacaacbdcbaddacbbccbdcdccbcabdabacaccdaabcabcaddabacadccddcadcddbbcbcdcdccacaabdcadbdbdbdcdaaccdbabcbcaadcadbbcdabaabadbbadcdbaadcdcbdcabaaaaddcbbaaccababbacbcbcacbbccaacadadaaacabbcddacadbcabacdadbbadabccbcbccdcdabbccdddddcacddddddbbbaaaccbabbacaddbcadbccdddcdaacadaacbbbccdaadaadabcabaadbabccadcabbbcabbcdabbbbdabbcbbaaccacaacbcdaaaaaccdabddddbaabaacbbabcbacddacacacabaccddbcbacaacbcbbbcbabcaabaccacbcaaaaaaadbbcdacacdbcdaaaacbddddbacdcacdaaaadbaaabddcdaccbcbdbbbaccdadcbaccdadaddbacccbacbddacddbbcbbcdcdabcabdcbabdcdbdbabdbdcbdcaaccbdaabdddbdcadaccabdbdcdacbaaaabbdcaadccbcdacccadaacccacbcbdccdbaaddabcddcbbaabddcdbbcbabcdccacccadaadadaadcbcdcadabaccdbbcbbbadccadcccaabddacbccdadadbcbacabddcdabdabcccabdbdaccbaaccbdbdcbaddccdcddaaaacbccabcdbcadbbcbaccacdcbdcdcbcadbbdaaadbbbaabbddcdacdccbcbbabcbabcbdabcaadaaacbababddbcbddcacadbddcbdabdaddccdcaababcbbabadbcdabbdbdaaccbcabbdcabcccdbabdbbdacddccabdcaacabdabaddddaabbdcbadcdaddcaaddcdbcadddddabddcacaaabcccdbdddddbdaabbbabcdabbccccbbbacccadadbccaaaaadbabcdaabbbdabccbaacbddcbacaaadbdabcaccadcdaddddddcaddcddbcdadbdaabdbddcbacabadbddccabccaacbaacadaacdadadaadcbbdccbdabccdcbbbbcacdadccbacbaacdddcacabcdbcabaabcdbbddadacacbadbaddcacbbcaddaacdacdccbaaabbddbdddbaadacdbcdcdccdcdcddccccadadbddddadcabbdbbacbaddbdbdbcccdbccbcbabdbababdaccbdbcdbbadcaabdccccccabbdbcccdcddcaaacdaaaddabccbcdabaacddcccddcdccccbbaabccbdbabadcbacaacbdaacbdbbccddbabbacdbdcacbcadbbbcbdacabcbaaacabbcbcccacdadabcbcbcaabbdbacbacbaddcdaadcdaccadbdabbaaddcacbcbadadbacccccaaacbdcdbccdadbaddcaddbbadcdbcaadddcbdcddbcbbcadccccadabdaaabbcdadbcdcdababcbdabbcdacadbdadadacabddbdddccabbddbabbbdcbdadabadbabbabcdcbababcdabdbddabcadcdcbddaddadddabdccabacacbcbbdbcddbddbaabcadbcaaadbdaddaadbdbbdbbadcccdabdacddcacbaadbbcbadbcdddaadcbcddbadaaaaddadcddbbcddaaabbbacdadcdbcbcccbbbddacdbdbccbaaabaddbdcddbabddacccbaacddcdadccdacaacbacababdbaddbcaddaaabdcdcbbcbcbabbcbdbbbbdbbcdbcdbbabdbbbaadcbddcaabcbccccdccddadcaccbdacacdcccdbdbcbdcdcadbbdcabadbdddddbddcdddabbbaadbacccbaacccbadadcacbaabbabddabcadccadabbbdcabbaccbdbbbcacdcddaccacadbbccdbbdbabcdadcbbabacaabdbacaabbddbbcabadbaaddbbcbabbaaacbaacbababbbdcdcdaabdcabacabacdabbbccdadbccadbcdaccbbddaabccaccbbccaccbdbdaacdbacbacdccbacabbaadaaddbabbcadadcccbadcdacabaadbcdbabbccabddcbdacbdbdcabdbacdaddcddcdaccdcaccaacabcbbadbdbacdaccccccabcaccaadababdaddabbbdddacacccddccabcdaaccbadbddbddaccadabcbbbaadcbdccdcdbaadbaabdadcbddaccccdbacddabcdadbbaaddddbccccbddacaabcccbccddaadbbccdbacbddbdcccddcabccdcdbadcacccbdabbbaacabddcdaabcdbbadccdbbabbcbdaddacdbddcddcaddcbbdcdbabacdcadcadcabccabcddcbbacaccabbdacaccbdbbcbcaaadacaadbbdccbddaaadcbbcbaaabccbbbbcaabbabdbcdacacaccabacbcdbadcdbbdbbcdabadbbcadddbbbddaadaaaccddbcbcadaabccdcbccbdcabcbdcaccadbbaadadbdcdccdccaddabccbbcdcbadaababbccaccbccdaadbbbdcaaadccbacbadddbdaabacbbdcadbdddbabbcdbacadabbababccbbbaadbabddaccccdaddcaabddbdddcdcdbbcdbcacdcbddbdbcdaaaaabdcccbcdbdddcdcacbcbcddcdcdcacaccbbbdaaaccbbdacacbabbccadbdbabbbcdaabcbcabbccadadbdcaababbccdabdcaccbcdaccccdcbcbddacdcdddcbdadabaccacddadabbddcbdacdbdabcadccbddacacbbdadbacbdaabccbbcaabdaadabcadcbdadabbcaabdcadadadbcbdddcbbadabbdcbdcddadddabacbbdabbbacbbbbdcaacddaaccdcacbcbccdbcdcdcabcbcadadabcadbadcabadcdbabbbbdabbacbbaabcbbaaadbddbdadbbbabbbbbadabcddcacaccdccbccdddadbacbdbdddbddabbdbbdabbbadbdabaacbabccacdbbdcdbcaaadbcddcadccdcbbcabddcdbacabcccccadaddaabbaadbcbcdbacccabdaccbccccaccaaaaacdbbcdcadddbdcdcbbbbccbcbbbddddcabaabccbbdcdbbcbbdabbcccdddbcaacadbcaccdadadacbdddbdbdddbccabacaaaacabbbacbcbbacdaadbcbddcbcbdaaaacadabcacabbabccbcdaabbaabccaaaabcbaccdaccabbdbdcadaaabdcbdcbdbdbdbadacaddcbbaaddbdccdbcadabdccbadbbdbbcdadcdcaabbbaacaabadabacacdadaabaabbbdaabccbbdadcbbcdaddddbbdbcbbbdadaccdddddccabadcdcdaccbcaccdabacaaadbbbbbcbcdbacadaadcacaaccccadbcbcadbcbdddccddbaacabacbdccabbabbbcdaddcbbbcddcbacabbbbccdbbacbcaabaadcdadbbdcadacbccabbdddbaacdabbcdbdcadccaabcabdbadcdccabbbccabdbababdaabacacbbcadbacdbccbbdbbbdddcabdcbaaaabbdddaacddaaaabddacaccbacdaabcbbdccddaccdaddcdcddccbdcbbccdbabdbdabbcadadddcbdbcabccddbbcadadbbadadcabcaadccabadaddcbdabacdabaacdcabbbcadcbdaddcadccccaddacbbdbdbacdddacadabbacdcbccbcccbcbbadadabdaadabdcccabaacacdbabcbbabdccdcbacbcaddbbaccabccdcccbbdbaaabcacccadaccdcbddddcbdaacbcaccaadccdbadaccbbadbacdccdbabdbacccbbacccdbdacbdcdcbcabdadccaabaaddccbddbbcaacdddddbcdcbdcbcacbabcccbbbcbdcccabdbadbbadaaacccdbabbbdcdaabdcacabdacccaccdbddacbcdbadcdbdcacaadcabbddbbcbbcbcdacbbbbcccacaabbabbdacbcdcabcbbadaadcbdbaabbbbddcdcbdbabbcdacbcddddcbcbdccbcbabcaccbbccabcbcabbabacaccdaabbdbbcbcacdbabccaddbdddabadbcabaccbddbcdcbccddaaadaabcdabdacabbddccbaabccabdbdbbacbcdcadabddcbcadabdabdddabddcbcdbddcabcabcadaaacddaccbaadabbbadcccaddacabddcbbcacadcdcbbcbcadbcdadcdcaddbabdcccbddbdcabbcdbbaccadbacababcaacadaabbdaddcccccaacacacaaadadddcccacabacdcbdcacadaacaacdccbbacacccbcdbbcacacddccdadbbabacabaddbdddbbabdbaddccbddbdcbaaabdcabdbdabbcbadaddcadcbddabcbacdacccaacbbdcdcccbabaddcbbcaaaccbdaccaaacbcddcaccccaadcbccbbcabacccaccdddadbcbbbadbdcbdaddcbcbdcbbccddabcbbcacccddccddcbacaaadccbdacabbaccbbbcadcdabadcabbbabadcabdcbacacdacdccbbddbccdacdabaccbdcadadccbacccdbbbcdbcaacabcbdabcddcacacadbacacbbbaddddadbbacdbcdacacabdbbabbabacadadaaccccbcbcabcdcdcdcdcbcccbacdacdcdbbbadddadcdbcdbadbdbacaccdccbdadbcdcddbbcadaacacaaadddbddccabaddabccdccbbaadbaadaadbdadbbdacdcadaccbbbbddbadbbccbadddbdbbabddbccccdccbdaaacbaccbbadbadcdaaddabadbdcaaabccadbdcccaabadadbaadccacbdcadbaacdabddcababdcbcadbdbbdccbdbccdabbbdcacabccbadacbbcddcbdbdcbdbdabcabdaacadcbbabcacaaccdbddccabdbbacacdadbdccccbabaddbacaaddbdddaaccbbaaaabaccacdccbbdbbcabaaacbbbcdddadabdaddaabcbbbaacbaddddaccacbbddacbaabaddcaccacaddbdacaaddddabdbbbbcbdadbbcaddcabcabcdccdaadabacababdcadabbadbbbbabcbdddaddbbdbbdcdabaaacccddccbcccbdbccacdcdaacaadccbcdddabcaaacbbcbdacaccacbdbcbcabbacaabaacbdcdaadadaddbcddacbccacbadcadcddadcacadacbabadccbcdcabaaaabbcbdccdcdaddbddacbacdcabbacdbdacbaadadbdadbccadabdaabccdcdacccccbbccbbbadabacdacbcddbdabcbdbddbcbdbababacbcabbddadbdbcacdcaabdbddcbcadaccaaabaccccaabdbbcbbcbccdcaadbcadccdbaacabbbadcacabccadaadbbaddbdaababaddcaaabbccdbacdcdcbaacbdaadabbdbdcbcbadbbaadbbdacbdaddaccccbbcdbcacdcccabdadbacddcbaadaadabccacbdbdbcdcdbabdbbdaaccbdcdcadabbdbacccdaaddcdaccababdabadabbbaaadbbabcbdbccbbbbbbdcabcdbcadbdccdccdbccaacdbbbadbccbbabcdacadbcddcaccccadacdbaaaaaaddaabdcabbbadcdbbbdddbbaabccdaccdbcadcbcadacdcaddcddaaddcbdbcdddabbcbdcadcbcccabccbacbaadabaabccddbcababccaadacbaaaaacbbcbdabbdbdaccdbaadcbbbcabdaabbbddaccaccaaabcababbacadbdadbacdccbddcbcccaabcdbbdbdddabcbbdacdadddbddbcddcbddabdbcbcdcddaaadbddbababdbaddcdabddcbacbdddaababddbadaabdcadbabaaddabddddccaddcdcbabbccadabbbbbabdacddcadbdbbadcdbbcacdaddcdadcaaacdcaacaabaaadcdcccaacbababbaccdbbadcadaadabbbccacdddbddacabcdbccbcabcbbbaaaaaddccbccbaadbdabcdbcacbacabbcadacdababddccabdcbdaaabdcbaccccbbbdabbbaacacddbdcbdadaaacadaabcabcbdaddbdccadaadacbabdcdacbdbbdddadcaadbdacdacdccccdaadaddbdcbbdddbdcbbcbdbdddccbaaaccbbdaaacdccadbcaabaddabccbbdcbadbaabcdabccccccaabbacdbaabacccdccdcbccaabdaddcaddabbcabdbcccabddbcdbcbdabdcddaaddbabcadbbaddddcbcdccdbcadddcaacbcbbdbcaacdbadabbdbdaaddcadcdbaaccbabcadcabcabbaddbbbbbcbaaccacdcadbdbabccdbcddaacdbcbbabcadcbadcccdcaaaccbbbaacabcaacbbbabcacccbaaacadbaabaaddabddacdcbadabacbabacbcbccabcbdbbcdddadccbddacaacaabcbdbadccdabadabdccacbdbbcbdcbacccaccaddbbabcaccbbcacbcddcbbacdacdadbaacdadcbacadccbadcbdbbabadcdbdbddabacbbdbccdaabdaccdbcccabdacaadbadcdaacabddacbbaacbabdccccaaacbadcdcbaadbdbbdaacdddcdcdddbacddaadaadabbdcbabbdccadaabbcaddabdcaaccabbbbaddaabdbbcaadacabbbbcbbddccdbbccbaacbbbbccddddadcdabdadcacadbcaacddbccdacdcdaabbabcbadacaadabbbbddaababdadaaadabaabdaccbacadabdccbcdaaadbcbbadacccbcdbccbcadcccbdbcabbbdacaccdabdbbccdbacdbcbbcbddbdccbddcccbadcdbcddbbddbcbccdbbdbbbdddadccabccbccbacabddbccdbaacdbdbbacadaccaaddcdbcaaccbbcddaabddccaddccaabaaaabcdaccabadcaccacaadbbcdcacddacddadccdacbdbacbabbdcdbcbbcccdbaabaadbbcdacabddbaaddccbccadadacbcdacddbadbdcbdbacddbacabbcaccdbbaadbbacaddabaabaacacabbadcccbcbcdbadcdbccacbdcdccbadccabdccbbbbaadbacbdabbbcdcbbcddbadbabbababccdcddabbccbbdabbcddccaccaaccabddaddcacaacdddddadaaddabccaacdbbbddcdbaabaccbdccbbcbddbcdcbccddcacadcaaddcbadadadddbcccabcdabdabdaacabdcbadcdbddadacdcdaabdcdbcddddbbccbdcdddcdccbdbbdbbdbacbacbabadddbaaddbcdbbcabccccadcdacacdcccbbcbcddbbbabdaabddddbbaaadddbddccaabbbccddaadbabaabccadaadbbacbbacadcbbcccbdabaaabaabdcbcdbbbdabcdddacadacdbadadcbaadccbccacdbcbcadaacabdcdcddbddcbdacdbaaabddcccbcaaccabbcbbaddbacaabbabacdbbccbbdccbbbacbbabbcdacdbcacbcaadccccadacccdbdcadcdacddacbcdaabaaadcaaddbddbbccacaccdcbbbccdbddbdbbbbbbbccdcabcdacddadbaccbccbcdabcddabbdabaabdbaabaddaabdccdbabbdabdbababccdabbcacdbacbdaddaddcabcacbccabcacccbcbbcbdcccddcaababcaccaccaabadadabbcdabadbcbadbdabdbacdcacdadcdaccccadbcdbbaccababddcaacdbbaabdacdbddabcbccaaddbdacdcbbdabbbcdbbadcabdabcdbccaaaddddcdddccaaccddcbcaccabdbadcaddcbacccadadcbbbacbdacaadbcabdcacdacddababcbcacbcabddcdbaadbdbcacdcbbbbacbadababdcaddaabbabcdcadbbdadaaacdbdbadadcadbccddbcaadaadddbaacbacaccdbcaacbabbdaacddadadbbabbbddcadbabbabadadccdbcdcaccbbdcabaddbcabdbcbabccddbbbabcadadddbddbdbcddabababdcccaaababacdbdaddccdcddabbbabbbbccbcccacdaddcaaddaddbacbcbdddbadadddaddabadcbbabdabcaabdbccacabdacbaadddabadabbcbddcaaabbadabaadbbaacacaccbcacbcaccbcbaddadbcbadbaadacdbccdadbdbbaaaabccdbccbdcbdaabdccdcbddabddbabdcdbaddbdbbcbbbcdcbcccbcbadbdddbcacddadadbbbccdbcccaddcbaabacdcdacddbddabadbaadabcabbdcaaadbbcbdbbaabbbdbbddacccbcbacabdcaadabbcbadbcacbdbacdacacbdddacdabcbcdabbcdddbbbdaabbbdddbbbcccddcbbabccadddddacdcddbdbdacaddcdccbabacaddcbccddbdacddbbbdaacbbcadaabcdbdcabcabccabadddbaccddaabdccabdbccbcdacdbcbbccacdabadacacddddbccdabbcacdccadbcdaabadcbabdbccdacdbabacdbbbabadacbdabcdaaccbdaadcbdaaaadcddabababdcacdbddccbdabbaaabbbabcbdbccdabdbbddddaddadaaabcbdcdabccbabaacbbaccabaabcaacdabdcbcababbabbbbdbddaacdcdbcbadaacdbbdacbdcddadcacdbbacaccccbadaabdaddbaaddaabbadbcabbdacdaababdbcdcadbcbcbcbaacdddbdbabcddadbadabcddabdabcaaacacdddbbcacbabdcbccabbccbdbbcbcbbdcbacdaadbadcbaabbbbaaaacbbaadaaadbbcaadcadaddbcdddaccbcabdadcbcdaccaadccadbdadcaaaaddbbbabccadddacbbabaaadcaccbacddabbcdaadadaadbbbabddbaadbcaddbaabbbbabddbbdccaadddabbddddbdbbbbacaacdcbcadddbabccadbbdcddcccaddbaacdbadcacaddbddcccaaabdddccdcdcbaadccbacddcbbcaadacdbdadccdbdcadcbacdcadbabacabbcababcdbbddabcabbccabbcbcdaaabbcacbcbcbabdbccddbbabdcadcabadaaadbacacbdcaabbadaaadbcddadbcdbbcbcdcadacadddbcbdbcbadaccbbddcdcccbcdbaabdddbdbaaaadccddbcbbcadaacdcbdadaddbbcdaabdcbcacdbcbadcddcbddcbbccdacbacdacdcabadddddddcadcbdbbcacdabcdbcacddbbbbaddaccdaabddbcdccccddccbadababddcadbcccdabdabaabbbbbddddacddccdddabaadaddbbbddabdaddbddadbccbadbbddbdbcdaacdbdbbbdbadabcbcddcccdbbcdddadaccccbbccbaabcababdabbadddacbabcaacadabbcabbaaaaaadbdabacbccbbbacbabdcacbddcdbacbcccbabbbcbbaaddbabadaabcdbccbaccccbdbababababcbbaaacccdbddbdaccbbcaaaccddcaaadbbbbdbcbcacdbddbacbaadbbaaaacbddcbbdbcaccbaddabbddcbbbadcabcaccbadaabbcabaaddcdbadccbaaccdbdbdcbcadabdbbbaccbbcdddbcaadbdcbdcbdadbccbbcddcdaacdddbdaaabbddcabaccabaacddaaccddcbadcdacacdbdddcdddbbcdaababdacbadcdcdddddbdbcbcdabdbcadbaacccdaccdbcbcdbabbbdaccbababcddcbbaadacacbbcbdbdacbabcadbababacdddacdbcdcbcabdccdbcdcadbabaccbbababbbabbcabddadcaaadadabbcddbabcaaaddadcccbccbcbdcccbdacdcbcbcaacaabcdbdbbbdaaaaabaaabacdccacccdcaababaaaaccccbcbbaaadaccabacabbcacacbcdbadcdccbcbdbabccaddddcbddccacabbbbbdaacaadcabbdddbacaaacdddaaacbaaadcdbdcabbaddcbdccbacadcdbbddcccdbcadaccdaccbddabdcdbabdbddcdbdaacdbcadacacddaadbdabddcbdadbabcabadbcaabdddcbbdbddbdcccaaabddbacdbaabacdabbabbbdcdcabdbdadadacddbaaaaadddcbacbdccaaccbbadbcdabdbdaabdbbadcabdcbdaabbcbbbbdcbddadddddbdaadcbccccaabdacdbbbdcdabbdadccbccccbcbddacbadaccadacaabbbbabdcacaabacdacbdccaaaacccbbbddbaccccbaaddbabbadaadaaabacbdadadbbcdbaaaadbabcaccdddccdcccabbbacccbcaaabaabccacbcbbdddcadbcadcbcdadabadddaccdadadbbbdabdcaadabdbacadddbbbaadbbccadbdabdccaabdabdacaccdbbdbaccaaddbdcdbdcccadcddbddbbdbacbdabcdaccbcdbdcabcaccbaccadabbbbcababcddbacbbaacabdcaabaadcacccadcddcbddbccddabdbcddabcaaabbdaadadcadddcddddadaddcddaccbcacdcbbbcbabaabdaddddbaaccaccbdbbdbddbcbbcbccbdcadcbadadcdbdacaaaabcadbdcbaaddaddcdbadbccbdddcdaacbacbabcaadbcbadbadcbadbaddabbadbbbbbcdadccdbdacbdbadcdbadadbcdadcaddcdccddabbbaacdddbbaadddbcdcbbcbdddcddaddcabcccdccaacbbcbdbddbccdcabdbabdccbbcdadaabbccbccadbdddacbccbbddcbbabacdccadaabdadbddabbccdbbdababcbdbdbaccbaaddbabcbbddccdcabdbcaddcccadabdbcaaadcbabccabcdcbddaccdacabbbdcdbddbcbddbddcdbbbcbabcbaabdcdabcadcdbddaadcdadadbddadbbdabddcaddbabdbbdcbdcadbaabadcbaacbbbbbaddbcccaddccbbbdacaacadaacaadbbbbddaccdcbbabdcdabcdcadadcbbbccbabbcddcaababdcacbacbaaadbadcadacabbcadadcabaaacddcacbaacbcbbcabdddcbdbbcbdbbdbcddadabacabbddaabadabbcadcdaddbdaabbbadbacabcbdbbccdcacbacddddbbccdcddbcbcaccbadaddbcbcdcadaabbbcdbabacddbdacabdbcdbccabcbddbacbcbbbacccbbbbcabddadcacabdcdabaaacbbdadcbabbaaabcdabbcdccbbbcbdacbbaabbddbccddcdbacdbababddbadbacadcddbaacbbaabbcbbcacddbabbbbcadcdcbccbbdbdabadcbcbdbcdacbaadcabbdaadbddbcaaddacbbdbbaababdcbadcddabccbcdaacbabddbcbbaacccbcbaaaacbaccdcbdaadbbcbbdbacdcbcbcccadccabacbaaacdcaadaddcbbabcaabdbdccdacdbcacbbbddcbccbbbabddabbadcbcbcaacaccdbaacccabbdbadddbaadbbadadbadacbcdadaccbcdcbaaaaacbdadcccadabddcddbccdaabcbcddcddbdddbcadcdadcddabdabaccaaacaabddbabbbbcdadbccbdaadccacaccdcccccbbbbaccbcddbcacbdbdbdbadbcbcddabbcccbcddaadcbddabbccdcabcdaaabdccacdddbadacbaadabbadadcccdbccbadcbcddddbaddccdbbacaabacdddddbcbbabaaadbccbbcdaaabbdaccdbdbdbbcbdcbacccbddcdbaddbbacacbcdcdabcccdcabbaabbbdaddaababaaaacbbcbcdbcaadaaaccdacdddadacaaababdbaaddacdadbcbabbcdbcbaddcbbcdcdaaabdabcbabacdcaddcbabaabcabcdcadbacdaddadbcdbdcdddadbacdadbdbdacacaaadcbaabbbcabaadbabdaacddabddccaacadcbccacaccacadbcbdbddabbcacdaabbbaddbbadbbaaccabddbbbaacdcadbcabcbcccbaacbddbbcdccdaddcdccddaabacdadbcdbccdcadadcadbabadbaadccadbcdbbcaaadbabaabcacacdbbdccccddddabbabdbddcbdbacabcbbacacdacdbbddadbbbdcaccccddcbacdbaddaccdaacdabcbabbcaacbbbdadbadddcbbadcddacdabaccaababbaaadacdbcbbcbbddcbabaaabcbbddcaabbaabbcbbbdcbadcbdacbbabdcbdcaabbaabbcdddddcdccbabbcbdcbaacdcbdbbcabcdccadbabcadccacdadcbbbbcdadabdabdbbdccdabaaacacaccaadacadbbcbccdacdacabadcbccaccdaacbacbcadabcbcdbbaaaabaabaccbbabcacdcddcddbdbddadbddcdacbcccbdacdbdbcbacaaaadadaddbdbdacaacddabdacccccaccbadcbccbbbdcbdcccbbcdbddacdbadbbbcbacccbcbcbbcbdadacbaabbbbacbaddccacdbbbaddacadbdbbcadacaddaabdabccccaabcadcdcdcbdcddcdccaadddcdcbbcbacdbcdcddbddcaacadccddcdcbbccacbadbaddaabccaddabccadbcbabcabcaaddddabbaabadabacdadadacadcdbbaccddadcadcabdbacdcdabbbdddcbcabbabcbabccbdbbcdbcbdbdccdbbccdaadbcdbdbdaddabacbcbddbadccdbcaacbdcaacdcacdcddcdcbcbadcbdccdadcbdcbcbbadddddaacbbbbdcacdbbbcdaadbdcabcbbbaabdacdacababcdaabdaabdbacccbcbcadcdcccddbbacabcadabaccabccaaccaaaaabbcddbdacadbcacabbcbadcdabdbdaccccdbdcdcacabbcaaddbbcdacdccaadccaadbdbdccacdcbcbcbcbbbccdbdbcbbbdbdbdadbadbdacbabdbbbbbbbdabadbaddbabcdbcbddaaccddcdcaacabccadbbdacbcccddbccccaaadccadbddcbbaaacbcacccaddcabadcbcdccdbadbcbadcbccbbdbcdcddadddccbbbcdddbcabdbbccadcadacdaaacdaabcddcdcdcbbdaccdcbdbdbdbaabbaabbcccbdbaddacdbdbdabacadaccbdcacdbbadddbcacbccbcabdcddadbadadabccabacaccbcacbacacdddaaccdcaddcbccabbcccaaadbbadcdcdcabdadbbababcdabcbcabdaaddcbabcabdabcdaadadbddbcaaabcdaabccbdbbdadacdccacacdaacbadabadbddacbacdcdccbcaddbdbcbcdcbcdddaababddddbdcaabdacacdbabccacabaaaabbdbdcdabdcbcdccdacdacacaddbccaaabcbdaddabbadccbbbbdbaacdadaadaabbababdccadcaabaaaacdccdcbabcaccadacccadcaabbcdacdbdccadddcacddcbbaacbbddddcacbbaaabdcbabbbbdbcddcbcbcdcdadddcacadbacadadcdddbdcabbcbbdcdabdaadccbaccadbdbdcbbaaccddddacbbcddabdbcdbdcbacabdcdacddbdddcbcbaacbabddabcddddaabdbbcccbcccdcacbbcdaabcaaddbaadccdddccbdacddabcbabcaddcddccdcadbacbbdcdccbadbadcbdccbadbdadcdcbbccccdcbbaaccbddabcbddadabcacdbaaccdbccacbdbbdaaaccccdcbdaaccaadcdccdcaabcdddbdaabddccdadbbcdbbadddcbbabbadddacbddcbcccdacdbcdaaadcdcaacccdaddadbbaaaabdacbadaddabcbcdbbaaabadbbdadbbdadaacdbabaadbbccaabadbdbbbdbcaadcdbdcbaaaababcadaadbacdabacdccbaccbbdbbdccacdcacabcddbaababbdabcbadbacacdaaaaabdbbcdbcdcbdcdaabbaacaacaaaabdbccabcbcdaabcccbacbbcadadaadccadbabbcacbdcbaaddcbdbbbcadaacaddbacbdddabaacbccbaddbccdcbdadccdddcabbbbacbadbbacaadccbaaaccdddbdbadcaabdacbcddbbaaabbbdbbdbdcbadcaaadddacdadadcbddddbdacbbabbbccdbaadcabcdabdcbdabaccaaabbaadddaddcdcccbcbdcdbcbdabdadabaddabcdaaabccccccccdddaacbaaabbdadcbdcddbcdbdcaaaacbdadcadaacaddaabbaaaadabdccadacdadaccbcbcbdcdbbaccabbcaadddcdbdacbcdacabcabcaabaaccddaccacbaccbbddabbdabbdacdbcbccaacdcaddbdbcaabcadabacccbacabbaacdaaaaaadbaadccdaabbdcbcdbccdccbcdcccbcddbdbacbbbccccccadabcabcbcbdddddccbdbbaabbbddbccacbdcbbbcadbbddababaadccccbbacabbbbccaccadbbdaaadcabcbddbcbaaacbcadcbcaccdbcacbadaccbaccbccbddcadcabbddcdabbcabcddbbaacdbdcdadbabaddcdbbdcccdbdddbbdcaddddddabcccdcabbabdbcbcdcdcddaaacdbbdcbbcdacdaccdcdcadaabcddcdaaaaabbbcbabdaaaacbbccaccdcbaacaabbadddaadbadddadbccdcdacbbbaddabdcbacbaaddcbbdcdababbcbadbcaacddaddacaaddaadcaabacacdbdcdadacaddddbbabdbbdabdaadbdbadabbabcbdaadbdbbbcbbaaccbadbbdcdbdddaabdddaabdcdccbabbcbcddbbabcdaaccadcdacbaabaabcadcccddbaccdbcaacddbccddabcdcdbdcbabaaaaadccaacdcbccaacdddddcbbcdbacbcbacabbcbbabcabccadadbdcddddcbbcabaadbbaacacaadcacbbadbaabbdbadbbdcaacbbdaccbaabdaadaacacbdbdadcdddbdaabdbaabdbdccbbcbdbdbcddbbccacacaccccddbddacbdccadcbdccaabcdabadcbbbdaadaccccbbbcaacdbdcddcacbdbddcdbbabbdccccabccbcacacacdbcbdbcadcdbadccabbbcbddaabdacabdaabacaddbcbdcddaabdbacddbacddabbbcdaaddcabcdcddabddbccaaaacbabdbcbabadbdbaddccbbdbdcacbccdddcaccaacbacabdcdaacbdccabcdadbdbdcbcdabadcdcbcaaddbaabdbdaadcbbdacbbbaaabadbbbbacccabdbdcadbaadaaacadaababccaccbdcbcbbbbbbcbacccbbbbcccaadacbaaadcbbbccdbbcdccdcbadbbddcabcbacbaaaaccddbbcaacabcababdaaccdadacdadddcdbbddabdadcbbddbcabacadbdabcabbabdcbcbcacacabdbcbaadaabccaaaaddbbdccbacbdabaaaaabcdcaddbddbcaccccccbaddabdddbcbddcaabbadbabbdcbacdddaacbdbdabccbddccddacdabadcbacdaadcdabbaaacdaaacadcdaddacbacbccaddbccdcdacccccdcababadbabbbabadcccacbacbadcdabdbddadcbacdabbadddcdbabddbccddccaddbdcbbbadacdbdaccdccbbbcdcdbddcbdadcdacdbcdcabbdcccaacaaaadcddbcadaacaacdccbddbdccbbbccbdbcacadadcbdbabccbbddccaccbdccddbdbdddbdcdabcccaaadaddacadccacdbadabdddccbbaddddbdaccaaadcccbdddbcaaadbcbcaacbacbcbaccabbddbcadbcaacacbbbaacbcaddcccbaddbabccaabbcabdacddbcaabacbccacbabdbccacdadaadaababaabddccccabbabddbdcacdabacbabdcdccabdacacbdbacbadcbadaabddbcabdacbdacabbbcaadabdcbdcbcdbbbcacdcbbbddddbddcbcccbddbbbdbaacdcdaaabccbdbbccdaddabaacbdaaadcbcadbbdddbacccabbcbabbcabddbcddbabbacdabadbdaacaaabacdbadcbbcabcddbcddbaaaddbaddadbbadccdccdbacbbccaadabccdacbcccaaddacbddaccaacbddabccaabcbdaaacacdadcdaaaaaacaabccddbddabadddccaacdcdddacadcabcaddacdcdddbaddcbbabaabbcadbdbbdbccacabcaaddbabdcbdbdaddddbbbadabbcaaadddccddbdbbbbbcbbcdbcacddbdccbaccbddddccbaacabcbbbbddcacbacabddddccbaaddddcbbaccdbbcaabcdcadcdbbdbaadcbdcdacbadbdabacddbcaacdadddccdbdddaadcddbccacbbcbdcbcbbbaabdbbcccbbbaaddcbcbdbbbacbddadbccdbddbbbdaaadbadaacacccbabaccbdcabbcbbdaddbadaacdbdadaabbddaaccdccdabcccdaabdbaacdadacadacadabbccdabadadcdcbaadccaacdcadbdacdbddabdadbdbadaacabadbacdddabcbaabbbabaccddacbbcbdaaadacdbccaabbaaabccdabdadacccccadbcbdcaacbadccbacbabdbcaddacbcaabdaadcbabddddddccdadcacbbcbaabcbaacacddddccdbdddbcdbbbbabadbbbacabcacadccdadbadcbacadcdcbbcabacdaabcaccddddbbabddbbbdcdaccacabdacbabacdbbbdbaccaccdbdacccadbadcaccbbdabcabacbdbcabcbccacdbbbdaacbbadabaaccccddbdbccdbdabaaabcdaccdadbbadddccccdccbbddbabcbddcdbbadbbbbbaddababbdcadbaababdbacccbcccbbcabacddcbbbcbaabddbcbcdbacabdbaabbaaddadcccacbabcbcacdbbdcddbacbdbbacbacdbddcdcbacbcddaaaabaccbdbddbddacdbcaccbdbdbadcdcaaabaccbbacdbcadcadcbbcccccddbccdbbadbabaaaabcaabbdacbccaaacaabbaadadcaaabdddbdcaacccababcbaaccbaaacacbbdbcdbadaddcdcbdadddcccdcccacbdacdddbcbaccbdcadcdddbdcaddaccdadddbccbaabaabcdcccbadcadcddcdaabbaabddabdacddbbabdabbaadcbcadbaaaabcdaddbcbbdabcdddaabadaddbcdaabbdaadbbbbadabbcdbddddaacbcaaabbdbddbcdbaadccdcaaabbdccdaddbaaddccbcddddcadbddaaacdabdbbcbdcadbcacddabbadbbacabaadbdbcbdcaddbccabddabddabcdcbbcbdaaddbdbdcbbcccbcaddaccdacabcbbcbdaccccaabbabacaccbcbbbacbcdabcabdbddbcddcbabadccddadadabdddabccabcdbdaddbcbdcdcadbcbcabbbdcdbcaddbdabbaddaaaaccdcdddabbbdabdccadcbbccdcbdbbabcbacdbabcadcabacaaaddbbbacbdbabcddcdcbcbaddbddbdbdabbcccdbacbbaccbbcdcdaaaadabccacbabacdacdbdbbdacbbabcacbbaccaacbabaddcdbacdddddaacaaccadcddccadcacbbbddaddbdaacadcbabbdaabacaacbcdcacabadbcdacdaddcaadacddcbccabbabccdaadaacddcdaadaaabcaabcdacadbcabdbcbaaccdbcbabddcdcabdbbacbbbbcadaabbbddaadabababaccabbabcaabcababaaadbbcadddabccdcbbbbdcbbcabbacbbbbabdaccdabbaccccbdbccaddcaaccaccbccaabbddbcdbcddbdacbcddbccddcdbabcddcccbbbdcabccabcadbdbaabaacbbbdbcacdadcccabcdcabddccccccbcabbadbdacaccdccbaccbccddccdaabdccaaaddcdadaaddcbdcccaadcddcadcadbbdbdacdacddbaddbaabccbddcaccbcbdbdcadbcbdaddadbdcbcaddbcabbdddbcdcdbcabaccaccaacacbcbdabaddbabaabcacdbdbababcccadcadcabdadaaccdcdcbbdadcdddcdbbadcabbbacadcdcaabdcbbbdcdcbacbdacdacbcdbdaddcdbbddcdaadaacbbbbabcbabaadbbcadadbbbacdadadbbcdabdbcdcbbbdbcaaccbbbcaadcdababdccaddbbcbcccccbcacadcccabaccabdacbbbaaacadadddababdadddccdbdbacadadadaddabacabcbdbabbcccacdddccbbacdcaaaacdbbccabcaaccdacacabddaadccbddcbcdaaddcdacccadcccabcadddcaacdbcacaaabaabaccbbdddbabddbabcadbacbaadbdacacabcbbbdbababacdddaaadaaadabacbbdacbbadbcdddcdcdabacaadbcbdbccaabacbacbcdaaacaaabcacdbdabaddbdcbabbaadacdcacbbcdbbddccbadaadcababccccbaaadacccbbadcbbdadcdadcbacccacadcaacabbcdcaccdbaaacbdccddcdbdbdadbcddcbcddccabbabcbaaacbdbaabaaacabbdadbddbacdccccacddacbdadaabadaddbbabcdccdbbbadaaddabbdcabcdaabbcdaacaaacbcbbddcabcdddcbbddbdadddccbbcababccbcdbdcdbcaaddcdbcaaddabbdcdbbaaccdacacacdadadaabdadbbbaacdbcdcbabdccbadcaccdabcbbbddaadbccbbdcbbbbcdddcdbbbccdacdcaabaacdbbbbadabcaaacdcdacbbbddcdabcacadbadcaabccdabbadbcdabacacabdababbadcbabaaacaaabccbdcbdacacaaccbdacaaccdbaaadddcbacdbaddacabcdbcadccdcaacacabbbadaaddadbccbccbbadaddacdaaddaaadddccbacabbabbddccdacddadcadbabdbacccddcacbcbdadccaaaacbaccdbadddccbbbdddaaabcdccadbbcbcdacacacadddbcaaccbddbcaccdddacbacdddddbcbcbccbbccbddddbdcbbcbcadabaadcadbdbaddbdacddcadbbcabbbbcddacbcbadbbacadabccbacabddabdcdaabacccbdddbcadbcddcdadbddabaddaccddddcaaaaccbdccbadbdacccdbddcdbabacdcbcccadbddabdccdddabbbccdbbbbcbabadccbaccbddacaacbdbdbdbbbcabbddadbbdadacddcabdccdabbddadbddcdddcabddcaccdabcaddbcdabccbbcaccbbabaddcbdadbcadcdbbccbccaadcdcacdbdcbdacbbbddbcbcdbcaccdbcabcccdcaccbdaadddabadcdbadbbaddbddabccbbbaacbdbcadacbcbadadcdbaddadadbcdddcccbccaccacdbbadddadacbcbbdacabbdcdbbaacdbadbdccdacdaccbbadaadcabdaaaaabaaacbaadbaccaaabbcbbdccccbddbdcbdcdcbdcaabccaacddcaccbbbdacabacdcadabbcacdadbbdbdaddbdcabdabcabddadbaddcadabdaaabbbcaccadaabbcbacbdaacbcbadbcdccacadddadddbdbcdbbaacabcaacbadbcddadcadbabcbacbcbdaaacbbbcccdbcbdddcdbacdaddbaaccccccdacdbcacbdcbbbddbaabbbccadbdbaccaaadddddadbccaadcabcdabadaabdcbddcdcddbabddcbaddbdaaaddadccbddcaddcccdcbcdddccddbaadbcadabababaddacbbababbdabccdbbdddcdaabdbabacbdabddbcbbdcaadbddacccdbdccbaadacccbddcdbdbbccaddcdabcbcbbdbcbcbcccbdaddaddcacccbaadcbbbcdbabcaabababbabcacaaddaabccdcbbdaabaadccdbddbadcababcbcbcdbbcdcdabcccbbaddcbdaccbbdcaddbabdcbaccbacdbdbdabcabdcbaacbabbcdcabbbddbacabacacadbbdcddbddaccdabcddabdbdbddddbbaacbddccccaadbdcacbaaabdcdcdacbcaddadbccdacacbbbbccadcdcacdabddcacdbbdbaaddbcaccccdaddccbdacdcccadaacbddadabdcabddbbadaccccbcccdcbdccddabadcddddcadbbbbbacbababacadbdcababbdbdaabcbdaaadaababdbbcdddcadcadcdbbcbaaadbabcbacacacdaccbdadcddddbbccadabdcabbdcbdddcbddacadddaddcabdbbdbddddadddbbdaaabdcabbadcdccbdaabddadccacbbadaacaacdcddadbbdacdcbbaababaabaddacbabdbabdccabdccabddddbadcabcbcdbdcccabcddbdccabacbcacccbaccbbbbcacabbbcdaadbbcbccadaabbdacdaaaaabbcddddddaacbddbcddccdccdcacdcaabcbbbbdbcaacbdbadbcdddccddabaccabddccdadbccbaaaddadbdcbccadcacdacccdcccbcbdcbdaaaadcccbaabdbaadcbacbccdcdbbdcdabcdbcdacdcbaaddbbcadcbcabdccababdbddbcdbcacdddadddadcdbbcccccdaadadbccdbcccacdccddbdcaabaabdbbdbacdacaadaaaadcdbbbbabbbccbabdcbbacabcaccbcdcccbcaabbbaaccdbcccddddddbdbaadccbacdbadcabadcacddddabaacbccbbacbddadacbdadcacbabcacbbcbabdacacbaaababbcdbbdbddadcbdbccccdcddcbbcdcaaddcddbcdcbbdadbbcaaddddaaaaaacaadcbacbddcdaabdbacbccddbcdcabbacdbcadaabcdcdbacdbbcbcbbddcacddacbabbbaddcbdbcddbdbdcbddbcbcccccbbbadbddadbcbbbcacddccdaccaabbcbcdadbbcbdbdbabdadddccbdabacdcdabdacbacbadbdccccbdbadacddbddcadaabababbaaccccaddbadcddcdacbdbacdbaadaadaddcdabaaabcbcdaaacbbccabadcabbdacaababbcbccabbaaabcbccaccaaadbbbacccbbdabdccababbbaaacddaadbaaadcadcddccddcdddabdbbbbabadddadadbbcddcccabdcbaabadcdacaabddbccabbdbbacbcbaaabaaddcccbacdcbbcaabcdbdddccaddcbdbbcacbdddadccdaccdbbcdbabacbabaccaadadabdaccadcbaccbdcdadaaacbdabbcacbdbaabcbbbabccbaaccdbcaabbcabbbdbabbbaddccddbbbbabddbbdbbbbbadacaddcbacdcadbabcbaacccbbbdddababbcacddbdacadadddddcddbcaabaadaccdcddcbabaacdbaddcdccdddcccaaacbdadccadadaabdbcabcdacdbaabacccccbdbaaaadcbdcbabcdabdcbcabbabbcbcdcdaadbccaddbcdadbdadcabbddaabbbdacaacbdbbddbacdbbcdcddbacccdacbcacccbbcadbbbacbacdadcbaaadbbbdbbdabbddcacbabbaaadddcdaaabccbbcdbcddaddbbadbaddbacdbdccccacadaddddbaaadabaadcbbcaddcdccacbddabadbcbbcabcbbcbcbbaadbbbbabadabbaadadbdbbdbcdccabdcccdcdccccccaaacbadbcdccdacbdcdaaaabbcaabacbbabadcddabcbbaaacadacbdcbcabddcdbcdbcabbcdabdcbaaaacabacccbcbaacaddbacbdddadaddcaadcdbccbbbbbdccacadcddcaaacbcadacbcbabdbbadacacbbdabcddbcddbbdccadddcbdddddcaabbdbbbacaacbbbdcccddaacadcbddcacddaabccddadbdabcbadccdacaacbabccbbdacadbaacbbaacbdacbcbbcdbccbbabacbcbbadcccddccaaaaacaadbddbddbadaaabaddadbdabdacaddccddacadadbaacbdccaacbcabdadccaccbbdaaacbdacdaccadbacbdcbddbcbdabbabddabacabcdbccbacbabadbcdcddadbcbcccddcdaacaaccddbaaaaddcbabcadccabdabdbdbcccdcdccbdbcdddadacaccbaaaccdbcccddacdaaacdcdccccabcbddadcadcdaabcbbdccdaaaacbdaadbdacaaaddbbdcbdaaabcbddadcbcdabaaacbcacbcdcbabacbacdccccbadadabcaaaababcadacadaddbddcdbdacabddaadddbcacdbaaacadbacbcdaacbcccdaabaabbccbacbcaabddcbbcccadcdaabbccdaabcaaaadabadcacabddcbddcdbbdaadcabadadbcabccbbabcdbbaacbbdbcccbcbdcdccdaccdbaaadddddbbadaddccbbcdacbdbcbdccabccabaddadbbcaadcddddbbbbbabcbadbbbbbadbbbcabcbdbdabaadabbddabcbbccaaddccabbccbdaadaacbbababcdacaaccbbbbcbbdacbcbdbadbdbbbcabbdcbdbbccaaccbbccbddcabbcabcddccdbaadccdbaddbcccccbcdaaacddbadbcdaadbcbcdbaccdccddbcccbacdcdaacbdababbddbcabdbdddcbcdcdbaababbaaaadbadbbbccabddbdcaccbcccbacaadbbbcacabacbbcbccaddbdbdddbbcdbadccddbdbdaaacccbcdcaaddacdaaacddacbdacbdaddbccabcbaacdaadadaacdaaccacabbbaddbaadaaabcbdaacbcbcaccbbbaaabdcbdadcdabbdbdaaccaabacdacbcddadaabdadbabdabdcbbcacacbdabcbccbdadabbaabddbadaacdcdbadbcdaaaabaccdbaaabcdcbdbbddcbcbcccdabddbbdcaaccbdbaccdbdbaacaaaadccccdadcbcaaaccdaacddadacdddadcbbcbadbdcddcdbcadbdcdbdabcaaddbbdbbbcaaabccbabdacaabbdcdadccaabdccdcadbdcbcbaadcdbbcadbbbbcbbcbabbbbbacbdcddddbcbacdbbbabcabcdabdaddcadddcadabdddacdbdbadacaadaabadbddaadaaabdcadcadabbddbcdddaccbadabbccbcbccdcdabcaabadddcaddaadbaabbbbacbaadddbabacccdcbbadcaaabcabcaacacadbddbabdcdbdabcddccdbddabbdddaddaacbccaaaacbcaccbdcddabcadadababdacabcdacadcabbdcaddabacabcdbcbcabccddbacbddacdaaaabadbbdacdccadddbbabbccbbbcaaacccdbaddaadccaccdbcdbdadcbcdcbcccbaabbaabcaadbdbdbcacbdccadccbddaccdcdcddcaccbdbcabcbacababdabacbdcdaadbbdddcddcdbcbcddacabdbdaadddaaabbbcccadbdbbbdbcadbabcbdadbbcdaacbcdabbdacbbabccbcbcdaadbabcbcacaacbcbbacadbdddcaacccdbbbbcdcddabbbbbcbaababbadabbabdccbbcddcdcadbdacddabbbcbacbaacddcaccacdababdacccddbaddcdaadabbcdcdcccdaabcdbcadbdacacabddadaaabaadaadabcbbbcabdcddaccbabccadccbcbdcbabddbbacbcdcddcaddccdccddcacbbacdcbadaabdacadabdaccdaddbdabbacaacdcdbbcbbaacdbccdbaaaaaadcdabdaccbbdbcdcccdcddaacaaabacdcbcbbaaddcdcadddcadbadadcbcbcaccacbabadccacdcbdbccaabadbcdbcabadcddbadaaaabadbbbbdadbabbabbbcbcabbbbabbdbadccaccaabbbaadccbbdcbaccbcbddacdddcbbbcadbdbdaccddcddbdbdbbcacaabcbaccccdcccaccddbabcdabdaaadbdbaabccbaccdbbcdbcabaddcaddcacaaaacccbbbdcaccbccccddcacabbabddccbadccdacdadccdbcdbcdccadaaacddadaaabaaaacccdaabccabdababbddacabbbdbbcabbbacbbdaaadbabdbdccbbbadcbadbabababbbadabdccbabacbcadbbbacddcccabadabadcababaadccbdaddcadcabccbcaddacadcabccbdbabcadddadcbddbadaabbacdbbddacdcbbaacbddbcabcdacbaddbbdbcddbadadbbabadbbdcddadabdbdadcddbbbaccbddaccdddabdcabbcdbcbcdcdadddaabbcdddbbdbdabccdcadaddcadbdcbdddbdcaccdcdbbaaaaaaccabcddcbcbbdcdcdddabdacdcddacccbdbcaddbbaadcdbddcbdbaaabcbbbabccbccacadcccccdaacdbadcacbadcdacdcabdabdcccbdbcdbcaabbdbcaacdbdcbddabaaadbdababacabdbdadbdddbdbbbbdabdccabbbbadccaccdbadacdbadbbcdbdabbbbcadbbdccddbadbcdbaacacaabaadabccddaddcbacaddddabababdbbabbcddacccabadacadcacdcbbacdbaabcbacaabbbbbbdaccdadcbdacabdabaddcbcdddabdbddbcaddcabcbcacbdcadcddbcdbdbbcadaacdcddaaccddbadbddbcbcdccbdcdabbcddacdbbdbaabbaaacaccadbdccadaabdbbdbaacdbccaabbacbacddcddbbdadbadccdadcbadcbdcdbdacccccdcbacaabacdabdbbadcadadabdddacabddbdacccacdbaaccadabcabcccdadcabdccaddcadddaddcdbbcdbdcaabcdcdcdbacabbaacabcaabccbbbaaaaaddbabbabbcccdbcaadabdbcbbbddbdddabaaaacdacbcabcccdbbaddcddcbbcbdcdccdbbbdcbdbbcdbbabacdbbbddbcbbaadbdbdccdddacdbbacccadccddacdddcadcdccbbcbddcdbcbadabcccaadbbdccbaacacccbdcacadbdcaccdbacbdbdcddbbcbbadaaaabbcdcdcbcaccddcacccddbbadaadcacbbadbdcddaabcbcacadadcbbddcaaddccbbbadacbcdbdbbbaddcbddacbcdbbbdbcadcacdbabbaddadccbccaadbcddddcacdbcbbcbcbdacccccabbcaddcbcbdddcbbadbadabcabbcbcdcddbbddabbccddcdbdaababaddadabacbabcaadacbbacbaadacabddbddbcadcddbcbcdaddabbbabbabdbadaaaaddcacadbbcbabcaabdcadbabddcbbabacdddabcbbccdbbabaaaabccaabdabcabbaaabbcbaacbcbdaaaaccdabaadddbddbdcbbdabaacbddbcbaaaddcdcbcbdbddcacbaabbbccdacaacbbcbccbabbdacccacabacaabdddbdbbbbdbcdccadccabbccdcadbcccbccdccacddabcabbddacccdaddcdcbbbdbdddbabbbcbbdabbbcdcbdccdcbcbcacacdbbccccbacdadcdcbdccbbdadcdacaaabdcacabddaaacadcdacbbacbbacccbabbaadcdcabadbcdbccdccabcdddbccaabcddcdaaadbbacdcddaccadbdddccddbbacadcbddbbdcaadcbadabccbbcbdbcbcacbcddbacdbccdcbaaabcdaddcbcdbdabdbbcbdaaaacddcbdddcbdcdabbcddaccbcacbdcbbdcddddacdcadaababbcddcbdddcbdbbabddabcdadbdbcdbbdadabddbdabbdddbddaaacbaaaabadbdcdbcbabdcbcdbcaaaabdacbcaccbaaddbbaaaddcbbaddacabbabadbdaacccddcaddbbdaaadbdbaddcccdacabacdbccdcaadbccddcdacdcbabcbddbcbabaaabcbadbabcdccdbaaaaccaacbdaccbbdcdbccabddabbbbdbabccdddaddcaadbbddacabadabbdbcdaabdaddbddccdaccbadbaaadbbacaccdccadccbbadcccaababbdbdccddcddbcccacdcaacaadbbbbbddaacacbcdcbbdccdcbbadddbdbdddabacadabccdacbcadbcdcbcbabadccbbaadaadadcbbaacccbdbaadccdbcadcbcadbbabacdacdacadbbadabdabdbbbbbacdaddcacbbcdaabaadbbdadbbbdcdbdaaababddcbbacacdbadaccbdccaddbacdaaabbdccaadbadbcacadbddbcaddbbbaaddccacccccaccbcbcccdcaccbbccbbdabccbabdcbacabcabddaabdbbcdacacbbbacdbadaababaadbadabdbcbccaacccabdbddccabacbbcacdbbabcadaaaabdcdcacbbccbcabcbbabacdbbcdcccbabbbcbacdcbbcbdccabcddaacdcbabccbcdbcdacbbbdabaaaddccbbbbacadacdccbabdbbdcddadbacdacacadaacbdbaddcdbdabbadbcbbdadccbdcbdbabacaabcbcaababcbddaabbabacbbadabcdaaabcaacddbabcdaabbdddccdacdacdbddbbdbcadbdccbadacddabadcababbbcaadddbbdcabcadbcccddccdbcddacccaaaaaadcacbabcbbbbadcacbbcddbccaccabcaddacaabaadccccddbdbbccdcbcabdccccddbcbbdadcaaddccbdccaabcbdbbbacdbabdacadbbacccbabdcbbcbbaaaaadcdcbacdcaabddacbbaccaaaadbdcbbdcadbaaacbacbbcbdabbbccccbdadbdcbabccaccbbccadaddddaccabcdaabcadddbcbcddcbcbaadcdcbbbbdabcaadbaadcddcdabdaaacdcdccdccbcccbcaacbcbcbcaddacbddbbcaacbcdaddcdcadacacbbbcddbacbbbcaaabaabbdddcabaaddaabdcdacaadbadbbaaccbaabaddcdaaacccdbabcdddabbaadbbbdcdabdacbcaabbdbacbcabaccdbabdbdcdbcdddbbcdbbbbbbacabdcaccdccdddbdbadcbbcddccadacdbabccdacbdabccbcbbdabdcdacaaacddcaadbbccabaacdbbcccddbcacaadacaaddcadcbbbcddddcbdacdddcbbcaabbbddcccbdccbbbbcbbdcadcabaddbcbcccdccccccccdacaacddcabdabdabdaabcadbacdacccabddbaddbbadabadcbdddccdcbbccaabcddcadbcbacaabaaabadbddccadbbaadccbaacbcaccbccccddabdbcacbdcbcaacbccbcabddabacbbcbbbcdbccacdcbcbdbbabcdbdccabdadccdcadcdddcddccdaccadbbddadaacbbbbddaccbdbdadcadaccdabcbbababddaacbcddcadcbbaaabbacadabbddaaaabacaacaaccbcdadbcbdbbdbabdaabdabcdccadabbaababbcaccaaabcacdbcacabddbaacbccabcacddbaccddcdcccccadcddabcbcdacdddaabddbdcacdcaccddbabaaaaacbdcbbbacddbabbdbccbdddcbbcadcdabcaccdcbbbcddabaaabbbcadbbdcacbdcbcbabbdccadcbbdabbbdbbbaddccddcababccbcddaacacccbbdaacbddbdabdbaccacccccabccaddabdcdbbdbdabbbddbcdccdbcbbdbcddccacabadabaadcabacabddabaacbabbadbbcacddbbabcabcbcddccbcbcaabdccddcdcbbcabddcdcdcdbaadcbcacaccdabababdbaacacdacbcbcbdcdcacabadbacdabbbcccadaabcdaccaccaacbdbcdbbbcccdddaaacdcdbababcdabdcbadcccdcbdbcbcacacbbabbddaaaabdadacbccbadaadcdbbbbaaabbbcdaddbddcbabbcdccdddadaaacbadccdddbddbcbcabadadacabbcbbacadcbbbdbacddbaaccaddbcbacabbbdcbdabddcdcdddabddbcbbcbbbaababbdbaacadbdaabdaddbdbacababddaddabacdbdcbdaacbacbdabccadccdbaddcadabcadcddccdccabdccbcaddcbbbdcbdbaaaccdbcdccaaaabbcccbcadcbbbdccbbadcbcdabdabbbaaadcaaadadccaddbadbcbcdaccbdaacdaaccacdbdcaadadbcdacbdccdcadbdaaddcaadcabbbddacacadcadbccaabdbaabbadbcacbcacaabbabdcddabcabddcdaacabbcadcbbbbdcccadabcbadccaaaaabdcaababacabbadbddcdadacccbbbcbabbadaadbacabdcddcadacadcadcaadadbdcbbbcdabcdcabbaabbaadbacbdccbbaacbdcababdbbdcccacddcaaaaddbdbabbdbccbbcccdcdccabadaddcccbcbbddbcdcadcdbcddcbccbaabdcdbaadcbdaaabcbbdcdddabcddbcbbcbbcddcdaabbcdaaccddbcaaccaddaddcbddaaddadbdacdbbadbcbbcbbdbdcbbdbdddaccbbcbcadcdadbcdbabbcbdadacbdccacdbccabdbbcabadddbbddcbdcacddadabcbcccadcbbccadacddacacacbdacaaaabadddcdbbadbbaaadaccdbcccdbcddccaccdacbacdacadadbbbddcaadbcadccadbdacdcbdabbcdacdabcddbdabbbdbadabdcbcadbdbbaaacdadbbbaabacddbbabaadbddaaacbaaaabbbaabcdcbdcbabccacaaddbcdccbbdaccabdccdbbddbacbbcdabbbdcbcbbadabadbcdacbaddaccdabbbddbdabbaccccaccbdddcacbdcbccdaccbadcdabdddddabbaaccbabdbcdabdcbcaccdabbdbdcadcccddbbbcdacaaddcbbaccbbdbadcccaabbcababbdbdaaaacbbacbbdcdcabcdbbaadacccbdbdbcbccbabacadacdbabdadcadaddccadbbddcddcadacaddbdcbcabbcaadddacabadbcbcdcdbcadcabacdcccdbdcbccdaadddabcdbccaccbadcacbbadcdcacbbacddccdbabdbbcbdaaacdcbdadbaadadbaacdbadcbbabcdaacccadcabaadabbccabccdbdadcdadbabcdabdccbcccdadcbcaddbbbacdccbdbccdbccacdcdcdbabcadcdddcbabaabbadbbadaddcbbcaaabbcbdddacdabaaaaddaaacbbccdcbaacbcdadbbbdacacaabdccdbcbbbdabcbabadabacadacddddccbaaabcabbdaddbdbcdcbacccbcacbbbbddccdacbdcbacaccdcbcaacdaaccbbaababdddbaabcdcdbddbbdaaddadcbdaabbdcabcdcbaccdccbaaacabaccdcdbdcbbdccbcdbdbdbaabaddcaabdbcbadcdbcdcbaaaacaccdbcdbaacdadcdbaabcdcdacdbcbdabaccbddcccccdcccddbbbdbbbaaabbaddaabacbacbaacdacccdbddaabaadcaabcadcbcbabddcddcbbdaccdccdbbcccbdbbbbccacdbccaacaacaaddadccacadbbbbbdcdddbdbcadcaabdaacbadbaccccdbcdcdcbcaddbbdacddcbabddabbdaabaadaaadabcbbacabddbdacbcabadddabddadbdabcbdadcbbaccbbabcacadbcddcdbbbddcccbacddaccbabacabcdbcbdddadadddcbbbdaddccbaabdcdccbddbbadbccbacaacdaadcbbdcbbcdcaabdacabccabcdcbcacdabaddacccbaacbadcbcbaaaabbdbbbcacacabcdcddbadaadbdbbbcdcbadacadccdcbdcbccdbabcbdbbcbacddabbadcbbcdbccaacbadaacaddaccccdaabbbcdbadabadbabaadbcbbcddacdaabccbddcabbaaabbcbaaaadcccacccaacaddbcbdbabcccbbacbaaacabdbabdaccdcccdbadcbcacaccacaaccddaccdcdcbabcbabaabaadaacdddbaddcbaccaddbdbaddadacbbcabacdddaaaaabbbcbadddbddaaabdbbbaccacaabcbdacacadcacacdabaaaaccacccdcaccabbcdbbaddbdbddbbbbdcadccaccdadcacddcacbabddabcddccbdacabdadcbadbbdabaccddbbbdcbcdccccbbacaddacaaacbccbadbdcbdccbdaaacdddadacadaccbcdcccdbcbbadccacddadcdbaabddcdbbccddccdabababbaddbdcbbcdbdcdbdbccddccaddcaaabbbddacacbccddbdcaadaccbabdcbcbbbdccadabaacacdddcabcbbccbdadbbaadaadbacdbbdbcbabcbcbaabbbacdbabaccacbdbbacbbcbdabacdddddbbbbcdcdbdbdaadbdacaddbcbadcdccbdabdabaaddacdcacadacbcbbbaddbbddbbbdaddcabddbadcaacccbbccaaacaccaaadcdcdcaadacadccadababbddccdbbddccdcadbcdbdddacddccbcdbcdccdaddaaadcbbcbbdcaaaadbacbbbabbbbaaabccabcbaacaccdcdddbaccbbcadcdcaccaabcacdbbdbdacadaaabcddcbbbdbacbbccaabcbbccccdbbbacddcadadbcdacaddcccdbbbadcccaccdaccdbdcabcdcacacabaccdcbdaaacbacddcadbacdaaacacabcdcccbdadacaddaddabbcabcdcbdbddbdabadcbbcccccbbbbaccacccadbabbddabdbdabddcadbdbddcccbddabdcaaabcbbaaacddcccdccddabbdacdcabbaccdacdadbaccaaacdaadbcaaadaacdcadbbabccabbcabbadcabcbdbbdbcacaabcdcdbbdaaabcccacaabdcdbdbbdaadbbcdddddacaabddbabbdadabbbbacdacaabbbccbdabdacacdbccbcbbadcbcdabdaddaadcdaacaccaadbadbaabbdcaadddbddacabdbabbcdccadbcbaaaaaccdcccabcbdbaaabbacdcabbbabbbdbddcbdccddccccbdcdbbbaacdcaaacacbbbdabcbcabcacccbccbddcdbbbbcaabbbdcdcdccccccbabaddccdcadaacadccdaacdbdccbcabbaaabcbbbbcbdcccaaadccdaaabbbaadcbdaacdbcbcaacccdaaaccbdaaadcbcbbcdabcabdbaabbabdcdcadddbaadabccdaabacbaadbbaaadbccadcaaaccddacdbcbcddadcbbddcbcadddccbbcaacaddcdcacbdcbbcdbdcbadbbaababddbbbdccddcbacaccabdbadcdcbcacabdadabaadaddadaaddbcaabbbbadaacdbdabdbbcbdcdcabccccadbcdbaaccbadbcddacdbddabaabdcbcccbaabdcacddcdbacdcbcdddbccadcaabaaadbdbcadaacaacadaababcccddadaddabacbbcaaaacbdbdcbacaaacababdcddcaddacccabdcdbdccbdcdbcabbdbbccbcbcbbbbdacbbacbabcccacdcbdcdbbbccccdccbcdbadcbcbdbddbccdbbbaccbddbacabdcdccccdcaaadbdddbaccbcbbcccbcdbbcdaacaaadacdabdcbdcaadaccabdcdadddcdbccdabcbcbcdbcababdccdcacdcaabcbbbdcabcabdcdababdbdaadcabadbbbcdacccdcdcccadcddbdcabaaaabbcddbcbbabdaabdcabccabcabdbdcbbcabbccbbbaccccbadacbbacbdbcdcbaaaabbbaaaaadaacbcdbcdacbbcbcdcabadbcdcadcdbcbdbabbbadaccbcdbcbdacaddbbabbdccabdccaabdbacbbcbbcaacccddbbaaadcdbaadddacdbabadcaabdacdddcacbabbbaaaacbbcdacadaaabacacddbcdcbbaaaccaabbbbdcbabccdcadcddccdddccbdccdaabaaddaddbdddcabdcaaaababaaabbdccdcacbadacaacacbbdbcddaabbbdddbdbccbbdacdadcdaddcadbcaabaaccccdacaaaaadcabbbbdacaaaccdbdbbacddbababbdcabaacbbcaddcddaaccaaadcbbdcdbbbaccddadbccabadabbdbbadbdcdbadaabbaabddaaaaadabadbabbdaaadcaadbdacdbccddbbabdabcbccddccacddbcbaadcbccabaddcccbbabcdaacacbcaddccdaacbcbbcbddbcbbdbadbdcccdbadaadbdadadadcccdbaadacdacacdccadbdbacaaacabbbcdadcadbcabbbdccdabbddacdddaadcacabbdccdddbbccccaabddbcabbccbbbcdacccccccbdcdcadabacadcbabadccdcdaacdcaacdacacadcbddddcccadbdacdacbcccccabadacbbaacaacadaccbbcccacaabbbbcbacddaaccabdbaddacccabdcbdcddadadbbcadadcbdacabccacbddbbccabdabbbdcdababadaaadbcabbaddaadacbbcdcbcabdabcadaacdcbcaccdaacdacccbbadcbbadbdcaadbbdaccaabdcccacbbbbdcbbdbdbddcadbcbdcacacbdbcbaaddbbccaababcdccbccdabdcaccbbaabbaaabdabcabaacccbbddccaabacacdcbbbabdbcdccdaccdbcdadbddacddbacaacacabcabccabbdbdbadccccbcdbcbbbdacacababababddbabaaccaadccaaaacdcddbabcdddbaacabdcdbdccbabbabcadbcabbaadcdaacbdbddcdbbacacaadbaccadabaababbcccbbddadddbabbaadbbbbbadcaddbbaacabdbbcbdcadddddbbbdbcbacababbcddcbbbbaddccbdddccdabddbbcaadcbcdacaacdbbcdbddaacbcaadbacdcbdadabbcdcbccdccbbbcaabcaadcbdcbaddbdddcbcdaadbabaacdcaaadccbcbbdbbdabcdcbadadddccbdaaaabdaabcbdcbdaccbabcdcbbdcdddaaaacbbdbdaabacbbababbcddabdaaaccccaabddcabcaabadcabbdacccaadbcbdbaacdcccbaaaabaababacbcdcddccdbdcdcdacadbbcdcbadaabbbdacbdabdabbdabcacccababdbbccabcddbcbcdccabcaadddbddbbacdaacadcacacbbacbcccbbccabdcbccadbbdaacaccbbcabdbdadbadddcbdadddcccadbcbbccbadbcbddabdbbbccccabdadadddadacddbcdbbbbcdcccdaabdcdbbcdcabdcdccdbccbcacbbcdbacccabcbaadbcbacdccddadabcbaabaaacbcadbdbdcdcbdbdacddbddcccdacdbcccdaabdcacaadcccdbadaddcacccdbdadddabddcdbcbdadbabacdbbabacdaacadcaddbbacbbacdaaabbaaaaddbabbaaadddadbcdabddaddaadacadccdadacabacbdbcccabcbacbbcaaaaaacbcbabaaabdbbbddacbbacabbbdddabccdabaabcdabccdcbadadcccdcabbcbdaacdabcdcdbcbdcdddccdadacccadcdbdccdbadcbbbbdddcabdcadbbdbbbdbadcdddabdbacabddaaadddaccacccdadacadbaaccdaddacabbadacacdaabbcacababcaacabbabccaaabbbbcdbcbcabdddbcdbcbaddadbaabdbcbaadacdcbccbcadabdbdccdadbddcbabbcdcacdadbbcbaaccdbaaadbddcaddaaccccbbacddbddcbbacbddcdaccccabacaccbabacaabaddbbcadadddccababacbbbccbbbaadabacdccdbbacadcbbbdcacaacadbdaccddbdadbcbdcacbdbdbcdacabdddbdddacabdbaccbabbddaaaacbcdbadacabbbcddcbccadbcaacaabddcddbbacdacbdaaddcbcbacacbccbaadbacddbddbbabdcccdbabbabbcbcccccabbdbabbdacacdcccbdabdaaccdabacdacbdddbcccaccdabbabbbbcacdbadadbdccbbaacbdcdcbdacddacbbdcbdccadcdabcdddccacdaabcbacdcaccaaaabaababdbbbabbcbbcaacdadbcbbbadadbacdaabddbbbdcbbacbcabddcaabdcdccdbcbcbbbacbadbadbaacccbabaddcdabadacdabcdacbacbbccacbbdccbacbbacdabacaaddcddbdcbddcacabcbaadcdadadaabbddadcdcacabadbbcdccbdbaacddbadcabadcdbcdabadcbdddbbcadbaccbcdadccabbaaabddbbbbdcdbdbacdbcccdbcabbbbcdcbcbabaacdadbbabdcbadadcdbabaddddadaadbdbbdbbdbabadbcaabbbddccaaccbdaaccdcabcbdcaccdacbdcdbbabdaabbabcdaaabbdaaabbacadbdabddddabbaadcadadbccbddbdaabcbbbdcdaadcdbdacbacdabdccaadcdbabdbaddcbccdacddbabcacbbbbbaccdaadbbdacbdddcbabacbbdccabcdbbacabdcbacddcdcacaccbaadddbddacbcbbdcddacabbbcbccccadbbdacbadcacccbbbadbacacdcbbadabbdaabdcaacbdacdbccccacccbdddaddbadbabbdbcbcdabdaaaddbbccbcddaccbdacacdabddbcaaabaddcdcdacccddddbbbccacacbacdcabadbbdbbcdcdcdddddabdbbdbdaaaddbdadbbaddcbdcdbaaaababbbddacbbaadbccdaaabcaaaacbadcbbcdddbaadadbddcbbdddcdcbdabadbcbadcbbabbbbcabbdbcbcdaddddabbddbbbcbdccccddcdbcdddabccadbabadddbaabbabdabaaddccbdddaccddbcbadddbdabbacccbbccdbdbcaaccdcbdadccdcbacbadbcabdaaabdcdcaddacdcdbbabbbbaccdbadbdaaaccaadcbdbbcaccadaabcabcdddcbcdadaacddaabcdbdacbdacbbbbabcddcdabbadbacacdaccdccababdbadaadadaabcbaccdccccbadcdbacddcbdabdbbacbabddbbcadadcdccaccbaabdcdcbacadbddbdbcababbbbdaabcaccaccdbaadcbddbcbdacbaccddaddccbdbcbdccdaddabbbcbbdcaaadabadaddddccabdaddadbdbccabbdbadcdaccdbaaccbccbbcabddbaddbbaddcacaaaacaadbadcacbcbbccaaabbadcbbacccaccaadaaaddaadcbdadddcdcbddcdbaacbdcbbbaababdccdcdaccbbdadcbaabddbacaddcdaacccbddcdddbbbcbabcacdababbcdcddbcbbcdbddacdddadcbbadcddddbdbacbdcccdbccbcbadbddbcbabcdcabbbdadccbaccaddbbacbbcdcccdaadccbcadbdbcaaaacdbdbbbbdcccabaacdaabadadbcdcbcdabababdadacddadbacddbdbcaaabdcdaaacdabdbacbacbdaacabbcdcbcddaaccdbacdaacaccababdddcadabaabcbadadbdacadddbcacadacbdcbaaaccacdacdcbdbdddccdbcddbbbcbccdcaaaddbbadacbabcbbbabcabbadbcadbaccacbbdcdcbdbcbddacbccdabdcbcdadbbdabcdcdcddbdccadaaddbccacddabaabcccaabaadcccdabbbbaabbbacdaababbbabbaaadccbabcadabbdccaddcaddacbbccbadbbbbdaadaddbdbabbcddccdcabcacaababdaccabaaacaacdaabaabcdbdbbdadacdaabcadccaabccbdacdcbdbabbbdcbcacdcdcdadbcdaccbbdcbabcbddbdabbabbdacadcbdbddcadcddccabacbcbbbacbbaddbbdddbadbcddbbdbaaadacababbdbaaadddabbadadccaddbacbabacccbcadadbdcbbbbcbcabbbbcabbbacbbcadacdaaaccdabaabacddaadbdabadcbacccdcccddbadbadbccacdadaabccdcdbbaaccccddbaccbabbcadcacadadaabbbcbcabdbddcaacdaccbbbbddadcbdbdccadacdbddccaaadbcbbdbddacbcbcbcdbdcdbdabcbaddccaadbbadcddabaddabaabdccadbacbabdbdacdaaaabbbdcdddbddcbbbdbacbbdccbbadaccabcdaabdcabaacddbdcaabaddadbddacbddbbacbbabbdbbacddbcaabccdacbdbddaadaccaaadcacbcbdbbbccbbbcacbbbcbbdacbcaddcadddcdaddacdbbbaabbcccaacbbdbdcdcaadabcaddbcbcbdbbccbddadcaacbdcaacabbaccbbbaccddcddabcddacadcabababbdcbcabcbbcbdaaccadbadcbdbcacaccabdcdcaaadcdabbcadaccaadbbcbdcbbcbddbcdabbcbaccbaaabdbdbdbaddccdcabcbdccbbccccdbcbadbaaaddaadcadababcaacacdacadcdbbaacdddabaccacdaacccdbddcbdacadacbaaadccadbabccbddddbdbcdcbcdddcabaccaabcddaadcbddbcbbcbcccdbcdccaadacaaadbdaacbcbccddbcdbbdacdcacdadacdbdbdbdcbbbbccacccaadcbaacccdcabbcbdbddbadbdadadaadbdcdbbdbbadaacabacbdccaddacbdcbaacabdbbcbacccaacbcadbbaaabddcdccdbcbdbacaabadaadddcbacaabadddacbdccbcbdadbdbccadcccaacbadbdbabdbacbdcbbbcbbcaabdbddcdcdaaabdddacccdaaaabaadccccaaacbbdaacbdaddabdadcddcdcdadcaacacaadabdbcdbdabbdccaccdaaddabccccaaaccbacdddcbdbcdaddabddabacacdcbcbcacaaaaabbacabacdbabcdaadbbbcccaaaabdcaacdacddddbdbacdcdaadbabdacadbbccdcdbcadbcbccccddacaddabbbdddabadcdacdacbbaacdbaaadbddbabdacbbbbdaacbbaaaddbcadabccbbadbddbbaaaabcacdbdcdaddbbacaddcacbabacdccccdddcadbbcadbccabbbadaacbabaabcbaddbdbadbddcccbddcbbcdddacddabdbcbcacccbdccddbacbacccadaabababaacdaacbcbdacaacaacbddaaadaacbcdadbababcaabbdbbdacbdaaacbbcabaabbdadccbbaadddabcacabdbdcbddcadabdbdbddabaccbbbccaccdcbdadccbbdcbdbbbaabacddabaacabadcdbbdcaabbadcbcdaddbadddddcaabddabccaabbccbaadacaddbadcdacabdcbcbbcdddabcbdccccadabbbabcaddbacdcdccdaccbcacaaccacabbcaacddbbccdabacdcbacaccdbcbbcccbbdcaabcdbbcbaaaccadcacadadaaabacbdbbcbdcdcccbbdbcbadabdbddbaacacbbbbbdbdadcddaaaccddbbcabccdddbddddddabbdaabaddcbbcbdaaddadabcdcbadbcbdcdbcaaadacaabcabcdcbadccabddbcbbbcddddadaccbaacdcdcaacababcaacacaaadcdbdbccbbddcabdcdbadbdaaadbcabddaabbdcaaacbcaabcdcaddcabcadbddcabddabddacaddbdddbdaccbcbbdcdcbbaadcbbdbdbdbdbcacabddcdcaadadaccdabadabbabcadbcaabcaaccbccbbbabcaddadacccbdabddacbddaadbbaccadcbddadcdbcdaaddaabcddddbccaabdaadbbbcbcdaacacaabddadcadcdabbbdcacbdcddcabcadacaddcdcdabdcbbbbccacddbbadacdccbadadbdbdccaddcbcaddaabbdbdabddbabbbbbaaadbcadadbacccbbbabcccaadcdcadaaaacddadcbdaacaadcccdacabbdbcdbcbbdabbbbdaaabdbdcdcdcdadbaaacabbaddcddccabbacbaccddcdcacdaccabdccabddabdbdcdcadbaccbadbdbcdcadccabaaacccbabaaddacdacadabbcccddcbdbddabcccabaabaabadaacbaadcbbaccccdccddddbaddacadcacbdacdbcdcbcbccacbcddbbcabcbaaabaadddacabaaccbcacbdcaacdcaadbddbacddbdacbccdbacacaacaaaaadabdbbdbbccdacbbbdacbbbbadabcacccdadaaddbbdacadcdadbccbdadbaccbacdadddccbabbcdaadbaadcaddccbaccbccabdabdadcacbaaaccacdabcaccabdbdcbaadddbcdaacddccaadbcacacbccabbcbbcdcacbbdadcdbdcadbccbbbbacacbcdcabcddddbbbabccaccbbbadaacacccbddaabdacbcabbbbbdddcdacdcaaabccdbbaaacdbcbbacaaabbcdaadcdadcdccbdcbabccaaccaddaaaacaadabcbdbaaaacbccbccadcdbcdabbdabcbabcdbdcddccaccdcbccacaacbbdbbbccbcacbdcdddddcabacabbabdabdadacdbaaabbdbadccbbddacaabcbacadaccbbdaccbdddccbbdadccbcabdbbacdbdccddabaacbbccdbdaadcdbdcdbbdcbdaabdbacbbabdcbbcadcacabcccddacabaacddadcbdddcbacbddcbbbcadaacabcbaabcbdbdacbccdbdacddbcbbddccbabbccbacbbcbdcbbcdacdcbccaccdbbadaabbadcbadaabcdadcbcdcccbdcbddcdcadaadddcdabbdcbdbddbbcdcbacddbacbcdcdcccbcadbdcdaadcdbbcddddbdacbdbcaabaabbddcbccccdcdccddccaabbabdccadbcdcabddcbddbcadcbadadbdbcabccbbcdccaddbacbbcccbdaacdbcbcbddaabdabdcbadccdccacbcdabdccdababadcdaccbaccddabdbdbaadbbabbcdcdcdbddcabbbbbacddcdbcddabbcbcccbbbcabddabcbcaaccbddccccbbabbaacabadccbdaccbcdbddbddcdddbabaccbcaadcdbbabbbddcbbdcdadabdbbdaaabacdbbdbdbacdccabddbdaaabcadddcbadcbcddaacbacacbbcbcabddcdcdcbcabcdacbabbbdddbadcaacbccbabaddcaadabadddcbdbdcbdabdcbbccaabddddcacdcbbbcadadddabbadadaacdabacdacdacbabdbbadcbdcaaacbccbdccdcaddddacbababccbcddcdacaddbddbabdbbbacccbbdcbcbddbdadbabdbbdbbabbaacdbadababaddbacdbacdabbbbbadabbacdbabdcdccbbbbadbbcccadcbcdaacadcddbacdcbdcdabdddabbcaacabbcabcadcaacbdaacdaddbabddbaaddbaaadbbcdabacabdaabababdbbcbdcdbdcccbbbdaabdbcbadbbcccacbaadcbdbcaccbcdcbbbcabcbadcaacccdacbdccdaaaabaccdabbbdaddcaadddcbcaaccadccabcaadcbcbaaccbddbbcdabaababbdbcaacbccabbdcdabbbbdbbdddbdcddbacbbbcbcccdcccccdcdcdbcbcaabdddcccabbacadadbdadbaabdbbbdbaabdddcccadbdadacccdddadaccacbbcbbabdbdaacbadabdbbbcbacacddcbdacbdbcbbbdcaabacdaabbcaaacabadcdcadacddbacaabaaaaadccbadacbcacdccacddbdbaadaacabcbbcdabdaabccbcbbdcdadbcbcdbbbbddcbacbddcbcdccabdddbacbdacaadcbcacbbbaabbcacaddbcbaddcaababccadbdbabccbaaaccaddabacaacbacddcaadadababdabdabddaaccdacacaccbadaddcccdbbabcccdbaccadcdbaadcaadbdacbadadababddddcabaadadabdcdacbabcacbdddabbdbcacbbacccbdcaccbdabcacadabcaaabbbdaaddbcccbaccdddbcabbcbbbacdacdaadabbddbcaadaccbbadddbbdbcbcadacbabaabdbcdabdcacbaacccccdbbababaddcacdaabbdaccddacdadaddabbcabcacaccacacdacacddbbaacdbdbdcadccabcdccddbbccacbadbccbdacbcabcaaabccacaabcdadccbddcddbdbdccacaaddacbddadccdcdacbbcccabdccaaaaccdbdddbdbcbcddcbcbdadaadadcaccbccdcaddddaddcdccdbdbbdbddbdaddbbbdbbbbbcaaddbcacdaccddbcdcdcccbdbadcbccdcbbbadaabbbcaaaccaaddcddbdccbbadbccdaccbcddadadaddababbcaabddadaaddccccacdcadbdcbdacadcacdbdabbccbaccdddcbdbccabbdcacdccacadabddcdbaacbccddaddbdcddbadcacaacaddbadcbcabbccccacdaddcbddcdcbcbccbdadadaddcacadcdbdaadbadbbdcbcbcaabaccacacaccacacdadadcacddbbdadadbadadbabccabbdcbcccbabaaababcabbabbabbcdcadaacddbdbdbdbdcbccacbbdacdaaadcacdbdccbadddacadaadbdbbddbcdbcabdcbaaabdddbaadcaabcbdbdcabbcacccddababdabbcaccbcccdcbddccbddabaccccaaccdbccdaccaacdddacbccdddbadcdaabbaadaabadbdddcbbbccaadcdadcbaacbadcdaabdbabbbcdddaabcdcddadacbdcaaabaadbadcbbbabbaaadcadbacdcbdaacbdacabbabdaccdbbbcddcacbababddbaabbcbcabbabcdadadabdbcabdbbbdcbdccdbdbbcbbbbabbdbabbadabcbcdbcdadbbbbdbbdccbcdcadadbaabcbcbbccdadccbccbbabbbbbabcaaacbcbddabcaacdbababccdacaadaddacaacacdcadddabcdbcacbabcddbbdbcbbdccbabcaacbdcbacaaadaddbdbacdacbbcabcbabbaddabcdaadbcabbbdababaddddabdbbdbdbaadcdcddbddbacbcdaacbbdbbdaddbdcbbcadcacccbcbaccacccdabbcbbdccabddbdcbddcbdadcddcbcbadbcaacbcbababdbacbabddddbdbcbcdbdbcdbbadcadcacacbbcbbcacdacbcbbaddbbbadbcaddcccacbdddcabdddaaccddcacaddcaaabacdcabcbcbddaddbbdabbddddbdaccddbcdaaabdcddbddaccbadcbdcdbbadcbbccddccccbabbccccbccaaacccbbcddbadbadadbdbcadcbccccaccacaabcbcbdbbdbbddbcacadcbdaacddccaadbdcdadaacaadcddabacaaaadbbbcdbadcdcdcbaabaadddddabdbbbcbdbaadccddbdcacaaaabbaadabbccdcaccbaadbcbdacbcccadbacbabdbdddcdbccbaaccdcaddcccbcbdcacdbbdbbcadaaccdcacdcbdbcbcbbcdabcaaabcaacbcdbdccdcababccddbcdbcbcccbbadaabbcabbccdbaadaadacbadbcddaccdccdbdbcacbabacadccccdccadddcdcbdcbcdabadbdccddccbbcbcddbccccdbdddcddccaccdddddcbccdabbbcbbddababbdbcadadbaacaddbdaddaabddcdbcdcbbddcbdbbadaaabbdccbbdacaaddbdcdcdaacdbbaadbbdbcbddaabacbbacacccbbccabdcaaacbdaadcaccdbccbbbddcbcccaccddcdbdcaaaadaacbaaccccccbaadcbcacaaabaacbaaaabaddcdbbccabbdcbcabbadaacdcabbabadccdaababdbaaacabadbacdbdaddddddddbdcdabcdcdbbccadbacbacdcadacbaaabddbddbbcbabdacbcbddcacadabdbbababccbadabaadbbddcccacbbdbbaacdcadabdddddcabbbbdbabdddbadbaaaddccdaabcccdcdbcbaddddbabdbadbdcbcdcbaabddaabddadbbacddbbadcadcadcbadbadbcadababcacbcabdbcbdcabcccadbbcaadadcadcddbcccddaccacadbadbadcdbdccbdbbbabbdbddcdabcaadbbcbdcabcdbbaabbaddabacabaacdbcdcbadacabadbbabddaabccbdcddaadccaaacdbbddcdbbadccddbbddbcbcbbcbbaaaaacdccbacdaabbaadddbccccccbaadcbcbacacddbcddccbabcdabadabcddaabcacabbaadaacadcbdcccbbccccbadcdbdbacacbacdadabbbccabcadacbababaaaccaaacccccdccdcadcdbdccdcbcbbbdabcbdcccaabbcbaaacacccbdcadaaadbbdaddbbaacbbdbbddbbaaadbcadddadacaaaddcbddbadaaddccbbabddbaaaaddbdcccabccdbdccacdbbdaccacdcadbbacbbcacbbdbbdddcdccbcbabaccbcacdaddccbcabbabdcaacdcabdccbbccdcbcccaaccaadacdacadbbbccbbbddaccdddcdbdcdacbbddcaabcdadbdcaaaabacacbddddcbcbcdaaadacaaddcdbaabcaaccdcacababddbcabdccdccdddcaacabaaaaddadcccaccaabcaacdbbdbbccbdcbbdbadddcbdadcaccbddbccccccbacbccbbbaabbddadbbdacdadddadaaaacdadddaabbaddaadcdbcdccbbaddbaaadadbadbadacccaacbbdaadacaccababcccbcbdabddadccdcdcbcccdbcaacddbddcbbdbcbbccaacbccbbcbdbabdbdbddcaabdcdabdcdcdbbcbcadbaadacccacbadbbcdbaacacbcdccbacdabacddacdbccdcdbcddcccabbbcacbdacdddaadbcbdccaabcadcdbcddabddacacbcacaccacadccbcdacdcaacbcbdcddacbcbdaacdbadcbacabadacddcbcacdbdabdcbaaacddaaddccadddcccabccbbaadaccdbbcddbbccdbbbbbdbcbaaaccbbacaccaddadacdcbcacbbdaabcacdcacadcadbdcbdadaacccddabcbccabcdcbbcacbcabccdccaabbbbcbccdccbdaccbcbccbddcbcadaadccdabcabcdddddcdadbbadaabadccaadabdacbddcdcaccbbabaabdacccdaababbdaadbdbcbcbaaccabaddccdcbbabdcaadbdacccaccbcdcdabacddbabacdadcacdccacdbdccaacdcddcddaccababcddbdddaabbabdccaaccddbbcbbdcabcabbbcdbdabcccdbcdbdbacaddbadccdadabaaacdaaabbbacadbaaadcdbccadabcaccbaadaddcaaabdbbcbccdbabcbbbcdbddabbbbabadabaadadaadcbaadadcaababbbaaddabddcacbcbcbccdacaccabdbcddcbaababccdcbbcbabccbdaaaadbbcbdbadadbaccbaccdbadbddcaadbacacabaacbbcccbcbabcaadbaaabcbaddbdadbbdcadaaabbdbbcdbbcbccdacccdbdacdbdbbaabbcdbabdcbbdcabdbaccacbdaddcbbcadabddaaddabbbbccddbcdccdabbaaaacdcbdcdcbcacababdbbcaaddccaacbbdacbaccdabbcbccabdcbbbdbccdcbbbbbacaabcacadcdadadacadbbdadcddbdaddadaccacbadbcbbbdcbcbccddaadabccdaabbabacdbaacacbccccdacbcbdcadbddbbdbcdadacacdddadcbbcbdccbbaabcbbccbdbacaaddadcdbbbacbdddbaccadccccdaabaadbaadacabcadaabdbbcddbcdbcdbbccacdbcccbcbbaabdbbcbcdcdbbbacccbccdccbcbaabacdbdacaacadaaabdbacbdabaaabdcabcddccadaaacdaddcacdaabcdddddccaccdadbbaddabdbbdddcbabdbaadddbaaddaddcccdcdccddcbcaadabddcadbbddcabddcbcaabcbccdbdcbacabaaccacbbbcdbbbbaaabdbbcbccbdcddbcaccbbdacacccbacdbcacaacaacbddadaaaadcadabddbbddbcacbbbddddbcdbdadbdbcaccaabaaacaddcddaacbacbccccdadcdcddcddabccbadbadadcdcacbbbbdbaabccccbbcdbdcbdccdcbdddbacaabadddcaacbaccbcacbdacdbaabbbccadbacbbbaddaabbbbaabccabbcbcdcaacbaaacbdaaacababbbcacaadbcbcbdcdbaaaadacbbccdabcbcacabcadaaaddccdaddccdacccbbdadddcbdddddbddbdabbabdbcbdcadadacdbbcabbadcddccccbccdcdccbbaaddaacabacdbcdbbddcddccababaadabaacbdbdadbbbdbbcbdbcdadaadbddcbbadaccacdbdddcdabdaddabbbdbbcdccbbbddabaaacbacabddcadbccbcbbadaccdcdbddcbcaddbbddaacdaadaaaabcbbddbdccdcbdbbacdbddabcaaacdadabbbbccaabdbcddacddcdcdbbbabaddbbabdcabbcacbcdcbadbbcadbdadabbcadacbdbadababacadcbacdbdcbaabcbcdbcddcddabcbaacaaccaadddbbdcbcdbbdbabaddccaddcaccacbacacadbbdbcccdabbccddcbacddbdacadbddacdadbcabaddbabddadacdcbabdddccdacbacabddcccbccaaaacddccbadabbcdcccdccacccdcadccabccbbcbbcdadaddddcaabcbdbcbbaaaaaaddcbdbccdcbcbaabddacaddcbccdaacababcacbdaacbccdccaccddacbcbddabddaaadadcdabadbbaabcacdbacabcdbdaccccbabcaabbdbcbdbaccaabacbbdacaabacdcccbdddbcddddbbbcbaaddcdadadacdcaccdbbcccaadbdbcddabcdaabbccaddccbaacaaaddaaaacddbacdcacbcdabaaccdabcbbcddbcbbdacbaaadcaccadadbdabacccddcccdbabbbccddcddbabdabcaaaacbbabbadadbaccabcacacccbbbcbbaaabdbdcdccbabaacadbcabbaacabcabbacbbcaaabcadaaacbaaabddadcbcdbcddacddcbacddcccdabbbcadbddcbcddaabcbccacccdcaabdbaacbbadbcccbdccbcbaacdcdbccaaaabaccabacbcaacdbcccbabaaacdacacdcdbcddbaddbbbdddbcadcddaaaacabdccdcbcdadbdddcadcacabcdcbdababcacaaacbcbabcadbcddabbdabacbbaacdbadcdbdccacbbbadcbadddbcbbabaacdbadbdbdcddbcabcddbcadbbbddcdcdcdccddcdaccbaaadcdbcacabdddcbdccdccccdcbcddcbcadcaddcabdcdbaabbdababcaccadbdaaaccdbdaabdcdcccacdcdbbdabccacbcaabdbcbddaccabacddcbadcbadacccddadbcbdcabcbbbccbdaddacddbcabbaddbdcacdcdacdadcaacdbbdddcadbbcccdddacdcdddbbacdbdcadcbcaabbcacdcddcaadaabddadccbdbcdcbdcbdccdcbdccadddcccdbcacbcdbdbdcbbdaabbabddbdacaadbcccadcabaabaabdadbdadaccaacdadcddbdaabcaddcddbdabddbdddbdacbddcdaadcdccdacbbaacbabdacddbccdadaacbbdccbaacbaddadbabdcbcabccbcbbbbcccdbacabadbdcbdcabdccadaadacacadaaadccadddaacabcdabcdbdaadadcbbcdaaddaddbbbcddcabdaccaacaaadcabcbdaaddbadcdcbdccdcbbaddabcadcccbcaccbdddcbbcbbbdcacadbcdcabcaabdadaadbcacddbdabaaaaadaaddbaababcbcdbddabcbadcacacddbcacacadbbbccddaadbdcddaacbcbdcdaabbdacdbbaabccacaaccddddccbcdadbaabcdbabdcbcdcdaabddcaaaadbcbbdbbdaabaccbcaddddbbadaddbaabccddbaaddcaddacadcdcddddadccaababbdbdaadbbcbaacddbdaabdabbbadcddddbcddacbccdabaadccbbbcabaabcbcccbbdacbdcdbdcbadddacdaadaaccdccbbbdaabcddaabbbaacdcacdcacdcdcddadbabdbabadacaabdabbbbcadddddcbdacdbbcacddbddbccadacddbdadadaacbabbdadaccacaacaadabcacdabacbacbaacbabcaaadcabdcdcabadacbdaacadbcdcacddacdadbbbbadadcdbaccdddccadacbbdcccdcddddccacacdaabadbbcdbbdddddbabbbcccabcdbadbcdbdacccccaddcccccbdbdcacbbdacbdcabbbadbcdbbcacbccbcdddcdaacadbbcccddbacaabddbcababccdbdcacdcaacbcaccbdaaabdddbaddbdaccaacdcbacabcaadcbcbdcabbdcbccdbcbabadbacbcaaadaaacccdcddaacdadbbbdaaabbdcdbccdddcbbdcacdbdbbbdbdbcdadcaadabbabcbbabcdbaaaddccbbcacacabbbcdddbadabaccddbadcbabbccaddddabdddbbccdcacabbcabdbacbbddbcdbdaababdadbbaaadddcbbdcdddcddaacadadadddbbadbbadccccbddbadbcdcddbbabaabbcadddabbcdaaadddaadcbdcbabadccabdadcccaabcddadbbbbcbaccabbabccbababbadadcbcbcaaabadbababaadadacadbbcbbdcadaaadcccacbabcdacacdabddaaabccbdbbacabcdbcbdcccdbdadbbaaaaabbadcabbdbcdcdacbdcbcaabbabdcdcbadcccaabddacbcdddbbccacccacadbcbbddadbaddcaacabdccbbabcddbaccbccbddbbababcbbcbdcacabcadbcdabcabcbcbcbbbaabbcdcbcacccaaddabadacddbacadbabcdabacadcabdbbadbabcbbbabcddbaccabdacbcccaaabaabcddbcbcabdbadddaaddcbdbdadbcbcccdbcccccaccccbaabbdabbaabdddddcbbabaadddbabdabbddbaabbbcdcadcccddcaddbaccdaddadcaaddaaabbacadcadbddcaddadadadaaccbaabadbcaddcacbaacdcbaaccddcbddcdadcccdabbbdddddaacbabcbabbbcaadbbacdadcaabbdcbcdbcabcdcacbddbabdbacbbabcbabadcadbbabcbabdccdcadddcdcbaaabbbbaddbdbadbbcbaacddbbdcacbdbdddabcbdcbadcadbbcccacdddcddbdccaacacabdbdcabbbbacacbacabccddacdccaaabdacbbcbcdddadaadbacbbdabacaadadbabbaccdabbcddddadaabcdbadbdcbcadaabdcbcbddbdacbdabcadbbaaabcaddbacbaacdcdbbdcccccccabdcbdcabcbbcabaabaaadbcdbcaacacccadcdbbabadcbdccdabbacbabaaddaaabbcbcadcabbbbacdaacddadddbdaadddbdcacadbabbacbdbcadadacabcddbcaadadbdbbaddcbdbbdadaaacddbcbdadbaccabaacddadaacadddbbcdccbabbcacabdbdcdcdcbcdaadadbcadcdccaabdaadbbdaabaccdbbdccdaaabcaaacbbdcbdddbcacdababcaccaccccacccdbbadbcdbcdccdcbadbcdcbaddaabdaadacadcddddcacacdbcbcddbcaacabdbabccbcbdbaaacdcaccabbbabddcacccbddbbdbbbaabbacbdddabddbbdcbcadacabcccaccdadcddaccbbcaacdaacdacdacbbbadbdddcdddcbbdbccdaaaacdcbabbdbbdcbcdacababacbaacccbdbdddccbdabaddbdcdcdbbcaddcbabbaaabdccdcdaccbaccbaccdadacbdaadbaccbadcbdadabaabbbcbdaaabcaacccdadddacbadccbddbdbddddabbdbcdbcccccadcbbdcadbbadaacbcbdcccabbadcdbbadababbbcbacbdcccaccbbcbcbcaaabacabdccccacddccbbbcbddcacbabcddbdbdbbaaacbbbcaadccdacbaaabaabdcadabcbacdbdccbbdcccbdbdaadcdacacbbbccdbddbddcdccdbbcababbcbdbdadbdacabbcadcacdaabccccbaacadbdcbbdccbadaddccdcaccdadbdacaacccbdccabbaacbdbaccddcaadcaaadbbcdaacdcaaaaacaddcdbddbaaddadadadaaacdbcaddbadbaccbadcddddcacacadaaaaabccaaccdadcacdabcaadababcddbcdbdbdcaaaadbccbcbcddbdbcccddaabadaccdccbabbdbcdcbbbaabcbccaaccabdbbcdaacbbbdadddbbadbbbbbcbddbdcdcdabdacbddbbaabbcccdcaacccddcbdcabbbdccacaddaacbacbaaabadbadbdacbcccabdccaddaddcccacabcaccbabacdccdcabdaaaadbadcbdacbccdaddaacdabdcabcaddcddccdcacabbacddccbcadabbdccdaacbbabdaacddabcdccccabaacadcacddcabacddaaabaaccdccddcacabadbabdbdbbdbaacaccdadadcaabbdbbaadcadbcaadcbdabadbadbdadcddccbcbcbbddcbbddbddcbddaacadabbbcdddddcddadccdcbcddccaaadcaaadddccdaadbbacdbcaaddcbcddcccdcdcdacabdbcbddaacabdaaaddabcbdcbdbddbbdabdcbdddadddcadcbacbbbddcddcdacaabaabaabcbccbdbabdbdddcadcbbcacdcdabcacadababdaccdabadbbddcddabadacbbcddaccacbbbaaaacbdcbcbdacbdcaabcabcbacbbbacaddbabcadaabbdbcbcccdabaaacbaaccccaababbdbcdcdccaddcddbcacabccdacacaccbbbcacbcdcdbaccbbadcdbadbbdbcaadbcaadcadddaaabcbcbcacbbabbadacbbabbcadadacdccddacbaabadbbbcbcbcbcabcdcccbbabdbbccdcaabacbdcbcccdbdccaddaabdbcdbdcaddadbbadacbbaadbdacacacdadbaaaadabdabaabbdcacbdbacbcbdcaababdccbdadbacaabadadcddacadcaadcabddddaccccabbcdaacadcacddacaacbadcbdbcabaccadbbbddabcdbbcbdbaacdaadacbcbcdcbabaadadcccbcdcdbdbdbcabaadacbaaadadbdbabbadcdadbbaabcdcddadabdbdddacacdabcdcabacbddadbbbcadcbbdbbdaaaabdcddbccbbcddaaabccdbcdbadcaabbcbcaacabadbddbcbaddbcdabdbadccbdbcccabaababaddcccdcbcacaadcbcddaabdccaaadddadccbabcbdacadddcccbbdababcaaabdbdcaadbdcdcbddabccdcabdcbcbcbaadadddbbbcacdacabaddcabadccaaaabbbaccdadddababcacdabaadcccbacbdbbbccbcddcacabacadccdbcdbcccbbdbbcaddcdbadbdbccbdacaddccdaaaddabdcadaabccdbcdbcccbdaddbbdaccbdbbdbadbbcbcdcbabcbccddbcdcdaaacacccdbacbbbcaabbdbbcacbbacddacabcdbdbaccbcbcbbcbdbcbbbccccbcbcccaacaacaababbbdbccccbadbcdabbbbaaddcbbcbdccabccacabbbdbdbcacaccdbbbbbdbccccbdcabdcadbadcdddcabacbcccdcbdaccdacddbddbaadcdcccdddaccdcccdbcbccacdabddbadccdbbbbaddabccabcdcdabbaacddaccdacbccadaadbdbadddccdadddbbbbbcbadcdccadbccaadccadcbcddbbcbdcddadbadcddaababbabdcbdddbbabdcbabbdcdabacacbaacdadcacaadcaadcbcacacabdaaaaaddcbadaddcdcaacbddaabbdbbddadaacbabbbdaaaaddcaddadaddadbcdbbcbdcaaadbbcccacccdbcabbabbdcabccdbadadbacdbbbbaadcadbadcadabcbccaaadacadcbdabadcadbcbcbcabdbdcabbddacdcdcaadbdbbdabccbcbdcbddaabbadccbccdacbdadadcaacdcbdbbdacacdcadcdaacbdabcdbcacbdcaddbacbbdbabbdbcaaadacddcabcdaacdadbacbbdbaaabdbacdcacdccdabbcbccadbadcbbdcccccabdbaddccbccdbbabdcadbabcdcaaabbbdaccdaccdcbbdadabaddcddabdddbddbbccdcddcbdadbcbbaccccdbbcaaacaccddbcaaccbaacbddaddadabdbcdabdbabbccdcbcdbbcbbcaccdadbcadddddaaddcdddaaaacdcabddcbbcaccaccadcdcaaddbbbadbabadcbccadabddcaccacbabbbabcdbcdbdbcbcabbdbbaddacaccddcdbcbbdddaadbcaaddacadcabbbabaadddbbcdcadbaaaaaacdabcbcabcdcbbcddcccbcddbcdcddaadaabccdccdaddbbacccacabbbcaddcbbbaddcbcccccdbdcccbaacbdcdbcdcbbccbbadbbdbbbdadbadaaddadcdcdacdddddbbabaccbdabdaccdbaaddabdbdaabcabaacdccdddbbabccaaabcbadaabdccddabaccbacdbdbabdababbbaaaaaaacddccabcdaccbbbdcabaddcbbacbcdbcbcadccbadcdabbcbbdddddaaadaccaddbccacadccddddbaabdcabaabdddbcbbbdabbdadcdaabbbccbbadcddabdbcddaaccdcddbcdddbcbbbcbcbdcdacccacddddacbdcbbabbcacadabbbdacbccbbccbadabcddbbdcabbcbaabdbacddadacdcbaadbccbbcdbcbacababaccdbcbbdaaaacdabccaaccccaadaabadcababadbddbbcdcaabbbbbddcddbdbcbdddddaabcabdaaaabdaacbcdbcbddadacadaabbbcdaccccacdbbdabbccaccbccbdbdaaabccccacbaadbbbccabdaaaccdcbdcddadcccacbddccbabdcddbdabcbbbacaacddbdddccbcbddbabaccbcaadbadadbcbcabdbbcaacaacabcbbbdabdcdbcaccdbdaacabadcdcddaccbccdacccbaaaacabdaabddcabacdbbcbabdcacbdcbcabdabdacdcacabbbdbcaaccacabdbabcabaacdcdaddabcbbadccccaabddcabdccbcdacbdcdbaacccdcccbddbbaccaabbaadbdbaabcdbdbcbcdbabcaddcabadcdbaacdccbbccbcabbcbddcddcccbcdcccbdcdddadbbcdddcbabbbdcddbadadacddbcbdadcacababdddadabcbcaadaadbccdaadabcbbbbdbccddbdccabdcddbbbbaaaddbdcbcddcabdccaacacbbcbabdaacdbbacaabaddbcbcddddaadadbadabaadcadbaccbaaabacbcaaabacbadccccdddaaaccccadadcaccddbacadaaadaadadddaddaddbbbadccacddacabbdbdacaaaadccdabacdcaabcadddbddcdaabcdcccccbdbcaaadbcaacaabdddccdcaacdbdbcaaacdcacabdcbbbabccddabdababaabdcbcddabdadacbbabacababdbddcadbabbbadbcddbacacabcadddbabbbbdccbabcddddbddbbdcddabacacaccbcadccaacdccaaddbcdabbcaaaaccbdabbcdbcabbabacdcabbdcdccbdbbdddddaacdabcdcddcdaccdacdcddbdcbbaaccadbbadcdbcbdabacaaadacbaddadccdacdbdcadbbbbcddaccaddadadcddadbadddddacbacaadccdbbbdccdcdbcdabbdbddbcbbdcdadccadbbbbbaaabdccaddaccdddddcdbcbababbbccaadcbaacadbaaaaacabacbcdaccadaadbadddaacbddbcaaacdbaaadaadabcacbaaabcbdbbdacbcbbbbcdcdcbcabbcccabcbabcaabbbddbdcddddbabaadcbadbcabcbbcaababdaacadbaadbccddddacdcabaadaaadccdcdccbcaabaaabbcbaccdcadabadbdadbdbadababddaabbadabdaccbccabbadcccbbbddabcabdcbabccadaaccbdabaaacdccbbbacadacbadcbbbdaddbadaacbdbdcacdbdbdadcacbcbbccacdaacabbbcabadacbcaabdccdbccddcddcaacbacdcdadddddabadccacccadcadcbcadaaababdddbdcbdabcaabcaacbcccbadbdabcdbaddccbbabadcbdaddbbaababaaccbadbaabbddaaaabdcdcdaadccddaabdaadbdddbccdaaddbbaaacaddbbcbcacddddcddbcacadcccbdbbdcddbbcdddadbbbdcbddbbacdaadcdbdbbddaacdaacdbaacdcccdcbcddcdadddacbacddabcaddbbddabdbbbdacdbabcdbadabdcadcaabbbcdcadddddccdbcbdbbcdabbaabbabdcdbbdbcacbacabbbbbdcacdbdaaddacacdbbcbcababdcabcadabaaadddaaddcbcaaaccbaabbbdbcadcadbddbccaaaadcacaacccaabcbdccdbdadbcdbdaddcaadcaaabaabccbaddbcddbbdababaabddcabcaababddbcabcbbacccdadbcbdabbdcbdbbdbddbdcaadaaacbcabdbbdaabaaddbcccaddbabcbbbbdcaabcdddbdccdabcddbabdabddabaaaacaddaabcacacdccbbacacabcccadcbdcababcbacdadccdbcddbcadbbddccdccaaddbabbcbcccccdcccccbdbdcdbabdbabaaaadabbacccbdcdddcbbbbbbabbcbcaacdadacbbdacbcbaadaabaacbcacbbabadadadcadadbabcaccccbacadbbcbabbacbbabcdabbbdaddaccbbdcbbcdcdbacaabbcbacaddbaaacbcbadaddcdcddadcdaccccadcacaadbaddcacccacdabdcdacddddacdbdcdacbcdcccdaccbbbacccccddbcdaddbcdbdadabdaacaaadadcbbcaaadbbaaaacdadcbdaccdabcddbcabbacbcdcbacadcaddcccacbbbaabbacaaadcaccadcbdccaccbbdccdcacabdabcbabacddcccacaaccdaddbbbaabbaacddbdbdcbdbcaabcaaadbcccccbdbadbddbcdaacddabacdcbbbcababadacddcccbbbdacbdacabacccbddbaadbccdbdbccaaacddaaccddcbadbacdbdcccadaaacdcbabdcabddcadaaaadbddaababcbdbbacbcbacdadcabccdcabccdbcccbbadcbacbdccbdddbdbadbbcadacacbdddaccdaccdbcadcadadbdcbdccbdbccbabcccbdabbacdabddddbbcdbdccabaacaddcccbaaaadcccdbcdaddbdabadccaacbbddbcbbbcabcabddaaccddcbcbaccaabdaaccddbddcabbdacdbcddbdacdbbbdccbbddaadacaddddccabbcdccbabdabddcabbdaabcdbadbdabbcbbabcabddbcdadaaccbdbabcaddddcaaaccbcabdbacdadbdcbadbbdcbbcddddbbccdaadaddbdbbaccbbdacabaabdbcddbadbdbcbdcddbbbcacbbabbcadadacbaabbbdccbdbabacbcdcaacaccbbadcabddabcdcbbcaaaabbcbdacababbddbdacdcdabbcdccbabaabddcaabbdccbacdddddccbcabbaaadcdaaaddcbbccbabbcdadabbbddddbdbbbbbbacaddddcadacddcddbabcdbaadaabccaabcaccdbcccbcbabbacdbdddddadddbabadaadcbcabdbcddccdbacbdabbabaaaaaadbcbcbbacdaddbaddbcabddaaaacacaabcadbcaddcabbaaccabadcbbcbbcaabbbcbcbbbcbcccbccacddbccabddbcddaccacadcaccccadaaacacccadccbaadbbdacacdaddacbdbdddccdccdcdadcacbcacbadcaaacbabaccbdbccbcccbdbccbdcdbccdcabdadddcdbadadbdbbcdbccbcabcbdbccdcaacddddbbdcbdddcabcbabcdbbdacbaacbbcbdabcadbdadbbacdcdbdccdbaddbbbcbdccdcacaabbacdadacddccdbbbbbadabaacbabdcadbacbcacadcdbbdbdbaccccccabacdbcaadababdbcdabacabdcacabbdbdaccdbdccaccbbabaaabdcabddbacbbdbcdadaccbcdadbadddacaabaccdddabbdbaabaaadbcbcbaccbbabdcaaaaadacbcaadccadadababccdcbcbbdabaacbbccacbbbccabccacddcadcdabdbacccdbdbdddacacacccdaaabbcdccddbbadaabbabccdcdaadacdbbddbccbcbdadbbddccaabcabcaccbdacacbbabbaacaabdcbcbcadddcacabdadaaaabdadbcccdbaadbbdbdcabbddacbdbdcaaddcdcddabcdcabdacccddbadbbdcacbcddabcadbbaacdcccadddabcbabbbdbddcddbbccbccacddaddccadaabbacbcacabbaccabbcbcbcabcbcbccacadcbcdacbdcbdaaccaccbcaabdcaabccbabacbcdccbcaccacdcdaaaacbdbcdbaadaadbdbcbbbbddaadccbcbdccdaabddcdabcbcadcbcaabdbccbdddbadbcdddcbcbcbabdbadaccccbdccddbbaddabacdbbcccdddccaaddacacbaccdaccaddadddcdaadcdcbdddcccbdcbdbcaadcddabccaadabdcbabbbdbbcbbdbaccacaaadaabddbaabccadcdaabbbbcbcdcbddbbbbdbadacaaaabdcdcdabdadaabaddbacddadbabbbbbbdddcdacbdbaadaccdddbadcddbacadbbddbacccabbcbdcdcbdaddcbcdacabcbccbbcddadaabaadddbdccaabcbdbddbbddbcbbccadccbbccccbadbdccdbdadcbdabccbabaaabaddabbcbbbbdccabbddaabaacaacbbabcaadabcbdadabccadababdcbadaaadaddbabaacbaabcaabacddbcdcccdcadbcaccdabdbabbcdaabaccddccdacbcbdbdbbcbaddcdbdccdccaadcbcccbcbcdabbaababcdcbcabccdcaaaadaccbdbddcdcddbbaaccbddbcbddcacacccbcadcccdbcdadaacdcbdabcabbdabcbbdcbbddcdadbbbcacbdddadbbbaacddcbbdddddaabdbacbcdddadcbabdacadadaacadabcbadaccdcdbbdabaadddbcbcdbdbcbacdbcdbadccdddabcaabaaddbbbdbcdcbbacdcadbcaadcdbabbabbbbdabaacadaccccdbdaaacbcbdabdcbaadcdcdcadcbaaadacacbadccbcbaacdcabddccaaadccbabaddacdadddddddaaccdbbaabaddacaccccbaddbdccabaaadbbcbccdcdcccdadbdcbabddbdddcbcabbbcaacdcbaadcddaadcddbcddcaabcdcbccaabccadaaccdcbcacadcdaccaabdacbdcbbcbcaadbdbbdcadcbcbccbbddbaaccccdaaaddcbabddbaacacbdcabbaccaabccccbcbbddcdabcababcbbbcaaccaccbbcdcabcacabbaadcbcddbabbcdcccadbaaddcaabcdddabccbdabbdacdcbcbccaaccbbdcdacaabbccddccdcbccaabccadcabdddccddcbadbdabcdbddaddbbdcadcbcadacdcbccdaababdbdababddbbacbacbcbbcbaadddbbdcdbcabadbcaaabbbadaabbcadbdcababaddbdcbdaadccdadadbccadbdcdadbacabccbaabddaaadadaccdcdbdadccbaaacccccdcdaccbdabdcddddbddbbbbdbbadccddccdcbacaaababbdddbcddbcabcaccdabdccbbadabdcdcdadbcccaaacbdcdbadcabdbdbbbdbdccddbbbbbddcabdcbbabdcabcdaccabaaaccddabacabdadaabcacdbadbbccaabccdbddbbdccdbbbaababbcdaddcdcabdbcbadacdacddbcbaabccbdccdbddadaacdabacdccbbccbdbabcddccbabbbacbbdbbbadbbdddbbdcacababcbabdabaadcbcbaadcbadabadbddadcdcdaacadcddbdcddadbdbbcabdcbbccadbcbddcdcaccbcaccbababacabcccdcdbbacdbacadcccdccaabbcadcaacdaacdadadcdbccdcdcddbbddadbdacbadbaacbbcdcbabaabadacdddddcaacaababbbaccabacaaadcdbdddacccdcdcddccabbaddacddcccdbcaabadabbcccdacbcacdaadacccbddccbcdbcbacbdbcdccbbcacccdcdcabcaabdbccddccdbcaccacddbdbbbadbdbddabbbbdbbcadadadbdcbabdbbbaaadadaabcacccddbbaddaacbddbacdcbabdddaabddcdaaaabaacddabcddcbdcdbcbcbaaddbcdaaabcaaaabdaccbcabcabbbbbdbddbcbaccabddaddabacbcdbcdbccaaabaabadbacacbaabddaddabddbccddcddbddddbaadccabddadabacacbaccadabcabbbadcbcbddddddbcaddccddbadcdadbcbddbcdaabbbbbacdcbbabdcddbdaccdaaaddcdddccbcaaacdcacaabcbbabccbddabbbadcadcbdbdcbaaccdbadaddbccadbacccbbabbbabccbbadacbadacdddcbbbdccbaddadaddcadcabdbcadadcadbdaacccaaaadcddcbbabcaccaaabddaaacdddbadcbbacabdababaadadbadaacbcbbdcbacacdaccacaccdcdddcbbccdaabbbccbdbdabddabbbcbbbcaaadbacbbcccaccdddbccdbdadcddcddddbbadbcccacbaddccccdadcacccbacbddbbbaaddacdbcdbcbddacccddbaababcdadbcacdcabddaadbbdbbbcdddabdbaaaacbdbabadcbbdbbbbcabcdbacaacacbaaadcdacbabddbdbbdcadacadbdcccaaaacadbbdbcbddccdbdbabcdccdacdaaacadbcbbcdaacdcccababdbcdcdbbcdcacabddddbacdbdabddaddccbbbbcaabbbaaddaddbcaadadddabcabaaadccabadccdcdcbbbccabadddbbbddcdbbdbcdbcbbcbbcbabdbcbdbabbdcdbddcdbcdbbbdcbbacbdadabbabbdcbbcadcccbcacbbaabaadbcaabacbbbcdbabcbdabcbbccccaaddbbdcccdcdbbddccdaddcccddddacbbcaccadbccdacbbcaddcbcddacbaadabcbbbddccccdaaadddddbbbcaacdadccdcdaacbaddbbdcbcacccdddbdbbdacbcabaddddcddccbddbdcbccccbccabaabddbcddaacdbcbdadaadbabddbddbdbdcadcbaadddcccddaccdbcdcaaacbacacdaaaaadbcdbcadbcdbdddadbbddcdadabcdbdbdadbaabacabbaaaacaddaaaaaacbacbadcbbccadadbbddccaacaabcbbabacddcdbaaabdbacdcddacdaaddcdadadaddaaabccdbacbcccdbbaabcaacaabcabaacadbcdcacbabccdcabadbcdcbabacaaccdcbacbcadbbbdccdcdaccbcdbdabbabcbcdaaacddcdddbbaacbabaaacbdbbdbbabbcddbcccacbddbccdacdbcaddbcacabaabbdcbadddbdbcbddadcbcabccaddddaacbababcdbcbabbcaddabbcaccaadcdbcccddcaccccbccdbddbcccabcdcdaccbabbcccdbbacdaabdcdbbabddcccbdcbaadbccdbbadabcaadbaaadcadacacaccadadbbdcbcabddbacacdbaccacbbacdcdcdcdcacbabdaadabbcadabcdabbbaaaacabdabacaccbcccacacbddcddaccabcaddadcdadcdabcccdbcaadddacbabbabbccbdacacddbcbcdbdddbbcddbbdabbbbdaccccacbacdaccdcbddaaabbaadabbdbcdccbdadbbadacdbdddbbaabcdbdbbbcaabaacbdaadaacdabcacadcbacabccdcabcdccacaacbddadaacccccdbcabdadcadcbdaacabbbcbaaaacbddacbccadabdccacdadcdcbcbbadcdbdcccadbacdadaccaadaabbdbddcdddacbdbadacbbddccddbdbdbccacbcbbbbaccaaacdcaabbdcacccdacdbcaadbcbdccbadccaadbbcbadbaacdabaddddaaddbcbaccdbcacacbdddbacadcccdabcababcadbbccbdaccddadcbcdbbadcbdaccbcadbddbbbdccbccadbdccdabccccbdbaddabbcbdcabacadbaddabbbddbcacadaaccbdacbcdddbbacdacddcbbadddbacabcaabbbaaabbbcbaddacdcdabdbabbccccdcacdacdccdbbdbcdacacaabccbbadadbadaccaacdcaccddcbabacbcbbacbcddacdbdaaccacabccddddaacccbabbabbaddcaadcdcdbaccaccaacdaadbdabcdcdcdbdcaacddbbacbdcbaacddcdcccbabdaabaabacbbbabacbcbdccdabbcaabcabaadcaaadbdaadacadacbcbcddabaaacbdabacccccdadabbbdbbbdacaadbaadcbbdadacaadcabdaddbdbabaaddbcbddaababdcbbdcadbccaadbbbaadacadcddbccbdacdadbaabcaccdaacdcdadabbdbabbbddbdbbbcabcaccdabdccadadbcdccaabcddbababccbcabcbdbcdaaacbddccaabdaddabccadadacbabbdcdbdcdcdcabdbbaadaccccadcbadadbabadadcdcabbbdadbacbadadbaaadbddbdacccdcbcacadabdbcdabdaacddbccdcdabadaaabddbdcbdcacacbcbdaddacdbadacabdcdcababdabcaacdccdbcdbabbccbaaaccabbaddabacabddddcbddacddbbaadbccbdcbcdbdbbabaacacbabdcdbbddaadddbadcbdccacdbacdaacaaadcdcbdaadcaddddadaacabaadabdcbabcaadbbcacacccbdacaadcaccaaabbabdaabccadbacbcbcbcbabcccddadbabbadcbddbbabbcdddccccbcdbcbaaddcabdbbbabdcaaadcdaabcacbbcdaccaadbcbaacbdddddbccbaddddcaddadabccccadbadddabcadccbbcdbbccdaddbccbbcbadddbbcddabdbacbadbdcaabadbadbadcbdcbdcdaabdbdcbdabadaccccaabaccdbbacaadabdaddcccaabbbdacbaadaaddbaddabbaadcdaddbccdbbcabdbcbddccbabcbbbdadbabbbcabbabacddbacacbbccddadaabaadbcdcdddbbbdacdcbcbacadabcdcaacccbbcadadcadcbcaabdccbbcdcdcadabdacabbcddbcbbcbcdacbdbbabdaaacbbbcdacdcadbcadbaabacacaadacdbababadadbadabacbcbaabbabcdcddaacdbddbbbcddbbbadbcccaaccbcbcabcccccdcacbbdcdbbbdbdcdadbdabbabbcdaddccdbabbcaaadcaccbababbcdabdcaaadcdabbcaabcccccdadcacdabdaaabbdddbccdbbdacddaaabdbbcabbbdcbdcadcbcbdadacabccadccaacbbcddadcddbaddcddabddbdccbdaabbcdcaaabadcbcdaacbdbcacbadabcbcdbbdacccbccbddacacaadaadacdaaddaaccdbadababaccdabcbcdcbbdbbcaaaaccadcccabbccbbbbdaaaccabbcccaadbabdcdcbdbcdadbdaccdabaaabbaddabcaabbddadbcaaacaababcaccbdcadcdaadaccbbaacbababdabdaabbbaaaadbdcbaaadaaddabacdbbbcabbccbbbaacbaabcdbbbacbccdaaddbcbbdccddcdacbcddadcdbdbbacacbbdabcdbabcbdcddaaddbcadacdcadcccbddacbcdadabacaddadcdcbdaddcaaaaddadcacadcdcabdbbdccccacddbcdbbdbbcacbccabbcaabcdacbaaadddabcaacbcbbbbbacbabccccacbcdabcdccbacbdbaadddbcabacbdccabbacacbacdddbcccccbdbbabcdbbcddcbcadacacbcabbbcbbbbaaaaacabccabbccaaddcdacaabbccadcaabaacadabacddacdcbdbbaabcddaddbddbabcddaaaabdcabadcbcccdaccdddaaddccacdbddbabdabcabbaccaadacbbcbaaddacadddaddaadacdbbdccddaabbccaddaabbabacdcdbcdacbbdadacaabdddccacabcdbccbddcddcdccddadbabbabbcdbdbadabbcadcabbbabaabcdddcaddaacbabbdbccaaccbabaabadcdaccccabccbddcbadaabbdaccbdabaadcbaabadabdabacccaccaadcbdcbdbbacdcdbdacbbacaabcbbdbccccbaabadaccabbddbbccadbdcddcacabdaaabccdbabdaabaadcccbadababadccdcddcadccacacbdcdaaaacaddbdbadabacaadbaddaabaabcbbadcadcddddadbbdbccdcbaabaccaccccdcacbaaccdaccccdabccaccacbaaccccadbddbccaccbdcddddbddabcdacdabbcddadbccdbccbdcdcaadadccbacbccdadadaaddbcdaddbaaccbbddbccdabdcbdadaddacdadbddbcbdacdbacabaadccddacdcdcaddcabaddabaabbbdbcbbaaadacaaadcabcadddaacdbcaabaaabcaaaaccaddcdccdcddddacbbcdacdcbbabbddadcdbbbdacbbdcbccdccdcccdcdaacabcdacabaadccccacbcdaddbccdddddccbacaddcddddaaddadccabacbadabbaaaddadbbabcdcaddcaccdadccbacaacdbbacbaaadaddcbadcacaccdcdbadcbaadbaabbdadcbbadcbbadcbdbadaddbdbcaccdbbbcddcbbbbdbdcbaabbcbdaaabadcabdbdbbcdccacdbccbcdbacadabcadcbdcccacbdbbcbcababababcbbbaddbadaccdcdcbacabbabcddcbbdbbadabddccbccadabddaaabcabdccddacabbadacabadacbcdadcbbddbdcddbaaadcdaccacabccddbacdadcdaabcaaccdcdcadcdcaaaacccdbabbadbbdabaccaaaacccbcabbcaabcababcacadbadaabbbbdbdacbaadccaaaaadabdadccdacabbbcabdbbdcacbacdcadadbdddcdbcbdbaaadadaacaacaadbbacbdddbbdbccbdbdcddcbbbbbcaabbcddacbbbccacbbbddbdadbbdccdbbabcbdccacdbdddaadaabdbacaabdaabaacdbdaaacaadbaacbdadbdbbdbbbdccbcaaaaabbcdcddbadbacadbdabbbadacaadbcdabadccabdadbaacdcadbdcabcdacdadccabcbbcacacdabcddbabbccbdaacdbdccbdbbdcdbababdbccbbcadbbcadbbcddcdadabcbddcdbccbbbbbbaadddbddacdcdabaaadbaaccababdcabcdabbabddccdccabaddcdcbcdcbcbbbbdbbadcabcdcbdacddbadbcadcbdbcbdaddaccaacaabcbcdaacacdcadbbcacbcbbbcdacddcabbcaadbdcccabcbabaddaacccdbcacbcbddccdababdbdbcbcaaabcdcdcdddccabcdabbabdbadbccabdccaabdaaadbdbbcacddcbdcddbcdbccadcddcbccabaabdccbdadbcaaadbdbdcbcadccbabbcccdbadadcadcabdaddddbccddabdacddaadbdbcdbbabbcaccbcccdbdcbbcaabdcadbdccdcbaaaadacadbaddddbbcbcbaabbccbcadcabbbdbdbaacabcdcbcddbbddbadacaccdbdccdaccdcbcaadcbdbdbabaddbcabcdcbcbbccbadacbadacaadabbddddbdcdaadbabccaaccbdabccdccdbaabbababbddbdcbaadddcddaaabdbdcddcddcbaddbdbdcababdccaabaccbdadadacacccdccaddacbbccdcadcddcacdcbbbbbcdddcababadaaccbababbbddacadacaaabbdadcddbcdcbcdcddccaccbdddbcaaacdcdaccaabcaddcddcdcaddabbcbdababcdbaadddadaabadadacddbcdccacdaaddabdaabbcbccbcbcccbccbbbcdddcaaaadadcacdbaaaacadccdaadadbdbdadddddacaccaaaacadcdbdcadabdacddbcabcabdabaaaabbadaccbcccbcadddcaaaabcdacabbacbacdabbcdccbaabdadbbcdadacbcbbcbbddadaaaaadaadaddadbbabbdadddbaccbdacbbcdcdbacaaadcbbdcbbbccdbddcbbccccccccbacdacdcdaacaacadddacddcccacccdccaadccaddbcdbcbccbdbcddbaddbbdcbccbacddbbdabbcabbaaaaddbabcdaabbabacccbdcadcdcbcaacabcbdbdccdabbaaccccaccadbdbbaccdccabbccccbcabbbaabddabdbbcddcbcbbbbbcabbbbcababbbdaadacdaaabaabcbdddacccacaabdcbbaaaacadbdcdbcbccadbcaabbbababbabbcaaacaaccdcccabaacadbbdadbcacdbdbdcbddacacacbddccccdcbcccacccdabacbacabdccdccacdcdbabacacbdbabcddadabcbdacbcabcdcabcdadbddbbdabaadaaacbbcacbbadcabaddddbbabaddcacaabdbdbcbbbcdbbadcadcacddbddbdbbddddcbddcbdcccdcdbccdabcbabdcbbcacdbabaacdcbcbbbddbcdaacdccabaaccbddbbdbbdccdacbbcccdaaaadaaadabcdcbddccaabcabbdbabdbcadcdadadddbcbddabbadbcacbdbbddcdbcbdcadaabdcbdabddbbdcaccbcbabcdacbccdddaadbbabdbbcaaabdbdbcbbbdaadbdcddbabcacbbccaababcbdabadbabaabddbbddccdcacdabcdcaddcaabbdbbabadccdbbaaddbcaaccccbdaabccbdaacabadbadbcbccbadccaccdcdbcddadbbbdddbddaadbaacdadccacbaadadccbccbbacccdccbcbdaccdbaccabbabdcbddaccadaaccadabbbadbacaddddaabddabacabbcaacddcdddbccbaadcdcbdabbaccdacddabadabbadbdaadacdbdabdadcdadcdbdbbadbbbbadcbccabcaaabbddcbacddaacbcabdbdccdaabaaaaaadabbadabcbbbcaabaabddddaaadbadaadbaabcabcbaddadcccabbdaddcacacdbcddbcbcdbcbbdbbdcdacabbabbccdbdcdabbabdaadcddcdbacbbdaaadcbcdbaabaadbdabacbcbbdbdaaacbbdbcadbacddaaabccccdadaaabbacdaacdcbccdabbbdcbdbcadbcbdddcbdbcbdbdbaddbbcdababbadcbbaadadbccbddbdcaacbddabbaddcccdaccbbacdabccbdcdcaabcbdbcbbbdbcbbdccddbdccbccadcdbccbcbdcbbcacdcbbadccdccaddcccaadbabadaacacbddaccccbcdbbbaaaadbbcbdbbadcadcccabbddbabddbdbbdabbdbccadcbdbbcadadcdaaaaadbbbbbacdbbbadccaddbacaadbcddbcaccadddadbaccbaaaccdbcdbdcaacadabbbaaadbbdacdcdcabababdbdcaabcccacddbcbbbbcdadacabbccbbbadcdbdcbbbbbaccabdaccabdaacbadcabddadcaadabacdadbbdacccdbdacdcbdbcabcadadcdcbbddabacbdbacdcdababdacbaccaadbddbabcbbdaccccaabdabaccadcbddbbcaddbacadbccdccdbbbbbaddabaccdaaaaddbbbadbdcacbdacaadddabbbdbccadcbbbcdcabdadbbaccbcaababacbbbcdcbdcadcbadbddbbbdbddadcabcbdabbacacbdbaccbdbccbdadbaacdadbbaddbadddccbbcadbcbcdccdbacaabadbdbacbdccacbcadcbccabacccccadcabdbacdacdbbcbbbbcddadcdaadcddccdccadaabcadaddbbbabbbddddcccccddbbacadbbbdaaaccaadcbacaadaabbbabcbdbbcbcdcabcbdadccddbcdbddabdacbcabadaccdacaaabcaabbacadaccccddcbdcabdbccbdcddbaaddbdbdddcbdbccddadaabaabcccbbdacbcdbcacddaddbbcadcaaacddacabdabdddabbddbadddbaaddcadbadabdcacccdaacabaacccaddabbccadbdbbbacbcdadacdcbcadcabbcdacbbcdacddaaadcbcbbabdcbbadcbcacdaacbababdcdbbbcdbacbcaadcaabaacbdccccacabbdbaadccbddbcbcabcaadabbdbacbaabdabdacbaadcacbdcdacabcabddbccaaacdacbbdbddbccbbcdcbbddadbdbdccaababaddabbbdbaababdbdbadccddaaabadcbccccaacdbbcdbbacdabccadcdbaadddaadbddcbccddcdcbaabcccaaccddbbbcaabbcdbbcddbcacaadadadcccdbabacdcabbdadcbdcabbbccdbaabdaaadccacaddcddbddcdbdadddbdcdcbcdbcdbaddcbabcbdaccddacddddbdbdbdcacaddacbdccbbadddccbdccbabaacdcdcbcbddacabacdbdbaabcdcbddabdabcdcddddbcdacabbbaddabaacbcbbcdbddccddddabbbddacaaccbacdcabdbbbdcabcdbbadcdcdbaacdabcbababbcbbcacacdcdabaaaacccaccdbbacdacdcaacbccdabcbbdacabdabcbdcdaaadbaacbdbccbabadccbdcbbaacccbbccadadaddbccacccaadaaacadabdcbbaacdababdbcccabbbbccbddaaddcddbbcbcbdcabcdbdcdcaadadcbbccddcacbdbcdbdcbdacaacdbacadacdbcbacbcbadcbbabbbaccaaaccddddbbcccdcbcacadddcbacabcacdaaaaaaccaadcbbdbdbdadcababddbabcabccadacabbaadcbddcdccdccbdccabbbdaaaccaaadcdcaacabcbacaaddccbcabbccaddacdbdadbddaabaabdaccabcabdadcbccbbcaabaabddabcadcabdccaadbadacbcdbdbdddabbcdddbbddacadaaabcdadcccadaadbaaaabdbbdcccccabbdbccdacbbccababacdbacdaccbcbdaccddcbdbcaccabacbaadcddcbbaababdacaccbbcddcaaddbbdcdcaabaddbcbdacddbcccbbadabbcbdcaddbdcbbacdaccabccddabbcacbaddabcdbbccacccaabbdbdacbbdccdbacdbaaaadcabcbdccaadcdabdcabbaccccadbbdbbccaaadacdcabdcdbbdcdabbddbdadbccaabcaadaadcddddcacddcccccbadadddbbcbbbdadcabdbacadbcacddccddacbdbcdaaccabaddbbdacadabaacdcbadbbacabdddbcdbabdaadcdadbdbdddddcdbcbcacaabbaddabacdbcccacdbcccadcadccaabbbbabbcbaacabaacaaaaaababdaacaaabddcbcaddcdabdcbacbbdadcddbbcaddbcccdcadadddadbbdbcadcabdabbcabcddbcbaabdcbacbcbdbbdbadaabbdbbdccccbcbaccbdaaccdbbabaadbdcbddadcdaaadcdddbbdbcaacdbdaababbdbabaddbddbadaacdbddbddbbdaaccadcabbdabdadcabbcdadbcdaadddacbbdcacdbabbcdbdabcbabadadbbbacddbdbdaadaccbadabdbcbcddbcbdbccddabccbabcdbcdabbadbcacaacccbbdabcabcdadccbdcdadbaccbabcdaacbccbabaabcbabaacddddaddcabdccadbbdbcadbddadbcbddaabcbacccbccdbadcaddccdadccabcbdbbabadbacbaadddbcbddcacbabbccaccdaabcdbacbbabbaacdbacbbdddddccbccccdbbdcccccacdbdaddaddabacbcbcddaacbccdbdccdcddababbddbcabdcbdbcacdaddbdbcddbabaddbabcdabcdaddadbdddddbacbadccdbbcacdbbccbadbcaaabababadcdaabbaaddccbbbdacacbbbdcdadababacdcbbccabdbacdbbcabcaddaaacbdadbccbdddcbbdbacdbccbbacdadcdcdcdabbaaaacadbdadacdcaddcacdaccddbbbcccacabccbbbbacabccdccadaacdabddaabcdbdcaddcbabaacadcbbbdddbcdddbcabbcdcbcabcccaacdaadbbbccbaaaddddbcbdabdabbbbabbadcccbbcaaaabbdacccdbabbbcbdcdccbcdddacacbdadbcabcdcaddbaaacacbadadaaabbabbacbdcddccabbdbdbcacdbaadbdbdcaaabdbaacadcbaaddbcbdabdddbabbcdcdacacccdacbdccbddacabdcdbadcadccaaccdbadacdccdcbcdbcdcaaadabacdcbcadddaccbcdbbaddaddcaddbbddcdcccccdcdadcbcdbbacdbcdabaddadadadddccbdadbcbbadddcdcadccbababbbcabdabdddccdddbabcabaaadbadadcabdbbaabcdacadccdaaaccdbbbcdcbadbbccdabbdbacddbadbbdaccbbdbbdababbdcccdcbabadabdbbdcaaddccdcdaadacddbbbdaadadcabdbccbabbabadbabcccddcdaccbabcbdcadbdbabcdddadcbcbbbbbcdbacdadcabaccdcaaabcddbadccaacabcabcbcdbbacabaaddaaaabdaabcacbdbbaacbdacadababadacacbbabddabbccddbcaccbacbdddcacbcadcdcdbabcacbbbdbccbdaddbbacdbcdacdaabdcbcaaccbcacbcaccbbbbabbdbacdbcccdbdbbddcadbbdababdbccbbdaddbddccabbdbddbdadcdbaddbdacbccbbacbdccadcddbacdacbaaabaaabdadbddadaacbabcddbabddaabccdbcbddbcccdabbdddbbccccccadbdccacabcdbcdbabadaacbcacabdacbddcbcdbacbdadadcdcdacbccbcdbcdacacabccaabbabbaacbdadbdadbddaabacdcbdabcccbddbcabbccdccbacdaccdabdcaaaadbcaadcaadcddcdccdbcbabacaadcbacdccddccbdbbccdbacddbdadbbabbcacbddcddcacbaacabdbacabcaadbccabcaaccadaccaaddccdacbdadbbbbdcaacbbdbbbbdbadacdcdbccbbddccdbbddbcdaddbbbdbcbddbadadbcabbcbbcaacdcacdcddbddddcbbdbcdcbdacadcbdcdbcaabcacdcbdcbcdcbcacabdbdbacddbbcaadaabbbaacabbbbabdabbaccdabbddbdbcdbbdadadcbaccdbbbabcaddbaaddaddcbddbdcbabcbabdbbccaccbbabadabdbacbdaadcdddbbbcddacaadaadbdbddacddbcbbccbadabcbabcaccdcbadaabdadbccbcbbbadcbaaccbacadabadbdacbaccadcccbababaadabbbabcabccaddcabcccdaaadaaacaaacdbadbdbbacbbdccbacaaddbaccaddbcbcdbddaaadddaaacbbcdccdcaabbbcbcbbaaddaadaccccbacdddbabccadbddaadddaabbabacbcabcccadccdbdaabacbdacaddddccbbdabdbbccbbcabbcdbbdbbbaddbaabadcdbaddabaabccbccdcaabdadadbbbbdaacddbccbcadadcaadadcaddccdaccadcbbbdabcbdcbadabcddcadbddcbcdddcdbdabaaddbabaabddaabaadcbcddaabdbabcaabccccdabbdbcdcdabadabccbbaaacabbbbcbcccbdaabccacbcccbbccbccdccbbbaaddccbcbbcabbdaaabcabbdbdcdacdababbcdacbcabaccccabbacdddadcdbdbbadcabbcdadddbcabdabbbbadbdccadbaccbabbadbcabddccdbcbbcabadcdadbcaabccaddabadadabacacddcdcadaaadaadbbdabbbbcbcdbcdcaddcbcabbcbadbdccabadbadcccddabadbcdcacccadcbdaacbbdbcdbbadbbbaddabcbddcaddcddacddaadadaddbcdadbcabbabcadcbbddddcbbcadccdabcaddbccdacacdddbdbcbdccddbbabddaccbcadabcdddcacbcbcdccddcbcbddcbdcbababddabaaaabaaccddcdcabccdacaccbcbddacdbccbbacdcbcadacdaabcaaaddddaadddadacddcccccdacdacbbbcdddcddaaaccacabdadcbbaadbaabcbdaacbcbcadcdbadacbbaccdabadabbccbccaaacdddbbdbadbbddddbaaacbcddcaacaabaaccbbabbadaaccabaaacdaccbabddbddccbccccbdbcdcbbacdcadadbdcbacddbaddbadbbdacdacbbbadbcaaddadccdaccdbaaccddddddaaadcccdcbdbadbccabdcbddbadadabbbcacbbcbbddcdadaabbbababdaacaaacbbcaaabadcdbbbbdccbbbcbabadbcabbccddbcabddacaacbdaaddddaccdcbacadddbcbbbbdcbcddbabacadbbacbddacbcaccbcbcdaaaabcbbaaadaddbccbaabdddabcdacdacabdbcbaaadcbacadcbbabbbdaaadcccccdcacddcdaabdaccccacdabdacaaabdccdccdbcaacbbccababbbdcbabbadbcdcccdcdaacabadcadbabbdbcbcdddacbadcbccaabaccaddaddddccbdcadddcacddddadacacdcadbaadbadbabdbbaccbdcaadacddabccabdbcbabbdcababcdabcbcbdaccdbbddbdcbdaaaadcccbbdadaacdcbabcbadbdcbaaadaabccbbacbdbbccbcacbddababcabbdbcbabaabbccbbcbabbbbacacbcaadcbbbcacaccabcacbabccacaaadcbbbbacbbbddacbcdbdabdbabadbcbbaaddccccdcbbacbbccbcbabbbacdccaaccadadbcbccbaadbadcdcbdccdbbbcaaddccacbacabdcdbcdbcdcdadbbcacbcdaabdbdcbdadaabcbdbacacbcbdcbcdabadabaaaaabdbcbbabadddabddcbdcbaacdbcadbbcbcacdddacddccdcccbddadbdbddbacddaddcdbdbbadabbcbdabdadbcdcbaaddcdcdcdbccdbdccdbdbdbabbadaacdcbbadbbdbaaccbadbcdcbcaaacbbbdcadbbbaaadcadadabcdacbcbbcbbdcccbcdaabbcaaacaccdadadabccaaaddacccdacddaddabcabdddbcbbbbddbbbbcadcddadcdbdbadadbcacdbbacbcdbcbdbaacbcbabdcbdadaabbddcabddbbaaaabbddcdacdaabbabaacabbcccadcddadaadcbdccdaccbaababbdabcadbcbaadccabcaccdabaacacdccbdddaaaaaababdcddacdbbbdacbcbbccdadbcdaaadaabdcacbcbdabdbacaddcbcadcdaddbaaadbcabbcbbbcdccbdadcdaabbddbaccabacbbdbbdadabdabaaabdbcddbacadddbcbdbaadddbcbcdadabcbacccabaacdcdcdadaccdcbcadcdcbaabbcbbacababacadcccabbacacacbacbcdacabbdddadaaabbabdbdaadbbdaccbccabdbbbadbaaddadcdaccabaacacaaadabdbbddbbdaaaadccdaaaacaaacbcbdacaaaabbbdaccacddcaddbaabadabdbaaabaacabbbadbddcbaddbbadaabdaddccddacacbcbbcaabddbabdbbccaabbabacadaccadbcddcdddbabbccacdbdbcbcacabdcbccddbacdcaacddcccabadcbabbdcbbacbccdcbbbbbccdccccacacddbdbadbcbadacccabbbbacccdbccccacabaaccabddadbbaaadcccddaddcccbbcbcbddabacadacdcbccbbbcdbadaaaadbccdaccbddadacdbdbddcbabbcabdbaccbbdacdaabdbcbcccabcccaadaacacacbcdbcddcccbbcddaabaddcdbabcdddacdacdcabaaaabcddcdbbaabbcdadbbbbdabbbcdbddcacbcabdbddabcdcccddbacdbbabacdbacdbdbdcaaacdacddacdbdbddcbcabcaccabbccabddaaadcdddadaacdbdbddbababcdcbcbaadadcababcbcadaaaaabbcdbbababdabbbcccbddddcbbcdacdcbacbcbccaccdccbbaabbabbccdccacbabbadbacbaacacbbdbcbbcabbcdccccbcaacbbabaccbcbadcddbacddbadabaacbcdaacdbcabcaaccbbdadbdccdabbaaabcbdacdccdcbdabdcaadabadcacadcdaaddbddbcbadbcccbcbccdaaaccaaaacabdbdbbddadbadbcbaadbbadaabcddbbcbccacbadadccadbccacbadcacbacbbbacaccbdbacbababcdccacdacbccbabbbcddacdcddcbdadaabaababaddcbadbcccadcacaadcccdabccbddbacddcbcaaccdbaabaaadadcccadabbbacddbbaadadbcdcabcaccbadbacaabcbbbbbbcccaccaddaaadadbddbbcaccdacbddcbdddabbddcbbcbabdccbacbdbcabbbbddbdaddbbdadbabcbbdbaccabadbddbdadbadcdcdcdbddaccbcbbaaadbcddcdbadcbabbcdacccccddbcddadcdbacaaaadbabbadddababbcadbbdaaaabacdbcdddcbdbdabadbabbacbcbdabdaabdccbddaddbdbbbddcbacdcdcabdaccccbcbbadcbccbcacbabcacbcddbdcadaaaacdaddbaccbddcbbbababdacbbbcccdacddcbdbbddcaabbacabbdaabccacccbbddcdcaadcbdccdcaccbbccdcbaadcdddbacaacaaddcdabcdbdaddbdbdbbdaadbbddbbdabcacdcddbaabdadadaaadbcdcbdcbdaadacadcbacbcaaabaadcbbbadacacadbccccabacaccaaabddabacbcbacdadaacdacbbdabadacacddacbbddddcbbcdbddbcdccaaddbadbbcddbbcaadadacadcbbbaccccdbcdddabcccdbacbcdccdbcaaacbcdbccdddadbdabddcdabaaccddbcadacdbdadcccccdcacadbcdcccbbadbaaccacddbbaabbbbcaadddcccdacaccdcdddccbabdacabacdaaddccdcdbbbbdaaacacbddddadaddcaacbbccdacacbbbbdaabdbbbbdcccdcbcdabdaccbabdcbaacaabcbbbccabadbdcbdcbacaabccbbcaacbdadcdcaadbadbbdbbcbdaddaacbdbaaccabdcabcbaabddccdacdbacaabcbadbccbbdbdabcabacccbdcccdcbbcbcbaabddacaabbbadbadddcacbdbccbadbaacaccabdcdddcbaaacbadaabadabbbabadcabbbccdabdacccdddbaacbddbdcacbdaddbabcdaabbcddcabccbadcdbbdadadccbcdbbdbddabcdaaddaddddabbacbdadddaaacbcbdcadabcbddccabccbdccdddbcccaabbcdaacdadbdddcbbccbabbdbcbdcbbbcdadcdcccabdddadcdccbabcacdcbadbabdbccaacdbcbacaccadbbcabbcbcccabbacdcbbddbccdbaaabbaabbddbbcbcaddacbdbadcddccadccddcbccadbadbaaabaccdbbcdabaaadbdccdadcaccdcacbaddbdadccdcadaacacbddbbbacbdcacbdaabccadadbcbdbcdcdaaaddbdcdcabbdbbcdcdacdcacbbcccabbdddcdaadbddcdccddacacdacdabbacabbaddcaadadabbbaaddaaaacbcdaadbbddcddddcbbccacbccbdbdcabdddabddcbbdbbdacdbaccddcaaaadcaadcbabacdadbabddbcdaaccddadbabdaaadbdbacdaddddabacacccbbababadadbbabcbbbbbbdaabbbcdbddabdbaaaaaababccaadaabdabadbcdbdcacddabdabccaddcbcacacbcabcdcabbacdabbcdccacbdcabcdccacacabdbcddccddababbbbdabbacaccdbcaaaaddcadadabdddbbaddcbbadbcbaddcbaadcdddcacacbccbadaccdbbaabcabdacbdcbbcdaacacbccbdaaaddccccadadbaabcddcdacddbadcadbabcbccacaacbcccadcccccdcbaddcaaaadcacadabbcbbdccdbaaccdcddcabdcdcddbabbbbadaddcdbccbbaddcdabcbcadbdcdbaacccddadbaddcabbbacdcbaadbddccadcabaacabbbdadbdaadcadbaaabbbadcaadadbaaccbccadadddddadacacbacbbabddabccbdcbcbbccdbdacbabdabbacaabdcdadcaaddaaaadbccbdbcaadbdcdbdacaacacddcaaccaaacbcaaabdbcbdcdaabcbdcbacadcbadaaacacabdcbbcbbbbacadcdabcabadddbadbcaddbabdacabbdabbcbadddbcbdcbbbaaacacdadcbdcbcdcdccadccbabadddbdaadddccbbbccbacdbcbaabcaacdadccbbcdddbcadcbbdaabadcbddbdcdadabaadcadccccaddcdcbaccadddacdaccbacbaabdcbabaadbbdbbbdbacbaaccacccbddbacccccdbbabbccacddacdabccaccdbcadcddacddaccaccadccaaadabaccccbcbdabccddbaddbcbbabbbdbddcdbcadbdccccdaccdbaddccbabcbaadbabadbcdabbaadaadacacaaaadaaaddddaadcdbadcbbaddbacdcbababaadbddadddacbaabdcaccccaaadbddadaccdaccabdddcabcabbaaadbacbdcccdacbddcdddbcdacaccdcdabbcccccbddcaaddacbaabcbcacdcddaabdddbdadcbccdbadabbccdadbacdddacccbbabddabdbcaddbdaadbcdbabcaaadcccadbbbddabdbbaabcaabdbbaaadabcabcccaaccbbdccaddbcddabdcabcddbdcdcabccdccadcbbacddccbddbcbccacbdadbdbccbbdccaaddbbcadadcdccccabbdbbccabbdaddabdaabbaaddcaccbdcbdbdccbbddddcdcdbbaabccdabadccbcaacbddbbdcdcdadcdcdbdddbcaacdcdaaaabdaacabdbabccccbcdadcaaadccdccddaabdcddcddadaccabaaacddbdbdddbbaddbddabcccbcbbacbdacdbbcdcbabaccbaccdadcddacdadbadbbdbaccbdabbbcbaaddbdbddbdcbcacdbdddacdbbdddcbacacaababcbbacababcddbbdbaaabdbcaaacdbddabdddaabcdbbcdccabbabcaabbabbddbdcadaccdaacdcccbadaccaacaaaddacddbabcdcbbdcbacddaabbccbcdcbbbcaddbdbdadbcdbdbdddbdddcabddaadcdabcbdabcdcdaabccbbcdccdbaaaaaaacaacdddbdabcaacbdcbacbaabccddbbcdabaccdaacabbabcbdbdbdabbadaaaddccbcdbbacbcbdccbcdbccdadadbbacabbbcddcdbbbcdcacaaccacdcadbdcdaadddcbcaabddabcabaaadcdccdbbdaaaadaddbbcbcabcdabbccddabcdadbadddaacaaabbcabcbbcbdadcbbdaddbbdaaadaaabaadccdbdabcbccbdbdccadadbcbbaaaaaaacdccbbbdcddadddbbbdacbadccadaaadbabacbddadddcbdcadaddaddbacbcadbcdbdcdaacbcaabbaddcacbcdcabcbbabccdbbccaabdabcddbccabaddcadbdbbabbddbcbdadccccdaddbbcbcbcdcdcdadadaaadabbddddccdaaabccdbabcdcaabaaabaaabaabbcccdcbccccdcaaadcccdadccadbabcdcaaaadbaddabbdddcacdbcdacdccaddccabdadabdacacbcbabaabddaddcddbccccadababdbbaaccddbcadbbdabaacacaaaadddccdbdcdabaabacbbabadcbabdacadcaddbdcacbbddababcdbbdbcaddccdcacbdcbbccbcbcacbbbcadadaddcdbcdabcdcdabccbaddabcdcaadbcababaabaacdaaaadbbccddccdbaaacddaccdccdccaccbddabcdbdcdbabaddbbbabdccbbacaacbbdbbbabccacbcbcacbacbacaadadcdababcbddbcabacdbccbaccbbccadacccdcbdabdddcdabbbcddbadacbdcaadbcbadbcbcdbbdacaddbbcdcdddcabacdcccaaacabdadbccbcccbabadbcdadcdabdadbcdcbdadccbbaabbbbdcadabaddaacdadcbdcacaddbcdccccbbbccbadbddcdabaaacbcbabdcdbcdbccdaabbcbcdacadcccaccbbbbddacbcddbbdbdccbbdcdbddacababdbabbcdcbbccdaccbcbcdacdddadcdbdcdcddcbaaabcbdbcadbdcabbabbbcddbbbccbadcdbcbbdcccaccabbbdddcdadcdbccdbabbcddbbbccdadbbcbdaacccaaccadcddcadacbcadaddaacdabdabbccadacccccbbabcacbbbbbbbadddcacdcdadacadcaaddcdabacbbdbdccbdbdcdbbaabdadaddaddaaacdadbaaabdabdcdcaaddabccabdcaacbabccdcaccccbbdcabaacdadccaddbbcbdaacaddbbcacbaacbddcccadbbbcbadbaabcaddaaaabccdbaabdbbccbabbcddcabacbdcadddccaaaaccacbdabbcbdcdddccbbaaddcbbdacbdcddcdabbcabcbbaadbcbaddddbbbdaddabbbcbbbccabaaddaddadbbabaccaacababdbbbccdacdcccbcdcacacdbdaabbdbabaacbadbcdadadcacbdacdcdcddacacbcbaadbbcddcdccdcdbdacaaddaddcbdcddddbddbbbcbbdbbcabcdaddbcdbabdddddaddbccdccabcdcdbabcbdddccccbcddaccbdbdcbadbaddabadacbcccdbcddaadccadacdabcbbcbccbbadaadbacbdacbabaaaddbacbdbaddcdbbcaacacbccbdcdbcbccbacababcbbbacbbbabbcbdddddbbabbcabdcbaabdacccdbabddbdddaacdbbbdccbbcadbddabbdadcaabbdcdbdbaaadbbaaccbaaabbcaddbcaaccbdbaabbbccbdcddbdddabddabbbdddbbadcbaabcbbdcccabcddcbccaccbbadbcdbdadcaaacbdccdbaaadcdbaaadacbcddabdbabcbdccbbbcbcadbdbdccbccaadcdbbdbddaabcadabcdddbdbcadbdcddadaadacabbccaadcaddcddccadcbbcbaadcadddcaaddccaadaddadbdadabdcbbdbccbdacacaddaadadcdaaadddcdabacddbdddcddbbbbcdbacdbcbdbacadbdbbdcaabcbbcabbdbccadcacaaadadddacbacddbdddcdbadbcccabddbdccaccbacdaccbdcaacbaadddabccdddccbaddadcbcdddbbcadcbdadabddadbcbbcbaddabbdacdbaabdbbbccdcdcaabacdddbaaaddbaabdaddaddbddddbbcbdabcabdbcaaaabbbddcbaccbbccbbdadbcccaccdbbbaadadcdabcbbbdacababadbdcadcacbaccbdbbcdcdbdadccbbbbbdbdabdbaabbdbddcdbabcbccdcbacdcdcbcbabadbdbbdacccdacababadcaaccccbddaddcdbcdbbbdaaddaacacdcbcbbcdbbadcabbdadbbbbcbbdabbddaddccccbdcdaaabbccdcddddaacbdaddaddaccbcbbcbadcabaabcccabcacdcddcaddddbdcbbcddbdbccabacdbbcadacbbaadbddcaccdcdcdabbcbbcabcccadababcbabdbbdabccccbdddccdaadcbcbacaacccccdacbbdcdbbcadcaabbdacacdbdbcbbacdcacabbcddaaadcabcbddaddcdbbdcddbbcdcdcaabcddbdbdacddbccbcbbccdbabcaaaddddddccdbddbcdddcdcddbaaabacabcdbbbdcdabbacbadacddccbcdaabcaccddddaccacbdabdcbbdcdacdcccbbbdabdaccdaabaabdddbbbdadaaaadcbbcbacbababaddaaccdadbddadadacdcdbccccadccbcaaaccadcabdaacbbacdababadcdcbadbacaacbcddabacacbacaaacbcccaadcadaddadcbbabccaadcbacbccacbbcdcbdccddababcddbbbadcbacadcbcbabbacccbcddbcdcacaacdccadbabccbdacccdaddcaaccbcbacdacbbddbcbbbdbaaacccbddbddbccdcddaabaaadbdbadbdcabcacdcabadadacddbacbaadddbbbccabbdcdaabcccacabbbddaaccabcbabababadaaacccacabbabacccbdabdbaccabbaadbaacacdbbaaabcadaacbdadcabbdcdcdbbdcdbcddababbbbaaacacdcacddcdbbcbcabbdabddccdbccbbdcccaabddabddcccaccdddcabbacabbcdcbbbccbcddaacdcdcdcbdcbcddaabacddabbcabcdaddcbacaadcbababdcacaaccccaccdbbacaccaadcdccbbcccbadbbccbaababcbcddbccacbbddbacbbaaacadcbaacacccdbcdcbcdcbadcacdccbcdbbaddcaaabacbbbabdaaccdabaacdbbdbaabddbddbccbdbddbbadbbdcccbadbbdcacdbcadcdcabccdcbacaacacabdbcccacacbcacbdbcaccaaadcacaaddaacdaaccdaddbbbbdcaadabcdddcbcadbcabcdacbabadadcbbbbaabbcacdabcdbbadaadcaadccadccbdacbcadaadbbcdcadbcdabbbdddbbbddabbbaddddbcbccdcacabdbaadbadacadaabbdddccbadbadaadcdccbcdcdbadbbddbddcdddadddbdcaadabdcdcadccabbabdbadabaadadcdabdbdbddcbaabaccaaccbdaabdcadaccdbdcddbbbbddbbcadbaadbaddaabadbdbabdabcbddbdccaabdbbadbbdadaccacadcbcbacacbccdadcdbddcdcdbcbcadacddbcadcdacbaabcbdadabbdcacadcacacbdaaacabcdaacdcdccdacbcadbccbbbdbbbbbbcccacdbbcdcaadacbbdabcbcbacabdccadaddadcdcaaabaddcddbbdacaadbcadcdcbdadcacddcdabbcbdaacaadcdcaacabbacdcccadcacbdcdbbcbaddbdcbddcbadadbbbbcbcabdbdddbcdccabbbbcbdcdcabacaddbdacbdbbcacddbcdcbcbabaabaacbcccbcbaabdcdabdcdabacddadabdbdacadaccbbddbbcaacaacdcabcaadddccbaaaccbadbccbadacbccbcccbbcdaabbaacdadaadbbbccaaaacccdadabaabbbddcbbbddbabcbdccbdbcddabbbdbddabbacabcdddbcddcdccdaabbcbddadaadcababdbcaccdbccbacacbcbabbacbadcbdddbbdddccccaaddaabaabcadddbddcbdccbdaccaaaacddbbcaabababdadcacdcccbabbbbbcabcdccdcdaddbcbdacdcabcbddcbcdabddadaccaabdbbddacdbcacabcdbdccaadcabbbbcdabdccccbdbdbcdaccacacbddbbbabbdbbaacadcdbdcccdaddbbddbacbabacccccaaaaabcddbcaabdcabdabddcbcaddaaacbacaaabadbddddabdcdaaacdddbbbdbaaadaabbdaccadbbbdbcdcdcdabddadcdddbaaccacbbcbdcdaccadacddcbccdddcbdacacddbbddaacaaadcdabbdabdddcbbccdbcbdbbbbcbcababbdadaacdaccdcdbdacdbcdadcdbbbacadcaaaababdcadaaddbdaacbdcddabbdcddaaddddbcacaadabbadacbaaacbdbacabcccbaccadaddabbdcaadcddbbddccddabdcdbabbabcdbdaadadbdadacbcccabbbddbcccbbaadbcccabcbcdabacdbacacccbddbddbbdbccacccadcbbccbbdccdcbddbcbaabcdbdcdccbaccdaadbbaacddabcddcddbbcbaadaadddcdbaadabdcaccabdacabdbccdcbdbcacabdddabbdddbdabaddccbadadcacdbdcaadccccbbcabbbbbcabbabbacaaaadaacacdaccbaaddbdaddadbbbcddbccacadbaadbacbdbbdcaacaaabdcdadbbddaddaacddcabdaaccbaabbccdbaacbbbdaadaabcabbbdccbdbcaabcabdaddacbdbbbbdabacadcdddccaccdabbccabacabcbbbaddbdbdadbabbcaadcbadbccabbdbcabdaddabbbbddcbcbabdcdbaaddcbdbbcdcdabbbcdccacaaaaddddaaddcbcbccdbccdaababbbcaabcaaadbadcadbbaaadbdbdbccaaaddcbabaccdabacccdbababcddabbcddacbadcddbccaacaaadcacbabacdddcadabaadaccdddcbbcbddbdcaabbdaabbbccdaccdadddbdcbacbaccdbdbacdbdaddaaddcbacdbbcccccaabdbaabcbaaabbbaadcabadbdcbbcdcbbbacbcbacaacaadcbcbcadbbaccddcdadbbbcdbccbaadddcaccacadcddcdcdcaacbbaaadcccbabbdbacbabdcbaddcbdacbbcbbabbbaabbaccbccdabcdcdadcccbacdaabdbcdabbddbbaaadbaabbcadcbbdaaabaaacaabcdadbadacabbacadcacadabdddbccbccdacdabdcabaaaccbdabbaaabaadbccbbaabacadcddcbcbcbbaadbbaaadbdbbaabbabdccdbabccbabdacadacabadbcabbbadcccaabcbdbabdcabbaccaadbcddacbbbabdbbadcdbacbcadbbcbcccdacbbacbddcbcbdbabcbcddbaabaadcaabcadddcaddcaaabbbadbbadcaabdaaddbaaadbacdccabcccbcaaaaadbbaabbadbbabdbabcddbbabddbcadcbbdaaddbacbacdcdcbabcddbdadadbadadcccaacaaccacaabcbcadddbaaabacdbdcacbdcccaadcbccdadaacaccdcacbabaaaaddacacddbaddbccaaababaccaadaddcaaadccacdaddacabccaacddbccaccadcbddbddcdbddaacddbddbdcbbdccdadaadbabacaddacdddcadcaabadacbaccaaaabadadbacddadcaabadbcacdddbadcacaabddaaaabdbddaccdddabcccdddbdabacddaadcacddabbaddcdcbcddbababdcdccbabcdaaadbaaabacdbbbcdbddaadbdadaccadbadcabadbccacbabdaccdbacabcabdcdccbdbcdadbcbaacaccaabdbbbcbccdaaacdbdcbccbbaacbbddcacccabcbdadbdacccabbcaaacdcaacdcdcdaaccbcadbaabbbaaaaabbcbcbcdcadcbbaaddbbcacddabdcabdbaddacababcbdddcbbcbbabaaaabacbdccbaadaabcadbcbccabbcbcbddabdcbcbaabdaadbdabaccadbcdadbbabdbbdcdcdbabdbcbacadbdaaabcbcdbbbadbabcdcddacacbadbbbcaabdbcdbddbacddccccbaabbabddcccdbcbbcbaddcbaacaababddbdcdbacdaabdcdaabbddbdccdbbdbdcdabbdbcacbccbcdadbadccabdcaccdadcadbddbdcddcaadacdacacddacacbdaacbaabdbdcbaddaadcbbbaccdcbababbdbbdcbbacbdbadcbcadbcddadadcdbbdabbadacdddbbacbcbdbddcdbbabbadccbdbbddbbbbcdaadcbabdccabdacbddbcccddadcdbacaccdacdcccbdcddccaccddaabbbcaccbcbbacbbddbdbabdccacbbadddabddaadcbadbbdabacadabaddcacdcacbcbbcdcccaaadbdcaababcbbabccbccdbdddaccadbcbcabadabaccbacbbadbaabbcdcdbbccddaaddbcbbaccbbdbccdabdadbddbccbacccadaabdcbcbaddabbaadbbddaacacaccbadddbbcacdacddaccbbbdcdababbdadcabdcabddddbcdadcbdcacaaaacbadacbcbadcaddcabcbdabbabcdaabddaabbcbbadcbaadbaabccaccbdbddcaaccadbdbdbacbabcaddbbcccaacadcaccacabddcbddcacbcbbbcbaabbdcaaddccbacaaaacaaccdbbaddbdddadbdbbcbbaabbadabbccbccabbabdcdbaaabacaaadabcbbcdaddbcdbaaaccaadabcbddbbcaaacdacabbcabcdacdcdadccdcbaaabddbcaacabacaabcbddbbbbcacaddbccacdccbaccaadbacadcacbdbdbdcabcadabaaaaddcdbdadaaddaddcdabcbabcadbbbbabddcacbaaddadddccbbbbdbbcddadbcbdbdacdabbccabdbabadbcdacdbcbdaacdcdabcadcdddaacabacadbbacbbadacbbcdcbccddabddcaaaddabcbdcccbacddccdcdbbcadddcbdcbcbdababcdcadcadddaccdbdcbcaadcbadbdbbbccbcccbaddabbbbdccbcbbbbbdaadbcdddbaccbbcdbadddadabdbabcbddadbbcaabbacdbbadacdbabbdbbadabdbbdcccbaacaaabbacabacaabdcadbdccaaaaabcbbdadddcabdaccabbaabdabbbbcbbbdabadcacbaddcbdbcaaddaacaaadccbdbaddacabbacbababbdbcddcdddcdbcadbdaddccbadbbdbbacddbadbddddcaaaaabdaadcbcdddbddbbbdbdbaacdcbcdaacbdbcacbddddadbbaaacbdcdccdbddaabdbdbcabacadbbbabdddbdbcbcadabbcdabdacbdbdabbbbcaddbdababbbbcddadaadcdacaccbddcccbacabcacbbbccddacadaadbbcdadcbbaadcbcacdcdbaacdcaadddbdcbcdcddddcdcbccdddccddabbbbdcbddcdccaadcbdddcdabaccbbcaddbaaabaaccaccdbbaccbddabadddddabddcbdbbaadbacbbddaaadabddaccbadaadacdaddcccdbbdaababcaaccaddbbbcababbcbbdaabdadcddddaacdacaacababccdccdbabaccbdcdbdcdacccbcbbcdbaddabbcccbacccbbacddcaadccaadabdbdacccbdacbbbcdbcbdccccbdacacaccdbdcbdcacdbabaacdcbdccdcddbbdcbccddbacbadaabbababccdccbaacabaaaddcacbaabbbccbcdacacbbcdadaadcabbcaddbbcdaccdaadbcdcdadbbbabbccbcaccadbcddcbbabaaacbaaccbdccacbcacabbbcbacbdcbcdbcdbcbaaddaaadaddbbdccdcdccaccddacaabbdcbdbbdcaabbdbcacdadbacbdadabbbadaddcbdacbcdadbbbabbadccacdabdbabcdcadbbbbddcdcbcccacbdaddabbbdbbdcbbdabbcadbdaaccbadcabcaaaabadcaddabcddbcabbbdddadcbbbbadccdaadcaadbcbbabbbdaddaabdaacdabdabcbabbbbcbdbdcbcabaddcbadbbcabcbbacddbccdcadcbbcacbcddaabccddbaccbddabcbdabdccadacbddddacbbbbdcaaadadaaacacdbdddbdbbacdccbabaababbbcacddbacbcbaadacddcbcaacdcacddbcbddcaccdcbaddbadbcacbbadddccbdbacccbcbbdadcbaaadaabdacbbddaadbadacdacccbaddcccdcabaddbacbdccbabccaabcbdabdbdddddadcadddccdbadbcbcccbddabdcadbaddcbbabbbabbdddddaaacdccdccbdbacddbddaddcccbddbbbccabdbdabdbbbdbdcdbcbabbaaacccccdbdbdacabdbcadabbacdbbbaacaadbadcdccacbaacbdbdadbdccbbadbbabbcbbdaabcbaccbdbcdcccdbbddcddcdddacbdaccdcbcdbdcdddacbbcbdbaddbabbcdadcbdbaddbcbdaaadcdbcaacbccbbdbbcabaccabdabaccbacacdbbcdddcabcbddacacababcbddcbdabcbcbbcdcdddbdcabddbcbbdcbdacaccabaddccdddcccccdbabdbdcdadbcddaadbcacccddaabacbaacaaccbdbaabbbabbadccbdaacacbcabbcaabadbccdbcdacabbdaabbbccbdcdcccbbaacbaaabacdacdacddabacaccadabadbcaabdbbbdccbadadbbdbacbabcdabbdcdadcaccbaccacacdcbcccbbaadadbacbcdbcbadbbdcddacabbacdaacdcacbaddddddddcbcbbaccbcacddcadbcadabdcdbbaadbaaccdcaaadacdccaddccccdcacacdbccccadadbdcbdbbaddcdbabbdcbcbdbbbcbbdbcadcaadacdbadcbabdcccdbbbddccdcbababbbdbbbacacbbdcaccddbddcaccdadbdbdacacacbcbbaabbdbcbcdbabaabbdadaccccdcababadcddaadcdcdbabbbcaabdabccccaccbcabdcdccdbbbddaabbccbcbcbbcccdbdccccdddbdaccabaccbdcbbccdbcddbccbcbdadbcbdaadddaccabccbdcccbababcabcbdacaacadacdcbddddddaaaabddcdccadaadcbbcdccdbddaababacaaabcabdadbdbbbdbdabbdbadadacdccdbddbbbdbaaddadbaaddccadabadadabaaabadbadadbbbdddadaccccbccbbbcacccadbdcdaacbbdadbcdccbaaadbcbdbbaabacdcadcbabdacbaadaabddcbaacbcacdcdacbcdaaccbcdaacccdcbdddddccbbbcdcbacddbdbdddabcbaadccccbccaacabccdabcaccbbdacbccaacaaddbbdccdcabdaacdbabddadbddaadacdcdcaddcddacadaccaadabbaccaaabbaabaaaccddbcccddabbbbddaabbddabbdbabdadadcacbdadddabcdbcadabccddccbccddcdadaadbbacdacadbdcbbccacddbcdbbdadadcadbcddcaacbdcdadcaacaddbabddccbaacbbcbcdbbcdddbbdcbbcacdcdcdbbaaacdbdabadddbbcacabaabaababaacaabcbddbdbdacadaccbdbbdcbaacccbbbabadadccbcbbdaaabdbbcadbcbdcadaaccdbbaadaaddaaadadcbbdcbddbdabbaddddbdbbbdadcadbabbbbadcdcdcbcdcdbacccdadacadccbdbdadaccadaabadcccaacaaccccaaacaabaddcadbddbdbabacbdaddbbbadcbaacccacacdcddbcbcacabbbdddaddcdccbcabacadccabaabdbaddaabaccadcdbbdddbbcbbacddcbbbdcbcbdcbdcdbdbbaabdaadbbcccbcbcabdabcbbcdddcaabcbcbbcdaadbbadacaddddbababcabcbbccbabcdcaabdccacccacdbdddaabdacddbdddadddcdcaabdbdccbcaccddadcdbbdadbcabcacabcaabccacbcadbadaaacaadaaaaddbcaccacadbbddddddadacaccabbaacbccddcddcbcaaaabbacdddacdabdcdcabdadadbaabbbdacccadddbaddaadcbbaaddcadccdadaddcdbabcdadadddabbaacbdcdaddaccccbadbdcdaddbcddacbbbbadcdcbcdddddcbdbbccdcaaabccdacdccdacdcbdccaccaacaadabaccccbabdbcdccaacdaccccdcabaabbddbbbaacdaabbddbdbaabcbccbadadacbbaabcddcacbaaaabdababddacabbbabcdcdcbbaccdadbbabcadacaccaccbcccbddcdcdccbdabadcacddccbabbacdaacdcbadcbabbcbbcdcacdbcaaadbdbcadcddbaaaccccdbaccadbdbccaabababcbdabaaaddbbcaaaabacbcdaddbdbdbddbcddaaabdccadcabcddcdcaaabaddadbdddcbccbbbcabdcabddcaccacdbabdbbababcdbacdabacccdccddbcacccbbaaaccbdbdccadddacdddbdacccddbadacdcccbcaaaacaabdbdcdddbacddbdbbbabaabcbbbdddadbddbdccbbdaaddcddbcacdcbddddddcccacabcacbbabddbcbaccccdbdcddbadadbabbdbcbdbcbcaddabcdcdacaaaadadaddbaccadcbadbcccdacccbccccabdabbddacdcccaccdcaaabcdbdddcccdaccbadbaccbbdacccbbdcbbacacbcdbdbdbacddddcddbabbdbccacccbdadbcbbdacaaabaabcdcbdbadabcbabdaabbbcabdacdaccadadddbbbbbdccccdbaaabbdbdbccaacabbcacbddaacddbdbbbbdabaccdcdbaacaadbcbbabaabaadbccaabcaaadcbadccaacaabaacbabdacaaabccabdcdddadaddbadcadbbccdccdddcbbacddbbdcbdabdbacdbccbbadaacdadbaabbabcbabaaaaddaabbcdaaababdcddcddbabaacdcadaaadcccdbcaccdaccbbabacdddccddacdbabcaaddbabdcbdcccbdcadcdaccdcbdabbcccdcddcbabdaaddacadccadaaadbbcdadbabbdacdabcadacaaacaaacadcbcbdbdcddccacccdcabacaaadadbdbabbbdcadaddcdcadadccaadaaaccbaddaacdacbacbcabdbcabdddcbdcaaabcdccdbaaaadbbaabbbcdacdadcadddbdccbaaaaaacaaadaddbcddccdbbadbcccadbbbcbdcaddbaccdddccbdacacabcdcacaaabbdcacaccbcaadccadccbabddcdbdacadaaaadcbddbbdccaacababadabdcbbdccdcaadadbadaccccbabbbaddadbbaadbbdcacddabbbbbdabbadcdddabbdabccbcacadddadcdbccbdaddbccbdcdbccdcabcdbdadcabaadacaaaacabdbdacbccdbadcdacbbddabdacbadccadbbaacddbcdbaaacaccaaddbbdcacdaccbadadabbabbdcccdbadddadcbbdcdbaaabdcddacadbdadadbcbaddbcdadbabaccabbbabbacabbcbbbbdcccbcbcaacaabacbdabbabaadbaabdcbcbcddcaddcacdddcbaaddbabdccdaddadcdabccdacdacbbdabcdcbcacabcbbaaaddcbbadccdcadaddcbacdbadaddccdaccaddbacbabddcdccacadcbaadcdaabaaadcccbaaaddbcadbdbacddaacdacacdccdbacbbddcadadcccccabbbbadabdcdbcbdbaddabddbbcadcdbdccddbdbaabcadbadbacbdcdbdcbcbaaddcaddccdccdcbdcdcdacacbaccacccbdcadccabacbdacbccbabcbdbdaaacabbccccbdcaaacdaadaaaddbddbbddaabaccbaccccadbabbacbadcddccaabdaadbdbadadbdccdbcbcddabcabccadaacdaadbcdbaaaadbabdbdcdaddbcccbbbcbbbbbcaaccdadabcbbcbbbcacbcdacddbcbadbcdbaaabcdbdcbcccabcbaddccbddcadddadadbdaccdaadbabadadbdddbaaabdbadbdabacaadcadbbcddbbdcbdbabbaccdbacaddbdbcdccddbacbbadccdcdbadbbcccdbdadbcdcababdbcaadabcbcdabbdbddcacdaddcbdbcaacbbacbdccbdcbbdacdbaacbbabbbbdadbbbdcdadbacddbabdadddabdaaacdcccdbcaaddddccabbdbcddcdbcabdbbbdaddacdbbdabdbcdbbcbcddbcaabdcbbbdcbdabcccaadabdabcbcbadcabccbabbbabcbcbbcacabbcaadcbdbabdabdcbcacccddacabcaadbcdacaccdbbbdaccdabcbabbabbdbbaacadbbdacabbdadbadaaaabdcbaaddbcccabdbcccbbaacadadccddbdcdbbadccbddabdabdaddabacdaabcccbbadbcaddbdabdabddabdcaacbbccbbadaacdbbadddaadbbdbdcaaabcbabacccbaacbcdadaaddcdcbaddcaabccabdbadaadcbcbdddbbcacabbbbbcccdbbcaacaabbbacdbcacacdcdccbbdbaddcddadadacaaabacadabbdadcbacadaabbdadcdaccadacbacacbaddcbcabcbdcccaabcbbcbacbabbcbbabdbbaabcdbaadcbadccbdabbdcbbabccaadcdbaadcccabbbadcbcdabaaacccadcbbbbdcbddaacddadacacbbbdcdabbcadacddcdbccdbbacddcacabaacbcadbdbabccabaaccddddabbdcadacbcbdbcdadbddbcddaabadaabadbaaccadddaacaddbbbdccaacccaabdabddabaddcdbcbbbcddbbbdaacadbabbcbcbdcdcdbcacadbbdadcaacacdbbdbbdcadbcbbbddacccdbcdcbbcacbcddcdcaabaadabcdadbaadcabddddbdcdbdaabcdcddcadbdacdddcbddbbcacbaaadacacbbaaccdcbdbbddcdbadbdacbabadbcaccaabcdaddbddabcbdcaabcbbbbadcbdbabdbdcddbbcadcadabddabbccdbadbbbaddccdddcbdacdaaadbddabdcccccbcdaaadbccbcaaacaacdabbabdbbbcbcabccbcbddbaaaaaabadbbaabaccdccdddaabbdcddadabbdcbacababdaaaaccdaddbcbaabcaaaacacccaaaabdbacbcadbcabddcadabbbcaccabdbddabbddaacaadaabbdbbababacbaadcaaacabbccbccdaddcadcbbbcbbdddaccdabbaaabbccbbabdacacbabdaabcdabbaadcacddadcabbaabdacbbadcbcadccbaadacbadcabdccbbcccdbddaaadbbbacdbaadbbcaccbccaccbbbbddacababcacadadbdaadcbdcacbcbcaabbccbaabcdccacccdbcdbbdbbadbddaacdddbbccccabcdabadbcbdccbbaabdabcbacccbdbcdabbcbddcadaddbcbdcbdddaccaccdabadacbcccacaadcbccadccdcaccbacbabdbdaadccddcccccbcbbbcbbabdccdccaabdbbacddbbbddccdacbdcbcbaababdddaacbdabadadcadbbdcbbbcdcddcbdccaacddddbdaacbabbbcccaaccbbcaddabddcbbdddddaaabbaccdbabacbbabcbbcdbdbababaddcddadbabccbcaabdcbcbdbdabacaddccadcccadcddcdabcbbdcabbdcdbbcabbadabdbbaacbccacadabcccaabaccbdaccbcaadddcadbbdadabcdbaccaaccabbbabaaddbaaddcbabccbbbbbcbadddcbbbbccbccdcbbababadaccdabcaaaaddccababdcdbbdcabbcaadcccbdacaadcbccdbcadbcabacbbccabcbddbbddddcdbbbdaaacaadcaccbdbbadacbdbdbbdaadcbbaabbcdbbbdacdcbdadbbcdcdbbddcaaadabaaaaadbcacbabaaadcbadbbabaabbccdcddbdcdddaabaddbadbcacaaabbbcdddaadaadbaaadadadbaaacbacdcdadddcbdcdbacdabadbaabdcadbbbcbcccdcbbbbaccdadcadcbbbddccacbdddbcdbbabbbddcbccbbdacdbaabccbacbadbdbddcadbcddbcabbbbabdacbbadcaccaacbbddddabcbaddcbaadcddacaacccbbdacaadbdaccbddadcbcaacdbacbbababaaccbdddbcbcbbcaaacdcdabbddacdbbcccaaabbbadcabacabbbbbbabadcababdbbdccdddabacbdbdaaacbacacabbccbadaddabbcbbddaaabcbacbccdbdabbaaaaddbbccdbdacbddaabbaacbdacdbaccbdcdbdccdbcdcacbcbabcacabcaaddcadbddbbdcabdcbbbaacabacddcbcbadddddcababcdcdbbaabcacacddaabbcccaaabccdcabccdacdbacabdcbcaddabaccadcbddbbcabbdcdcacdacbdcacdddddabacbcbcaddcacacccaaaacdcbdacdcbacdccdccdcccadbacdaadbbdbaccdbabcccabddcbdcdaaaabadbdbacbaabcddacbaadbdcacbbcabbddcbacdaddccaaacccaccaaacdaadacbdcaabdcccdbbbddaccaadbaadcacccaaabbdaccaaadcaacbabbbbddbbaabddaacbaaccaabbcbbacbabaacdbbcbcccbcaadbcbabcdccbadddddabccbdaababadabbdcaabadbbdabcdbdadacbbccabcbcccadbcbddbaddadccbdaadbdcbbcaaabddaccdaacbabdbbadcaccccaadccbadddddcdacdbcbdbacadbaabbcbcbbcadddbaacbabcdabccddbddaddccdcabadcbaabbbcaddacbdbbadcbbcaaaddddacbdbcdbacbdaacddbdaddbbbdadbcdcadcbdabccbbccbacabbababaddaadbacccbbccbddcbdcbabbcaadccaaabbbbaacacddcdcdbdcbbdddbdccaabddbbcababddadddacdddbaaadaaddcaadacacbabaaabddabaadcabdabbadddcbbcabcabaadcbccaddaddcdbbabcddbabacdacbccbbadddaabdccabcbdcbbdabbabaccbacbdccdabdadcdccdbacccbbabcabdcbabbcdcdbadaacdbbdabbccddbbdbcadddbdbbaccabccaabbdabbdcacbcaabadbaabccdddbcbdadbbbbadcabbabaccbbbbbccdcadbdaddadaabaadcddacaadcccdbbbbccbadacaccbccdbddbdddddcddcccacdaaabddcbbaaaabaddcdabadacaccaccaaacddaabababdbbbcbcbcccbbcccabcaddabdccabaabaddcbdadcdbbbadcacabcccbdabdddaaddbdbbcddcacbdbaacabbdcdbaddbdbbcbcddacbbcdbdccdcccaabccbccacbccadacbabcdbdbbcddacbdbbcdbdacbdccbcdabdbcadabcdbbaacbcddcccabbbaaabcbdbcaaacaccddabadcaadddbdccdacaccdacccdcbadadcdcdcaaddbcacdbbabdbaacbbcbdbacbdaadbadaddacaadcbbbddabaacbcbbbdabdddcbaddbaabcbcaabcbccbcdaddbcdbdbdabcbbdcdcdcdbbadbcabbdddaadccadaabdccbdcbbbaccccdcdabbcdacbcacadcbaddbdabadbbdddaccccdcbbddcbcabccdcdaddcdcbcbcdccdabcaacbacacdbbbdbaddaacbcdbcabcccdbbadadcacccaabcabcabccbcaadddacccccbdbdbadbabddcbacdaabbaaaccbddcbdbddaabcccdbcddcadbaaadbbdbabbcdbbaacabaadabbcaadadcacddadddadddbcbdcadaacdbddabdcdcacbddabccbbbaadbcbddacddbadcbbbaddcadbbcdbcdbdbadbdccdccadacbadbccadbabbdcbadcccddcccbcbdccaabaaacbdadbbdbbabbcdbdabddabcddbccbcddabccbccccabccbbdcabcbcbacdabbbbbadbaabcdcaddbdbbabcbadbcdbabdaacbacccddcaccdcbdbbccbcacdcdcdacdadcadccababdadcccbbbcdbabcdbabacabddacaccbdbaabcaabdbdacbaddcbbdbacdcccdcccaddcadbbadddbbbcbbaabcaccbaabbddbdacadadcddabbccabccaaccbadcaabbdaacdcbacadbadbacdcccddbbbcbcdcdbcbcbdaaaacdaadddacbdbbbdacabbaacacaaaccdcadcbcbdddacbcccbcdbdbbbddbbbaabdbcdbdbbadddbbbddadbbcadaacacbaddaaabbcdbacbaabcbdacbbcbbcdcadbdbacabcbcacabaaaabaabcddaacddbaaccdacbacabdcbbccdbbacdaabadaacaadaaddbadaacbdbdbcaccdcbddcacbbaddcdcabcbcdbbcdcbdbcddbcbaabdaddccdbbbddbccccaabbabdbbadcbbdbddbbcdbabdbcddddbbbdbcccbaccddbbbacdbcbaaabbdcabbddcadaddbbdbcbdadacbcccdbbabcdbacbadcbdaadadaccbdcbcdbdaccddcbbadddabbccdccabcdbacdcadaabdadcbaccbaabbccaacaacbacddbbcddadcacabdacbabbbbbcbacaadcccacdabbaaacdaaabbcabccbcbdaccacdcbadcdabbbbdbdcadbcacaaddbaaaacdbababbcbaacacbdccdbcddbaabbdabdaddaaabdddccaaaacbabcaaacdbccbdbbcbacabcdcaaccdbcbabdbdabdaaaccdabcbcddbdaabcabdacbbcccdaaabcbbaabbdacccbabcbccdadadbcacacbbbaadbdcbbdccaadacbbadbabaabdacbadccabcbadcbacbdccccadcabacbaadaccaaddcacabaddaadddbaacababddddcbadaacacbbdbaaaccabaccaccdbcdcacdddddcccdcacbbaadbbcbbcabccdbcccacaacdbdadbcbbdaabbccbdcacabbddacdaaabbabccdcbbdccdcbbdcbacaaaddbcbdbddddbcdcccdabdcbbddabbbdcbabcdccbababaabcdbccbbdbccbdddcbdabadbacdcbcbdaaddacabcdbdcddbbdbdabdaababcbbbaccbbababbbcbbbcccdaabbcdaadadbbddbcccddabdbbbcbcdcabcddbbcbaccbcaabcadcacaabdacdbbdcdaadbccaddbcaaddbcacccccbaacdccdabacbcdacdcbcbdccccbccaadddcccbccdbbccdabbddaacabbccdcbbcddabdaadadbdcbdcadaacbbccacbaddcaccccaccbccbdaabaabdacddccbcccabdcbcdaaadddbbdcbacbcbbabbbbacdacaaacdcdccaaaacdabaadcdccdbbbadaaaadbdabccdaaaccabdabcadcaabadbbdccbbabbadcabdbcdbbaccdccabcacdcddaadccdcbcddaadcdbccdcbcabaadacdabcabdbbaaacdabbaabbccccdbdbdbbabcbdbcaabadcacadcdccdccadcdadabddccdadabdacbaaddddadcbcdaabddbbdcabbcbddbaddbbddbaccabddddabcbabacbacabcbacadcdddabbadbcccbbdaaacbbadaabacddbbaadbdbbacbbbbbbacdaaaacaabdbcaddacbbcccdcbacbddabbcadcbadddcdacbcbbacbcccabddccabacadbbdcdacccbdcbdcbbdbabaaacdbcbbbdadbbbdcddcaaabbdaabaddabacadadacaccbcbdabcccbbaaccaccdbdbdcdbdbddccccabaaccbacddcdcacdddddacaacdbbdadabdbcdaacbbccccdcacbaddabdadbaabacdbcdcdbdbabbbcbdadbcdacdadaddbdbabbdbadadabcaddcacccbcdcabdcacbdabccdabbbcccbdbcaaccaadcccdcaacbdabbcbcabaacabcaccbdcbabbcadbadbacddbadaacbabdbbcbdabcdbcdaccaaaacbddddabddbcbbcdadcaadabcaacaaaaaaacbccdbbbbccacccacbbdbdcbabcacddbbacbbddbccccacaddabcdbacdbacadcdcbacdcacdcadadcbaaacddcacabbcdbbdccdbaacacacddbdbcddbbcabdbdcacbbabaabbbddcbacbccbbdabbcdcddacbcddbdddbcbbdddbccaacabadcadbacddddbbcdcadbbaacadcbddbdcdcbacbbccaabddbbbdddcaabcacdbabcbcbbcacaabdbadbabaddaddddcbcabdbaddbcacdaaccdddddcbdbadaabcabdcbcbdaccacdcbbababaaabccadbabaabbbdacaacacbcccabaacdbacdbacbcccddbbadbbbaddacdbadabbdbbbbbbddbdacccdbbbcdaabaccbdbdacbabbadbbcccddbabaccddddbccddacaabcdbddddbbaddcbdbaadcdaccbcbaccccddaabacccacdcacaaadccadccddbabdddbcaddbcadbcbdbddcdbdbddbacabbaddcccccaadabaaccabdccbcadbccbadcdaabaaadbdcabbcddbccccdabdabcbdadcbabbdadddcabacaabddcdabaddadbbdadcddbabddacbcabaddcbcadcdbcccabddaaadabbbccacdbcbadcbcbadcdaccadcbbbcdbdccacdbcbaabbacaadccbdcadaacbcdbcacddbdbabbcaddabddacadadcaadaddacdbbddabdccdaccabccbdbbdbdbbbccaaccacacddcdcccdddcdddcddacabcbdbcbcdbacadcbbcbbbabdcdbccdadbcbddbacbaccabaadcadccbcadcacaddcbbdabdbaaaadbdcacbbddbadcdcdccacbbdcadbbbddbacccabdaddcbccccadcacbaccbcbbddcadccccdaabddabbdddaadbcbddcaaccccdaaaacdadaabdccbdbabcddddbbcacbbbcdccdcdbaabcbacddabacbababcccabdcbdcaadabddbcdddabdaacdcdcacabbbdcaaccabaaaacdccbddbabbacabcacbccbcbcbacaadbbcadaaacbdcbdcaadadaadcdcbdccddabcbccdbcbdaddacccdbcdbdcbbaacbcacaacadcbdccbbdcdbacacabaacbcdacaadcdcccccadbddababbaadaccbdaaccbccdddbbcabbcbccaccbaddcbcadcaaaddbdbdaaddddbcabaadcdbcbacddbabcdccbbaabbdccccbddababbdccabbbadabaadcdaabdbbdbccacbcddbdcddaabccccabadccadaacbabddbdcbbadabbaddaddbddbbaddbddcbbcdcbabaddccbadbabcabcbccbcdaaadcdcbacdabbdaabcabddadacdbdccbaaaadaadcdbdbadcaaddbaacbbccbaadbdccdcdaabbccdaabdcdcbabaddbddadbbadddacadcabdcaaadbbabcaccbbccccccbadcaabdbcbcbacdabcdcbcdbacddaccaaddbaaadbdcdbccacaaddcddcdbdabadbdbadbacccdbdcadcbadbbcdcbbabababcabbddbdbacbacdbbabddccbadaaabdddddbbbddcadbbcbadbcbdddbbbdddabdaddcaacdbacbdbbadcdcccbcbdcbdbcddadaacdcdbccddbbcabbaacabcbcabadacadbadadbcdbcddbcdbccabdbbccabaacbaacdcaccdabdbcccbabcacdcdaaaadbcbdcddbbddcadabcbaccaccccacacbbdbcbcdcddcbdacaacaadcaacbadabdcbdcddcbdcbadaacbccadcccbcddadbdbdcbaabacbcabbcdbbcacdabaddbdadadddcbbdadcccaadbbcbddbbccdbcbdbdadcabdbcbcbcccbcabcbdabbcbdaaabcbbbdbbddddbbbaadbdccadcbacabdcdabaccadadaabbbcddbddadcdaddbadddcdcacdaaccddabccbadccccdccadcbdbbacbbbadccccddabaacbbcbbbbddcabcdcbbaccccbadddccdabdcbabdcacbacacdaacacaadccbddddcaadddababdcddcbcdbbbbcdbcbcbddbcaddcacdcbaabcccdadbcdcaccabcbabaaaabdaacaddbbddabccdbaccbaddcdbbbcaaaacbdadbdbbacbacdabadbbddcacccbddcccdccdabdbdddadcdcbcacbddccbdccddbdaadccadcaccaaaccbdbaddddbacaacbabcdbacabddbdcbddbdcbbcadaadcaddccdabaaaddbdabdcacbabcbabacadcbacddabadacbbabdabacdccccbdcacdbadaccbcadbbdbdcdbacbcaacddddbbadddcbcbcbbadaabccadcbdaddcbdccaccdabbcbacaacdcbcdcaddbcbacdabbdcdcdacdccadddcdbabbddbdcccbaccbbdccdcababbbcacdababaaabcadbccdadbbcbcadbbabbcabadbdacdcaddbbcabaaadbddddbadbababbbdbcdcadbacdbadababbcbbdacaaaaacbdccddddbcdaacdccaabdacdbddcbdcaccccccbcacbdddcddbbbbddadbccbcbbcdddadaddaaaabacacdcaaacbdacacdbbdccbdabccadbddbbbbdacaaabacbdbcaccbbcadaaccdbbaadcbbbbddddacababddcadcdcabaabcbbccdababcddbdcbaabaaacdaababacccaabdddcbdbdcbaaacccbccdcadadaaadabcbdbbddcdaddccbcdcadcbdbaddcdbdccadcbdcbabdcdabddaaccdcadacbdbcdabcdcbabdcdaccacadadabbdcabadbcabcbadbabcdacbccdcbdcbbdabaaacbcddbcccddbcaabcadccabcaacbbdaddccaadbabbdccdcbbcdbaccabbdabddbbbcbaaabcdaaacbddcadcdaccaacbdddabddbddbdbdaabaaccadbcbbdbacadbcbbaabbdbcdacdbcaadbbcbbabccddbbaccbaadbbaacbabdcbcdbcaddcbadbbdcbddaddcddbbbbdbdabdabbaabdaabcbddcbbbbcccababdcbdcbabaaacbdbadddadabbdbccbbabdcccbcaacbcbdacddabdacbbcbddcccbabbadcdbddbcacddbdddaddbabcbbaacccaabcaaabbcccaddadcbcdbdcbacdadabaadbbdbcbaabdccbbcbadcdcabdbcbdcbddcadabdabdadbddabbaaaabcbcbbcdaccbbbbddcacbabacbbacadcadccaaabbddbdbccadbcbcbbaaacdadaccaabdbbcaaacdcbbbdacccbdbbdccbcbbdaaaacaaabdddcacbabcabaadaccabcabacacdcbcdacbadaccbdcaadacbbcaacddcbcdccdbbdbbbdbdabccbbdccbbdccbbacbbaccbdccbabcddaadcbadababbccbdbadadbddaaadacdbacaadbabbaabbadacbdbdaccdbbaaccadacbcccdbcddadadddabacaadbadaadacddccbdabbddcbccdcdaadabdabadddcdcccdaabcabbbdadbdadbddacbaadbaaabcadaddcddbdaabdcaadcdbbdadabbbbbbdcbbddbcdbcadcdbcaaaccadccdcdddbdcccacdacbcbaadacdbaacccbbcbaaaaabcacdccccccabbcccdcbadddadadaacbdbaadbbcbcdadbdbddddbddbcbcbdbcaabbccadcacbcdabdadacdccbbbdaaccadcaccacbacabcaaaacaaccddbbbabdacbdbddbbbacbbcaabadbabccabbdbccbdadbcadbcaadcabccddabbcbaadcaabcbddbdcbbaadbbbdddbdbdcdaacaaddacdbcdaaaacdabdadabaaddaadbbadbcabaacbdbaabdbcddddbaabadccabccaddbccaaabddcadbdbbdbdbacabbdaddaddbcbacccdbbbcccaacbddbacabdcdabddbcbbcabbdddadaaaabadadccdbbbddccdcdcbadcdcbbbadadbcbadacadccddbdcdacdcbbccccddabdaabbbdaaabdaccaaadbbdddbcbacdcdbacaddcdcacdcdaccabcaadcdbadbdbcaddbbacbdccabacdacbddacddadacbcbadbcbccacbabdcddbacdddabbdabdaadddccbddbcbaadbdacdbaabddacabaaaadadcdcacdcbcaddbaddbdbaaccaacbacbdbcbdbbccadbdcdadddadcdbccbbabcaaacbdaabdbcdadbddcdcdddddbcdcbdaddcdddbddbcaabdaabbadcaadddbdbcbcaaadcadcddbaddcdcaadaaadccdccbbdcdbddabbbcaacabcbbacbccccbcbbbddcccddcaadcdbddaadadbcabdabaaabbcaabdccacadddabdcbbaddcacdbdddcaadcbccddbabacacacaddbdbbbbcdcabdbadbbaabccbaacbabadccbaabddacdcdcbddaadacbcadbddcdacbaadbbcbcbccbbbdcbaadacbbadbbcbcdaacadcbccabddccb
cddadacadbddabbbbacdbdcbddcccbdcbddbabcdbdbadcaddddaabbbdbddbbdcabbcabdaccadbcdbdacccbacabcbbcbcdbbbacdcdbdaaacacacabdcadddcacaccacbdbccabcbdbadadaadcddadadcdabcabdabbcddddbbaadaddbbbcccdcbbcdbbbcadaaabcaabbcbdcdadddbaaaacdbdbdbbdbaaabcdbdcacaadbbcdaaadcbabbbcdacbbcbcacbbcccbadbadcdadabadcbddadaaadcacdaadddabcdabdbaacacbacbbbbcadabccabcddbbdbcbdbbdbbaccddccdbccbababcadcaadbddcddddbddabdabdbacdabccccdddddcbbcbdbaabcdadadddaababdcabaccbbaadddddaacddbacabaacaacbdaccdadbcaaaadccbddcacdbddcbdcdbbacbcaacaacdadbadbbccdcadbbddaadacbddcbcdbbadabcababcadcaacdcdbccddbadcacccbaaababacaadacbdbdddccddbdbbcadbcbbddcbabdcaacbcdbcbcaaccadcadaaaaccababcdccccdcacacadabdcadddbdcdcbddcdadbaccbddadcbbbcdadccdbdcbcdccacdcbcccbbbdbddcbbccaadddccbacdaadbaccbbbaccbbbcbabbdadaaadbbbdaaddaabdbaddddbdcabdcdbabccccadcdcdacbdcdacadcdcbbdaadbaaaacbccabdcdcdbdaddbdccbdbdaacdbdbdaacdbaccabbadddcdbdbadcabccccdcbddcbdddcabdcbdcaabddcaaaaaabaaaacacbbdcdabaaadacbdccaababddaacacdbcddcaadbcbbdccccdbccdbaddabadbdaddccbdcdbbaaabdbdaaccccbbddabbadacccadcccdaacabddacbacbcacdbdbcabcacabdabdabddacbabccccccccaabaaacdccacdadcdccbccddddddbbbaadddcbcddabcbbdaacddacbbbdacaddcddbabcbddabbaabbdaabdddaabddbdcbabacadbdaabacdbabbabcaadbdbdacddadaddcbcdacddccdbcacdcdaaaaadaabcacccbcccabdbdacdddabbdadadccdaadccbadbadbddbdbbbaccacbdadbaddcdccadcacabbbadcbbbdbaddaaaadacaabdbdbddbddaccadcdbabaabdbcbdcdcabdbcbcbdbaaaacdadabbaadcdcdabcbaccccadccccbabbbdbbabbaccccdbbccddcdabcddaacaddaacdbabcacdcccdabaadbdbaaddbacdacadacbaccbcbcbddaaacadbdaadadcabcbaabaacbbbcccdddcbaaabdddcdbacbbdaadabbbbcdabbaaabaabdcdacdbdbbdddcbdddaaaaaccdbbcacdcdbdcdcbcddacbdbdcbbacbacabadabddaccaccddbcdbbbadbaaadabcbcdcbcbadabacdbbcbabdcbbcdadcdacadaadacdccdacddaaccdaadaddcdbbadccdaccaabcccdaddabddcddcccbcccbbcbbccdbcaaddbbacdbddabdaadbdbabbdabbddabdabbddacaddaaababcbdcddacddaadabdaadcacccddbadbadcccabccbbaddbacaddbdcbadcdcbccadaddccdaaaaadbddacdaabaddcbbaccdddaccdcccbdddcadbbdadadcbddadcbabcbcbbcdddacbaccbabcbbcccacddcbdabbbddbacdbabacdabcbdcbcbadaabdcbccababcbdcdabacacbbadccddadbabbbadaddbbbbdabdcadcdaccbcdbdddbcaaabdcdacccdbbdccdcadcbbbdbbdcdbbbbdcaacaabdbabdacdcabdadccddcdadccccbbdaddccaadccbbbaaabdacaadbdcdcaaaacddacabaaadddbccaaadcaacbcabaddaddbbcbcdbaacbccbdbadbbccbabdccdabcabaddbababcbccdcadacbacdbddcbcbacbccdcdddbdcadaaababbbdbdaabbccddabadbcbabbabbddaadcadbadaaccaaaacdcdbbaadacabadbbaaddcdbcbdacddaaacacbaaabacadacbdaaddcadacbdaacbdaddbbcccadbaacdababccadcbcdbadddabccaadccdbaadbcdddcdcdacbcdbcdbdcbcccabadbdbdabcbadcbdbdbcdddadcbacbcacbabcaccdabdcbccbbcaacadcaaccabccaccbbbcdcaacdabccdabacccaabbdccddcddbabbbdbbacababcdbbbbbdabcddccdbdacccacbcadbdbbadbcdacacbccadaccadcbcbdbdcccdbcadaabdadaaadaaaadbadacaaaacdbbddcbcbabcdbcabcbcbdccdaaccbcbcbbaadddbbadddbbdddaabbbbbcacabdccbcacccbddcbbdbaadbaacccbcacddadbbcccbabacddcdabbdccdbcbadbbbdadcbadbbdcbdcaadcabccdacacabbbcbbbbccacbdcaaacdaaddbdcbccdddbacbabdabacbacbdbbcbbabccbabdbbddacabcacbddbacaaaabdbcddabdbcbcddbcbbbadadadcbcbbbbcbdabcdadaccadbcddddadacdbbaadaabbaabccbcbaddcbacdbcbcaccccbacaaabdcdbcbcacbcbcdcbdaadbdcadcacadbabdddacbbcbbdaddcbbbcdbbbaadccbbbdcdacadccdadcdabccdbbadbbcaabaaacbcbbaabccacddabadcdddbbabdabcadcaccabccdcbbbdcbccdcddcccabdbcadadccdcdacddbacaddbacdccbddcbcdccbcacbbbdacbcbdbadccacadacdbcbcdadaaadcdadbacdcbcccdbcdbaacacbccbbadaabbadcabdbdccabaddbccdbbbabdbacbddaadddddabaaaadcaabdbaadcadadadcdbdaabcbddcdaddbbddcdbdbdadcbbcdaacdaabbcdaabaddacdbbddaadadabbdaadccdaadcbaadadabbcdbbddbdcdabddcaccddddbaaadcccccbcbacaddccabcbbbacbbaaaaacbbcaabaadbadcccdcadbcbaddcaaacdddacbbdddaadbabbadccadcbbadacabcdcbccbbcaddacdcbdcddadadacadcbccadaccacbbbddddbbabdacbddccdaccbdabdcbadddcbacbcddcdcaaaacbccaddbbbabcadcdcabddddccacbacaacdccdbccdbbddacabaaccbbcacbbcaddaddddbdbbcabbcadacddccccaddbdbddcaababdddcacbcbacccabcbdbadbcbbcdbbdcbaaccdaaaacdcdcacdacdbaabdacbbbbbcaddabaabbccbbddddaacaccbbbbbbdadccccacbaadbbcdbcadbcacacabbaabcdcbbcdbacbbdbbacabacdbdccddbbacabbcbbdadaadddaacbabbbddaaabddccbdbcacbbdadbccdbcacbddbcabbbbdbbdacddbbcaadccbbcbbabdabdaaddbbddcddadacaabadaabdacbacaaabcbdddbdddbdabddaadaadbbbcdccabdcdcbcbacddddabdbcbdabcaaccbbcddabcbaddcaddabbdcadcbdbadadddabcadccaacdcbbbabbbcccaccabdaacbbccbbccdbcbdcaacbbacaacbabababccdcadbcacacabaddadabdbaddbcccdcdaabdabaacadcaaadbbbbbbaacdcddddbdbcbbabdbbbabbbabcccaaccbddaacacbbcabdcbbcccbccadcadbaccbadbddbcacdcdddaadacacacbccacbdaabdbcbcbddcdaacbcdcbabbbcdbcabdbbbdccdacaaabccbcabddaadadddcacccdadabcacdbcadcdaabbdadbbacdbacabcccdbabdbbbccbdcdbbbddbcadbbbabadabbbcdabcaababdbccacbbdcabbbdabdbaacadbcacdabdaaacbbadccacccccaacacbababcddbbaccddccacbcccbbdacacdbbbcccaaaccaaccaabbcbbbadbcacbaabdcdcbcbcbadbbdccadbdcacbbcdacdddcacabcaaacacbacdbbccabacabcabdbcdbccabaabacdcbbcdddaddddbbdcaadcdccbddbaccccdbcaabbcbbcbaccbcaabaccccbccadbcdadabbbcaadbbdcdcdbdbaabcbbbabdbdbccadaabcbbbaacddcacbbdaccbacadbbcbcdbbbdbadccdbcbbdbcdadcdccccdcabadccdbacccddbadbdbccbbdaddbcdbacdcbadadbbbdbabaacdadbadabccdbbbddbbdbbaaaacacacbbcdadbcdcbcacdadccdcabdaadbabcdbbcbcbaccdaaccbdabbabdcdcaadbcdbbbbacccbdaccacbcbabbccbdcdaadcdbcacacbdbbdaddacaaaddcacddaccbbbbcabcdadaccababbddbcabaaddbcabbdaabcddcbddbbabaacbbaabaaacccbbadadcdcaaccbaccbdcabdabcccdababdccdabcdbbdbbbaddabdadccdbbaccdaabddbaadaddbcccaacbdddbadccabaadbdacbabcdccdaddbcbcaddbdddbbcddabadaabbdcbdcaddbacdadbbcdcadaabcdabadbccbcdacaadadbbdacabbcbbadaddbdaccacdcabcacbcbacabcbdbdaacdaaacbcdbaacdbccdadcccbcabadccabbcdbddadbccddcddbddaaccadbddbabbcbbadddcbbbbbdbacddacdabccbccabbaddcbbaccbcdcddbcbcddcbccddadaadbdcbdbdbcdabdacddbadbbabdcdddbacaccdddbcdddbcccaabcbcacccdadcbabddabdccbbbcbbbcdbaacaaabacbcacababddadbbbabaacbacbdcabdabbcdcacdcadbaccbcddcccbbbcabcabdaabbaadbdacbbdcaaacbdcdbcdadcbdcccabddddaabadccbbcaabddaaddaabbadacbaddadcadacccccbbcacaacdbcccbddcddbbbacdadbddbadacabdcccdcbddcbdaddadccdbbcccaccabbbdabbdbdcacddbcbaddcdbbaacddbaabacbdbcdbbaadbccaabcbbbcccacddcaddadbabbdbbbcaaadbbcaccaadbdaaaabadcdacddbcdbcdacacccacbddbdcdccaadccdcaaaabaccabdddcadbacbbbddddacccbbbbddbbabacabbcbbdaaacdccabdadcbaabacbbdacdcabcccdcccaaabccadbddcaddbbacddccdacaddadacdadaacbaacbaaccadbcbccdddbaabddaacbdcdaaccdbbabbbaadbdcdccdbdbcbdabaaddccbcacdaaabcaacdbdcdbdabbddddadacaabdcdccdbababaabbcdaaaccbadaadaccdcadbcbddbadbddbcdbccccddacdacccabaadbaccbbcaccabacbbaddaddaadcbaabbbbbbabbbccbbbdabdabdddcddcaaabaccbbacabbbccadcdbcdcbdaadcabbcdcdcdddaacaabbdcbbcaaabcacbadcdacbaddbdbbabcccabdbccabacbbbdddbdcabdccadddbbbddddbcdadcbadcbaaaabcdacddccabdabcdaabadcaddcbadcadccddaccaddcaacbbacddacbadbcbacdabaacaddccbcaabddbadccdaacaddbcdacbcbadabcbacbddaccadcacaacdddabcdddcbcbcaabbbdcaabcccacbabaacbcddddacbdadcbaadaccabdabcccbcabaabacdbadbacdcccccabadcadbccbaaadddbaadccaadbabbbdbdadcdbbbacbdcadaddbddddcbcabaaacddccaaddddbddccdbadbbadabccdaaabbbaabaccbdacadbadbddabdacadcaaacddcadabcabbccaddcccacdbcdccadadcbddccadcbbcaacddbccacbabbabcbbccadbdcdcccabcdbbcbdbdcdacbcdbacadbdaacababbbdbbddaccbcacbbbabcbddddcabaddbaaacdaabcbccbaabaaddabdacbbddcabacccaddaabbcabdaacadbbadcacdbddaacbcdcbaaabddacccbdaddcccaaddccdddcadccdbcaddcabbcdcdcaaccdbcdbbdbaabcccbcdbccdbccdbbbdcabadbbdcbbcbbcbbcabaaaddbcaabdcccbabcacaaddbaaababdccaaacabbdaadcacaaddbadbcdcdbddacacbcdaacabdccdcadcdcadcabaaaadbdbaddcbdcdcbcbbccacdbbadcabdadbabaacdccdcbacddcabdddacbbaacbcbdaaacababacacabbcdbababddbbacaccaddcaacbccbcdcabadddadabcdadcbddccbabcdadddadbccabacbadbcacabddbdaacbdcdbdcdcbdbcbdbbbbdddccbabbabbdbdcbaacdbdacbdcbcabbccadcbaaddabccddadacabaacadccdddcaddcbacbbaabcdbccabcbabdadbcddccddbcdcacbbabacddbbccdbcddaaccaaadacbbaaaaccbaaaaccbaaabcddbccadcbcacaaadababacddbddadbbacdbaaadccdbadbbbadcadcdbacbdcddcbabbaabaaddccbbcacdbdbdccdadacacacdccbaccabdddabdadcccddbbabdbacaabdbabbdbdcacdacbdccabadadcddcdadccccaccdabbacacccadcbcdbabddbaacbacbdbcbcadbbacadbdccccdccccbdddcdaaccbcbcadbdabadabaadbbddcadbbcbccddcacdcbddcdabacaaabbdccdcadbcbcbdcaacacdddbadcacbabbbbdbbabcaaaadbddbdaabacdacdcbacdadcbcbaddbbccaabcbbacdaadacababaabacbabdbbbccbbcdbdabaacacbddccacbdabaaadbabbbbbaadcbdbdbcacbbcbaabaccaccababacccaadaacaddacdbacabbddccdabdbbbaabaacbcabaaaabcadadbdaadbbcacbbbcdbdbabbbdbcdccabaabdcbbddbbaadbccdaddbccbbbcacbdddbddadaabccccdcbaacdbadacdccabddddcbdadbaaabdccbdccbacacacaccddddbcdcabbbaadbbddccaddcbdbbacbcaddbddacbbbdbcccadbbdbaccccabcaabadaacabaabcaadcacbddcbcddcabbbcbdacdabaabdacdccaaccacbbddacccdababbadccbdabbaccbacbcdccbcaacbdabacbcccbbdcbbcaadccddbbddccacdccbdadcdccdcbbabcbbabcddadadcadbdbaabdbcbbdaacaacaaccdcdcaabadddddbacdbbdaabadddbdccacdcdcddcdcbaabbcaddabccaadadaddcccdbcabddadcbadcdabbcbadcbddabbbdaaacaadbbdbbabacbbbaadcdaaccacbdabbbdcbbbbadbabcabbbdbdcaddacdbbdcacdaabcddcabbabddacbdcadbbdcadccccbdddadadcaccacbdcdcbadbaaccddddacbbdbcaccdbcdcddcacdcbcbdcaacabbbdbbdccbcddbaaccaddcdadcbddbbdcdaabdaabbdbbcdabbbdcaddadcaabdcbbbacdbaabbbcccdddddacabaacdbbddabbdadadbacbbbcbbdccbabbcaccddccbbadcaabdbbccccbbddaadcddcdaabdacdbabcaacaacdbadbdaddabcdacbadbcaabbcccbbbbdddbdabdbdcccbcaddbdbcaddccbbcbdacacdbabcbcdcbaabaabacbdbbbbacbbbbacddbdccabcadbcaacaaaacbddbdabacadcccbacabddbabadcdddcaaccaccdddacdbabdcdabdabacddccccbbdaddbddbcabccacbbcdbcbbbadbcdaddcbcbbdcbacddddaddbdbcdabacacdadcdccaadcdabcaabccababcbcbcabcbdbbccbddbbdbaddcabaaacbbccccddccdccdcdaacdcacadbbcabcdcbadaadcdaabccadbbbdacdbdbaabbccdacbdcdacdcbbccaccbdaddabcaaddbbbbcbbcadcdcddddbbdcdadcbcdbcaaabadcccaacbadcaadadaaabbabaadccdadddccbcaccababcbdabcabcadccdcadccacbabccdaadcaabdccbadcbdcaaadabcbcabcdcbadcddcdbcdcbddacddddbacbaaaacacbcbdcdbbdbababbbbdddadcbbcddbbbbdaaadacaddabbbcabcacbbdbcdddddbaaacddabbaaadabddbcdcdadcdbbaabaadddcadaadccacdccadbadccccddccdaabdadcaccbbcacabbdbadbacbdcadabdabbdadacdcdcabccdddbddcbdadcddddcaaaaabcbdaccdaadbadaadabdaccaddbabaadcbcdccdccbcbcbcdddabdbbaccaadbcbcacadbcbddbcaaaabbcccdadadbaccdbcbbabaaaaacdbdcbabbabbadddcbdadddccccdaadbabcabacacabcbcccbdabcbcdabbacadcdcdabbaacccddbadcaaddbbadbbcbcdbdababdbbbdadbdcbdcdcdacbbcbcabbdbcdcdbacabbaadcaabdbbabcdddcaabcdbccaabbdaddcdddcadacbcddccabdccaabdcbcabadbcbdbdcbdcdcdbddaacddbabacabcaabccbcbbcaaacabbbadabdcaabdbbcdadcadccabdbcdadaddbacabdcccbbaaddabdcadbddcdccdbaaacbccadbdaddddcdaddbbbcbabbaadaaabbddbbcdcbbaabbccbddcacbdcddcdbbcbddbaacacdbbcccbbdccacdddabddaaacadacbabccbbacbbcabacbdbacaaadccaadcbbdbdcbdcdccdcaacdcabcbaaabbcdabccccbabbcbddaacaddcadbbadaaaacacbccdaccdadccbcaddddcdcabbbcaaccdcbbadccdacadcdadccadabdcabbabbcbdadadadbcaacabadcaddccdaaabdbdbddcaddaaccdddcdcadacccabbabbbcbcddbcabadccbdaccbdbdababcbbbaaabddbdcbdabcacbadaabcbacaacccacabcdddcdabcacbaaabaadcaaadbbdbdbddcadbcadccddbbdaaaaddacdddccacaaacbabaaccbdacccacaadcbddcadccdaabdbdbdacdbcdbacbdcddccdcbcbdaddabbcdabbbbccaddadcaaaabacbdbcdcddbddadccacaadcbdccbbcdbdbcbcbbaaadcbbdcacdbdaabbcabcccbbdadbcaabbbdcdcaabdbbabdbbdadccbcbcdaaacdcdcabcacdbbdccacbdcdadbcacaacbabbbddddbdacbabddcbdadbbcabbdcbabbccbbdbbdbbcacddcbabddacabcaddcdccabaccdadbbccabddabbddbacabdbcaccbccbcddcadabcdadbbcdcadcabdddadccadcacacadccaadaabbdbccbaacbaacabbcbabcdcdcdccacbcabddbbcbbbcaaaddaacdcccaabbacdddbabbbcbbabadbcabadddaabccbdcccbcdbabdcdbbcbbbcccbdacacddcbdddbaacdacbdaacdacdddbdadadabbbdaaddacbdcbcadaccbabadcbcdadddbacacdccdbdbddbacdcaacbacdcbdcccbdbbbcbcdbbaacdbccaaadcddcaaadadaabcacdbccbdbcbdbdacadcbdcdccacdacbcdddcbbaabcaabccaacdaadacbdcddddbcdcbaaabdbacdddcacdddacadacccdbcdbaabccbbcaaacbdcbddbdcbdacdbddddabbadcdaadaddacbdbbccbaacaabcbabddddbcbdbbcdcaaabdcdcabadaadadcbbacbcbaabdaacdbccadcbdabcbccaadbbbaccaaacbcabcccdddcdbcdcabddccbbaabcbbbccdbdadcbaddcababccddaaccbdaaabaddaaaaaccbabdacacbaddaddbabddcbcdcbacdbadabaacadbcddbabacadabababbcadababcabdbdaacccbadbcbddddadbcabddcbdbbcacdaadbbbccddcddacccccbacaddabadbbabbcccbaabdbadacbabaaaccaddcbdddaaddcbbacbbddbacadcccccbcadacacbbadacdbadbcbdaabaaccadcadcaaaabcbadbbdcdbbbcdbbdddabcddacaddcdbbbcacabbdabcbababccadddadbcddcdbdadbddddcadbddcdccddaaabbddcbcdcbcdaacccadcbbacacbaacaaaadddbdadaaaadabbaddaddbdbccacaadddcbbdaacccacddcadbbadbaabddbdbdaabdaccddacaadababdbabbaddbbccaaadbdbddcccaababbcbcccddbddcddcddcbaddcdcadacabddcacbbdaddabdacbddbcbdaddacabcdbbbacbbbbdbdadacbabdadcaddadabaaabddaaacadbdccbddcadbccccdbdaccbdbcacbcbbdbbcbdbcdaaabbaddaaacdbcbcaddabbccdaaabaadaaaabccbbcacbaabccdcaabccabdbaadcadaaaadcccddbdbcaabcaadcddcaadbabbdcdccaadbadccbbbbcbdbccdaababdccbacccaadaccbbbdcabbbabbbbbcbaccadbcbbbaccbddbddabdcdbbddacdabdbcdbdbbcadbdbccbabcdcabcbccddadcccdcacbbabaaaaddbdddabbdcbddbbcbcbbcbbbbababcbdcbbbcacdadcccbabdabdabacaababcacbacdccddacbcacbabbaadcdcbbbaaccaadadbbadbddccdbcadaacbaddcbbadaaacaadbaaddbdccdadccdccbadaacbbadacdaaabacbbcabddacdbcbacdacdacadaabcbabaadcddadadadcabcacdcaabcabbcabbcbbadbaacbdcbbcbdddcbbabbbdacdcacdcddccbcaaaaaadbcddadadbbbdaaacdcacaaacaadaddbcdcabccdaaadcabcabdddccdbaadaacdabddcdcaacaaaaccadbdccbabacbcbcbaccbaccbdadbccaabcbdaddcdcbdabdcccbadcaaddacdacdbbcbcdbccbcdcaaacaabcdcccadaacadaddabadbbabacaccacdcaabbddbabdccbccbcbacabbdbdaadcbccbccaacadcdccccacdacaacadcbdaaaccddccbcbddbaaaddccccccdcbbabaddbabbababdbaadadababcbbccadadbcacbacddbacbbadacabbdcbcbdbcabcdcdbbdadbaadacbccaaadcddaadbdccbbcbbcbbdbbddbbaaddaaaacabcdddbdcbabbcbadcddccddcbcddddcbbdabbabcdbbbbbcadcdcaaaddaadcbacdbdbccddbbdacdabddbbadbbcbdbbbcccddddbbdacdcdbdcddbcdaadaabacbbaccdcbbcdcdbdbaaadbbcaabccbbdaaadccbaddccbcaddcbdbacdbababbbacacccdcbcbaccaddddbabaadaccadbddccaadbbbbacadbcadaddddbdbcbdddcdaabbbcabcdcadbcdaadddcbbdaacadbadbaacddcaaaaccdcabccbaabccaadddbdcbcabdadadddabcdcadbadbdcaaaccabaaaddcdaddacbbdddbaacbaabbbcbccbcbdbbbbbdbaaccdacbdbbcabdbbbcbddbbddccadccccabdaabcaddbbbdbcaabddbadaabcbdbacbcaadadddcdbddcdadbdccddabcbabbdbaadbaaddbcddccdabbbccdcabaccaacbcdaaabdadbcdbaccbbbccbdaaacaccdbadbabbccacbbbbcdbddbababdbadcbdddacdbabaadbbbaadacdbcdddcbcdadbbcbbcadddabddcacdcdbdbacbddcccabccbdccccdcdddbcbadddccaaccabdabdaadcbccadbcbdcbcabbaadcbcbabbaaddcccbcacadcbdcbdbbddcaabddbaccddacaabdcccabadccabbaabddcadbdddabdabccbaabcdcbdadbdcbccdaddadaddacaaabaddcddbddaaacdadddabddbddacdbabddbaadacdbdddbbacdacbacadcbdddcbbcbcdacabacbaaabbabbabcbddabbcddadadcadabbbacdbcadbbabddddcacbaadccccdabcbaadcbcacbaaaaabcdbadadacbadaadcbcadbddacaddacaccaddcbbccbdcbdabbacadabaaabdbdbcbaddabcdbbcbbdbcddbbcbdccccbaaabcbcbabddcaabbadbbcdbdadbaabbdcccdcddaacdccaabdabddbacdaabdbbdacbcaaaaadabdcbdcbdcaabbadacbdbbbbacccddccacaadcbdbabcdbaacacbdbcdbcbaddbbbaadbbdaababbadbbbbdacddddaaddbaadbdabccaaadbadaabbcaaacaaabdcdcacbcbabdcacbddadbacacdbbdcddbcccaacdcaadcdccdabaacaddbbacdaddbcdbbbaaaacbdbaacdccdddcccaacdddaaababdbbbacdbcadadbadacaddcbdabaabbcddabaabcabaccabaacbdbdbbbaacdbdcbdaabbcdbaabaabcddbccdbbabbdcbbcdbcdbcdbbaacbcbcbcadbdccbaccbbbcaabddcadbbbbdcabddccbabadaaccbcbccbcbbcacbddcbbacddaadddadbacdcdaadadcbbbaccdabbddbadacbbcdccacaddcbbbcddcdcdddccadadbcbbcdbccababccdbbbabdcbdcabcaaabbaddadcbdddbcdbaadbcadbddbaddcadbccddcddadcbcbbbabdaabdbbbcdccccdcbbdbbaabdcadaaaddcdccabcdccbbbddbdcaddcdbcdcccabcaaccdddbabaaddcdcacbaddddbbcadcadbdccbcbbcdbadbadcddbcacdccdbbbccddbdccabdbbcdacdbccabbcdbbbcccbbcbcdbcdbccccabcddbbccabbdabdacccabbcbacaccacacddccbbaaccabdbcddaccbdbadcbabdcadbddbaccabaadadaaaabcddbaaabacaadaaabbacadccdadbcbcccaacdbbaacddbabbcadbbbccbdabccccdabdabcccadcbdcdadcabbabcdcdacbccdaadbddddbacdcdcbccbabadbccbabdcdbadbcabcabacdcadabdddcaaacbbabbabcadbbabcbccaacddbdacadbdabcbbdbcdddbacbcbacadabbbaddbdbdacadadbddbbbcbbbddbaabbbccdcdddcdbbbcaacdcdbbdcbdaccbbcbacabcdbabddababadabdcdabacdbacdbbdacbabadaacacaccddadbdadbadaadaccbbdccddcbdbdcdaddbdaaccadacabdabdcbdabbaadcabbdcdabdaccbbdbbbcaccabcddcaabbbcbcbdbabcaabbadcbadcbabbdcbdbcabbcbaadadaaacbdbaccbdccddaaacddaacacabddcbcdadaaabbccdccdbcaabadadadbdbaadcadadbbabdadbcbacbcdaaacdabaaccccabdcdcdaccbbbadabcdcabccaaadbbccaabddaccacbbdbabcbdabcbdcbccacbdbbaddcadcbabdadddccdbdcddbccabdcaabddbacbabcadaacbabbaabdbdbadcddbacddbdbbcadabaadbdaadcaccccdbadbdbaadbadcbdbbabdbcbdbbbddcdcdcddbccdbabddacbdcadcdcacacbbdacddbbdbbaabbdcbbacaadaddbddbacbdbdacdbbacbccaabccbbcaaacbccccccdbcadbdcaabacdbcbbddcccccddccddbbdcbbbddcabccdbdbccddaddcacbbbacabaababbacacbacddbbbdbadddaddddcaddadaaabacbbdbbcabcaacabbcabcaabdddcbbabbbcdddcbbadbcabaaaabbcbcbbaacaacbbcddcacabbbcbdabcabdbadbdccbbbbdccaccbddcdabcdbaccaabbdcaaabbbdcbcbbcbaacdaabdcbddbadaddcdbdadaadccbcdadddaaccddbabadddaabaaaacbcddcbabddccadadbabaaccbacacbbdbbdaaaaccabadacdcccadaccabacddacbbbccccccdacabbdbdbdaadddbbababbbbaacbcdabadacaadacddcabacacadbdbdccddcddbcaadbdbbabbcbacbbbdbdaddbacdaaddaddcaaaaccbbbbcbbcabbcdbbadcbcbadddbcdcabcaaaabbabbddadddaabbdaabdababacadadbddbcdddccadddccbcdbaddabbddccdacccabbdbbdabdabbadacdcccabbbbaabdddadcbbabcccaaaccabdccddbadbaabcbbdaaacbcddbbaccdcbddcacbbadadacbcdbcbbaddcabdcccccddabdddcccacddbcddaacbabbadbacbabadcdbbdbcddbcdaccacdddcaabbabcaadcaaaabbacadaadbbdbddbccdbabacabbbbcddaababdbdccdbadcaadcbbaabcdaadbbabcadbdbcbbacbbbaacddbabdaccacdcaaccdbcaaabccdbcbbccdacacbcdacddadbbcdbbdcabbcccddbbbadbaccbbcdaabbaacadacdbaadbdddbacbbcacdbdbacbacddbdbbcdcabaabcbbddcdbabbbaccaacacdbcaccbcabcdbcbdaddacdbabaabbbabaccaaddddcbcacdbcbbbcdadcdacbadadddabbbbbddddddcccbbbcbacdbccbbacbcacdcdababdaabbdadcccccbbdcbaaabccdbbcbdadaadadcdbbdcbbacdbddcbcdcbcbbcaaccabddbbbbdbcabbcbbccddcdbdccccbacddbacbdaccadddcdbddbaddcdbccccadaaaacadbccdcdcccabaccaabdadcabcbaacdbbaccadbcaddbacadcadabadddccacddabcaababcddcccdbcadbacacdaaacabdcdcabbbdabcaacdaaacbcdbadddadcbddbccdbcaaacbbbdabaccdccabdbccaddaabdccabdbabcbdbadbaadbdbddddadcdccbcdaddbacbcbdcbdbaddaddcdaddbddcdbaadadbcadaaaabcbcaddacdbaababaabadadaccdbbbcbaadddddbabaabdcdadbdcbbaccbacaccaabbbacbbaddcaabcabbcdbbabbcdcddbadbdaccdcbbbaaddcddbacadabdbadacbcadbbbaabaadadadcbcabcbccbdcadcaacacdbdaaabadcbcddbbadaacddcacdcccdbdaccdadcacbbaccbbddacbccabaccacdcddabbdcdddccaaccbccadabdcbccddcadcbbacbbabccbaaaccdaaacdcddcdcbdbbddbcdcaaddccaddcdbaacccdacdccacddadaabdbbdddaccbcbcdcaabadaababdadabccbdbbacbdaadadcddacadddbabacadacabacdadcadacdadcadbbbabdbbbdcdabbbbcadccadababcbddbbbdbbbabcbdddbbadcdcbdaccbdaabddccbabdbbccccbaaadaacbacabdddaacbbdbbcbcdbabbadddcabdaabacaddabcbbcdbcccddcdbcaabbaccdabbdbcbabdbbdddacaaddcddaadabbbaacbcabbbcbbccddccacbdbbcbbcbcdadcbaaadbbadaadbbcacdadbbacaccbaabbdaaaadbcacbbbbcaddaacacabbdbddddcbcddcbcbaaccdcbabdddadaabdcbccbbdadcbccddbdbbbcbaccdcaaccadabdbdbbdaccddadacadadbbdcbdbcaccdbcddbcadabadadbcaccaabadadbbccaaabcacbbccdbbcdddcbddbacdcdbcababddabcbccbabbcacadababaadaacbbdbbcdcadaddcccdbddbaddbaacadddcdddcbbdabbbabbdbcbaddcdbadaabaaabbacddddbcaaacaabccbadabcdcccbdaabcaddabcdddcabdbbdbbdaadaadadaadabcabcdacaccdbacbabddacddaddaadaaabdbccbaacbdaccdcbacdacccdadadacbcaababbbabcdccdacdbabdbddaddbcacddbacabbcaccacbacdbcccacabbbccacbdbdadabaddcddbdbcababbbbdcccabbbbdacdcdbdbbdddacaccbdbcacbcddccaddcbcbbabbcbacbbdabbbdcbadcdaccbbbbdcdadbdabaadacadddbcccacddcbcccdcacdcccdddbdadaabcacccbabcbdadabababbbddddaddcaabddbadcaacddddbdcbaacbcbccdcdadbcaddcbddbcbbdcbabbcbbbdadaddcabadbddcbaaacabcbdcabacbdacbaabaaabdbbdbdacbbcbcbcaacaabbbdacccdcbdbcbddddccbcccdcadbbcbbcdadaadddadcadacdaacaadbdbadddacacadaccadbdadbccddbbdcababcccccbddddcbadbbccacdbbccbaaadcacbbcacddabbaabaccacabadadcbdbbdbbcdcbcdabadbbaaabcacddbcdaadddabbabcdcacbadbbacdcbbbddbdadddaacadccbccdaddcddbadbcaacdccabddbbcdaaccdabaadacdaccbaccbadddbddbcbdbbbbccbcabaaabdcddaabbacdaadcbadadccdadabacadabadcaadbcccddcbcdcccaadaddabdbbccbddabbcccbcdcacbccabdccbacddacdbdabccdbbadbbbcadbbbacdddcabbdbdbcbbbcbbbabcdcadaaaaccbcbbadaccdcbdcbcadbabbdcacdabcbabababcaccbdacbcbdbdcbcccccdbdccdbdaaadcccabdbadbbacbcdddacacddcaddcccbcbbaadbcccabdadaaaabaaabdcadcaaabbaababdcbbdadbbcbdcdadbdbdbaaaccccadbdcadccdbcaaaabaaaadddaaabcacdcaddabbadddccbcadabcaaacadcaabacaadbcdbccbcdcccabdcaadbabacccdabdacadabcbbcadcabcdadbdacbcddabbdadbacdccbdadacbcccdbcdbdbddcbbbcadadbbabcadcacdccdbdbcabdcacaddacbcadcbcadaaaccaabbababdbccaacdbadddcbbbbabcbdcdccaddacdbddcbcdccaacbbacaaacaadbbabaacadddadaddcbacaaaddadbcbabdbdcabaccdbcbaadbcbbaaddabcdbaadaabdcaaccacbbbddacddccbadacaacaddccddabcaccaaabacdaccadbaaccccbabbcccbcabbbaddbbbbbdbaababddddbccbbdaabcbacbbcdaccbdccadbcadaddbcbbdbbcbdadbdabcdabccbacbcdccbcdbbdbccdabddbdbaccaaabacddbcadbdaadccbbdabadddbabcdccdcaaadcbdddccabccbcacacabddbdcaabdbbacdaaaaccdadcbdadbdbbdcdacdcadcdbccccbcdadddadcaaacdbaaabbbcadddbddddccacdacdcadddbbcbcabbddccbdbbdcdccaabbcacaaacbcbbaccbbcdacbbccaadadbcbacdccabaaaaaddbbddcbbacbcdbaabdbcdddbccaaccdddabcacbbbcccddcdbccbbabccbcccdccdcdcabdbbdbcdbcdadcbcdaabddacaaabbccbcadccddddbcbcababcaaabcbadcaacddadadacdcbcbacbbacbbdabcbddadccbabbccbccbcbdbcadaadbdbdbbdbcbdacacccddabbbbbbbbcddbbdacbbddddbacbcabbbcdbcddaabcacbdadccacccbccdbabcadadaacadccdbadaabaaaadddbbdcbcdddbcddbccccdcaccadadbcdbdaabccaadbbadcdcabbbacbdbdadbcadbbaabcbbcadacdabdcbdddacaadddaccacabaddbbbbabdbccdcdaddbcccccdadacbabbabbbbbcaadddaaacdddcdccddcadbddbdccbccbadcbdabdcdcddbccbadabbabdbcdabcbaacdbacabcaacadcbacababbbdcdbbbbccdbcbcacadadbbbccdbcbdbadddbbaccabbadcaddcccdbccbdaccbccacaabdcbacaddbdcacaacbcbaaccbbcacddcbdcdcdaabbbabdcbdcabadbbacbbbdbcabadbadcdbdbdcdbbdbabcacbaacabdacddcdddccbccccbbbddbabccdcddcdddbcddccadbcbcddaadbabaaddbbdbdaacaacaddcdbcbcdbaacbddcbaccacbaaaadaadcdbcddbbbbbbadcdcabbdddbcccdccadcbdddcacaaaccbaddaaadbbbcbccbdacbcabacdaadcbadacaadaaddbcbacacacdabbaadadaddddacaadbdbcdcbcbcdaabdbbbdbabcddaaacdccbdabcaccaaacdcdcdaabacaccdbcabdcdcccabdcddbcdddcbddcdcaadddadacaabdadcbdbcdacbccbcdddbcaddcccacdddbccdcdcbdbabbadbddbaccbbacdaacdcbabdabbdaacdadaddadccbbabcdbdcccdcbadddabbcdbdadabccaadbddabdcacbcdadababcbddadadaccbccdabbaabdabacabbbcbddcdbabadbcbbcaadddadabcdaaaacacaccacdddbdaddbddbaaabdcdaccabbddcadbaaadcdacbacacbcadddbbcbdbadbcacbdcdbbbcaddcdbabcccdbbdadcbcaadddbaacdbbdcadacabdddbdcbdcacbcadddacccbabadbbaacddaaabcbcadbadcbbbabaacdabdccbdcbbdadbddcbdcdbaabacaaccccabcdaadddabcbbbaaddacadbdbdbcbcadddbadcddabcaaaddbbdaabbccadbbaabaaaaaaadbccdaaddacbabbbddddcbdddcacdccbabbcdaccadacbbbccabcadcdbcdabddaccbabadadcbcaaaddabaaadbaddabdbcaadbbcbccddabcdabaaaaccbbaccabbbdbdcbcdabdbddbadbcdccbcadcdbcbcbddaacdaddaabccabbdadcdddcbbccbdbdaddacbdbccadcbdacccdccadbdaabbbddcbddccbdbabdbcdbaabdcbcccbdadbdbddababbadbbaccbcaddcddcdbaabbcddcccddccbbdcbdaacaadcddddcacdabadcbdabaabbbabacababaccbbdbadcddddabbdbccbcabcbbccdbccccaabcabbadbdacbaadcbbcaacdbaaddbbbbddabcbbdddcabcdaacbcabcaadbddbacdbddcacdbbdcbadaaadcbcdbbbcaddabcbddadccaaccbbdcacaaaddaaabdbcbddbdabcccacdbcacbcdabadbacbccdaacadbabbacadbbcabdadbadbbacbcbddbdccccddcabaddcaccbadadbdccaadddcbbbaaadabcdcdabcdcbaccdbcaadbddcdbaacbcaadcddcaccbbbbdbdadbbaacbcccaabddcabbdddddadcdddbdcaaddaaccdadcdccabbdccdbddbbdcdadbcbaacbcdadbbabccadbdaddacaaacbacacddacdaaaabadcbbadbbbcaacaddaaabccaaacaaabdbadabacbbdcddbabdadccbaddaadccabdbbcddbdbbabdcdcdaacbbbabbbbdcbdcbbbcdcbabdbcdbccbccbbdabccdcaaaadccbdaacaccddddababcdaddbddddbbdcadbcdccbbcdbdbadadccdcddcdcdcbcacbbdccbcacbbbcdadbcbddddbabdbabacbcacccbaaccddbdddaacdadcacbcdcacdaadcbcdcdcaaacdddababbadbdcabbaddcbbbbdcdbaddabaaabbaaacdcacabcbbbddbabadccdbbbddcddaabbdabccbadcdccdaabadcbccdaccbccdbbdccdbccbdabcdadaaadcacababdbbbdcbccdacdccbcddaccddddaadbbaddacbdaddccaddbdbacddacbcdacddbbaacbabacadaddbddabacdadacaacdddcabbccaabddcdadabdbcdccddcbcdacbbdbcabaccdbadabacddaabaaacaacdccaccbbacdbadcaadcbadcbbdcadcaaabdadcdabbbdddcadbcaaabcbacccdccdadabbcdcaddaabdcbcdbaadbabaadccacddcbbadbaccdcaaabbcbdccaddaacabbdbddbabaadacbbcbdbdaadbdcabcdccbadcdddaacccdcbacbaccdbbdbccaddcdbcdaccdcbdcdabccccbadabdbcbacaccdbdbdcadaddaaaaabcacbdcdadcbccdbaccabcccdaadbbaaccaabddcbbccbcbadbbbdcccdddabadccbdbbbaaadbbcbdaccdccabcbacbaaccbabaabaaacdcaaaddaccdbaccdbbbbdccaadbcaccdccadddcddcadbcdbbbbaabcaccdaacbdadaabcdaaabddbcaadadbcaabdccacdacbbcaaadbcccadbadacacddbabbbcabcacbcdbbbbaaccaaacdbdccdaabaddaadbdbccbdcacbdbccbdcdddaddabdcbbdcdacaaacbcadbcbbcbbcaacdbcdbcbaacddcbcdccdccabcadbdabdbadabcbbcddaaccabdcdcbdaccdcbdacaaacdbbbdcdcdbcdbaccacbabbbcbbdcdaaccdbabbdbbdabccdcdbdacddbccabcbdbdbbcdadccadabdcbdcdcbdcbbacccdddcccdadbbdcbddcdccbcbadaccbcbbababcaddddccbaaccbababaddaababaddccbbaacccbacdcdbdcbdadaaadacaccdaabcabcbaacbbbacabbccbdbcccadddbcbcbdcaacdddbbbbdcaccdcdbdadbdbbbcdabbadcdbdaacbaccdaccbccadccbabcaaddcababbcadcddbcdbdadccccdadaccbadcdaaabacaaabccaabdbcbadadbbabcacbdaadbaccbdadaadddbbabdddcbccaacadcadaacbbbcdcaaccadadcbbbaccbdbdaadddcbabcadbbabbbccbacdbdcacdcdbcddcabccdbdccadcaddbbcdaaadbbcbabbcdadcbacdcdcddcadcaaaddbbcabdbdacdcadaddbbacdccddccdbaaaaabcbbbbbcbacdccbdcddaaccbccabbcbcdcdcadbbaddadddadabdaaccbacabdbaaaaadaaadbabacddabccadcabaccbbaaabdbaddadcdabcbadaaaadddbacaaadabbdcbcdcbaacdbaaababcaddbbbaddcbaadccacdbaaccbbacdddaccbdadaccdcaacdcccbacbcdbadbddaadcbacdcbcdaacaadcccadaacadacacbbdacbbbcccaacdbddbbaabaacdcabbaabbcbdabacbaddbbbadcdbdcacbbacabbacdbbbcbadbdcbdbaddbcbbaadbdcbdacabcabbdbadcbddabccdbabbbddcccacabaddcabcbabcbcacaaabcbbbaccbdbacddacdaacbabaabbdaabbabccddbbcccdccbacdbbaabacadbbddacbbaaacacadadbaadbdadbcbdadccdabbdacdcbaacdddbdbdcbcadbabbcadddcbcddcdcbcabcdcbcdbcadadbdddaddacdcdadbdbdbacbbdadbbacdabbbaaccbcdbabbaddacdcdaacadddabaabddbbabaccadaacdcacabbdacaacccdcdbbacddccabccdacadbdacbcaddbaaaabdcabcdacdbaaadadddddcccbbaaaddbdbddbddabbadadacdcbacccdbddadcccacadadbbadbbdbdbccbdccdcaabdcbdcbbdbacaddacdddbadddcdccaaadccccdaddbbdcbabbaaaacbacabcadacccdcdabdabccabadbdcddbdcbcdbdcbabbddababcadcabcabacdabbcdcdbcbdcbbbaaddbbadddcbabbaddaccdaaabcbddacdbacbacccbdabacdbaddadbcaccabdadcaadcccdddaaadbbaaadcbbdaabbcbacddbdabadbcdbbbbbcddbccaabcbcbaabdccdbccacbdbaacbddadaacbbcccbddcdcacbdadbadbdccdcdccaaaacaaaddbaacbababcbbbdadbcadbaddbaddbbadcbbdbaabaaddaddacbaacdcbddbdcbadddcdcdaacbccabdadccbcaababbbccabacabdaaccacbccccdabddaccacaadbdcaadadabcdbcacacacaabaacdbdddcbbdbcdbdcdccabbdadbaacacabdbbcbaadbadcbdddccdabbccdbacbbbdddbbcdbbcaaabbccbccbdacbbdcbacddbadcacdaddbddbcacbbcdcaabdcccdabbcdcacacadbbbcbdadbaaddabcdddaddccacccccacabcacadbaaacdadccacdbdbcbbabccaabdccbbaabbabbbcabdccbaddabcdbdbdddbbabbacbaddbbcaccdadcdcbdabcdccbdbbdaaddbbcdccbbcbacbbacccddadcddbacbcbcadacdcccacbadbabbbdcccccabadbdadccddbbacacdbaccbdadacbdacbddcdabcbcdcbbdbddcbacaabccbbddddddadaacdbbaadcdacddaabcabccadbacacddaabdaadaccbdcbabbabcbabcacdddadcbcdacacdabdccdabccbbacabcabaabbcbdccaabddaddaacddcddabbdcbaabbababcababaaadabbbbccbddacaacccddbbcadcdbcdbcdbdcaaccbdbbcbdbdcddcadccbaaacbdbcdcdadabdcdccadbaccdcacadcdbcdbabaccccbdbdddccccdcbaaddcabcaddbbcbadcaabaddacbaacacdbdbdbbdcdbdddbadcdccbdbcbadbcacadacdcacbbdaddbacbcabcbbadcbdbbbcbacdbccabbbdccdcabbabbacddcdcbcddccccddddcdddbadadbadadcaaddbccbddaccccabdacbbaaacdccbcccbddbabbbcaaaddbabadabaadacbbccbbbbccbbcbdbbcaaacbcabadbbbbdcacdbdabbcbdbadcadaadacbacaaaababbdccaadccbdbcbacacbccbcadacbbaddccacabdbcaaabbdbbcbadccacbdccadadbdaacaddbabdbacddccbbacbdbdddcbdbbacaabaadccabbcdcaabcbbbccdcadcbacbdabacbdcddacaacdbacacdbaabbccccadadcbacdacdcdddcdcbbbbccbcaaacaddaacdbdcdbcbaddabcbcacadbcdaacbdccdbcdbdcdadacabaaadccbdbbdcddbdbabbabbbadaccacbdcaaadbacddabddabccbdabbacccdccabcaccccbaaaacdbdbddabbdbbbbdccdccbbaaaaddcacbaaabdccbabbadacdcbdaadbabbdcbadcbddacabcabcabcaaccdcddabbadbcbadddabcbbaadcabbcbddbadbcdcdcbddccbccacdbdcdddbdcabbdaaacabbadacdbdbbcbadadcdacacdaddcdbcddcdadcacaddaabdabdccccbdddbacddcbcaabcbbbdabdaddcaaddbcdbbbcdccaadaabbdccdbbccdabbbdbadddaaddcbcaabbdaccbdbbbccacabaadbadbccdbdcdcdbcbcdadacacbbcdcdbacabdcccdabaccccaccaabcbdabcaacbccbcdbaddcbbacacdacbcbccbbdcabcccacbdbaaccdadddbbdaaccacccddbdadddabacdddbabcaadababccddbbbccadacdacdaacbbcbdaabadcccdbaaccacbadbadcdbcbabdbcacdabdcacbcbcdcccdbadabcaddbccdbbcdabccadacaadaacbcbcaddaabcbabdbbaccaaababbaadacbaaacaadbbdadaaccabcbbdbbbacadcbdacbdbbbaccccabdacbbbcacabbdcddbdcacbaacacbbccacacddbadddadbdddaadddbabadcbbadcaadbdbcdadaabbcbabbadbadbbdacdbcbbbbcddccccadaccbddaabbcdcdaddcbacccadcbacccbadaabcdaddccbababaaddbdbbdcacabcabacdaaadcdcdcdbaacbacbbbbabcdbcdddbacbdbbbaccbacadadacacdbadacabaacccbaabdacdcbdabcabdbacbddaadddcdadabbcbdacaddbdddabcbcbacbdaacbddccddadaacdadbbaadabdbdccbbaaabadaaddabcdaaabbddbbaabadcbcaddbdbcdbdcbadcbabbcaccadbcaddbdbdaabbbdbabbbbcbbaacbbaccbcdddadacbddbddadacbbcbadadccbccaadbbbadaacadccbddbbbcdddaacbbbcdccaccbaacdddcbbabcdcaabcbaccbabdaaadababbadccbadacdcbbbacacaabddcbcadacbcddabcdaddccacacbabcbbaaacddbbddcdcacdccbaaddaabbcadcdaddaadabbaadbdaccbabadbbccbabdcabbbdadadcddcdbddcbaabcbbdaaacadaccbdaadcccccabaacbcbcbdcbcccccdcdabbacabdccabbbbabccabdbabbbdcbdadbbabaacbabccacaddabbabacaabaabcbabbcbbdaccbcdbabdcbddadcbadadccadcadaccdaacbcaacabaccddaaaaadddcaadadcbdcdabbbabaabbabbcadddcccdccdbcbdccccaaaddaadaadbbddcaccdaaabbbaccacdbdcbadacccdcbabbbaacbdaaccdbaaadaabcaabadcbaddbacbdaacabcbacaabadbccacaaacdaacbbbaababaaccbcccacaccacdbadacacbbabadbddcdadabdbbbdabbcdcccabbcdbcabdaadabdcadbbbcacdddadcbcbcbadacaacdbbcdccbdbbacdabacaccbaaccbccddadabdbddcadcbbddcbdccadacdadbdbaaaadbbccbcccaacadbaadacbbcdacaacbcdbdbcbabadaaabaadadabbdaabadcdcccbaccbbdbaacadabbdcdabddabaabdaaccaaccadadadbdbddccaaabddacbcabdabcaabbaadccacaacadababdbddccaacbcdbcbaadbddabdabdccdbbcaabcbdabbbaccabaaaadbbaaabbbdddcbcabbdccdccacccdadddcaabadadbbddcbdcbbbbbddbdabbdcaacadacbcbaadadbacbccacbadacddadcdabddacbaddaaaabdabaadbaadadacdcdbcbcbaadbaccccbbcbddbaacdaccabdddcbabcdcacbdabcddacdabbbadcdcbaacacdaacccdbadbaabcbcdadaaacbcdabcadaadcbbacdabadaadcbbdddddadaabdbcddbbdcbddababbbaaabbabdcdbaabccdcdaaadbbdcadbbdbdbbabcabbccdabcddbababccaaaddaaaadcaababacbbaabdccddbcbcabbbcaabbaababdbcabcbcddbbabbaccbbbcccaadccdbcadcacddcbabdcbbadbaddcdbcbbdbccbdaacbabddcaaadbbdcadcdddcbcddccbaabddbbccccdcabcaabbcabdcbadbcbbcbaccddabbbbdccdaaadcbddbbcdabcdcaddbaadcdadabcaabbbbbdacddbcbadadbcbbcabcdbcaadacdadcaacccacadadccaacabaacaaadbbdaabddcbaadabadaaddbddcacdccddcaabcbdbaddbcbccacddbdaddbddbddabcdacddadcccbcacaacdabcadbbadacdaddacdadbbabdadbacdbabcaddadbadcbabbbacdabcbdbdadaddcbbbcdbbdabcaadbcdbadcababadcbdbadadabbaaaaaabdabbdbddcdcdcbaadbddcbdadddacccdadbdcacadcabddcddbdbcdadbbadcdbbaadcabddaadbcacbabcacdddccbabbabdcbaacdcdbbbddbaabcdbddcadbcacacadadcbaccaacbadacbccbcabcbabcbdabccdaddadabcdcccbbbdacabcddaabacacdcaddbdddccdbbdaaacdcbdcbdbbabbbccbccdbbdddcadaacccbcdabbaacaccbadacdccddbaddbacdbadcaacabcacbddbdbacacbdbbdcbbddbbaddddbbdcbcaababdabbbcaccddddaadaabcaccddabbdbdddccddcddabaadbbdabdabadadaaabacabdacdbabcbacbcbbdccdacbcdabaccdddbbcdbddadddbabbcbdddddadacaadaddabcccbbadbdadcbadaaacadabcccdcbcbbadccbabcbcbbadcbbdcdabdcdddddaaadbaabaccddbccdbddbbbbdbabbbdbdbddcaaddddcacaccacbbdaabacaaaadbddcbccbacdcdccdaacacddddcddcbdadddcdcddabbcbdbabdbcbccddcbdbaadcbadaddadbdcddcabbddcdddababbcdadcacdabdbccbbadcacddbcdaaaaabaaabdacadacaddacdacbcbcacbddbccddadbccddacadbcbbcbadacaadccadbddcabbddadcdcadcadbcbccccdacaaddadbccdaaddbaabdccbcdbdbcdcdadccacdcbddddababcadddbadacbcabdaaadddddbbcbabcababbaccddabaaadaddcabdaaddcdcdaccabaacbcacbbcddcdccdacddbbbbabdcbbcaadcbcadccdbddabdbabcbdaadccacacbdaababdddabcdaddcbcdbcdbaccaaccdccbbaabbdcacdddabcbcbcbcbbdcacdaacbcbddcbddadcbddbcbdcdbaccddcdcddbbcbcbcbbdbcbdcacddddbaccccbdcbbdcbabcdbdacbdcddbabcbcabbdaadcddccdcbccdaddcabdabbdbccbcdaaadcabacbdcdcdadabadcadbdcbdbcdddaacccccdcacdbccabaabcabadabbdddbbacddcbdcdcdbcaacacbcdbcdccacaaaddbdbdddcdbcabaabbccbaccabcbabbdcacadbbbdaadaabdbdcbdacccbaaadbabbbabbaccbccacbbadbdcadbbaaaaaaadcabdcacabbcbaacabdadbbabacaaacbbabdaabaadbdbababcaadbdacdbabccdbccdbaacaaabbaccacacdbdacddbcbcbdcabbaadbcababcbdcdcbddacdaccacdbabdbdddcdbdcaabbdaddacabaaadcbaacdbbdcadaabcbbdaacbbdbbcaacccacabbcdbabdccccccadccdbaaacdadabbdbbaacbaaabbaadbcaabbbaabaabbbcdddccaabbcdbcbbdddcdbdadbbcaaccbbbcbcaaabdddbdbcaaacdcbddcbbcbbcddbbbadaddacbcbdaddbbababccaccbabccdacaaadbddbbdabcddcacaaccbbdaabaacdacabbddcbbacbadcdcddcadcbdddcbcbaacacaddaaddbdcbcacaaddddcccccddcccdacbbbbddcabccddccacadbadabaacbbdababddbaadbdbbbcadacdccccaccdbcdaccbdcbaadaccbdbcabaabacbccbbcadaacacdcdabbbbddadcadbbdcdbdbadddabbbccaababdabcdcadcadaaadbcbdcbabdbdcacbcccdaaaabaccadbbacaccdbabdcdadacdbcabadccbddbcdbbbaaaadbbdacdbddcabccddcdabcabbccadcddbbddbacbbddddbbcdcbbcaacccbdbbdccccdaddaabbbabbaabdddadccbdcddadccadaadcaadbcbbccbddacaacddaaaccacacbdbccdcdcaddcbaccaacbadcbcccaccaaadbadabacccdbddadcacacbbcabdbccaaddbbdcbaddccdddacbdccabbccbadbbadacbddccaacbaabdcadcbccbcdcddabdddaddbbddadcbaccbabdcaaabaacdbabbcacbaacbbccababbabadacdadadabcccbabddddbaccccbbddcdabdbdacdadbbdbbbaadbcbbcbddaaaccaccbdbdcccbadccacababadcbdbaadbadaddaccbcbbcbbadaccbccddcabcbccbadddaaaabbbcddccdadcdabbabadcbdcbadaaacbaccccdcdbcdacdcdcabaabdaabcbcadccdacddccbcaadbcdbacbcabdaacdcacacabcdcdbacbdccadacababccadddcbddbcbadbcaaaabbaacadcdbacbcddabaaadccbbbabcdacbabadcbddccbcddaacadacbdadbbdccddcacaabaccbadaadbcdaacddaaddadaaabbbacccdaddddadaccbbddaabbbabadbccacdacbbcdacaadacadaacbbcbcaabdabbcccbcbaddddacdbdcbacbcdcbbdcacbbabdcaaccbabababdbbdcdcaccbdacccdddabcbdadccddbdabdccaacbdcadcdadbbbabbbadabddcadcdbcbaaacbbbbbccaccbdbaaaddcacdadbcadbdadddccacadaacddbdcabdadcaabcdbaaccdaaccbdadcbbacdbaaacdaddacbbbccdabcbcabbdbdadaadbdcbdddbacaaacbaccbdacddcdadadabbabdcabdccbbbcdadabdbaaabacbddccddbbdccbbdbbcabbabbaddbbbbbbcdbdcababddaadaacddcdccdddabccdacbaabbdbbdabbbdbbdbaccccbddcacbacbbcbacaaacadacdccddbcaaddbadbbbacdadaaaddccababababacbabdcbadbcccdcbbdccbabaaaabdabacacdacccdccdcbdbbccbbcbdbbdcadacbabdadddbcbdcbdcadadbcbddaddbadabcbbacdabbcbbbdbdbcacbdccacbdcaddaacacbbcdabbcdddaacdcbcbbaddcadddcabdbcddbdabdacdadbdbdcdaadabdbdcadcaacdaabaadadcbdcdcbacabadccabbbbaabbcadcadccdcbdbdbddcdcdaabccdbcbdababcbcbdccbdcbccbdcbccaaacbdccbddbdcaacdbdcadbaadccdacaaddaadbdcdddacdbbcccbaccdaaddadaabccdcbaadddccccbcaabbbbdadddbcacdababbdbdcbbddbddabbccadcbdbabaabddaddadcabdbdbcdbacabcdcdbabdccbacadbbdabbaccdddbcdcbbdacbcbcddacdccaaddabaaaabacddcadcbadbbbbadaccddcdccbbadcacdaaccacdbdcdaabcadcaabbaadbcacddcaccaadcbddbddabbaadcacbdbddaddaccacbdacabddadcbaacdccacacadcdbbdadccbcbbdadbddaaddbcbadccdaccbadabbacdbcddbabbcddadadadcbbccaabdaaabadbdbdcadadbaacddadcdbcdccbaaaadabddddaddcaadabbcccddabcddaaadbacdbaaaababadccccadcdddaddbdbcbcabdaccdcacabbccdcbdacdddccdccbddbadccacbdbcbbbdaddddbdcbadcdacabcbccabdaadbabbbbacabcaadddacabaaddddcacccdcdcdabbcaadccbbdbbcabadbcbbaddbdcbcbcdcccddabaabccdbdcadaaccbcadbaccbaadbdaccdbbdbabbbcaaddbdcaabbcacdbdaacdcdbdabbabbbdcaddcbaacaddbbbcdaacaadaabaaacdcbcaaadcaddadddcddcdbcabcaacacadaccbdaddcdccdcacbbcadcaadddccdcdccbbaadacacdaccbcaacbdcdddcaacdbbcbbbabaddbacddcaacdcdcbcdadbbdbacdcddabacaabbbcbadbaacccdaabdcadbdcbcadccbabbcccddbcaddcccdabbcbbabcddbbdadadcbcbaabdaabacdaccdabadababdbdccbaddcdcddbabcacbccaaddabaccdbababbaadcbcacbbcabcdccbdaddddccdcabddaabcadaaccabacccacaabaddbacaabdabdddbdcbbadaacabddbdaadabadbadddbbddaadccabcddbbabbdcbabadcbbbbbddcdbddcdababbdacccdbbbddaccddbcaaabbdcdaaabcddabacaaaabbbccdadddbcbacadaaaabbbccbbadbcaacaabadccbddadcacdbbabadbcadbcbcccabaadbddbcbacbcbcdbcdbdcccdaabbbcadcdbabadbcbadadbbaddabdabcccbcbbcddabbdcababbdabcdcadbaabcddabdddbabdbcdacdbbbbcbdbabddaddaddabababdbabbadcccbbdbdbcbccbccdaabbaccbdbbcadcbdbabdabbcbabcadcccaabaadbccdbdcbbdaaccddcaaaddcdacbacddabdcbdababcdacbdcbdccccaacacacbadadddbadbdcacdcddcbccabccaccbcdaccdcdadabddacadddabdbbbaaabccdbcdcccbccabbbdcaabbbddbcdabdabaccdcabcdbcbaaabdbacccdbbaadcbdcbbcacacdbadcababdacdabbacbadbaaadccadccdddccaadcddbaddabcbcbddbadaddbdaaabaacadddacdccbbdcbababadcbcabdbbacbdabbacadbaadcbabcaccabbdadabadccadccddcdcdacbcccadbddbbcdcddddaadbbbcbbcaadbbcbacaabccbcadbacabdcdddaadcadbcbbbbcaadabacadcaaabdaabddbcdabbbabcaadcdbcacdaccbbadbabbddbdbbacbadbbbbccdbdbccbadcdbbccaccadbbbdddbdabdaacbbbbcacbadbcbdbcbbcdcacdcaacaabaaacccaadddcddbbccdcccbccccaddbdcccabcacddcccbdcacbccbacbdbbcacaacaccdddacdddaadaadbcaabababcaaacccccdcabbbbdcadddcdbdcbdbdadaadccbccaadbdcbdaaaadcbbcacbbcdcabaaabbcaaccbacbdbdcaddaabccddccdbbcabdadbcadcdabcdbaccdddcaabbcdbdaabbdbacdbdadcddbaddaaabbbdbccbacacddddcacdbdddabccacadaacccbccdddbdcadaaadbddbdbdbccdcdaadabbcadcccccaabcbcbbdcdcddcaccaddaabcbbdbadcbcbabaabcaccabaabbbaddaaccadabcbbbaddcdcabdbaaccdccddaddabbadcdabacdcbcccdadcdcdaacababcdccadddcdbcccddabdddbdccccbccdcdddbcbcdbbdbccccaddbadcaadbabccdbadbabdcbbcbbabbbbdcdcacddadacccccbaddaadccbdccbdcdbaddcababdcdddbddbaddcdbbbabccaacaaabdcdaccdadcadcbcadbbbabcbabbbdadcdabacbbbbbabbbcadbacbddccaacdbaddddbabaaababbbbccbadadaccdcdaabbcabcdaacccdbaddbddddcbcdcddbabbdabddaaabcbaaacbdddaddbbacdbdbdabccdccbbcadddbaadbdadacdcccaaacaaabaadbcacbbadacccbcadbacabccdbbcaccbccdbbbdadddbddccdaacbacdabaababbbacbabdababdaaabdbcbabbdbbbabcdbcbddabbabcdbdadcdbaacccbccbadbcadccdaabdbaabdcdbbaddccdbcdaaccabbbdddadbcbdaaaddbaabccbccabdadddccbadaccddabbcadbacdcccadcaabddbabaabacacadbddccabbcbaccaaccbbdcdbbcabcccbbdcdbdbcbdadaabadacdcbabbacacddbdaaccababbcbbddcdcccbaabaaadcdcbddbbcaacbbcbbdcacdbaaabbdbdaaddccaadaacadbbbdbcdddbadcdcabcdcdbcacabbdacdadddbcacccbaaadddcddacdabbdccccbddcdcdddccadcbcccbcdbcbbadbcaabcabddaacdaadcaaacbdddbadabacbcabddbbbcacdccbccbaaddaacbaaacacbbcdabcadcdaadbbaadbdbcacbabbababaacdccaababdbcddcbacaccadaddaccdbdacbadaddbcbdbccdcccdbdbdcaadcdcdabdacbbabcbdaddbabbbdbcbcbbdbbacdadabddabaadbdbccabbcddcdacadcbadcacbbaaaddcdbabdcbcdddddbddcdbccaddcddbddaddaccbbbdabcbacdacadccaccdbbcddcbbcacaddddabacccbdbadaadacbbdaaddabaacaccadbccbdaadccdbbadbbbbcabbbcbcdbcbddbbcdaacacccbabcbdbdbadbcccabacddcbbdababcaacbbbcbadaaadddadcdbaabccccbacaddbcbbddccaacdacadccddbbbddabaabacbbaabcdcadbccbdadadcaaadbdcbcabacbdaababdbdccbcbcaabcbdaaaddaddbcbcbbcdabdbccbabadadaddaabdbaccdcbdbbaadcbcbddcbcdbdbabbdcccadbaaddcddddcbdcbbbdddaddbbbdabadacdabbbbddcccdcbccaacbbcbddacccdbadaccbdcacbddbadcbcbdccddadcbacbbbbbdacccabadddadddbaddabccddacbbdbacacbdbdcbdacbabacccbdcdcbacaddbaaacaabbaabcddccbcadcccabbdbbdcacdbdcabcadbdaddbcddcbcabbaccbaadbabcccccdbbdbdcdbccbdddbdcdabbdabaddabddcaaccbddaddcbbcdbbdcbbabbacbbaabdaccabaccbaccdcbccbdabacbbaddbccbdddacddbcdaddbcbadbdcbdbcddcbaadaddcbccdacccababdbbcbaabbacadbbdabbbbdcbbaaaddcbdaacddddbcabaccabdcbbddddaccbacaabbbbabdbbacbaabcbacbcdacadaabbcababbaccbcccdbaddadbdcdbdbabdcadbbcdabacddabcdbcabbadbbdcccabdabccccbcbacaccdabccaabdabdbacccbadcadcccddddbdbbaaccbbcdacdaacdbccbbdbadbcccbaaaadcdbabcbdadbccaacbddbcdbdcbbbacbaadbbcbcacacadaadcaacdbddaadccbbaddababdadbaacdbadbbbbddcaadacaadbddcadcbbaccbbcdccdbaddcddbcbadbcbcbdbacaacbcddcabbbacabbddaaacdaadcbbcabadcdaccbbadbabbbdbbcbabbccdbcadcbaadcabbacdaddcabdabdcacccaabbcbbdddbbcbdacabbbbdbbadadadbabadcaaddadbdcbcccdddabcaadbabbccaccdacaaacaaadabadbcacdccacbbdcadbacddabbcacbaacdbacbdcdccdacbacbddaaadabdbcccbddcbbababccccdcbababaddadadcbbabcbabbcacbbcabcbcaaaaddaddaccacdabacaadbacabbbcbcaacdcaddbdbaccbaabcaadacdaababbabcadabcbbbbbcccbdbaddacadcdaacaddaccdaaabbadaabdddacddbcbacbbddacadddbcccddbcbdddcdcbcbcddcbaaabbdbbcbddbdaabbcbddacdaacabccbccbcaaaababbdddadbcaaabbbabbccbccdcddcabdcddcdbddbcdcbcacdbdbbcaccadbbaddbadababdbbadaabdbdbbcacaacaaaababdddadbbbcadbaacbaadbadaaadadcbdbcabcddbdcadbcdddbdacbbadcacabbaaaabcacdaacddbbccdcadacadaaddbcddcbcadbcbcdacbbacabbadcdacaabadcbbaacdcbcaaacccccacdabbcdddcababcbcbdccbdaadcabdbcabaccbddbadaabcdddbbccabbdcdbbccaabddcaccbacabcdaabccdbccbbdacdaccbaadddbcdbdcacdcdabcdbcaabbabcdadcddacabcdbadabcdddabdaddbcaadbccaadcaaaccacbbdbdaacdabcbdbbdbdabaaaabbabaadccbddabbcdaccdcdaadcadbcadadbcbaaaabdbdbcbbcabdddadddbccddbdaaaadbdcbaccbdbdccdadcdbbcdccbcadbdcaacdcabbacdabbabddbaabccdacccdcaadaaddccbbaacbccadaadaddcbcadbcadddcacadcadbcbbbbdcabdbdadaddbbddaaddcdcadbcbacadbdbdbcaaccaacbdadbdbccbaacabccbcdaacccbcddabdddbabaaccbdcacdcdbccadbaaabcaaabaddabcccbdabcbddccdababcdabdcddbbadbbadddcddddcbacddaadcbbabcadbabdcbddaabacdcaccbddbdddccaccbddcbacdddcbdacadadaaabbddcbadbabadacadcbcbaddcacdababdbbcbaabcbacdadbaddbadcaaabbbdccbbacacadcbbbdbccdbabcbbabbabbcccdbdddacbdccdcbddbacadcaabadacddcbdbcdbdbbbadabaabccbdaabcbbcbbbccabdcbccdbbcaacacaabdddcbbddbcacdbaaccbbbabddadadcacacdbadbbdccdcbdaacddcdaaccdbabaadaccbbadccbdacadbbaddaadddacdadadcbababbdcbdccbabdaccdadcbaddadccbbdddadbdadbaaccdbdbdbddabdaadccdbabbdddabcbbbbadbbcaabccacdababddabcbbdadabbabdbdddcdddbaddddccdcabbbdbddbbcbcaadbbbdbaadbaadaaaacbaaaccacabdcdbbddbbdbaabcbdacdbadcabcdbdbadbcdcbbbcbbacaadbdbbddabbbbadddaaddccaaacbbcaddaddbbadbdcddaddcacddddccbcbacaddcccddcdadbdaacdcabbbabadbbbcdbbcbdcdaddcaacdbabcdcddadbdbbbccbcadbcddacbcbccaaabaccadcacabbadadcbcddcbdabbbbaaddcabcbadcdbcdcabbcccbbdcdaccaadccbcdadbcaadddabdbbbadcbdcaccbbaaddabdbddaccadaadbcaddacbdcdcaacdbabbbaccacdbadbbaacaadcaddcdbcbbabbabbaddbcabaadbbbaadcdbacaccacbdddcbacabdbbacdababdaccaddcccbacdadbaadacdcdddacbadaddadacbcdcbbbcbbdbacdbaaddaabababaaaddaaddaccbabacdaacadaaadaacbdcbcabacdddcdacdcbabaccdcbaddabdadbdbdbddccacabadaccaccadbdddaddbdcdaddaabaaadbadabdcdcacccbcdbacddbddcbbcbadabbddacbbbccbdabcbddcbdadddbdbdbccbadccaddddbbdbccabadaddbbadacaabbaadcbbdbdbbacabcbbabcbcdacdbcbdacbcacdddbaadbbdcbddaccdacbbcddbaaabdcbadaabacbbadabcddbcccbdbadaaabcbadcccbdbbdbcbbadaccdcbcbabacdacccadcdaddaadbdaabbcbdcbcdadabdcabddaadaabbabadbcddabddadbddcbdbdaacacdccbcdcababbddbdbcadacabdcbacdabccbdcbcddadabcdccdaddbbdbdadddadbacabcabdaddbccccdbcccdcddbbcdcdcddbdcaddbbdbcadabaadaabcacdbdbbbcdacdcddabbbcbbcbbdbcbaacdabddbcdcbcccccacaadcbcaaccbddbbadabbadcabbbdbcdacbdbaddbbcbdbadadacbcdcdbadddbbabaacccdababdbdbadadaaadcccabccbbdacbaadcbdbacdddcdcaabbdddcbbbbccdddaadaddabcbdacbabcdbcaddcabdbbdcdbbadbbbcdccadddddcacdacdcddddccddacabcddcccaaccbbabbbdbadaccbcbdbdaabadddddcccddcaabbdbbabbabbbadbcadacaadbbbacadaaadddcacbcdcadccbdadcabaaadbcbabbbddbcabbabcacdbbadcccacbddbcdbdadacddcbabcbaabbadbcdabbddcdacbbbcbddbddabdcdadbcbddcdbaadbdcacacbccdacbdbbaaacaadacccdbacbabddcbaabacabadacccadddccabaabddddcbbadccbddcbcacacaadaabbdaddbadbbcdccdcdbdadaadbbbdbcddccbcacaabbbbcbdabbcdcdddaccdacaadcddcbccccdccccacbdddacbdbabcddcdaadaaadbccbcadbdcccdcadcbcacdcccddadcaccaaaadaabacbadbbcdabdacacdddacdbbacbcbdbdcbcbabdaadcccaaaabaccddbbbcbcdabcaddabcdcdbccabcbcccdbbdbccbacddccdcbcabaccbacdcccacbcdbdaccdcdbdbaddddabcacaabbcacbdbaacaacbbbcbbabcbacadddbbbcdddbbaccdbaccbaacbacdaaaabcacbdabccbbcacaaabaccbdaabcccbababbdbbadbbabdcabdcbbadbaaaddccdbbccabbdcadabdcbdadcababbcabcbcbcbabadbdcdadbaddcdadacbcaabbdbaacccabadcadccddaabccbdaddabdcbddadbcccdcaaacdbddaadbddcdabcacbcccbcdadbabcccdadaacadaadddccccdcdbcbcdbbdccacdbcabdcbbabcacacdcbcabaadadddbdcccdacddbbabcbdaccdbdaddaabbccdbddadcddabcadcddadddcacdbacaddcaacbbdbabbccddccbcaaabacbcbbdbdccbbabdcacababaabbcacaacbddadbccccaacbdadbbbadaddbbacbbdcadcdddcaddcacbcdabdbdacbbcbddcdacaccbbbccaaccddacbabcbdbbabaddcbcdcbdacaaacdddcbdbbcbbdbdaddcadaddacbccaccccbbacababcbcbbdcdddbbcaaaadccbaddcbdbbcadddacbdcccbbcacccbacbdddaabdcdadcdadbddcaacbdabccdbacbccbbcdacabdbcbbddddccbbbbabacccdcabcabbdadccaaaadbabdddaccddcdcdabdcabdbdacaccccdbcdaababbacacaacdaddabcdabcbccccbbbcadddddacbdadcbacacdddbaadddddaabbdcbcadbbdcdbddcabbdacadcdbaabcddbbcacadcadadcbcdddccacacdcbacbbaadbaccdababbbbbaddadbddabbcbdcbcaabcababcacdcddccccbdccacacbcdccaccdaacccbacbabdccdddbdcadcdcdaaaccdcdddcbacbcdbabdbadbdbcddacaaabdcabadbabcccaacacbdbccbddaabbbdcccabadaddcacdabaadadabcdaabbbdccdbcdaacacacacdccdaabbdccaacbcccbacadaccaacacbdabdcadaacccddcacbbbaaaadadcacbbdcadbccbaabcbbdaabbbdbcdbcddcdbccbbcdbbbccaabbcaddbbbdbbcccaabddcbcbadddbcccdbbdcccabcabcdaabdbdbcabbadaddbbdddadcddcacbbddccacdcbcdcbcbdcbbcbdcbbaddaaaaccbdddcdbbdbbdaadaaaacbabcccdcbdaccbacaccbccaddcbdadbbbcbddbbbccbcbadcaacdaccdbcdcbaaadcbdbaadbbccbbdaaadadccacdadcadcbcaadbcbaacbbacbccccbaacdbbddcdbaccbbbddacaabcccabbdccdabcddadbaadccadccdddccbddbdbaddbddacdacdcabbbcbddccccdbcbbabaabddcdccbbcdadcdbdbdabbcdcbcbcdadbadcbdbcbbdbaaacadbabaacbddaccbbacdadababbdaabdbdbbacbccdcddadadbacbcddbbacbcabaaaaddbdcbbcbabbdbcabbcccdbddddcacadccadbbacbbdccaabdaddcabbbdbddaaddabdbbaabbaddaaabcccadcdbacacbdcadbaaccdccddabcadadddadcabbbbacbdadcbdabbaddbbbcdaabcccbcabaaaabccbbabbddcaccbbbdacccaaccccbaddddcadddbcbdbcabdbacdbccdbddbaaddacbaabddaabaccadcdadadaccaacabaadacbdbcbdbcbacabdcaaddbbcaabcdaccacddbabcbcbaccdbdaddadcdbbbcadadcdbaccddaaaadcbacbacacacdacdcdcccdbccbbdbccabacbbdcddaccdabdcbadbbbcbdbdaadbacbabcbbcabdccbababdcacbadaadbacbcdbcadcdbdaabbabcdbcddccaaccddaccbaddbabddbaccabddcdabcbdbaccdacbdcdaaaaadccbcdccbcdbaacbabbbdbcbdcdabbaacbadbbdcacbcccaacbbcaabbcdbcaccbaddcdbaacbdcbbaaaadddaddadbbdcaadbbcadbbdbaadadbcbbdababbdbabaccbaacbdadacddbcadcccccbdcaccaacaddacadcccdaaaabddbcbcbcacbbddcadadcdcddaabbbaadcbadabbcacbbdcabdcbaddcaddcdddacccbabcdbbbdbdcbaabdaaaddcdddddbcabdcaadcbdcbaaaaccbaaabccdcdddabaccccacddaadddcdbbacabccaccbadbcdcadbaadddbdbcdaacaabbaccbdcbcddbbadbbddcddaacdbaaacaccbcbaccdcacadcbdabacaabcadaacadbbdbdabbcbaddacbbcadcdbcddbbbddbdcaaaacdcbdcdaddbaadaaacadddabacdbccabababacbbbdaabdabdbcadddcacccbdcaabdbcbbdcabbbbbaccbbdbaabacadcdacdbdacdcbaacbbbbcababdcbcbaaadadbbbdacdbbaacdacabdcdadaccaaabcdccacccaabbbaddcdacccbccbcbbdcaccddcbadaadcaaaacdcbaccbbacdcabdabacbcbddbcdcbbddadccdbdcaabbdddbdcdcdabcbdcdadadaacbbddbdadadbbbdcacaddbcaabbabbdbaaaadcaabdddbcdcddbcdcbcadaccbdcabdcdcabaacdbdbdadabcadacbdbdcdccabbaacdadccdddaadcaacaaddbadddbcbbcabcccaaabccaaddbdbcdbbabcddbcaabdbccdaadabdccdcbdbadabbccbccdddcdcccbcdaacdbcddbcadddbacdddbbccacbaaccbccdacadccaabdcabcbcddbabbcccddbbabcacddbacccabcbbcacabcdabcdbbabccadddbdacdacccababbcbdaadcbbaaccdaacdccabccbbcbbcabcdaccdadbaabdbabbcadbcccddbcbadadcabadacbddddccccdcbbdcdadbbadddacbccabaaccbbabcaadacbcdabbbaabbbbdbcaadbadccaaadbdccbdbbddaacbbdcbdbbbddcacdaddbabbcadaccbaadcbdaaccaadabbabdadaabcaacbddcbcdadbddbbbabdacdbcccadabababdacabcbcdbdcaacdbdbdddcabcaacdcbcbabbabcacdabbbacddbdabccbbdbddbdaadabcbabcdbdbadaddcdbdadccdddcbdbbbdcddbbaaddddbbaccbbaccaabccacbdcccadcbdbcbdbddbbbbbbdcbdcbdcbcbdbbdacccaddbadacadcbabbaadccdcacbadadcbdbaaabadddadcddccabbdbdcdbbddabcabccddcacdbabacacbbacdccaaadacadccbbdbabbcddadccacaadbddcadbbcdddbbabdbddadbdabadbcabbdaadccdbcabdcdbddddadadcabdccbbadacccbddbadbccacdcbcbbdcaaacbddbadddccbbacadbadadbbaabcaadccaccdcbadaccaacdcabcccbaadbddddbbadccadacbbcddbdaadcddbaacabcbcbdbaadddbabbacccbbaabadaadadaccdaaccdbaabdcaddacddaacabbcddbaabbdbdadaaccbcddcddaccacbcdcbdcdabbdbcbcccbdbbcdbdbaccababcbdacabcdadacccadbdbdcbbaacbaaccbddbdadaaadddddaaccadbccbbcdbacbbdcdadcbbdcdaaabdbaaaabdaabcddbddbcacaaaaacbacbdcbccaddbdccccadacdbcadbadaabddcaccdbbbabbbbddcadcbdaaddacdaccdbbbbdbcaccdbcdccdccbadcbacbbbccdaabcddabcbdcdbdbcccbcbcbdcacaacabacbcccdadacaabccbdaadadbaabdbadabacaadbdddcbcbdabdaabadcccbcbabbbcbdaabcdccbdabbcabccdccabddacaaddabaadabacdbbcacbabbdddadadccaaaacdcdaadabdbdcbcaddacccbcdabaddcbdaadcccccdbbbbdcdadddbdcbabaabbcbabbdaaadbabdddadabdbcbcdddcddccabddddacbcbbcbddaaaadbccbddadcacaabdbcadadacacdcbddbacaccbddbddbcabcccdbddabbababbbbbdbbddbbdabccdaabcaacbaacddccdbabccdadabacacaadacbddcdbdabcdaddccbdabbbcdcaaadacaaaacdbacbcdccdaadcacbdcbadcdbadcbddbbbcdbadbcadcbacdcdadadcdacddbbdbccadbddbcdaabbaabcbbabccbcbdcacaabbdcbdcbccbaaadabbbcbbbbbadddbadddcbcacbbacddaabdaabcdbcacdbbabcdddaadacbdaadbacdbbbbacabcabbbcbdddcdcacacbcadcaccdbaacaddcabdacbabdacdbdbccddcacaddbccaccaadbbababbabbabbddabbdcccdadcabbcaaddddcabcbaacababbbbcabbcdccbbabccacdcbadcdccbbbbababdbdacaacbcacdbdcbcaaadaabbdbbbbcdbbbcbdbcdcbdcccccbbdababdbcadcbabccabbadbacdbddabdbdddacbdbbcabccbdbdcddcdabdbacbbdababbdaabbdadddbbadbdccdcddccdacbdcdbbdbbbaabbaabcbbddbdbacaabcacddccbddabdbadcdbcdbcccbccdcabbadabdbdcccddcbbbbdcddcbcacdababbdaaacdccadccadbccdbacdabbadddbbcdadbaacbdbabbddcbabbbdaddbdadbaaddcdbadacacbabbbadddddabadbdabddaaccabdaddbbdbcaddddcbddcddbbddcbbaabcccccdbbbbdbdcdbdadbabcdbbaacabbdabbdccdcdbdbbadcdacdcaabbaddabdccbdaabbacbbdbdaabcabbadbacbdcbadcbadbbbddaddaabbdcaddadbdbcbcbcdccdacadcbadadddacbccdacddcacbaabcbabccaadcbcbadcbaaddadbdbddaaacccabbaadaaaacaddadddacddbacdbabcbbccaacddbcdccbabdcadadddbbdcddbbcaadadabbaacdbdabdaaaabbadddbbaccbacdcccbcbcabcccddbcabbbaacdacacaddcdddcbdccabccbcdabcccacdcdadbdaaaaabbbcbdaacccdbaacccddadabddbbdbcdabbbdbbcbaabacdcdbcbccccbbdbcbcdabadabcdabcdaadadabbdddcbddcccbacaccbdddccddaabdcddcbdcaddbadcdaabdcdbbcdccbdccdcdcbacdabbbaddcdbdcbddccddaaadacbddadcacacddcbcaacaaccdcdbbcdcdcdddcddbdccacaadabbbcaadaddaabadbbabacbdddadcccdbbbbcacdcccbadcccbcaaadbacacdccdbccbabbdbbadaddacdaaaccdcddabdcbcdcdcdcbddcbbadaccbdbcadabaaaaccdccddbbadcbdbccbdbaabdaddcabaacccaaadbaadcddbdcdcccdcddbbbddbccdadcccbdbbddbccdcadbadadadcbcadddbcdabbbbbadbddccadabbbdbdccbcadcaacdccadaccbbdbcdcbcbbddcadbaadbcabaadbaaacaaadbdadcdaadacadcdddbaaadbddbcdcabdbabdadbcabadcbbbdbabcaabdddcacbacbddcacbabcbabdabccccbddacdbababbbbdddcbcdcadccbbcddadacccbaccaabdbbdccddbbaabcaaaaabcbaccaabdbbbddbbdbcaaaaacddbdaaacaddbaadcdcaddbcbaacabacabcdcbabdccbacbdccdaccdbabcadcbcdabbadadabadccdacccccadbbccacaabdacddadcacdaacacababddacbbcdabaabdbdbbbbcadbaabadbbcacaadcabddadcddcacbcabdcdabddaddddddadacbddcbacadadabcdccabacacabadaabcbcdacabdcddbacccdcdcaacabadaacdabccbaaabcbcdcacdbdaacccbaadbabbcbdcbabbabaaabbdcccacadaccdcbccdccaaaaabdcdbacacbbccbccaaadbdbabcdcbacdbacdcbcadcaadbdaaccccbabadaadabdbacacbadbacdcbccdbbabdacacdbdcdbaacadcabcacadbdcabbdddaddbcabaabdbdaadcbbccaccbcadaabbcbcbdadcddacdaadddbcacdbdccbaccddcadaadabdadbabdcadacdbbabcbaabadbbdcbcdddaabbddcacdbddcdaddbacbdcdccadbdcadbcbbacdbadcdcaaddddaacdabdbbcdababdbcbbacddcadcabaacacdabaacccccdddadcdbcccbcbcadadbcacdddbcdcdcacaadaaccaabacadbaddcbbbccbcddddddbbdaccbcacbaccccdcddbbcbdbdcadcbddbccaddabbccbbcbbcbcdcacbbcdddabccbcbadbacbdacbccbbbaaccbbabbaaaaccccadaaabdacdcdadaabddaacaabdcbaccaabbaaddabddbbbdcdaaddbcdaaddbbcbabbadabcabbaaccbbbcdaaacbdcaaacdcbacaccbcddbcbaccddacadbabdadadacbcbbbdcbcdbbbdbbdcdcaaabaccaddbbdcdcdababaccbacadababddadccdbddcabddcabacadbdacdacbadcddbbccdbcacbacaabbdccbbcbaadadaaabababcbbadcbbdccccdbddccdadbdcddcbbaccdddaaccabccaccbabdddbbcdcddbcbadcbdbddacccdddcadddbacdabccccdcabdaaabcbadccbabacababdacdbabdbbaabbbacddccddbadaadcbbccacbcacadcddaddabddbacbcddbddcdbbbbbdddabdaabaababbbacaabadadaacadcbcdabcddbcdacbbcdbabddbbcbbcaaaaddcdccbdbccbdddbadcbcadcbbbaacdbccdcaabbcadaccbddadcaccaccbbdbbcbadccbacbabbddabaccdcdbdadacbdacaadbdbadbbbbdadabccabcbdaddbbbcbbacabbbbadddddccabcdccdccdbbadcdcdcdcdabaaabaadcaddbcadacabdcaacadaccdcacacaaaaaacbabddbbdccaccddbdaabdaaabbbbabbbdaacddcadddcdcbbacdcbcadabacaabcbbbddbcbdbdccccdccbbcdcddddbabccaabaddcbdcddabbdccacacbcdabacbddacccabdbddbbdbcccbcbbbaacdadbdcaadccdababccadadbcbaabbbcaaababddccaacddbaaadcdbccbbddacbbdadcadcbaadaaadbcabdcbbcbbbdaacabdbcaddacabccdabaaacdbcbbdccdadbacdbccbbbcbaddbcbdbbdcbcdaababcbbacdcacbccddcdbcdbbbbdbbaccdbdcbadbdadbcbdaddbcbbbddaaddbbbdddbadaabacacdaadbadaadcdcdaddbcbccaccbbbcbcbdaccaddcacabcacdcdcdcdbcaccdbbaadbbdbbdadadbbddcdcbdacccaddcbabdddababddcbddcbcdcacacaadbbaabcaccadccbddabddabddccbbbaccacdabdbcadbadbcaaaddbcdacbccccbbaaacdabbaadabccadabbccccdbbadcdacaacbbabbacaddbabbbcabccabdabcaabcdccdddaddadbabbdbadcacddccaccaaadaaadabcdcabaabdcbbdaccabcdbaccadbcdcbcdddaadcdaddddabaaddcdbdcbbbcccbadccaabccdadcbabdcadbdbbcdabcaccbcadddadadadbdcbdbbadbaadcdcacadbccacaaadadcbcbcbccabdcdbdbdadbdcbabcddccddccbbbddaaccbbcbcdddacddbcadccdbccadbbdbacbabcacdacdadbcacccadbdaaddbbddbbdcabcababbaacccdbbadddddbddcdccbbccbcadadadbbdcdbcbcaacacbcabcdbabbcddadcdcadbdbdbadcdbadadcccacdcddabbdcbcdabccabbcbcaccdcdbdbaadbcacacdcdbbcacbaddacadddcddabbddbbcbbdabaaabbaaadadcdacdcdddbccbccdcbdaddadaaddbddbbccadccccdadabdadbcbabbaacdadaccadbbbbdbcaaabdddbabcbdccbdbccabdbabbddbccdabcaabadccdadddddbcadacdcbdbcdbbbccacddadbdccdbdbccacddccbbdcbbdbbcddbaadbbcddacbdabababcbaadaadbccaabaddacddbbbaadddccbacdcbdadaccaabdbcabacbdaddbdabcadbbacabbcabbacadcbdcaddcdcbddcbcbbcadddccdccbcbcbdacbbbdbcbbbaadddbbbccbaccddacabbdbdbaddcdcdcbdccbaabcbcccabacdccbccbbbabdbcdddccdcbdbadccdccaccabddcbcdcdccabddccacccdacccdabaadaabadbcaccdcdcccbbcacdbbbdccdbdaddaabdbdabbbdccddbadbdacdacdddbbbadaccddadbacadcdbcdabdbcabddabcbcabacddddbdcdbcaddcdcdccaabcadccabcbabccccadccdbcaccdbacdbcacacabdccdddcbcbcdacdaaaaccdbdcddabdddbdccbacdaadbadbbacddabadbcccabcddbbbdaaccdcbabcbabcdbbcbdabcaddaacbddbccbaacbdbccbccdabdbccdacdcdabdacadbcbddbcccdcdddbbccdcadbcdadbddcddddccadbadadbcabcbaacdbbdddccbccaadbcabdcbabdbddddccdadaddbdaddbacabccdbdadaadaaacdabacadbabacaaccbcbadacbccabadcccbcbbccaaabcdacbcdbbcbcdabcacacddabbabccbcabdcaabbdbcbadaddbbbcdbbadbabbbcbcbcabbcbcbcaaadaaacaaacaabbbaaabdacacbaccbdadacbdbccddadbadadaadcbbaacdabaaabdbbdcabcadadbbabaddcdacaacddcbdaccbbbadcadacbccabcbabcbdacaaababcccadcadddcdbbbddbcbabdcbcbaaacadbcbbadabcabacacbdddaddacbbdadacdccdaadccbcdabcbbabdaabaabaacbdcddabacccddabcdcabaababadbbccdbbbddbcdccbaddaccbcadabbabdcadadcadcabbbcdbdddaadbbbabacaadcdbaadbcdbdddacccbddbadbdaadadcbbbcddcdbcabbdcbcbbacbbbadbdbdbdddcbdaddccdccdbdcdcbcabbcabbacbccadaddabcddbcabbaadbdcdacbcdadcbdccdbacbbcaabdddcadcdbaacbdbcdadbbaaddbabcccbccacbbcdcbcacababbdbcdbdddbcadddaabcccdbabacbddbbdbacaadacccbacdbcccdddcbbcdabbcbbdaaddddcddacbdacddbabcdcdcbdcacccaaaddcabcdacacdcdbbcaabdccdbccbbacabddddcbdadccdccddbdbddcacacabccdbadbddcbcbbbbcccadcdadadbdcadcbcaabdbdcdaaccbadbddbcdbdbdddbacdddddbdcdaddddbccaccbccdbdaccaacbabdbbcbcbbcbcbddbaddcdcbcbdacbabdcdabbccdadabcccbcbdacdcbccadbdacdcbdaadbacaddbbabdcaddcdbacdbaddcbacdccbdacbbadbddadbbcbdadbcdaadaabbaaadaddabbddcbddcddddbcacadbbcdcdcdbcabadabcbbaaabbabaabacbbadbbbacbbabdddadccababdaaddbadbacabacccddbacddabbaadadaccbdbcbaaaadcaaacbdcaabbcddbbcbccabbbaadbbcddbbbccbabdcbacdcacdbdbdccaaddbdbdbacccbccbcbabdcdaadadaaccbacbcdadacccbcbdccddcadaaccbdccdccddaaadbdcdaddcaddddaddccaadcdabcdbdabbdacbcadaccbaabbbddcabccddcddcabbaacacddccacabcabaddcdadaacdbbdccdbdbdaaacbddbcbdcadbabbdbdbdcacababdbdcbccdcaaaddcadbdadbddaadcbaadababddaacbbadbbdacccdbdbbbcadccbdabccccbacddccdcbbbbbdbacbbbcabacdddcbbbacbddabaaccbaacdbcbcdcabadcdbbbbcccdcabacbbbccdddbbdabcbdcbdbccbddadaaccbdbccdabdcbacdbbbdddcccdcabcbbabcdbaabaacaadcaaccbcccaaadcadbdddadbddabbbbdcccddbbdbbaacbdbddddcddbbabbbdadccaaabaaabdcacccbcacabdbcabaababcacccccabcbdaadddbdcbdcabdbadbaacdbddbccbdaabddbbbcaddabdcdcacbbadaadbaadcaddccadcbadabcaabdcdbdcbabccacdbbbbabbddaddcabcacacaabddbcddbacbbcdadacdcdabddbdcbcbbcbdcaabccabbdcbbbaadbddabdddcbdabbcababbaadccdbcbdccaddacbbbbdcbaaddccaacacabcbcaaabbabdcbabcacdbdbccadbbcccbdbbabcbabbdcadbcccabcccdbdcadcbcccdcddabaabadddcdbcababcccdaabdacccacdcbbaaaadabacdbaccbaaadbaacdddabcaadcbbbdddddbddcddcdaddcdabdbacbaaabbcbdbabcaaccbdabccacdaaaabdddcaccbddabcacaaaadbcddacbcbbbbdacaccaadccdacbacddbbbcdbdcbdccbccbddcddcaddcddccacdccddbbadbdaacddbadbaabcdbaaadcbcbcaaaabaccdbbbccbdaddcdbbadddddccdbabccdcaadcbaaaddacdbcbacccccbadacacaddccbaadbabcadddbbadaababbdbddccddddcadaddbdbbddbbaadccabaddbabacabadbbbacacaddcccaddabdccdddadcdbabdbbdbccadadbcbabaaadbcdcdddcaaaddabcacaaccdcaddaadccdcabaaadcdbdabaccaaadbaccabaaaddadcddacabdcaabbabcdddaaccacbdbbabadbaddbabbbbbababbdcdbcdcababccdaccccbaccdadbdddaabdabcdbbcaaaaadbdadaccccbccbdbdbdacbbbddccdcabaabaadbbcabcaddadadbbccccabaccddcdcddbddbbbcbbabbccabbacadabcaadaabccabbddbdbdddaacdacdbacabbdccbcabbcbccdcdcbcacaccaacaaccabbddccccacbdbcccabaabccdbdcaacdadbdbbdcddbccddccbcaddbddcacccbbdcbddabbbaddcbbaacdcbbabaadaabbdacaabbdbcbbbbbabdcddacabaadaaabbcabbaddbdcaabbaccabccccaaaaabdcdbbcacdadaabbbcbcabdccbcadcdcccabcdabcddbaaaaaccbbaccaaccaddcdadcccbbcaaabbdbaccddaddcaabddbabddddaddaadcdbbdcdddcaccbcdaaaddcddadcdbdbbdbbcbbabcbdcddabaadccbadbdbadbdbcacccaccbbbaacaaabcccccbadcadcaddccbaaccbdadcbcbcaacdccbbccdcbadbbacadcbadaaaaadadcbaabbadacbddbbddbaaacddddccbaaabacdadcdcacccbacbdabbbdabcababbdabdddbbddbadcabddaddcaaabcadbcbadddaccbdaddbcabbaaacbbcbadaacdcaddcdabaccabadddccccdcadbcaaadaabbdabccbbbabccaaccbbbdbdbbccadbcbcdabadabbdbbddccadabcddbccaabacbabdbcccbdcdadaadacbcadccbbbbaacacabacdcbbbdddabbadddddacbbcdbccabdcacabadcbabdbabacaadaadccabadbdcaacabbabcbcabcbddbaadaadadbddccbdcdddcbdbbbabdbdacccadccacacbdbabdadabccaabcacdcbccbbbcacbcadbabdccbaaddcdbbaaadddcddbbcdbadccaacbadbacccadbbcddcacddbbccdbaaacbcbacbcbabcbcababdbddbddbacaadcbddbcabcdccbcacdcdacbbbabbcbcdbacabacacaabacbbdccbaacbbbadbdcdbdcbcbcbdbbaacbccadbccdcbcdccbabdcaacddaaabcdabbaacabadabbbabbbcbcabbaacbbbcaacbabbdcdcccbcbbbdacbacbccaadcddcbdbdbdacddbdabadaccadcaaccbcbacbddccccdccacdccbdaadbddcccbdbabbcdabbacdbbadabcddbcbbddaacbdaabadbbcbbbdbccdadcbadcbacdcdbdcdbcccdccbdbbbdbdccacdabadccdbdcaacdbabbbcbcccdcaadcadbdadcaddbbacdbadbdddacdcbbadacbabcbbabddbcbcccbaadaccaacdacbccddbacadcccdadbaaacdbaacacdddbbdaccadbcdbbcdccdbababaccbcddaadddaadaabadadcdcaabbbdbcacdcbbcaddacbbabdcdabdaccdbdaabbbcaacadccadadbaabdabaddccdcdcbcccacdaddbacaabcdabbdcdacabbbbcabdcabbdcaabdddcabaaaabbacbcccccdacacbbbdcbbbbddabacdaaddacbccadbadadabaabacadadcbbdbadbadccaaadaaccbdcaadaddabdbaaacddcaaacaabaccbddacdaddaadabbdbdcdbccacccdabbddbddcdcdbcbaabaabdadbccbacbadccbaadcabdacdcbbadccdcdcdcccdbdbaababbddbacaadbcddbccdcdbbaaaabdcabcdcbadbdddcaacbdcddabbddabcddbabbbbbccbdaadadabddcbcbadddacbbbadbccaadbddbbaaccbaacdbabacccabcccdbbcdcdcdacdbccbadbdcdaabaccbcadaabcddacdcbddaabccaccadbbccaaccddabadaacdddccabcdbcdcadbabbacabcabaabddbbbdccbabdcbbaddabaaacbdbbbaabddadcbcabcdabbabcbddabadbbdbdaddcadbbababcddbcbddcdaccdaaddcbccdbddddbdcccccbbacdbaacaabbbdbcbacccdaccbccdbdcddcdbbbbcbacabacaadcbabdbcddbaacacbbbcdbdabcacadaaabdbcbccdddabcadcbdddcadcbadbdadcaabdcbccdbbbadaaadcccbcaabaccaaddcdabcbbaacddbccabddaabacbaaaacadacabaadcaccddbadbadbaaadbababacdbccdbacbccadaccaabbdccbddbddabdcabaadcbbaccbddbbabcabcabcbcdabacccdcbddcbcaabadabccaadacdaddadabbabdcbdcadadadcbdcbbccbaaaaddccbcbabaadccdbdbccaacacabcabadaadbcddaacdcaaccccbcadccbdcdadbbbdcdddcabaaadacdcbadcadbbddddbdccbbdabdbaabddbdbdcbbdcbbaacabadbbdaaabcbcaadadcbdccdaccaddaadbdbcadabbdcccbcabbcaabddbcdccbacbbabddccdcabbbbabdddcaabadaabbbdbdbbddadbdbbbabbaaaadbccdcdbbddabcdaadcbdaaccddcdcbdddabcbccdbcaccbdcbcdddacbbccbadcbcabadbaabaaaabbddadcadcbbccbabbcbbdbbdaacdcbddadbcccdddcbccbcaacabcabddbdbbccbabbbcacadcdbbcdadaaddcdccaabbdababddcaddacbadcccddbabbaabbbdbddddbcdaadcbdcbdcdcdcbbbbccadcabdddbdcdacbdacabcbcaaccabdaacdabcdcdbaabbcabcaacacddbcddcaadbadadabbbacdbbdacabbacdaaadccacbacbdbcadcbaaacbabdbcdcbddcbacdcbbacacacabccabdbacaacadcccdddcacddadbbaadabbcaabadbbcbbbdbbbbcaabbbabdbbcccdddbacaabccddbdcbccbbbacdbbcddcabdbadaaadccddcadbdddcadacbbaaabbdddcccbacdbddcaadccdaaaababdacdcadaccdbbbcbaadbadbddadbccbbdcdccccbbbcadbcbdbbcdabdbdbdbadddaadabbadabddbabdccbacacdbcddccbbadaadddacaabadbbbcacbdcacbdaaacaabbcbaddaadcccdaddcadccccdbcbaaddccaaacacddcbcdcdbbaacacaaabcbcddbbdcdbccabcabcdbcdaadbbabcdaacbbddacdabbbadbdacbbbdabadadbbaccdabacbbcbcdababaadbdaccccdccabdcbbdcaadaaaacddbccccabdbcbcbcccbbcbdbdacacdcdadaacbccaabdcbbacbbcdcabdabdadbcacdbbabacbacbbbcdaaddcdacccdbcdabdabacddaadcaaaddcbaacddadacbddabbadbadbbaaabdcbabbdacbaccbabcccdbaddccddccaaababacbabcccccaadacbabaaccbbbbbcddcbcbbddbccddbdaccbdbdbadcccaaacacadbbdcbaadcbdbbddacdccabbadddbccadcddcbbdbbbadabcdbdaadaabcbdbacbbdcdaaabbbbaadcdbcdbbcdcaadbaaadbabacdaabddbcdbbddbaaccdacbacbdbadbadbbdcccdabbdcddbaabaddcdcddbbccddaadaabdccccacacccdccccbcabcbabcccbaccdbbddcdddccabddabddaabccacddbdaddbcdaccdddcacabbbcdccbbcaddbddaabbcdccddbcdaabcaccbbcbcdcddcbcdcbacacadacdcdccacbbdcbccbadadaadcdcccddcdbcccabcaddbaadabbcaadacccbcbcbaaaadacbccacaadadddbcdcdcccdcbbcbbacddccbaabcbbdaabccdaadcaadabcbcacbdacdaddcacacdcbbcabccacaacadcadababdbabcacaabdccaaddbdcaaadcacccaabcbbaabbdacaaadddabacaacbabbdcaacbbbddaacaabcadbddaccdbcbcacdadcbcbcabcbddbbdaaddcabaaaabdadaabbaacdbdabcdaaabaddaaadabdbdbdcbadcdabaacdabbbcccbbaaaaddcccbddcddabcacdcbbdcabccdbbaccbcddaddacddbaacbbbaadabcccbadccabbcdcccabbddabddbacbdbaaabbcdddabbbbbcbbcbabbddddcdbaabddbdaacaabcaddbadddaabbadabdacbadabbdacaddbcaddbcbcbcaadaccdbdcaddbcadbcdbbcdadddadbacbdadccdadddbbadaaaaabcbdcbcbacbdbddcadbdbadbdcbcbbccbddaadcdddbbadcbbaccbddbdbaabadcbaacdbcaabdbcabcadacacaacdddaababaadacdbbbbdbcdadcdbbcbbbdbbccccbccbaccacbbbcacbcdadadabaadaaccaccaadcdddbbddbdcdcaadcdddcdaabbbccbcccbbdbdaccdacbacadddbabadbbbaddbdbadaccdcadabdaccdaaaabdcadccdddaddcbabddccddcbaccbcbacabadcacacddbdcadbcdbbdbccbddbbadccdddcdabbdcccdbbaabbcbdccdbbcadadcaabccaddddaacbcadacdccacdaaccadcdadcabbcccbbdabbcbbbaabcbbdbacdacbddacaacccbaabdcdaadbdcdbdbdaadcbaabdbbbcabcbaaacacabddacddbacbaacdcdddddabccaabbccdcacccacabdaaadcabdccbbbadddbccbacaaacadbcddaabcdbaacbdddabcadacaddaddaccbaaccdbddcadcabbbcccbbacbcabcddacbbaccaadbdbcdacadccbdbadcddadbdaabbbabbbacacdcbdbbaaadabdcbadaaccdbaaaddbccbddbbcbbdbbcddaddcdaadadcabdadccdcddaddbaacccabacbcdbaaaccdadaddcabaddcbcdbbbbbaddcaccbddbbcdcdaacdcdaccdababbaabbbcacaadadbcdcaddaabbbccccaccaacbbdadaabccdbcdacbbbadabaadcbababaaacdddcdcdcbdddcbcbcdaaaddabdddaabbdbbbdddacbadcdbccdbaadccdbacdacdbadaacbbbcdaaddcbdddacbdbddcddbabcadbbcadbabcdbaddadcdcbdabbbccbccbabdddaddbbcbcabbaadacbcbbbcccccdbccddbaccacaccdcaddaddadabadacbaddcbcaaddbababdcaabcbddbcaaaacdacabccaccbaddbdbdaadddaabddddbbdcabcbbabdcbbddcabaccbaccbdaddacaabccaddddadddbbdadadbcccbcbacdbdbcacdbbaaabbabacacdbcbcbdcabcdcacabdcdbaacacdaddaaabdaaaadbccbadddbcaabddabcdcaacdcbbdbaabacbcacbdbcadabddcddaddddddcbcacbbbcddacccdbbaacdbbcdadcaaaaaccdcddaaacbaadaabcdaabacddcdbdabbccbcddbaaabcadddcabaaaccabaddaddacadabbabbdcadaccaabbaababaabcadbdbccbbcbbacdabbdbcbaddbbbbdbaccacccaccddbabcabcdabaccaddbbdcaacdccdbbcbacaadacadadbdbcdbcbaadccbdddbbcbcccbdbdddaacaaaadabdddbdcdddaddddadccdabbdcdddbcbbbbddcdcbcadbbcccbcdbaaabbcddababbccdbbbdaaadbccbdbddcccdccccbcbadaadbabaacbdbbcccbadadbdccbdcaabbddbdcdaccacabcdbbbdbadbccabbdcacbcabddadcdbbabdadacacdcaaabcdacdacccbdbcddbbacdccdaacbdadabbbddccdddcbcaadcacddaacaabbaaaadcaccacacccacbdddcaaddbaacbcbcbbadadbaaacccdabdbdddbccddabdadcdadbaaaccccadbdadcadcdbcddddddbbacacdccccbaabdabcdaacbbddaabacaaaaabdbbdddaacbcaabccbcccdadddabdaadcbacbbcbbbcbdbccdccbcaaaaddbdabdaacbdaadbbbbadacdcddaddadbbabbddcbababcbaddaaabddaabcdbdadbccadcbdbcbbdbddcbcbdbddbcabbccdbbacbccabababaaabdcbcabbbbdcbaabcdabbbbbddbdbddadccdddcbabcbdacabcbacbaadadccacaaabcabadbbbcdcacbddcddbbcccbdbbaabdddbdbacbbcbaccaccdbbacbaaccbcdcdcbcbdcdacbddbddcaaddcaacdcccddbbdabbabbaccbcbadaadaccdcbdcadababcbbadcdbbdadcbaadbdbcaaaaabbcbdccbddcdcccccbbdabbbdbddccdabaabdaaccadabdccdcddaddcdabacbcaabcbdcdddcddadcccdacbccbbabcdadbdcdadcaadbcbbacbdbcacdccabcdbccdddcbdbbdcbbabdbaabccabbabccaddabddccddbbabcbcdbbdaddbdadcaaacddcccbbadcbdcdcadaabbbbcdcabbcdaabbbcabccaaadbbbacdbbcbabbdacbdbcadcddbabccbdbdbdbcbaacbbddabdccbcdcdadbcadbccccaabcdbdcacbbcddcccbacadcbcadddaddddaabdbccbcbbcaadabdcabbadcbdabdddbaacacbdaacdcacabcbabddcaabdbaaabccbbabbcbbcbdbdbabcdaccaabdcacdacacdaddcccdcadddaacacccbadddbdcbbbdcbababbbabddddbcaabbadccbadbbdcbcccdbdbbadbaacdbaadaaaaddddcdabaaaabccdadcdddbbccacbbbdcdabdaadbbdbdabbacadbcbcdbdccdddddcbbbacdbbdccaddacdadbaabddbacdaabadddbdbdbabbccacbddabdcaabadabbbdbabbbaaaacaaddbcddaddbbaaadbdbccbbdcdbccabbdcccabbadcdbbcddabbbbccaaabcadaadbdcabbbbddbcabddccdcbdacdbcaadadbacabcadcccadcabdacbcbcbbacacbadddbdcbbabccbbdcccdadabcdbdbdcbcadabddbcdccadadcaacdbccbcabcccabbacbddcddcdcddbaacdacbdbdbcccbbbaabbacdccdacbcbbcdbdaabdbcbbaabcabaaabbbcabaccbccbcdcbababdaaadcabbaaabdbacbcbdcdbbbcabddcbdccabdadddccacbabcaacdcdadacdbcbcaaacdcabbdbbbabbbdadcbcaabbbdcdbdccbabddbbbcbaaaddaabdbcbaddddaacbbaccdaaadbaddbcaaccdbdccacbcbbacdcabacccbadacacabdcaccbcadcdbaccaabcdcbdcdccaddaddacbbdcccbdcadccbdacdbcbbabdcabcaddbccbbcdabccadbbacbadbdaadcccbbbcbbcbcadcdbcccdbabaddbacbadadddaadcbbccbabaabcdbdcadccbcaacddcbabcbbccbbacbccbabbadbaabbbdcbacdcaadcbbcdcdabcbdcdadabacaaadcacbcbbadabddbdaacabcaddcdddbccdbbcbdabaadbacdbccaacddbdaaabbbadacbaccdaabbabcbacabcadddacadabddcbcabdacdbdbdcddccddbcddbaacbababddbcabccdcdcbcaadaabdcacbbdcdabccdbdcdadcabdabacdcbcbdadaadddcdaadcadccabbdcbdbccbadcaabddccdbdcaabdcabbdddaaddbccdcbbcbacccdaddcadadaddaaabcabdbddccacdbdcabdddbccaccdcbdacaddbacabcdcdcacaddddbdadcdddbcbbcdcccdacbcabbcddacaaacadabcadcacdaabadacbbdcadaccbabdacdaabcdcddddaaaababdcddcbaabcadcbdbaddbdbbbdddabcbcbaacddddbcddbbcacaccdcdcadadddcbddcadbcadbcbbbdbbdcabdabadbbadadcbcddcabcbcccadbacddccdcbcabdabccddcbddccbabcdbdadbdaabbdcdaaddaccdbabdcaaccdbddacdddababadccbdcdabaadcaadbddbdbccddccacdcacadaadcadccaacaadadbbacbbcabaabadcbbbcbdaddadccddabdcabaaccdadcacdaddddbbcbdcbacdcaaabbbcbadccdbdabbbddcabdbacdcbbdbcbcdacddbcdbaddcaacddacbdacabacddcddcdcdcdaacacbaabcbdacdbadacbcddddddadccadbcbdcacbdadababdaabbabacdaaddcadbbcdcaabbbacabdddcadacdbdcdbacacbbdddbadbadabacbdaacaaadbdadabbbaddccaddbaaddacdcdcbcdcccdadbcbbddddccbacdadddcdbaacbbccdadddbadddbddabdcdcadbbbaadadcbddccaabdcbdcdbbacddcdacbcacdbabdbacbacbcccacccbabadbaabcdbddbbcbbadbaaaddadbdcccbbdcaabdcdcccbacccbbcacacabaaaabddacabcbadbcbbccbbaddccaccacbbdbdbaaadbaacaadabdadacddadbcadbcacabcaabaaadbddccdadcbdddbbddbccacabddbbccbbcacbdabbddabadaccccdcdcaabcdddccaadcabdacacdaacabadadccddbabbbbacdadaacabcbccbccbddbbadbabdabbbbbacacacaddacddadddadddbacdbabadbbdbcabcacaadcacaaaaaadddcbdbabdbbbaadaddcbdadcdabbbcdadbdcbdbabadadcdddbbbdccddcbbadcadacdbccdadcbdcaacdcbccbdbcbddbbbddddacbbacdcbcdbbccacbabdcddcbbaacdcacdccdddcbcbbabbcabbbacbacddbaadaacbdddbbdbcdbabaacdaddbbddbcddbcabaadbbcdaccdaddcdbacbadaabbcbdbbacaadabaddbbacdcbcccddbaabddcdbbcabaadcacaacddcbcdbbbbabcddabbacbabdbbbccdddbdcaadcbbcacdcdbdbabaccdddaddaccbabcaaccaddbbaddcbaabdcdcccaddbdaddbdaaaccbaadaadadbdbdaccdbdadddacbcccabcbdabbdbcccbdbaabbbbdccddccabdabcadadccbcdbcbcdacbcdbbbacbbcddaadbcdabccdcacddaaabaacdaaddcacabcbbacdddddcbbcdbbbcadbbdcddbddbcdbdcccacbcbacadbdbdbaccdcabbacbcacbaddcdcabdcdccadcbccdabdabbbbbbcdbddbdcabdcbabddcddcccccaaacddccaccaacbddcdcbcddddcababcacdbdbabddacbcbcdcdddbbcdddbbbcccabddaddaabddbdcbacbacadbdccdcacdcaacababbbdaccdddcabbbbddbaadacabbdbdbbdacdbcadddabbadadcabaaacaccabcdbbbabbacdcbdbccacaadabbbbcadbcaccaddaacbaacacadcbdcaadababadbdbddbcbcbcddbbdbbbcbcacadbbddbabdabdcbcbaacbdadbacccaccaddacabdbacaccabbbcbdbccddacaaabdbaabaaccabcdbdbccadcaccadbbcdbacbbadbcddccaadadbdaccbabbabbaccdbbbaabbbcbcabcaadcdcacbacdabaddddccadacbaaaddabbbcbaccccbbbdbacbddadddbdddaabcabcbdaccaadcbcdacaaccaadabacdabadacdcbabacdcbabdaaacabdbbadcadbbbadbdddcdcacaccaadcdbadbbdcdcddccccccbcbcaadcaaccdbacdddabbddaccdabcbbdaaaaaccddbbbcadaabbabddbccaabbaabaccdaccccbadabcabdbcaadaabdabbabcdacaadabbbaadcbcbdcbadbcacbcbbacbabdcadacaabdcccdaacbaaadbaaadacabbddcbdbcbabdbaadadccdaabcaccaadcbcaabbababdbbbabdcbcdcacaacbadbddcbdabbdcabaacaadaadbaddbabaacddaacabcbadadadabbababbadbcabbbdbbdcabcccdddbcbadcdbbccddcabdaddccaccdbabaccbbbbddcaaccdacbdcbddccdaabddbcdbbacbcacaddcdbcbbccbdcaccadbaabdabbdabacdadbabccaadcbcbdbdadaddbddcccbbbcbcdacbcdaddadaabddcbadcaddcaddbabddcacdcbbbabcbdbaacdcbabbdabbdaddddadbddbcaabdbdaacdadacadbbbccbaaabdccbcaacddcccbbcdacdaaadbcdbbadbcbcabbdbddbacadbcdbccaddacaccdbcdbbcdcabadcdcaddccadaccaccbadacbaaddccbdbcddcaadcacbaccbcabbdcddcdcdcdabadacbdbbcddcddcaaacabaddaacccbbdaddaabbddbcdcaadbccddccdadababbbbcbcdabbaacabbddbddbaccdbbdbbbaccdaabccddadabcabdcadabbadbbdcdddbdcbcbbbcadacabaddacdcbcadbabcacdabcbdddbbaabcdbbdbabbccccaacabbdcadbbcbacadbcbadbbdaadcbddbddbdccdbaadbcadbacbabdcbbdbccccbcdbadddcadcbdbcdbcdbacaabcbccbcaabcddadcabcbcbadbbaabdbdbbabcbaddcbdcbcbaccadadaacdcabbadaddbddaadcdcdadacacbdadbbbaddcacaadccabbdbadcaadacadacdcaadacdababdccaddaaadcacbbbddcddaddbaddbcdbbadccbbbddbcadaccacdbbabbcbdbabdcbdbacdacbdbaaabaaacdcbbcdcadcaadacccdcabbacdcbddaadccdcbaaacadaabbcaaaabcbdbbaaacccbcdcbacddbacacbdacdbcdcdababdcddadbccaacbaadaabdcabccdabaaddcccacddbdccdbbbbcccccaacdbbdadbcdcbccdcbdddabbcdcdbdbbdbdcccddacaaabaabcbdcdcacacabbbadacdbdcacabccddcbdcabaacaaaaddcbcdaaaacbccdcadadbaccbbddabbabaadbdadccacaddbabdacccacccddbddaaadddadbcdacdbacbdbccabdcccabbbbbdccaacdcaaadbbcdadacdbdbcbdaaccababdcaccbcbcddadbcbdbbdcdbdcdacaabddbadadcdaabdbcadcacbbcdcadbdbccbccacddbddcbadcadcbaaadcaddacacdccbabcdcdcdbbaadbcaadbdcaabdacdccbccacdadbcdbdbabcbbcbdcabbbbaadcaadddbccaaddbaaabdabbaadcdcababbdadbbbdcbdacccdbacaacadcdddacccbcababdbcccaacbcacdccbdabdaaadbcdabbcabbcdcbdcaddcbccabdbbbdccdcbdcbdcabcdcdddcbdbdbccdbabccadaaadbacddcdcaabacddaccadabbaaabaabbaadccdbadcbacbdcbabadacbacacbbabcccdbcaddabcbbaadbdbbbadacbdacbbddbddaddbbbccaaadddcddcaabdbbbacaacaabccddacaabcdacdcddcdaacbcbcddcbdddddaabdadccdccbbabbcbcbcabddcadaccacacdcbccdbbbbcccdbbacdbdddbbcdcbdddccacaccbdbcbacddccdbaaccdbddddbcdabbacabaaccaabdbbccaddabcccacdcdadccccabbdabadddbdbddddcaaadbdbacbbdadbcaabacadababcaacbcdaaaacbadcabaaababcbbadccdbacaaaddaabaaabddaaadcbbccccccbbabbcaddaddaaadaaaaccbcaaabdddddcabaacddcadaababadbddcaddbcdbbdabadbaadabbdadabacbccaddacababbbaaadbdacacbcddbdbddabcdcbcbcacbdbadadcaaaacacbddabcadaadbbdbbcaaddbbadccdadbdbdabdbcadcbbaadcabbbcbaaaadbddccdbaccaacaabccbcdcdddcbcccabdcdabcbbccddbbbcabcbabdcaaaabbaddbaacdcacacdcadacdbaabdbdbdddacdadbbbdadbcbacaacbddbcbbddcadaabbcbadbcbbcadaadcdbabadcaacaadababcccccaadbccbadabbbbbdabacccbadcbbbacbdadcdbdcbcddcccdcabdabccacdbbadcaadddcadabbdaacdcddaccaacabcabacaaddbccbcdababaaaabdbdadadcddbabccbcddcccdbccbcbcdbcccbbddbacdbdcccbcadaacdaccdaabddacbababcbcbddbcbccacccaaabacdaabccdbcabbaddbcbcadaadcaaadcdabcaadbabdcdddbcabbdacacabcbbddbdacabacabcccabacdadcdcabacacbbccbacdcbdaabbbddcdaadccdcadcbbbcbabbdabacacbdabcbdbccccbdaadccaaddddcadcddbaadddabddabbdabbdcaacabdcacbddadacabdcbdacadbddaadaabcdadcacdcdbcccbbddaabcaddcccdcbaaaabdacddaddcbdacadcdcdbbdcdcbbdbadcaccdaabbadadbacdccdbcdadbbdadbdadcbbcdccbbaaaabddcbbdccdcbadbbabcdbbcccbbdbacbaaaccbdbacaadabbbdadbdbaacccacddcacbadbaacdadddbdacbbcdabadaccbdcdbaabcdbcabcbdcddabdbacaccdbdcdcdcadabdbcbdcdcadbaabddbdccabbdabdadaddcccadcbbdcaacbcacaacdcbabdcccdaacccbbcbbbacdddacbadbcbaaadcabcbcbbbddbcabaacbbccabbdabdcaaacddbdacacababddcbbcbbdaacddbadcabbababbcaccbacddbccdbccbbcdbaabcdcdbbaabaaaccabbddccadabaccacacbabacdbcddccbcccccadaabddbccacacaadadacdcbaccabbdbcaacdbbabbdcbbacbadaaadcdabbaddcbcaccaaccbdaabdabcacabcbcbbccccdbcaaddcbcaaccaccadcacdcaadcdcdddccabaaabccbabbcbcbaadcdbaddbbbbdbcbacbcacdbdddcdccacdacbcdbadabdaddbadbadcddcaccabbadbbccacdbabcdcbacbbaacaaccabbcbdbbbaacaabcbcadcaaabbcbbacddbddacabdaadabadddacabdbdcaaaacdbcaacdabdcabbdcdadbdacddbcacbdccccddbbcbddddbdcbdaadbaacaacbabcddaddbdbbbcadcccaccddbbcccddadcdbcadabcbcdbbbcbdcadbcbcdaaddcaadbdbdcbdcaacaccabdcbdabaaabaabbdcdcacdaacdcdbbddacbbbdadbdcbcaaaacbddbcbbadcadbbcbbaddcdcdccdccacaabcaddbcddcbcdcaadabcadcdbcaadbcbaadbbbacbdcbacbbbacbccbcdccaacbcbbcbdaababdccabbbbadbcccaddbdabcbcabdcbdddbdbddcbbacccabbababbacbbcddddcdcbadbbcabdbadbbcaabadcdcaccbccadcdcccabdcdacdbcbcdacacabbaccbdcddbcdcbccacabbacbdaaacbdadcaadcccdabbabdcaccadbbadbdddaabddbdcdcabdaabcbcdabcdcdaabdbaddabbcdbdacbdddcdddddabdbcbababcbaadababcbaacacdcbdabdcaddabbddbabbaadddcbabacdacdddbbbadbacddabddccccaccdbcbbabbbbbbcbcdacdaabbcdcbdbcddddabddaaabcdcbcacdccbdddaaaacabcabbcddacbbdcacbaaddcdccbabcddcadddcdbadbcdaabddabccbbbdcbdcddbdddccdcacbdacdabdddddabaccbbbbadadbacccacbcdacacabaabbadaaaddacbabbbcddaccacbcbbccaabbbaddcbdacbbdbbbbabcccadabacccbaabaadcccdccbbcbdddacadddbdcbcbdcdbcbbacbbabcacacbabcaccdcdbccddbaaaadddcbbdcbccbbbcdaddbacdddbbabcdbbbbbbbbccacbbdcbdbcbbcdadacacbabbacbddcabcbabddbcadadbbbacbbcbbbcbbcdaaacdaaaddcacdbbdcdcbaacdbaccadbccaccabdcaaacdbcbbbcdbccbbdcbaddbcdaaacbcbdbacdccaadbcdaabacdacabbdcdbbdacacbadbcbcbcaabbcbbcbbdababcbcccbaadddbcdcbbaddabaabaabddacaaaaccccbccadbccccccddacccacbabdabcacbaaaaddddadbdbacacabdacadddabaabccbccbddaacbcdbbdacbddbabbbabacabccbababcdddcbcbbdcbccbdbddacacdbaccaccccdddaacdababddddbbacdabcdadbddacbccacccbdabcabdcbcadabadcdccabaabdacbbccdcddacbdcddbdcdccccbcdbaadbcdcddacdbdcdcdddbbccacaccdabcacbbbadbcdcdccdcbcdbdcbdbcadadbcdcdadcccabdbdaaacadddadbbaacdcdcabdababbddacbbdcabdbabcadccacccabcbbbcbcadcbcdcdacdcaadbcadbbabdacccdcadacabaaddabdadccdcbccccdabbccdadcadadaaccbaabacdacacaaaaacbbcccbdddbdbccacbcddcbbacaddbdacccabbdabdccbbbbddadccbbcadccdbdcbcdadccbccdaababcabacaadabbbaacbbbabdbaaaadadcbcaddbbbccbabdbdaaddacbdcdcdaccababbbdcbbacdcaddbbccabbcddbbadbdddcbdcdbdbacbcccddbcaaaddbddbdcacacacaccdbbddcabacbbbabaadacdcadcdadaccaabbcdcdbcbcbccbdbaaacbabdbdbcabcdbcdababaaccddcdcbbcacbabcaaacdbbacbbcacaabbbaccbbdabbcadcbabbbbaccbadbcacacbbcccdbbdadcaacdcdadbdabbcacdbdcbaabadbdabaacabacaccbbbbdabddcccadbbbdcdabcdbbdabadaaccccdcbabbcbdaaccdbbbdaaacbbbdcbcddcacbdaadabbdccddabbbabaaabcacccdaaacbdbbcaaddcddcbdccbaaabdbbccaaddcacadcabbdbbddcbddbccddabbcddcdcbdbbcbdbcabcdcddbcacaaaacccaacccdccbcaddabdaadbcacccabaacbaacdadcdcdabbdcadbcaaccadccacbccadcaccdaadabddcddadcdaacacaacadddabcadcccadbbbabccbabcaabbbdbdccaddbacbbdbaadaddbddabbcdcaacddaccabcbadadbccaabcccaccdcaddadbbbcddbdbbdcabbbdcddbaccdcabbbcaccaabbacacaadcdddbacdcdabbbdbccbcddcdcdabddcddcdccbbdadaacabdabcbabbdacdacacabcdbacadcccbcdaaddccdccbdabbaabcdaadaadcccbbcabdadddbdbacddbdcbbdcbcccbdcbbdadaadacbbaddabbdbcccbdaadadbbcacddddcacacdcdbaacdabbcdbdbdcccdbdabcaadabbbbacdbdcacbbcdbcbadaaacabcbbbdabcabccdcdbccaaacaabcbadabbcdcbddcdbcdbaadccdccdcdcabbaabdcbdbbdbdcbcdddddbccabccbcdbabcccdddaddbdbccdaacaabacacddccdcbbaacaadacdbcaabbcccbcccabdddbdccdabcbcdaddbcdbacbcabbbbabacccbbccacdddbdcccadcddaabaacbdbbdbbdadbbdbabcabdbddcacbbacaabababdadbccccdbccacbcabbcaacdbccdddddccddcddbbccbbacdacddddacbcdbbaddbaacbccdcbabcdccddabbbdaddbbddcdaccdabbacacdaddbccacaccccbdbcadacccacddadbdadadccbdcabbdddbaabdccdcabdbcccddabadabaccaccbbcccaaabaacdbacadbaacabaaaacdbbddccccaabcddbbbccdbcddccacdbadbcbccdddbdacbbaddabdcababaddabccddcacddbabaacabdaaacddabadddcaaaabcaacbcbacccddacbdcbcabcaacddcacadbdacacbcbbcbddadbbbaabcadcabadddccdcdcbacbbaadcbcbbabdacaaddacacabbadbdcacdacddbbbddaddbacdacaaaadadadcbdcddbcdcbdcbbadadcbdacdabdddaaddbcbdbadbcabcaccabcbbdbdbdccbdbbbdbdbbaacdaaacaabcdcabbbcdddadbdcbdcbdcbbcbadbbdcaccdabbadcaacbbbacdbbbadcccbbabcbbacddbcccacdbabbaddddaddcdaccaccbaccddaabcbbbdcdacdaadaaabcbacdbbabdabccdacbbddaaacdcdadcbbcbbadaddbcccbddabcdbabcddbbbcbbaacbaadcbcdbccbdaccbdddadcaaaabcaabaddccdaabaccaaabaddcccbccabdbbabdadaaddcabbaccbcbbcaabbbdaabdaacdabadcbdddabdbdaadbccbababbddaabcdaaabaaaabcadddacdabdddccbabadaaccbbdadaaabcdcdccaadaaacabcababadadbaaccacadbdbaacccadcabdadacadbbaddbcaaccddbcbcbbadccdcbcbcbbbdcbddcddbddccaabadccddbdcbaaccaabbdaaddadbdbdbabbbbdcbdabcbccbaddccdcacaaddbddcbacaadcdadbadbcbdbbcbcbbdbbcbcbbaddbdaccccaadbadabbbdcadbacabadcbbbacdbdcaddbacbdacdbadbdcbbbaddaaababbcccaabdbbcadabadddccaabbabdbdababbdcddbccbabbccaacbacacadcbadcbbdaaadcabbbbdcdbdcbdababcdccdbbabcdbbcdcaaccbdaadaabaababddacdddcabaadabbbadabccdddcaccbbcaabbccaddcccdaddabbadcdaaccadbddaabcadcbbcdcdddacdccddcacbaabadaaacbaaadcadbaddcbcaddbaacdacabaccdaaadbccaacaababdabddbddbdbdbdcdbbdbaabdaddddbdbcbbdbdbcbaddddaacdbdbbabcababcdcadccdacddadacdcabbadbbccddabbdddcadcaccdcdabbccdcdbabccadcddabbbaccaabddcacccdcadaacddbababcbdacbcaccbabcbbaaadaccdccacabcccddcddabdcbbdccaadaaddccdccabaddbdaacdcaccccaccaddaaddcdbaaccacccabdddbadbdbdbcaacaacbccdccddddcddcbdabbcaabcaccbdcbdbaabbababdbbbcccbaacacccbcaaccadadbdddbbacaabdbbddadbcdbbdbcdacbaacbdcacccdaccccadccdaccaaaacdaabcabaacaadbddbdcdcaabdbacdcdacbddabaabcbbcbacbacaddaabcaccadcbbcaadbbddcbadaaccabdcdaaadbadbaaacdaadbcdaaacccdacccdaddbaabcdbbcacbaddcbaabccdbaacdbcbdaacadbcbadadbdbbaacccadacccbbcbacbccdbbacacddcbadbdaddbcaddddacdbdcdaddbcabccaabcdcccdcabbbbccdcadcabadadcbcabbdccadccdaccdbadccdacaaadcacaabaddcadbcdaabacbbbcadcacacccdbbcbcaabbaabbdbdaddbbdacbdcbdcacbcaadbbbbacacbddacdbbdcbabcaaaaddddadbbdcbcdadbaacaccaddadaaddbcadabbdabdbdbbabcabdabbddbacddcdcbaaaaddadbbcabcddabcacdadcbabdabcbadabcbdbddcbbcccbddbddcdbbcdacbabaacbdadcaaaaccbadbbbabaddcbaabdadbadadabbcdbbccbdacaacddacdabccabadcabcddaadcbbabcbbadbbdaadddcdbdcdccddcbccdcaabdaccacaddbaaddddaadaadbbdbcbaacadcddbcadbbbbbabdccbbdbcddacabbcbdaccbcaaccaaadbabacacdbbbbddcdddddaabbcacbaaccacbbabccdcdaddcbccbdadabcbbbbdaacaabaaacdbcbababdabadcabcabcaaaddaacdcbbddcddddcccddcdbbccbdbdcdbbbacbaadadddbbbdacbbbbdbdcdbaabccdadbaaabbdcaccbbdccaddbadcaaccbcdbddaddccbcaacabacbaadadbaadddccabbbcacabcbbadbbdbdddbdbbdcadcccabdbaccbbcdabacbaacdbbddbbacddccbabdabdbadccdaaaabbccadccaadcbcbbcadbbabdabccbcdadadadccbcdbbbbccccabccbccacdcacdadddbadcadcadabaaddbccdcbdddcaabcdbbcabacccaccadbabcdbbaacbdbcbbccdbdbdbcccdcabdaddbcadacdbbdbdbbbdbbbcacdbcaabdacacdbcadcbddbcabddcdccaadddaacabccacbadaadccabdbcbabaacdabacabddcacbdcbadbcddbadcbaddcbdaddabccbdaaaacbbadbdbbbcaccdabbaacddcaaccdabbdbbcdacdcdcacbcdcbabcaddaabddbadddabaabaabadbccdbbbaddbdadcdccbbadbbdddbabaadbbdddbbcadbacbbbcbbcbaabccaababdcbbdacbbdbdadddacadcacdcdbdcdabbcaabbcbccdadcdacabbbbbcacddadcabccbaadccdcaddcbcccbaccaadbbdcacaccbdcaacbcbbabacbdcbadbbddccadbcdcccbadddadcaacabccddcbacaaabaacdadcccabddcdcccbaadaaccacacdacbcbdbacacadbcdabbbccbcbcadabbadbcdbadabbabaacabccccccabbbdaaccadcdaaaccccbbdadcdaddbcdbdbadaabbbcbcbabaabccabbaaabbacadadcbdccdccaabdacadaaaadacddcdbcaacabcaccdbcdddbaacdbcdcbcbcdbaadddcbabbcaacaababbdaccaddadddadddccacbbdbdaacabbadadabaaaaacadccabcbbcabcbbbabacbbcababddccadaaabdccdccbdcbdccbbdaabddadbbadbbcdacacbcabadcadcdcaddddbabadcdbacabdaacaadbabacbcabdaadabdcddbcaabaadbbdbccbddcdaabbbdbcccddbbbdaabbdbcdcdbdadcabdaddbccabcabbcbaaaccdbaaacddbabcbdabbcbbcadaaadbadabbccdcdaacdaccaabbbaadccabcaabadabbcccccabcdcddaaacabaddcdddaabcabbcdcdbadcabbabbcabcaccccbdabcbdbccdadadacdadccaddbbdbbbdccdbcaccccabaddbbdcdbccbdbdddacbaabccabaabdadddcacbdddaadbcbcccaabbbcccadbdcaadaabacaccdbbacbacaaacddccadcaddbbacdcabcacbacdacaddbbbcbcbcccbaaabacbadaacdabddbaadabdddcbbbddabbbdddcbdddcccbdbabdaadaccdabbbdcbddbbcdbaaaaccaabdcccdbbccacdacbaacbdbadbcbcdbcadabccddbbdaccabdcabbdaacaaaadbddabcbabdcaaabaddbacaaabdbccaaccddddadadacacdbcacaddaaacdcdaaccadaabcccbcbaacbdaadbabcaaacabacccbbcbbcbcaacddccbadbddabcbcabdabccbdccdbcbbcdbbbddacdcbbbbadbacdbccbdacababaacdccaaddadbdbccabddadcacbdcdbbcdbbbbacbdaaccdadccbbdacbacaabccacbbbbbcbadabacccccadccdacaaddabcdcbcaadaaadbbdbdaaabcbabdcbacabddaabcbbadcacabacaaaadadcccbbccbdccdaacccdabadadabcdbaabcbbcdccadabbbcccaddccddaababcccaabbabbaddcababdaccbacdacacaadcbdaabbcadaabcbcaaddddcbbbadadcbcddbabbadcdaadabadbbbcccbbadaaacaacccdcaddaccadcbcbccaabddcdabbbbbbaabcabcbabdbacabddadddaccabbcdaddbaabccbdaacaccbacaacdcabcbacaacadcdbaabacacdaddcbaccacddcdabaabdddcabdcaadacbbdcdadcbdccbbbcbadcbddcaddbaccaadadcddbdbbccaaddacddcdcaddcdbcadbbaaaddcbbddccdaaabbdbbaaacbadbbaadcdcababbbcddcaabbcbccbbcbbcdadabcdcdbccbcdbaabdbbabbbbaccaabdabcabcdcabcabdcbccbaaaaaddcbddacccdcbcbaadcacbcacdcadbdcadbbbcbcddbcbdbadcddbcaabcacacdabacaabdcbaadcbadbbabadaaababadbcdcdbcdcbddbbaadadbbaacdcddddbacccaadadddcbddddccaaddbdaccdacbadbdadcbcbcaaadaddbaddbbdcdddbcccbaabddacacdbbdcaddccdbdcddcdaadbcdbdcaccdabdabcbbdcdbbadbabbacbabaadbaacbcddbcdbddccbbdbaabdbdcbcaacddcbdadccbdbcdbaccadcbbadbabacdcaaaabdcbbccadcacbaabcadbcaaacdcddbbccaaaacbdcabbacabbccdccaacaaddaaaadccabdccbbacabccaddcdcaabdbabbaaddbddacbccbbdcacddabcccdbabdbaacaadccbabdbadccccadadaababddccababdaccacdbbbbacabcbcaaabdadbcddcbdadcdddabacaabcdbcbadcbadaacbabaaadcaadaabbbccaabdbdbacdcdbaaaabbdbcaddadbbbbbcbdaacddaadbccdbdadccacacbbbbcbbbddacbaddbbbcdcdbcaabcbacbdaaccbcaadadaababccaaacdcbabadbcbdacddddacbbdcbbbdaabbddaadcacccbaadccbddbdcdaaacdcccdbaaacacdbbcacacbabcabaacdbaadaabbbadbbcddaaacdadcbcbdbbacdbbcbbaadddaacbcacbbcccadababacdbcdaccbcabaccdaadbdbcacabccbcdddabcaadcbbaadcaaacdadbadddcdbaccbacbcdbbaaaacbddcbbcdbbddbccccaacdcadddcdacdbaabbbadaaacddccacdaaddacbcdbddcdadcbabcbadcdaccabddbbddbbabccdcbcbabcaaabbbcdcddadbbacddabbacddaabdcbcdddcbdcbdabdaddbbdaaaacdcdadcdbccaadcbcadddcababbbccabdcdccbacbacbcaccbcbaaabacbcdaddcbddabadacaadddbdabbbcacdbdaaddbabcabbbbacddabccbaaacddcaddaccaadaaaaaabddccaadaaadacbabbbdacaacbbdccaadccbabcaccbcaaccccbcbcbddbcacdbdccbccbdcbaabbacacacdaaddcbabaddbabccabbaaddcccdddaadcadccaadabdaababbbaabdaabdbadbdbbddbbcaaaabdabcbbcdadbbbddddacddbdbaaacbbaddcdbbabbdcacbadacdbaaaadcaddaddacdbcacaaaadcaacccacbddccbcdccadaadaaadbddcabadabcdcddbdcadacaabbccdbdcdacbcbbccdccaacbacabaabcddadbcadbbabbccabbadcbbdcaaddbbacbbaaddbdaddbaabaaccdddcadcdcdbcabdccacbacdadaacaadbcaadcaaccccababcdabacbabbdddacadbbabcaabadcdbdcaacdddbdbddbcbacddcdaddddbbbbbcacacdcacddcbbdbadcabdabaddababaabcbcabcabccbccdadbcbbccccbdcbdcbcacaaacaaccbcdbaaadcdbcdccbcdacddbbccbccaddacababdcccbabccbdcdcabcdbbacbdcdcabaaacaadadccacdbcaadcaccdcdaddbbbdbdacbacacdcaabcdabcccdbcdaacbaabcabadbbcadacbddbbcadbcdbdcbabbbdacacddbdcabdbdbddccbaabbbadbbcaabacaaddbcdbaccddcaddaccdcaaabdcdddcbcbccbabcdccccbddbcdcaabbbdabcaaaccaabbacacdbbacdcaadcdcccadadcabdbdacccabdbcdacdcbdcdaabacccbbccbdbabbcbbddadaddbbdddcddddcadcabcbabaabbcaaadccaadcaccddbbdcdaaddcddcddcaadacddcdbdddcdbcddcbcdbcadbcaddcbbdbbcddabaccdddadccadaaddbddbaadaabccabcdcdacaaaadddcdabcbdbdcaabcdabcbacacabccbccadbacbacbbaccccbddaadacddacdacdbbdaaacbcccabdaacdccddbbbaaaddbbdcccccbcdaddcbabbccbcddabdcbcccdbbbabbaabadcdcccabdbbddccaabaddacbacabadacabacdabbcbadbcccbdababbacdcbbbbdccbbbabbcabaaccdabbcacbdcacbdaacbaccbaaaaacbacbccaccbaabaabaacaadadddbacaaccdbccabcbbabcabaddbcaddbadcadadbbddcbaaabddaddadbbaabbadaacccbcbbddaabdccababcadcbcbcbadcdcdabadbdccaadccaacabbbccbddbaadbabbcbcccdccccdcacdaabdcdbddbdbacbbccdcbadbbcbbdacaccbccdddcdcdbddabdccbdbbbbadcaabcdbabdccbbbbabccabbbdbccdbacdadcbcccdbddddddcadbbccbcbaacbbcddcdcdccaaadabdbccbbcaddcddbccccaabbabccbcacdaddbacccbbdbadbcdacaacbaabdcdbccbadccddcbbdaddcadcbbbaadcbbdbcdddcaaabbddbcaaccbddddccabdbaaadaabdbbcccbbacbdbbccdacacadcacaaccabdaaaddcabadccaadbbcdcbcbadddabdbaabaaadbadbaccaddcdddbadccacaababacadacdadabacbbaadcadaaabbccddbcbbdbacbcbcdbcbcbbcbabddbadbbdaaacadcbdcacdbccbcdbcddcbadbccbcbccddabccacaddadabddaaaaabaccaddbddcdcdbbbacdbbdcdbcdcacbddbacbcddcaacacbadaaaddcabdcdbcbdbacccdcadbdbabbdbdbadcdcdbddbcadacccbdcbacaacacbdddacdcbbdaacaccacbbaadacbaaabdccabdddabcbbabbdcddaababcdaadbadcbbbaddcccbccdbcccccccdabdacddcabbacdaddddbbadcbddcccbbbacbbcddaccbbccdcabbaacbbdabcbbdaacdaccdbddadccdbaaabbddccddccbaabcdcdaadaccbbbbcdcbcdcbdbcbbaddddaccabaccadcdbbcddbabbcbabdbacdcddbdccbccbbcdcabbcbaaaddddbbacacacadccaacabacacdbcbbdbdbddaccabbdcdcccbddbbbdbbaccacacbaaacdaabcbccabcaacccadadacbdaabcabcaaaddcddcdcdbddacdbabaddadbaddbcdacdcbaadabddabcbbbaabcbbbccbcaccddabddccdbacadccadbadaaadbabdddbaabcabcaccccdbbbbcddabcaabdcbbbccabddcdacddaabddcabbbadabababcadabbbccbdcabdaccdbbccdbaabacabdcaddaaabdcaaadbbbdaadadaccabbaabcdbbdddbbbbdaabbcacdbaddcbaaccccabdccdcaacddabbddbdaadccacbddbaddddbaaadbddaacadbbadacdbdadcdcdbdccadbbdcbbaadbdbbcaddcccaaaabcaacaacbaddcccdbbbddcaabacbbbcaacaccddddcdbabcbabdcbbabdccbbbbdbaccdbadbbcccabbdcdccbabdabaadcdaaddbdabdcdadbaabcbbbabcaaabdbcdcdacbadadcacdbbcacbadddabadadbcccdbcbacbbbaccabdaccbadadbdccbdbadddaadbcadbbdbbadddbadbbbcdcccddccadabcadaaadcaabccdcdcacbccbcabccaabbdbbcaccbccaccbccbdadaaaddaacaaddbbcaddcdabddcbdddbaacadacdababcccdbcccbbbbcdaacccabbbccccddcabcbcabdbabdadcabbbdcddbdadacdccdadadbcadaaccaadbabbaccbacccdadcbbbdacbbadbaadacdddaddbcadacbcdbbdbccabdbaaabaddbabaadccdabaccdaacccaabbdbbacdadbbcdddcdccabbbbdbcddcdbadaabcbcabbacdacbcdcdddcddcdcbadbbacdadcbaadaadaddcbdabcdaababdaddcaacbccacbbacccdbadbcdbbbdcbdcbdbabccdaddbabcaadcaaacabbaaabdcacadcdbbbcbcabbbabbdcbbabcabdacadcaabcbcabdbaddcbddbbdbddbcdcdbbdcbbdbdccdbadbcddcbcccbcdabdaaddbaaccacbddcdaacdbcbdddbdababbbdbdbcdbbcdcbdacddacaaaccabcaababbcbaaadccccabbccbbcababcbadabbaaaadcabbacccadbbaacbccaaacaddbbdcaddcbabcccbcaddabcdcbccccbdbdcccddacbbccaaccdbddcaababbadbbddbcbbccabdcaadacdabcdcbdcacdcddbcbadddababcadccdacbcbcddaabbcccbccddbcaddcddaabccdacdccdbacccccddccbcbbbdbabaaddadbcdbaacdcdacbbadadbbddcbbcbdacbbacacbcbdacddbcdadcddddaddccdcddadbcccccadbbbbabaccddbaccbadadcccbcdddaddcddddbcbcbcabbccaddbdbcdbabcadbbccccbcabdbcccddaaccdaacbbadaadddacbdacadcadacaaaabbdcdccbcabbaaccacadcbccdbccbcaabdddbdabbdcaccaaaaabaabbabcbdcbcccacadccddcdccdcccccdcdcccaddbaaddaaabbdcddddccdcababcbbbacccbbdbacdcaaababccbcdacbdcaddadbbdadadaccbcdbdaccddbbccbabdadadcddccbbddabadadbacaabcabcbbadbcddaddccbbaaaaacabcadbdccbddaddabbcccddbdbacbdbabbdabbccabaadabdddbdccbaaddaaaacbaabbddacdbcbdddbaddbddabcdbdcdaacddcabdadcbbadddcbcccccabdddbdbbbbdbcbddaddadbabddaddbdbbddbdbbbbdaddccacdbaababddcdbbaadcaaaabcbddadabccbcabbbccbdacccacbadcadcaadbcbbaabdccabdcdccddbdbadccbabcdbcbadcadcbcbaccbdbacccbccbbccdaabdccdaadacaaaaaabaabcdcacbbcdcbdcbcbaccaaaccacaaabcdbadabddcaccacbddccaddaacbccbaddaacbcbdcaabddacddacdbdabbbcbadbdaaccddaaaaacbdcbabccbdbdcacbbcdbdbacdbbcdbddcdcddcdaaacbacddcabbdbbdbccddadcdacdbcadbccabcdadcdccdbdcdaaabcadaaadccbbddadabbbcdcacccdadbbabbbdababcbddcccdbbcbacbacabcdbcacacadaabaacabbdadaaadaddccadbdadcbddbaadadbcaddddcdaccaacdacbbcdbbddbbbccdddcdcdbabaccbbcaaadbacbbbbdbdbacddabaabdbcbadabcbdacbabadcbaadcbddaacdcaddddaacdbadbbcaadadbdbddcdcabacbcdcbacddadadcddadabbdddbbcbbcdbbaccaabbdbcdaabacadabcabdccdcabbababaccacbbcddacccaabcaacbcacdbccbdccccbcbcbdbabcaaabbcdcdbbdcbacbbdadcdaddbdddacddbacdcdcdcdbbcccdccaccadbadaccdbbddadbccbdcddcbccdbdddacabdbacadbdcabdabcabccddddbbdbbacdbcdbdcdcbccbcbababdcdadccaddbddccaabdaabcdabbdbcaadaacabdbaabdcddcaddbaddaddbdaadbbddbaaabbdbbbbadacaddbbdcbdacdacbbdcbadcddddcbcbcddbcdbdbabcbabdbcddbdbabcdcaacbadaacbcbdcaabbacdcdccabbdbdababaddbabcaaaabccdaddacbbaabdbcabaccdbdabbcddbaacdcdbbdcdccabbccabcaabbcaadddbacdcbcdcaaadcdacddcdccaacbaacabdaadbaabdbcadbacaacccbbdacbbadcdcbbbdabaccbccdcccbccadcbcdddacbcdcccabccaaadccbdcccddcdddbbbddccdbaadbcdbbacccbdbabcdbdaddcbbcadacaacaaacddabcccccddacdcdcbabacddacdcccaadcdcccadddaddabccbbccbbcbccddbbbddcdacccddabaabdabacbacabadccacabadcabdbbdbbcddadacbcbabadabbcddadbbcbbdcabacbabdadaabdadbcdbcddbddbcacadbdbbdcbbadcadddbaabbadaacbacdbbccdcacadababdbdaaaaddbaddcdbdbdadccdcddbccaddaabbaadaddcaddacacbaddccaddbcaabdaddbbdaadcabdababbacacbdbacdabaccbdbbbdbcbaabdcbcbbcdabbacaddadadbdcabadddaacacdadcbdbcdcdbaaacaaccbdbcbbacbbbbadbdabacaaabaabbdccabdbacccccdbbdadccbbbaabbdacdaabdcbbacbabcbabbddcabdbabdbdadaccacdbbcbcdbbababbabbdcdadcaabcadaabbbdccdbbcadccbcdbbbdcbaddbbbacaadcbbccbdacadadbccbcaabbbdabdaacccddbdcdbcdbbbcdaaaccdcbbbcbbbadddcaadacacdcddaddbdcbcddccdddccaaddbcbbdaabbbddacdbbcbbbcccbaaddcbaccacadbadbdccadaabdbcddddbacaddddbaaadaacddbcdddabaaabcaadaabbaaddaadabbdbaddccbbadbbbddbddcbdcddaaabcddbcddcaccbdccdddabbdacdcbadbcdbddcababdabdcdcaaddbbbcaadddaacbacabccddbcacaaadbacaaddadadddcdcbccdcbadaaaabdbacabddbadbddcaabadcbaabbdbdbcacccdcbdbaacddacacbbaabcdbcbcbadacdddcbdddbcddacacccccbccdadbdadacbbcbbbcbbacddbddcadbcadcacdccccdcacbabdbcdbbdadcdbadcccdaacbaacbdaabdcdadaccdbdacbdacdddaacdcdbbcbbdcabddbcadbcbcabbddcacabcbcbbadddccbdbabbcadbacabdabddcbcccdaacccccdcdccccdaaabcabccddbbbcdddbcaccacabcabacabdaddacdacdbbabdbacbadabbbccdaaccddcadbdacdbccadcbbbbcbcbabdbacaaddccabddcdcdcccbddacbaadbdccdcacbaccaccaabcbdbcbaabbbcababbdabbabdadacbdcdcbcdddbcbadbcacccddbcbaccdaccadabaabbdbabbaaabdbacadabbabbccbacdbbbbcbcdbdaadbbaaccbdadccabdbddbabbdcddcdadaddacddcbbacbcaaacbccdaaccdabcbcdddabcccdcdbaaccdbaacdaacaacbdddabbabdcaabdccbcaccaaacabacddccabaadacbdaaacccdbaacabbadcdcddbacbbcaaaacddbcbcdbabbbbacacabdbaadabaddbbacdcdcbddbadbadaaacccbbccdddaccaaadbacbababadbbadbbabdabadbacdcbbabdcbcadaaccabdabcbdcadbbddbcdbcbacacaddcddadccaccdcdbbddadbdacbdcacaaabdbbacbabdbcbaddccdcadbadbabbadacdacdcddacdaadbcbaddadccbcbaccbaaccabccbcdacbbabbccabdaddbbabdbbdabdbaacbacbdccdcccadaaadcbcccababdacabcadadadcbbdddbbbacbaabaadbcbcbdadadaaaddabccbaccabacabccaddcadbdbbbddcadcdcbdcabcbcbbccdacabbbaacbcadbdadacbaacbcaddadadaabbbacabbbdacddaadadadaabbadabdbaacbaaacadabbcbbbdccdaadacdaaabdbabbdadabbcaacddbbcadcdbabaddbbdbdcdcbaccacbcdaddacacdddcdaacbbbcbcdbabdbdcabaccdabbaadcbbbdacadcddcbdcdcbaabbcabbacbabdcccbbdbcbbacccadacbdbdcdbbcadbbdbdcdbaaacbcaaacabbcbcdbcbdcadcdbddddacbcccbbccabbccaaaaccdbbddabdcccdbcadbbcadbaaaadbaabbbbbdcddabbacdcbbbcabbbdcddaddabdddadcbcdaaccabababdadcdcbdcdadcdccdadbdccdacbcbbacddbbabcabcadcacadbbcbaacdaddbdbbcbcabddbbcdcbadbdbbddbccdddbbcbdcaabbbaddbbacaaabbbbadbdbdabbcccaaacadcacdaccdcdddcbdadcaadadbacbcaaabaaccadacdacccaddabbbadddaddaaaaaaccbaabadbaaaacaddabbdbacdccaacddacccaaabaabddcabbaccdabcdccabdaadbdcccbababbdbbacabadddbcbcccbcbdcacdcacdbbadadaddabaddcdabcdddddcabdbcbabccddcbbaacacaccacdcbbdbddaabddbdcaadcacaabbabdaccacbbccbdcbdcddbdabcdbbaddbbcbacbcadbdbacdbcdbbcbcdacddbbbaaacbabbddddcbadadcdaabcabcbcccccaacdccacbdabbabbacdbdacabbbaaaddaacbabbdcaacadbabbcccdbdcdccdbabacbcaccacacccaaadbbcbaadccdabaabdabacbaddcbdddcdabbadbadcccccadadcdbcadadabbccabbcdaacddddcacaddaddbbbdbcadccaabdccabccdbcbdcdcaaaacababbacabaadcbdccbcccadbcdddacdcccdbdaccbabdbddadcdacdddddcaccadabbbacbdabdabdbddcbdcdccabccaacacdbdcbdaccbccbdaabcccbaabbadabdbaccbbcacdaabdbcddaaddcdbbaccbdcdcaabddbbacbbcbaaccdcddbdcacdaddcddcadadbcdbcccadccbbaccbaaadaacaaabcddbabdddddcdcaaaaacaadadcdddbbaccaaacdacababccdcacbacbbcbabbdbadbaadbcccadddccddbdbdbdacdaabdacdadcadbdcccabdbbbbbadcabacaaabdcccbcabcbdbbbcddbacdbcadabaaabbdbdbcdadddacbabdbdaaccdabbaacabdcbcaabcccbabadbbcabbdccdbddadccdbbacaadccabbcdaddcaccdbbdaccbddcdccdddaacbcdbadbcdcaddbcabcdadaddddddaccddacabacccbadddccdbabcccababadbdcacddbbaddbcacacbcacbbbdadccddbacadbdacbadacddcbcacbdabccbaadddacaccbccccbabccabdadbaccbaaaacdaadcdbbbabbdabdbdccbadddddcadcabdabccaaddcdbcbacbcbbdadcdbdbadbacbbddbbadbaaadbdaaacbccadabcdbbdcacacaaaddddcdaaddbdccbbdbacaddacabddcdcccccbacaadbdddcdcabadacbaabdccccbcdbdcaadacabbcaadbacbbdaabdbdccabccbcddbddcccaabbdabcaaacadbdddaccacbadaabcbbdbbdbdbdcbbcadacacbccdacdcbccbaccbbcbcbcdcbaddccccbdaddbadcaaaaccbbcaaddcccdbaaacaacbadddccdbcbcddadbbabacdbcccbbcadcbdbabbcbcaccaccddaaddaabdcabadbddcdcdabaaaddabbaabddddcaddbcbcdbcacdbbacdcddbcacabccbabcccabcabcdccbcbddabdaadcdabcaccaaadabdabaddabccccccaacbbcaacdbadcacbcccccdbdcdbcacdddccaacabcbabdcabcccdadabcaaaaabdabdbbcbdacdcdddbacbdaccdbabbcacbdaccacbdbcdaadabdadbabacadcbbbacacdcbabdccbddddbcddabbbabbbbadabaacadbdcbccdbcadbdbaccbdbbcbaaabadadabbdadbbcdddbbddaaaddbdcbdaccbbbddabcbadaccdbcaccadabbdbacacdbadbadbbdbdbdbcbdacbcaddddcdbbdbbbcdaddbbbdbdcdcbdacabdadabdbaaaabaccabadbcdcbccdaabdbcabccbbdadbbbddbcdbbcbbdbdaabccacdcddccddabbdbadacaaaaacdadabcbccdcbddcbbdaabcdcddbadaaaabdabcdcadacacdaccdddcaccbbdcdbdbdbcbddbabbbccdbaabcdaddbddcddadddcdacbdaaadbcaacdaaacbddbdcdbabcaaadbcacccabbabaadbdcbdbcabdbcddacbbbbdaccbcdccdaddaadddcdaadbabddcaadcbddadddbcabccadcadccacbacbcdbdbdccabccdcccbcacbbdbcabbacdbacbadabdbcbbbcabccdcbbbcaadbadbbacbdcbbdabbaacccadcbccccabbbbbbdaabbdddaccadadcbacacccdaaabaddcbcdacccaaddabdabcacbdcbbdcbcabdadaabaaaddddbbddcdbcbbbdbadaabcdbbbaaadddcaaddccbbcacddccacdabdcbdcaaaaadcbcbbbaacbabdcaadcdacbdacccddccdcddadabbdbbbacbdcabcddcdaabcaadcaccdadaaadaccbdcacdbdccddacbcbccbbddcbcccabcccbbcbabacdcbccddadacabbbdaabbbcccdaccddcadcddbbcbcbdccacdcdaadcadaaddddaabdadcdbcacbacbddadadabbcccdbddaddccdcbacddccadbbbcaacccdcbcbcadcacaccccaaccdabcbacacbcbaadabdcacaacaddccadccadabbdadacdacbbadbcaccabdbbcacdadbaacaaadbddadabcabbaaadcdbbdacbadddccbdabbccaabddbcbbbcdbbbbaacdbcdbbbbbdadbcdababbbdadbdabaacbbaabdabbadddacdadbbbacacabcddcdaaccdabcbaaaabcdbbaaaaacabbaaaadddabbcbcbccbabcddbddabddabddadbdabdcdcdcdaddadcadaadddbbaadbbadaaaccbaccbbabbaccdabdabbaababbcacdbddccbaaaaadcbbabaacacdcbddccdaaadaccbdaadbbcbabcaadbcdbdcbcbbdbbadbaaabadbaaacaaaaabbcbaaaadabdcaabcaddbcbcccddabcccdabadccaddadcbbcaccddbcbacbbcdddbbdcbbaabadbacdbddbdabbaadbdddcacccabbcbccdbbcbbbdacbdbbaaacacbcccddcabbbaccdcbdccaadbbbccdcacaddbcbabdacaadacddbbccbdbbaccdbccaaadabdaabacccacddbabcacdbccabacdcdbdbadbacbabdcadcabadaadddabcbcdddbcddabdabdddcaddbadbcdadacdbddddbcaaaddcbaaadcdcbabadadddddcbacddbdaaddadbdadbdabbaccdacbcbababdbdbccaabadccbbbdccabcadcbbabababcbbccbbbaaabbdabacabbbcbbabbadddaabddacacdddcdcabacdbacdcbbccabcbbddddddacbdcadabbcbdadbbdbababadaabaccacacadcaddbdadadcbddddaabddacaacdbdbcbaadccbcadcdbbcabdbbcaadaddaadabbddcbcdcbbcbaaadacccbabdbaddcdccbbdbbddbbccaccdadaabaabaabbcbbdbaddccbcabddbbccbdbccbbbdaaabbdabbaaabacdbbbabbcdccccabcbacdbcaabdbccaacaadadcaaacddacacbbacacddababddbbadcbcddddaacbaddaacadaaacdacbbbaacdddbdbdddbbbabcdccacbacdbcadcccdccccadbbbcdadcddaaddcddaddbaaddbbbbdbabdaddbcdabdccdbcdbbcdacdccdbbbababbbdaaddcbbadabaaddbbabbbdbdaaaadabadccbccbbddbccddbababbbcdbdaacabcadadbbddcccabbcdcdccaacbbacabdbbdbdcbdadacaaadccbbdbdadcacadbcdadaadccbdcdbbbccbccabdacbdabbbccbcbbddbcbacabcdcaccdcacbbadaaaaaaaabdbdbbbdcdabadbbadbdcbcabdbdacbbaababbdbcddadbadacddbadacaccdcccbdbbddaccddaacbaaccdacdbccddabaadccdbaabdbdbcacddbddcbacbcdaccaadcacdcdcadbcacabbdbaaaaabcabcccaccdacbabcacabdbcdcddbababbbddbcacbdabccdbaababbdabcdcbadbabdbabbaababcdaabadbcdacaacccaacccabcabdcdaaadbcacaabcbbbbaacaaadcdabdbabcadabdbcadbdbabbdaddaacabcdcabadaaabcdaadaadccbcadbbdaacaacbcddcddcadabcadabccdacdcbdbbdadcabbccdbddadaacbdddddabdddaddcbdababbabdadbadaadaccabdbbcdbcbbbbcbadbaddacccdcabccddcdbaaadaccddccbaacacbdbbbbabcdcaaaabbaadccddabaccbbcbcacabadddaadbbacaddcddaaabdadcccabbccbabacaadaccabcbddaddcbdbdadbddaddcccccdaacdadcbbcaacbbcbccccdcddbcdadcddbcacabcadcaaacddddabcaacbddaddddcabdcdbbdbbcaaabbbbcdcabadaccdacbcadaaccddaabcdcdababaacbcaabcadbbccabcdddaacabbdbcbdcdddadcbbcaabbdadbadbdbcacadcbccdcabbbcdabbaadbacaddacdbabbbcbabadadbdbbbdddbbbdcbbadacbdabcaccbadbcbaadbbbcdccdbcaadcddcbadabdcadcbaccddabdaaadccddbaccddabddcdaabaabbcccdaddbadacbcdbccdbdccabddbbcdcccadbabccdacadccacdbacdcbbbbbbbcaaadadbacbbdbdacaccaddacbdddaccddccacaabadacbdcdddbbabcbddddbdaacadcbccccddddbbdbbcdaacbaaaacdbdcddddabbcccdddbdadbacbddcadccabddbddbabdcacdcbcccbdaadacbaadddddbcbccdcdaddbccccdbacbadabadcccaaacbabaaaacdccabdcaccdadabcbaabdbbdbdccbdcbccabacccacabbbbbaccccabacdccaadccddaadccbabdaddadabaacdcacccabbbdbccbcaaabbbacbacaaabaddbbadaddbcdabaddddbbcbbdcadbccbcbbaaadbccbabcadccdcabbdbadcccaadbdbcccabcdbdaccdbbbcaacaababacdcdaacddabccaaddcabaabcadbbccbcadcdaadcbdcbacbacbcacdadbbddabddcbababdcccaabaaabddbcccacbcdacbcdcdadcaabdbcaabbdcddbddccabcaababbdbbddccaabadbcdabdaabcadaacabbbcbcccaccacdccadcabcccbbdadcccaaadabaaaadbdccbddcbddabccacddabbcacbcdbaaabbcabccbbcbabddadbdaddadcddbababbbcbbbcdaabaadbdbdcbdadbcbbbccbaddabcacaccabbdcdcbbbbdbdaddcaccbdbbabddcdadcbcdabdbadbccdcdccbddbbbbddabccddacdaaadccacaaabbaabadbdbcbacacbadbcadacbbdddcccababadbacbdbabcddcaabddaaacbaacbdbbbddcbbacacccacacddcbabdcbdddcccddbbcccbadcdaaabaaaadccaddcacbabdbdbabadacbcabcabdadcbddcdbcbdacbabcdbbcbdadadcbcaaadccdcbdcbdddcdbcbbdcabdbbddadbababcccaaddccbcddcdccbccccacbbabacbbbaadabadbaacbcaabcaaabbddcddccdaadcadabddbccacabcbaddcdddacabbaacdcdbdadaaccddcdabbdaacddadbbbcbdbbddddcbcdabbdbccbbbcbbcbaacbcabbdcbbbaddadcbcacbccdccaadcbabcbbbadbccaaddcaccacabacbdddbbbbccaaadcdaacbaacdacbacccabccbacdbdaabbbabdadcbcbcaadccdcabbbdcbdacbdadabcbcbacdbbbccdacaadaadbadddaadcbdbdaaadacddbdcdbbbbcbcdddbddcdcdbcabacbadbcdacabddcdcddadabcbbcaacdbdaadcbbbbbdbccbbdbbdaabcbacaddcaddbbddbdaccbbcadbcaabbacaadcbdcdbbcbccdbccdbbaccabbdcdccbdbbdbacadddbcdadcbacdccaacbdddddccaaaabbacabdcbabbdcdbdaabddcdddddacbadbcbacbaadbbaddcabbcdcbcdbddbdbaccdabaadacddbcadadcbaaaacccdcdddcadcabdbacdbbdcaaccdaccaaadabadcccadaddbaabbadddcdcacaaacdcadbdcdbcbcbdddbbdaacbddaccacadacacbdadbbddbadcadbcababbbbdbddbaacbddadadbdddddccbddaddcbcdcbbbcbabadbabaaacadcabbbccabdacdadcbacacbadcbcbdbcdbadcddabddbcbdcbcaadaadccbbbdcbcdbbaddbacaddcdacbbbadaddcccdcadcdbacaadaadcadaaddddbabddadbccdaabdaaacbdbcdaacaabcbccabadbcccbdddabdbcdbbbbccddbaacadabaccbcbaddcccbcdaddcbccadbabdaabdbcaacdbcdabdaccdcbcbccdcbabdddaaaadaacdaddcaadcaabdcdabbdcdabdaacdddaabcbcccabbddcaaadddadaababaaccdcbbdbddcbcacbabcdbbbcabbcbabdccbddaabbabcdadbcabaacbccbbdacadaacbabddbadccbddbaccabacbabcbbbbdcbbbdcbdcbabaacddddbcaacbbbadadcaabacdcdddbdccacbcbcbddaababdaaaddabbdcadcacaccbcbbbccaabbccacdabacdccdcdddcabdabdbcbccdabaddbcddadbabcbcdaaabcdbaccaddbdbdbddcccdddddddcbababccbbddbccbbaacacbadcacdadbcbbabacaccacabcdaaacdccbbaddadbcdbabddddcaacdbaabcbccddcdabcbbbccbdcbbaaacdabbccbcbcccdccddbcccabbccbcdadccddcdbdacdbcddadccdaacbbdbaaacddbbcaddcaadacdaacccadabdcccccdcadbbbdaabadcccbabdbaccdddccdabdddddcbbbdacabcbabcabdcabdaabdaacaacabbbadcaababcbbbbbccaccadaadbacabcbadabcaacaccadacbcbadccabdcabbcdbcbabcccacdbbadaadadbdbcaccdddcdddbabbabdbdbddddbdcabcccbbbacddcccadddbdbcdcbbdcacdddcaaabcccbcabdaacaaaacdbcdcaadbcabdcbdaaccadcaccccbdbacbaaccaabdcbbcaaacbbccaaaddcadbdcdcabacddcddabdaccadacbcadbbabbbcbcaddbabbdaabbdcdcccdaaabddcccdbdaabadcbdbbacdcdcdcdcccdcadaadabcdcdaacadbbbccdccbbadaaddbdbdbdcaccbacaaaccaddddbcacbddcbbbcdccdcbcdacbbadcddcadaaadaaddcccbaadbcaacbcddcddadcdcddacadbdadcbbbdcdbadaabdcbaddcabcbabddcccdcacbbcdcbddcbdcbbcbdbccdadcccddcacddbacaabacbbcaccbbbcbcaaabbaacccdbcadaaabadccbddbacaddbdcbbbbcdcdcabcccacdcbdcbadbabdcaabbaaddacdcbbcbcbddccdbabbddacdbcadcadcdabcacbddcdadbccabdddbcbbabaacbcbcaddddadadabaccdaaddcbbadbcacbbdccdacacaacaaddcdaccdbcdcbbabcaddbacadcdcbaccbabbbbccddccdacccdbdcddbcbddadbbaadcddacacddbdcadcadadddaacdddadbcabdbbcdcddddcaadaaddaaccbabcbbadbccdaacabdaacdbcdbddcbabccbadcdcacbdadaaadbbbadbdcabbaddabccabbcabdabadaddbcddccddccabbbccaaaadccbdddbbaaabcbabacdcddbcddcacbdcddaddcadccbacaacbacaabaccddbcbbabacbddddbcaccdacbbaadcdddadbacabdaaabdaddbbaccadadabddadaaccdabbaaabdadcbacdaddacadadadccdacdddcdabdcbbbdcdbbaaccbcaacdddadadddbddaccadbdcadcbddadabbcccdabdcbbbaadcccbdcdcdcbbdbddacccacabcdbdabbbacbdbcaddbdacaabdaacaaacaabbdccdcdbbcbdcbcbcacacabccccdacacadaaacdabcdbacbdbbbdaccbcadbdaacbdadbbddcacddabccacaacacaddbbbaccdabddbdaadbbabcdbacaadcbcdadabcdcccbacacddcaaccdacbcbdbabadbdcacccdddadcadddccdccaaaaaccabccbbaadcdbaaadadcbcaacabdccaaadcbcccbdbdbcabbabdbcdddaaabdacbdaaddbddcbadadbaddadacaddaabdcaddcbbbadcdaccbcbdaddcdccbddbbbddababaaabbbbbcbbcdadbaabbddddadbcadcccacdccddcddbbadccaccababadcbdbacddaabbbdabcabbcabbbdbacddaddbdaacaababccaddcbdbadaadddddcbdaddbcadbdaccadadababcbbaaacbbbccbadcabbaaabdacddabddbacccaacdbdaaabcbaddcdabbbadabadcbacbcbdcccadbdcddadaddabdddbcaaaccadadaadadbcddddadbabdbcdcaccabbacacbcdddcacddbdbabacbccccaaabccbbccdcdaccaabbdabcacbdbbdbbaccadabbbaadacbcddbbabcccacccbdaccacbbbcaadcbaabcadadbbdcbaabbadacaacddbdddabbbbbabddaadbbacabddbbabcbcabadbdbbabbabddbccdccbdbbcddccabcabccbbbbbcabbdaaabcdadbddaddcdcbaacdccccabdadcbdaaacaadababcdacdacaabdaabdabbbbcbacbadcdbbcdbdbdbccaadcbbbccacdcbdbcaaabbdcdcbacbaccacdababbcdcabcbddbccbbacbbbcacacdcccacaabbcdaaaaadddbbcbbaacdcadbacbbdbacacdbddbcccbdacdbbdbdabdddbdaacccacdddcbdaadbbbabbcbbcaaadcccbaaadadddabdbbbcdcabbcdcbbddcdcddcccbcddadcababdcccdadbbbbdadbbbdaabddaadadabbdcacbccabdbbbaadcacdbcbacccabbbbcaabdaacadbabbdaddaabccaccbddadbbabbbabdccddcbccdbdacdcbdccccaddaacddaccabdacadddbdaddcdcddaaddbabbccabaacdabdaaacbacadbbbbbbacdaaadbbdabbacbdabdcbabdcdbdccaadbccdcabcbbdbbdbabacddcaacaddacbbcdbaccaddadacbbcacabacaacbcdbbdbaadbabddcaababcdcbccbbacaadabcabccdddcdcabbbdcbdcabadccdabadaabacbcbdcaababbbdbcaddccbdabdbcbbcbcccccbbbcdabcbddddcbcbcbcacdddcbbaddbabdbccaabababdcdbbbcaccabcbdabbabcaccbabdbbacabadaaccdbdcbcdabaadaabbabacdcbabbcccddcbcddbaadccbcdcdcaaaabbcdabbcddaaadddbbacdbccdaaaaacbbcbbcdbddccddcabdaadbbdadbaaaaddabbdbadcbcdaaadccdacacabbccccbbadcbcccbdbdbddbbcdbdacdbcadaccabbacabbaddbbcddcddddcbbacbabaccbacdaaadbdbbcaabadaabaaadabdcacddccbcbbcbbcdddcaccaaadcadbccdbdbbbcdabcabadbdaccbcacbabbabdcbcbcddcbbcdbcbdcdcaacbadcddacdcbdcddaaacdabbaaadddacbadcbbdabadacaddadccbabcabccbddcdcccccdbcbcdadddacacbdcbdcdaaacbdbddcacabadbccdccacccdbcaacabbadabacdabbcabcdabddccbccabbacddccabdabaccdbdababccccdabcdbdaaaaaababbcdcddbadbdbcdcbcdaaddcdccacbbbbaddadbccbdacbcaaccadddbaabcbbbcabcdabcddccbaacdccdaddaacaabbaadddaacbcacddcdccacbddddcdcbaccbaabdabddbbcccabdabdacabdbdabdcadbbadccdcbadcacabdbcdbcbddddddcadcdbbbbbdbadbbdbadbcacaadbdccbcaccacbadaacbbcbaaaccbcbbccdccccddacdddcddddbacdbacabbaaacdcabbacbcddadbbdaaaaaabbbddbbaaddccadaabbadcbdbadbddcbadcdcdbdbbddbdacddbadccabddcababdbdbbaccdacacbacdababdcabdcadacbcacccabbacccaccaabbbcacbbaaaaaaaacddcaddcbddddccacdbcaacbcdaabcaadacdaaadccddbaaddbcabddcdbcdcadabbdbbcadadaccbabdbbcacdcbacabaddddbdcdacadcabdcadbaadbaacbbaaccbdbdbdaaadccdbbbddcccdbababdadadaddbadabbbcbacaccabcbbcddcadcadacabbacdcbadddbdabcdddbdcabdcabdacbdaadccccccbaacaacdaddadbdcdacbccdcbbdbdadcddaaacbdccadababaabadcddbccdbdbbaaabbbabbccbcdbcbadbbdabcacdcddbabadccadbadbcddddabccacbdbbbbbabbcabcbdbcbbbacdadaccdbdacdccacaadcbdbabddcacadadbabddadcaabbbdccaaabdcbbaccdbdddcaabcccabbccdabddcacabcabbdbbbcdbbbcbdbbdbacbacdcadcbabbbdbbacabbbbbabaacbbbcbdcabbcaaadddbcbdaacdaddaacacaabcddbccdadddccdcbccccadccccdaccadacbdddaaabacccbccdcbcdbdbbadbadbdcaadbccacaaaabbddbaaadcabadbdacacdbbcababbccdacbbadccddadbddbdbcddbcbddddabbcabbbdcadacadadcabbaaccbabddbbbbcacdcdaccccdacbbadabbdcacdccdbbcdbcabacccddbddbccadcaadbcdbcdabdaacdbcccabadababdaabdcadcccacdaccbadcbbbdacbdacbacdcabcadabacdbcdabddaddcaabcbccaccbbcaaccddbbccdbbcdcdcaacdbcdcaaaaaadbaabbaacdccbdbdbdcdbdadbcbcbccdaabddaddcbcadccbcdcaabdcdcacacdacabdcbdbbdddabccbdabacbdccbabcbccacdbccbbccbaabcdcabadbdabaddccdbdbbdbcccccbacbbbcaaacaccdcbdddccaacabcbdcdcadbbdcaadadcddabbdbdccbcabbdacbdbadcacccaadbbbaddabcbcbbaadcbbddccbddcbacdbbababbaaacdacdccbacdccacabcdacbaadcaccaaaababaacbdaddacdadbcdbdbdcdabbcccaadbadddddbaaccbdcaabcccabdcccccacacdbcdadacbcbdadcbaddbddbddbabbdbdcbbcddbaaccdbcbbdcdddacccbdacabdacccabbbaccbccddbcccdbcaddcccacaaabbbcaccbabbcdddbccaabacdbdbdaadbcddccccbdddbbcbdbbbdcbaabddadcdacbdaaaabadadacbcbdaaacaabadcdbccacadaabcbdbbdbadadccacdcbcdbabbddcbcdcbcbabacdddaaabcabccacaddddacaadaadaddbdbbaaaabddaadbcdcaacdddacdddcadaadccccdaccbdbbbbcbbcdcbcabdccdbbaacbddcbcacdbbbdacbbcbcaccbbcbbcbdaccbaabdbbccdcbdcbbddcbcbdbbcbdcbabbddaabccadcdabcbaaadddcaadccccaddaaddacdbbcbabddadacabbbbcabbcdcaaaaddaabcbaaabcdbccaabccddddcccdbbdcaadbbbaaabbcabccaaddadcdbbbcccadbaabdbcbdaaddcbbaddcbddaaabcdbcdaabcbabdcbdccacabbccacccbabcdddcdbdccccbcacacacbacbcdcdaacbdbbcddbadcaaaccaddbddcddacccddcbccacadadacdbabbaabacaccccbbbacbaccaccdcbdadadababcbcbddbccacdcbbbcaccdcddddddcddadcdbcddddacbcbcacdadbdbaaabbcaadcadcaddacaddcaadcdcbcbbbadbbbbcdbacdddcbbdcbcdbdaadbcabddabcbdcbcbdbbdcddcacbdcbabbaabbcbddacdbbdabbaadacbbccccbbdbbbddcbdbdcaddbcbdccbddcbdbdccadaaccdcbdaccbacbcabbbbcdadacccaaadcaccbcbcacaacdbbccccbbacdbccbaadaaaadddacaadabdadbbbabbbdcaaaabdccbacaaabcaacaacacdccaadddabdbbaccacacddadddaadcaabbcbbaddddbacccaaddaaacadbabbbddcddddadadacbabacabcaabbbbcdbbcdbaaaccadaddbccdcdabacdcbbbcdcbdabdccbbdccbcdbdbdcdbdbcdddbcaabdbdcbdaccaabcdabcaddcccadcadcccbdcbabbbbdbbccaacbddbdadbdaaacdbcbdbdbccdaddbbcbdadddababbddbadbdbcdcdacdcdbcdbaabbcdadbbbaabacdddbbbdacbcabcbbbddacbdacdadacbdcbdbaccadcaacaaccdbcccaadabbdccbbcaaddcbdabbcbbcaadcdbbabaccbabcdbabdacdaddcddccaacdbaabbbcaccabdabadcbddbddadbccadcddbbcdbbabacddddaccacadcccccabcddcabbccacacadcddcbdacdcabcdadcaccacdcbaadbddbdbdddaddccdaaaacabcddccadbbccdaacaaaddadadadadbcacdbcccacbababaaaaaccdbcadaddbcccaadbdcdcdcbabbbbbdcbbcacbdaaababcdaadaddaaddcabdabacddcbadacbdbaaccddaaaccbacbcdadbacbcdadacbaaaacdabbacdabacacacbabaaadaadccbccabacbacbcbdaddacbddbbaababccbcccabbbdbbcbbdbdbccdddbbabcbadbacdadacbbdbaabcacabbcdcabcadacaaacbcdbbcdaacabddcacbdbbcbcbbcbddaacbabcbcdbdaddddcdcccacdddbadddccbdacddbdcccabdbbdaadcbadbdccdbabdcccddcaaaaddbdcacbddbabcbbccaadbbabcdabcbdddbdadcbadcadbbcbdbdababcccccbdabbdbbbcaadacacdcccdbbcbcbddcdcabcccbdccbccaccccddbbacbcadacabcaaacddcdbcbababcbdcccdaaddcdcbacacabadbaacadbdbadcdaddaaaccbcadbbdcbadacabadccccbacbabdcddbabcdcaaaddaabbdbdbadccbcdabbadcbbbadbbbbabbbbbccaadbcaaadcaadbcdaacbbdcacdaaddcacccbddbbddcadcbbabdcacabbbaadcbaadbaadccbaadbbabdbbbadcbaabcbccbabcbdcaccbaabdbdadaddbbdcabccaccbdbbcadcdccccacacdbbddabddaabdbdaddcbcdbacbcccabbddadadcaabcdabbabbbbbcacaacaaabddadcbbaccdcadadddabcaddbcddddcbdcabadaadacdcdbccbdadbababaacbcacadbdbbcbdbcdbbdbbabaddacadbdbbbdaadbbccacbbdcbbccbbdaccacdaabbbdccacaacdcbddabaccbcbadaccacddcbcdbdbccddcbcbdccdccabddacdcbbaaabbadddbddaaacacacaaadbbcddcacddbbcbdcacaacababacadbcacbbaadbaacacabdbcacbddbaaaccacbdcacdacadddbabbbcbdbabbdbbbaabcacacccdbbaabcaddbdcbaccaaaccbdddacdacacbbbbdddadadacadcbabacbbacdccccacdcddcacdbdaaabbcaacdccaaccdabcaabbddadcbbdbbbaddbaadbdbdcadacdcdcdcbcbdbdcdaaaababdbbdacadcacbacdccbabbadbdabccbddbddbbccbaccddcaacbadcddddcaddddbdaacdabddcbbadccdcdcbdacbacbdbbdbdbcbdcdbcdcdbbbacbdbbcccacadcdbbadbabdcddaddccadbadcabdabcdcabddaddddbbbacbcccbabbdaaddbaccbcdddcbcdccbbcacabbdbdccdcbdbccbbadcddcbddadddbbdcbacbaabcbdbdcabdadbdaacccbbdabadcbcdcacbdabbbadbadadbbabaddcadadcacbbacdbacadbabdaabbbdddcaaadcbbbcdcbdcbbdcabddbbcbabbbacacbbabdcabcaddcaadaaaadaabdbbcabadbbbdbcbaadcbdcdcdbdaaadabacbabbbcddcaddadbcbaaaccbccbdabcaababdbaddacdbaddbccdbbbadccccddabdcbcccbdbcbcabccadbbabaccbbccabcdcddaddadbcddbbdbcdbbdcabacbcdccdacccdadcaaccaabaaacbcdbdbbccbdbadadcacdcccabacdacaacbcdadbbddccbdaaccaaaacdaadaccaaabdcbacbddcbadaaabcacdbabccabbabcdacaadadbbcddabcbdcdbaddacddbcbcbbaccbbbbdbbbdbdbaaabdddcbcaccdcdcddbcacdbabbbbbabaaadabddbcdbbbadcdaabcacdabdccbaddddddcadbcbbcbadcbdbbabcabacddddaacddcccddbdbddbbdacbaccddddcdbcbbdcbabccbddaacbbdcdaabbdadaabdaacdbaadbabcabcabbadcdbcbbccaaabdcccdcbacacaacdbddcadbcdcbddbbddddbacaddbddcddaaabcdbbcbddbcabbbadababbadddabdcbaddadaccadddccbadbbccdccdabdcbacbaadaabbabadaadbdaddbbadcbbccbadadccdbaabdddcccdcabaaddccdabcbabbdaabaddcbcbaadaddbccacccdcbbaabbaadadabdcbdcbbababddaaacbabbddabbdaabdacbdbaabbddadabdbacdaaccdbaddbccbcbcaddaaacadbbcacbbdcccbcbcbcbcaadbaacbbacdccdbacbbdaaacdddcdacbabadcdbddacadcacadbdbdcdbcabacdabaadbcacdabbcbacaaacdbdbdcdbbcbdccbabdcaadabdabbabdadabdcdbccdacddadacbaabcadbadbcbcacbcacbcdbdbcdbddcdbababcabacdacbbbabdbcacbdcbccdbdaacccdaabdcbcacabccacddddabdbddcaadbbbacbcbccaccdddddbdbbbabcbdaccaaadbddadcdbcdaaabbbaacacbbddccbcadacbdcacbbcaabdadadbaccdccddbdcabcbdcdadabdcbdbaccccbcdbabbcadacabbcdbadcadddadadaddbdbdcaaabcdddccbdbbbabddcacacbbababadddcbbabaabcddbbbbbaabbdabacdababddacabdddccbdbbdacdaccdccbdcbbccbbddcdbcbbdcdbdcdcbcaacdacbcaacacdcccbaddddabaaadadddccccbdbcdddbbcbbdcbcccbbdcabaadbdcdbaabdaaababcbaaadadcdbcbadcbcdaacbcbddcbdcbabcccbdabdabcbacabcacbbbabdddcbacbacdacddbabadcddcbcacbacbcacaddcdacdadabdcccaccaddcbccbcdbaacababcddacaacbbcbbcacbabccbddaaabbbbacdcaccccabbbbdacccbcaddccdddabbcdbabcbdcbbbabaaacdbbaacbbadbdccccabcddcbdbaacdbbcdacdcddccbacbabcddacbbabbcadddaabcadcbcdcaccaccddbdcabbbcabacdcbdacbdbdcbbdbccbdbaccacaadddbbdacbdcacadadcdaccbcaddadcdddabddddccbaacbdbaadbdaaabdabaddaadbbabadbdcdadaaacadbcccabbabbdcaccdbcbbaadcccbadbbaadcbbdcacbcaccabdbcacbddaaabbdccbbcccbccdbacadaadcdcbcddccccdccbdaaccbbdcbddbdbdbcadcbbbbdcbbdcacddbbdbcddddcbddaabdaccabdccdcbbdabdaacbbdcaccddacbcdcabdbbdddbaddddacadaaddddbbddbadbdcbcbdabcddbdcabcbbaaadbcddcdbabcaddabbbdbdacdabbdcbdddcaddbdcddbcccccadcdacbcbbdbdbbdbadacbacabbbdacabdcdbcdadaabaadabdaddcbabbdaaacdccabbdbbccbcddcddccbacbdaadbbdabdacdbbdcdccbccdabcdcaddacbcacabababbabaddadbbddadbaccadcacacbabddccabcbaacccacaddabdadbbaaabadddabaabdbbbcadbaddcdabccccbaadcddcdddbbddcccbddbaaccadcbbaccddcdacbdccdcaddbbaadbddbbdddbddcdcdaaccdbddbdbdababdddbababccbcddbacaaddaadcbabbcbbadddaddbcddbdccadddcbbacadcaadddadcababbabbcaacbcaaabaddbdcbbdcbddbdbcdbabdabbcdbaaaacbadccbdbabaaadbbcbddbaacdcdbdaaadbcdcadacbccdbcbbaabdcbacbcbdbadddbbcbbaabaddadddcdaccbbababdcbccbadabcbccdacaacdabccddacabbdcddcbacdaccccadbddcdbbcdcaccdaaaaaddaaccdabadbdbaacadcaccccabaadadbcabadaacdacacaaabbccdcabdbcdbdbdbccbbdbcadbdabbdbcbccdbdbbdabbadbabbddcddadbbbccdbbcacbccdddbbbaaacddccabcbdbdbabcaadadadaadcbddcbdabccdabdcadcaccacdcbdbbdcccadaabacaabbbacaababbbaadcbcbaaabcabbaacdbdcaadddcccaadcbbcabdcbdcdccacdcbabcbcabbbbaadcdbcaadcabadcaddddaacccbacbaacdaaccddadbccacaaddaabacbcaddaadcabbbddcddddbabbacbdacddddcbddcdbcaaabbaadabdbaadcdccddcadcccaacaaabdcabaccccadbacbccaaadbcbbcccaddabddcbdacbcbbcbdcbdbdbdcdcbdcbddcbcdbaaadddddacdddbababaddbbdddbaadbbabaabccadbcbdbdbdccaabdbdddbbdacacdccbdbcabcbbcaadaabcbccddaacdbbbacbabbcbcbaabdaccbdaddbadbccddbcddbbbaabdaacadaaccdddaadbddbbcbdbbcbdbaaddacadbbbbbadadcbbddcdbddbbaacbcdcaabccacdcdbaddaaddacabaabdcbdbcbcabadddbdcccdddaddcdccaccdaacddcdaacbdaaddcacaabddbdaccadaadbabacbcaacbcaababbcbbaabaadbcbddbdddcbccabaaddbadabbabacccdcdddadcbabdadcbbcdccaacacdcaccaabdbbcbbcabcadababdbbddbdcabdbacbaacbddddbbaacbdabdccaadacdcbbcbadcdaabddbabcbacdababdcabbddbddbbbccacbddbaddbaaddddbccdaaaadabdcdadabbdcdaacdabcacacdcacccccaddccabdcbccdbbaadbcabccbbbdbcaacacabcbddbcbdcccdcdcaddaacaabddaddcbbbcaddaaaabcdddbadccadadddddadbadaaaddadcadaadabaabacabccdccbdbaccccaabdbbacbbbcbbbcdccadddabadcadacdcabcbaabdacdcbabbacaaaadbdaccabcdcdacdadaccdabcbadaacdbbdbcaddcccccccacdddccdccbacbbccbcdadcabccbbcdcbddbbbdcdacdccbcacddbcdcaabccbcaddcbabbbaabcbbcacbcdadcccaddadbaacdaaccbabddacbbacddbcccbdbbccaddaccccacddcabacacbcddbcbcbbdacabbbadcdbcddddacdaadcaadcdadbdccccacbbccbcbcdddcbacbcadbdcddadcccccbbadaddacacbbddbddcabaaabaaadaccadcbabcadccccaacdcbadcaaccbadcbbdbabaacbdcabaacbcabccdadbcabacbcdcdbaaaabbcddbaccababbacbadcabcaabbdbcdabcabcacbaacbcdacaccbcddbcaabcbdadaddaadadbacbbdaadbbbbaabadabcbcbbdbbcbbcabbdaddbabbdbbcbbbaacabdabaddadddacbcadddbccdcadcaacdcbcbcdccdacccaabccabadadccbdadadabcadcddcbcadacddbaddbbbadadcbdcdadcdbcbabcddbcdcccbdcddccdcdabbbbdbbcaabadbbbdbbdaaddcbdadbbcccbbdccadbddcacabdacdcdbadbcddbbccaabbcccaadbdddaaabdcccdacddcbbcdbcaadcacbbdccacacabdcadabbbaccbdacbbcdcaddddbbcddbccbbbccddbcaabacabcabadccddcdacaadcdadbcdcbaacccadadddabccbcadbbdcbcbdcadddaabaaabdbacabccbdabccccbbdbabdbdaccbccddcbcbabcdcadbdbbccdcdbadcbcacadcacbadbbdaabcbccbdbdbbcdcacdcbabacabdcbbcadadacbccaabcddaddcabddccbaccbdadadcaadcbadddadbaabbacccddabbddaaddcdccbbbcaaadbdbadbdbddddddadccbcbadbdcbdabddacddcabadbddbbbacbddabcbcdabdbbbcbdadddcadabccabcdaabbacbbcbbcbadbdabcabaacbcabdcbdcadadacbbcdcbabdcbacdaddcaabdcddabcbbcdcddcdbbddbaaccccdaacadabaabdacabadcdacdcacadcbacccccadabbccbccbaabdcbbcbbccbaadcbbbbcbbcddacddcbaabcbbcaddabcbddabddbdcbdadcbaddacbcbcbbcdaacdccaddbbcdcadbbaacbdabbdaababadaadcbabbcddbbbaaacddcccbcaabccabdcbadcbbcaadaddbdbdabcbbdcbcdbdcdcabacdaddbbacdabddcadcddabbbdccbddaabdadaaabddccdabcbaadccacddadaababbaadcdabdaacdcbcadadbcadbdadcaabadcadcddbcbcacbadcdacababadbbbaaacbcaaadddaddaccdaccdabccacbdaabdccdaabccabaaacbdaababadbadbccdacdcbcbacbbaddcdacabbabbcabbcdabbcbdbdbbacdaacdcdbbbdadcbbccbcacbdcbaadcdcbcccdcaadcaadbcdbdbbdbdccccabccacddaabdccbcdaabaddbacacabaaddaaabbcbdbddcbaabaacacddcdabccabbbaccabcaaabcdadbaadcdadaaabdadcabbbdccadcbddbcabbdaabacacdadddbbccdadcdcaccddccddcbaadcabbcdbbabccbcdbbcddbccdcddabddabbcabdadabbaaacccbdabbabbdcbdaaccaddbccdbdbbadbbabdaadddcbbbabdccaacbbccbdaccbbdbdaddccccacbabacbccccbacdcdbdbabaddabaaadbbaaddcbababcbbacbbbcbcddbdaddcccbaabdbbcacbaccdbdaddbdacdcbbaccacbbddadbcabbbdacddddcbaabbdbdccacadbdaaacdaaccdddabdabdcbcacadbddccbbbbbdcdcadabcdddccdaabdcbadbcccdacddddcbdacbacdcdabbabdbcbcbdbbacbdbbaddcdcbbadadcaabbabccabddacaadbcbbddddddddbdabbdbbaaaabcddddacaadaadddacbbdccabbcabacbccbadcdbdddabbcddbdabadccabbdcadcbadbbdbbddcdcdcaccbdccdcbaaadbadccacadacbabdaacadadadcaadbdacaacacdcdbbbbacbdbdbcdbbbcbdadcbacaccabdabbdbcabbbadcccbdcccabacbabbcaacccbaaddaccddcbbdaadaaaacdbbcdcdbdbbcddadcddabbbaccbaacddddccdaaaddbbdaacdbbacabcadcadaabbdcbdcbcdcccdadadcdddbdaabbbaaacadadadbdbaddacdbacbbccbdbbbdddacccaacccabbadbbaddaacdcbddbaddcbcbbccbadddacaadbabddbcbcdcbbdbbcdadccddbaddcddcabdcdbdacdbcaacaddcbacbbdddbaadbadccabdcacaabcaaaaabcdcbbdcddcdbcbcbdbdbcbacdbdabcdccdbddbdaacabbbaabddbddaabddcbccddddacdcdbddadbbcdcdcadbbcbaaadcdbbaddbacbbbddcadcdabdaddbabadccadabdbdacdacdabacbaabcbcacdabcbdbdbcabdabccccaadacddbcddbdbccabdbdaaabddbabbabcddbbcbbaabcaaccabccbadacbacabaccbaacaacadbadacccbaabbcbcccdabbbabccbbacbcbcababcacbccbabbcdcdabbaddbdcdabbdbbabcbdcbadcbdaacdbcdaabcadadccbccdcdbbaccbbabbdadcaddacabcbbbdbaccaddccdccaadbbdcdddbbbaccccccbdbdaccdbcaacdcaaabbbadbbcbbbcddbbdbdaabbdcadcbbdcabdaccbbdddbccbbcadadbcccbdccbbdccddcacadbbbbddcbbcbccbcbcdcadcbcadacaadbcadbadabbcdcbcbcbdbbcbdbcabbabadadcdbbddcdccaabdcccaacadababcdabdcccbcdaacbdaddccaabdaabdccbdadccbcadbbdacbacdccbabacacbaaabbccdabddbaaaadccadcabcdaccdaddcbbbbbabcdaaccaccccbdadacbdbdacccadaaadacdacbbaaababdabadbbcadabdcddbbbcabbacbacbccbadbcaccadaaddacbaddbcacadabdaccaddaababcdadddbdaddbaccaadccdccccdcadaaddacbcbbdaabdcdcbcdbcddaddbaacbababcdcccdcdbcbdaaabcbadadcccaabcbcbddcdaddddcbdccddabaddcababaccabbacbaaaabdbcdabbaacaacbcdbcbabdccccabdacdbadbbbaadbbacccdccabbacdccddbcbbacabdadbcababbbbdacbaabccbbddcddccbdadbbdaddbbcabbadccdaacccabcbbacdadaccbababccabccbcabacbddadcbdbaadbcacaadbddcdabbbccaaacaadbbcadadbbddccddcdcabaccdaaaccbbddaccaaddcdcbaabbddbacbbbdbcacddbacbbacdaaadbacbacddacbbbaddccdaddcacdadaabacaabaaaabaaadbdcdacaddadabccddbabaadddcabcdbdbdbcadbdcbbbdbcccdaabcddacccbaabdadcbdbdbdaaabcddbadcadbacbaabcaddacdcabdacccdcacbccaddaabaaacccdcdcbadcbdddbbdcdabcabdcacbdbacbaacccdbbabcdbbbdcccadbadbcbbbaddacbbbdbdccbabbddbcccdadbddddaabbaddccaaadccacbbbabccdaccbacadcdccbbcdacbadadbbbcdbbcdadcaacdbadbcabdaddaadbdababcbddbabcddcdcbdaacccdcaacbdcbcdcababdbcccabbdbcbcdccdaccbdcadbabaddbadaddbaadcddcccacaaacbcaddabbacdbadcbadaccbaddbcadccacaccadcaaccadbcababcacdcdaccdcddabddbdaaabaaaaaaadcdcdacadcaacdddadbbbdbcbbcbcaddaaccbddcdbbaccddbcacaadbdacacacdacddccdacdcacadbacbbcbcdcccadbdccadbaabcabbcabacbbcdaaadcdabbdbdddadcabbbdadbbadcacbcdbdcdadcccddbaddadbaddcbdadadddcbbbdbdbccddacbdccacaabbccdcaaaacdbbbcccaccbcaaabbbddcadabbbbcbaccdcdabccdabaabcdadccaabdadcaacaaddbbccdbcdddbadacbdbdabaaabcdaacadcbabcacbacabadadcdcaadadbdddcbcaaddadadbdaadbbadcdbdbacacbacdbcdcdcdcdbcaaccbcbbaabadaaaaccdbadaddaaacacaabdbdccddbdddacbaccdbcbacbaaddacadcdcddcaacbadcacadbcccbcddadabbaadcdaabbaaccaccdaadaccabadaabbaaccdbccddbcabcccdadabcdbcaccbacdcbbbdccaccbdccaacabcacbddbadbbcdbbbbbcccadadcddadcbbbbbbadccbcdcabaadabbcbbbacbcacddbcdddbcbcbbdacbcbdddbadbaabdadbbccddbcdcbacbbcbdcadbadbccdcdcbadcaadcdadddcbcaacaacaaabddaacabdcbbcacdcddadbaabcdaaabccbadabbaaaabacbabcabdaadadbadddbbaabdbbdccbcbbaacbadddcdbddddaabdabaaacbbaaacbccbdbbdbcdcdcccbbdacddcdccacbccbdadbdbbbbacbbbcabbbbadaaaabcbadcccdbdadcdadbbdbbccaccbaccbcacacbbbabcaddbbadbcaacbccdccdbbdbcadbacbacabcbcdbdbcacbacaabcabdbdacaabdcdbbdbbbcbccadbcaddaddbbacbabbbbacdacadbdaacdbccbbcaacbadaabababcdbbbabcaadadabacbbcacbcadabbcdababacacdbbacaaabbbaadbcacdababccddcccbdcdbadcdcddcbdaabadbbddabbcddcbbcbbdcbabbbaaddddddaccbbdbbdadadbdbddaaddbadbdaacbadababcbdbdbaddbabcdbbdacaddccaacbadcbbabcdcaddbaccdaaaabacadbcabddbaacbddcaaaccacbbcdddcddbdadcbcacbbbbddcbcbbdaddadabaadabccbcbbcdbddddadbababcaabdbcacbabdadabadcddcadddbccddbcccaccbdddbadaaadbaaabbcadbbabcdaccaabaacdabcdadcdddaccdaabbbdbbabbdabbcdbaaaaccaadcaabaababcacdaaddacccadcaaadbdbddcbdcadcbcbccbabccaadabcbaaacabaddcdcaaabdadbbdbabababbadbcdbabbabccbddaacbdcdcddcdadbaccbbacaddabababbadccacabcddbacbcabbdabbbabdcbabadccabccbcddaaddadabcbacccbbacbdcccdcdbadacaccadadabdddaaabcadbdbdacacdbaccacdcdbbacabdbbcdacccbbcbcadccabaabbdadcdadcccdaacdbbbdaaadbbcdddaabdbbadabadcbdbaacabaaddbcbbaaadbdabadaaabccbabcadbccabdadccdccabbcbcbcbbacbcddadbbbccddabbdccabcdbbcaaabbbdbdbcdabbcdddcabcbbcbadbdcaabcdbddacadbbdbdcddcccaabbdabbcccbaaccccdbdbcccaacbddbccdbdaaaaaadddcccbcadbabcadcaccccdbbddbdbbccbabcccbbbdbbdacaddbcdbcdacdadcdacdbaabdcbbccbaaabdabddcdbaabcdbdbdabbccdabacdcdbaabababaacbbddbdcccbccdddcdbcbadbdaddcadddbbadcadacaaddcabcbabcadadaadbbdcabdadcdddcdaacbccdaadbcdababcbbbcdcaacacbccdaddbadbbbbbbcdbbadbbabdcdaddbbadcdcacdbcbacddccddbcddbddbccaacbdbdacbaacbdcccaaaccccdcccbddbbcadbcdcbababcbabcdaaabdbadbaaabcccaadcdddaadbbbdadcdcdccbbdbdcabaadddbdbccbdbccadbbaabaacacbdcbacdbdbddaabccacdcabdaaabbbabbcbbbddbaccbddaccbbaddddaacdbacdadadacabbdacccbcdbabbcadddbbbdacdbdcdadbaabdbbaccdddbabcdcadabcaadaccbabadbbcbccbacdabcadabdbcddccacdcddbcadaaadbcdccaddbdaaabbaadcbbaacbcdcbadcbadbdacdbcbcbcdadabcbdcbdbbcbddadbbcdcdbadaaaddadcbcacbcabcddcacaccabcccacbdbbdbddbacadabdadbdbdddbaddddccccbaabdcddaadbadddcacdbbcccccbcababcbaacbddbacddddcbccdbabbdcbabcbcdccadadbcbbabaccbcccbaacbdbadddbcbbcbdacacccbabadcdbaccbcdddcbbbdbcbdabdbddddddbbbcbaccaabbcdcddcbabbbabbcadbccdaadaddccdbbcaccbabbdaabccbcbdcddcccdbdcacbbddddcdbcccdacbbaadbccbddddbdcdabcddbdcbbcdddddaabaddbcbbaaddacdcdcccacdabbdbbcacddcdcbabaabdcbacbbbbdbaabccbbacdaccbcbcdcabcbbbcddacabaccbbadddaddbbdcaacbdacdbbdddacbbadaaacbbbdcccdaaadadccccbadadcbcccacdbbdcccaccbdabcaabddaabcccacdadccbbdbacbcadccaaadcbcdddcadbadabacabdccadabcdacddacaccbbcbcdcccbbadbaacacadaadabbbcbddaaccadbbccdcabacdddcacbdcabdaabdcaaacdddabbdadcbcbdabacddbabccbadaabdcaaaacddadcdddcbcaabcdddbdcdbccddbadcdabdabdacdcbbdaccdcaacaccdbaabdddaadaabdccdcbdabdaabcbbbbdacdcdaaccdbdadaacabacccdabbcbbbadcababcadbacbdacbbdcddacabccbccbdcbcbacbabdbddbbcabbcbbcbccdcbcdbacddadaacdbbccbdcbdbabcdadacacbbadbdcaaadaacdbcdbcdccaaacacdbbbdbbbbdbdddcbaacbdababdbcdcaadacddabcbcadacbcbaacbbcadcaadacabadadaabaaaaccabdcbddaabdcbbabdcddabbdcccdbcccbcbbadadbadddddbdabcccacaddbacaaadbacdadabcabdbdabbabccabbcaabdddcddbcaadcddacacbdaadaaadaccadcdcbddbadcabaaaacbaddcacbadcdadddbccdacdbacabcaccaabbbdcabdbabbaaccabcbdcacddddbddbacaddcbcbddbbaccbabdbccaabdccabbbddbdacbbddaddbaccdbdcbddddbbdaccdbaccaadadbadaabcdcbdbbbbabcdcdaccdbdbdacaadbdabacdccaabddbcccdcbbabacdbacabacccadabbbbcbbdcccacbcdbbabbbadcdbcbaacacadbadabdcdcbcbacbddbbddbcaadaddbccbaaaddcaacbddbccdbcdbbbcdaacbbbcccbcdbcccbaddadcbdccabdabbaccdacbccbddaaccdbcbadbacabdaaddabdccabcccabcbdddbcdcbddcabdcdbbdaccccbdbadccadbacbbdcbddcdbabccdbcaacdbdddbadabbcdacbccdadbcdcbdbadcaaaabdbddbbccacaadbbaaaadaadbbcacacbbaabaabcababdacadddaaaddbcadcddcaacaccaccabdbcddcccacdadbcbdabaadbbddabbaacaddaaaadcacacddccabcbdcddaccccdddacdbcaaddcddbddbcccbdacacabaddcaadaccbbccbbbcbbadacdadcddddbaabadbcccddddcddbdadcccdcbdccdabadbabcbcbbbcdabcaccbdcacaddcbcacdaadaaddbcdabccbaaccdcbcdacbbdbdaddbadbdcbdbacbadaaababccdbdddcddbbbdcdccdddacccbaddbbdaaaacbdcdacbbabadcadccbccaaadcbbbbbdcabbcddaccbaabdbcbcbbadcbdbdadccdbddaccabacbababadbadcbadbabbabcdaaadbcbbdabbadadaadadbdcbbaccaccccacbcbcadddabaddccaabadcabdaabddcacdcbadbccdaccdaacdcbbcdbbbabadcaabdaaababababbbadcabdddddcdbaabcdcdbdaadaddcbdcabadabbaadcdacaacdbbbbabbcbbbbadbaddabaaccbabddbcdcddccdbcdaadbccccdccbbdaadaccbddbddddaddbdcbccbdbdddbcdadcdccaabcbacbcacdbbbdaacbcddcbbacbccadbbcaacdabababcbccddadccbbdabdddadaacdbcadbcddaccbdacdacccddbcbddbaababadabddcdbdddbacccbbbccbcbaabcbbabdbdbabadbcbadaccdcbcbbbbadaaaddccacdccdbabdaaabbbbadacddbacabdcaadcaabdaddbbabdbbbddccbbccaddabacadbacdcbdadacabbddcdcaccccbaaadaacddaccccadcdbcababcaaaaacaaddaaaabcdcacdcbbccbdcbdaddcddddbdbcbbcdbcdcdccadcccbbdddcdbdbcbbcbcbccdbabcdbcddcbcabbcacabaaadbcacbcbabbbdacbccaadbddaadbcaaacdaddccccdbbabdacaddbcbddadddacbcbaadaadcccbcdacddbbabdbcdcaacbddccbdcdacdccdcdcdbadbadcdccccdacabdbccdcbacacbaddbccadcacdabaabcabbbabccabdbcdbccdbabbadccadbdaabadcacccdcaccaadcdaabbaadaadcdcddcacdaaaacbdcbbacaddbacbababdbaacccacacccabbdbaaacabdbaabdbdbbbcdbcbbcbcabadcdadbbcaccaadcdbbbbbbdacddcacdddabaadabacadadabcccaadaddadcdcbdccddbddcbaadacdacbccccabcaaadcdcbbdcbbabaaabcbdcdcbdbddacddaddbddcabbdccbacaccdbccbaacbcdbcbcadcbccdaaaaaacabcbdadbccdddacbaabbcbacdaacbcdcccadddcaadcbdacdbdbbaddbbccaadcbbaadbbaaabbccccdbacccacdbdacabaabaaacddacabaabaccabacbbdbacabbcadbdddbddacbbcbbadacbdabccbdacadbbbaccbcdcdadcabbcccabaaadbbaaaadadbbbdcdddcbbdbccabbabaacabacadcdbbacaabaddabbdcaabbadbadcacadcccdaabcdcabddbddccaabcbdaacccddbbacaaabacbacbbddaacddabccbabbbdddadabcdabbcbcbbdddababdbabcccdaadaadddacadbacbdbbdcaddcadbcbbdacdcabccbccbcbbdaaddbccbaccbcbbabdaabcadbdbaccbcccdadabbcadcabbcbcbacbccbdcaabdaadabaabaadacadcdacccacacdcbbadcdcbbabdcdbcdbcdccaabbccdacddccabdbbdbccbcadbcdbdcaadacbaabaacbbdcacaacadcdcdcadabcaabdabbbbdbdadaccadbaabacadacdabbabbcddccaaccabdbbabcadadaadcabbddacbdbcbcbaccaadcadcadcaadbbaaadcdbccaaabddcadacbddbadddbbddbdbccbcbbacadaaddbccabbcacdddbccbcccdccdddbcccdbbddacccadcdbbcacddababaaababcdacddbabccbbbadbdcaaadddbcadbbcbacbcadcaaddaacccacacbbabdacbacbcccccdbcaccaababbcbbbcdabcadcbaccaabcaddabbdacbaaccccbdbcdbbbaabdbacbdbddcddadcbccdddabadbbddcacdbdbadadcabddbaddbaabaadadbaddabdcccdbaababaaadaaabcbbabacbdbdabbbabbccadcdcdbdddcbaadddaccddabcdaababcdbcdddadddccddabbabadadabcdbdbadabadbcbbddbabadcdccbbbbdcbbadccabddcbdcbdbccaddadcbacbabbbaddbbbacdbdabbdcacdaaacbbcaccacddcacabcbabcaadadbddccccddadbdddabaababacdabbaccadbabcbdccadcddbcaddacbadddccabaaadcddabcadbbccaacddcdcaacadccddccddcabdcccbddadbcdbdbdbbdbccbbcacbcdbbbdaccbbdbacdabbbdcbacbaaabbbadcaabcacddcbdddcccbcdaadbcbabdacdadbcbbbbcdbcdabbcccabcbaddaaddbabadabdcbdddcacdaddbdcababdcbacbaddcccbaabdddbaaaabdbddadcdcabcaaabaadbbccbadbabcdbbbaacccaddbbacbabbabababaaacaaacccabcbbddbbccababbaadcabbbaabbaabbacabdabbbbbdbbcbcadaaacadddbaabdcabdaababccaacacbbdacabaddcccacccacbaabcaccaacdaacdcdcccbdbadccbccadbadaccdcdbcadcbcbcddbbbbabbbbdbdadadcaacddbbacdaccbaadaddabbcddaddcbadcbddbbbdbbaccbddabdcbaacdbabddcbdadcdbcadbbccaccbcaacddbcbabcccbbaacabdddbabdcabcabbdabbbcbbcdcbacbcadbcbbcadddbdcbcbbacdadcacdaddccabbcbdddccdaadddcbbdccaddbbcdbcdcadcdaabadcaacabcdccdbcacbadcbbaabcbbddddcbdabbccacacaabbdbcccccccbbadbcabdcaaadcbabcddcaccdccddaababcbcdbbabbcdadddcacbddacaaacacababacbcadccdbaababcddccadbbcdddcbbdccdcadabdddbbbcbcdacbdddcacbcdcdaddcbdbcddccdcbacacccabaaaddddbcabdbddbdddcabdddbdccbdcadccadbaccabdabbbababbdcdabcddbccacbcdbbacdcdbdcccbaacbadaaabdaacaaaaaaadbbcbdbdbbaaadaaddbaccdbabbbdbcdababccccbbdbaabbcdacbdcbbbbcdddadccbacbdddaccadbbddcbbcdbcbbdddaddbbadccbacbcccbbbcbcaccbcbadcdcadcdbaddcabcbdabaabdbdabbdabdadbacbcccdbcacbbdabacdaacdccaabadabbcddbadaadddccdcbddbdcdcdbdcadccdcddbbbbcaabbdcbddaacbbaadcbcccabcbdbdbbacbacadabdcdcdbdaaddbabaababaadaaccdabdccdddbcbadaaacbbcddcccddacbcdcaddadccdabcbbccccdbbccacdbbdacbbdcddccaadaadbbcaabccdabcdadacdbbdbddcdddbbcdbaaaadaaaccaadbbbadadcacdaddaccacbdcbcdabbbbbacdcacccdaadbdbdacbdddbdcbbcddcdacaababccdbdcadaabddcacdcdcbcccccacdaadaabdbcaacdcdcaddbabdcabbaadaccadbdcdbdcbccbaddbabdcdddadacdbdbbcaacddaaadddcdaaadcddccaddabdbacdabbdbaacbbdcabadbccbdadcdbbbbcccaacddabaacdcbdacdcdbacdcbdadcbbbdacacaadcbdddbdacccabdaaccadaaacacdbaabcccbbbaadcddbccadbdccabacdaabbacadbadbaadadadaadadcdddbdacdddbcaabdbbcddadccdcacdbbbadaababbcbadaababdbcdbacbabdcbddcbaaabbbcdbdbaaddacaaaabdccdacdbdabddbddcddddabadcacadaaabbdcddbcdacbbcddcddacddbdacdcacabdaccdccccbbdcdbdbaddabbbdabcbddcaadadbdacaadaaadcbbdabdcdcacabaddbbcbcaadbbdbcdbbdbacdaaaadacdabaddabdcdbaaabccaccadbadbbbccdbdaadadaabdcabbbcabaabacadccacbccacdccdaacacbaddddcbaaabccdacbdbdacbbcabcacdddccbababbaacbbbaabdddcdbacdddabdcaccbddccbbcaabcbdacdcbacacbadccbdaacbaabcbbabdaadddaadcdcabaabcdbcbacdccacacdadccdbdadbcbadcddabacdacccccdbacdbdbcabcbccaabccdaacbccdadaaccdddaadccaadcaabdaadbacddcdcaabaadcdbbdabdbaddadbbccaabdbacacacabbbdbbaccdabcdabadaddbadabcaadbbccbdbcddabaadabaadabdbbadbdccbccdcbbadcbcadccabbbdcbacddbacdcadbcdccbcdcbdaccdaabcbcbcbdacaadccadcdadcbddddbdcdbaccaadddccbbbaabbdbabcaadddcdbcbcdaacaddcbdaacbdcadccbbdccddcbdcbcccbaabadcdbadbddbcbbdaaaabbaabddbadcadbdccccdabdbbcacadcdaabababcbadccaabbbdcabcdabdcabcbcdcadbdacdcccdccddbabcdcbabcaccbdbccddddbbdcdcaababdaacaaccdbabcaddbbaddcabddccbdbddcbabccdbcbdabdbadadaccddbaaabacdaabbacdaddadcdbcbdbaddcccaddaddcbddcacccacabbdacdcaadaddababbcdcbcabbbddabddddadbcdabadbabadcbdddbccbadbccdaaacabdbaddacddacdcaaabcadacaccddcdccbacdbcddaaccddbbdbadcdbbbcaaccdcdacaabacbdbbcaddcdbbdadbbacadcbdbdcbdbadabddbdddddbbccdabcaabccacadcabdccbbdddadbdcdbcbaaabacaccaaaaababadbbcbabdcdbaaacbddaadcacbbadbdadbdcbbbcacdbbdccdcacbcbbdddbbbdaaddcacbcdaaddadaabdaccdbbacdbbdbabababbaccdccccdaabacbbcbdbbcdcaabdbbdadaadbddaccccbcbbbcbacadbdacacddabacabadacbbbaacbcdcabdacbcbbbdcaaddcadaaaacacdaacbbaddbbbdcdbdbdddbaabccdddacabdacbddacdacdbaaacbddacabbaabddabbdbdbdabdacacbdbbbbabdabaaacaadcacbcddadaadddcaccbdbaabdabbdacdbdcccdcadabaaadbbaddbabbacddddadcbaacccdbdcdddcbabbcbddbdccdddcadccbbbcbcbdcccabbcacbddbbaaaadacdddbcdbdabbaaaccadbcbaacdcddbccbbbbcbbbcbdadbbdcaadddaadbaacaaabddbcbcadbbabbccbaacdcbcadbcdddbacbdbaadcacadaccbcdcdbbccabdbddcbcdabaccabbacbbbdacdacbcaccdbbcdaccbbbccddbbcaadaadcabcabbdaadcdaadbbcadcdbabcdaacdaabaacdaacdddcbbaccdbbcbcddbbddbdbdacaccddccdaddabadbdabaabbbaadabaacbabaabaadcaabadddbabbbcdcccdcbacaadbdbbdcadcabddadacbadcccadddcadabcadbcbbacacdcbbcbabaddbbabdbabdbcdaaacadaadbdcdadccccddcdddcabcacdbbcbcdbdccdadbcababaccbabdcbadcaaccacaaddbcbabaadcddacbadddadbcbbcabbabbbaabaccbdbadaddacababaddbbdbddccdcbcaadbcdaaaadbcaccdbccbbcbabdbddbdcdcabcdcccbbbccabdbdbbddbccdbddcaacabcccbcddbddaacdcaadccbdccbccdbcbabdaaacbbbcdbbbcdbdbddcbbbcabacbccdadccabaaaccadbbcdbccbddaacddbdbcbddadddbdcbdcbbcaadcbcdcabbdddccacccbcdadcdcbccdaabcbdcaaaacbccbbccdaabdbcadabcdcbcaacaaabcaaadadcddababdcbbbaabbabdddbdcadccccbdcacaacbcccaddaacccabadbabcaadccacdaadacdbbababbdacdcdbcadbcaacdbccbbdabdbbcbdbddbaaabccdcbabbadaadbcdcdaacabbdadbaabbccacadbcdbbbdcdbbcbacdccdcbdbaabbdabdbdaabcaaabbbaccbcbabbcbdddabddacdcddcaabccadacbdcadddadabdbbbbbdcdccbaaccbcbabcbddbabbccaadbbdcdbcaccacabdbaacdcbdcdcaaccddaaacbadddbdbdcbbccacacbbcdddabbcaadbddcdcddacbdacbdcdcddaccdbcbadadadbbcbcbcaacbbcdcbccbdbcbbdabbacacaadbdbcaddbddbccadccccbadcbbbbcbdcdaaadbcaaacdabdddabbcaddcadaadaccadbdbacbaacaabdcccbbddddadcbbdccbabcaabdbadddcbbaadaccbdcbdadccddabdbabdddaddaabdcbdcdbbbaadbbdbaaacbbaaccdcaacddccdabdbdccdabcbacaabdadadcdbbdacacadccaabacdcbcdaddbbddcddbdbcdddbbdbabddabadbaccaaccdbbabcdcaaaccabddabcbcaadaaaaccbdddcbaaacbabbdaacdcdcddacabdbcbcaabbacadbbbbcbcbadabddccbbdcccaacaabadddabacccadbaddadbaabcdcbcbabaacbbdabcadcbcacdacccbdacdbdaddccbdacadcccabacacddddacaddbccdacdadcacbddbdddbacacaadaabdcabacbbbcaccbbbbcdacadcdbbdbbabcdacbcacadaddaaabcdbabccabbababcbcdddbcbdbaccbddadaadacbbbacdbbbdddccbcaccaacbaacaccddbbcbcdcdacaabdcbaadcbcbbbadbabddcaadaabacbdbacdddcbcaaaabbdabadddcbdcabaddadbaccbdcbadbddbbdadaabbbbaddaaaaddbaddddccacbdcdabbbbdccbdddcccaacdbdadaadabbbbcacaababcbabddcdcbddabadcbdbcbddbcccdcadbcbacbcdabadbdcacccadacbdbbbacabdbbaaccdaccabcacadcbcaacbabacbccdaaadccbbabaabaddbdcbddbccbdaacddbdaaadcaddbddcdbbccbabbcccaaddbddbcaadaabdcabaabdddabbaddbbdbbadacaaacbadcdbcaccbdabdcaddbdddbadddaabdbabbbcbdacaccdcbbcbabdddacddaddbcbcccdbababaccbdddddcbcacddbaccbcddbbcaaaaadbabcbddabbbcaddbdadccadccacbccabcabaadbcaaababadabbcadcdbacabdacbbbcdbbaacbcbbdacdcdddcdccdcdbbaadabbaacbbaccbaabcbdbddbdccbcbbcaaadbbcbcdccbaabbddcbbadbbdbababcbddcbddbdcdaadbdabaaacbbdcbccddabcbabcacadbcddbccdbdacdddcdaadbabdcbbddbadbddadcdddbadadccbabaababacdadcaabadbcbcbacdcbddddbacacabaddcdccbacacaabccdadbabdadbadcbdbcdbbdcccbacdcabbdabccaddbdddbdadcaabcdcccabbbcbbbdbacbbcbababddabddccbdbbddacbbaaaddcbaabaccdadadbadacdaddabadddcaabcabdbaddcdcaadaacdadddabdbddbadcbcbadacabbcdbcdcdadadcabcbaddacadccdbcbcbcabdcbcbccadbadabbbdbdacbbdacdddbadcadcdccbcabccdcaadcccdaaccadbdcbbcacbacdacdbaadccdaacdabdadbcddcabdcdbcccabcdabcbabddabdaabcddacaaacadccbabdcccdcbacabccccdcdaabacddcbdbcabcddaddbdababbcaabcdbccddcddbdcabaaccdbaaacadccbbdbbdccacbdaaabbdbdcadbdbbbcdbdacabdacdbaabdcdbdcbdcddcaabbbcbbccbabacabdddabddbcaabacbdddbadaaabbbacacaccaddccbdcdbdcacbdbdadbbbbcbbdbcadbdacadbdcddccddaabccabcdddbbdcadbcadcaccdabdcacbbdaaddcaacbcabcabbaddcdccacabbcbbabcbbccaadbaabcdabadddbccccccadbcbbdadcdabbdbdacababbacddddbadabcddcdaaacdcccabdcacadbbbbcdadacaacbddbbcbdbcacdccdbddbcdababacddbabbdcacbadadabacdabcaadcbbcbcccbcbcaddddabaabcaabcbcdcbdcadbbbacddcbbdcdcacabcaadadcbbbbcadaccaabdacbcbbacbbddadcddbabacbabddbadadaaaababcadcbdaacabbcbbdccbadccccdbccaaccababcbdbbcdbddcbbcacaaacabbcbacbaadacdcadbcddcaabbbcbbacaaccbbbbddacabbdbdbcbccccdbcdabdcdcaaabcccdbaabcdacddcdaadcbbbcbcddabdccabbdbaccadaaacbaccabcdaaadccadbdcbcabccdacbdcdbbdadbabbbcbcbbadbbbcabcbdbcbacaaddabcbaccddacbbaabddcbcacbaadcdddabdacbdabcbaacbaabddababaadccbaaccdccbacdcbbdbbbcdbcacbbddddcdbbabbbacacbbdcabadadbcbbbdbdbaaddabdcbcbadcbdbdbdcdbbaacbdadaccbbddbddcdaccdbbbabaadcdacaaaacaaccdabbdcccdbccccaaaccccbaaacbaccccbbcbabcbabcdccddbbabdddadbbababcbaddaadcacdbbdbadbabdccacadbacaddcaadccddcaaabcbcadabbdccddadbdbcbbaadbcdcdccbccbacaaaaaadddabbccaadbabcdcdbbbcbbbdcaaaadddbbdcdabcbdccbbaadbabdbdcbcdaaaabaaabadbacbbdbcccadcdbbaadbbaccbabdcdcdaccbcaaccbadabdabdcaacddcacbadcbdaaaddadcaddadbdbabcaacbcbdbdcabdabacbcabdcbcdddacaddbacaccbcddcccacabcbdcdbcadcdddaddacbccdbdcccbdbcbaaabdaabaccdabcdcaaabacacbbccbccdcdcccbbbcdcdadccddadccbbccbddbdcabbbadbbbddcaaaaddbadacbcddbddabcbaabaadcdddcbaaacaabbcddddbbbbcdabbdbadaaacccccdccadaccabaabaaacccabbcdbccdddcabbbbdcbdabbbacabbcbbdddddacaacbaabddbadcacadcbbbbbaccdcacacaadcddbabdabdabcacacdcadacacddbbadacdddbadabcbdccbcaddbabcacacddcadbbbddcccaaaddcadddbccadbdddbaddbacadbdabdbabddaccaabddbdcdbbcbcabdcbacccddacdacbbdcabdacadbdddcabbcdbacbbcbcaacababdbcbbdbaabbadacbbaaacbdacacdabddbcabbccbdbadaaadabacccddbbaadbccaddbbccbcabcdacadddddacddbbbabcbabcdbbdbbcbbabcdaabbdcaddadacbabadbbdbabbddbcddddcbaacddacabcbdcaadcbddaaacdcaccccbcdbacdddcccadcabccbdcadabbababcacdbaabbbcbbcbcaadbcaadababbabdacaaddbabcbbacbbbbbabcdbabcbabccbdcbcbdddcbaacacbabdbccdcbbdadaaabaaaccbabcddccabdbbdcadacabdcacddcacbcdbcdddadaacacbccdaccacabcbbabaacaacbbbccadbddbbdddacbdddaadddacbdbbddbdcbbbacbbdcddbcacacacadcaadccbdcdcdbabdabaacaaccdadcddcdddcbdccdddbdaaaabaccaabcbcdbccdddadcbdcdadacddaadacdabdcccccacbbbddaaaadcdbbcdacbcacdbdbacdccbcdbcbababcdddddccaadcdbbbcdbbccdddbbacaabbcadaddadbdbadacccdcddcabacdcdbcdaababdabcaddbcccacdbcdaaabcddbbcbdbabcccbdddddddaddbdbaadcaaabbddbcdbdddccbcbbddaadcadddbacdbdbddabdccbdacadaccaadddddcbaaacababaaaadbcabdabbcbbacddbcccdadabbabaaddbdabcbadddcdabcbdbcbbadcddacddbcbabbdcdbcddabdcabdadbcadadbcbcacbdbcdcbacddcdaabacaaabaabaadcbcdcbbbacdcadadbbcbdbbbbcbabbbbcdaabcaddbaaaaadabcadcdcaacadcbddaaabdabaaadccdddbacbdddbcbadcaaadcbdddcaccadabddadbabcadddcccbaabcbdbbbbddbcddadcbddadaacddddccacacdcdcabbdccdbccdcdcbccbcbddaaabdddabcadacaadbbddccaccaccabbaddbdbcdbaddcbdaaaabcadcabadcbbabaccabbbdadcbcbabbaacddbaacdacaabbabdaaddcabccddabddbddcbbaccabacbabdcdcaabcdcbdabcaaadbcbadcdbabcccbcbcdadddacacbdbcdbaadddcbadcaadaaaadbbdcbdcabbacbddcaadbdcdaccbaababaddacdaabcbdbabcddcddbbbcbbbdbbdbadbbacacddcaaadbabdbaadadcaccdcabdbbaabacbbcddadcbcbadaddcbcbcbbcabbdbadacdaaddcdbbdddadcbacabbabaacbddcdbbbcbbbadadacbddddcacbaadacbdaacbdacbcdbcabcdbbaaacbbbdccadabaadaddaacbdbdabcbddaccaccabcabadbabdcacdabbacbbdaccadcacadbcaabddbdbdaaacdccbcbadaacccbdccaadddaddbcbcaaadbddaadcdbbbdbcacaddcdbdacabbbbabbaaaccdaaabbbcdcccaadddbbbaaabcbddacbacaccdbaababaadbddccbbadcbdadaabcddccbdaaccbbabbcdadaddacbdadbcadaabcacaaaccbaacbbddbddcabcaabddbbdadaccccbadcdbabcabdccbccacdcdbabbabcaabadaaaabcdbdabbcaddaabdbdcabcbcdbbcccadcbadabcccbddcaabcdddacadadcdcadaacadcbddcdcdccbcdbcdcbcbbacbbbbdcaaadbcdccbcddacccdbbdbcbdcccaadaaddcdcbbbbdbcacadcddbcbacababddacbbacbcdddabdcddacbdbdcccadbccacbccaaabddbaaabdbbbcadcaabaabbbddbcabbbdabbbcaddcbbbbbcddddaddcaacccdddddddacabadcdbcbaacddabddaddacddbbaaabbaadacdcdcaabbdddccdacadcaddbdcbbaabadabccdbcadaacbdbdbbcbadbabaacabdbdcdacdcdbddbdcdcadcbbbbbbabadcdbaabbbdaacdaacbcaadcadcadbcbcbbddbdbbbcabdaacdadbdbddcbbbcbabdbccbadccaadcbcdcaaaadbbccbbdcbaccddbdbdddcbabadcdcbdaadddcddabccbcdbccddadadbbdcccbcddadbcbddcaccbaaddbdddbacadcdaadbccbdadbddbaabcaccaddabbdadddddbbdadabadabcabaadbbcdddadabcdadacaddaacaaddbddcbbdacbbabbdcbdccbddcccdadadccababacbaabccbdddbaabccdbbddbcbabcdbaadcbbcccdaababbcddbddddcbccdacacabcdaabcdadcddbbaacdcdccdacdbbadbabbcdaccbacdababacbabacabaaccdcdbdbaabababdccbccbcdabcdcbbdcdddbcacbcdcbaacbbcaaddcdadcacacdcbabbdddbddddbbabdacacbbaabdcbbbdadbddddbddcadadbbbbddcbbdbcbbaabdbdacdaddccbadadbbabaabcccbbbaddcabcaabdcccddbacadadacccbbabdadddaacbdaaadcdaadcddccdbccadadabbbbdacddacbbcccaababbacdacacdbdbaccdbabcabcddbbccddccadaccbabcbdbcbbaabddadcccbcbdbacabdbabdcdbdcdcbabaddbbcbbcaaabacccbccaccabdbddcccbadccddacdbdcbbcdddabccaaddcadaccbdccabcbcddcbaddbccbadcacccccbabaadbdddcdbcdcabacccbbacdcaaaaddabdbcdbabdcdcbbabadbdbbbbaddabdcbcbbbdccbadadbddbaabbdaabaaddcccabbaaacddaabcdbacbddcabcbadcbcdbbcbcabccabddbbccddaacccbbaccbbbdbdbaabbdccbdababdcdaaadbdbbbbabdaacbdaaccabadccbacbcbdcbaaaacddcabdbccaddbcbadddccdddaabcbbbbccdcbbbdccacdbbbaaddbacacbbabbaabaaddaccbbaabcccacaaaababcaaccbccadcdbbcbacadbdbaddacacabcbcadddabddaaccbacbcdadbdcddaacbbcabacabddddbaaaacabbbabbabadbbacdcacbadcbccbbcbbabcdcccaaaaccccbccbaacadabdcdadbbcbabcacdbcddbccacadabdcdbacdcdcdbacadbddbdddddcdaddcccdbbaadaddcdccbdccabccbbbbdadbcaddddcbbabcdcccabacccacbbbddacbcbdcabadbbabaccbacdacaacaaacdcaccbbdccdddacaaadccbcaacbaadddcccbacbdccdbbbccbbdadabcadaaacaadbdaddcdbbbbcbdbabdaaaadccacbabddbcbbbaabdacabadbdddbaaddcabcacddbbddaadbcbcbcaddcdabacbcbdcacaaddbabcddacaccbdabaddbbdabcabdcccbddbcdbdbaaadcbdddddcccacacacdbbdaddddcbbbcccbccdcaadcdaadbaaadabbddcabbcdadacbabdbcdbcaddcbcadcbadbcdccbbaacccddaaddbdcadcbbbabbbacadbbddddcabcdbccbcccadcdabdbdccbaccacccbccdcaaacabcacacadaaaaaaabbababadbabbaacabadabcaacbbdbaccbaabccbbbccdbadcdcabaddbbaccaacacaaadadaaacdcbaddaabaccabdaabcdaadadcddddbcdbacabdaadccacddaaddcababbccbabaabdadacadcccaaadcbdccbdcadddccaccddaabaaddacddbbbcddbacdbcabcdcbdccaccbdabcabacbdddadddbbabcabbdaaaccdaddddacbdaaacaaadddadaabcbdbbbbbdabbcacdddaadbbdccbccbcbcaaacbbccbbbcbdabdbbadacbcabddacabcbabbbbdbcccabdbdbbdabbacaccdadbbdcccdccbdbbacdbbbadcdabbabccccdabdccddbdaddcdacaccbdaacadabbbccabcbbbaaabdbbdddccddbaabcbccdcabcacccbaddabdbdaacdabdbddcadbadaddbcabdaabacbbdcbbcacadaadbcbcdbbadadbbbdbadbdabdddddccaadaaacbbaddbdbdbdbbababbbdbcdcdcbaccacbdcabaccabacbdbbdbaacbacdaaadaccdaaaccaacbdcbbddaabcddbcdcbadacbaadabcddacccddbadcccbcbbcccacdcabbbdbbcdddbabccccdbccbcbccadacccbdddaaccabadaabccadadbddbccadbbdadcdaccdcdcdbcbbbadbbacbaddbaaabbbbcaddacbdbdabbcbcbcbdccdaaccddccbbcabbbdabbabbbbdcbdccbbdbbcbbaaaaaccaaabdaccccbdbdadadddbdbcdbbcaadcabcbdabdadbdcccbadaadacdadcbcbccbcdcbbacababbacbcccdbcdbbccbdccddaaadaadbcacdacdadbcacadcdabbbbacadbaadddadbcdccddbbcdddcacacbaacaacdbcaacbcadbcbabaccbcdccabbadbdbdbaccccbcdbbcaacbcbccbdcadabccadbabadccadbaddbccbbbabaaaccbaabcadbddbdaddaaaaaacacbbcbdbdbacccbdcddadbccbaaabbcaabbcdcccaaabbdbabddabadccbbcabbdbddaddadbdcdcdaabcaaacdbadbbbbcbddcbdabcacccbabdcaabcbdddbaadaaaaacacbbaabcaddaadcaaacbccdbaaacbdcdddcbbcabbbdbcdcaabdabcdbdbdbbdcddbbbddddcdbbaacdddcdbcbdddbabcdacbbacadcccccaadabbdbdbdbdbdbbabdcbaadaadccddbabadbadddacbcdcdcdccadccccadadbcacdabadabcdcbcdbcdddcbaadbcabdabacadababaacdbcdcddacaaacabcbbacaadcacbabbccdaabcbdccabaabadccccbcaccaddbcbaaadbccbabaaadbccbdadcaaaacbadddacaccbddbbadccdaabadcaaaccccdbdadabdaccdadbdcaaaccdcabbcacdabaadadabacaadacbddcadbadddbcbaaaadddddbdabdbcdccbcdcdacbcdcacdccaadddcbcadcbcababacabdbbcbcadcdddbacdbdddcacdcdbcababbcaabacddacdbcabdbccbbdcacacaaadcbbdbacbbaaaccdddbbcaadabdcdabccdbbbcbddadcdacbadbbcbdabcaacadcbbadccbbdacbcacdccccccdcaadcdaaacaaadcadabadcdbdbcdcccaaccbcccdacdcbabdabbbaddddbbaaadcbabcbbbbcbcababcadcdbaadadddacaaccdbddacdbbddacdbadaddcdddcbbdcbdcbbcbadcdbdcddbbadbaabadbabbaacddacbdabbbdadcabcdbbacaaaaadaacdbbbdbcbbabcaccdbddcdcbdbbadccaacbdaabcbdacacdcaabddaaadccaddbaaacdabbdbcbaccaaadabcbdbcabbbadbbadcbbadabcaacaadcadbcdbddacdaabcdddbdbdcbacdaadaaadbabaaaabdddadcadbaacdbabcbacccdaaababbcabbaabccabcbaadbbcbabcaddddaacbadccdddaccbcabdcdcddaacccbbaabcdbabaadcaddcbddcdcbbcaaaabaddcabdaaadcccbbccadcdacadcdcdbaacdbbbdaaaccccdcbcacaacadddbccaacdcaaaadaddbcddbdcdabcaaaaabccbbcbabbbcaaccacdbaabbdbbddcbcddddccbccaadccbabdbbdaadacacbadcdaacbdaddccbbaaabdddaabbaaccaaabbaadcacabadddbadcacccaaabbbdacbdaacbbdcbabadabcccddcccabddcbabcbbaabbacccccdbdccaacbcaababadcbacaddacbbacdbbcdbdacaddbaaddbcbcacbacccaccbacdcdcbdcdccbcacdbddbaaacbaadbcabbacaaacbddbdaaabbaaaddacdcbcccdbccccbbddacadaaadaabdaabaacbadbabcccbacbaaaaaaaabdbdbccdacaddddddaccdacdcbccccddcccdcbaddabddabcccaacdccaabaccbbdadaacadbddcbadaccccaaadddbcddbacddacbaccabaadddcadcdddadcaaadbdadcabdbabcdddccccbcbbaabdddaddbcaadbddaacaadccddcbbbabcdbbacbadcbccbbabaddbadbbcabdcdbcaddbcbdbcaacaacccbddddaddbbcacbcccdcbdbaadbbacacadaddcbadcaddbaccbbccccbbaabdcdcabdbcdcadaaaababcdccbabdbadadbdadbbaddcaaacaabbacaccaddaabcabbcadcbdaaaaabaadcdaacdbbbbdacaddacbbcacddbdcccbdddbddbdccabbcbcbdbccbbabacabdaacdaabcbbacadacbddacbbbabdbaadcabbdcbaddccbdcdaadcbabccdabcacdabaadcadaabbccdadcbdbbccdcbaddcddbbaadacbcacdcddcdacddcbabbdcdacbacabbbdaacdbcdadcbdbdbaddbcbcbbcdaabbbdbdbcdccddababacacaaabcbcdbaaccaadccccccdadcaddcacbaababdaddbdcaadaadddcacdcadccaacddccbaabbdbbabcbdaabdbbbbcaabaadbdcddbdccbcabcaddcccbddaabbaaaacdbadcacacacccbdbccccadbcdadaabdcddbddbcaacdccdbdaddbcdadcbcadbcccdbcddcaabaacdccaabacbddcbcccacbabbdbadcdcdbccdbdbdacaccaacacaddcaabdbddbbdbdbdcaabddcdaccbcdbbdadacacdbaadbaddcbacacddabdccccdccdbaabcddbdcccaacabdbdbbdbccbaccbacdcdaccbdcaccbcaccbbdbabddbdcbdcabbadacdbcccaaaadcaabadacccbbddabbaccccadacdddcdbdcdbddacaccbadababcbdccaacbdbbdcaddacbcbaacbccaccbcacdbabaddcddaaabdbdbbbacbccdadcbcbcaaabdabcadddcdbdabcbdbcbbababcccdaacadbdcaacababbcbaddcbbacdbdddbccbcdbacaaabcbdccbdcaddacbabcbaadacbadbacdcdacbabbbadbcdabdacbcbbccdabaddcaaabcababcaccbdbddabbcdbacccccabbbbbbacccbdbcdbadaddcadbbabbbcaacddccddcbadbcaccaccbbcdbacdddbcdcadbcbdbdbadcdddcdcbbccacdbcabdabdbdcadaabaaabbaadccdccbbbddcbaabcdadbdabbbbbccbdacadaabbbccbbcacddaccbdbdaabddadbdbbdaabcbcdaaadcdcadcdcbdaaccddcdadaaadcabbcdabdbdadddddcabbcacdccccdcabcddcccbabcbabbbbddabbbbbbcddabcdcadadbabcbbdbcbcdcadbbaccaaabbcadbdbaddbcddaccbdcaaabdaccbcbabdcdaaabbbdaaaddcdadcbcaadddbabbacbbaaddadcdbdccdcbacbdaddbcabacacdcaaddcbbcddcaaccacacabdbddacbaaabccddabdcdabcdadabdccbcdaddcdbccddddacabccacdcdaadddacdcccdbcdbddbcbbcabccbaacdcdbadbbabbdddcdabdcaaacddaabdbaaddbaaacbbccccbddcbddbbdaacababaaabdcddacdcbccdcccccddadcdbbcacbbccbddddabadcdbccabdddbadcbbbbbaabbcbbcacbdabdccbdadcdbaddabdadabdbdcbbddbcbddcddacddbadbddabdcbbabaccbabaabaadadabdcddddbabbadcaadcddcccdbacbccbbacdaaadcccacdabdacacbbcdacaabbbbcbddadddbabcacaccbcaddbcbbbcdccdddbccabbaababbdcaaaacbbcadabcdcddccdadaaaacabdddcbdcccccacbcbadbdabdcccccbbcabbdacadcbdbcbdbdbbaadacbddccdcdbbbcbcabaacbcdbadcaabdbccaaadbaddabbbcbbbdbbcadbddcadacbabcbdcdcdadbdaabbddbdaaddbbcadaacbcbabaccabbcaacdccaabcccaacddcdbdacbccdbcbddcccabbdbabcdccbdaadbaccccaddabbbdbbabdbbbbdacbcaaaacaaacaccabdbcdcacdaaccccdaacbacdcbdacbaddcadbbabdabdddbadddccabbcbdabbacdbbddccadcabcaadcadddadaccbabdabdcccbdcdcdabbcddabcbaadcabdcddbcbcaddcdadcdabacdcbdadcbdbccacbcaacbadcccacbcadcaccdadaacccbdbdcadacdaadddcabcccaaabccdaabbdbdacbdadaaabadabacbddacbccbaadacdcbdcadcadacddccdcaacbdcbbbbddddbbcbaabdddaaddadccdcabbabaacacdbcadcbdbbddcccdacbaaccccdbcacacdbbadcdabbccbcadadccdccaaddbacccbadcdcbaababaaacdcdacdcccdddbcbbcbbacbcbcadccdacaacaaaddcbddcaadccbcbcbdabdddcdddcadcbcaaadcddbddbaccdcaddccadcdaacaabbddaabccacbdcbbcdaadbaaddcbbbadbacccbdaabbbddccbdacbbabbcbbdabbdcbacdbccccdadabaadddbccbbcacddadcccaacabaaacdcdcccbbdaccbdbaacdcabdbccddcaccaadcdcdcbcbdbbcbbadbbddccaaaaacaccbcaadabdaaabaaaaadbdbddbcaadaabccdbacabdcdaabbbddcccbbcabdaacaccccaadbbdcadcacdcbabdaacdacdbbbcddacbacccdaaaaaacdcdcbadbbababbaabcbbddacabcdcddaabbcdbccadcdaccccdbcddbddaacaadbccbdbdbbadccbbdccdacdddcdcadcabbbcbcdbacdaddddbcccdcdacbccccbaacdaadbadabbdbacdacbdbdabbbcbcbdccaddadabbaadacaaaccdabccccdbaaadddcdbadabdacdabbddbbbccbdbaadabddccbbaacbcbccbdbabddacdddaadcbdcbacbdbbbbcacdcabaabbbddcacccdaacdbaabcaddcdcccbabdcdaadccacdabcaadaadaaacbadabacadacaadabcccdaacacdaabcdbabadbcdacbccbddaabddbadcbadccbaddbacacbaccccdbacacdbdbdbcaabdabccdbbaccbadabddaaaaaadbcbcaccbcaadbcbcbdadcaacdccabdcdbacdabcdaccdbacadaaacdccbbdccbcdccdadbbcbcddaccaabdddbabdddaaadaadcabdbacbaadcbabadabdccdcbdccbbbbbaacacbcdaaaaacbbcdadbbcbcbbacbabdaababbbaacabbbacdbdadbaccdcbcbdabbdacccbddcacadcccabbaacbbdbdddaabadcdcdcbadccbcdccbacdccbcacdbdcdcabbabdcbdddacdcddcddcccadabacaddadbbcbcbacabbcdddbabcdaadbadabadccdacbbcaddcdddabccddbcbbbadcbddadadbcabbbdcbbccababbdcbccdcaccdabdccdaabdbadbcadabdddaaddcbcbdbdbdcbbdbcaccdccaadabaadbcbbcdaabbcbcadbddbbcddacdcbacaccddcbbbbcaccaababccddaadacaacaaddcbbaaabccddbabcdbdaaacdcdbcdbdcbcaddcdcbacdccbabacbadddacacaacbacdcbcdaabaccaccbdbabbcadabdbbcacbbbbccdcdcadadbbaacaddddbabccbcddbadbccadbccdcbacdbddcbdaaadbccbdcbabbdccaddababcaabcbccccabbcbabaacbabadabccdccbbaaaacadddabbbcdbabcaabddbbbabdabaddcadbcaddcaccabdcacdddcdddddcccdbbaaadcbcabddcbbacddcacdacdbdaadbacddaaabadbbbbcbbdccacccaddabbcacbccdcdbbbbbddaacccacabddbbdccdcdbdaccdacddbbbcbbbbabadcdddbacddcbdbdcaabcbbaacbdbabbddcabbcbbddcbdaacdaaddaccadbabbdcdadaadddcbdcdcdbabbabdbbcaccccdcdaabccdaabaacacadbdacabbddaddaadbbbcacdbdabbcbbdaabaddbcbcbbddbbddbabdabbccbbdbabccddabaaaaaaaaccdbaaddcacdabdbcbdabbdbdcddbcacbbbdadcbacddbabdadddcdbbaddbabaabbdbcaacacadcacaadbdbbbcdcaaaaaddbaccdbcbaaccbcdcdaacadbcccbacabaaddcbbdcaacddcbbabdbabaaaacbaadaacadcaaabdbbbababbdcbdaabbccbcdbdcbacddbdacbcadccdcbdaddabaaddbddadbcdbdcddbdacaadadcdadbbaadbbdcbcaaadabbacdacacdcccbaaaaaadcdbadbbdddcacdccadaccdbbbacbccdaaccbccddabdbdcdaccacbadbbadadbacadaaddbdaddcbcbbdddbabcbadaadabddbcadbbdacbccccdaabbcccaabcabdadaaaababcbdbbcbcaccddbccdcbdbccbbaabadaccbbdbcddbccbbddbadabdbdddcbbbdabcaaadbaadacbbbcdbccdcbcdcabadabdadccbbbbcdbdaaacdddbdabccabadddbcbaaddbdccaaccadbcbddbadbcbdcbbdbbabbbbcbbbabadccdadcddaddbaddccbdbadcdbacbcbcbdcbcacacadabccaacdbbaaddbbcdcbcdaaadddcabddbdccbddbbddbadacbbdaadababacccdbacdaaccbbdccbdaddacbddcbdcadccdbdcbbddbdadcaacbdddbddaabcacaaadbbcbcabaacaccdabbdbcdaacbcadacbbdaccaaccabdccaccadbadbbbccdbabaabcbccacadcacdbdacddcbaccaaacccabdcccacddacabcccdcaabbacddbbacadccbcacccaabbbabbadccdbddbbaddddaaacaccddbdabdcdccbadccbbcbbbabaacadddccddcbadddabbcbacccdbbbbbbaacdbbacbbbacdbbbaaacccbdcddbabaaacacddccacdcbaccabaccbaacadabaaacbcdcdadbddcacbcdcbbbbdcadbaaccdbbbcacbcabdcddbbcaddacbbbdbabcdbcacddbacacadacbdccaaabaacdcacdaddcabbadddbbacbaababcdcccaaaaaaccdaacbbbcdacdadbcaadbabbbacbdcdabcdbccdaadddcabaabdbcccaaadbccaabdbbacacbadacadabdbaadbbdababcccabdbdaddabbcaaccdcbcacadcaccbcacccaacdcbbddbcddacadadddbdbababbaddcabcdaaababccdacbbabcbcdbcbdcbcbbdbabcadbacbdabdbcccabdaababbaddcacddcadbacbaddaabcddaddcbdddaaccddadadbddbdabaabbbbadbabaababcddbccbaabccbbaabcbaadaacbbbbddaaabccdcdabbdccacdcccbbcbcacdcdccdbdbbddaadaadbabcdacacddddccbbcdbddbddcabcbcbaaacacbaaaadccdddbcadabacdaaddcbbdbbbbdcdbadbcacdccdbdcdbdbbbabcdcbcabbdccaaadbbaabdcbbabbbabbbdadbdbcbccacabadcdddbaabaaccaabcccadacbdaccadcbcdbabcdcddacbcbbbcadadbacbcaaccddaaaabcabdbdacaacadabcbddadacaddcdbcbcdaddacbcccaaabcaacdccaddcbbbcacbbbddbdbdccbdbbdabdaadabaabdcbcddbbacabdbabdaacbdcabdabdcbccdcdbabadcacbcadbbddadaabadbbbaadbabdddccbdddcaddcddabcbcacdabbcbbbbcccaaaaddacbbdbddbddbbddbcbbdabbbdbbadcdbdddcbabcbcddadccaabccaabcaccbbbacccbbdabcaccadbbcdabddbcdbcbaadbaaacbabaadadccabcdbadddddbbbdbcdcdaaadaacbccadccacacbcdbbbcbcaacadbcdbccbaadcaddbcbddcaabddbcbddabdbdabdcacdcbbbbdcabccdaccaddcbabddcabbcdabaaaddbcdccaabdbbcaddbddaccbdbcacdcddacccddaabacadcadababdcccdccddacbcaddbbcabaabaaabbadbbddcaaabaaabdbdbcadbdbadbbccaaccbbcbacbbdaacdcbcbddacdbcdabaddbcccdddadbdacdccbcbacbbcbacabadbacaadddbcaacbddbaadadabbdcdaadacbbbdcbbcbdcaabbddbddbddcbabddbdcccdabbbaccadcbdcccdaabdcccaaabdbdcbcdccdcaacaacdbdddddcaaabdabacabacbcbddccdbccbcdbabbdcaadbdcdbdadaddcdadabcbaabbbcbbbdcbccdbdbcbadbccdaccabbadacbcdacbaddcbddccccbbbaabbcddccbadacabccbbcbbcacdacbaaddbbdbbbdcabbccdccdadabadaabbbbdadcbadcdbdbdbdbcaacaccbbdbdbdbbcaabaabcbdabccadbbcacbccbdbbdcadbbdcbdbbdaccbdbacacdaaccddadccadbccbbcabaabacdabcbcdadbbabacabbadacdccaddcbcdddbcabbadbaaaadcbcbcaadcdcdabdbbbbbdddbdbbaddadaaddcabaddcbddcccbdabdcccdbdabaddccacbdacdaacdddcdbbccdadbbadcccbdadbabbbbbaabdcdabccadbbbdabdabdbadbcbdbdabadbdaddaabadbdacdacdddbcbdcacacaabaadaacbdabdadccaddbcbdbcbaaddacadaabcbacbcaacbcdbccbcbaddaabbadddccaabddadbaacbabadabdaccacdacaccccacabbdbdacbacdabcddcdbcabddccdbbdbbabdddbdacbaddcbdcdcadabbcbbcababbadabdccaabaacbddcbcbdcbabcabbdacbdabdadbcabbddbcdcdaacaaadadbcaaacdaadbaacacdaacaaadcacdbbaddbcadcbdadaddbadcbabaacccacaddbbacaabdddbcccdccdacdcbcddcdacdcaabbdddaaaaacdaaddcdadccccabaabaacdbbbcbadabdcdbbabcaddccbadbacdcacadaadbbcacccaddcddadacdcbcdabcabbdabdbccbddadcbcdaaaddbcabacddbdcccbaaccadbaccaaaaaaddccbbadcadbddbcabaccdaaadbcdadbadbabbadaccabbaaaadbdabacaddccaabddcdbadbababbbbdcdabdcdacaacabcdadabacbbdcbbdacaddbdcdccdaacacdaabcddbabcacbdbcbccabdadbadcddccdddbbddaaccbdbdacaadaabcdddaddddccaccbdaacaddbccbcacdbcbcaaacaaacdadacdcadaddbaabababbdcadbdbbbbdbadcbacbaacdcbdddddbbdddacddbcdcaadabddacbbcdadcccabcabcbddcadcacdbcccbbacdbacbdacdcdcdbcdbdacbcabbcccdadbbcabbddcccbcbdaaccdbccbcdcbcbbcbdaddbcaadcabcbaccdaabdadcdddbbdcbdcdaacaaccdbbadcdabbcddddaccbaaacdcbddcacccdabbacddcaacdcbdddacdcbdacbbcbdbbacccdccadcdaadcccacbdddcddbbacdaadbcadcdadcdacabbdccccbddaacacdbaccdccbddbcaabcdababbbcccadaadcdaaccacdddadaddbadbdcabcbcbadbcbabddbdadadbbcdccbabbdadcabbcccccdbcaccbbddcabbaddcdabaaadbccabbcababbbbabddcadbcabddbbddbdcddcbbcbaccbddcbdbcdcdabdcdddbaccaddadbdcddcabdcbcacaccacbbdbbaccdadbaacbdbabcbcdbddccbadbbabadadcbccbabbcdbabcddabcacbacdabaaaaddcccabddccbaacbaaddabcdcbcdbcaddcbdbddbbcbdbadcacbbdbaccaccdacbacacbdabdbbbaacabcaddddabdabbdbcbdcdbcddadbdaaddaadbabababbbbdcacdccadccaaddadcadcdaabbaacccbcadacdbbabdbacbdcbadabdbcccdcbcadacddacbcacbbacaddbbccbadbaaabbcbccdadbcddcdbbbbbcaddbddbcacddcdadbabbcaadbbbbdddcdcdacdcbdbbbdcdabddddcddbddddccabccccaddbcdabdcdacdbadbacbdbdddbbaaaccadddddbacadbdcbbcdcbaccbbddbdbbcdadcddadbadbccadcdddccbabbccadcdccaccccbccdcccadbaadabdccddabbbbbadbbbadbddbacbbbddcbbadbbbbcbdacbddccbbacbabacaadaddacdbdbddcbcbcbabcbdddadddacbcddddcccabbabdaccbabbdaaaabbbddcaccddbabaddaccadbbcaddddbcaacbdacadbbbadaabcadabaadbabdddbaadddcbdaacbcbcadbddbbcadccdcbaddabcdbacbdcbbddcdcbdaccdcbdcbdcccbbabbdbcbadccdddbacbdcbddbcbbbcabcdabbcdcbcdddcababdcabcbdadaadabbbacdaadccdbaaadbcaaaddaaabadcbdbcddbdcdcabacdbdadaacbaabdadddcabbdaddddaacdbdbcbddbabcccdccadccacddcddacdababdbcddcbbbdbcbccdcddcabcdddcdbcdccbcbbbddcabcbcabbacdadaaadccabbdcbbabdaaadccacbccdcacbdddadbbdcddbdaaacacdbbdbdddddccdcdccaddddddaabbbdcccbabbbaacbcddddcdabbdacdcbacadcaadaabaaadbdbcadbadacbdabbdabadbadabcdbabcccbcdbacdcbacbcdbbdcbbbbbddbdccbccbcbdbbdcabadaadccbddcadadcccdaccbccbdadcadaaddccbddbcaddbbccdcbddcbbabcdadbabcddbcabdcbaaacabbaacbbdbcbacdabcacdbdabcdbbcaadbdbbbcbdddbadacccdbaacbcdadbcddabadbdbcdaacbbcdbbcbcadddcdddbdcdccbddbcccdcbbdaccddbbddcccbaaabdbaabccaccdbaccbcdaabadccadcbaabdbbbcdbccbdabbbdcdbbacdcaabcdccbbddccadbbbdaababcadcbcaaacaabccbbcdcccdccbbcdacababdbdbddabdacdcabacdcaaccccaadddbdbabaddcbadbbbdbcbadddccbbbdbbacbabacadbbcbaaadadbaacbdbbcdbbbadcddbaabcbacdbcadbcdbbcccabdcaaaaddccabcabbdcabaaabadbdabacbdbbcabddccaccaadbabaccacdbcbbbbbacbbccdaabcbddcabdcdcacccdbcbadaabaadadabadccdbcbbadbdddaabbadccacabdbdadbabbcbbcddcacddbaacdbbaacadbdcaacacacabddccdddddcdccdccaadccbddadbdccbababcadcbbbdaabccccadbcdbcaacbdbddcdcccbcdccaddaabdcbaaccdbbbaacddcaccdccbabaacaaadaacdadbcaaaabcdcbcccadadadaacbadcacacacabaadabcaccacbcadacbdcbaabdbcbbddbdcbcccadbcabcdbddabcdddbabbaadbddbdaabbcadddbdcbcdbccbadadddabbabdacacdcaaabbdcbadccabbccbadadbbdcbddcdcadacdacdccdadccdcadcaaaccaaccdabcbdbdcdccdabacaababdaacbccbdbabdbbdddbdbccdbbcdcdcdbbdddaacbadcbacddaaddbdcbbdbbabcbbadcdabacddacbadadddacabdcdcaaccbdbdabcabcdaddbcddddbbcdabaadbcabcadabdbdaccdbdbdddaaaadbabdacaabaaabbdcbdcabcbcdbcccdbdbbddaacacccbbcabdaadcddbdbababdbdbaddabacabdbccdbaacdbccabddbdaabaabcdddabdbbdccccabddbdbccadcdddcccdadabdcabaabccdcddbacabcadbbdadbadddbcbabdbadbabccccdcbaacbdbababcbdcacabccaadadcbddbdcbdbddcddbadacddbaaccddddabdadbcaabadabbdcdcbddadbcbaccccbdbadabccbcdbbbdabaabbababaadadaaabdaaadddcdabcddccdcabcacaabdabcbdddadaabbbabadbcbacdddcabccddcadcaaaacbbcdbdaacbcadcbcbdadcacbdcbcacacccddabadaccbbcaccaabbbddcbbbdbbcadcbaadbccababdbbaabcbcddbaacbaaaaabacaddadcdaabdadcccbddcacabcddadaacdaadccbabbcdabcbabbaadaabddbcacddacbdbcbccdcbdabcaabcaaddacbadbabccdadbcbcacbccddacdaabdbbdbbbccbcccbabcddbdbbdaddccdcdbdcacadcadcacbcdacdbccccddbbccdbddbbcbdbabcbabdcacacbcadcccbaccddbbddddabdcacdcaabdcadcababbddcbdddadaabdbcabdcdaddddddacdbbadbabadcabbdabbbcbabacbadcddabbbdacddacdbddbbcdacaaacdacbbcdaacabdbcabcabbbccabbabbcaaadbddcbbdcaadabaaacaacddbaccaabdabcbcabcadcdadabbadcabbabccbcacdccbbbddbdacdcacdccdbcacbddddadcadcdbdacadadabaaaccbdbccdaccbbbbacadcddcccacbccaabacbbdabbdbcadcbacccaccaaabdaadabbdccaacacdcaddcacabcbabcdbbcbbbadcadbadbbbbbacaacadacadbdbcbdbccddabbbbabdabddcccadddccbdbbbaaadbbaccacaaabacaccbcbcdbabacabadccacacbddccdbbbdabccaccabdcbacbaaccaaabaabdabbdabbbbbcdaaabcdcabccacdbacbaadcdbdaabcdccaacccdcacbbcbcdbabbadbbddacdcbbcccabcabcbccacdbacabcdabbdcddbbbcbbdadacddaddaadbcbcbacbddcacaaccaaccbcabacbbdabcacdaaddabbadbdabbabdbbbdcbabdaabbbbabbdcacababadadaacadcacabdccbcdabdccdbdadccbcbbddcbddbccaacbbaddbaddcdaacbaadadbcaacacddbccacbdbabbbabacccbccadccdabacbbcddabacaacbbabaacccddaacbbacdbcadcdddaabbbbaaacadaaccadbcaadbdaaabbcbdbbabbaddcabbdbddcbaccdcdacccabbadbbcdbacaaacdadbcdbccdbcddabaddaacacdcccddbbbdcbccdcabddabcacadaadcacdddbbbbbdbbbbabcdbdddbcadcdbacbddbbadbbddabbddbddcdbacdbabcdcbccabaccdbaabddabddccbacbaccbdadddaadccdbbaadadbbbaabddcdccbdbadcddbabadddddcdadadcabcbddadabcaadbcdccaadccaabbcddbddbbddcabbddbbcdcbdcbcadabaaaacaaaddbdaacabdbadcadbcabdadaaccbbaadababcbabddbcadaaccaaccbcbcdbadcdcddcdddbbbcbcdcbdacccdbdbaccbdbbdacccbbbbcabccacdabbdadaacbcbdbbacdaddacddccaddaccdacabaacdadcadbcbacdbccdbcacdddbaadadbabbdcbbaccacabacabacbadcbccccabbaccbccbbacddbcbdacdccddcacdcaacacccdcbbdabaacacaacbcaacbaabbabbaabcbdcdbacccbaaddddbadbbddcdddacadcddacbcdbadadddaaaadcddcccabbddcccccacaacccbdacccadbdddddcbcbbbabdacadcabacaabbbddaadabdacbdaccacbabbacdccccabacccddacccbbbadcadbdadacaabcdcaadcccbabacccaaccacccbadcabddbbaabacbbdbaaabaabdcccdbcaaabbbddbdcbbadccbbcbbdacbddddcbcbadacadcabddaddcbbddccabacaabddabcdcccbcdbccbdccbbbccadaadaacbcbacacdbdcacddacdcbcacddcbdcabcdddcabcddabdddcddcbabdbdbbcbddbddbabcadbcdbbaadbbdccbaddadadacacdcabbbbbbdddcdaabdbaaaaaaaddcbbbcadbddadaaccaadbdcccabcaadbacdbdcbaacbdadbbcddcabcddbacaaabcdcdacabdcaacccacbcdddcccaacbdddcbbaaaabbaaccaaacdbbbbabbdadcdcbdbbcbbcaabaaddacbbbaabadacbddbdbccdccccbccacdbdddaadacadcaadddddabaacacbcbcdcbbaddbabadccaacdbabdcdcbddbddabcdbcbaadbadaddbdccbaadcbcbabadbadabcacbbbdcbdadbddccbbbbbabdcaddbcaccbadddadababbaacabccdddcdddcbcbacbdccabddddbccddddcabbcdbbdbadcbcdcddbadbbacdcdddbbdaaccbcabcaddaaaacbbbcdaaaccdacadbbdddadadcdbdaddbdbaaddaccbbaccaddbdabbbbaddbcadaccdcbaabbbacaabadadccaddcbccbabaaaabcaacadaaddccaaadbcaaaadbcbbcdbddcaccdbcbbddbcabaabadccbdadbaddbcbdccabcaccdcbcdccdbbbcdbdddbbcabccbcaacaabbcacbabbcdaabdbaccbabbaabcbcabbdddccbdbcbbbddaaaddaaadbccdcdbdddabaabdaabcccdbbbcbdbbbaccbcdbddccabbadcadbdbbbdcdabdccccbdcadabcbbcdbdaadddbbbbbdcbccbccbbbdbccdddcacccadccaacaaabddccadcadaacbddadbbddacdcdabdadddaabdcbcacdddccabcddcddaacbbdcccbabbcbacbbddaadccaaabacdcacccadcaaddbddccbbadbbacdcdcaadbcadaacabcabaddbcdccdaccabadcdbbadcdbadbdbaaaabbddbcaadcdcaccdcabdbbcbcacaaacbcbcdaddbaabcacddadabddcdadabadadccaccadbabbdcbdcbabcaabaaadcbdcaaacbcacbddccadbaaccccddabbbbcbbaaccaadabcccdddcdddccaaddaaccadbcaacbbbbbcabdaddadcbaccccddcaccabccbdcdabdcbacbbabbdbddaddacdbdcbaabaddadccdbaccdcdbababbcdcaccbdaadaaabcdcbadbabdddbcacbbddbbdbbabadbccaaadbcbcaddbccdadacdbdaddbccadddbaabbacadadacacdddaacdbabcbbaddccaabbdddcbbaaaaadbdabbcdacdbcdaddbdbdcbbbdddaccdcbdabadcdaabddabbadacbcdddabaabcbbacbcbbcbbdccaaabbccccbdbddddbabbdcaaababccadbbddcbcdccbbbcaacabcbcbbbcddcbccddcdcbdbddcadaddcbacaacbcddaacbbbbabbcaadddddccdabaaaacddcdccaccdcaccabbbbdddbbbbcbdabcdddabcbbccdcabddadaadadcdbaadaccdcdcdbdcccbcaaabccaabacdcbcacbabaaaccbbdbbcbdaababddadcdcbdaabcbccdaadaccbadddbaabdccbdcadaaccbbbcadddcdccabaabccdbcdaadccadcbcccdacbcbdacbdabdccddadaabbaaaddaabadabaccdbcbccbaadccdabbddaaaacdacdbdcdbbbcbaccdbaabcabbbbcddcabcbcaacacbdcbbacadcccccabbdbbdcddccabdbaaaccaccbdcacccbcbbdbdbbddbddccccbccaccacbadccdbaddbcdcccccddadacbdbdadcacdbdcdaccabaaabdadcabacbbcdcddddbaccbdacbbcdadbbbddbadbbbbbbcaaddcdadbbdcaddccbbdcacdccababdbbbaabdbaccbbcddbcdbcbdbbdbaadacaaddabddaddbdabbcabbcdaaccdaadcaccbcbcbbbdcddbcdacbcacbcabccbbdbcaabbbaabdcdcccbaaccbbbdccccdccbacddcdbbcbdcbaaccdbdcbdbbbcddbcadbccdcadbdcbabddadbaaadddaaabcbddcadbcadddaddacdbbabadbbcbaadccccdacccbbabbabcdcdacacaaddaddaccababbdccbbddaaabcadaacaaaddaddbdcacdbbacbdbcdabcbdbcccbcbacddcbdbddddbaddaaacbbacadabbbbcbdbabcbaacbbbcdbcccbbbadadbdbdccbbbcdcdcacdaabbcadcdbcbbcbbcdcbbabcacabcdddaacbbdcbbbcccddbacdabddcddaddaddaabdcacadddadddddbabdcadccbbbcddbdddcccbcbbcbcdcaaacabaaddaaccdcddddabbbcdcdddcaabddbabbddbbcbbacdbcbbbdadcddcbbadcccbadbcddaabdcccdbccbdbaccbbbbcdabbdcdddabcadbccbaadbdbccbcbcccadbdcdadadabdaaaabcababbbccbbcbabdcddbdbcdbacbdbabadacadbbddcabacacaddadcbcddccccdbbdabdcbaccddadddbcbdcccdbdbbdababbbcdacacbbbdbdbabaccbcdcddcabbcbdcbbccaabcbabbdccdbbbccdbacabbdcbccbbacccdddbcabddcdbdbbbbccaaadaaaabddaabbcdcdcbcabaabcbccbbdcbbdbadddacddabcccddacbccdddbbadccaacdddddbdddacbbadcbbdddacacdabbdaadbdbbdbbdbcaaaddcddcaacadcaacaaccbcdccbdcaaaacdcabddddcbccbcaabbbccaacbabdcacbbadcaabaddddabacbdccadbbbabcadbdbcbbdacadbabadbcdcaccadccabdaddbbdddadddbdbdcbcdcdbbadaddddaddbaadcbabbaadababbabbddcdcdbbcddabaadbaccbadcaabaabdddcbcdaacccdacbaaadabbbbbccdaacdddcdddcdcdbcacbdacdbddcdbacbdaaccccdacbccdcdabdacbbacdcddacccacccbcaabbddccdacaaddddcbbbbbbcbdadddbbaacbabddccdaddabbcaccbcbcadababdbadcbadabcbdccbdccaaaadbdbcaaccadbdccdbaaadaaabaacbdbddcbccbddbdabadabbbbaadcdaabdcccaaadaccddcbcbccabcaddccabbaacddcbdaadbcdadbdacacaacbaababccaaccddacdccadadcdbccbdaacbbaacbbcacccdbaacdbcacddacbadbaaaaabdabababaacddadaabbbbabdcbdccdadadaacbbadddddabaaaadcdbccdabcbdbaaddcccacaddadaacaaadcacadbdbbcccbadcbbdbbdbacadbabdabcdbdacddcdaaadddbcadccaadbbadbbbbcbcaddbaacdadbacbbaaacaccdcccbaadbdcadcbbdbcccdccacdbcdbcdbbdbadbbcbdadcaabbacabbcccaccbbaddcbaaaaacbcdcddbdcadbaddbbbaaaaaaaabadbbdcdcbaacaddcadbbccccccbcaadbcdbdcaaadaadbbbacbdcabcdadddacadaccadddabbcdacddabbabdacdaabaccdbdadccacdaaadcccdabbaaacdcbaacddcccbdaaddbccbcbacbdcadcbdcbccbbdabadccabcdcdddbabdaaccbbbbcbbbabbaddbdcbacdabababbadcaadddcdadbbbdbdbbdcbbbaaccbddcdadabbdabaaacabccdbbdbadcdabbdaadbaccaccacadcdbccdaccdbbbdcdabbaacbaddaccbcacbdbadbdcadcdadbcccbbcdbcddbbdcccabbcbcdcdbcbcbccadacccbdabdbbdbdadbbcbcbcddbcccdddbdcbcbbdcbdabdbbcacadbcbababaccdaccadddbbabcdbdaacbdbbadcacdbbdacddcaddcbabccdcdabccabdcadbabbbcbcbbddcccbadabcbcacbccabdddcdbcccccabcbbadbabacdbcbbdabccbccdadbdabacccbdcdaaaddbacaacdacaadbdbabdcdbbdbbdbdcbabacacdcbadbbcadcbaddabcbaaccbdcaabcbcccccddaadbcbcdabbaccaabbbadcaaadaddcbbbccccadbbdbcddddbabcbbacacbdddccbbbdddcadbbacbdcbacbddabddbbccabacdcdbdcbbbdbcacabcaddadcacabbabbddddaddaabbddcbccadadccdbbbdbdcccbdcaddacbdcadcbdabaabdbddcbcbcdbabddaaacacdcbcdcbccbcdccdadaacddcbdadadcdccdadaabcbcdcbdabdbaabdaddbccbbacbdcddbddccdadcbabcbcdaadaddcdaddaccacdcccbdbdbbddcdabdccabccabaddcadbcaccadbabccdcbaabaaaaaadbaabddaabddbccdcccdbddbcacbbcdbdbdbabbacabdccdbcaaadabdaadacdcdbdcbadacdccbdddacddbbcadccdbdbccacbbdbdcbbcbadcabbbdadadababaaccaabbaadcacbabcbdcbbbccabccdbadcdbaccbdaccacacbaddbdcdccdbabddaaddbddbbcaddababbdbcbbbaccbaacccacbadcddddacbcdcdacdaddcbcaabbdabbcbdaddaaacbcaccacaccddcccaaacbdbdbcbadcddadbbbbdcbddccddbbcbcbbddaacdcdaababdbbabcbccccadccaccbaccdbccdddbbddcadadcccdaacadbcbddbccbdadbcdcadcdbbdbbccbbbabadacaccabcbdaddacbdddcbabddacbcacabbaddcbdbabdccbbdbdcdbadbdacbbaabddbdcbcabdaabcccccadbbdbbbcaddbabdcabcbcabccbaadcdcabcbbacbababdddbbdcdadcdadbbbcbbacbbabdccbbaadbcdabadbcdaddcdaabcdcdabbaccdbccdcddcdbbcabbbbabddcabaccdbcabdbdcdaababcbcdbbaaccaaccbcbcaddbdabadbadabbcbabacaacbcccdccccccdacddbadbbcddbbbcdccdacdbcbcdbcbbcabbbcaacbbacddcdbabadaacacbbababcabdaacdccccbdabdcbadcddacdadbaccaddabadbccdabccbcccaaaccdbddabdbdbbdcbacaacddbdddabaacdbdaddabbabbcaddcbcdcdcccadcaccbcbbacdcadcaabbdccbabcbbadbccadabbdacdaabbbdaddbcccbdaaaccddababbaccbaadbcbdbaaccabcdcbdcbcbcbbabacbadadcbddacdaaabcccbabbbacabadcccabdbdcbdaddadbcbcccbdbaddadbdaddcbadbcabadabbadcccbcadaddbbcccccdccaabdcbddcbadaadbcbbcbbdbdbcbaddbacdaaacabbbcbdbdcaadcdccdddadbdaacbbbcdbcbcdaabcbbcccbcdbbccbaccbadadddacbbaabcbaadabcaadadbcccbdcacdccbbaaadaabbbcdbdaabcbdaabbabddbaaacdcdbdabadcccbbccacdbaaaacddabbdaacdccabcabaadbaacbdbcaadddcdbbbccadaccabbcaababcbcccbacdbddddbccddbaadacacbacdcadcaadcabdadbbcaaccaddcbbabdbaadbdbbcdcadddaaaaacbcacabdbcadbcdddcdcccacabaabaddccbaadccdabcbcadbdcadabcbdccadabcaaaacacccdbddcdcbcabdbaddadadccadcacbbadcbdaacabbabaccddbbababddcdadadabdabaccacdcccddbcddddddcccaacdbddcbccadddccddbbcbbbcccbdbcbaddbababcdccbddbabadabbdbdbacdbabcdcaaccadcdabccbcaddccccaaabdcadcbbddcbdbbbcbbdacacdbccddbcdbadcaabdacdbabbadbaabcdbbddccabacdbbbddbcacbbdbcaaabdabbcabbaadbcadbbacbaddbabaddcbacabcddccdccccbacbaabbbddcbbbbdabcaacbbccabdaacdccadaaddacdcbbaabddbcbbadcbbcdbddcdbaccdccaabbcdadbbbcacbcdccdacdcbaabddcaabdacccaadcbbcaaddadbdbdbcdbbdcddaababcaacacdddabddbcabbbccdadaaddbdaddccbcdbbdcbadcbcdbbacdbcdccbcddcdcbbcccddadddbcacaddaaaaaacaaacdccddadcbcabaacaaaabbcabcbacddcdaaabdcacccdbdbcdbbbcadcaacadcdaaacccdadacdcdaabcdbaabcadbaacdaabadbbddcdcadbababacdccdbbadbcbabdcabdccbabaacbacbdcdddbdbbcbccabddbbaddddbcdbbcbacaabcdbdabcccccbdddddadadacadbabdacadddadcccddbdddbaabddbcbdcabdabbbadbacbdbaabdccbbdddcadcbbccbdabbabbcadadbbbacacbcabdcbabccbbdcdcddccacdbbcdaadaaccadcaaabdbdabdcadaaabcdadbbcbbacdabaacddbbdaddacccbadbdbbbbbcabbabdddacbdacdbdcbbbdabddbbcdabdacbadbacbcbaadacbdacacdcbacabcbdcbdbdbabbadbbcbbacadcbacabbcaccbaddabaadacbdcbbdcdaaadbbbcaaddbcddcbdcbbcbacaacdccaccdbbadbcbabcbcdbbdbabadabccdddcbcacdadbdbcccbbdabcccabccbbbbbccbcacadbaabbaacdbbcbdbdabdabbadbcabcddddbaadbaaddcbccdaccabbbadccbcdcdcdbaaadbdbbcaabbbcadaaabccabccaaabbbcdaabadbcccacdbcbcdcacdddacdbccbccbcdcacdbadbccdadadddcdccdcabdbaccdbdaadacdbbccdaadbacddccccbdbcbaaaddbadcadcaacbbbbaccacddbbbbdabbdbdcdbadadddbabacdcbbbccabdcadcaadccbccbcbadcadbaadcdccbbdbdadbadbcaccccacddbacbdaaabcbdbbdcccdbbcacddacbdcbdddbbdbdddcaabbddacdbabdaababbbddcbacdbdcbddcabddddaddddbcaddcbdbaddaaadddbcaaddcabdbbbcbdbcbdccdabbdadbcddaacacacbbaaadadbdddbadccbabcdadccbdadcabbddcbabacdcccbacbbcbdaccacaaddacdccbddbbdacccadabbbacabaccacbbbdbccabacddbcabdbdabcdcdacbbaadbaaacbcaabdccabddacacaacadbbdacadabdaacdcccadbbcbdabdbbcccddcbbcbacbccccddcccdcaadacbbbabaddcbcdccbbbcaddcbcbbcadbdaadcbdabdbbbcacbccacbdddcdabddcdcadbcdbddcbbdbadbacdcacbadaacacbccccabaabcdcbbabcaddbbcdaadccdadcdcaaadabbababaccbbbbdbdcbdddaacccabcbcbaabaaddcacadabcacdccaabcacbcbbaacdbbcbdbabadcabcbadabaccbcaaadcbccccccdbbbabdddbcdcdaadcddacbabdbcdbbaaddaccccbaadbaacabdaddbaddbdbdbbcbacddcbadabaddbbdddcaacacccbbddaccaccaadcccdadbdcccaccaaabcbaddcbdccbdcbbcdbbbcbcaddbdbcaaddcbdcabcbbaacdbbdadbabbddabbdbbdbcdadacaadabbbbadabbbdbbcadabaccbadccabbaaccbcdaaccbcbbdbddcadcdabdccccddababdaababacbbddbbddbbbdcbabbbaaccacacbbbccdaaabcdcdbabdcbdbaccabcddabadddacccdadabddaddabccacbcabdbaabcaddddacabbccadbaaabbcabbabacdcabccdbcbdabdcabadcbbbaaddacbaccbcaddbcccbdddbdbaacaabacacadcbdbcbcdbabcbbcaddbbcccabdbadabdadcbdccdbcadacbacbcbaabbcdccdaaadbbdcddaaaddbbcddabcabdcdaacacccbbbdaacabbdacabddadcbdadacbaaddababadadababbbbdbadbcacccdddcddddcdcbbcccadaccbadabdbdadbbdbacabbbbbcddcadcddbdcbabbccdacddcdaacadabdaabcdacdadcbbddbabddaccdcdabbdabcabdbbbdbccbabadcbdbbccddaccdcabbcdabaaacacaccacbaccddbcdaccbdadbccbddbdbcbdabddadbaddbccdbdcadadcdcdbdcadaccaabcabcbdacbbcbacddaddababcbdbacdbbdbaddbccbacababdcbbaddbacddcabcbcbadcbdcaaccbbdbbcacdbabbcacdacadcacdacbdddcadbddcbbddcdcddacddddbbadaadabadcbadccdcacddbdcccaddddacaadacbbcccdacdccbaccdaacdabccccaacbbcacddacaabacddbcacacadcbbcacdcaaccddcaacdccdccacdbaacdcaabacddcdabcdacdcbbdaaabccccdbacdbbccdbabdddcdcabdbdacdaddcbaacacadadcaadcbbaaccdbbdccbccbadcbddcbaababddbaabcbbbcdbdbcdaaccbcddcbcdabccbacddbbdabcdabbdbbdcdaabdabdddbbcaadbaabbbacdaaddbbabbcccacbdacaacdacddabcddccdadcbbcdcbbdabbcdbdcbbcdadddabcbcbbcabdbdacaabccdcababcbcabababcaaccdcdadaabacacddcaaaabccbadabababbbcbacbddadacabaaaaabaddcacacabcabcaabcaccddbbbbbbddacabababdbdddaccdbdbdbcbdbabbacdbcdbbdaabbabbaccbbbabcccdbdbbbdbdbdcdcaaddbabccddbcacaadaccdddacaadbabdcadcaacbcdbabddccacadacacbbdacddbcbaacdcaccbdadbabdbdbbaaaadbcccbddabbcddadbdbcdcbcccadabdccabccaadbbbcbbabbddccdacbcbbaadadabbcaacadabbadadccdacbcbaccaacddacbaaddaaacbbcbbbddadcbdbdcddccacbbbddbddaacaacadcacacbdacabbdaaccbdabbcacadbccbaddaccbbddcbcbaccccbcbabcaccbddcbccbbabdbdacbbadbbdaaabaccbddbdcdbdcdbdcdbdcabcaccbcddcaacdcbccbcbbbbbbaabbadbcaacbccbbcadccccaddbacaddcdadcdcdaddaccbabdcdbbcaccdddddcddacabcadcbadacbaadbaacbbacaadbdbdcaabbcddbacbddcabdcccacdcccccabdccbcaacccddbaadadbdbbbcadabcabbccdcccaabbaddbaccddcbdbdbcbdcccdabaccbaadccbcbadcadbddabcaaadbdbacbbdbcbddccddcdbacbdabbacdddacbcadcabdbcbbdbbbdbabbcbbadaaddddadacbcbbcbdbbdaddbcddccaaadbcadbcbccbdababadaacbadccdcbabdadddcdbdbccddbdcbdcdaaccddcaaaabbddbdcccbabdbbacbbcdcbdcadacaddaadacddbbadcaacadbcbbaabdbcadbaaaccbbccabaaabcdcaaabbadaabcddbbbbacbaacdbccddbbdcdaabdbaccbcbbacdddaacdcadccddcaccbcdccbcaadbcccccadbcbbcbaabdcbccdaaaadaabacaadddbadbdbbbaaccacadcdadcdbaacbdbaaacaddbcadccddddadabbdaaabddcabbdcabaabaccadabcaaccccdbdcacadcaacbaccddaaababdcdbccbdbbabbbbddccccddddbadabcaadcdabcdaccacabccdcbddaababacbaabdaadacccbacddaaccbddacaaadaddbcbabcdbbbaddbadddddbddadcdcadcdbaaaddadccbbdadabdadbbcbbacbcccbbcccdcbddbaddcdbbdabcdacdbabccdabdcbbbaccddbacbcadcadaddacabacdcbbbdccbaaaadaabdbcddcbabccbdcbbccdadcdacbaddbbbcabadcabcdcdcabbcdddbaabbabdabbcdcababaaddbdbccbcdacbaddcbbacbdddcbdaaaaacbbadadbadaabbcbaacbddabcbdbacacdaaabbacabbcdcaddcadcddccbddcacbdbdbdaadbbdccdadbccddcdccaacabcaccbadacabbacbbbbcbbbcccadadbbcdbaacbcaadaabdcbdcbaaabccbacbccdacadddbdddddaabccddbbdbbbacaadddcddabcadcbddbabbbadcddccacdbaacbcbbabbcaaaabdcbaaadbadaaacdadadddddccbbccbabdcbbabbdcdddabddadbccbcdabbbaadcabaddcbaaabbdcdccbcdaadadcccacaccbabcdabcaabbbdccacdaacbcdadcbdabcbbbccabbbcbcbbbabddcbdbdbddaccddbaabacabccaadcddcabbbccdcbcccaddbdcdcdadacababbbbaddcdacddacaabacddbadcabbcddaaaccacbbdbdaaaaadbcaacdcddacdbbbabcaadacbcdaabdaaabdadbadcbcbbcbaadbcaacdcbddaddcdacacdbdacddcadcacadadcdbcbabbccccabdcabcabcddaadbcbdaaacaccbdbbbaddccaacbbbccccdbcaddbbbbbdcaabbcccdabcbacbabacdabdbabcdbbcacbdddddbddaddaacaabbdbbcbbaacbacbdcabccdbbacbabccdcaaacddabbbdcdcdbbadaddbdddcbdcdabbdbbaaabdcdbdcaadccdcbdbcaaccaccaaaccadaccbdbbcaaddcbdabdbbdaaddbaabcadccdbbcadaaaacdbcaaadbbbbdabccdbbbddbbcacddddbdbcabcadccdacddcbdccdaacbadddadaacabbbcbbccbabadadccbaacbbbbdcacacbccdddcacacaaacccddcdacaabaccadadacbccdadaaabbacdbdcdcdddcbbabdccddbdbbdaadbacddaacaccaddabccbcdaaabbdbbdcacbdabaaaabccdbabbbdcbdabcdcbaacbcdccbbdcddaccdbaacdbbdaccbadddadbacccadbadbddbbddadccbcbcccaadbbcabccaadddddbaddbbbcdacdabcbbdbccabaaabccbcddadcccabcaddcbbdaccdcabcbbbbcbabacdbdcaddbadacabdcbddbacdccdbcaaacaaacbabddcccadacccabcdddaccacabcbbdaaccaaacacdbbddddccdbdbdddcbddcdbdcbbbabcbdbbbdbcacaaaacaacbbadddcbaacacbcdbabdbbacdcdcbcbbbbcaddbcccdacdcbbcbbbdbbccaaaadaacbbdbccbcaacbaaadcdadbbaddaadabbacacbdbcdccddbbcbcdcccbdccbaabadccbbdbddccdcdcdbbcacaacacdbcadabaaaabdacabcdbbabddccaddbacadccddcbcbbcaaadbadcccdbabcdbcbcdacaddbdccaadcdabdcabdabbaabcbbcdcabdacbdcbdbabccaaccaaadbbdcacbdabbacacaccabbaabdbddbccdcdcbdcddbdcdcaccdcdadbaabbdbcdbddacabddbddbdbbacdacadcbacacdaaaaaadbcbbacaccdcaaccdbaadcbcabcbbbdbdbcbddccbdbcaaddbcdadcabbacbbbdcacabccdadabcbdbaababcccbbaaccdcddcbccddbccdccaaaccbabdadabccbacbddadccbbccadbadacaadacabbacabdbabdcadabadcbdaaddadcccbcbcbdcdbbdcadaadcadcdcabddacacdddabccbbcccacbdadbcdadbbdbabcdbbbbddbaababbcbababbbacbcdccaacccabcbddbdcadacaccdacaddbcbaabbbdcaacbdacdacccdbbdaaacbabdcbaaaccbbbaacccabdcbcbbaacaabdbdadbaacabbdbbbbddabbaadaabbdaabdabbacbaaaabcbbbaaaadaadddababbccbabbcdbbbccabacdaadbdcdacdbddcbdacccacbdadcdbbbccdbdaabddbccacccddcabbbbcbdbcdacdcccbbcddadacaacbdbdaabbbabcdcaadaadcdbcbacbaddbcabcbccccdbcabaadddadacdcbdcbdbacddddcddcbbccbcdcdaddcbbdddbdbbbcbacdcbbdabdddadcdbcbcabbbbdbcddddbbacbbcaaaacabcdbdddbaaacbbaaddcdcabcbccbbbadabacacbacddbcdccdaaccdbbbaabacdaabaaaaacddcaabdcbcdaabcbbbcdabbabbdaccaccddaabddcccdbdccdddbacbbadddcdaadcdabbbcbcbdacdbddadcccabbbabddaabadababbbacadadbdbbddcbcbbdddddcaadabbadbbdccbdbcbddbbcbddcaaaacaacaadadcdbacadbcdcddbbddcbdaccacabccaccdaccbcbccacaacdabbadacdcacabdaaaddababdcbaacddcbdaadabdadcadadbadcdaaddbccbcadaadbbdabccdacbbcbbddaddbbbcaadcbddabcaabdacdcaccdadcbaaddbcdadcbdcddddccddbcbbbcddcbaccaabdcccaaabcdaabbbdaabcadbbaddbbdadacdcdabacbbbdaaddcdcacdbbbbdabacdabbdcbccbbbaacdcaaababdcadcdbdbbbaaacdcddadbbbadaddcdbabacdabcabbadbcdabdaacdccddbadabdaaaabcbdbbacacaacddaacadacacacacdddaaadcdacaabaacdddacbdabadbbccaddcccccccbaaccadbdccabcdacacdcabbbdabddcbbbdbaabdbcdaaabbabdcddbadcbcabaabdbbdcddaadcdcdaabddcdccaaadbccadcdddaacbcdbbdaaabbdcccbaabbaaadcdccabbcccdbdbdaccaacaadbcbbbadbddbacddcbbbabbcabbbadcdabdccdcbddcdddddacddcadabcdcccbbcbaabbcaacaaaaaddddbbdacbbcbbaaadccccbdbadabbddaaccccabadcbcbdbdbcdacdaaddacabbbccbcbbbbbcabcccbbaabcaabdbbccbbccabcacccbbdaadccaaccaadacbdbabcddbdaadaacddabdbcaabdbaabacbbabbdacacbbdcddacbbdaaacdddbcabbdadbaccbbaaccdaddbbabbcdcadaabaabdacbcaacbacbcbacabdabdcbcaccabdacdbbbccddadaabccbabcdcabacbdbdbaccacddbabccabcadbacbbbcdbacababaabbbacbaadcccbadaadbbdabbcbdabcbcbabddcddaabcaadbbabdcaabacbaacadbbbacbbaddcddaddaccabbdcbcadbbbccddcbbacccaaabdacddbcdabcdaacbdbdbcbddbcaadcadbaacadcadbbabbcbbaccabaacbabbabdaaabbccabdabddcbcadbbadadabaadcdababccabddaababdccdaaadadbabbdbbcdcbaccacabdcbccdbbccabcdadcccbadabcaddbacbcbbbccbacdbbcbccadbbddabcdaddbabcdcddbaaaababdacacaacddbabdacbbaacdabadbacdbbdaaaaaddbcccbbbabccdccbadbbcadbdadcdcdabcabbdbdabbbcbacbddadcadacadcddcbdadaacbbadcccadbabdcddbdaadacbadabbcaadcababcbbdaaabccbcbbbccdbdabbabddaccabccdbcadadcbbaacdcdacdaacaadacccdacddbcbcacdbadcbbddbbbccaaadabaaaccadbaaccccccadadbcbbbbacdcdcccdaaccabddadacdcbdaccddbbcdadbbcabdcaaabbcdabacddbcdbdabcbdcbacabdcbbadccdcbaccccbdcdddcbcccbaadaaaccdbccdacbdcbabbdbabddbdcacbdaaabaddaacbccbacbaccbdaddbdabcdadacddaaababbddccadbacbddccbcbbdcabcccddccacaccdaddbccdbdcdbdddacbbbbcbddbbacccdadcadacbcdabadcdadacadddbccbaadcacdaccbdcadcbcadbcbcbbabdddbddcdbaccacbdadaacbabcaadaabadcadbbbbddaacbddbcabdaabacdbcaabdcbcabcbbbcbbdaadaabdaccaddacaabbadbbddbabbbcacadbcdcbaaaacbcddbcbbbdaddacbdccdaaacddacdbadddbddcddbbabaabadbdcbaacacbaadacdbdacddcbacdaaddbbdcbcbaccbaacacddacbdcdcdcadbadbbabcdcbcdbabdcdbadcabbdcbbbadaabbccddbabdbcccccbadadbacadcdccabcbcccadcdbaacdddaadbdacbbbdabadddccaacbbbcccbbbbdddddccbbaccdcaddabdddddacdbcbddbcabbacbccbddcdadbdbaadaccbdbabccabddacaabbbabdbdbbabbbadbccddbdcabcbdbbbdbbdbcdbcabcabdddcadbbabdabbdaadcacbcacacdbdcdbcddcdbcdadcabbdccccacbdddbbcdbbaabbbcdddabdddadcacaacaddcdbadadcdacbbaabdabdbcdbadccdaaabccdddbaaaadbaabbdccadddccadcdabccdcacaacdadbbcadabaccdcbabaacdcbabacbccbbcdbcbacddabdadcacbcaccaabbcbbbbcdcbbbdcbcabdbdcbaaddadbbacaacabbcabbdbdcccbdadacbdbcdadcbbacbadadaaccbdbcdabddbcdaacccacbbacabccdabbacdbbacbbaacdccdacbbcaccaaddbacdbacadcbdadaacbdbbbadbabaababcdaaaccbbdddaccbbdabdcbdbabdaaabbdcacdbbdaccacacabcdaaaadbaddcadbbcdacddcdbdbabaacbdbbcbdaaabadbdbbbddcadbdbcddbddbdacdcbcadbbcbcdcdaadaaaaccbadadaaddccbbcccacbcabbbaabbacaabbabdbbbcdbcdadbbcdcdabdbbccaccbcbcdccddadabcacdabaabcacdcdbbacacaaacbdbbcdbcdaddbdadadddacbcddaadddadaccaaacdbdbaacdcabadcaabccabdacbdadbdbaddbadbadbccacbdbcccbdacbbcbdbabacacdcdccdbcdcaaddbabcacccddbacbababbacbacbaacbabbbbcacdacddabbadaadadabbcabbacbaadcaddcbdccddbadcbbbcbbbcabcbaccbccbddcdaadaabddbddcacccdaadcccabaddbdcbcdaddcbbcabdaaddbdadcbdacccbcdacbdbdbaaddcbcbbdddabcabddbcbdbaabcbbdbdccbaabcdbaadbcadbccbacbaccdacadbaaadbcdcbbaddaccadcdddcabbcadacbbdbccdcdcaaaccbcbbacdbbadbcbacdbbacadbadccbbcdccadbdbbbbdacdbcbbacaddbdddbbaddccdbdbbaccbbcacaabacddadbacadabcbcbbcdcacaacbdabccddbccdcbcaddbbacbadddadacccaacadcbcccbdadbaaacbaccbabbadcbabddbadcbdcabdccdabaabaacadacabdcaccababdabcbadabcdcbaccacdcddcaccadccbacacaddcdcaaadcabaaddaccbacdcbadbbabbbbdbacbbccadbdbcccadccdcacabdbbbaaccdbdcabaabdcaddddaaacabdbcabdabbbbcddbcdcbdccbcbcdbcdabbcbacbadbbbcddbaaaaccadddcbbdaccddacabacbbabbacbddcddccdccbbdbbbacabbababcaaabdccadadcadbcbcdbbdddbcacacacdcbabdaccdabdcacbabadaadbaddabcdddbcbadbbddccdbbcddbabaaddadddacacacaababdcdbacddddabaccadccbbcadddbabbaddbdcddcbbbccacbdbdabbcaddababcadbddcdcadccbadbcbbcabcacaabccbdbbbacabdbcbccdcdddcbacbccddbcbcdaacacaaaccacbcacdbbdaacdccbaccccdacddbdabcadabbaccbcbdabaccadcbbbdddbadbabaacadcbbcdbddcbadaddaccbdbdddadbaaaaaccbacdccbabdcbbabdddaacbdbbcccdddcbdcdadccdcaadbbdcbddcdabadbadcaadcdacbdbbadadcbccccbadccbabacaabdbbccdddbabbabcbbbdababcbbacaddbcbbccbdcdbcacdcbcccbabcabccccbdaaacdcabdaacaaddcbdcadddddbbbcbabbbcbaccaaaadcabcaccbbddbccdbbcaddbcbbaabcbacbaddadbcacbabcadcdbcbaabacccbbadbacaddcdaabdccbcdcbdadcbbabaccdbdadcbddcdcbaacccbabddbdaccdbaaccadcbcbacdacabdaacbcbcdbdcbdddcbdddcacbbdcaadacbbcbdabccdcbaabdadddabbdacbbbdbdbddbcdcaadcaadadbbadcbdbbcbcdbbbcdccdbcbcbcdbbcaddccdaddbabdcccadacdacbbbdcbcddbbdaababbcbaddabcdccbbdadaabdbabaadccaccddaadcccccbbbaadccababbdcbcadbadadacacbdaddcdcdcbaaabdbcdcacadcbbcdaacccbccdaabbbaabcabbdcbdabdcdbccacbdacdcccbacbcadcbdaabbaccbabbccadbaadacddbbcdcddddcbabbacbaadcddbaabbbdcbcbbacbccacddadcddcabdbddcbabbccabddddaacbdadbbddcbbddcbdcabccdabbadbcdbaacacbbaddaacbdaababacabadddacbaccdcdacabdbddcabbddacaadbbbcddaddabddcaccabaacdababaadadddcbabacddaaddaaddddccbdcaacdacaccdaacadaadcabacccadcadcaccbbdaaabbdaabdbdaacbcbbcbabbbbdbaddcabcdaaddbddbcbaddbbabdacdbcbaabddadbdcaccbabccacbdacacdcadbacccbadadadcdabccdddbabbcdbcbdcccbdaadaacaabaccbbadddcccbcaaadcdddacbddacabdbdddacbbadabacbbdcbbdabdadccabbdcccbcacabcaabccacdcdccdcbdcabaddbadcdbbbcccdbbccdcbdcadbbdbabadddbcbacaabbbbdddbaabccaccdbdadcabcdaccbaacadbcadbccacddbddbbdccbcbddcdcadcddbabcdcbcaddcdaabddcbdabbcadbabadbdccbbddbddccdccbdacdddabcdbcbdddcddadcbadabaaabacaabbbbdbdacdcdacdcdddaadcdadbacdacddacdabaaaabcbbbadcaadabbadcadacdaaddddcbddbccabaacacbcdadccbdabbdabbdcddcaaccbdbcbdaddccabbaaccdcabaaacddbbdacaddacaaadbbdbbbaaaabaadbccdddbcccabadcabccacaababbbbbbdbcdcdbdccacaddbbdaababadcdbcdbbbdadcbacbdbdddaacdacccdbbccaadcbdacbacaaddbbcabdbdacadbbacbdddcbacbcbccbacadbaabaadababcddadbcdabbdccdbcadabbcddaadddaddcdcabcaabdcddcbccadcaaaacdcdbbbcccaddbadcbccacddacdadabbcdcaadbddbacacabaccabbbcccdaddbcacdddddcaccadadabddababdcdbaaddcdbdcbdacaacdcdcdddbaccadabbbbbcdabcccddabcbdcdcdacdbaaaaccbbcadccacddbbacadabcabdacbbacdcbabcbcbadacaaadccdaccacbbddbbabcbaddabcbabcbaccaccacabbadbacbadbcaadbbccaccbbaacaacdccbdbabccdabccbcdbaabbabaabcddacabdacbaccadbbbcdbdbbbbbdcddbddbcbcbbdcdbbbaadaabbcbdbadbdaaadbabcacaacbdacaddbacaddadccdcaddacaadabdcaccaccbabaadaadbacacaccdcaaaadccccabddddbadbacbccaddbddddcbddbaabadbcbbdbddaabdaaaaddadcababacadacdbcbdddcabddddddbbbbbbcccbbcdacccaaaddadbccbbccddbdcbcaccdaadbaadcbdacdcbdbacdcaaabbacbabaddbacbacccddddaddbcdaadabcbdbdaccadaacabacdaddaacabccbcaaababababcacaaadbbbcbacadbbbacdddbacbabbcdadcdaabcdcaaadbadcbcaacacbdbddacdcabaddabaacccdbacbcacbbbbddcbccdbdddcacbcabadaadabacbbbbaddaabaaadcbabcdadbbdaaddbadbdcddcbdbccdbcccbadaabdcadabaccaaaddadadaddddbacacdbcaabaddaaaadabdddbddadccdbdcabcbddbcbccdcdbbcabababbcdcaacdcbadccbcbbcacccdcadaddadcbdddccabdbaaaacccdbdabbddaadbcbdbcacaaccbacaddabdaccaddcdcabaaddabdbcacccbbbbcbbabdacabbcccbacaaddabbaacacbbabacdcabbbcdacabcaddbaddbdbdaaccdaabcdabaccbcbbbddddcabbadcdbcbcdaadaadadddcdabbdbacbbaaaabaabcdcdcddcacbabbdcbaabdccbcdabcdacabcbcbcbcbdbcdbbccbbcdbabaabdaaaddababdbcaabaddbcadaddcaaadcbdccaaabbdcaabbccbadadccacacccbaaaacacadcaaddaacdcdcccaaaabcdccdbbccaabbcbdbacacdcdccdcdbdaccdccbadbdadacdabcadbbccbdababaccacaadadabddbacabaddacdadcbddbddbacbabbcabddabcadccacddbdbdbdacaccdbcadcbccbcbaaaacddddacdccbccadcadcacaaacacdcbabccddccdccabbbadadcddaaacbcaddadccabbcabcadabbcddbdcabacddcddcbcbbddbbcddadcdabaddaaddcbaddbadadadacccbcacccaadcaccbcbcadcdacdbbaacacbacdcdabccbcabbacbbddbdaaacddcddbaccabbbadcdabadcbcadbdacccbccdacdbacaabbadbbaaadabadaccbcbbdbcaadbbadadddadbcbccbbabbadbaccaaddccddcbdcdbcbdcdbdbcdbcababadbacdbbccaccacadbcbccbcccdbbbadbddddccbaabbdbbaacbdbbdadcbdabdcbabdbbdddadadacbcdaaccbdbdbbcbdddbabcadddcccabbccaddcdadabadabbdddcdbcabbaccdbaccbcaaadcbdaabaddddbbdcccbbdddbaaccdabbcaccdcdbdddabbddbcbbccccaabdbdadaddcaabcabbaddbdadabaaadcaddccbbabcbcdaacbabaddbcbdcddccdddaabbadcadccbcbcdddbaddcbdbdcbdcadcaaaadcababdaabbdcdabdccdbbbacabaddabacccbddaacdaccccbbbcccccccacaaccdabacdacacaadbdacdacdddbdddabbdcccddcbccacdddbacbbcadbacddbaccbdddacbbbabbbbccddcbabdadacacdaddddccdacaddcddbbadbdabbbaabbbacbdddbddababdcbbdacaadaaababdbcccdcbacddaabbbaaccdacdddbccaacddcbcabbcdaadbdadcbcbcddbabdbcdadbadbdbabdabdaccbcababcbccbcaccbcbbbddabccaabcbadadbacbbbbcaadaacaaabcddbaacbbcdcbbbadcabdbcbbcccdaacbbaacdcabcaabbccbcbbdcbaccbbbdaacccbcacbbdbbadbaadbbbaddcbddbaaabbccaccbdaabcadbabadbcbdcbdadddbbaabaccdacbddddbdcabdaccbdddcccbcacbcccddcaddaaccadcbccccadbbacccadbdaccacabaccababbcbcbdcdcbcadddcabcacadddccabdcdcbbcbcaaaccadddbcbacbabaacbdbdccadcbcaddcdcbdacccbaabadcdadcacacbcddcbbbaaccadbaccbadccbaabbdcaddbadbcbabdcdacbdccbdcdacaccadacbdbccbdacdcbdccaddcaabdaadabdcdaaddbbcacbdbbcbcdaacbadcbdbcbabccabaccdbbdacbabcdadaabaaabaddbacccdcbbacaacacadbbbabaddcbddbcacccaccadcabdbbdadcabbacbcbacbbadaddbadcddabdbacbadbaadcbcdadbabdabdabbadaadbddbdabaaddbbdcbbdcdddcbbdbdbadbaabcbcacccdbcdbbbbbaacdbbcdbababacabbbbdbddddabbaddbbcbacccdcaadcdabdcbcbaaacacdcabbdadbaacabccacdabbbdcacbbaacbdcaadbdcbbcccacbacbcdcbdabbaabababcbacacaddabcdaaccbcabcaadcdccddcbaccadabbaadbabdcdbabcdcdddaadaccdcdadaadcabddccbbddbbbcdcdcbcbdbbdadaaabcaadacbbbabadaadccaaccbaaacbaaccbdabdbbaddcdcaabdbdaabacdbccdccbaaccbbdbdabacbbacccccbbbcacdcadccbababbbadbdcddaabcccdbabdbabccbaadabcdbaadcbbdaddcbdcbabaabdbcadcbcddcbaaaacdcaaccacbbbdcdacdccabbdaccacddaddcbcdbaaccdacbdbabcbcbcbbcbcdaadabddbadbcbbdbbdadbcdbddadacaabdadbbcdaccdbdadabdccbadaaaaaabcbdbbbdbdaddbcbabcbacdaacabaabdbdddbddccdcbadcabcbccbbcdaccaaabdacbbdcdbaabbadccaaddbcdbbbbbabdabacdaddccabcccacddabaacccdccddacadbccdbbaaddbbbbbcdadddccbccddccbdbabdbbccccbabbbbcddbcbaccdcbaddbabbdabdbbddabbcccacbaddacbdbaddccdaacbababbcdadddbabacabaccdbdbbbacadcbbaaddabcddacaacbcbbbadbbbacccabbbdbdbadbdacdbcbcbbdbddcacbaaabddbdaadcbbacbdbcaddcdddcbddbacddbaaacbdabdcdcbbabaababcaacabacdcaaddccddddcdbdbcabadddbadccbcaccbdaccdccdcddbaabdadcaabbbacacccdbbdbbbddacaccbdcbdbacbcacdaabccccbadbcbcbcdbbbbdabdaddcbaaacabdbacbcdabbbdaadadacbcbbcadacdcddbabcddcaaadcabcbcccabacdbcacabaddbacdcaacbbcbdacdbadcaaaabcbcdabdbcabddcbcdadbbbbaddbcabbcddbdcbcaddaabcaddbdbbddcadaaddabbaabcbaabccccdacaabcabbaadbdcbcabcbdacbdaccdaccabddbdbbdadcdbabaadcbcbacbccbcccabbbbccdcddcbbcacdccddaadcddacababbbaddbccaccabccdcdcdabddcaddbbccbccbaadddcddbcabbbdccdacdabdadaaacadddaadcabbaaabbbcadddcadadbbcdadadadbbaccdcddcdbaddadbcadcabcacbadbbbbadbdaaccdabdabaddbcccadaaacdbcaddcdcdabbdcbcccddaaacbaacbccbcbdbdcaacaaadcddaadabcdcadaabbdbbbccbdbbddcdcdbabdbcadcadcaccbdadcdacdddbabbcddaaccbcbbaabaadbbadcabadbcacddbaabadabddbddaaabddcdaacacbbdbddddabbacabdcabacaadddaaabcaccaaacdbacddaaadbdcabdbdbadacddbabcabcdbabdbccdaabdbbbbcdddabcbbaacacacabbaaadbdccbcdddbccbacbcadbabccdcabccbcbabccbcbcdaaacabccaabbabcbadbcbbccddbbccccadcbdcaddcbdacbddcbbcbbcdcaacaabbcbacbbababaaacacddcdaabcbbaadcadbdaabdbbbadcdddcaadcccacdcacddcaadcbddaacbabaccbbdacccbcaccadbacadddbbdaadbcbcdddabcbdabcbdcbdbdadaddcabdadaccaddababccbdddaacbccbccdbdbddbbddbbaddbbdbabcdddcbcccdbbaadbacabbabaadabadbbbbacaabcdcccccbbccbabdccdbadadaabbbcabbcbbadaabcdcccdcaaddcddddabddadbadbccbbcdddcbbdbdcccbbbdcbbbacbbcbbdabdacaddccadadbdabbccaddcccabddaddaacdddadbbcbbbcddddcacdcbcdbcdcdacccccbcacadcaaacdaaccccdbcbdadcabbbccbdcadaadabcdcddcacadcdaababddaaabddabaaddcbabdbccbbddacdabadacdcaabbdabddcbbadcabbdddddaacaaaadaacdacccbaacbcddbdabdaaccabcacdbcbddadaaddaccacdbaacabdbaacabbcbcbbcaaadabacdbaabbbdbccdadaabadaabaddbdbabdbccbcdadbadcbccccaadbaacddabaacbcdadcdaccbdaabdacbdbdddadbadbddcdcdcaddbcadddcddcadccaacdbadbccabbabbccccbdbbddaacddcdccbcdadabaabcbcdadabacbacdaacdacabacccbdcdababbbdbbcbbddddbdbadacdcddabbacdcdbcdabaadacbbaddcbbbaaaaccadbaddccadcbdcbadbacaaaddbbcaacdbddccdbdbaacabcbbcbcbddbdadacdaabdcddcaccbddddbdddbcccbbddbaccbccddbadabcbccaabacbdcdbacbacdcaacdbcbabacccddccaddbababaccdaaacccdbddbbbcbcdbacabcaaddcdcabadddcabaacacccaccddddbdadabdbcbadcbccccbbdadacdddaabcacdbccaddcbbaaaccadabbddacdbddbcbbbdccdcdcabbdbccdaccabadabdacaabadaaabdbbdcdacdbcbabacdbbcaadabcdbcadabbacbbaccddcadbcaabbbaabcabbaaabacabacbbaaababccbbdcadabdbcbbaaadcbacddcbddddaadabaccccdcdcadcddcddbbaadcbddddaaababacbdcabddacbbaaabbcdadcdccadcabbdbbaabaccbbcbbdacaaccaccccddbbaddaadddbcdbccdcdacdbddabccacbaaabbccbacaacddacdbabcbdaabbdbabbaaacbdbabdadadccabacacabcbdcbbabadadcbacbaabacbaacbcdabccaadadaaccbbbcdaaadcacadacbaacbaaadbddbcbbadcdccccdadccacdbcaacacccccbdacbccabcaaabaaadbbbcabadddddddbdccacadaddbccdadadbbbbdcaacaaddbccbabcbdbcbcdccbacccbadbbcdccadcdbdbddcbbabcbbabccccabaaaacbddddbddcaddbbababbcdddddbdabcbbabacdcccbadaddacadbccbaddddadbccdcbdacaacdcddabbbbdadcbcabccbbdccdddcacdcbdcbbdabcbcdbbccdacdabdadacddcbdaaabaaabddccccddbadcdbcababcaaddddcccdcaacabdbbadabcaccdbdccddaabbdacaddccadbcabadbaddcddccabbbdcbdbacbbccbabaabadbdcacaadacbaacdadacbcbddcdbcbcbdaabcdbbbadcbaabbbdaccbdabbacdbcbbbccdcbccacbbaaadbaadcbaadcaccadcdaaabcdbcdbacabdddcccaddadcdaaabdbbddcabbdacbccbbdaddabdcbadbbccbddbccdccbdcacbacdbddddccbdbbbaadbccbaadccccadadbacdaaadcadbbdbacbcabcdbdcdacdbbacadbcbcbababbcddaabbbabdbdcbaaabacbbcabbbadacdababcddddcbbbcbcbabdcbbbbadaabaacabcaacdbcbdabacbaabacccdbaadcccccbacbdbcbdadbccbabbdcbcddaacdbdbbaaadaadaacddcbcadddcdbdcdcaabbacbabddaaabacbdddaadbdbadaadcdbcacaadababdbbdcdcacdbdacbcbcadadcbdcdacbccbbacbccdbcddcccdcabbdcdbbaaddacccadabbbdbcbbaabbcccccbcacbccadcdacadabcdbbadaadaadabdcbdbcdbbbbbdcddbadadbbbbbbdccccacaaccaddacbcaacadbbabcabdddaaadddbadccbbbdcdbccacdbcdaaacaabcccdcbabbbbcddbcdacbcbcccbcbcbdcadadcddacdabbcbccbadacaccdbdadbcdbcbabbaaabddccdbabbdbbddaacaacdabcdcddcbbcbdadbcaacacbcadcacccbaacccdaacabdddcbccddbaaabddacbccabaaabdbadacbddddabacbbcbbddccdaadcacdbabddcdacccbcdabdadaabacacaabadccbcbbcabaadacacdcbbbdacabdabcddaaddbccaadddcbdbcdddcaccccaabdccdaacdabaabcdccaddaaadaddcbccabbdbdbdaacaddacdccbcbbdddcbdacaacdaccdaaaacacaaaacaabddaddaacccadbccbccdadcbbccdabacaadcbbbaaccccbbcadbbdddcccbcdcdbcaacaaddadbbdbaacbacdbcadbcbbcbaccddacababdddccbbdbadccdcbcacccdcdcddddcaadabbdccdbddcbcdbacbddabdaadadbdbdaccdadacacaacbddabbabdddcbdcaabacdaaaaccdaacabccdbdcdadaababcdbbccbdbadcabacbbccbcadccbcdcbcbacbbdbacbbdbaddcccccaadbbabdbdccdcddabdbbabcccdaaacddcdacdadddbbcaccbbcccdacdddbdddbbbabbacddbabdbabaddabcbbadacccdbbcbcdacdcdcadbbbbbbaadcbabbadcbbcdcbcaaddbacbcbbbdaacacddcabacbcccadbdcaccbabaccbaabbbdbabdcdbcbdaaaaccbadcaccaaaabaadbcabddabccccbdddccbabadddcbacdcccccdddadddaddbdbbdaabdccadcdaadccacadcddbacddcadaaccaacddbddabcbababaabdabbcdcccddbcdccbddcdcdddbbdbcbabccbadcbbaabbacbddbdcbdacbabadddbbcdbccacbadddcaaddbcbbbacdbdaacccdadbaddddcbcaadbccabbddcaabdabbaacabacbbccddcbcadabacccaadbbbccdaacdbbbcbbcccdddacadacaddccdddbddbaddacbdadbddddaacdadcadccaddbdabaababdabdaaacdcccbbdccacacbdccdcdabacdccabbabadcbdbdbdccdcdabcccdadbadcaacdacccdbacbabadcacbcaddbddddadcbdcdbdbcacdbcbddbadccadbbbbacaaccaaaccdadbccdadbabdcbbcbbcdaabcacdcacbccdbaaaaddcadadabaccdaaaacaddcabdcaacbdcddaaaccdaaadabbbdddaabddbabcbdcbcdcbcbaaaacbdaadcdcdcccddcdaadccaaabbcdbbdcadacdcdcacdbacabcbbddaddaacaaacdbdbbdaadbbccdaacbdcdccbaccbaccdaacaccacaadbccbcbdbcacdddbdbdcbbcdaaddccadadbdcdbcddddaaaadaadcccadcaddcdaaadbccbacbbacdadbdbcddaaaccacdabadaccbaadacddccdcaabcbdbdddacbaacaddccddabbcbddaaddbccbabaddddbbbbdbbddcbbccdaaddccdacbcadaacdcbdddcbdcbddcdbcbcddcbbbbbdbcaddbbdbacbddcdaaddbbddadbbdababadcdcdbbbddbbbbbbaccdbbadadccaacbadddccccdabcaadcadadadadabbacbbcccdcdcaaabadbaccddadddabccdcdcaddadbadccbbbbcbbccdbdaccdccccbdbbbbdabcddbbcbaccdacdacccdababbccccacbaadcbadbbdcaccdacddbadbbdacbdaccbdaddcadcaacbabbdccbbdadacaddddacaadccbdadbcaddccadcdabbdaddbdadcacbacdcdcadadcbacbdbdcbdaacaaadbdbcdbbaddabdbbbddddbccbcccbcdbbddcdbcacbbadacaddacacbacacaccaddcbbaadadbcccbdaccbbabaadddacabaadbacacbccdbddbdbbcadaccdbdcbbccabdcaccaccabcbcaddbbacdadcdbcbbbacababccbdabbaabdcadcbbabccdcbbdbbabcacaaddddaadcccbaaadaabdcdcddacaacdcdbccbaddbbdcdbccaddbabdacbabaaaabbbbabbccbaadddbcbddbbbabacdbbdbdbbcaccadbbbacdccddcacbddabcdadadddddcbadcaddababbdccbcadbbacaaabdddcacdadbdcddbdddadddddbcdbcbcccbaabadabccdbaabdcdabdcdcccccabcdbcacdabcddacbcdbcacddabaccbbccaacbbddacadddaadacdbbacbbbcdaabcbacdabbbcddbdbcccdacdbccaacbbbbbbccacddaacbccbbaadbcadabadadbbdaacbdddcdbbddbaddabbadbcacdccabaddcdaadabaacbabcbcadabbbacddccbdacababbcabcbcdbaabbcdaaaaaabdacacacadccadcdbdbadaaddaadccdcaabadabbaabccacabbcacabdadadcdbaddbcacacbdabcbdbcdbbbcbddcacbbbbbdddacbdddddbabaadaaddcbbacbbacabbbacacabbaddadcdacdbbacdadcaacbacbdacbacbbabbcaddccbacabbdbaacabcbbbdddacdbcccdacdaaccbaaacababadbcabacaaaddabdddcdcdddbcbbddbdddaaaacbcbaaabbbdcadcbdbabcdccadddbaabdacddbadacbadcaaaacbdcacdaacabaaddaaddbddddbcadbbdcadddbccbadbdbaacabbdbbacdaaabcabaddbdcdbdaccdcbdaaadaadbdbbbdcaacbbdbbdbcbbbbcdadddbccbadccbcddbbdadadddaabccadcdcbcbadadcaabadbaddacddbcbcbaccdccbabccbbdddcdcabbbdbdddbddadbabdbaaccccddbcbdcbbbcbbadcdaaacaabbbbadcddcbaddaabaddbbadbbbbccbbdcdacdbbbbddbddcadbbddcadabddbcdbbbbdbcacbcccbcbcddbaacbdccccabddcbacabdcdabbcdbbadbdaacdadbcbcccdabcccabaabbcbdccbdcacdddabddcabbdcbaadbabbcdaddddbbccbbdbdcdadcadbadabadbbdcabaacddaabbabadcaabbcdbcaaabbcdabddcccbdaacacbddcaaadcbcadadcbccdddabcacbcacdbbacaddbdababbadcddbcaacdbbaacbbdaacdcacccbdcacdbacdcdbbcdbababacddadcbdabbdddbbdbadbadcbdabcdbcddcaaddbabbccddbccdabbccaccadaddadbaccabcbabadcdbbbbbddbddcdadccdbbcdbcccdcccacdadaaabadcdccdbdbaaaadbccdaacbabddccbadaccdaddcbaccaabcbbbbaadddcaadabbcabaadbdddcacaabacadaabddbcbcaaadbddcbddcdaaccaaadcbdbbccddbacdbbcdbcaababbadaabcbaadccdacadbadccbdcccbacbcadcabdcaccccbcbddbdcbdcbcdbdddaddbbddadcbdbbbbbadaabbadabcadcaabdbcdcaaabbcacbcccadaaaddcdddbbbcdbbddcaacaaccddbdadbacdaadddddbdcbbabbdddbbbcacaabdcdccbbbbdabbcaabdabacccabdbbbdbcdadcdbabdddbbbbcaaddddccbcbbdbbbadddcbabdacdbaacbabbdcabacacdccadddabacadcbdcbccdccaabdcacdababbadcccdaccdcbbcddaccaadbcdbcdcbdaddbabcacdaccddbdaabcccaaccacbbacaabbdcccabdabbcccddbdbcdadddbbdadcbaaabcadbadadaddaddaacdcaccdcadbbbadaadaabdcbbddbaacdcbcdabccbbccdddadbbaabddadcbabdcacdddcbababdabbcbbccccdcaabbbabdbacbcdadaddccaabddabbacdccabaabcbabacdccddbcdcddbdcbbbbddccaabababaacddbddcacbdcbcbbcbbdcdaabbccdcdadccbadbddbcaaddabaadabcacdcdbabadcadcdaaadabbaabcdacccdaabbacabcdbdacbabbbaccbcbbdcdcadcccdccabacdbddadaabaadcbcdbccdcbbabaadcadbabbccdccaccdccababbbaccbbaabbcaaccacaaabdbadbaacdaaddbacaddcbcabbaccbadcdbdbaccbbaadbdacbdabdbabbcbabcdbcacaddddbacadacdabdabdcdbbbaabadacdbadaabdadaabddccccddcddddddaaccdcbddbcadbaaacbbaabdbbaacbbccddcbdcababaaccdbaddcdcbcddacccbadbbaddcbadbddabbadbdbabaddbccccaddbdbdcbabdbbbdbacdcbbabdbacacbcbacdbcadcbcabaacccddbcbbbadbabdbdcaaccaccabdddabddaabdbacbdabcacdabadcddcdbbccabcdbccdbaacbbabbbcdbdadaadaccabdadcabaaacbcadddabdaadadcabdaaddccbdbabbcaddbaabdbcdabacbaddabaccbacabbbdcdccacdacccbbddcdadbdaaacdaaaaacadbcddacadbabaadabddcdabadbacdcdcacdaddcaddadcbddabdaccddaadaddaadbbcbdbbbcccdabbaaadbbbdbccadaaaabddadcaacccbcdbcadababbabaabbcdacbddcacdddcdcabcdbdadcdcaacabdaccbcdabccdcbbcacbdbcacbbcdacbacccaabbcdbcdabacdcadaaadaabbabaadcbadaadbcccadbdbbacbccdabaacacddddcccbaaadbadaabcabbddcdadcbcabacbdbdcccbdabcacbcdaddddaababaacdcacdccaadacddddaddaccacddcacacccdddadbaaccbababadabdbddddadccbcbbcbcbaacaccbcdccabbaaadbdcabbcacaccccbadbdbccddabcbbdcbadacbcccadbdabababcccbdcdddbcacabcabdcadbbdadccaadbcccaccccdcacdbdcaaaaabbdbbaabaacacaaacaadaddbdccbadaacbdcadbacdbccaacaadcaaacddbcabbabbadaddbdcbdaccbabaccdccadcccdcaaaccbbdccacdcbcdccadcdcdccccbaaccbdbcbbbabbccbcabcaacbcbabccbbcdccccabbabdbcdabddbadabdadbaddbadddaddbdbcdcabaabbcbbccabcbacacbbcdaadaabdbcdbacbcccdcbcbbccadddcacbadadaabaacdaabbbaaabdaddccdaadcddaddaddaaadbdcbbabadcdadccbcbadbabccddcbcabdcdababbccbcbaaabccaacbddbcbccbbabaccdbcccacaabaddbaccadcacacdbddcdcadadcdbaccbcacbbaacaddbcababcaabcdcacdbcdddbbdacaccccdbccdbbccacdbcabdbacaaabcabbbcabbbdbabddbbcdcaaacbbdcaddbacbaadadbbdabadccdddbcbdddbcbdbcdbbbcddadcdbabdbaadbabddccbbbabbaccaccaddcbcdbbbbccccdaddbbcccbcbacdbdccdbbddabaaaacbcbdcddbabcdaddbdacbaccdbcaddabcdcaaacdddbccabbbdbbcdaabbccacddcadbcddbbddaaaaabcdabacbcabcbbdaadbcbbdadcacabaaacddaaadcadbcddddbddbabdaaabccbbbcabcddcacadababdbacddababdacbbaccabccaacbbbdbcabbdaccdaccdaddabdbaddaddbdacbaccddcaccacacdaacaadddddabcbdcacbdaabcacaabbacadadbbbacadbccdadcddcabdaaaadcdccadbaaabaccbacbcabbbbbbcbdadccdcadcbabbcabdcdcdddcdbdbbbabacbdaddcdbbabacdaddbacbbcbaadaacadbabbabaccdabbadcabaadbbdbccbccacababbbcdacdcbaacadbdbbcbcdbabbbccbabdbacabbcdccccddcdaddccdcddccbdcbdcbcdbbcabadacdcbbdbacdbddaddccacdbadddccbdadddadabdcaadaacdbcdcaabacbdabbdcabbcbdcbacdbdbdbaaaaddddcbdcbdcccccbbdcaadcbbaaacccdcdbdcddccdcdabdabdbdadccdccadcdcbbaddbbcccabadccacadaadcacaccdabdcdbdbcdadaacdcabcdccdcdbcbccbccdcbccddcddbbacdacdbdccddabbbdbbcddcbdcbdbabccbbbadcbddcbbccadadadcabaaabbddccbaabbbadbcdabcbbacddacdadddaaacbacaabaacabadbbcbdabbdcbdbacaabaadcbbcbdabdddbaacbaacddaaccccaabdddaadabacdddccacbcbbccabacabddcdbdbabbdcbcaadccacdaccdadaabbbcaabdababadbdaadabcadcdaccccbcdddcbbdcadcaaacbdabbddbabcdabacbcbbcaaaaddcdbcdcbadddcaadadcdddddbacbbdccacdacbbbdcabbdbbccdbccabbdaadaddbdaaaccdddcabcaacadaacbbdbbdaadcddbcccccdcbcdcaacdccacccabacaaacbbddcddddcbdabcdaccbabccbdabaadddbaabdbcabaacbbabcacdabaccdbcbcdddabcaadddcbdcbccaddcadcbbbccacadacbcdaaccdabbdbbdaddcdbdccaadbbdcdcdbcbacaacddcaccbacabcaccbbabcababadacdccaacaaaccdbadcbcdddaadbcbdddbdababddacbadbbdadccdddbddddcbccadddbddcdabddbdaadadbaadaddcdcbbcdddadbadacccccdcbbaaabbcaadcccddcbcdcddbbcaddcbddabcdbcdabdddcccdddabdcdabcdabbcaadbbadbcadaccbddbaadcabdccbdcbcbacddaccccacabddadabbadbcbacacaadcbccbcdadcbcbdcddacacdddbaacdcbbdaacabcadabbdaddadbdbcbbacbccdcdccdbbbbdabdadcabccddabdccbddcbbaacadaccabbbdbcbcabbcbaaabaabdcbdbdcdacbabbbddaacbacaabacabadacdaaaccbbbccdabbaacddaacaddccddbadddacabadbaaaacaaddcddcbdabcccddabadcbdadccdcccdacadcccbdccabdbaabbdcdcdababcacdaabbabaccbbbabbcbcccadcdbbacabdbdcbcdcaadddcaacaabbbcabcdbcccabbccadcdbbacabbbdabccbacddacaadaadbddbcdcabadabbcbbcbbadbdccccbcdcbdaabbdccbbcbbddbdbacdcbddaabcacaddbaaabbadcccccacabbccbbababacacdbbadbacbbabbbdcbbccdacdbdcadccdacbaadbaaaabdddbdcddababbdaadbccbaaddabbcdcdccdacdcaacabdbdbdbdbddababccdbacaadbdbddcddcabbabaabbbbdacaadcdcddababbbbccaaabdbbabcbadaaabdcddaaaddbdccbbadaaabbcbadaacbccccadaacddacbacdcccdddbcbadbabbdacbdbcdaddcabbcbcccaaaadaccaadbddcdcbbdbdcddcaaadaaabbccdbcaabcccbdbacbabddbbcbbaccbdaaadbddcbbdaacbbabbdaadcccaabaabcccbacbcccbacbdcddadacacccaaaccabdadbcccddacbbabdaccddabddbdbccddadadcbacdcbbbdddcbbbaddadabacdabbbccdcbdabbadadcabdbdcbbacadcdcdbbabddaabccbaabbbbccbcdbcaabacbbabadbcddcbbadacdcdccddadabdaccdabccdabababadbbbadbbdccacbbaaaabbacdabcbbccabbcacabcbdddbbbbabacdaacdddcdbaabbbdcccbdbadadcdbdabbbddacdcdcdcdabaabddcdbacccbbbdbcbabbcaaadbabbcddadbcbdbabaacbbadaccaabdbcbabbacccdbbcdabcbbcdaabdabdbbadbacbddcdbaaacdcccdcbdacdbdcbcacbbcdaaadcadaadbbccabbcbbdcbabcadccbaabddcdadccaadbaddbdcbbdcbbcddcdbcadbbcbdcadbddbcccacaadcdbcbddbbbcbdbaccbacddcdbcdcccbcddcadbbbaacaacacbbccdddccabbcadbbddddccbbbabdddcaccdacdacbcbadbadbdbdcdadcaacaabbcbdcdbadbbdaabbdacbaccdaabadcbcddaddbccbbbaadbaadabdbdbccdcbcbbdaadabbaacbcabbbdbbccccbcddaddcdcbabcbbadabbcbcadaddbdbbcbdbcbcdaaaaccdaacccadadcddcccbacbcdddbdadcdbbdbddcbdcbcbbabbbcaabccaadddbccbcddacbbcaadcdabdcbcdbdcbdababddbdddbcdadcabcaabcccadcbcbbbdbbcbbcbadcbdabcdaddcabbdccacadadbcbcccdbccbddbcacaddaaddacaaaacbcaddccbddbcbcdddbddcccacbacbddbabddcddacdbbdbdbcadbdccadcadadbadadabacccaaccdabccabcdbcabaadccbcbbaacacadccccccbbdaccacabdbbadcbcabcaacbcdbbbcbddbbccabaadcdadacbbbabcccadddaabadadbdcbacadbdcbadaacdacababcdbbadcadabcaccbcbcbcdbdbbdacadacbdcdaddbdadcdaabdaacbbaabdaacbacdadcbacbbbcdcdcdbdaadcadadddcababdaddcbababbccdbdacdbdddcaacdddbbccbdcbbadcabadbcbbbddbccdcccddccacbabddcdcaaacadbacccacbabaadbdbccdcdacbadcadaabacabcbadabcddccbadadcaaabbcdabaabadabddbaaaddddbcdbacbcabdddcadabddddccbcbbcadcabcddcaccdabbdddcdbaaaadacbcadadabcccdabbbcbabbbcdabdddcbdddcbabbacddcbbbbaaaacbbbdadbabacaabdbaadddcaccdacbbdbdbcacdabbdaaadcadabbcccaaddccabacbbaccccadcbdcccdcaababdcbaaddaadbcacccddcbcbbbadcdaabcbbbdbacdcbbddaddbaabdbdcacadcbabbccdbcaddbaddadcdcbccaaacdcbbbbabbcdbaadbcbdbbbbadbbdaabaabcbbdcabcbcbabddacbaadabcadbbddddaaacbdadbcdcbaabccabaddbcaababddaddccacbaabbcbacddddadaaaaccbaaddbbddccccadaaaadadbdacadbccdababdaacadacadbabbcdcbbddadbbaddadbddbccbccdadbbccbcadccdcaacccdbadababbcdccdbaacbaaccccbbabccabccdcdbcddccacabcbdaaabadcaaccdaaacbdccccbbcbdcbbdabbbadcdaabddbdadbbbabacbddcbbdbcdccbccbbaaadcdbadacaaccabdaacadddadbbbcaddbcaadcdadcabacbdddabcbacddbdbcdbbdacdddbbaacdcbbaaacbddbdbcdaaadbccbdccdcbccdbdcdddbdcdaaaccacdbcbcbcbaccdabababccbabaadaddabaddcbacdddaccbbbabadbddbaabacbbddccdabddcaddaacaccbdcdbbcbdcdbcdcaabbdbccacbabcdcadbddbddaacbcababddaddbaabcaddccdcabbdbabaddabbdaacacdbcabdbcdbbcccbdcbcbaddababdddcbabccdbabbdbdabbbbdbdbadbbbbddbcccccdaaabbdcddabaadacacbaddcaddbcabbadadcdddbcbaddaaccdbacbbadaacbdbcbcddcabbbbbcaccacaabdcadccacdbaabdcbbdbbabbbaadabadabdbbaaaadccabaccaaadadcdbcccacccbdcabbabadcbdbaccbdacadcaccabccddbaccadbacdcacbadbcbbdcbbdabdaaccdcaddcacbcbbcaabdcaccaacddccaaabdaccdcadbcabdabacdcaacaaaacaaddaadbcbdbcbdaaaabdbcabcaabbddbdaaabbcbadcbbdaccabaabadabcddbbadbbbbdcbbccacaadbcdaabaadddbbbddbaacccaccdccabadaabdcbbbdcbccddcdcabbbacacddcabadcdbadbcbdaaddddcddbadddbcaccdccdacdcdaccadbdcdbbdcdacadcbddcaacadbbbdcdddcbddcdddcdbcbbdbabccabbdbaddbcdabbcbbdabdbdbdbcccdabaaccbcbbabaaacbbccbabdaaabacaacdadbcdddcbccabacbcddabbaadaaddcbdbdacadacdbcbcbbbcaabacdadbccaadcabddddccddddcdabdaabbddcddcabadbadddaaadadabdcdbbaccdbdaabbbbaabcdcabbcdccbccdbbdaabdcaadbacacdcdbddbbdbbbacbcddbbcddcaccdbbdacbadcccbbabdbcbccaaadcadbbdacdcbdcdaabbbdcbcbbbcacdddbbbaddcbbbdcbddacdbadababcccdbddaabaddbabdcaabdaccaaccdbaaadbbaaddddaacabbbccdbcbcadcdadcaabdcdbabbdbdbbddadcdcbcdbbaabcbbacbdabccaaaaaddaadcdcacccbdaabaccabadcbcaccbbbbabaaccdcdccabcacbbbddbdabbacdacddddbcabcdbadcbabbbacadbbcaccdadacbbcdadacddaaaadbcabbdacdaccdcbbbacbbdadbadaabcacabbababcbbbcbbbdbabcbcbaabcdbcaadabdcdcacbbabdcbdaaccdaacaacccaaccabdaddcbddabdcbbcabbcdcbccddabdaccbdbbdadcbcbdaacdbcdaaacbdaaacaacaddccbccabaadcdccbdcbaabacbcdbacdbddacdaabbaabbaddddcdaaadcaddcdbbababbabbaabababadcdbbcdabdccdbbacddccccbcdcacdcddbbdadacbbbdcdcdcaddcbbabdacabcdccaabbababbdadacbcacbbdadbbadcdcddccddbdccdbcadadcaddacaddacddbccabcbbbdcbdcbdaddcadbaddddcacccddcadacbdbdaacabdbcdadbbcbcbaccabdccccadbdaacabbbacbbdbaabacdcadbbbadccbbcacdcdddabbbbbcacbcdadddbdbddbbdaaacdcdaadabdccddddbabaadcaaaabdbaaabbcbcdbadcccdbcddaacdaacdccbbcdbbdbaaccccabcbcdabbadadccbdcdaaacdbcddcdcdccdcdcbabcdbdbaaaddbbdbbbcdbabccbbdcdcdcccdaccdaddbbcbbdcbddbcbcabbddacddaaadddbaadadcadcdbbcbabdaccddadcdabbababacdcaacdcaccbbaddaaacbdbbddaccaddbcbdaabcbbbcddcadcbccbdcbbabbbacddccacaaaaacdaaaddcccdcabcbbbccdccaacaadcaadccacdcabcbbcbddbcdacaaabbdbdbcaaadbcabaddcabcbaaccbdbbdcbccdbbacbcacdabbdbadbbbabcdcbccbcdcaabbbcccacbdbadcdabdcdcbadacaacbaddcccbacccbcadcabbadaabadbaccbbcddabbbbdbbbabadaabbaabcbbbbaaabdcbddccdadccbcaccdcbcbacdaddbcbdcbabbacddcddccbadbacbbabbdaddbaacacabdbcaaddadabcadaadbbddcaccacbabaabddbaacbabbaadacbdadcccbcdbabadbdabcbdabdcadadaaadcaccaccacdadbdaaaaccbaddcaaadbaadcacbcaadcdaccbbcdbbbccdcbdcddacddbbdbbbcadcdadccccdcbdddabdbcbdabacacabbdcabcbcaacbbcbccbdabcbdbcbdcaccbaadbccabcccdbadcaadabcbbcdbddddcccaaabcbdaadabbabddacacdbbbadabbaabacbddcabddcdcaaccdbccdcbbddbbccbbdbabdaccccaccbadcdacbbabaabdbabcbbadcaacdcdacbbacbabcdccddadbdbcacdabdbdcccdddccacaacdcacaaccdcdabbddbccbcacbbddcacbacadbaccabbdbdbddacbabbdccbddbccbcddcdbdababbcadbdccddbcaaccbadabdbbbaabbcbabbdbbbdaadabbddcaccdadbdacaccbcbbbabbdbbaaacdddbddbabdacdddbddccdcacbcbcbcbadbdacbdabcdcdacdbdacccabcbacddbadbcdcaadcbdddcdcacdbabcbadaaaaabddccaacdbbaacbbcdadbacacdcadbbcbcccabddbcdaadcacdaddbbaadababbcbcddbaddbadcbaabddbdbaaaadcdbbbdcccccaabaacdcdbcbaaaccbcbbdacaadacbabcabbddacbdbdbbcbbaabddaaacbcaaaaaadbbbacdbaccbcbccabcbddabcbadcdbbacbdcdacbabdcabbadbcccddabbdaadadadbcaabdcadcdadabcddddaddabdabcccacbdabbddadcbdcdcdacacdcbccadbbaabbcdbcbaacbbdcccaddaadbdbbadddaacabccdaccaccbdbcccdacccdaadbdcdbadadacdabbdcabccdcdddcbdadbbbadbcaacbaccccbdbacbadccadabacbcddbccbbddcacccaaddcacbbbadbbccccabaaadabaddacbdaaabbaabddcadaabdcbdcabddaccdbcccccababccadcbdadbdbdcabbdbbbbacbcdabdaadddccadabbccbaaacccaabaabcadacdbcbbadcbbcbbbccddccababaabbbaccdabacabbbaabdbaadcbbcbbbccbaccdccabdccadbcacbdbddbbbbbcacdccbddbcaaccdbcdbbabbbcdabcacdcbcbbdaddddabbdccaccdacbdbabdbdcccabaabcacaacdbbbbadcaacbccabccaccbacbaabbbbdcccadadabaddbcccdcacaaaabbdcbbdadddabadbaccbabbcbdacbddbdbbdabcadbaaacabdabbbdaaabcddbabcdbcabadbdbddcaadbaddbcacbdacdddddabbdaacabdbabaabadcacbadcaddccaccdcacadccbdaabacdcdcdbbbbaaadaddbddbabaccddbdadbadccbbacbbdaaabdbdccddacacccbccbbdcdaabcdbadadbaddbcdcdbcccaccbcacbbdbbcdbaacdcccadcabcadbbcaaaacccaaccabbbaabadcabdcbdcbcacbaaaccdaaddadaddbbdbaabbcacbacddcbdabcabdbacaabbcbcabbacbddadbcccddbcdccadddbccabdddbadaddbdacdbbbdbddaccababdbbbccbddcaaadcacaadccddcbccbdbdccabccabddadaabddababaabdacbdcbbddcbaaacbbcdcbadabbadddcdcdbbabcbbdbbaccbdabdbadabdcbaabbbadcadbacbcddcaccaabacadcaaddcbabdcdabcababbdcbbcbabccccccbbcbdcbcddaaddcbacccdbbcbddbdccbbcacdacbbbabacabacadabdadbddbbbcbdcdabdbdcbccbccbaaaadddcdaacaddcddcdabdcbcbcdbcddcddbcccdbdaadbbdcbaaddbadccaababbccaaccdaacbdcbabdcdbdcbccabcadcdddcddacbadbaccadcabbadbdadacaaddbaacbcddbcdddbaadddccbccddacadbcaabdcaabbdcdbadbbbbdaaabcbcdbdbacbdbadbcbbbccdabddabdccdcadbbbacdcaaaaabadcabbbdabadbaabcadbddbcdcbddcabcbdbccadaaadaadbacbddcadcbccbcdddcacabadbbdbbadccadadadadaabaadddabbaacbdabcdbadcaacbcdacadadacdadbbcdddbcddacbcddbcbcbcbbabadbcbacacacdacccdbddbbdbacdbccdddbcdcbdacacadcaabcbdabbaddacdccacbcccabcbacbbbdddabacbdaaddcdbcabcacaabdabbdaaacbacccdbabcdbbcddcbccacddaddadcbcadabbbaabbbccccabccabdacdadbdbcdbccddccdaabcddaccdcccdbbadcddbadbadabbcbbcadcdcccacbaacccaccbdccbbdbadddcaabccacdbcbbcabbaaddcdacbbcabcabbacbaabcaadccbbcdbabacacdbaaacbdbcabbaabdcaabbdaacaccabacacddacbddccbbbdcbddadccbcabadcaddabadbbadaaaabbbddcccccbcdddcabacbbbcaaddacadbabbdacbbadcdacaddcdddcdabddaabddcbabcbacddacacbcdccadacdaacccccdcbcbdcbbddaaddabbdbdcadcdcbbdbadccaadddddcbbababddbbddcaacaccaacacbdabacbbbcacccdaabdbcbcdaabcabadcacbdbcaddbdbabcaacccaacbdbdcbabaadaccadabbbccccbdacdbbdbcbcaadcddcddbabadaadadaccabcbbbdbbbcdbaaaddbaccdbabdbcabcbbbbcccbaaadbdcbccbdcaddbabcdbdcadcacababddabdadccdcdacbbcdbdbcaabdabacacacabddaccdaabdcdcbacdddaccdcbbdabbbddcddddababbbbcdcabadbaccacbbbcbddcbdcaadabdaaacdbabbcddccbcdcdaaadcbdccadbadcdaacdaddaaaaaccbcaccdcbbadbbbdccdabaabadaadbdaadaabbbcbcbcbdccacdbabaaaaabdcbdbdacccbbccbbcbbccccacacaddbaabdacbcbccdbdddbbadbcbcabdddadacabbacddbbcacbcccacdccbcdaaaabdbdddcaaccbbcaaadccaaacccdbcccbbaccccdaddaaadcadaadbdbbcbbbcbbcbdadbbdadacdbbcadcdbdbaddacddbacabddcbaddbcadcabbdacaabdacbddadadbcaabbbccadcbccdcbccadcdbaadccbcdbccbabacddaaabacbdcbccabbabdbddcaabbcacaccbddbdacdbccccaaddbcccdaadbcadacdcddbabbadbdaaabcccadacabbbcbabbaccbcdcaabdacabcaccbcdbbbbddbbccbbaadbbbdaaaccbcddaacabdabccbbadacddddaabcbdadacbdbccaacaabacbbdaddacdbcbaacddbdddbbdcddbbacaabbbcbdababcabccccdacbbddcadbbacbdacabaccaddbdbcabbaaccacadabbbcadaabdaaacdacacacbbabbaadbaacaddcddbdabdbaaabbddcbdaaccbdaacacadadcadbcddddabababcdccacbdbbdbdbddbbdcacbbbbadddaaccabbcdabbccacaaabbddaaccaddadddadabcdcbcddabcdddbdabadadbcacbdbdbdbbadaccdbbddbcdaacbdbdcdacacdcddbcdbbdadbabbccdbdcdbadaccdbabcbbcbbdcbbddcdbccabdccbbccccbaadaabbbdcbbdcadaababbbddbcaadbbddccdbaaacdbcbddcbbdbbadcccbababadcaaadbadcadddcbaabaaadddcadaccadccbdbabbabaccdbaaacdcacabdcdddbdbbdaccbadbbabcaabdcbabaccabdaddcddbaabbaabbbbddccdaacdcabadabcaabcaddbabcaacccccdcbdbbdbdccaccaacacdacaabbacbdcbbcbabbddcaadddcbdddbbcdabadbbabdabddcbdddacdcbaaaaaaabcabcbcaabccadcbbbcabbdaaaaaadcddccbaacdcacbcccbccbcacccbacdcbaadabbddbcdbacbccbbaddabbbcaaacdabcabbbcbcdabbaaacadbbacaaaaccaacadbabacabacacaabaabbbbaaadacbcbcccbcbaadbabaacbcdbdaccbdcabbdadcbdacaacdbcdcddacdbbadddbbadddacadcccbacaabbacbbaababacbdbdabadaabcdccbdcabcdcbcacbacdccdccabbbaadbacdadccdbbacabadcbdbbcadbbaadbddbcbcddccccaacaacaadbbcadabdcadaddccdddcbcabccabcababbccbcddbadbdbacddbaddcdbaccddabcbbbbbbdaabddbdacbcccabaddabcdbaccccbacababaaabbacaaadbdbabaaddabdbbadcdbdcbdadaaddaadaaabbccbaacaaaadbacdaabacdaddddaadcbdbcccbacbdddbbcdbabadcbbdcaaabcbaaadcdcbaccdaddcbcadcaacadbadcadadacabcbabdabcbbabddabddddcabdbcbadaaaacabdddcaaadbbcdddddabdbbbddacbdacdacdbabbbddaaacdbbacdbbdddaaaabaddaacbabdaadccdbdcabacdaccaabaccdbbdccaaaadddbcabcbaabcadbadacbabcaaacabaaadaccbabacbccdbcddaccabcadacdcbdcdcbaccdddddaabccadacdabdddacbcbdaabbbacddcbdaaccaddacaccdcadbccdabbdabddcdbbbdccacbaaabaabddabbbdbdadaabdcdbdbbbabbbcdccbadacacbbdabcdbacabcdbccdcbcdabbcdacabddbbcadadcbccdbaabdaddbadddabccddadaccbbdbcdcccbbdacbbbbaaabddbcaccbabcaaaadbcaaddcdadbbdabbcddbacacddbbbcdadabddbabdadabcdbbdbacbdbccbdccbcdccbdaacabacaaacaccaabababbccaacbcdcabbdabcadcbdaaccabdddcccdccddcccbcddbabcbdacbabcabbaaabddbaaaabbacbbcaadccdaabacdbddbaacbaadbbcabcacdabcaacbbacbdacaddcbbcaddadcacabdbdacdcaaccccabadbddcadcadadcadbaddcabcbbbbcbcdcaddddbabadbdadcacbdbabcaddcdcbdbcaabacacdcdaccaadbaddddadbcdbcbdbcabbdccccdaddcadabbadaddabababcdcbbdadbbacccadcdbbcccdaacadddabddbdccbbcbcddbaacddcdbdabbbacaddbbbdcbcdcddaddabbccabbccdabdaadbabadaacaccaacaadadcdabbaddbdbdbcbaaddababaadcdcaacbaaccaabbdddbdacbbcccdabdccaaaadddbccccbbdcabacbbdacccaadaaadddaddccbcbacbabbbaadbcdabbdbccddccadcdcacaccddbbcbacdbbdbdbbabddbdcacacddbdcbdbcbdcabdcaccaccbaccadcddbccadcbaccaacccadcaacadcbcaabbacadbbdbcbdadddbcdacdadabaabdabdcbccaaababdbcabdbdbaabddccbaaaacbdcddabdcccadccdbcbdcdbbdcaddabddaaabbbccaaaabcadaaadbcaccbaabcaaacadaabcbacaadbbaaccdbcabbcdcccdcbcbbccadababdabddbbbbabcaabadbbacbdbbdaddbadacbdbcccddbbbccadcaabbccaabacccadcbadacdaaacccdcddaaddaddddccddbadbbdcbdcabdcdadabcababbcccbdbbadcbcbbbcbabbcdccbbbaccdcdcaaaacdcddabcabcadbadbdaaacdbbadbdcabcbabddacbaddabcbbdcdcdacbdbacccacdbdacaccdddbadddacbacacbbcdaaabbbdbabcccdcdabcdaaabbbabaddadbaadcddbbbbbbaacbddacaabacddadbcacaaccdbcbbdacccddbcacbdcdccaaccaacbdcaddbdbdbbaccbadabcacadbddaacddacaacacbcacccbbcbbacbdbaadbbababbccbbcdacbdacacbbdaadbdaabdbbbcddbaaadccdcccadccbddadbcacdcacdbccadabcbbdaacdcadcbcabbcbbbccbacabadbcabacccbdbdddbbcabbccdbddadcbbcbbbadbbdcdbcdbbdbddadbaaacdadbbccabaadabddbaddbdaacdbaddcbadbbadaabdaacaaaddadbaacdacbbbbadccbbdcbdaadddcadcabdcacddaccacbdcacbdcbbaaddcdacaacddbaadadccddcdbccccabcacbabdcdcddcaadcccadbccccaaaababcacbabcbaddcddaabbdaaccccadacddbcdcbbdccccddccdadbadacccabdacddadddadacbaccbacdcddddbabacccdadccbacbacadbbddcacbdcccdabcaadcbcbadcdacabdcabbcccabddbdacbdaacaccdcababddcababdbadabcaabbdaadcbccaddcdcaaacdadbbcbcbacdadbbbbabaddccddbaabacdabdcdcaaabdbbbbaadbaaddacabddbccdcccaacbcddacbcbdddbcdddaaddccabbcadcbdccbcaababdccbadadcddcadcbadaaaaabdadbcdcdadbcdbcabcabcacacdbdaababccccdcbadbaccdddaaacdcbbbcdcbbadcbdbabcdaabdaddccaabddcadaccbdbcbabdcaabcdbabdadbddaccddaacbaddcdccaacddcaacbdcabbabbaacbdacdbcbaabdcabbbdcdaadcbcacabaacccbbccadbcbaabaddabdbccdcaddbdadccccacbaccdbdabbbadbadbdabdbdacadaccbbddacacabdabddbadcddbadcadaabadbcdcccbcbdaabccbdddccdbadbdabdabdddcabbadccdaaddbaadbbabaddabbcabcbbbacdddabdcbbbdddacccdcdcdbcaabbcacdcbccadccbbbbdbacacccaababbdbaddaacddbbcaddbbcdcbaccbdddcabddcccdacdcbddbadddbcabdadccdbdbcdcabddccbbdcbcdddaabcdaabacdaaacdbccaabcdbaabbbbbaacdcaddabdadccdcddddbbdbcbbdbddccbdacdcbabbbaaddaaddaaabddccbdccdbdcbaccabbbbdaacbaaacbbaaabdbdbabadcbbccacaacdbbccaabadbbdcacbaabcdcacbdaaadbcbadaaabcbcadbccbacabcacadbabaacbbaddacdcdadacacabbcacddbcbaddbcdaabbcccbabcacbdaccbdbcbadaababddaabddccadcbbbadabaaabaaccdcbadcccabbacbbbcacbabcadbdbcbcacdcadbbccabdddcdcdabcaacccbabccbbbcabbaaaadacadddbccdcbccaddbcadbddcadaccdacdbccddaccdccacbacdbbadddbcaacdccdcdcbbbcddcaaccaddcddbdcbccdaaadacacbdccdbcaabbccbcbdcccdddcdcddcbadcbcacadbcccacbaabcccaccdcccadbcbdadcbdbcdccabcddacdcbbaaddbcbaccccbabbbadabaadaacadcdcbacbbaddddcdcbbdbccadadaabbadcaccdaccaddaaadabaaacadcdcbbdababaadabaacddcadbbbbaadbdbcaddaccdcdababcdcaabadacbdcbadcbddbbaaaadabbccbacdcacdbadabccdcddbabdbccdddbdddadadddacbbabbaabaccdaabcaacdcccdcbbdbcbadbadbddcbbbbdbccbccddaadadcaccbccdbbdaacacccdacdbccacbcabdadaccbdddadcbcaddaabcdaadbadcdbbccbadbadabdadcadabcddbacabcbbbacdaacaccadddcacccaabcbcdbddbbadaccabcdccaaacacdccadbcbacaadbddcaaacabddaabbadaaccddbcaacdcbaadddcbccdaacbddcacadcbcdcaadabbadadadccbadbbaaacbbcdccbdddaddbdccbccdababadcdbcddadccbadabaddddcabcbddbacbadcacbdcbbcdcdcabdcadcbcbcccaaabddcabdcaddcbbdcbbdddccbccbbcdcbdcacddacbbddbcdbddcadccbabdcbaccdadbacadaaacaaadccacbdbdccbcbdbdbcccbbadbbaabcaabbcdcbcacbddaccdbabaabdcdaacbcddaadcaddadabcacccdbadabccadbbbdcbbcbbaacbcdddccaabbcccdcbdcbdccbacbbdbabcacbbdbccbbcababaacccdccbccaacbbadbaabccbdbcbacdcdbaabbcbcddcbaadbbcdcbaabadadcdbbcbbcbcccdcababccdcdddaabadbbbbcdabbdcabacdcabbdaddabbdcbacdddaccbaabbccdadbdaacccdabccaacbbaacadabdcadcadbabdddddabdbabdbcaacdcdcdadcaaabbdaadcbcbdadbcccdabdbbccbbbacdcddddccadcabcbbbccbdcbcddbbdbddcdcabcaacadbdaacabcabddbaddcddcdcbadabbddbccdcbcbacdcdbabbaabdbaadccadababacbacdadcdbaabcbbdbabcabbadcabcaacddbdbcdcabbadbcaabadbcddbbcccdbcbadbcacccdbcaaddcaacbbbcadbdbabdaadabacdcdcacdbaacadadbccbacbcddbdcadcabdccacbaccbdabdbabcbacdabbdbcddaccbbddadabcabacccdbdcadcbddbbcbdddbdddacdbbaccbbccddaadcddddbaccbaaabdcacdbaababdbcadbcbababcaabbabaacbbadddbdbddcbcdabdabdcdbbacdbbadaccadcbbbdddcdccdbccbbdddbadabacddaaacbbdcdaacbadbdcbccacbdbbcccaaaaadbaacbaabaddadddccbcdbbbaaccdbcdaabbaddabcbcbcbcbdabcaabadccadcbbadabbadcaccbcdbbaababdcbdcacdccddabcaccbdbcdacdbcbbaadbdccacaaacabbbbdbbdddaddcacbadabaadaddcacadccadbbcdbccdbcdbcaccdaccbaaacacbcccccdcdcdbcaadbccacaddcaabdadddbccadbdbadcbddbddbcabddccaccbadddbcdadaccdaccdcadacaabdbddddabbcccbbabcbdcbcddbbdaacccabaddabdacbbadccbcbbdcaadcbcaacddbdbbabcdbddcdacadacbdacdbbbdccbdaddddbcaabddcaccdcaadbbadcbdbadabcabbbbadacdbbbadbabcdabaaaabacaaccbbbbabcdabcccdbdadbadcabcdcdbdbdbabbcddaccabbcadacdacabadccacbacacbdaccdcdaacddcbbabacdaddcbbcbcddbabccaaabdbadbcadacbdcbdbbdbbbbdaddadaddbbcbcccaadcbdbbcbbbddaadbaaccaadadaabddbdcbcabbbabcdacaddadabbbbdccddbaddccbbdbaabdcdcbcdccacacaabacbccadabacadcbcbabccabbbdbddabcbcccaadabbaaadbaccbcaabdbbcaddaacccabcdbcccdccdbddcabdaacdbcdcdaabddadbdaadddbdbcbbabbbbccdccbdbbaaaabaadbcadbbbbbcdbbcbdaddbadbaabbadbddcddccbabcacabdcdbcdacbdacddcdadcbcddcaaddbbdcacdcaccdcbcdccdabacdbbadaaddddccbddaaddcaabdcdbbccabdababbccaddcbaaabbacbcacbcbbadaabbddcaccadcdabaaaadacdbdbdbddbddbabddacaadcddbbbbbbcbbccdbbdddccbdbbbaabcbcbdddbcbcbbdccbaaaacabaddccbcabbddcbcdccddccdcbccccadcbdcdbcbcaacadcdaccccdddacdbcaccbacaacccccdcdabbbaadbcabccbadccddcaadcbbcbcdcbdbdcbdcdccaaacbbbdbdddddbcdabcaccdaadbaccbabbdbbbdaadaaabdbbcbdcbcccacabbdcacdbcaddcdcdbdbaacbbccdcbbbbbaaccdcdbacdcabcddbcbdbcdbcbcadadabcaacddaabaacaaccbbcdacbccbdbddddaabcddbdbaaabcaadbcadadbcbcddbddccccbddcadcadbaaabbbbdbabcdacddcbbbcaabadcccaaabaabbbbbaabbdabccababbdcbcbaddbddcbcdacabbcbcbabdbaacadabdcddbcddbcddbdcaaadddbacbbcbbdcbbccbacdccaaccdbcdcbbddbdbddbcdbaaacacddabacbacbbcaddcbddbaddbaaabdccaacbbbbadacddbbcadcddbadacaacababbcdcabcaccbdddcbcbdabcaacbcdccbaaccaabccbaaadacbabaccccaddbcbbcbddbcdbcbcaacbbcdbbabdbacabdcccaabbcacdaccaaccadcdcbbadcbadbcaddbadbbbacaddadcbaddbdccbbcccbcbbdaaddaaaacbcacdaccdcbbbdaabaddadbaaaaabbbdabadbbbcdccbcdbbcabcaaadaccbadbdcacdbaabcdacbdaabaabcdddacbdbcddcbaabbcababbdbabcbbcdabdbaadacbbcbbbdddbcadbbdadbddbdbcbaaccdcaccdaccacdbbcaacbcdabdaadaaddbdcccdbadadddacbbbbaaabaacddaaabbacabcbaccacdacdcacadacdcabbaddadcdadabacbaaabcbbbaabbdcddacbbdbaddbbdbbbcdaadbdbbdbbdbbadccaaadabdbacddaadbcaadcbacbadcabccdcababdccacccbabaadbdbbacaaacbdacbccbabcbddabbbdbdcdbadddabcbccbdaaddaabaabcaccbccccbbacccdcdcdcadbcaabbabbdcabbcdadcabaadbadbdadaacdddcddaadcddcbcabcacccabcbcbccbabacabbaacbacbdadbdcdbdccbddbccdccccdacdbcadcccdbcbdddcbdddbdaabbcadddccacdddbdbbbcabcdddcdcaaccbcdbbddcbbadbcdaabdbabddaacbabccbdbdbccddabcadaaaccbbacbbbbacaabbbdccbbbbcaacabaccdbcddbaccbdccaaadaacadaaaaccbdaccdbdcdbadccdadcaababbcabdccdbbbcbccdccdabacdbbdddcdbacddabbcbbdbcccbcdccdabdddbbaaddaadbaabbbbdbbbbddabaadccbccbcdccbacdabacabccbcacacdcabbdbacdadcddaacaadccdadbabacabdccbbacdabdaccbbbabacddabdaabbbadcacdcccbcdbcacdacbddcabadcdbdcbddaaabddacadbbabccacbccbdcababaaaddddbdacaaacddcbcddbcacadccbdbadaabbcdbbbdcddbdccbcbdddbbaddccdababbabdcbcbbdababcabdbbadcbadcbcccaaadaadabacddcacdbcbcadcabbaddccdbbbbbcbbddcaddbdbbcbbcacdcadbcbcdddbacdaaaabddaabbbddbaadadcabaccadbbabcddbddabcacbdadcbcbcddbaacdbccacacbbadcbaadcddbabaaccdbccbbaddaaaaabdccccacbaccddccbdddacbcdaddbddaccdcacbbabaaccabacccddbdaaaccdbcbaabdbdaabbbcdbccabdbabcddaadabaacccdadadcbdbdbadabbcdbcaccbdaaaacddaccabbbdbaddccabdbcdbbbbbcbababcdbcaabadbdcbaddcdbbcdbacdbcbcdbbaaadddbdcadaddaabdddcabadadccbcdaddbbabbcdababddacbdcccadcbdbadbbabddbbdccbbdddbbdbaacbcbccbdabbaacadbbddccbaddccdbbddbccaddbaccbdaddbcdacbbccdcadbcaaacdcbbaadbabdcacaacaaadddadbcbadabdaadbcbddbbbbbabbbbcddbadaababaaddcbbddcadcdcddaacbcaaacccaddcdcaabadacbadbbddbdaabcadcdabacbadbacdbbcbcdcbcccbcdcbbdaaaaddcbccabdcccdddbbdaaaccaabcadbbddbbcdbdbbbbaaaccaaabdbbbbdcbdbcbccbccacaacababbacdaaabccdacdbbaacaacbcbbbcbbabaadbabdbbcaddacaddbdbbddacbacbadbcaadacccadcbdddcacdbdbaddcbdcdaadccbcddaccdbdabbacddddaabbccabcaaccbbdbcbcbaaaadccaaccababbbaccabcbacccacdbdadcccabababcabbccaacaaacbbacabcbcddaacadbdaaacadcadabdbccadaddcbbdaccdacccdccdabcdccaabcbdabbdadcbbabccbcdddcabcbbadcbbdbbbcbccdbbcdabcdcaabccabcadddcdbbccdbcbbdadbccbbdbbcbaccccabaadccacaacbcbbddbdbbbcacdccbcabccbabdaacbaadcdaddbabbbabcccaadbcacbcaccddbcddabaccdbabadaabbbaccacaddddacbbacbbbbbabbdccbdaccacaccdddbddbbabbbbbaaccddccbbdbdbcbcdabcdcbaddbbdaccccbbabadbdacdbbccbbdcaddbdbcdcbcaccaaddcadaddccdbccbdadacccdcbcbdcdcaaddcbaccadcaadbdbaaadbadcddbbabbbcdbcccbbbadabacddbacbabbabadaaadddcdcdbddbdcdabbbdbaaadbbbbddbadbadccbbcaabbbdbdcacacbddddabdadbbdadacabcadabcaacddcbcbdbccccacaaaabcaddabbadacababcaabdcaadcacacdaacabadcdaabadacccacbcbdacdadcbdbabcddbabacccaccbdbbacdbbaadccbbcacabcbbbcacccdaadcbaaabbbbabccabcbbdaabdbcabbabccadcbadcddbcccbdabcbacddbcbbdbaaabacddaabdcacdccddcaccccdcdcbacbaddaadabbdaddacbaaddaaabaaaacdadbabcdcbdddbdaadbdbaccccdcaabdabcaadcaccccaddccddcccddabdcdcaadcbabddaccabbdcbbcaaabaddcdcbcaacabdacabaccbdaddcbbacdbcdadaccaddbbdacbaaadabbaacaccbbacaddbcbacdabbdaadddbbaadaaabdcbdccaabacabdbcddaddcddcacadadaddbbdacdcdddccbccdcdabcdaabdaaaccbdbbddcbcbbaccbddaddabbddbaabcdccaaaacbdccbacaaabdccbcabbddcccddbbbccaadbdbadaabddaaabacbccdadbacbdabaddaddcdacbaadbabdbaccadaaaabaabbbdcacccabcdaabbbcadbdbddcabddccccaddacbabdbacaaacccabcccaadcdbdadbaaddcdaaadaaacbdbbaaacbdcacbccaacddddaddbccdabdabbbbacccdbcdddddaaadcabccaacccdabbbcddddbbcccbcadbdcddbbdbcabbcdbbaddbabdcdddaabacacdacbdbbacaccadcccccbbabdbcaacbbbabcaabdccacacacabbbacdbbadbdccaccdacdabadbaccacbdadbdaadbcbabdababcbaaaddbdacdcbcccbdddcaccdbdacbcaabaacaabcaadadacabcabcbdbacbabccccbdadacdcaadbdcbaadcbdacabbddbddddbdaabcadbcadcaadabbaccabbcbdbccccbcaaacdaadbbccbcbdcccbcabaddaabccabcdaacddcacdbcbbaaaccddbbddabdddcbdbcbcdadbbdbadabdacbdbaddccdcabccaaabcacdccbbdbdbbadbcdbbaadbdbadcbcddcbccabdbdabcbcacccadcaaaadcabbcaacdcccdcdaacabbccbaddabbabababacacacdabcbadadbbabdabcbccaabdcddbcbdacabdddbaddadccbdaccadccaddbdbdbdacdccdbaabbbdcccdaacdbddbdcabadccbccaddddbdacddaabbcaaddadbcdadadbdcdadbcbbccbaaaadbccadcbdbdbddabcccbbacccaaacaabcbadbbdccabbdcccccbdaabdcbdadbbbdaadbbdddadaacbbdcdbabcbacbdbbcbaddaccbbddacbcbbcbacdddccdbdbbbbabadccadaabcdddaadcdddaddbccbadaabbabbacbbcddbbddbacdccdbadbbdadcbdcddbdabaaabdcbabaccacbadccccbabbdcaabbbdabaaadcaaddcdacdaadddcdcbacdacadbbaabddacbaccaccbaddccdbccbcdacbadbbadbabccaddcaaddcdbadbabcabbbacbcdcdccbaacbaadccbbcccadccacdaddbdddbbacaabdadaddcdcdccbccaddbbccbdbabdadbbcdccbcacddbabacbacdbabbaacbccdcdddaaadadadabdabaddaddbccdbbdcbcdbbdadaaaaadcabddcbcadaaacdabcaccdcababdddaabbcbbacadaabdbaabdaadccbbdbdbacdbbcadbbcbddbdabcbbddddcabdbdddcddaacbcacbadbacdcbdbbdaddbccbaabadaaaadaddcaddcbcaacdaaddcbdadcdcbcbdbdccaadabcbbbcdabbbbbdbcdcdacadbbcbacbddbdbdbcdcdcdabdbabbbdacaaccdccbdabbccbbcdaaaccbadbccdcdaabbbdccbacdbbbddcbcbbbbcabcaadddcaddadabdddbcdbabaddcbcaddbaddbccbcaccaccbcabcddbcdbcdbbabbcbbdacadacbaccaabbbcadbddbdbacbcdabbdabbabcaadcdddbdbbaaadbcaabacabaabdbdddbdacdacaacbdaadaabaabddddcccdcaccacdbddacbcacccdcdcdbbbcdddcdbddbdbbaaccbdcbcabbbdccabaddddbabccdbbaddaabcadacccdcaaaddccabbbccdccdccdbbdcbbbbcadcdcaddbcccddbcacbbddabbcbdbabbbdaccbbcbacccaaccabcbcddacbdbaadadabbdcabaddbcdbddcbcadddbbccaabdababdcccdbabdbdcabcbacccbcddaaabaccbcccacdcacbdbbddbcbcadccccaabadccaadadbcdcccbaabbbdcddbacdbadbabbccaacadbaacdbbcbbdcbbcbcaaccbabccbbaddddbdbdbddacdbcdbcdcdbcbddbaabdadcbaabcbdcccabccabdbadabdbbbdcdbdcbaaabcccdbcaddbdadabdaaadabbdabdadcadcdbcbbacaaaaacbdcdddadaccabdabddccdabdddcdccaddcdccadcdcbcaacbdacdcccabaccacabcddadbabadcdacaccabaddaaddcdddccbddbadaabdbabadcddccbbbaddacaccddacaabcbdacdadbaaacbaccbbbaddbdcdaadadddadadcacbaccbcaaccdaaabbabdabadddcbdaddcdcdadbbbcddbabbcdabbcdadbcdbcdcacbbcbadadabaabcadddabcadddbadcdaccabdaccacadbaaaaacadaababcddcadcabaaaacaadabdadbcadccccbabcdabddbcbaccbaadacbdbccbabbabaabbabdcccdabbbaddccbccbdadbacbdbdaaabbbcadcdadcbdcacdbbbcbcbbaacccccbbdaabccadabcabacddabccadddaabdbccbacbbaadaadabadacdddbbbabbbcbacdbdbbbddadaccabdabbdcdaaadbadccbbacadbcddcbabbdcdbabcbabaacabbbaadbdacccdabbcbcbdaccdabcdacdadbbaaccbadccbbbbccbbddbccbdccbbcdddbbcbcbacaaadccadacdcbbbaaadaddaddaccabdbbcccbddcaadbcbdddbdcabccdbbcbccddcbacdddbaacacdbabadbabdddadcdacaddcabcdcaacbcdacaacaaadcdacdcdbaccbcbbacdabddabcbabacaddbaabdcbcabbacadbabcbbbadccdabdcabdcadcbaddabbadbaacbabacbaddcabbbcbadcadccddaaabbbbcaacdadadbadabbaacdacccaddbdadcaccaccbbdbbddaacdbcaaaacddaddcdcaacdaaaddaacaccbabddbcbddbaaaabddcdccdabcacccabaccaaacdddddccdcbacbcaabcabaaabdbacbcaababbdbcaabbabdbcaaadbabdbbbacbdbcdadcbaaababacdbbcdccdbacbdaadacacdddbcadcbaddbcdadcaacbabccadabcaddabdbbbbdcaacddcbbdcdadcccdaabddaaaadbdadbbcbbabdcdbdbbbdbbaddabacadbbcbdddcabcddbaadbabcaaadacbacdadbaddbbdcbbbaaaabddbbbbcdbbcbcbdcaddbddadccbccddbcbdacdbbcdaadaaccabacacbcbcdbbaccbdccacbccccccbbcddbbabbbbcaaabaddddbdaaabcbbbaccbbbabacbbcdadacaddbabcccbccdddaaadcbbbdbbabadbdcddbdccdbbdddcccdcccadbccaababddaaacbddcacccbbcdabadbbadbcdbbcabaaacaaadbdcdbdcaddabccdcbccabadbdbccdadacbcdcadaadaacdddddcdcdcccdadddadbbbdadddcdabcbbadbdcbdbcacbadddcadddbabadaaaaaacadcbcacabbdccabbcddbccdbadabdaccbcccaaddcbdcaaddbcdbbcbcbbbabacabcabcbbbccddbaacadaabdcabdccddcadcbacdaadbaacdcabaacadcdaaaacdbcaddccdbddcbacbcabbacacdaccadaddbabddbaaacbacbcbbdddaaaccbbdaaddddaabdcacccaadcbcdcaaccdabbadcddaadbcaaabcbcbddbbdddbcdcbbacdbdabcacbacdbacaadccddbcadcabccadbcabbadccbcaaadababdcddbcdbccbddbaacadbcabcdabcdbaacdccddcdcbadcacdbbcdccccdbabbcbbaabbbbacccbdccaccadbbbdabacadaccbcbcbddcdbddcbaabacacadbbadbdbabbaaabacdcabcadcbbbaabbacdcbacdbaddddabbddabcbdaddababcaaaabbdacdcbddacadabdabcbacabbacdcddbadcdcdacacccbddadcbcdbaaccdcbbcdbdbcdddbcbabcaccaaabbdaabdcbcaacccbcabbabcadadacdcbdbddcbccdcaabaaaadacdcccaccaadbdadcaabccdddabacdccbbdacaaaaccadacaccdbdacddbbdbcdbdbbbcbaaabaccdbbbccadadbcabbcccacdcbdadadcabddbcabaadcbaccaabacdbddbbdcdbdabdccccadcddaccdbabcdbaabdacbcbcdaabcababdbdddddcacdbadbadadbbadbbdaacdbdcbbbbcaaaabcbddacaacabccadabcccdcddcdabbcacdcdabbdbaababbdabdabaaccabbccccacababaaadacabbadbcbadaababcdcbbadbadcdbbaabbcdbddabadbcacdaacaaacadbccacdabaaabaabbbdcdbdaaaabdcaadcccdbdadbddacddabdccadcccdbccccbddaacabcddcdccccacccaaaadcdcbacbbcddcdbcccccdbacdacbbcbcadacddaabbadbbabdcbabdbcdbdbdaaddbaccbcacababdaabbbbddababbbaaadacbbcdbbbaddbcbcbddccadaddaccccccaddabbcbdacadddbbbdaabcdbdccdcddadadaaaacddccaacdadddbbcabddbaddcacdccbaabaddcadaddadbabadadcdadccadccaaabcabadabdbbbccdcccdaabbdccdaaabacadabacaadccadcccabcbacdabbabbabbdcdccdbabaabcdabcbacdadbcabdccbdaddaadababddbbadcddbaabbbcdcadacbcdcaadcbbcbddbccabbbdbbbcbddadcdaccddccbcbbcaacadbaaacadbbddcbdadbbbdbadacdbaacaacaccaddccbbdddadcccadcadddccccdddddadbdaacaccbdbabbddcccdcbbabdbdccddcddcdbdbccaaaaabbddbcdcbadadadbccdcbbadbcccaddbbcdabacdaddabbbabadbcbbabbabcddacaddadbdabcdabddddaacaadbaaabccadcbcacdbcddbbbcaaabbcbacddaddbcadbccbbcacccbbacbaddbddaadbbcbcaadaadacccddbaabccbadcbdbccddacbaadcdbcdbdacbdddddcdbaadabddbdacccdccbabcaddccccbddacaaabaaccbbdadbacabcbabaddacbbcdcacabcabdccaddbcadaabcbabccdbacccbbbdcbcabdaccdaadcaaccdcbcbccbbcaaccdbcbccabddaaabbadbbcaaadacacbacbacbdcabbbbccdbdaacacaacbbdbababdddcddbcaacaabaabbadddcadbcbadacdcdbcbccbccacadacbdcdcbdcdadccbbcdcddaadabaaddccbbdcadbdacaaaaacdabbccabcdcdadacbacacacddbbaccabddccbdabdabdacbbdbdcbdbccaaadacacdacbdaaaadbccdbdccbcdbbddacbdbcaaabbadcdbdcacbcdadcaccccdadacdcaddbbbbacaacacacaaadadcdccbacbacaccbdbabddccccabbbaaadbbbbaaacbdbcdcacacadbdbbccccdcddddacaccbbabddcdbcaadcbacbddcbacabccabbdbacdccbbcbbcbbcbcdbccdbabbddcccbbbbacbabddbdcbccdbcccddaddbaddbcccdddaddbdddcbcbaddbbaccdcabcdcbabcbcaadabaabdcccaadabacbaccbdababbddcbcdbadcaacbdaddbbdcdbabbaddbcdbddaacbbbbbddccacbcadabdcabcdbbbdababacccacbcdccccacadbdabcaacdddabbbacdaaaaacacbaacccddcbddadcbbcdcdddcdbdbadadadcdbabcdcbbddcccaddddaaaacddddadcadbcdcababccbbbabbdadbadbdaccdccbbaabcddbbcacdcaadadcbdcadcccaacbdabccdcddcaaddcbdcccaacccbdabbbcdcdbabbaabbbdaccbdaaaccbbdbccddcddccddacbbccbbacaabdbdaaaccbdccaacabdcbaaaabaaabaccacdccaacdaaabdadbcdbadbabbbbcabcabcbccdabbddcadcdcdddbaabddaddabdadcbbcaccdadbadbcabbabbccbabcddbbaabbcccbdaddcaaccadabdaabcaddaccadccbcbbacdaddbbbbddacccbcbcabcaadddcccbcbdabddcadccdcaacdabbdccbbbdccdbabbabcaacbaadbababdaadcabdaacadbbbcdcaaccdabdbccbdbbdadcdabaccadaccddbbcbdbadccdddadbabcdacdccdcbaccbdaaadbddacdcbaacacbcbaaccadddabbcacaadbccddbbaabcdadcaccacdadbadcbddccdacdaadaccbbbbddabcdccaddacbbbcadcbdbadccacbdcbaadbcbbcbdcddcabdbdabdbaacaaadabbbcacbdbbcacabdcdacdccdacccbabccbcaacaababdcbdaaabbcbddacccdbdaccbddadbadadabdbbbccbccbbabdbbccbcaabdccdddbcccccbadcdbddbabcbdaabcddbcadbaccdbcabacabdbdccdddccdbbdcaacbbabbbabcbdbacdcbddadabcddabbbabbbbdcbccdcdaaadcabdbbccdadccbacbaadaaccaacccbbbbbacbacadcbdacbadddddbdcaaccbdcaadbdbcbcdcccdbddaaabccabcaadbcbbabcacccbbdabcdacadcabbddaaddcdbabdccacdaacaddbddddccdbabbcbcababadcdbacddccbdccddcbbcbdbdcadcdccbbcacddbcccaabdababcadcddbcabdcdbadddaacdddabdcbacdbbabcaabccaddaaccdcdcddbbcaaabcaccddccddacaaddddcaddddbcbcdacabdabdababbdccadcbddcabcbccbbbaacaccbbddbccaaabbaccabbacddabdaacbbbaacbcbcdaaddbcddaaaabbdbaaabdcbcbbdccdcabcdbdcabdddadbdbadcaaaddbcdbabccdcbccbbdddadaacbacadddccadbadbbdbccbaadbdbcccdbcbcdbaadcbacdaaccdbcbadbbdaddbdbdbcabdcccdcddaacbbccadabdbbbbddbbccbbcaadbaabaabcdaadaccddadaabddaabbaddbaaaabbbcdacdcbdcbbacaabadacdacdcbdddcadccaacababbdbdcdccacdababcadbbacbabccbddcdcbbcccdddccbcbabdbdbdaadabbcabbccabcdacaddbcdabbbacacbacbaabcabbdbaadbcdacddabddcabdbaaabaddcabcacabbddcbdcbabdcbcbcdcdcbdddddcbbaddcaccbcbbacdcaccaacbdbdacdabaddcdaacacabacbadddbadbcaddcacdbcdbacccabacaacaacbdaabccdadcadcbddbbdbaadcbbdbcdbdaaaaddcbccbddcacacabcdcddbdbbcbabbbabcccdbcbcaccdcaddacacbababdabddabdbcbddabbbadbdaaaadbcaabcbcdddcacddacdbaddacbabcdcccdcbbadcaddaacdcccdaaacacadbdccbbcccdaaabdbdcccbcccbddacbccbdbdaadcbcdbccbcdcadbaddcbdcbdabdbabbdcbacdcdcaabaddbabcdccabbabccdcabbabbbdaddaddcaaabaabaddcbcdbccccccbbcabdabdadddbbcdddbccbadbdadcabcdccbadaddcdccbdcddbabdbabbcbaccbcdcaaabbbaabdbcbbbaabaabbbacdbacadadcabccbbadcdcadcbcdacacdcabdcdadbcacbcbbddaccdcbcdddbadcacbcdcacbdaababcccadcdbdabbcbcbcbdabcbbbaabbcaaadaaddacabbbdaadccbcacdcaaddcbbbabbbcbcbcdabcdacbccabdbaacaadaddbdcacbdcddadcadbbdbdaabcdccaadcbacbdbbbcabbaccdcbcdcaddbccacbabaabcddacdbaacdbaddccccaccdbbdbbbcbdbbccbddccabbbcdbcdbcbacbdbcdbdbaabbbadbbbbacaadcbcbcdccadcccdbaaccccadacacccacdcbabcaacbaddaadabdddcacabbdddabdccdcbbbbbbcbbbadacabbddcdcbcaccacadadbabbccbbaababaccaacbaaacdacbbdbbdbbbcaddadbbbdabacddbbbcbabbdddcdabcaddcadbdadacdcbbbcbdbdcaaabbbcaccdbcccdcbaacdbbacbcbccabbadacdbcbcddaaddbbcccadbcdabddbdbbcadcaccabaaadccddaabcdabbcaccbacccdcbcdbacaabdababcdcccabbabbabdccddacacdcaaadcbaaaabcbbdababaacbabcbbdadcadbdbcdbdcbbbdaaaabcbdbaccbcdadbddccabbdcbdcddacbdcadddbdcdbdccababacccabaccdbcaccbccbaacbacccbaccccdacdcbbdaccaccccabcbacbcbddbcdbabdabccccbcacadddabacdbddbbbaccdaaddcbcaacdcdcbcabdcddbbdccbdaacbcdbdbbccccdaacdabdacadcabbcbbdbbcdaacabbcccdccbaadaacacbdadbdbbdddcbabdcacaabbcddacdabbbcabbabbcdddaddddddbdacdcddcddcdaccacaabdbcacddbcdaadacddbcdcabacbcdaabcaccdbbdcadabbaaabcaaabcdcbccaccbccbddbadabccbacbbbcdcdbcdaabbbaabbbbddcbacdbcbcdcbaccdcaabbcdbadacbcabdabcabddccbbadbccddbdaabddbadcbcaccbcbdcdccbbcdcacbbbcdddddbddcbaaacaddbabccbaddcbccadaaabccaacdccdcbcbcabcaadacaddddabadadacbbaaabbbbcaaabbbdacdbacbdabbadacdddcdcdabcbadcbbbaccddddbbabaabbacadbcbdaadadcacaacabbabbcadaaacaaabbadccbacbacabcccaaaadaddaadbdabbcccbdcbcdddbccddacbdddbdddadddccadabaddbcaccccdbabbadbbbcddddbbdcdcddccddcddabdabbbdacbbacdbbacadbadcacaaadbbadbacdccdddccabaabdcacddbbadacddacbabdcbbcadcbddbdbbdbbdabdadbcdcabbbadaaddbabbdaabdadabcbbdcdcdccbcaabbccdcaabaccdbdaccabcaaacdcabbbdaccdbbbdabcaddcdcbcbbbcaddbbaddbdcabdacdbbcacadcbabcdbbabbbdadabdaadaaacbdbacabacadbbdbcaaaddcaaaabccdaadcdbaddabaaaadbdbcacabcdcccbcdabccbadbddadaddbabdbadccaabcacadbadadacadcaaabddbddbdccaabcbbaacdddcdbdddadcadadcbcccddbdccddaccdacddbdbbcddaacadcdaaabdcaadcbbbdcaaacaacdccccaacabcccccbabcccbbcccdbdbadadcbccbacaccdaadbbadadabbadadddcdaababacadcacddbaddbcaaadbcbdaabbcbcdbbaaddababcabbdaabcbdbdcadddcdcdbdbaadababbdbbdaabddabdddaddaadbacbccdddcabcabdddcacdbcaadcdcccccabcbddabcbdbdbcbcacddcbddddddbacdddddbbabcdadbdaabbdccbcbddbddbdcbdcabdcdccdbbddadbcaddcaaabaabbbcbcabdcdbcdabddacdabdabdadbaddcdabdbcbbdbcaabccccdbdbacdbdcbbcaccaaddbaadabbdbdcadcccbbaabbbbacdccddcaadabacbadabbbccacbadddbcaaccbabddacbacbbbcaaacbcdbacbcbbccddaabbcbdacabbbcbddcdccbcbddbcacddacbdddbbaadddacdcbbaacaccbdbdbadacabaacdcadacbaadacccbbdccabacadbabbbdaaccdccabbacdacbdcccadcabbcabbddbddaddccddcaadbbcbaaddbcbadcaadcacaacacabddadbbdbcaacddacbdbdbcbccdcbbcabadaaddaccccbdabccacabdcbcdcccbaaccbcaccbdaacadaacdaddbcacdaccbbacdbdabadbadbaacdcbddddcdcddcddbbccadbbcccadbcdbdacbccaadaababbdbcdbbccacdbabcdbbccdcaacccaababaadacdbacdbacacbcdbaabdddbbddbbdabcdbcddbbdbbbacccacccdcbbadccacbdbaaaccccdaacabbdcdabbaaabbccadcacbcdcaabbcbcabdcbaabddddcccdddbccbcbdddadadadcbcdcbbbbcaadaddbddbbcadabdcdadddadbccccddcbababdadccabbbbaabdcbaacccddcddbaadbbabbaacabcccbdccddababbdacadbdbdccbbdbcaaabbdbbdcdadaddababaabbacbaaddacdbbcbdbdcacdcccdbdcabbccbdaccdaabddbcacababdbdbbadbbddcaabbaaacacdccdcadbcbcabdcadbcdaabbaddddbbddbcbbadadccbbdaaacacabacdcdbdbaaddbacdbadadaabacdaccabacccdcaaabddaababbcdbdccdbabbddbbcadaddcaacbbdcddaddbbbaacdcbaddbdabcbccabccbaabbddbacadbbcbabddddbdbacabbcddddbcdbaacdcdcaddcdddcaddabdcdabcddaabdcbabdcbcbddaacdaaacdabdcdbcccbbbbdbbdddddbcddbbcbbbdbcdabacadabadaddbaaadaddaacdcdaaddbabcbabacdbdaccdddcbdcabbacdccabddbcdaaccbcbacabbadacccaabcbbababddbbcaaddccadcadbaccdaaabcbcbbbbacdaccbbcbadcbdadcdacbabddaddabdbbadbadbdabbbbcccbbaabdabbdadbbcbcaadabccadddddbcbbbaccaabddaddccccdbdbcdabaadbcdbaabdadcadbacdcddbccdacccddaddcaaabddaccbaddddcccadadbbabdabbdccadababdddcbbdbbaadcccbccdaabccadacdddbcbdbabadddddcccabdbcacacaaccacbcababddbdcababccabddbdbaaadacacacbcddccbdcdaaadcdbaabccacbccccaadbdbccabbcddabccbabbddddadcaacdacbaccaacbaadbbdabdcccdcdccbadadbdcbbcdaccadddaacadcbadbadcadcddbaadbbbcdacadcccddadbdddddcacaabdaadabcbacacaaabbcbdadadcdcddbcbabdbddadcbbababdbcbbbbcabbacbabdabcdbadcdbcadcabaaacadcacdadcbcaacddccdcbacbddbaabcabbabdcbddcddbbacacadbcabdcdccddbddbadbcabdaadcbcdabcbaabddaaaabaaadbbcadcdacbbcbabccacbdccabadcacbacdcdcaaabaccdbbbdbcbdabbdddcddcaadddbbbaacbbbcccddbdaaabbccaccbcdacbccbcccaccaccbbcaabccabbbcdbabdccdabdccbbbccbcdcdcacdccdadddbaaadbddaadbbbadcadbbdacacbbcbbbbdbbcadacaadccccdccccbbddcdbddbadadcddcccbbacdaddccbbaabaddaaabdacbbbbacdcadbcddabbaccabbababcabcdcadbccdcccdcdaddbdadcacacacabbbdbbddcbcbdbbdaddcacbabacbddbcddacbdbddbadbbbabbaadbddddaccaadababdbcabdcbaadbdcdcdddbbabaadcdbabadbcbdadabccbddccbddadaaccddbdbaacbdbbbaadcacaacdddcbadcdbbcabbdcbdccaaacccddcbadbbbadddacaddbbdbacccbbbaacbddadcadcdbbaaabbbbabaacbbbccadbcdbcbbcccddbddaaccbbcddaabbbabadcababcddcacabbacaacbddabbacdbadcdacdcccbaabdccbdaacaaccbbcbbcadadbccbaabbdabccbaacaccdacbadbbccacaddbdabccbacbdbccacdbdaddaddcbbdcbbdabbacbabacbddbbbddbaaadacccccdcaabcdaacdaadcddaccbdccbdabdcdaddcbcbabbadbbcacabddbadaaabccbcccbbdbbaccaabcabdcbbcdbbbcbbbbdadbbccdabdabcbabadbcdbbbcbbddadbddccdbbaaadbbccbcbadbbdabbdaddcdcccdaabbdcbdbccaccacacbaacbdcabcddccbbdddbabdcacadacddccdccadddcbcaaccdaccacbbbaaadacadccbabbaadaddbababdcbdccdcaaadacbbdbcdbdccbddccbcbadbcadcaaaaccdccccdcadcbdcbaadbabccaadbabcbcdbccbaddddcdccdaaccadbbcddbcdaadccbaacadcbbbbbbbdcbcabcacdbbbcabadcaaaaaccaadadddaddbacbdbdaacaababdcdbbdaacbadacadaaaccbbacacaadabaaddbdddccdaaaacaddacbbcddbdbdddcbaadbaadbbabcbbcdadcbcbaddaccbddaabcdcaadccdadccabcbdadbdbddbabccbcabaddaaaabdbdabbdacdadbbacabaadaacbcdcbbbcbbbbcdaacbbaaaaacdbacddcdaacbbacddcbdadcdccaacdcbcbbdbddcbabcbabaaaaaacdbbdaaadccdadbbdcdcbacadbabcababcaddbdaabbadbcdaacadbbbcbdbcbdbbdbbabcdcdacbadabbbaadcdabdddabadcbcabdcabcacacaddabdaddcbcbaccbaccaaccaacabccdbccacabbadcbbbbcdadaadaadbbdaabcadbdbadbadaabccbcccbcbdbdaddaabbbbabdcaababcaabcbcbdbbdcbdaddadcbcbccbaaaabaddbabbcaaacdabbadddcbadcdbaacabdabacdaadaadaabddcabbbcadaacbbacdcdabdcabbcbbbccbcbddbbaaccbbbaadccdbccccbbddabdbbdacacabaabacbbadcccbaaaabaccabdbdcabbbcdccddbdacabadbdbbbbddaacddadddaaaadccdcdbbcacdcdbaccdcbccbbbccacbbcaacbabdcbbbcdbadaaabbacacaaadbdbbadcddbdbdaaadaacbbacdabdbaaacbbddacdacadbdbdcdcabdccaaabbcbaacbbcdbabbabcccdbbbddcbaaccdddbadcaadbcccccacdbcbacccbbbabcaddcdacbbaadabbaccabbadbcbcabadcbbaacaacbaddbdccadacbbdaabbdcdddbaddacaaadaddbdadccddcabddaccabbabddcacbbdbacaabccbabacacdcdcbdaccacbcddccabddccabcaadcadddabbbcabbbcdccbccdcdbcccdddbdcbacccabbbadaadabddcacdbdabbadbabbdcdacabdbaddcdbbabcdcbaaccadaccbbbbadbccccabbabddccdbccdabacaabbdccabcacdcccddacadcdcacdcbbadabdcaaccdbcaccaacddbaabdaaadbcdcadadccacaaabccddcddbddbbabccbdbdcbadababadccccadccdcdccdbcabccaddabbdcbdbadcbcbcaaccacccddacadbbbbccbdcdcddabaabcbabbcdabaacaddbccbaaaabbbadcdaadaadbacdacdacbadaddaadbcbbbbbacdaccadccadddcbbbccdcdabbdbaaadddbdadadaaadbdaabbddabbcaccddaddccdbbbcdcaddbdcddaddbbcbadddccdadcabdcacaabcdaaaabccdddcacdcbcbbadaacabaaaabababababdbabacdabcdacdbdbcbaaccadabcaddddbabdbcbbbaaaccababdddbbacdcadcaddbcbdacdacdcdcbcbaaccacbbccbbbbdcbcdcbdbbacdadcabcdcccbdacddaadabcbbbccdaacdadddabcccbcbabbdbacccdaabbcdcaacccdaacacddaaddabdaddccbccabcaaabcaacdbaddddbbabacdcbdbbbcbcbaabcdcaababdcbadcbcaaaaadaadaaaabdcdbadaacddbacaabbcabcaaadabbaacaaabbccaddaccbdcaddbbcdcadddcdabbabcddbccbddccbddcbcdddbbadbbcbaaacdacdcaabaadccaabacbcbbdccadcaddaacbacbdabdbdabcdbacbcaabbdbabccbbdddbbcacaaaadbcbdacadabbcddaadcddbddbaaadaabaacdadcaddacbbacbabcbcaaddbbcabcdcdbdaccdbdbadbadbadababaddddbbabddcdbbbaabdabcdddccdbdadbcbddcdacaabcdabcadaddcbabddccddaaddacdcdbdacbadabcbbabbbcabaddcddccbadabddbdadcdacadadbadcbbbbcbadacacbabbbcaacbdabcacddabdcacbabccbbcadcdbcccdbbdcdbbdaacadadaccdccbbbaaacabcaabacbccdabaadccccbbcccdcaddcdbdcadcbaaccccdbabacdcabdcabadacadcbbabaccadbdbabdabbcbbccccaddccbbcaaabdcdadbbccbbadbddacaabbcdcdcbabbbdbbdadddabacabcbdcbccccdcaddacbcbcbbddaabbbbbddaadadcdbcddadbbbddcbbcdadbcabcbbccadacbaccbccbddcbcddabdadbcabababccbbadbcdbdbacdacbacaadacccaaaccbbdadcbbaaaabbddacaadaacbbacaaddcaddabdbdadcacdabcbaaddcddaadbbdaaccdbacdddaacddbbccacabbbdbddbaaadcdcdddcbcbbcbbddcdbbccbcccbadaddadbdaabbdddbdbaadcacbcdadbdbdbbdcabaabadbabdadbabccacabaddccdcdcbcdbcabccdddbcbacbcbcbcaabbaaaacddcaccbcadaabbcbdadabaaabdaccdbbbbabaddacbbbcbcdbaccaadbdbddcaaddbdaaacdbbddccbccdccacaaddcbddcacbcacdbddabacabcdccccabdbcacdbbcbacadbbaabcaaddbdcadbcbacbbcdddadbddcdcdabbdddbaabbabcbbaaccdccdbdcbdcbcaacdddbbbdcaadcadcdccacdccbcbdcdcacacdbacbdbcdadbbccddccddcaaadaabaabbdcddbbdccdbcacdaddbaadcccdcbbcbdbadacdacbacabdabcabbbadadccccbbddddadcbcdabddcbabcaadaabdccccbaaadabadbacdabcddaadacdccdbdbaacdcccbbdacadccddcbcbaccbbdbdabccbbdadbdcbbccdabdadddddadcdadbcdbbadccacadccbbbbbabbcdacabcadacdabcdcdcbbaadcababaabcddbbaabbbbccadcddacaacbbaaddabdcbddacddcbcdbdcdbaaacdddacaaccabaabddadcdbacaaaaccdcaccdaabdbdbabcaccacaaaacaccabccadadaaacdbcbbdcabdbabdabcdacadbcabcdddacbbdbcbdccaaabcacadbcdadcadaaacdcccdabbcddadaccbadbdcddaacaaaddbaccdcababdbbaddaadbddcadabacbaccadcbaaaaabbabccabaccabbdcbdcccbbdccbbbcdbddacdbdcbcabacaddaddaacbddaacaaddaddcdbddbcbddcccbabbacdbaccabacdaaacacbbbcccababaaaccabbbdbbadacbacacbddbccacacbdcdadcdccbcabccaaddbbcbccbbcddabbdbdcabbcccdadcbcbcdbddcbbcdcdccdccadacaccdaacdbccbaaccccdcbababbcdcdcccbdbdddbddbddbdacabcabccbcadabadccaddaaaaddbdacbbbdabacacbabacbaddacdacbdbccabdccdcddddcacdadcdcaaabdbadcdcdcdbadabcabbccdbccbdaddbcaababacbbacdcacbdabababbcadbaababdaaacbbbcdcccbdcbadbadabacabddccdabcabbabbdaaaadcddaadbcdcbbcbabbabdbbcbaabdbdaccabddabbbdcaaadabdcdccddaccdcbdaccabbadbddcbbcadaadbcbddcdaaabcadbccbaabaaacdddaccddddbcaccbdcbbabcadcddabcaacddacdcbaacadccdbadbaacbdcbdadacacddadddabcbadbbddaacacbbbadaccbcbbbbcddbadbdabcdbdabcbcbbdbbdcbccbadcabddccbcbccadccbadabdbaccdbdbadcbcddcabbdacbabcabbbdddcaaddbbdaaaaacaddccbdbacbcbbbccacabaabaccbcdbaadbdbcacdccbbbccdddbccabcbddccbdadbddcadaacdbbaaabdcbadbdbadaabbdaaddbcdbadadccacbadcbcdadadabbccaaadbaaccccabaabccddcbbdbddaaabcbcbdcdddabacadaddccdcccacacbcbaabbbbdadcdababbbaabcbaabdbcacdbaabacbbadbbcbdcbaccdadcddbdadaaaddccddbdddcddbcbdbbcabcdbdcababbcdbcdaadbdbbdcbcaaacbbbdadabcbaddbddddacdabddcddaababaadacbdbbaaddbccddabdcdcbabdbabcacbaddaadbacbdbdcdcbabbdcbdcddcaadacabcbdaadbcaacacadcbcdcccbdbbbbcdcddadcdbbcddbcbbddbabdabcadcaccabdbccccabccbbabacbbcdbdacdcccadbcbccdbacabcbbaaaaabdabddbcdadbdabdccabcdbcbabcbbadadabcacdaabacacddbcabcbabaddddccbbaadbbadcdabbbdcdacbdaabccbabbbdadacccdccdcaddaadcacdbbccadbdcadbdbabadbcbbadadbcdcbacaabbbbbcbcbbccdbdddaddcabdabbccdbbbbabbdacbadadcabcacddbbcabdbbacaadbacdcdabbbccdbcdcddcaaccbdddcbbacdcadbdbddadddddacccadabdbdbabbaccbcdccaacadcbbdacddaaaccababaccbbacabddabcaaccdcccbcdabbbddbcaccdcbdababacdccccacdccadabcccadaddaccbaccdabdbddaaddbbdcaadbabddbcbacabbcacbcbbbddaacaabcaccbcdcabccadaaabcdbbcccbabaacbaabacdbcbcdabadbdabacccdadcbaadcaddaadabbcaaddbbcbddbccdcccccbdbbbddaddaababdcddabbcabaccbcccdbddcdcdabcddcbbdbbdadbbbcbddacadabcaadcaaaadacbacacbaccadadbcbbbbabdddccbaddbccdabdbaabccbabbcccccddcababcdcddbabddaaabadaaddcbcbdbdbadadadaccbbbdbcdacbbcbabccbbdbaacadbbdabbbdaccbbbcbabdbcdacaccddbbdbaccccccbdccddacabbbcbdbdcccbdaadcadcaaadabdacdacbcbccabcadbaadccadacccccbbbccdacadbdccbabddcdbcdcbdcadddccccbaccabbbddbdbbdabcaadbcbcdcbdddbcdaaddabbaaccdcbababaadddacacadbacdddabbabbaaccadcdacdabcbdcaaaadccbbcadcbccbacaadbdddabacbcdccdadbcbcadcaabaabcdbcccaddacadbdbabcddaddbdbabdcdcbbabcdddbaadababbcdbbcbbcbdbbcbdaaabcaacddcddddbbacabbbadcadbcbabadacdbccdbbcdbacbddbaabbcbaadabcabdcacadaabdccdadccadadcbacdaacdbbbbbadaccbdccdbadbbdddbcacacbcdaddaaadccacbabacdabdcdbbbccbbcbdcbbccabccbcbccabbdccdbdbcbbdbcacdbddaabccbcacdddccbbaddcdbadcbccdcdaccbbcccdadcacbabacccbbdbadacdbcdbbcaabcbabdabbbdbcaccdcdadaacaddccbcdbdbadadbbdabdbadacaccaaacaadbaddaaaabcadabdbbcacaaaadbdbbdadbddddcbcbbcbcadacddddcbbccddaaabcacacdcabbacccdadcbacacbdddbdbaabaadadbbbabdbbccabbddcdabaacdcdccccdbcaddbddddaabbcbbacaadaaadadbacacbbdabacbdbbbbddccdbdcbbadbbcdbdddddaadcdcaddbbacdccdccbcbccbaacddbdbcbaabcdbbbbdccacccdcaaacdcdadccdcbdbcbcbadcacdcaddbacbbdabdcaabaadacddbacbbcdcbcbdcbdcdacbbccaccdabdbdcdbdcbcacacdcacaabbabbbcaaadbacbdbdacccbbbcbaadcdabdabaddddcbaaadddabbcbaacdcdbcbbbcbbccaacbaabbcccccccadadbcbcbddadddcabdaccdabbcacaccdcabbcbaddcdbdaaaabcbcdacdcddbabbaccaadcdbaabdcddacbcbdacdcbddccaadbbdacbdaacabacbadbddccadcbabddbdabbccdabdddbdcaaacabacbcdadbaddadacaccdbcbbcdbaddaadaadcabbadbdddacbccabbbbdbddbcacdbbcadbdddcdabcaabbcdacbccadcbaddbbcdbaddddbdcdbbaabbdadacbbabbdabdacbabdbccdbabcbbcadbbdaabcccbdbacacacabcdacadabcbbdccddbddcadccdbbdadabbadbaacadcadddbcdacdbabddcbaccdabbaaabcbdbccdddccdbddcdbabbdbcbaaadaadcabcaabbaccdaabcdbcbdaabbcadbdabcbabdcddaccacbcabbbacdcabbdaabdbddcbdcabdddddccdacdaabcbddcdcccdbbbcccdcbccdaaaddccdcbddbddbbcddbdcaacacdabcaccdcccaccdbdbcbccadabbddcacccbcaadbbbbcadbaddbbdccdcdcdaccaaaacbaddadacbcbddbddacaaadcddabcacdbdbacbbcabbbdadbadaacaccdcaddbcabaadcbadaacbbbdcacbaddccbdbbbbcccdabcaddbaababadccbbadbbcaaaadbaadacbaaacbbaaccbabbaabbabaccbbccbcddaaddccccaabddcddcdbdddbabcbbcccbaabbddacacdabcabdabaababbccdaddcdcaccbdbccacccbdcacccbaaadacbccabbbdbbcdbdabcaddcbcbbaaacabbbddcddacbaabaacccadcbbcbdcbdbacddadadccdcbdcbbcbcbdacabdcbcdbbdabadddbbbbcacacbcdcbaacbcabaccbbbcdbdbcadabbdaddcbaddadbcadcdaccacabbabdbdabcbbdcacdccababbbddbbbdabcddbabdbddbbbaabcdaadbdcdcbdcddddbadacddcadadddabacaadbdbcacadcbcabbcdcadcdcaaaddabbadabdcacccdacddddcbcaabccbcabbdddadaadabbcadbdabbdbbcdbbbbbdcbaacddbbadbabcdabccccdbbbccddbbacdaacdbaddcddaddcdbddbcbacabdaabbcacbbdcdcacadcbbbbbacdaaabdadcccaadbccaaddbddcccbaabdadbdabcdaccddaadbbbbcdbdbccacbcbacbcdadbdaadcdadaacbccddaabacbdbbcacaacabccccbcbbbabbdbbdbbdcbbcdbbbbbdbabdcbdbadcaddccdcbdcadbddddbabdabcbadbdaaabcacccdccacacacbddadccbdadcbddbababccaadacccdcdcbdbcbbdbadddbbdbbdadabbbbabcbdaccbbcccbcadaacacbbcdcaccbadacccdddcacacbacadabdddbacbbcabcdcaadcdcddcdadbbcacbaaadbdbdcdbbdacddddbbaddddbccbdbdcbadcdccdbbaadcaaddcdbbbabaaaadddadabbddddacdbddaddabaabcddbcbcdccdaaadbcdaaaccabccadbcabacaaaaabbcddddcbdbcdaaacdadabbcdbcbacbdcbabdbbaacbbbcabbcadcdddaccdccbddbdcbadabbddddbcbdacbababdbcacacdacddccdadcabbcbbcdddddaadcdbcbdabbbdcdcccdcbcbaadbbadadcdcaadcbddcacbdabaaaabadabcbbccbdcbbaabbcbacaabcadcaddacdddcdabbaaabcbbaadccbcdacbdddddddbaacacaddcdccdacbabadacccbbbabbbcbaabddbbccccdcababbcccdcacbbcacbdacacabdcccabacacbadadacbadcbaaadbddbcddabadbdbdabcccaadbaddaddcdccbccbbbadaddccdbdbccaccaaccdaddcdadcabacccbdccdaacaabacbbacddaaabbcbbddaababcccacbcaadadcacabdccbddddbdbcbbdbaaaddadbbdbcbaacadcadbcbbabcbcccbaccdbbddadaccdbcadcbbcbabdacbabcdbbadcdddcadddbdcababaadbaddbaacbcacddcdccbdaabbbdaaccbccdcaadcbcdadbbcaccbbddabaabcbbaacbabadcbbaacbcbbdbbcaaabbbbacaadcdcccacdddccaadddcdcbacbcdcdcbbbddbabbabbcabcadddbbabcbabcadbbdbabaadbababcbddbcbabaaacadbabcdaaccdaadcbcdaadabababaaacdabdadccdbaaaacdadacbdcccbdacbdccdbcdddacadaccdcadaaadcdbbbdaaabacadcbbddccdcbcbcbdbbacbbbbcddccbabbbbcbcbbcaacccaccabacadadbcdbbcdbbdcbcdbdbcaadacbcacbbcbbdcaddaadddbdcbbabbadaaabaaccbabcaadadadbaacbacbbdccacdcccabdddacadbcdccdaabdbddddbdaadabdbacbbbbbbbbdcbcdababcbbccbabcccddadadbdbdcdcbdcaabdbbdbacdddabbcbcacaacbdcabcdbbddacaabcdcaaccdbdddcacddbbcdcabcbbbbacbdbcaccdbadbbadddaacddddcbbbaaabaddaddcbbbaacdcabdbdbaccaddbdcbabdcddcdcccbddbdbdacaaddcdabdccdaadbdccdbabbbbdbcbdbcddaccadabbaacaacdbbdadadabccccaadbbbdbbadbccabdaadabaacdddbccddaccbbcacaacacadcaaacdacaabbcabddbadadaccdabaaddddacacaccbccadbcdcaccdcdadacbdacabdccaaaacaddacdabbbaabcbcadbbcbaabdbcbbacccbaaacababbacdcbbcdcabcbadadacddbbcdcacabbccccadbbcbaaccacaddbaacaadbbabdddabaccbaddbcacddbdbbabdbccabbbdcabbaaabcddadbcdbbcdcddccbcadddacaccddaadbadacbaddadabdaabbdcadcdabaabbcbcadacbaaadcddaaabcccddcdbdcabbbabbaadacdcccbacbbbdddbdcccbdcddaddbbcaddcbaccdcccabbbbbdccdabcdacadbcacdbdcdbddcdadaaabdabadbbdccabaaaaccdacadcccbcdbcdcddcddcbbbabadbabdcddccaddbdadbddcbdadbbddccaacdccdddcccccadabbcaaddaddadddcdccccddbdbbaddacabddcbbbddbcbcabbabbaabcadbcbaabbcaddacbdbabcaacdcddccbccdcbcababcdccdbdcbdbacadaccdddbabadacabdddcdacdabdbdcaccaddaadcadcadcbbcadacbbdbbbaabbabacbbdcbbbbadcddbdcbcbdccabacbacbdccbcbdadbbdcbbdddabcacbdbcaabbdbdcbcdabdaaabaaccbbdcbaadcbbcdcaabcbdaadddacbcabcaddcacccabaaadbbcdacadcdaddaacbadcbccaccacaabcbdbacccadadacbbddadadbacccaabbdbbbcbaaaddabdaadbdbdbacbabdcacacbddbdababdaabcadcadbaadcdaddccccbbdbcdcdcbdadbdabdbadadbdaccaccbdabddbaddcaabbaabddccbcbcadbcadccdcdccabcbbbdbcacdaabbacccdcbcbbaadbcaaaaaacbcacdbabddbdacbcdcdcdbccbccbdcdaaaabcacbcacdaacbbcbbabbbcdddbbbbbcdbdbddbbddddcddcdaaadbdcadacddadddacabbbcadcddaaaadbacdadccdcbddadaaadababacabbdaccbddbacccdbabcacaaabcaccabcbdbdcabbdbdbbbbdcdbaaccacadccaaabcbbaddbdabaccaabbaadbaaabbdccaacbcaacbcabccbdbcaaadacbdbbbbcabcdbbbbaabbbcacabccbdabaddbbbaabacaaadddbcddbdcdadddbabbacbbcddadcbaaadcbdbcdaccadbddbadcabaccbccdccacdbccbcbdcdbadbbbbacdabbcddabcdcdbdbcabbcdcbdccdadbbadabcadddaabdcacdcbdacdbcccbbdcbadcbdcbbcaacadbddabcabcccdbacbbacacaacdacdbcacbacbadacbbcddcaaaabacabdaacacddbcbdbbaddbabcabccabbabbdcaadccaaddabddbaaaaaaaccccaaadcdbadcdacabadabcdccdcababdaadcbaadaabbccdacdabbbcbbbacadacaabddddccdbaaadcaabadddadcbbadadbcbacaabcacdcbabbabdccabbdddbcdcdaadbdbbdbadcaacabdbaabaadcacccabaccaaccdabcddcabcdcbdadbbbcdaccacddcbbdacccccddacbacadacacdcdddcbdcaccdabcdbccbcdbbccabaccbcccbbcbacbddaadbddbdcdcdbbcabcbddbbbcaaacdddcacdcdcaadaadddbabddabaddccadadaaccadbabadccbcdbdabbdbdcadbabacbaacccdabcbcabadacbdccdabdaddccbcdccddcabdacabcddabbabcdaabbcaababcccccdadccdbddcdbadaaddcbabcddacdaaaaabdaabbbdcaadcaacddbbcdcaddbdaccbccdadaddabdabdcddddaddbbddaadaddaccadacdaabcdcbbaddcbaddbddbccadaabdbdacaccbbdbabccbcbcccdbdccdcbdccaaadbbbbddacadcdadccaacaaadccdcdbaadbccbdbdadcbccbcdcbacccdccaaccaaccbacbcabacdbddbdbbbbddbdbccccbcbcaaccdccccbbdadcdbbbbcdccddabcaddacdbbbcadaabacabbdbbdabaabccabddcadddcbcdbacbadcaabbdaacabbacabbacabaabadabbaaddaddadbdaadcaddacbbdadddbdaacdaabbbaaadcabcacddabdacbacbddabdbaaddbcdacabdcaaaccbdcdabbdcdaddbddcbbbdcdcddbaabdcdbdbccdaaabbbdccbadadaacbacabcbcbddadbcabcbadcadcacdbdbcdaacabdcadccadaaccdaccacbaddcdbdcacaccdbcbccbdcaaabcadbdcbbcbcbdbddbbbaadababaaddccacaadddcaaccdbdcbacbcadbadadcddbcdbcababdccababbadaaabbccdddacdbccbdbbcdbbdbccbdcdacadacbacccbcabbdcababdaaaacadabcabbcabccdddcbdadcbdbddddabcbbdbbdacbccbbadaaadadaaabdbbabbdbacbdddddbbbbaadcaddcaccaacdbcdbbddbcddcdbcaaadbbcabccbcccbcdbddcbadbacbbadcdaacdbbaccdbdabdccacacaccacbdcbddbaaaddaddccbcdaccadabddbadcaacbdabbccaaacabbccaddcdddadaccacddcbbabcaaacadbabbccccabbbdbbddabbdccdaabccdcbbbacccbdbcacdacdacdaccccbbacaddbacabbbaaaccdcdabdabccaaccbbdccbdbccaabcbabadddbadcababaaaccddccabcccccbdddabbcbdcddabcbcdadbcbdccbdbdabcabcabccccbcbaacaddbbbbbbababcbdcaccbcadcddaaacdbcdabacaaabadadcbbbbcbbcbbcdcbddcadadabbadabbdbadabbcbabdddcabbbaaaacabdbcdbdabaccaddccccbdabbccacbbcccddddccabbcdbbdacbbbbcdacbaabadbcabddbcdaaacabbcdbaaabcbaabbccbabdaabddbabacbcdccbcacadccdcddaaacababbbadccbbaabdbbcdddaaadadbbadccdbdabdbbcdddbbcbbaabdadbcccacbdcdccdbcbbaddccbccacbbdaaabcbbccddddccacbbbbcbaccdccdbdadadbdabbcccacaaaadaaaddacabadbdcbadabcdcbaacbdcccbddbdccbccccbdbadbdbcccbdcbabacbadccbdaaaddbacccadcadbaddabcbaadcddacdccaaccdddbabaadbbbabcabbbabddddddacbcacdbbdddcdacbbcbbdccbdddbdcbacabadcaccadbccdcadbdacbdadbcadbacdddadadddcdbabbbdaaadbbdadcabddbdbdadbadbddbddadbbcbbcadabaabcdabbdbbddbaddadbcaabbbacaaaaddabadcdbdcdbcabbababccddccdbcdcacdddccaabacdcddbdccacabcaabccddddcbaaabccbbadaccabcdbbacaaaccddacdacadbcbdaacccadcabdbbaccacbabadcaadcddabacaabcbabdddcdcabbaccabddbdbabcddabaabcddcbadbbdccabcacdbdabbbdaacacccbcbbbcabaabddbdaccccadbdccaadbbdcbddacdcdaacabcdccbbcbbddacbbbbcadccacbbabbaaddacacbabaabadbabacaddbdcbcddbddcdcbdaadaadbccbcbccbdacbddadcbcadbabaddbccbadabacaadcacdbbdbacaddcddcbdacddadadddbaaccbdabcbbbdacdbadcabcccdaabdbadbbaadbaccbadbadbccbbccdcbdcdaaabdccbdccbabaacdbabcbacdacdcaccdccbaabbbbcaadaaadcccdcacdbadadbbdbdbcaabbbcddacbbbbdbbcdacabbacbbbabaadbaacdcaaaaccbaddbcbcabcdadcbdcbabdddbbdcabacaabbacdbdbbabcbbacaacadbdbccaccccacddabcdccbccaaadbcbaacddcdacdabdbbabddcaaadaccbddbaccbddcccbcdabdcccdbbbabdbdcdcadaccadacaabacbdddcbbcbdaadcdbcaaaacaacddabdccaccbbbdbcaddbcabbddacadabdbccdbdcbacdaadbabbbcbbdbbcbacbaacbacdbdddbdabdadbddabaaadbbcddaaaddadbabdbbdbdabacaaacabbacccacaadbbddcaabbaaacbbccdcdacadbccaaacdacccbacdccbbbbbccbdbacdccdaddbcbdccccdbdcadbbdbaadaaadaabccdacdacadccccbbaadacabaadddbaacccaadcddddbacaabdcdabbbdbbbadbadbddbcdabbbbccaaaaabaacbbbdbaadcbdcbdcdbadabccccbbdddbcddabacabaaaacabdaaadacbaccadbcdcaacdabacaaabadaababcddbacdcaccbccddbcbddbbcdbadacbbccbbdcacddddacbabcbbacccdbaddbbdcacbbbbddadbdccabdabcddccbbbbcbddddababdbbbbdbadbadcbacbbdadcbdddabdcbbbacbbcabaacdbcdacddaadcaacddbacddcaccacdaaabadacbccbdacbcdabcbcdabdddcbdcdaacabacddcbdacdcabcdacdaaaacbabcacadacdbbaddccbadcdbbcabbbcadddadbdbcccdaddadbadddcccaacbbcdbbdabdccdcddddccaaacdcadccdcdbacabaacacdccabcbdcacbabbcaccbcbdaddccaabdbcdbddcaaaccacaadcacbccaacbdaadcbcdbbbacdbdcaddcbdaabddbabcddabaddddbbbadaccdcdbcdbcacdccddadacbaacaccbadcdabbdcaacbdabdcacbbddbccbacbbbacddadbcccbbcdbdacbdcabbabdcbddcbddadcdaaccbbaddcbadabbbccdacddbabcccbdadadddaabdddabdbdcbccdbcbdcbacbabadbdaacaddcdbddddcbabacacaaddcaacdbdbacadddaccdcbacdaaacbdbcddabbbcbddbaaccaadcbbbcccdcccaabdddcbdacccbaadbbdadcbaccdbaaabbddddbcaacbddaaaabbabbaabdadcccdbaadcbaaabbbadcaacbaaccabdaacaaccadaacabddbcddcbacadbdbdadcabdbdacadbcbcadddccdadddddbcdabcbbabadddabcdbdcbdddaacacaaddbbabadcadaaddacbacdcbcddccbccbadcdaccdbbcbbdaaaaaccbcdaacddbbdccadabaaabbadaabbbbaccadbbaabcbdbbaddaacabcdbcaacacbcdacadbbabcddaddcdaaddcbbcaacabcbccababbdbaddabcbcbabacbddcacdbbdbdadddcbbccbddddabcacdcbaccbbddcdddadcdbdaddcdcccaaccbcaadcbcddacdcdbaddddbabcdabcccbcaaccbbbdadcdbdcacbddcdbdddcccacacaacbbdccbbcdcddccdacdbbcbdcbdccacbccdacdbbddadccbabadbdcccdcdbabadbacccbacbbabcddacbabcadbaabaadddccbcdbdcbdccabbbaadbadbcbacbddadabdaaaaaababddccdbdbdacbacdbcdaadbccadbdacdbbcdbcbacbdbbbbbbcbbcdacaadbcabdccbdddbbbdbbdddbcbcbabacabdbdacdcbaaaacadcbdcaadaaaddadadbadadbbccbbaabcbbcdcbdbccdacdcbccdbbaddadaaccabacaccbacdadbbaabdbaaadcddabbcdacbadcbadbabdacabccbbaaaaabbcbbdbabdadbccddccbdaccdaaabaabbacaacacbdabbdbcddcbbccccbbbadbdabccddbdbcdacbcbcdbaacadcdccbddcadacababccadccadaacdbbabacacbcaabbdbaaabdbbdaabbabcdacabadcdbbacbabacddcabbcabccbdaaababacdaacadabcacadcdbdbacdddabbabbadabcbabdccaccdcdadacbcaddbbddacababadadddabccbbabbbabbacdacdaaaccddbbccaabacbdaccddccddbababcdbdcbbdbbaccaabbdacccadbabbcbddcccddacbcacdbaaccbaddadbcadbaddcbbaabdcdbbcbbbabbcbbddbaacccdbbcddbabcddbbabaabccddaccdacbcabdbaccadddbbbadbbacddcbbcacbdbdbaddcbabdabdabbdddadaaddcacbccacadaacaaacddaddaacdacbccbbcbccababbcaddbdcbdaccdadcdbbdbcaddcbbccaaaaabdcaccbbbcbdcdadaacdcddadddcbaccbbaddbbdbccbadbccaabbdaaaccaccaabddcaacdbbbbbaabbcbcacbbbbdadddadbacbcbbdbcdadccccdbdbbcbaccddabbaaaabbaabcabbabdddbaccadacdbaadbcdcbdacacccbbbadacacbacdabdabacbcaabdddabbcaddcdbcbcbddaabddadbaaabbdacbccdbbccababcdaaadbaaacddbddbccaaaadadbaabdaadacaacccbddbbbdcbbabbbbdcabcacacaccaaaccbbdddcddcdcbdabcdadcbabcaaadddcdacdbbcbddbbccdbbbadbcabbddddcacccbbbbbdcababbaccdcbdadbacdbdddcddccaadadaccabcccaaadddbdbcbadaadbdacabdccbbaddddbcbdbccdaccbbdcaacbcabaacddacbacdcdccddcabcccdabcccacdbdddbaadaacddbbadcbabbcdbbdbcbdbdcbadbadcdddcbdcabaacccdadaaabcbdabbabddcccdccbdbadcbdaadaacddbbadcdbbcdbadacddaadbabbbaadabdcdddbbabdacddcdcdbdbdabcdcddbdbadcdbbcbbbbaaddbdcbccdbcbddbcbaaacdcdbbacacddbdcabdcdcdaaacdcdbbabbbcbcccabdccacbbdaaacbcbbbcbcaacbbacababacbadacaacbbbcbdadbcdadbbdcaacaccddbbbbadbdbaadcabdacbddadaabbccacddcbbcddbbadabaadddbcddaaddbacccaadccabcaadbaacdddcbabaddaacaabcabccdabcadccccabcbbbacdbabdcbadabbdabaaaadcabcbcdaccbccbccbdbcbbacdbadacaabdbcaadabaccadacbdadccdacbbbbacacabbabdbccccbcaccdadbccbbbacdcbdacbaadbdbdadcaacdcdacabbdbdabbaaacddcdbdabccdcbabdbbbabbadcaddbbcaaccccbdbcdbbddbdcbcdcbddcaddcbcbcddacadbbdbbcbbaaadbadabcadbdcdbaadccbbcabcdbcbdacbbabbaabbacbbacbaddccbcbadddabcbcbcdadcbbdbdacdbadcadacbcddadbdcaabdbbdcccbaaddbbacdaadacadaaddbaabdbbbcddbcaacbbcbcbcddbdcaaaabccdbcddcdcdcacadbcababdbabbaabaaaadbabbacbdccaabbbcbbcbdbbdadacadabbabbddacabcbbdbbadcbdacddcadbbcbaababacbccaddddcaacdadbcaabcbbcbcacacaddcaaacabdbbbdaddddcdcbddaaaabcabbcdcabdccadaddcadddcabcdcddcbadcbbdcbaaacbcddbddabdcacabaabdaddbcdaadaacddccccbdbbbdaacbddccacabdaaabaabbadccaacaacacccacabbdcacaccdbcbbccbabdbcbaddabccaacdbbcdddacbccbdcaacaddadaaacbbadbabdcbbcdadddacdcccbddddcaabccabcdbcbaaabcbcbdaabdbbdbaccacddcddabbbaacbdcbbdbcacbbbbdbdcdbcabcbaadcdbdbabdcacbaaadddabccddcacdacaaddadabacddbadbdadacdbabcdcaadbccdccaddadbcaadcdabdacbcccbcbbbabaadcabbbccdddbddcdbbaaddbddcbbcdbadcacddcbdacdacbccacbcdbccbcbbcbcadbcbccdbbccbcbdabdacaadcdccadaabdcccbbcddadcadbdbdabdbadccdddbabcdbadcdabdcdcbadddbdbddcbcaddaacdcdbadcacbdbacdaadcaddbdccddddacbbcabbdacaabaacaaadacabbcbccabadccbbbbabccbcadcacdddaabdaaccbbdbbbaccbbccabaaccdbccaadadbbbbcabddcaabadbddcadbbcdadadcbccbdabaddcacaacdbcdaaadcbabbcccaabbcdcbddcdadbabdadcbcddcbcdbbbbbdbacdaccdaaabcbcdcabbdcccdbddadbaacbadbaabbacadacbbdccbdaddabbbcccdbbdbbacdacdaacaddbccdacdacbdcbaddacbddacccdccabadabbabcbbcacaaaaccbdaddbcddcbbaadacdbacbdcdbaccabcadcaadcaccbbaacbadabccddacabacdcaaccacbcccccbabacbabbbcadadaadcbbbdadaadcdbabbdabbdbabbcaddbbadcdcdacbbadccbbdabbabdadbbbabbcaddccdababbbbaddadbdaaadcdbddbcbdadacbbbdddbbabaccdcdbcccddbaddbdbbbadccacbacbabadbadbdbdadcacbabababbdbcacbdcdacccbcddbbdacaddaacaabdaadacacdadacbcdbbcdadaccdadbbcaadcacabacbaaccddcbccdcbcbbbcccbccaaacdddaacbdbbccaaccddadbcbbcdbabddacbcaadddacbccbacaaddbddccdbcbbbbdbcbccadccccadcabdcabbadbdddaaadaabdaaabbadacaadccddadbbcacdbbcdababdbbadbbbbbabacabaadadcbcdccbbababaabbbdbcabdddaccacdbcddaaaaaccadccccbddccaddddccbcabcccddbbcacaddbdbdacacdbdbadddcacbcbdbcbdadcccabacccbaddadccaddadbccddabcbcbddccccbcbcaabdbdabbaaadadcbabcadcbcbccaccabccabcdbcabcdabdacaacbcbadccdcdcbdaddbadbbdddaabaabcdaaaddabdccbcbdcbadbadccaddddaabbdcbccbccdadbcaacbdcddbdccdcadabcacabadbcddbcdabbacbddcacaaddcbdbdbaabaaabcbdacdadbddbbcdccdcbabbbcdbbcbacacbbabbdbaaadccbcddcccacdbabccbccbdaddaaadbabdddbdccdddabdcddbcbcaaddcabbdbcabdbacaaaaaabbcdcabdbdaadcacdbccaccacdbdbdaabdbcdccaaccdbccdbbcdbacabcbccaacacccddaaaaacddbcdbcdcabdcdcbbbadbabccdbcdaacacaaabaabdddadcabddacaccadacaacacccacdccbabdbdaabbbdcadababbbacbbadbbaaaaabdbdabdccaadcabdcbdddbaaccacddbbcbbcdddcdcadacdcbdbbadaabbababbaabdcdacadaaabbcccabcaccbbbbbacbadcdddddaaddddabbccbbcbbbdadccbadccbcaacddcccdbdacadaadbbcbdcacbddddaabdadbdbacdcbbaaacdcddabbcabbcbcbcacddaacdabbcaaaacdadccbaaabddcacaddacdaabbcccaabcaabbdcdcaadacaddbcddccbaabbabbaabbadacbdabacabdadaabdababddacabdcbddbcabadaaadddbdaadccbbabddcbccbbbcdbabcadccddbcccdcdcbbdddadccadadbbbdddcacacadbadcabddbacbbbadcbaabaabcbdcaabddddccdcbdadccbccdabbcdbadcbadbabcbcdaaacadbacaadcabcdbadaabccbbdcbcccbbbbcbcbbacbaaccabcabbdadbbddabdccacaccaaccbaacaadcaaaaadacbbcbdbdbcabddbabcdbdbaabddaacccdddabdcdabdaaadddababbdbaaacdabadabcbbbaadbdbacddabccdcbdbbadbcdcdcbccbcabacacbaabcbbdbadbdcbcddbdaccbcacadcdcbabdcbaabcadcadadbacadaabcaadbaddddddadddddbaaabbccdcabdbaabcacdaadababcbcacbabdaabdcdcddbdcadbbdbcdccbabbbdbabbddccbccbabdcccaaadaadbbcdcabbbcbaadacbdccddcabccbdaacbcbadcdadabdaacbaadaccbaaccacdadabbddbddbbbcaabaddaacdcccbdbdbccaabaacadddaabbbadddaabddbdbbaaaacabbbabbadabcacaadadaaaadbdcdcadaaadacbbccaccaccbaaacdccdddaabadabaaaacbddaaccacdccacdabcddadbcdbacccddcabddccababbccdaacbabbaabcacbacbcccbacbccddbabccddbadaddadddcaaabacbaadbdabaadbddccadaaadadacadddbcbaddaaccabddacdccbdbcddaacadccabbdaddddbbbbcbccbdccabcaabbbabcdcdcbbdabdacdcacacadbbcbabdbbcaccbabadacbacababcbcdadaaddbbdbccccabcdbaccbccdaacddcdaabbccdacdcbbcdbcbcadaaccadadbdacdbcccaadccddaacbbacbcaabcbcaaccbabbabcccbccacbccccdacbcabcdaacbabdbdabbbadabadcdddacadabbbaacaccbcdccabdbcdcadcadbdcadcccabacabbbcdadddddbbdacbaccaccabacadadacdabdbbaacdcdbdabdbccbabdaddaaaabbcbcababbdbbacbbcdaddbdbbcaacddbbdabddaadddddbabdbdadddacbbcdbdabbacacdbacdbaabdaaaacdbbdbdadddcddadacdcbbddbccbdadbbadccacbbadbbbbbbcddaddabdbaccabdaadaccbcdbbaccbabdbdcabdbbbaddbbbcacbbaddccabcabbcadcaadcbdacaccaaabaaadbdddabbcbdbbadacaacaadbcaadccbdbdbccbadcddbbcdabadbdbabdadadcdcbcdcdddabadbcabdcddcaccbccbacccbccaaddcdbdddcdabccdbdcdacbabbdadabbaacdcdaccbcbaccaaabbaaccdbbaacdddcaacdbdcabddbcdaabbabcbddbabbdaabbbccddcdabcbbcacbabadabcabcddbbdbcdbbacccbbcbcacbcbcdcaadcbbbabcdcadaccadccdcacdbcdccbcbcbabadcaccbddcadbdaccaaaccadacbbccadbbdabbccddddccabbacdbccabcccdbbcaaddbbdacaabdddcbddcaaccabbdabccbacdddbcdbdbbaddbaddcadabbbbccadbdacacbabdcaadbcdaaccbccadcddccdaadbacabbabbdcadbadaddcaaacbbaccaadbccdacdcdbcddcbaaccbbbbcabdcbcadcbddacdddcdabcdbaddccabdbccbcbcddaddcdcdcbbdcdabbccbbddbacdcdbbbacccddcadbbdaaacadbccabbaadddbdccbdddddcddaadacaaaddbcbdccdcdbbccdcadcadaadababddddbddcddbccdbdabcaacbaabdcdadcdcbbdaabccacddbaaccdcbcdddacdbadbcdcdcdcabadcbadbddcdcbdaccddccbacdaaddbddbaacbcbdbacbdddaacacbbdaaabdbccbddbbcdcaaaabcccaacccabdcbabbacddbbbcbaacbadccdbccaacbbcbcdaaaacabbdcdcacabbddddabdbcaccccccacaaabcddacdadbadcbcbdcdbcdddaacabdcadcabdcacbaadbbdccbbaacacadbdababcdcadabcddbadbddcaabbbaddbadcbbdbcbccdadccadaccdcdbadcdcdcdaaddcaacccdbddadbdaccbdbacccddaaaccacccccdaabdaaccbbdbabdaaabcdaaaaaacdcbbdaabbbdbdabcdcddbdcbcccadcbbbdcdbabbbdbcdccdaaadcdbaadaadbcbaacbbcbbdbbadddcbaabdddcddcaadcccbabbddbabcbdcababbacbcbcbadcddbbdbbdcccaaababdabadcabbcdccadaabbdccaddbacbacadddbdabaacaacbcbcbbcbccbbadabdbaadabccbddccdcacdbccddabdcdddcdaaacddbcccaadcacaccabddabcbacdaabbbaabaccbadbdcddbcccabcdadbcdcccbdcbccdbbcddaddccdcbadddaabcacadddbdccaacdcbcacdbcadcbcabdbbadbadadbbdccdacbddbaabbabcadddcaaddccdcccddacbcaccadcbcbaaaaccdaccadddbadacdacbbdaccdbdaacdadcbbcbcadddcaddadbbcdadcdbacdcbcbbdabbbcbbdbbbcccbdacadabbbbabcabdbabccaccdcaabbdadbaabdddaccdbdddbccbbdaacabddddaddbcbdcbcbbbbbdddbaadaccdbcccabdacddddaadcaacbcccabcbbabbabbabcdadcaadacdbbacbabdbaadcabbadadbbcbadcddaaccbccdcccdcacadbdddaddddbdcabbcaabadbdccdbbcdbdacbbdbaaacbbccbddbbacacdddabbbcdcadbccdadadbbdabbcaaacadadbadaddadbdbadcababadbccdbbadaadacbdbbaaccdbaddcdaadcccabcdbddbbddbacbdbcdaddacddacddaddadcdcaaddcacbadcbdddadccbcddcbbcabaddababbdcdcddbbababacddccdcbdaabcddacdabaaadacacbacbcaaacbbcbdbabccccdcabadbddbcabcbccabcdbbbcacbcbdaadddddcdcdbccbbacacdcabcccbcbbbcbcbdbdddaaaabcdbadddbaacbdacbdddadbcbdaccbcbcbbddcdbddacaddaddcddcdbabcdacddbdacabbddccdabddccdadbdddddcbacdacababddcbbbccaabccbbbbbbabdbcdcdccccbbdacbbadacababbbaaaacadbccddcddbaabcbcdcdabbdbbbcadacbdacacaabcccadacabcbcbccbaaaccbacacbccadabaacaaaccabadcaadadacababddacacaccdadcdabdcdbabcacdddbbcbcccbcacbbcdcccaacdacdccbdabbaadcdcaccacbcdaaaadbddddcacbbdcdbcbdddbaaacaddcbdcdbbcdbdabaabdcddbacdddabdbdccabddcddbccdabaacbcbbddcbccbadadcbabaaadbaabbabbcbdbaaabbcbabcbcacbdddcabbccccccbdbbcabaabbaabacbabbdccbdcaccddcdacaddadabbbcbadcbcbdbcdadcbacacbcabdbdbacadddbbbaabbddaaddabacdcbdadbbddaabbbbaccaaccbccdacadcdbcabdcbcdbdbddaadbddccbccacdabdbccbaadbadbcabacbabbbacabacbdbbabdcdacbdcdcbdbcdddcdacccaacbabdddcbbcbbbdadcaabcaccbaaacaaccccddcdbbcdcdbdbacbbdcaacbdbaaadbbdaaadcabbbaababcbcadbdbcddbccadddcbbadabaddbccddaccabcbdcaadacbbbcbcbbacdbdddbdcaaadcbadaddaccccaccddbbdcadacdacdacdaccdabddabdddcacababaddaddcdbbcddabdddddbbdbacacdcdaabcababacdcddabacdcbbadbbdccddbdbabcabcdadaacccdbcbbccddbadddabcaadbcddbcdadbaaccbbdbcacdbdadbdcbabcdacdacabacaacabdcaaabadaaddadccaadbcbbbbdbacdababbcaabacbbcddabbbcadccbabacadddbbadcbbadbabdbbdbccbdddcdadadcccaabdaddadbcdddccbcababaccacacbdaccbbdcbcdbbacabdbdcaccdcadcaacabcaccdadabdbbdaccaaccbbbbbcdcdacddcacccdacaadabacccbaabdabcdcbbbdbbcaabdbbdcdcbaccddbdcabacaabddbdbadbbbbdbacccacddccaddaccaabccdccaadccdbdbbcdacadadcbdabccaababbadcbbabbbbcbcdcbdcdbaaccbacbcadcbdaadbbcbbdbabcbcbbbdbcdcbaddbdcbcdcbddcbbbdcbcbbaabcaadbbbbdbadadaaccdbdddddbbbcdbccbaccdcaaaabccacaabdadcccbdcabcdccaaddadbbcccbdbaabccccbbdddbccbddcaddbbcadbbdadaccdbadbadcdababcbbbbdaabdccccabddcbdbdbbbbabacababcacdabdaabcdcdacacbccacdcbcbcbacdcbddabcbbbcccdbbcaababddddcddcbaacabaccaddacaabaaddabaadddbdabbbdbabcdbcddbbdacdbcdcddccadaaadabccacababbcdacbadaabbcdacdcbbdaaadaacababacccababbbccadcbccbbadbbcadadadccdaddccdaabcddbcacddababdccdbddaaddbbcdbccdccacadcddbcadbacdcddacddaabdababdacdbdbaadcdddadbbbbbdddbabddcadbcbacbadbdcccacccacccaccddadabaadacaadccbdcaaadadbddbbdcbccbabbcbadadbcdbabcabacabbcadaacaaaccacacabdcddcadcbbbababdaccddacadbbccdaaadbcdacbbdcdbabbbbaadbcdcbcaaabbcbbddbbaadcbbbbccbaaadaabbdcadaccdccabaaabdcdbccdccacdabbcabbddbdddadddbcbdcabadcbcddddcdadccdccaccabdaabababdbcbdbcdaaddbbccbcabaaddbccacadaabbccbcdbdbdbacdacbbaccdcbbacbbabadbccdabbabcdcbcadbabcbcdaccdbbcdbcbcbaccbbbddcccddbbbddaaddcadbadadaabdaccdabacdbbadbadccabcabccdbcbaabbbbcdbbdabbccdaadccdaddcadbcabbccadcabccbddababdaabdcddadadccdbabbacbccdbddccddcaaddbddabddaccccdccccdcabbdddcbaadadacdacdcdbcadddcbbbabcdabbbcdcddaadcbcacdacaccadddcbcbbccadcacddbadabbadcaacbccbbbdabcabccddadbbadccabbcdbdbddcbacccbcaabddbbddcbaadacadcdbcaccddbaabcacbbaabaddcadadbcddddbabadbadccdabdcaddadcdcbcbabacdcabadddacabddacacdaabdaccbdcddcdcdadddbddddbcadcaacadcbddcabacbdaaacbaccbabdccaccbaabaadbdcbbbdbcbaacaadbadcdbaaccaccddcbaaaccbacaadadccadaadcbadabcbdccaabacaddaabdadccddcabcbaaabcbaaadadddbddbdcdaabcaabadaaaaddddcdabcccbadaabcdbbbacbcbcbbdcbccbabddadaddbadddbabbadbbcaabbdaabbbccabbccadcbccabbbadcadaacdbabccddbcccdddddaadabcccbcdcbdcaadadbbbcccacccaadbcadcddadabcdcdcacbddcaabccbbcabcbaabbbbacbaddbdaaaaabaacdbcbdcbbdcdbbdcdabaadddddcbccdcaaccbadadbddadbbdbcdaddbabadaabcadaacddadccacacccacacddcabbacdbabcdaccadcccababbbcdbccbbdcdabaacaddadbccbdbbabccdddccdaaacbbbbbccabddacbaccdccccabcdcabbdcdadbcbbcbaabbdcddbdcbadcdabcdbaadcbccbcbabddcbbdadbdbabbbadcabbadbbdadcdcccaaacabbadbbcccbbbdcbddaddaaabadcbcacacdbdcdbcadcbabcaaabcaccdacaddbdabcdbaaadaadbccadaacdbdabadbbcccbaabbabcacdaddacbacbccccbbcccadcccbadbbabbbaccbbcdcddbbdcbdabbaadaabbcabbbcaaccacacadbdbbdcdccbcddadabbbccdddccdbccddcdcdbadbdbcbddcadaabddcbabbcacdbdbadaadbaccaabcabcbbccaabaadddcaabbdcaaabdcacbbacbdbddcbbacaadcaacabdbdcbccaaccccabaccbddcdddbacbcbccbdbdadbbcdbdcaadacacacadacddcaddcacbabdbacbdcadcadcaaabbcddcbddabdaccacbbcabcbdaacdabdddccbcddacbdcacbadcdadbbdcacdbabcccbbddcacdacddddaacaddcadbadccbbbddbcdabcaaccbadcbcddbbdacadaddabcbaaabcdddaacacbcdacdcccacbbdcbcdcdbaabccddbddcdddbcbddcdbccbdbdcbddbbdadaddccdbbbababccdbbccabdcdabccabdaccbcbbbbcacaadbcabadcccdaaabbbadbbaaabcaaacdccabaabddbcaabadaaddcdadcaacbbdcccdabcdaaaccadcacbddacbdcaaacbbaaadcbbdccadbadcdbccbcddbbdcccbbccabdddcdddbbdaadaacdbbacdbdcdbaccccbcbcbabdbbcbcccbacaabdddbccbdaadcbdbdabdaacaddcacbdaddaaacdcbaacbdcbccbbbdabaacaaaabcbdabdbcabccbacbacdadaccbdcdaabcabdddabcdadaccdcbddcccaccccddcadcbbbdacccdbacaacdadbcbdbadaccdabcccddcbadabbcacbaadbdacbbadcadddaddbacabdbacbaacddcaacaaabcddbadbcdcdcbbcdcacaaacacacdabdbbacbcbdadbcbcbbbaccaddbccadaabdbcccdcbbccbcbbdbddcabbaadbbdaaaacbacbacddcdbcdcdacabdbacbacacccbdacabdaddbacacaabcdbdcababdabcabadcdbadcbcccbcbbcccdbbcadadcbbddaaaaadadddccabdbbdacbcaadbadcbcdcdbcbbcbdabdaccccaacdbcaaaabcbdbabcadacdbcadddbcaadacacaabcddaabdabbbbacbccdabddabcaddcbbcadbbbdadddacaccbadbcbbcbbbcbaacdbbaacacacdcdaabcaddddbabaacccddadaadaddbdcdddaabbccabdbbcccccbdcadacdbbcddcddbadccdcddccddacccbcaabcbdaaddabcadbcdccbddccadbdaccacaabbdbadabacacadaaccabbabdadbabcbcbccddbcbddacdcdcaddbadcbdadaadbbcabacaaaabdcdaadcbbddbdadacacbaacbbdbadcbbdacbcadbbdbabcbbdbaaaaacccaadbacbddabdbcacacccadbdddcddacdcbbddcddadccddddbdcbcdbdcbdddcddccdccddcabddbacdcbccbaaacdabdddbdbdaacddbcdbaaacbcdbcdbcabcaacbbdadccbababacadabbaacccdadddbababbcdaddbcabbacbbaabdaabbbdccaaacdcabdcbdaadbccaacbbbccaddbabacdabbacbcaaabdddacbcdcdbdabbddabddbaddccadabaccbdcdbdbdddddccbdaccddcdbbbccdcbabdadcbcbdabadbdbabbdaababbddddbcadddabcabaabdaadcddcbadddcdbbddcccbbcbadcbccdbbcddacbaabbdbbbbbaabadbcaabdadbdcaabcccbbababcccdadcabbdbdcbccadccbcdcbabaaddbbdcbabaabdcacdadddccbcbcabbaaacbdcdcbacdaddbcbcbbbdaacdddcaacdddccadacabacdcdccdaabacabbabdbbcdbbcabcdcaacbaaacddacdcbadcdbcabacbcccbbdabcdabcacbbadbdddccbbdcbabadadadbbcbdccacadccdcdddacdadacabdaccadcbabccbadabcadacbaccacbbabaccbadbdbdbcdbdcccdbdbabcbbdacbbbcaddcdbcaabccacbbacdcdbccdcbbacccccddadcddcccabcdbbcdcbcbdaaddddbccaaccbaaacbcacbdbbcabcacdabbcddcadadcbaadcdbdcdaabbdcbaaddbcdaaabbcbdcbbacabcdbbbbacdabbadddbacdbbaccacabaadcabadddccbcbdbcdcbdcbcdadddcbbdbbbcabbbdadcaddbbcddcdacdadbbbbccaadcbcbcaaabaaddcbbadbccccbbacdaccbdaaacacccbdacdbcdacacdbcccabddbadabaccdcaacaabbbdabcacbcbccbacbacdabddabcbbddadbbcacacdcadcaccabcbabdadcbabcaacbccdaabdddaddbbdabbdcbbbacabbadbcdbbcbadbdbabbddccacbacdcbaccdbddcdbbbccdbaccdcbbbdcaaacbddaabdadadccadbccccabadaaacbaccbbabcbddadcdddadbccacbbddabaabaacdaadddbccaadabccaaaccbddbdaabbdddccadaccddbbdcddddbdbccdbcdbcddcadbcbdcdacbbdbaadcdddadabdcdabdabdbcbaacdaaabaacabbbbbaacabcdaadbddcccdbbadcadbbadbadaaaddbacdbcbcddbbccbabdbbbccaaabbdbbdcbbbacacdaddcbaadcbcbcbcaddcdbbbabcaddbcababdccdddadbcaabaddbdcbccbcdbadaaccdaaddbabbcdccdcbadbbdbddbdabaacbddabddcdcbddddbcaaabdcbaccaacabcbddbbbaddcccbbdabbbabccbaacdbbcbdbdbcadcbbadbdadbaccbccbadcdaababbbbdaadbcbcabadadcddcdcccabcabddbbcbacddaaababcaaacddbacababcadadadcdcccdbaccbdaaaaadbccbcdabbabcaddddcddbacdddabdbbbbdbcacbabacdaadbcccacdadccbbacdbabbbcaddddaacdabaaadbcbdbbddbbddbacdccbacbbdbdbdbbdcbadcaaacababbababacacbadcddbcbdacccbddacbbabdbabdddcbddacdbabaabaacaccbbbcbdabbaabdddbbdcbdccbbbddbbbabdddacdcccbcdbcbcbacdbdabadadaaddbcaabacccbbabbccbbcddcccdbacbbcacddabcacaccbdaadbbacbbabaadbcbdcbacbddddabcadcaaddcabcdccccdcbbadddbbadcbaddadbccdbdccbdacbabbbaccbccbdcabdbcaaacbaaaccccaabcaccaccdacdabbcddbbccbbaaaadbdddbdacddcbcacdcadaaadcbdabbdcccdcdbbbdaadaacdbaccbadcbabddbbbdbbccbadcddbdcbccbcddaccbaacbacddabadcabaaacabbadccdccbadbbaabaddbaccadaddcbdcdbcbdccccdaadbcdacddcbbbdaddbacdbddbadaabbbdaddddcbcbbacaaccadccbccbdbccbcdccccdbbbacdddcbabadcaabcdabaacadbcbdccacadbbbbdddccadcddbabdcbdbdbccbacbdbcdababaadabacaadacbabcdacbddcdabcdbbcadddcbbbbadcacbaddaadbcacdadaaabbddddbdcbadccadbcdabddadaabbddccaadccdbabccccddcddbcccdbddccbabbabacbbacddacbcaacbadbddacaccadaddacdbdbdaaabdaccdbddddaccccbddddcadbbdbcadccbcdadbdaacdbdcdcdcdccacdccdaababdadcbdacacacaaaccbbbaacbddababddcccdcdcbadabdaddbccddbddccccacdacddadaddbbbcbacdcdbccbbbabddbccbabdbccccdbcbaddbdbdddccddcbddadbadcaacabaccdddbbaadabcdbdaaccbdacdcabadcdddaabddbacaabbbdadbaddabacadbadaadcacccbdaccbaaadbbbdccabcbdddaabbadbbaadcbdcabdabccabaddbbbaadacdcbccaaababdccccdbdbbcacadadbcacaadbdcdbcdcddcabadabcddacbcccaabcdbcbabaadddbcbdcdaddccbbbbbbcdcdbdccbadbdadcbaabbacadacacdccaabbcdabdbbbbadcbadaabbbdabddbcbdabcdbdbbdcadcdddacabcddccdbcacaaacbaaadcbadadbbcbadadcccdaddbbbbdbdadbaadcaaadcbccbccdccbccbdbbabacadaaacdadcbddcacbbdaddcdcaccdddddddacbdccccadddbddddbccdddbbbdbdbcddbccabbbbcccbbbababacbbacbdaddcdbadbaaaaacadbbdbdccbcbaaaabbadabdacacbbdcbdbdbcaccccbbcaaddbcccaaaaabdddacbdbbbacdabcbbccdadbdbbbccbbdabadaadbcbddaabacbddbdacdaacadbbabbcacbdbdbbbcaaddaabbbbcabbcabaadbcadcddcdcacbccaabaacddbdbadcccccdacaadaabdabcabcbdbabdcaccdcbaacadcadddaacbbdaaccabccbcbddbdabbbdaadabdddaccdcaadbdcdadbdbddacababdaabddbbbbcbdbcbcddccadcdbadbadcbbdcbcaadadacbbacadbcdbdadacdcdcdcabdabbdcaacabdbbaccbbbdacbacdbdcdabcaabcbdbaddbbdaabaddddbddbbdbddbbcdabdbcbcdddcbddcaacbdbcdbcadccbaacdabdbdcabbdcbdaaadbcbbacdcbcdbdaccdbabbbdaadbddcabbdcdcbcdbabababddcdcbcbcccacacdaaabbadabbbaadaaabcbcbacbabddcaabdddbaaabdcaacccccadcdcdbbabcddcbbbacaadadcdbbacdddbccbaadbdccdacaacbaaddaabdcdbaccdaccdaabbaddadddabdabcaacaaaadccdabcbbaacacdadddabcaddadbbcabccadabaccaddadcbcbbbcabbddbccbaccdabbdbbaacaadaccabccdcacdcddddddbbaabcbbbbcdaaddcbbaacbdddccaaccdccccacccdbbabbbcaacccdabccddcabadcdbacbcbcddcacbcaacacbdcbbcabccdacbbbddabccaabaddaaadcdadcaabddaccacdcdbdaadcbaacbbdadbacbacabbadabdcccccaccbacddcbbdacbdaabbdabaadccbcbdaddaaccdbabbcadcccbadbccbccccbddcaccbadacabddccadadcdaabbbdacbcaaccbdbbaaddacabdadcbabddcbcabacababaaccccdcbacdcdbccacaabadadcddaaadbdadddaaacbcabccacdbcdaccbbdacddcdaacbbcbabacdbccacbbdaccbdabbbcbbcaaacacdcccbbabdbadadcdacaccabadaaccacbbcdacaaaabddcdbbadacdbdbddabaaaccdaaaaadcababccbdcdbbaddbbabbbaacdaddbdcbcbacbccacbcbbbdbcdaabcdcbbdaaddcabccccdabdacacccaaacbdacddabcbddcbdacbaccbaccddddaacbdbbdccccdbacbccdcddadccaabdaacdcdbabaacdcaddcbdaaaccaddcacbddcadbaaacddccaccbaabbcddabbcbadcadaabaaaacbcaacddbdbcddacbacdcddcbcadcbaabdadaacccacdbbabbcdccacadabdbcbdcbdbdbdddbbccddcaddbcddcdaddacbbcbdacdacbacbbbbbdddadcdbbdcaabbdbcdadbbbbbbacadbcbbbdcdcddcacbdbacacaaabcdcccbbaaaddddbabacddcdcdbcdbbaadcccacdbdbaddbcdcdbacadbacadbcddccacbadccbcccbaabdabaaaacaacddaacadabadacbbdbcacbbcabdbdddccbacbbcbaadbbddaacaacadcaaaddddcdbababadddabbadbcccdaabdbcacbdaadbaccccdccbdccbcbcaacdacbadddbdbaddbcddaabbbcaabcdccbdcdbaccccbddccbbcdbabacdabdbcbcbccddbbbadabcdacbbbcbdbbabccadcdcaacbcadcdabaabdcadcacadcbdacacbdbaaabadabcacbbaaaaaddbdbddcadcadccdddddbcbdcddbacabacabaacdbadccadcaadabddacbbcabdcbddcabbbbcccacaadcacbdbabdabcbabdcbdddacbbddcadbdbcaabddabaaadbddbdccdacabbacdccadcdccacacbbcbdbabdcdaabbdaaabadddbbcbdbbadabdbaabcbaaadbdcaaaadbacdcbbcccbabacbadbcacdcddbcaaabdbabdabdbaadbaddadbcccddbadcabdbcadbaadaabcdbcaadbcaccccdcbabaacabbadccddbcdaacbcdaaabcdabacddabacabcbbbcbbcabdbdbbbdabbbbddaabbdbdaabacbbcbdabadcbcbdbdaccaadadccddabcdabcabacadabdccbabbbabdcdadadbbbcdadbbdbbcdaacdadddbcbddaccabbdccabdccaaddacccacccbacbacbbbdbcadabbabbcdbbcacdcabbbaccbcbbdcdaadbdcabbacddbabbcddcdabbcdccdaaadbaadddccddddbcdaccdaaadccbacaacdddbdaddbcdcddbacaabdbcaddcaccbadacdbbdcdbbccbcdccdddacaddacacdbacccbdbdcacaddbdcaacabcbccadbbacadccadddbaadaccabdccaaabababddbabaabdcbccdcdaddabddbcbacdbcbbacdccacbbcaadabccdbbcbccddadbddcdcddcccbacdcabcccadadadcccdcdbadcaacbcbaaadadcabbabbcbabcdbbccdcdbaccdcacdddcadabdbbddcabbbabcbcaabcdbdccdaaaacadabbacbcadcbdacdbaddbaadadcaadcaadcdcddbbdabddddcdbcacacbbddbdacacbaaabbccbddaccbdacacbaddadbdbabccdbaddcdcdaccdbadcbddbddccdabcbacdcbaaabcdddaaacdbcccccdacdcadccdacbadbabbbddacbbabdcaadabaddacbdacaabcaabdbaccbbbdbadcccdddbddddbabaabaadcddbddbadbdadacabbaccaadcababdbbbdacdbbdbcabaccbaadabbbcadaabababdaaadddbbbcdbcbcdcadccdccbbacbdccddaccdaaaccadcbaccdabcacadddccdcbcaccbbaabdbcdcbaaccdcdadbdcbddcadabcbdcdacbadbbbaccaabcddbacabcdbbbcaadbaacabddccaacbacccacbccbbbccdbbaddbadbaddddacaadbbadbdccdbddacaddacbbcacbdcccdddadccdaaaddcbdcabccbcddcbdddcdddcacbcbdbcbcdbbcaddbccacbdcacdbcbcbacdbddcaddadaaadaacabaccadcadccdcdccadadabacacddbaababddbbabadcdbdacadaadadbdaccbaddcbbcaacbacbbbbbcdacdbdcabbccbdaacddbbcdddddabcacbccadabdabcabbcdddbdabbdccbcccadbdacbdaadcabdabdcadabbcaddcaaccaacbbbbabacddcacbbcaddbacdddddaccacddaccccbbddcbcbacabbdddcaacdccbddcdabcbaaddcaacaadababbddddcababccbcadadacbbabdbcdbdaaaabcddcaaddddbabaabddaabdccdaddbacabbcbaacdbdddccbaacaddacddcadcddcabddcbbbccbcbbdcdcbbaaddbbcccbccbacabccadaabadbbccbcddbccdaaacddcdbbdbaaccbdddacacacbaddbaacdacbdbadaddbcbdbcccddcadbddbcdbbccdccaaaddbbdbcaabcabdbdccddbaadcbabaadbbaccdbabcdbacaccbaddadabdbdacdbcddabbcdcabcdbdddadcbcbbabdbbccbddabdaaacbaacdbacbcdddcccbbaaadbcbbcadcdaacdadabddbaabacbddbabbacddadbcaddababdaccbbddbbdaacdacdbaabdaabbcbcaabdccbdcdabbcbcaaadccdacbdbbbdaccdddcaacbadbabacadacdbbbcdcabbaabadbabbdcacccbbbbbacddabcdbdbadabdbadbbabdaccbcbdcbbddbdabcbdbabdccdcccaaacacdadccadcadccbaabcbbacabdbcabbabcdaaacaccacbcaabdacaccabbbbccbbddccbdbcbbbadaadaddccdcabcbccbadbdcbbabdcacbadddacdbcccacbaccadbdcabccbbcbaabdcacbdaddddbacddbaddccadcaaaaacdbbcabacddcadcdacbacccaadcadbdadabccdabdbaccbbddaababccaaccbacacadbaaddacbbddbccddcaadbbbbaacbabbdcdaaaddacacaccdcbbccdaabaadbbabcddbccdaddcbbcdbbbbbddaccdcbddaddddbbbbabbdccbcaadccaababddbbacdddbacabcadaccbcdabadbacddbcbbdbacbcccdbccabddddacdbbcadccbdcbbadcdbbabcccbdcdccaaccddbdacacddadcadbbdbadcbdaaaadbdaacabcbaababaddbdbdcabdaadbddcaccaacbbbdbccdadaddabadcdababdddbccaaacccdcbdddbbbcaaaabaaadccdccdababbadbadccacadcabaddcaccabbabdacacadbdbddaabadbacdbcccabcccbcabccabccdcdbccacbbdbabacbccdcabaacdaaadccccbaacacddbbdbcdddadbcbbaaaabdcaabbddbdbcdacabcdbdcdbbaabbbbbddddabcbadcdacacbddcbcddacbddbcacacdaaaabdcbdddcbcccaabbdbdbaacccbdbbaadccdadcbbbddadbddadcdbaabdacbccdbcddcbdbcbacbcdddccdbcdcbcadcccdbcbadcbccaabdcaddbbaddcdadabbcacadbbbdcabcbbdabacabddcdaaaadcccaaccaaddbcaccbdcccdbcbabdbabdcbababacbaddcbbcdbbbabddddbcacbadaccaaddcadcbabadadaacacaccdaaddcdabcbcbbbabcdcdddbbaabaccccabbcaaacdadddadaabddbbbdbdcbacdcbaddbdaccabadaabadadcadbcddccabdcccccbadccddcbbbcddccbdaadcbdababbdcacddbcabddcaddbabcddbbcbabdbbabbddcddccbcbaddbddcaccabdcababdbcbbabbababccacbddbbbbacbbdaaddbaddadcaaaadbcaabbbdacddbabcabdabdaaacbccbdcdaaddbcbacacacdaddacdddaaadbaadbbdbcbbcaccbcaccbbcbadadbdbddccccbbdacabcdbacdccdcbabdacdbbcddcaabbdbcaaacddccaccddbbbcddcdbcdaaddcdabdcaaabacaaddcdcbabbcdcbdbccdbbadbddcaaaaabacbdddddcbaddcbbbbcbbbcccaabdcbadcabdbdccbabdbdbcdbccbaaccbcddcbabadddcdcabacdaadcdbdbadadcaddaadabdbbbcaddbdbdccaadcdcdbdbbacbdbbcaabdddbcddaccbabcbdaabaadcacadadadbbdbacacdcaddbcaccbcddbdccbbbdcbbabcccbddaabdabcdddadacbaaccdcdbabddcabccbccbcbdbdbbdbaaabbbdaccababbabbddcccabadccbbbbbadcbcaddbaddacdccdcbadddaddbaacdadbbdbbcbdbdbbbabddbaacaabdabbcccccdabcaaabbaabadbddbdaaabdbdddacbdddcbcdccbbddbbaadbadababccdcbcdcdcdcdcddadcddcdcbdccbbabcbabbcbccbdbddacbcdddcdccbcbbacbbcdbacdacdddcbdbbdabaabdcaaccbaccabababacabcbdcdacaabbbbdacdccdbccddcbbcadacadcbcddadacbadadbbbaccadaddcacadcbacabcdbaacbbbaccaaacbcbacbacbbadadadbcadcbddbdbcccacbacbaccacbbbaddbadabdaccbadabbcadacbadbabddacbdaadccdbdadddabdadaacbcdcdbaacdbccccdbbaddcaadccdbbdbcabcbbacbccdbcabdacdbdddaddabcbddcdadaddaccabaabbdcbaacaaadbbabacadabdcacadccdddcdccbbbbcbdddbaadbadcbccabccbadcdcbddcddbdadabcbbbcccdcbddcdacddcddbadbccdcaddcdaaddbdbabbadadadbcbbaccccbadccdddddcdcdbddbacdbcbcbdaccdbcbdcbdcbadbbabcbbabaabcdddcbddabbdccdccdcccbdbaccbbdabcaacdddbbadbabbadabbbacbbddaadbcdbcdddcadaadbccbabadcbacbcbbabcadcaaacbcdcbcbdbbbdaddcbdbddabaaddacccbdacdbddbdcacbaabddbadaaaddadddbdaadbbdbbcdadcdccaaaaaadcacdcdbabcadbcbadcbbbcaaccabaacddaddbdcbadbabacbcbaaabdcdcacbdbddcddcbbabdcaccbaabacacbcacdaacbccdcbdabdaadcaaddbccbbbbbaacbbcabcbcbddabdacbcbddacdacadaabcbcccbaadacaabaccbadcacadcbaccdaababbbacadbbbdabbaaaabddbbcbdcacddddadadacddcbcbadcbdbbbacccaacbcadbdddacccbaadcbcadaacbdcbbcbcbccaacdcbdbcacdbabbacdbdcbdcccbdaaaccccdcbbcdabaaddcbdcddbacaaddcbaaccddcdcabdbdddbcbdacbdcaccddcadcaacabcacccbccccbbacadadacabadaaacadddcbbbabaccdccdaaacbacabcaadcbdcadbddbacdbadabcabbbdddaaddcdbaadabdaaaacdacdbcdadcbcdcacbdcaabdcadbaddcccdbdbcdcccbcacddbbadcdddcabbbcadcdccdbbdadaaaacbaccbcdaabbdbddaadcccdcadcbaadccbdacacbcacadbbbacabbacccadcdaddbbadabcccdcdcbdababcaabbbaacaccbdcdadccadcdccbbdaabcdcabadadadcaaabbadabdccbbccdbdabcdcddbaabaddadabdbbcacdcbcacdbbabaddbbdbdacdbcbcaacacccccdadbbdccbbbababbddbddddadcbadabbbadcbdcbabbccaacabadacaaaccbccabcaadbbbddcdddacaddaddabcdcacbcdbcadaccacacddabddcbbbbdcbccdaaadbaadcbbbccdcbcddbadbcaccddddaadcbdbcbbabaacaadcdabaccccdcbbabdadbbccabaabbcccbbaabaccdabbbbbbbcbcaacdadccbbcdbabaacddcdcaadaddcbbadaacbadbabddcdddcddbcacbccdbddccbcadadacdaaabcabbcdddcdcacbcadcbabacddadacadaadacdbbacccaadbbbdbaaabcbdabbaaaacbdaacbabbabdadaacababdbddcccbbcbdcbbcdaccbbabaabccdaadddcadccadccbaadbddcacbcccaaaacdccbbcbbbcabcdbcaccacbdcdcabbdcbacaacdcbadcdcabbbddccbbcdbabddabdddcacbcbabcbdccabdddcbabdddbbddcaddcddabdbabbdaabacbbccdaabaacdabbabcbdaabbbcabaabcadbdbdadadcbcdbbcbcddcaabaacdcacadadacaacabdccddbddabdbdcdaddaddccbbdbcdcbdbcdddcbdcbcccaadbddacbbabbcaaadabbccabcaadaabcddbbaabaddddbcccdadaddcdbbdadcaacbcccddadabccadadadabbabababdadcbbbaaccacabdaccbbaaccdbccdabcabaacaaabcabdadccdaacdbacdccdadabbbaabddaaccccbdcbbacbdacabcdddcbddcabcaaddbdbcacaacbacbaabcddaacbadacddccbbccbaabacadacabcaacdaaccccaabddadbabaadabcbbbbbdaabbacdcdaaabacdcbbadbbabbccbcddbcaadbcaddabcbabccdbaadbdaabdcdcdbcddcadabdcabbdabdaaadddbabadbcccaabbdbcccbdbadcbcacaaabcdccdbbbdadddaadccbdaaabcdddaaadacbbbacdcaddaabadacdcddccaacbdbaaddbabdbdbcaaccadbcbcddadacbbdccddbbcbbdcdbcccbddabcccacaabbbcaabcabcbadadadcbbcdcddcdbdbddcbddcbddccaabccdbadcaddbcaabdcabbccbabcacddabaadbdcbddcbdcdacdabbcdbbcbddabbcddbcdcccdabdacbabcaabbadcddcdbdcaacdcdbcdacdabbddddcacddacccbdcaddacddcddddbdabcaabbccabdadddbdadbccacbabbddaddbbcdabbcbbaaaabdcddbaccaccbbcdcdbadcddaabdcbdcccdbbacacddcbcabdbbcaaabcbdbbbcdbdabbcbacabacdcccddcdbbabcbbbabaadcdddcbddacbccbbbcbaaadccbcbdcbcbdbdaddcadbabcbccddbbacbbadacabcabbbdcaacabaacbccabbbbcbddcdddcbdccbccbccccacddabbdadaaddcabdcabadacbddcacaaaacdaabbbdbbadbaadbccabcdcabbdbcdaacdcaddaddcadbdadcacdabbabbaddcddcdbaabbabbbbaddabaacaaccdcbddbdcdaaadcaccbddbbcadbddabbadaddcbaacddadcbbcbdbaddacdccbbcaacacbddcdbdabdbcccbbadacccccbbccbabcddabdaacdacbbdcbcabbaabcddcdbddbbcdcdcaddbdaaadbccabbbbddbabbdcaaabbcbcacbcaababdcdaccbdadcdbccabdcbaacaccccdaabbbcaccdabdbccadbddbdacdabccdbcbcaacbcbcdbaaabcbacccbbdcdbabcababbabacabcdcdbaabdaccddcadddaaccabaadbcadaaababdabadbbdbbabbcdabdbacadaacadbcddaccbbcdbcbbadbabdaacadbdbcaabadcbccddbdadcccaddcaccaadcdddbcbddadcbbdadbdabccddddbbdbddbbbddbdbaabcbabcaadcddbbacdadbcbbadabacbdabcddbccbdbcadaaacabcacddbcdccababdadaaaabaadcdbaaadcbacdbcabbbddaabbdaaddabcbcbcdbcaaabadccdbabddcbdcdccacddcddcdbdcacaabcaccaddcbbaaacdbbcdaccbcadabaaddcccadbacdadbabadabdaaaadcdcddcbdcabdbaadddcadccccabcabcbcdacacdadbaabbcabdabdadacbaabadaadaacaccdbdcbcdbbcdbcccdaaacdcaabcbbaaadbaddadcbcbdcdcbcadbcabcbcbcdaccabbddadcdcbbabbccddddbccbcccadaacdcadacddaacbdcabacabdddacdddabcdccabddbcbccbbadbabdabbccaabbadddcacaaacbdacccdbdcccbddbdbbadadbcadcbdbcdbdadbcccacddccdcabddaacbadabcabccabacbadccbacdbbbcdcadaaabdaddcdbbabbddbdcbabdbdcbccbbdbadbadacadcdcbcabaacbaaaaadccaabcdacacbbbcaaccdddadbcaadddcadccaaaacaaacbbcabbdadddcacdadddbccaacaacdbacacbcbdccdaaaccdcabbaabdbbdaccdacbbadbaaadabdcddacbdabbbaaddccccbcdccbbcdbababbadabbdaccbabdbadcdddbadbacaadcdcbadcadaabddacbccbcdabbbbdbacddaaaadcabbcadbccccddbcdadcdbaccdbccbdadbbabcccbbacbcccabacaaababbcabdbcadadacccbadbdabdcbbdccbccbacdaaddccddbabbabcdbccdbacabdbbaabddcabcbbdbbddcdbbbdbaaaabcbddccbadbacccbbbddccadcbcabbdcdcaaccaabaccdbcbcdabddcabdbbbbbbcbdacbddcccdcadcddadcdcbadbcacaacbcadabbbbbbbbccbbacabadabacaddabaddcdaaadcaaadacabbcdcdccccbabbcacbccdccddaaaacbdadbbbaabcacbccdbbdabacbaacccaadcdcbccbdddbaddaaabcacbbdcbdcabadcbacbcabcdcccaacbdabbbcbaaccabdaadcccdadaadbaaaadbaadbdcdaacdccaaababcbbcdddadcbdcbacccbbccdabcccbcdcddcbbcdcadbcabdacaccadacbacdbbdabbabcadcbbdadbadcaaadbdaabbababdaabbdaccddbcbccabddbadbabcbcbabbcddbbaccbbacacacddccdcacdddbcacabbcbddbacaddbdacbddcdadbbcdccddaadaaabdccbacdcabbacbdbbacaadccddacacabbcabcabadcdcdbbdcadbdcdbcabbdbadbbbbddddcadcddaadcbdbdcdccdddadcbcbbaacdadabdadcdbcaadaccbacbcaddcbbadcacabacccbcbacdbabadcddadbaccadaccbdbaaccadbacbdadccbadaacadcbcdabddbaddacbaacbacdbdcdddcabddadbacacbbbddddacbbcabacadaaacaddbddddabadcddccdaaabbbdaabacdadddacddbbdadaaddbbdddaddddbdbcbadcbcbdbccadcdccccabcbdadcacadbbdbdcabdbabcdcaaddccddcaacccabbaaaacbccddcaccdbaabccbdadcadddaaaaaaccbdcaddadcaadbdaabaabbbacabaacddddaaacabbbbccbacdaaccbdacabbadcbaccdabbdccaaaabcbcdcbbdbddcbbdabcdaaaccdadddcdabdacbdccacbbbabccdcdccbdaddacaaadddabdccaadbbabddcaabaddcacaadbccacddcbdabddadcbabbaaaccbdaddddbacbddaaaccdbcdcddccbbdcdcbccaaabadaacadbcdabcdaaddbcbacacddbacacabdacacccbddcccdcbbccadaabcbbdaddbddbacbdcbddcbcaccdbaaddadcacdcddcbddbcacdaccaddcbaabcccdabbbdccaabdcacbaaccdcdabbacdddcccdcbcadbacacbccacbbddbaaccddcbbcddabbcccddcddbccbdbdbadddcabbccdccabcacbaccddbccbbcadcdbcaaddbbbcaddaabbcaaaaabbddbccdccabccbccdadcbccaccabdacbcdcdcaadaccabbdcbccabbdacaababbbabddcbddddabbbaddccddccdadccccdbbbcdddacacaddbacdbdbbcccbdadcacbaccdcabcdadbdddcaccbcdacdabbcdbbbdbbdcdabcdddbdbcabbcaaacbdcbdadbdcdcbdabddbbdaacacabddaabbaccdadccabaacbababadcaddadbbcdbcacddacbacdaaabccdcccbdbddacbbcacaabbdcdacdcccccadbadddcaccdbdcadcdbabdadaaaccbadbabaabdaddabbdadbacaddbdaddaaabdccddbaabcaaadbdbcbdbaddacbababbbdadddcadbbcadddbccddbdaaddcbadcacdbaabcbaaccbddabbddcbbaddaccadccdbdcacdcdccbaaddbdddacabacdadcdcbdbddacaabccbdbcbbbcaadddcdbcbbcccdbdababacbdbcaaaccdaaacdbabbcbdadabddcdabcadbbdcadacdacbbdbddabccacdccbbacbbabacdbbdcbdccabaccadaddacccdccbbbabbbddcacabbabcadcdacccdadcbacbcbadcbdcbcdddacdcaddbaabadaaabdbcaabbbacdddabcbdbdbbdcbcabdbadbcaddaacdccaacbbaddbcbbdabdcdccdcacaaacacaabccccaabbdddaabbacddaabdbadcddcbbaaaadbcdcaddbaacdbcdaddabadaabbbbbcccbdaccaadcbccbcbbbcaaadabbddbddaadddcccaadacbcacaddabbdddcdbdbcadbaddaabccdccaadabcdbbdaccabaadbaccabaacaddddbdcabbbaacabdaddcbcabcaaaabdcdcadcabcdcdababdcbaaaddacadbaccadcaaaadbccbaabdcbcaabdbcbbabbdbabdbdbbcdbabccbabcbabcabcccbcacddbcbaccdabbabacdccdcdcbbbddcccbbcccaacdababbbdddbddcbdadccabacdcccbacbcdcdadaaaaaddaacbbcaddacadccddcbaccddcaadcdcbddcabdadacbbcbbdaddabdcaadacabcdbaaccabadcadbcbbdcacdaaacccbdabdbddbadabbaccddddbcbcdccdaaccaccaccbbbbcdbdcacbdbacaaccabbbababaacabdaaddabdbaddcbddccdbcabcdddbccabbddcbdbbacbcaddddcccaababdcddcdbcbcbcddddcddcbaaccabcaaccadddccccbdaddababaccabaacbdbbcdabaabbcddcddddbcbcadcabccacaababbacbaadbbcdccdbbbacccdcdabbbdcbaabdcbadacacccbabacddcdcdbcabbcaacaadbbcccaabaaccdabbccdaddbddaddcbddcdbdcbdcaadcabadaabcdaacdccccccdcaccbccacbccdcadcbdcbdabdbabbacabcccabcbacbabaadacccdbbdaabbaacbbbbdddbabadaabaacbcdbdcccdcbadbaabdcddbcbccbdacbcabdbabdcbbcdbcdbbcaabcaadbacdbaaddddddbbbbacdbacdbabaadcbbbcbbaacaabccabdabdcdabbacddddbcabdbaadddabcdcadaacadccbcdabcbadaabcbacaabcbabcccdbdbdcbccdcbbdbaababcadaddccdadcaacabccacdcccdbdbdddbcbacdbdcaacadcadacacabdadabbabcdbccaaccbccaaabbccbacdbccdabaadbabdadabdacbcaababcabaaddabbacddcabdbcadabdacdddcbccbabbaccbbabaaadcacacddadacaddaadcbcbcaaabcbcacacccdbabadababdcadbdcabbbdbcbcdadbcdbacbdaabbdaadcdcdadbbaabdccadcdccdabcdaaacacaabaccaddbdcbddddcdabaacadccbbdbcdadbbddaaadcdaadaaaacabacbcdcbcddcdbcacaccacaaacdcccbcccabcbacaacabdababaadaadddcadcccdcaadabbdadadbcaabdabbcddbcdabdcbcddcdcaccdbbdcadcabcccababddadcdbccbdbbbcdabcdbcdabaaadaadbcbdcbbdcaddbabaacbbddbabcabdbdbccbcdacbabadbacccdbccbabbcccdddbadcbaccaacddacbdbbdddccbddbbcbadbddcaadddaabccbdcabccdcdccbcdacaccbabcdababdbbdcccadbddbcddbcbbbbaaddcabacbababbddaddabdacdbcabcbdbcbadaabacdbdaadbbbbccdddcbcaabcdbbbcddbbcdbdabadccbdccbdaddaacbdbcdcbdddcacdabdccbdddacbdbbadadccddccdddacacdddadccacdcdbbbcaabaacbdbaccccdaccddadbcaddadcadabdddacadacaacacaadcdaaabbaadbbbbaadaabcaaadbaddbcccddbaccabcbadbacccccdccacbadbcccaabadcaaadcadbbbabcababbcabcbcbbbddacaaacbcbccbaccdcbdabaacbcbcaadcbcbdadbbdcaadbcdbcbbdbccaadcddccdadddcbdadcbaaccacacbaaabababbcdccbdcbacbdaacabadddabaabcabdddbccdbdcbbaadbbadbbacacccddcddcbacaadbcdaaacbcaadbadacdcdbbcbdbdcdbadcccbbdabbccddccadaaabcdbcdcccbccbadcbaabcaacdbdbbbcabdccabccbddbdbadcdccddaccbdbcbcbaabdcacbcbcbdaaaaaaaabbcbbadadacdcdbaaccabbcadadddbbacccdbcdccaadcaadbcbbcdacdbaccabccbcacadcadccbabadbcadacdaddcdabaacdbaacdabddbccbcbbbaddbdcacdcbcdaadbdbcbbdacbdbbaaadbccdcccdaabbbccdbaabaacadcbbccdcbccabdabccaadbcdabdabcabbbbabbcddaccaaabacbadbaabadadccacbbdcabdcdddadcddcadccbdbdcccdcabdbccacaacdcdbbdcabbbdbbdabdaaadababcbcdacbcbccaadbacbdbabdccaccbbbbdcccabdcddadccdbdccaabcbddbcbcdabddbddcacababdaaadbccbdbbacbabbaaacdbbcabdbbdcabacdcaacaadbbcbcbadacaaaccbdbdccbcdbbaacdcdadbddbcbaddbcadbddcbcacdcbbbabdcdbcadddacacacccbdbbddbbaddbcddccdadbccaabacbcbdbcddbdabbaacdadcdadcbcbccbdaaadabdcdaabbdaaabcadabcabbadccabdaabddcdcdcbdbbcabbabababcdcaadbddadaacdabacdaddbcccdbccbcaadadcaddacdcbabaadbcacdbdaacbabbcbbbbcaadcabcdabdabccdddbbdcaabbbccaadcbaabbdcdbcbabcbbccbdddbcacdadbbcbacaaabbdbadbdcaabbbbbbcbdbdddacaaddbbabbccabbddadbcabadaababacaaddcadcbddcdccacccdbcbddabcddbccdcaabdbbccdcbdddabbccadaccbcdccddcbbddaaaaddddbdbacdbddbcddabaabacdcccdbcddacacdacadabcdadcdbabbcadbbcbcdabbaccdbcdaadbadcacdbdaabcdadbabcbccabadccabcbbcbbdaaacdcbbbabbbcbcbbaccbaabbabaaadcdbabbaddccdbcacaccdcbddbcadcdcdaddbcbbdadcbadbbbcabadadabacbcacccdcaadddbcbcdcaaabaacbaacdbddbaadddbacbabcaabaddbacbddbaacbbbdddabaaaaaddcbdbbdbdbddaacabdaddaaabddbbbbdabbbccabbcddacdbdabddbccadacaacacbadcbacbcaacdbacacadadacadacbddbdccdabaabbcbddaaaaabaaaacabdbaccdbadcabcdbaccbcdabacccbcdaccbaaacacbcdcacddadacbacdaacaadabbbbcdcbbdaddccccbbbacbadabdbaaddadaabbcdcdbcbbacbbcabcabcbacbdaccdbbcdaddcbdbcadacbddbbbdcabdbdabccacbcbbadbadaddcbbadadbdbddbacdaddccdccadbdabaabcadaadccabdbabdabaddcccacbbaabadcdbdcdccbcddccddbccbaadaaaabcaaacdabdbcdcdbabdbdbcbcdcbddbdadcdbabbaacababcacbdcdadbcbbcdbacdcabcabcbdccbcaccccacdddbaabbdaaaadcaadacbbbadcccbadadccbcadbdbbcdccbbbcbdbcdbabadabcacbbacaaaaabbbdddbbcdcabacdcabcddcacabdaadbbcdcadadabdabcbdadbcbcadbacbcadccbdbbaadcbaccbaabcccddaddcdddaddbbadaadcccccdddadaadbbbaddcccabddcabcbcacbdadadbbaddbccdcaadabdcdccbcacdbcbdbdbadbdbdaddbbbbacaddcdbddcccadcadabdccddccdacabadccaabbbacbcddcbcadcadaadddcaddaacbbadbadacaabacbbaddadcccdbbacbacbadbcccabbbdddaddaabcbacbccbcbaadacaccbbcbcdbbbcabdbbbbcbcadcbdcbaacacdacbcbbbadcddbcccdbbbabdacdbabacdddbcddbccacdccaacaccbcddadbdacbacaaddcccbabaabddcdbccabdcbbaabbbaccaddbdddcaadabdddadbcacbbcdccdaddabbcabcbcacbbccbdaabddbbccdbdabdaddbbabcdadbbcbddaabcaccaaccbccabdbdcacccaadcbdacdccdadccbcaddbaccbacadbcbdadddbaacaabbcaaaaadddadadbbdbaaccdaccbdaadcdadaababcbcaabadbbacdcbacaacbdcacacacdbbaaabbaddbacaaccabaccadcdcdbdaddaaccbaccacacbdddbbbddaddcdadccbdbacbacaddccbcbacacdadbbabaadabbcbbaadddcdbbabdcbabdabddabddcdbaddccaacaaaadabbcbdddccaadaaabbadacdadcadcccbdbabbddbadabbdbddbcdcdacbacdcbddbdcddabccadbcacbcbdcddbadababcdcabacbcbaacbbcdddacbcbccdaddabbabbaddccccdacbcbabcbbabdcdcbccdbbabcbbacadcbdbcccdaccabbccdcbccbcccacacdcaadacdaddadadbdcbcbacbcaacacdbbaaacabaddadaacdabbcacbaddccaabadbaddbabbadcddbcadbcdbcdbbaddaabbbbbaaacbbbcbcdbbcccbdcbddbdbccbbcacbadcdddabaabcdbbddcddbbcdbcddcddbadabdaaaaacddacdabccbdbbcbdcaccaddcdbddcdccbdcbdacbdadadcaddddacadaddddddbbccadbaccddcbdccdadcaacbddacbdabbbbcabbddcaaabbdbacccdcbabdbbabadacacbcdacccadaacbcbddccbbaaadbbaabccaacdddabdacddadbacabcbcdaddaccddcdbcadaaaaaacaaabbababbaadbdcabadddccababadbdbacadaadbcccabdbbddcaabdbbdbabadcadbbbcaabbcbacacdacbacdcbcddcdacbbdadaddbdcaaccbadbcdcdbdaddababbdaddbdccdbddddcdccbbdbcacbdacbbccbdabbdbdabcdaacbdaabdabaaccaddddcbcbbcbcdadacdcdabdcadbbacadabdacadbbbdabddabbaacccccbddcbbabcbbbbdbaaccacddadbcdddbbadadbbcddaddbbdabdbdaabcbabcbcbbcddaabaacbccacdbdaaddaadacbbcacdcccaacddddbabcadacbcbcdbbabdddcddccbacbccbaacccbabaaabdadcdbbddacdacdcbddaaadbaddbcacacddcdaabdbaccdbccacccdadcaaaabacdddaadddbbbdcdacdccadabbbadbaabcbbbccbbcabaccadbcdcaaabdcbdcdbcabdbbababaccdbddbbcccbdbaadcbdabcadaddcdcbdacbdcbbacdcbbbbacddccdcadacababbccccbddbdadbccbaacccdbadabaadcadadcaadbbcbacdbdddaddacabaabddadbbacbbacbabdacaacccdcccddddcbdbaabddddbbdbadcabddbccccdbcdccacbdddccccddcdbdaabdcdbcadbacdabbbbabdcccaaacddbababaccccbacbdbbcaddbdbbcdbaaadcaababbdcccbdbabdadacbcccadccacacbcbdbdbcdadcdbbcbaccbabcdadbcbbcdaaddcbbacbbaabcbbadbbdddbbddabacbacddcadbdaccccdcccdbadabbacbcddacdbcbdbdbaddddbcccbbbbcddbdcdcdcdcbadaaabcddccbabadaddcbbccaaacdaccddadbdbbabbcacdaaddbcbdbcbaabdbddccaadbdadcbcaaadbdacabcdcadbbcddbacbabbabdadadadabcdcdaaaababcbddaddabcacddccaacbacbdbaddccaabcaccddaaddbabdbbcbcadacadaaccdcadccddddbcbcbabcaadbccdbcdabbaddddcbbaaacbaabbcdbaaacacabacddadaabbabaddadddabdcacddababaabccbddaaccbbaabbcbdbdbbddcdbbcddddbacdcdcdabccbbdbdbcdadacdddbbadbabbdadabadbabdcbadcccdaaddcbdddccdddbbaddacbdbdacabdcdacaababbbbaaacabcaabddbaadddddabbbbdbcadbacdcabaabdbadacaadacbbbaccaaccbadbaddbcaccadbbccbddbddcadccabbdccbabdaadcadbbddabacaadadbcddcacacddbdccddbccacbbbccabcbcbdabaccaaddacdacbbcccdacaccddbbcbddaadbbcdabdacccaabbcbacbbbdbacadadbaabdaabdaacadddabccbcdadbcccccaddbcbdaccbcdacadbccdccadbcbacabacbbbadcbbdddbdccdbdbccadbaaadcbdccabddcccbacdaaadbbccccadcccccbbddcccdbababaddabdcbcdbdbdcbadccddacdabddbddbadaabdbdbbddaddadcdabaaacacaaababcdaddbabaddbcabdddaadabcabdcbccdbaddcddbaaddcbadbbbcaccddccdbbcaaaaaacadbdaddbccdabaaacccdbbcdacdacbabadcbbccabaaccbacdbbaddaccacddaccadacacddadddccdbcdbacaabddccadabcccddcbbcddcbbbaaddacbbbbdbacdcacabbdaacdadddbabcdcbdccbbdbaabcdcbdbdcbbbdbaddabbabacccabcaacdbaaacabbddbbbacaadaabbcddbdccaaaddaddacaadcccdbbbbadbcbddccdbadbaaddbbdcacacbdaaabcdddcdccbcbdbcbcdbbcaddbdcddabdcacddbcacbcddccaadcdabcadcbaaaddddbbbbabcaacbbdaaabcbbcbcbbdbddcbdddacddacdabbdbbcbadcccdaacdcccbaccbbaacabbccddaaaccbacaaccbddcdcccbadbcdccdadbadbdadcdcddbacbbadbbbdadddacbcdcbbddbabcbacdacdcbccddcaabacdadbdddbaacaadbbbdbaaabcbdddcbdbabdadbbdbadbbdaddbaabababbbcaaaadbadcdccdcacaddbdbbcabadcdcdcdbacbbdbcadccbcccdcbacdbabaacacbccbcdabdbdbcacbaaacacbbddacaaaddcdbacaadbcdbbdccdabbaacdacdaaadcbaccabdadbacacbcbbabdadcbbaadadacaaaccbcadbacbdcaaadbadcbcabdddcaadcdacaabbdabbbddcdacacdddacddabbadbbdbdaadcbaaaadaabbbbabbccddcaacbbcadccdcbcacbbcdcbabccbcadcadbdcdbdaccaddadccbbadadbccbabcbbbcabdcdddbbbdadbbaddddcbdcdacdabdbbdacbabbaddddcabbadbcbbaccbcacbdcaadaabaacbdcbdbccdacdcaacbbdcadaadabccbdacbabcdabcadbcbcbcbddbbaaacdcaabcacbbcbdbdaccbacadabbdadbccaaddcbbacbdcccabbadddddbddcccaccbcabccdcadbabcccddccdcbbabbababadbcdbddacccdbaacbadcbddccddcbabcdabcbabddaabacddcdcddbbccaadaabacccbdddabadabdbaacdcaccbadbcacdcbaabcdadaccabdcdcdaadaacbccacdadbbcdadcdbcacadcbbbcdadbbdaadcccabbaaadcdcacbdaaacccaccccdddadbdaaaababddcccbaccaacadbacbbcbdbddbcadccbcccddddcadbdacbbbdaadcdacbabccbccacbadadcacddaaaaaabcababcdddbbacacaddcbbbcddbcdcaabbaddbbcddccbbabbbbcdcdbdcdaddbbacaaddaaadccadcdbcdccaccddbddadbaabbbdbacdbbbdababddbaadbccccbcbabddadccacbadccacccdddabbbdcddabcadacdcbabcdcbcaadabcbbdccdbaccdcadcbbdccbaccdbabbabdcdccadadabccbacdcdcbddddcbdbdaccbdcdcdbabccdbdaacbbbacbddccdbacdbbcbadbaadccaadabbbabcdcaacacbcaaabccdbcbacaacaccbcdabdcbacadaddacdbaabaccbdcacdabddaabdaadddbaabbbcababdcdaccbbcdccbaccbcabbcbcdcbbbcdcddacabaaddcdcddcccbbaaccdadbcccdddbcddcaabbbdaacbacaabacaaacadacdbcaadbadbbabdabaaacbbdcaadacdddaabacbaabdadacdcadddadbdadcbdacdccaddcacbbabbdddcabaadddbbacbdacabadbdacbdbcaacaaaadbdcbdbadbdabccadaaccacddccabbdcbccbababcbdcddbccdbaaacbdcadcdaadadaabdccadccdbbdbddcbcdcdcaacbddbbcbbdaccdadbcbcacadbddcbcaccddbdbabcccaddacdccbbdcddcbaacdbadcbbbddbbbadaaddadaadbdcadcbddddcabadaaacddcbddbabbbaacbddacbbacbdcbacbdbcacdbdacacbcccadcbaaaaddaabaccdbaccdbbaddadddcccbadddcbcaaadcbaabaacbcdaaabadababdddbcdbdcacccdbbdaaaddacaadbbbddaacccaabaddcadcdabccddcacbccbadcdcccacdbcdcdddbbddaadbaaddaddacacccccaaccaddbddbaabbadcaccbcaacaabbaccacabaccacbccaaddbcaadbdcdaccccacbbbddbbdbaacacbddcbbdbadabddbdbbbddcdbdabcdbddcaacddabacbbddbdcdbbaddbbabbabddaaadbbddcdadccdaccbacdadbcacabcdddcbcdbbacbdaaddaaccbbacacabcacdadbcbacaccbadaabdacabcbaaadbbabbadacbcbacaddbbcddacaaabdbaadcdcdaaabcddbddcdccaaabbadaadadbcacbbddbbcdcacccaaacdddccbcddabcbaddcdbddcccacdccaabcdbbaababbadcbcbbabdbbbabadaabdadcabcdbbdccbabadcabdbbabcbbdacbcacaccadbbcaaabdadbccddacbacacddaddcaacadbaddcdcbbccbacbbdcdacbacdbdccccddacabdadbbaddcdcbddaabbccbcaabccbdbcadbddabcdcbdbccacacdcadcbcaabcddaabacaddcbcdcccbbbaadacdccbaabdacbbcdcabdabbdddadaaabadcbdbdbaddbdddaccdddaacdcdbcaacbacbdbabdddcdabaadbbccbbdddccaabacddccccbcddabddccabcbcbdccabddacddbcdbdcdcaccccbabcbacbbbabcacbddcdddbdadddbdddaaaccbadabbbbbdabcccbaacbadcbabdcbbccddbccabddbdaccbabadccccbdbabbbdabcaaadbbaadbcbcbdbbdaccbcacccdabadcccbcaadcdacbcbadbacaadbdbcadcacacaaaacaabcddccddadadcbabcbcdaddcbcbcaacaacdadcddbabccbaaabccadbcdbdcdbddcabaabcdbdaccbcccabdcaabcddcdddadcdccbdaddaaaadcaddddacddbbbdbaacbdbbcdbdbbcbcadbdcbbabcddabdaabdaabcddadccbacdabaaacdcdbabbbaddacbccaaadccbccdcbcbcacbdcdbcaadabdbdccddbbbcdacccdcdcadccdbadbdddaacbdcbcbaaadbdadaccdbaaababcbdaaaabaabcdcadabbadbcabbcdacdcbdbabdddaddaacccbddaaddccdcbcbbabcabcccdbadbacbcdacbddacdaddccbdbcaabbdacdaadadcabcacbdddcccdabcdcbdbabacdbaaacadcdcacbdabcadddaccbaddccccadcbaacddaacaaabcdbdddadcabddaccdadbcacdcdadddcdcaacbbbadabacbcddcdddbccbaabbddbdaabbcbbdbbbbdaabaaaacbbcbbcddbaaabdcabdacdbdaadcaaccccdadbbddcdbcbcccacadcdcadcbbadcbcdabcbbbbbccaaabaddbaccbbaadcdcbbbdacdcbabdcacccbabcbcddddbcbadcdadbcbadaaaddaabbbaadadbcbacacdcdcbdaaadaaadcadcbdbdadbcddadcabdddcabcdcaacddaaacbcaadaddacdcadcbddccbcbadaadbdbcadcbdcccdabadacabccddccbdcbcacaddcddcbaabadddaccdccbaddbbbdacaaddbbccadaabbacccddaabadcddbacaabcadaacadabcabacabbbdccddaddcbcbbbaddacbbcbbbddcaaaadaaccabbbcdcaaacddbbaddbdcabbaccbaabbbddaadbbbbdadbaabdabccbacddadbaddabbddbabcbdccbdbabcdccaadcbcccaccdabdabbdadacbdbdabadabbbabacbddabddcbabbbabdaccdbaadbbbabbdccdcacaaacdacdcccbcacacaaaaddbccbdcbcabbbbaabdaddbdbabbbbaaadbcddccdccdadadcbdbdabcaaabdabdcdbdccbaabadccdcdcdcabcbdbcdcbbdbcddbdaacadadcbaccddacaaabcccaddcacdbdbbcccdacaababbacdaaacbcdcabdcacdbdccacdddbdadaccbdcaddabcddbddaadccdcbcdbdabddbbcbcdcdbabcadabcccadcdbbdbddcaadcbbaabaadccbcccaaddbbdacccddbcddcbabccdcadaadacccaaddadbbbbdacbdccbcdcaaaccadbbbadbcdbabbabcbaaaccadbcbbbbaabcbcddbccbdbcbbddcadbdbbbdbcbbadadbcaababdbdcbdaadbdbbbdcaaccdcaaadaccddabbbdbbddacbcbcaccdabbdbdabbddbccddacccbcabbcccddcacdccdbcacabdbbdbddcdcdadbddbadaccbdcaadddbbabcabcccdbbacdcccaccbdbddaccbcacddaaabbcbdbbbacdbcacccbbcbabdabbaaabdcdbcbaacbdcbdcddbcccabaaacaadbdccdaacacbdbbcbbdaacbdddabcaacdcdabbbcccbbadddbbcabdcbacccccadcaaabbdacbbacbdabadddcbdbbcadddcbcddbacadcaaddcdbacbdacabaabaacadaadacdcccdcbcacdaabbcdaacbdbbadccadadddcbdcaabcdaaabbbcaadbdadcaaaccaabddbdbbcdcdddabddbaabbddbdcabbddddddacdacbdaddddbacaabbaccdbdbcaaadabddbdabadbdabbdadacbbdbabaacbabbbadcbcaacdacbdcbbccdbaaacbabdabdabbcbabacdcdbaddbbbdcdbbbcbbaaacbabacdcacdaacadcdcdbadbdbcabacdaacdcadadcdabcdadaddabbdaddcbbbbbbaabbbdacdbbbaddcadabbbdcabcdbccbbddbbdccdacbcbdddabbdbadcddbdddabadabcabbbadbbbdbdbcdcdcacbabbcdaddaccccdaaaaccdacdcbaddcbcdcdbacacdcabcacdbcbbbabbdbbcaacdccbcddbaccdcaadaacabcdadbcbcdabbaccbccccbacdbbbcccadbbdcccdbbddabddbaabcbaddbcdacbccdbddbcbdbdcdcadaddcbabbcbcadcbcaaccaaccbccadacdddbaccaccdcaaadcaccadbcabaaaacddcbdbcdcbcdcdccbccbcdbbdacddcbdcbdbabdcabacbabddbccacdccaadbcbccdccdbbabbcdbdabcbccacbbdbdaaddbbbdaaacaaabababcdbcbbadadadadbdcbadadcbbaababadddbddabbabbcdaccdddaacdcadccabccabddbcbadcbdcccaabaadabddbbbdbcbbdaaaaaabbacaaacbddaababdbdddcdbddcacacababdcadbbddabdacdaaabcbcddadababdbcdbababdbbdaaadaadbcabadddcadaddadaccacbacabaddcaaccbccabaadbbbbdadadbbaadcaccddacdbdbcbcbaddcacbacdabaddacccadbaabddccbdddbdbdaaadbaaddaacaacccccbccccbbcddbdbccaccbcdddcdbbcaabadbadcacbdcbdcdbccdadcadcbbacbddaddcbacbdcabdabbdacadaaaadccabccabddcdcaabbbdaacddbdcbbbbdabbccddbdcdadacbbcbdbcaccabbaadccdcdddbadacbcdcaaddccabdccdcadddccabddbdbddbcdadcbdcdbdaddaccdcbbdcdabadbcddaddbbacbccbacdcaabaabcbddccdbdddccdcddcdbdbdddaadaaccccababaacbcbabdabccbaccabadcabbcaaccabdbbbabdadaacbadacddbaddadbabcdbaacdabadcdcaadaccccacbdbbadabcccacaabdbcaaaadadbbcaaacadadbdccaacbacacccbbdcabdcdbcbbbdbacacdcbdbbadaaadadacaddddbddddcbccabddbaddababbaacdabbccbccaabdaddcbabcadcbbacabbcdbbcdcdccadaaabdcdabaccabdcabccbaaabdaddaababdaabbbcccdcbccccbadbcbaacabcdaaabadbcbbbcadbbdbacbadddcaadbadaddacadcbbcccaddabcdabdcddbbbcaadbdcbdbdadbddabbcddacadbdcdccdcbbbbccbbadbbdabadacdabadaacaddcadcccbdbcadacbccbddaacaadaccaabddbbbdcbdbbcbacacaaaaadacdcccadccdbdbbabbccacbabbccbdcddbbdaddbbcbcdbabddbbaaaaccacaacbbcdabccbcddcbbbbdcbccdcdbabbdcbddcdabddcabdccdcbcccbbcbcbddbcacaadbacddddcabcdcdadabcddadbddddcadbcdbacabddccddadcdbbadbcdccddddddcbbbbddaddcdbaacbcbccbbacdbdaabbcbdacbadbcbcbaaddaaccaaaadddaaabdabdbbdccdcacddadacaabaabcacdbcabbcdabacaacccababdcbdbacdaaabbccdbacadacadcbadacdbabacbdccabaabbbdcabcaabdabbdbdcdbcdbbbcbadbaddbbaaabdddacaaacbadadbbddaccaaaadcdcddbcdacbdaacdbcbacaacabacbaadbddacbdcccbadbacaddbcbbdbcbcbbcdabcbbcbccabdadcdccbdabbbacadbbbcbdbccbadcaaabccdbccbcaccbaaabacacdbabdbcbccabcabccabcaaadcdcdcacbacbdbcaddcbdacdcbbabdabddbacdcabbdacbdaadbcddacadbacaabccbbbaccdddacadbbbcbabacbdbaccbdbbdabaccdabbdccbdaacaacdcbbdddabbdcdbdbddbdacbbbaaddcdcadbadadbbdccdbbcabdabddadaabcabddbccdbcaaaacbdbacaabdbacbabbbaadadcdcbbaaacdbcbbcacbdbdcccddccddcdaacaddcdabadcbcadacdadcadaaddbcbbdcdabaddbbabbcbdddcdbaaabaabaccdbbcabaaccabbcbbccdcddbbbbdbddbbadaaccadbababbcaccacaccdcdbdbdcdcbccaabbccbabbbdbdccabcabdadaaaabddaddcccacddaaaaccabadccdcaccdbdbccccacbbcdaabddccccadbcbbbaabcccbdcbdcdbaabdcbdcaabccbbbabcaddadcaddadbdacbabaacbaaaacbbacabadaabbadcbbccaccdabcbcbcdaddacbacabadccacdacbcccacacbbaaaadcbdcbadbddccabccbbdabcbdbbbccccaddddbdddbcbdadaaabbccddcddbbbbbdbaadbaabcbdbabadccbdcbbabbbbababcccdcabddaccdddcbbbdcaaaabcabcadbbdacddabaddcacdaccaacbbcccaadcabdbdcccccbdbccbaacabcbdddaaaabccdbdcdcbdadbdcddcbbbbaddbbdbcbdcdbdacacbdcddbaadbdadccbbbcbddadbcccccccadabdbddcbcabbbcdccaadbccdbbaddabddacbaacdcbccbcadbdacdbbccacbccabcccccaccdbacbdcaaddbddabaaaabbaacabbdcbbabaddadabadabaabbddcbdabdcdadddbcaddbcadcacdadccacaadccdaadacbdcdcdbacdaabaadddcacdaccadabddaaddaaddccadbbabcabbddccbcbcacdcdbcbcccacaadbdbdcdddabcdcacdbccccaacaccdabddddddbbddbbbadbaacadaddbcdccaaabdaddbbbbcadbbcaaadbdbadacbacdccbcacadacadbdccbddbcadbcdabddbbddbbdcdcbdbcacdbbccdcccddbcadaadbcaaaccbdcbdadcdbccdbddcaabcdbadaabdbcdacbbcbabadcbcbdabbcaaddadbcbdbcddcbbdcbbbbbdabaadccbbcabccdaaacbddbababdacddcdcabdaadabacdccddcbaadbbdcbdaabdbdbdbdadacbbccdadcddbbbbcdacacbcbddadbcacbdcdcdabcccbdbdbbdcbdcabbbacabbbabbdbacbcbdbcdbccbbccdcdcbcdacacbadcacbbbabaccbaabdaaaccbbcbcccbbaadaddbccbbbbcbddbcbbbdddbdadbbdcbdabbcdadbcaddcbccbbaaadbcdbbcacaaacbacddbdbabacaddccdcadbbabcabdbbbbbccbabcdcbbbdbbaadcbbdbcdacdabbbabacdcdcdccbdaccdaccdbaadacbcbdbbadcdabbaddcbbaddbaababcbdcccaabadbdcccaacacadcacbddabdcaabcdcbaacbcdacbbbcabccbcdbabadbabbaabaaacacbdbdcdbcdcbabdddbaacddcabbddababbbaaabbbadcaaaaddccccdcccbaacdccbabccdadcababddbacddadbadccdadadbbdbddddccadbbdbddcadadaddacdbaaddadcdcdacadcdbdaaacacacbbacccbcdcbbdacaddcacaaaaccdbddababddacccadacdadcbcbddadaaaaddbacdcbbaaccbdacbbbbadcbccdcabaabccdcdddaaaaadcddcdabdbbdcabcbddbbaabaaabcacacbbbcccddabbcbacabbbbcdbccdaddaabaddaadcdaddaacdbcbadcbdcdcddaccdadaabbadbbbabbdbaccbabcccdbcaaabdcacddbbadcacabcbdadccbbbadbdcbcdcdcdbddaddbacbcaacaccbbaabaacaabbbdacbdcdabcdadcdbbaddcbdbadccaccccabbadacadcbbdbaabbdbacccbbdbccdbabddccbcaaacdcdcddbdadbcacccdcdbbbadccccaadcdddcbccaddacdbbcdcdcaaabdddacbcdbcaaabcdcbddabccbacdcbabaababbbdbdadcadbaaccdaabaddbbbcdacbacdcacdaaddcdacacbbddbaaadbbadbddbbddddbbcddbbdbaadccaabadbababdacbddcabacaccdabdbbaababdaabdbdcbaaccabdadddcdacdacdaadcbdbdbaacdcbcbdbadcaccacbdcbdcaaaadcbbbcdabcadaaadaacaadabadbcbacdcddcaacdcddabddbacbcaaaadccbbcadcdaadadccacbcabaccaddcdbbaadbbcdbbaacaaccaacdcdddcbbabbacbadaaaaaddaaccccacdbbbdcbdacbbadbccbccddadaaaddcbbccbacdddacddddddbdaabadcccdaadbadbbbabdcdcdbbdcbbacbaddcacbdcbbbbccabaddbaadcdacacacbcdccbbacbadcdddabcbbbbcbbcddbaccacdaadcadddbdaccaccdadbccbdbdbccccdabbbddbadaaabadddccbcaabaddcdcacbdcbbaadbdbdbbdaabdcbadbaddcbcadbbbdaccabcaabbcdadabdabbdccbaacadbaddadddcddbcbaadabcaabadbcdbabaccbbdcbddbcccaabaacbbaabaabdaabddadddaadcbadbdbacddabaacadadabacbadddcbcbbbdccabdbbddbabcacdbaabbcaaccddcbabdabbcbdcbccbdbcdbbdcabbbdbdbcbacdcdccdbdcdbabcbadcccddccbdbcbabbcaccaabacccdadcaadabbcccddcbdbdbbbacdbaabaacccddabcbaaabddbadbddabdacddbcdbcdccdabddbaccaccbcaacbdcaacdbdcadddadbcdacaaacadadaacaaaccaccabddacbaacdcadbacbcabcdadabcbacdbaacdddabbbbdacaddcbadbbcdbbbcccddddccacddbbabcdcaccacdaadbadcdccdbbbacdbbcbbcdbaccdcccdbdcdccbabdacaddaabadcbadbadadcdccdcdaccddcdadbcccacabbcdcdcdcccaddaabcabbcdcbadaadaaddbbcdbdadcabbaabbcacbccbabdccdccdbcbdcadcbdcdddadbddcdcbdaccddccccbaacadbcdddabaabaabcbdcbcbdacdabcdccdadbcabbacaabddadaadbddaacbbbcaacdcddacadcddbdccaddbdcbadcdbadabdbdbbcbdbababcdcccbccbadaacadabaccbbaaddcbcaddabcdcdababdbbddcdbbdaaadaabbcaddabacbbdbcabbbdcabdaaacbbcabcabdbbdaadcacbbccbcaaccbdcccdaacdaacbcddbacbdbadcaaabaddadcbcbcaabaacbccbbdcdbddaaddbdadbbccddaccaaadbcbbadcabccdbbcbacaabadbabacdcdacaabbdcadccdacddacdcbbcddccacaabaabcacbbcccbdabcabcbdbabdcdcbcacaaaccbcdcdbbbddccbbcdaddcddbbacdcccbdacbbdcbccdcaaddbbbbcadcddbdddccbbbdccabdbcbdbcabbbcabddcbcdcaabacadcbddadccdccdabbdbcbccaadbdbbbccdbdadadccdbdbdcadacacbcdadabdbcbcbacccbcaccadcbababbbadccaccccbcccbbdcdbcdabaadbbdabcaabdacddcbbbccddcaacbdaacdbdcbacdadaabbbbcdcbcbbbdbddbabddbbaccdddddcbcdbabcabadbdccbdadbbacadacbcbdbdddcbcdbbaccbbcdababbbadbccdccccbddbadcbdbbdcabcaccadcdcaccdccdccccbbcbbbdbbdcbbdadddabbdaaadacaabbcbbdadadbdaaaaabadbbbdbadaccbdbdccbbbbdadbbabdcbbccbbdabbbacdddddbdcbcabcdbabaccacdccbdbbccabddddacdbcdaddaadbcbcdcdccacaadcacaabbbaadcdaadbcdddbcaacbabbdddaddcdabdccdbdcccddcdbbdcaadaccabbabddcbcaaccadccdcbcbbacadabadbaccacccacabdcacbaddcaaccdabbdbbbddbdbbbbddcbabdbccaaccaadcbcacadcddcadbcadbdadabdadbccccccabadacbdcacaabcabcbdddddaabdbccabcabbcbbdaacbacddbbdccaccbddcbacdbdccbdadddababdacadccaacbadccdacdaddddbdacbdaddbdacbdaacdbbcbcdbcaaddbabcbbcddcabacbbacaadcbadcddbadcdbbbdcdaaaaaaccdcdcbacdcddbbcbddaddcbababadabdbdaacbdcadcbcabaccaabddddbddadbbcccdabbcadaddcaadcbdcdaaadbddabbdabdaabbbdcbcabcbacaaaaacbdadcdbbdbddbdcbabbdbcddabdbcabddbadbdcccacabdacdccdcdcddcadaadbdbcdabccbdbabddadddbcadbccdccdacbdcdbcacbcbccaacbaaccdadbacaabdccbacdbadabadadddddbadcbbbabccddcdbbccdacbadcccdcbdadbbacadacddbaadaacdaddcddaaacdcadccbadaacdcbcdbccbbbbacaabdbddbcbbbacadbdbbdabacddbbbbadcbdcadbdddcbcbcdabacdbcddadbabacbbbdccbcdbdddabacdbbccddbdabaadbdaaadbccaadccdbdbbacbbbbdaacaccccacbcddcbaddbbbcccacdbbbddacbabcdbaaacdaddaadbdbbbcbcbaaacaddaddaacacaadcacbcaadabcbddbddbdadcccacdadaaacadabadaaabbcabbbcacccbbadbaabcdcdbbcccadbdcbbcacadaccbcadbdcdcbabcbcdbdbacdaaccaadaccbaabddabbdbadccacaadbdacbcaabddadacaaabccccccdaccacdacbcbccdbbcaddddbcadddaccccbbddacbaadddbacbdbcbacdabbadbacaacccdaacdbcacdacaacccbcaddbaacddbaaddccababdaadabdaaddcbccccbcccdcbacbcdabbcbdcbabbbbdccaccbdcdabbdbcadcbaabacddcbdbccdcdbdaacababacbcdababdcbbcbbacbaddbdadcdccccaabbcdbaadbddabbbdacbcccbdcbaadcddaaaccbbdcabcdddbdbbabddabadbabccbdcdcaaaccbdabdbadbcbaccdabcddbdddccaaaabdabacddcbddaccdaaaabbaadabdbcdbcadcbbddbbbabcabbabcbbabbaabdccbbdaccdddcbbdccaadbbacacbdbcccbbdcbacbadbcacbaabcbcacdacdbdadbababdcbbccabccddcdcbcbcaaadaabbacccaacaaddacddacaacdaacdcbcadabcadcadaddacbcbbdbdadcddcabaaaaadccacbcdccbccabbdbcdccdabddcaccaadbdabbdccacadaccadbbcbdbcccbacdcabcbdcaadcabcacbacccdcdbcbadbddbdddbadadbbccbadcbcaadbbadcadddbddcdbcdadbcddcddaddbdbbdcbaadccbaadadaabbcbddcabdccababadaddcabbdabdbdacdbcbbdaabccadcddcbdcacbcbaabbbbbbcabddabaccdbbccddcbdbdcbcacddcaddaddbbdcdddaaccbbbbabcbbbabccccbbccbbbaadbbccaddbcabaabaccabddccddacdbadccaccddbbdadbbcabdbbabcccbdccddacdcddacabadbadacacbbcbcaacddbcdbadcbddcdcdcdcdcdccbadbcbbcbbcacababdbcdbcdadbcbddaadaadccccacbcbcccdbdbbdbcbbcdbcdbddcbabbbcccdcaaddbababdbbcdddbadcddbdabcdcbdcacbcacbbbdbcdaabaccacdbcccbdadadbbbbbbadacbbdcccdcbddcaabacbcddabbddccbbadbcadbdaadaaadadccdacddddcdbacadddbadbadadddbdabbbbddcdabacaabdccbcddddadabacdaadabcbdbdbcdddaccdacdcbbcccddbabccbcbdccabbaddcadadaaaaddcadababacddcccbaaaadadbdabdccbcccdccbcdddccdcbdabbcdbcccbbdbdbacdcddaccaccccccdcaddacabbbcaacdddabcbdacddbdaaacacaaaddbacbbaddaadcddbacbadccccdbacddddccdabacdbacdbcbababddcabacbddaadbbdadabacacbcdcccbddbdcbdcbaddccdcdcaababcdcdcacacabbbaadabcbcdbabddcbdddcbaadbbccdcaccbcddbabaddcbccaacabaddbcccbddbcacacbdbadcbccbbdcbdaccdddabdabaabcddcccdcdcddaaccbaaabbcbdbacaabdadccbbbaccaabcbdaddabbbbabbaddbadccbbdbdcdababdbabbccdcddbbaaccdbddacccdcdbbcbadacdbadbdaddbbccdacddbcdacadaccadabdaadccdcbbbbdcbbbddadadcdcaabdcabadcdcdbdcbaccdbcdcabcacaadddabbdcbdbacdbacaacabcaadcdacbdbbcdadadadbddcddcacbcaccbacaabddadaaaacbabdacbbbccbcbbbdcbddddcabacabddcdbbbddabbccaadcccdacddacacdbdcadcacdcadacaabadaabadbcabbaadcabcbabbddbccaabaabaadbddbdcdabadbdadccbaccdbbcdcddadcbacdbbdbbbbbcaadaddcaabacccabbababbdadbbddbadacccdbcbaaaddcccaadbbabadbabddadadbcbccdbcacadcdbbcaadadadbbbadcbabaacdbabdaacbdbdaacdddbdccdddcdbacccaccdbcdadcccbccdcaccccadaaccddccccadaabdaadadbbcddcdabdadbcdcaddddbaadadaabbabbaddbcadaddaddababccadcdabdccdddbaaccdcdcadaaabdcabcbbbddccddbaddbacbdcdcbabccababaabcbbcabadbaaaaaccabcbddbcdaddcdcbcdabdaaddacaccbbbcadddccadaabcaacdddbaaadbcdbbddacdcdbbdabbaacdcaccbacababaabbdacdbacccdbbcbabacbcbbcdcccdcacccddbbccddcddccbdaccbdbcbacbabdaadbaabddcabddbcddbbabaaacbdabdcaabbdbcddccadcdcabaccccdcbdcadaccdcddbdbabbbaaabbddabcdbbbbcabdbbccdbbbcadbcbcddcabbdbcbbadadddacdaccdbdbccccbdccbaadabccbdbdbcabcdcdabdcdbaacbdaabbbabccacaacbcccbddcbbcdccabbacacddcaaacddbccbbdbdadbaaaccdbccaccdccadabdddaaddccaadadcdbacbddbabdbdbbdcddbccaaccaadcbbbabbaccddabbdcccddabacddcdadbdbbdabbcdbdabaccbacacdbccaddcbaaddbbdabaddacbadbdadaccddbbcbbdabdcabacbbaadcbabadcdcdcdcbccabdcbbaadbbababdaaadcdcddacbadbdcaaacdaaabaccccccdabdccaddbcaaaaddabcbccbdcadbaabdccbcbddbdaccaacdbadbdadbbaaccbddccddadbaacbbacaaddabbdbcdabdbddcdddcdbdcabbdadcabbccbaaddbbabcbdccbbacbbdaadaabcddcdadaadcabbadbcbbbadbbbdbdbcbcccddcdadbcbcbacdcdacdccbcacadabdcadaacabdabaaaacdbdaabddabdcabbadcdbacaabcaddbbacbcddadacbccbbdbcdadbcbbddbdcbddccbbbcbccbadbbbbdaccbbadadacabcacdcacaabdcbadcaccddaaaabbcddbcdcaccbdaddacdaddaadcddcdacbadacdcdaaaadbbccbddaacabcbdbdacbcabbbcdaddacdaccacadaccdcdbadabbbaddaaaddcadcbacbcbcbbabbcbaacacacdbcddaadbddcaacbdcdabccbbcbbcaabaaaabdcbdccbbaabdddbcccacbddcaabdbdcccbdcbdaccbccdddbbdcddddbccbdbcccccbdbdbdaaadabbcadbbbbaababdbbddadccaacbcccdbbabcacadccddcbdbbabadaacdcdbadcdaaddbbadabbaaaaacddacabacaabcadaacacdddddbcbacaddaaaadacaaddbacaacbdccccdcdaadddabdbdacbbbaccdcabbddacadbaadcaaadcbccdddaaaccdbdbddbccbcacbdccbababbbcbcabdadbacdbcadcbddcdccccaccdcbabbdbcacdbabddbcbbdacbbdcddcdddabbddcdccacbabbcacadbcccddacabababccadaddbddaaacbdcdaddaabbbccbbdcbdabdbcaddaccdccbbacccccbddadddcacdddbcacdcadcdbbbbbddcbbcdcbbccbadbbcccbacaabcadbcabcbbbadbbbbdcabdddbbdbccccdcdacdcbdcdaaaaabbacccbabccdabadccdcdcdddddbddaabcadcacadaacdadbcbabaaaabbcddcbddadccbbaccacaacaaabccbadcaaadbbccabbadaddbbdbdaaabbcccbcadabbcacbdacadcbabdbcabccbaadcdbcadabdcdddcacadbaccccacbadcbadaccdcbcbccbdcabcaddddddcdcaddadaababdbbdbddddadbadcadabdbabcadcdabbabdabcccbbbbddbddcdbabcadababababcdcaabcddcddacabbbbcddddbbcbbacabccbbbbcddbabbbccaadcbabdaacbdabdddbccaacbcdccdadbacbaabcadcadbccbdccddadabdccabcdbdaabcccacdcbbdadcaadbdbcbabaabacbcbcdacbdcbddabbcdacbbdaccbcaaadccbadcbdacbbbcccbbdbbcdddbdcdbbddadadbdccccbdcddddbbadadababbbadbbaaabbaabadbacbcabbddaccaaaadaddbadaadcddbdcabacddcdcabbbcaadaaaacbbbdccbbbdaacbabdcdabbdaaadcaccddaaddcddcdabcaddcdbbdbddcbaacdccdcccbcadacbbdadbddcdaaaaabadddaadcbdadcabadcaadabbadbddbdaccadbddddcaddcbcadcddadbdadccabaaddbbcabdbdababddcabbbcddcaaddbacdabdbbaacabbcdcacbccadcdaacadcdaddcdcdddadaaddaccbdcbaacbcddababbcccbbcccabcabdcacbcaabdbbbacdaacddbdcdbcdaaddbbdaacdbbbdcbadcbbabccdabdbccbddaddbbaacbdcddbbdcdbddaadaaadddbaaabdaabadaaadbbbbcdbcddccbddcdbabaabcbcacdcccdcbbbdabccbbccadcddcbccabcdbddbbabdccaccabdbaacacbbcbdcbddbdcaadccaaadcbdcacddbacdabdbdcbaddbdaaddacbaacddbaabddcbcacabbbccbbadacaacdabcbaadcabbcbddccbddbabdacacbdbdababdbbbddbadaaacdcbcddbadcdabcacbcbbcbbcbcabcbcaacdbdbccacaddaaadbacabadcdddbacaaccbccbaaaaacbbddabcbacddadadbdbbdbabcacdcccccbaddaccbacbcdcbaccabcdddcabccbdcbcabbbcbddbbcdcacacaaabcabbccbdbcdccdabcbacabdddccbadbbccaccbcaabdaddddcdabdbabaadadbbddbdddbacbadbaadbacdacddbbdcaddcddadabaacdddadadcdcbbcdacccbaadcdbbbccacdbcbababddccbcadbbadbabbdcbabaaadaaccdcdbaacacadabacaacbcbbdcabcbcaddccbcbccbcaaddcacdbcbbbdaabaaccbdbabdcbaadddcdccabadddabbccccbcdbaacaadbacdbdbacbbddbdbbcbdcbcbcbcddadaccadabddbabdaabcddabdcdcdaacdbdabaaacabbbaaaddcbcacccdadddbddcbbdadcdbbddcbcddbccdcccbacdcccabbacaabdaddbbcbccccdbbdaaacabbcabdbbacbbcbdccdaabcccbcddadddddacabdbdcaaaddbbaabbdcdcadaccabccdaddbcddcbadccacbaaaaccdcbccbcdcbccaabbddcdcbadcbbbadcabcbcccaccbaabdcacccbbbbaccacddccaacbddbbbbcacacdbcbdbdaddadbaccacbcbaadadababcddabadbccbacdbbaaadbdcdcadacabbbbddccaacdcbbcaacbcbbcdabcbbaddcdadcaacccdbcddaaabacaadcddadccbaaaccbdbddcbbbdadcbaacbdbcdacdbbdbbacadbcbcdccdccaddcdcbbbabdaccbcccadcbdbabbbcbbcabccdddcdbdadcaacacaaaacbddbacdddadbbbcaddbdcdcabcabbcbddbddccbbcacdbaaacadbacadabbcddcccbadcaacddabaacddabadcabbaccaaabccdabdaaabbaaddbcbdaccbbcdbdadcbacdabadccdcbbdbdbadabbbdbcacbabcbcccacbccbbbaacdbbcdcbaddcddccabacdaaccccabcbcaaabacdbcdccacdcdaccbcadddcdcdbccdadacdcbcbacdaddabcbcbbcbabbacacdddadaccdbacabadcbccaaaaddcbccdababddcdaabdbdbdabcddbdbcdcddaabaddbddbcbdbbacdbcdcbabbcabddcccaabadabbcabdcdaaddbacdcccbcbabbabadcacbccbbbacbdbcbdaaacdadaaaaaaabbbdaacddcbdaddbbdcadadbdabaaaabbaabacbaacbdadabbadabbcabbcbbddadbcaadadabaabaacddaadadcaaaaacdcddaccbdacdcbdbadccbbadadddaaaaaaaccacbbabddcbbdbcddcbdaacdbccdbbdacabdcdaacccbccdacbdbadcdacbabcccdabdcaacddaaccbdcdcaccdabbaaccbabdaabccbdcccdbdccbbadaaabdabbdbaaabbcbcdadcdbbbccddcabcdbcdacbbbbabbcabbcdbbaabdbbcbcadbabcdbaaacabcbbcaabddcddaaddbbbcbbdddaccccddbabdddbccdcddddabdbbdbcabccccdabbabdaddadbcaaaaadbbbdbadcbacdccdacbddabdaccbbccbcaccddcabdbddadbbdbaababaccabddadbcbcbcabbadcccbbcdcacbacadaabbbdcbbcdccabdaabaabccbbdaaabbcdabdbaacaaddcbcaacbbcaccdbdcdaccaabdababdbcacaccbdaccbcaccbdabccabcbabcbadcaccccadadccacaabdbaacbbcbddbccddaabbcacbcacbaadbbaacdddabaacbbaddaaabbacdabdacbdbadaccdcdccbddbdddadabdabdddcdacbdabbdbdaabcacabcbdddacaaacbaacbbddacabcccabbcbaccaccbdbadcabcdadaabbcbdbbdcadcbddabddbbdadddcabacbcaabbdcdcaaddccacabacaadadaaccdcdbabddadbcabbdccdcbcabcbcbdabbbccbbbcbdccdbcaaabaddbacccabbdbbaadacdcbdaacccbbbbcbbdbaccdaddcdcdbcbabdadddbababacaaabcdbddcabbbbadabcdcabcdabdccabaadccdbbbcccbccddbdcadddabdcbbcadddccdccdacdaadbadadddcabcbdbdbbcbcccbddccdcabcdabcbcaccabcaaacdadcddcabcbcdcbbddcbbdbbabadccbdbbdddccaacbbabaaacdcaaaacbdbbaacadbcccaacbadacbbaddbccddcabacdadbaaaadaddabdbcdacadcabddddcabccbdadccbccdabcbbdcbababdcbddabdcbacaccbaaaccccbdddbbccccbbdbcdcabadaacccbcacbcbbaddddabbdbcbbcbdcabbcdddcdbcacaabbcbabcbcdcbccdccadcdbbabaddcccdbacacccacddcbcabbbdcddbaacdddadcdcbaccdadbbcddabdbbbddcdbcbcacbdacbdcbabdacbccadcddddcababdccbabdddbaabbbaacccbdbadacbcbcbddddbcdddcdccbacbacbaacdbdcbcbdcdbbbddbdbadbdaabcbbcadaacdcbcccbbcacabaacdbbabbacdcaacdbbacabbabdcdacbcacbbadcadbaddccdcbaadbaacaaadddabaabcbbdaadbbbbdbbdbcdbabdbabacacbcaacddbcddaccdcdcbacacbbdcaabbbcbdbbcdabaadccccabbdddacbccbdacdcdbcaddbbcdcaaabcbbcacdcacbdbdacabbdaacbbbbbcbdbdbbcdbbcdaabcacbcbddadababcadcdccacbabadaaaabbcddbddbabcdadcccadaacbcacabbcddbaadcbacbdbadaacbdacabbacbbbacabadddcacbcacdaadbcdcadbdaccacccbbcdcabcccbcaadabaccabcbddbdcabdabcdbddcacddccdaaaddabdbbcaddddadabcbdbbccacaabcdacbccddaadcabddadbabdbaaabcddabadcdcadccccaabdcbabacbcadabaabbacbcdaccddcadaccddbabbccacdcdcdabcdddabdabadacaaacddcadccadbdabcaaabbadddcbbacbdcdccdacbcdbadadcacacbddbdbcdbbcabbaabccbadabcdabdbcddbcdacddcccccaccbacdbdbababccacdaabbcabbdcccbdaabdcadcdbdbccabdcabbdcabddaddcadcaacadaaddbcbacaadadbcbcadbcaaadbddcabbbbbcbaddddcaccbabddccabbcadaaddacacadbbccbbdcbdccaddbcbacdcbdbadbcbabdabcaabcaadddcaaabdbdccbaabcdabbcdacaadbbccbdcbadddbcdccddddbabaadbdbccbcdbbccbddccacbbcbacdabbccdddcbabcadaacabccbdbadcacbacbddcbdbaaaccbbcbdbccaaaccbacdbbcaadddccacdadbdcdcbacbdddbbbdbbbdccdcbaadcddbadbdcdbdaadbcbbbbaddacaccabdddcbbbadcbbdbcdabdbdaadbaabbdbbaabdbbabccdccacbabbaddcaacadabaddbababcbbacbabbbbacadadcbcaabdacbcbcbbcddbcabacabbbdcccdcdcacbcaabcbdcbccbddccbdacdacacbcddbbadcdacbdddbcbaabbcdbbccaaacdbdbcdacabcabcadaaccbdccbbcadcccaabbcacabbddaabcdcbbddbdabcabdadadaacdbccbcadccabdbccdbbbadccdccbadbccbddacdacbcdabaccbbabbcdadcddacddbddadaacdcccdddadccbdbcabcdabadbcaaddbdcaccdcacbacdadabcccdcddcabbbaaccaddbdacadbdbbcbbbdacbbcbbabcbdcacdbbadbcacaddcadbadcacaaaacbbbadacdbcdbadaabbaaccbdadccdadbdbbabbdabacaaacdbddabaaabcdddcaddcbcabbbcbabbdaddcadaaccbdcbaadcbbddbcdabbadabaadbbdcdbcdababdddcbcabbabdbccbccadbccdbddabbddbcdcbcddbddbcacbacbadcdbacaaccdabbcbdddcaadcaabcbccabadbbabbdaddacdcbacbdbdaccdddbcdbbccdadbdbbaadacbbadbcabcabcacbaaabcbbdccdaacabbddbdddabbddabbdddaabdabbbcadbdbabbddbdcdcaddcdcdbdbabbaabaaaccbbdcaabddccaaddadcbdbcdcbcacbdddbaddabccbaaaccddbbddccbdaccabbcbaadccabdabbacbdcbacabbbabccbcdddaadaddaabbcdcddbdcbddbccbdccbdaccdbbaacbddcabcacacbdddcaabbaccacaccabacbbcacbadcabddbcbdbcddbbcacbaddbcbccddbdddbddbbacddbcddaacbdcddabbbbadcbbaccddabbcdcadbddbccbadddbcadbbdcbadbdadadcadccbdbacccabacacccbbcbbdccbccdadbdbbbccddadbabdcbdaddacdbacadccbbcbdcacbaaaccdadcdcbcabacdcddcbaccbcadacddddaaabbdbbbcbdcdcdacdbcccaabdccdacaccabdbdccbcacadbdbadaddcbaaaabadbddadaaddbcdccadddbbdbbaabacacaabbabdcadacacdcdccdcccaadbbdbabdaddbbcbabdbbcaccdbadbbbcaccaddaacddadccdbbacabbdcacdababddccaadbcadbbbcaccbdbcaddacdbdbcbcdddbcacbbcaadbacbccccaaadaaccabbabbbacacdccdcadcdccabbdcddbadadcbbdddcacbdbacbcaddbbdaadcdabdadddccadbdbbaadcddcadaabcdcbbdacdbbbcbbbcbcccdcbdddbabcbabacdcbbacbdbabddcdcdddaccababdbcdbaadaddabdbcddccdaacbbacdccbccdbadcabcdacddcaacbaadbddcddcbdccdbbcbdcaaccbdbcbaabbdbaddbcbbbddbbabacacddbddbcddddbadccdacbaaaaccbdaacacbbcdbddbaaddbbabdabdbcbaacddcadabacdacdadddaaaccbadbcddabcdacbbdbadcdcbcbbbccdcbdcddaacacabcbcbbdbdccabaddbdddacddcccbdadbdbacdcccacddddbccadbbcbdaccdcaadbdddccdacacccbcadddddabbcadbddababaddcabddacdabdcccbdddbabccadabdcdabcabbdadabaccbbadcaaaaacdadcbabacccdaaadabdcbcbbacddcdbadaaadbaabcdbbbddbcdaddccbbccacddacdbdadacbdccbaabbdcaaabacdbdcbcdcdbacbacbcbcdabacddcabbddbdabbdcaddddbdbbbccacdadddcbacdabdcdaddbdaaaabacbdbbbbbbdcabcddbdacdbbccadadbddddbbdbcdddbdcaccdadaaddddaadabbbadbdccddbcdddcaaabbaababcdcbddcacbbcacaddabddabacadbcbaddccacbddadaabbabbdcbadbccaccacacdabddbaacccccccdcddddbdccadabcabaccdcbcadddadcdcaabcdbbbadcdaddbaabdccaadcbbdabcacddadbddbcbcbddcbbddbcbbaccbbddbddadcaaccbacabccaadccabadbaaccddccdcccabbaddddaccccdacbcadddacabaaccbbdbdbaddbcdbccdabaaabaddabdcddbdbdaccbcddbbdadbdadccccabcdbabadaacaacadabccaddbacbcaddbacbbbcdcbccdbbabadcaddacdcccbddaacadababadbddcccbcbbabaccacbadddbabcdaacaacdcaccaccbdbdbcdcbcbbdcdbbcabadddbcaaacddbbcbbadadbbccaacbcccaabcbcaaabdccbcdaaddbcdcddbcccccbcbcbdcccbbdaaaddbbcdbcbdaabddbdbcdbcdbdddbacccbddbcadccbcaacaabbcadcdacbabdddabbdddabadccdaaaacacacaaabaadacaabdbcdcdbdadbbcbcaabacadbbadbdcdbdadbcbaabdbbadcbcbbaaabbcabdcacddadddadacabaaccadbabbdcbaddbcadbddbdbcbbbdaacabdcdbbcaacbdcbbdcddabcbdbbdcbcabbaaddcdaadadcbbadcadaccdccddbaabdbbbdabdcbabbcabbbcbcbaccabbbcddadbaabaaadadcccdbccdabccdcbccddaccbdbabbadcabaabbccdbbacbbdcdaccccbadcdbdcbdccabbcacdabccdbdbcbdabbddddbdbdcbdadacadcbddddadddccbbabdddccccccccbbbdacddabaacbdacdacdcdddbcddddaddbcbbbaaadabccccbcddaaadbdabcccadabdbdcbcaccdabbddcdadabbbabadbddddadbddcddaadbddacbdadcbbbbacdcbabbbabbcdcdacabbdbbcdacddacdadddaddcdbcdbcccbcbbcccccdbbdacdcbabdadacadacddbddaccabdcaacdacbdcdabccaaadbdbdabcbcbdbbdddcccccbcdccaccdcdcbcbbabcabbcbbdacbcbababdbcdbdbcddbcbbcbddcdcddacbabbbcaacdbacadbcbcdbcbddcabcabbcdcdcbdcccdbadccbbaccdcaaddbdabcddcddacadcbcbbbacdbdadcbabaaadccddaabadadcdcbbaabdbadcddbabddaddadcccaaababcdaaccbacabdabcbcdccccbdbbaaddbbbbbcabbadbcbcdccadccadcacabbdddabaddccbdccdddcddababdaddbcadccacaacccccbbbdbacaddabdbddbacacbbabbaaddbcbdcbdaacbaddaaaaaaabbbccaccadaacbbadabbddaaaaddddcbbdbccccbaacddddabcbcbacddbabcdaddcabdbbbbbbbccaabbbcdbbabcbadaccabbddccacdcacadaaaabccccbaccbdabddcababdababdbbadcacbcbcacbbbbcdabadacbbbabbadcdbbdcddcbccddbdadcaadddbaacdacbcdbcddaccddaabbacdaacccaaddaabbddbabdbaddbdcaabdddcadaadbccdddcddcbdbdcdbcdbcacdccdbbbabddbcabbddbaacccabacbabbacbdccaabcabadccbcdddcdccbdaddcaacdbbaadcbdbbccaddabaddcbddadacaaacbdadaadbabdcbdcaabcccbddcdacbaccbdaacdbaadbbaccbbbabaccbddacacdacaddcbdcadbacbbbddaccacdcccdadcabcbbddddadcdbacaaddccbdadaaacbcbcbdbacaacbdbdccdacaaabadcccacdaddbacabdcadadddbaddacccccbdadbbdccaccdbbacccbabadddddcbccaaddacabbcdddaacaccccacdcacdabcccbabbbcdbaaaddbcbbaabaadbcabccddcccbcccddcacdcdccbadaacacbdaacaaaadadbcbcadbbababccacdcaaaccbbcbbbcacdcdcdcadadadddbcdbabdadabbbccbdababddbcdddddababdbacaccbcbaddbacbbcadabcccbbbbddbbbdbabccaccadcccdbcddcadddbcbcccbbbccdcddcbdbbccdcdbcabbbdccaabccbadbbcaacdaaaaaaabacbbadbdbbdbaabbdaaddbbcbabddadbccbdbcdbaadddbcddbdcadcbadadadcacaabbbdbdcbcdbdcdcbcadaacdbcaccddcdcadbacbddcababaabddabcdccaaadcddcbaabddaaddcbdbdaadacbddcadcabddddbdcbcadaaabccbbddbabcbdddacaccccccdaacbccdacbdcacbdcdcabdbddbadbddccdaaacdaadbddbbcdbdaababbdddcabdaaccacbddbabddbbbdbbdbbccdcdcbcbdddaaaaabbcdddbcaaaadddcbbabdbaaacbbccacacddbdbaabcdaaddaabddbcbcbdbbcbbaaaaaaacdadcccdbcaabcdacaacababaaaccbadcaaddbcabcccacadcaccbdddcbcbabddadcdaccbdcbcdbbccbabcddddcbaacacccdaddcdcaacccbbcacdcdddcbabddcccaaaaddabcbdddbcdcadacdadcbdddcbbadcbaddbcbadbcaaadabaacbcdcccadbabbaadbadacdcdbbcdbddaddaddccacadaaaadcadcacbbadbdabccdccdcdaaabbbaacdbcbccbaccdaadbaabacdbbbcdacaaaaabbbbdadbdbdaacbaddbacadbadacbccbabbbdcbddaacbbcdcbcbddbabcaaaaaddacacacdbcacadbcacdadbcdcbabbcbddaacdacaccdadcadbcbadbadaacacdbaadcdbdbadcdbdabdaabddccbbbadacbdbadacadddbbdddcdcadcacdacdaacdacdddacbadcbbddddabbdcccbdbacdccacdbdbabcbaddcbbbbbcbccacdbbbbccbcbcbccdacccadabddadcdacacccdbbddcdaccbcdcbcdcbbaadaaabbabdccbacbabcddcdcbaaaccaccbaaadacaadbddddaadadaacbaccdccdbddaadadaccaabcbbbbacdabbbabaacddddbdbdddcbcdbadcbbdddabcacbacabddaddaddaaaaaadcbaaabadbacaacbcdadbcbbcbabacacccbdddcbddccdcccccabcccadbbababacbdbdaccddbdbaacacdbdbcdbbdcabddcacccadcbcbbdcaccdddcccccacaddbadabdbbacaabbadbbadddcccbadccbbdcaaabdaacadadbcbcabbdabdbdabcdaccdbbaacdadbddbccadcdabaacdabcdbadbcbaaadccdacbbcdabdacaccaabadbdbbaddcacbaabaabcbdadabbacabccbbdaaaaadcadbadddcabadbacddaccabcdabbaccacbdbdbbdbdacbdcbbcadacbaacdabbddbacbbddbddaaddaddacdacdababcdcbbcabdaaddddaadcaabadacabddcaddaabbbbbacdccbacaabcbccdcdbaddbabddbdabadcabcacbdbadbbbcbaddaaadbabbabadaacdaddcbbcbdaaccdbcdacdcabcbadbabcdabadcadcdbdbadcbbbcdccbddbbacdcbdcaacbaddbcaddccacadacabadcddddcacbcbbaadbaadaacdabdababbabdcbddadcadcbbddcccddacaacdcabdcbaddcbcbbcdddcdccbccbadbccbabddbbaadddcdcbdcbbddabaacdabbcccbddcbdabbadcdccbdbbbdbdbcdbcbacaacaaaabdcbcadaccdcaabcddcdcacdcdcabbaaacacccabcbabddadcacadccddcdacbbaaaabbbddddaaabccadbaddcbdddbbaadaaaadadbbadaaddbbbbaaacdabadbddccadddcdcaacbbddaaabdbcacccaaabbbccdcddbaabbdaabacbbcbcdaddaccbcbddbbcbaabbbdddadbbcbdbcacbabcabbccbdddbdacbbadcbdddbcbdccbbbacbabaabdabaddbccdcdacddcdcbdcbcbbbcdccdabbadddbbaabbabdcaacdbbddacbabcabdccbcdbabbaadaacaccaaabbddadaaabdcdcccdaaccbaababbbbabdddbacbbdcaacaabcbbadbdaadacaccdacdcabccadabbdacbbabbadaadadcadcbdbbcaccabbbaadbcbdbbaadcbacdcbabcbaddbadbabddabcbcbdbbbacaaddabdcbadcaaabbdcbcccbbdcacbcadbaabbdacbcbadbbbccbbccddcbbcadaacdadcbcccacabcbcccbbcaabacccdccbaccccbcdccadbcdbbbcbdacbadaccbcabacdcdcbcccbbddccddacdccaacabaacdadabcaadbdcbcddbbddbbdccacaacadbdadaaaadadacabddadbcabcaabbabdbbdcccbadaccaacddcaaaababcaaacbaaabdbdacdcddbbbadababddcbcdadabbdabccdbbbcabdadbccddbacaacbacabcacdddcaddddddcddcdccddbadbbcaadbccbababaddccccdcdaabcaabbccbcdddcadbaaadcbdbcbcabbbcdaccdacbdbbcbddaaaccbabbdbaaaadbcbcacbcacddbbabadabcadabdbaddcbcacdddbcadccbcccdcadddabcabadcdddbdccbbdbadabccbcdacbaaadbddbdcabdacbacbdddaaadabbacbacacdddbdbacaacccdbcbcdbbaccabcbdbaddacbccacbcadbcddcdddababbbdcdcaaaccbbadbbbddbccbadbcaccdbbabdcadbbbcadddbcddcbcadaabaaacabaccacacdccbdaabdccddbacabacbabdcddbbdaaabcdcccccbcbdabacbdcdccccadcaacbdcacaadcbdcaddbbaaabdccacddacbcacbadcdcbbaaadabaadcaddbcabbabcadabbbcababbbaabdacdcacdbdbddababdacaccbdcbbcdabdbcdcabcaaccdcabbaccadbbdcabadbcbccaaccddbcddacacabdacdabdcaccccabdadabdbaaabccdbdadbcccdcaacabbadbdcbcaddcbbdcadcaabcdaddabbdbddacabdabbdbdaabbbaddaacbccccbdbbcdbaddbddbacabbcacbbdccbccbbaacbcccacbdbaabdbdddabcacaaabaacacacaacdccdacdddcaabcadaddaaabbddbdbccdbdbbadcdbbdaccccadbdcbadcbcccadcbacdbcacacaaacabacdcaddbbcdcdaacdbbdacdccbdcdcdaccdbacdacacbbbaacbbdcdbacccaacadbbadbabadcdaccacabcdbdbdbacdddbbaabcdcccaaadddbddcbdcdcdabadbcbcacacbdadbaadacddcccacaadcbddbdcbbbbddccbabcbacdbabacabbaadbbaadaababadcbaddbcbbdccaabbaaabdbcbcdbcadbacaddbcbbcbacbdcdddacaaccdadacbddabadcbddaabdcacaacbbacbbaacbccbaddacccdccddabbacabcbccacbdbdacdbbccaacdaabadabcddbacbbcababadcccadaccacddddbbbacbdcbbbcabbdababcabaccacccabbdacacbabbbbacbccaabbaadaabdacccadbccaababdacbdbbadcccadabcdccdaadcbdbbcaddcdaacbadbabdddddbdbbdaccacadccdbacdbadabcbbbcbbcaabdddddcdcdccbddccaadbcddacdacabbcbccdbaccbabbcbbabcdcaaaccbccccaadaaaacdabdcbaacdcddcdaaadacbcccddcbdbdbbbaddbdacccacddcbdcbdcaccdadabadcaccdbbbaaaddbdbdcacbbbbdccdbaddccdbbccdbdbcbaddbaaddcbdddadbcddbadcccbadaabccdddadcbcdbbabbbaabbbadddbaabdcbaccdadbadabaaacacbcbdddaacccdaabdbbabdaaddadcadcabadacdcaacaacbbccdcbdaaccaaaaadbacdddbaacbabdcbcbadcaabbbaabddddbbaabdbbacccccccdccdbcabdcbcabaddabbccdbbdabbdbabdbdcccaccabccbdddcabcaaaadcdcdacddbcbcadadcadabaabdacacabbdaabcccdbdccbababddcdacbbbacababcbacdbdadcaccbbbccacbbddcbabdbbaccbaaaadbaabccccbaccaccbbdbbccdaaccacdddccdaabcdcdadaadbacbdacbaacabbbacaddcdbcdbdcacbadccccdbbaddbdcdcdaacbabdcbbccbcdbcacabddccadacccbcdcadbbddcabccbdccbcaddccbadcabaddacdddadcdcaabbdaadbaadcbccacaddcbccddccaaddbbddacbccbbcdbccacabdaccaabacdbddabaaaaacdbbcaabbbaacbddcddcbbcbbbabaadaadbdbbdddacaddcbddccbdabbcabcbbabdbaccdddddaaadbbababadcacdcdaacccbddbdddddccdaabbccbdcacdbdcaabacadcacacaabacabcddacbbadbccbdaacbacabdbaabbcabadabbaccbcdadbcacdcdccaddcbbcdbabcaababbdccdcdcdacaabaabbcbcaacdababbddbbdaddcdccbbddcaadcbdaccddaccbddbabbccbdcbcbbdbdddbccacabbaddddddaaacbdcddadabbbababdccadbcdabdddbaacbbdbbaaacddbbaacbbaabbcbbbbddbabcdbbddabbabcdbcbcabbadabaaccbacaaaaabbcaadbbacadbcabbddcadabdbbadcabadbdacacbccadbccdadabbbaabdabcbcccaddcaadbcaabdadabdacadbddccbdbbbdbccdbbbcadcbdccdbaacadadbcdaddaaacacadbdbdabdacbbbabaabdaaabddbbbcacdbcccadccbabcbdcadcbdbccacbbdcbccaaaddccbbbcdacccccdddbbcbcaaaaabbcaadcbdcadbdaacaaabcbaddccabdbccdddbcdacdddccbdacccaaaccacaadcbabcdbacaadacbcdbdacdccbaaaadcdbcaadabdddbdadbdadbaacabcabadcddacbaccdbaadbdabddddbcbbdabcccddbdcdbdbcddddbccccdabacbcdccbbadadbccdcaaaaaaddbdabdcbddbcabbccaaccaaddcdddbdacadddcacbabdcbadcdcbbaddbcabcbcababdababddacbaacadbdbdbdaaacbddbdccbddcdabaaadbacadabcadadbbabbdaacabadddaacababbacdabcadaccbccccdadaababdbacdaabcabbdcdccdaaadddabadaacdbabbcccaabdaaabccdccccaccaccccbbcdbddacacacddcbaacbdcaaaadacbaddcbabdbdbbdaadbabdbbacbbbcdddadabbacddbcbccddccaddddadbcdaabccdacbbcadcadabaacddcbcdacaacbcdaccdddacdbaabddcccadcaabdbbbaacccddcbaacadcabcbdbbaabcacdadbcddddabbacbddbcdbbaababddddacbcbcbbdabcddaddbccbaddacbbdcddbdabacddabcaaaaaacacadabbcdcbaacdcdaccddbbadbcddddbacbdddcdbcdddbbaaaaaaccaabbbabacbddbcdaccababcaaddbadccdcbcdbadaacddbcddccccdbadacbcbccbabcaccdcbdacccdbdbaacdcdbaadabdabcbdbbcbcccdacdcbcadadbdddccbbdcabbdabcdbccbbdababcacdacacbdaacabdccadbcddcbcaaabcdcaabaaacababadbaaddbaccbdbbccccaacccaacbaaabbbababbabcaaccdbbccaddacbcccdaaccddadbddbcccdcddddbbcbbccacacabdbcdccacadcdddcccaacaabcbcddaadbbabbbddcddbcadddbbdcaabaaddabaccaccaadadddbcdbadbabcbdcbbaaccacbcdcabbcbbadcadbaadbdbdbacddbdbcacbbacbbcaaabbdaaabcdabcddcadddcddacbacbbaadddcabdacddadccdaacddcbdbccacdcbbdaadcacbcbdbcbcaddbbabdbababcacdbdccdacadabdbbabdacbcadcccccbdbdbddcbcdbddccdbcaadabacbbcaddbbbabccbdbbabaddcbbbaabdccdcacbcaaabadbbdaaabdccdadbdbddbdccccbbdadaaccdbabdcdbbdcbcbaabaddbabbacdbcbcadcccdadadccccdbabcdbaaddbdddddabdbbcacdabdcabcbdccbacdddcdcbcbabaaaccadddcabbdbcbabcaacbddbddaacbdcdcbabdbdcbacdcbacbccbacbaccadaadbcabbbdbbdacadbcaaabadacabcbcdbbaaadbbcdbcbcbcdcbdbbcbbcbcddcccddbbddbcddcbcbdbbaaabdabbcdcbddabcccbdacaccdaadbbabcbdbbcdbbacabaaabadacacaadcbbcdaabcdbbbcbcbcbdbbccacadaaabdcacbdadaadcbccdaaacbaadcaadcaddcdbcbadbccabcabcaadbadabbddbccbabdabcabdbdcaaadaccccbacbaddabbdcbacabdbcbdadadbbacccdccddddcccbdacdddaadbabcadbaaadcdbbdaadacbacccabdbcadbccccdbadaaaccacbcdacddbcaddacddaadcdddcabdddabaacacdbdacaddbbccabbacaaccadbcababcabcbccacbbcaddcdaabdbcaabcdacaaadbbccadbdadadbbdacdcbddccdccdbaccdbccacacaabccdcdaabbadbcbbbcbdddababcdcabdbaddaadcbdabbacbddccddbadcaadbdaadbbdcaabcddcbdbdabccddcaabbccbcdbcacdbcdaddadaabddaadcccdbdccbdcadacbacaacabcdaccdbbabcdcaabdcacbccabdcdbbbddbdbdddccdadcacddddabdbcdbccaccabccbbaadaccbaadabbddbbcbdbddbbdbbcabdabbdbccbcabcacdbcdcabbdcdccbbbcabdbbcdbcaddbcabbbbaddacdccddadaabadcbcacbadcabdcddbabacccdddabdbbbcdcdacbbcbccbdbcbbccbbadcbabcdcbcdcbdbccbdadcccacbdbadccbdccabacacbaadcccabdcaaadadaacabddaadbdcdbcddcadddacddacbbaacbccddadddbbabbdccbabdbbdbddabaacdddacbdaacdcdadadaadbbacaddacccdbbcdbddcadadcbaddccdaadcbdbcbbacddacccdaacbbbddbcbbdaaadadcacdadcccddbaaabbddcdcbbdcbbdabbdbcbacbbddadcdddcbdaaadacbabcbbbabdabcdaaadbcdcbbcbabcccccbccdabcaaaadcaacaadcbcaacaccdabbddabcdaabadacabdcdbcdabaccaddbdbcbbddbdbacbbabaabcbabaadbcbdabbacadbdbbadcacdddbddcbacabbcbdcdcdbcdcdacbdaccddbdaabbddcbcbbbabbbbdbdbdcbbbdbaaabccacccacbaabcdadbddaacbcdbabdbabccdddaadacbbabcbddddaadcbdbcddcaacacacdbbbbbcccabdcdadcdbcbbabbddbacabcacdbddddbdadbddaacbddcbdabcbacabcdbbbdabdacacabdcaaaddacadaaacbbaaccbdbbbbbccdbcacaddcdcbbabbacadadaacbadbddcbbaadacdbcdbaacbcdcddbcdbcbacacdbbabbdcdaccdddababcdcdcacadbacdbacaddbcaaaaabbbccbdadacbbabbdcacdbddcdbbacbcdcdadadcbdcadbdadcaccbccbcbccbbcbbacdaaddabcacbbcaacdbcbcdbddbdacdababcbbbcbacabbcdabacaabbdcbcbdabbbaddacbbbadacbacddbabadabdaddcbddddbbcaaadaacccdccdbaacdddabbabdccbdababdadbbabbadaddbabbcaaadbabcbdbbdddababbaadcabddcabbdaabddadacbcdbaaccaabbdcacddcacacacbccdbabbcbdacabcddcacacddaabdcdcaccaadbdbdaacbadbcddcbddbccbaddbccadbdadddadbadcabaacdccccbbbbabadbddbdcdbabdabbbdbddcdbabdbbabccdcaddabcaaadacdcdcccaaacababdbadacbacddbbcaddbcaccddbaddadaddccdbcaddcbddacbddbaaddbcabdbdadadadbbabcdbdbacdccdbacbddcddcadacbaadadbacdacbbbbcbcdacbaacadabcddabddcaccbacdcdacdcddcccaddbbdcbdbbdbcadabdcdcbbbdbcddaabbbcbaaddabbbadddddbccabbbdccccbcadbbbbabdaaaabaccacbcbdacbacbbcbabddaabbdbaccccbbadbddbaaabddadbcbdadbcbcccdcabaccbabdacdccaccabcacbcdcccbdbdddaadacccacbbabbddacddaadcddcbcdbcdadaacdacbbbdcddabdcaddcdcaadcaadcbaccbadadbcadddababaddcdcbdccbdabcbadcbbdccbddadbabcdcbcabadadddbadabbdadcdaaaadaabdadbdcbbbccdbbaaaddcbbbbbcccccabbcdadabcbddcbcbdbdcdabdccabdbacbbddaabbdbaaddbabdaadbdadadcddacdaadcbabacacccadaccabbdcdcdddacacddbdccbbbaaccccaadccabbbdddcdbaabaacaadddabacccbcdabcaadbbbccbbdcdbbdddbdbcbdcbabdababaababdcaacabbcbbabddaddccadddddbacdacaaacdaabccaabcaadcbaacbbcdddaabcaccacbacbaaaababadadcbdbbddbcadabccccbbbddaccddbddcbbacccbadbdbdbbccadababbdddcaababcacacbacbdbbdddcaddacbdbaaddcbdbdbdbbbdbdadacaaddaaadadacabbabcdbbcddaadbaabadbbdddacdadbaacacddbacbaddcbbbbddccaddacabccccccbdbcbdbbdbcabadddadbcdcdaccbdaacbaddacacbdcbbbbcabaabbbadaccdbbcccdbcddbcbacdbcdaabadbadcacababcdbaaddbcdcbbdcabcabbdbbcbdbcbcdcadbadcaadccdaddbbdbdbaccbabacbadbacbdadadadbbdcaddabaacbaaacbbbbbdbcadbadaacacbdadbadbbdcbdcdabbadbccdccdcdbaacacbdbaddaabadaddbbcabcdaccdbdabababdacdcbacaacddddcdacabbdcadbadbabdbdbbcbcaccbdcbcdcaccacbdaaddabbbdbabadcbcdbbcababadcddaddadaabccdcdcbbacdaabbbcaadcdcabbaaddbdbdcbcbdcdcbccaccbabbcdbbabcadbdcdaddacdddbabcdadabaadbccbbdbababcabbbaacbcadccdaadbadbabccbcaadbaadabadbdbaaddacdabcbdabdaacddaaacdadacbccadddcacaacbddddcdcdbbaabaaacbadadacccbdbdabdcbabcaaccacaaccdbacdabdcdbcbbbacbcbdddcdcadadbcbbbbbaaaaadbabbacaabbdadcddbdcbacadcccdaddcabcbdcbcbddcbacdcbbddbcbadbcdbbddbadacaadcaccdcabbccbcccbdddccadbbbcccdcbcdbdddacabcbcdcddaabbbacddbbccbbdddccbbddbcabccaccdccbcadaacabcdaaabaabdadbddabcddadcddbdaabadacdbabdddaccdccddcadbacbcacddcccacbbcadbacdaaccbacabdadbcdadaaccdcaabcaaccaccdbbaccddcdadddbbcdaadbacbdcaaaccabcbbbcdbbcdcabacbbccccacdcbcdcdcdbacbaababdacdbcdadacaccddbdadcddbdabbacbbcdcdbbadbabdcdccadbaccacddaaccbcbadbcbbcddaccdadbabbabdbcccdbdaaaadcdcbbccaaddabbaaccabbaccdccacbadccadccabbdacccccaadcdadddcbdcaccccbcdaabaaadbdbacbadbadcdadacadddaccbbcdcdbbcbaacbcbabdcdcdabcddbbcbccbdddcabacccaddbaccaadcdddacdbdadbccddadaddbdbdacddcddbdddcdcbcbcaaddaccdadcabacbcdbcacccbadaabcabbbbabacaacbdaaabddcdbdacddbccadaaabbbacadddbadcaccbcadaabbdddbaccabacaddddcdbcbaaccaadcdcbdabdabdbddaaaaabacbadbdbacaaacbbabbbadbacbbdabbadcddcdcbacbbbcbdbaddcdcbdcadcabcabcbaaaacaccacabcaabcdacdaccabadbdabdcacdabbddbaaddcbacbaadbbbbdbbbaaabcdacbdbaccaadbbabdabdabdbbbaccacbbcccbbcbdbdbaabbdaacdddcbdadbaabbcabbdcdbaaccdcbacacadcdcddabcdacaadcdaabbacacbcdcadcdbdcbdaccaabcdacaabdccbcbdbadadcacabcbaabbdabdbadcdcbabdccaabcbaccdcbdacbabdbcaddbbbacaadaaddbabbdccbdccacbcbcccdabaddbadabcbbcaadcdbadcddadcccabacccbaadaccbbddddbbccddbcbbdcabcbdccaabbdbcacbbbaadbcdcbdbbbcbbadcbaacbdddcabdadbacadcacacdbcbbbdddbdccbccdbcbadbbdcdbcbadabcdbcadbddddaccbcabdccdbdadddcadabcbcdccbaccbddacabcaacbbcaabcdacdcdbadacdadbaccdadcdabdcabaabdadabcaaaacdcdacbabdcabbcabbbacccaacabdddadaccdbacdcbdcdbdadabcbaaaccabdccbdbabdcdbdcbcccbccdaaabaaaadddababdcdcadabbdaadbcdbacbcdddccdacbaccaccdbbccadcbcccdabddcbbbbcacdaabcabbdaabcbbdacbcbccbdacbcaabcbccbcdabbdadaadbbbbbbddabbcdcbbddcbcbdbbbacabcadcaccaccdadbbbadccbaccbbddccaabbcadcddadbcabcabdabbcdbddbbdadbbadbbcdbdbcbacabaaddbacbbcacabacbdabaddbdbddccbdcbbcddbcaaccaadbddccbcdcdcbbbcccbdbadbdadbbdbdcaccacacbccbbbdacacdcdddcbcbcacbcbcacdccbcdcacddaddcbbaabcdbbbaababadabccccabcdacaaaacddabcabbdbadbbdbbcacabaacbddddadbbddbcccacddbcadabcdbbabbcacaaaababcddbaddabbccaabdbbddbbbdbaadabdacdbdadaabdcbcbccaaadaabbbccbcccccdbabacbdcccbccdbdcccdaabbbaacccdadcaabdbcbaccabcacccdddcbdabacadddcbbdabcddbccbbaaadcaabacabcdaaacdbddaaccadadaddddaacabbbdccbbcddcabdbaaacacbdbcbaacdaaacaddbcacbccbcbadcabdcddbaabcabcbbaddddcadcbcbaabdbacacbdbaadddbdcddcacbdcdbdacbbdadcccbbbaddabbbadaaaacccadcbcaaddccaccbbdabdadbbadcbabcdadbdbbadbaaacdbdcbdcbdcacbdbcddbaaadcbdaddadcccdccdcaacacddbbcbbaaddacdcdadbdbdadbdccbabbcaabdadadacbddbaacbbccbbcccdcbaadcaaccbabcbaadcdccacaabadacddcaddcdbabddcdbdabcddcadcbbcbbbbabadccbccabacbdcdbdbcdbcdbaacbcbaabdbbdcabcddabaacaacdadccabdacdcabccaabacbbcccdcbcccdabdddcadbdacccbdcabdadabcbadbaaacdbbddcbccbacaabddccbcbcadbacacdbacbdaddbabbcacddbbbacbcaadabbdbcdddaccdaaaaacdbdadccabcdbdddcbbbacddcaacbbcabcaabbacbbcbcacbcadcdcbabccacabbabadcdbaacabacaadbcacabbbbccdbcabdbcdadbcbcdaadbbbabaddaaadcbbbadbaaddcacadcbbbcdcaddbaabcdadddddacadaaacbddcacccacdbbbdaaddddcbccbbcccdddaabddbbcccaaadadacbbdccacabbddddbdacccdbcdabcbcbadddaabacbcdabacbddddbacabadaddccbadcdbaabccbbacccbadaadbaccadcbaacbacabbdadaabaacaabbbabccdcdcacbcccabbdcabaacbdacbdccbcbbadacbcdadadbbbdddddabdaacdaaddcbbbccbcdcadddcbaddccacbdcdbdbabbddcdacdbadddddccadbcccacbddcccaddbadbcbdacabbdbddabdaabbcdcacdccaacccbcdbccbbdcadcaadcaabaadbccaabbcaacdabbadadcbadabbcbacdcdcbccbdbccccbadadbcabccadddddccacaaadbababcbbbdadcbbbcbabdbaddacdcdcbabdadcccbacdbbabdbdaadbbddbdbbaccbbcbacbbdbbabdddbcbddccdbdbcabbbabcdacbcaddabbdbddcdbcaddccdabbcbbdaccbcbabdbddacaaabbdbdadabbaaabbdbbcbcddbbadbacdcddbadddadbcbaccbcabdaddabdbdddddbbcdadacaabbadbbbcccbcabcbccbddbbaaaddbddbcacbbbaddcbaaadcacabcaccdaacdddaadcaadcadcdaacbababcadcaaaaacadcccdaddacbdddabbadbcbaabcccadccaadbbcacacabbcadbcdcbddadcdbdaabbdbcccddbdbcbbcdddcacacccddbddcabcbbbdadcadcbabddadbccbbabcccdcbdccbbbbccdbdaccabaadabcdacdacdbbcadacdbcaabcddcccdabddcdcbaadbbcabbdcbdbdbbbadacaaccccbdbdacbcddacddccacdcbaddacddddcdaabacccdcdbddbaccddbacbacdaadaddcbbbaaacadcbdadaacbcccaabcbcccacbaabcaacbdcccdcbcabdbccacdabaacdbabdddabbbdcbacadbbadbdbcabaddcadacbacddbbaaaabadadccaadbcadbcadccdcbbdbbdcaacdccadadbcaacbabbcaccdaccbddcabaccaabbdaacddabddccddbcaaacdadbcbbccaccacdcabcaaabbbbaddbaabcaaaadbdacddccbbcdcdcaabcdbcadcdbdabbabdaadcdabadccddbbdcadcbaddabbccbaabcacddaaabddbaadabbdddacddccbacaababcbcdaadddbabcbbdccdbcccabbcaaabaadccbbadbbcbbdcdcacbddaabccdcccddabcbbabcaacbbaaaacddbdbcdadbaacbabdcacabcddababacdcaaccbddbcbaaccaaadadbbddcbbabbccbdbcdccadbdbddcddbcdcaaadbaccadacccbbadabbdccdaddbdccdacddadccbbbcdbdcababcbcacabbdbdbdbddcbaaabdbdaacbccbcdcbacccaabbcbdbabacaccacbbcadcbbaccbdadbaaddaabacbcdadddccbbbbbaccbadcbbabdabacbdacdcdcbddcbaddbacabcadbdbaaabdabcbcacbcbcaaccccdcbcbccdbadbdbccacccddbaaaaccdbdccbaadbaaccdaaddccbddaacbdcadaddbddbbaabdddbcdbcaddcbdddcabadbdbbacaaacdabdccaaacdadbbcdccbaacbbbaccabadcacbbcdbcbcacddbabbbbadddbcdbbcbcbcbbabdcdccccdbdcabdddbcdbadaddbaddbbbbaccaabbcbcbacabdbddadabbcbbaccdabbacdabccccbdcbdcddcdbabacbadcdbbcbdaddaabababcaadcaaaaaaabbcdbbbdbdbbbdbaddbdddcdbccdbaabdbddaaaaccccdbdcbddbbdccdadaccdbdbbdaacacacbabbdcbbbcbcabbcdccbcadcddcaadbdbcdaddcaabaaacbadccabaccccccbcdcacabaabdacdccacdbaadbdbcdcdbcbadcdbadbbbcccaaddabcdbbacdccbaadbdabddaccbcbdbbbdddbbcadcabdbdbdacbcbbbcbacaabcdadbabcccadadcadadaccdbbadaadbbaaabacadcddadbcadbbbadcacadbdbbccdbadbadabadbadbdbcbdcdaaddbdbcbccbbbdaabcbacbabacbdbdbdcaabaacdadcdaadbcdaccbddbbdadccbdaccbbdddbbddcbdbacccdcadcaaadbabcacbcacadacacabbcaddbabcdbadbcccbacbdddcdbabababdccbbccdcbadaccdaabbbaadbabdabacddacaaaaccbbcdccbbbdaabadbabdcccbaccaacaccaabbdcbddbcbdbadbbaacccdbccabbadcbacbddbcabdabbbabcaddaadcdcacbbbcdabaddaddaaccbdbddbddcabdbaccabbbaabbdadccdcdccdacaaddbbaabaddadadbdadbdbcbbabaacaadbaccddcddacdaccdcbaabbcccdcabdbabcbbcddccddadcacadbccabdccadbacacddbadcdaaccaabbdabcdbabddcdacbdadccbbbcdaccbdbbababacddbaacbbabdcccccbdababcccddaddbaabbdbdbdbabbccaabdaccadbbaaabbbdcddbdacdcabaadacacdaccadbcaccaddccdcccdadadadbaddccabdabbbccadcadbbbdcbbabacbcbdbbbcaacdccbddacddbcadbdcabddbaccccadbcabccabacbcbadadcbaaccbbcdcdcbdabbbbdcdcbbbccbbbbacbbabbacbaabbcacacccadbacbdaacdbbcdddbaaaaccdacabcddccabbcdcbbcdadadcdbababaaccddadbabdaabaacabbcbbcacbbdbccbcabaddccddbdbdcccccbbcdaccbcaddbadbddcdacdbcabdcbcdddaaabbccbcadadaddacddbbbdaadabbddcccbdabbbabdaaacadadddabdacbdcdacccbccacbdbcacdbbacbbdddaccbbdbbcdbaccaccdacdacccbdbbcdaddbbbabbbbbbaccbadddcccabadbdcbaddabbaccdaaccddbcbbabdddbccdbbbbacdcabbbcdbbadbacbcaddaacaaccbbaadcadaacbcbbcbbaaccadadadcababaacbaadacadddcdbabccccdadcddccccbbbdccacaadaaabddddadaacbbacbbbbdcbcdbddabbacdbcabdabccbccccbdadbbccadbdadbbdbbdacdcbbbddabcddacbbabbdcbadaddcddcdaaddbbdaaabcbcddcbddabdbadbdcddddcdbdccbcaacccaaddbacddabcdaadadacbadcaccaaabbccbdabcbccdaabdcccacdabccdabaabddbbaccaabcdbabbcdbacbcababbdacdbdbddccccacdabddaddcadaddcbcdbbadcaaaccbdaacbaacdddbbacccbcbbbddbbcbddabadabaddbcccbdbacadcbadbcdbbccdbbccadddcbdacbaaddddcadcabaabdabcddbcdbdcbcdbcadddcdbcbbabdacbbaabadadbabdcccbbaccdabdbccbccbdddbaacccabacdbbdcddadbbdbdcaacbacdbaddbaabccbcadacaaacbccbbdaacdcdbccdcaaddcbaabdcabdcabadcabcbddacacbbabcbbccbccdabcadddbabbbadcbababddbcddaacadcddbbbaadaacdcaaadccabbbbabdabddcbbdadddcabacddacadbdbbaaccadaabccdbcbbccabdaddddaabadcdacdadcdbacacdacbcaadadcdcdddaadddaaadcacbdcadbcccaaddbacabaadadccaabbddabbbbbcadbbacadcbdabcdbbbbbbaabcccdabaaddbadbaadbdacdbbadcdbdddbbacaacabbbdcbcacadcabcbcccadcdbdbcaacddcdabcddbadadbddcbdbddbbbbbbacddaabcaddcdbbbdddaabcccaddaadccdccaccccbcbaaaacdcdccdcdbdbccdcdcbbdcbdaaadddaaadccacadacaaaddadbadbddaddbcbabbbacdadaadcaccacccddccadccdcdcbbbdbdddbadabacdcbddcaabccaaabcbdaaaddbadbcccbabccacbddbcbcbbdaabcadadcbdcbddddddbddbcacaadbbcbaccbcdbbadbbbadaccdcadbacbdcdbbbdcbaacaccadacacdccdbbacdadbbdadcdddabcabbadbbbddaabcdcaaaabbaacadbddaadbccbbaabbcdacdbbdabdddbabbaccdbdbcbddadcccacacaadbcbbbcbdcbdacdddadcccaaacdcdbcdccaaccccadbbccdcddbccabcbcccbdbdcbdcbddcdbcacdcbbabcdcbbdaaadbddddcddcaacadababbaaccabcdcadddbadbdaadcdaaadacbaabacccbdccacdcaaabbbdadadbcdbcacabadcdaacbbacddbdacabcccbccdbbbccdddacdcaaaccdcddbcabdcbcaccbdbcbaaddabcbaaaaddbcbacbdccadcbbbdcbccacdcaddbdbcababbdbaaaacbddabddaaadacdcbdbdbadadcadcbcacaaaabdbdcbaccdaabbcaaaabbaacbbdddcabdbcbadcbaaddbcacadbcaaadcccdddaadaaadbddcadbacbadaddaacaaacadcdbaddccdaccaacaaaabdadacddcaddbddbadabaccacaacaaaacabddbbbbacacdbdcdbdadbdadabcbaddcdccdcddbaadbccdddadbdbcbbbadcaadbcdccbadddacacaccccbdbabdddddbbabdabcbaaabacbdbccbcabcaaccacbaaccdcbddadaabdcbadbdaaadbdcdbdccbaacabaacbbdccccbddaacccacdadadccbbbcaccacabcdcbcdddbabacaddbcbcbdbacddbadcdcbcdccbbadcabcbadaadcaccacabccbdbacbdcbbabdcaaddabacdbadcdccccddaabbbacbcabbabbbcacaacddccaacacdbacccacdbacaaddccbddabbacadbbadaacbdaccaaacbcbdacaadddacaabdddbddaabbbddaabcccbcdccacbaccbccbbacacbdddaadcbdbabbaccbdbcabddbbdddababaaaabcbbdbdaccadabddbbadccbabcabaabadabbadbbdadbcbcbdccabcdcdbdaccdddacbdcbacdaccdaabdcababbbbbcabddaddbcdabdbddabaababbccdacadcdbbdcbadbabbbcbadbcdbdacdbabcbbcabccadcbbcbacadbbabacbdbabbaccbbaacaddadcaadaaabaddccdbcaaaaccdddacbcdaddadbadadbddadcaaddbbbbcbbbbbcbdccaddccabbaddaddbdbabbaddbaccaccbbabdcbadbcbdbababdacabdcbadaadcdbdbddadcaddbbabaabddacdcdbdccdaddabbabadbadabadabbbdaddcabdbbdbabdcadcdaacdcccbcbdaabccccbbbbdcadadabdcdcabdbcaddbccabaaabaccbdddbacbaabbdddbaabddacdcaabaaabaabdacaccbdbaddccdccdcbbdddbdaabbdbdddaddadccbbcaaccbdbcabbadbaddccaaccccdcbacabddcbbdaddadabbbcbbdcbdcbddaaddbbcacacadcdcdadadadccdbadcbcbccbcacaadaabbaadacbbaaacbabacbcacbbcbcbacbabbadccdbcbbbdaadbdcdaadabbaadbacbddabadadbccddcbdbddcbaabcccdcacaaccbdaccbaccbacaddcaabddacbaaddddaaabcbadcaadcdbbdccabbbacadbdcdadbaccccdbacdcaccaabbbdadabcbadbcdababcdadbdaccdccdcadacdbdbbcbbbabddbbadcdaaadcdccabdbcbcbdabdddacadcbddbcccbadbaaadcccaddaadabbdbbabcaacadacddadabaaccdabdbbcbddbaaaddbcbacabccaacbdabbccbbddbbbcdbdabdadbbddcbcdcdbcdbccddabbcacabcacdacbaadcdadcbabcaabbddcdabbadcadacbbdbadadbddddbbdbdbdabdbbcbdcbcccabbdccacdaccbabdacdbaaaabbacaddaacbdddcdcadaabcbaacdaccdadbcadaadcbdccdcdaabdcabbadcadaadbddacdacaccaacccbccabaabdaccccbdaaaddcbadadddbdbabbccbccbcbcbcadbadacaadbdaacdbbdcadccbadbdbcdbbadcccaabcbcacddaadbcabaaaadabdabacdaccbcaabccddabacbdbccadcdbadddaabbcbbbdabbbcddadbbddcbdbccaacbadbabdaadccaaacbabaddddacabadadcbdcacadcdbaaaaddbaddaaabddcdcdabbbdbcaabddbcaacbddbababacdcbddddcadbadcddcaccadcdcbaadddcbbbbaaaccccdaddaaadbdbcadabccaabbaadadacbacccadccbbcdbcdcacdaacabacaaaaadadcaddcabdbdaacabadbddbbaacbaaabadddbcacbbaaadccbdbdcbbbbdcdcaddbadacabbbbbcdcddcabbccdcdbbacdcaadbbcabdaaddabcbacbdbdccdbbcbbccdbccbccbdbbdcaabcdbabdadaccbcdabccddbacaacdaddccddddcddbadcdadcbabacbcdcbbbcdcdcadaabcbbdabbadccdcadbbbcadbbadaaaaaaaddcccdaabddcdcbaabdaddabdadccbdbabdddaadabadddddcccccacdbbdccaaaadbaabbdbcccbacaccbcaccabaababaacacaadcadcaadadadccbaacaccdaddccbcabdaaaabcbcdbcbcaddbcabcdaccabbbaacdddccccbadcbdabcaddbbdacdbbababddcabdabdddcbcdccbadaddcbdcabddbadaddbbadccaddbcdacacccbababacacbdcabdbbcacccabaabddddbcababbccdacddadbcdccacbdadaabccbaadcbadccabcddadaaababdbbadcaadbbddaabdbacccacdacdccabaaadddbbcbdcbbbdddaacaabaacdccacdbacaaaccdddcdabdcdcccdbddcdcbdcddcdacabdddabadabadbacdbcacbaabbdbdbbcbaacabdbabdbcdcddbaabbcdcacbabbbccbadbadbcdbbccaabcaacccdbbcbbadcbabcbabcddbbcbbbddaaccdacbaaabcadbcbcbaabccddacacdddddacbbcacccaaadddcdaaddadadcbccdadbcdabaacdbbcdcdbcbdcbadcacbaddbdbccacccabbcacbbbbdbccbacdcaabcdcbbcabdabbdacacdccbccaacdbabcdcdacbabaddbcbbbdccdacabcbccccccdbcddbacddccdabaabbdcacbbabcabcadacdabcabcddcbaabdbdabcbdddbdaacdbabccdbaabcacacddbcaaadcbaaabbbabdbdabacbbadddcabdaacdbacaacdbdabacbdccbcccddabcbdadaddadaacadaadbbddbdacccacacbdabbadcdddbccaccadabbcbcbaccabddbcabdbabdbccdbcbdbadaacddaabdabcdddddbacdadddcadbacabbbdaaadbcbaadadaacaabbbcababcadbbddcccdcabbcdccdbbcbcccadccdadabbcbcbddacadbdcdbcdbabbdaadbdccdddaccddbbbaccdaadbccdcacdcacacacbcadcbdcbbbccabdabcabcdcdcddaabbaaacdddacabdbbbdaaacccbbbccadaccdddbaadbbaacdccddaacbcdcbddabccaabcabadaabbdabcacbddccaddddbccdcbcabaaddcbbbdbbdabaaaadabbaccbdddddbddccacadbddcabbcabcbcccdcbaabdcabaccabcaadccaaddaaccddccbdbbbabbcdaddddcadccbbcadcbbcabcbcadbddadddaacccdbbcadaadacbbadaacbdaaabbcdbbbcbdaaddaadbdddddbadaddcaacddcddcaaddabaabcbcddabbabbdcbdbdcdcdbcbabcdcabccbaacadcdabdbdbccabddbaadcacbacadaacdbabbdadbbaadcccabbbdcddbbabadcdadccdcacbaacbccbdcbddbdccbdabbddbddadcaaacaacadbabbddacbacbdcaccbdccadaddcdbbccdaaddbdabacdcadbbddbadacadbaacbddabacbacaaaabacadbdaddbbcaacdcdaadadcdabcbcacbbddddbdcadcdccaddabbaaacdbdcacbccbcadccdaabdbaaaacbcadccdacabcbadaabdcaccbdcdbddcaccdddddadbacbadbadbbbaccbdccaaacacbcbdadcdadbbdaacadabbcaabbcccbdccdbdaaaddbbdabdadaaacadbbcacaaaaaabbbbabdddccbdddcbacdbcadddcbadacacbcbdaabacbcbdbccdaaddbbbbbcdabcdcdacdaadbbbccdbadccbcbbbccdaaaadaabbaccbaabbccaaabdbbdaacdbdbabbccaacaacdbbddbaaaddbcbabccbbcdcdddacadcbcacccbdacdaacbbacbadbdaddcbacdbaabacabaaadbbaccbbbbcaccddccdccaacbdcbbbbdaabbbbcddcbdaabccabbbbaadaccbaaacabcbaaadbabbbcbbadacabcddcbbcadabcacadbdbdcaaacaadacbbbcabdcdacbdabbbdaaabacbdabbbcabbbacccaccddabbabcbddbabcdadabcdacabbbbaccdaddbdabdbdcabacabcbbdbbbbddadbaadbacabbbbaacddadacbcacacbbccacabcdbbddccdbdcbbdaccdcbbbbcbbbccadadabbdcaabccaaddacdcbcdccadadcddbaaacacbdabaacccaadacbbbdacdbcbdbabcbbcdcabdbdbabbbacacaddbaadbbbdbadddaabccbdbcdaaacbdcdcbddbdabacbacccddadabbbdddabddbdaddcddcacdddacdbbccbcadcabbabdbbcbccabcdaccaacbcbdabddabdabaacdbbbaabbcaddbbdabbacbcbbccdbbbdadbadadacbaacbcdbadacbacbcddabbaccccadbcacccaadcbabcdcddadcadbbdbbdbcbcaacbcdaabbdcacccbdbaacdacccbdbccdbadcbdaadcdacabccccbccbadbccacbbbdbbdacbcdabbcbabcdbacddbaddbccbbbddcdabacdbbbadbdbbadbccacbdcadaabcacdaaadaaddaccaacbbbcbdcbdccdbccbcbdbccddcdbccdbbccbabaaabbacdcdcccdaacbbadccdabdadcacadaaaddbddabbbacabadbaaddcaabcacccccddbacadcdacbddcbbddcddccbdbdddbacbaaaadcbbcaccaadcccdccbacbddacaadbacabdcbcdcdbccaabbcdbbbcddcdbcbabacddbdddbcacbbacaaadcdddcdcaccdacdbcabaaccbcdddcaadbbcbcddbdadbbbbdddbabcdbbccccababdaddacbcccddbcbccdcdbdabdcbdcacdbdbacdccddaccccaccaddbadbbbdadcbacacbcaaaabaaccdaabaadbabbddaddbcbadacadcadbadbccccbaaaadaaadcdbcaadcbbcbccdbaaaababacaabbcdaadadacaabcabbbccdcdbbdcdbdccabbdcacabdacbbbabbbabdabdacbaabcacbababccbcbcbcdbdadbccbaddadbddbdbdbcadadbbdccaacbabaabdacbbacbccbcdcaacaaadabbdccdcdadcacadacdccaadbabbdbcbbbaacdbddbabbdbacaccddaabcaadadabacaacdbbcdbcabdaaaccaaacbadddacccdaaccbbdbdcacabcbdadcaadacddbccadcdbbbdcccdcccabcbadbdabdbbcbccacdbcaccdcacdddbbddbbddaccacaaacaaacacaaaacdddbcbccddcdcdbbddbbdbbdbaaddbcbbddcbbaacbabcbdbdcabaddbcaccacdacadabacaabcbcacccdbdcaccacaadabcdbaddbbdaacbabccbdcdacadadabadbdbccccbcaaabbdbcbbaabacacbdbcabbccacdcbabaaacdbadbcdaccddadcabcbcadbcbacdbbccbddbbdbcbdaaadbcbcaacdbbabddcdbdbdbbaadaadbccdbcbaacdbaccccdaccaaccdaaadbbddbbbdbbbbdbcddabbbbbddcbbaadbdcaddbbcddcdcccbdbaddcdabcbbbcbbdaaddaccaabaccdcdbbbcddabcddcabbcbababccdcdbcbbcdccddbcbbdadadccccadaaaaabdcaccdaddbdbacbbadcbacbcabdcdbccdabdcaddadbdbdcbdcacaadbacacadccbcddacdabccdaabbacacbcadccccdcadcccbabbccccbdbbbbdabbbacdbdcabdccddabccabdacbdbcdbacccdbddaacbbacdcbdbccdbddabcccabddadcccdaadbcccadbbddcdadcbcbbacddbcbccabccacbbbadbacadcdadcacccdccdccaaddddddaccbcbcabbaaabdcddccccdbbdabbaccaccdbbcdadadcacdbaaaaacbbbaddddaddacadcdbdbbabbabddadcadbbabdcbddacddacadababaabbbddcdbbdcbaaabdccababcbbabacbbacdaaabddadaacdbbdddbababcddcddaddcdcabcdbbdcabddddcbacbbbabdaacbbbdaaaccbdaabacbdacbdccbaddabccccabdacddabbbdadcbcbdcadbcabdbbdcdbaccbaadcdadddabaaaddcdbabdbdcddbcdcbacbaabbbcddddbcacbacadaacdcdbaccdddcbabccdcbddbcccbbcbadcccccaacccbddbdbdcbddaacbdccddcacdabbaaccdcdabdaccddcdacdbaabccaacdbdbbbbabcababbaccaacabbbadbdddddcaddbbccbaadaaaacddcbdabdcadbacabbabcaacdcacccbbdbdaacbbbbcacadbcadcbcdacccccabccacbcccabccdcbadaaccaacbbaacbdcccaaaaaababbcdaacadbdcaccaddaddadabccdcbdbbdcdcabbdbcacadacbacbcbaadaaccddabcbbadbdaccddcbadcdadbabcdccdddbdddccccccacbbaabbaccaadbcadbdabbbdbabcaadccbdadbbdadcdcdbcaacadcacdbdccdcbbabacbbcccacdddacbbddcdbbadacddbabdbbcdabadbdcddbbaaaadcabbabadadccabbbdcbbdbabdcabbaabcdabdcbcdbacabcabdcccbbaccadacdbcdaaddbddbcbbbdbbaaacbccbcacaccacddaabdbccdcacbbadbcdcabdbcbadaaccdcadccdababbcbdddbcbaddbdacbddcdccbbcacaaacaabbabdbaadacaaacbdcabacdbabcdbadaabcdaccbdbdacbbbabddcdcabdcbacddddcdaabbcdcbdcbbcabbaaabadcabdbbcccaababccdbabadcddbbdabbbabdadabccdddcabdddacddadabbcacacbdadabbdbcaaaacabbdaadcaaababcdadbcbbbcacadababdacacbcadcadccccabdcdcbabcddddadbbbadacddaadccddcbdddadacdbbaabbabcdcccccabdbadabddadadaaabdccbbdccdaabbcdcbbaddbaacdaacadabdadaacdbbbacbaaabababbdbdbbbbdccacbdaacaadabdabccaccbdacabcbabbdbdcbdaddbcaccbdaacabbdadbbcbbbcbcdbdacdcacacdcdcccddcddcdbbbcacababcdccddddbaddcaacbcdbcbdadcbccdddabdbcadbbdddbcddabcaadcabacabacaaadbddbccdabdbdbddaacbccabbcddbbdcbadbccccaaddbdaabbdbacbbdccbbcadcaabbcbcbdcbaddcdccddaccaddbcaabcbcaccaabccbadcaaddaababdccdddddbbacaacdccacabcdccabccaddcbbbcdbccabcbbcaddabcbbacaaaadcbbdbbcacbcaddcdccacbaacbbbdabadcacbcdaccdcddbcbcbbbccbdacbadbcacbdcbbdbbcaabbbcbaacdcccbdabcadbcbcbaaacddaabdadaacdcbcdaaccaccabbabbbcbabcdbccdcdadcbdcaacacdddbadbdadbccbdaacdbaaacdcdcaacddacbdccdadaaccbcbbcbbcacaadbacabacaaaaacbabadacaaaccdadccbcccbbbdaabbdbaabdaddcdcdbabacaddaaddcbdacdccdbddadcdaddbadcbadddaaccbbacbccbbaddccacaddabbcdddaccaaddbbcaadbadbabbdadcdbcdbcadddaaabdccabddbdacddbbcbcdcbdaaccaabacaadabdadbdbadcabbbabbcdbaaccabcaccddccdcddacdcbadcdbdacddbbccaddbabdaabcabbbdcdddbbcaacbdbbcbdbdddcbbbbddaadadbcabbabccbdddbcbccdbaddcbdcbbdccbcbcdadabbbcdcaddbcaacacaacddcaadbabbadcccccbcdcabbcabdcbacdabadaddadcddabdaadcabbbabbabbbccacacaaacbcadcccbbabdaaacdcdacadbadadcbadbbabdcbcaccbaacdccaccaaadbdaabbdddbcadcddcccbbcbaacdaccaccaaaddccdbdcdbdbcbbccaabdabcacdbbbbacccaabababaaddabdadbacacccdbdcacbcabbcbadcacddbcbdabdccabcbbcaacdbcbbadcddbaadbcaabcdbbacbbaddaadcbdbddbabdcabbbdcbaadabbdadcbaababacbaadacadcacbcbcbcbaddabbddababbbdddddbadbacbdcaacdbadbccdbccbbadcbdcbadadcccabcadddcaabccbcbaabddabcadcdacabcaaadcbbaacdccadacdcacaccbaaaccbcbaccdddbcdcaddcbcdbaaacacccccbaddddcabbddaaddddcacccacaaadddbdaaddcadcccdcdddabdacdbcdabdcacccacacadcdddccaaabcdbaadaadadbaaaacccaaaabbdaacbaccbdcaccddaacdacbadbdccaababaabddbdadccadccadcaabbabaabacaacdacccccacaabbaacacdacbdcccacddcbcabbddcadbbbcbddadbbadcbabbcaaaccbcbcdbbcdabddbcbaccdcddbcabccaacbacbcdcaacbcbaaadabadbcbaacddacaabcaccbacbaabcbaaddccbcbccbdabdbabababcacccbbcabdcbdabddbabdcdababdbbbadcdaddcaaaccacabbbaacaabdcaadcbcdbddabccabbdccabcabccacbbbcdbdcdccaaacbbcbddcadacddddaabaaacbbbaadaaddcadddbadbdcdddcdddccbacadadbacdacbdbcadbadacaaadadccadaccdccdbabbdadaaccbabccaddacaaacdcbbdaccababadbbadcdacbcddcbdbcdccbabcdbcccbadccaccadacacbbbaddccdddabddbaccdcaaaddbcdcdadacbbcdbdcacdacaacccacaacaadbdbdbccbcaacbaddbbdbdcbcbbccabacaaccacdbbcbdabcaaaddcdcccbddcdddadadbccddbcabaacacadaaadbccdcdadcbabaabacdbdabcbadbbabddadaacabbbddcbcdddbbdbddaabdabdacbcabbbbabdccbcacdbaabcbbbdabbdcbaaabacdbcdcbabdbdcbbcaccdadcbcabcacddcdaaabddaaabbdaccdbbbabcaadadccdacbaddbaaccccaaccabbdaccdccdbaaadcccbcbabacdabddbdccddddadccaadcacbacbcccaddbbbbacdacdaadbadcdaacbcdacbcdddacdaddbcbaaaccdbddabbdbddcddbcccccbaadcdabbbbccbdcbabbdddcaddadcddbbbbcbddadcbcbaaaadcaabaddaacbbabcdddccdacabbbddbacbcbbdcbadcacdddacadbbbdcaacacbcdacbaabbbaddbaddabbabbcbddbdbcaaadcdcaddccaabddbdbbdadcbabbbaabbbaacaddcdaaabacbdcdbdcbbaaabbcadcdbdbaabbbdbadcacdcdccccabdabdadaaadbabaaabbdacabdaddacbdcdcbacabdbdcabaacbdcdbddddadcbcccdcdadcaacbccbccdacdabcccacabcddbbddaccacadcbdaacbddacdcbdccbaaabdddddbaccbdaadaddbcddddaaccaaadadccbbbaccbcabcbdaabbcaccbabadcbccadbadcbadbbcdcbaabbacccdacabbdabcacaacccdadbcdcbabacadadbbbdbccbbbadddadaaccbdcadddcbadbdbbcbbcacabbdacabbdcbccadbccababcbbacdbbaacdadadaddccbbcddadbadcdcdbccdaaaaadbdaacdddddbbabdcbaadcbdbacaccbabbdbbadacabdaaadbbbabcacdbbabbabccbcabbbbbacababddabaacdcdadcacabccdcbccbdacddabddddddbcaabadccbcddbacdbaddcdcccabbacacaaccdbddbcccbdddddddcbaccddcbdddcdbbacdaabbaacdcaddbabccccbcbbcdadddbbdabcdaddaabcaddcbacabcbbadccbcddaaaacacbcbabcbcbaabaacdbabddcaadbbcbdbaabdbbdadabcbbbcabcaacccaccdcbacdaacdbcacbbbcddbdadcbccadcbbaddabcbdbbcadadccbdddadcbddbcbbdcaaaabdbcdbaccbdbcbdccdbcbcabddbbddcdcabccbbacdaadbdcdbacbaaddacadabbdbcdacdaabababbbacadbbcababdbdddbcbcbaacacaccbbdcddddddccdbacadcacdacaacbabacadbdacabcbadbcbddcbcdcaccadcabcdaacacdcbaaddccbcbcabbbdaaabdddbcbdcbcbbadabcaabcdbbcbbaccdcacdadbcacacaddabdbadadabacbbccdbdcccdaabaddbabadbddccbbdaaccadacdbadadcaadacaddbdabcdabacacdadacbdcbbacaddabbbdbbccdbbdadbdcdbbdbacabddaaaadcdacaaabbbdabcbdccdabbabadaabbbcacddacacbdaaaccdabdadbabddcdbcccacbbbbbdcbddccbacccadbcdbacbdabaacabcbddabbdbbbddacdcbdccaddcbdcadddbabcdadadadbaaaabbcbaddcacdcadabbbbcbccbbcabacdbddcaccccadbabdcaacbdbadaacbcbccdadbcadbacdaccbdcbbbadabacdaccddccadabddbbcddcadccbdcaccabaccaabbcccdacabdddbaaddaadcaccababdabcaabaacdbdbdadacdcddbcdddcaddbcabddbccaaaabdaaccddcbadbabddaddccadddbcbadacbcaaccabadacbacbcddcdddcdcbbdccabdaadbdbcdacabbcbabbddbcdaacbabcdccabbbdbabbcdcabccbdbcaaadabcabbbabcccdcaacccdccbccbcabccbbddcbadccdbcccabdaaabddaadbbaadcaccaaadabcaadaaabacbcdcddbcbbcaacdccbbcacbbcbaccaaaddcbddcbbdaaccbbbcbbbdbdacbcbdcbaccddbbabccccabcdaaabdcbdabdcacbddddabcbbbddccbcdacaddbaaacaddccdbdcacacdadccbbaacdaabdbcbbabacdadadacaaadddaccbbcdddbdbddccaadddbabcbbbccaddcaadcbcdacbdcbdbadcbbcddaadaabccdbbccbadcbbdccacdbdacbabcbbbacaabbcbbbbabbdcaadbcaabcbdcbadcddccaabcbadcbbadaddbccdaabccaaadacccddddbccbdadcbbddacadabcabbddcdcbbcbbdddbbadbabbaacbbdaabbbbcbacabddcbbabababcadadaacbdcdccdbcadbcacabbadbbbdcacaabcaabdacbadcdcccdddcabdacbadccbddbdbcaccaacdcdbadbaacdbccbcdbdcdbadacbbddbdacaabcccacbbacddaabccddcdadcadcddbdddabadacbbcbcabbaccbddcbbcabbaccccdaddcacdbbbcbaccdcabcadaaaabbcdcdbbadaabbcbbdccbacbabcbbcdaccaaaddcccacbdbcaddcddbbcaacaaabcddcdbcddaacbdcddcaababdbdbcaacbbbbccdcaabcbaccdcdbdbcbaabdaaadccabbcabdcbdbbabcdddbcdddbcbbaadcdabbbbacdbacdcddcbddcbadccbbdbbaddbabccbdbbccddbadadaadcdcacaadbadcdadccadddcdacdbdcdcbbbbbdddabdacabcdcabbcacacdbcdbbdabdcadbbcdbbcabbadbbabadaacbcabdccacabdbbadbadcbbcbacdddaabddbcdddbccdbcdbacccccbcabadbbbdbaccbbddccaaddbdbdabacadcbdbdcdbdbcaacbcbbdadccddbdddaccbdbbabaacabbdbddabaccdcabbbcaddacacbcabbabbbddcbdbaccddaabddabadbbdabcabdcbcbbcddaccddcdccdbbdcccdabdaaabdacbaaacadacdadccacdacbbbbaadcdbbabcbcbcdacdadacadcdaaccdabcbdadabcacbccacccbbdacdbdccddbccddbadbccdcdcbadacccdbddccacdbadbbbacdbcdbcdbdcaacdacbdbcdbbccaccaabbbdadbdaadacbbaccabbddacdbdaabaaabcaaabbbaabcabbdbdaabdccdbbaaaaaccabbccabbbabcdcaaaaadbabdcaacadbadccdadaabddbbbcbacdbdcbabaddabcddacbbadacaadadbaaccbcacacdacabdcdbbbbbbdcdbbacaadddbcadbdacddbdadabaaabcdddaaacddddbcbcdbbcacdddccbacbcacabbbdbbdcbcaccdbddcddcaccaaadaabbcbcbddaadaabcdbcbaacbbaddddbbcdaacabbbacbcbacadbdcdbacbbccaabbabbbddbcadaadababcbdbdbcababdcdbcbccdcbdddcbaacbaaaadaacbadbbaabadbbcbcbbbccbcdddadaabbaabbbbdcaddcccbcadaaaabaabbdcadccadcdbaacdbcabcdccccbcacbaacaacaccccbbacababddddcbdbbaacccdbbddabdaaaadbccddcbadcadcdbbccdabdbcdaccbdbbaddadabcbadcdabddbadbbbadaacaaaccccdbadcdccdddcabacbddbbbacadabacbbdabbcadabcbcddadbaaacabcdcdbddccdccdacbaccadacdacdcbcabbbddaddbdddddaaddcaabcbbcbbbbbdadbbcbbaabbbbddacdaadabbbbbdacdaacacababcbccdadcdccacaadccddddddbddccdcdbdcbaddccbabbcdabadbdabaacbacccdbaacccccabdbbbabdacaaacdababbbadadcbccbbadcadddbaacddcbdbbbacbbaababdbbaacbcaadbdacaaddabcdcacaabccacadaabccddcdcacacbbabcdcbbdccacdbaacbcdbdcadcacddbcdcddcbabdaacccdbdcacbabadcbdccccbcadbcbbaabbdaccdddcdaccddbaaabadbacdbadacbbddbdbacdcaaddbbdcbcdcabacbaacdcdcdddacdccacdcacbbacccdcacdbaccdbddabcbdcdcacdbacdbbddddccababaaadddbaaccacabdaaccbdabadddddacabcdadcddddbdbdcaadabddbcbbbacbaacccbcdabbaddccabaabddbabcababbcbbabbcdbddadcabaacabaaacaccbcddbdbaacbcdaabbabbdcdadadccbddcbbacdbaddaccddcdcaaadaabccdbcddbbabdcddcbdabbacadddccbaddddddcbccabcdaacaddacbcbdadcdaaddaacacadabdccddacdacabdabdcbaacaabcacdddadaabaddabbbaaacaccbbdaacccbbcaadcccabbbcacbccdbcaaaaaaacacdccabbabadddcacaccdacdbdcacbbcadcdccdabcaaccaaabbdcacabcbddcbcdddddadacdcddadcacadcbbbbadababcbbaadddaacccbbcdbbcabcacccacddcccdbababaaaddacaaaabacdccbadcdccbacbcdacdabdccccdbdacbdbcbdacbabadcbccadcadccbdabbddcdbcaddbaddaabcbdbccacddcbcaccbccaabcccdacdadadaddaccdcabadcaaababdaababdccdadbbbbdbdcdbbdcdcbdbabdcbdcbacbbaddacacacaddbcdcadbacaccaadddadbdadbabbadcbbbbbdabacabbcdabbadbcdabacdbabdccabccdabbcabbdddbcadbbacddbcddccbcdacdbbbccbcbadbcccaabccbddcabdddddcbbabdabbabdbbabcababdcdcdadcaaccabbdaaadbdaaddbabbbcdcaadbddcddccbbbcbcacdbdabbcadaabcabccbcdcabdabcdaabadcdbdbbddbbdabcbdadcbcbbcbaabdddaccdadcbadabddabadabbaabbaabcdaaabdcabccccbbccbcbdacaccddacadadabbacaddddbccbdacdbabbddcadcbccbddcbcdadacdbaddbcdbddabacaacdcabacdbbccdaacbdcbcccbcbbaacaabbdcbabdbbbbbcaaaadcacbdabbaababaacadddbbbdbdcabaadacbacdbdacabcabcdadccccdccbcbccaaaacccbaaabbdcabcccdcbdcccdabccdabcccaddaacdbbcdcacccdbdcbbcacbbadbcccaddcbbacdbbddcaadbccbcadaaacbbadacaccdbcbaabcbbaaadcbcddabbdbacbdaccbacbacdaddcdadcdadcdabdbbbadcbcbbdbdcbbadbccbaabdcbabccccbcdcabadbdbddbabdbabdcbdccabbcbccadcdbddccadacccdadadbcbacbccabbaacbcbbccbccabacccabacbdcabddbbbacbccdaadadcacaacabdabcbcababcdcccaadaaaddcacaacbccdcbadbcbcaabdccdcdadbbbcddaabdaddcacddacddcbcbcabbaabdacccbdbadcdcbddcdadcdbacbccdbccaacadcbbdccdbaacadbabbacbcadccdcdbadbabbdcccccacccaadacdacbcaacbcbbdacbddaccabcbcdbcbbbadcbdaaaabacadadbccbbaccbdabaacbcaadacacccabaabaddcbcbabbaadbddbccdabbadcdcbadccdadababacbbbadcdacacbbabdbadcbbcdabdbbadddcaccdcacadbdccdccaaacdaccbccdccdddaabbaccbdddaadaaccabdacbccbcbabadcaaadadbabaccababaacdcaaadddbcbadccdbddcadcbaadcdbadddbdbbccbdacadadabacbadadbcccdabddaadcccdbbabcbabdbccbbbbcdaddaabccaddbdaadccdbacbddcddccbcbdbdbbbadaaddbdcadcbbddaaddccdcdddcaadcdcbccdabacbcbabcdacbdaabbabccbddaacbbabaddcacbcddccbdcbabbbddcadccbadcabdacbbcabaadaaadbcdcdabcbdccddbaccdbcaccbbacdbdcdccdcdbabbcacdbcabdcddccacccacaddcdacbacbabdbbaddaabdcaaaadabbbddadccaddcdbdbbbdaccaaabbadcbcccddbbdcdbcbcbccdcdaadcbadbccbdccbbccacaabbdbddaadccaddcbbcaadbdcddcdcdadbbcbbcbbdaabdbccbbcbdacaadcbdacabadcbadddddcdbdcbabdabdbbcaadbcaababcccccdadaccbabbbdcaccdbdacadcbadbadaccddcbdcacccaaccbbdddccacbdddccbcdbadcbbbccbacccabdbdcacbacbbacbdabddadddacccbcbdbcddbbbbabacdcdcabccabcdcdccaacbbddcbdbadadbabcbdbcacdadadbcacbcabcbabdcccbcaacaabcdaccdbacdcbccddcccacaacdabbcdcdadbdcacbaddbabbacccbbbcbdbaddadbacaaddcdadcaccddaddcdcdaacbdaaacababbdbdcbccacbccbadbbdaabbadababacdadbbcdddcbacadbdcdccbadbdddbbadaccdbadbcdadcccbacabcbcccabbcdbabdadaddbcbacbcbbdbaadcdabcbbbbcbbbbacbbaabadddddcdcdccdbaaabaacdaadcbdacbdbbbdaabdacdcadccbccccbdddbdcadacdcacccbcdacdccdcddcabccbacbcccaddddacbcdddbbbacbcdcacdcabaabacdbdbccdaabbadacdaadacbcbcdacdaabdcddcadacddadabbcaccacbbddadcbbbdadcbdcbabcdcabdbdcaadccadddbccaaadacdaabdacdaadabcbcbddbcbbabacccaaccccccdbcadccddbbabcbabcbaadbcbcabcdbcabbaacbaabdcacddbdacdadadacdbdbaacdabdbbcccbacbdadbaabcacbacdbabacabbadacadccacbacdbbbbdbaaadbadbdadabdccdacbdcbbaacdccbaacbacbbadaccaddadbabbdcbabdccbcadabacaaddadcbacdccacbdbbcccaadbccddabcadcadbcbadbcbbbbbdbbcbddbabcbdaddabbbcdbdcdbbcacccdccaacadabcbbbcadaddbccbcaababadcbabddcdbbddaabaaacacccccdbdddadcddbddaacabbbcabaadaccadacbbcdbcccbbbbabcbaaabcabddcddabddabadddcdcbaadddabcaaabbcacccbcbcbcbbbbabdadacaabcabdaabdbdcabdacdbdccabcdacbccccabcbddbabbbcccadbbccaccabdbabdacdbdcacabaacbdcccbbabccccdcbbadaaadcbabcbdaccaabcbbabcbbbdbaaaddacacbabaadbdccbaccadaddcddbacdbadcabdbbadbddaacabccddcacbadaadccccaacdcbdddabdadabcaaabcdbcbdaadbcdabcbbddddcccbbacbccdbbcbdcaadccdaabcbabcababccdddabdcbdcabacaacbdcadabcaacacbcbbbabdbdcccbbbbcaabbcadacdaaadccdcdbccccbaaadddcbbdacbbacbbbacdbdcbbccaadacbdccbacacaaacbadbbacbbdcdcddbddddaaacaaacbccdabcccbccbbabbdcadbdbcaabbdddcacbdabbbcadaccaccbcbbbcbcdadabbadcbaccdcacdaaaaaddcdbdddcddcbaabdddaccbadbaddbaacaabdadcbababcddaaacbcacaabddbcbaabccaacdcadaccdabdbddaacaccbbdababaaacabdddbdcbdbccdabddabaadbcacbcaaddcccbadcdacbaddbcaaacaadcdaacadcdccaacbdaaccddbaadadaaacdbbaadcccbcabdacacdaabdadbcbaddacddacccdddbcabbcdaccccbbbddccbaabdbbbabbcaadcbbabbdbbdcdadccadbbadadccdbbbbdcacdadacaccbdddcaaadbabccbdcbabababadcccabccbbbbabbaabcdccbbdaaaacbcddaddddabbddddcccbcdaacbdabcbdbcacdcddcddabbaadcdbacacccbbddadbaabacdbaacbbccbddcbdbcacdadaaaddbbaabbcdbdabaadacbdbdbbdcacaabbacbbabddcddcaaddbadbbdbcdbabccaddabdcdbbacbddbbaccaaccddaccdddcbcdcbbcbddbdaddabddbacaccaacdcaccbacdaaddddbddbbaababbccbbcddaabaccccabdddbdbccbadbaaccaaadddbdcabbabbbaaaddacbcdacacaccabaadaddacbadbccdbbbbddbacccacbabaacbbbbcaacbcaddbdaaddadcdddcacbbadacddbcbbbadacacacadacbdaacadadadcacbccdbddadddabcbcccdadbabbcdccabccdcbbbbbbdbcbccbccbdbabbddbbaccccdaabddccdbaaabadcbcaabddbddbabcbccbcbbddaacacacbdcdbadadbdbcbbcbabdccbcdbbbcbdccadaddddadcdddcdbddddddaaaaaababdbaaacbccddccbcadcdbdccdcdaabaccbaccbbabadddcbcadcacacbccbabaabdaacabdddcabccbabbccbabcdcadacaaadabacdaddaabcaddabbbdacaadbcbacbabbaaccaccbbbaccddaddcbbccbaaadcaccbbcbcccccbaddcccbacdbbbababddaabdcbadbbcbbcbabbdccabddcabadbdbccdcabadddbbadcdadadddccbbdcbdbbbdcbdcaabbbabbdcdbbbddbccbbaaadbcdbdaaaabbcbadccdcdaddbbbddacbadaadadabbcbaccccbbbcbdabbbbdbaadaacacdacbdadaacdcbbbbcddbabdcacabcccbcdbbccababacbbdddbbdbbbdbccdabaababcaaadcadbbbaadbabbbaccbabcdbcbdcacdbccdaccdadccadddbaadbdccabbcdadadddbdddabbcbacbbadbdccbddcbadadbbadbbcddcbdcdcdccdbbdddbdbddbdbaaaadabcabaddbbcbcbacacddccacdaddacacdbadacbbcbcbaadbdbbacccbabaaccdbaabbaddadaadbbbdddbbbbdbbaadccadabddcbddbdcdacbdadbdabdccbccccdaabdbbbcbddcdcabccdaacabcdbcddddbbaaabdbccdcadbdacaccaaabcddbbcbcbabadabcdbcadaacadadacdbcddcdddcbabccdcdbaddcabaaacddbabccbddcbdbbdcaacbcdbdbdaddddbdaccdaddcddbbccbdabcabbcccbcbbbbaabcdbbaabbcbcdcdddabbddcccdbbdbdcbdbacacdbcbdbdddcadbacadcaddddcbadbddcdcccbdaababaddadabcdaadcaddcbdcaadaaaccbdaccaacdbdadcabcadaccbddcbaadddcdacaaadbdccababadddbcbbcaadacaccadcddcdbbddddbcdacaababbddcabcddbdccccacccdabcaaddaccdcacdabaddacbcdbadabbacaaabdbdcaadabbdcbcadacaabcacccabcadcbdadddacdcbbaabbabbaabbdcddccddcddbcddababadbaaaaacaacccddbcdaaabbaadcdccdddcaacadaacaccaacadcddcccdcbadcabdbcddabacacbabdcacbadbcbadaccdbbccddbbbaacccdcccdadcbacaabddcaabcdbdaabddcbdadaaccdaadadccdbbacababbbdadcdaacbdcbdccdaabacccddadbdacbcbbcabacdddabddbacbbabccabdcccbddaddacaacaacbcdbbbbacdadbaaadadbccacbdaabccabaacccadbddaddccccdcccdaacbddbcdddcabcbabdccacdcbadbcaabaaaaaadbdbcdcbbddcddcabcccbcabbcacdaddadabadadbabcabbbcacbddbdaaabdbdaaaaccaacabbacbbbdabbacddaaacbdaaacbdbddabbaccbbdaccbcbaaaacaddcddbdabdabdaccdacbccddaaabaccbdcbcdadbbacdbbccbadddcaaccbbaaddbcddcdbdbaddbbadabcdbbabcaaadbadabacbddbddcdbcbdcbbacabadabbdcddcadccdbbdcacdbcbcdbaaccdcaadaadabdadbdbabbdaadbbcdbddcdbbbbbbbbaccacaacbcdabdaadbacbcdbbaadadcdabacdcdddacaaabaaddaddabcabbdcaabbacadcbcdbccacacddcabbcabbaaabdacddbcdadbcabdcadacadddbccdbbadcbbcbcacbbdadbcacdbaabaaddbccbcdbccccbcbbaabadcdcdaddbccbdadddabbdbaccdadadaddaaaddccbddddadacaadccbbaacbadacccdcbbcacbacbdbdccdbbccbcdbcbadddbdcddbdbabddcabbdbbdbccabdccadadbcbabbaadabdbcabadabbbdadccdddcbddccadcbcbcddcbcbbbbdccdbbacddddddccccaaadbddccaadaaccaaacadcbdaddcbbbdaadcbdbababdcdbccdcaccdcbcbabbddccccbaddcdddadadcbcabbbbcccddabaddbbabaabacccdccccbdabaaaddcbccbadcccccbbabccdbabddbcbaaabbcbdcdabcaacccbabcababdbccbadabcbaabbcccdcdaabbccbacccbbaaabdbbacdaaccdcabbddbacdcbaccaddddddabccabdadbcccdbdcdbbdabcbcabdcabdbdbcadcabacbaaacbaabadacaadbdbcabdaabaaabdaddcaabaaaaddcadbddbcadccdcccbaaabaaababcbacbadaccddcbdbdbdcaaccbaaabbcacbaddbabdbcadbdbbadcccbaddccabbcdcdadaaacccbbcaabdcbbcdabdddbddadbcadaaddbbbabccbcdabbdcdadcaaccccbcccdbcdcabbbabaabdadacbcddcbbcacbcbaccbbadaddcabcbbbdaddddbdbccaabdccdbcababbddbbacbaccbdabdbaccabbcdabbdadbcccddcaddcbacbcbacbbababdcbaacaddccbbdbcbdcbcbcabcbccabddadaddcbbdddadadccdadaddbcdaaddcaddaccdacdbdbbdacbacbccacaddacadccdabacaacdadbacacdaddbaacdcabdbcbbbbccdbdbaaddcdcbbdcaaccbddadadbcddbadabdcabaacdacbccccdbbdbdbdbabbaddcbdaddabcdcccbccddcdacdccccabdbdcdacdbaabacabcaaaaabbccbaccbbbaaaaaabbbdcaaabcbddcbccdaccbbcccbcdbbabbcddbdcbbaadbdbdacaaddbddcaaddcbacdcccbdcbaabaccbcdcaacbddaabadbacbbccbbccdcababcddabdbbdbbbcaabbcadbccbdcbbdcbddabccbacbbccdcbaabcdadcaadabdbdcadbccabcdaccaacabddccaabaddbcbacaaddcaabccbbaadbdabaccdacdbaadbcdbddcacddaacbaacdcdbcdddbcbbdccbaabdccacadabadadaabacccacbcbbabcaabbdcdadbccdabbcadcdcdbacacdddabaaacdabbbabdccdcbacadddcbcbdacbbdbccbbbdbbacddacaccacabbdbddbaadbdaddcccaadbbbbdddccddccacbdaddccdacdacdaabbdadbbbadbabdabaccccdcdadabbbccacaaaabdcbaaaccdbacadcabcaaabcdddacccbcccabaadaadacaaababbcabcbbcdddbaadbadabdacccbadcacccaaaaacabcacccbbcbacdaccdbbabcacaacaaaddbdbbccdccdbcdccaccbcbdbbaacacbdcddcbddacbabbaaaaacadccbbcbccccbcddcbcbcacadccdbabddccaadbbbacdbbcddcababbddaadbababbaabcdbbaabccacddddccaacacbcbaacbdccbcaacadcbbbbcbcbbcbadddcdbaccccddcadcdbcabddacbadadabbbabacababbaadcdccbcacddbcadcbacadcbdccbbcbbbbbdabbcdbcabdcdcbdabcbcdcdaddbbdaaacaadadaabdcadddadacdbcdcbaaadacabbbabdddcdaabadbaabbcabdbdccbdaaaccacdccaccacdbabcabbdcabaccadcccbaddcdacbcccadaaddaadcbadaaaacddbdabacbbbcabbdacaadbadabbbbccdcdadccdbcddcdbdcbbcbaadddbdcaaccadbadcccbbbcacaaacbcacbcbbdcabddacdabcbbdbbdddbabccdbabdcccaacbbaabbbcbcbbaaccddddbbadbbabcddaaccbaddabadacaadabbdbaabbdadbdbacddabbcdbccadacdadddbaadcddbabbaaaabdccdcabcdadccaaaaabacacdcbddbaacccbdcbccbbbdacdbbabbcdadcddbddbadddadadbcdababdcccadbcabcbdbdcacaccbadcacccbbcadadacddbdacacaaccccbdbcbdabdbbccabadcbcaacabccbbbbccaabaccaacacccbbabdbcccabbcbaaaaabbbcaddaccbdccacacabdbbaaacaaaaaadcccbacaacdaddcccdaaaddadbdadbaacbddabcdbabcaaadccbbddcabdabccabcbbdddcaddcccdccddaaaabcdadacbcaacdaadbcadbdcbdbabdaabbdacadbabdccaaccccacaddcabcbaabadaaccbabbdcdcadbdadddcbcbcdabcadddbdbbdbcaadccadbbcbaccaccccdccacacbbabbddbdcdaadadaabcbdbacbcccbbdddaabbcacdbbdbbccaccbdbbbcabbdbcadcddcdaacbadcadcccbccdababbdaadadaacbdbccddbbdccadbbdacadddcdbaabdabcccadbadabacaacaadccbbbaccadcdbcabadabdbdacaaabddbaddadbabccccdaacaaaadbdcddcabcccbccacdccaacdacabcdddbccccbdbaccaadaaccbbbaddddaddabbabbbcaaccbdcdcaaaacbcaaddbddaddccbcacababbaccabbadaddbadbcbdcaaaddbacdcbdcaccbaccadcabdcbdccadbbdccddcbabcadabccddaddddddbacdccdbcacdaccccdaaddddddabdcbdacbaaaaddaababcbdcbbcaababcccddcadddbdbcddbabbddcacbaabcbbbcdbcbbaabbdbdddcdacccccddddccbacacaacacaddbcccdbabdbbbcddccdadadcadbacbcadcccddbcacaabdbcdaaaabdccbbbadaddaaaccbacabdabbcdacdbdbdbadccaccbcbccddbdcbaadaacbbadbabdcbacdabbbaaabdbcddcbbabaaabbcbbcbcaadddabdbacdaacbcabcbccbaaddbbbdcababaabcdcaabcbdacbaccbadbdabcddcadcacbdadcccabcdbdddbbaacdaaadacacdbacbcaddadcdbccdacadbacccbbccdccadbcbbadcdcbcbaccbadddcbbabbdabacaabdadccdcdccbccbcaadaacdccabccbcbccabcbbdacaccdbbccbabadbdbbaddaabdddcabcdbaadabbdbdabdacccbabcdbdbaddddbccbadbbaddcbbacdcacdbddbdabbbacdabaaaabaacaaddcaadbbcdacdabbbdacdbdacacbbccddcbaccdbbdbcaadbcdaadcdbddccabbbcddabdcaabacadccbcadccbaadadccdbddcdbdaababbabdbcbdddbaacdaddcbabbddacdaabdbcbddaddddbdbbbdcadabccaaccadcacaaccbcbbccbbaddadccdadbbcbdcdaacbaddcddddaabddcabcaccadbbcdabbcbadcdbdddadaccadcbcadddabddcacabbcddaccdacacdccacaaaddcbddbaacbababdbbcacabcadcdbdbdcabbdaaabadbbddcbcadbbadcadbbbabbbbdbddaacdbababddaacbacdbcaddcbbcbccdcdcccababbcdddcacdddadcadbbbcdabaaccdbdddbccbacbbddaaadaabddadcaacbccbdaccdbacbbcadcaccbcabaccdbcacaaabdcbddabddbbbcdacdcadbdcdcaaacdabdcdbbdaabdacadccdadbbbcabcaccdabcbcdbaacabbdcccbadbbbaaabbddbddacaabcbaccccabbbdabdbadcbadcdbddadbbabbabbbbbcbbdbcbbddabbbbccbdabdbccbcddbacacaacbaabddbdaacbcaccddbbbdcdaaccbadddacbcbadddacbaadcdbddacbcadcccbaaacdcdaccdcbcbbccdddaabdaccadddadbddddccaccabdbdaaddcccadcaaccaaabcccddaddbccbabbbacbddcdbaaccbaabcdcbbbcadadbddcbccaccaccbccbaaaaaaabcacbbcbadbbcbadccdaabddccdbbacbdcabbdccbccbacbdbdbacacbabdbaadbbcbbaadabacbaabaadacdcccbcaacddccbadaaaccdcdbdabaabcbbcaacdcadbddbaadcdaccbcbbdaddcbcbbbdddcacaaaabddbaccdacdcaadbcaddabcbcadbcabbbbbabcdabcccccaacbbcbdbdaabaacdbcdabddbbbacacbaaacddbdcadaddbbdccacababcbddadbaadcccbabbcadbbccdcccbbaaadbcabddbdabdacbbcbdbbadadcbcbbadbcbdaadabbbdabbbcacccacbcbabcadbbadcbdaaadcbdccdadccdccccdddcccdcacbccddcccadccabccacdcccdbdddbdbdbcbcddacabbcddbabbbaaacaadcddabbbcdcbddccdbbbdaddaddbdabbaabdccabcbcdbabccabddacabcccbaaccbaabbcbdbddadbabbadabacaccbdadccaadaaccbdbcccddddadccbdaaadbbddbcdbacadcdbcccdddccabbabdcabbaabbdaacbbcddaaacbccddaccbcabacbdababdcbdbdbacacbbdbcabcbcbbabbadadbbbbcaacdcdaddacbbdccdcbabbbdbcaabdacadaacdcbbcabadbbdaacdadbbaddcdbbdbdaaacbbbdaabcdabbdaddcbcddcaacbcacbbddacbdbcadabbdaabcabbababcbacabadbddbbddbdcccbacbddbcbcdabbdbbcaaaabddaaccbcbddbadaabadddaacadadcdbdbaddadadbbcddacdcdddabdcbdabdbadccbcbdcdadccabcabccdbccdccdabbbbaacdaccabbcdcbbcbccdbabdbacabdaacadbabbcabcabcbbcbababcdbdababbbbbacacadcbabbbbbacccaabdbababcacdbcadddcacbcbabcdadbdaaabaacacdbdaabaaccaaabaabddcbbadbbdcdbbacbddbbbbcadaabacacdbdadbcbbdbbbbdbdcdacbdbdcbdcccdbbabccdbcadabcbbadaacdaadddccaacddacdadadbcacbdbccbdbacacaadcabcdbbbdbacbbdacabcdbabaacabbadbbccabacadcdddcacacaaabbaaaacdbbcccbaddcbbcdcabdcdbbdacdbbbaccdaccababccacaccabadcaadcaaadacacadbaaaaabbbddaabbdcaabaadbbdacacaaadbdbdbaddbacaadaadaddbcabbacbcbacadcbcbbdccddccbccbadbcdacaddbbdcbdbadbcccbbdacbcaaccbdbcaacbabbbdccbbdaaacdbaabccdcbdbcdbcdadbddcadaaaddddbcddbcaabcbbdccccaaaacbbcabbcdbcbabcdbdaaacdbdaabadaaabbabdacbcacaacbabcaddabbaccbacacdcbdbbdcddcdbabccccdabcabdadddcadccacbccbadbdcadacbadcaacaaaababcbdabacdbabbabcccddccccbacbdcabbdccdddbdcccabcacbcdbbabcdbcbadddddaadcbdabaacccccbdabbbbaaddbdbacddbdcbcaccbddddabbdadacaabccbabcacadddbdababbcdccbbacbabcbdababcbdadaacdaacbacabcdabddbabddacadbbacddddbbaabdaaaddbccacddadabbdccaaabacbbdccbbbbabbcacabdbbccbacaaaadbabcbabbbdcaccbacadcdddbaaadddcdcadaababcbbdbbaccbdcddbdbcbcbbbaccadabcacbcbbcbcdbacdacdbabbcadaabcdaaaddaabcdcaadbdbbbddddaaddadbdddbbddaabdbbddacccccbabcaadbabccddbaadadacdabcbdabbdbdcabdbdbbacbbbccacaadadbbcddbdbcdccacabdcbaadacddaadcacbcadcddbbbaabbabdddbacbbadadaaddbaaddbbadcaaaccadabddcabcbcaddcdbaabbcbdadcbdccccdbbcdcabbdbddabcaadcaabcbdacadacbaababacabaadacbcbaaddcddacdabbacaacdabdbdddaabaddddccbaaaacbdabaabbddaaadcadaabccddabbbdabbcdbcddaabdcdddaaadcabcccacbdabcbcdddddacdabbdabadbacdbcccadadabdcddbaabbacdbdbacdcddacaccbaccbdadcaabbabacdaadacbaabcacdbabbaddaaddcbbddcccbbbdcbaccbbabcaabaabbdbadbdcabacaaccbccaddaadbacdbacbbccdbacbcabcabbbbdcadbbdcacdbbbdcdbbcbacaaadbccabbbbcdddaaabdcccacabcbbbcddbdbcbdcacbcbacbbdbccdcbbcbdababdbaabcbaacadbadcabddacadccbcaabbaddbcbbdddcabbccdbaccddbdaaddaacdaaacbbdabdabbdadbcaaaaabcaddbccbccddbcaaabbccbdcadcbcbaaabccdcabcdcacddbacdbbdcaccbcbadbcaccdaacddacadbbdbaaaccbbacdbddaadddcdaabdddcdbcccaddacbbdbaadabbcbbacccbdcdabaccdbacacdadccaabdddbbdcbbdbccbdcbadddddbcdcccddcaababaadccbdcacbabdbcabbabcdddcbdbaccbcddaccdbacaddddbadcdbbcdabcbdcdabbbdcacaaabbbbdbbbbbbbadccdaacbbbbddcccaaaacbddddbbcbcbbdcaabcbbcacbdbbbcddaaaaddacdbcdadcaacbbbbabcadbcdabbaccbcdabcaadadabcdcbdaacdccdaccaccddbbbbbbdddbdbdbacccdcbbabddadabadcaabababbdddbddbdbadcabacacdbdaabcacbadacbaddcdabadbcdcacccdaccdbcabcacdaabadaaacadacbcdbbbdaddbabccbbcdaabddacdbcacadddaabbbacdaacbabaacadbddbdabbcdcacdbddabbbbbdbacdddaadabcbaadccddabaacbdcbbcaccbabbdbabaccccbdcccbabadabcadaaccabdcccbdbdbbdacbadabcabdccaacdaadbbcaabdddddabdcadaaccacbccbaadcbdacabcaaddddcaabbccdcaaccdccaaddabbddcadacbdbacaacdbabcdccdcbdacddaccbbcaaccbcacdcbdaaaaddbbcdccddabbdabdaaadcbddaacbdacdacbcaadbdaddcabadccabbdbcdadbbcaaabddddcaaaaaccbcddaccbcdccacdbbcbccddddcbacaaddaacdcdbbabddcccdacaddaddddabdadcccbdbcdcacddacbcabbbbacaabacdcbaaadcbddabbdbbabcadcbcdbccabdddccbcbcadaadacadccaaadbbbabbaadbddbbbbacdccddbacdbabbcabcdccdcccadcacdacdcdbbcbdcdddadaddbdbabddbbcdddaacaccbabdaadcbaaaacadbbdddcddbbaacdbdabdabdadcdddacbccbdbcdbcbabadabdccdaacbcbaacacadbbddcdcbaccdadcbcbdbbddcbccdbbdbccbaabbdacbbcddaddbdcdaaadbcbbdcabdbbcbdaccdabadbddacbaccdcdacdddaddcbbbacdabbaacbadbbcbcacbacacbccbbbdcabbdcddcdaaccacababddbddacbdacdbabbabcacbabcbcacdcccadbaaaabadcbbdbacbbdabacbaaabcddcaaddaababaadddaaccbaadbcdabdabbadcacaacbcabcdbbbdbcbcbaadbacdacadbdbcbcbdbacbabadddbccabcbcdbbdbcabcdbcacbcdcadbbaaacacdbcdbddcccbaacbcdadbadaacccccdbbbcdccddbaacbcbccccacaaccbabcccbacddaacccbcddcddcacdbabdacabdbbbbdbcbacbdabbcccacbadbdabaaaadbbabaddcadcbbabaaabbdccaabaabaabdbbadbdccbddcbbdbcbdcacabadbddbacaccaddddcabcbadcddddcbcdaaabaaccbbacaaabdbccbcbdccdbbdccacacdcdacbacdddcccbcbaddadacdddcccbdcaaaacbdacbdcbbaccaaabccadcbdcaaccaabcaabbbddadbccadbaccbbacbbdcccbcaddddbbadbbdabadcadacbbcaaaaccdacccaaadcdccbacaddaccabadaabddaacbbaaabddabbaadcccdcacaabcabbccdddbbccdbbcbacabbdacbbabdbaadadbbcaacdccdcaaacbcdaadaadddacaacbaaabbaabdddadbcacbcdcaacaadbddbaaabccdcbcbbdbaddaccddddbdbcbbcaccdcaadcaabbbcddbbcbbabbccbccabadbdbbdaadabcbbabbccccbbbdabadccdaddccabdbacabbdccadcbbaaabdacbcdbbaadbcdbacdcbbddccdcbacdcddbbbcbccbadcdacbacbabdcccadcdcbdabadbbdbcdcbdbacbbdcdbcacdacbcbaddcbcaddbadbddbcbdbccaabcdadddabccbaccbbbbcccadbdbcbdbcbcdacbaaadbbabaabccdccccbbabbbcbcaaddacadabbcbcadaaadcaaadbcaaacabadbcddbcdccabddaddbcdbbbdaaddbddddcbcdacabadcccaaaddabcbbcdbbdbaccacdaacddadbccccabbbdcddbbaccdaccbaddcdcabbacbcdccadccadcbabdccbacaadddcaddbddaccdaabcbbadcddccbdabdbcdacdacbcaddaccaccaabaddbcdbabdacccbaccbbbbcdcbacbbcccdcacdcdadbddabbabccabdbdababccbbaaddbacbdbaaacadacbbbcadcdbabcbaacddbbbdbdbaacccbcaaddbddbbabaaaccdddbbcbdaaaddbabdaaacacbbdcccdbdbcabdaadbcadbacbddccddbdbdcadadbdbcdcdcdccdadbabcdadabccadbdcbbcbdaadabddcbabbcbbbacbcabcaabacaacadbddaacbdbabddbdddccdbbcddbccabcbbcbbcdbcaaadabbdacbcbbbdbcbaabcdabcacbdcbaccbccdaabbcbddaccaccbcbdbdcadbbcdcdbcadbbddbaaadddadddadccbdbadaaabddbaacabbbcbcdcdcdabcdacdabcaabbaadcbbcacdacbaabcdadbbbdccdcaccbdddacccdaaacbbbacbadabcadcacdbdcdacddbaaabddddbdcccbdccdbdaadcdccacbaabdadabcabbbdacaacaddaababdcabccaaabdcccccbbbadbdbacabcdadaccbadcbbbcddcbbabdbacaddbccddcdbaccaccaaddcdacdbaccaadcabbcbcdbbaaacacbdddabaaacacbaacaaadbcddaabbcccbbddccbcadcdaadabaaccddcccadacdcacaaddaccdbcbbacabcbbcbdabcabbdbcdcbcacdabadadbdbccabddcdcccbccddcaaabdbbccddbcaaadbdcbabcaddbccdcabdbacabaacbdccbcdddbbbbccbbdcdbcdadcdbbbaaacbddbcbbcdcadcbadcdabdaaaddddaaddbaabbabaaabbccaddbabddadbbdabbbbbbcaadbcbccddacdaaaccacdbbccaacacdcaccadbabaddcadbadcaccddbbdbcabbabdbcbbddbbadaaaadccbabdaabbbacdbbacbcdbcadbbadbcdabcadcbaccadbdcabdacaabadacddcdccbacdacbbaaaaadaccbbaccabcdcccdbaadbbabbbadcbdcaabadccddadbacbdbbddadacadbdbcdcdcaddaabbacbaddddabaaaabcdaadbdaddacbdbccabacadbbcddccadaacacbaaacdbcbbbcbaddbacdddacabacbacabcbcbacbcdbccdcbadbacacdaadbdbdbacababbbbbaababadcdaaccdcbaacdbbacddabdcccdababdadadbccbadbdcdddacccbccabcbbbdbcddcacdbbdbbdabdadbcadbdcdccbbbbbdadcabddbdbcbbbabbaadcbacbccadacdbacddbdcbdcdcaadaabacdabbddcdaccdadbcdcabccacabcbccdacbacabcddadcaaccdbbcbdbbdcdddcbdcbaacacabababbbbcacdcacbaacccadcaadccabbbcdcacbaaacbbdbdadaddacaacbcacccaddacbdcbbbcadadcaabcadabdbabadddcbbbddcabdccdcbcdcdaaddcbbaccdacbbddcddabaabccbcabccbaaadaabdbbaacacbaabccababddbbbaabddcccccdddddcabadbbdabcbcccbaadaaacacdbddcaaaadbcbababbdbddbddacccbbbbdbcaaacccabbbbdbcccbcbdbdcdbccbaccbddbbabaccabdcbcadacddabaadbdbcdadbcbadcbbbdbdbaccddadbadcbaadbaddabdccdcdaadddabdadcddccadddabbbdcddaaccdababadbccdbdcadbcbdbcbbadbdaaacbabcaaadcdacddbbbbbcabcdbcabbbabbaababbcabdbcbaaadbccbcbcccdaabadbbcbddcbbbccdbacaccbacccdcdabcdcddaddcbddcbbcbabbababcbabdcadcddcdbbaacaaaddbccbbdbccdbbbbbbdaaacbcbccacaacdcdacdcccaabdadcccbaaabddbbcdaccdbaccdabcacbccbccddcddbcaccdbccbccccaabccaccabbcadaabdbabdbaaaacbdbcdcdaaddcbbcbdaabcdddbddabbccaccadbbcccbcabaabadbcdaccbbbcadcbdacadcbcdbbaadbacccdddccbaccabaacdcadbdaaacdbadcacadbbcacccadcdcdcbccbdcdabaaccbcadcbbdbcbbbdddcbcabddaaaadababdcaabaabaabacccddacbdddcdbdbbadacccadabaccabadbccbcbdabdaccbabaadacbdadbbdbabdbccdccaabbbabdddabbbbbbaabbdddcdddccbcadcadccdcbcaadcabccbcdadcccddbaddbdddbdcadacbcabacbbcbacccdcbddadbaddabbbbbacddaddaacacdaccbcbdcbccdcdbdcbddddbbacabcadbabcbbccdcddccaccacbaaadbcabccaddcddcbacbdbacddcddacccbbaccabaacadccbddbbcbbdacdcdcbaabddacbacdcadbbacaccbbcccabdcccabcccaddbddccdbcaaacdbaacbadadbddabdccdacdadbabbdbcdacbbcacacaadbbaaccddaddbdacaccccbcbddbdcbbbbcdabcddbcbbadddccdbcbdbcccabddddccccbbbbccbcbadbbccddccaccdbdbacadadbccdbbddcabbdcdbdcddcbdccccdabbddbcbbdaaabaabcddcddcbbdaacccadcbaaacadbacbbdcddddbabcbbcacabdcadddaaddaadadcdddccabaaabbcbbbadccdadadbbbacccdddcbcbddaaddbbdcabbdcacabdaaabcdacccacdccdcdddbaddbdcaaddabddbacbcdaddddbcacbaccddcbdbccdbbbaaacdcadbdadcacbdabdcbcaccacdcabaccabbdacccacbcdbdddadbbdccdbbadcbdaddbcdccbdcbcdbcbdbabbddccacadbaabccdaadbcabaabcbdbcadaaadbdbacadbcdadddaccddbabddcdaddaabcbaaadabcccacdcddddbacacbcdcbacadbbcbcaaccdabdcabaabdadcaaaacbcadabbdacbdcddbcabbaaabdcddaabadcacbaadadbaccbcddacccdcbacabcabbacbaaacdaacacbdaaabcaadaabdbcccdcbadabccadcccccaacdabbdbdcddcdacdadacacdacabcccdcbbaababcbddbcabaaacbdcbbadbadbadbdbddccbaababacaaaaccdccdaadcdabddddaddbaddbbdcbabcadadacbcbbbcdbdcbcadbdacadbccdbddccdadacddabcbacdbcabbbdccaaadabbcbbbcdcdcabcaddaddbbdbbadabaccdcbadcabcdbcccadbbccccbccbdbdcdcaccbddccadacddddddcdbcbcddcbdacccddcaabcabdbbbddcaadcccbadbccaccacbdaacccbddcdcccdadacaaddccccacaddaabaacbbccbaabdadacaddbacbacabbdbadccacdaaddbbdacadddaddcacaacbcbcbbbdadaadbabcbacaccbdbbcdcdcddacccadccdaaccbadcaccddaaddbdbdacdcbcdddccdbcadcbcbbddcbdcabcaaadbbbcdccabacccaabbbbccbdcbdbabdbabbccaccbbbabcaabadbaaabcbdaabbcddcbbabadadcdacbdddbabcdcdccddccbacddaddbdcadbddcbbadabdcccbdcdbbaabccbabcdccbbcaabdcccaddbcddbccccdacddbcadaccbcddbaabacdaacacabaddcbcbcaabdbbcabbdbaacdbcabdabacdccbaacaadddaddaaaadbbbdacaaacbdacbabdaaaccdcdccccdcbbbabadbcacdcdaadccbdccdadabaabdaccbdbaadabaabcccbcdcaaabbbadadddcbcababacacbbdbcbcabbababbdccadbdccccdbbbbccadbcabaababccadaaadcdbcbcbabbcaabaccbdccccbdabdbacabdadddaaacaacbdaccadcacddcaadccdaddcbaadbdddabadcbbaabadbbbdbcddabacaddddadbdaabacddbdccacbabddacbdccadcdaccbbacccdcbacbbbdabadbbaaaabababcaabbdccbacbcbdccbbabdbdddcaabdbbdbcbdbdbdbcadaaababbdcabdcbacbddbdccdadacdbbccbbdbdbdbdacbcaccacaddcaadacccbdbcbbccbabacdbabdaaccdbdadbcacacdadbabbbdcbaccdacacadaabccdaccbadbdadaccdaddacdbbdadcadaaccaadddbdaadddcbbbccaacabccaacdabbdbcdcdcbaccaaabdbdcbbdcaddcbcaddbddadccbdabcbcbbbbcbbbdcbbaddddcccaaddaaccabababadabcccdadbcaddcdabdaddaaccbccbdabddbcbcccaabbaddbdbddbabbadabcbdbbadcaccabbddccdadddaadccaadaddbacdbaacbdcbadcdaccccababbcdbddcbcbcddccacdccabcdbcaabcaabcaaccbcbbbacdacbaccdcbcdacdccbdaadacccbaaaccbcdacccbadccadbdbcabdcccddaadcbabbcdbbabcadaabcccccbaaadbcabddbbbccdadddbdabacbbdadbcbadabdbbcdddccbddbadacaccdbcbcdabaaddbcaabccbcccccbacabccbdcbacaacacaabbddbbddbdbccaabacdaaabdcabdbacccdcadddddaadccadadbabbdacacbdbdcbbcccbdbcbadbddababcadcbbdabdcaddaaddbbbadcabbdaacbdbcdacbbbaaaaadcbbbabaabaaadcaaaccddbdaccbdbbcabdcbadcadbcccccbaaacbcaadaccadbcbdbbcacaacccbabadbbbacdacacddaaabcbcabdbdbcadbababddcbbaddbccaabababbbaadbccdaadabccadadaddadcacbcadacddbbaadcbdabaacbbcbadacdbbddcbdbcbadadabcdaadccbbbcaabbdccdbaababdabddacbadcdadbdbbbadbdacccdcbcbdacdbaabccbccabcdbbddaaacacbdabcadbbcaadbaaacaccdddbaaadbcccccabaabcdbbccbbdaabcaacaaadbbddcdababcdbdcacbabcbbdaacabcdabbbdbabadadaaabdcbdbcbcdbaabcdabaaddcadaaacdccbdadaacaabadbbdddbccabbbbacbbccacaddcdddcaaaabdadacbbcccabadabaaccbababbabbcdcbdcabaabdbaddadadcbcbdbcdcbdccbaacddadbacaaacdabcdcdccddbdabcddbbdddccddccbcaacbdbbdbbbcabdbcdabbdaaabcabbbbdaccadbdcccbcdccbccaccbcdcadcccbcdbdcbdcdccdadaacbcdcdaaaabdaaacdabbbdcddccaaaabbbbbaacbbdddbcbddcaaabccbbdabccbcddaccabadcbcccbabdabcbabdadcbbdbddaaaaaccaadccdcccbbadccdcddacaabcacbddaabdbbddbccccddabacddcbdddacaccdccaddddbbadcbdaabacccbddbdccdacdcadabbabbcbcdcdcdccadddadbcabbabddbcdbccadaadcdbbdbbcbdaacdddbcabbcacccbcbadcdcbdabdbadcddaaababccabcccbdacbadbccabcccbbaacacbcbdaacbcabdcdbcacadccacdbbaadaacacbbccddabacbdadbbcccbabadcbddcbdbabcdcdcbcbadabbbddcccaabdaabcbbabacdaaccbbbabababcacdadccbbddacdbabddaadcabdacbcbaabcbcbdaddcdaabcaacccaadcbdddbcdcdbbddaabccddbcbdababaddbbaabaddcabcdbbbbaddbbbbcccbbacbcbcbacababaccaaccdadcdddacbdccaddcbaddbacdbddaaacacaccdbcdbbdbbbcbabccadcddaadddcbdcbcdcbdbdccbcadbbaccaadabbbbdcbdcdcdbbacbcbaccdccbbcbbddddbbdddcdbdcdbbadbbcbbbdcabdabacdacbcccbddcbbdccbcabddddbccdbbdccabbbbaacadccdcdbadddcdddbddccdaadbacccaabacbaadbbcaccbdaacacbacdbbacdbbdbacadddcdacbcdbacbcbccdcdabccbabdbdccdbddabcbcddbcbadcdcbddbbabbbbdadbcaddaddddaaabcdaadbddcbbbdcabbdabbcbbdbcadbdcddadabaccbdcbadabbcccdaacbadddbcdcacddabccaccadbdbcadbdbacadacdcccdbbadacdacdadaadaaaaccdbbbcacacbddcccdbddbbaadaddbabbdadbabcaaacaabccdbaccdbabadccdbddbacbcbacacdbabdcbbcdabdddacbdabbdaddcccaddcccbababaababaaabbadcddbadaddbbaaabdaacbdbdadacaabacbbbdccdaabcabaadbabacbddbbbcccacbabcbaccbcadbdcaabadcbccabdcbcdddcbbadcacccbcdabbbaabaddcbabbdabcdbcbacadaabbabbaddaccccccbdabcdbadbbbbccabcbcacaaabccbdbabcdcabcaddddccccbdbacdbcbbcacdadccbcbaaadbbddbcbabbcdbbdcbabcbadbdbabbcdbbacacababcbacbaaadadddcaabdaacdcbcaddbaaaccacdaccaadbbbcbabdaacabbaabbaabdddcdaaabcddccbcaacddccacccdcbbdcbbacbbdaccacdbaccabcbacbdadadccddbddbdbabbdaddaccbdbabadbdbbaaddcdbaddbddbccdcbabbaaacabbaacccacabcadbddaddaddbbbccdcbbcbadbbadadadcacaabcabdcdddcdbbadcbdbddcbabcadbbabbdacacaabaccddaccbaacbaaddbccdcdcabdcbcdaddbbcdcddabcacdbdbdbadabdaaabddaccabcddaddaadbdadccbbcbccbddbadbcddbcdbaccbacbcadbaaddccaddccbcacaadbdabccabacbaacaaaddabccdcadadbadcaccdabcdaccbcccbccdcdbabacbdbbcdcacdbadddcbdbbaaadddadbbbbbcddaacbcddabbcddaddcadaccbdccbadbabcbcdcbbaccdbaadaabbababadaaababacdcccbadddcadacdbdddaccddcacaabbcddadaabddbadcababaabadbbbdcaccdcadddbcbbccccdacccbdbcbacabdccdaaccdacbcaccdaaadaddbadccbdabbabdbdbdcbcbabccbadadbcdbbadbddaccadcabdaabcbadaddbbcddbbacddbabdccccddadbacabcbccacbbcddbacbaadddcabdbdbaccbccdbaadbabbadbcdbdbbbadccccbacbaababbaabbcdbbbbdcacddaaacbcdcdadbbbddaddccdcddadcbcdbacbbbacaccbdaaacccbbbcababcddaadccacbbbbdaabcbdcadcaddadbdabbadabdaaadadadbbdaddbbcbbabccbccbdcaabcabcabdbaaacabbdcbacbcddabbddcaadccbdcdabcdbdbbccbdcbbacdcbaddbdadbdcbcaabdcccbcdddcdabdabdbbdbcdcdacadaadacbaddbaddddbdcdadcbddacadcaacdadbadddcdabbbcaaababdcabbdaaaaabbbcaabbdacccbcbdaccbbccdcabcdbaccaabdccbbcabddacddccbcaaabaabdcadaadadcbdabbdcddaabdaadcdcbbdccdcbacbaaacbdadbcbdcdbdabbabcbcddbdadbacbadaaddaaacabdbbacbbdcadcdbbbbcddcddcadddbabbddccbdcccbbbdaccbbbacaddbcdcdccdbdccadcbbccbbadadbadabdbbadcbadacdbdabccbdcccbcdbccbdcddcabddcaabbbbabdadbdccccddbaaadddcccdcaabcadaaacacbbcabbcdaabdddcbdbccdacacdcbcdbdaaaacccbcadccbacccaacdadcadabadbcadccaaaabcdbbabcccdbaadccbacbbbababdacaddadbaccabbcdbdaaaaadaadabbacccabdccbaccbadacddbbbbaaaacaacdbcbaacbdaadaaaadcadcacdacadcabbdacbcddddaddcacaadcdabcbadcaccbaabadadbabacbcaccaccddbabbcdabbaadaddaccbcbdcbddaaaacaccaabdaddbddaccdcdcacabcbdbccbcdcdaabcdabaaddabdadbaabcaabcbbdbccdbdcddccbacdbabbcaacbdbcbccbdccdacdbcddcdcaadbdcaccdaacdcdbbcddabcddbaabdbcabdcdadaddcdbcdbaaabbdbbbddabdccbdbaccaccdbcbbbccddbabcaadbaaaadcabcdabacbaaaccbbaddabcddbaaadbbcdabcbdaadbbcbacbdacdcaaaddaddcbbaabdadcabcacaabcdacdabacabdbabcbdcbacbbbbadcddcabcddaacdbaccaccaddabccdcbbacabbcdbcdbdcabaaabdbcdacacaaadccacbcbcdbcbbadbcdbacbaddcbcddacadacddbabccccadadccddadcdcdccaabdcddaaccbabaabdabdadabbccaaccddbabbaaacdddcaadbcbacbaacabcccdabadbdcadadcbbcbdbdadaaabcbccdcbabccdbbabbbcccbbadbdadbabacaadcddcdbcccdddbadcbcacccaaabccbbacabddccdbcadbcdcdccbccccbadbdbccbcdcbcaddabbacdbccbccdcaabbdaaddbbadbdcbddcccddacacbccdcabdaddcddaadcbaabcbbbbccccdadadcbacaaccacdcbcadddaadaccaacadccdaaaabbbbdcbbcacadbddaadcbcabcbccacdaabbaadcabaaadbdcddadbabcdacadabcddcdbabcccabaaddcdcdabdcddbddbbbbbbccccaddaddcdbbbcabcbccdcdccaabacbcdaadbcdbaadbaacdaccabbbcdcabddadaabaacacbcbbcccbcbcbaabbdcbabbadacadcacabdbdccdbcdaacbddadaacaabbddcbabcabaddbcccbdbdacabdacadacdcacadddbdbdbcdcccdabacbdcbdbbadaadacbdbabbcbbdbbdabccdcdabdbdcadbcdaabdcbdabbcaddaccbbbdbabaadccddaaaaddcabbbbdddccaabddcadcccaaabdbadaaabaddcdbdccbabaccdbabcbabbbbaddaacdadcadcaabbdcbbacbbbbcdabcabbdbddbacaaddacbdbdcbadccadcdcdbcdcadaabccaabcacabbabcdcdcabbdacdcdbcdacccaaccbadccbcbbadcbcaaacdacaaddcaccdbabccdbcddddadbcccaadbbabbbdaaaccdcbbbdddcaccacdaddcdbdbccbdbcacdadadaddbabbcadcbbbdabdbcabaaccccaaabdacdadbacbddcbaadaaacdbacaaccaacdaaccdcdbbbdcbcdbdcbcdcbbbcabaaaadcdcccdabbcabbaaaddacccdabcbcbaabbaaaaccccbabcaaabddcdababdaccaabddaddbddacbbbcbbabcadabbbabccacadaddbbbddcdcbacbbdaadabdbbbccddbbdbcdccaaacacdaddbdbbaccddcdacadbcacddbaacdddbbbddadcbddadadccaacbcddddccbddcbcddcbdbcabdcbbcbcadccaaabacdccddcacacaacaadaabacdbadbbbcbdbbbdbaccdabdccddbcbddcacddbbbacddbbabaadabcacbbdaabccabcccbcadbdadcacdadcabdaaddbcacbddcbabbbcccbadadcacacddccdbdadbcbabaacbcdbddacbaacdbaacaaadaddcaaabccdddadbbabcccbacdbbbdddcdcdcbcccacbabbcaddddbdabcaadabacddbbcdabaaaadddaadababbcdaabbccbdbdbccadccdccbcdbbbacdcabbcadbcdbcbccbcabbcbcdcdddcabacbdccabbcaabadcbbadaccacbabadbddcacaccacdcdaabdcdaacbccbbccacadbdddcbdabbcbccbcbcacabacbbdbbacbcccdbdacabbdabbcdabbaaabcdacbbacddbcbbdbbbdabdbbbacdacccadbccabadadabaccbaddadcabccbcdabdabcdaaaadddacaaababbccdcabdaadcabcacabaccbddadacccabaacbabccaacdcacbbccdabcdadcabdbcbaacccbdcdddabbdcdddaccacccbdbbdcbdbcdcaccabbcbcbbcbccaabadacddabdbbbcbcabccadbbddcbddacdbbbccdbdcdadcdbacaacabcabdbbbaaddbbabccbadabcbcbdacdadbbaabbccaabcddabaabcbccadaadbcbdbababbaabcacbabdccbcbaccabcaabadbcacaddbcccbacbccdacbbcdbcbcccaacdccaaddcbcadcabdbcdbcdbadcaabcabaccaddbdabcaabcbdacccadddcdddcbacaaadcaaabcaaaabbcdacdadbbdcadabcbcddbdbdaacadbacabbadccbadabaadccddbdcbbcbdacdbaaabdcacbcbacaadcbbcbcabdcccabddcadabbdacbccabbcbbcbbabcbcddcbbcbcbccadcaddabbccbdddcddcaadcabcbcccdaacbaabbddddbdcdccbbadcabdccabbadbbdccbbbcadaaaddbaccbcccaadbccbccdaaacdbbdbdcbcacbcbdadbaaabadadadcccaaaabcbbabcdddbcddcdbbcaadccdbbadcddbdddabcaacacabcdcdbaaacdbdcddbbbacbadadddbdacbcdbbbddbddcdaadbbbdbbbadcacaaadacabcabaaaacbcbaadbccbbbbdcbaccdcdbaaddacdabcdaddddbadcabdcbbaacdbdbbbbbdaabbcbdbcccabdaacdcacbdbacbadabdaddcdadcacddcbacddaaadcbbbbcadcadabbccadbcbcadaacbdabdcdcaccddacbaacccacccbcadacddacbdaacaccdcdddcdadadbccddabdacadbbcccaadbdddbbbadbcaabadbbdbabbbabdadadccddadabbcddcaaaabccbdadacbbcdababbccbdbccbcddcabdbbadacdbbabbacbdbcaaadccaabaacadbbdccccaddccadccabcacaabaabbccadcbddddcdacbbdddbddbcadbdcbddbbdddadcbaaaaadaaaacadcaddadcabcdcbbabbdddcdcbacbcbccbbacccbbdccdacdabccbbaddbadbdcaaaadbaddaaaddbdddbcadbdcbbccccbbdadbdbdadadbddcacabbaadacdbccbabdddddbccddaabdbaacccbdabadacadbbdaabddabcbbcbacddadabacbaaccccbdbdcdbcacbabcdbaccbbbabbbdcadccabcbbbccbbcdadcaaacabcddcbaccdcbbacdcdbcbddabcabbdccdcdaccdcbcddacbcabbcdaccbcdcacdcbcdbdbdbbdaaadbadabbcabbdbbcacdbcbbadbdcddbcbaacbccabbdbbbadadbaaaaacdddbbddbadcacbaccbaaacbccbbbddacccbcadddaacbccaabdcdcbcccdccddcbcabbabcadabcdabbddbdbcabbaaddcdbaabdccdcbcdbddacadbccacabdbaacbccaabadddccbdcdcdcdbbccdccdbcbdcddccabdbaadaaadcacaaaadcbddbdacbccadbaadaabcbbbadaacdcbbcacbdbadcaaccdbabaaadcbcdaacccbbddbcdacdcaccbdbdcbbacccccacccadaaaaaddaadaacbdbbaacbbcaaabaddadbcbbbbbadcbaaccddcbbcbcbbcddadcabadbbdbdadbcbcabbdaaccadbacdaadacdbbddcaacccccdcdcabbcdcbcddadabcbbdacdbcabbcbdacbdaccbaaaabbabcbcdcdbdbcabdaccddbbbabadccadbaddcbaaccbaaacdaccddadadbbbdabdabdbccdadcdcabcbaddbccaacdbadaacdbcadbcbcbccdadbcccadcdbdcabaaccddadbccdddaaaacbadddcaccbadbacdbcbaccdbadddacacaacbddcdabddadbaaaccdaadcccbbcacdbcbdccbcdbbdcabdaabadcabcaacaacaaacbbbcbbcbdccbaddabbccdcdccdcabaaaacbaaacddbdbbdcbdcbacacabdabcdbaacccabcdbbcacddbcabacdbbccbbcbbccbcbadaddddddabacaabbcdbacacbddbbcaacbcdbdbdbbbdbcacddbabbbabcabdcaccbcbdbbbabbadbbcaaccacdbdacbcacabdabbaaabdcddadcbaccccabdabcaaaaddbbcddbcdaaabacbcdbabcddabbddbadddccdccbbaaddaadddbacdabacbdadcccacdacdbaabaaacbbbcddbdadbacbbcbcdaddddcddabbbcbcadaaaaabaaabcadcdbdbdacdddaabadcdcbcadacdcacacaaaadbbcbddcbbadbddbbcbaaddbcddcdaccabcdbacaccbdbddbddbccddbccbbadadacbbccdabbcadbbcabbacddabbabdddddaddccddccadcaaaabcbdbcabdaaccabccbbabdabdadbbbccbbdaacdddbabcadbadacbdaaabdbaabdcbaabdbcbddbdadacabddbadcbbabddbbdaaadcaaccdddbcaaabcdccdcbcbddddabdadddcdaddbdbdaadabbbaccacccbcddaddaccdbadadabacabddaaabbacdacbdbaddbdacbccdabdbabacbcbbcaccdaacdadddbabadbacaddabcbdbdcdbbccccacabcdaccadbaaadbbacacaaabcadbbdaacddcdacabaaabccbcdaadbcdcddcbbadaabcbdbcdacdbdccadcadabdbbdddbcdaddacbcacbdaabcacbdabccbcccacaaaaaacccbadcdddaacadbbbbbacdacddcacbcccccdbcdbdcacbbabbaabbaacdcaacccdddadccacdddadbacccabdcbadaaddaaabcddadbcacbbdbcbaaaabbcbabdbbcdbadbdbcbaddcbdcaadacadaadcbdcdacbcdabbadaabacdddddbacdbcbaabaaddcccdcbadbbdcbbddacdabaddcbbadacbcabdddaadcdabcdaaadabdbcacabbdcaaaaddcbbdddabadabcdddaacbcbbdaccdabbdccadccbbbabbcdaaddaaabcbbcdcdbcdddcaddcbdddddbaccbcdccdaaabaacbaabddbadbdacdabababdcbcdadddbbdabcbabbcbcbcdbbdbbddccabadacbaddbcaabdbbdcadbdcaaacccccabbaccaddabdaabbcdccdbbdadbcaacadbaadabbbbaaadabccddccabcccddbcaccdddadbabcdabcdcadbbcadcbdabcaadacaacadcbcbaabddbcabbdcaadaaacaacdaaacabdbbcdbbbdcdddabcaacaaddcaaadcdcdabddbacaccccadcaddccddbbaadacbddaaadcdcdaadcbbccaaabbaabcbcbcbcdadbdabadabbccddaaabbaabacabcbcdddadcbbddbcdcdbbaadbccbabbbdcbdccdadccaabcadcbbdcdbddacaacbdcddacbbcddccadacbdbdbbcbaccddaacbcbbbacccbcbcdadbdaccdaccccbdbccaaccacbacdacaccabaccacbaccbdbacdadbbccdababbaccacacbaadaadbcdbdccbbaaaabddaddacbcbbbbcbadccdbcddbacadbcdbabaadcbbbddcbdaccbabdcbcabdbbbcabdaabdccddadaabaddacabcbdcbadaaccbbdcaaaadadcbcdcbdbddbdbacadcdccacbbacaaababdcccadaddbcaabccacbabdddadaddbadcabcdbbbaabacddadbabbacbcabcccaccbbadccbabccbdabaaaddccbaccabbaddcabcbcbbdddabbaabaaaaabbbdddcacabccaccddbbaaacabadbbbaacbdddbdabdbabcbbdccdaaddddaabbabcbbbaaacbbcacaddcbbdbdabccdcdacbdaccdddadbcdccbadbadbdadbabdccdbdbaaadabbbbabadccdbaabaacadcaaabcadbbacbcabbdbbbbcbdacccddbcadaabbdaaabaadcbcddadcbdcaccddddcaaadaccddaccdbacbcdcaacaccbcaaaadabccacbaacaacbaccddccaddadbcadbccbddadacdaabaabcdaabbacdddaadbcabbaadbddbaaaddaaadcabcbdcbcddddcddacdbccdaadbcdaddbacdbaadaaacabcddcbdbaabcadaabbbbaacbcacccbcdadacddcbcaacdccdbccdbadaabbbbccdadabcabaabccdbcabbdcdaccdadbccbbbdccdadacadadbcbbdabbddbcabbadbbabdacdcbbacabbcdddcadabbbaacabccbadcddcdddbcadbcaaddcdcdbcccadcadbadabdbcaacaaccaccccbdabaabbadabdbdbbbccaddcbcbdcaddadbdcabccadbbdccdbacbbabcabacbacacbcdacbdbddadbbbcccccdcdbbdabbabbdcaddbdbbadcdabdddcbaccdbcaddcacbadaaaaaabcbcdcccabddbdaadaacabbccaaaaccdcbacdbdcdcbdcbbbbbabbbdadacbddaddacccacbbdbccbbcbdcbcaccbcbaddaacccdaccbdddbcbacadbabacbacdbdddccccbbadacabccabbbcaabdbcaadcdaabbdbcaadccbccacacbdcbdcaddddddbcdcbccabadacaccaaccaabcacddcbdcbaaacddadbcdaccbbdadacdbcddcdccdcbcbcaaabdbbaaabdcbadbbaddbcdbbbbdbaabdaabdadbbaabacbdcddcabbdbbbabbcbdacbaadcabacabbacddbcbadddcbadaccababdabbcbbaaabdcacbaaccacbbaacdbbdbbdbbbbbddccbdacddbbbbaaadacdacbdddbdadcdabacabadbaacdaadaadbabaabaacabbcbcacaadbdabcabbbddbccbbaadbcaadadcdbabcddaaddbdccdacadadacbdccbbaaaabdbcbdaadbacbdccbcdccbdababcbcdaccbbdcbccadaaabdccbdcacbcbcabcacdbaacdcaacadabdcbdccbdaacdadadaabccbddbbacaabbcaabbadddadacbaddddcabdcaccdbccddccdcaabaacbddcbbcddbbdadcdbacbcaaaacdbaadacabadabcccbdbaabdccbbddaaccddddccdadcbbbddcccbcbdcccbcbbcbbbbcdbddcbdddaadacabdbbdabbcddacbdacbccccbbbdaadcddcccdcdbaacbbcbabccabaadacdacddcccaaacacdacbbaaddbddaaadbabacdcddccdaaabbdddabcadabddcccbdabddddbccdddcaaacbdcddcdacbaaccaadaabcaddbcaddacaaacbbbddabbcabdbccbbaadbaacbaccabdabdccbccdbcabbccccddaaaadcaaccacccdbccdbbcdbaaababbbcabccbdabbabdbcaddacdadadabaacbadacbdadbadacaacbbadbccdacdbccaddccbbdacbbcbaacddbaacaabadabdbababacbdbbaaabadcdadaabccabcdaabbacabdcbbddcbabbddaacbabcccdadabadabaccaaacccabcdbccdaaaccbdadbdbdadabbbbbaddabdbcdccdbbdbbdcadbdabadbbdcadddabdaacbaadadddcbdcaaddcbdcadcbcbddddcacbcbacbcaacccdabaccabdcaddbacccaacadcbccbdcadbacdbdbcccbcdaacdcddcbadaddcdabacbaaacddacaaadaddbacbccbbacabddddbbacbdbcccdbbaabacdabdbdaaadbaddcacdcdaccbbcdaacdbbcbcdcccaadbadcabbdcdbaadadabbcabbaabcbcbddbccbaddcbbcdbcddadabbbdcacbcabddccdcbcdddbbcccbbcbbadcdbbdcbdcdabdbdacbddbccbcadcbcccbdbcadbcbbdadbacdbaadbdbddbaaaccadcbbddadcdddcaadacbdaccbbdaddcadaaddcccbdbcdcbbaacacabcaacbdabbdcddaababdaaadccabbbcbcdaadccddbddbadbabcabccdcddcdccdaadbddbbabcbacbcbcddacabcddbddabaabbbadcbdaabdcdbabadcdbcbababaddbcdcadbdacbcbcababaacaadacddddbcaccaaaccbccbcdbbcbddddadcaabdbdadbbcaaccacdabbcdabacdcabaabdaadacdabcaaadabacabcbdbabaaddcadbbdccabdbdabdabaacdcbabccaddbaadbdcadabcabddbdabcddbabdbcdbddbbcddaabaadaadcdacdacbdbddaccabacaddcabbacbdaaadcaacabcdddccacddaaaabccacdbadabaccacaababdcaaccadbddbbdbbddadbdbbcccddcaccadabdacdbbcbcaacabdddddcdadaadabccdbdbaaccaadacdaadbcbdccaaaaacbbcbcbddbdaacbbabbbcbdbbddabbbcaabdbccdadacaacbbccdcbdcccddbdbcababdcdaaabbcabdcdbbcbadbcdadbbbdbbbbbbbbcabddbddaccbcaabdaddccbcbbcbacdddbbbbbacdbccdcdacdcabcbbcbbcddccdcaabadbcbabaaaaadabdccaabbdacdabbcdcaddcbdcaaddccdccbddbcbbddbcdcddbabddcdbaadadababacccdabbbcdcaababdcdacadcabacdbadcaddbaacddbacbabadadcbddbdadccdddcadbdcdbbdaacbababdcddcacbcbbcadaddddbbcdaccdaaccccadcadbadaabcacaddabdbdcbbaccccbcbddbddacaccadacadcddacbbdbbadacbccbbdabadcadccaabaaccbadbdbbbdbbbbbabacdbbbdddbdccddcbbaaacbcdcbbdacdddacdccbabcdbaaaccadcacbabbdadabcbacbacbbbcbacdcdccbbbacaaccacdbccbababaccdaadcccaccbbcddccbabdbdddbccdabaabdabdddcbaacbbcabaccbdcccbdbbaaabcbddcccddaababdadbcbcccadbcbbdcbcbabbbddbaaadcdcbbccabbaaaaadcbabbcdacbcddbcbddadbadadccdcbbadcbadadbccccdddbbdccbabdadcbbdccdcbdcdaaaddcaadabdcacadccabdcadcbcccabdbaadbcdbcbbdcbccbbcddbbbbcccbcbcdbbcbbcddddcbadcdcdcbaabadccdabccabbcacdbdcaaccbcbcdadccccacadbdcddbcaaabaacccbddaaacadbbcbbbdcbbaabbddcccacdbacabbadadcdadccbcbbbbcabcdcdbbdccccdbcdbcabddcadcdbbddbdcadbbdacdacbcdacacdacaabdcadcddbcbababddcabdbdbbacadbcbdcabbbddbdddaadddbbbabddccccdadacbcccccccbdddbadbdccdbbbbbcbbcbdddaddcbbdddaabcbabcccbccccaadbdcdaccabbbddcddbbbdbcbdabdbaccccbbdccaddccdcbddbcbadcbaaabbcbddcbbbbcccabdddddbcddbadadabbcadbdcabadbadddbccadcbadadcccbcdbadaccadcdbcdbccdbdabbdddbddacccdabcbbdaaadcacadcabddcdcdcacbdacaccabdbcddbadaaacaccbdaccdbdaddadadacbdcdbacbcbabaddddbbaadbdaddcadbbbbaaccdbcbcadbabdccccaacddaadbbbdadaaadcbddccaddadbdbbccdbcdadaaddacccbcbbaaccccaccadaddaaddadcdcccdccdbadcdbdbaaadaacadaaddabdcbabdbcbaadcacadaccbadddbdabdcbaadcacacaccbbdbddbbdbdcdcbcababacdcbadaaaabcddadcbcabbccaccdcbbdabcacbaacaacbabcdccbaddddadbcdcadbbbccabbbbacbcccacaccddacddcccdabaddbddbbbdcbddbacdddbdcabcaddaddabddbbabaaabbdccdbabbbccdaacabbcdcaccdabbbaacbcdddaadadddaccdacbaccabdcccdcddddcbcbbccdccdaadccacdccaabddbdadbdbadacabdddcbcdbaaacaadbdabccadaadcdbbdcacadcabcacbadadcaacddabbaccababcacbbbbcbcccabcbdbdddbcadbbabbabdbbbcbbcbccbcbdaaadadcaaccbadbbbbcbcddbdbdccdccaacddccbadcaaadabdcaddbbbacdaccccabbbacaacaaadcdbacaccbdbbcdcadddbcdababcabbbccdbaadacdbbbabccdccdadadaddcdabddadbaacdabbccdadacbdbdabaccbbdccbdbdbccbdbddbdbdababbcbddbddaaabddbabdcacaaddddcacacbadadbabcbabccaccbbadbcccaadbaaacbacadabaddacdacbaabbdbdbacabdaadaddbbdcbbcdbdddbcdabadabbbdcbacbddccabdbabdcbadbdcdaddbddacdccaaabdcabadccbccdbbddacabcbcbdacddcdacacdabcccddabccdbcacaacdbaacbbdbacddabbcadabccdddbddabdcccbadbcacdbabddbabdaaddbdadddbabbaaacbcbbbbaddbcabcddccdaadcbcaaadbaaadcacccdaacdababdccacbddabcaacaccdcbcddcccdcccbaadbbddccacbcdbcadbbbadbcbcbcadadddaccbcdabcbdaabaaaabaddabbdadcbabcccbadcdbacbcabbdbccadcadcaaaccbbddabbddcbbbcbaaddcdbabbcdaacdddbcddbbbcbabdbdcbbdacacdaaccaacbacdbccababcccdbcbdcbbabaccbbbbdaaddabdcdbaaccbbcadddbcdacabbacbbadbdcbbbbbabcacbdccbcbcacdccaabdabcabdcdbbdcacbacbaacabcacaabaadadddddbdadcdbdcabacdcddcdadcdadcbdbcaaaddcaccccdddcccbdaabacaadadacbacaadadbbacadddaacddddbadbadadcdacabdbbadcdbaacadbaadbacbddbcdbdccabdddddbcaaadaadbdcccacadcbddaadcadcdcdcdaaabbdbbccbcadbbbaccbacabababbadcddcdadaddbcabdccdddabcbaaadabcdbbbcbaaadcaaddcbabddadccdcdcdbcababaaccbdcadcadacadacdaacbdbcddcdbcdbdbcacddbcbcacabbcccbabbcdcbbcddbcadcdaadaccddbbcdddbadcbcaacaacbbccbcadcdadacbcabddacdacabbaddaabbbaddbadbbabcbbbdaadbccbbaadadbbacadbcaacdcbbcacbcbcdbbdcadbaabccababdbdbdcdbadabcdccbdbdaadbdbdbbbccacbcbbdbbccaadbdbcacdbbcbdbdcacdccbbcacddbcabcdacadbccaadccdbddcadcdbdddbbcacdabcbbbcaabcdddbaaccdacaaaccaccbdccacdccdbcaaaadacdbcbbddbddbcbcdaddcbdddcdabbdadcbdbbaabbdacbcddddcbddbadbcdcadacdcccaddbaddbdaccdcabdadddbabbabaabadbccdcdbabbbabcdabaccaccbcbabadcddbcdcdccadaabddbaaccacddcabbbccadbbacbacbcbdaccbcccaccbcccbbcadaabbabcddcddcbaadbdacdabcadcdddbbbdccdbbbadbbdcbaadcbabdaaacbcbcacbacadccdabcddacabbdcabacccbadacaddabbdcabacdbbdcaddbdcbcdacabaaadcbadcadccdabbacabbabacdbdcccbdcaccccbabdcdacbcbcbbbabacbaadcaaaaadbbcaadccbdcdcaddabbbcacbcadcdabccdbaaaadbacabaacbabdbbddbadbaddaddcdcdddcbcdddacaabbdbaaababbbaddadaabbcdbbdbbacabdbbcddacadbdaadaccbcacaccadbbbadccdbcbadcaacbaadcdacadacdaaaddbdacdaaaddbdaaadcccdabccaddabbbdcaaacbcbbccbacddddacaabcbbcabdaacaacdacdbabccaaaadbacdcabdddddddbcdcacdbacdcbcbddaadccccaadabbcccbbcdbdabbacadcdbcbccacccadcabcbbccadabdaaacadbcddcdbcdccbbbddacbaccdadcaacabcdcaaabcabdcabbdcccacdcaaccbaadbbbcbbdccbacaabbdcbbddccdddddacbdcadbdababbbbbacabbcdaccbabbbcaccdbcbdbcabdcadbdbbcdcabcbadcabdcbbbcbcbabcacbadcaaabcdacbcacdcbcdcdabadbdccbdcadbaacbdbabccadadcbbaaaaccabbbabcbaabaccbcccdbdcbcaababaabaaacdbcadbcbbddaccdbcdccdbcbbadddbabacdadaccbbddcadacbabdbcbbcccaadcbabbdcdbacbcbdbaadbbcaaaacddbbaabbccdaacacbaaabaddcbcbbcabcddacdaacbbbaadacaddddacaabbabbaadbbbcacbcddddbababcddddacbddcbbdbcdcbdcdaacbbcbcbaccdadccabccbdadcabcdcbcbaadcacaacadaacddbcacbadcbccbbcccdcbdacdbadacbcdbabdcbcacddbcbcddcbbababadabbddaabbbccbbdccaadacdbbbacadbdbdcadbbadcbdccadccdcdbabcbbacaddaaadbadadbabddccacbdbbcabdbcadcdadaadcbabcadbcdadcbddcbdacbabcbbcdacbbacadcaaadcccdbaaabcdadbcddbcaaaadadaacdddbcabdbdcdbaadbcdbaadbaadcccbdcccdcdbcbddcaddcdbdcbdabcbdcdbabdcdbacadacdbabddaacccacabcbdabdbbcaabcbdbdaaaabdbadcabcdbdacadccbcccabcbcadcdcbaccbbdbdcbccbdabaacaabcacbdbbcbcdbbadcdbdaacccddabbcbadcbbbaccdcbacaddcdbbaaabaabdcaaccadcadaadbdcaaadcaacadcaaaaacaadcbbbcdbabcdaadcdbbbddbccbcddbaabbdabdbbadbadaaccbbdbcbcbacbcacdadacdcaccbaabbdcaaccbdcbacadbdcadbcbaaddabbcdacaacbdbcccccbaadabbdddcdadcbbcdcaaacccbabacadcbbbcacdbcabbabbdbbdabccacacdbacccacabbcabacabccadccbbdbcbbccbbcbccdbcdbcccaddabcbaddccaccbacdccddbdaddbdbcccadcadcdddbcabdddbaadddcacdacdccbcddacdaaccbbaaabaccabdccbccaaccccbbccdcdbadcdacaaccdbcbcdbbdbdcadcdcdacdbcddabccbbbccacdcadcaadcdcdcabaaddbbdbbbcaabaccbabcdddbdbdacbadbabbbaacacbdcacdbddcadacbababcddddbdbbcacaabaabcddacdbcdbbdbdcccabcbdcbcdcaaacccabbcdaaadabacccdbbdaccabcaadddbaddcadddcbdbcccdcdcaabdcaadabbcbccacbccbbcaaaaababdbdbddabbacaacaddcbdbbdcaadbdcbcadbccdbaddacbdadcccaaadbdabaabbcabcaadddcccbcabdbdddddbcbdbadbcdbddacdbbbddacbbbcdddcdbcdcdddcdacbcccdbcbdbadbcadbdbbadaabdbaaabababacaccccaaaadaddadabcbdabbdcaacbaaddabaddaddbbaccbbbbbcbbccaddccaaadadbbbcaabaacaabbbccaccbcabccbcacdddbdabbbaabaadccdcdcabdbadadbdcccdabaacabaaaaaabdabdbbcddadddbacdabbbaabcadcdbcbdadadcbaccbdcadcabadcdacccdcbbaccabcdabcabcabdbccdcacddbcdbcbdbbbcdccbbbccdbcadbbaddabcbcccaacbcbacbbaadccdacbdbdbbbdbdcdabcccdabcdbbcbbdcaadbbddcddadacbaccbaccdadadbbcbdbbaabaadddddbadacabaaaddcadccbadbbadacbcbccaddabccadcacdcadcdacaabcccbdaccdadbdbaacadacbcaaabccdbbcbacdbdadcacdbcaadcddacadbadacccbcbdadcccdaacdadccdcdadaddbbacaaacbaddbcdcbdccccaacbccbddabacabccdbddaacbccbcbadaacaadbdcdbbddbddddbdddbddcaaadbbbadadabbcacacabadaadadcbdcdcdaadaabbbddcdaadcbbbbbbdddcaadcabbabdaaddadabcdaabbaacdacadacdbdabdbdbabdccaaccdabbddaddbdabcdcabadbaacbcadcccbcddaadcabdddbabadaadcbcabbaacaaabbabbcddccaaacbcaddcdccccddabdaaacdbabcdbabbbadddddcbbdacabbcccdadcccdcdbcadbbdacccdcadacbabcbcacdbcadbbcabbacddbbadcdaddaaacaddbbcbbcaaacdcccddbaccccaadcbaacadcdccacaddcaabccccabdddabaddbbaabdbdcddacddbcabcacabdcbcdcbdcdcbcacaaacadbcaddaabdbcdcdacccabcddaccadcaadbbbbacbbcbcabdcbbdcaccaaabcbdbbbccabbadbbcbdcdadbcbdbbcacdadbadadccaaddaabaadabcabddcdcdbddccaaaacdabbcddcbdaddaddabdadabdcbccdabbabcdbdcadcadbacacdcbdbbaccaaccbdcbcddabbdcdbcaacaadbaaddddbdbcacaabacaadbaccaddcaabaabbdddacdcddccabdaadadccdbacccbddcdacbbdcdbbabddcababcbadccbcccdaabbabadacdcbaccbabdbbadbbdcddaacddbabababbbaadbddbbdccadabccbaccdcaddadbaababcdcaddddbddacdacccadcaddcacddadbbabaacccbdbabbadadcccaccdbbaddbbaccbbcbacdbdbbbcadbccbbaaaadacddcdacadbabacddcddaccacbbcbbbdbcadbddcbbbddabbddacbadbcdaacbbcabdbcbaacdabaaaacbccabdddcbdabcbccaddbabbdabcbadadbadabaddaaaabacdbbccabacadcbcaaccdabccbdddbcbadbdcccbcddbbaadadadbdbaccadabddbdbccdbbdacdbddadbacdbcacdcaaaaacbdacbdcbadaaacbdaaacaacadaccaadcbabcaacaaadabcbcdccbcbabcaadbabbccbdacbcdaacdadbaacdbccbcdcdcbbdadbdbbaccaacdbaccabdbbbacbacddcaaaddaccbbaccabbbdcbdbbcccddabacadbcbdaadccadbbbaabacbdbcbadabcccbdabcccabddacccabbcbbacbaaadcdcbddaddaacadddcacdbbbcbcaabddcdcaddbabbbbbdbdcaccbaadcdcaccaacabdbbcaaaccbbbbdbadaacadbbaadcaadccdabcacdabcdbacccaccdaadddaddabbcaadbaabcabdcccbbbdaaacdbadacaaccaaacddacabdaddbabbadcbcbddcbddaadabadccaccbdcbbcbddbbabcbccdcccbbcabdccbcdddbccccbabaabdbaaacaabbbdaabcabacdcaccbdcccbcbabbacadadbdcaacaaddcadacadcbbddbaccaccaaadcabbdabbbdbaaacaadbdbcccdbdadcdcaccdbdbcdcdcabdbabcdcaaadabdabdadacdcbcacadcbdbaddbabacccddbadaaccdcbcdbacdaabcbadbabbdbbdcacbcbbcbbbaacbdaccdadabbbababdaaaaabbcbaaabbddbccdadbbcbccccacccabacadadcdcacadcdbbbddbadcddbdadbabbdbbbdbcabbddcabcabdccaccaabbdbadabbcbcacddbccccdbbdaaaacdcdcddbcbdcddbdbcbddbbbdcaaacddbdbccabdcadcaccbddbbccabcbbaabcbdabaaaadbddbcaccccccaaccdccaadcadbadaaabacbddbddaddbddbdbabcbbabcdccdbbbdaadcbdacdbcccccabbcaaacbcbbdbddcacabdddcbdabdbccadbbbabaabdacdbdbabcbcdcaabdbdbccaabdacbccddabccdaabdcbdccacbbcdcbcddbbcbddbdcdbdcaddbdcbcbccacabcdbcacbcabdabacbbabddccbbaddadbbadabbadacbbbbbaddadbcaccdbbdabcaddaacdddadccbbbcacbacdbaddbdbbcabaaccbaccbadacaaccccabccdadccbbaaadccbacacabccbcaabddaabbdbacdbdaadbbabccacddaddbcbbaccbcbcadaabcacdabdbcbdcbccbbabbaadabdacdbadcbbaabccacddbcdccccaddbabdcddbccabcaabdcdcaadbdabbdcadadbacadadddadccdbbbaabcadcbbbbcabdbaabbacbdbbbbcbbcdadccddcdcbcdcabaccbcdbaccabcadcacdccbdbaddbadbabbbbcaabbcbdbdacaaddaadccabdbaaaccdabcdbbbcddbabaabbcccdcbcadcccaaccdbdcabbacbdbcdabdcabddbdccdcacbcbdadccdcdcbbabbcbabcbbadcdccccdbadadccdbadabdaccabccddccbacacbbabddaaccaaadacdccaabccabddcaabcdcdccbddbacabadbccbaaacbdcddadaacbcccaaabaadcccbaccbacbcaaccacadbbabdaaccddccabcccaabbbbccddcbcbcbaabbdcdbcabbbbdbacddbaacbdcaaccdbccadddabcdbbcdcdaccbbdcbbdcdccabdbbdcabbaacdadadbddbccbabbadbaccccadaccdcdacbcabacddcbaabadbbacdadaccabccdccaabcacaadabbbaddcbabcbbddddacacaaccccdbcdaabbbacaacadcdbcabcbbccdadaaaadbadcadddbbbcbacbcabbabaabbbcbcdaabadcdacbdacadbbabcbcadabbdaccccbabdbbadcccdbcbabdbabdbbdababcddbaddabccdbaadaddbabcbaaccbbadbaaaadabdacaabcdcdacbbbccaacabbabcbbcdababdbddcbdbcdccdadaccbbdddbadadcacadcdbbccdabdccadaadcdbcbacdddaadacaaccaddcbbacbabaacabcaadbbcbcabaccddaacbbccdbdcbbbdcccdddbcbaadacadcdaabdbabdabdbdabbbcadbabdbbbbbddccdcabbbccccdbbacdcaaaacbbaadbabdccdadbdbddcaacddcddbddcdbaadbcbcaddcccdaaadcaddbbbdcddbbadddaaccdcacccaaabbbcdccbcabdcbdcaabbdbcbadbccadcabddaaabccbaadacabacdbbabcdabaaadbcadcbdddccbdababdaaccabdccacbbcaabbbacaabcbcddddccbbaaaabddbaddacacdabccddacbbdbababbdacddacaddddbacdccacaaaccdbaaadacaddabcabcaddcbacbcbdabaaaabcdabcabdcabbddabdccabcaaacbacccccbacaacbdcaddbbadcdcdcdadbbaaabdcbaadabddbcdbbbdcbdacdddacbdaadabbcdbbacabacdcbacdcabdcbcddadcacaccbababbadadcdcddcccaabbaaabcccdbdbdbadcacbddcacddbcbcdbaaddcaababadadddabadaadddcddbcbccbbcbacbbcdaadcdbcbbcaccdcbbabdcbaacbadabdcbaadcbaabcccdaaadcdbbbbaddbddaccbccacbababadddcbddddbdbccbdbdbbbcdaadddcacddbcabddbacbbaacabccbbaaaccacdcbaddbacccdacaacbcbacbaccadccdcddddbacdcadaccbddaccbbdbdbcdadcaddacbbcacadaaccacbbddacbbcbbbcdadaabacabccbccbacddcbbbdbcdbabcdadccaaaddaddbbbdcbabadccdacdaaabbccbdaadbdaacabbcddddbbbccbbdcbbddbcabdbbacccbdaddddcbdbccccdbbcdabbbacbcadbbcacdcdccabdbcadbddcbccbcbadbbbddadcadaadddbbacbaddddcccaccbbdddcabddbdbaabcdabdddcdccbabccadabccdbdbdcbadbdacbabaaddcabaabaaddbccbbdcbbacddbcdcdcacbcbadddaacbbcacbadbdaadadbaabdadabbcadbdbbdcdbcbcdcbdcdcaddbdcabbbadaddbcbacbacbbdcdacdabdadbbbccaabadbdaaaacdbbddbdcaabccbddcbdccbadbbabcdddddabcbcddadbcccdcadbbdaddcabbbdddddbdaaccdbabacadbbccdabacddddadbabcabadcdcddadcdcbbcabaccbdbbacbdacbabcbdaacacaccbacabcbbdadabbcbdabdddbaababbdcaaaabacbbbccaadbabacbbddbacaabababaccaddbdbcccabbaccdcabaacacdadaddcacaaddcddcddaadccccbcccdcbcbacdaddbbdbbccbcbccddbbbbbcacbbcdcdbbbdcbdcccccdccbbaccccaddbbdccbccacbcdabbcdbbdaabbdbccbabccbdddbcbdccdcccbcbacdadbbdacbcbbaacdccadadabdadbddbaccbcccdcdbdaacbdcbbdaadddadaadbdabdbdddbbddabdbcadbbabdaaddaaaccbddccabbbbacadacddbdbccaaaddbbaddabddaadaabaacaacdbccbadbbdbabcccbbacccdbdaddcdbdcbbccbdddaaddbabdaacaadacdbdccdacdabccbabbcccacbdcbbcddcdbcaabdcaacdcdbddacbcbbdddacadbdcdddddbdbccccbccccbcacdcbabdbdaddadaabddbbcaaaaddbbdbdcacdbcbcaccbdaadcabbdabdaabcdddaccbbaadcddcaccbaacbdcbdacadbdbbcdbcdcbaccdabadabbcacdbacbacdcdcaaadbcdccbdcdadcbdcbbbbdbaacbcaacabcdacbdbaddadbcaccadbbacaaacdcccbabccaaddadcbcdcdacacbbadadcdabdabacccbccbacaaaacbabbccaacbcbdabcbbdacaabadbcddbbddbbccbbbbdbddacbdcababdbcadccdbcccdacadbbcadcdababdbadcdabcbdbcbcacdcddccaabdbbacaaaadccbadcbaaddbcddcdbacddccbbdabaaaacaccdcbbadaaccdbbcbacbbdcbbababbdcdccdabbccaaadbcdbcbccacabdccdbabaccabacdddbccbbbaaaddbbcacbacbdadabccdcbaabaaaadbdadcabcbabccaacdddbdddaccadcbdccadacacccddcbbbbccacbdbccbdbcacdcdbbacbcabbcacbdbadddbbbaadaaccccabccdbcabddbccddbddabbdcadcccdbdaaacbcabdcacbadcdaacbccacccabccbabaacadbddccbcacbdababcabacddbcddbbdddbaddbaacbabcccbcdaddaacbcaaccadbbddcccabbcdabaddacbdcacbdddddbddaabdbbccccacdcbbdabaddddbddcdbaaacaacbcbdaddadbccabaababdccaccdaaaacdbddbacbddacccbcdbaabaabddcaaacbcdcadbccaddadcbcaacadcadbaaccddaaddddaabcdccdabdaccabaccbabcdbcdaabcbdaadbbcdbdaadccabdcbaabbddabbaacdababdbbbdabcbddadccadbacccaacdcdacaaadcabdabbccbaddccdabcdddbdcadddbaaabaccacbaaddaabdbbbcdcaacbbddaddddcbdcbcadcaddcbdbabbabdbcddccdbbcdddbcdabdadadcdabdcabcdcdccadccdbcbddbdbcccbbaccdbacbccabbcdbdcdcacadcbdbdccabdbadccbcddbdbbdacaacdbbaaccccbcbccbbbacabbcbcaacdcbdbadcabbabadacbdcabcacacbadaaddbbdadcdcadbbbcabbcdbbccdadcdbabdddccbbcbdddddbcdabadbbdcaddacadccdaadcaacbbadababaacccabdddcbcdcadabdbcbbcbbacdbbaabadbabbbcbdaddadabadbdbbcaadcbcdcccdcbaacbdcccbcccbdbcbbbaaabdccacdaaaccccacbdcdaccbcabdbbbcddcadcddcaaddabccabcdcacaccbbbbbcddadddbdbadcdaccccbadcbcccabdbbbccbcdbacbcacababccbcabddbcaddddcadbcbdcadacacdaacbaddaabdbbdaaababccbaccaadaadbccbcddaacbcbdacdadadddccabadadcdadcddbcbdccddbaabdbdbcccdbaaacbcddadaccbbccadabdabdcadbbaadddabddbcdabdccbcddadddbcccabdacccbdacdcdcbdaddbccbadaadbabbcbdbcacbbdccadcadacbcddbbcdbbcaababdbddadccadbabbcdcabdcdddcdaadabcadcbabaadcbbcccbbacaddbdbbbabbbdddccdcdcdabadababddccdccccddccbaddbdbacdabbdddaddddcaaaaaccdbddabcaabbabdbdbcdacbccddcbddbccddbcdccabaabccbddbcbcbdcaacddbcacadbabdccadbacadbddabbacaacbbaddcdbacacacbbbbdbaadccddabcbadbbddddcdbdcccddddcdacabbdaaccbacbcbdcdcdddaccdaddabbbadacaddadaabdadcdcdbcabdaadbbdddabaccdacdbbbbcdcccadaccaababdbbddacbcbdbdaabbddadcbbabdbdabaddbaadbabdbdacbabdcccccddccccbcacbabbdbbddbaddbccaadcdcdbbdddbbcbdcbabdddabaaddbdbddabaabaadbacacccdaabdbbbdadbbddccbcbbabbdbbdddbadbcbbaddabccdddaacacbcbacccdddccdaccbbabcddcbddaacdcbbdcacdcaddababbbdbcdcaaadacccbbbabcbacaacdbdbdcaaacacadcbdadddbbbcabcddcadabcbdbcdcbdddccbddabcabacdbaadaaadbbbdcbcbdbcccdadbcadabacabaddaaccaabcdbcbdcccaccbdabdbcdcaddaacadaadbcbbadabbcbdaacbbdbdcaccbcabadaabdbccbdacdbdcdabaccabadbdbabccdaddadccbbbbbcbbacbcdaddccccbbcdadbaccabadcacaaddbdababbcbccbcacabdccdcadbacaaadbdbacacdbabbbaaccaaccabdcbccaccadcadddccaddaaaacadccaacacccdadddbbababbcbacbaacbcbbbddcaadbdcaacddbadcbbbdcbabbcbaadbbbcbbdabadabdcacbaacbccbbcbacbadcabacbbccdbacaaabacbbdcbbabcbcabdcbdadbdacbcadaaabbadbcbcddddabbadcbccbcaddbcdcdaadbabdbaacacbaabaaaaaaccadbacbcdddccccabcccdabcaaaccadabbbabcbcccbadbacdbaddbcccdbbbcaacbdaaadadbabddcacbcdacbacacdddcdcdbcabbaaabacaababbdbadcbbcdcbababbadccbbbdcaaaabaaacbcccccbdabcaabcacbaaccbbabcbbadbadcbcbadaccbcbddcccbaddbcbbaddcdcbabcbdbddcccabcdadabbddcdcddadcabadbbdabadaadaaadcdaabcbcbcccadabdaacaaadaccacadcddddcbabccddddcadacadaacdccbdddcccddaddcddadddcaabccdadadaccddbadddcbbbbbddbadbbaccadcabaddddabbabdbcbacbcadabccbacbaacaaccbbcdaaabdadadbcccdcdbadcbcabaccbccdcbccdaabccdbaabbcaaaaddddaaaadacacddddcdabddabdacdbcbadbdbabbcbdacaaddccabbbcacdcbabbdbaaacadbdbbbdaaccccbabddababcdacdcdacccbbdacbcdddcbdccbbcbcaaaddbaadddcbcbbccabbaddcdcdadbdabccccdaccbabaaccbbacddcbdbbbbccdbcaadbdabbaccadabbaccdcbbdcbdbaadacbcaccbbadcacbcbabbaaacadbcbdabdcddbbcbdbcadcaadabdcbaccbcdcbbcdadbcadbcbbcaaacddcdaddacbadadbcbabdbaabaaddcdabadbadaaacadcdaabddbddadbcabdbdccdcdbddbaabaccbcadcddcbdccddcdaababcbbacabddcacbacbbbbcadacddbbabbbdcdbbdcccadaaabaadddcaadccddacbdddacdccbbabbbbcacaddccdbdbabbbdbdacdbdcdcdadadbdcdbbaacccaadbccacdbcdddadaaccdcacbbbcdddaabdbdcbbcdddacdabaadabcdadbacabddabadabbdbcabcbbccaddcaccdbcbdaadbcabccbdcabcacdabbbdacaacadbbcacacabbaadcdcdbcdccaaabbabacbdbcbcabaaaabddccdbbdbacdcbdaacaaaccabaddaabaaadaabdbddbdddcabbddaadaabbdabbcdaddbcbcaaccacadbbccdbacabbcaaccbcdccbdaccbdababdaabdacaadcdcdabddadcbdbbbdabdbcbcddacdaddcbcacbdbddbbcdcdccbbdcbdbcaddccdccbccdadaaddcdcddbadcdcbaacabdbaacabdcbdacabcabaadbbbdababbcaaadbcddabaccdabaaacbcaabbaccbbbdddacdbaabbadbcdabccdcbdcaaadddccbcabccadbccbabadbcadbbdbbddacacbbdcbadbdbbbaccdbdbdddcbccadcdaacdabcdcbbaadabaacbbadcbbcaacaabbdbadbdabdcbdaabdcadbcacdaddbaaabdbcdcdbccbbdbdbbcbcbcdabbddbcbcabbbccddcacccbbbabbcdcddacdccdcbaddccdbdadcaccbccacddcbadccdbbcdbbababcacbcbabdddcaacbdbdbcbbbaccbcaddababdcddadccabaabdacccdcbaaaaabdabddcbacacdbcabdcabacbacaabddcdbcdcabdbddcacdddcbdcaacccdccdabacdadabaccbbdbdcaabaaadccdbabaacabaaaddabccccdaaadaaabdbdaddcbddaddbbdbabbbaddcacadbdbabadbcbabcddaaccbdbddccbbacdbbdbcaabadabbbaadbdbcdcabbcbbdcacacacbcdbdbbbcbaddabddcacbbbcbdacacccdddcacbacbaadbbbbabccabaaabcadcadbdbabccabadbaadbbddbaddcaddcacccccbccbbbbddabaacaddacdbcacabccaaacbaacdbadcdcddbdddabdbcbbadaacbdbabcaabdaaccdbddbacbadaddddbcbadcabdacccaddacbcbccbbcaddbccdcbacbacbdbcbadcdbadabccbddacbdcdadbdcaddbcadadcbcbadbbdbcabbbcdddbddcbadcddcdccddababbdccbbbadcbccddcdccdccdbaabdadaaacadbcdbcbabddaddadacaabdcdbbbccdcadcdadbcccbadcabacbcdbcacdbcdcdcababcacdaadabdbcdcdbcacbbdaddbddbdbbbdbaddbbcaadbccabcdbaadcbacaaaaccadbdbababcdcbcdccccbbcbccaabcaadaacacbcbbadcaaaacdaaaddbdaaaddabdabdcbdcbdbddadacdbaccbdacddaaadacdadbdcdcddcccadadbcbddcdbdbcacdaaadbbbcbcbbdcbdccbcdbadbdaccccadcdcaddbcabbbcdaaababadbbaaaaabcaacbabdbcaadcddaacdcdaacccdcbbaaacbbbdcddcabdbbaccbacaaddaddcdbabacbccdbbcccddcccdccbdcdbcbcdabcbcbddaddbbcbdcbcbbbbabbdbcdbaabdacbdcbcaddbcdccaccddcacddddccaacbdabcbcdcadbbcdbaddacacdbaccbdaadbddccbbbababcaabdddaabcdcdcaaadabcdcbadbccdabbdcdbbcacddbcbbcadbdadabbbcbacbaadadbcdcbacaacccbcbcbacddbbaadabacdabdbbbddbdcbaacbacbbccbdbbcccabcbccbdcccbadadbcbdcbbbcbbcacccbcdaaccaccaddacdccdbcbbbbddbadcbbdcccdabcbcdcacbdabacdccaddaadcaabbabcddbccadddbcbbdbdbdddbcaddacbcdccadcbbdabbaccadcacdbaddcadbcccabbcbbbcbbcddbddabcdddbbcbcdadbdbbdcbcdcbbadcccdcbccbcbcabbbbbdbdbcbcbcbccdacababbbaddbcdadbcdbddaadbcabcbaaccccbcbbadcacbcadaadbcbbccaabdcbcdaddbcaaadcdabcdcacdadccdcdabbadbbadbaccbaaaabbbdbabccbbbdaaddacdbcadbbbcaccbbddcbbddbddbddbabcdddbcdacccdadbacacdbbcdddccabdaddcdcddabaaabbccdadddaabdadadddbbaadbcbabaabdcbdbbaaccdbbbdbbcacbccbdacbbcbccaccdccdddcabbbadacdbdcccdacddadcbcbbcdaadacdadccadacacaaabcaadadccdbbbcccccaabdccadcdcdcccbabbacacddbdaacaacdccbadaaacbabacacaaaacdbdbdbcabbbcdabcbbababbaddcadbaccccccacadacabccdacddaccddbabdcbacdcbdbdabcbaccacbbdbcbccbccabbbbbaadbddbdbaabdcdadccbcdbbabbcbddbccddcbacdaaacaabcaadadbcbcdabcdcacaacadccccabcdcbabcbdaaaacaacdccbbdadaaabcdacbacbbdcbdbdcdadadcabcddbdacbcacddbcdacbbcacadabddcaabddcaddcbbcbdcdcbcdcadabaaadbabbbbcdccbbdcdaabbbcbadcccbbbbccacadcacabbcdcdccdbaddbbbcdcdccabadbbcadaacdadcadbcacaccbacadbabdcddabdbbbdbdbcbdbbbdaaaabbbcdbabbcadbadcadacbacbababdcacadbdadcabadcadccacccacdcbdbbbddddcacdabbacddddaddcaccabadabdaacaaaababcacabbcadcddadbdabdabcbdddbccbdadbbcdabcbbbcdaddbdcbdaaabacbdbbcbbaacdddababbaaabacaaccdccccccdcabbbcdaadcbbadcbdddbabbbbcbcccdccdcccccdcdaacadbcbcbcabddbadacbbdbdacaaddaadaacacccdaababcabbcbadbdbbcbdbdbaabddabcbbbacdaddbccdcdacadabaddbdcdcbddabbdabdabadbcccacacadabcdbccbaddcadcbaabcdcbdbdccababcbaacdacdbdbcbaabbcdccbcdbbbbcdbbbcaacbddbbdadabddbadccccdabbddaabbdadabccacbbadbadbcccbdcdbdabcdcabbdcadacaababcadbacbcccacbaaabccccabbbbcbcdaabddbbccdcabbdbbdddbabcacacbdbbdacdbbbddddaacbbadcdcacabbabaaaddcbdcbdbaaddbddbbbabcaaadaacdbdabacbbddbbbdbddaccabbbcbaccaadbbbddaddccddbabdbbadcaaccbaabbacdcaacddccbdbddbcbbcbdabbddddabbbbaadadbdcaacbccbbaddbbaddcbbccdadbbacabdabbdaabcdabdaddbcdddbcbdbcccbcccbbdbbdcdaccbccdbaaccbaaddbdbcbccdaaddaaabcbaccacdddbabcdcdbaccbddadcbcddbbbbccaddccabddaabbdaadccdcdbdcbbbccccaadacccbdadabbdcabcaaccaaabadccadcbaddccaaaddacbccabcaabadabaaaaaaaacccacccbdbadcacccbdadcddbacbccdcbddbdcdcaaabbdccdcccbbbadaccbdbdbdddadaaccbdbbaddcbabcdbcabccdbdbcdbbaacbadadcbabaaccbabdbddaababdaaadccccbbcadacbdbdaaadbabcbbbadbbbbccabddbaabccbbabcadbabcbadbaabdccdbbdcaacacadcbccabbdcbabdabacbdaabcbbdbcadbdbcbadcdddbdadbadccccccaddcbabdabddbcbdbddbdbccacaddbbdddcacdbccdadbbcbcbdcabdccabacddaadaaaacdadabacacdbaacdbacddcbbabddbcabddcadaabdccacdcbbcbdaddbdcacddcdadccadcdbcabbdbcadadaadbcadbdabcadadaadadadcbdbbacbccdbcabcdddbdddbcadaabadccadaacbbbdcbbaabccbdbbccabacbbddaccdabbbdaddacbbbbcccaacbcdbcacdccadbddddbcbaccadbabbbabbddadcdddbacadcdaadbbcbcdbbdcdcdcbdcaacabacddadadbcbaaadcaaddbdcbdbbdcabdabcbdabaabcacdcaaaacaadaddaadccdacccaddbddccbdcdddbbbcbaaadabdaaccccbdacadcaacbcdbcabbcbbcdcdcbbaaaccdcccdbddcacbbdaaccacbcdacddbbddaadccdcdaccbdadacddbcabcccbbbddabacdaaacaccadcdadcddabbccabadbbadbcbcdbacdcbacadcbdddccadcbdbcdcbcccadacacaabbcdcbcbdcacbaabadaddbacadaccbbababdbacbabbbbaddadbcdbbadadadbbacbbcbabbdacddcdcabcdddbcabdabcbcdddbdcabcaddcdcbbdddcddbabdcbcbccaaacddbabbdddbacaccaddabcaadcdbdbddbcbbdacdccbcaabdcbdadabcccbdabdddcbcabbacdbcabaacbbcdbdabcddcbacbccbcdbbabccadbaadcbddbacbbccddbcabdcbdabccbbbcaccccbddbbdaccddaacabbaadddbcdccaccdcadaaacadbdbababcbbcaacbccdddbcddabbbddcdbabcbbdcdaadcddbcdcbbbaadbcbcddccadbdbccddbcbacadcbaaabcadbcacbaaacadadbbdcdaccbaaddbddddcbbcabbbabccdbccadacdadcdabcbcdbdcbbccdcabbcadbbcccccbacacbcbacacbaddcbccadccbabaabaabbcabcbbadbaabbcacdccacabaadabccdbddddcbadcacdbdbbadcccacbddcadadcbbcaaabcbbbadabcbbaadaaacccbacdacccbbddcccadccaddbdccbddacddbcdaacbbcabdcccbaabdadabdccdbadbcbcbdbacbccddcbcacabbbbbbdadbcabbaadbaddabaddbdbdbdababdbdcbccddbbcdcbaaabaabbbddccbcdbbabccbabccbbcbdaabcbadcbdabccbcdbcdcdccadcaabdbbcbabdaabaabadaddddbddccddcdbdcddddabdbdabbdbcbddcbacbbbcdbdadbaddccbcbdaababddcbaabbabdcbbdccbadcdbacddcaccdbbddaddbaddaabaadbccbabdcccbddaaabcbcbcbddbdcaddaaccccbadaabadabbbaadaabbaabbccbbacdacdbcdacdccbacddcccadacbdabaadcbdcdaabdacbaabbaacaacbcdddbccaacddddbabcccabbcddaccacdbaaadccbacaacbaaabdbacaddbcbbcdacccdabbdcbcbadbabdadcbbbdbdabbbdcdccbbdabbadcaccadbdcadbdaacbbdbcccdccacdcdccddbbcadacddcbacaddddddbbcbbdaaadccdaccbcabccdbcddddabababbaabbccabcabacbabaadddbacbccbaccacbbddbacaddabcbbbcccbdabbacdcacabbdcbabccdaaccbdbdbcddaadaaadabccbbdcdbccccdabcbacaadacacadaabdccaacbacacdbbddbddbccaddcdbadadbcbacaaddabbdddaacbaddacadddddbdabdacacabbbadccdadabbabbcdbdcabcbcacabbbbbdadaadcddcccadbdbbaacbbbddbdbbdbbcdaaddcaadbaaaccaccdcbddabdcdbadbcdcadaddcbcdacbcbbcabcdaccbcbdbdcccabdcbddddcadabdcbdadaaccaccccaabddacaabcddabbddaacdccdbdabcdbbccacbdaddddbdbccbbaaacdaadabbaaabbcaaacadbdadddbbaadbdcdbcddddbaadbcbcbdccdccadccddbcddaabbdccadbbdadcbabbddaabbdacacddccbbacbbadababdadabccdbbacbdcddbacddbaadcccdccdbabddcabccdcaaaacdbddcbdabbdbaddabcbdddcbdbbacadcbddccdbccddaabbdaaabccabbbdccabacbbbaccdccbdcccdbbcbdbddbabcaabcacaadcbbcdddaabdaadaaabbbcdcbccdadbddacabcacdaddbbadcdadbddcbaadbabaadcaaacbacbcadaaabdaccddcaabbddacbdcabbaddbdddacdcabbbcddbbbabcbdbcbacdcaabacadccbdbbdaadbdbdbdbcbbadacaddbacabdbbdaaaaaddaaaabdddaadbbcacadcbdcabccbbcadaabbbacbddddccddabbacadbcadcbbcbaaaaabbadcccbbccdddacccdddccbdabbbacbadacadcdccdbdacdbdabdadbaadcaacaddcacaccdbddccabbbdbcbcadacbaddbdacccdbdcdbbacaabcacccddacadddcbaddcadbcaddbbaddbbddddcdabbacdbbddadaddcabaaadddbddcadcadcbbddcdccdbddabbbcbaacdccaaabdbcbdaaddddcbadddcbccaadabdbabccadacbaacdbccabcdcacddbcdaccbbddacbbaacdaccdccbadcaccdabdaccbcbbcacbacdcddccddaccdddbdacdddccbcbccbdbdbcbccacabbbaddccdabbabaabdbbccddacbcddabaddbdcccccabdaccbbaaccaacabaababcbbcdcdacbdacaadadbbdaaaadbabcacdcdbaacdadcbbcabbdbbabcadcccccaaadabdcacaddbacdccaabbabaddbbaaacccccddadbbcddbbdbadcbdaaaacaddaddbcbcadcacbaaadccdcabcdcdbaadbcdbcddcabdaaddabccaacccbabacbbdcbcccddcdabaadaadcccadaaaaadacdbbbbbbaaadcddddabccabddbacdbacbdacbdcdaccbcdcccbcbcaabddcbbaacbbadabcaadbdcadbbbddcddcbacddadacbbbadacddcaacdcdadbacbdbbadadcdddddcadccbbdcaaacdcacbabbacddaadddbcbdddbaddddbddbadcbdcdacddbcbcbddabdaddbcdddccabcaadaacdbbbcdbcccbaaabaaacccdaabddcddabccbcbdcbdbcbdabcabdacaaaaadcaaccbdbacdccbdcaaccddddddbbbddcbdcaaaabbcbbcabbbadaaaacbcdabcabdacdddadadaadabababdccddcddbbbdaadbabaccdbcbcbacddaaacbddbaaacddcadabcbdaaacabdbcbdbddadbabcaccdbbbddaabccdaadccddadaabcdcdddbabcabbcbbdccaabdbbbbdcbdaccdcbbbcbbbddadbabcdcaddadcbcabddadcdabdabcbcbdacdcaddabbabdddacdacdacbaacbcacdaddbbacbacbddbadbdbadcdbbdcdcadbabdaabdaabababbbaabbabccdcaaabccdbddadcddacaacbcbcccdcaadadccbcccbcbbdbcacbacdaaabcbcbccbcddaddacbcaaccadacaaaabddbdcdbbbadaddacbdcdabdbbacdcdaccddadabbdddbdbadbbbabcddbcadbccddaaacbaaacdabaccaddacccdbaddbbbdbaaccbbadaadcbccaacbbbacdacaaaadadaddccdbdccabcbaddcdbbdadaaddaaabababbdcadacbbabaaadacbadadbdccdbcbbccdaddcdacccccbccccbbaaabcadabaadabbdcddbbdddaaacdcaaccbdbaadabdddcbbbcaadadcaaacaabbaaadcaabdccabbccbcaabccacaaabaabbadaadddabdcbaadcadaabcdddbbddcbccbbbcadbaddbabaadbdabbdaaabaabbbdcaaccbcbcddbabdcaacccddcbbcacadcaaabccbcdaabbdcbadcabccabdbccaaadadcddbbddbcdaccadccbbcadbaccbdcddacaccaabbcdcacccadacbcaaccddacaccbcdcbabababcabaccdccacdddacbbbcccacabcddcbcabcabccbdddaacabbaadadacddbbabcbbccbbbbcacadbdaacdaacbcacaddabcabdadadddcbaadcbcddabbcbbdacaadbabdccbacbabadababbbdbaacbdaabbccaacdabcdaacbbbbcbbbadcbbbdadbdbbbdddbcbdaadbbccacdcdcaaabbabdaabccbaacddcaabcabbabcaacaacadacbdbacccdbabcabbbdcacaccadcddcbdccbbccbcdacabccbbbabcbdbbdadacaabdabaddbbcbacbcddbddaabaddbacaadaadccaddcabddbaabdbbbcddcabbdbddaccacbdadacddbcdcccdcabdabdacdbaadbbaadbbdaabcbddbcbcbbdddaaadcaccdbcacaabaaaaaccadcddbadbdcabcaabaddabbbddabbbaaaaaaabcdacadcbbadcdcbbaacccbdbdaacccabbdccdddadbbdaabccdbdabccbcadddcdcbcacacdbabaadbabcdcbcdcdbcabddacabcbcdaacacbcddbcaacabbaacaabacdbbaadcaacaadbcacacccacdabaadcaacbbdbcacaaabddacaddbdbcdddccabcddcbddbccaddddbbcabaddaccbcdcbabaaabdcdcbcabdbcdacaccbacabbbcbbdacdbdbccbbdbadcdcdaadbadbcababdcdcdcdccbdcbaadbcccbbbcbadccccaacdaadcdcbbaccdbcbcabbbccddccacbcaaddaaabbbdbaacbabdadcbdabbcbcbadcddcaacdcabbaabaacdbccbdccdcaacbddabadacaccdacadabdbdabddccdcbaacdaddccbdaddadbacccbccbdbadcbabaabdaacabdcaddabadbbbddddcdbadcbdcdbcacdbcbcaaaddcbbcbddaaccdbcccabacdacdddccaadccdcadbabacbdccccdadbaaacbccacbccdabbbcdbcbdbdccbaaccaacccadacbaabccaddbadadacbcdddaccabdcbdcbdabbcbacadcbccbadcbcabdbbccacdddbcdbdaacbdddcdbdaaadacddcacddbbaaabbbcbabdcbdcbbddddcdccbddabbbcdbbdbbbaadaadcbcbabcdadcddaccaabccaaaabdddaabcdcaacabbbdbbbdcddbbabcaddaddddcbcaccacccdbabaaacdadbbdabcdddcaadcbdaaadcdabbaddcdadcbbcdadacbabadcbabbcacdadbddbbbbdacdddaaaddbaadcbcabacaadbaddabbbcaddbabbbcdcdadacdcddcabcacacdbbacdaccbdacdcbdcddadbaccddddbadabdaabaddadcaaadabccdacabbadcccadcbdacaadbabdabdbcdcdcbcdcabcabdabdcdacdabbdbbdabbadabcdcdacccbddccdbbcdcbbadddadbddccdddaacbddbcdaccbdacdacaabcccaaadcabdcccddaddccbbbbabdcddcbadbdbaccdbaacabbacdaddaadabbbdacbbcdacaabaaccbaadbacacbacdbdaabdbabcdcccdacaddcbdacabcbccdadadbbddacdccabbaadddbddcbaadbcbccdabababadacabccadcbbdddbcbdabcddbcaadccacbdbaabdcbcaccacbbbdbaabbabadcccccaaaadcdaabbccbbacddcbcdccadadcdcccaaaccbbaccabddddaccabaddcadaababcccadacabcbcbabbacbadcdabcbbcdddcccbdaacdcbaacbbbdadccaddadccaacabbbdccbabddabcabaccdbbacdbdaadcdabcbadbbcdbdacbabbcdcddbbbbbddabbdacadaacacadccabbbabdcddaabbcddccadcbcbdadcadcacaacacadadaddcaaaacdabbbadacdabaacdabcabbcbdbdaaddaaaadbadaabacbbdbcddcddaccccbbdcadabddacaacabdccdccabadcbbcdababdadaaaddcbcbbbababcdcbcdacabcacbdaabbabbdaacaaabdaccadaaabddbcdccbdcadcbdcbdaddaddabacdcabdccbddcaccadaddcdabadcaccacbbdaccbdabbbcbbacbaaadcbdbdbdacdaaadaaddaabcbbbcbddcabbdcbdccabbbcdddcdccbbdccadbcdacabdcdcdcadcdcccadadadbdbdcdccaadbddcaadddaddbccbabacacabcbbcaddcacdcabdcbbbbbbdcaaaacdcbccdbcccdaccacbabacccccdccbcdcdabbbaddcbbbdbaabaddaacacbcddbddaccbccbaddadcacbcaddcbdbadbcadcddbaabbcddddbabddadaaaacdcbbbbbccccadcbdccbccdcbadcdcbddccbdcdbbdbaaabdbaadbadbabbcabcbcaadcbaaccbcbbcabcdccdcacdddacaaccddbccccccacabcbbbaadaabadbcaadacdbbabcbbbabababddbdabdabbacbdabddbdcacbdbabddadddacddbadccaaaccbaadadadbdaaabcbcdbbbdbcdcdcdbbacddcdabdabdccdbcdccbacbbbabbcbcacbabddabcdbdadbcbcdabbcddbcacabcdcbbdcaaccddadccdbdddadadadccdbabdbaccacccbabbddcdbdacdcbabccccbdadabccaacdacaccdddddcddcadbbcbbcdaccabbbdbadbddcbabdbddcbddcadcbddcaabccdaadbccdaaddacdcdaddccdcccdaaaddbccdcdddbadccbccacacdbadcbcacdbbdabdbdbddbadabdabaaadbbdccdacbdccdbadddacadcdbaabaacbddaabbcdcdadbadccbbcdccbcbcbcdbcacaccbdbbbcadccabcbbbcdcaaddbbacccddadbadbaabacbbdbbcdddccbdabcabcccaadcddbcdbdcdaabbcbabbadbdcbacccaabdbaabaaadcdaddbddabacbcaaacdccbddbccacdcadacbdadcbdabcabcbddadcccbbadbdcabdaacacaacaacbdbcbadcaababbacbdcccdbdaabbccacbacadbdaaaabaaacaabdaabdacccaadddcdccccbcccacbdadbdbadacbdaaaadbbccbcbbacddacdbaccbdadccccaaaddababccbcdcadabcabbdcdcdcacabdbbcbdaabcacaccabacbcbabacdcccdbdbddaacbaccdccabaabbbbdaababbbdbbabbdcbdaddbbaccbdcbdbadcdbdabccbbdccabddadbabcdddacadaccbccababdbbcdbdadacbbdcdccdcdbbbabbdccddcdadadbdcddbcbaaaadabadbbcdaaccadcbcdbbadccdbdbbacdabcdbacbcacbbaacccccddbcdcbbbababbccdbccbaaabcabcbababcdbbcdddadadbccaadcdabcdbaaadddbdbbbdcbcadacadadaacabcdbabbbbacdcaadbbbbaddbaddacaaddbcbddcacaadcbcbacddadbcbdcadddbabddaaaccdacbbdcdcdabbbcbbddccadbbdacdbbabaddddcacbbddbddccaabcdacabccdcdbdcdccbcbabdaadacbdabcacccccbaaddacacbcbbdabddcacccdddcaaddcbdbcdccbdcbdddcaabacadbaddcabccbdcbbadcdddddaaadbcdcbccbabbacbbbbaccdbcdcacaccdbdcbadccacdcacdaacdbdacacdccccdcabaaccdddcddbababdccccdaaadbcbdbaadcdadbbdbdbdcccbccbbcbbbcdadcccbbdddadddadaccaacdadbaaccbcacbbcbaaaaacbacaadbccaccdabbadbddbaabccbccbaacdacdbacadabadcadadbbbbaaadddbadcaaadbcaccbadaccaddcddabcbccaadccbbcbbabdbadbcacccccaabaccccbaccbdcbcacbbdbddbadbcbabbadbdcbbbaaccddabacaddccbbabdddcdadccdadadbcddadcdcaacdadbcadbbacbabccbbbbcdbaddacdbbacadbbbcdbddbbabbcbcadadcabdbbdbadbccabbbbdcdddacdbdddabddcbdbcadddcbcacbcabbdacadaabddcdcadaaadcadacbddadccdbbbddbbbacaaadcddaddabdbadabdcbbbdcdacaccabdbaacbcbacbdabbbdaaaddbaaddbacccbdcdbbadddacadcbcbccddcccccaaaadcabaaaabdbcdcdaaabdadbcdabbacacaadbdabacadcbadcdcbdadcdccccbcdabadbcaddaaabcdbccdccbbacbdaccbcbddcdcdbdabbcdbdccccdcabbbdcaabdbbacbddbbccaccaacbddbabdbdacddbbcbaabdcbbbaaddbacacbddadaddadcddbbbbccacdcacbdbcdbcdbdcadbcdbcbddcdacaababadddcdbbaacdaacdaacddcddacadcaadddcadddabdaacddbbbbbadacaccbcacbddcbbddaaacbccbbbbcaabbcacadbcddcadcaabdddaabaadbcaaaaaddddbbcdaacbabcdabdaacdcdcdbbcbacddcddbbcabbdcdadcbdaabbcdcdadadbaacabcccabbcbdadaadbdaaccccdddcbaddccdcccabdabbccbabaabdacdcddbbddbddbbdacdbcabcbcabacccdbddbabcacdcbcccacbbbdadcdccddddbbabccbcbcbcaadaacadbbdaadcdaabdbbbabaccaabaaabbacaddbcdcbbcdccabddbbbadbaccdacaddbaacdcadcbbdcbacbdcbbbcdbabbbcdbbcddcadbdbbcdbcbdaddccbcccbcabacabcaddacbdabbcdbdbacbccccaacbbbacbadbcacbaaabacbadaddccadbcaadbcaccbbadbadbadbccaaababcabccaabdadacabdccdacadccabddbdcabcbcbabddcdbcdddaddabbbdbbccbdbbbdabdabdccdbcdabbabbaaaacddcbbcbbcaadbdccacbcdcaccabdaacdadadbcbcdbacadbbaadbcaabbcdbbbabbdbcacbadbdcbaadadabdcadcddaadddbabbdbccddadddcddcdcbabbddaacaccacccccdbaaadcbbbcbbacccdbaabcaadcbbaccacddaacbbcaaaccacabadcbaadabbadaddcdbaadcdddaaacaabacaccdadcccbabccbbdabcabdcadbadccbcbaddcbbdcdacbdcbccdaccbabacbdccbcdbcccacbdabcddbccacaaadccbddaddcbbdbccbbcddbcbcbcdbbcacaabdccadccbbdbbbdacbbbbcbadcbdddacbadbbcbbbccdcbcadadcdcdbbabdcdabddadabaacacddbcaaacacbcdbcbbdbdaabbddcbadbccdaaaddbcaacbaacaabcadadcabdcabcadbccdcdadbabbadddaabbbdbadbbdbadcaddaccdddabdcdbbcccadcacaacbccbdaabadddcaddbbccaadcdddabbccddabacbccddbdcadbdadcdbabdcbddbaadabcdbdcccacaabbababbcdcccdbdadbabbbcdddacdbbbddaabcabdccbdcbacaddaaabddbdacabdbaccbbdbddccaaaccbdccadbacdaadcbdddadbcdaccaccaaddacbcbabadbadbadadbccdaabbbcbabaadbacdcbaddcdbdabbabbbdddddcaccccbaddbaabcdabdcbbcabbdbbabdbcdccdbbcabdbdbdccbbbacbcabdcacbabdddcacabdbdbcadcacdbcbbdcbcbacbcadabccbbabdbbacacbdccbcbadddddcbdcabdcbacdbabbdbbdbbdcadccabbbdddacbadddacabbcaccddccbcacbcdbdcdabcdcaacbddcdadcbaabcbbccdcddadbdcabadaacbcacadcdacccaddaadddaccbbbcdddbddbdddbbacacdcbddadadbbdbabcbcacdcbccbcbacbdbbbcadaadacdbadbcdbcdcadcbacbbabdbbadcbacadaabbcbddddcadcdcbacddaabdadccaadabbcbadcacbdaacddcbcaababababcbabacbddaadccbbbbadabbacdbddcdabacacddaaabbadbcbbdddcbaccdadacbcaabbdbdacdaaadbcbbcbbdbcdccdcdacbdaaccbadbcabcabcbcbdccaabddcbcabaabccdaddacbbdcdacdbddcadbdcbdbabccbacacababdcbccabadadcbdcbdccdbbbaabbaabaccbdcddcbbccbddbaadcaadbccbcdaddbbddcddbcbaadcdabbcbdccdddcabdcaaacddcbacbacccadbcdadbdccdddcabdaabadaddcdccdcbbdcbcaaaaaabdbdcacbbabbbcccccdbbcccbcdbdacdaacbabaccdccbccccaaaadbcdbccdaabdbdabbdbadddcbacaddbbbbadaaacddddadcabcccdbbcaaccccacccbaaaaadccdadbabddbabbcdcdbcdaababcaddcaaaddaddaddcccadcddbaacccadbddbdadbddbddbcddbacdadaadddbbabdccdabcddccbbddaddbacbdbacaccabbacaacdcbbacddacddcdabbddbacdcaadbaccdccddbabcadbcabcacabdccaacacbbcccbdcddcdcaaadaacaacdababbbacaaaabccaaccaaaaabdbbaddbcabdadccbcbbdddaadcddbbbaaddcbdaacbcaacbaddbabadaabbbdbbbbbabadbcdbcadabdabcdddaaadacadcdcbbcbaacddabdbdadcdccadccacabbbccbddaacacaddcabcdadddcdacbccbbdbacdbcbbdcddcbddddcbadaadcabcabaaababdbaccbbcdadbdcabaacbaaabdabbabbbcdbaadbddbcbbacccdcbaaabccccaaabaacbacbddddbccadacadcccccbccdbcadbdabdbdabdbcbdadacacccbbbaccdbddadddadccdcddbacacddbabcbabbccabdababbbbabccaaabccbbdcdaacadcbccabcaccabdcddbbdbccdbabaabdcddbcbaddbdccbacbaaadaddcacccaaadbccaddcdccbcaccadbbddcadcadacdadabddabddaccbddadccabaaadddadacabdbbcacdadbdddcccbddbacbacabdabcdbaabbbbbbdabacbbdadabbbccacabcbbdcbddbbcadaaccbbbbbdbccaacddccabbbccbdacadaaababbabcbccdbcadaacacabbdbdacabaadadbbcadaacccbcadddcdcacaaadbcdaddcbacbdcddbadaccdaaaaaccbacacccbbbadcbcbdaaaaadacadcbcbddbcdddccdddadabaddaacadabadcbccacdcdbcbbccccadbabbacdbbacbbcddcacbdcbbdccacabbdadbaaddcdcbdbdbdadaadacaddbdbcdacbdbabcadadcdbddcbcccaadbbbcadcccccbacacabacdcbdaabbdbdcaadcbbbdabbcbcdacbbabbbcbaaabdaabcbcdacccadadadaddbddacbcaaadbadabdccbdbdabbdcaabaddbdaabdbacbaddcdbdcadbddadaadccabddcbbbbbcabaabcccacacccadabaabcccbcaacbdadddcbcbbbbabbbbbdadaccbbbccbcbbdaddcabbdcaabdcdacccacbbbcadadbcaabddbccdbbbabcccbbbabdacacbbdccbaabbdabbaddbbaaccacabccababadcccaacdddcadddaadcbddacaaddacaddbdbabdcacacbdbbcdabdaaadbaacacdbbbdcadaacccdcacdbadbbaaabbacdcbdaabaaadadaaccddacbddbaaaccabbbcbbbbcbddcbdccbdbddbbaabbaaaaabbaaadadababdddacadbadbcbdbabcdbbcdcbddddaacdbccdadcbbbabbdcaababcabbbbcddbbabcbbacbaadadcbccbdbbdddddbacabcacddaccccdabbbdbcdbadadddcdddbadcacddbcdacaaccdcadddbbdcbaaacdbdbcdacdbabaccaddcbcdbbbcdcacddaddddabdbadaddcccdbcabcdbbcdddcbddccaaacccadcabcabdccaccdacccdccdccdadaddabadadcabcbcddddcccdaadddcadbaaadacbadcdbdcdbaabaabbcbbadbdcbbdbcbcacaddababddbbbdcbbadbbcbcaacddbdaaddcacaadcadbaaaddaacbcbbcacacadbbabaccccbbbaccabaaaadbabdcaabcdaddbccdacbadcaadbcadcdaaaaacaccaadbbabadbdabbcdddcbabbababadabaddbdbdbddcbbcbccdacdbababaabadbdbdaacaddcacddacabbbabaababcdcdabaddddbccdddbbaabadadccddbadbbbaddcbdbcaccaaccdabbbdbaadaccadbdddaadbcbddcccadcbbcbabccddcccdcabbddbdddccabdabbaddbdacdbcdcbbdabadabcdabaabcbbadddddbabccaadbdbcdcadbbcacacccbacbbdadbbccccacbdacadabbbddcdbccabdddbbbcdddddbddacadabdccadcaaccdcdadbccaabbcdcdabdbabaddbddbcccaddaaadaadabcddcacbabbdbdcddcdbadddacddbcacbadaaaacabcacdacdaddddcbbdabbaaadbdbddccaaabaaddacbccaabdbcaacccbacdcbccdabddbdbcdacddcadcdbbdabddccacdadccccadbadddcabcbcdcadaabcddcaacaccbbdbdacbacdcccdbbcdbbbabbabbcdbcdbadcbdadbbdaacdbdcdcabbcbbaddaaddbaabcabcbbcbcdcaabbbadadacbabadcbacbcbdccbdadcabcdcccbdcdabcbaabcaabbcdbcabbccdabcbdbaacbaccdabbadcacbbaadbcdcbccdacaddcdabcdabbbabcbdbbcbdbcaadadbaaccaccbacbdcaabaabbcccacddabbbbdccacaadddcbcbcbdaddabaaabcddcadabcbabcdcaaadccccdcabacabbaccbdbaccbbcccccacadbcbdcbdcdcabadcddcdcaddcbaacaadacdacbcddbbccadcbcddadcaadacbdcbdbccddbcccbadcdbaababcababadbdbadaaccacababdcdacaaabdcbbbcbacdcaaaabacdaddcadcdadbdbcbdcdbaacbcadcddbacbcbbaaababcbacdaabcbbdbdacddabaaddabbcdbccbcbddaacadbccdccdacdaadaadababcddabdccdabbddaabbbcbaacbcabddabcbadbdddddbadaaaaadcabdaccdabddbadaccaddabcaaadaddbbaacdacadbdbadbcacccbadcabcbbbddaaabdadbcdabbadabbadcbabbdcdcbdadadbdcaaaddbadddccccbdacacbdbcacadccdbdaaddbccaccbaccdcddbcbadbbdbbcdaaadcdcdbabdddbdbdbabaabbddcdaddccdadccbdddbdbdcaaadcdbddcdccadacadddbdbccdcdaadaaadaacbcadddaccdbcdccbbcadcddadabccbababcbbcabbdbcaadbbdcaccdccaaacdbbadbbccdccdbaaacacabcabaadbbbbdabcbbaaadddcbbcacaadadaadacbdbbabaacbabbcbcbaacdcbdbcabaabdabaccacbdcacddabcadabcacbbcbabadbbcaadacaaabccbddabccaadadbabddadcabaabadcbbbdbcacdbaaaddbabcccccbdcaaccaadbcbdbccdbadbabdabbbdcacbddcddcabbbdbbaddbcabadcadaaabcdccccdbddbccdbcbadabbdbdcddcabcbbdcbcdcbcadaddbbbccdaccabcddcabacbabdbaabbbcabcaaccbbbcaddccbaddcddbddcdbaabdcadbabbbdbcdcccccdddcdadadccdabccaaacddcadccddcaacccbdddbbbabbdcdbbbabacbacdabdcbcbccbcababaaacbaaddbdbdabccbabacdcdaacbbccadbcbdaabcdabdadaabcabcdddadccadcddcdbaddbcaacbdbcdbbaddbbbbadabaacbcaccaddcbdbdbbbbadcddbbbbdabdddcabdcddabcabaacccdbcbccdddcddcabccaabcccdcaadaccdbdbabbddccbcdcaadcdccabdabbaaacdaadddacccbcbbcbbadcacbdacbbcddacdbdcaddccddbbabadacacaccaabacdacccbacdacbddcbdccddadbcabaddcacaaaddabddadbccdcddcbcdcabdbddccbdaccdaabdbabbacdbccadadbdcbacdddaacadbdddcbbddadbcdaadbdbcaacaadcbacdacaaaadadcadcdcdbbaadcbddbddcbcacababbdacadaddccbcadbaadabadcdbbcbdddabcbddcdadcdabaaabccabcdbdcbabbadccdaabccbacacabbbbabdabbbbdaaddbbdbbbcbbdbdbadabbcdcdcbddbdbcbdabbccaacdabaabddcddaddaaddaabacaccacccbbccacbddcccacadbcaababdddabaacbcacccbdaababbabbdbdddbadcabdcdadbcadaddaacbdabcaccbabbdbabdddbaccdcabadbcabdcbabcbdddcbcdaabccbccdaaadadcbbbdacccddabbacbaacadbadabaacbabcababbccdbcaaddcaadcdcdacbacadaddacbbabdabbabbdbcacdbbdacaacddcddccbbccbccdbbcbacbbaabdcacbbcbabcacdacccbdabadadaadddbcbaacabbcbdbbbabdcacababbdcddcbcbccaabccaaabcbdabbbddbbaabaaccdcccbcdabdbcbbcddbdccabbbbbbacdcbbbabadccbbdacbadbcbbbcabadcdbbccdbaaabdbacbcadccabadadcaddcddacbadaadadbdadbdcccdbcaadddddcabccbcdcbacadddacacacbbddadacbbadccaadacccccabbdaabbaddadbbbcbdaccacbaddacdcbaabcdccaddcadbcbbbdcadddabdadadbadabdccccbadadbaabbaadaabbabbbabaaababdbcdbabbabbccdbcddadacdbacacdbcbdcaabbddabbbdadddaddbbabbbdaddcacdcadcaacabbdbabbadccdbabbbcdbdcbabcabaabbababcbccaaacbbadbdbdddbcddaababbdcccbbbddddcdcbbdccbdcdadacdcbddbcdaaddbbddddadbadbcabdacabbcccdaccaadacbabdbbcddbbaccdbaccaccaacdcddcaadaaaacdbdaccccdabadaadddbabacbccaccadcdbbcbacbdabaaaaadbaaacdbcddccabddaadbcdabbcacdbadbacbbddbdbbddaaabcabbdcdddbbcbaadadbdcbcdbbbcddcaaacbbcaacaaddadbacabaadccabbccddaacdcbdabccacddbdaadcdabcabbccdabaabdcaacabbabbbccccdbbdbbcbaadbbdadbaddabcbbbcaadcdbcacaddaadcdacdcbcbbabababccaccbbddbbcdcdbcabadcdaddacbbaacaddadbaddbdbcbcbabdcadababdddacbacdddcadccbacacddbacbdcbacbddabddbadcaccbdbcabdcbaddaaadcdaadcaaadcbcadbcaabcadbddaacbbddccacbddbbcbcdbbccaaadbdbacadcddabdcdbdbbdcccaacbcdaddabdcbbacbabcbddcdacadcdbdcadcccaacbababdadaabccaddabcbcccbcaaddddbbbccccdaacbcdcbddcdcbcddbbadcdcbcadbbdabccbbbbbaccabaabbcaabbaaccbabbabaabddabacbbbabbcaadbdcbdbdbdaaabaddcababbdabddbbadbaadaabbbcddbbcbdccbdaddaaabbcbbdadbdacdabbbadbccbcacbdabbbddabccdaadbbcbbaccdabccaadbbdadcdababacaadaaababccdbacccbcddddacddacddbcbbccdacdaaadbaabadabadaaaddcbbbbaacbadcddbadbdccadcdddcaccccdcbacadaaabddbcaaddccddadddaacaddaaadabddbdadbdcbabdbbbbdabdbbcbdaccbaabdbbbdbcaababcbdaabccbbccdbadcdccbcdabdaaabddacaaacaccbcbcbbbcdaccdccaccaabcbdddcabbacadbdbcadbbbaaddcacccbacdbbcddbaddcacdbcdbcaabdccddddbddacbccabadbaadcccdcbabadddabaaacacbcacdaccbdbaacadaddbaddadcdbcaacacadcdbbadcdaddbcdddbdbdbcabdabddaaadcdabdcbbadbcbbdcabaccdcdbcddbccddacdccadddaadcacccaabcbbbaacbabdcbadacacbdcbacccdabcccacabacdbdabadabbbbbaacdbaadabdcadabbcccabcbdacabaddadbcabbdaccddabbdbbbdacacacbdcddddbcdbddbccabcbcbaddabddabbbdabbadcddbbbbbaabcabbbddbdbabcacccbcbbbbcbccacabdbcdbcdcdaaadcccaccdbabccdbdaadbcdcbbacabaabcbdabcdcdacaccdbbaccbdbdcdabddcadccccabdbccddcacadddcddabdbbcdaadccccbbbbbbdcddbbdbcccadcdbbbabdcabcdbddabccdacadabdbdccbbbbbdababcdaabacdcccbbbadbcdbcddcbadccacadbdbccbdcacacadbbdccdaccbbabbbbdbbccccbabdcbddbaddadacdababcdbaaaddbdccdbaddccacbcbaaabcdaabcaacbcadddcbbacdacbcbcdbdcbbcbdbbbaadaccdbbdbbbadcbdadddbbcabaabcdcabbbddacccddbcbbcbccacabbbabdccccaccccccabdbabccddadccabadcacbdcbcacbaadbacaabbbdaddcbdcbdccbadcbdcabddcacdbacdbdabdbddbddaacbdcccabadbcdcacdabacbcbadcababaabbbbdbaadbadcaadbccaacadaadbbaadbdbcabcbbbddbacdbcbdddabcaadcdabcbccbacadaddcabbbdaccbbdaccdccdadcadcbacdcababbddaccadadccdcaddaddcbdadaacbdcdcdbaabcabaaaacddaccadadabbadadcdbcbdbbaaacbdcbaccacdaadacbccccdcbcacbcadbddadcddcddaacdcabddaddbacbcbabcdcbccbddccbaabbcdabbccbbadaabcdcbbabcdbbbaaacbcbbcbdabdcacddcaddbbbcddabbbcdbaabbaaabcdbddddbbdbabddbdbbacadbcdbaadccdcadbbdbbaadbbabbbcaababddadcccbccdcbbcdcbadcbabacbadaadbdcdcbddbbdbbdddbabdbcddabbbaabcdbacdccadddcaadcdaadaabadacbcbbababcdaaabadbcacabbbdddadcdacabdcbdcbbdadbdaddccdbabdaadccbadcccbcdccbadadddbbadbddbbbacbdccbcddcadabacbdddadacabacdbabdcbbabadadccbddacdbcbdaddaaacbcccaacbcbbbbaabdbdccdaababbcbaaaadaccbaddbadbaaaaddacdddabadacadbbddbddaabddbdcdcaccdbaadbbbadcbcbaacdaccacdbbcdcaaadddcccbccddbaaabcabdbcdcccaccacbdddabbbaddccdaaddabbddbaadaabbdccbacdbbbcbdbbaaacbbaaaddbccadddcabdbddcccbdaadabdcbaabcbabadccdbbbdccbdbaccadadadcdbadccbbcdbbbdacccccbbabddabbbbadacaaccdbabadccccaadbdbbbddadccddaadabdaacaccababacaddabdadcabaacbddcaadcdddbacbbbddccbdabdbccacacccdcbcadcdcaccbdccbdcdaccdbdcabcdcbbadccbbdabbcdbdddbaaaadccaaddabbdbcbbcdacddccbdcbbdaaabadbbbbdaabbacdcbddbdbddcabadbabcddbaadabccdbaaacdccabcdbcdccddcbccabddcabcdddabcadbbacdccaabbbbbbbdadccdbbacdadabbadddcabacccbaaadbdaaabdcdaadadcbbaacdbacbddbbacdddcbaacadddcbcacaacddbcccaaccaaacbabbdcdcbccbbabbddadbcabbacbaaacbbdacaacbddaddddcabccddaabdccbccadcdadcdbdcdacdddcddcdaaadcbbbdbaddacbddcbaddcadadcddacabddcddbbddcabbbbabbdbbbdcababbbadbabcbabbbcdaacabdbaccdcaacddbaaccdcbbbdbdabcbcbdcaadbaadbabbddcbbacabccdbcdaadddcbbcadbdadbdabcccadadbdcbcbdcaddbbdabacdabddabaabbcdadabbbbaadbdbdbbabcdbaddaabcdbaadbbdccadcccbaaddcadcdccdbcbdbdabccdcbdaabdaabcdabcabcabbcbcccbadcabdcadddddaabbcdacacdbdbbccccacdacbbcbbbaaccdaddbdcbdacdadaddacccdaaaadacbcdadccabdccccdaccccaabcddbbbbcdcccabbcbbbddacbdadbbbbcbbbbbbcacdbababbcdbdcbdbcdbacbdaddccccbbdcbddbbcdacbaccbcbbdcdbbcbadcbbbabadabbacdddbccbddacdbdccccdcdabbbadcadbbdacbcdccdacaccbabdaabcaaacbacdaaccbbdcddcdddbdccabbabbccdbbabbdcbddbbadabbdbbdbdbabbbabccbbabaaddaabadbbbbdadccccccbbbabdcdcadbbbcbbbdaabbdcddaabcbbcbaababdbcbbddaddaccacaaacdaccabaabadbcbddaaaccdcbccbcdaabacabcbddbcbabdbdaadcdadccccabaccdaddccbdbbdbabaabdacdabaccaadacadcddaddabcaabacbbcaabcdbbacbcdacbdbdacdacabcaaaccdbcbadacdbbdccadbabdbbcdccdddadaacdccdcaaaccdabbcdddbccdcbcdbbdccdccbdabbbccbddbbbaabbccadccaaaacbcdaaccacadbaabccbdabaaacdcdaabddcdbbbcdbdbcdbcabccadddaabbbdbbdabccabbcadbadddabbcbddcaaaccdbabccccbabccbdcadbadaaadbcbdcbccbcadaacccadbbcdaaccbcbdadbcdadcaadcacaadaccbcdcdabdcbdbacccdcccdbcdadbdbaabdcdaacabbaaacddbbccaaaccdbaaabacbcdddcabbbbdddcadbbcddddddcccddcbbccbcdcbacdaacdabbdabbabcbbbabddcddacdcddcadcaacbaddcaaaddcbcbacddcccbadbdabcdacdddadaadcdbbcccdccbbbddbdbcadcbddacbdbccadbabcaabdbdcaadcccbdbddcdddbbbbaaabababacbabbccbdabdbdcbbdcabdcbbcbacbdbddcbbddbdcbbcabbcadbbcccaddaacbcbaccbcddbdbbdbcdbddadacbbdabacbaabbdacdadbbdcaabddcdcdbbbacabadbbdaaaccabddacccdacadcadacdbbdbbbcdcbadcdcbdbcbbabacdbcabcbccbdcabadacdcdcdabddaccdbbacbdddbbbacbddcadaabcdcabcdabadbcdcddbaaaccdcddcbcdcccbbbcaabbaaacbcaddadddbdcaaccbcaacbdbcababacabdabcddcbadddcdcaabdcccbcadcabbcadccddbadaaadabdacadddbcdcdcbabcdaacaadcababbcbbaccacbbbddddbccbcdccadbcdccbaadbcdbcccabaaddaddcbcdabbdddaabbddaacacdbcbabbbacbcabbddccccabbdcddddacddcbdaccadabdbdcdaaccdacacdddabacdcbdbbbcbdaaababbcadbcaaacdbcdadacbcdddcdaababdccbdbbddbababbdacadcccdaacccbbbbddcbcaabdcdbbccababcdaddadbbcbcaaaadccdcadddaddcadacddaabdddbcdcbbbdaadbbdbcdaacadaddbddbadcbcbacdcddccddccacddddaadcaccaadccdcacbcacbdcdbbccabcbcbaddbbdabdccbabbaccdddbccdaabccdcccabdcabcadacbddbcadcdbddbcbcdcabdcabbcdadabcabccacccdadbddcdbcdacbbcbaaadacaccdaabbabbbaaccdbaabccbddabacaddaacdcdbccdccbbbdcdbddcbbbbcdcddbbcddccaabacbdaadcbbdabdbaaaadcdddacacbadbbdaabaaaaacbcbcabddbdcacacbccdddccdddbbcaadacdcdcbdbddcddacbbcddabbdadccadccbacbcabcaacccadbadbabbbbdabaccbdabdacdbdacaabdccbabbaddbcaacdbacbcbddcbaadcaabadcbaaddacadaccaacadbbabddbcccbbbabbcdaccbcbadbbccdccdbcaabcbbdacddabcadabcbbbbcbaccdabdadbcdbbbbaabdaaccdacddabbbcccbcbbabaacdcbbcdcbddbdbcccccdddaabbcbabcaadabcaacbbdcccbbdddbaacadbcdbdcdbbdbabbbcbadcaadbdddaccdaacadbaddbcdabadaadaaacacbdbbacaacabccbaacadcbabccdaddcacddddadcbbcdddbdbbbbdabbbabaacdbcdbbaacdbdbcaddbdaadccadbccbcddabaaadaabcccabbdbdccdadaabddccbbcbccccbabdcaaadbaccabcccdccbcdaccacadddacbcddbabadbccdbabbcacacdbbabbaacadbcbbcbcddadcaababbadcdbbdbccdbbbcccadacaddcbcdacbdccdcdccabadbcbcbcddddadbddddccdbdacacdcabbdabadbcbcbdbccbbbdddcacaacbdcaddcddcdbbbddacaadabcbbcdbdbbbdbaadbdbbdcacbabdbbcbbbcabdcbaadcdbccaaaabcabcabcddccbddaaacadabbbbcdadacccbddcdccbddccccdbbcaaacacabdaaadddacdcccbbbaccddbbbcbcabbbabdcbbdccbbcaadacbbdbdcbddcdabadbcdbbdcaccbdadcdacbcbbbbcbdbdcccbaaccabcadbbaabadabcabcbcccbcbbddcdcaddaaddbbbdbaababbabbddbbaaaccbadbbdcddcccddacbaddaccadccabdbdcadbbbabdcabbbabbdabbdccccadcccaacadcbccdbdddaaadaaaacadacdcabdddcbabccdbaabaaccadcaaccbdcacbdccabcbdcaccccbccaaddbbdbbabbabbcddaaabbadaccaabccbcdccbbadaabdabdaccdaccddabccbbbadcadddcbbbadbddaabbaccdbdccddbacaccbacddabcacadabbccaadcabbaccabcbddcbbbbbcacbadcabbacbaaacacabcadbbcdccdcaabaaabbacdddaabbadbbbcddcadcbdaaaabbbdbddcdccdbdbaaacccccaacbbccbaacabcdbcacabdadadcabdabacabcaaabdbcdaaadaabbddcabdadadccabcddbabcbaccbbbdadcccaadabddbaaaaaaddcaadcdbcdaaabacbddabcbcbcddddcacbabaadcdcdbaadbadbcdbbacacbbcbddcacdcacbcbdacdcbdbcbdccadddbabdcdcbcdbacdbaaaddcbddddbbadbdbadbbacdcadcccaddcdabbddbadcbbbbdacaddaacaabbdbcabbdcbababadbbabcabcdacddddaaaacbcbbbbddadadcdcaacacabacabccdbbddcdddcdaadadbaaaadbcacacdcaadcbbccdcbbbddbdccdaacdcaddbcacabbaddcacccdbabbbbdcbcccaacccdacaacdbacbdadcccbadccbbbbcabaaacbcbcdbcdccbbaacbcadaadabaaacbcdcadabddcdbbadcabdbcdbadadaadcacbcbddbbcbddccddaccccbabddcddbbacadbdddccbcccdddcacbdaaaddadcadbdcbccacbcaadbbcdadbcabaabbbadadddcbbdcbbacaaccaddbccdcbdcabaccdcbacbcaddaabddaabcdadcdbbaacbbbddcadaccdcabacabdacddcadcccccccccadabcaddbcbddbabbabcabbdcdabadaacbcdcaacadaabcddbdaccccbccbcabcdcbbbcddbcdbbbcaacddadcbcddbdcadbaabbbccaadcabcbddacbbbbbcbbddcabbdaddababadaabbbdbcabdacaacadadaaddabbcbdccdcaaccddcacdddabaaabbbbbbbdbbabaaaccbddaccdcbbcabdbaaabcdabcaaabdddaacdaccbbdcbdcdadddaadddcbccddbbacaacdaaaddccbcadabcdddccadbbabaabddcbdabcdadcddbdbcdbabadbcdbdbaaabcbacdcdccdbcccadcaabadaddbdabcbdbcdcbdaccdabbaabdccbcbdccdcaaacddacabbcabbdccadaababcaaccbcddaccbcadadadcdbbdbacccacaabdcddacdabbccdabbbdadccbadaaaddbcbbbaddbbddbbdaddaddbccdcbacddcbbddaccbddccbddacbbabdcbccdddacdddcdcccdabcdaccdadcdaddbdaaabcadadabbcdcaaadbdacddaadaadbadcabccaddabdbcacbdbdaccacbdbbcadccddaababcdadccdcadacabcdcbcbdddcbaaadbbddbcaababddbbcdacacacbaaabbdbdcdbdcbccdcacabcbddcacddcdbadacdaacccbabddbabccbacdabacddbacadcbbadaaccdbbbcadcdcbcadcacdbbabaaaccbcbadbdadaddbdbdcbcdbcaabdcccacbadacacadbadccadbdbdadcdcbcadaadabccaccadccccddbcadcdbbaaabdbddaddabcaddabccdddcddbcbacdbaadcccaadadbcbbaacbadbbadcdcaaaacabacabdbbbdcbdbdaacadcddacaadabaaccccbbcdbdaaadbcaccdcbddbcdcddccaaccaaccbaadcbccaaaadbdcbadcaccdbaacddaaabdbcbdacddadbbdabddcccccbacbddbabaddcaccadacbcbddadbcdacdbababaabcaadbcaadbdddbdacdababcadcddbbdbdddaadadbcdbdaacaacbaddbdbddbbacdaccabbbbcacaacbabdaaaddadbabbcbcddaacdadcaddddcdddcaacddcccaaccdddcbcdaadbdbbbbccabddbbdadacaaadabcdcbcccaababbcaccdcbbbcacdbadabcdadbbcccddadbbdababbccacddcaababcdaaacdaacbaadaddbacdcdbadbaaabdacbcccaadccbbbbabcddbdbddcacaaccbcacabcbccabbbabcbddcdabbdbadbddadaacdbbcbbdccccccacdbccddbcdbbacbdaabbbbccabcddbcdcbbabbbcbcabbbadddbccccdcbcdcbcbbadbbdbbcdadabcabccaaccdddbbdaaaadbcbdabbacddddddcacbcadabccadcaaaaddbbcdbdcbdcbacabcabaabddcdbbaacbddababbbabbbcccbcaabcbdabcbcbcbadbbccbaddcabacabbbabbacadbbbcaddcbaabadbddadcaacdbdcacabbbdbccdabdccbbdaadbbadccbbbabacbcabdbaccdacacacdcbddddaaadbdcddabbdcbabdddacbdbaaadcbdcaccbacbaddaabbcddbabbaaadadccbbcbddbbbdccdcdbaccabcbacacadacbcbdacbdabdcbcdcdbddabdadbdcacadbcbbbdaaabacdccaccdccacdbbababadcccccddbabcbbaccccbacdbbcbbcbddccccdcdbcdadadccccbbdddbbbddbaccbabdcbcbddddddbabadccacacdbbbcacdbdbaccbbccbdacddabddbdcbacbcbcddbabbacbdcabbbbbdabdcabaaabccbaadddcaabcaabcdcccbcdbdaacabcbaadbabbaddbbdbacccdcaadadaaaaacdbaadaaaddbdaccdcbdacddcaacdaccaabccbaccdcbacbdabcbcadbdcadbbcacddaddbbdddbbccbdbbdccbddaaadcdabcdbabbaaacdbdabbaabbbdbcabccddadbbaababcdcccbcaccddaabcdbcaadaaabcdbadaaaddcddcbcbaddacdabaccdaccaccbdddaacabadbcdbbcdcacdaacabdbbdbbabcbdccacbacdbccacdcdcdacacabcaabadcdacaadbdddaacdbacacabcaccddabddbddaccccabdbdabbcacbdabcdcbccbaddcadcbbdcddabaddcddcdaacaaccaaddcaadcdabbdbdadcacbdcdacdcbbdccacddabcbacacbdbaabbbbbcdaaacbcddacaaacbaaacccdaadbbbbccbcacacadcbddcbadbacbccbbdddcbcadcdbabddcdbccbcdcdabdacabdbabcabcbddadddaaaddadddddbdcbbbdbbcdcdcdcdbbbdbacccacadabdbdabbcdadcbaadbbaacadaaccdbdcdbcbdcaaaccaabcaacccbbacaadddbababdbcbdbdddcabdabbbaaabbcdacbbbbaaccddcbbdbabccbdbbdacddaaaaadcaddabcdcabcbbdcacbcbabbcbacadbacdcaddbaddbdbcbdabaacccacbdbdacbbdcbbbdcabbacccdcbabbcbabdadabdaabbaacddbbcbdddcadcabacddadbbacdbdacbbdaddbcbdccbdcbdbabdaadbabbccddddabdbccdbccbcdccddddcbabdbcbaaaaacbcbcabbbccaaaccdbcbbaadbcbcdbcccbaacaabcddddbbbbaaabcbcdcbcaacbaacdacbadbccdccccbdccbddbbaaaadccccacaadbbaaccbcddbdaaaddbbddabddcdaaacabbddcccdadbcdacbbdcaacadddaaaadddabbbdaddbbcbbcbaaadaadcdaabcaadacbbccccacbcbdaccabddabaaccabbadbccdaaddcbacbdddccddcdcdbacbaaadaddcbcbbadadbdcbbdccdcdcdbaacacbadcbddadcabacdbddbdbdddbbcacabbacccdbcbacbccdacaddbcbddbbabadbddaccbabbacaabddabacdcbdbddacabcbdddacababcccdcabdcdaaddadbdadaaabdaacdaddcbaccdcaaccddccdabdccbcdbacbbdaadaababcaccdbdbcdcaccdcadcaaccbddbbbcbdaaacbcbadcdcadbdcaddbcbddadabccdbaabcaaadcacbaabdcbcbdcdccacdaccabaddcabcadcacdacabcbbabdcadddcdadadabcabbbdbcbadcadbcabbcdddbcbddcbddcbcabddcbbadbdabcdbdbddbabbabacccaccccdacaddbbbaaabdcdbaabcdbcdacdbbdcbacdddbbaabccdbcddbaabacbbcdabdcddabbadcadcadcbcbddcdbbcdbbdbaaadaddbbaabcdcabcdbbacbbddbbabcacadccbcaccbcadcbacdcacbcccacbbbcccbbacccdbdddbccdbbcaabccddbdcccccddcbcdbddcccccbaddbbaacdbbcabbcbcccdabbaadbbbbbddacdabdacaddcabaaabcbadccbbddaaacdddbcacdcabdccacadacaccaadaaabcaacccadbaacabbbdbabcabbccccccbcdaaadccbcdbdbcbcdaadbcabcdcbcccbdbacabacdbbbdaabdcbdbcacdaccaadcadabdabcccbbadcddadbcaacadccbcdcbdddbdcabbbddacabbbcdddccaaaacdcbadcccdcaaaadbcdddccbabcdaddbbccddbdcbbdbbddbbcadaadcabbadaacbddaadccdddaacddcdcabccddbdcdddbdddbabadaabdbbdadbcacadcaabcdcdacdccddaaabbacbbccbcbccadcbbaacdbaabbbddcddddaaddcbadadbabdacbcddacaadbaaacbcbccbdaacbaaacacdcdcbdcaababaacdadddcbdcdbabdcbbcacbbacbcccadbcabbdddadcabaadbcddacbacabbaabcbcaaaaacdcbccddacdacbcaddbdcdaccaccddcaccdabcabaaaaabcddccccdddbcacddbbbcbabccbdcaababdbbbcdaabacddaabbcbcdddddbddccadabbaaccabbbaddbcacbaadddcbbdbcacaccdbcddbacaababccddaddbbcbabcbdcaddaddcabcbdabdbbcaaadbdccbcddbcadbccbcbbcabbbbbaaccaddaadabdcdadbaaabaaaaacbbbcccabadbadaabbddadddccbadccadcdbacabcabbdadccabbacdaccabbdcbaadcdbadbbadddcbabbabaaabcccbcdcaacbbabacdbcaabbbddaaabdbcdaacaddacdbccbcdabcdcacdabdbcbcdbbbacbbaccacbdcbadddcdccdbdabcdcaccdbacaccaabaacbadcbcccbbbcccdcaaaadcbccbdabdddacdcdacdddbccbbbccbddcbbbdddbbdbaacaabcddadaaddddacacaabbbabcccadacbabaddcccaaacccbadcdacdbaabdbaacbaacdcbbcbbdaddbdbbbcdaadabbbdcdadabbccbbdcccccacbbcddccdaacbcbcbcabacacadcacaabaaacaccdaababacbdccaaadabbdcbcbcadbbcbaaddcbdadbdcaaacaadbdddbccadcdbcbdadbccddbadcaadcddcccaaccdbcaddabaddcbbdbcdacbbdabbcccdbccabbdbcabacbdcbccbadccbccbccabbbcccaaddbdaaacbbabacdaddaaadcdbdbbdddadbaadcdacbcbdadabddcdacbcccacbcdcccacabccdbcabcaadbcaabdaddcdadddcddadcaccdbdccccaadbaadcaabbcbbddcbababcbddcccdddadcbddbabcabcacaccddcaccaabddcdbcbabaccddbddddabadacddbccbdabbcddabdcdbbdaacdbadcabcddacbcdacbdcbbdbdcddbccabdbbacdcababcaccbacbdaadbbcadabbdcabacddaccbcaddababbdddaacdddcbdabbdcbcabcbdbabdbabbabddcdccdcababacdcbcbbdaadddadbdcbbcbbabbdbaaccddabaacbacbbcbbddcddcdbbbdbccbdddbcdbcaacccdadabcabadaddbccdcddcbaaabbcbaccacccdbbadbcbccadaabcbbabdcadbbddabbcdbddbaccacbaddbddabcaabbadadabcbbcacbdabbbbabaccabaabcbbcbcdadbbbadccdccaacdaadbaadbcccaabccbcaccbcbaadcccacbdaadabcacdcaabadbccaadacddbbdbbabcbaddacadacdcaaaccbcbbdcbcbdbcaadcdbdcdccaccdaabcddcdaddabadababdbbcababcbaadcdbcbdbacccbcbdaaadbabdababbabbacbcdccaaacaabdcdcbadabbbadadaadbdadaddacdabbaabcdcabbababcabcbbcaddbcddcdabaadcaadbbbdcbbbadabbaadaddabcadadbacdcbccddcbbaacdabababcbcbcaacbbadacdbcbabadccccccdccaabaadcdaaacbdcabbcccccdadabaaababdacbcacbdcabbdcbddcadccaccabbccacddbdddcbcbacbdddcbddadadbdcababdbacdcddbdabbdaacacabbdbdccbcddcaddbbbcdabbcbdcbbcdbcadddabddbbabcbcdadccddaccbdddaacbdcdaaadacbbdadaacabbcbabbdaababbcdaacddabbdccbaacdaddcacabccdabadabddadcdcabdbbacdccdcacdaaccdbcaacdcbdacadbdddbddcddbadbcbbddadabcabaabaabcdccdadcbdabcadadbbcdadbbbaddaabadaaadaddbdacadbcadbcdacbcaacbacdbaccdabcabdbcdcbadaccdacbcabaccdddccbcbcdcddaacbdadacabbadaccaabbdbccdbddcadbababdbcbaaacadbbcabaddadabbbaaacaacbcadbabbcabbddaccddadacbabaacbbaaaccbbacaabcacaacdcaacdbcacdcdbbcbdbbacbabdacaabcddbdcbbddacdbccbcdccaaaaabadcabbccccabbaadbdddbabcdcdaabdbdcababcbdddbdbbdbbcaddabccbcdccdbbacdddcaacacacdddaacccdcadddcddaadcdadaababcbbaccbccdaddcaaccdbacbcabaacdbabcccbbaacdbdbacadcddccdbbdabadcccacacccacacadaaabbbaccbccdddacdaccbbdacddddbbbcbadaadabcabddadabbaaaccbaadcbacaddbddacdacadbdadacacbacccadacdddbaaaacaacddbddcbabddcabadcadbacabdcabbbaadbabdcdbadbbdaababaccbcacbcdcdbadcbcaacbbcdbadcaddbabbbdbabccccbbcacddbbadcdbcccbccaadbabdcacdbddddabacbcabcdacacccdadbbcbdccadbacbdbcdccacccdabdbcccabbcccbdaacddbddaccdadaaddbadddccccdcddbbabdbaababaadaacbdacbdddcabcbbbaabddcbdcdbaaabddabaaccaabdddaabbacdacddbcccbacddcddabbdcbacaadbddddabdbddcaaadbcababcabdbdadacabbacdaabbdcdcaadaddbaabaddadadbdbbbacbdbdbcbbcdbcdddddbbaadbdadbdcbacadccbaacaacdabdbddcdaacaddaaadddcabbcbdbcbbabccbdacaaabcdaababbdabbbcaabaabadbdbdcbcccbbbdbcdddaacbadadcdcadccbacababddcbdccbdabbaadbaaccdaddccdccdaabbddbcccdbdabcddcbcaaccacdbdbaabbdcaccccbbbbcdbaddbabbadccabdbabcbadcabaabccbacbcaaacadbcbbddbdddacdadcbcabbdcbbdacaccbbdcbdcabdddaaaccacccbbcddcababdbcacdabdbdbdddbddbbbabbcdadbbdbaccabbacbccdcddbccbaabdcaabccbbdccdcddccdddccdbaabdbacbadcacacacdcaacbcaaacaabdbadabaabbbddacaacdcddaddbbccdcaddbbaaaaabaccadccdacdcbcaddbbdbacbbddcaaddbbcbdbcacaaaaacdbaaadabbbdcdccdabdabdbbaacccadbcbcacaddcdcddddacddbaddaccbaaabbccdbbabdbbcabadccdbaddbabdcdaacabccccacaccadcacdabcadcadcccbccdbadbacaabbdcdbbaaacccaaccdbaaacdbdcaabbbdddabbccabcbbbbbbdbbcaddcacdccabcccdbbcbcadaccbbbdbdbccdcdccbbbcaaaabcadbbdababcbbbaddababbdabacddcccbcdaabacddcbaabbdddbbdaaaadbcbadadaadcbcabbdadcdbbbaaccdbdadbdbcddcbdbdacccabcdaccabdcdcbbbddadbccdaaccbbcaccdcbbbabbaacbcabdbdddccaccbbbdcbbcadcddbbcaabbdcdcbcbcccadabddbacbccbddddbaabbacdcadaccbcbbabadbaaccbbdbddaaaaaddbacabdacbbcddddddaccaddabddbdaadcbcdcacadbccdcccbaadcccdcadabbccabdcbadaabcdcbbadcaabadddabbcccdbbccbcbdbccbbcbdcddaddcbbcdbdccdbabaccbdbadaadaccacdcaddbbcdcbddbdbacbcbddadddcababadccbbcbadaddbbcaaadccbadaddddaadcbcbcdabbbbcaaaabddadaaddabddccabdbababbddabdbdcbbaabbcdcadabadccccadbbbbcbbcdbbdabcdcdadbbadddbadccbcdcacbacddcdaacbcbcadabccacadbcabaaabbccddcbcccbbaccadbbddbabddbcaaaaaabcacbdbcdbcddacacdcbdbcacabbdcbaddaaaabacbbbdacdbaacbaaabcadbcbdcdbbccabdabddcbcddaccbcaddbdddbadcddabdaacdbcbccbdbccddccadddaddabcabacbaadcbbbcddaacddccbaaccabcdadbaddbdaabccbdbdadcaabaadabdbbddbdaabcccdcdcbadabcaabacccbcbddcabbcabcddaccdadbadaddbbbdcddacbdabacbdcbbdbdaaaadddabcddaaacbcabbdcccdcbcbcdbaaaacccdcbaacdadccdadadaacadcbdbdabbdbccdaddacccbdcdcabadabdbcdbddbbcccdcdcaababbdaadbcababcbcdbacbcddbdacaacacabacddbaadbddabcdbcabbcdbcdcbbcbbabcbcdbbdaabccbcdaadbbabbdbdccbbdacbcbdadbdacacbbcdcdbbacbbccdcdabbbdaccbababbabbadcdaabbdaaddcddaadcabdabcddcbabbdabaaaddcccbbaabdbbaabdddbaacbadcdcdacacbbcddbbdcadadabbcaadbabacadbcadbcaabbababcdcbcdacadcaabbccaabbdbcccccbdabbcbdcacabdadbcccbbcdccdddaabbcacbcbcacbacadcabacaddaabcddccacbcbabbaaadcdddacadcdbdaaadbbacbdcbbcaaddcbadcadbcbbbabbddaddccabbddabdbdbabbddccadbbdbbbacbaddacaaaabcbaacbdcddbbaccccaddcdbdcadbbbacbbcdccacdbdbaddabcbbdcccbadccadbdbaddcbaddbabbccbabdbaddbacbaabbdbaaabaaccdcccccdabdaadaacdbccddaddaccdcbacccbdddcacdbabdbcabdddcbbbddbbadcacabacaabcdbbabdcbaadcbbababbaabacdbacdcadbbbbabbbdccaabbcdaaadcbccacdcbacbbdaccdacdaaaadcbcaccdcbccbddbacbbbbcbaacdbcbdbabbaccdadacdcdddcbacabaacadaabacaccaabddddaddcabcaaccabbbbdbddadbcbabcacdbcaadabdacdbbcbdbadacaddddacabadccbdddcabdcddaabdadadbaabdddbdbaccacacacdaabbdaaddaccddbcbcdbbcbabcbddbdbddddbadadabaadcbdbbbadcdbbddcdacdbcbbcaacabccccbcdaccbbadbcaabdbdbaaabdaaadabccdacacadcdbdbdaacddcaabdcbbcbbbbddcdcbdacbddcbbbacaabadbcccadacabdadacccbdbdbadcccdccdbdcacdbdccaccaabaadbabdbdbcdabbbdbdbbaaddccbabbbcabcacbbadcabaddbdcbaccacdbaccccdddddaccbcdbbcabcbcccaabbccaadbbbadbdaadcbbabbbdacabbacbcacddbddccbcccabbdcbadcdcaacccbbddcdacdaacccdcaabcccbbbbddcacaaadddaaccdddacbdacddcaabcadabcdddbdadbcbcacdbbabdddadcbcdabccbdaadbdabbcddbbcbcbaaccdccdaabadabcaaaaadcabacdccaaaaadbcdccbbadcbbabdcabacccabcbcdbddcacabacbdbbbaabbcbdaacaaadbbdcaaddcaccccaccabbabaabccbdadcacaadcbcdadbacdbdcababdbbddadcccadbcabcbcdabdabababaadcdddbcdbdacddaaacbddaaadcaabcdadddbbbacaaabbdccddcbbbbcbccababbbdcbbbdbdbadabcdaaacabcdccbcddaccbddcabbbaabdcdadadbbbbdabccaadcacdcdadbcaddcadbcbdabaaaddbacabddbcbbbacdabadabaabbdbddabbbcddcbdcdbbbbcbbbdcdabaddbaabddbddcaacddcbacbdaaddbdcccdbddcdbbccdbdadacbcabddaabcdcacdaaddddbabdccdaccacadcaaddcabbcacaacacccdbbaddaabdbcbcdbdddbaaddabadccabdcccddbacbababccabccabdaacddaddacdccaccdacdadbdcbcaddaabbcbadacdcdbaccbddddcbccabcaaddbcbbcdcbabdbdbddacadabdaadbcaaacddabbbaaadbbacdbbacadbaaddcdcccdcbacbbbbbcadbbcacbbabdcadcddababadaadaccbcacccdcdbaaacabdaddcdbdbbadbcaddcddcabcabdadcbabcccdcaadcddacaadabadbbddcbaccaddbdbbcbacbacaaadbadccbdabbccccbadbdacaaacdbdaacdabbccbcbdbdadadcdcdcbcbddbaaabcabcdcbadaacbabbdacdcabcdabaccbadabdaddbdcdabaaadabdbcdbcdcdaadbddbdbbcaacdbbaabbdbbadcbbdaccbbabbcddaddccdaaadbddcdaaadccbcdbdbdddcadddadcdaadbaaddddbcdaccacdbdbcdaccaadabbccdccbdcbaabbaabacccbcddbaaadddcabacbadbcabccadacdbdcdadbbcdccdadcaccbdabcbcabddcddcbdcacdcbcabbbcbbacdddcccbcbabcacdcbdcbccbdaddaccddccbabcdbdbadadbbddcddcbadaaaabaacccaadacdacccbadbddcaaccacdacaabbabccbadbcbdabdaccabcdaabadbcbdbcadcbadbdddadbbbccbbadccacdcddbdbcacadbbccabccadcaabcbdacddaaadddbcbbcddaaaacccbdadbbdcccaacdbddcddaabcccacadcabaccdaadccbdbdadacabbcabbbacdadcccadcbbcbacbbcadccbcbacdbdbaddacaddcaacaccdcbabcdcacdacdccbcadacdbdbdbcacacddaaacaaabdbbdadcaacbadabacdbaddcbccdddcbbcccdabaadcbacbaacaccccabbbdddcdbbbacacdcadacdbcddcdcccbcdaabcabbddcddccaabdaaccbbdcdbccbacdcaaddcccbabaabbdaabbadcbabbcaabcaadcbdddabcaabcbbddcccccacddaadddcadcdccadcbdbacdaddcabcbadbdabcbdcaddaaacccaabbcabbddbddbdbcabcadabcdbabbcbacdcdaabaaaddddccdcaadaccccccbdacbcababcbacdaadacbdcdbaccdcbdaacbdadacbddaabacabdddcdabadbabbbcabadcabcbaaaadcddadabadddacbaacdccddabbbacabbcaacbadabbcdacbbaabadbabdabcccbbbbdcbcbbadbacbacbbaaaabccbcacadbccbcaabdcaccbbcbabccbaacbccbbddcdbddbddddccaadcadbccbbaaaadbadbabddcdcbaaabcaddadadcbadabcbabcbcaddbccabdacbcbccabcbbcbdbbadadcdaabbddcacddcacdccbcdcbcbbaddcbabddddcabdbdcadcddccddaddadccdbcbaaaadabadddbdbcbcdccaddabccadddcbaabbbcbcaabbadbacbcaaacdcacddddcddbaaacbbdbaacbbcbbcacdbaaacbadbddadcdcbadabdddddaacdccbbcdaadcdcadaddbccdcbdbcbcccdbbbbccdcbacadacadcabdabbadbdbcddcbacadacacababddadadccdbbbdadcaaccdaacbbcacbabcaaddcccbdbabdacbdccaadccbcbcacababccadcabbbbbcdcdaaaaddcaacddbdaaccbdddcdbcbcbddaacaaacbabcbcadcdcdaaadbcadaaccdbdabccaaacbadaadccdbdcbcddaaacbdbdbcccbacbccbadadbdaddcdcddbbcadbccdcbbbaccccbaaddbcdaacdcbaddcaaadacaccaaabbbdcabbbdccbccbacadddcccadcdadbbadcbdcaabbccddcaccccadbdbaadcdbcaccabbbdaddaabacddaaabbaaacbcbccaadbdbdabdbaccbabddbdbdcccdabadbdcccabcdadcdccdbcccbcacacdabccbbbbcaabdaddabbaacdbbbcadcdabdaaabdaabcccbbbaaabcaacdbdccadadaccabdaacbabacaacdbadbaddccabacbdcdbbcddcaddbbbaacdadacbdcbdccbbcaacbaaadcbdaabbcbdaadddbdbaabbdcdbcdacdbdcadbddcbaddbddbccdaadcbaccdbacdbbbccccdacaddcddbabcdbaacabdcabcdccbacbaddbcbbcccbcbbdcdcdbabbddaccccddcbabbadaccccdadbccdaadbccdcdaaacbaaccadbbddbdabadcbdbdbddaacadcbaabaccbaacdddacdabccbbddaaddbbaaaaadcaddadcbcddcacabccabbccbcbdabccbcabbdbdabdcdbacddaadcccacbdbcadccaddcdcaccccacaaabbbddaabadcdaaddbddbcaabbddadddabddacacdcdbcddcacdabdccdcdcbdcadbcbaaabdccaadbdbccdbaccdadbabcdaaaaadaacdbddaacadddbbbadcdbabdccbbcdbbbddbadbcaacdabcdaabababcddcddaccdabbddbbbddadbabddbddbccbcdacbaddbdababdccbacbacbbcccbacabcdacddacbcaadbcbabdbbddddbbdaadbdabadaadbdcaadbdaaacccbbbaadadbbbbbcbbdadddcaababcccdaaacdcdadbacdcbbccccbcbddcdcdabbcbbdabbbdbcabcdcccdadaacadccbcaddcdaabadbbddbddabcabbabacbccaaabdbcdbccccccbadbbdcbaccbcbbadbcdcccbcbdcdaaddcbdddbdbcddadbdbddbcacccdcbdcaaccdacadddbdaddbadbbabadbbbcdddcddcbdcabcacccabaababbdbdcdcabcdaacbddcadbccbdaacaccccadbdaabacccabdcdaddaabbbadbababadbbcaacbdbacbacdcbdabcacabaaaaddaacbccacddabcbdddcdcbadaaacbdaacdbbdbbbbdbbacdaaabbcdbcabbbbdaadbabaddacabcbdcbcbdcabaddabdaacbadbdbdaccbcacbcbccdccbdbdbbaaddcdaaccccddddbcbbabdbdabdcaaccbdcdaadbabdabddbccaadaaaddbcabbccbccbcbccbbacbbaabddcacdddbaddcbddaaccbacdbdadcbbcbbcdadccabbcacbbdbcddabbcbdabdadacdadcbbaacddddcaddaabaccdcbcbbcbabdbcbccaccdcacabbbaaddbbddbdcbbcdadadcabaddcbaaccaacccbbddddcaaccddcbbbcdcbcdbcbabbbcbabaabbdaadcaccbaadbdaadaacdcdcbabbcbdcadadadacdabdacbbbaaccdcbccccbadbddbcddacdbcaaabddbcabddddaadabddccadbadabccaabacbdcdcccdcdbabcddabcbcabdbadcbcccdcbdbbcbdddbdcacdaaaaaadcbbadccddccccbddbdaabbddcabcbcbcdbabdaaaddadddcdbacdabcddbbacdaadaccabcdcbcbdbcbddaacdccdbbdaccbdabbcdbbdccddadbcbbacddbcdaacacdddacbaadbbdbbbabbbdaaaadcabddacdbcbaacbddcaacabcbacdccbcabbcdbcabcdacdddbdacaacdabddbbbcdddacbaadaaacbcadaaabacbcbcdbbabacdaddaccacbcbcadaddbccdbbdbadbbddcdbcdcccbdbdacbccddddcbbdabbcacdcdababbcdadbcbdbaaccadbddbabbbdadbcbdaabaaddacbcccaccaabaacacadccbdddddcabcdcadadaddcacbadcababbaacddbcdcbcccabadcbccdcccabcdbbacbbacddaacaabbadccdabaadbbdccddbacadbcccaaccbddccacaddbaacacabcdaacaccddbbcdbcbcdabaaabccbdbacabdaaaaddbbaaddadbddcadabdbbccddabbdcdaccbdaabdaacdabdbdcadbabcdcdabdddccdaadbcbcadaaadbdccadcbccaccbdabbabdbdadbaddaababcaccbccbbcbdcabbcccdbaccdbddddadabacaadadabccdbacaaababacdaadbcaabaaccbbccdadddcaabacaccdccccaacdbbbbddaadabcbacaddacbadcaadadcaccbcadbcdadbaaadaddcbcbbaabaadababbccadabdcacbccccadccdcbbaabdbbbcaaddabcadbdbabbcabbddaddcadabcccddbadcccabcdababdbcdcabcbbbdcbdacbbcdaccbabcabbcdcadcbbdadcbbcabcdcbcacdacbabcccbccaadaacbdbcdbdaddbbacccbdddcdadacbdbccccaacbaadcbbaaaacacdbabddccadccabcccccbbcbdcbaacbcabbbbccccdbdaaabcadccbdbcadcdabbaacbccbaabaccbbbcdcbdacbbcbdbabddddbabadabddbdcdccbbdcbddcddcbccdcbccddddbcabaabbdcbbaccbbddcabbddcbbbdabadabcbabbdacddcadddadbaccbacabbdbbddcccacbdabdbdccdcbdcccbdaddaaaadadbccabbaadbcdbabdbcabbbdbabdabaaaddddaccdacbadadaccbcdddcadbdadbccaccacdadddcbdcbccaaaaccbbacccccdcdaaddaaddccdadbaabcddddcaddbbcbdbdcbccbbccadbbdacdcbcbdcdccdbabdbcbabcadaddbadcbcabbbcdcbbadbbcabaabdcdcbcababcaadbababdaddabbcddadcadcddabcccadbcabaacadaabaccabdbadcbabcaabccdbabbdacbadbbdcdbbdcbbcdaaabbaacaddacacdadbbbaaabbadbaadabccadbacbabdbcbaaaaadbacbcacbcdbdabcccccadaaddcdcddcdadaccbcbaaadaabbaabaaabaabbabaddadccbcbadadcaaddbaaaadccbdcababddadcdccbbdccccbbacabbcaacbabaaadabcbbddbcdbbcdcacbcbcdbccbcadccadccacababbbccacdaddaabbcacccddadabcaabadbcbdacababdbcdcabcccdcbadaddddaaddccddbaaadbaadcacdabcddaabaaadbcdabbaacaacdbccabbdcacabbdaabcabdbbbcdddadbdbcbbabdcbbdddcabcccdbcacabcbabcbbadcabcddddddcdbbabbbdddbacadcddccdaadcdaaaadabaccdaaaaddadcbbbcacbddbbddaadcabdbaddcabcaabdaacdbdbccacccbcaadbaccabcdcaabcaddadcdcadaddacddbcccbacbcacbdadcccacdbccdbdabbcabbacdacaccabaacbcacdcaddadbbcddcababbacaacbdddcabcbbcbaacbdaacdaaabddcdaadccdaaaadbbabdabaacddddddadadcdaabcadcbdabaacadbbdddddbdabbccabddccacacccccabadcbcaccddaabacbbbabaadccddbcdaacaadddcbbabccdbcdddbabddbaccdbcdcbaaaaabbccddddacddcddabaabdddbbadbcdbccaadaaddacbbbbcbddaabbacbabcddbacdccccccbdbbdaabdcaaaababacbbbbbbbcaaaaddcaacdddaacdbbbccdadbacbcbadbdaaaccadccabcccbbcbcbcadbbcbaacdcdadcccabccbbacabcaadadddcdbbdabbcacdaccabbbbcdbccdcbabadbdcbccaabcadbcddbdbbbbabaaabccabcdaadbabdbdbbacabdabbdabbacdddbbdcdadadcadbccbacbcbdbdabcbbadccabaaaaccacddddddbbcccbcaddbcaabbcacdbcccadccbbabadadddcddddbcacbbccaadadbcbccabbaddabaccbbdddbbbbbbccdcadbcabbcacdabbccbbbcbdbbccbaabaaacccdabbdcacaccabaaabcbddbbaabbbbaadacaccbdbcabacbdbadccbabcdacabddacbbadacdcadccdabaabacaabcabdcdadaaccaabadaaddbacccaaaabcdcccadcabdcabbbdababaadbdcccdabdbdddbcbddcdbdababbdddaddcadbaaacaabdcbbadbadbbdcccdcdabdbbcbabdabdadccdaddcabdadadcdabbbacabbdccdbddadcbcaccdbbcaccacbbcaadbacdcdbbddaaadaaccdbdaccdccdacadbbbadcacacacdbaababdacbbdbacbbdcccbdcdbcabadbbdcdcadadcadbccbadddcacadddacbbbacacbdcdadcabdcdccbddbacdbbbccbcbaadaadccbdaacbbacbcaddaadacccbbddbbadcdacdaabaaddbdccbccacdcbbdabcaccbbddbcbdcabacabcbbddcacccacccadabbcaaccbccdabcbbacaadcdadadbabbcbdddbabdcbdaddaddbbbccccccbdaaadccdccacbcaadccbaccdbccaaabbcbcaabbacabdbacabcddcdbacbabcacbbdabbbacaadbcacdcaccabbbcdcadbcdcbcaadbdddddccccbdbbddcacaaddaaaaabddabbabbcabacbaaaddbddccbddaacbacaacbcccacccacdcbbccbcbaddacdcbcaadcadbcdcdbddddacabcaabbaabccccaadcaadabdddcbadabbdcbccdaabddcbbccddaaddabbcabcdabdbcbaddbaccabababbaabddcadaddbccdddbacbbaadcdbbabdabbbadabbdbddcdbdcadcbbbdccdbddbdabdadaddaaaaddcbbabdcabbbadbbaacbdbbcdcadacaccbcbaadadaacbddaacbcadcccacbbbdaacdacddababcbbbbcdddbadddacdcbbcbaabbcbcddbadbaaadbacbbabcbdaacdaabdbbccdacaaaabbcaccabacccdbcccabddcbbbacbcbbbdabcacababbddbbbadabacbccadbbadcbdcaccadccabcacabdadacdaacddbaaacdcacabacabcdcdcbdacbddcaddaabcbabccadddcdbbcaccacbbdcccbcabbbdacbddcdbccaccccabcacdcbbccabdcbdadcaabdcabcdcbbabbdbccaccccdcbccddaccdaccadcccadadcdbbcabdddcccaaabcbbbccccabdaaccadcaacaaccbcadcddbbadbcdcbddbcdccbcdbabbdcaaaddaddbaabdbaadadcccddcabbdcbcacaadddabaaaadbcdadccbcaaabadaaddcababcbddbccccaaabdbbdccadaccbbbdaadabacbaacaabdbbcbdadbcccbabbaabddacadccaadccdcaaadabdddbadaacabbaddadcdbdababdddadddddcbcbbaccacacbdccbdcaadbbbaaccabbacbcddbabcaacddabaaacacaacbdbbbcbbdacbcadacdcdcdacbdcabaadcbcbaadbccacacabaabdccdddddbdaadcdcbbdbddbabdcbabccccbabbddaabcddbcaaaacddddbdbcbbddcdaadabdccacddbbddadccbbcbcdcdccababddccbbdacaccbadbbbccddddcddddccabacbcccdbbdacbcaaabadaabadabdabbddcddbccbacccbbadddabbbccdcbabddcbccccbdcdcbcaaabbacabcbbcacbcbababaddbaccbbabcbccbaabdcdabccdcdddbccccbccbcbaccbdcbdcdbbccaaccbbadaadabdbcacdadcccdcbdacabcdddabdbbcdadabdbaddbaaadbcbacdcdadbbddbaaddbbcbbaabbcadcdddcdacbbbcddaaaaacabcdcdabdddabbaccbdaacdaaadcdadcabcacbaadddbccdcbdabccbdaccccdadadcbadadddaabbdbaaabdddbbccbbddddcdbbcccacaccbbacbabacdcbddbacaacccabbcbacbdddbbadaabdbcbccdbdccaaccbdcacdcdccdaacadbddabaccbddbdbbbabbdddddaacbdcccbbdbcbcdbcddadbdbaacdbacadccccddcaccdbdcaabdbbbdbcbbcdcbdaacadabbcbabbdcdaadcddccdaddbccbcabacbbadbdcbaccadbbdadbddbccaacacabacdbacadddbbcabaccccddbdddacacbabbcdbabddabdddbdadcacacbadcbbbabdadabdabcacddaadbdcddbadbcadcddcbaddbadcaacdddccddbdcacabcddcdcdbbdadabdddbddadbababbcdbccbbdbaacaadadcdcabcaadabbdbacbcacbbcabcbdadaadddaaaacabadbbabaabcbabadcdbccabddadbaababdadacadddcaccbdbbdcaabbdddbdaccaacdadadccbbbacccbdabbbbabadddcabcddcbaadbcadabbcbcabcbbcaccaaaabddddcdacbacadadcbcaaacadddadcaababcbabcabbacddbcbcdacddaddccbbcbbdacdaabbbbaadaaadcdbcdbaabddcabddbcbcddadcbccbcdbabcbaadcaccdbddbbaacccbdcdbdcabcbaabccdbdddbbcadadcaddbdbcdaadcdbccbbcbbbddccbddadbbcdaaaccdbbaadaacbaabdcdadaaaaadbbddbabcaaacbacdbbcaaaadababbcadccdbbadcccadbaabdbbbdcccbbcbbddcdcacbdccdaababcacddbaaabbaabdbcdbcabacdadddadbbdccdabbcabcadbcbbdddddbcccbbaadbddddcbbbbacdbcdddcbcacadccbabaaaabdabdcabcabcadaaccbbbddbccdadbddbdddddabbcacdccabbcbadbdbabcbdddbaadacddaabbcccaaccbbcddcdbadcbadaadcbdbcdbabbcabaccaacbdabdaababbbadadcabacabcabbacbdadcaaadcbabcbbbccdacbaabcdcacacbcdcadccbabdddcacbdaddbacdcadccbdcdcadacacaabbabbdaaadbdabbbbcdacccaaadbbcadadaddacabddabbcacdcddbdccadbbbddaccbabacdacbbcbdacdbdadabcbcddbbbbbdcbadacaaccabdaabcbaaddcbaccaaacdaacddbaadaabbbabdaacbbaaaacbbababcdcaddbadccdcadbdbddccdbbcbbdaddcaadabbbdaadbcdcaadbcaadbaabaaddbdbbaaadccdcdabcadaccdaabdadcdbdcbbcbdbabdacdadabbdabadddacccacaaddacbabdabdddabbbabcadbacbbdccabadcdabcdbbaacdbadabababddaabccdbddbbcabaabacacbaaaddbdababdcbcbabdbbbbcccabcbdbaabdbbbabddacacabbccddccdcccaacbcdacadaccdbcbbadadadadabddbbcdbdcacdadbcdaaacadabddcbdacbbdbaddabdaabcbaacdacbddcbdcbddddbbcacccbddbcddbcddbbcdbcbabdcbbdbbbcacbdcbcbbbbbcadaaaabcddcdacdbcbdbdcaccdccaddabcaaddcbbaacabcacccbcbbbaabcdcbcbbcdbaccdcbbdbaccdabadddbddbbbdaabdabdbbccddbccddbcdbcbdcaaacdbbcbadbbccbabacccacbbddddbbbacabcdcbcababdbaacdadccdcdabbadccbbcdddcbaaccdccbcadcaaaaddbccabbbaabddabbdadaaadcdbacaccbcddaddadbcadaccddcdacbaddadcbdcbcadacbcaacccbcdccbacbadaacccacbcbcacbdcdbacbbbdbcaacbaabdcacababccaabbcdcadcaababacbbdbccbcdbacbcddbcdcdcadbbbcccccbbaccdbbdbdbdbcbdddcacdbcaadbdaaacdcbadbbcabaadacdccadaadbaddbdacdccbbadadabaacadcabadcaaddbbbdddcccdacadbdadbdbabbdcdbbcaacbcaddabdcbaaadbbcbababccbcacdddbaaccdbcdabcaddbcbcbdcdabddbbcdcbbbbdcbcdcaadbcbcaabddbddcbadabcabdbcacdbdbacccadcaabacdaccdadddacbacdadbabbdcbbccbcabcdbacdddddaaadbaadbccadcdacdbaaadbccbadabdadacadcabcbaaadabcbcbcccddaabcdccdabbaddadabddbbbdabaabddaccbbbcbcbaadbcadcccbdadbbaddcbcdbccbdaaaccabbbddbcbcaadabdbdcddadabbbcacddabacddaccbacccaacadacbdabdabdadbccddddbbddacddddcabcddbacaddddcbdcdbbcbccbbcdcdccaaacbdbacbacabdcadcbaacadbbbcdacdbcccdcacaddadddbaacddaaabddcaaaabcaacdabccccdcbacbacdbddbddcdcaacbbcddadacccbdbcdbbbdbbcbbaccacdbabaabccdbabacddccdaaddbbbbcbccbccbcbbdaccabbbbddadccbabacdbcabdcddcaaaccadcaaccacadcdaddacbccadddcaacaadaddcddcdddccabaccaacccbabcdbdcbdaadcabdccacaabdbcbcabacdccbacaadddccddcdaccbbacaabcbadccdcccaadddccabbbcbcdcdcaddacddcacabbbcabbdcdcbbdbcdccbdbbbccdcadcacaabcaccccdababacbbdbaaaabaaadaddbcaadcabcaadaccacaaacadbdcdabddadaadccccbacbcbdddaddacbcdbacdbccbadbacbcccacbdcabbbbdbbcdbbccaaacbbcbdcbcbbcdacdcdaabcdababdbbbadaabadacdcdcccdbbabdaddaddccbacbdaddadabcbacdaabaaccabcbdddcdbcbccacbbcbcabbaacddaccaabbbbacdacbccdddabcbbcabcbcbaddbaabcdbbcaddddddcbccccdbcbaadbcaddcaaddaccbcdabadccacccbbdccaabdacbdbbbdcbbddbbbdcdbadaccacdacbdabcbbcdbacbbddbdbabbdcbccbcdabccccadacdccbbacadcdbaccdaaccadcdcaacbbbbdbbccccbadaccabaccddaacabcabcdcbbcdccbdabaadbbdcacaccaadacccccaacbdccabdccbacdabddaabdcbdaaccddaddcacacdbadcbdbabddadcbaddbddcbddddadacbbbaadadcbccdaddcdacddaccbccbdcdabbabcabdbcbdbdbcdadcbaaddcccdddcbcdacacbadcdabcccdbcddcacadaaabbcaccabddadcbabbbbdaabcdbbbdbbdaabaaddcaccababdbbcdcacdbbcccdacbbacbcdbaadccbaadbbcccdaaacddadcdbdbdbdabadcdcbccbabbababbcbacdddbcabcbcaacaaaacdadadccdabacddcbdbbcdcdcdbbcabbdbcabaadcabccdcaacbabccbdbdbbacaccbdabbdcababdcbadcbbbcdcaaabcabbdabdcaccacbdadaadaaacbdacbbcaddbdbbdbbbbbcddabaaabbccbdddbaccbbcbbaabbbabcaacddcdcbcdacaaccddbcdcbacbcadddadcdabadadcacaadabcbbbadacdcbdcbcdaccddbaacaacbbddbcbbcadcabdacacaaddbaadbccdbdcbdbbbcdacccacaccbddcabcdddbaddadddcbbcdbabaabcacbaaacbaacbdcbabdcaabababadaabcdccbccdbbaabdbcbdadbaadcacadddcaaaccddddaadcbbbbadacdacddcbdabcbbdcddbdbcdacdbbcadbadbddbbadbbccacadcaabcacbddbdbacccdcbdbacddadaaadbcbccccdbbdacadcccdbdaaccdabbbbaddbbbbbddbcaabadddcccbcdabaadcbbcaaaabacabcbcdabdbacbbcadacaacbccbddcacbacbdddddcacbaddbacdabcadaccddbbbabacdcaaddbdcbdadcacabccdcdcadbcbdabccdadbcaaddddaacdadbbaadbbbdbabcddbcbcaacbdbbcbbadddaadcbdabcccdbcdcdaddbddcccbcaaacbaddcdcdcddaaccbdaacbcdaacaddcbaabbcbabdbabbbccbddddacddadaccbbbabacbcdacacadcbccbbcabbdcabbadaadcdcdccbbcdaaaadbdcccaabadcdbbaddcdbaadaaddbccdcccbaddbdbdbbdcbcbdcccdbbdbdaababbbbbddcccaabbcadcbcabbdcbabddcacbaddbcbbcdccabbbdacccbdaaaaccaddabcadbbabdadbdbdcabdabcbbdccaddbdcaccaabdbcaccccbbddbadcbccccaaabdcacddbacbdabbdacbabdbdbadbadcdddbcdcbdaacadccbcdcacddabaacddbabbacddccbcacabdcccadccdaaccddbddccbccbabbbdadaddcdcddccdcabccabaacaccbbbccbcadbaaacacddaddcbaaabbabadcaccadcaadddbbadaaadbcaabbccbcbabdabbacbcabcbbadbabcdacacabaaabadacabbbdbcdabbcdacdaabdcdcdcdadbabdbacdbbadaaaabadcbabcbddbadbddbbabacccbdccadcaabcbcdcaaaabcdbcdbbaccaccbcacbcabddcaddcdcbaaadadadcddabcabbdcaccbbcbaaacdababdaacacdbbbacaddcaccadbcbadcbcdcbddacdcbcadabaddaabaaccdddcdcddcdcbbbbaadababbdcbbadbcadbaabbcdadcacbbdbdbaaccddbdddcddcbcdacaaddabaacdcccabbabcbcbcacdbdacdbaccbacccadbaadabbdabdaababbabdbcbcacdcaacccbbadcdbdadadaddbcbabbaaccdcddcadbbbdcccccdbaaccadbbbdaddbadbbbbddbbccaabaaccddbcbbdddcaacadbacabcdaaadcdcacadbdccddcabbaabbdcbadcbcdcbacdddcbbacbdacbccdbbddbdbacdcbaddbddcdbcbccdbbdbbadaabbacdabcaabddbbddacbdbcbbcadabcbbcddcbccaaabbdaccbadcbbdccadbbcdddbaacbcdccacdaadbbadbcabdacdbcdaadddacddddcaddcdbadaaadaccabaaadcddaacaabbbaaadabcaccaccabaccbcbaccaaccbbdacdcdacccbdadacabbccadbdadadcdabcdabbdabdcdbcbaadacbcaccbcdbadabadbcbacbaaccccdbacbbdbddcdbcccddcabbddaacddacdadccddadaaadcabcdbabccddbaadddcdaaacccdaaabbcadbaadccdabcdaddabaddddbbdccadcbcadcbccdbabbcdbdcaddcbbbadbcbddaaabcabaaacaababdbababbcccdddcaaddbabcdabdabbbabcbdccadabbddbcadccbccaacbcbdcdaadcddacadccbcbabddcaabddbbddcaaadabdbbaccadaaccdcbaaaadbcdbcbaaadbccbbdbcdadccddaccaddaacaabcadacabbdcddbacbadbccabdcaacdbbdccabcaabcbcbacdccdbdcdbacabbdbddcdbbabacbbdcdaadbcaacdccaccacbbaadaaddadbddddbdacccdccbacbaccddbbdabdbdbdcbbbbbbbbaabcbacbcabcabdcccdabcabacabaadccddacbdbbdddabcccdcacddddabbadcdaacbaabbbcbdabdaddaddbdaadbabadcbccbacdacdcbadabdcdaadbbcbbaacbdbaaaaddacbdbabcdbcbbbaacaddbdbbabaaabbbcbbbdddabdadcadcccaabbadbcaaabddccbdccbdbbbdcbaccbaadbbdcabbbdadbbdacadcacbabaaabccdddbbbdbbdacdbcddbddccdaacadcddaddaaabaadabcaddbddabaaddccaadcbdcddabccdddacdabacbdccbbcbabbabdababbbdaccadbbbcbddbdadabacadacbdacbbdddacbdbdacdbcaddbbdaabcddaddabcbcbadbabcbabdcdabbbdbadcdcadabbdcaaddaacadadcbddbbbddbcdcddbdaadabaadaabaaadddcaabdaabcbaccbabcaabaccbaadbbddcdadcdaacdccbbcabadaadddcbdabcddbaaadabcdaddccdaabcdcacdacbadbcacacacdaaaabdbacdddbbacdcbadadacbbaccaadcdddbabaabcbadbbcdbbbbbadcccdcbddbddcbbcbadabcbcbcaaadababdbcaababaabddcbdadcbdbcccbcdbbacdacccbdbcdccabaccdcabddddcccbcddbcccdaddbaccddccbacbbabaacddddadcbbadbbcaddccadccaacacdcdbbdddcdacadbabbadcacccbdbccaacadcaddacaaaadcaaaddbddabcabbbcababccbdddcbbacaddaccbbbabbbcabbaccdcbaaacdaccaadccccaddbcaddbadaabaaabcdbdadbaabdaabadbbdbccddbaabcbcdadacacbddcddbbdcdabdcbaabbbdcdabbabdcadbbddcdcddcbbaccdcbabddbacdcccbdcbccaaabbbcccadccadbdaddadcbadaacadadddcaadbccacdcbabbbbdcabacbadbcdcbddcdcaadcdbccaacdccbdcacdbdaccbbbcbbaccdbbdcbdabadacddcadbbbbdbdaaccddbdcbaaccdabbadbddacaacdcccddcbcadcacbdbddabdaacaacdbdbcacbcaccbccacddaabbdcdabbcdbcdbcaacbbddbacadbacbbcacdadddcacbabddbdcbddbaaabdbadbabbcaccdccccbbccdbdaaadcaacccbaaabdccabcacaaabbdbacbdacaddbcdcadabcbadaddabddbbacdcacdcbdccccdabdcdbdcbadcdaddcbadaadccaacddcabaccabcacaabbdbcdadbcdddccaadaacadaaaddababbbcccddbaadacdcbcccbdccddabcbbbccabaaadbdadcadbacadcbbbacccdabacbbadbdbbccdaaabdddadcbddabcbcdddbcdaacbdddcadccbaabcbacddcbaddbdbbdcdacabcabcdcacacdacdadacbcaaccdbccbacccbcccbaabcbacbabcdddcaccacbabcdbdaadaacacbadcbacbcaacbdcaddbabbacabbcbbdaccaacddaacbcaddcddcbccbaaaddbbdddcdccddadbcadcdaddcabacbabcaccbbadaabddacbddcbcdabdbadaccbdbcadcacacbddbcbccbbbaabbbadbcdabadddabdccabdcbabcaccdbcddaacbadaaadccdddccbacadbbbccbabdadbcbdcdbbbddacadddcadaccddaabdcbadddbabdbabbcdddcdbabbacabccdaadccdbcdbadbbdccbddddcdadbdacadddbcaaababaabdcacbccbccbcbbbbadbbcbbccbabbdbbdbbddbcdbcadaaabaadacababcbcabaaddaabbabadccdabbccbadcdcbbdaacbbbbdaaacbcbbbabaabacddbbbccabdacabbdacdbbacabcdccdcddbaaadcacbddbccabcaaccccbacddbaadcbbaccbaaabbccbddabbdbddcaadbabbdbaaaabdbdabcbaabcaababaaadcccdaabbcdabbdcddadcbdddcddddcbabdcbddbbbbcadbdbadbacaaddcbbcabdcbbabccdcacccadcabcaacbaaacdbcabccabcdaaabaadcbbcbaacbbabddbabaacbdcbbbcbbbbcdbcaddbadbdabaccbabadbdadacbbbaadbadcdaabdbbdbddbdbcababacdadacaabccddcaadbbddbbccdbaacbcaacdddbdccdbdbaabbcdadcddaabcabbcdcabaacabddcbdadbddaacbdcbdcabacbcaccdcdacbcdadabdbcdacadadabddacabcaddcbdabdcdddacdccddaaadabdbbdbadddbdbbaddaacddccbabbabdacabdbcbababbaacabbadabcbabcdcacbccadbbdbbdbbbaccaaacabdbdbcaadbadcbbacbadbbdbacbcbabccaaaabddbacdcacbbcaccdcabbaddcbdcabccaadbaccdaaddacbaacdbbdcbadddcdaddddadbcbaaadcbadcdddaabdccbcdbbacdbbbdacadcbacccacbadaaadcabbcdddaaabacddbcadbddcdabadcdbdabbacddbbbcdaaaccdbbadbcdbadadcbabcdccdcacadadaaaabdbbdccadbaccbdabddabcccbabcaacaacbadccaccdcbcaadbbbccabadbbabccbcabccdddccbbacbaabbdbbacadacaccccacabdcacaacacbaddabbcaaddddcbcdcbbaacaaaaabacbdbdbdbbbcabcaadbccdaadcdbccccaacdcccadcddddbaaaabdbcacbdbbbbabdaccacdbcadaacabdbaccbbbcdabdcdbacdbdbacbcbacdacdbabbcacbacacaddcbbadbcbccbcddccdcccccbcdccddacbdaddbadcbcdbacacabcabdddabcccdabcabadcdcbdababbbaaaaadcdcbbbadaccaacdcdaaddbbddcddadbbcddadccdddcadacdccdbcbbbacdacacbdcabadbbacaabdddacababaaccbdabdcdbccabddcbdbbadbbbdcddcdabbcbddbdccbbaabcbcabbbaabbbcbbbadcbddbaacbbabdcdddcdcbaaacadbccbacbddccbacdcaabcaddccdccddbaaccaacaccdaacccdacdcacaaccdbadaaacbccacacdcabcadaaaaacbdccadcdaaaccbbdbdccbbcbacddaacbbaccacadcdcddbabcbaadbbdcbbddccacbcabcabdcbabcabaccbdbdbbdbbbddabcbbccacacccbabcbcaaccdaadcaaaccdcadccbdcacaddbaabbcdcbcdbdacbaaabcbadaccadabdababdbdbbcbabcbddaaabaacaddaabadbddbccbabdcbbcdcacadbdcabbcabbacbcddcdbadababbabbbaabbbbadbcdcbcbcbccccbbbddddccccdcadcdccdccdbdbadaaaccabcbddddbdccddaccbbdadbdbdcbbacabdcbbcddccaadabdbddadbbcddccbacdcbccacddaaabcdcbdabbcaacbabdcbbdbbbbacccabccdcbbccbbccacdbbbadbddccbabddbdcddcbdcbdbaccbbbbbbadcadadbaabdabdbcdbdabcdcbbdddbbbaaacbadabdaccaacaacbbdbcabdddddcadabccbcdcbadacdabbaacccccdcccccaaacddabcbacdbdadcccaacdaaddbbacddbdaaacccddaabaddadccacccaccabbaddbccabbbbbbdaaccdbdcbcdddabbbacabcbdabacaccbdacaccaddbdbaacadbbacadcbcdaabacbdbcbbccadacccbcbaabcdddaccdaabcdaacadcaadccbadcccddcaaccccbbacdbadcaaaacddcdbabbaabbcadacacbcccbbabbdddacccdadcabbdadabcdccacdcccdbacdaacacabbdacdcbbcdcabddccdcccdcdbbdabdbdaaadbcabaccaabadabdabadbdabcbcdabaaaabadbacdcbacabcbdadabbaaddbbbbcbccbdacbdcdbabdabcabcdbbcdcbabacdcbbddbaccdadcddbdcbddbccdbbaddaddbbdacbbcdcabbddbcdcdacadbacccbccdbbbabcacdadbbdbbadabccbdabccbadbddcddadcdcdaaacacacadcbadcbbaddddbaaddaccabdbcaaacadbbdbdaadaddadbabcaadcbcbcbcddbacccdbcdcbcdacacddccdbabdddbbabdcdccabccabcccdcccababddcdabdccdaababdbbdababcbdcbcbbcbcabcbbbabcddaacadcbacacbbaccbcbacacddaaadcacbbccadcdbbaaadadcbcabcbcabaacdadcbcbccbaddacacbdcaadddcabcdcaddabdccaaabdacbdcdbacabddbcdacaddabacddcbbcdacbabbbcacbbdbadaaadaccadabcdabadcdacbdbbdcbaaabddcababcdcacccdbbaabaaddacaacbbdadcbddccaddaddbccbaaddccddccdcbaacababdcccadadbddcabbcbdbbadcbbadbdbaaaccbbbabdcbaadbccaadbcbcbaaacbcbbdcbcdacbdabccaccbabaadbcbcabccdcbbbbadbadbcaacdcaadaacbdbcccdddbbbacddcacbcbbddbdbdddadbcbbcdccabcdaadabadacddddbcddaabdacabcbdbddbdabbbacdcbaaccdcccbdbdabcbacbacbcbaabadabaaacabdbddbdcabbdabccaabbabacadaacadddddbdbbabaaaacbdbbbccdccccabbaccbcbacbbcdbcacaabbddddabddbbccddbcdbddbbdcbbcaabaacdaabbaccacdbbbbcdcbcdabbbdddcbccadcddabccacbaaddcbbdccddacaaaaddcdbaaadaacaadbaccbcdabaaccbcdcdacbacaaccbdabaadadabdabbccababbbccabacbddcddabbdcaddacdbcaddadddabcabdbdcdbccddbdccacdcbdcbadabadbcabaabcddbcccaabcbdaacacbbabcbaccdddabbacaaccbdaccdccdaacabcddacaabbaccadcdddbdbbdccccbccbadacdadabcbcaacbcbbdddcbcdddccaabaddbccabdaacacdcddcbbadddbdabccabccbaadcbadabccaccbbadbbacbabacbabbacbbdaaadaddaccbbccddccbbaccddbbabbdcdbaccaacdcaccabaddbbbccdcabccdaddcbccbbbcabcdacaabdacaabbcccdcaaadbdabccadacaaddbdcabaaadaabdadcbcacdbbaacacdabcabdcdcddcddcdadccdbcabdcaacddacabccbdadbdcbcacabbdcaccabdcdbdbbbadaaabbabaccdcbaaddbadcabdbcbaacaaadcdcaddbcadddabbdbdbdcaddccdbddbcbccdbbacaabcccddbbddcdbabbbaabcaaacabbcbbadbbcaabcdcbddaaaccdcbbbdabbababbadccbcadbacbabcddcccadcaabacdbadbabbbbadbcdadbbdcdbaabccbbdcbabdaaccddbbccadbbdcbcbcdddabdaaaddadaaaddbaddcadbbcbdaccbdddaadaddaaababcadbbbdccdabbaddbacaadbdcccbdaddaaccaaddcdddbadbccacbddbddbcbbdcadadacbcaccbdabaabdcccbabdcaaacaabdcbbbdcaadddbdcccbcbcdccdbaaddadccaaddcddcabbccaaaaccbccbbdbbbcbaabbbbabdcbdbccbacbbdcbbdcbbcccdaddcbcbcaabaccabccabbccddaabbbbcbadaaacddacbbadddccdccabadacbdaddadadadbbdbaaccdaadbbadcaadddacaaccdadcadaaddcadcbbcccdcbadabbcaacacadcdbccccddcbcdccccdaacbcdbdcaddbdbadcddcbbdcccbbabdcbdbbbabcacbbbbdbbaacbacabbdaacaaddacaaabbbcbbbbcacdbdabababaacdbcddcbdacaaabddcaccbcaddadacaccbbaabcdbcaadbddaaaccccadcaaddbccadccccbdcbdddddadbdbdbacdcaddcbcddbbaacbaddbbcdaaaababcbcbcabaaaccbcadacadcacabbdccabcabbdbaababbccadcdddbdbbdbdabcdaccacbbbbadcdabadababcbbcabadbdabbadaacbbbcccddaddccdcdcdaacdbcaabacabdbaaadcdcbbdcbadbdccabcbcccdbbcbccdabbcccbdacbddcdacadddabaacdaadccdbbaaaacbdccabcdbccdacbdbbdbaddbdcbdabbdacbdaddcdbbcddcddacbcaabcbdbdbddadbabcadddcdbdbbcaabaccbaccbbdcdadaaabcacddcaccacaadbdaabdbadbaaaaddcdddbaacdbacbccbaccabccbcabddddacacbcbadaddcbdaccdcaddbccbabcbbddbbabaddddadabdcccbdcbbabaaccaccbbdadddaaabdbddacbbcaabbddaaaadbbcdccbdacdababbacbcbcccbbdcadcadadbccbbdbdddaababbddabcdacbccbcbcdddaadadcaadddcadbdcaddbdcddddcddbaadacbaabdcbdbbcbdccddbadbacbddacbbabbbdcbaacdbabbabaabccbddcdabdddadccccdaabdccadaccdbdcbcabcdadbdacbdbbbdacaaacddbdaabaadbcddacdacdbccadcdbacdcdadbdacdbadcabbbbacbbaaddcbaddcaabdbbdddcacbdbaacabbdbadcccbbdcdcbadbcabbccbccbdddbadadcbdccbaccacddacddaadacadbdabcbdcbdadcacdaacababaadbdadabacdcdcbbbbcddaddddccbdddcdcbcaaccccabdcbaaddbaaabbbdacaaaccccbacbdcababaccabccbadacdbaadddaabdccadabcbcaabbdcbdaaddbdddcbbddcbbbcabdabaadddcdcaaccbabdbacaddccdbbbdbbddcadabcbbcdaaddcdccccdbcaddabcdcdcbacccaaadbdadaccdbcdabcbabaadabbbcccdbacbcdccaaabacadbaadcccadaabbadccaaadaadcabdabcddaaabdbcdbcadbbdbcccccdcbccbacbddbbabdcdbcdcabbcdcddcaacbabbabbbcadbbadbcabddbadabccbabaadcabcbcaadadcbcdddcaccdbcbaacdbadbddbbbddccbabdcadadabcbaddddddbdcdddcaabaaabdccddbdcbbdbadbcadaacacddccbbdaaaacdaaabaacaadcbabbbcdcdcadbadaccbaabdaddcbabacbaaadacbbabdabbdbcacaddabaccbbaccbcbaccadbcbdacadadacdbbddabbbcaacdacbadbbacdbbaacaabbadcacbcbcbcbdadbacddddcacdcacdaababacdbcccdaabbcbcddcdbbabbcbdccbadccbdddaccbbcabcabcdbabbcdbbcdddaddcacdcadcaabdacbabaacdadddbbdddaabbcdcdabccadcddaaddbbcdaaabbdccdcbcddabcaadccbcabaadaaaadcdacbdbbccddcaadcadbaababbaddabbabaddcdbdbddbbbaddbccaabcdbcbadbccacdbacaadcaaccbadacdbabdcabdddbccbadccadbabddcdcbbcbdccdaacccdccacaadcdddbaacaaccbcdbbccbacbdbdacbbbdcacadabcdccaabadbbadbcadcbcbdacdcabdbbbdabdabcadbcdbdbdddbacbacbdcccdcccbcdbdaaabcaadcacdbcaddbcbdaaabbdaaccbabaddddddaddadbbdbcbbcdacabcddddcbbcababadcbdacdaadcbcbcadbaabbdabdddccadbacaddacadacabacbaadadbacccbbbddaaacddcbbadaabcbcdcaaddcacdbddabdbadbdcbddddcddaaacbbabaccabdbdabccadbdaaaddcdaacaaabbbdcbbcabbdcaabcadddbdadabbddcadbcaacbbbbdbabbddaaddaaddadbdbcdabcbabbbaaccddcbdcdbbbbdcdaaddccbcacbcbabdcacabddbbbadcdcabcadabbbcdcdcbdbbcbbcbbbaadbbcddcbbcdaddddcdccdcaddaabdcccdddaddcdbcdaadabbaaaaacaaccdccaddaadbacbbbbbcbcbdaadcdddddaacbccdcbbdccbababacaccccaccacaadabdccbdabbbdbcccdbabdbbacabccaabdaacdaabaccccbcccaabdbbcbbbadcbccbdcdcabdcbadaacdcccaabcbdcdaacdddddabbbccdbbcbadbadbacadbabadbaaaabadabdcabcdadbabcadaaadadbdcdacbabcbacbdbcbbbbdbbbabaaaaddddccccabaddabcbbdddcbdbcdcccadacccadccdcbadabbdabbdccbbaaaadacdaccbdcbbacbcbcabcbcddabaabdcadbabadbdbcaaaadaddaadcadbcbdbbccbcbacdcaaabdccaddbbbddaddbadcddcccacdabaacccdcaadaddacacacaddadaaacabdddbabcabbddcbaacbbcacaddcacabccbccbadacccbcabbdccccbaddccdcbbaddcbdbadacdbcdabdabddcaadcbaababaadbaadcbdbccbaacacadcaccbddababccdccdcbaacdbbaacadbbbcacddcacacdcbcdbaabccdbbdacadaccdadbddaaacabdadcbcabdaccabddcaaacaadabdcdbaaabbddacbadbbbcbbacbcdaabccddbbdbccdcccbaddacdbdaabdaddbdbaababbbdcabdcdbcdabcaccdcbbbdcdddcbadcdcadcbbcdaabccbdbcbbcdcacdcbbbaacbcacbbcbcbcacdbbabcdcbcdbababacbcdbdabbabbbacdcccbcbdadadcabbbbcbbccdbcbbdbaaadbabcabbaaccdddcbbdaccbacacabacacbbbbabdbbcddcdccbcbcdcdaddcddcacabdccababccbddddddbcccdcbbcddaaddbcdcbbaadcabdcbbcbcddcacdcdadcbabdbddddcabcaddcdbbbcccacdabcdbbadccbbcdbdcccadddddacbadbdcdcacdcccaccdadbccbbbdbbaaacbadcdccdaaadacccabadcbaaccbadcccabbaaadbbcdaddcadaaacdccdccbcacdccccdbccbaddacccaaadaddcdaaaacddbbdadcadabcbcaabdadcaadcdaccacbabbacadccadabadaabcccdabdbabbcbdcdccacdbbdadbbcdacacadbbadbdadabbcddbabcdbacadcbdbaacbbabcdaadbbbbbdbbdccccbddbbbabdacaacaaacbbcdbcbadccdaddaabbdabcbbbdcacabdcbbaaabadabcacdbadcdaacbbbcbbbcbbcdccaadbbaabccccdabcdacdaadcabddcbbddaabccdaaaacdacdcbaaaabacdccbabbcbbcdcacdacabdddabbdcdbbcdccacddbdbabadadddadcddbababaacbaddcabaacabbcddabbcaabbdadddccaacdcaccbcadbcccdbbabbaaacdadccadbadddacbadddacaabcbdcbbccaacbdababadccbadbdcaaaababcddacdbadccabaaadcacaadbcaacaaabaaabbdcaabbbcdbbaabbdcdacaaddbaadadbcacacdacdbcdbbabdababbbddddcaaadbdbaaacbbbbcbcdccadcdddddcbacbaabbbadbdbbadbdcdcbdcaabbaacaccddbbacaddacbbbaccdcddbcdcaaaccacbbcdbbdbdcdabbbcbbccdadadbdddbcabbaabdadcbbdcadcadcbaabccadcdadbcdccaacbccdadbdddcdabddacbbacbbddaadabaacaccbbcadbcaadcadbcccbcbdddccbccbccdaaccccaccdaaddcbccdccabcccadcacdbdacbabdbbbbacddcbcabdbdcdadaabcbadcccbadbdddbbddbddbcdccddcadcdddacbaabcaaaaddbbadbadbdcdcdcdbdcbdcdaabcdbcababdbdbbcbcdacaadddaabbdcbcccacbaababddcaaabbcacbdcdcaadacbdcbabbddcdccdaadbcdddadcabaabddbcbddccacbbcadbacbacdbbacdcdacdbbddcdbbbccdbcdbcaabdaaadddabdccccaabcbdabcccccccbdcaccabadaccacaacdbddccbbcbbbdbadbacadacbcbacdaabbcaccabcbabbadacbddbadabaabaacdbcbbdbbdaabdadddacbdcddcdbccabaaddccccdbaacbadcabcacccccbddadabacacabbccabcbbbbbcbbbcbabbaccbacbccaabbaaadaccabdaaaddadddbadbaccbbdbbdaadbcabcaabadcbcbaaadcadbcaaccabbcaabdcaadaaaadacdcddbabbcdadaddcaabddbbaabddddbccbdcaddcaccbaadbbddccdcccccadcbcbabcbcdddacabadbcdbbbbccddacdcdddcacdbaccdacbbaaacccdbbcaabcabbdbddabddadaaaacdbccbbbcbddcdbdbdadaacbbaccdbcadcdcbdbadacaccdbdbbacdbdbbbcdbdbcbbabaabcabdbdbdababbaccbdbdbcdddbcbcaddbcbbdcbcddbacbbadbbbaadbbcdcbccbcbccbdbadbbaababcadccbcddcaabcdcacbddbcbbaacbbabcaacbaacbdacddcdcbabaaacccacbdcdaccdccdcdcaacabcdcccabdacdccdddaacabbcbddabadddaabbcccdcdcdabdbbabdbbdbbcbabaacaddcacbdabcadabbbaadbaabcbabbbbbaaabbccdaadcccbacdccacbbddaabdcaccdabccdbcaccbacabbbddbddcccccdabdacbcaaabaacddacdcddbdbbaadaacdaaabcdaadbdcbbcdaaaabdbccdaddbcadabadbcabbddcaaaddbbbdbbcadbbccbbdbdddcbbcbaababcaaddaabcaabbdaabccdddbaadccdbbbadadabaabbbccabdbdbadddaacadbddccdbaacbacadddcbccbabbdaadcdccccbcdcdbdcababdbadccbcadcabacbaccbabbdbcbbcddaaddcbdaadabaacbcbdcdcaaadcaadccadccaabbcbdddbdccbabbdcbdaabacbabbdacdccaccdacabbcbdcdaaadcccdccdcdccaadbddaddbccdbbdccdbccacbbbbdbdbcdabdcacbabbdbbbdbadcaaaccbcacacddcaaadcdabaabaaaaaccacbdbaaadddaccdbbbabdcbcdddddcbbaacdaabcdadccbdaaaaabddcadabcadcbbcbbccbbacacadcdbbbdbdbdccbcaccdcbbbabddacdabccbabcbbdddccccacbabdabbaacdcbdbbaddacaaaaccacdddccdacbacbcaaddabcbadcbccdcdcaaadbddbadcdcaabdccddadbbdcababadbacbcdadddabcbcaccdddcdcacdbbbcbaadbcadbadbabbbdacddbcbaadcccddacaabcadaadcbdbddbbccbcabcddbdcbdcccbbdcdbadcaacaaaabbaabbbcabbbbcacbdbbccabdabcacbdbacaabacbcddcacdddbcbbacabbdcacadbbbcbdabdbcdabbdbdabbdaadcbbcabdaabdcacbaaacabbcbadcbaaabdbdacadbcaddcddcadddaaaddacabcabcbdcdcddbdadcdcbdabcbdcdcaacbaaccacbdbadbcbddddbddbcabbabbbbdaccbbddabbcdaacabcdbbbbdabcdddbccdccaccabacacbbacaccccbabbaabccadbdbcbababbbadaccbcbbcaddbddccdcbcbbacbccbdcbdcdaccdbbbdacbddcabaccabcbabacdbbacdbacbbbbcddaacbcccabadadbcbdcbcaddddcdcbddabcabbdbddbcbbaadbdbccdcdcbacddadbbbbbacacdcbcbadcddbddbdaaccacbcbcbaababdbddcbbcaddaddccdacbbbdbccaacdaddccccabbcabdacbdbbcbadbadbabbdbcdadccbdadbbddbdcbaadabbcdaaaaadbabacaadddccbcaadcdadadadbabdcdcbdddcadababbbbddaadbdcccdbadaddddabcdcddaccaadbdbabbcdddccdacacddccbaaaacaababdaabbdcaacbccdccdadbaaccbadbddcbadaddccdcccdbcaccbbdccbcadabaabbcabaccbdddbabcbcbcdcaccacccdcdaaaabbbadddbbabcbdbaddbdbcbadbdbbcdddcbcdcadccbbdbacababaadddcdbdadccbddcdcaaaadcccddbcdbacdbcaaabbbabacbbabcadabaadaacbbdadabaaabbcdcddababdccbdcdaaabbaccccbccadcaacbbdccaacadbaadbddcbcbddcabdabdccaacaaccccdddadbcadcbccbdbcbbacdcbcbddcadccaccddccbbdcbcacbdabccabcacbbbbdbcbddaaacbdccdbdababcccccbcbcddcbaccbaabcabacccdbacbcbaadbbcaaabbaaaabaaacdccbaddbbbcdaccdabbadcaccdbbcdcaccbdabbbcacdbaaabbbbabdcccbaacdccbcdcdbaabbdcabcbbbaaacaabbcbccbbbddbccccdddacdbadcddcbacbcddcdcaadacbbccabdbdbbaaacbaadcaccadaabdcbbddbdddcddcaaaaaacbdcddcaadcbbcbaadddcabcdabdcadddcccdcdccbbdddcaccdbabdccbbdaabcdcdcdacabadcaadbcaacacbcaadcacdadcadaccabaaaaabcdcaabdcadbbbccacdbbcabbbaaddacbadbbbacbdcdcdbdcabbacbabcaadddbaacaabcdbcbbdababacbbabbdbcbabbcbbbcaccaaacbaddaccddcbcdcacdcbccbdcbbbacaacdacbbcacbaaacaabbdaabaacbddcbadbaddcbadbbdbccbbdacadcbdaccdbadbbabddbacbddddccbdbdabadddaaabbddacdbabbaaaaccacbdbbbaddacdabcbdaaddbadddacddacadcbbacdacdbbdcdbbabcbddccccacaabbccddbabdbcdccaaaacaccbbacbdbdcbcdcdbacdbccabbacbdacadccdadccbcdcbcbccbbcaaaaaacbddcadcacaccdcddbddbcacadabadacbcbadcabdcbccddccacdcddcbcaccbaacadbaaccbcacacdcbdabccccbaddbdbdbccdbcddabbbddddccabccabdccccdbcddbaaadbaaadabcbabaabaabbbdcddcddddbccdcdacaacabbdcccacadbbbcaadcaadcbccccbccaddccccdbaaadbdaaadcdddababbcccbaccdcdadcdbdcdddabdbbbaabaddadcdcaabddccbaadacaadcadbdddaadbcbdbcccbdddcbbbdcbcadccdaadddbcbbcbdddddbdcbdabccdddbdddcaabbbcbdbacacdbdabbccdadcacddabaabbdcbacdaddaddbbbadbbbaddbbacddbcbbbcdcdbbdccdcbcbaaddcdddcaaabdadbddcdbdabcdbaadddcabbcbbdcaabbadcdbcaaaadcdaacbdcabdbaadbdccbcadccacaabdbbcabaaddadcdbacdbdddacbbcaacaaccadddddadaddcdadbbdddcadcadaabcdbdcacbbaadcabbdabdccbbabdbadcdcbabdbbcdadbabcdddacdddcadcbbdccaacabadccdadbcacdcbcddabcbddabbcaabdbbdbbdacdbbbabcdaaaaacddcdbadcccabdddaccacbbddcadcaccdadadacdbddadbccabaabbabdcbbdbacddcabdcdbbddabccdcadcdbbccaadddcbcbcdcacbabbccdaccccabcacdbcdaddbbbcddabdbbccccaadbccdddbcbbcdaacdbbdccccadbcacddacdbacbdbdccacaddabddaaacaadcccccdccbbbabbdbdadddbdcccaddcbcdddcdaccccaacdddbaddddabacadddacaaabccbcabdcaacbacddcddbcacbbdcabbdbcbccccadcdcadacabbcbdbcddadaadadbadbcdacaadbcbdabaccdcacdccdbbbbcdaddbcbbbccdacbbaaadccaacbcccbabaddbcacccbdbddacbcaadcbacdbcbcbcacdababaabdcdbadadcbccabcadddacccbdaabacdcccddabacabbdaadcbdacabadcacaccccbbadacbcdabcaaadddbdbaaddcbbadbdbaaaccdbccbdbcbbbcbbabdcacdbdbdbdcbcddabbcadcccbadbbbbacbabcaaaacacdbababccdbdcacbabcbaaddbbcabcccdbbcccaadacbbcddcdacbbdddaacababdbbccccbacbddabcbcacbadcccbabdccabccacddbbabcadcccdaaacdcaaabbbbacacdabadcacababddcbadcdbbbcdbdbaddddacddbbabacdbabbadacdccdcbdddadcddabbccadacbcbaabccbdcaddadccddbbcdaccbacdcccbcbbbbdbdbdcaaacdbdcabadcaaddcbcbadadcccbcaaaaddcaaaddaacdcdbcdadbddccacddddcbbacaccdddbabacccabdbabacbcaaddbdbccddcdadaddbbcabdabbacccbbccbdadcbbbcbddcbdbbabbaddcdaadaadbcaabadcccabaaadabbddcdabbbbaacadbcbcbcbbcabaaabddabacbaacccdacbaccdbdcaadabbbdbddabcdcaddcddbcacdbcddadccdcaaddcbcdbcbdaabaaabdcbcaabacdcbcccaabdbbbdadbabadadbddacdccbcaabacabcbdcdbdbbcbadcabcdbccbbbcabddbbdcadbcdaaabacdadacbccbbadadcaccaddbbbbaddadbbaaccbcabbdaaacdadbcbabdbcdabbddbcaabdabdaaabbddabbcddddccabbdbbcdcdabbccbbbddadbbaaacaaaacddbccacacdcaabbdccadcddccdddcbaaaabbaaacaccccbbcaddcabdacbabdaacbbddcccabdcbbdcaabbbacccaddbbbbbcabdbcabaaddaacacdcaaababcdbabccdabbdacbbbccbaaacdccbadcddbcddadcabaaddbabcbbababacbaaaddacbdadaaaccabcbdcddcabaddbbbdaaaadbcadadabbbaddcaacacdabbddbddcacddcdadcdbacaacdbaabaddacbabacddbacdcabbccaabdadaaaddccadbaababddcbcaccababbaabddaccbaccbdabdacbdbabdbbcadcabdbcadacbccbaccdcaacdcdbaacaabbadcaaaacdabacacabbccddaddaabcdbabbbaaaadcabbdcddbcbabaadbabdcdaddbcadcadaadddbccbabcdcbbcadddaaadbbcdcbdababaddabdbdbcaabdcbdabcadbcaddbaddadbabcabaaacaabcacbbcbacadadadbadddadaddacabbdbbddbdcacbbddaabadddaadbaadcdcaaccbcccabbcdabccddadcbccbdcbdcddbccdcbcabaccdabddacadbcdddaabdabdbdacbbaddcbbbdcdcbbaaaabcacaddabbbddcccbdcdbbbbdcddbdadbbaddcdbabcbbcbcabdadccbccadbddbabcabbadbccbcbbbcabcdaadcbbacccddcaaaaabdaddaadbdacddcaaddcaadcddcccabbccccaabbdbddbcaaabbbcccadcdacccbaababcccaadabbadbbbaaabdccbcacbdbdcaccbdcccdbbdcadaaddcbdbdbcdaddccacacccabacbcabdacaabaabbdcccdaabcacccacbcabdbdcababdcadaacbccdaacbabadabcdbbcbccaadbdaaabadabaaacbdcbaccbadcbbcbcaabbabcdcddcbdddbdababdabdcdccdbaadacadadcbbdcbaddcabdcbbcddbdbabddaaccadbaaaacccbcbadcbaddcbaccccaaacccdbadddbcbcabbccdccabaabbbaaabbdbbddbdccdbdbdcddcbadccabbbdbaaccabcbdccabcddbdbdbdadaddcdddabbaadbabdbccaaadbcdccbdcbabbdbadabdbaadabdccadddddcabcbcddbbbcdbccbcddcabcbbccbbaaaaadcaabcdbaabbbabaccbacbabcbbccdddacdcdcdabdaadabadbbbbdbcdcdadabacccbadaaddbbacbcaaddaccdddcdcbbaadababcddadaacccaddbbbdcccbdacadabdaacdbcdbcabdbaccbdddcbcdadbcccabcdabcadcbacdcadaabdbcaabacddaccbcacabdbaddbbadccbdaaddadbcbdcdddadcbadbdbccaccbccbabbabadbbdbbaacadcdaadcccacbcdccbaacdcddbcdaabaaabaacacdcbcbaabdaaccaadacccddabaccdccabbacbddcddabacdadcdbadacddacccdddbabdbccbcadddadabbaaaacbabbbdcbbaabcaabadbddadddcdbbbcbaadcddcccccbacddaccbbbcaccddddcaabcaabbaccdbbcccadddbadcbcbacaccabdaabacbbcdcaabbdabaacccbdcddcddabacddddccabdbcacbbddcaaacdbadcbaaabcbbbdbbacdbddcccabcacdadccdcddccdbbdbaaacbddddbdcbcdddadddcacdbbbaccbabbbcbabbaddcabacacbbacbcbcdaddacddccbcdacccbddacacdbdbbdcdcaaacbbaacccbcbadcabbbadcaddddcacdcbabcdccdbdabccbccdddbcdaccdadcaacdbcdabbdbccdabbdacddcbacdbdcacacdcaadadcdccbbaaacdadbdaacdababcbccdbcdabbbaddbbcabaccddddacdcaabbaacddbbbbabdbabddcdbddcdbabdbbdbcccbaccacbcacacddcdccacbacaccdbccaaadaccdcccbabcccaaaadbcadaaacccdbcacdababdadbbaadddbdaabdadaadcbddadbcccbcabbbcdbcbbbdccacdaaaddbbbaaadccbccdacaabddbcccbacdacddabcbbddcddccacadbdccdabdccbaaacbdaacddadbccbcdddbbabdaaccabbabddbadabbbbbaddcccbdbcbdcadcbcacacaaadaadddccdcababcbdbdaaabaddddbbcdbccabdddbcdbaabdccbabbbdbadccdbacdcdacaccacbdcdcdcbaacddddccaabababbacaacdcdbbacbbbaaaadbacbbcaaddcaaaccccadcbadaabcaaddbaaccdadbbcabcacdbdbdadadcabccdcbcbacdccabdaaacdcccbcddcbbabdbcbaabbbadcbbaacccbbbbdacbdcadacdacdabdcddccaabbddcbaabbdcbddadcaabcabbdabdcbcbcddddaacbbddcdddcbbbbcdbcacccaaaccbadaccdbddaddbabbccabdbdddcbbddacaaccabdaaaabbbcdbdcacdbbaaacbcacbccdaaddbccccdaddadcddddaccaadabadacadadbcbdacddcdcadcddbaaaabaaadadabbcdaabcadbdadbbaccddbccccccbdacababdbbdcddbaacacbaacdbbddaadbdcacccbcdcdbbcbabacdaabcdbcdabbbaabbcbaddcccbcbaabdacbbdccbcddaadaaddcbacddacbcccbaabdbacdabcdddacbcdbbddccddaabcabbcacabbccdadadbbddbabdacbabbbbabbdbddcbbdcbcdadabbaacabcabacaabbccddbdcbaaacadbbadbcacaabbbbbcdbddddabcacdaccbbbccacaadcabdcdddabadcdbaacccabcdcdcdcdcaaadbddabababdbdabbaaacdcacdddacdcbdbcbdbbbbdcdaccbcbdcbacdbbddbaaababbcbddadccaccaabacccbbddacccabccaacddbcbdcdcdbbaaadacaadadaabbdbddbcddddabcbadcdadbdccaacddbbcdbaadaccbabcccbbdbdbdbdbbbcdadabdcabacaaddabdcabadddadadbddadbbdaabbabbbdadbbbadcdaaadacbdccacacccccccdcacddcbdcccbacdbadaaddcabddccbdabbcdcbdadabdbaacabbdbbababcddbabaadbdddaddaacddbcadabbaddcdbdbabcdbcbdadacdccdbbbcaccdbdbddccadaaabbcbbacacbabdbccddcdabcbbabbaddabdadcdccbdacadcdaadaadccbddccadabccccbcacbbdbaaaadabddbccccacaccabddadddacccdabbdcacccdddbcacccababbdbdbbabdadabcdcbcabbbdcdabbbdbddcadadbaacccabdcbaddbdbdbbccbabcadaadbddcdbdadbdcdcbccabbdabadaaabadbddaaabdcdbabbbdccbbdccdccdabcadbbcacaaadddadbbbdaadabdcbbcdccdcacabcbcdbbdabadcdcbdacdaabbdddcacbcddbcaccaccadcbbcacadcccaaddadbddddabdcbbbababcdcaccbcbaacadaadabaacbcdabcdabbcadccccaaaddaddcadabbdcadbbacbdcbabccdcdaacabbccdcddcddbaacaacbbaaacbaaaacbacaabddadcddbbadaacdbadcacabdcddccacacdaacacccbadddacdccdbbcbdbabcaddabadcdadaaccbdddcdadaaacbabbdadbdaabdacdccabbaadcbdbcbbccbddbbdbdbdacadcabdacbddbcdaddcdddddcbdaaabdbabadcacbbcbccddcaabbccdddbbacbacdbbdbcababbacddddcbdcdabdbbddabaabbccaadabcabaccddaaadabdadadacabaccaddadcbcbbbccadbabcbbdbddbdbadcacbbcdaacdbddcdadadcbbdaabaccadccaacdccccabbdbdaaddbddabddbbccdbbbadccaccddbbbcdccdbadabdccadadcdbdaabdcbbdcdddaacaaaddbbdadababdbdcbdcbdcdcdddabcbcdcabddbcbbcdddbdcadbadaccddbacbbcbcdcbcddddabdcbaabdabddbccbadddcbccdcccabdabdbddadbabcbdcabacadcdabbddbcabbbdbabbdaaadcdcaabbbcdccbdbaddbcddcadadbddbcddabcdcdaabcaacbbbcdcddaccbbdaabcdbcdaabaddddcbdadddbaaacdbbdbbaddcadadabbdbabbbbacbbddaabcabdbbddbdacdabcbddcdabacbbddddaacddbdcdaabdcaccdcdddccbadadacaabcaddccdababadadabdddacadddbdcdcaaabcacadbcccabdddbbabaacbcdcadbabdddbdbcabdddbabbacadcbaaacdaabddbacbcbdabaabcaccddacaacdcacccbcaacbdcdbbcacbddcdaccbbcbbbdbcadcdbbbcbdbccbdbcccbbabdbbacccbbddabddcadcaaadaaaabbadddbddbbbbbdcbbddddddcddbdccdadbdadcdddaabdbbaddddccbbdbdcaadbaabcdccbcdddaabacccadadccaaacdbcccdaddbacaccaddbbbaccbcacaccdaabbcdbaadbbbdabccbaacddbcdbabbbdabbdaadcacabcaadbabbcdcdbccdbbbcabddcdbcbcbbbaddddaacdbcbabaabbaddabddcbdcdaacadabbbaccccdacddcdccdbdaaddddbdcbccaddddacdabcdaadbcbdbccdaaadccddcbaadadaadbabbacdbdaaccaadaddbbbcdababadadbababcadaccdcdbbbdbadaddbddaadcdacacbcbbacbaccadadcaabdbcdcadbbccdbdacdcbcbddacaadacddaaaabcdbccacaaaadaabbbdacabbdddccbcacdcdbdbabaabdbacbbacbdcadbccdccdbbddaabaadcbadcadbdcaccddcacbdbdabbbababcbdbdbbadbcaacdbacdbdacbcaabdddccbbcbbcbaadbcbdaadaacbbbcadbaadabcabbdbbbacccacddaacdabbacbcdcbdddadabdbcaacdaabbadccadacaababccbabccbbaaadcdbbdddbaadbbaddcdcbbbacdcdcaabcdaaacdbdaddcbdaaabacdbbcbbdabdcbcbdcaadcccbdadbaadbdbaadbadbaaadaaddacbccabbcbadbdccacaddbdadcdcdacddbbadabdabdacaddcacabdadbcaabbdbbcdcacbdbbcbacccacbdbdbadbdcdddddddacdcbdadbbbaaabddaddbccacaaddcdacbbaacdcdaabbcadbacbdaabcbddddacacbabbcdbbabdbdacdddbcbacbcccababbddaaddcccabdcacdbbbcbcacbbaaddcacbcdbaccabcdccbdcbaddbadbdbccdbabacabcbdcdabcdcbcabddadbcabcdcdacbcddbacccdbaabaadbacdbddbbbaccbcacdaadbdaabcacbabbbdbdabcbcdadcdcdbcdabccaccadbcabcdaacadbabbbcbcccddadaddbddbacaadaabaaaabaacdbabccdcadbacbdaabcbadaccbcbcbbadcddcdddabbacbadabbdbadacdadcaabdadcbcbcaaadcddaccdbcbbacacdcccbabdadaacbdcbabbddcaadbbcbcccdaadbadcbdcbddcbdbbdddaabddaddcddbdcbdaddddaddcbcbcdaacadaccadcaccdbadcbcbcadddcabcbdaabdbacdaccddcbbbcdaaaabdddcddbcbaabbcddabacacbdbccababbadaadacccdbdcabbdbaaaaccdbbbdbddbbbcaabbdacdacbdadcadcabbcbdcbbbaddcacdabababacdbbadbdbbdacadddcadacbbcacaabadbddcbcdacdadcccddcddbabdabcdbaddccbacbbbccdaabcdcabdadadcdcaaddaaadccabbcccbcaaddaaabacdcbdccbdbcbcccdaabcccbccdcabbbbccbdbabcadacdccacbdadabccbdbbcbdadbddbdcdadacbdbbbbcaaaabdbcdbdbcbbbdbbdcbaadacdccccabbabcbbcdacddddaadcccaddbcabaadbcaccbddccbddabbadadddccadcbcacdabddbbbcbabbbadbcaabcdcacdadbcbccabbdbdcbaabaadbabadbdcaddbbbcaadbdbcbacdcdaabdbbbacabcbbdaabbcdbcabcbbccbbbcdabbcacbbcabbcabcacaccadabcddddbdcdbddbddbddabbadbbdcdbccbbdaccaabbadaacbcddbbcababbcccccccabbccddacababccbaabdbddccccbccbdbbbcacddbbddbcccbddaacaddccdcdccbaccbcaccacabcacbaaacbbdacddbacddbdcbbcaaabddacdcdbbbadcbadbcbbddaacdabacacacabbbdaaccaccdbbbcccacbaaaaabbbdbaaadcbbdcdcdadabbaadabbcbabdaacdacadbdcbcdabcdaacaaccccdaccbdabaacaabddaddadcadbaddbdacbdbbadaaaccdcaaccacbdcdcbdaadbbbbaaaccacdbbcdddcdbdabcbcdbdabcadbbbcadbcdbaccbcbcbadbbdbaadabbbbdaddbddcbccdbcabcbddbcacdcdbaddacadddabbadcabcdcbddbacbbcbcdcaccbccdbddbaabbcaacadddbdadddcacdbaaabccaccaacbcccacaadcaaabdbbadbdadabaccdaccabbabaaddbabdadcbbbbccdaabababbbcdacdbdaccabbacadabdccbbddccacabcbbcacdaadccdaddcdbacabadbaccddabdbacaddcbdcbbbcbadcadabdadddbddbabbccbacbacddabcccaddbabcddacdddcabadcaaadababdbabbdbadaadcabddbdabdccaddcbacccbbcdcaacbdaadadbadddcacadbcdbcabcccdbdccbbccdcdaddbddabbabaaabcdbccbccabcbdbccaaaddcbdddcdbdccaadcddccddbbbccaaaabacacaaacabdbabdcbdbcbdadbcdcacadcacbdddcdbbbddbaaaabacdbdacdcdddcdcddcdcdcccccbcdabcacacaddacdbddddcbbbbbdadabcaacccbabddaaadddadbcdaabddbacbcbcacdaacccbaddabdccddbbacaabcadbbdbaabdddabcbaabccdbacbbdbcdadddbbacbdddbcaabacdcbdcdaaadadacddccbabbbacbdcbaadbcacbbbcbbbbdbdaddaaaddbcaaddbdbdbcaabadaabcdcbbdcbcdcccbaabadcccdbabbdcbbbbaadbacdcaccbadacbcdcccaaaacbbdbabbdbabbbcddccdddbccacbbacdbbabbcccbaaacddabaabbacbbadbbcdaabcccdcddbdacbbdddcdbdbcbabbbcbabccccdaacbcdadabbccadaabacdbcddddbcbcddbddadcbdcbddcbdaadcddadcaaadcabaccbaacbbdbbdaacbcacabdbaacabcabadaacacddcccdaaaacbacabaacbddcbdadbccddcdadddabadbcdaabcabcddaccaadadabaddcbccabbbadbdbaccccbaccacccdaabaaaaaddbacabbccdbbabadbaaddcdabdacddaaccaadadaabbddabdcbdabdaccabbabcdcaaccdbddcdcbcbbdcbbcbcaadaccbcbdbdcdaddcbdadadccbbadddbcccccbbbccbbaaccdcbacabbcbadddacccaddaabddacdbabcbccccdadddbccacadadbbdccabbabcccbdaadccbbbcbccabcaaabcbdccdaaabdaaadcbcdcabbbccabbacabdabbcbdbdbcdcbcaddbbdaaadbcadabbbcdcdbcdabdcbccabbabdacccdbbccbaccabdcdbdbcddbadbacccbdccddcbddaadbdcaabacbaddcbdcdddaacacdccdaadccbdabcacaabbcbaaadcbcdbaaabbaddcdabaaabdddaddccbaaccadbadaabdacdcbddcaddadcbddaccdddbcabdbacaabccaabaadccdcaaddaabbabdaddbcccadadbdbdbdbcaccbbdcdbaaddccddcdabccbbdbcbbbdccbdddabbbcccabcacaababcddbaccddbaadaacabbcdacccbadbabaccbccbbcdcccabcbabcaacccbcabdcbdddbaddccaacdbdaddaaacbdddbabccbacbdacbacddddbaacacbacbababbbdadcddcaccdcdacccdcabddaabbcbccbbacdccaddabbdadcabaddaaaaadcaddbcbdaacbddadbabdadabdcdbbdaddcbdcadbcbcdbabbbdadcdbacabbccdcbbcdadbabccdacaadbcadbbcabadacaaabbaabbbadbabdaddcdbacbcababdbcdcdbcbdcaaddbbababbdcbddaddddbadaacbcdaddadaaaccadddcbcbcdbdcacbccaaddbdccdddbcababcbbabccbbbdcacdbcacdbcdabdabbcadbcdaaacbdbdbacccbbdadbcdbddcacbaabdddadaabdbcccdacacccccdbacbacbddadbdbacbdbadbbdabddbcababcbdbabdddbccaddccaaacccbbaaddccccdbbbcadbbacaadbcccacabadaaaaccccbbbdcdddccbbbbcacdbddbbbcdddbcabaddacadabdbbcdabdbcddacaccbddcbdcbcbdbabcbcbadcbbbacddddcacaddccabcbcbdbbacaaddbcbabcdcbadbdcdddcbbbbccbbddacdbdcaacdccbdbcccbbddbdccaccaadacdadbbbbcccbbdccacbbdbcdabacaaabbacacbdbabdbdccdddcdbabdabdbaccaddcbadddacdcacaadadddbbccbcddadabaacdccbbdcbdbbbbdabcabddbddbbaccaaabdccdababbdaccbaaadacbcdbaaadacbdbbcbbdcaabcacbcdbbcdcbbcccabccdaaabddcdacacdddbcabdddcbdccccbbaccabaddbbddaabacadaaccbbbccabbcdcccaddbbbdcaabadcaacaaccaddddddccaacabadabbadcaacdbacccacdcdccbcddbbaaddaaaddaadcbaadadaaadadbdaadbcccdbaadcbccdbbbbdaccadccdcabcbaabaaaadaaacbdacdbbabbaabcbabbdadccadcacacaadddaaadbabcddccccaaaaccbadbbcaacadaaaabcbdadccbaadccadcddcdcdccaccbabacbbaabbbcddbadaccaaadbcbcbddcdbadcabcbcdacbbdbcccadabaabcbdcddacdddddddbcabccbadcbcacaadddcccccbbcbcbdaaabdbcbaaacbbadbbbccccadacdddcaaabdbdcddbadbacbcbccbccdcdacbbacbccccccabbabcdcdaadbcacbdbdabcdaaabacbbcddbbbdbdddbbddcccdbacdabaacaabadcbcdccabbcccdbcdcdccadababdcccccbdaddbcbcbcdabbbbdbdddddaaaabcdaaabbabababaddabbcabbbacacdcdddbdbabbabcbdcbcbdddbdbbdcaddccddbbdddadbbcdacccbbdbacccadabdcccdbdcddcacbbbccbdaabbcdcbbdaaabaaabdccadcacbccdddbaddcbaabddaabcbdccaabcbacbcdccadcdcaacddadaacbaabaaacbbddacbcbdddbdddabadbaaaccbabadcbbcbcdddddcdcabbccbbabbdadcabbbcabccabacaacbadaaaaabbbabbbdbcdcbadcdbccddbaaccbaccdbabbaddbbacccbadbdabdcdbbbdadbccacbbddbcaddacdaddcbabbadadcaccbbcaddcdadbdacadbaabababbbccabbcabcccdadacbcccaccabbaadabaccabbcbbcdaabdbadaaaaabdabddbbdbbcadabdcbacbbbadbdacbcbbabdacbabcaacbdbccaadcbbaaddbdbacabbadadccdabdbcacdcdcbbdabcdbabacdcdaaabbdbaaabdbabbbddaaaccaccdcacdacaababdbcdabaaccaadccabbbdbabacdabcdaadadddabcbbbdaaaabaacbddadcbaddcabdaacbddbaabcacabbdddbcacccdcacbbcabccbccdcdbdaacdcbddbdcdbcbdcabcdbcbcdbbaabaabbcbdaadcbbaddbbdcabbabccaccbadbacacccbaddaaddbacdcadbcccdcbcbbacccbaacccaaabdacabaabdbbcbcabcacacdcdabcaddbdccbccbcccdbcbaabcdadcabbddbbaadacacccccdaabcbbcddddadabcddbcbbccaaccaddbcbcbabdcaadddcadcadddbabbcdacdbcddcdbdbddcdaccdccdddddabcdcbcadaadbbdadbbbdbaacadabccccbacbbcacbddaaaaadcbdbadabcbbdbcdaacaabdaacacadabcdbddbcdaddacdddddddbbddaabddaabadbbcabbdaabdaaaaaccacadadacbabbcdabcdabaaadcaabbcdbcccadbdaddddbabcbbcdcadcdacdadbdbaaaaaccbdadcccaacbaaaacbcbddbcadcbdbbcdbbcdbdbbbdcdaddaabddbaaabcdaacdcbadcbbdaacdbacbacdccbacabcadcbbbbbcccbbbbcbcdbaadaabdadabbadcacbbdcdccdcdcacacbacdcccadddabbccdddccaaccacccacabcadadbadcdaabbdcadadbbbbadadbaaaabcaadbabdcbbcbabbbadbdbbaddbabbdbdcbddbddccdcaacadbddccaaddbbaddacaccddcbcdbdcbacaccbdbddcdcdbbdcadcbdbcabcbbdaccbcccccbbdbbabcccbddcbcaccaddabdbbdbaccbbbdccbbadacaadddcacbaabcdaaaacacddccdbdccdaccbdaccddbbaccacdcdcdbabccdbadccbbabadbbcabdccacbacadccadbcbcaddccabdbaabadccdbbaddcdadccdabdaccbbcdcdaabbdbbacdbbcadddccbacbacaacccadbacbcabdcbababcbabcacaacadccacdaabadadddaacdbbdbdbaacdbccccdccddaacbddcddbbcbcbdcddcaaaaddcbabdaacdccdbdbccaadbacddbabccbdadcccbcacdbddbdbbcabbcddbbbdbcabcbabdbbbaaddaabcaaacbdddbcbacbaaccbcdbbbabdccbadaadbcaabcddcabbdbccdcdadddacabdabcbcdaaadbcbdbccbadddbcdcdddddaaadcccbdcdcabddaaddadadaaddcabbddacbcaccbbddadbcdbddccbbaacbdcdbababbacaccbbccdcbadabdaccadbabadacdbdbdadbcdccacacabbbdbbcdcccbadddadbcabcdbcababdcacccaacbbdadadcbbbddbdbadaabcadabdbadaabbcddbbbdccdcdbccbdbcaaaddddbbaabbbcdcbddadacadcbdababcadcaabcacccdbcadadaaaadbaadabaccacbbbcbcbdccabadcdbaddabacccccaababddbbababcbcbbcbbadaabdadbabdadcbdddbcabddcbbbdacbbdacdbccddbbdddbaadcdabacbdbaababdaabcbbbbdadaddccdbbabcdabdbbdacccbdddcaaaaaadcacdbbcbccabcdacbcccdcdccadcbbbaddccbdcbdabbadbaadbcadcabadccdacaababccdaccababbadadbddabcbdddbcddbccccddadbdbbcadacabddaaaaadacabbdbccdcbdbbbdcbaddaccadaaccdabadbacdbdbbdbcabcbaaadbacdcadbdbbadadabcdabdacbccccacaaacbaddbdaacaadbcbacbcdccdbbdbbaacbacbbdcddbbdbcaaaacbcdbbcbaaaddcabbbbccbbccccbaccaabadbdcaabababcaabdaabcdcabcacdbddcadbbcaabbdaadbbabaaaabaaccbbacdabcbacbabcdcdaaaccccddbabddbddcaddbccabaccdbaccabdabccdbbbddcbabaddaaacbdbdbbbccbcbbadbcddbbbdcbcdcbbbcbbaacaccddbddbcdcbdaddaabcdcaacaccadbdadcabdaccaadcccbddbbacbddbacdbbaabcadaabccbbddbcdcbdbaddbabadccabbcddbaabcbdcbdbcdddaadadbddbdccbddccccdcacbcbbccbbddbaaccbcadcabbccbdbbbdccdbccabbcdaccdcacdabbbdaaccaaacaccaabaabccaaadcabdaadbbcccaadcabccbbcdbacddaabdaaddcbbabcbccabdcacbbabcacdabbbbaaccccaaddbcdbccdbdcccabdacbdbcadbdddbcccacdabdcadddaaddaabcbcdbbbdabaabcdbcacabdacbdccababdccddacddabcbbbbcbbbdbabacacbaddcbbbbababcbccbacbbdddbcbbdaadbbabaabdadcbdcdccdadbadbdbbbbcccaabcacccacdbdcdccdababacbcaabdbdcbcaacddcbabcbdabcddadadcdcaadbbdacaabaddabcdddabadbddbcccdcaadbacadacadaaccdaccccdbcaddbbcbdcdbcdcccaabcdcddadbabcdbcdabadcaabdbabaddaaabbbdcacabcdabbdcdbcdcaaacdbadacdcdcbbaccaadcdbcdacabacacdacabcccbdbaabcdcbbcadcabcdcdcbcacbacdaabdbaaddbdbaadaacdccacddcbbaaacdabbcbabdbdadadcccacccaddbdcbbbadddcadcbdadbbadabdbaacaaabcbbbacacdbdcdadbcadadcacbbdabacddbbcacaacbdcdbcabcbdadcdbdcaadcdddcaadadbcabdaacbbdbbcdbbcaaadaacabbcaabadcadbabbdccabaccaabbbdbbbbbcbbbccdddbdbcbdccdcadddbcaccbacbbccabadbbacadddbbacbabbbaabccddbcbddadbdbadbacdccbbacbdbddaccdbbbabadddbdbccbbcbdabcbaadcbcbbccccbcdbbcaadaadbaddbbbadbddabbcabddaacacbccaadcbddaacbdabbdabdabddcabbbcddcacabaaabaccbbbaccbadbadbbbddddcccaccbbdcdabcbcccacabadbdddbbdabbaacbbabbbbbcbdcadaadbdddadbabbddcacbccbaaacddccdcdaacbbccbabddbaadabcdcbdabcdadacccbaddbbdbcddcbbddbdacbabacccbbbccdbbbadaaadccbdcdccbcbcbbaacbbdcbdcacaabbcccbcaddcabbaadaacabacbadaacadcdacabddccbbdbaacbccdcaadccbabdaabbbcddacdaacaacabdbcdabbbdcbdcccbbdcdcbadddccbcdadddbdabcbdccbadbcabbbdbadaaaabdbdcbcaccdaccdaddcacbdacdbccdcdbdddcbdcdbcddaaccaadccdbabaadbadccccdccdbbcdcdbbcabdabddbcdddcacaabbaadbadcdacccddaacddabcddabbcdabdcccadccabdbcddccbdbabbbcbadddcadbcaaacbdcdbcbcbcdadcbbdccbaccbabdadccadacdbacdcdaabdccbdcdbadabddcdaacbaaacddbdcdcdcddbbcbbddaccaccaaccadcbddbcaabbacaabddabddcdbdaacbdbbdbddbcdbadcbcabbaababdbcbdcdcadbcddcbccacdcaadcdddbbcabaddcbccbcaacddbadabbdcacacdbbbdacaacddbccaaaabccbcdccaadbdaadacbbcbddbbacacccdccdcbcacdbbbaddcbccaabbbdbcbdacccccdccdbbddbcaccacbdcbacbdaccdbbddaddadcdbcbbabdcadbcccdddbbdaccdccddbbbcabcccdccbabaabdadccccdacbadbabdaaaaadadddbccbbdaaadcccabcaadbddbadabbacdabaabccdabdaabbcbcdbadaaabbddcbbbdbcdcabaaddbcbcbabadaadbacddaaacbadbcacabddcdaabcdbcacacbdaaaddabddadcbddaccabbbcdbccadadabbdbdbddcdbddcdadaaadbbabcbacabdacbdcacbbbcdaddacbabbcdcccccbdddaaabcbddddaccaddbbcbdabcabdadcccbbcdaaaddcdacddadcdacadbacacababbcdadadcaabbbdcaccacabbaabdbdbccadacdcdccddddcabccadddadacaccadccaccbdacbaacdbaaaaddbabcbacccbbbcbaaadaadcbccdabdbdcdcadaccaddbaaacbcbbbbbdbbcbddddcdbdcdbacaaacadbdaaaacaddabccccdabcababdaddcbcbbdacdaadcbabababddacadadcdccacaadaccddcddbbbabcadbdabbdccbbbacbbdacacdbddbcbbaaaaadcbadbaaaccbbbacddbddaabdcdbacdcbcdcbaaaaabddbcccdaaaadabddcdcdbbcbdddbdbdcdccccdacdccddbdbbdccbdcccdcdababcccacbdddadaadcbcaaacacbaaadbdcbcacccacaabccaaccdadcaaabbddabacdddaababaadddbdaacadddadbbbdcacbaabbddcaacbdbdacddacacadcdacdaccbbcbabdacabcdbabdabcacadccdbddaabccccacabccbcaccdcdabacbdaacbbdaccacbbadbccdbbaddcbcdcbbccacbdcbcacadacabacccbdaabcbcbdaadaabcaaddbdbadcccbbcbcaaaacbcabdddcbbaaddbdbdbbbdcbcddabbabdbddcacbccadbcccddcaaabaadcdcaaadacddacaabcbadbacbababadbbbcdbcaaaddcadabddcdbacddddcacdcbdabcadaddbddbdbcbbaabaddbbbbadaaddcdaadcdccbacadbbdcdcccabbbbabcddbbcccbcccccdbcddcaadaddadcbcdcbdcbaacbdbccbaabdbaaddccdbaddcdddaaadcadcdacbdccbdadbcbaddbacacbabccbbdcadbdddddcabbbcabbdbcabdabccbaadaccacddadddbacacaabccccacddbaacbdcdcdbbddacaddacaaaacbaaddadadcbccdbaacbdbabddaacacadacaabddcbbccddadddbaadadcacaababbcadcadcdcbcccbbcbabbacacbbdcbdddacbdbddbddcbccaadacddbbdacadcccbbdbcbbababaabcbbddacdadcccadcabdbbaacaddaabbcdbdddadccbbababcdcdadadaadbbdddcabaacbabcbddbcacddacbcbbdbbbcaccdbbbddbcbbadcbcdacbbacbdabbddbbdabddbdddbabbabadacbaabcaaaddcbaabbbbaaccadcaddccdcacdaddadadcadbaddcbadacabccbbbddddacaddcbbcdacdccdacaadbbcbcdddbdcdacadaabaaaaadcbcccddabccddabdbbbbbaaddaaddbdacdbdbccabcadddabaddbbcdadddcdbaaddbdcaaacacbcddcabcbabcccacbcdabccadcbdabdcadcddccbdcddacdddacbabbbdbcaabdaaddaaccdaabdcaadadadddadbddacbccbadbaadbbcaddcbadaccacbbddabdccacccddbacbacbdabbaacbcbdcadbccaddccdcbdaccccdddcbabaccdcbddbdbdccbbbbcdaadbabbbbcdaaacbccbbcdbbadcaaadadabcaadabbbaaacdbacbcccdbaaabdcdbbbadccbdcbbbbbdcbdcabbddabcbcddcacdbadcbcccaaabbdacdccacadbbbadcaadcdabcbaacaacbcddaabaadbbbacbacddaddbbccbacaaadadbddcbbcdcadbdacccbbbbdcbbbacdcdbabbccadabbaaccdbbcabcdbbadaddadbcdbbabbcbdbbacacbacbaacaadbdddbbbaadaacabbcadbcaadbbacdabbdcdccdbbdbcacddcbccabccdaaabacbbaabbabbdaadabbdbdcddbddcbbcbcdddaaaaaaadacadddddbacacadaabddcdcddabdbccdccabcabddaacdbcbaabacaacdddbbacdcabbcdadcddbbaabbadbcbccabdadbabadcaabbadddddccddbddacbacddcadcbcbabccbbcbbcdcaadccadadaabcdaabacaabaacdccdbdcdcbdcbbddbcaccdaddbdcddbddcbacddddcbbdddabbcdadcccbabccdccdcbacadddccaacbbaacdacddccaaabbdbabdadacdaadbadcddbbbbcdcddabcccadabccdadaddccdadbbddacdbccbbadbcdbdaddadacbdbacdcabddbcbbcdbddcbacbbbaadacacbdadacacdadbadddacaaaaaabacbdbbacccbcdcabbcadabcccbcadddddbaddcaaaacacddddbccabbdadcaacccddbdbdacaaaadcdbacdcccacbdccbcdcccdadcbccdbaadbddbbdabdccccbbcabddaaacadccccbcbbddbcdadbaabadabaaccddcadbcccbdccddccabdcddcdabdaddcabdcbcbacaccbcbbcacacaaaaddcddadaaaabadcadcbbbdadbabdbbacdaababbbcdabdcababbadbabaccdaddacdcdbaccddddacdaccadcddacadaccddccddbcdababcbdbbdddbbcbbaccacabdabcdcdccaacbdbbbdcbaadcccaacabdadcadcdcdbbcbbabcaccaaaaadbabcbaccadaaabdbdacbabbbdaccbcdaccbacdacdabcbadbadbbdcdbaabccdadadbbbdcdddbacadacdacacddcdcaaccaabbbdbaaadccdcbbbabacbbcccdccadbbbbcdcbadccadcdabacbbcdbabcabbaccacdcbddbbbacbddcabcdadaaacdcdbbcdacacacdbcbadbaadabcadcdddccbcdbbdccddaddbbcdcbccaddddbaddbbdccdabbbdddcaaadcbdccbbcbcdccdbcacaadddccbddbbbdcddddcaccbcaadadcacdaabacbdcbbaaadbacbdcacabddbcdccaddcaadbcadabddcdcaababddbcadadabcdaddaacdacabbcdbacadaccbdadabbddcadaaadccddacaccacbbdabcdccaabcbdadbcbaddbcdbdccddcbadbdadabcbcadacbdbcddcbcddddbdcdbbcdccbdacbdaaacdbcdbcdcccabcadbddcbdadddddbdcadabacbcbbcdccacabdbacdaaacadbccdacbccbddacdcbdcddcbaddbcccabdddacadbdabadbdcabccdacaccdaccbccccddcdbcdcdbacddabdcdcbdbddacbbbcdcbcddcbbcddccbdbacbcdccaacacdddbddbcbbcbacaabbbcdbcbaaddaaaacbccdbddcccdcaddccdacbddcadbcadcdbaccaddcdaaadacacddbcaabcbddbccdcbccaabcbccdabaccbbbcbdaddccbbcbcdbcccbdcbdaadbacbdddccbaadacccbbaaccaaddbbddaadabccdcbabbbacbddddabccbabdadbabddadabadbdcddbbbdbcbccaaaccbbbbbcdbdbabcbcacddacaadbbaabdababacdaaccabdcadcbabcdcbdbadddabcddcbbccdacdcabadddadcabbbdcdcbdcadabbadabaadbcbbacabacbbdadaaadabdaaccbcbacbabddabcaccbbbdcccdbcaabddaaaddbabbbaaaabaaccbcaadcbaaddabbcadcbbdcccdbcabdbbabccbacdcdbdacbbaacdcbdbdddbdddcadbbcbbdaaccdbdbccacdadaccccbdddaacdddcaadcccaddddadcdcdbddaacacbccdbbcaabdcaddbdadaadaabcabdaddaabbcaccccacaacdadcadbadcbacabccbdccacabccbccaaacdcddabbbaddbccaacabbccbdcddbdbcdaaabcdcdcbacbcbbcadaadaddbcbabbacadbaaaaabcdbdbdbcdcbbbbadccaadabbbcdacbbddcabbdccabcdaaadbddcccbbadddcaabadcbadbbbdbacaabcdabcbbcbbadbbccaabcddcbdbdbbdbdbabcbdaacacdbaaabdddaaaddadaddddacccdcbbdbdbccacddbccbacacccdabccdadcbdaaadcadbbaadbcdbdccabaacaccbabcbdbbbbbbddcbabcdccdaddcbcbadddcabaadabaccdaacbddabadcadccbbbacadcdacccdddaccbcbdaabbbbbcadcdccadacabdcdddcbcacaccaddcbdabbdbcaabadbbdcabdcbcdcbdabbbcacaccbccabccbaccdbdbdadcbbcbdbaaadbacccdacbbcdadbddadbaabbdcabddccadccaddacccaaddbabaabbcbdbacbddadacccabccabbaababadadcddcdcdbdbcddbbdaddddaaddacaabbbdbaacbacadbccaadbbabdabbacbabacbaadddccbcacaadccaabadbcddbacacbcadadccbbbaabdcbabadbdccbabcddbdabdcdaadbbdccbcaaabbcdbaccabccacabaaacdaddabdacdacbbcddbccbddbadbacbcdabcdabccddacccbbbdbdcdccadbbdcadcbdaccbdcbdcaadacabbbcdaddcadddbbdbcadcdbbdbddcadcccbddabddadccccdbdccbbbabbacaadcdbbbddccadaadadcdcbcdacbdbcccbdbcdddcddabaddacbdcadcbbddbdbcbcbbcbdcdabcccbcccaaaccccbbcbbccadbdcddbacdcdcbadbcabcdaacacabacdcdbbbabadabbddacbccaaddaacbbbbbcbbabdcabbcadbacaddbaccbdcacccdacdabdbcdadaddcacdccbbbbccacaccdcdaabcdaabccccddbacccbddbcbddbabcbddbbbcbacdaddcdbacbadbbabdcccbabbdadadcdcdabddbbbcacaadddcdabcaadacbbcbadbccacbdcdbdcddadccbbaccddadcdbbaaababbdadbbcbcbbccdbcbbbaadcccaaadbcddddcbbadbdadcddbabdbcdccadcdbabcabcabaabdbadbdccaadbbbccbbaddadbdacdcbddadbddbadabbbdbabaabbbdabcdadaadccdddcabcdddbcbcbcaacdacdbcddcbcbabcdadcdcdaabdbddbdddaabaaacadcaaacbdaadbaacdbadcbaaaadaabcdabdadaddcdcaddcbabacccddaabdababbdababdaadcccbbdacdadbddcdbcadcbbcabcbaadabaccbdbbddaddbcdcaadbbbcbbcdcacbcaaaccdbbaccbbacbdaadbccbddcccdcdbddbcbaddabbacaddbdabcbaadcdccbbcbcbbbdccbdabbdcacbccdcbdbcacacadcbbdaddcbadaacbaabacddbdabccddccadddbbadcaccbcbcababbbccbbacacbddbdbddcbaabbacdbacbacdadbbacbbdcacdcbcdacdcbbabbdccccacddccdcdabcadbaabdcdbdcddbcaacbdbdddaddbacabccbdbcaadbdcaacdcbadbddcddddccbaccadabdcbbadaddbadcadbbcbbadbcadaadcccaaddbdaadcabccaaadcabcccbbabcaadbcddaaabacbabcacabbdadbccbcaadbbabdacbabcdacacabcacbbbcdbccccaabcdcdacacbcaadbadcdcccadcadaccbcbdabdccbdcaaccccacccbcabcdddcbbcbdadbbbabcbbdaabacdacaddadcdbdaaaabcaadcdacbaddbbbdacbcabbdadcddccabbbabcacabbacabbbddacbbbdcccbbbaabbbcaabaabdadadbcdabcdbcdddbcbdaabdcdabdcdaabcabbbaccdccdccdbdadacacccaadcdcadddabcabcbdccabbcbcddbaaadcbadacbacdadbcdddaacaacdcbbbccbdbbddbbcaababcacdccddcabdcadcacdcaddcacaccdbababaccaacaaaccaccadbaddabbccaacbcdcbadbddccddccabadacbaddcbcdaaadadcbadddbdbdabaacbbaddaaaccdbabababdbcdacabacbdcaacdbbadbccddbdadaaddbaadbcaacdacadadabcbbcaaabccadadbbcdbbababacdbcaabcabdbdadaacbacbaaabadccaacaccadabbdacaccaccdaaabdbdbabcbbdbadccbdcbcccacabdddccbaabcabccbadadcaaabdbdcddcdcaaccbacddaaaccdbcdadcbcdbbbacbbbcaddaadcddabbdcbaddadbacdcaadaaadaddcbbcbbbcbbbdcddbdcdacaacbbbacaaabaddcbdaaddbddacabcadcddbacddbbbdaaabbbbbacbaaacadbddbabbccddacacabdaaacbdccbacbacdccadbdcbadcddabcdcbccbbccbaccbcacdcacaabdabdcbcacaadaaaaaaabbabdbcbbdadcacaababaabdbbddcbdbbccddcadbccacbaaabdccacbacdbacbbadbcbabaabddcbbabbcdbbcadcdcddbbddcccbdabbdddbaaddbdcbcdbcdbcddcadbabaadadcbbdcdbaabdbcddaacbbcbabbacbddbccdcbcbacacccdbdcccbbcdbadacccadbbabbbaddcaaacbabcbdaacdababaabdadcabdadaadbccbbdabbbacbcacdccbacddbbabbdcccccacbaccddbbadbaaaacdbbbcddcbccbadbbdadccdddcadccaabbcccdaacbacdcdccccbadbcacccdacacbaaaddcdabccbdcadbdbdbaacccdbabbdaadabcdabbdcdddcddcacddbbbacbdddbbcbcbbbabdcbdbacdaaacaddbccbbcdbdcdcbbbbbbadcbdadbcacadbbaccdaddaadbaadacdaccdbbccaaabbaccddcbbddadccccabcbdaadcbdcbdcdabccbbdacccaddacdbccbdcccbcbcdddabddcadbccabcadcccccdcaccdbcbababcdaabbbbcaccdcbaaaabbbdcbdadabbcbcbababcbaccacdacdcadaadababbadbdcacdccbcdcdcddccadbbadbbddbdaaccbdddbcbcbbbbccaabcddacbdacddcadcbddaacccdddcdddaadddbddbcccddbbcdbbcbaadaabcadddddcadacdcaccabdabbbcacdbdbaddcaadbccadcacbabccacbbabadddabdbbbdbaadbddabdcabaccddbabddcbbaadcbaaacabcccdadbbbbabcbdcbcccdaddabcbbbabbdcadcdddacdcacbbadacabdbbbddbacbdacccabcbabbdbdadacbadccbadabdaadcbddaaddaaabdbadccccdabddacbbcdaacccddcbdcbcbbbddcabdacadbbbacaadadcbcddcaaddbdccadacbaacdbcadbdbbcdbaabdbdadccaaadcabcbdaccaccbbcbbbcaadbcaccabbacaabbdccabccdaaddabdbdcddddcccbaacdbbbadcaadadcddbbddacdacdbaadbbbbacabdbdddcacabcdabbdcccbdaabdbabacbbababdaddbcadaaccccabbddcaaabcbabdabacabaaadcdbdcadbbbddaaddbcaabbbccddbdababcbbcbbccaddccaabdccacaadccdcaabbcabdcacaccdabcdcaabcbccaccbccccbcbaacaccacabbbdcbcacdcdbacabaabbbdcbbddacaadbabdbcccbcbdcbbacabadbbcaabbbbdcaacacabccaaddaabccbdbdadaacddcadddcbabcdcbaccbbdbcabddadbdccbdccdaaacacbabaabadbbbaabadcabddcbdcdbaacdddcddcbcbcdbbbdddabdabdddcdabcabcaacacdacdbccddbaccccadbcdbbbbbdacbdbddcdabdadddddcccdabbabcbcdddccbcabdbcbcbaddbacaabaadccaadaacadbdbbaadabcdacdadccdbccbcabadccccdccdaabddaabcbaabbaaaaaccbdbcdcdcacdccadbdbcdadcbbbadcabbdabaadbcdcbbbcdaacabccdddcddaadadaaaaccadadadabdbacadcbdbaaaddbddbcadcdccdbaddcbcbbdbdcdbbddcaccacdaccddcbdcdbcaacbcacaaddbdddcaccadddcacdbcaccaddcadadcbcadddadcdaadbbbaabdacdaaadddaccbcdbacccdadccacddcccdddcadccccbaacddcacdbdddaadbbadcbadaaadcabacdbcbaabdbcbdbadcabbddacacbdbcaacbaaacccaacabcddaabbbdcbbdadaaadaacabcccdacabdbbbbcdaacdbcccaadcadaabaaddbccbccbacabbdacbbbddbcddabcababbabbbccaabbdbbcabcdbccdcdddccabadcaaccbacaaabdaddcabbbdddaacababcadcacabbdaaddabcacaccbaacccaddaaccbbcdcdcbacaadcabccdacbbddcbccacddcadabbabbbbddddacaaacdaabaadbbaacdbcdabbdcdcadbdbaabcabcaccbadbcabddbbdcbabdbccdcabbbabaadaacaacdccbbcdccccbdacdbdcbbbdaadaaccdaabdccbbdbdcabbbbdabadabdbddbabaaaacccbaddbabddbadacaabddbacaddcadddddabbcadaacddddcbddacaadddbcbbcaabaacddcbbacbcabdbaacdbaaaabaabbcacbbcdbdcdabbaadabdcdcdcbcbadbcbacadbaccbdcaaacbaccbbaabbbaddbaaaabacbbbaccdcbadbdbdbababdcbcadbbbcacdacaccabdbcddaabdcddabcbbbbcabcaaadcbdadbadcbcbdbbcdbabaacbcddcdbabccbcdbcdcaaadcbaadabaadaacbadadaaabbbdabbadbddcddaaddaccbdcbdadaddacaaaccabcddccacdacdaddbcbbacdcacbcdaccdbbbcdacdcdcacbcaccbaaadddbacbadaabcdaacbabdbaaabcddbbdbbaacabaddadcdabaadcdaaccaadaddcadccccbbaacbccbccabbdccddadcbddddbbaabaacbcdbacbadadcbcdcddcdbabbcbbabadbdadbbdbaaaccdccbcbdbbbdbbbdbabbdaacbcbabbbcbbcadaacabccdbadabababababadbddbaccdbdcdbbbaabacadbdcaabcadbabaddcbbaccbaaadacbabdbbadcaaddccdbaaadabcbcbacdadacccbbdbaccbbaaadacbdaadcddcbdccababbabcdababadabcbbaddaacccdaaccababbcdcbccdadaddbdbccddcdbacdbadadbabcccccabdbcbaccababbacbdbcbbaaddadcababadabbdbabdadcbbaaacddcadaadddcdccdddcabdaddaccbabdabacadcbcdcaccbcdbadbacdcdaddaaadddbbaccaaacbbbbbdcacdcbaadcdacbdaaabadbddbdbcbcbaccadcaabbacaacbcdaadbbdbcbaaababcddbbdbdccbdccabaddbabacdcdcbcbadaaadcaadddacccdadbcacacdbdbabbdbdccbbadddaaababbbacddbbbcbaccbccdaaacabbccddacbbbbadabaccbbdbabbdcddaccccbcdaacadadbabcbdbbaaccabbcacbabcddadabdcabcccbcaddcabdbcadcdaadbdcbbbbdccdddcadbcdbcddbdaacdbdbdcbabccadccadccabbccbdaaacbcdddbacbdaaccaaabaddacdcccbcdcdacbaadbcbbccdcdbcaddaaadddcbacbadbacabadbbaaaaabdaaccbaddbadbbacabbadaaccbcbcbbdaaccacbaaabbbaaccacbcbdbbcbaddbaddaaaccdbdcbcaddabaccaccbccbdacdaacaabbdddbbaaadbdddbdccbbbccccbaccbdbdacbbacdacbbcdcabcdcbdaccbdcbbaccdbbdcdbdacaaadbbdadcaaabbaddcdcaaaadabdcaaadaabdaacbcbcacccddadcdcbccdccadcddccaaabcabccbcddccccbdbdbbdddaddacdaadababdcbcadaacacccdbccdbcaddabbccccbcdbbcdadbcbacaacacdccbdbabdccccdbbdbdddcbdbdabadbcaacdcdcaabdcacdabbdccdbdcbcabbdbddbddcbaadcddcddadaddcdccaccdbdadcdaddbcbaddbbbcdbacbcddcdacdcbcabbbadbacaaaaccbdabdcaaabdaaaccabbaacacbaadacdcaacadcaddccdbadabcdbacbadbcbdcddccdadcbbabbcdadbdacbadddddaabcaacbcacadbdbdccacabdcddabdbdbddbdcbcdcdbbcadacbdacdacabaabaddbdbaaaabbdcaacababcbddcbcddabcadcacaabbcbbcabbcacbabcbcbdbcacabddaacdcdcddbbaaddbbbbadbaabbcdbbbcdbdabccddbbdcbbadccabdccccbadbabbdbdccaddcaadbcdacbbbcacacbabbadbcadcdadccababbbbbcabbbcddbcbbdcdddbcbacbccabddbbcaccccadcaadcabcacdabccadadaaadcabdaaadcbcbddcbabadcadbcadcdadaabacbbdabbdcdbbcaadbdadddddacadbabbbabcdabbdacabbbababbcdcddaabdbadddbdbdcaaccdaadacdadcacddbcabbdcdbaabcbacccbacbabdbbdabaddadbcadbdbbacbcbabdaaadcbacddcbddcccbbdcababdbccdbaadcbcaabdddcabdaaaccacdccccbddadbdbcbcaccddcbddcadabddadabbdabddacbcacddcabddbbdbcaccbdacbadadcdbacbcdbbbcbcacccaccacccaddbdcddbcaccaababcacddbadddaaaabbaaaababdcbacaabbdcdbbdacaccdacbdbdacabaabaaadcccbdcccdcdccdcaacdacbbbdabcbdbdaacccddadbdccdbcbdcdbabcbadaabbcbcacbadbbabddabcaadbaddbaccadcdaabdcadaaaadcddcacbcbdcacbacaadacaabcddadadddacdcaacbdadddccacddbbabcbccaabaabdbaadbccdabcbbbdacddbbadddadcddaacbcaabcaadababcdddcccabdbcacadaccdcbabbbdcababccaaccccbabcdcbcdbacccccbbacadabcbcbadbcacddcbdbbacbaababdabdbbdbcabaadbbdbabdcacabcdcbbadbdbcccacdbaacadcdbadacbbbdbdabbbdaaddccbcbccbccaddcdabbbcdccbccbdaaccddcacdaadaacabccaddadaacdbbccbccacacccabdbdbdaaccadaddcbdddddcccbaabddbbcdbcbcaabdcdadadadddadbdccdabaaabccdbadacadbabcdccadcdbcdddababcbbbacaacccbbccaadbbacdadbbabcbbbbcbbdcadaadcdcccbaaabdacacbbbbdccddabcdacbbcdacaacccbaabaaabbaaadcdcddcdbdbbccbbccadbcbbcdbaabbbcbabbabcdacbacccdbabdacbacbdcbadbccabdabbbbbdbbdbbaddcccddbcdbabdcacccacddcddbdaadcaabbbddcbabaacadccabcbbddbcabcdbcddbdccdbcdcccbabadaaccdbccadbadaabacbaaaccadabbbabcacddacbbbbccdbaadbccbcadacbacdcddbbadbcabbcbcdbbcaacdcadbadccdbbbcbddbddbddaddbcdbcabbdcdbabbcbddcbabcccbadddbcdaadccabccbcbbacadddababbdbaadcaddcccdbbadcdaccaacaddcdcadcdcdabddcdabadabacbadbbabdcccbabaadbdaacdcbaccaaabaabccbcdaddabbcbddadcbabbbccbaccabaccccabcacadcacbbbdbbcdcababccdbaaacbcacbcbbbbadccadbcdcbdbbdccababdbdbdbbcdccdaddaadacbacacadddacbbaaaccadcbabcaadcdcbadcdaaadbbabbacdcdcaadcccdbcdaabdccbdacdcbdbadccbcdbdccbdcccdaaabacddddadbdccbdddbcabcadadbbdacbabcaabbbabdbaadcaabddbcccbbdbccccddddaddadbdabdbbacaadabaaaabadbddbcbabadddbbbacdabaabccddacbbbccaaacacbaadacacddbdbbbccdadddacdbdcbbadcadbbcabaaccadbcabdcddcbbcdbdaddcbaaddcdbcbabbaadbbcdbddababdbcbbcbbadabacacbbaabbaccdcaacbdbacdaccccdbdbacbdbbccabcaaabbcabcbadcdbcddbcabbccdbcdadbabddddbbadadbcacaddababaabdacabbddccbbadbacadbcbacaadcbcdaabbdacaacdabddddaaabccdccbbddcddcadbbdddbabdcbdabbabcddadbcadccabbbdccddccccaadaabbdddbdccbaadadaaaccacbaabdcbdbcbbadcbcbccdcbbdddabbddbaccdadcbcaadadabbaccbdcddccbadbbdbcbdcccaaacabddbcccaacbcdaccdccbabdaaadaccbcbadabaabbcaabdbbacccaddbdbbdbcdabbabdacbabddadacbaadbbdbddbdbdcdabbacbdcbaddcacabbddddacdabddaacdbcbdddacccdacacaccddadbddccdbdabcbbdacdabacdcabdbbccbdcbaccababcdaacdbbaadaadddacbbcaddcbbcadbbadbbdacbadcbcbbaabdbdacbccbddcddcbbbbadacbcdbabacdabbbbcdbaccddbadbdadabcbccdccbcbbbcbcccdaabcbdacbdcabbadbaaababbdbdaabcaaabaabdbbcbccbcdcccdadaccdddbdcadddcddaabaacbcacdcaddabcbbcbdacccabbbabbdaadcdacbdaccadadbbadcbbcccbdcdcacbadbcbccbbabbcddacdaadaacacbcdcdabbbdadbddcbadcdcdcacddcbddabdbbadacdbdcccacdbcbdcbbbabcdbbdbcbaaacdaaaddccbadcbcacdbcaacaaddddbcddddcbbccbdccbccddadabddbcadbdbccbdbdbbcaacbdcbbbbcbdcaddbaacbdddccaddadaddbbccbbadbabdbbacddcdbddcbbdbdcdbaaaddccacaccacbcdbbdbabdadadcbaabccdcadadbbbbdcdcbcdaddbccbbaccbccabadbdccabcbbddddccdadaddbacbcbbbacabcadcadbadadbcbbadbccaaccbbdabadcbdbbdccaaabbcbbacabdabbcadcabbdadcbcbadbdababbdcadaccccaccccaddbacbcdbbbcacdbddcbccbaadbbaccacccdcbbbabcbcdbccdbcbccdbdcadbbadddababdbbcdabbdbbdbcacacaacaabacabbbcdabdbdbadbcaabbccacdbabdddcbdbccadaabccdcddaccbddcdcadaacdcaccdcabccbbaddbdaaaabcabacbbdaddcacaaabccdbbcacaabbdddcadddbdaadddaacbdbbacccdaadcbdbcbacddbbdcaacaccabdbcbdaddbbbaadccbaacdabdabdbcdcbaadbadccaacbcbcdccababadbdccdadcabcdaccaaadacbacbabccbddcaaccbcbcadddbbabaccacdacbdcbbcbccbbdcaabacabdbbcaccccabcbdcbcdabdccbbbadbcddabbabbcbaaabadacbbddadabdbdadccbbacdcadbaacbdccabcdadaccaddacdccaaadcbdcdbbbabdbdbaaabcaadabccdccdddbcbaaabacdccbbbddbaaccdacaabdcabbddbccdcccbcccacaaaddddcddccaddbdadbacdacadbcdddaaaccabcadddbcdcadcacacbdbddbbccdcdaccbaaddcbcbcadcabbcdbadbdadbaacbccbacbbabbdabacddbdbdddcbcbdcaccddddcdbaaaccaaccaaadcbdcdabababbcacdcabbccbcbcacdcacdcaabcabbadacabacdbcaabdaabbdcbdddbcddbaaddaaaaabaadaadcabdacbdcdccabbbdaacddacddacaadcdacbacbccbdaabdcacdbaaccdbbdbbdcbacabaaccbcdcbaacbdbaabdbcadaabdddcaaccadbaaabbcdbbcadbacdaabdccabbbccaccdbdacbadcdccdbabcdbccabdabccbcaacdabccbcddbadccabadcbdbbcdacaabadcdbddbbcdaddbbdcdcdcabbdccdcddacababcacacdccdaaabdaccbcdddbaacdccdadbaacdadbadddcbbbcabccaacbcbbabdbbbbcdcbcadcbdabaacaacbdbbddddbbadcaabadabadbddcadcdccdabadcdddaabacbddcbdddabdaadcdddcbbadcbcacaacdbcdddbaaaabcadbbcabcbdbbbaddcccbabdaacbbdacaacbcaccbbadcbaacbbdcacddbabcddcabdcbcccddaddaacbccbccaccdcdddaccaacbcdbabbbabcddbadddccadaccbcbbccbccbbdbadcaaaddadaacdaabdcdaccaacaaabacaabacababdcdcabbbaccabadbadbaddacdbaaddbbbcbdabbcbccccacacdbabbbcbabdcdadcabababbcdaabccddaaadcaddbdabaabbdcccbaccbadcccababcaabcbbbbcbccdabddbdaaabbbbdcbcaaddbacabbdccccabccacdddbcadddabaabcbbcbcbddadccddadacabbddaaabdaabcadbacbdbbbadaabdbdbdcdbdabccabddbaaddaabccbdadbbbbadabdcbdbcbbdaaccbbcbdddbacbccdadbacdaacdbaaabadcdbaaabbcbcacaaabaaccacabdbabdbbdbdbbbcbababacacaadbcddddaccacacadcadbccdcddccbbabbbadabbdcdcaadccbacabbbdacddcbcabcaddcdaccaccabababadbbbddadccbbbabddadaababbddbaadbadbabcdbddcacabacbbbcbbdaabddbddddbadacdadcdbdcdbadbccaabbdbccbaccabbaabcddaddaddbdbdbbbccdaadaadadbaabcddcdacbdacdbbccdcddbacbbddadddcbdcbadcbdcccccaacadbcbbbcddcbdcbaaaccacabbcabadbbcaabaccbcabccbbcadaddcdadbcdaacdaabbacacdaddadabaabbbcbdaadcbbddddccccbadbacbacbabaaaacdacacadaccdbadbcbaccbabdbdacadddabcdacbcaddaccdcabdaaddccabdacbcababdaadbdbcbbcabdcbbaaccdadbccabcdacdbcabbadabcaadddaadcbcbcabcbdaadbdaaabadaabbbdcbaadaaacddabdaaabcaaddcbcbdacaabddabbbadbacadcbdadbdcabaadcacaaabbbcaabdbabaacadbccbbdabcbacccdaddbaacddbcacaaddbbbdcbcdcdcdcdbbbdcadcacbbcbdddcaacbccaccdabdbadacddabdaaaabbdcbaaaaaadbcaaddbdacacccdccbaaaddaadcaddcbbdacdabdacbdcccbcabcdaabddbbaaccbdbabcbdabcbdbcadbdbabdccbcdabcaddabbdbaaddaaccaaaadcdbbaacddddddbbbcacabadddadbddcacccbadcacccdcacaadbdbccacccddbcdcbcacbaabcabdcbdbbcbdadcdbcdcbaccddbabbdccadaaabbdbddcadbdadccdaacbcdabadadbbbbccccbdbcbadbadddadcdbacbcbacdbcabdddcdbcababbbbdbdbdacddabcacddbaacdbdbbcccccdcadaabbcbbdabdabcacadadddcdbadabbdcdbadcbbcdadaddbaddcadaddcbddcccaabdabbbcadccabcabaacabddababaacaabadbadccbbbcabbcbbbdabbddbbdccbcaabbbcbaccbadcccdabcabbbddaddbddcccabcbbdadbacddcbabcacdbbacddcdadbabadadbccdbcbaabadcbaddcadcdccaaddacdabcccdacaadbbcaabbabaabdddabbabcababacbcbaaaccacbbcbabbbdbcacadbdddbbadccbccbbadadcbcbadaddbddacccaccbaabaacadcdaacbbbdbddaddbcccbaaacbcaccbdabdbaabacdcdacccdcacdbcabbdccdaacabbdbdaabaaacdbabdddbddacacccbcbaabddcabbccadbacbabbbaadabbdddbdbcddbccadbaadcbbccbabbcdcdbabcabdbddddccabddbcbacddbbcabcabbbccaccbaadcbbbbddbbcaddbbddbcdaddcdbacddccdaddccdcbddccbcbddddadddaccddbbcacbccdbddccdbdccdddaadbcaadcccbbcbccadcdcacaddcdcacaddcabdbbdcddddacbaaadbaabccdabacabcbdddbcaacdcdabddbaaacabdddbddcaaaabaddbcddcdadabccbbbdcbcccccbdaacccadccbcdadabadcbdadaaadbcaacabbdaacdcbadcaccdbcadcbadbdbbcabadbcdccabcbabcababaacbaadcbdcccabadaccdccadccaccadababcbdddbbacccdabbbdddadcbadaabbbacddabadabcacbadcaccdcbbdddbdaadaaadcbdbbbbdaabcbabdccbacbacdaadcbaccdcdbabcbadbabadccccaacdacddaddddcacdcccdbabbbbaabcccdadddbbcbcccbbcaccaddddddccbdabbacdabdacdbbcbaaabcbbdabbdcdcbbddcddcdbdadccacbbbbbaddacbcadbbdcaadbccbaadbacacbbaaaddaabcbdcadcbbadaacacdcbaaadbdbbadcabbdabbaccdabdddbcdbccbaccabbdbcdbacccadccdcddcacaaaddbaadcaadadbadbaacbcabccaadbaddabdcabbbadbadbaaabdbcaadbcbdaadcababbccaaabdababdaddbbdbdadbbaddcdaadddcbdbdcbbdacadcdcaadbadcacbbcbbbdacccabaadaaabcdaccbabcbddaccbddbbcabdbbdbbbbddcabbcbcaccbbdcbabbbdabcdbbadaaababbacabbbbbaaaccbdbcdbacbcddbcdabaddbddabaacdcbadbabadcabddbcbbaabbddbcbcbbabddaddcdddcaccccdbdcbbabadbbcaadbddbdccaacbbbcdabccaaddbcdcdcdbacaadcacdcacbabadbccacbcdbdbaadcacbbdaadadbdacddcbdcbdbcaddbcdcdbbabdacaaaadcaccaabdddccbbaaccadbdbacaaadcdbbbcbaabcacaaaacccaaadcbbbdaaadbcdddbcccaabbcdaabcdcacccdaadadacaabcbabadcbacacbbdaabbcdadadcabccaaabdacabdddbdccbccdcbbddccbbabbddaabdacccdccbccdacbbdaabadcddbddaccaabcddabcbccbcbcbcbcacbbccbcddcbacddcbbbcbbacbbdddcacdaadbcbbbbdadcbdccccabddbcabbdcdbadbcdddabdbbcdadcacdadaabaacdaccaddbbcabbacbbdbdabbcccabbbaaddbbaadbcbbcacddacabbbcabadcbbaccbcbcbcddaccddddbacbcddaccdddaabaacdcdddadcadbaccdacdaabbdccacaaaddcccbabdcbcacbdaccbbdcbadaaacbdbaababcaacbdadcbbbbaacadbcbbdadccbadbdbcaadcaddabccddaabcadbbabbaaaacdcabdcdabbdabdcadbcbcbddbdccdadacbcbdadccbabaddabbbbcbdacbcdabdbdccbdbabcbbbbdbbacababcbdcbcaddbdbdaaacbaadabddcbadcadccaacabacabddddddaadabbdbadaddacdcccddbaadbadadcdacaddaccaaacdcabdadccbbbdcddacccaaaadbbbabdadbbaadcccaaaaabaadaaccbdaccaddcdbacdabccadcaaadbccacacddcbcdabbdddaabccaacadaaddabdbdbbdabccadbcabadacadaacdbaabbcbbaccddabadcbcacadbdddaadaaaaadcaacacadacbbdabbbbcdcacacaadaaddaadbbababcdddbcdbabacbcdccabbddacdcacadbaacbdbcccbcbadcbbddabdcbabdcccacaabbabcbabcbabcccabaabadbacdcaabbdabdacdbabcdacabbabbadbcbbcaddcccdadaddcdcccaccbdbbbcbaaccddbacdcaadbadccccbaacadabcdadcdabacbbaaccababcbdaddcdaddbdcdbacaadcbaabccacbbcdbcababaddcbbccaacdddbcbccdaadaacbbbdcbdccadccaabbbdccacbcbdcddcbdacddaacaddbaabdabbcbcccddaaaaaddcbddbcccabccdbbbacadbbcddccdaaaababdbddbcbadacbaabddbdbdcddbacbbbdcbaaabdaabbcdbcbaadcdabcadacacaadcbbbdbaadbdccdbdddbcbcacaaaadcdcbccadadbacbcacbcdcdbcdbbaccdcacdbbcadacaacbcbacabbcdcadaacacdbbdbbdbabdcddcccddbdccdbaadbbacddbbabcbbcbdacadaabaababdbcbacbaaccaadcabcaccbcdbdcabbcccbbbbcaabbddccbddccdbdbbbdcabccaddaacbdaaadccddbcacdabbaacdbbbccadddddbcaabdabaaacdddbadabcadcbcbcdbbdcbcabccbbccaaddbadadabbdccddcdbdcbbdcabcbbddaccabdbcacdbbbacdacdaabbadccbdacbdccdbbcaaabbbbdcddcddacacbdcbcadccbdcddacabdbddddaacccdbcddbaddccadcabaacadaaabadbbdadbcadaccddadcbadbaaacbbcabbcadaaabbadcbaccddbdacbcbcabbbcddbbaababdacddccddabaccbdccccacddabdbaaababbccacbcacbbabcbdcddddbdccacacdbbdddabdaddabcaaacadccaadddcdddcbaccbbacacbcbcbbdbbccbaaaabddcdddadddababadcdabaaaaddacdbddbcbdadcdadbcabbccabddbbacbbccbcdbbabcdbadabcacbbabcdccaddcdcdcdbbbcbacacbcbbbdbcabdcdcbaaddbddcdaabcbcababdbccdcacaadcbbadbcdadccdababaccadccbbbddcacccbcacdacbdbdbcdcabddbbdaacdbcadcabcadaaacaacacabcdbcadabccdcaaddcbcbcbbddccbbbadddbbbdacbdcbabcbdbccdacaaccaabdbccccbbdcaddcdcabaddabcccccababcdbbabcacdcbabaabcddcdcbacddccacacbcddcabdbabccaadcdabdbdbacbbabaaabcdbddcbcabdbccddcbadbdaabadcdaaacbbdaadbbdaddcabbabbacbdcdcacddabbadbddcadcacbbccdbcbbaacdabcdacdacdabcbcddcadadadadcacdabcdccaacdabbdddddaccccbcccdaccbbdaabbcccddcaadcaaaddbcdbdbdadababcacaccdcbdbabbabbbbbabbbabadccadbadbcadccbcbadcaabdcabbcccbacaacbacacbdbddcaddaadccacadbcacaaccdbacdcdbadadadccaaccccbdadcddcbbcccaadddbbdcdddacacddbaccadccbdaacbadbadadddbbacdddabdcbaaadcbacaabcdadbdadcbbcccccdaadaabbadcccadbadaabcdddbccaccbbbbcbacdcbddddcbdbacabcbaabcbbacddaaaaacacababcababdadabbaddaaabcddcacbccabcaabddaadabddbbbadcabbddbdbadcaddaaccdbdcadabcaccdaddddddaabbdcdbccdbbcbadcadbaddacaaaabcaacdbbaddadadcddbcdaaddabcbbdaabcbbddbbbcbaccbbcacacacbbdccaaababdcccddcbabadadcdbbadddbddbdabacabcadaaddacaabacbabddadcbbcbdbadabdbdaddcdbbaababdbcacacdddabbdcaddcbddddcbbacadcdcabcdcbadcddcadccadcabacddbdccdadaddcbbdacbaacccbcaabcdcbddacacaacbbcadbdbbbacbddabcbbaaabdbcddddbbcacdbbbcacddcaaadaabcccabaccdbcdcbacbbbdacbbbcdabddbbcaacbbdcbccdddcaccbdaadcdccccbaaababdaaccddacdcadbadabacccacdcccddcdbcadbaadbdbadcdccaadbdcbaaaaccccbcdcdcbdbdbbdaaaccdaaacbccccbcbddaabcbadbbdcacdadadddbbacddadaccbbdccabdbccbcccddddcbadbaddcdbcabccddabddbdacbaaddccbadddbcbcddcdabbbddcdcddddddbadbaddacadaccddcbcaadabacbdccbaddbdbcbcdaacbdbddacacbcdddaccbbdbcbdadbdcddbaddcadbccbacbbdacccbccdbdccddbbabadccddabbadbadadabacacbdcddbbbdddccbbcadabbbbbacbbbacbcbcaddbabacabbbbbabdddacaacaababdbccddbcbdbcaacdaabaadbabcbcaacddddcababccdbbbacccdbbaadccdcccbadcaacddcccaabbbcbaabddcaadbaacbdbccbaddddbaaaacabdbddaddabccbdadbbcdbdbbdbdcbcbcaacbccccbbdadbbbadaacdbdaaaabdcdaccbcccbcbbccdccadbbcbdbbaacdcbcaabaabbcdbbabacdcdcacabcaaccababcbccaccccababaabbbcbbaaacddcaaaabbbdcabdcddbcbbbbadbcadacaaadabcbacbbcbbdbdabdabaddbdadabcdadbbbadadbbbbaddbadcabdbacbcbaaacabacdbccccbcaaadccbabaacabbccaccbddcbdabddcdacabdbccacdcbaccabddbdabccacadbcdddbcdbcadbbbdcadddabaacadbbdacbbdbcdaaaccdbacbbcdbdcbacaabccabdddcadacbbccddbcdaccaaaabdcaadddacadccbbbaabcccacbdbdccdaddcdccbabdccadbaacddbcabddbbaadcbdabbaaabdbdabbdcaddbccacdcbadbcdbddcbcbdaaaaadccccddcbcdcdccaddadcdbabcbddcdddbcbddcdabcccacaaddcbbdbacccccbadcdabddcbdcacbacbabbbdaadccaacacbccbbccddbddccccbdcbdbbacaaaabdcabbbcbbacadbcaabaabaabcdbdbdbdcbdddababcabbbaadaccdaadadbadadccaaddacddddaabbacabdcacdbdbdbabbccdadcdabadabbabddcbbdbcabcdabdaaddbbbcbdaddbccdbcdbaadddcadddddbabbdccbaaaaabcdcdbdacbdabadbabcaadcbabbbdbcdbacacbaaaccdddadabcbaccbcdcabbdbdaadcdaaddddbbbacacacbccaccccccbabcdbbadbacaabbacaccdcccdaadcbacccddcabbbbaaabccdcaabcabbcaaaaabadbbbbbbadaaacacadbbcdabdcabdbdacdddcdcdadadcdddabdaabdcbbbcbbdcabbdcbbbdaadadaacbcbaadbcbaddbcdaadbdbcaaccabdadadbaaccbaadacdddbccbaaadbdcaababdbcabbbdddacddaddaccbdabababbddcbbbdacdddddadabacbdcddbaabcdddadadbcdcbbbdbaaacdacccddccddadcabadcabcddbbcbdadcdcbabdbcababbbdbcacaacbcaccdbbbcbcdbdabacdaccdbbddddcddbadbabddcabcddabcdcdcddbaaaacbbbcddaaaadbbaabcbdaccbbcbbcbabacdbdbccdaabcbdbaabcccbdddbbdabdddbabbddccdddbadddadbaacdcdddbcbaddccdcdcabbabdcaaaaabcbdcddbccdcccccddbdddacbcbcadaadcdbbaccdbdcbcddbaaacaddbbbaadacaabcadaaddacccdccbcacdacdaccdcbcbdcbadddbcddaccabdccbcccaacbdbbadddbabbaaaadcaabdcadbbadadccbcdacdbbdbdadcdbccbdbdccaddadcbacdcbbacabdacabdbacdbdaadabbdcddcdcdbbcaaaabbcccdbbbbabbbadabccbddbdacddbdadddcbcbdddacbdbdacdbaaadbbbcaaccdcadbdbbaddaabcadcdbbdaacddbaacdcbddadcddaabdccbdbccbbcbdacbabccccbacbaaaacbcddbabbbbddacbaadcacdababaabacacdababadcbbacabbacdcbdcbbcdaaabacdadacadabdcdcacddadbaaccbdbbcbadadcccdbdddbbcbccadbaadabacadbabbdcdcddbccabaabbdbcaaaadadcbdaccdbacbccacbccadbaddacabcabdbbaabbbdadbcadcdadbbbbdddbacaacbdcabcbacbbababcadaabdacbbacccaacdcacacddadccabddcdbabccbaadbbdbbaddadabcaaabbbcdaabddbddadddbddcbbbbaddaaaddaacbdabcddbaddbdcbdabadacbcbcadadccdddacbadaaaccabbcaabddddadadadaadbbabddddacbcdadabdcdbbdccbcadbdaaadcddabaaddbdbdacbdababbccbddccccbbabbdbcaacbdcbabddcdbddbccdaccaabcadbaabacbcbdacbacbbbbcdbcadbacaacbabdcbdbabacadadbbcadcaaacbcacabcdcadbabcbdadbcbcdabcadcabbccdaaaadcdbcaddcdacdbaccbaabdaacdcabddcdacacaaabdaaccbddddabdcccacabcccbbddadbbaaadaadacaabaabccabbcddddbcadbbccdccadcabdacabcacbbddcadbcddbaddddabdcdaaaadcdaacabbdcaabbddcadabbcbadcacbbbccbbadadabbbadbcaccabbbdbbddbbaccddbabbdcbbdbcbdcbacabbaddaacaabccaccbdabbaaccddaabdcabbcabcabbccdcddabbccacdcccbccdcdbdabdcdabbccdaacddadccddcdadcdcdcbcaabaadcadbbcdcbaaacbaaccbcadddacbcbcacdcdbaaabdcdcdadaacaadacddadacbcdabbbabcacdbbaddabbbccdccdaaadcbbcbbcaabaddadaddbadccdcadcddbabcdadddcaccabbccacaccbcbdacdaaacbcccadbaacdbccbcdbdbddbbcdbccdbaddcabcbcbcbdabcaccbaaaddadccaabdacabbbddacdbcbbcaabddcccacbdddccacaaaaaabbabaacdcaadcaadcddabadccdadadccadababaaabdadbaddbcbcaccadcbbbabbabdabddaddabadabadadaabbbbabcbbdadacabcdcacaabdbdcdaadadbabcddaccdbbcdbdbadbcaadababdabacbbbbbbaddbbcccabbcbddbababbcdbcabccddaabcdbcdacacdddacbbaadcbbabcdbacdcbbbbbddacbadcdabdbddcdccdcdbbbbbaaaabcbccdbaabcbcbbccdcdbddccbcbdbdcccdccccccbcdbdddabccaccbdbabdbaacabccbbcdabdcabadbadccdbbbabaccbbdbabbbcbbdadbacdaaaacaadacbddbacbdbbdbccadacbdbdcdcaccacbccdaadbcabcccaddccccdadadcbcddbdacbaaacabbadbbdcccacbcbcbdcccdddcbacdcabccbdcadcddcdbdbcbcbdbdbcbcabcabccadcdcbddcaadbdabdcaaadabbaccbadbcdcadabbcabccabaabdacdcdabddcbccdadaacabadabccbdbdbbbaccaccbbcbdccddbdbdadaccdaccabcbbdcdabddccddbabbbdbbdbbabbbacbdbccddabdbbccbbcccbadbbaaacdcbbbccdbacbdcbbcccaaadcbcccabbcadbddcacabccaabbcbdaddcbcccccddbddcadabdacaccbcbcaccdacbbbabdddaabdddabababaacbddacbdacadcbbbddbdaddbdcdbcadcababcaaaaadbddccdbadcbdacbccdaadbadabaacacbdabcaacacdcbababdadccbbdbacbcacccdabacccbaccdccdbcbdaacaacbabadcdddcdadcbcaacddbcddadadccdaaccbbabdccdbddcdaaadadabacaadbdcbccbbdadbbcbabbdddddddbdadbdcaccbbbbcdccdbbbcbbdcdbdccbdbdbadaacacdbaaaadacaaadabdaaadaacaddaacadadcdbabddcbaccabcabbbdddadcadcaddbcdccbadbddadccbbcabbbcdababbbabdcbbbcadbaabadbbaadadaddacddbadcbbdbacaaddacabadbcaabdbbacdddbddaccddadbcbcdcdddbcabbcccbcbbddccadcbcbdabbbadbbcacdcaccacacbbbddaccbdbabddabdcdddadbaccdcdddddccdadabaccccbcdcadddaaadcbadadadcabcccdccdbadbccdadbcaaabcaaadaccbdcddccdcddadddccbaddacdabdabdccbcbabdcdaadbdabcdacacdbadaaacaaccdbbbacdadcbbacdadbacdbdbdcaccabbbadcdabcdbbdbcddbddacbaaaddabadbdadadadcbacacbdbbadddcbadacdbdadccadabbcbcccbccadcdbbccabadabddbadcccdcdccbcdadacbacbdbdbadbabcadbbacdabcdcbbaabdbcacccdcbdcbabbddbdcdaddadcddccaacaaccdbbcabdbdbaaabbddaaddccbdbbadbacbccdbbbcacaccbcaabddcdcdbccccbdcbdbdcbcddabdcbcbaadccadadccaccbacddacdabdaacbcaccdadbdcdbdaacbddddacbbdacbbbaaaddbddabaabdadbbcbcbbacabacdcccbcbbabdccbdbbddbdbbbacddcdddcbacaaadbbbcaacdaddacdcdaabddccbdbbadcaddbaccdaaaabadccadccbdaacdcdbbacaacadcaddaadaaacccdcbddbbbaddcbdbaadadabbdcddaacaccddddbdbdbccccccaadccabbcdbdaddccacbdacdbababddbaccdcddbdabbadccbdbbbcbcdabaababcdcaaaaacaaadbcbdbcdaccbdabcccbadbdcbdbbadacbdacdcbdadccdaacbaccdadbadbddaaabddcbabbcdbcbdabccbdbbbabcdbcdbacaacacdbccdbababdabdacadcadacdadabcbddbababbcbbaadadbaaadcacbbbbbdabbccacdcdacccccbdadccdbbdcccbcbabaaccbbacbbdbabdbbaacdadaaabdcacabcacbddbaabaaadbdacbbbbacccddbccdddaacdadbbbddadbaabdbabdddcbddbbbdccdcddcddcacbcbcabbdadddccbccacbccacadbabdcccdcbddabcdccdcccadbaabbcbddbbabbdddddbddddacddddcdbaddacaadaabcabbadabcdcdddbacdaccbdbddaadadbddcadaaaddbdcbccaddbacabbbbacddbcddcaccacbcadaddbabbbaadbbdcbbbbcddbaddbaadbaaabddbdbdcdddbdcbacaccadbcbbdbabdddbccaaacbbddbcbdbccaddbadbcdccaddcbcdacbaacdadcdcccbabaaddcacccbdbdcbcbbccbddbcabcbcdaaabcbdbdbcdcbaacbcacdddddccbbdbbdbbccddaccaaccabbbbaaccaccccdbbdacddddabacdddbbdcbdcbdcddcddbcdcdbcdabaddbccbabbbacdbdcddabacdabaddaaaabcbbdddcabcdaabbabcccddcaadccdacbcbaadaadccbddbadabdccdcddccbbcdbbbbdbccbcbaddddcddadaadbbbacccabdabdadaddabcccbbbabbacbcdbacddabcdadbbccbbacdccaabccbdacabaacabbcaabbcdabcdaddadabdcbcbcdabbcdacbacbabacbbaaabcddaabdaaaadbacccdadbbdddbbbdabdbaccbaddadacbdcddbbbadbaadabcdbbaccccddbadbaaddcadcccabbbacddbacccbbbabacbdccbaaacdbadacaddaadacaddcbbddcaccdcccccdcacdbdaaccdddbbcbaacccccddcabbbbcdadaabccdbccddbcccaabcdddbcaadadaddbaaabccdbdabaadcdbccabadbcbcabcdcdbcbabbdacdddbbaaadacbcdbadcaccacccbaddacaddcbddddbacbabdcadbbcadaaddaaaadcbccbadbacadacdacbcacccdbdddccacbbbbdadaadabcabadcccccdbcbcddddaddddbcabcbdcccbabcbacaabcabdabadacacdadcdbbadcdacacacbbbadbcdddbbbcbbcdbbcabbadbdbadaadadadddbbabdcabdccbccaacdbdaccbddadcbcaaaaaadadadcbdaaaaadabdccbabcccddabbdcbacacdcdbcadbdccbdbbbdbccbaaaabcabcadbadbcbccaabcaacdbdaaabdccdbacacdbdccdbbbadcddcdacdbdbcaacdbaaaacaabcbddcabcdcbcbdcacdddbabcaacdaadaacdabbabaddddabbadcdbaaccbbddbcababdbadadddaadbdacabacbcbcddbadccddbbcbbcaaddcbdbabbcdadbcccbcbaaabdaadcbdddddcadddabdcdbbcdabbcadbccbcaacabbdccdddabbbdbadccadbcdbbcdbaddabbddabdacacddccddbdadacacdbddbabdadbbabcbcdbdbbcbaadbabcdcdadaacddddccdaadabacddcdaacdbbbcdacadbcacadccdcdddacccbaabaacbdbabacdbbadcbddcbdbcaddabbabdabacdaccacbcacbaaaaaccbbddbaaddabacdaabdbdddbdaadadbcacddccbbcabbdbdcaccddddcabbdbdbadbbaaadcacccddababcbdbcadabccdddcacadbbaaccbcadaaccdcccabbaadbcccbadacdcabcdcaaaacdaadabdcddbacddbddadacbabcacccaadbddbbdacdadccadcdbbbcbccdcbcbacaabddabcdddacadcacacdbdabcdccddadadcdbbbbbddbacaddcdccacdbcadddddbdcacbbdbcbdcbcdcccacdadcdbbaadbadcbcbcbaacddddabbdaabbbddadadbbbabdaadbbccdcdcdabcadabdbcadbabdabbaabbbbaaadccdacdcccacdbcadbcabacadcccaabbcddcbcddddbbdadcbbacbadbbadacdbadadbcdbabdbdcaddbdaccaccbbcccdccdaabcbabbbcbcbadbadbbcdabcbccabcadaaabcbcdbddcbacbdcddcbcccdbbdcbdbbaddcbbdcaabbbddddadadcbdcabcdaabdaacadcdbcdbbcaddadbcbdcdbabaaddbddadccbcaddbcacbabcdccacddadaacaddbddabdcacdbcaabbdcdbacadbcdcbcddaaddaadaacdabdbaaaacdacbcaabbcacbadaaddbbbbcdbaacaabaddacdabbbccbabddcccbacbdbaacddbbababddccdaddbbcbbdbacdaaacbcddabddcdccaadaabdbcbabcbbdababaaaaddacddccdbbdccdcaaaabdbbbabaccbccacdccbcadcccccbcbaddbadcbbbbcadbacbaaddbadccbabccbdbdbabcccdabcaadcaacaabcddabcdcddccaaacbabbbddcbdaaabcccddbcbddccbddacddbadbcabcbddddcccbdcadaddbbdbdaccbbddadcdddadbcbaabdcbdbbdbaacdacddaaadbbddcacdaddcdabcdbabdbabcdbdddddbddddabbabbcbdbbcabddbdabbbabdadddcdacddaacccdcdcdbbdaccccccdaadcbadabbdbbbcbbacbbcbbaabbaabdcabaaccbbcbbbcadddbadbddcadddabaddbacbabccdbbbdbacaababbddaccadbcadacbbbacbaddcdcaaadacdcbaddadaddbcabdbbabaddcdacdddcbaadaacccdbbbacaccbdcadcadbcbadabbadcadabcdadaabcbdbcbabbccbbdcdcccacabbcadcaccdaabcccbbaacaddbdcacabdcccbbcbbaabaadbbcaaddcaadaabcadcbbbabbcdcacbaabdcdddadbcaddbccacadabcbdcbdccabdaccbaddcabcdddacdaadbacddbbcbddbacccadbbdcabdaccbadbacdadddacdcccacbddcdbdbddaccdcadcaccddccdcbcaaddadbcacdabcabdccccbabddbaadcbcdcbbaaddccdabddcdcdcacaaadccdacbadaacddabadaaabdbccccbdadccccbddbcdccdbcdcbdcacadbdaadbdabdaaaaaaacdbbacacaaccaddacaabddabababdddaacbccbacbacacddbabcbaddacbdaacbdacabcdcbadcddcdddcbdbdcaddaaaabbdaabbadccacacdacbabaddccddbacbacbbdcdddadabbdcbdaabcaccaddabdccdaabbadbdaaadaaaacabdcdbaabcdabddbbdbacbbaddbabbbabbdacaaabdabdabbdddbbdbcacbaabdbbddcabbcdcdacbabdaaaabdacdabbdbabbaaacdabaadcddcdcdaacdbccaaddbdbddcdaababbbdbdbccbdbbacadbacaaccacabbcdacccdabbccbdaadbabadaaadadacbcbabdcbabdbddbbbbbaccabacacacabacadddbbccddcbadaaadbbcbbcbbacaabbdcdcdcccdbcbddadaccdcbcabdcacdcdcbdccabcbbcaabadbcadabdabbdcaddaacbcbbbcacdaacddbdbdcaadacdaaacadaacacacccacbacadccdcdddadcbbccdcacaacbbdabcadadcaddbdcbaaddaccabddadcbcacdbaddcacacbcdaadabcbbadddadadbacccdacdcbdabdbdcaaabdbadbcdbdccdbdbcacdbbabbcaacddbbbdcbcbddccbdaccaaccabbbaddddadbcbcaaacdcbaabacdaccdccddcacbcbdbdbdcdbddbddcddbdcadbdbcdbdbbdcbdaadbdabdbdbcbaddcaaddacabdddacbdcbacacbbccabdddcdcbaaccacdacacdbbbbdddbcbcbadbbdaabcdccbbdbadbbcbabbdcdbbbbdacdbacdbbcdddaaadbddbccbacadcdabbcbacccbacbabdbadaaaddadbcadbcdbcdcbccbabcaccbadcdcdbaddbdbcbaccbddbcdbabddccdbdddabaabbdbcbcaccdcaaaccdbddaccdaaaaacaababaaacbddabcbdddbcacabcdcddbbdcccdabbbaadbadddaacbcdddbacdcddbaccbcaccacdaacccccabadcbacbcabcdbccacbbbabacacdbacbbaabcadcdaadbacdabbcbbbbddbbddaacbdcdabccbacddcccbccbbabbaaaaabbaccddbddacacdcdadcccbccdadcccdbccdddcbdccdabdabcadaadbbbbdbbabdcbbdbdbccbbaadadadbabcdbcabaabdbaadcdaadbcdaabcccadcdadaadabdddcdbadacabaabcabbddabcddacccbccadcbbbbcabdaddacaadaadcacadddbdacddabcddabddcaacccdbdcaadbacacdbaabddbcaadcccdbabccbabbdccdbbadcdbdabbaabbdaadbcbdbdadcdccdbbbcdbacddbdbbabcddbccbdcaadaaaddddabdabccacaaddbdcbcdbbaadbbcacddbbdaaabcbcbabdbcbcddcacbacabccddadcadcadcaaacaacabacbdcbabbcaaccdccaabdbdbdccdcaddabacacacdacbddcbcdcdbddbdbaccccaaacdccdcacbcaccdbdcdcabdaadabbdbdaabbdbaabccbdddabcacadcbadaabaaddbabbbcadcccbcccbbcacdcccbdadaadaddcbdadddaacbaadadddacabdadcdadddcbbaccbccbccbadacbcdbacdbacbaccccdacbcbaadbbdbaccbbdbdbcccbbcbddbcccdadcaddabcbdbabaaaaabacbdcacacccddabbdaacdcbaabbbdddadbccbbcabdddbbaabbaaddaabdcdcdaccbaadcdcdcaabbdcacbddbcbdccccbdccdacdacdbabccccaaabaddccdcabdbddbbabcbdadabbadcccdbcdcdaccdddadbdadbbababdadabbdbabdbccdbdbdbaaccbddaaddddacccadadcbcdcbcbaddadbccdaaacdbdbbccbcdddbcccdbbaccabaaaadbbbbcbbbadccdbbadccaaabdbdbdabdcbdabcbdaadcddaccdddcaacbcbcbbddacddbccbacdbaaacdbcbcbdcbcacaaacbdbacbcacadbbabaccbadccbabbcddbaccdddccddbdccdddcaaaadaacddabdccccadbabcbcbbaaadcadbbbdbddddaccbbbbdbbbcbdbbccbabdaccacbaccaccdaddccdadbcbdcbbccababbcaddaabbabcbbddaabbcdddbcdbcadbddddabadacaabacbaccccabacbabbcbcabcbdccdcbdbdcaabbdcccccbcabbadbcbdaabdaacccbddccabcadcddaabbccbccccaccbaaddabbbacbbcdaababacdaabdbcacaaadaccadaaaaaadbcbbcaacbcbacdcbdddacbcbddddbbabcdaaaacdbcadaaaabccdaadbcdbacddbdddbdabbcbdaaaacdccddabdaaaddcacbbccdcdbdbcadcbdbdbbbaddbbdaacaaddcdaabdbaaadacbcbcadaccbbcbadaaccaadbccadbabdaabdbaddbcccacaddbdcddaaacadcbcaaacdbdacbcddbbbdaddaabbcdabcbcbbcdbbdbbdddcdbddbaaccbccaabaadbcabcdabcadacadbcdabcbcdcddadbcbdbbbcbcccacbcdaadacbbcaadcabadccdccdbcadccbddabbbaacacadbbcddadcbbccbbacddddddaabbabcabdbddbacaccbbcbcacdbcaddcbddbbbbdcabbdcbaddacccabcbacbbbcacacbbdddaacbbdbabbacbbdbbabbaadbaabaaaadcbddacaacadddcbdacddadbabdcacccaabaadbcdaadbcabddcdcbbaabbcaabbcacdbcdadbbdbcccacbcccaacddadabbcbdaccccaccaccadcbaabbbaacabdccbaabbaddbaaaadcabcdaddcddbdbbddacddbdbbcabdaccdcdbbaaaddbdbadbdadaababcdaddccabbacbcbccabbcabbbdbdbdadcccadabadcaccbabcbbdbdbabcddbbcdbbdcdadabcdddcbbccdcccbdaacdadaccdbccdacbccdbdcbbabacdaacbbbcadcbcaaadcbbdabcddaddacbabcbccdadaccaddcaacbddcccaccabaccaacdadbacabaddbdbccddaaadcddacdacacddaababcddbbdcbdababaabaabdbdbdabdabbbdcddcbdbccbbbadccbacbaddaccdacdddcabbdaaaddddaabdcbcdbabadadbbaababdabbbdbdbabcddcaacddaadcddaccbabcccbdccdabaaccadbccccdddadbccabbddcabdddcdcabcbadacbcaaabcdcbdcbdabccddccacddadbcdadadadcbadccbdcbbbbbbcbbdcbdbabbbadbcbaadcccdcccbbbbccabcacbaaacbdbabbabdaddacbbaaacaaabcbcdddcaccabccbaadaaddcbcbbbbdacdcdcdaadcbcdcdbdccabcdbcdbaacdbabbbdcdcdbabcdaacacbabbcaabdcdabbcdadabdbcbdcccdcddccabcbacccbabbbabaacbaacdadbdacadbcadbbbbbcadddbdbadabbcccbcaaacadbddabbcdcdaddbbcbbbbbdbaabaadadbcbbdbbcccdcababddbbbdcdabbbbadadbbacabdbccddadbdbacdbbddbaacdacabcbaabdcdddabbddcaddbaadabdccacddacdbdaadcdbccbaaacaabdbbbbaccbdcaaaaabbaccaadcdbcbababbbcdbcdacabbccadccddbcdadbcccddcbabbabbbbcdcacbaddddabdbabbbcbdddadbddbddacbacaacbdddcbbabddcbdabaccdaccaadccbcbdabcdbcabaabddacbcacddadbcaadbdadbadddacdadcabbbabdccadabbbbdccaaabbbabddbccabdcdbabbbcacbcdcdbadcbdbbcddabdccdadabdcabcbdbaddbccccdddaddccbcbcacacdcaacadcbcacbddcbcbcadcdcadcaddabdadccabaacabacdacacaabdddcdcbddabbbcaaaaccbaacbbaaaabbdabaaabdadaacbaccbadbabbacabbabcacdcdbcdbacaabdbdabddabacdbdccdaaadadaccaacbddbbbdcaddcbbaddddcadcaacbcacdbbbcbbbaacbaccbaaddabbcdbcbacdddccbdcdcdddacbdadcdcddbddcbbccbbbbddaccdbbddacdadcbacacbabcbcdadbbcdaccbaaddbacaadacdaadbcdcdbbdadbabacbcdcccadbaddbabccaccdacacbcabcbcbaaaaadbcbacabbdacadcdcbddcadcbdabccabbcaaccabcdbcccaddbbabcabadcbdbbcddbadacbddbcbbbdbbcddddbbbdadbcddbcdaabcbbdcabdbbddbbdbcbadbdddabcdcdddbdabaacdcbdabdbacbadcccaacbdbcbddaabbcaaadabdcbcbaccccbdcbcbcbaacadcccbcaaaccaaacadbcacaccbddbdbcbdbccccdaccaccdccbaacaabadbacccccadcbcccacccdbdbaadbadbcbadaccdacdbbdaccabdbaaaddaacbabbcdccbaaadcadbcabbddaaadbcccbccadbbacadcddcdabcbadadccbccdacabdcccacdacaaccdbdabcbcacbccccacacaddbbcacacccababbaccddbdacccacabccddbbacaacbbdddcadabbdadacabbaaaddddbddbcddbcbbcabdabcaddacdbadaadccaccdababcbbaabbbbadaacaacdbcadacdbabcabdccccbaaccdcdbcdbdadbbcbbaacddbcdaaadbbacccdddbcbbcaaabbaabacddbcaccbadcaabbbdbccdacdabbcdaabcadcabdacadabbddddadaaadccbabdcabbccabbbcbbaaadbdccaababddbaaacadbabcccdadddadcbbbcaddcbcbdcaaaccbcdbcbbccacacdcdbcabcdccddbdadbbaadbadaaabcabcbccdbdabaabddddaddabbbccaddbabbcdcbdabaaddbbddddccdaccdbdacaccccddccaabaddcbbddcacccabdcaccdcddaddcbdbbcaaaacdabacddaaadbccbccddabadcadacccacabadddbddabddbcddccbcdcbbdadccdddcadbadabdaccccbcbdbdabbddbcdabbaaaadbcabccabbccbabcabacaaadabcddadbcbbccadabbdbcaccdcacdbcadaacacaabcddabcdcbcdadcadcbacdabccdcdaaccbbadbbaddbbabdbdbcacbaaabccabcdbabadcbdbddaaabbbcabaaababcbabaaadaacdbdadbaddbdcaabbcbbbbbadaaddbdacabddcdbacabcbcbccbbbbdaabacacabccdcadcbbbcccddadcdbcbcaaacacadcdbdacbdddcacddbcaccacdabbccabaadadcbdccbcdcbaaaacacbcbadacaddabbabcbddbcbbabbbbbbcdccbcabbcdacdbdaaccdccbacbccdbbabadabacccaadcadbcbcbdcddbdbccaccabdaaaddaabcbcbadbbccadbcccbcbcabcbbdddaddaabcaacdaacabbdddadcbbcadadaaaadbacdcbdadabccdcbcdbccacccccccdcbadcbbcaccabcbcbdcbbaabacdccdcadbdccbcccbcbcaaadacbadddadcaaddcccacabbdddabadaddbbcdbcdbcacbbbaabbdacbbcbddccdccbdabbdabaabbcbbaacadaacabdabadcbcdcdbbbdbccdaacdccdddabdbdabaddaadbcddabdddcbbcadbcbdbddbcbdcbbbbbbbacaaccbacccdababbdcdcbbabaddcdbacbbadcdcaacccbbcbdbdcdbbdcbbdbbdaadaccbaaddcabccbddbcacdabddacbcadbdbababcddccabbbababdcdbdabccabdadacbbcbcbbadcbaaaacdcadcaacaaaaccaabbdbcdbaddddbddccacbdbacccddbaddcbcbdbadaaaaddbbdcccaadaaaaccaabbcadcbbacbcdcdaacbabbaabdacbdcddbbabaadbdbbdaddacbcccccbacbabdcdbccddcbdcccdbdabbbcacabcbacaaabacacdddcabcdcccdbbbaccccccdcdbdbbccbdbbbbbcabaaaddbabaacbdbddacaaadabccdabddaddaabdacccdccbbaaccdbcbadacabdcddddadbabdadddddcdaaaabdcdadadbddcbcbaadabddbddbcddadabbcacaadcddbcacbabdccbdadabdbbaaacbddddbadbbaabaaadaaabddabaacadcacdccccddccddaccaaaaacbaaddcaacdcbddabacdccdbadadacbbdbabddadbadbddccaccaabbcdbbcdaccddbddaaccdbcadcaadbbdaabdddccdcdbcacabaccdcddcabcaddccccadbcdddcdbddcbbbdadccdbcabacbdcddadccccabddbbaacabacaaaccabaaadcbbbabcabadcbddcbbdbbccaaccbccaddabaadccdbdadbaccadabdccaccbbcadacdaabadbdacaacbbdabaadbaadddcaababdadaaaaaabccaadadabddbbbdbccbadcdbabcddbcaacabacdaadaddccabcdaadbbacadadbbcbaccadabaabcacdbbbaccaccdaabbbccbbdddcdaaacbbaacbdcdaadccdcdacbacaaccbcaddcdbbacbcacbaaacacbccabdcdaddccaaccbadbadaddcdcaadaddcbdbaabdcdaadbbadccaaccccdaacdcabbcabddcdcbbcbcababbbbaabcbdacacdbcbbcabbabbaadbccbaaccdbdddccacccacbcdcbddbbbcdbcacdbdbaaabdbacccdccacacdacbccccdcdaadaabcdcdbbabdcddaacdbbaaadbbaddbcdbdcdcbdcabbaadbcbddcbdbbaccabbbcbabcbaccbaddcbcdacaccbddbdcdacacadacacbabdaaaddcdbbbdbcbcbcddbcdabbaabbbbdcbcdbdbcabcbabcbaccabadaccddcdacacbcbaddcaadbdcdabadcbcabaaacaacaacdcadccbbdbacdcbbadcddacaadadddbddddcbcdbacccaacbcdadabdaddcdadabdbcdbdcccadccdcccbdcbdadddbdabbdccdbbccddccdacabdadabcadbcadbddcdcdbabdabdacddbcdbaabdbbacbbabaadccdcadbbdadbaacccbdaabdccadbbbcbdcdabcdddadcdbdccccbbdddbbbdacacacacadaabddcaddadcdbabdcdacbcaaccdcdcadcccaaaddcaacacbcccaadabaddddddaaacdbcaadbabbdbdcbdbbdcaacadcccabdcacccabcdabbdabbdadbacbbcccbcadcccbdadcddbabcdaacbadbbbbadbdddddacadbaaccaacacddbcabadacacacdaadcbcaccabccabdaddbdacdcdadaadbcacccccabbbdcadadcbccbababbdbccbaaabdaaababbdacabdcbbadacabccbdcccbdcabdaccbacaddccdddbadaccdbacdbadccacccdddadbdbdbbcccbdaddbcbabacdabbdadcbcbbcdadcdacbcddcdcbbacddabbcacaabadddddacabadbacabbbcbbcdbabbadbaabbdaccccbacbacacacdadcdbbcadbddbdabcaaacddddcdacdcbaaadbbcdabdcbbaddbbdcdbdccabbdbbaababbaacabbddbaabdcbcaacdcaacdbcbccdddadddaabbccdddacbdaacbdbcacddccbddcacbdcdddddbddcdcbcccabadddbddacbbcbacdaaddcbbbccccacacddcddbbabdbcbbcaccbbcadabdcdbdcaccaabcaccdbdbbdbcdbaabaabbccdadcbbcdadadaddadcabadcbadccdacccbbacbdaccdbddddbadcaddbbadcadbcbcccdaccbcadaccdbdddcbdabacbdbabbdacbacdabddaaaaabdbcbcaadacadbadccbdadbdcabaadacabccccdcaadccababdcacaddcbcabadccbcbcabbcbcccddabaccdadcbcddddcbaddbcacdacbdbdbacabacddadaaabbbccdaadddcbdacbdaabcabddabdddbcbccbbaaabacdabdcbcadcdbccaddccddadbdbbacabaccaacbdacaddcabccababbbcbaadbdacccacadabccaadcabbacbcaddbaacbdbbccbdcabdccabdcdcbabcccbadcbbdcadcbccacabbddcbdcdcabccdaaabdddccbbbdcdabaccaacdbcdbbcdacbadcbadbcababcbbacddcbdbcbbcbaadcaabdadbdcbbadadbbdccacddaaadbddddabcaabdcacbbdcadbccdcbacbddbcbbaaacaabdcccaaaddddbabccccddbacbbcdbddcaacaadccccbbbbcddbcdabaacbaaccbbacbccddbadcccbaabddabcdabaaaaaddcddcacdbcddccbacaaacddddabdaabdaaaadcdbcbbcaadbcdcdcaaaacaaacdcacddbbbcdbcddbbabbbacbcccdbbaaadcdcdccbcaadbcbbcddacccdadbbaadcabcdaabdccdcbcabacdbbcdbbadadcacbacacdcaadbcdcacbcadcbbbacbababdbbccdcdcdcdcbddcdabdbdaabaaaddbcdddadcdbdbbababbbabbbddbccbddabaadcdcaaacdcabbdaabcdcdadabdcbacdcdaabbcbdbdbdadcabdbdddbabadddbbbaccccbbbbdabcdadcbbcbaabcbbbcbbddaaddbcbbdbdcbcccbddabddabddaaadcadacaabbbaabbcccadabcadccbddcbdaadabdbdbababadbbdaccacbdbacdbdcdcbcbcadcabcacbbcbaaadabbddbbbdbacbddcabbadddcccadbcdcddabcdbaabcbdbaaadbaadccaaacdbdccbdcbbaabaccbcdcaacbdaccdbdbdabcbdbdbadccddcbdbdabcccdbaaddbdabccddaccdacaacbadbcaabbbbdcdbcbbdccdddbcaadccacabdbbabcdabacdabbcacccaaabdcbbcdccddaddbcbdbbcdbbabbbbbacbcdcccaacbdbcbdbaacacaacbcdcaadadabdccdddbadcabbdddadadbdbdbddbdcccbcbadbbdabbadbddccabbaadbaaaabacccdcbdcccacbddbccaccbdaccdcdcadcabcdbaccaadcddbcabaacdbbcdbaddcacbaaaabcdccbcddbdbbaacbddabdbddbcbbccacbacadcddbbcccaaddabaabccbbcabdbabbbccdabadbcadacdcbbbdbabbbabddbadcbcccaacbbacbddddddcbddcdabacabcabcbaaccbcdbcdccbdccbaacbdadddbbbcaacbbbdbddccccdccbaadbaaaadcdccabcccaabdcbcdcdbaadccbccddbbddccbdaacadbcbacbbddcaddbdcaaaaccaddcdccdddacbabcacaacdadcdadbbddcbbbadbacddddacdaabccdbbaadaccacccddccdcaabdabdacadaccabdcacadcdddccbddabcdabdaacadcadbcdabdabbadccdadaaabbacaacaccbdaccacaabddcbdadabbdddbdcddcccaabacbcacdaddbcbacbbaaadbaaaccbaaaacdbdaaccbadcbbdacacdabcaacbbcbccdcbbbbbcaaadaadddcdadbdcccacbccacdabccaacbdacbcbdaacccadcbbbbdabbcaaccbdbabdcbabcdaadaccbcbcbabcbbbcaaadaccabdadabccadbcaaddcbdbbcdbcaacddbddbcbcbaaadcbbcacbbcbccbacadbcaaaccddccbdddccbbacaaadaccbdadaccaababcbdcbabadadabcbbbbdcbdabbdbabcbddddccadaacccdcdcaccdaadabbcddcaacdaddbdcccbcdbadbdcbbcddccbbcddbbababaabadcbaabadddcdbbcadbdacbdbdcacaaaddbadbababaccdaacdaaaccbbacabdcababdcdddaadabcddcddcccbddbabaacabdcadbcbbcccabbaaaaddbddaadcadaabbabaacadabccbbdabdcdcccababacdcdadbababcdbbbbcadaaddbcbbdcdadaddcaacdbabcbaccbbaabdcacbaaabcdbacbddddbdbacadbbcbacacccdddcdbbddacdbacccbbbdccbcdadcdcdccacbbbcacddcaccacdddccaabccacbacccccdbdcdddbccdabcbbcbbabbdbcdbabacddadcbddddadcbcbacbaaaaabdaaabaddcababdaaccccbaadbcacdbbadbdddbdabccdaddabaaccdddbbdddbcddadacbbbcaacddbcadbaddaccdbbbbdaadcdbabacbddbcbdbcdbcccdcbdcbbaacacccdabcadabaadaacccabadabdbcacbccdaddadbbdddacbcbbbaabaacbdcbdcdbbaacccdbbcabdddcdabdbddbdcacbdcccabbababddabbdbaacbcbcbbcbccdcddbbbcdcddccaaacddcdcdbbdcdbcacbabcbdcadbbcabaadaddcadbbddcaadcbbdacbaaddadbcdcdabcbbdabacdbbadbbccbcccdaadcbabcaccbbcabbddcccccadbdddbddbdbbabaccbdbbdbbccbbadaabbabbdaaaacbdcbabaaacaddbacbbadddbdacdcddcccacccdbcbdbbbccccdcdbaddcbcacccccbdacbbdbbacbcddadbcdccabcabddbdbbdbbbdaccdbbdacbcccacababadabdadabcacbdbccaaccbbcaddabcdcabaadbdcbbdadbbcdbbbcccddcbddbbaabdcbbaddbcddccdccbddcadcabacdadbcddbaccbdccbdaaabaaddaababddadccbbbcadcddaddbddcccbdaaaccdabbbddbbddcbbccadccdcddddaddadabacacdcdaabcbabddcbdbbdaadbadadbadadadabbccabadccbaadcdbbbdaccdcbccaaabbbddaccbcbacdacaacabdaabddddddabbbabcbacbbaadaaacbacdaaddccbbdbbcbbacbdcddbaadcdddddcddaacbcbaacdabdbdbccbcdbadbbaccbbdbcdcccbbcdbaacbbddbbaaccdccadaddcdbddcbacdbbacadbdbddbcbabacccabbdbcddacdbbbbbddcbdbcdbdbcdcadbadccbacdcaacacdccbbcddabccbbbbabaddbcacadbbdbdaabbcabbcbcdabdcdcdcadaaccddddcccbcdbbdccadbcdababccbadcbddadcbcbabcdabacdbdbbadaddaddcabcacbaccdbaccddaabaaaacbaaadddaaccbbccacdacacacacdabbdacaaacadddabdcddaccddbcbacadbadcbccacbcbdadbdadcbbddcabbacbacabdcccbacacbdbdbccbdacdcbddcbbadcacdaddccbabaccdccbaaabadabdccbdddcdbdcbbaadaacbbbbaccbaddccbaabcddcbaadbbdccadccdcdbbacccddbbcbbdaddcaddadbcaadcabcdadbcaccacbcaccbabdaaaadbcdbdbacaacbbcdabdbaadaadbaaabdcbdadbcdcccbacddaccddbbcdccbbabdccabcdbdacbcbdaaacbcbbcaacadddabbdcbccdddababcdddcbadbbbddccccabdcccddcacdcacddbdbbdadbbadbcbbcacdadbdaaadbbdccdcaabdbdaadcddbbaacaacbccbdcbdcbbabadccbbadacbdcbbaccccacdbabbcbadcaaabbccdbaacadcbdaccbbdbddaaccccacddcaaabadacbccbbbaabdabcaabbbdadbaaabddacbdacabddadcddacdbabbdddbabcbaccdcdaaacaadaaacdbadcadcdbacccaadbddccdabdbbaacadaaddbbdacaccbbacbbadbbadaddbccbbdbaccbdbbdcbbbccdbacccabccaabbccacbccbbabaddaababccbddccabaaabdabbcbcbbbcadbbbdcddcbacdccabcbbccaabcdcccaccbdacccdacbacdddbbadacacbadddadccdcadcacdabbdaacbaacccbdbbbbacdbbdacadbdccacdcdabcbddcddbdbcabaccbcdaadbdabdcbbacccbaaaaccdaaacaabccacacacdabaabbbbaaadcdacdaddcdcbcccacacbcccaddbaadbdcdddacbbcbbdbadcdcdacdabbddabababadadadbbcdcdabddbcbbbaccdadbcdddaccadaccaadbbdabcbddbaaaaaddcbcabdbcaccccbcbacadaadccaaaaaacbbabbbacdcbccaaaccaadabbbbdaadccaadddddadcaccabbbabcdbcdbacccaaccbadbbdacbcabbcdddbcbbddcbbbbdcadccaabdbaabcaddcccabddcdbabccddcbddbbadbddaaddccdcbdcbbcbbcdcacdcbbcdcabccdacbbdccbaacacbccabbcddbcdbadcadbdcdcadbccaaaadcaddbbdbdccddbcbbddcccababccacabdaccddbadbbbbadabbdaadcdaaddccdbaabccddaabcdacbcdcddcacddbacacbabbccaddcbcacbccddbacbabcccabaaabcddcaadadbddbcacacbabbbcbccdadcdcddcaaccbddaaaaadabbaabdcbdcaccdbccadbdddbabcacacaabcaccababddcabcabdcaadcccdcdacabbcaaccbabbaccbbccdbbadcabddcdabbbbdadcabacdadccddcccdaabcddddcdadcadaddabaaddcaddbbddcadbcbbdccacdcdcbdbbbadcabaddbbdcbaabbdbccdccdcccbbdbdcacdbcbdbadabbdbbacccdacadbadbabcdaddbbbddbbcdcbcbdcdabddbaccdcdbbccbbaaabcbbcddabdcacacbadacabbbaabccbbaacaaabcabaccadaabbcacddcddbddbaabccbcdaacacbddbcdabaadabbabbdccaaacdcbddabaacaabccadcddbdddbadcbdcdcccbccbadbbdddddadadbdcbdbacdcbdaadccbdbcbdaccbbbdccbcdcbadbcaaccaacdbddbabdcacdddaabbcbddcbbbdacaccbbcadacabdbbbcaadabadabbbbaabadaaabccaaaddbbabdcadbcadacdabdbabddbdaabcdbadbcaacbccdabacdbdbdcccccaadadbcddcddcbdcbaccacddddcabbaadcdccaacbdccadadaaaabaadccabcdbcbcdddbdcabbbaccdccaadcddababbccccdcbbabdadbadadacbaadcdcdbddacbadcacbdbbcdcdcaacbdacadbdbcccadabdcabbbdacabdccaccdccbaddacdccbbaadadbbcbdcacadcadabccadacbacddbcaabdbcbdaccdcbbddaddcaddbbdaadbcbaadcaaadabbabddddabcdcaccddbbbcdbddbcccabbcdcdbadcdbddccdbbaddbbdcaacdcbddcbcccbdacaaacbcbccacdbddccaaaabbdccdccaddbcaacbababcbcbdbaabadddaddbdbadcdaacdbadbcaadaabcdaccddcccaaaddacaddbaacdacddbcacbcdbcdddadaaaacabcddcbcddcdadccabacdddccacbcddaadbbdcdcadaddbcaddbbabddcddbccbacacbdbababcdbaabbbdcbcdabaadcadcbbccddabaadddaabdddaaddacbdddcddabdcadbbdccbbdcbcbdbacacbbdbbbcaccddacbcadadacdaabacbacbcaddaccdbdadbdadddcbddcccdaacdbacccbbaccbbbabbacbccaaabcabcccbbacdbcbacadcbccddcbbaccdadcaacdabaaaacaccadabcbbbcddcccbcdccddbdbbcdcbadddcdacbbcccabcadacdcddadabbacabbbbaadaabcbaacacdbbbbaaccbaacaaaddbadabacacadabadabcdccdabbadcaaccdbdccbbccacbcccbaacabbddbaaacbbcaaccadbddddcdbabadcddacbdcbadbddcdcbdcdcddbabaaabccbadadbbbbdcdbcdddcbbdbcacaaddadccbacbcaabcabbcbcabbcbbaabdbaababacccabbaddaadccccadcacdaaddbabcdbdaddabcdadbdacdaadccbbdccbbbabbadddadddbcdccabccdaddacccdaabacbbcbacbadcdbaadbcddbddbdadbddcbacdbbbddaddadabcababadaaabdadbddcccccbcdaddaccaacbbdbacbcdcbcbaabcccbbcaaabcccabacdbabbbcbddacaccadcbcabddddababcbaadabacdaaabcdaaaaabccacbcaabdcdaabbcacdddabdaadaaccbcabbacdcaadaaadcdadaccbcdaadbaccdbdcdadccbaaabcdcdbbbdaddbbbaadabcbbdacadcbdddadaacadcbbdbabcbdacaaccacbcbacbcbcdddbbddcbacabadbadaacbcabcdaadacaacbabdbddbaacdbbddcccdbccbccacdacccbbabcdbabddaacdbdcddacbcccaaaaccacadddbcbadcbccccbcdcbbbcddbddddbddadcccccbbabbacdcacaadddbdbaaadbbcdbdbdbdacbddadbddbdacbccbaadaadcddbcdaccbaacdddadbcdcaaaccbddcbdcdbcddaabadccdbcacdabdcabdacacbdbcdbaacabaabcddaddbbaddbccbcdccddadccadcabaccacbcaacccdbdcdabbdbaddcbaccccdcaaaddcdccdccddadccaddcaccccbbbacacdbaaddabcbaacdacdbabbbcaacbaacbdddababbccabacdaccacdcabaadacbacabbbbdbccbbcdabcacdaabbcadcccdccacdbbaabccdbaaabddcbabdaacbcacadacababdbaacdccbaddcdcdddcbdbbdbaddbbbabbdacbbacadcdbccddbbdccccccadbdbdcdbaadcddcdbbbcbadddabbbbddadcccaaabcdabbddcadbdbbcadabdcddcbdddaddddbcdaabadbdacbbcdaacdcaabacbaaaaddcddddbacccbcdccaabdaacaabbabaabaacbcadccaddcdcbbdbadcabacddacdcdabbbdcbbdccdbdbcbcaabcaacbddaadcaaadcabadbbcddcbaccbaacbabcaabdcddcbdcabadaadbbcdbdbbdcdadaaaddaaccbacccacababcdcabdccddbabddbcadcadbbbbcdbcbccdacbcdaadccccdbadbdcccdbbcdddcdccdcdacbdddcaaacaccddcaccbadcdbdddbadcdcaabaddcbdadabccacbddbdacbcbbbccaddbdddcaccadccacdcbabbcdaabddbcdabccaadadbbaaadddbcbabcabaddcdbdadbdadabadbcccccaaddddadbaadcbccccbcccbbcbddddacabbcdbcacdadbcabcbdbbbdccaacdabcdaccaddabbabcabbbbbbbbdccddbcccdccddacdaabacdddaccbabacbacbdbdbbbbcbbaddcbacdbccddddbcbdaadaaccdaababcaaaaabdbcbcdddabbabbbadabdccdbcbdbacdcadccccbbacaaacccbbccdaddbadcccaacdaabbbccbdabddcaddcabdddadacccdccbbcdbaaaaaddccccbdbbbdacacdaabcbbbabdbacdacbbaccdaccbbbccacddaddbbbdcbdcdbbadbdddacaabadbadadabcdccbdbadddcddbddabbdaccbbacaaccdbdbbdacbcbcbacbbaacddacbdcdbadcbcdbbabbbddcacaaccaccaccbbdbddbbabbbcdabdbdadcadcadcdaacaaacccccbcbadabddbcabcccaadbdacdcdbabbadabdaacdccccbcbccbbacabadbbdaabcabaccdccdbdbcaacbbdadccdcaabadcacdababccbdadaabdbadbbacaaccbcddcdbadaaaacbcdbaaccbaaaadcdcbdbccadaadadcdaadadbccbcaaacbdcadbacdadabbaadcacacdbabababdbcdadbcbbddccdabbcbaaccdcbcacacddbcacdcabbdaaabcadbdcdcadaadbbabcddcacbcbabbdbccacabcdaddabacaabccbbcbddadbadbccbcbabbaccaadcdaacbddbdabbddacdbbbcadbbacdddcbbaaddcbbbbccdacbbccadabdccbcacdcbcdbdbdbbcdcbdaacaaddcccdbbdacbacbabbcadccdccdbdbddbdcbbdcbddddcbbababaadadaddbdacdaddacbcbcbddcddcddaaaaacddbcdbadaccdabcbbadbdddadccbdcdcacbddbbcacaacaadbcccdacbdaabadacddabdbabbdcacbcabacbcabbbdcbcbbcdcccbdbdbaacccbacaabcaabcddcccacdbaddbbdbaadbbbbbcbbdcdacadcadcbbbcacbdbccadcbdaddcabcbacaaddacdadadabaddbaddaddccdaaaaccacbbbbdcbcccaababdddbdccbcbacbdcabbdbacacbcddaacbddbdacdcaccbcbdddbbbabaaadcaacadabccaaabdabadacbddadacbcadabbdccdabdabddcbcbabcaddaddaacacbaaaadcccccbbaadcbbcabbbdadbccabcbbccdaccbbbdaadbdbaadadcaabddbadadccccadbadbbdccbbdadabddcccbbdcaacbcbcabbbabadaacbbdcdbadadadcabcdbccdbcddbbccbdacdcadcbbcdccbcbaabadabaabacccccacbddccdbcdacabcdbbabdbbcdacddaaabdcbcaccaccbabdbbcddcbcaabacabacdcabbcbaacccabcbcbdaaacbbaadcdadbcabdbadabdddbdbbadbadcbccccbadbbddbcccddbccddbaddaadcdcbacbabbadcbadaaacbbdcbaacbbdbcbdbacaaddbbcbdbbabdbcccaacbbbbacadacbdbcbbabbbcadbdccbbdacbbdcaccdcabbdcabaccbdaddcaddabbacaccbcacbabbcdadcadbaddddabaccdbccbbbcbddbccbbccadacdcbabbabcbcddbdddabbabccccbccbddacdacbddabadbbcbadbbadaacdcbbaadcdacdddbcddccccddacdababbcabbdddabaaddbbdcbdaadaabccccabccbbdbbbbabbdbaadcbcbabcdabbcdbdbcddddaadcbdadbddcdcaabdadbbbdcbbdbbcacddcdccacbdacdcabdbbaaaabccdbbadbacaadbdcbbacadadadbcddddacdbaddcadcddbdbcddaacbabaadcbdcaaaaccbbccbdbcbaacbdbacadddcdcbddccdbcacabbccbcbcdcdabacabdbabcbdbaabbadbabaababdbddbddcacaabcbacccdadccbbabdddbbdadddabcadcacbdacdaadabadddcdaaaabcaddcdccccbbaddadcddbbcbccdaabdbbcbbdacbdbbcbbcbccdabadcaabccbbbcacccaabccdddcdbacadddacbcbccdbcacccbddcabbabcadcbddbdaadaadbaaacbaccdbbabadbabbabdbdbcccaaadccddaddbcdbcadaaabbdcaccccbcabdbcabadcddcdcbdbdcbccbcbdbababcdbadcbcabaacdccaaccabbcaabcdbcabddadcbbcbacaaccbcacdbdabdcdddaaaddccacdadacdabbbbbdccdadcccccbadcbcdbdbddacccddbcccaabddbcbcabcdccbdacbdddbbdbadaaaadbabdddbccbbdaadddaaabacbaaccbbcdcadbdaaccabbcaacccabbddcacbadadbbdddcbabbdcbdaadcbcabcadaaabccdbaaabbbdcaabadcbccadccdacabadaadcadbbdcbbcadcaadbdbdadacbdaadbabccaccbddaabdddabaabccadabbabdcccdbccacdbddabbabcddcdaccbbadcbdadbacaaabcbdbdadadbcabaccddadbcbbcdaadabaacbdadcbbaaadbccaddadddccdaccdadbdccdddaaaabcbcadbaccbcdadcdccdccbbbbcabbacbaaacbdbdbaabaccacadbadaccccabcabcacacbddaccabbabaddacacdbdacccbddadcddbcaadcdcbcacbdbbdcacdadcccdadbcababbcbddcabcabbcbdddabcdcbacacbddddddbaadbdcbdbabaabcbbcabcadddadbbddcabcdddbbcacbdbbdcdcbdcbdcbdbcabcaabdbcccddccaddacbcabcacaacbcacdbcabdcabacbadcbbbddaacdacddbdbdccacbbdaaddaabbabadccadccbddbaacbccdddabddccdaabcdaabddadccaacbbadcacadccccaabbacdbadcaadccbdaccbacadbdcccbbdbbcdbcbacbcaaddddaaaadababbcacacbbdadabccbbcbcbaaddacccbccbaaabdcbaccbbcbabccacdbcbcbddddccaacccdcabbadacdabaddadbcadcdbabbacbcaadbcbbacbaacaaddadadbadddbaadacbcdacaccccabbbcddbdababdbabbdcdbadbdacaacbabbdddaadcbcbcbcabcbadcbabcadcadabcadababbdcabdcaaaddaccaaaadaabdcadadbcdadcddbaaabaabbccaaccaddabcdbcbcddcdbdddbcdaadccdddacbbcbcdbaadccadbbcaabbbcbdbbaadcbdccaabdbddbdbcbccbbdcbacadccbcadbacadabacabaadbdabbdcbadbcadcdbbccaddababbcbadcbadcddbcbdbbaaacbacbccddaaddcacacbbbdacbdbdadbbdabbdbabcadacccacbcbcbddbaabaadcadccabdabbaaaaabacbcbbbcddabccabcacabcadbabadddccbbddcbaaaccdcdcbccbcdccdcbccabacdbdcbbdbaadccddaaacdadadadcdcbaddcaababacadbbdaddccdabadaaacaaaaabdbadcdcdaddddcbadddabacbaaccdbcabcbbabdbcbcadbacadcbcbcccbbbbaddabdddcbdccdbcacbbaaadddaddbdddbcdccddbddcacbbbbccbbbacadbadabdbacccacadabcadbaabdabaddaacdbdbdbbdcdacdcbccdcacaaacbcccdbcaaabadadadbacccaacaccaabbcdbdbbacbccdcbbcabcabcacdaaaabcbddbabbbbcdbdbcdcabddbadcaddabbdaddcaadbaabacaccbbcbaaabbbbcbadacdcabccaacbccbaacccddbbdabadbbaabbdbabcccddbcccddbdabcdbddcbdaaabbbdcabdccacabddbdadaaddabaaabdbddbcdccaccabdcbbdcbbddabaccbbdaaadbdcadbbbccbdbbbbdadbbddbbabaaadabcbbabcabadbccdbcddcadadccdccdabcddbadddaababcbacbadbbbbbbadabdddbcbdacccbdddabadcadabdcdcdcbcccbaccacadcacddcaadbddacdcdbcbdcbbbbdbababaddccdcabbbdcddbaddcaadddbddbbdcdcbbdabdbaddddddbbdcaccaadcacdbabcabcaaaababbdbddbcdcabbcdddbbdbbacadccdcdbbbdcdaaddddcbbaaacbbdadaadadbbccbcdcdbdcccabbbbaddcaadccbdbbcdccaaccbacacadaaaddbacddcacbccadaacabbbdcbdbbbadbcccabbdbacccaabbccdcdcbabaadccbccbccbccaadbbcabddbbbdcdcdcaadcdadabaadacbcdcaacbcdcadababbcccacbdcdaadcaaddbadabdaddaadaddababbaadbacacabdbbbabbdcdbadddbcdacbcdcbddbaacdacddbdcabcacacdaccaacbbabdaacdddaaabbdbddaaccabddbcbaaccbbcabccabdcabcccaaadcccdbabadcccbabaacadbadadcaddabcdaddbdabaaabccccdbdddddcdabbbdbdcacbaacddcdcadaaaaabdcdcabacadbadbaccdaabddacdcacbabdbbcbbcdccbccddadacddaddabadbbbbbbddadaacadcdcaaacbcdddcdddbccbabbcabddccccbbccdbaacbcbbaccacabdcdbbcdcabbadccdadbbccadccbddcbacccbdccdbdcddbddaabcbbabcdcdbcadcbbddadddbacbcddbdacadccbcccbdbbdacbdccbadccdcadcdabbcacbddcaccdbcaacbbcddcdbbabdbcdcdbbadaccbcadaaabdcdacdbccbdaabdbddbdcbdcbdbbabcdabcdccdadabababadadbbdddccabdbdacddcdabbcadbcddabacdbaaaacbcddbcdddbbaddccbbabdacabcbdabccbdbdbdaaccdbadcabbacabdbccdbdcbcadcbdbabdcbdbaaacaccadbacaadbcdddcaacdabccdcacaadbcdbcdabaccadadcccbcddcbbcadcdbbbbbbaadcddccccddbaabbcbaadadaadadaaabcabaacacacacacadcaabddbddbabcbdadabbbccabaaaadccadcdbdbcddbadbdcaddaaddddcabdbcbabbcbaccddccdabbbdbcccadbcdcaaaccbbcdcdadcbdddaadaabbdcabcbdabdbbaccacadbaccaadbdbdaacadcacbadcbddcbaadbccccbbbaccacababdbddaddccacbacdbcddbdddabbdaccccbaaaaaddabcacaacdcdcaddaacababaabdbdacacdbabcaaaddacccbacabadccdabbcddaccabbcbdbdaadbdcccccaaccddbbdccbcacccadbbbbabddccbbbacbdbdcdabbdcdcbbbbdaccadcdddadbcdbdddcddbacddcbbcbdcbddbacaacadaccbacccbcddbbbababdbdcaabacdabddccbaacaabcbcadcacbbacaaabdadababdbaadbbcacdccbadbccdadadcabccdaacdaadbdddddbcbcbbbcdddabdcaabadcaaddbaddccaaadbcccbbbcaabccaadaddadddcbdbdadaabddadadbbddcbabcdbbacbcbbbccddabcbaababdccdbcacddaadbbaadbbbbdbcaccabcddabacddbcadddaddcabaccadabbcbddaacbbdcdbabdddacbcbcdbbabbcbcbbcbddaccadbabdcddbabddcaacbdddcdadadcbcacdbadaccbcbbccabbdbcaddbdccbabbccbaccbaaaaadaadaabbabbabacabcbcacccbabadcdddacdaddcdbccdacbaaaaacdbcabaabdadacbddaabdcabddcabacaaadaaaaccbbddbdabcdadabcdddbbabdcbabddacdaaaadadabaabcbdaaacddbbaccdbdbbddaacddcbdaababbdaccdccddbbdcadccabbcdaabcddbdaaccccbadabbbdbcbddcdbbddacbcddbdbdacadbcaaabbdaacbdacdbddbbcccacbbabdcbdacddcbbaababdbddbacbabbddbbcddbbbaaccdadacacccabbbadbcbadbdadaccbbcdcacabdcbabdbacbacbbbdcabacbcdcbacccadbdbabcabbbbddbccaaccbaabcbdaccacccbbcabadbdaccadadcccaaddaabbcadaabbbbddbbcbbababbdbcccbbadadcccacbddbdadddddaddcdbdaaaacbccdbdddabcbcdccaabccdcddccccccdaabacdcccdbdaaaccdacaadcddbbcdacadaacabaccaaadbdcdaabbdccbbaddaaddcbdbdcdddbdacbacdadbdccaaddabdcababbadbdbbacdcdddbaadbadcbbbdaccaadabbdacdadaccaccbbdabbbddcabaaadddcdadccdabcbacbabbbbcabdbbccbcdbcccbbbabcaccadbdaadabccaadccabcabbbcbacbaddccbccccdbdadbcbaccacaadbadacbccaadccccaacadcbddaabcabcacbadabdababcdddbaddbbbdbbbacbbdcdccaabcddcadaccdbabdcaadadaddadbdabbbbaaabddccbacddbcdadcadcaacabcdcacabdcddcbdbbacbdabbbdcccbaacdbbbbbaccccbadccbdabdbcbcabcdcbbbbbdbbaacaaadaccabcaaacabbaaacddabcdaddcabcccccbbdbadbaddcaadddaabbdddadbcccdabddbdadccddaabbacbdbbbabbbcaccacacbddabccbdbdadbabbbcacbdbabcbcdcccacccabbdacabdbcdcadddcbadabdaddbaadbbdabbddaaabcbaaacdaabddabddcddcdcadcdddacadacbcdbccbccbddbbaddbcaddddbabbacaddcbdccaabbcbadcdbdcbdbbaadbcdabbdadbbbbdacccabcbacbcbcddccbdbcabcaaabadabcbdabdbdaccaaddaaadcdbaddabbbddccdacdbddbabbdbddacccaccbabacdaaaaddaccaaacdbaabddadadbccbbabbbbabccdddcdcdddbdccbdcbababdbacbccbdbacaddcbcdcbacdadcdbbdbddddcbdddbabddcaabacddacdccbdbbdbabbccddbabcbbadcdabbdabcbdcdcadbcddcdbbcbddbbabcccabababdcadbadaddaabbbbdcbacbddacadbabbcdbcadaadcabdcadadadbbcdbbbdcabcbddbddaccdaabcadacadcdbbacbabacaadbccabdbdaaaacbacadcadabbdbbdbbdadaabbbcbbccaabbdcbcacdabdacbabbdcacdcabcccbcadaabcaadcdabccaaaddabaabdcbcccbdaaaabccaaadbcbabacababdaabbdaacbdddabccbadcbdabdddbbcbcdcbacaccaddcdcdbcddabcabacbdadbdbbdbbcaaaadcaddaaaccbacaccbdaddcdaabbbaaddbdccabccddbacabadcaddddddcbbbdcccbdbcaaccddcddcaabaddadcbbcadaadaadabbaddddccddbdaacbabbddcabcadbbdacbcaabccdbcbcbddbdaadabdabbdbddcccabcacbbdddbcadcbdbbddcbaabadddccbcdadcddcddccadaabdbadbaabbdcababdacadaabbbccdbacbabaaabbcdbadcbadcbdccddbbbdadabcdcbcdacbadcbbdacaabdaaddacdacccabcbddacadcdadacadadbdcbadbccadaccacccbbccdcdaddabccccddcccacaacdddacbbadbadcdcbbabcbbbcbdbcaccbcccdaadcadbdbaaaadcccdcdbdcbabdddabaadacaabaccdcccdcdddbbbcaacdadbddcdcbddbabcdbaabbadbaaaadbcadaadbabacbbccdadccbdbbddcbadbbccbcacdbdcccdbcdabccdccabcbbbacbcdbdbddbbcdadaacbaddbddcbbcdacdaabbbdbabdabddcdbddcdacaabaacdadcbdaddbcacdcbbbdcdcaadaadabbacbcdabcacdacccadbcddaaacdbbaabcbcadcaddadcaacadcdaacadcbbdadcaccddcaccadcacdadcabababcabbdcdbbdbccdadddccaadcadbcdaabaccdabbbbdaddaabacbddbaaddbabaabbbcdcddabdccdabdacadadcddccababcbddadcccdbbadcdcabaabbdbabbdabcbbbdacdbcabcaacdcabdbcaaddcdadcdaabaccaaadabdbbacdcaadbccdccdbbcdadabdbdaadbdadbabbdcbcddccbdccccdacccacaddbcaddaadbcaabadcacccabddbdddbdadbbbbddabccdadcbadbabccddbbbcaccadadaddaddadbccbdccabdddcaaddbaadabdddccaabdcdbdcaaaabcacddaccbdbbaadbaddacdbcacbdaadbdccacdcadbcaadaddadddbcabadbacdddbbcdadbbdccacbadbacccbbaccbbcdcbdaadbcabddcddbaaabcaabbbcabbdddcbcbdbadbaadcbcbbaadcdbadaccccbaddcbbdcabbcaacbabbbadcaacadbddcccddcadabbaadbbdacbaddbcadbbbbdddcbcbccabdddcbbbdcabcacbddcadddbdabccdddacdacccbcdcdabbddccacbdcdcbbadbdbbbcbabaddbdddbdabbadcbcdcacddaababaacbaacccbbbcbcbbadcbbbacdcbdadbabbaabaabaadccbdbccabddcdbaabccbbccdacddaadcacdacbcbcdbdacacbccabadbadcbdccdbbccbaddcadaabccbcadacddbcacbaabbadcbaacbbbbcaddcabcbcbaadddcbdddaddcaaaacddcaabdadbbaacdccadcccbccbacdcbacdbcdcaacbccaabdbddbadacbdbdaddadaabbcdcaaadcbcccdbdbcdbadcddddcccbbabddcdcbaabccdaabababccdbcbacdadaaaadacababbccacbdbaadcbaaadddbcaadcccbcdbbabbcaadaababcbacaaacacacbbcdbccaacccbbcdccbadcdddccccbabccccabbcbccdadccbaaddbbcbdabdacabbdbdaddacdcbcdccacbcbbacddaaababccacadabdacbacbcbdcccdabdacadacbbbbbcddadcdcaaaacbdaacaadcaccdcbccbccabdbabcddbcacdddcaadbbbcbcbbaaacbacaccbbcdcdbbbdcccaababbcbaaadbccdddadbcdcaaccaaabbdbdbacabbdbdadbcbabbbbbbdcdbddcbdcdbcadbbababaacbdcbdbcbdbcbbbdbdadacdcbcccacabbbaabcadcddcbbdcaabcdbbcaabdaaadccdbbadbcccbcbbbaadaadbaaacbbdddccdaacabccaacabaaccddddcacdbbdabacbabdacabadaaacaddccdaccddbcdddadadcbcbadaddabcbccdbccdbcbdaddcdddbcccababaabccacaacaccbcccbbadbccbabdccccdddccdcaddcbcabbddacabadcababcadbdbbcdddddcadbcdcdbdbddddbcdcbcbcdacdbabadabcbcbdabccdadcddcdabaacdadbddabbabddcdbbbccdcaaccbbbcdcadaaaabddcacbdcbbaccabcccaacadabdcabdbaadaddabcbbbcabaaccaabaacdcbddadaaaacdadaccdadadcacdddbaccbdcddcdbbdddacbaadbbcbcadcbdacbdcbbacbbabdcbbcbcbdadabacbdbbdbcacdccdcddcbaacabbcdadbacbcbabbdbccdabcaabaadcabdddcabccdaaaddbcbaabaabbdaabbcacaccdadadcddabdbcccadbbaccbdcbbddbabdcdccdabcddbadaccbddddcbdbabdacbdbdabcbdaaadcacccaabdabaabbcdcccbcdbaacbcdacadddcbdadccdcddbddbdcbabddcdddccbbdddcbabbbabcbbaacbaddbbabdabbdabdccdabdaadddbabbbcdcbcaacadaacbbdabaddccdabbcacbacbdaabcdcbdbadcacdbdbddcbcabadbcbdbdcdcaabcabcdabaacccaacbbadaacdcaddbdaaddbbccdacdaddddabddabdabaddddcdacabbccdcddcbbcddccddbcdbbaddacaabdaadacdadacbddbaaccbddbadadbddadaacbaddcbadacabadadcdcababdcbdaccdddbbbdbccabacaabdadbbccacbddcbdababcddacbbccbabdbaaacdbdccaaaabccbccbabbadbcbcbcbabacddcdbcdbabacbadbdaaddccbabbacdabadddbadabadbaaadddcbbaabbacdddacbbbbadcaaddbcabacdbacaacbcadacaccacbabbbbaacdcddbcbdcaacaccdbaaadbdddbdadcaadcacaacddacbcaaabdbaaababdaacdbdccadcdadcbddbcddadbaabbcbacccdbacbbbaaadcccbdccccdcbdadcbdbbdbabdbdbbacbaccdabadaacaccddccbbccddcbcddbbbdaaacaacbbaabcbabadaaabcccdaaacccddbcabcbacacacddcddabcbbdbcaccdbadaadbbdddaacbdaddaadcdacccbaacadbdbacadacbdbacbabcbdcdbccdbbbbacbacbacadccccdbbabdcbaccccdbdaacddaabacaabbcbbdcacabbbacdbdbbbcdcdcadaddcdddadababdddcccacdbcaccabbbdbbcabddbadacdacbabadcadbbabbbdccccdaababadbaddddbcabdbdaabbcbdcdbdccdccbccabdcbccdcddcbcacdbbdbbcaaabdcbbbbdabccbdbddadabbdcbacbccdaaaddadcdcbdbcbdbcaaaacdcadbddacdbcdcadbbcdbbabbacacbaabbcabbaddcadacccbdcbacaadbbccdabadcbbcbccdbcabccbdbacdaacbcbbdaddbccbdbddbbaacadacddbcabcbcdaddcaccdbbadccdacbdabbaabdbccddabdaacbcaccbcdbbcbabbdbcabcbdadcbdddcbbabdccbbddacddbddccdaacbcbabbdbaaabacbbbcbdacacdbcadcbbbddccaddcbddabdaaabaadaabcdabcbcbaccbbbcccbcdaddadcadcabbaaddbaabbbbbdcddabbaaacabcaccaaabbcabadbacaaddaabbdadccbcdbbaccadacacbdacdabbcddcabdcadddabdbdbdabccbcaabbcddcbbdaaddbddcddcccadadbbdbadcbcdabcbabcadcbcdbcdddbdcaacdabbbcbdabbcdaacadccaddbcddcdaccbbcdabacabaddaccdbccabcddabbaabaaadaadadbdcbacdbcdbabdbccdcbcadddcbbbbccdddcdcddbdabcadbbdbaadddbddaaaabccbdbccbbbdbccddcddcacaadbabaacadabdbcacbddcacdcdbbcdacaadbcdaccdccdabdcadacdadacaaacbcdbdcabbcbaddddabccacacbdcbddcdbcadbdddcabaaadacbbcccaaddbadaddddadcdacdbacbbcbcaacaabdcddcdbabaadbdcbadbbddcdabbccbabbacdcdacbadbdcbdddcadcccbabcbbaadbcbaddccadabddccdbccaabdbccddcccabbbdbdadcddabdbbcdddcadaacbbbbcadaacaddaabdadcabdadbcdaadddcdcdaaabdddcaaabadaaabbaaadaccdaccbacabcaaaddcdddddaacaaddbdabdcbcbbabdbcaadddaacacdabdcddadcadbdcacbdbabcbcdaddccbdcddcbaabbbbbabddbcccbabbadbdacbdadccbddabbbadcbbccdaacdaabcaabdcbdcdbbcddadcadddabcacbcbbcabbdacaabcdcaabcaacbabaadbdbbabadbdbbcaaddaadddabbdaccdadabdabbaaaabcddadadcbcbdabcbddabbacabddddaccdcbcdccccbcdcbdbbcccbcdcbbbbbcaaaadccaaacbcdcbbdcdbacbacacbcbbbadbbbcbbcabbaacdbbdcccccdabbabddcababaaaabbbaadadabdacdbbcbccdaacaacabaccbcbcddaadadcdbabadcdcaaabdcccaccddaaaddddabbbbaaadbadbbadcacdcabbacdbcbabcbdbacdaaadabcaddbabdaaaadadcacbbaacaabbabadabdbbcabdacbccddbbaaaccbaccbddbaddbdcccacadcacbbcabdabdcbbcdddcacccdcccacaacbabbabbaadbcaabddbdddcbaaadccabcbbadacabdacccacbdacaaadabccdbdcbaabdbcbbaaacbabcadbabcdbdcbcdcccbdaabcddcdadbaadabbdbccdaddbaaddacbadaadcdaaacbcdccbadbaadccbcaccbdddcacddbbcacabcbdaabccddcadabadcddacabdbcddbabcccbcccdcacccacbabdbcddcbdabcdcbddcaaaacdbaabddbdbbcdbaaddaadaaddaacacbbdcbbaaadcdddddcbccdbcaadcbdadbbacddacdaadbbcabdacddbddccbbacbccdbddcbbddbbabadacccbdbadacabdaabddaadbacadbbabcdadaddbbdbaabdadadcadadcdcbacdadaaabcabbcbbcacbadaacdbbacbdcdbbcdaabdbabacddaddccacccdbccdddadccdcdccacdbcbbadadabdbcddcdddadcaabccbdccdcdcbdaabbccdcaacddcabbcdaaabaaaccdbdbabdbddcbaddadcddbbdacbddddccbbaabacdbaccdbdadbcdaddaaadbcabbcdaabcabbbbdcdbbcddacaccddbbddadacbbdddabbcdbbdcbcdabaacccbbbadbbddcbcdcddbcabaccbcdbbacaaaaddcaccacaccabcabadbccdadacbdabacbdacddcbbbaadcccdaabdababbcdabcacaaababddcbcbdcbcccbccbacabcbdcaabbcdadaddabccabacaaddbcaadcaabccbdacaaccbadcaddbbababbccaabccdbdbccdcadabccddadbaacabacaadbcdbbbddbbbacaccabbbdbadbcbdacbaccadabccabacdbcadacacaddccbcbdccabdbbaacaaabddacbcbdadadbbabdbcdddcabadcdbdbcbdcbadadaabcadccadbdababcabbbbbbcdbbbcccacadcddbccdadabacacbdabbbdbcdbadddaababcaadabaaacabdacbcbcdbadbcbdadaaabdabacdbacbbacbbacdaaacbaaabdcaccdcbdbcadccbbbcdccaacbacbadbdcbabaaaabbdbbdccaaaabbcdbadbdccbbdbacddaaabadbacadbaccaabaacbdaacddadbcacbaaabbccabacddbabadbcccbbbdbbcdbdcbacdbdbacabaadcddaadbdbddbababbdbbcaadbccaddacaaadcbcacadbccadccadabbcbcdbdcbbaaabcababcdaaaabbaadaacacaccdbdcbcdbbbdddbcaadcbcacbcddabbbbbbdbbdbabddacaccdccacdbbbcccbdcacdcabacacbbdbdbbadcdacdcdaaacccaabcbbbcbcacdcabadadcaabdcaddaaddbccccaaccddaddcadbaaddbcbaacbcddddcdacabadcdaadacdcddacaccacacdcdadacbddcadabdbdbbcdacbbbcbbaabdccabcbccdacdabcadadbbdccbbaccdccbabababaacadddbabdccbadbdaaabdabbaaccccdcccaaabababcabccacdbcccbcabcacbbacbdcddacdddcbcbadaabaabdcadaadbacbccabcdaaddaaaadcdbabdacacaccdbbdcddacdddacbddcddbcddbcabdacbcbbcbcbcbdacaddbadaaaaccddabbbcabdbbaadbdddbddbcdadcccdcbcadbccbdaaadcddcbcabcbbdbbacddbaccddaabcacccdaaacacddbcbcbcccdcccdabacbddccdabddddacbdbccccadddbcbcbcbcbccddcdbcbadabacdcbdcabadadbcddbabbccbaaddcddbdccaabaacddaadccbdbbdddcdbddacdccdbaccdabdcaddcdcacdccbbadaabbddbbcbbcdbdbbcaadaabaadccbacbccabdabadbbadcdcaabddbccccacbbcbddcadbdcbcdcbaacdcacbccacbabcdbcaddcbdbcddbccdaaabdbbdbaacbbbdacbccbdbcdadaabcbccbcbcbdcdcaaadabccbaadaabaaddbbacabacbaddabcbcdadacccabcdccdbccdcdadaddbbcdbcdbdcddcbdcaacdaaacbbabaddcdabddccdcdcabddbcaadcbdaacddacdbdacdddcbccadbacdbabacbbdccaabababaddaacbdcbcbddcaaabdcdccddcaabadbdddbdddbdccaaadaaddbdddbacacaaadccbcdbccdbcdabacacbdcbdcaabbabcbcbcbbaadccdbdbadaccdcabdbccacdccdbdcaaabaabdddacdaabbaadadaadbaccdccdabaaccdcbbdbdababaabcddbdacbbcacaacdabddbdabbbdccbcadbdddaaacaddabcaaadddbabcbabdcadbcbcddbdbacbacaddbdacabcccacacbbddcacdaadddaacbdbdbbaccbaaccacbdacbcbcbacabdbbbdddbdcbabcbacaadddaacadddcbabbdabbbdcccadcbcccddbcaabccadbabdabaccaabbbcddbdcbbdabacbdbaacacdaabbadcaabcbcdcabbcbbccbdddadcadbaabbbbcadcaccddcabadcdabdbdbdcbbdbdabababadbdaacbbddacdcbacdaacbdddcdddaaccaadcabcdaadcacccdcaaadbdabdcbdbadcbdbabdbdaacaadcabcaabbbcbbcaacabcbbabbcaaaddbadbccbadacbdcabcbbdcbcbacddadbcaccdcbdacdabdcccbaaaaabcdcdbdcabacdaaabbbcaabaabcabddcbaacbadabcbbcababdaabbadadacbccbcbaddddcbbbccddcadcdbddddaddbdcbdaadabbdbdaddadddcdbbaddabbabcbcdcadabccdaacaaacddaacdbabadaaccdaacbacbacadbcccbaacdcccaddcacdcccdacbaacacbadaabdbbcbbacacaaccdbdbcbadabdccadaddacbcdcbbabaaccdbcdcdcaaacbdadcdacabbbacdddaacaadadadddaabacccbaddaddbbabccbbccbdbaddadbdaacaabdbcbdbcdbcdbacdadbddaabcccdbcadabbcbbccddcbaababdbadaccadbdcccbdacacdcaaadcacdaaccddcabadcabdabcbadabdaacddddcabdccaddbbacadddbbbbddbabcabcdadccdcdcabacaaaaddcdbccaacdaabadcabaabcbbbcbcadaacccbcdbcadbbbacaaaadaaccddbddadbacabcbdadcbccbbadccdcacdbbdadadbcacacababacadcbddbbabbbaadabbabdcddaccaccdddcbbbaddddcaccdbbbbcbcccdaaccaddddbbdbaaabbadccdbaadadacaadbaadcbcbdaacbadbcbbadbaabbadacdbccacddaacaacabdcadaccdcbcaadbdcaabbcacadababcdaaccdaabbaacbaadccadaadccaccbacdbcdccdccbddabdccdccabddacbadbcdadabaacbdadaacacacbccdadbbdccdddddbaacadacbbdaccadbcabdddadababcabcddccccdcadacbbbcccacdbdbbdbdbdcbcdccdcbcdcdcacddcdbcacbcadbcccdbddaacabbbddbabbcaaaaadbdcccccdddbabaaadccdbaaaadddbacbdcdabadadbbaddaadcdcdbacdcdabbcdbaddabcdccccaccddbaabdbadbaabaccacdcbdadcddccabddadbbdbaccacdddbbcddbacadcadbbbdbdaccbbacadcabdbabdaadacddbbacddadacbacadcbabcccaabcaadaadcacbdaddbbbcccbcbdddbbccabccddcddbdcbdabcccaadbbbddccabbbccbddbdbaabaddadddbaaddbacacdcabbcbaaabdcdcddbcabbbdddaabddaaaabdcabadbdaccdcdadcbcbaabccabddbcbccacdacdbcadbbdddbcdabacbbaacbbcdcccdbaaddcdbbdcaaacdcdbaacbcdabacdcccdbcbacbabdcacbabddbbddabaccabbdcaabdbaadbccdcdbaddcccccadacdcbdaddddabddabbdabdddcaaabbaddcbdccbcdadabddbbaccdbdbbdcddacdbdaabcadbcabbbabccacccbcabbcaadaaccbabcaabababaaaddbbdcbdcdababaaababddbaddddcdccaddaabbacaccbddcbacacdcddddbaaaccdaaccbaadddcbbabdadcbcbbcabcbdacbacaaacdbcbcabddaaaccdddbcadddabcbacbddbddbddcddbaabbcbbcdcdcddcddbdabccaccbabbbcdaaabdacddaaccccddcdaabcbcacdabdcbbcdcaabdcccaddadcbcbadccddaacddbcdbcadbbdcbaaccbbcabdbaddcccbbcddaddcbaaaccabdbccbdabcadcabddbdbdddaaaaccbabaaacbbdcabbcdaccbbdddacbdbbdbdbcbadadccdadadcabaabccadcbdabacadbccccbabcdbacdaddabdddbacdaabadbcddacdcacbbacbccbdcdaadadcdcdabdabbcadbdccdbbbababdbcdcbddbcbbbccbcadcbacddbdbbbcdbdccaaaaacdcdadacbbcdbccbcbabddababacbabaaadbcdcbbcbcabdaccaadaadccdaadddaaddcdadbbcadccddbccbccddcccbbadbbbbdbbbaddccdbdbaacacbacdcadadbadcbdabdcdadcbddbdbcabcbaccdbccadcdddcabcbcdbddcdccbbaaacddaabaddbaacbaacbcbccbaaacbadadcbaaabddcdbbdbbdacacdbacbdadbaaabbacdddcdccdacdbbbbcdaaacddddddadcbdaaabdabdbacadadacdccabcbdabdcdbabacabbbddbabcdbbdbaacacdcaaccacdbdcbbdddcbdbbcbcbbdcbdaabaabbdcdaabbaacdaddacddbbadcbcbcdacbcabdbddabbcbcadbbdcddacaabbadbabccadddccbacdcbdcbbbcadacbdaccddaabbcadcadaacdbbadbdcadbcbcdbdbdcdbadddcabbcacabcccbbddcdcdacccacdccdddbabcacbaddbaaabdaaacbabcbbabcaaadccbcdabddccdddacadbdabbbaadbacbdbacccbbbadcaacccddbcbddcbadacdaddbabaacccdcddcdadacbbcdabdadaabbbdcabadbabbdabaccccbbcaaabbadacdcbdaabbbbaacacdacabbbddaaabaccadbcabddabcacccbccdcbbadaabadccbddddbbadcabbabdacacaccbcacbaadcbbcaaaaacbabbdbdcabddcabcdaacbaaaddacadcdcacccbdacdbdbddcbabdaaaddaaddccdcbdbbaabcbbcbccadbabadcadbccbaadbabbbbbdbdccdaddabbabbadcdadccdcddddcdcabacabddcdcbcaabddbbaabbbccddaddadbbabdadbddacbcdcbbaccddacbcbddcddbdddcdcccbbabddbadadddcaaddaccaaccdaaabcccacaacbcdcdacdbccababdaadbbaabcdcdbdbadadabbdcacaaaddaabccdacdbdcdcbdcbbcbbcabcabdcaddbabadbdcdccabdcadbccdacadbcbbadbbabcbdbdbaccdcddcdadcabbdcbccbcbccaddccdcdcbcbcacabbabcddddacadabcbaabdcccdaacddaddcddbcbdacadbdadacbddabbcbabcdbbddddaaddbbdaacbbbdbcccbaddcbadacdabdbabbbaabcbdcbdcabcdcccccbcccaabddbcbdcacdabbdbdaddbbbacbccbaabdbbbcadabcdbadcddbdadadcccbbcdbbddcadabbacdccbadcdbaabaadcadacaccddaccdcbacacabcccaaddcbddddcabbcddbacdddcdbdbbcabddcccbbbccddadcdccabbdccddddbdbaaddadcaccaccacddaddddbbbcbcbcbcabdbbbbccbaacdcadcbcdcbcababbdddabbbdacbdadcabbccbccddbcdabbaabdaccdaddbadaaadabdadaaabddccaabadddcbbbaccdcbcdbbdaddabbcbadddbdbdbdabcbccddcddcbabdbcdbdaadcaccdcdcddaacaabcbccdadcdadcaacbaccbcaccbacacbaddbabdacbdadaaacbaabddcadbbddbcabacdddbccdcabdacdbcadbbbdcaadddaabbababcbdabdbdbcaccadbbddbdaddcaaacbaccdbacacbcbaccacdccaccaaababadbacbbaddbdacbcdbbdaacabdccabcbbdcbbdaddcdbdcccabaacdbadbcdddccbcaacbdaaccdabbdcddcbabbbdcacabbdabbdcdccaccbccdcdaaadcbddbbbaaabccbacdcdddadadbcbacdbddbdacbaccaadccabdbcdcdabbaacddccbbabdbaaccdabdcbddcbcdccadbccaadbddddcddbcdbbdbcbadbbacbddcaddacadddcacdbbdadacbadadbdbbbaaadacdbbadadabcccddcbabacdcdcdcdddcbbadcadcdaaacdccdbabdbcadbacadbaaaacbcdabbadbdbabdbcbadbddbccbbaaacaccdcaddcdcccbdbaaccaddddbbaaaaccacbbcadabbdbcdaadcddbbcabcbabdcbccbddaacdadbadbdbaacaaddcccaabacdccdcadcbabbaacdcbdddcaccdcdcbaabccacbdadcacdadacdbbbdddcccaabaabcdaccbbdcbacbadadbaccbbbbcbbcbbbbccddcbabbcdbcdabccbabcbacacdabcaaaacaaaacbddadadbdabaaaacabaadccaabaadcbdddbbadadaccccdadbabcbaccaadacabaacbaadbabdcdadbdbbcdbacacabccdacabbbacdbdcabbabccdcaccbadadaaabaacccacacbcaabbcdddcbbaccabddabcbacccdbbadadbdccabbdcabcacdbabbdbccaabdbdddacbcdaadbabdbddaaadcccdadcacbbcddddcaccdaacdcaaaacaacbacacadcbadabacaccbcbdbcacbbcdcbdddbdcdadbadbbcbabbbbcdbacbddbbadcbdaadaccbacaccddaccdcccdccddcdcacadcdcbdbcdcbcdddddbdbaddbcbcabcdbbbbbbbcdcdcabddacbcabdbbdcbdccdbccaacabbdababadabdcddaabcbbbbdaabccbcddacadccabbbcbdadbaddcabaaddaccdbcbcabbdaaabcbbccabbccbccabacbbacbadccbcaccbaddcddbbabbbabcbcdabccacbabacdaccbdbacabadbcadbdcadabccdacaaadadaabcbdbadaddddcbbcdcdddcdbdcadbacbcacaccddadbbbadbdbcaacddbcbaadccbbbacabddabddacadababcdadbadcdbbdadacadbadabacdcccbddbaaadbbbdadbbabbdacbabcbadcbaabacbddcbabdadcbbcdbdbbacacadcaabddbaaabcddcaaaadbcdaccadbabbddaccbcdcacaddbbdacbadccaddcabacdacabbaacdabcabdbbcaaabbccddbbdccadbbaaaddcadcaadcadddadbdbddcaadbcabbddccbadbccbacdbbaadcbcaadccddbcaaabdabcbccadbdcaddaccaaaadcadcabddadcabaaccacddbbacadabdcbdbcbcccccbccccdcbdcddaaacddbdabbbdacabddaddadccbadabcdaacdbddbababaaddcbadbddccccaccdabccdcdcddbacaadbabaabadbbacadbbbbbcbbdabacaaadacbdcbcdcdddaaaacadaaaaddabcdcbbadacabccbbadbbcddddabaddcbaabbdaddddbcadbcdcdadcdbaaadcbddcdcacccaadaaacadacddcdadbbdacbbcaabadbcaabacbcbddcdcdabdaaadacdbccbdbacdcccaabadcadbdacbaaccbbaacdddbddaaabbdcbdbccccbaaaadaaabacabbdaddbbaaababddcaabbaacbdcaadcbdaabcbbccdcdccabcadadcadcddccacabdbdcacbddbbcaabbdbcccdacdbbcbcbdcdccaccbbdbabdcaccbcabcdadcdcbaddaaabdcdccaabaccbbcabcbccbaaddabdbcddcdcbddcbbbbbbaabcacdddaadbcccbdaaacbbccdcbabbadaababccdcdbbcbbdbdbcbaaccbdbaacbacbcbadabbddddbcbaabbcaacddacacadabbaaddaabbcddabddbbaddddabccbaaaabdaabadbbbbbdaabcacaaacaabdccdacccdaabdbacbdbacddabdacabddbabacbdcdccbbccdbbaadcbdcddddcdcddccabadaacbcabdadbbabaaddaccbbcaabbcaaabaddcbcbdcdcdbccbdbbbaabaabdcdbddacabbadaccadbbbadbbabadbbdbbddcdaccabbcddbcdcbdbbbdcdacacdbaaadbbcadcbbcbadbbcccbddbdabbcdcbccabaaddadbcadcbcadcaabbdbcaddabddcadbdcadcdcabdcdbcbbdbdccabaccaacdddccddcccddaacdcadcddabccccdabdbdbcddcbcadccdbdabbdbadadaadcccbcbbcbbcddadccdcdcbbddccaaaadcbbbadbccddcdcabcacddbbddabbdcbdccabcacaddcbbbcccccdaddcbbdbcadcadcbadbabcbddabaacccabdcabdabcbdcdddadbbdbddbacaccdbdbcbabcacbbdbcacdaaaabcbdddaddacacdbddaddabacbdbaccdaaaadcbbdccabbdbccdabacaabbcbbdaacbdadcccbbcdcdbbdbbddccdcbaccdbccabddcdacbdadccdbcdaacccdbadbcbaadadcacaddadbdbcbdbadbdcaccbcaddcddacdacccadcdccdadabbabbbbdacacdcbabadcdbddddddcdabdccdcdcabadbdbcbacccaccbdbcbccbabbbbabacaddbcaddbdcdddcabacdbbbdbcddcdbdcccddccababdbaddbddbbdbdbccccadadcadcdcdadbdabdccabdadababbccaddccabccbccabcbccdbdcbdaaabbadccbcaccdcbbdbdacdabbaacdbcadacbaadadadbaaddbcbbccabaaaaacacbcbabcbabbccdbababaacdadcacdcaccbbbbbdaaabcbaadcacccddadacddcacdbabaccdcaaabadaabbacdacdddbbcacabdbdccaacadcdbacaacbbbdbcaacacbaacdadbdcdccbbbacbdcbadadbaabadbdcbbdacbaaadbacabbcdddccccadbdbbdacdcdbaadaabcbcbaacaacddcbcdccccbabaaddccadbabddabcaaacdacdbadddacbbddddcbddcabadbadcacaacdcbcdaddadbcdbbcadadcbcbbbbdadbdddadcbadabbcbbcbbbcccbbdbccbbbbdccacbccaaaabcbbacacbabdbaccdbdbcabbaabbcbdbaacbcdcdadacbcbdadcdcdcbdbccbddccbdbaaadabcbccbbdbbcdbdabdcbdcccbddcbbddbbcdaaddaabadccdabadbbaabdbcdccdbaaccabaacddcabbcbbcdaddbcbbdcdcbbacadbbccdacdbdacccabddaabbbabadcacdaadbabacddabccdaccdcaddaaddbcbddddcbbddaccaacaababbccdabccdadabbdbdbddabbdaacbdbcbcadcaabcbbadbdcbbcadbacddaacadddcbdcddbacbdbcacaccbcbccbccdbacdaacdbbdccbccbcdcbcbbdccbadacdaaacdddaddadacdcaaadaacaabcaccdaadabdbbdccccbcadcadbcbaacdcbdbbcacdddbdcdcdaadaabccbaddabcdbbdadcdbcabbcbcaacacdbdddaaadacabdaaaaacaccbcbaaacbaaccadaaadcbcabdaadadcdcdbbaadccacacdaaccacacbaacaacacaaccacbadadaababbddcabddddccdcdbdaddaadbbaabcdccaccadcbaccbdbbabcabbadcbcccabdcccdddcdaadbdadaccdbdacdcacabbbddddaccadbaccdbddacccbbcddccbabbbbdacbbbcabcacbccdccabcacbbcabdacdabacabccbcdcdacabdcdacbcdcbdccbaaccdbcdbabdcacadbaccaabddacbcdcdddbcddcabadbbcaaadabcaacddddcacccacaaaccdbbdbcadbbaabdbbdbcdaccdbbaacccdadaadddcbcbacdcbbabbcbbcbdacabddcbcbccbcdccabddcbadddbabcbccbadbddcbcbdabddbaaaabdcabcabcdbcdddabadbbcadcabbdbdcbdddaaaacbcadccddbbcbdaabbcddcccacdaabadbbadadcaccdcbbbbcbdcaccadddcdabdcacddbbcdbccbdcdddbcdcbacaddddacaabcbcbcacabccbbbacbababcadbdcdbacbaddbdbddbbacbbbbdabaaddccaddddaacbabbdacacbcdccddaaaccbbdabbaaabddadbbbcaadaaccdcbccaadddacddbabdccccaacaaaabcbabbaadcaccacaacdddadacaacbdbacdcbcbccbcbdbbddbdbacbdcadadcadddddbbbdaccbadbadcacabaddabbcabdaabaabbbbddcddadbaddcdcdacbbcacaaabdcbbdbbccaacdbbcaacdadcbdbbcdcbaadbaccbcabacadababadbbbbdabaacababbdadbaadddadaddbabcabddacbdbbbadaacaaadcacbcdccddcdabcdbcccdbbadabacacdaddbbadcdccacaacdabcbbbcaacdcadbdbdcaddacbcacacbbcccdbaadcddddbcaabbcdaabdbabacdabdbadaccadacacbbacadbabbacadcaacddcaddddaabbcdcacddddbbcaadddacddbddbaabddbdccbabbbbbccdaddcdabadbbaabbaaaacdddddacbbabcbabbcbbbccdbaabdccabbdbcbbcdaacbaaacdbcaccdcbcbabacabccdcaaacddbcbddddcbcdbdababaacadabdacdcadaacbabcccdbdadccbacbaaccbbcbdaddbbbabbdabacddcadccbaaaccdcddadddacaaabacbaabdadadaadabadccbbcbcbaabaccadaadabcdacdaaabadbaddcbcbddabddbbccabccccddaaadcdbbdbaadbcdbaacdacdbbbddccdcbdacccabaddacccdbccbdadcbbcdcbcaccbcccbbdcddcbaddcccccdacaccdacccababbbcbdacabadbccccbdbdbcaadbdabbddbaddddcbcbbccdbbaaaaabdccccdcbacbdcdccbcdabbbdcdbadacbaaaddaaadabaaadbadbddddabdababbaaccdaccabadaabddccccdadcacaabcabbccbbadaaaacaacdddbbdcadbadcdadccdbdaaaacbdadcaaaabacdabdcbacaacabadcdbcabbdccacbaadaadabbcdbbbcbbcdccccacadcabacdbaabcbccdccbbacbacccdadadbaabbcbbcacaccdbbcbbbdacddcbdabcadccadbadbdaacdddddaccdbbbacbbaabcaaccddabbdbdadccbbbbdcbababbbdcddcbabcbcddcddbccdcacdcddadccacacdbaacbbcabaccacbcdaabcdacbaddacbccaaadbbaabbccaddbabcbbbddadcdacdcddabdccdbcdabbdaccaacadbcdcdccabdcbbababbdaabaaccadbabdccacdcdbdcdaadbbbdaadbbbbbcbbbbdccaccddddcadbdcadcbbddddaaaacdddababbccabcbbddcbcbacadacbadadcbbccbdbdaadcbaaaccdcacbbcdbdccaccadcbdbadbdbcaadcddbadccadaadbaaddacdbdbdaddcaadbbacdbcbadaacbaadaaacdbbdcdcdbcbbbdadbdbbcccbadcadddbdaacbaccddadaaccabddbacdbdbcdacaacabccddbaacbacbadddcadccdabbaadcddbbacbccadbbdbccaadbdbaddcbbddbbbcdaabaacabcddbbdcbccaaadcddabdaccdcddabdbdbabddcbcddccbdbadddbdaddadabadcaddadaaaccbacabdcccbacbadccdbbbddccbabdcaabacbbdbaabcacdbbbbccdddbdbbbdcdbddbcbcdaadccbcdccdacaabbccaccbadbbdbcccbbacbdcdccbccdbbcccccccddddbdcadbbcdbbcabcaaccbbdccadccbbddbcdbdbcacabcccabbbddbbbdacdbcccddcdcadacbbbbdcaddcaddaaadabbdbbdbbbadcdbcbacacadbccdcacabbcddbdcbcacdbcdbabbbabcacbcdacbdcbacccdabdadacbacdbbdccdddabacbddcacadaccacbdabacbdcbcbdadccbcddbaadbddaaaacdbbcbabacadcadcbacaddacbaccadabcdcccaddabcbcaaabbbcbabaaccbbbcaaabdcacbddbcdcacabcbbadbabcdbddadaabdcabdbcdbababcdbdaacccbdcacbdbaddcbbdacadcbcccacbbdcabdcccadaabbbbabcaddddbaacadcacccddacbdcacadaaababccccddcdbadbaabbcaabcacbdcabbbbabdbbbadbdbbccbdbcaadbdaacdbbbbdbbbccadcaadbaaadcaaadcbbccabbcadcbdaadcadbddbbbdadabdcdccdbabcdcaaaabcbcaaddddbbcbcabdcbcbcbbbddccdaacccbcbaacdbadccbcbcbbbbdababdabccabdaadbaaadacbadcabdbcabbcbcddcbaabddcabcbcdacacbadbacddbbaaadacddbbbabbbbaddacaaccddcbbdddbcaadaacbaadaabcaddabdadabbdabbabadacdbddbbbddaddccaaaabadcbbbabddacbacaaadcdcbdcbdcbbdbbbbdaabaddcbadcbbdccccacdcdcabdcdcadcdabadbbbcccdaddaddaadddbbcaaabbcdbcddbbddcbcabcbbacccdaddbaaddabcdbbdbaabcbbcdaacddddddadcccdabbacbcacaacbaadcadbdaadbbaacbabadcbcccaacbcbcdccbcdccdaddaabbadacdcbaabadcabaabadbbdadddabcbdaabdbadacbacdabcdababacabbcccadbaaacadbbcacdaabcdadabacddbdcdbdddbbccbccdcacaabbcbaddcbaadbcaabbcdabcbcabcabdddbbbacccaaabcbaaddbbbcbcacaabbbcddcbdcdacccdbbdccdcdabacccbbdcddcbacccbaaabbdaadbdccdbbdaabbadcdccccadbcacabdcaacdcaccaccdaccdaccaaddaaacadadcbcdcdaddcccdbdccabcaadccababacdabacccaadcbbbbdbcdaccbdaabbbbdbcbadadaabbdabcbdcacaaacdadbdbcdadbbadddbdaabacdcaadaadaccacbacbdadacdbcaacaaabcdcbabaaddbccbdbdaacbbcbaddbbbdcdbaacbbddbdadddcbcbbdaccccbcbaadbbdccdcdadbcdbdabbadbabadcddaccdcbabccacacdbadddbccbaccaaccdacbdcccbbcaadbdaacbccccdaaaabddbddbcbadabdadaacacdddadaabddbbddcbaabdcabdbaccbdacbbccabbccbaabdbdcdaadcddbdccbabccbaaaddbaacaacdaabdbacacdbddcacdcbaacdcabdadddbabdbaabbdbcaadabbbddadbcccbbaacbadbabadacacaccaacadcbcabacacaddbbbbcaacbdaadcdaacdbbbcbdcdcaabcccccdcbabcbbbaddcbdacbacddbccbbdcdccbbcbdcabbbddaabaabcadacadddcbdcdaabadbcabddcddccdcabbcaaabdccddcabbdbdadcabccadacbbbabdbacadadaabcabccdcddbbbbdadcbbaddcdcbaacaccccdbddcbbcbdbbbcbddbbaccccadccbbcdbbdcdddaadccbbbabcadabbcbbbdcbbdbbabcacbbcdadcabbadddbbcacdddadbcbcabbbcdacaadbdbcbdacdacbbacaabccccddacabdbcdabcdbdcbdabaaacbaabaccddccccbcabddbababcabcaccccdcddcccabadbabbdbabaacaadccddbcddbbbadbdbbcaacbbccbddabcdbababbbcbacccadbdbacdddcbcbbaadcdcbadcaadbadcbabdacccbcadcddacbacadadaccccadcbdddccacdcccdadccacbdabacccbadddcccacabbabcccbaacacccdbcacddbbacbbabddcacdcbbbabdcbcbaaaadbacadcbdbbacaabccbdadabcdcadabadabdbdcaddaadadcdbabccccccadcaabbddacbdcaccadadbbabbaaadccabdbcdbdaacdadcabcaddccabadaaccdccdccabbbcbbabccdbcddcbcdccbbccaaadbccbaabdbadcbaabbccdcdbcadabadcacaacadcdbdbcacbaddaabdacadbadacccbabddbddccbbddbdcaccaaadbdaaacbcaccddcacbbacabbbdaadcdbdbaccbabdbbcbbabaddddadddcdccdddddacbdccacabaabdadaccbacadadabddbabaaddcdacadabaaaabdbbbcbbbacdccbbcbbbaaabaacbadcddaadadcbcbdccacdbbcadbdcbdcbaddcbaccabdbdacaccdccadbcbaddaaddcdaabdbcaddbcccddadadccababddaccbbadccdabbccbdbcbccdaccbdacbacbdabcbddbdcababbbacaadbbadabcacbaddaaaccbdbcccbbddcbbcabdbdcbbcbddccadcccbcdbdcbdcdbbddabdbadcbcddcbbccbbcacaaaadadbdabbbddabbcadcbadddcccddbbcacddaaaccbaacbababbaddbbdddaddbcabdacdadbdbdcbccdddcbabcdcbdbbaabbbdddbddacddbbcccccddaacacaadaabbbdabaabacacaadbbcbbccbaabcabaddcccdaaacbdcababccbabcaabddabbcccbcaacdbbbcbdaaddadbabaaacdaddbddacddabcacbcccaddbdaacdbbaacdcacaabdcaacddddbadcbcbbacabacabdbdcccbbadccadabbddddaadbcccdbdbccdcbbdbdaadbbddccdacccdacadabdabbdabddacdcacdcbabbcacaabbacdbcdbccadadcacabaaabcacccacbdddccbcdbcdabbddddcdbdccdbdbabddbdccadbcaaacdcbacdcaaabbacabcdcccbadbadddbcaadacdbbaacdddbdcccadbbcdcacddadaaacaadbaaaccaabcaabcaadbdcdddbaaaddcabcaabcdabaabcdcadadbcdbcabaadbdacdacdcbabddccacabcdccbcddcabbcbdcddccdbddbdaaadcdbbbabdbbbadacbcbabdacdbcaccccbaaddcbbdbaadcdaaabcccacadbdcbcaabcdcbddacbbacccdccaacdcadbcacaabcabadccdcdbababbcdcbdaacaaadacacaabbbbcdaaacacdadbbbdddbdabbadbbbdddadddcbaddddcbccbabddaacadccbaacbcbcddacbdcdababccddabdacccddddbacaddaabadddccadaacccccacdadababddbccccdcddabdcaddcacadcdbbdabdddaccabccdaacdcbbdcccdadcbdcdcdddbcbbdadcbdcadbccacccccbbadacbcdbdbdbddaacacddbddbbdcbbbacaddcbdbbabdaccdbcaacdcbaaacbcddcddabaabbcbcccbbdccbcdddbcdbbacccadbccdcdbdbcababbdabdadbabcdadabbaadaaccdbdcdbdbaadbabcdcaaaaccbaabddaacaaaadbabcbdcbcaabbdacbdacddaadbcbdbddcccccadbabcaaccaabadccabcacdbdacdbdaacaaacccddadadabbbbaababbcddbdacacdbbaacbdbddcdabbaabaaadadbaaaddccacadcbbaddddadcadddbdbcdadbabbabcacbdacdbacdddcbdbaaccbcdbdbabbcbadddcccaaabaabccadbdbddcadbdcaabbcbbdcacbddaaddddbcbdaddcdabbacaadddabaabadcddcbbaaadacdbbcdcbbacbdcdbbbddbbaddcdabdabcddcabdaaabcbddabcbbbadbbaadabcacabcbdaaaabadaddcaddacbdcabdbcbdaacabacabbbabbbbdbcaadddbdabdacddaacdccdabadbdadbdcbcacabdbcbabbdccaadaabccbbbcaadacabbcaccdddbddcadadabccdcccbcacdbaaaaacbccaddbbbdaddccbabbdabbaccbabdaddbccdbcbaadaadaaabccccddbbbaaacccabbdacddbcdccbaabbacdbdadadadcabccaacbbcbaacacbdabddbbdbdaabdaabbbbdacdbdabbdbdbaaabcbdcadcbbaadcbccbbcbcddcdbcddbdcbaabbdadccbbddadcdbdcabbccbabbdbcaabbadbbacadbaabacbdbcdabadcdabaccbdbddbdccbcaddcacdcccbbaaaddcbbbadcdbcccacabbcadbdcddbccdacacaddccbcacdadddbaaadcacdcbdbbbaaaccbbadadbabbadaacaddcdbcaddbdadbddabdbadccbacddcaabbddabddbdaaaacccabcbbcdbbbbbbacccdadccdaadcaccbdacbbcbbaacbbcaaaaabadbdcacbcabbabadbadacbbddaaacdaacdbcbbccdcddbcdaabdbdaaabbacacbdacaaabadaaddccabadccadcbbdcaabaccbdbababdcbcbcdbaaaaababadcddcbabccbdccbdcabcbabccbbbddccadcbbbccacabdbbccbabcdcbaccaabadaccacddaaaaadcddbacdadaaaaadacabdbadbdbbddaacabdddccdbadcadaadbacbbaabdacaddababaadcabbddcbacabcabadccbbcdaacdabdcbdbdbdadddaacddcbbcbbdadbcdcdcbdddcddbcaabaabccacdaaabbdbaadabcbdbcbcadcacadcbbbcadbdddacdbaabccadcadbbddaccbbbcacdabbdbcbbcdacddacacdbdacbbbcbbddbaaabdbbbddbbbdbbbaabbcccddccaacbcabdddddcbcbdbbadcacacbcacaabbaadbddbddddadaadacddcbcbaddbccccdaaacccbbdcdadbbddcbcdacddcabcabdcaaacaaaadacdbbcccdbcaccaacabcabdaddbbbbbdddcbcaacacddbcbbcdbbcdddddbaddadabadaccccbddcbabddacddbdcddaccccbbbddddcaabababbbcaddacbaddccabcdcababdacadddcbdbccbcdcddbcbabcccccbcabbbbddddabdddbdadccbdcdabdcdbabcbdbdaabbabdcddbadaddadbccbbcbccbddaaddbcbbbbdcbcbbccacadccadabbbcbdcdcbaacbcbbddbcdbbdccddacaaddcbcbbabbdaddbcdabaadccbcdbbdcddbaacaccdbabdaaacbbcddbdcccbcbcbbdbcabcbacdbaccbdcaabaddcbddcccbbbccabcbccdaddacbabacddcdbccbabcabcdcbaabdcdaabdcdbcbcaaababdbddbbadbdcbabaabbdaccbcddcbacadcadddcbbcddaaabbdbabaadbccdcdaababcbbbbbcddcaaaccbadcacbbabbbbbbdabdcccabdaadbcbbdbbbccdcdbccacabacabcdccbdaacadbbddaddbdbbdcabcbbaddcdaccdaaabccdaaadcacbcccdbcdacccacbddadadacddaabdbcbbccbabdabaccdadbdbbbaadbccdcdadbbacbbadddcbdddbccbddcdcbbcbabdadbbcddbdabaccabcabcccbdaccacbacdacdbcccbbacdcbdccaddcabcaddaadacabababbbaacaadbbdbbbabcccccadbaaccccbbcdbbbbadbdcabddabdadbccddcddaacacbcadcbaabdaddacdcdccbdcadddcaabbccadacdddabdddcacddbacaadddbadcccbabcacadbacbcabbbbabcccccbacdcadbbdacdbcaaadbaababcddbaabadadaaabbbbabcbaccacacdcacbcadccdcdcdbdacaacabdbbdcbaddadddccbadcacaacbacdcbabdbdccbbbabccadcdcdaaadcccccabcacddaadacaabcdbadbdcdccacdcccbdcddccddadbddbdcbbdbcdbcddabdaddbddadaddaaccddbdbdbbdacdbacddbdbaddcdaadacabbabadabaadbbdabbadbccbadbaaadcbcabaacbdddbcabadbabbcccaccccdbddcbdbdacbbcbaccdcacbcbaddcabbcbbdababbcacbbbdaddbdbccadbacabbdbddccbbaaccadbbdcdcaddbdddadddbaccbbcaddbadbdcadbcabcacacbaabbdaaccdadbbadcdacabaadbdbadbbaadadcddbaadddbbcbccadcbadbdccbcbccdccddbccdacbaaabaacaccbadcdabacdbddddbccdabaacaabadccabcbbcacacabacccddadbcbaadabbcdbdcbaccdcbcacababaabcaabddabcabbcbbddbadcddbbbbcbdacbbbbaacacdcaaaacbcacdaadbabcddccabccccaccacaadcdccbccabbabccdcaacdcdcabcccddccdcdbacbdddcdabddcdaaaddabadcdbaacccbacdbababcabbaabaddbdaaccddaacadaddabdaaccbdbbbdacbabadbcdbdccbcaabbbdcaaadddbdcccbdddaacaccaddaccadcbaadaaacabaaabbdddcababdacaabbdbccaadcadcbddbcabcababcbddddadccbbbccdcddbbdaacdddbdadcdadccdabdcbbdabbcbcdccabccdbcbbcccdcbababdabaabbcdbcdddcbaaaaadbacddcccaddccabbbbacbbdcdacaddcaccacbbaabcadcaddcbacabcaaadabccdbdcdcadcbcdaacdbcbdcccabababcaddbabcbcccadbcbdaaccabbddcabbddcabccaaaadbbccbaabacaaccaabdbbcdadbbcdaaacddabbcccdcdacdabcbdddbcbbcbacccccddbdaabccddccdabdaacadbddbdcdcddddccdddcbbdcaaddcadacbaaadadbcbcaaccabbbbcdacddcbaccabdbadcbcaaadaddbdcbdbbbabdadacbbdcdcabbaadcadddbcaacddcbbcdccddcdbdcdbdabbcdddcbacbdcddaddcabcdbddddcaccdbaadccbbaaadcddadddcabdaccadbacaccddadbcbcdcbddabbaacddccbdacaadcabcbcabadbbccbcaaaabbdccbcddbcddcdacdcadcacbcaacdaaacbbcdcababbbbdbdcdaabdcadccbbbbbaacaaacacaccadbababaaccccbccbbdbdbbdadabbaacaccbdaddcbcadcdaabbdaccbabcdcbdbbabdaabbcdcacdbdbdcaadcdbbdbcaaacdcddbaaccbaabaabbcddaacaacbaccccacdbbcdadbbbcabadcdbaccbccdcbddcddcdbadcccdddcbdadbaacbdddbbdcaddcbbabacbbacacdddaacaacaacacbadadbbdcddbbdcdbccadddabdabbdadccdbdcbccabacbdccdcabbddabdcbdbacbdaaaacbdccaacdaadaddaabacdcbcabaccaccbaacddaadbabddddcbbdacddadbcbacbcddbaccabaacdaccbcbcabbcbbacdbaccacbdcadaccdbdddabccdbbacdcabdbcabbbbaccacaacdbacaabbdcaadbcaacdbaaacadbbcdcdcddabbbadaaabccadcbbcaaddbdccbadabbcadcabdabacdabaccdccadaddadabccbcbbadcbcccbbccabbbcadbcacccacdddaaaaadbdabdcaaadbdccaabbadadbcbbddadcccaaddadaccabdcbdbcdddcbbcaadbdcaaccbacdcaccadbcdbcccbdaaaadabddcbbcbadddbcacccccbccdddacdadccaadabdaddccbcdbccccabddcadccadcbddbddbacdbcddbdbbaacaacaccadbccacbcdabddbdccadddddccdcadcdbdaaccbcccbcbbbddccbbdabdbaaadbbcaccdcbdadbbdabbacddccbaacbdcdbdaabbcccbcccbcdcaacbbabbddbddbcbcaadccbdbbcbbadcbdcdcdaddbaaaabbcabcadddccadbdbdccbcbccadcbadbcdcbdcaddabadccabbbdbdabdbbabbdddbcadcbbddcbbbbbcabbdddaabcdcacbbacbbcaabdcddaababbdcdadcbbcdcbccccbababdddbdcabcacbdbcdcacdcccbaacccbacbbaabdbacaabacacdbdbbdbabadaaddcccdbbbcbbbacbdddccacbadbbbddbcbcaacbcbbbcdabddbaacacbacabccabcccdccdccdbcdcbbaaaacbbcbaabccdbaaacccacababacaddbadddddddcddaabbbadbdaabbbdccbbcbdacacbadacdaaacdbabcdbacdbdaddaacddbaabadcdcbcbbbcdcbdbccadadcdbbadacddaaccddbbbdababdabbaadbcacdbdbadbbccacccadcacacadcbbdacadaccbdccccdcabbabaacbadcaddabaabaaddaababdbacdbbccbddbccdadaabacdbacbaacdadaccdbbdacadaaabddcdcadaacdadbdbddcbddaadbdbbbdcaccacdccabccbddbcabddbdabbadbbadccdccdadacddacbdcbbdaacdbbccacddddbaddbacaaadbddcbbadcacbbdcabbdcbdccdabbbdddbddcaccbbabcbcdcdddbaaabdbbbcbaacbcddabcdadcdccadcbbbcddccbabaaccdcdcdabdabccbccacacdbaccbcbcaabacadabdcaacbadabacdcbbaacaccbacbacdbcdaccbbddcbaadbbaaaaddacbcaaccddcbcbdbaabdbabccdcddbdccbabbcdabbaccdadccaabcadacdacaddbcbcacccadcbccbddbababadbccaaabdcabdcddaacdababaaabbbcdcbbbbccacababacbdbbdbbbbbbcbbcdcccbadddadbcccccaadbaabccdccdcacdacbbccaddbcbdcdddabacadabcadbbcddaabdbcdaadabdbbccbdbbdaccbdcaabdccddaadddcabcabdbcdcdddbddabbbdccdabadddcccbdacbaddababcabdbaabaaaccdddabaaaddaacaadadcbcbddccbaadbaabdbadbcbcdacacccadcaccadbbacbbbbadcbdadabbaddcddadbbbaacabdadcccacaaabdbaaacbbdacacdaccacabcdbaacbbbbdabccabaaabacdcbabcabbcbddcbaaacdcacacccaddbdcccbddacbdccdbadbcbbcbaddccdbadcbbddabcddadbdcacbcadbbdabcbaadbabbbcacddccbbbcaabcbcdabbddbccbccadcacdacbcccdadaccdbdcbbdabaacbdbcaacadbabcccabcadbabaddcabbccaadbcbbcdaaababbdabdadcdbdacbdcaabbcdcccddaaacccbbdbadacaabaaacbdaadbdcdcbcbcaddbdacabaaabdcabbccbbdcbbbabadbabbdabdbdaabdaccadbaddccdadabcbaacccbdccbaabcaababdcaddbbbddddcaaaadbccacccaacaadcdcdadbbbdbaaabdccabaabacadddadbcabbacccaaaddbbcccbdabadcbdaaacadbabbababbabcbcdbbbdbdcbadddcbbaacbcdadbacdbbbddaaddadbbabcbcdbccaddccbbdadddbdbcddbdaaccadcbdcadbdbbabddddacadbbbdcadacdbcccdbbacdcccdaacabcbabbcaddbcadddacdadbbbbadbcdcbacaadcbbccadaadbabcaaccbadbacdaccbdcaddaabcacbddacbbcbadacabdbbadbcbddbaccdccadabdbdaabcccabacabbdbbcbcbbacbaccbbabaddbbbadababbacccadbbdaaddacdddbddcddcbbadadccabcbccaaadadbacbbbcdabcbdcadcadbbbbadacacdaabacabddccdbcbcabdcaddaddacacbadbdbddbacdcacabcdcdbbdaddbacadccbbabcdcbccdcbcaabcdbddcacadcbddabbcadddacdadaaccdcdacdbdbcbacdcaaaadaccabbadabcccdbcddabcaccbbaaccbaabbbccbabdbbcccabccbbdcdccbbbdcadbddcccaaddbbbbbdccacddbdaabcdddcbbdbddabbbddcddccacbaccdddabdbaabddccddddacbdccdbaddaabcdbadbadcadbaadaabadabbdddadcaaddddabbdbdcdbdcbbcdbabcaccbadadacbaccddcbcbbbbaccaaabdcdacdabdcbadababcaddccdcbadabadabacbbcaaaccdbaaccdddabadcccddbdddcbcbbcabcacabaddbaccbabbcaddaccaabbdbdababbdadbbadababbacbbcabbccacacbddcbdddbddaccbbaadabcbdbadbdabdcdbacbaabadcdadbbbadacbbcdadddbacadcaccbddbabcbbabdcddddabdabdaaddbaadbddcccbccbaccccdcbcdcccbcdcaabaadbaccdbbbdadddbcbcadcacadcccddcdabaaabccbcacbccdbcbbbabaaccccaddcdaadbaaacbccbadcadabcbadcddbadbcdbbbccdacbbbabbbbdbbbaddcddadcbbbbadccadadddbddbbabadcdcadcaddbaddaabaccadcdcddcacbbcccdbbcaadadbaaacdcbadbdcbcbabcbdcababdcdcaccbdbcaacaddbbcacbbcababddccbbbcccaccdadcbababdabacbdbaabbddbdcbdbcdccbddabcbdacdabbcdcbaacdbdbbabdbbadbdbdddaddaaacbcccabcddabbcacdddaaadcdadcaaadccdbbcdcadaabbcbcccbbddaddbbbcbcdaabcacbbcabccbbacbccbdaacbdbcaaacdbdbcdaabadbaddacadcbaabaacdaacaaabdacdddacaabcbcbabababccadbccdabccdccbbacaccddddadbdadcabcabcdccdabccaaaccaaabdbbdbdbcddbaccaaaddcbdadabaddcdcdadbaddcaaabcaddbcccadbcabbdadcdbabddaccaaabdccbbccbbbbbacddadbcdddcabbdadcdcdaccbdcaddbcadddddcccbaabcccabbabbabaadadbbbdccdacdaabbbbccbacabacdbcaacddccdccdbcacccccdbbadcabacdbdbabbbadbcbddbadccadbcadcccadaabcccbdadccacdbbaaacddbbcacabcaacbcacccbdddaacdcbdbbdaadbabdaadddcadacdbbadcaadbcbdabacdacddbabadcdbdcbccacbadbcdadbbdcababadaabddcdbbcbbadbcabcccccdbacabbdcbdcdcdadadcbcacbccdaccdcbcadbdbadccccbabddcababbdddbdccbbdcdadadbadccdccaadccddadccabcdbcdddabbdbdcadaacdccbabcbcabbbdaaabdaccdbccaddccacabaaccccbccbbcaccaabcddcdddbdddaacbdbdbdcbdbacdcccbbbdcccadddaccdddaacaccddabbacadbbbdacbaacdcbadbaaddcadaacdbdbdadacadbcbbcaaaddbcabdaddbaabacddbdbbbdaddbdcdbdddacddadadbbbaacdbcabdadccbdbbabddddbdcdcaadddbccaacbacbcaadacabcabacdacacbaccadadbddbcddaddbacccddbbcbbbbadabcaaadbcaabbaacadbadabcaabadcccaccaccacbacacdcdcbbcaadcbdddbababbacabadcbacaabaaacdbcdcabbacddbacbdaaabbbbaddaacabadbdadbacdbaaabcdbbabbccbdadabcabadbdbcdabbbcacacccbdaccadaddbabbddacaddcadddcadbdcbdcdcaaaccdcbdbddddcdcbbcacbcdaacbaabccacbcbabdcbbbaaaccdbadbcdbabdcdcaaccbdacacdcabaabcbaabcaaabcddcaccaadcbddddbddcbbaaaaabbbccbaacccadbcbbdbabbcbbcbdcadacabbcdddddabbbbcdcddbddddbdbdcbcbacabdadadbcaaccadbacbacbdadbaaadadcccaaccdbbdcbbbddacdcddbcaacddcbddddaabdbbdbabccccdaadcbbbdbccccccbbccddcacbaadaadaadcacdcaccabbcddcacdbdbbbbbcabcdbcdacdcbaaadcdddacadbdbdaadacdbbbdbaabbbaaddbaaaaaaaaacddbcdacacdbabbdaaadcbdadacbdddacccadaaabdadbbdbddddccbdbcabdacccdbcbbbcabaadbddddddadaadaaaaaccccbdccbadcacdddcbaccdcabbcddbabcbdaaaccaabbdbcadbaccbdcbbddcacadaabaaddcaabdcadadadcccdaddacbbbbaddabadccddacbcddadcacddddabddabbbbcbddacdbcaabdbccddccccaaaddadcbdbabaacdcdbaadcbaccbddbdadcadadbdcdbccdaddccdbacdbcacacbcbbcaaaadcdbcabcbdbaadabcbaccadcacddcbadadcdaacdbdcbabbbacdcbdbccabcccdbbdcbdadccbdcbaadcddcbaadaadbaabcbbacabdcbcccaddcbadabaaacdabbdaaccabacddaacabcaccddaddcbdaabadaccddbcbbcaacadccacdccdababcacbaaaaaccdaccadcbabcbccdcbabbbaaaadadaddcccabbcbccdbcccabddbdbdcccddcbdcbccaadbbdacbdaddccbbdabddcddacaaabbcdcacccaddaacdbbdbbcadbbcaabcadcbccaadcddbcbbbbaacabdcddcbcbcbdccadcdbbdcddcaddbdbccbbbcaaabbabdbdcbdcdabaccddaabdbddcadddbdaaddabadddadbacdccbbbbcbabacbcbccaaddccacbbbabcbddcdbcbaacbaddbdaaabbbdbbddbabbacaabcbbbaabbcddaaddddcacaaadadabadadbdbabdaadacbddbabdcccdbadadacabddccdbaabccadccccaaabcbcabdbbbaccacadcccacbdccdbadbcbbbacabababddcbdbcadcddcdaadccacabaccddccbbcbdacbdabdabbbbdcbaaaadabcdccbcbcdbbadababbddcaadaacabddbddacdcacccaddadcaccacaaabababbabaadabadbddcbdabbdadaddacdadabddaabbaddabaacddadbbbabdbacbabababcbcccababbbbadbaabcdabacdcdcdbbdcbbbdaacaadacccdddbcdccbabbdddddbadacaadccddcccdabaacddcbaccdacbcbcccadccdbcbcbdbcdddcbbbbaccbbaccdcbdbacdbbcababdcaaacbcabdadcaadaddbadccbcabdbdaccccdacdbdbcddcabbacccdcbdbbcccdadaadbacacddcdadbadccdcbcbcbcabccacaabcdcbdabbbdcbccccaabacdacaccadbcaacdcbcadbaabbaddbdcbdcbabcbabaddbccadaaaadbadcbcbbbddcdccdbdccdadddcbbdadaddbcdcbdbabbabacdbbcbbaddbaacbdcddadcbdbdbaacbcdbcccdaabcbbacbacccbbdbcdaccbbbbcaaccbbbcdcbbbbbbadcbacabbcacbbbbccaadcdbbcaaaabbbcdddbdabcbcacacdbdcdcdacadaddbbccbdbabbabacbbdcbadddccdcabdcdadbacabacbcbadacbadaaacdbccacbdcbdadcbbcabdaadbaacbcbcdaaacdbdaacbbcacddccbdaadaaabbacdcbbaddcdcaadacdacbaabdaddabbdbcdddbbdcaddbadabbbbacbbbbbbcbcadcabbdcaabccababddabcbdcaaddbcaaaabaabbbccbdcacdbbaabacddaacbbaadbdabbaaaabaacdbbbbcddbcdcbdaadddbabdcdcdcbbdcbcabaacdaacddcbcbbcbcdbbcacaccabdabcaaccbcabbababcbbbbcadcadbdbdcccbcadcbcbdaccaacbabbacdbdddcaccdddcdddbcdbcdcbdcabccbcdbacbacddcbcdaacddaddcdccadbabccaaccddddbdacdbcdddaddacbbadadaaacaacdbcababdcadddbaaabaabddbcaabcbdddaddbacbcbdbadbbaccbdbadbbbbaddcaabcadaccaaabcbdcadcabddccdacaaacdcabcbcaadaacaabbddaccdddddbdbacbadcbbdaaabccdcdacaadbbcdbbaaddcbdcbcdbcbadddcdcdbcaabdbcbadbdacdddadcdadccbbbcdabacbbbbcdbbbcbcdacbccabbddabbcaaadcbdbbbcbcdbdabdbbddcdccbbbbaacbdbddbaaddddadcccbaaabcbbdcbdcbbdcbdbccbccddcadbaababddbcadbbcadaacddaddadcaccdddaddbccbbdcababbbcbbcdccdacdcabcadcdccdadaaaccabdcabacdcbcbbcdcadaacbcdbaddcbbbadbdbdddabbcaaaacdadccbccbddbdaaacabcddaaadbcdbbdcdddababacdcdbcdabcacbcdbcadddcdccddabadbbbcdccaacabcacdcdccdbcbcdabacabdcdaabcbabccbbabddbbaccbddbcbcbccbccabcbbbcbcbbcdadacccbbacbcadabccbbccdccadaaabbcabcabdaaadbbcccdbdbdaacdcbabcababcbacddbbdbcadaabbbdaadbbdcadcbaabddabbbccdccababdabacdddacaaadcbbdadadbdcbcdbabdbadadbddcabaccdbcddcaccdbadddadcaacbddbdbadcbcbbabdbccdcdccdcdddacddbadcadbdacbabcbadbcccdbabacadbacadaabadbacccdbdadcbbcdcdbbaaadcdcddcabddadbacdaaccabdbaabcbcbdacababdbbbddccdadabdaccccbdbcdcdcdabdddbabbaabbbbcbdadddbbbbcdbdcddcddbbcdabbaccdadcacbbcbbdbbcbdbcccbdacadabcbcaccbbcbcbbdcbababbbdccccdacabbcabbdbcadbababbcbbacaacbbcadddaaacaaaadcdcccbdccccbcadaddadcabddbaddccbcbdcbccbabcdbaadbacadcdddbcbbaabdadcadbbcbdaccccddcddacdccbcacdcadcdbddaacdbddacdccabadcaabbcbddbdabdadbcbdadddbdbcacddcddabdaadcbcbdcaaaaaadcdabcbccccbcbababdabcaaaccacaaadbaabcdaadaccacbbbdcdbadccbcaccdbbabcdcddabdbccbbcdbdaddcbaaacbddacbccdbcbdaddcbaddbbbacbaadcddbbbccddbcbbbcaadcdbdccbbdcbdcbddadbabbcddcbabbbcabcbcbbccadbcdcbbbdcacbbdacabbadcaadadcabcdbbbccccdbdbaddbdccdadabcabdabddadddbadccdbbddaddaddbdacdcccddaadcadcacccccddababddcdccaabaabccaabbcbdcdcbbbadbadcaaabdcbacadbdbdabddabcaacbaaaddcdbcadadcddabbcacaccacddadcbdccccdaccddababcaaabaddcdcdacadabcdadaabbadaacabadccbddbcbdabdcdadbdaadddbddadddbbcdbbbadcadbacbddcdccaddadddcadbdcdcbdbacacbddaccdccbcbbdacbbadabaaabdbddcbcbccaacbbcdbbdacaadbcabdccbddadccbabdbdaacaccbabccaccdbccdccacaaaabcabbbbbdacabbcacdcbbdabaaadbbcddcccaaadadcbdbacbddddadcbbddacdcabaabadaccbddcdbabddbcdcbdbcaadacddcacddcdcbabbacaaccccbdcccbcbaccdaababbdacdbabadbdbbcabacacacdbcdaabbdbbbcbaacccabbbacdccbadbadaaaccabbacbcdbccbbddacbdbcccacbcccbdcdacaacccbbbbbbbabbbcdaacaabbbbcbbbccabcdaccaacbcbbacbbcddccadababbcdcdabdcacdbcddddabddcdbbcdbbdbabcbbdbbbcabdbbddabaacdbcdcdddccbadcbbddbccaaabcdcabcdadddabacaddbccadbbbacdbbaaadaccaadbcbbbcbcbadbabadbcdcbdabcbcbddbbcaccddacadcdaacbcddcdacdbcdccabadcacbdabdadaaddabcdcdaacabccabdddcbcbbbdcdcbabbbddbdaacaadccccbdccbcdcbccdddaddabbbdaabdacbabcdccabacccaabdddcaaadbbcbdacabacddcadddddaccbabdcdaadcccacdcdcbadabdbadbcaaadaadaadbbddbbdabbaddcacbddbabdadbbbdabbdacdddadcacacbcccacdcdabccadadabaacccdabdcabcaddaadbcddacdcbcbdbaadcdccddccadcbcbbbdcccbcbbadcbbbbcbababdabaccbacabbbcbbabbcdbbccabacadcdaaaacbcaaddbbaaadbcbbbbdaabcaccabbbcbadccaaaddddddaaaddcbaaabcaacbdcaddaccbbddaccacddababcbccdcbcddbccdcdacbdaadcbaaccdbdbddddadcdadaaacabbddcdcddabacccdcdbdccddcdbbbabbcacbadcdbcaabaacaaadcabdcbbcabccaacacadabcdababbbcdaacbdcdcbbdccbdaaddccdbcbdaadadaacbdaabbdbbbcdcbbbcaaaabbdadcacddccbcacdcdabbddcbcdbcaadbcaaaabbcacbcbdbabccdaadddaacaacbccaddcabbdbadaccabbdccaabdcbbcbddbbdaccadbaabbdbbdcacabcabbddadcacbbabbdbbdadbcdadccbdabacccdbabccbaabccadcdcbdcbcddbdcabaddccdcdbaabbdaaababdbbbccbbadddddcbdbcbdccbdbbcdbddabddcbbacbdbcbbbdacccacccdbbbdddadbcccbdcdaaccadddddddadbcadccadbacbdbaadbddaccddaabbcaabdaacccbaaacbdbbcddbdcddccdadbcbccdcabbbbddbdccbbdbdddbbcbdacaddcacbcddbdcabadbadbaadcdabbbdacadacdbbbcbbbdcdbdccccccadcddddbbaddbcbcdbbdbbbcaddaabaddccbcbddbdcbacbdaabddadbacbbdabdbdcbdaadbacaabcbddaabcdadbbcadcdcdbcbbaaadadcacccdaacadbaabcadabcddaaddbcbcbddddacbdcdbcbcabdbadcadaadccdbbabdcdbbbcadcacbadbdaabacdbcaacadbcdcacdbdaccbdbadccaabcdbcccdcbbbbaacddbbdaaddddacabdacdabccddccdcdbdcdddcdbddaaabddccaadaacaddacddcacbddcdabcaacdddbabbbbdbbbdadddcbddcdbccccabbadbbdccccbdbddabbadddccaccbdbdacccdbabbccdaaababadcccdccdbcaaddcdbbdbbcdaadccbddadcddbbbaaadbbddbbccbdcbccaddbcaacdccabbdabccbbbababacdbbcdcdcaaccbaabcbbddaaabbaadadacccbdddcabdccdddbcaacccccdddbcaaddacdbadaaddcbabcdddddaadbdccbaabcabdbbcdcdaaddacadcddbcbdccbdccdbaacdbcddbaaadcaacadabdacbccacbaccccbcadcbbbcbdcacddababbaacabccadabcdaaaacbddbcaabccaaabcdadabdcbdcdadddccccaccbadbdbaaccdaacdabcdbbbadcbdaaacaacdadbaaddddbbccdcbdbdccdcbabaabddaccbbdaccdacccdcabbcaacdabcdbadabadcbcdaadccdadccadacdbbdcbbadcccdabbbddcccbcbdbdcdcbacbcccbadadaccdccaacadcdbcccbcaddbbdcddbddbcdbabbbacacadaadabcdcdcdbcacabdbaabbbbcbddbdcacccabccbacaddcdbabacccdadddaaabbacccabbdbdccdbacdbccbadbabbbdbacbdcdacddbbcacbcbdaabdcdabcaccddcbdbaaadbdbaacdcdccadcbdcbcccacdacbbbacdddddddadcababcdddbbccdaacadcdaaacbdcaadddacacaadbbaacbcbdcaddaaadbabcbbcacccacbcdcbbdddacbbccdcbdbbacbdddaabdcaccaadaacbacccaaabbadcabdbbdbadcacbbddaabaadaaccbdccbbdcddbcddcddbdbddbcacadacaccbaaabcddccdbacdabcabbdcdddacdcdabddbcddcbcdcdcddacdabdbdacbbdabbcacabdcaaabacddcddaddcdcccddcadabdaadbbaccabcdaddadadbddaddcbdabadccadabbdaaacdccddbbbbbccbbdddacccacbdbdadaaacccbcddbbabbdabdddaabddcbddaaaddbccbdaadddbcadddbbabbbbbbdaadbcbbccadccdbacbadadbcbbccdcbadcbbcabcdbdbbddbadcbdbbddbdbbacbddbcbcabaddbbddcabcaabcbacdbbdcacabddaddbcbadbccacddccbccaabbdbbcbaadaaddcbbdbacdbadbcaccddcddcccaaadaddddcadadabcdbcdabababaddcdbcccdbdbdbbddabcdbadddbcaacccadccdacdacdadccadcddaadbcaadcdcdabadcacdbbaabcdbbadbabadbcaabbcdcabcaaadbcdddbdbaabdbadbbaacadbcbdadbccabbddadbaacbddbbdccacaaccddbbaacbdadacdcbbbccaddadbacdbccdcbdcacbddacabadbababcdaabccbbcabbcddbaaacbbacbadbbacddadaccdbdabacabcbccaacdbcbdbaaabddacbcaadddbdaddcbacaababdaacbbbdbcacdccccbdcbcbaadcabacbbccadbacdccbabbdbadbbabbacddddabbbdacdddbcaccccabcacdcbcdcdaaacbbacbbaaccbdbddaddddbdbdccbaadcdbacdbddbadaccccbaacadbabbadadddccccadaccbbbadcbabcacacdbdadbacddaabdbacccddaaccbdbcdacbbdacdabadaccdbcddaadbabcbdddacaaaccccadadadbadacdadabcdaadddabcbbcaaaaaddbbcdcacadbcabddabadbdacdbaccdadbdcaacaaabbddcdbacbababbabcbbbdcdcdacbaaccadbddccacacbbdadbcbbbabdcbbbccabbadccbaacdccbdddbddddcadcacbbdbbdcaacbbbbaccddcdbacbcdbbadcddbdcbbdcabadbdadddcaaccccabaddbdadbcbbbdbbcbcbcccbdcaaadcaddbabbbcbbadaaabccbacbdabadaddbbcbdbbdcdaacabbadbcbcccbddbdcacbdbdaabddbbacbcacbcbdcbadaaccdaacaddbcdbaaddcdcbbcdbdcabadbdcbcbddddbbcdddcbabcdaaadcadcacadaacacbbcdbccdbcabddbdcdacbbaddadbcbbccdbcdaabdcdccbbbcacbbcbadacccdcbabcadddadddabdbdbbdadbaacccbbbcdbdcddccccacbdadacddcaacdbbbdaaaccbbabbacaddaadaaaccaabdcadadcabdaaaaacdbcbabbdbbddcbcbadccccccacddabdbacabababcaaabcccbcdddaacaaccdadcaaabdbbccddbabcddabdabbadbabaccacacddccabadddccbbaadccdbddacadadababbcaacaccdadbbccdacdddbadadabbdcdababacdbdcddcbbdabadcbacabcabddcbabcccdcacddcaaadccbacdabcdacaaaaaadadabcddbabdddacdbdbdbaacaddddabdbcdcaabbbdcabcbabcbabaaaddaaaadcdaddcdbcbaddbbabcdcdddddbdbdbbcabbdcbdbbdbccdcdbccadbdcdcabddbdadbbdacabacbbaacadbadaaadcbcabcddbaacdddababbacaaacacacbadbdbabbbabcadacbdcdaaddccbdbdcbbbccaadccdbadbbadbbcbcdaadbaacbaddbdacdcbcbccbbacbbaccbccbcaaccdaccbacaadabcccddcaaabccbbcccddaddcadaadbbacbcccbaacbcbdacbdaaadaaabdacbbabbbdaaabbabddacbcbcabadbbddbdcabbadbcabccacddccddbdaaddbcabcdccdadbcdcacbabaaabcbdacaaacdcdaaaaccacdbabaabbbbabacabcbbbbbdabbadacdccaadacddadcaabcbddddacdbbbdcbaabddcacddadbcdcddccdaddbcbdbbcacbaddbbdbcddccacdcbcadddcacbdacabacabdbdbcacddabbbccdcdbcabcbbbdadccacacbacadccacacdddaaadabadccdcadadbcabbaaabdcdbdbcdddcccaacabadbcdcbbacbdacaaacdddabbbcbdacbdbcdddadabcabacccacadbbbbaaabbadccddabbadaaabaabcddbdabbaabbbcaddcbdcabadaadcddaacdbbbcbacbccdcbbbdadacbbccccbcaacaadbcbbbcddaababcdaddddbabccccdaacccacddcddacdcdadbcdadddabbdccbcdaabaddcbabadabbccbdcdbdbdcdacdaacaccacbcdcdccdcaabbdcbdcddcdbaacabbbbacccdabdadaddcdcdbcbcbcdcbbdbbccadacdabbdbaacdddbbaabababdcbdabbabaadccdcbdbabddbacbcdbddddadbcdbaabbdcbcadcdddabdcbdbdccccacabbdcaabacabbabccdccbbbccabcaabbbcbcdabcadbdabbabbbcbdccdabddcbbdadccdcdcbcbdadbbdadaaccccddbdcabadcbdccdcabadbbdaaabddbcddbbcddacadcdcaccbcbcdccccbabaaddaacbddcdcabbdbdddadaabdcadaadbadccbbbcccbadaadaadbbdccadaabcddcbaddcbbcbbbccbccdabaaaaabdcbbdccacccaddaacdadcacbadaccdbbbdcaaadbdbacacbddaaadbaabdabbbaadccbdbcbbccdcddadaadadcdcbdcbdabacaaacaccddbaaadcabbbadcccaadbbcdbbadbcddbccccccbbcddabbbdccdadbcdbaddadadddaaaddaadcbdccacbcdacaadbacaabadcdbcacbdcccbbaacbcbbcadbacdcabdbdacacbbbbcddcbcbacbbbdcdaadcbcdcadcacccaaaddbadcbacccbbbabbdadccacbcdaacbddbcacdadbabbccddabcadabdbdcaaccbbbcaaaccbccbdaddcbadaddbbbcdddadccaccacdabcaaabaccaaaccbcdcbddabaaadabcaaadcdbadbcbaadbcdadcdadddcabaccabdccbabaaadaddcbccadcdcdbcadadbbbbabccbcddbbcaddadaaddbddaacdacbdbacabcbbcbbbabdaaaddadabbbbdadacbbdaddbdcbabddbdcaadccdbcddaccbbabcdaccbbabcabbbabacaaaddbbcaabcdcddcaccdcacbbdadbdbaddbbdadccbacaabdcbcdabcabbccddabbbdcccddbbcbdcbdbbcddddccadbbbdddbdabcdadaccddadaaaabbdddcbcccaadccababdcbddccbdbdddacdbddaccadaacadadbaaabccbdbabbdddcbadddcccccdabcdcbcddbcdccddababcabdcbbabcbbbababacdaaaacadbcdddabaabcabcbadccadcbcbddbdbaccdbbddbaccdcdaddbbcacbdbbadcacbbccdcacabadddbadabddabbcdcbacdddcdabdabcbbabadbcdcbabbcaadcbadcadbbcdaccbbcbdabbaccbdbddcddacbabdabdacadbdbdbdccbdcabddabbacbacddbaabccacadabcaaabbbcdcdbaddbaaaccbdabacadbccccddaddcdbcdbabdbabbdcdacbbcadadbcbddadaadaabaababcdabadaddbaccddcdbbdcbacaacbcdbadddbbcbabbadacacddcbbcacccccdbaccadbadcdbbdbcdddabcddbcbcadbccadacaddcdcaaacdaddbdbdbccdbdcbbdcbcddddbdccdcbadcbaddbbbbcdbadccacdaadbaadbbacabbbcbbcbdccabdaccabdbcacccaddbbacadaccbacbbabcadadddcadbbddddbcdbaacaabbaaddcdbdbdddcbcaabaabcbddbcaccacdccddbbaacdaddcbdbbccbccaacbbacbacddbadccacdbbacaaabbcddcccdabbdbaabcabacababadddbcdacadbaacdcbbaabacccaabcabaddcabbacbacaadcbddccdadaddaaadcbbbababdbaacdacadddcbdbbbbaaadcbdbbddcabacbabacbbdadadbdaccccccbbdbdbccdbddbbcbabcadcdbbadcbadbdcccbcdabaadbcaadcbdddccdacddbcddddbdbadcdcacdbbbadccbadbbcccabbacdcadcbbccbbaabdccbcccaaccbcdcdcaacadabacbcabcadabdcdaacbbcbbacdccdddaaabadcddcbcaccacbbccdcdccadabdaabcddbabddbbcbbcaadacbdddcabbbabdddcddaddabacabbdccaaccabcbbbdccdaddbbbcbacdbdacacacddcdbbbbbdddabddaccbcabdaacabccbdbaddadacaabaadcdbabbbddddbdbddcbccdddaccdddbacbcdbacccddcccbbadcbbcdcabbaabdccaaaacbbccdaaabbacabdabcacadabdbdababdbaabcbdbcbbabababdbdbcacbdccdbbdcdbbadbcdcddaccdcabacdccbbdddabccbddbdbbabdbadbbddbccbaaadddddabcaddcbdbcaabbadacdadaaabddaddddbdaacacbcbcadbdddddcbcadcaddbdacdcbcaaacddcabcacadbcbcbbbddcabaacacbabddcbacdabccbdcdbbbdcbaaaacccaccacbadddccaababbcddabbdabccaaaababbacbcaadbcdccdbadbaddabdcbbdbcaabaabaccddcacccdddaccdcaacbaaaabaaaaadccbdadacccbccbabacbacddbcacdbaadbcdbdacdbcacbbbdacbdddccccbbddaadbdcbadcccadaddcbabcaabbdbcdcbcbdcccaccacaddaacdddaaaacaaccdabbdacaadaaccacbcdcbadbaabcdcaabbabcacabababbacaacdccdacacbdabcbbddbacbdddbcadcccdadbaaabaabdbbabaacdacbbccbabdbccdbcbdadbacadbbbadbddbadcddacbddcbbdcbcbcacbccadbdaccabcdacbcbbcabddcabbaddacbcdbdbbaacababdbbcabaaccbaddbabdbbcbdaadbbbcddbbacacbbdbdddccccdbadcbdbdbccccbacddacacddccddacdbccadabaadbaccabdbcddabdcdaacdccbcadbaabbddcacdaabbbabccacccccbaadbbddadadcdccacddbdbabbddbabcccdcdaabdabadbcdcacabbcdcdbcbcbdbabbbdcbcbdbdacdaddbbcbaabddddccaabbacbadcacabadacddadadadababadbdabdbdacbbbaaaaccbaddcddbbcdccbacdcdaadcdbaaaabcccbccdbdaacaaddbbacbcddadbacbabcbdaaaabdabdccdcabcbccdacbcbcbcdabbcdbacdaabdaccdacaacabcacddbbaccadddcaccddadacadabdbdaabdcdbabbdabddbabbabccdabbdcddddcddccbbbabadabcccbddcadcddbdcbccbdcbbbbadaddcbbcbdbaddcbaaabcadacdcccbdaabdbccccccbcadcdcdbadacdaccadcbcacdaadddbdbabacbdbbacbddbaccbbdadbaacbcdcabacbacaabaadddbbbbaaaccdaaacbcbdacccbbacadadacbbbccbaccddaccbbcdadabccdcbcabbaccdbbacbababccbdccaabbddacdcadbaaaabbcdbbaacdcddcddbcbddddcccdacaddcbcaccabcadccabcdbdbcbcdccdbdbdbcdbacbdbbbdabaccdbdbcaddbdadabcdbbccabcdadadadabcbdcdddddabaacdabbbacadcbddbaadcadabacbccabddcaaadcaadddcaadcabbbdaccbdddbdcdabadaacddccadbcaadacdddacdccdccabcbbdbbcccddabbbaddccbadcdbddcdbbbabbddcaccbbbdbaaaccaccbadbdadacabddddddddaccbbdbbdcdadcaadadaaccbdacaabdaabcaaabdcbbbcdccaadacbbaaabbcdbbabdbcacadcdbcacbacddddccdcdcddbcbdccdccabbccaddbacbccbbbaabcaadcadcbdbdbbabcadabadadccccdccbdbbcdacaccdcdaccadbddabdbcdbdaaadadcadadbdbbcbccbbdaaddbadabcdcbbcbcaadabdbaccbadcabdddddbccddbdbddcbdaccdcdaacadbbbadddcbdcddcaaabccddaabbdaddbdaddddccdacacadddccdacaccaacdbbcbddcadabdcdbcbbbaddaabdadbaadbcbbddcbcababbbdcdaadaabaaccccadabcadcabacdbaaacdabbabbaccaddadcdcccbdbccddadbaccabdcacabadddbadabcdbccbcbabacdcacdcaadacbcbcdcdcbbaddbbabccadcccbadcccadaacbcbbcdcbbcaadbaacbdbbdaddcccdaaddccabaabcdacdddabbcbbbbdadabcdddadccdacaddbdcadddabdabacbcdddcaddbdddcdbccabddadaabcdbbccbdaaddaabacbdbccccdcacdbbdcbcabccacbbddadaaadacacbdacdddbbabdbcababdcaacaddcbbcacbdadcccaddbbbadccdaacbdaadbbadcadbcaddaccddbaaccccdbabdbbacbddbddadcdbdccacbcbcadcbbbdacdbcdacdacdccbcbbbaadbbcbdacabbddcdacdaddadaadacdaccabbcabccbcbcbdcbdaaadbcacabdcadabddcbbdbcddadbadacdcccacccdaadacdbcdddbcbdacdbadbbccccbdcdbacaabcbdcdabddbbccdcadcdcdaadabcbaddbdbcadddabdacacddbcaddbcadadccadcccdabcccbcadadbddbbcbbcccccbdaddabdcbbbdabcbbcbadcadcdcaacbbcdcbcbccabadaddabbbbadcbbcbddcccbccdaabdbddaaccbabadacadadcbdcaadbdccbcabcbabbbdadccbbadddaabbadbaddcdacdbadcccbadddacdbcadcbcdddccdddabdabcacdadccabbacbadadcabbddacbaaaabdbabcbbbadcaccbbddababadbdcdbdbacbddbbdaddbaacaadacdbdadcdadbdccddabccddacaccacdbddbacabcdacacbddabbdabbadadcadbdbbbddddaadadcddbaadcddcbdcccbacdadbcabdddcbbdcadddabbbacacdaddbdbabdccbcbcddcdbcdcdaaccddcdacbadcaccddcdadcddbbccdcdddbcccbbaacdddbacaddccddabdabbabdacbcabacaabadabcabcabdddbcdcbdddddcdcdbabdddccababbabdbadcbcaabcccacdccacbbcbddaadbdbddcbcbbdcabbdcdcbbbbaabcddccbaccbdbbdcacaaccaccccdbaddcddbdbbdccadcaddbcadcdddbbcadaacbadbbcdbdaabbdaabcdbcadbbccabccbdbcbcbbaaacbacbcdacdbbbaddacddbbaccddbaaabcdadaddccbdacddccaacbcccbcbdaabdbcdabadbbadddbdcdbdcdcabacaccaccccbdbcdbcaacabcdccabdcadadaacbcabacaadcddbaaabcdadbdcddacacdcbdbbbccccaddcdccccddabccbcabaddbccbbddbbddadcddbdaabdbaaababcccbdcdcddacaaaccacbabbddadaadaccddcddddaaacadbbcdcaaccddabcdbdbabcadcdcaabbcbadadbbdaadbdcddbccabdacacbdcbccdaddccccddddccaaddcbdddbbbadaadcbbbaacaababaccdabacaaaccacbcbddddcddcdbcdcccaccbdbdadadbcbcabccbcbbbccddcbabbccacaadcabccabaaaacbcbbadcdacaacbddcabaadaaaadbdddabdcacdadabdddbaadcaabacdbdcddcbbbcccacccdcbbbcddbccccbbbabbacbababddbbababbaccadaacaddabaacddbadbdabaadaddddccdbdacacdabccddaccbddbbcdabbbbcdddcddccacdcdccddddabccadcbddddacdadcaccbdcadcdabdacccccabbadcbbdaaaadaacdabadcabacdacaccbdcadbacadbadcadccacdddbabaacdcbbdbabbabccbbaadacbcbadadbcaccddaadddaababdbbccccdacadcccabdcddaabdadcbbcaddddaabaaabdbdbbccacaacbbcbcadbaabbbabcbdcabaadcbcaaadbbbdccaccdcdcddbabbcddbcbbccabadccaacbddadcbdcbaabbdbcbacbadaacbcaaaccddbddbdbccbaadaacbbcccbdaabaaacadbdbabdcbadbaabbbdbbaabcdaadcacacdccaacabdadddcabcbbbbdcdcbccbbcdbacdcbaadcbbbbbbdcbbcbacacdabaadbdccdddaccadccabbbcbbddbbcddcbccccbdbcdaaacbadcdadddaccaacdcbcdadacabcbdaacdbbbdaccbaccbbdccbbccddadbbcaddbacabcdddacbcbbccdabbcbbdbdddbdadadcddcdabdaabdbdddcaccadbbcacdbccbacabbadbabacbacbcdddbcbccbbdadadacdcbcbbcbcbcdccbcddccbddbacabaddcddcccdadaccdbcdcbdbaacbacabbaabdacbdcbcdbdbdabadbadaacdbbdbbddbabaaccdbcbcddccadabcadbaccbabbccbdbaccddcbbbcbadbacbdadcddbbdbbdcbdacccaccbdcdcccdcadacbcacdcadaaaabdcbbcdacbabdaacdccadcdcbacacaaadbbdcbdcaaddcacbbbabcaabdaccdcdccbdcdbadcbcbcadddacacbdabcbddcadbdbdbcdaddbadcddaddcaacadaabdccddbbbbdacbbcddccbcbaddddbbbaaaacaaccddccbadbaaaaadccadcdbadccadddddbbbacddbdbcbacdacbcbdbbcdbdddaacddcdbaadbcbabadcdabadaabccdbcdccacdabbbdabdcbdabbcbbdabcdaabbdababdadbcdbdbbcdccababcccbccbcddacbcdcadcabdaaddadaadddccabdabadcdbbbdbaacaddabddccdcabddadbbbaaaadcadababcccdcbcbcabadbbbacccdaacbacaccbcbabbbabdcbaddbcdaaddadbbdacbabbabadcbadbbcadbccadbadaabbdbbaaabacbbbdccdaabdaddaccbbbdbdcbdbabcacdababadbcbbcdcddcbaadcabdcdcddbbcdbababcaadcddbcabdbcaddaaccccddccdaaadaaacaaadacbcbcbccbdcabccbdacccadccccdbadaaadabcbadcbabdabdaddcacbacaddbdccaabdccaccdaabcdabbacdacbbbcdaacbadababddcdcdaadabbabadbddadddcddbdadacbbcdbcdbcaadddddbddaaabaadbdadbabdbbccddcbcbbbaadcadaaadcabdaabcbccadadcbcdabbbdadbbbabdccbadbcadbaadcbddcaadadddbcadabadadddcbdcbbcbaabcacaaccccbdcabbccdaabcbbcaacadcadaabdabdcbddbadaccbdcdcdbcbcacabadababcbbaadbaababddabdcdcccacdabddcbdaaabbacdaccaaabdacdbdbddcacacbaaabcbbacdcdadcbcaabaaccbaccadaaacbccaccabddbcbccbdabadcacdbcbaabdacaccbabbdabbabbddacccbdacbbaaaddcccbccadbcaadddddabadabcdcabcbcbdbdacaaccddcccccbbccdbcdabdcbabbccbabbdcdbcbccaccaccadbbdadddcdbabbaabbbdcaddaacabcbaadabdcbcaabbabdabccbdccdcbbddcbacdaadcccacabdbacabddcbbaacadbaabaccaccdbbabdcacadaadabccbbbbdbcabadbaaddcacdabaccacdcdacddcddcdcdaaacdcbbcbbbdcbbcadcddbbbdaadbcaabccadabccbcabccccbcbbcbcddbbcdbbcdaabacbdccdbcbdcbbbaabddabbaadbacccadccdbccccbcddcacbddabbbbbcababaccadbdacaddddadadbbacabbdcbabbaccbbdbdbdabaadababcabbaadabdcadabaadaaddbbbcdbddacbbcaaaabacbddddcbbddcdcdadbdadcaadcdbcbdccdbacbdccbababddaabbccbdcbbadaaaddccdaacaadbdbdcbaddbaccbbcabbdbbdabbadaabbccbadcbadcdcacbdbcddaabcdcdcadaadadabadaaabadaddaadacccddaccdcddacadbdbdabbcaadbbbccadaccddaabccbdaddbdcdcdadddbdabdcdcdbbadaaacbdcbbcdbdababcddbbbddcadbdccbaddcabaddadacacddadabccdcdccbcbcabccacdddacccbdbbbbddcddcadcacaccdaababbabdbdbcdadccacdbacacbaacddcaaaaacccdacddbaabdcdbdcccccddbdbbabbcbdbdccccbaadadccacbbbdccddbdccbddcbbdbadbdcadcbbdddbadbaddaabbcabdacabbbaccbbcbcccabacdababababbcdcbacbcbbccbcbcdabbdbacdabdddcbddaccabbcbcdcbaddcdcaadbcbcccdaccbbcbddcccabccbabbabcbbddcbbbbcadbbbddccbbdaaccccdcaabacbdcdddddcbcaadabcaaacdccbdacaadababbdcbccadacbcccdbddcaddaacabcaababaabaccdabdabcbddacdcadabbacdaacccbbacbbcdcddbbccaccaacbaaabccbbabbcdabdbcabadccbbcbbdcbddccdbacbcbbcaadaadcdaaaadbbdadcbcdaabdacbdddbbdaabacbbabdbbccdccbbbcacbcbacbbbdcbbabacdadddbdbabcccdbcccabcadaaacbbbabcdbdadbcdcbabcdbcbcbadddadbbbbabaddaacbdcbbbadabccaaccbcaccdadacbcbbccadabbcdbbdbdbcdbabdadaacdbcababbaabbdaabdcdccdbbbadccbbbdbdbcddbbdaaddccdcacdbcdaaaddcbcadddabcbaccdbabbbabacacabdacdacbabaccaaadabcdbbcabddbadabdadbdcdccdbacabdcdbdadcbadbbddacdacbbaabbabadaacabcaddbdbbbbcdaadccdaaccdccdaccddccbaaaacccbcccdbdacddbdaaadcccbcddbbcaaacdadbbccaddabcbdbadcacbaddadcbcbabccbbaaadabacbcaadadccaddbcbcdbbadcbbbcbdccdbcbacaaaccdadbcbbaaadbbbabaacdabcbbacbdccbddcbbcbacccbdbccaabacacbdabccbccdddbadbcbabddccbbadbcdbcadcdbdcacdbbbdbcdddacaddcacbdaadbacaadbccdcacaaccbcdbacabaabccadcbcccadbdddbabacdddbcbbbdbacdcddadaadccbbdaaacacbcbbbbcabcacaadbbadbbabaddadacdddbdcaccabccddbbbdacbdddddddcddbccbdacbccdacdcdbbbbdcbaaacbdacaddbcddacddabdadbaaaadddaaabdbbcadbbcbbadcadcaadadabdbdabbcaccacdbacbdddbbaaaadbacdacccacbabdbcabbcbbcaadbcacbcacdabacbdcddccdcddbccbbdddbbababdbccddcddabdcdddccacbbdadddccddbaabccadcbdababcabbaabdbcaabcccdabacdababdbdbcdadcbdadbbbdbbacacdbbcbddbdddccdaadadabdaddcccbdabccacdbcbdbccbcaaddbcadaddbdcdcdcccddbabbadcbaddbddbadccbcdcbbcdbddaadbaadaddcbdbbaddaadcdabdccaaaadcacadacacbdbbdcdcdbcddaddcbbbccaddadaccdbbadbdcdddcbacbcddcdcbbadbabdcbbdcccddcdadbbcdbbdcbdbadcdcacbaabcdaaaccbbcccbaacacdadaadbaababdabddbdacbdaaaabaccacbddcaadbaaacbabaadadadcdbcdadccbaddaaaaddbcdcccbadabdbacaadcaabdcbddcbcdddacacddbcaaadcbbcdbcbccccaacadcccbdbacabddddcddcbddabbcabccddacacaddbcbbabcbdcccdbccbcdaaaccabbcbdbbcacbcbabacdbcbdbcdcaddbaacaaddcdbdacbabadacdbbdcadabbcbbbbbaacadacabaadadccbadcabbbcbcbaabbccabcdcbbbcbbacbaddcdbcabdcbdddadcdbddacacbcdcacadbcdcacaddcdcdccbabbddbcbbcdbbabccabacdbcbbcbabbbcdbbadaaccbbdccbacaaccdcdadbccbbbbaddacbdabdcdabbbdaadaccddcdcdcdbddbcbccbadbadacdcacdcbadaddaabdacbdddbadcdcbdddbacdcacacacbaacccaacdcdccbacccabcaacbbdbbbbcddddcdaccadcadcddabbccdbadadddbacdabcdcbcdccdaaddabcbdbddaadbdaadaabbdccdabbaadcbacbabaacbcaccaabcdcacbbadbccaacbdacbdcdacbadcdcababaaacaabdbabbdbcdacbacbdddadadcadadddabdbcbcdbcacbabaabadcdddcdcacdabaaabdbbacabcabdbbadcbbabdabdbdcdbcbcbaccaccbadcbcdaadabcbccdcdcabbaacacbdcdbcabdacbddbaccbaacbbcacccdcaadbadcaaabcaabcabccadcacabdcbdaaaaabddabadbaadddccdbadbaadcaddddddadbaddbbcdadabdbdbaacbdccbdcbdaccdbcdababaccdddcbddcacdaacaababddabcacdacdbadbbacddbdaddcccbcbccdbdbcdadccbccdcbddbabaabbdaabcddaddaddaaddbdbabcbbdaaabbabdacbadddadbaadccccacadbddccdcdcaccdddaadabaaadbcbdbdadaaacbbbacabcbbccadddababbacdddbaaccaddcddcabccdbbacdacbcaccdaacccbbdadbcacbdaacbbcdcbdacdddbcabbdadcdcbadbcccdbacccacadbdcdadbddddadbaddcccbdbadbcdcdbcbadcadbaabcdcaadbbcbabbccbddddaddabaddddbbcbcccdccdbbddcbadbbdaacbbbccacdbddbbcbbcaaccdaabacddccbbabbdbbcdbcbdcbadcdbcdbdbdcaaaabdbaddaccabddacccbcdbbddacbaaacddcbdbddbadddadacdcbaccbadcaaacbdcdaddbbdccdadacbccacacbdcabbbacdaccdacadbcbadbbcddbcdddcddcbabbbdcdbabcdaaacbcddbdaabcdccdbdbcdababdacaccabbbcbbababcbccbdddbaadbacdbcddcbdaacbacdbddbaddbbddaababbabcdcdbdddacadcdbaaacabdcdcbabccdbdabdccddacdbcadcddbaccadcaadccbbbbcbdaddcabaabbaddbdbadaadacccbdabbdadcbacddcaadcadaccdbbbbdcdddbaadacaccacbcaadcdabbdadaddcbaaacbcabdbbdccaccbdbdcbacbbdddcaadbaaaccbaaadccdbcadbbadaabacbdbdcadbbbbbdacdbbcdbababacacabaaaacbdcbbccbddcadacccccaacabadcadbdccbbaadbabadcbabddcdaacbcbdcbbbdabacbabacbbaabdaacabbacacddbdababbbbdbabcdacdccccdbbcacdaaaccacbbdadaabdaadaadccaaaddbcaadbaaadddbaacddacccdccdbabbabacaabddcdddbdccddbcdddadcaadbacbbccbbdccccdcddbabbbdcbccbabaadcabcccbbccabaaabcdcdaddaacbbdadacbabcbacdadbaddbaddbcbcabdaaaaabdbdcabbcbbddcdabcdacbdaadcaadddddcddabddbadbacacbcccdabadacaaacbddabacabdacaabbbadbacbbcbcacbadddcccbabdbaadaadddaccddcaddbacddaaccbdabaadbcbbccdbaccbdddacabdcccccbccaadddbbadbadbaaccabcddabbdadbadbdcacbbcacbbdcbdcbbccbaacccdbaabcbdcbddcccabbabdbbddcdadcbdbccdadcbbbddacaadbbbcabbcdacdaccaadadaabcdcdaaadccbbdabbbdcbaababddbbbbadaaaabbddccddbdcbabbbcbbbadaccabcdbacbbcabdbdcbcdadadcdcbdddccdcaabcaaadddacdacbabcbbcbdaadcbbbcbdcaccbaaadddacdccdcbccdcaddcdcccdddddddbdcdccbcabddccdcbbddacabcddaaaacbcbabaacddabdcbbabbadabcbdaccbadabdbccbbbccdccbacbccbacaabbdaadddcbdccacbacbccbbcdaadabbaddcbadcadadbaacdbcacabadacbcdcddbacbcbacbccaadacdacaaccaaaccadabcaaadcbcbcdcdbaddcbcadccabcbdbbdbaacbbadcdbdbddabacadbcccbacbcbadbbabaabadacbcccaacadbdabcacddbabcacbddabaccbdbbbdbabdbdccacacbdadacadaabdbccbabadbbaddcdcabdbbdddbdacbddbcaddcadabacaacacbadbcbadacdbcdcccadbcbbacbbbcdbcdaacdadbacbbbaaaabacdccbcadcbbacdcaacbadacaaddadcaadcdbbcbbdacaddccdacbccdbddccbddcadacdacdcbbccccadccdcddcdacbdcdcdccdcbaabbbcaadcbaddccaccbcaababbcddbbdbddcccdcadbddadaadddbdcadccbccbaaccbdddaaaddbdbddcddbabaabacddcadabccdbdadaaacacdabcaccccabbaaacbacdacdababccddbbdbaaaadadcdbdcbccabdcbbacabacbdbdaacacdcbaddcbddbabaddbbaaacdacaccdbadabcdacbbdcaadadddaaababddccdbcdddbbcdbbdacadabdcaddaccbbbabcdddbbdcbbdcbdddcdbbdaddadcdddcacddaabbcbacccbcbbbcbdccadbcdcbdddaddbcbdacabbaaadcdcacdaabcdcdbbbbcabcacdcbdcdbddacddbdcacbbbcbbcbdaaabdacdcbaadcdccacddbbcabbdcccabbcbaadbcbbbbdcaabacccbdababcbdbacddcabdadbabcddabcbcaadddcdddabcabcccababdbacbbdcabadddbddbdbcadbacaddcbbcdddcbababddbbcbdbcbdcdaabbdbcbbbabaadbbbabccdbcbcdddacaacccbabbbcbccbdcbbddbdaddddabbddabaccbaacccdccccaaaaaccaaacddcbcaaddcaaabaabcdbacadcddaddacabcadacdabccbbabcaadabaabdaaaddcdabdbccdcdbabbdcbacdbdddcbbaabdcaddbcabbbbacdcabcbdacdddbabdcaadbbccacbccddcaccccabdcdcbcbbbdcdcabcabbdbbbbaabbbdcaaabccbdbbaabbbcdbdddacddbabddacaccadadbbccdbdbaabadacdbdaccabacaddccbdcddcbbdbadadbbdcaddaaaccbaccccaaaccccdcadaaadccbdcbaaaadbbbbcadbaabccaaacdcbddbaaacddbbbbdcdabdbaccabdbcacbdacadccccdacbbaacbcbcaccddbcaddadccdcaadacdcbacaadbcbcadbacaddbbdacccddabcaccabacdcdbdbaabacccbdaddbabbdcbdabcbcdcbbcabdccdbaccabdcaacbbbdaacbccdbcacadcddaabbbbacabdccdadcdbccaccbacbabcbdbccbcbbcbbcbaaabdacbaacddcadccadbabccbdddbbdcdccbbacccbdabdacdddabdbaacbadddbcdbbacaaaadabbcaccbcaccdccaababaaddbdbaabaaabaaaddcbdcdaccacbcdacbdccacbdadcaaccaddacabdabccbcabdccbababaddbcaacadcadcacacccbaadbacabccdddbdabcbcdbadddaaccaaccbabaaacdbcdacdbccddaacbdddbbaddddabdcbbaacbddacdccddcdbdccadaaaacadcabbcccabaddabcccaabaddbbcbbbdabcccdaaccccaaabdddbddddcabaadaababdcdbddaaddbcacccadabaadcddaabacddcabccaaabddbadbbcacadbaddbbbcbccccadabadbbbdadbdadcbdbbbabadadadbdccddcbadbbdaabcdbdcbddacbdcbdddaddbcbaabddbabcccccbdacadbacdaadbadcdccdabaacacaaacbabcadcddcaccbcddacabbccdbcbbabdddcaaadbdacbbcbdabaaababdbaadccaddadbdbbcdcacaacbdcbdddbcdadbcbddcbbacdbcdbaddbccdabdccabbdadbdcaaabbdbabaaaacbbddddcbbbbababcabcdcbccaaadbaabaadbcacdadddadbccbcdadaabbadbcadbabbbadcbddacdbbcdbdadabbcbcbccdddcbababbdadcbdabbcbbcaddcaaddaabbcddcccaaaadcdaabcdaabdbdbddaadbcadcdaaaccdcaddaccdbacadddbddddcbbbbbacdccddbbabcacacccaaccdabcbdabdcbbdcabcaaabcacccadaabcbddaccdcbaabdbbadbccdbdbdcabdaccdbddccbaccdcdbbabadccbaccbccdcabaabcaaabcacccbdbccacbcbadddabdcdadaaacdcbcdacacddaabddddadabcaadabbcbbbaadbccaaccadbadbccddddacdbbccbbcdaddbaabddabdacdaaacbcdcbddddadbccdbbbacbcbaaadadbcabcbbcdccaddccdcbbddcadcdbcbcadacadcddcdcacdadcdbcbddddcbaccdcddccabbddccbdaacaabccbcccbaabbdcbaaddcbbdbcadbbcadbabacadaaadbdabaaabcacadcadabccaaccaaacdbbaccdddbabbdccdbbcdcaabaaddaabadbdbcacbcdacbaacaaabdbaadbbcdddbbbbdbccdbaccbaacbacbabccbabbdabddbbaacabadacdddcaccabbcbbbbbaabdcbdabcdcccabddaddadcdbddacadabbacbbddbddcdccdddabcbcbdcccaabcdcbbccbcacbbdbdbcadabacdccdabccbabaacbbdbacccbcccbbcabaacbbcbacacadadbcaadcdbaacbacaadbcbabaabaabaaadcadccbcabcdcdccadddaaddbddbbadddabadccbacdcbccbacabbcdddcccdaacaaccbadbdbbaddbbdcdaacdcaabacddccaadcdcccadadadbabadcbdacaabbdbacdababcbabbaadbaacbcaacbbbcacbccdcacadbbdacccccabdcbbdacdbcabcaabdadccdbdaadaddacacbbaacbbdacbbbbccccdadccbcdbaddbcababacdbddcdcacadbabbdaccbdbdcbadcbdaddabacccaddbadbbdaabdbadcbbaddababacbbdaabcddddbbbbdaadadbbbccdaacccabaabbbccddbcccbbddbdccdddacdddbccdccdbbadabbdbddbcabdbbbbcadcabcacdaaacbddcbbbbddbbdbdccbbaddcabccaaacacbadbdcddabbcdcdbbddbddcdaaadbbddcdaaccaddcadaaabbabaabcbddcddadbbddbcccdbcbacabbbdcacdbdcbbaabbbdcacbbadaabbcaddcdccccdaccacdacaacdbdcdacbadbdbadbcbddbbaaacabcdcdbccbcdadbbbdcbdaadddadadcabbaacabcbdacbabdcddcdbaacacaddabaabcbcccbdacbbaaccacdacaaaacbcaacbcdccaaaadcdcaadcaaddccacbcadcccbaabdcbdaabddbaacbddcbbcdddbbaaabbddcaddcbcdbaaccddaaddcaacaacbdccbdcbbdaabaabdaddcddbabbcdcdcdcbcadadbdaccdbcacdcaadbaaaddbaababbbccdacacaccbdbabddbccaadabbbbdababcacbbadcaadaddacbcbaaacadabcaadabcccbaacababcdbcdaabaaabbdcbabacdbcdbbdbacabbcbdbcdccadcbbcdadbbcaccadbabddaaccbddcdaddbdccddbbdacdbddbccbbcbdcaddcbcccdabaccadcccbddbbadbddadabdabdcbbbaadaabcbacabcbabdbbcdcabdaadccddcbbaddbdcadbcddbccabcacaadbccacbdbdadacddcddccbdccdbbddcdcaabcccbabbadddcbbdbddbbcbbbcaadcdcdadddcbaabbaabadbcacdacccbcbddcababbcadccabbdcacbabadbbbaadcdddcaaaccbcddcbacacabdcccdadaadcddaccbdabbbccabbccabddcaaaabbdcdbccbdccdadabdacbdaadabcdbcbbbdaacbdcbcaabccdcddcdbccaaaccbccccbaacccdacbcbdbddcdacbcdbdbbccdddadbcbabccaaaabdacdbadcbbaaddcdbabdbcccdbaaaadbbccacbbdabcbabcabddbbbbbacbcacdaddcacdbcacdbacbabdddbdcddccccbddaddabaddacbdddaadcbbbdadbaacaadccaabacddbaabcdbdcacdbdcbcbddcbabbbcbaccdaadaadaadbaadcacdbdaabbbabbddccdcccaadccbdaddbdbaacbbbcdbbcbdacdcccdddddbcacbaadddaabbcaccbbdabaabcabbdccbabacaccdbdbbdadbbabdadcddbbdcaccbbddaadabbcbbadcbadcdccbbbbbdbdddaadcdbdabbcdaccbcbdcddcabaacbabbccacdddddcacdacbbbdcbbaadccadcccdabcadbdccaccdddbadbbddbcacaacaaaaaccccbacbbaddbbacabbaabadbacdcabcddbcdbadaccbabcbbbcbdbcbbaddddbcdacbdbdacbbdcbaacdbdbdccdbadcdabaaaacadbbdcbacbdcaccdbddbddcddccdddaddacbbbdbaaabadadcbabacdaababbbacabdaaaddabbbabdccadaaccdaddbccaacccbbddaddddbbbddccbcdddccdbcabcdcabaacbaabbbaaadbbbdcbaccbaaabadcaacaadddadacbbbbccdcccddabcccdbdbcdbacdcccdbdcbdddddababcaabbaccabdccaccacdcbadbdddcdaccabadadacabadbbddddacadcaacacbcdadcabbddbccacbcbacbdcaacbaddacbccaccdababddbdababbaacbdddbcbadadbdbaacabbddacabadaddacbcadbaadabcadacddaadabcadbdaadccbcccbbaddacdccacdbadbccdaddbabcacbdbcdccbddacbdaacbaabcdabbccdacbaddddcaddaaabcabbdadadaaabcdccdbadaaabdbcaccdcdcbbdddadabbccabcadbaadbaaccabaccdbbddbacbcddaaddcabcaacccdacbcccdcbababadaddbdacdbdcdbbccbbcbaddbbabacbcaaddaacbacccbcbdadabcbbacdcabbdbcdacdadcaadcaccdbdccacccccbdcdccbddbdbcddcadabacbcabcbbbaaddbcbccaabbbccbadabdabddccbbcbaadaacbacabcbadccababcaacdbacbccadabccdccbcddcaacabcbdcaabbaaabbacddcbcdbbbddabcadccbcaabdbcccdadccdcdbdaaccdabbcdbccacbadbaadcdbdabdacdbacbadbabddacacdbccbbbbbdaaaacbacadcdccacdcadcddbcbcbddaababdbccacabdbbcbdbbdcddcbdbabcaabdabcaabcddddbdabadbddbabcadaacdbcdcccaabacbcbbbbaddadbbadcdbccdddbbacbcaaaaabcbbbcccbbdaabcbcbabdbabcdabcdbdccdaddddabbddcdccaacccabddbdacabbadbddbaddbccbbdbcbbbdbbbbacaddacccaacabcbabcdaabcddbdddcbcadbccccbadbdaccbdbcbabdcdbbbaaacbcaaabbadccbdcacbbacadcbacccbddacaddddacbddddbdbbccbabacbddbcddadbccbccadaabdcaaabcbbdaaabccabdaabcbddbbdaaadabccdcbbddbcddbdbcdaaaaccaaddcbbcaccccdbbdcdcacccdcccbddccaccdbaacbdbcbcaaabdadddbaabadcdccadcbdadcbbdacabcccbbdaabbcbaaccabddbacaacacabadbddadbccddcacbdccdccabacddadcdcdcadcbdbbcccbdbaabcccdaadbabdbdcbddbbadbdaabdcabcddbabdcdbcddccaaadddcaadddaacaabbcaaccdcddcdacdacccbaadbccdccacaddccdddbbcddbbaaaaaabcaacbabdaddbbbaaadcdadbcdbcadbdcadbdaabccbbddadccdacbcabcdbcbacabcbcaadbbcccbdcbdbabbaabbdbbcdbcdcbbbddcddabbbddbdacaabdbbdcbdcbccdccbcddaabbbdababbbbdabbddabccbccaabcbbccdddabbdbdabadbbcaabdccdacccbbdabdbbaababdbdbcaadbbbbacaccaddbcbcbabbabacbccaddabbcbbdabcccddbabdddbddcbddbaccddcdcbcaddbbdcabbadccbadccdcadbbdbbcdcdcbddbabbdadbccbbbadcddadabcadacbddadabcacabadcbdabdcaccbacccccbdddadbcadacbbaddcacaacaaabacabdaddabcbcadaabbdaabaaccbdbaccccccbcdddbcbcbbcdccdbabccababccdadaccbbabdadababaabdacabcaaaccbdcadbddccddcbdcabcdccbdbdaacacaacdadacdaaaaabbaacbbccacdcccdaddbbdaddabaadbadbabdcdbbdcbcdbcccccaabadabbdbbdaabbdcddbcdbbbabbccaadcbdddcbcadacddcaadbddccbcccddaadabbaabcdcbbadbbddaabdaadbdbcaadcbccdabdccdaccaacbbaadacbacccabcddabdadbbcccbcacbbccbbcbacdbdcbccddddddbdabaaadabdbdccdccdabbbdcdbdabdacbbcaaaddddbacabbadcdacdabcdcadacadbbadccbddcdcabbbadcaaccaabbaacbcaacbbdcabcaaacabbaacdccbbdcacbbdcaabaadcbdcccdadcabbcbddadbacbddcadaaaacdabbbcacbaaabbabbacbdbcdddccbdbdbbbddabdacccacadcbbdcaccdbdbdcbbdbddbbddddabacacbcabbacddbbabacdbdaaddbabcddcccbbbcabdcbabdabcddbcdddbacccdaacdadbcbacbaabcdbcbbbbdbccccbdbbacdcadabdaabababacdbbbbdbdcdbaadcbdcbbbbbdbcccacdcaaacbcdcbbbcaccacdcbccdcbbbcacbdaccbadabcaaabcdaadcadddcbacababdbddbdbbaccddbbcbcbaabbcacbabcbdcccabbaabdbacdacbacadcccbcbaadcdbcbbbaacbbbbdddbccaaccbdbcdddcbcdabccccaccaadcdbabaaacbbbababdacaabadadacccbbddbdbcbcadacbbccbabbbdcccabcccbccbbcdbbabaccbbdccbbdabadbbbcbbdbdbccacccacccbbbcbbbbccccbabaaabbdababdbbdbbbaadaabbbccccaccbaddcddbbcdadbcdacdadbdadcddcadbcbcdbdaacabdadcdcdacddddbbbadcdabddcbabcbabbdbdcbbdddbaccdddbddcdcaddccdabacbdbdaabccbbabcbddaadddbcacbcbabcacdbbdcbbbccbdababbccbdabccaabbcabcdccccaddbdbdacbbbdadbcabdaadabdbcaabbacacbbdbddaaacbbabbdbaacdddbbdcbbdaccdadadbbbddcbcbddaaaadbbaabccabdbcbbdcddadbbdcdddccdabaddabdcbdcdcadacacbbcccbdddccbbbdddcdcdaddbbddbcdacdcccddadccabdcbbabaccbdbbbdcacbbcdaccadcbbaddaabcabddbdadcabcbccdaabdacccbcaaaddaaaddbcdcaabcdadacaddacddaaddbcdddbbdacbaddadaadbccaddddadbaccbdddbbbbcbbbbcabcbccaadcadcdadcbcdadbbbaccbdcbdcaabbccaaadcbbabdcabcbbddcbcdaaabacccdcbaabbaaabbccadcdbabcaacdccabdbddbadbccabadbadccbddcdabbbbdcbbcbbbcabdabdaacdbcbcbccbaccadbcdcdbbabcddaaadadbabbdcdcacdccdabbabcccdddddddabdaaccaacccccccbaabacbdaadbcdbdcacbdbadbbcbbdaaddbcadacacbccdbdacbcddbababaabcdabdcdababcaddacddccdcbcccacddacbbccbaadcdaababdadabcabbcaccdabcdadacdcdbbaacbbbdacdabcadaccddabcadadbaddbbdccbaabbcdddcaabccaabbcdcbdabaacaddcbbccdcaabdbaadacdabbdddbbdaadbbabdccccadbacbdbdbdbcabcacbcbcaababadbdbbdacabdcadddbadbbabdaacacaaccdcdadccbbccbdbcdbbaabdbcadadbbbcadaabdaccacabdddbacdddbdbbacdadababaaabbbdaadccbababcccbccdccdacdcbcaaddbbbccaaadadcbbddabcacccbbccdabdddccabbadcdbddabdbdbddbadbbbddbdbbaccbabcbacccbbbddcbdbbaacacaabbacdbbddbdcabdbaabcabdabcabadddbbacbddbaaabbabcaacaccadadaddbbaadaccbbbadcbaddbddddcbccbaadddddabbdbbaaabadccbdcdcbccadddbbbdcbbbbcdcdccbbdbcbdddccbacadaaddcbdaddbddcbdbcabbbbdcbacdbcadbcdbcbbcdadacdcdccbccddacdcbdbbaaddddccdccadcbadbbaabbabdccbcdccbaadcacabbdacdbcabacabccdcdadabcdcdadabbdadcbcaabaaacaacadcbaaaabbddbbbadbaccddddcccacabccbcbccbcdccaadacdbcbddcdccdcdddbbccaaaacabddcdacabdcdbcbdbcbacccdcaacbaddbbdbcbdabbbaaccbccdacaaaabcbdabccbbddadccbaaaaaabcbacbbabddbddcdccccccbbbbabaacdbaabbdbbabbccdccbdaadccbcccbdabaabbdbaddbdbcdbcdbbbabdbacabbdbddadbbcccadbabdcabbdddcdcabadbbbccbddbcccbaabcbacbbbbaacbcdbdabadcdbddcadcbddbbbadddcabcdddaccbbadacbdccbcadadccabdbddacdabcbdbdddbccdbacacbacaddddaabcabddaccabaddabbaabaabaaadcabbdacbadbaccbadabaabcccdaacdbdcbacabbbaadbddababdabdddcbaabcccdbcddccabbcddbdabdcaacdccdbadbddaccbcddbcacbdccbdcadadbcbacbabbadbdaacccacbabbcdbcbccccaccbdddabccbacccacccbbbddccccdacccccaaacdbdddbadcdaccdbdbccbbaacdbdaddcbdadcabcaacdbdaaddacbaacacabcddcdcbdadcaccbcdcabcdcbdbbcaddcdbaccdbbdbaabccddccbaddbcccabbcaaabbabcbdcddacbbdddbbbcababddcbcdcabbbdacbdbabddaaacdbbbbabacbbcddbbdccdadaccaadabdadcadbcadabadaadcdcbbcbbbaababcdcdcacbaaadcbbbcbabbcbdbbadacadacddcacddcdcabdbddccabcbadcbaadbbdddbcdbacdcacdddccdbabccacaddcbdacdaaaccaabdddadddaddcdbcbaddcbbaadccdaaacaccbcbcdbbdbbdccbcbaccbdacdbacdbcadbdabbcbddaaacacabacccdcbdbccbcccbbbcacbcbdbabdcadaccaacaacaddcdbdccccbccbcbbaadcbaadcabcdbbcadbdccddcbabddcabacdbacddcbbadcccabcadabbdabbacbaacbbcabaaadaaddcaddcacadcbbcccbabcbabbbdabbccccadaabaadaccdbccbaaaadaacaaabcbdcccbcadccccbacbabcdbcabaaabdddadcaddbaabbcbbbcdbdbbbdcdadddbcddddccdccdbcbbccaaccabacbccaaacbbaadcabdcbdcaddabaadbabbdccdccadbcabddbcacccacaaaaaccbabcccbdcddbaabddbdacddaacadaccccbabddcacbbcabacdddcbacacacddabacbdddcbccbcbcabdbabcbccddccabcbdbbdacaccaddbcbbcddbabbdbadcdaadbbdddbacaabcdccbccdcccbcadbaabdacacabadddbacdabaabadbacdbcaacacabbbbdacaadbcabaaddadbcccbcbcdccccaddbdcbcdacadbaddbcccacbaababcadabbcbdbdadbdcdcaabcaadbbbccabcbaddbcbcccadabbbdaaadaacbcbdbddcdcdabdadcdddbccadcacdbadababbdadbaddcbabaaadcbcacdccdbaacddabbcaabaddcbcdaabcbbdcdaccbcbcdacddaabcabcbcadbaabbaabddcabbabdaadcacccdaadccbadcbadcbbcdacabbbccbcddbcacbddcbdabcaacaccbacacacbadcdabbbdbdacaaaccbdbbadcdadcbdcbbdcddcbdbdaaadaddcabdacbbbbdcaaacbcbaccccbbbdaabdabccccdaddbbadbcbbbbacddaccbadacbacccacbdbdbbbacadaabbccacbddcdadadaabddbcccccdcdbbcadcddcccbbacacacaaacbcdaadbadbaaaaabaadddaabddbbaaaddddccdcddcddaccadaabcbdddcbcdcbaddcbdbcadbcbdaabcddacabdcbdbacaacdbdbcadcaddacccacdddababaabcbbbcdcdbacbbdcdbdbabbaccacaccaccccaadbdabcddbcbccadadcbabcbabddabdbcbdccdbadcbadbcbcdadbacabdaadbdaabccbbaacdcaaaadbdaacacbbbdbbacccdcbbaaacacabccdaacbaddadbcacdadaabadbbaddaabcacacbccabcdaabbccdccccadccacaaddbcdcababbbdcdaadaacabcbbcbddcabacdcaaacbdabbbabaacdcacccddabcdbaabacbadbcbacbbdacccdaadbdccbaaacdcdcaddabadccbadbdaaaadbcbdbcccccaacbbabbddbcbbaddaddcadcaacdbdadbcbabacaadbddbdacacaccdddcbdddbbabcabaaadcdbdabaccbbcbddacdcddcdabbdcbadcbbbdbacccdddacaadcccbdacbdbdddcabdadcaabbbbcacadbdbbbcbdaaccaadbbcbdbaccadbdcabdbcdbacdadcdacbaaccadddbaaadbcbdcacccbbbbaddacadcbccccbbbdbbccbdcdacbbdbdbaccabbccbdcccbbbcdbbbccdacbbdcacdcabbbddcaacdccabaccbaddbcddbabdbdacdcaddaacbbacadaaaaaaccdcabbdbaaccabcdbcccaaaabbaadbccccabdbcabcbdabdabadcaaccdddcdcdadcdcbcbbabacaccaccbddacaabbacbcbcacbaadacbaccabcdbccdcbccacbbadaddcbdcdbdadcbdcbadbcbaabdcaadcabcaadcbcbdbbdbdbdbddbbcdabcdaabdabdccdcaddadcddcdcaccddcbbdaacdadccadcdacdbdccdaadddcdadadddcbbbbbcabdbcddaaddbbbabdacdcdadcabdaddcbccababacdcbdacadbcbcdaabacbcbddaadbcadabddcaadbadbcdaccdcdccdcbaddbbdbbcbbbccadbddcbcdababcbbabddbccacaadaaabdacddabacbdcccaabadabdbdcdcacbdaacbddbbadcdadcacccaaacbcadccbcdaacbddcaacbacbbacadbdadcaadcabcabababbaacdbddaaadbaabbdabcaadadaaaacdbdaadcbbaccdbdbdbabdddcbddaccbcaacbcacabdadcbbbdbbdccbccbaaccdadaccadabccdddccccccdaadacbcccaadcaabadbbdacdbcdabbadbccdcdaccbacaaadcccddbbbaacddbcdbbbdddcadbbcccdbbccbacccdbdccabcdbbcadccabadccccdadccdcacdacdaacddaddbddcbabbcbaacccbdaadcbbaccbdacccabbadddbbbccdaaaadcdcdbcacbcccdcdbabbabbabbcadbccbbccddbdbdbcdabbabbabcacbbadbbdabdbacbbcbaaccaabccaddcbcaabbbdacacdcbaabbabaccbccbcddbbdadbbbcbdbcdddadcddbdacbabdbcbbadbdcbabccbdababaacbccdbbddcdacbddbadbcabbabdababbbbcacaabbcbbbcadddbdddbbdcbddaacccbddcddbcbdccbbdcbdacbaddcddcccdacbcdcadabcaaacbacddcaabdabaabaabcddbbdaacbcdadababccdccbabdccdbdccbcdccbccddacdbdbbcdaacdbabccadbcbcaacbddbbdcaccadddcaadcbcacaaabbcbcaccbbadccdcbacbbaccccddbcdcdbabbaccbcaabaabcbbacdaddbbaabdaddcdcdababbdbbcababccbbcbadddcbabacddccdbbbacaadbdcdadadabcccdbddddddcbdccaaccdcdbbacacdbadccadbabddcddccccbbaaddbdbadbbcddbaddaadbdaddaabaabdbdcbddaabababcbbbdbababadddbcadabaabcbdbbccaccccbacdbacbdbccadbbbbcdcabbcccdbbdababababbaaccdbcbacbddcaddacdbcaabbcbcdcbabaadbdccddacdcbcbdcdcbcbdcdbdbddabaddaaadbcbbacccbcbddbacbdddaddcbbbccbadacacaabcabbdacbbcdddaddadadcbdddbbbbbabccdadabccdbabacdbbbacdbccbddaacbcacabcbccadbbaadcdccdddbcacaaaaaaaabbaacadcadbcabcacbbbdcabbccbdcdbbbddbabddcdaccacbcbbccaadbdbbbcddbcdcddcabaccaccabddaaddaacdbdbcddadabbaabaabbacbddcbadcaaaababcabadaacdaaccdddbddaacccbabbccccbabdadacbbbcbcabdcccdcdbddbddabbdaacbdcdbbcdaccabddccacdbdaacdabbadbcccccbbcccbdaaccbccbbccdcbddcbaadddabcaaddccaacdbcadbddcbdcccbbdadaaaccaddaaddcdbbdacbacddacbdabadcccacdacdcbddadbabbadaabddacaaabdcdadaabbcdcabcabcdacadaacacdabcbcccdddaacdcacbccabcdcccacdbccdaccbccccacacbccbbddccaddaadaccccbcacaccbbaaadcabaaaaddacacdadccdbbacadabcaabcbcbcadacacbbddcaabcacbaccddabcaaddadcddbcccdaacbcadaabdadcbabdbacabaacaccdbcccdcaddacacacdaabdabbadbdbdcbbaabdbccbdbcadbaadbcaabcabdcbdccbcadabcadbacdbbddcbdaddaabdcddbabcabddcaabccabddcaacbcbdbcbbcadacaabcbcdcdbacbcbcabadcaccaccabbadaccdbdbcddcdbbcabccaccbadacbaadbccbdbbdcbddbacabdbdbaddabddbbddddaccdbdcbdadcdacaabcccaabccddddccaccbccbbbbacdbdccacaadcaabaacaddabacbadcadaacddabddaaaddddaabcbaddabbadbadaaccdadcdacdadddcacbbcccccabbbdcdccdbdcdadabbbaddccabdaaadcbbcdabaadddaadbddcbdadabcadadbacbbbacbacadddbcbdcaddbcbdaabacdbbdadbacbabadabbcdabaacaccbcbacdbdcbacdcbabadaabccacaabcadcddbaccacdcbbbabaabbabacdbbcabdccbbbdacccababbabaaccdbcdaccabbabadaabbabcbcccccbabcadbcbbadcdcadccdaaacbbadccccdabcbbbacadcaacabbbcadccdadbbbbbddabacbddcacdbcdadacadacabdbdbbdbbabccdcaadbdabadacabdddccdddbcacadbbdadcacdbdabbdabaccddbccabadaadacbadadcacbbbbdbbaccbbccdddbbcdaddacacddcbbddbaaccabbcabacadcddadcacacbdbdadbcbdcbdbadabbabddccaabbadddacaacccbadaacbdcdddbbdcddcdabbcdbdabdacbbbbcbbcbadaacacacdaabdddbdddabcbaabbbcbbcbdadcdbacbcabddadadcacbcccabdbaabcddadadadbaadcbddaccbdccccdcadbaadddbcccdcddadaacbdabacaacbcccbdcbdcdabdabdcdbbacbcdacabcdaabaaadcabcddbdabdacccdcdccaccdbbddbabddcabbbadadacdcdbbabbddabbdaacadccdbcbdadcccbbddbadcddbaacbcdcaacaacbdbddbcaabbcbdcccbbdaaaabbbbccddccdaccadbbadabdcbbccdbdcdbccbcbdccbbdbdcadabadbbcaccaccadcbbadddbcccbddcadbbdaaacdabbadccccabdadabcbdbddcdadcbaccacbaabaadaccdbbccacbbbccaaadaccabdabcbdccabcddabbbbbcadacaaaabcdbcdaccdcbabbaabacacadaabcadcdabdcabbbabcaccddcdabcbbdaabbadabbbdccaaacbdadabddcbcaabacdacdddbbaabcdbbdbdacacbabbcdcccacdbcbdaacdccadabbdaccbbcdaddacdbdbabdbbcdbddaabcddaaaaabcdbddccbdaacacaadddbccabccbdcdabaddbbddcddcdbddbadbdbdcdadacbdddbcaccdbbdacacaadaadacdbbccccdbacdccbaacdadbbbbdccaadaacbdacccabdaaababdaccadbdaaaabbbbdbaadaabcadacccccbccdaaabcaadddcabdcbcdabaccabcdbabcacddaaabdbbddacbcdcccddcadccbaccaabadbbbdcacbcccabadacdabaccabcaaccbbdaccdcbbcabcabbddabadabbbccaacdcaaabcbdcdbcbaaabbabcdcbdccddaacbbcbbcdbbdababbbbcadbcdbabcacbabacdddacccaaabaabacdccababbddaccdbadcbdddddcadddbbadaadabcabcdbbaabddabdbdaadddbcdacdabaaadbbbbcaccaddcaaadadcbcbabbbcbddcdbddaaabadabdbbbdbaaabccaadbbcabccbdbbbdadabdcdbbadcabbabcbabdacccbdbaabdddaacdacadcaacbadbcbacbcbdabcbdacbcdacaccaabccbdbabcdddbcbccaabbbdabbdddadacacdcccbbbbdcdabcadcabcadaddabbacdbbbbcbdcbcbcccbbbbddcbdccdaaddbdabdbaaaddcbcaddcdbbdadcddacbdbccdbabcbabddaacbcadaacdbbdbabcbdbaabbdaddcaccaaddccccdcaabddddbbacdacabbccbdcddcbabadcdacdacaccaccaacdbdbddababdabbcdcaabbcbcdacdccdbccaacacdadbbdabbacccdbcaaaaaacbcabbbdcdbbdcacacaabcbddcaabbaabcadddbdacdcacbadcccccabbcdaacadcdaacbcdcbccdabddabadcadbbcbacddcdbdbbcbcccaadbadaadaccaaccdcbdaabccbdddbcaaacdbabccccaddcdbadabacbdddbaacaaabbcadcdcddaccccdacbccdcbcaccbdaaaccddcaacbcdbacdaaccaadbdcaccbadcdabacaabcbcbdcbbccaacddcccaacdaacaaaccdbcbaaacbabbbdadbaaabadaadaccddcbcbacdadcabccdbdbaaacacacdbcdbcdadabaaddcccaaabdcaaddddadbabdbbbddcddbcadcbdadbdcacbacddbaacbacaccacaaabcbbaccbcbabddcadbacddaccbccadbddcbabdaaabccbbcaddbdccccdddbcdccbdcabccccbaaabcbabcdcbcdbbabdaddbbcccbcadbccaacbaabbddbaaddabccbbbbbbbdacbcccacabdbcabdaabcaccdcbbdcbadcbcacadcdbccddaaadcadbcbabdababbaddadabddcdccdaabbccbaaabbabacdbbadbdbdaabbcdbccddbcccbddabcccabdaadaacbacbddabaccacdacdcdcbcabcaadcbdaabbabccabdaabcbdddddddadcdaccaadbdaddbcdbccdbbaddbbbadbcadbbddddcbccbacabaaaaaacdbbbdbcbacdaccbcdacddcbbdbcbdbccdcbdacabcbdbcabcdaabacbdcaadcccbcccdcadbcbcdbbdcbccababbbbcbbcbcdbcbadcaadbbdbcaddbddacccdcbcdaccdaadbbcdccdaaababdacbaccaccbddbbcddcaaadbddcdddabdbccbcadabbadbbbbcacabcccccbdacaccddbdcddabadbabbacbcddbdcccdbbabdccddcdaabdcbcdbabbaaacddbcaddcdbbbaaacbbbdaabbccccadbbbdbdcdbaaccbabcadbbddacdbabbadccdbdcadbdddaadbbddbabccadddbdadccaadcdbdcadacbbacdddbcbccadabcdcadbcbacabbadabdddcaaaadcdbbcbbcacbbaacacccdabbdbadddcdbadbaaacdbbbcbccbbabcdcaddbddbdabddcbabacbbaaddbabaccacdbadbadddcaccacaacbbdaccdadaadbddddddccccddbdbcdabbddadbcccbbbacdcabdcabcbababaabccddaacabcdbcababbcdacdcabcadddccadcddabbcdccbcabbbacdabdbddaadaccdaddccdbbddccacdbbcdabbbaabccddbcbbbddcabcdbccabcddcddbdbadcddcaacaddcdcbdacdaccccadbbdbcddcbddbdcdbdbadcacdbcadcbbbacbadaabccaabacbadbbdddbbabbbcdbdadbccbbdcddcdadbdadadabcdacdbcbabddaddbcbbbcaaadaddacabbacdabacdcddbcadddabbbdbbaadbcbabcacbbbddbcbacadcddabbbdadbadacaddccdabadcbbaabadbbddcbcbcaacdaaadabbdbcbcadaadcddbdbdccbbdcaaccadbbcbccdcabbbadbadadcabbadacdddddcdbaddadcdadcbcdcbcbcaabbddbcabacbacaabdbcdbccbcbbcaabaabbcdbddcacddbcabbddabdbbbdcbadccccadaccadbcabbabbdddcddadbdaccbcdbcbdcdaabbadbbcaaaabcaabbbdbabbabccddbbdccdccbbdaabcbddbcabdbaccbacdbbddcaaaddabcddaacbbcdbbaaabbbdcdbadbdcdabacaacbcaddadacdddbacdbbbbbcacbdcaadaabbcabcddbbbacccdcdcdddaddcddadcacbcabcdbabcccbbbcdbbabcdabddabcdcdaaadcabaacbdaadbcddcdaaaddcacaaddacdaadccdbccbbbaacbabbbdbbddabbdacbbbccdacccbdbadadcbdcbacbbadacbcbccbbcdcbbddddcbbbbccabbbcbdbdcbbbdbdcbdcdcdcccabcbdadcadbbdbcbbdabcbdbabdcccacccddbadbbabacdcbcdbbabaacdadadcdcaaadcdbaaabcdbaacababdccbccddaaadbabbddbacadacabacdbddbdcaccaaccdacbaadcdaadbacbcacccccbadacddbdaabccddcccabccbdcbaacccacbaccadcbcdcddcdbcaadaaaaddadacacaadccdcdcccaabcbdbdbbaddcdaacaacbaacbdaddabacaccbcbdcaadbacaabacbddbcbdcaaaacdbbabaabcaadacbdbcbaaabcaddbbcadcdaadbadabdcacdbbcdccbacabccadddacbddbadbdcccadbaabadccbbbaaaadaccadbddbcdddcbaaaadadddcabbbbdacccabdbabadcdadbdccaabbabdddacbccbcaadabbacbbbadcbbbdcabcbdbaabdbadbcddcccabcdcbbaabdbdaaacdcbabbccbcacdddcadbcbadcddaaacbbaaacdddcccabababbaaadbaccaacdacdababdcccccbaccdccbbcdbccacbabccadabaabdaadaacbdacddccacbbcdcbbaaaaabcaadacadbcddacaabccacbbbcdcabacaaabbaaacccbbabbcddacbddbdbacbdcaddaccdddbabcdbcbadcbabcbacdadbacacbdacadbdcbdadcaabbdcbdbbbbbbcababbbcaabbadabdaaacccadcbbbbbcadcabbbdcbcdbbdcdabddadbabdbbdbadabcbcbdacbcbcaacaaadbadccacdaccdcddccddcdcababcbdbdbdbcdbbbaaccbdcacbbccdbabababccacddbcaddaaabadbacabaccbcccbadbbaacbcaaccaacbabaadddacbdacadcbaddcbcccdcdbcbccbdbdbdccacdabababcdacddbaababbababadcbcbdadabdbaaccccabccbcadcaaabdddbacccbccbbcdbdbccdacddbcadcaddbbdccbabccdacaadbacaaaacddccdcdccdbacaacbddbbdabddddadcaadbbaadabdcaadcbdabbabbbcdacbadbcddcdcbdcaaaaabbdcadacdccabcaadaabbaadcccbbcdddcdddcbabacadcaddcadcbdacbdababcabadbbbcddbaccddbbcadbcdadbbbabbddaddbbdacccccddadabbcaccacadaacdcbaaccabbbbdaaabbaaadadcdaabdcdbadadacabccccddbdbdadcddbcbcdcabddbacdcccbadcacdddbbabbccdcadcadccbcbbabbdbccbccabdabdbadbbcddccacbdbbabccbdcdbcddcadcabdcbcbccbcddadacdbdbacadaccdbaccabdacbabbcbbcdccdaccacdcbacabcbacbbbcabaaadccddbddbddddccaabdaaaacbcaabdaddccacbdddcaaadbcbcbaabcdcacdcadbaacacdaaccadddbbabbbbabbbacbbadcdacdaddbbcaaadcbbacacbacbbcccbaddbccbccbacdccdbcadadcdbdcdbacabdaabaabbcadbadaaacbdcbdccaacaabcacccbcdadbbbcdbbbaccbcddcdbdbbbbaadbaccabcccbacbdbacccdcbabddaccddddccddbdacbbabdbbdabcdabadddaadbdcabadccaacacbddbdcbadbcaccdcddbcdabcadcdccacdbcbddddddabaddacaddbbbcddabcdcccdbbddcdcbadbcbccbdcdcacbcabbbbaadbbdbbaacabbbabcdbcbbcdabadabbddbdaccbcadcddbcccbacacaacadaddaccaccbccaccadcadbddaabcaccaacbbadaabccbcdbcadababccbdabcadaaddbcccdcccdbbdccdcdbdadabaaabddaabbdddcaddaadaaaabccabbdcaddbcbdcabdadacdcbabcbbaacabcbaacabbbacaacccdabccacddbcbbbcdacbbccdbabddacbcdccdadaaabcbadcaddcdaaacadcdbbcdbcabaabadcbcacbadabdbabbdddcbcbdbcacaacbbdbacdbddadcbcbbabbbbccdacadbdbdadaadbdccbbbddbccadbcdccdcdcbdbcaaacaacadadbbbdaabbdaaadacaadddddbaacabdacdabddabcdaaddbbcbadabcbaddaccddbabcababbaaaddaddbbcaacaadacbbcbbcbdbadbcadbbabddcddcabbcadadddcaddacbbcdbaddddbcdadbbbcbdccdabdabaccbaabbbaaadcccccadabaabbbcddcccaadddaabcbcbbcdbbdadbcbabcabcbdccdbadcbbdadadacbbccbbadadbdcbaccdbdccdccbdcbbdbbdcbacbcbdbcacbacaddbacbaabcbcdbacacbdcbdadbbabdcbcccddaadaacdccbdacdbacbdabdadcbdbabbabcbbddbccabaaadccbcccacbccbadabadccaadacddccdcdaacbbcbddbbbccadbababbcdbdbbcabbdaabccdbadacbcadacabddccbcbbcbdabacadbdbcbbdbcabcdbbaccbcdccbcccaddbadaadaaadadcbbdbaadacccdbbdacacccabbccdcaaadabcbccbbacddadcbadcbaabacadcaddbcbdcbbdccbacddbccbacbadcddacdddbdaddccccbcbcadacddbccaacccdcdcaabdaaadcbbadcdbdbdbacbdbbaadbadcaddabdccadaadbacbccaacddabcadccadababdcadabbabddbdcbcbdbdadbaddadcdddadbcdbbccdbcdadddccabbcbcdcadbabadccdabcabaddaadacaabbbdddacbaacdcdbaddddcdaabbccdaabbbccaadddacbbdadaccccbadbbadcaabcaabaaaacbcdacdbabbbacabcbaaccabaaacdbcdcccdbaddccdcccaabdaadbaadbaaaaddabaddabbdbccdbcabbbdcbccddcdabcdacaacaadcacaddbcacbcdcbcbdbbddbbcbdcbbdccdbdbcdddcdcaccdaacbdbdddddccadcabaadbdacbdbbabaacbdcbacdacadacabccacdcbcbbdacbadcdcabacacbcadddadadadadccacbcccccbdcdbcacddbdadcbdabbaccabbccbddccacbcdbabbdabbaacbdacbcdbdbcacdccddacaacadcbbcadbbcdadbbbaccacbbbbbddbbcacddcccaccbacccddaabddddbaaabdbbccbabdcdaccbaccaaadcbaadcdaddbcaddddbacacddaccdabacbbcdaccddbcbcacabccabbdddddbddbccbabadacadaddcacbbdbdcddaaaacadbdcbadbacadacababadadaccbdbaacddaadbbcacabbbbbabbaabaaccabccbddccdbdbddbcbacbcbbacdabddddcbcccdbdbdcaacdccbcabbbacabaaccaabdaaaaabddabddadcdaaccaadcbdcbcdcadacccbcaacbcdabcbaddccadcddbadaabcbbbcadcbcdcaabcaaccccdadcbbcdabdbbdacdcccabcdbcbbabbbdaccdbabbadccdaacdadabcdaaaabbadddddbbcaaabbdadbbabcaaddbadcdcacdcbbdcaadcdcbbacaaacaddacccddbadababcccbbdacddcdabbadbdcaccadbdcdcabaacacaaaabbdccbaccdaacdaacbaabddaabcacbcaacaaabbadcaadacaacbcabccdadbdbbbcabbcbdbdbbbdabacbcacbdccccdacdacaccbadccadaaabbdcacabcccdadcabbbddcdbbadcdbbbbccdbabdbbccdacbbaadbcaaadaacaabbacabbaaacadaabacdcdccbaccaacbcabcdcbcbbdccacaabbccdcdacabdadbbdbababbcdbaaadcaccacdcdcdadabcdcdcdddbdadddcddbccbdacbacdbbdcaaccacbcabdbcaaaccbddbbcdbdccdcbaaabdccacbabdbcdbbdbcdcacccacddbdacadabdbbaccdbcaabaaddbbdbaabdcbaaaddcddccabaabbbabcdccbbcbcadabddadddcbadcadccbdacccdcbadaddcbdbbbbaacbdcabaccdcdaddabaadabdcbbacccbbbcccdadabaacbaadcbbcadbdacccdabbacbbadaabaaabcbacbbdbaddaadaadcbaabddbacdbabcdddcdadabbcabcbaaacdbcbdccaddcdccbddbdcdaddaaaddbddbbcdaccbddcdbbdcdacbbcadaccddaaabddccaddacadbaabcbaabbdcccaaaabadcbabbcbbaadcacdcbdbaaadbbbddbddcadcdcacadbacbcacdcacbdbccaacdbbcadccacdccabadbcbccbcccaababdbcbacdaadbbcabdbbccdabacbcbbdacccadacbcabbdbbdcabbcbabcdabbaadccdcacaacbddcdabdbdacbbbdababacbadcabcacaccacabdacabdbaddbbbcacdddcbdbbcaaadaabadabdadddddcacaaccbadbaacadccacbcccdaabbcdcdbaacbaaddddccdabbbcddbaccddddbbbaccbacbccddabbbcacababacabcabbccdabbcdaaacaddacccdcacbbadbababdacbdbaddcccdccdbbadcdaadabadcaadbcbacbaadbdccaabdbababbcbdbcccabaddddbdabbbccdabcbadcdcdacbaccdabacadcdbcbdcdddbcbcabddbccaccdadbbdcbbdbdcdbbdabbcddbabbbcacbcdbdbabdcadcdadbbadaadbaabcdadaaabcdccdbcdbddcbbbaabbcdabaacbbbcaaaddbdbadaccbdbacaccbbbacadcbbbcaadccaadcbdbdccbabddaaddbcdbddbabadcaccabcbdaacacacddaabccccdadaacddacabbdbcdbdcbdccabbbaadbcdbdbcbadcaaddadadcbcbabbdbadcdaacdaccadabbccccaabbdaabaadbccadbacbcbcdbbbcdacccbcacdbdccbcbccdadaacdbcaccacabaadcdcdbadbacddbacdbadaadcdcabcccaddbacbcbbaddabcbbbaddacbcbbcaaacabadcadddccdbcbdabdcacbccabdbbcaadcbccbaaadabddbaaddaadbdccadbacdbacbbaacbcccccccbdaabbabbdaaccddacbccaddaaaccdddccbcbacabaababccbcaabbdccbdcccbdadcdbadcaaadcbcbadbadcaaabaccddddaddcbacdbdcbccdabbbdbabdbdaaabbcdaccaabdaadbabbdbacbcccbbccadcdadcababdbbcccdcccdacaccbdbcacbcaadbaadbdbbbbcdadcddabdadcbababddbbbdbcccdaaadabdadcddbdddbcacdabcdacbcaabbacadcbcbdcdddbabdbbbadddcccbcbdadbcdcacaacdcbdbcbdcaaabccaacaadbdcaddcabaaddddacccdacbdddcddacadbbbaccabcbabddbdcbbdaaaabacdacdbccadcdcbadcabaadbaaadbaabcdddbcbaccdcbcbbdcbbdbbaaddaaccdbcabaabcbaccbaadcccdbbadacbdaadadaaababcdbbabbbdcdacacdbbdcaddddbabdbcbddbbbbbcaadcddadbcdabaccdadacbabadddbcbddadabbbcddabbdcdbcbcdcbddbcacdcccacadccccdabbbdddcbcadaabbddcaaaababacbdccdaaacbaccdbcdacdccbddcbdcdcbdcbdabcbdaadcdababdbdacbadcaadcbdddaadaddbccaabaccddbcdbccabcbdbbcaddbdaabbbcbaddcccdbcdcbabaacccaadadcaadaaccaacabbabbdcaaadcccddcdbbaccbadabdbabdaddbabbbbacbdbcabbbacbacddcddccbbdadabcadabcacccbbbbbbcdabdcabaadbcabacadbcdccabcbbcacacdbbbcaadcdbcccdadccbbabddabddabadcbabdbdaccbbaadbbabbabbcddcccbabbabaacdcdbdcdabbbcdaaadbcabdbbbddbcaddbdbcbcdddbdddbcaacdbcdbbbaacbaabcccdaaaacdcdbdabbdbdbbbbbaaaaacbcadabadddacccacacdbbaabcadcaaabbcbbaadadcbcaccddcccabcdbddaddccbbbbdaccdcdacddabbabaacbbdcbabbbcddcddaabadbddbdbdabbbdbdabdbbcdcddcdacdaacbcadbbcdaaaadcccdaabbcadcbcdbbdabcacddbcabadbbacbabbbbcccdcdcbbcbabbccaddbdacdcadaaadabcbaadadddccbcccddacbcaabaacacdcbdaacbaddcbcdccdccddbbcddaaacabaaadacbaccdbcabbacdbdcddddaadccdaaabcdccdadbdadddabdcccadacbbacabccacabadbaaadcbadbbcbabbabbadcbbaaaddddbabbabaabbaaccbdacbddcbcbccbdddabbadbcdacccdaccbadadbaccacabbcdcaacdcacdccabbadabbdbabbbbbddddbbbacddbdccbccbdbdccdcaadaabdadcaccdcbcaadcdccaccbcdccadacddbcababccaaaddcbcbdadcdbcabcaabbbcbddacbdccaaccadcdbcdbdbaacbadbaaaadbcaacddaddcbdacacccbbdacbdcbbdabbcbccccdcdacdbadbbbbddbbdcdcababaccacbbbbcdabdccacdccabbaccabbdabccccccdccccccdbabbacdacadabdcdcddcbaddadacbbbcabbcdbbacdabbaddcaadadcdddbaaabbbbbcdaabcddddbaabdbbbddabccdabdbcdbbbdccdcadcbbabbcaddccbdadcadcacbbdacdaabdabbdbccabadabbddddbcdddddddbcdabbcabccabddaaabdabcbbbccababacbcadccbbcccacaabbbbaddcaadbdadbaddddaabdbcdccacbdbbbaadddcacbdaccddbdccdddcbadddabddcdddccdbadadccdbdacbbbbaaadaadcbbbccccbadccdccacdacbdaccbaabdcacdcdccbdabadbbaaacdabababccadbcdabbaccadbbbddadababddbcacbbcdaddddacbaabddaabbdacbcbdddddbdbbaaddbdccaacadabddccaaacdcbacdcaadbdbaadbaabaabcddcaaaabacbddacdbcdacccacaaaaaabaacccdcabddbbbdaaccccabdccdcdaddbbccdcddcdbabaadabbdaabcdaabdccddccabdbaaadcdacccabdacdbbcacbdadabdbbdbcabddcddbdbbdcabbdadcbddbabdbadaddacacaaacacaccddccbaaddaaaaddbcaabacacaccdbcaadcdcbbabbdcaaadbcdadcccaccbaaccbddacbdbcccbcadbacaadcbdbaaadccdccbdcdbbdcddcddadbdccaccacbadcacccabdcdbcadadbdabddccdbcbdbaabbdbacccadbdbabbdddbcadccddcbadcacbdbdbcabadcccddbcbaddcabdcbacbcdddadbbdccacaddcbdbbbcaadbcccabcaddddbdcaadcaababccbaddddaccbddccdababdbdbaacdccdaaabacadadaacbdbadcbadcbdcdaaaadddacdbbbcbcacdaccbddcbcddddaccddabbdadadddbdbbaccddbbdcdcdbaddbccbcbbbbbaaaabaccabbacdadaabbabdcbbcdddcbcdaadacdccdadacbcdccdabcbbcbddbacaabbadccbdaaccaccaadabccadaabcdcdddaaccdcbddaacaaadddddbadadbbbadaacdbbdaaabcacbcadabcbddccbacbccbbdbcddadadadcddccadddcdccdabcbcbccbacbbabcacaaacdabddbbbdcccdabbcabbcadbbcbaabdbbddcdababcaddaaccabddaaddcbadbddbcadbaacbbaaaabdcddacabadccdcbabbabbbcacbdcdaacacadbabadadabacbbbcbdcacdbcccaadababcaaadaaddaacabcbddaabaddbccbccddcdbbddddbbbbdcbaabaabcabdddcaabcabdadabcadbacaaaccacbabbaabcdddddcbccacccbbbbbacabddaabbbdbcddbaaadcaccadccadcdccdccdddcbcdccdcabababbdbbcdbcabdaadcaccccdacccdccbaabcddaadbccccdcaacabbaaadbdcaaddbaaaabbcadbdacbbcccccaabbacdadcabbcdbdcadbbdaadaaaababbadcdadbcbdddcccbacbdbadcabcbdcbbddcbdddcbcbbbabddcaabaccccdbabbccacddaddaadabccdddbbacaabccdabdacbbbadccdcdcabbaccadadcacabcaadcaaadaacdbbcaacdbacdbcddddadaddcacabdbccaaccdddbccabcaccaacaddacaaddbcbdccbdaaabacbababcddbadddddaaaaabdbaabbbdcdaabcdbadabcadcdcadbbcbadcbbcabadabbcadacddbdbbcddaacaccaacbddbcadcccacabdbaaaaabdaabccacccadbdadaaadcdbcbbcbdaaddccbabcaabcdabbddcbddbdddccbaabdddcddaabbcdacdccadbbcbccbcacaaaabacdbbdbdbbababcdcaadcbbcddcccdddadbccbdabbcacaacdbbdcdbadcabdddbbdbcadcdcdaddbadaadddddddbbbcbcababaddbdcdcdabdbbaabcaabbdcbabadccacdcacdbdadbadcbaacdcddbcbabaccabccbabadcccacccdabdabcdcaababdddabbadabddbacacaacddccccdadbabdddcaccbaccbaabdcaadadabbbccddaacdcdbcddccaadadbbccccaaadbbcadbcacbabdbdaabdddcacadcacacdbdcbabbcbabccccdadacbbcbdcdddacacdcbaaacacacbdcdaadcdcdadabbbccdddcdddbbcbcbddccbbcbbbbcadacacdddadabcbbbcdcbcacababcaccbdbbbbddbccbdcdaadbbddaddcdddaaabccdcbddbabaacacdabaccbdccccadbcaaacacccbdbcdaabdacbaddddabcbcbaaabadbbcadacbbbadbcdcabccacbbdcccbabaabcdacbcbbaddadbbaaccaddaccddcbdccdbbdbbcccdaaabbdaccbdbdccdcbabbdddacaadaacbdcbcdcddaddbbcaaabcaacacbcdcbdbcbdcddaadbbcccacaacdadddcbddbccbbcbcdacccdcdccbccadbabccddbaccbbdadcadcaadbacbccdbcbdbbbbdcacacaadbddbccadcddddbcbacbcbdbdbbacaabdbcdbcddcabaaaddadbbdcbcdacadccccbbcbbbdacabadbaccccabcaddddddbaccdcbcbbabddcdbaccddcadccccabbccddaaadbbdbdbdddabcacdaacddbaacaadbacdaaabbbabcccdccbadbabbacbacbccbbadcbabddcaaccddcbaddbcadddddccacddcacdabdadccdcdcabdbbcbbccaadccaaacdccddadbcbcbcaabcbcabcdbbabdaabcdabbbacdbcdcacdbabaaacccbbcadbabdbacdcccccdbcbdbdbcccddbacdbbdddadaaadcacccaadcbcabdddccbddadddabadababadccabcbbbaabaaaaabccdbcddcddcaacccdcdcbddabbdacdabbdcddadababdaddababaadabcbbddddcdcddddadabddcbbdbaadbbcdcbcadcdcdbbddbccdcacbabddbdddaadbbccadbabdcaccbdadcaadddddbcdabbcadabbcabccabcbacaadcdbcaacdccbdbbdbccadccabdbabdacdabccbabcacdbbdcabaabbdcbcacacdbaaacaaaabacdaadacbcdcdcdacbadaadabacabdadbccbddabdadcbaabdaabcdadcdddcbbbdbcbdaacddccdaccabbaacbaddbbbdbbdbdcdbaacdbaccadaaaddcbdcadcbcbcdcbdcbaacdcbcddadcccddbbcbdbcbbcaabdabcccbadbbbcddbadbdabcaacaddbbcddbcdcbacacacdacdcddcdaccdbabdccbbcccccbcbdaacbccdcbabcaaaddbadaddacadccbbcdbabcbcbbaaadcaabbbdcccadbbddbbbaababaabcbdccdcabaaadcddccbacdccbcdaaabbcccdbababbbdcccbbdbcabbadcaaabadabadbcbccbbdcaadacaadddccdcbbdbbbadddcdbcbadbacbdadabddabcaabbabcacaaaaabddadddbdcbcacacabcbbdccdcdddbadccaadadacaccdcbabaacdaacccdbabdbbdadabbacdabdbcbcddabbaccbabccdabccddaabaaabcddbbcdbdcbcdacadaaacdaaadcdcaaadddcaabbbadacddcababcbaccccdbaaacccddbbcaddaadcccbacaaaccdbcadddbcddccabddaccbaabbdabbbbdabcacabaabbadaccbaccddcbabbdbabbbadaddaddcbbaadcadcbcacacdbaddabaaacbdddaabdaacaabdadabccbbdcaaabccdadaabacbadcadcbcbabbadadbddbcbbaddcbadbbbbcbacacaabbcabbabcabaadaccbaaabbcdaccacbddcacbaccbbcbadadadadbaadcaacccacdcabcaabadddbaadaadbcdbdbabacdabbccccdacbcbadaacbabcdddcbabacbadababcbaaacbbdacbaccbacbccbdbdaadcdbddaaabbbcbbbbaadaaddaccacddbdddaaacdabbcbadcdcccacbabacdadaaaccccabcbdbdacdaaabdabcbddabcbdbcdacabdbccbdacacdbcabadaaaaabddccbdacdbdadccbbadbbcbdbabbbdabccacadcbdddcddddbbcabccaddbdbdcdddbccdcddcdadabdbcbadcbccaadacbccdaccdcdbbbcbcaadcdbdcaddaadccccccccbcdccbabaabbccabccbdababddbdcbabadbbdddcababdbddaaaccadcbadcaddbaccaaaabbdbcbbacccbccdddadaccddaabaccddabdbabbcaacadbbdacbdcbdddcbcabbbdbbcccbbcacdbaabcabdbddddacdaaaaddbabacddaaababdacaadcbaadcbbbbaaaaacccdccaddabbcbcaabdcbcaaaddacdbbbbcbcaadcbcacbaaacabbbccbdadaabdddbdaccdabdcaadbcacddabbaabddbccdaabcabaabcbaddbdbaabcabddbaaddabbcdbbbacbacdcadddbbaaadbabaaadcacbddbdabbaccacdcbdbaababbdccbadbadadabababcccacccdacaadbabcdadbdabaddbdcdabdcdddbbbbbabcdabcaccaadbcaaaddcbcbbacdaabbbcccabdbddbcccccbcacbaadbaddaabdcdabddbbdcaddcaaabadadccbddaacddacaaabaadcacadddadccccaccdcbccddaaaccaabaabddadabdcbcdcaacbcaaadbcadadbcbcbbddbccabddbaabacdccaabbdbbbabbcbbbcdbcdacccabbbcabdabaccccdabdbaddccdcaaabbdcddcbbddcbdcadbbcccccbacdabdaabcccacbcdacacdaddbcdcbcbbcdbacaccaabcbadddccdbdbacaccabddaddcbdcbadadadaddbaabbbdcabcadcdbaacbdadddcadddcdcacddacdacdbcbacaaccabcabddcdacbddbdcaacddccbdcbcbdddcbbcddcbcddddcddadadccaddacbdcdacaccbcadcccddcbccdcccddbdbbababbddcdcacdabdaaaadbcadcbaacbbbccddcbadbdaccddddcabbdddbcabdccccacbdaddbabdccbcbbbddcdcbbbdbbcbcbdccdddbddcababcbbbbbdbadbbacbadabcaabdbdcaacdcbbddcacdcdbcdbbddaadadabbdaabdbacabdcdacbabdacabccacabcaabccbcddaacccadccaabcbdabaacdbbdaccbcdbcbababcbcddbbbbaaacbdddcdcadabccabcdacacabbbaacccacbcdaaccbdcdcbabdacabaacccbabcdccaddadddbabbbcdccadcaaacaacbccaacbcacbbcbddaaadcaaaaccbadbacbbbbcacbaabaccbbcbdabbadbccdbacbdddcdbcacbccdaacddbcccdddbadcbbdbdcababaadccaddbdababdbbcaaaddbdbadddcabdddaadbcdabbbbdaabadcbdcacdbcccbdadcaaacbccbccdbcbbdacaccbcddaacdaddcaacaacbdcdbdadcbcdcbcdaaaabccbddabacdabbddcacbbbacbbddbdbbbbcddbdcabaacaddaabbbadcaccdbaddcbbaccbaacdcccdacbddabdabdacaccbbabbcadbbccbdadaccdbbcbbacaddacddbaaabbbdbabcabcdcdabddcdaccbaabbccbbcacacdacbcbbcdbbdcbaabcddbccccdacdbcadbacddcbccbbcaabcabdbbbcddddddbabdaacbcddadcdadbcaabdcbabbdcadbcccabbababddddccdaabdcddbbabbadddaddadaccdcacaaaddbcabdcddcadadbccdbdbbdcaccadaccccaacadcdcbccbcbddbdcbccacacddbdccddbbdcccbddbdcccaadcbcdbbdbcbbcaaabaccbdddacabcbabacbdbddbaaaccdddcbbdaacbdcbdbdbbbababadaadcdcacddadbddccdddababcadbbdcacdddcabddcdbcdccdbcdcadbadbdadbdcbadbaccbbcccddaadacacdacbbbacccbaaaddadbabadabadddbcbabacdccdcbabddbadcbbcacddadbbdaccbadacbbddcdbacbccdddcddbdaabcaadbdcbddaccadcddacacaabacadadbbbcdbccbacbabcdddaaaadbdcbdaacdacaaddadbbabcbbccbbbcdddbbdcdddddcbabcbcacbdbbbbcbcbbcabcaacbbbaacbabbaadabdcdaaabcdaabdabbdcddbbbbbdaacdbabadddccacadaabcbdbaddcdcaaaabacbdbdcaacacccbdcaabcacbbbabbbcccbbddadbcbadaaaadbadbaaccadacadcddbbbcadadaacabbcbbddccbcabccaaacadadbacdbacdabcbddbdddbcdcccadccdccabddabcdbcbcdaddadcbdccaddaaacbccddbaacaabcccabcbaadbadcbcabadaabaaddddccdbacbdcacbbbacbddcbdcbbbdcbaadaaccddbaadcdcdddccbccacbcccacbacddabdabbcdbabcddabbabcabdcacbcaaababaaaabbddcaabbaaddcccbaacdbabcdacacaccccdbcccaccadccccbbcacdbccacaccaadbccbdbcbcddbbacacadbabaacdcbcbbbdddcdddbbbcacccdcdbccdcdaaacdcccbbacabaccabadbaddbdbdbbdaddbccbbddccbcdbadddacbdacaddbacdcbcabbacbbccdbbdcaddaabddabbabdaddbaaabcadcbbacadbabdcdadabddcbddddcccddaadbbcbddccbdadddccdcdabdadcabcbbbcbdddcbdacbacbdcabdcabdddddbcacbabcdbbcbddadabcdadccdddaabaaccbccbcbcabdbbdcbddbcddbdddadcbbbbbdcaccbcbcdcadcdbdccccaadbbbdccbdbaccdbdbbbcddaacaadbddccdcbccbdcbdbdcbcacdbccddabbcdabbcbdbdbdbdacbbbaaaabddbaacccdcacacabcdbdddcacdbbdbbbcdbbdbadcdccbaacccdcacbbcbbdbdcbcdcddcaddaabacdcbcccddcaddcabcaaadbbdccddabdacadcbdcdcaababbcabbbdaaddadabcddcadbcaccccacabcdccdbdccaccbcaddbacdbdbabcbaddbcbdababdcaabcdcbcdbdbdcaabbdbadaabbbbabaadcdccaacbbccbbababbabcddaaaadbabcabdccacbbacabdcdacbadaccdbdcbbbabbdbaddbdabdabbaddadccbacaaadbbaaadccdcabbdadcdccbcbbdaabbbdcbdcabaadcdccbcbddadddcdaddcdaabcdbcaaddaacbcbacbbaaaacbadabaddcbabddadbdbcadcadabccaaaabaadddaaadadbccbabdaccccdddbbdbcddcaccbaccbabcadacaadcddaaabcdadbcbbdbbdabcaaccdacddaacaaadbbdaddabadbdbbbcbcaddbdcdcadbcabbdaabcadaaaddbdbdccadaaadaccbdcbdcdcddbbabbdadcdcbacdcadaddcccdaaddccbacddcddabcbbdaccaacbbcccadbccdadbcaaddbdadaddcbacccbdcccaadbbaddadadccabdcbcbbcacbdbccbcdbaccbcbdcdaabacdcbadcdaabdddadbdbcbacacddbaabdcbabcdddbaaddaddcadcbccbccdacbabccaabbdabaddaccbddababddaacbcaabcbcdacabccaddcbbdcbbddacccdbcabcbdabacaacbcdbadccaccaccaabaccababbbccbdaadaacbdbbdcbbbacadacacaddddcacacdaaacbbdbdcdcacddbcdddaacbacdbdccddccbcdbaddcabbabbbcabbabdbaaccdbcbdcabdcbbaddccaddabaaaddaabbaadddcdbdaabbbaabbdbabacacabcdcacbcbcacacaabcabacccaaabcababcadddabcaccbcacacbdbcbbdabbadcdbcbdddcddacbbabacddcbddcabccadabdbbddcbcbaadbaddcccdddccbcbbdcccadcdbabdbcbbccdaaabbaddabcaabcdccabcddccdcbcdcbcadbbccacccdddadadccdaacaadbaccababdddbdaabacddcbbbcdbbbbcbdccabbddbdcbcacaaaccccddddbdadaccbaabacbcadcabaddcacaccabaadabcadcdbddacbacccacaddacdbabaabddbdacabdadabdcbdaccbccdcaacccacadddcacdbcbdaaccbbdcddcadbccadbaacbcbaacdadabddcddaabcdcddcdabbdbbadbcdbbdbcaabcccccbaacdabddcacdcadcbdadcaabddabdbacacbdcabbcbdcacacccdcadacbaccbdbdaabdcddabbdabbbcbdabbdaaddcbabaacccbbbcdbdabcdbdacbbcdbcdddcbdabcacdcdacccbccacccbacbdaddcdadcdbcccbcdccbdabdccaabcbaadcabbbbbddddbddbbaabdbbaaabacdabbabbcdbdaacacdbbcadadabccdaabbcaddaacdabadcdbdcccddabbbbabcbdbdbbdcbaacbbdadbbbdcbcccbadcacdaccdcaacdadbdbdbcccabcdbaacbabcadaddbbddbbccbcddacacddaacbaaadadabbabaaabadbcdbbcbccbdcdddcdcaadbcddadcdacbccbbcacccbbccdbcadcdddbdbaadcccaacabbcdaaabcdcabdadaacdcddbadbcacdcdbcdbccccdbcadbddbbbcacccdcdbdbdbadabacbbbdbbdcdaccccaababcdadababbdbcababddccaabdcddbcbdbadaabacdbdcdbadbdacbdaccdadacbadabddcaadaddcbdbadabdadcacdbacbbccccdcdcacabcaddcbdcadadaddccbcadbcbdaabcddaccaabcaddcdbcbdccabaacabaddcacdbddcbccaacabbacbbabcabcdbdbdadabcbcdcccbacbbbdcbcdccccabaddcbaadacbbcddbbacacdbbdacddcdadadacacbaaadbabacbabaacbdddbbabcabbabdcaacadddcbbdbbbbbcdcdbbddccdaacdcacabcdabbbbcddbccabaaaacbabbdaccddadcccbcbabaadcbbaadacadcdadbdabddadbacbaadddddbcccdaddbbbdababbcbccbbabdbdccbbdaababbaddbccbdddbacdbabccdbbcdcbbddbbddcadcbdabcacabcaccdcccaabccaddbcdbdacbccdbddcaddbbbbcbcaabbbabaadacdacddbccaaabdadabdcadccdbdaabacacccacbaabacbdaaaacabdacabbadcdcdabdddcbddbccaacbbbcccbabbbaaaaccacbbabaadacbcddbccaaaddabbdddbccbdbcbcacbdccababdccbabacbbdbcdbacababbabadacacadbccbadadddcbaadcaddddbadbdbacaaadaccabaacabccccbdaddcdabaaaacaabcddbcdbbdbcaaacdbaaddbddbcdccbdacaaddaccadaccababadcacdbdddbbbcbaabbbcbdcdbddcdcabadacabbbbbdcbbacdaadbaddbcabddbbbccbbbaadbaabbaadbdbcaababadddadccaadddcbabcbcadccaccdabcbbcbdbbccdcbbdabdcdabaddddcabadaccaaaabcdcaddbbacbddbccccbcdbabcbbdaacacddbddacbacdbcbacdbddcabccdccaabcdcdcccbddbabdbabcbbdbbadbcbdcabccbacaccbaabbacabacaccadadaadbdbababaabadcadcaaacddabbcdabbadcacaaccaccaacaacbccddbddacdbccddddabdcdabaddcaadabbaadabcdadaacacabddacddbbbddcbaaaabacbcaccddabbaddbaaccabcbbabbdbaabbadcaabdbdacbbbadcadbcdbcdbdcadcbcabbabcacabacbaddbadbcbbabcadddacbcdbcbcacdbccabbbdacbccaadbabdcaddacbdcababdabdccdcdbccdaaabaadacddaabbcddaaadabbcdcabdabcdbbddddccadadbddcdaaabddaaadbcdccadbcaacbcbacbcdaddbdcbcaadbabaddbaabaaabbccbbaaabdbddcaabdaadccabcbdbdbacbdabcacdbbbabdcbbcacdaabcbabbcadccbdabbaddacdbbdacdbabcbcccaddbbccbcccbdabbcacbabbbbabdcdabcdbacccdccdcdadaaaaddcbbdacdbcbdddaccabddcdcaacbdbdcbdbbbcdaabbabbcaddbcacdccddbabdbabcdcabcdbadbcabbdbcaccabbddbbaabdcbddcaaaddcbddbdbaaacddabadbdbabccbbddbbddabccdabdcaaaacdacbcabbdaabdacdbbbbacdbbccaddcdbdabcbdbdcbacddacbcdbcdaddcadaadaacccddacabdacdddbacbaacacbdbbbbbcdcddabcaadabbdaabaddcbbddcbdadadabbcdbcbdbdbabcbbddaaccdddbdaacabcabcabaadbdaccbcdbacabdcccdacdcbacacdbbaabdddcdccadcbadbdcdbaaabaaadcdcbcddbccdbdcadcccbadddbbabbbcaaadbbabaabcdcbbcddbadddacdacccacbdaddbdcadddbaddccacadcbacaaccaadbbdcbdbabdbaabcdbcacddaabbdbdcccdbcddcadaabaadcccdaacdcaacadddbbbcbdbdbdbacaacabdbcbcbcaaaddacaaabcdccbaadbaabcaaabadccbabbdcacccaadcadabdabadabbbcdbaacdadbddbbdaabbaddadacdabdbcddadadbdcabccbbaacacbacbbbbcdcacadddcaabaaaadcddbdbdaddbccbcbdbccaaccabbdaadcadcbdbccbcbcaaaaaadcacccbdaaccddbacbdcaacaabdbbdbbacabbdddcccbabccabddcbdcdacbdccacddadadbcabbacbdccadadbabbabccadabaaadbbbbcbcaadcdbddccdbdcbccccbadbbaacbccdcdcaaaddaaadbabdaabcbaadbcdcdabdcadbdaabcdbadacacacacddbcaddddcacddadccccaaaacdcdbaabdcdaddacdbdcbbacbaccacbacaabcbbaacddabaddaaccbbadbacccaaaaabcdcbabcadbcabbaacbddcaabcbbbdbacddcdbbacdcdcadabadbbadadccbabaacddcddcabbbbbcccbacbaaadadddaabdaadddacbdbbccbaadaabcaddcccaacbcdacbabbaabcbcbddddddaacddbcdbbddcdacbacddadbbbbcaabdcbdbacdaabdbaaccaddddbaaccdddbaadaadacbcbcbccaddabbcabaccacabcabdabbccbccdaddccdbbbccbcbbbdacadaabdcacacaadddccaddbabdacabdabddcdbcdbacbcdadcddbcabacbbaaaadccaccbcabdbaaabcacdbadcacbaccddcbacadbbddddcdcccbdaccbacbbddcbdcbbdabdbcdcdbacbabdacdacabcdccaaccaabbbadcbaabcccbadacbcbcaaccdbbbadbaddbacdbcbabcdaccbdccdddccbccadcacdddacdaabccabdbcbccadbabcaddcbaaadaddbaabbbcccdbabccdccbbccabbaaabaacdcbabcbdcbdbddabccdbcbdbdadabdbadadadaacacbbccbbcdaaccbacbdababbddaadcddadabdcbaadbbbbccddbcbbdcdcbabbbdbbaabadbcbacabaabadcbbcbcabdbdddbdcbdddcbcccabcdcbcabccddcdbcaacccabdaacaddcdbdadacccbccdcdacbcabdddddccadaabdcadacdabcdbddcdddcdadccaacbdadabdbacccacccccddabcaacccdcbccbdabcbcdccdcdbabdbdcccddccadadbbacddadcbcbccdbaabdaaccabacdbbcbcdbaadbbbcbddaaaccbbbbadccbabbdcbccadcbcdbdbdcccccaccabcdcabcacdcbcbcbaacddcabdcdbaaaabcbbcbaaacbaaaadbbbbabaababbdcccdddcbdcddadccbdbdbbbbcdabadccadbccdcddbbdaabcccbaabdabbddaaddacdbbbcccdaabbbbcbabcccabadcbadccbbddcbdabdabbcdacccddabcacbbdadaaaacaccdbadddccadaddcbbaabdbabbcbdbdcdbbbccbddbdcbcdaaabcbccddbaccddcdbcdccccddaacdcabcaaadbdacbacadddbbaddccacbddcddacbdbdddbcdbbbcdccbaadbcdcabddbdbdabaccbacdbabbccaaacddaadcccbcbbccdbccdbcabbdabdbdcddaddbaabbacccbccdddadadbaaadccbdaadabbbaadabbacbabdcdcbaaaadbcdbbaddadadbdaaccbddbbcabbadacadacacbbbbacabccbcdbbcacabbbacbdadbbdcacccbdaacabddbaacdaaaccabdcaaaadadcdddaacbdccabddbcabdaadaddbcccbccddcaadadbcacdcadaddaaddddbbcacabbacbdddddccabcabccadcadacbacdaaabdcaabbcabcbddaacaabdaddaaddddbdbacabbbcabacbaacbacacbacadcccdcbbdcddbdbbdbacadcdcacbccaacabbaccabaccdcdaaddaababcdaddccbadbbdabadcddbaccadbddbadcbbdbbccddddaaccdddcdabddccabdccddbbaaccaccadacabcbdaccbcbacdbbcacdbbbbabacdbbdbadabacaddbbbadcaadabcabbacccabbabbcdabbccdcccddbaccbcdababcdaccddbdcaadacbcbdaacdadbaacbcbcdbcdcddbbbaadddcbaddddbdbcccadadcdddaccbcddcdcbcdcacdbabbaacdacccbdddcabddbdaccbadbcdaabbacbabcacbbcaacadcaadacbbddacdcabaaadddcbcacbddcbbacccbacccacabacbadadbcdadacccccaddcdbbabbaacbdccdcbdddddccdbbccaddbcaabaabacbccdbcdcddbdcccabbadaccaadcbdbcacbcdbaaacdcabcabcbbddddddcdbacbabcbcdddccbaacacccabaaadbdcaaddbddadadddcbddcdcdbcaaabbccadcddaabcccacbacacddacddadbbdcddacdabdaacadbdbcacbbcaadcacccdbaabadccbabadbbcbdbcccbbdcdaabccaaabdcbcbcdadadadcacaccbccbccddababdddcabcddbccccaabbadcddabcbbbccbdbaddcdcabbbdbdaadcbbaadbcdaaacbabdccacaddcdcddaaabbcaddcbaaddcadcbcdbbaddccdddabbbaddaaadccbdbdcdababcdbaccbdbddadabddcccdaaaaacddabccdacdadadbbcbabbadbaabadbabbbcbcabcddcdacbdbabbdaabcaacbcccbbbacdaccdadddaabadbdaaadadccaadcdadddbadcbabdbdbadcaadcbdbbddabcdaddcccccdbdacadbdaaabaacbacdbbacdaacbdccbddcabbbabcdccccdbddabbdcaadcccccdaaddcbacababdcdccbdddcbbdddaabcdbbabcaddbbbddbadddaccdbacabdbbddbbbbbacaaacbadccdbaccddbcbbcdcccbabdcdabbaabdaacccbadcacabbdbadacaadaabacccaddacdbcbdcbdbdcdbbababaababaaababbcabbbcdccdbddcaddaadcabcdbcacbbacbadbdbbcabddaaddbdbdabbccdbcbbbaccdcabcacdcdaccacdcdddbdacacccddbccddbdddbdaddbbacadbdabdbdcbadbbdcdaabaddbabacddbadbdbdbaaadcdcacaccadcdcabaabacdbdbcddcdadddddcdbcdacdbdccaddbdaacacbdcaccdacccaadacbccbbbcaabddccbcdddcbdbadabbabadbadcddabbcbbaaddbdadbcacdbdcbdcccaadddcdcdcbbcbcdadcdcdabbbbcbacaabbaddadaabbccbbcddcbdcbabdbabdacccbacdacddabbbacbcaadccdbcacbdbbbbabaadccdcbcdaaabbdccdddadcabbadbccbdccdbcbddaacdbaadcddaaabdcbabbdcbacacdbcadbadbcddacaabbbdbbaacbdbadadacadbddacccbdaddbbbdadbacbaaababcdcaddacccdcaacdcacbaadabccccaadadcbcadaccbaacbcdcbaaacdabccbbacccdbaddccbdacddbaddadcccaacbbcbacddccccbabdbaddccbccbaadcbababcddaacabaaacdbdcaddbbcbdabcbccdbdadbbbdbcacbccdbcbcdcdcacbccbdbcacaaccbcdcabbaddaddadcbccaadbadddcbddabddccaabdadcbaadaaccdadcddcbcddaaddabbacaaacdbbbbdbabbdbadddddabaddacbbdcbbbddbbdbdbaaacbcadccababdbbcbabcbdddabccdabdddbbddaddaadbbadbdddccdaabadaabccbbddbbcddcbddacabccdbbbdcadcbcbcbaacdbabbadccdacadbbbcabbacbddabcbddbdccaadadbadcbcbddbddbbbbabaaacbbddcabdbdbaabdcbdccacbdcbbacddbaabbccabcbccdabdbabccddcbbaabcbadbdabdaaaacdccaacaacacdabdbaabcbbcbdbcccbadbddcccbadcbbaaaccbabcdbacbbabaccaaddcbcbacbcdbdaabacadcabdcbcbaaaaadaadbacbdbcdbadacaccbcddabcdaacddacbaaacddadaacabaaaaacbbcacbbcddbcababacaabdddbcdbcdaacbcbadabbdbabccbbadddbadacacacbdadaabccacbdcdcbaabccbdbbadbcbaddbbdbcadccddbbbdddcccadaadabcabaacaddccadacdaccddcdddbaababdadaccdbbbcdabacdbcbbaacddcdbdcdddbcdbddabdabacddacdddbcaaadababdbcbddcaaccababcbcdbbaccbdbdcadbdadaadccabadabcaddbdddaddabdbaacbbbdbdbcdaaddabbdbaadaaccbddadbaababddaabdddabbddbdcdadabccbcadcbdbdddabbbadccacddbbcdbddbabadccdacccddadbccacbabacadacdcacabccddbccaacabbcbddabccdbccbddaacabccddacaacdccdadccacbbccbbdacaddcabdcbbacbcdccacadddbcaacbacdcbdcdcaacdcaaccbabbbbbdabccabbcbbdbadcbcadabbaccacdacdacbabaacaccdcacbddcdcdcabacbabdcdcccbaaccdbbccbadabdcbbccbdccbcaacdaccaadcadacbcddcadcbaacbddddabbbccaccccbcabdcbccbacddabaccbbbcbbcabcdccdbabbaababcacaccabdbbadddcbabddddbcadabcddddcbadaadaddabbacbdcbdbdacddaaaccccdcccbcabacdbaadadcbcbbcbdcbaabcdaddcdcdbdcbdccdccbdabccbdbaddabababcadcabbbcbabbbcbdccdcadccacdcdaddcdabbdcbddaabdbcadabdbdaaaaccdcbbdadcdaabadccbbbadbdcccaccabcabdcddbdcccccbaaacbaadcbcbabacbbdadbcbcaaccdcdacdcaccbbdababdbadcbcbaaccaaccddccccbcbcbdccabcabbccaababccdadccbbbaaaacbaabcadaacaaddacbdacaddbaaabcbabccddcadbbdccadcdabccbacccabddcccbddcddabacdacdabcaaabaabccbbdbdbbdbdddbaaaadbaccdbcacdabbbdbbbdbaccabccddbbddaaddcbadbadcddadcddbcacaabdaaddbcbcacaadabaacbcccaaacddbbbddbcbdccaababcdcbccbaccdcacbabcccbcababdbdadccbdcddabcaccbaadbadcaddbcadbcddbbacabdaadcbcdbdaacdbcbabcbacdcdabbdbdccbaaabccdbcdcdbcabdbbbcabbccbcdbaacccadcbcddcccdadddbaddbaddabcdccbbbcabadabdbdbaddadbacadbaabcbdbddaabddabdcdbdbddbccddbdcbbcabdbcbadacacddccbccabdbcbaaaccdbaadabccbcddaaaacdacbcabbcddcdaddbbcbacacbbbbbacbbdddcadcadbbabadbadddcacddddacaacabddadcdbcddaaadbbcadaaacbabbbbadbacacbdbdcbaaaadaadccbbcbdaccbbcddcaadcbcdabdacccdcbadbdbbaccbcababcdbadbddcabacbdcddbaabccbbbababbbcdadbdcabcddbbacadbabcbdddaccbbbcbaabbadcbbbdadbbdbbbaabdaabddadccccacdaacacddadccdbdaacdacdabccbddccdccbccccbbbabbabbdccdbcbbaadbdcddbdcaabdaabbdbaddcbcdaaddabccbbccabadabcdcacaaacaaaccaaccadabdddaddddbbaadaacdbacccaccdbbddcaaddbcbddbadcabbcddccadbcaddddcdcbddbccdbdababaccbdbbbbaaacdbabccbcbcaaddcdcbdbdaadaacbaacabbdcdacdcdccaccbadacaadddbddbacdbadacdabccacdbbabcbbdacbacaddcaaaddbaaaadbdbbbacdbdcbcbacddacacbcdcdbccddccbcacaadabbccbacaabbbadcdadaabdacccdccddccbabdcbaacacabccdcbdbccddadcaddcabaaacbbdabacacaabcbbbdbaadabdbdaadddaaadcdbdcdaccaaabbdbaaccccdcadaaccdccdccbccbbddbdbccbaacdccaabdddbdcbbcddabbdaabbadaccdccacaaccbadaacbcadabdbdbddbbdbbcdddcbbbbaabdbbaadaccbbdddbaccccabbbabbddadabaccdabcbabbbcabbabcbaabaabadaacdaaddbcbcbaabdcbcdadbbadcdcbadabadcbbbcacdbadcabdbadadbbbbdcdddabbcacdaacbdacbcacbbccbcaddbbdbbccbddadbabbcbbdbaacadbbcbcabcacddcccccdabcaacbdcadddcdcbbbcadcbadadbbdcdabdcacbdbccabbcbacddccdbbdbbbbbaacaaacdbaaaadadbddbacddaaccdacbcdcdcbbbcbdabdbcccbbbdbbabdcdddbdbcadaddaaaabcaddadaddcbbdbabdbdaaccccbacccddccdcdcabcddaddbcdabbcbbccdcccabdbdaddddccaaabbddcbacbdbbcabddaadcbcbcabdbdacdacccadbaabcccadabacdbdbcacabadaccccbbdcbbcacbbdcbbcccdccdcbcddcbcaddcbadbadcbacabacaccaacdcbdaadacddcbabbadcaddbdbbadabdcbbdbbaddadcaddbcbdbcbbbddbcbacabcbbcbbdbaaaacdcadaabdbcaabaccbbaabdcbdcdbddbbdacbaabccabbdcbbdcacbdccdccccdbcaaadacdbcbacdcbbdbddddcaabbabaccbdcdbddcbacdbcaacdccbbdbcbdcddbddcbbabccbaccaccdddbdbcbddbccbbddbbacbacaabcbcbbdaabaccadaadcaaaaabbaccacaabaacbacddccdbdabcdcaacbcdbaabbcbbaddddcabbcdbcbddbabadcdbdcccddacbcbcbaabaabbbcbaaabaabbbccdbdabbcdacddbaaadcbccadadbcbddacbcaaadccbbaabcaabccdbbdcbdbbcbabadddccabbabcdaadbcbacabadbbdbdbddadaccbbcdacbdbbaacccacdccacaacbaadbbbbacbccbbcbbbbcdbccdaaddbcdcdcdbbadaabccabbcadddbbdcabdacbcbcadcacdcaabdbbdbdcdddacacaaadcabdbbbaaacdcdbdcbadbbdaccabcaacbadadccdacdbdababadddcbaddacccdadacdadabbdbaababdcbbbdddcbcdccccddbbcccbacabcbaccdddabbbacaccabbdaabdbcaaadcdbdabcadccaabcbcbaccbbbcabdccdcaadcdbdcbbbacaaadbcdcdddcadcdbccdddabdaabcddbadddcacbbabdbaadbccbcbccbbbaacbbdabcdaadaaaadbdbcbcbaddcbccbbbccabcddbdddaabdaabdcaccbdcdcddadcdbbcbbbbbcddadcdcbababbbcacbdcadbcbdbcdbdddbbaddabdbbbcbcaaaacdaacabcacbabbbcbbcacaacccdaddadbbdbdbbdbcdcacdcbadabbdcdbddabcaccbcbdbbdacaacadbabaddddbbbdddcadbdaccadadcaababadaadddddddacccbacdaadabbacbcdcaadbcbbabdbcacdcaabccccbdddabdbcccdbabdccaddcaddcbbbaddbcbbcdcdbbcaadccccdacdbdaddbacccbbcbbbdcabcaddcbbcdbbadcabadacdcdaadbdddaccaadadcddcaaaacccdcadbbbbcddccbbcbadbabbdddabdbbddbccccbbbadcabcadabaadbbbdcbbbbcaacbbcbccbbdddcbcbbcbbcadaddacbbdcdcaccadccdccccacbaabddadabdcaacdbadacababbbaccdcbaddccaadbabbccdcdccdcababdcbbdaacabbaabdbbadcaadaddabdaacdcccacbdcacbababddadadddaadccbddadbccadaaabbbadadbcbdcbaacbbddabddbddbbbabbabcbadcbcccaaccdcacdcbcddddcdcccdbbbbcdccbabadbdcacbccadccddbaabbbbdbdaccbddcbccbcdbbbddbbddcacacddbccdbabcbdcabcaacdbdacaadbbdccbaacabacbbcbaacddbcacccacbacadcddaccdddbdccccbaabadbdacbabdcaccbcbbabbabddcbbcabcabdadcccbcaadbcaabcaaacadbcadbbdccdcddbcacaadcaddbbcacbdacbdcbcaadcdaddcadcbaddcacacdbdccaccdcabcdbdbcbdcbdbaddbcababcdabbcacbcbcbbaacaabbdbcbcaababbdbdbcbbabdacaaaccbbadcacdcdcdcadddbcbaabcbbbddcbbadadcddaacddbbdccdbbcccdcadbbabdcaabcadbdaaddcddabccabdccaddddccbadadcdbcaadbadbdacdcdbddcbcdaabccbadcbdccaabcddbbddabcbbbbbbaadbccbdcaccadaccbddacdaabcbacbcabcadccdabccddbaabcdaadcbaccbbadaaccabccdccbcdcbbbaaccaacbdbabcdbcccbcdabbaacbaddaccadcdcccbdacdcbcccdabcabbabcbaabcbdaccdbaddacabbbacdcdbaacdccadccdddacbdacbbbadcadddcaabdbdbcaccaccacdcbadcacdababdbadabadccbdbbcaabdbacbccdbabcabaacaadcbbccaaccbdadcdaadcdacccbbdaddbccaddbbacaabcbdbdabddbacbdccbdccbdbdddbdddccbccddacdcdccdcadadcabcbdbcdbbbdbcadccdbdbbddddddabbbcbccdbabbccababbcbaaccbdcddcccabaabdabcbddadabcabacaccddabadaaacccbddbdbcaddbaaadbdabaddacdaacccacacddcaabcbbaccbcdcbbadccbbaabbadadbbcdcabddacabadbadadcabcccbddaadbbdcabddccaaabbcddabadaadaddbdbadaacbdababadadddddaddbababbbcaabcbbaabbbdbacbccbbacdaccabaddaacdacaaadcabcbaccbcbbccdaadbdddaabbcdabbacbabddcabbbbacbbdaaaaabbdbcbacaacbbbcbbdaddccacbbadcbdcadbddaaccbdddcbadcbbdddcdcbcbdccbbcbdadcbbaadcbbacadbaadcadcaaadbdddddadcbbaababbcbcaabcabdcdadbdbcdababcadcbcbcabcdcdbabcadbdcbccbdcbcdbabcddbdadadadbcbcbcacbdbdabaccbacacadcdabbbccdbcabcbdbacaacbdadccbcbabcccdcbbbacdbabccddccdbdcccdbbcadccbccaddbbbdcbbcaccabbabacaaabaacbdbbadccccdabdabdabcccdbbcacddaadbdacdbdbacaddcbcdbddbbcaccccaabaccaaccdabaacdddcbdbcbacaaccbadbcbdccdccbcbbaacdbcaabdddbbdcbcdabadcabaacdddccbccdbcdcbcdcdbabbdadaaddbadcbddbaabcaabbccccdbaccdcabaddcbbbadacbbbbcdaabdcbdbdcdbbadcdbdbacdbcaacdadaaabbddadbabcadddcacbcbdbbadadcacbbadadaccdadbdaccbdaaacadaabcacacdbcadaaccdbbaaccbaadacaaabcaacdcdcdbacabcbcccacacbacddbaccbadabcdaaaddbdacbdbacaaacbbbdcdcbbcccbdcadddaadbcdabbddcbabddccccdbbaccbcdbdabbbddaabdcbaabdbcbbbaacbcabcbaccdacabddcdaacbdddcbdcdabccccbaddbcccdbaabdaacccdbacaaadbdbacdcdbaaccbdbacabadadbdadadaabcaadaddcdccbcdcdacdbbabcbabdcccdacddbbbbddbaddadbbddbdbdbaabcadcccbdacabbcbddaabbcaacbbbccdaabdacbaabbadacbdccddbddaccdcadcdccacbddaabbababacbdaddcccaabdddacdccdcdddbabbbbdbbcbdddaaccaccbccabcbcccdbbccbccbabdbbcbbdbaacabbbbbabacbaccccadacddabaccbaadbbbccabbcbcaddacaddcbdbbcccbddcaddcaacdadaadadddabadccbbdcaacaaddadaabbdcaadcadcddadccbbbbccbadaacdcddacddddaaabaddabadddaddbdaaadcccbbaadcbcadbcbcbbdcbbbcbdaabccccacadacaadcaacbbadccddbaacadaacbdcadbbdcaacddccbdabdbdbddcbaabcdbabdcddcdbccabbadbabbaacddcacdcdbddcadaabddbaccccbcbccdccbdcccaccccaaaaddcadddabacbadbbabbdcbdadcdbdcbabdabcbcbcbddbaaddbaacdaaabbaaaaadaccdbaddcaccbbabbcdadcbaddbddaaadaacbacddcdcadcddccddcdcbdccbcabddccabbadccacaacaddcbcacaddbbacaabcbbbbdccdccddcbcacdbcbdccbdbadcddaccaadbcccbaadaaacdcacbdadaadcdccbccdabcbcdbcdacbbaadcbadddddbccbdccdadccccdadcbbccccdddcbbdcbcccdacabcddbcbcbbacddddabbaacbccdaddadcccaadcbccddddacdcddcccbddadcbbcdabddacbcabdacacbabacdcbacbdcbbcbcbbddcbabccccdacdcccdbababbacabbbbadbabaaccddabbdbaaadbdcdadbcdbccddaaacadcdbadbadaabddccccccadababcadbbdcaabcababaaaabcdcbcddaddcbcbadabddcabccdbabaabdcbdaadbcbcbcddaddbbaacbcbabcdbbbcaadcaacadcacdddacccdabcacdbdbddbabbdaaacacdddbdacdcdcddcdaaabbdcbcdadbbcdcdadaccbdacccdabdabdababaabdaddaabbadcdbaaadcaaaacdcacddcbdccbcccbddcccbccdccbcdadcaaaccddaabddcabbcaccbabccdcaacdbadbababcbbbaccdabdacadddbacacddaaddbaddabbcbbbcaaabbdabadbabbadbdacbbbcddaabcdadddadadadbbbcdacbdaaacabbbbaabccbdbabbbdcdabdbacdcdacbddadccbdbdbabadcadaaccadaccbcdbdcabdbcbcacdccccbccbcdbacccaadadaddadbdcbbcbacdddbdcdbccddcadbbdcabcdbaadbabcacbcbabdcdddadabdaacddcbcbabdbaaacccdaaacddbacdcbabadacabbacbadcbdabcccdcbddbddbcdcbcabdbcdccddbcabdbaaaadcbacabbaddddbdbacdccbadcbcbccaadcdcabddcdcbbaacdddcdaabcacbabcdadbaacbbccddcbbbcdacadbdddddbbdbbbcbaaadcabccbaacdbabbbdbdbdcabbddbabadccdddcccbcdacccacbaacddacdcabbdadaccabbcacdbaabcdbaccacbaacddadaddcdbccaddaccccbabdaddcadbccaaadadabbbaabaddabdcddaabdbabcabdbcdbbdcacccacdddbbbdbcdadccdadaacbbbdaacddadbbbaadaaabdadaddbacdbabcdbcbbacbabddcaaacdbddddcbdccdcaadbabcbdaddcdabcdcbadddbcdbddcaadcdabacbacadabadbdadddcbbacbbacccdddcdcdcaabcdbdbbaacbbacaadccdbddaabcddaadaacabbccbaaaababccdcdabaaccdcaaadcabbccdabdaadacddbadbdbdddacaacbdaccbcadcabcddacbbaccabbbbdaaacacdcdcdbcccccdbccaccbbbbabcbacddaabcdcacbcdaddcdcccbbdacabbbbadbaadcadbdbdaaadacdddbbaacdcbdcacadaabbbddbcddcacdaacbabdbddccddbacdaccbdadbbbcbaacbaadcadcacbadbbacacccabdabaaddacaabbccddbdabdccaaacaaccaabdabbaadadadcccbadcbdabcbabbabcbbbbdaaddccaddabacaabdcaddddcacbcbaddddcadbbcdccddaacbbbccdbcaadccddbcbdbbcbcbbdacdaadbaadddaacbcdbcdcababbddccadaabddbbdccadcbcdcbbdccccdadccccccaddaddcdbbaacccdcadbbddcabdabdbabbccaacdaaacadbcbcbcdbaadbbdbcadabbacdbddcabbadaabdbcbdddcdbccaaddddbcaaccbdaadabdadbbadcaaacdcbdcaacacbdabbaddaacabcdbcbadbcdbbacaaacddcbdcadadacbadbddddddbbaacbbdccddddddddbddcbaaabdbcaddbddbcbaacabacbadbccacddcaccbdcbdadabacccaacabcadaacaacdbdddbcddbbdbbaaccadcdacacbcbacabcabddcadccadcccdabdbcdcbbabcbddaadabaabaaccccaadaadcddbdabadddbbbccbdaacaacbaabccbbdcdcbccabaacdbcdbdcbbaaaabcbddaaccabcdadbcccdcdaadaacacbbcbaabcdbbadbccdabbcbcadbdbaadcadccdabdbccacbbdbddbadbacdcdabbaaabbadbcadbbdabcadcbbbdacadabbbdadcddcbcbdccabbaabbbccccbacdddcbdaabddbdcbbdacbabdcddddcccdbbddddaababbaccdbddacdcdabbbaddbbbdbbcdbacbbccdacacdadcdccbadddcbdbdacbcdadaccccdacacbccdccbacddbabdabbcacbdacaccaaababbabbdabbccbcccabbbbdabadacdbdbaccaddbbbcdabbddcbbbacbbadbacbbbbadacddadbdabbdacbadacbddaccbacbbaadbbdadccccbbdadcaaaaddccccbbbcaccbacbccdcddcbdacbcddddcdbadabbacdbccdacdacacbdccaacbaacbdabdddaadcbcdcdcbdcbcbabbabdcbdddddcabacadabcbccacacdcccbacdcbdbdcbadbbdbbbacccbbabbccdacbdaaabddcaadbadacabcbaacaabdabcbbbcbcbdccddcddbcbcdbaddbcbbbdadabdaadcdbcaaabdcdbdccbcdcaddcdacdaadbdbaadacbcdaaadccbdddacbbaccbadbaddacabbdbbccccbacabdccddaccbabcdaabddabbbbccbdcbadadaccacdbbbaabbcdbbddbbadddabdabdadcddcbbabccbcabcaaccbacdccbcabddccbdabcacaababcbaddcddddabdcbbccbdaaaddbdcababaaacabcabacadcdacadacdcadddccbcdcadaaabaabbbdcccddcbdcbdbccacababadadaaadbbbccadcbacbadbdbbbabcbddabaabbcdbcdbcbaabcacaabdacdccaaacbadbabcbcbbacbdaacdcbbccdcddaadcabacccbdacbbdabdcccbddcbadbcccdabdadddbddabdccbcbdcabddbaadcddaacbcddcacbbbdcdaddddaacccdcadbbcabdabdbcdbddbcbabcdccaacbcdcccaaadadbdddccbabacdbaacbaaccaccabdbacbcbdddabcdabdcddabcacabaddbcabcbaddabdabaacdcbaabacdcdbbbdddcabdbddddadccbdbdbaaddadcdddbcbdbccbaaacaacbadbbdbaccbbbaaabbcdbddacdcacdabcdcccabaacdbcacdaddbbbacddddcbccaddbdddbcdcaabaaaadaaddabddcbacdaaccddcbdbbaadadadcdbcacdcaadabbbbbcacbcadddaadcdacbbdabcbadbdbcadadaacbacddabadcabadbabdcabcabcdcdbdacddcdcdbcaaadacaabdddadcdcacddddacdcacbacdbbccdacdaccbcbddddbdccacbcabdaaabbccbddbbabaddcaadaacbabbabacbcbbccdbcbbadbcdddacdacdbbdbccbabaccdbccbacbbbbdadadbbdddaddbaccdabddcdbbcdccacccdaaaaaadcbbcdadbaadcccbcacdbbbbcaccdbdbdbccbcdcaacbddadadaddcbdaddaabdbbddcbcacacadbdabcabbaacabbddadbdcadcacbbcadddbdbcdaccdcbdaabdccdabdbcabcddbbcacaaadbabdadcbabbdaccbcadcbabbcdbccdbbbbaaabadaadcacdddabdadaabdcbbcbcddcccadcbbcaccccdbbccbaaddacdbbdacdbccbcadbcaccbcbbdacbbbadaaccdccaabdadddadcdccaacabbcaaaddadbabbacdbbbaadbcddbcccbcaaadcdaccddddccbaddacbddbddcdaaacddddadbdbcbabbdbacdbdaddacaacddddbddbcadbbddddbbbbdabcdabbbaacbbccbcacaaacadaaabbbbaabccdcbdbbbbddbadddabbbadbcdbbbbdabccaddcdadbbbacacabbdccacacacdabadbbdcdadddcbbbdbacccddbabbbaaadbdbaccccaacccbbcabcaabdadcacacdbacbcadccbaacadabbbddbbcbcdabdbabccdddacaddadcdbbbccdadcaaabdbdcddcbddcbaabdcabababbaaaccdbabaaaddaddcdbdcaadcdccaaadbaabdccaddddbdadbcddcdbbabbacacaacbbcdbadccdcdcbbdcbccdbbadcbbbdcbaaababdbdbacbbbdbbcbacbaccdcbcbbdcaabbaddbadacaadbcddadccdbaddabcacbddbddabaaccaaabddbcaddcdcdadbcccdcbcccbdabbcdcdcaddaddcdddcbdabbdbabcabcddcbdbccdaddaadddaccdcacdbcadabdddbabdbdbcaaddcbdbdadddacadbccdacdaaabcdcddacdbbddabbaddcbcdaaabbaccdadaaabcbcdbaacbddcdaacdbdcdadcaaadddbccbbcdbacccbdbdacbbcbccadacbbdcbdbadacbcaabdcabacccabdcdcaaccdccdccbcbbcbbaddbbbdaacabbdacbacbcccabbabbcbdddcdadabaadbbcabcdcdcbdacdbcbbbccadbcdddabadacadbcaaaccdcacdddddabccbcbaddcdcaaddcaabcadccbdaddadbacccddabbdbbcbcaacdbddcdcbcdaacddddcbbaccdacbaddbdaccdbabcbdccdabbdbbaabcabbcabcbdcaacdacbaddaccbdbaabbacdacdadabbcabbbacadadcddbcdddbaacdccbddcdbbdacbaddcdbabbbbbcdabadadddddcbcddaccddabdddaadbccabdbccdccccaacbbdacbdadbddddddbccbaaccccacdcabadaddbcbcddacddbdadbdaacccbbdcacbadddcaadcbaccbdbdbbccaaabdaccbcbdccdcadcbdccdaaddcdcccbdaadbccbcddcccdaddbbccddbadcdaabbcccaaaddcacbbbbabddcccadbcdadabcbddcbbcdaacacdaabaccddaaadbdbaddbcdbddcbbabaabdadbacdcadbdbccbaabbddcbdbacaddcabcaaccadcaabbcadcbbadddcacdbddcabbadbdbabdbcacabbabbadacbbaddddbdccbdbacbbdacabbacdbdbcdccbabdacbccacdddbcdcbccddacccddcdddbadcccabcbdbabdaaadcbabddcbcbacaaaaacbbcccdcdacabcdccdaddadaaaddabdbddadcadcdcadadacdddabcaacabbdaabbddddcddbbdcabacacdccdcdadddbcadddbddcaabcbcbdbddabaabcddbcccaabdcddabacbdcabbbcabcbadcaaabdacddbaaccddabcaaaabbbbbcdbdcadadadabdbcdbcaadaacadbdabbaddbcdadbaacabbcddbbddcdbbbbdcbadbbcbcbacaabbcbddcbddbdbbbdcbbcbcbaaccdbbddbddbacbbadcdaaaaacadabadddadcbdbdccaabbcddcbadcdbadcaccbadacdacdadabddcdcddbdbbaacdaacacdbdabcdddcabddbbdddcbcddabbdddbcbbcbabaaadaabdddccababddbcbaabdbdcadcaaaaddadddcaacdbcddadbcbadbbabcaaccdbabcdbacacbabbbdcdcdbbdbabbbdcdbdbdcbccbabcccaddcbdbccccababdcbbbdbbcaddccaddddacaddacbcbcacbdabbcacbcdbdddccbddcdccbabaababababbdaccdadddbdaabaabdadcbbaaadbdbaadadcaadcdcdbdbcddaadaabcadbaadbddccbdccddbdccaccccbbacacaddcdbdcdaaacddcababdbccdbabdcdbddacbdddbdabdacabccdcaabcbdcbbccbabccacaabccbddbccbaadddbacdadacbcabbaabddbdbaacadabcdadacaabbcdadddbaacabdcbbdbbbabdabbdcbddaabbbccadcdadadbbaadabcddccabacdbcabccddbbcdbbadccdbcbdbccadbbbdbcbbbdcddaadcacaaaaaddadbbbcbbccddbdcdbbcbbdacacbcabcbabaccdcccabdabdadcccbdbdccacbbadacabbacbabbbacadcbbcdacbabaddabadabacdccbdacbddcabaacbabdcbcbbbdcdcdacadbccbdacdacdacbdaacacdabddbbadbacdbbdccbadabbdcbbcbbaddaadcacdaadccbccdcabdbdaccaabdbcaacbbbdcaaadbdabbdbabdbaadbbccbbdadaadddacdbadaacddddccabbadadbacbdccccccddbbadcdabddcddbbbdbbaccadaabaddbccdccdbbabccccadbccccdacbbaabaadbdbaacbccdccdcacdbaaaaabbaabdabadbacacddadaacabbdadadcdcadacdbcbbcbacbcaadbadbbbbbdbdbadbdadbaacccbabdadccbccbdbccadcdadcbbbccacbcadacdcdabdbadccbdcdcbababcbcaacbbcbadbbdcbadbccbbaacccccbabdcbbdbdabbacbadddabdcbaaababaabbbabcaccaaaacacdacabadbddddaadcabbabacbaabcdaccddbabacabcadbbabbcdababdcdadaaacaddaccddddaabbbadbbaaadbdcbdbaabbbaabcaadabbdacdaacdcdbdaddcbbcbccaaddbbdaadbcbdcddbcaccacbdaccacaccdabbcdaabadcdddddabbddcdbccdccdacdadccaacbcadbbbcbbacbadddbdbbcccdcccaaaaabbddabbabacadcacbccbdbcdcacadcdacabcbbcbabccadadbcbbbadccbcddccaaadcbabaaaaaccddbaaccadddbcdacccbcdabbaaccdadbaaccaaddbcbabcdcacbdddcccbabccbbbabcaacdbddabcccddacbddcaacbcabcacbcdacaadddcbbdcbcdcabdddacabdbcbbadddbdbaadcddabcabbdadcccdbcaaddcaaabacdbbabdbcaaaccdbdaacbcbdcbaccabaacbbdabddbbaccbbacbdcdbdddabbaaabaaacbabbacccbabbbaddcadbcacbbbcadbaaaadbdadbbdcccdbcbadcbcaacbacdccadbbbdcbabbdbaacdaaadbdcaadaddacbabbcccacbdccaacabbdbdcccdbadbdbbdaabcccbadbdaacbbdccaabddddadcacabbbaabcaadccaccbcdbccacccaaaacddddacaaabdbbccbcacaacdcdcabcaacddbadcbbdcdddadadadddbbcdabdcacbdabdbdaacabcacaddbbabacaccbcababcdacbdccbabadbcaccabbbadbbcddbabcadbabcacddadbbbbcaccddabdcdbacbadababbabcadccbcadcbbbabdbccbaccbbcabcbcacadcdbdcbacbabbcacdacaddbaacacbbbdacbabbccbaaadbcbccadbcababbbaccaaaacbcbcababdddbdcdcbaaaddbbadaaccccccacddcbcabdbdaabdadccdacbddcbabbcdcbbbbbaaccbccbadcadddaccccaaddcdccaabadbbcabbbdcbadccbbccdaccdbdaacbccbacdacbbddcdcadbaabcadcaadbaabbcdbacaaaaacddbddcdaaabcddcaccaabbdbbbdaacddccaccbabbabbaacccddccacdcbdddbcabbbcddadcdcbbacbcaacdcddccaccadcbbaabcbaaacbabccddcccdcddcddbbaabcdaccbbdcacdcdddadccccbbbbddcaadcaddabdacbcbbdaabcabdcaadbbdbaaabdadbadbcadcabbbdddcaabddbdccadbcababbddaabbadcdadbccadcdcddbaacdacbcdbdddbadcbbcbddbbbacdcbdbacdbbccbccbccdddcdcbccccddbabcacadbdcabadacdcccddabbabacbadcacdaabbdbbacdcadbdaabccadcddaabdbcbdccccdbdbcaacdccdabbdbacddbaccbabbbdabcdddccbbcdcbccdcbdaabaacadccacdadacabdccadcabbbdddbadcccdadbacacddcbbcccabdbccccdcdaacdacdcadaabdacccdabaccbabdabadcccbacddaacbbadccbaabbaabcadddadcbdbbbabdabbcbbbdccdcddcadcdbcdaacaadbaaabacbaadcbddacaacadcacdcadbcdaddbdaadcabdccaabbbcaacdcbbbdbddadbbadaaabcadaddbadbacabccdabdadcbdbbcdbcbcbbaabdaddbbdaabdbdccdbbddbcdccadbacaccbadbabaaddaddbbdbcaadcadddbabcbcccdaddcaccbbaddcbcdacaaacadbbdacccdadcdbcabddcdadbbdbbabcbcbcdcdacdbbdabadacbbacdbcdacadaacadabddcccdabcdbcccbabdcdaacacbccddadaadddccbcdbdccbabbbdabaddaccccdbcbccccdcacababaaaabaddddddbaacdbcbcccbcbbddbccbbabcadcdbdababbbadcacacbdaacbdbdacadcbdddbdbccdcbbadacbdbddadcdddadbaaacbcdcccbcbccdcccabdbbddaacabdcdaccbbbcdacadacbaabcdbcccadbbabaaccccaddaccdaadcdcdacabbdbadccddcacdaddadacbddaddddcdcadcbbdacbcaabbdcbbbbacbdddacabcadcaacabbbcbcabbaaadddbadcabbbbbadccaccadcbacaaaddbccbaacaaaabcacdbaaaddcaadcbcaaabbcbbadbbadbacccddbabbacaacddcdabadbcaaddcbcadcbbcccdcdaaccdaabbcdadbaccacbaababcbaaacbcdadaaacaccdcadccccadbbcdacdacabdbcddbbddbccacadadbdddcabdcddadcbcdcdcdbbcdbdbadadbcddaaacdaaddaccbcdbbcbcaccadadccacbcaccdacbbccddcbcbcabcaabbaabdbccabdcddbbddcdaabcadadccddadbbdcdabaaabbacaabdcddbbdacbdbdacbbccbbcdbdadbadadcdccdbcacdbbcbdbcdababdbbbdaadbbbdcaaccaacccbccdbbaddcbdddbbbaccbcbbcbdbbcccabbdbdabaccbdacbadbdbbbcabbccacabbdbddcbcadaaadddbcdbcdcbdabbdcaabdcbbcbddcbabdcaabadbddbbddccbaaadacdbcabdacdbdaaddabaccadddacccadcadacdbdcdcdbaddadadbaaacaacccdcadaddccaccabccddcbdbdcccadadcdabcaacadbbbddddcadcddddcadaacbcbabcbbcddaccabdbbabdcadaabbccbcabddbbddbbcdcddabbbbaabccdadcaddaaddacaaacbaabdbcacabddcbccbddadadbdaccaabbdddccdccdcabdadcadcdccabcbbcbabacaaabcdcacacadbbcdddabbadcbdcdcbdcabdadcdabacacaddbbdbacdadcccbaacaddcbddbabcbdcaaabbddbbbcbcdbadcdccaabaadbdaccccccacdcaccaaddbcbdbbcdccabababaabcdbdcbbccbdaccbdbbcdcbbdadbdbabadbcccddadccaacabbaadbbdcbaacdddbccaababbdadaccdadcbadbdcddcdadbdbbdbcacabaadacbacccbccbbaadbcacccaabdcdbdbacbcdcccaabbbdcdaccccdcdddddacaaaddabbccdbadbdaddcbbaccdbabbddaabaacbabcbdbdacaaadaaddbbdcabacddbbdaaaaacdabbcacaaaacbaaaddadaadcccccaadacdbddbcbadcbbcbbabcccaccababdbbdabbddbdcaacddbabbbddbacbdddaaccaaccccbaadccdaadcacabcddbdaadbddcdcdadbddddcccccbddbbbccdbbdbbbacddadddbddadcadcbddcbababbdaabbabcbcacbabdbcdacdbdbccbcbcbbaddcadcddccccdcbacdcdbbdcbcddcaccbcadcddbcbddcdaabcbcdbacccddcaccbcadaaaccacbadbcccacaabbcdbabdbabaacacbacddcdbcaccddcdbaabcbddbadccacabbccbdbacabadcabdbcdcaadcbdbbbacdcaaddccdaaaadacadddcbddcbaacdaadbcbabbabdcacbdadccaccbdcdbabbdabbbaacdddaaabcdcaabddcadbdccaacdccdbdcbcdaaabdcbbabbbaadbccadbbaaddcddaadcadcbbcddddcadbcddccdacbbabaababcdcacadcacbdadbabcbabbddaaabbcccdccbcbdcdaadbdcadbbdaadbbaacabbaabdbadaabaddcbcdbaadbdbabdbaabbbabdccadbbbccaaaabadabbdccabcdacdbdabcbadcdaacbbacddacbbdadbaddbaccdbaaacbabbcdcacdbdacdbdaadddabcbcbccabbbcdddbccabccaaccabbdcabcbcaddbbccbbcddcbcbcbadbabdddadaabcadccbabadacbcdacacaccaddddbcdbdacabacbcadacdaddbbaadaadcdaddddbdbdbcabcddaccbbcabdaabcbcaacdacdacdaccaaacccccdadacadbbacbbdaabdbacdacbbdddaaacbddcabdacddaaabccadbbbbddcbbbdcbbaaccacdbdacbabadacbcbddacbbabdabdaddbaadadabbbccbcbbdbcaaacacdcadbdddbdabaadcabdcdabccdbcdbbcccdddcaabadadcbddccdcaccccbddcadcdbcaccbaccaddcbcbacbcabbabdbcaccbcbaacdabddcddaddaddbbcbddbadcbcdacbdaccaaabbcddaaaacaccdbaaddbbaacdaacdccaabdcbdacbdcadabbbcdabdaadadadccbaddbabdbccbdbadabcdaacbabbabdcbaadddcdacbaadbccbccabadbbaaadbadbdadbabbbcbabcadddcbacbcbbdacdddcccccaabadbdbdbcbacbdcbdcacabbdddbbacdaabdadbababbaddacbcbdbbdbabcacbdcbbdcbccbcaacccdbcbbbbbccacbbcadbaddccabbdaaacbcabbccdbbcabcbadbdcaacbabcdcacbcbacddabdaccacbcbddcaaddbcbcbddccccdbddbabdbbaaaacdaadcbadbccacbaccccbbaaaaccbbdcbcadccbbcaabbcbdcbabbddcdcdbdddabaddbaadcadbdbdadaadaacacddddacdacdcdacacbbacbccdcccbaaabbdaaadbbbcaaadccbacadbabdabaddabdddcbcdacccccbbacadadbdbabccadadaddcbbdadcaabdadddcabababdbbbccacaadcdbadcaabdcaabbdaaddbbdccaabccbdcabccaadacbaaabbdaabdacdccacbbcddababdcdaddccbcaaacadadbaabaabccacaddaaaadacacdadcbdccaccbcadbccabbcacacddaacadcaabcbaacdbcdacbbcaaaadcacabcbccabbaadadbabccaadcadadacbdccdbbacdacccbcdcadccaddccbddabaaaabadbabccdbadbabddbaacdbabababdbddcbbabccddccdaadcacbddbadcacbcbdcdbdbdcacbbacacaaccabdaadadbaaaaabbbbdbadccdddcbbaddcdcbabbacaddbcbccdccaabaddaabbdadddadbbaadbabcddabdccbabbcdaccbbcabcbbbccdbcccaabcdcabddadacaaabbbbacbbddcaaccabccadabacbccdcccabadbaadbdaaaaabacadbabaadacdddabddcdacabddcadaccccacaadbccccadabbbbdaaccdaaaacdbcbadadabcbcdddbcbaaddbdcbcadaccdbaddcdbbabbdcacbcadddcbcbccccccababacbcadccdbcbddbaaabcdccacdacbccabbcdcdcdacaddbbbadbbcbccddbbdabbbabcacdddbccdbcccdbaabcaddadacbcbaaddabcacdbcdacacadbbbadddddbbaccbcccddaacadddccbcacdbdccbdacdbccddabadbbccaccccccdcbcdcabdabaacabcabdaabadbbdcdbcdcddddabcbabbcbbacabddacbddbdbbacccdaddcbcaabbacadbbcccbbadcadddabcddabccbbacabcaddaacccdcbcdddddbaddcbdabbbaacacdddbaacadcbbcaaaabadacbbdbbdcadaaddacaaddabddddcbaadbacaacbabbacbbdbddbdcdabdbacdccabcdccaccaaccbddcaccdcaaccadaddccdcccdbdbdcdbdbcabbbdcccbdccacdcdabaccdcacccbddaaddadabbabdaacbadbabdcaacdbcbdcaaaabcccababcbbcbddccbbbddacddcbccacdaddcabcaaacdbdbacaaadbcbbadacbaabadcacacbbaccccbdbdbbcddccaaaabbcccbbdbccdcadbbaabdbabbbaaddbadadbaabbdbdcdbdddacbbabcccbccddcaabadcdddadaadacccaccacbacbbdacddcadbbacbdbcbbcdcadcaaccbbccdbbbcccadacdacbacadabacdcbdbdbccbbadbabaccdaacbacaaccbadadcacaacacbdcdcacdccccdbccdaccdcddbddcabddbcadbccdcadabcacdbcadbadabdbdbbdbdbccbcaccdbdbbcdcddddddccacdcddbddcbcdcccbbaacbcdacaccbbdadbbdcadcbdbcaaaaaacaadcacbbaabbacdbacbcbcaabdadccaccbcaaacaddabcabdadacdbadadcbbddcbcaccbcbcacbcbacdbadbdbdbbcaaabaacabadcbcddbdccdbdcabbddabadcbdcbdbaadcbcccdbaabcbbbdccdcccbbddcaaccbbadcabbcdcbddbbbcadbbcddbcdbadcaaadcadacabbcdaabcddcccabdaadbbcaccbcacadcacbaabcbccccbbdaadbbacadbdcbadadbcbbaabacdddbbccabcbaccbcdaadddadbadcdbcbbbdcddcbccbbddbdbbabdcaabaacbbbadccbddcabccddcabcbabbaaaaddcbaacdbcadcabccbacacdbcbcddbbbddccdcdaabbcbcdbdcbbadbaadccadbbacabdaaccbddccbdaccaaaabbdbcdaacacdcbbdaababbdbcbbbaccdbaaaabdacbdcdacccaddbdabdbadadbcabdcbbbbdadaababbaccadbbabbbbabbcccdadcbcdcaacbcbbddbcadaccdccbcbcdbdbadddcabbdccdbcbcadababbaccbacddbdaacccdccacbadbbcabdbbacdbaddabcacdcdadccbcadbbbdbcabadacbbdcdddbacccaaccbddabbcdaadddbddddbcbadcbccdcccadcdaaaccbbbbbbbbcacbcdaadccbbaadaccdacbbaacaadaabadcdabadadccdccbddbacbaaadbddcbbcddbbcdabcadcbaabddcbbdaadcadadcadadaaaaadaadadcddbddacaacbaaaacaabbcadbbbcccdbdaaadabacacccabbbbaaddaccbcbbcddcdbbdbbdcbcbdaabddbaddcbdbcdcbcbcbaaacaddcdabdbbcdddcabdcbdaddcdcbcacababdccabbcccabdcbbcbcacbbdbdabaaaabcbcbbccaccdbbdabbbddbdabdcaddccabcbdbacabadccbbaccbbbcabcbbbccbdcddccdbcacaacddbcbaadbaccdcddbaadacbbbdbdadbabbcdbaabcbdcbcaadcdbdcddbacccabcbaadadddbdaabadacdcaaaaddbadbbaadcbbadbadbadacbacbddcbcccbbbbccdaaadcaacbcddbdbbacddcddcbabbaabdddabdcddbacbabbdbcdddbdccadaddccacbcacccdcdbcccacbdbdacbcdcbbabddcbbcbabcdcdacddbdcccbbbcbbbcccbaaacabdbcbaddbbdcdcabbdbdbdacbcbddaddcccaacbaacaccbaacdbdccbabbcdbdbbadbbdddddaaddcadbacadbbacddaababdcbdacbaaaadbaabdbcabcababcddcaaaacdabbadcaaacbcaaaacaaccbabaaaaccdabababdcdaaabacabacabcaadcbaacacacaccdadaaddcaaddbdaccddadabbbccbdcbbdbcdbdacccdbbcddcccbccdcacbddbcacddadcbdacaabaacbbcababaababbbddbdacdaaddababacaddadcdbadbbdadccdcbacacabdcbcacddcdbdbaadbddccbaabaddcbcadbaccbabbbadbaccaaadbddcacddcdbaadddbdaacabbdbbadbdbbcaddbcbdbbcbaccdccbbaaadcaaacbdcadacadaadcdcccaaadaabcddbaccdddaccdddbabaabbbaacbdaccccdcbcabcddbadcdcacbacbbcacddacacdbbdbcdbadadacbabdadbaadabcdcbbbbdcbbaddcdacccabbdddaacacccdccbcacdbaadcaddababdcdbacbbaaadadbaaacadaaaaaccadcdcdcdbbbcdccdcbabccaadcddddbddadbcdadcbcdcadcddadbaadcdcabdbadcdaddcdbdcdabddbbcaaacdabdbccacdbaddacababdcbdabaccbbdccbbcdcdbbddcbbbcbdccaacbcdbaaabbaaadabccdcbacacbcadacdddabcabbcdcdbbcaaabbcbacbbddabcbaabacabdacdbbbcacabdbaabdbdacabbddbcbbdaccaacbbcdaddadcdacacaddcaabbdcdbababdcadbbaadadabcddcbbaccabdbabcbbbaccccacbadacaacaacdbdababbbaaabdbdccbcbbbadccbabcbbdccddddbcaadddbbacbccaacccacabdabbacacacbbcbacadadaaddcdcbadcaacadbcdbddaacccbabbcaabccbdccbaadcaaccaddccbcbbcccbbabbcdcababdaccbccdabcbabdabbcbdbbdaccdcbacbbdacaddbcbdbdddacaaccdbbbadddcbbacabaadabdcabcbdcabbbaabadbacbbaaaabaabaccdcccacddcaadabbbbcdccdabbbdabbcaabacabbddbaacbddbcabcbbabbbdcacbbcbbacddbcaabacadbccbcacbdbcddccdbadbcbaaaabcdcbcaadcbadcadabaabaacaadbbbabadcbadcddbcbbdddaacddcdbccddcadadadbadbcdbabcbdcabcddddabadbbabbbdccabbaccccdabccacabddbccdabdccdccddcbbadcbaadccbacbdaddccbdcbaaadddbcdcbcbaaadcadccbbcdcbbdccaaaddcabaddaddadbbbabadbadabdbdcdadccdacadcabcabdacdcbbbacaadbcbddcbbcddcbadaddddadbccaabbddabdbcaccaadaabbcabbaddabbaababbcbdbcabcbcdabcdccdcabcdabaabcdbccabcadbaddababdaaadaddbadbacacaabbbacdbbadcacccddccabddbcacdaaabdddcabacccacddcabddacddadddddcabcdddabcabaacbbdbcdcaabbdddabbbbabdcacaaabacdcbacdbbdbbdacbacdbdaabbdaabbdcdddcacbaabcdaaabcccdccaaddddabbcdcaccbccbdcdbbdacadcaadbbbbbbadacaadbacbacdddadaabadccdbdcddbaacacadddabdbaabddbbdbdadcacbdbbcbddbcddbcdaaabccbabbcbbbdbadadcbacbcaadbccacccdadabddcccacbdddbaddcadbacccacddbbcacdbaabdabcaabdabcabbcbabcadaaaacaaacdcabccbdbcddbcacbddcaacbdbbabdbcbddabbcbddccdcdabcdbdaabcadadbcdddcbbbcccdabcacbbabbbadccbcdcbdbacbbcbcbdddaabbacdccbdaadaaadcdcccacacbbbdaaabbababacddacbaaccacbcbdcbbaddcbacddbcbacbcdbdadcacadabaadacbdaadbadbdabdccacdcbddbbadabbbdbaaaadcdcbdaccbddbaacabaccdabddbadbdddbccccbcaaacdcabccadddbbbcbbdbbbbcbcacadaaadcadcdbabcbdccdcbbbdcaacdcbbdcbcddaccbcbbdbdbccacaadbdccabbaaccaddacbdcdabcbcadabdcbaddaccdaacdcdbdaddbcacbaacbbcabbadaccccadccacbddcaaadcacaacddcabdcacacbcadcddbabbbcacacaacbbcbabcaaccdddddbcbdabdadcabadcdbdadaaadddcddacbcacacacabadcbcdcbbcdbddbbbaddcabbdaaddcacbadaaadbcbcdaddcdddaccacbdaaadbbbbadddccadddacbcddbbdcbcbdaaaaaaaadacddbbcdacbaabcbbbddddcabdcaccccdabacabdcbbbbcabcbdaaccdccdbcccaadaaccdadadcaaaccbdcdbcacbdcbaaadacaccbbdbccdbabcaadbdcadbbbcbccbdbabaaaccbcbcacacabbaabbaddaddbbdbcdbcacaacccaaabdbdbcdbdbdbdbcbcadabdccccdabdbbcabacaccdbdaacdaacbccdadabbabbdcccdbacbdbdbbaabdddcdbabaaccdbbabbacaaadaadbdcbbabdbbdccabbbdaccddbacadcbbcbadcbbabdabadaacdbaccaadabdacddaadaacbcbabbddddcdcdbadcddaccdbccaababcdddadaacbdbcabbdcbdadabacdbabadcbbddadaddbbabcbadcdcbbbccdabddadacdbbabddaaccaccaccbbdcaacdddbadddbdbcdbdadcababdcadbccbbbaddadbbdccdbbccccabbbcaaadbcabbaacccbdbabcbcddabddcaadbdbbdaddbacbbdaccbdaccbddddbacccbaaaaaaccbcbdbdbbdcacadacaadaaddacaacddcdbbadbbcbbbbabcdbdbaabbdcaabaadbaadabbcbaabaccaacdadabcdbddcddcdddacdbcbaaadacababaaaccacbccbdbbcaabdbcdbcddbccdcdbcbadbaaabdcacaddaccacacbcdbacaadcbadbdbaaddddbbcdbdbbbdddabcccacaddaaadaddcaaaadcdbddbdccabdaaaabccabcaabcbadbadcbccbadbababdbcdbdcdcddabacbcddacccaddcbdadacccbbbbbdcabbcbdcdabcbcbbdaccadcdadacaaaacbcbddaadbdacaccadcbaddadaadaacdcbbcccacdddadacdbbcacabcbbcadcdcddcbdacabadbadccabcccabdbcaabcbcdadaaadbcbabbcbadcdccdabaacadcabdbaaacbddaccbacbbbdbdacdddcccabbbdbcacbaccacdcbaadadcacbbddabdccbbaacbacdabccaadbdbdbbbccacaccadddcbddaddbbccdaddcabcccaddbcccbbdbdcdadbbddbcbababbbdcbaccbccbcacacbcdccabddbdadbaddadaadcdddbbdcbbcadbbbaaaacdbbdcbdaddcddbbcdacbbacbabbcadabdbdaddcadbbabadcdabacbbadbbcabcabadadaaddacbabbccacbccbdabbcdbaaabbbdcbbdadbabaddddadbadaadadddcdbbcbbaabdcdabaccdbdaddcdbacabdacaabdaadababacaddabaadccccddacaccddaacabcaddaabadcabaaccbaddcabbbbbdcabcddcadbccdbaadcaababbbdcbccabdaabbaabdbbcdccdcbdaccbcbbdcddddadbbacdadbcadbaddcbcbadcdcabaccddcadbbccabcdbdcdcdaccbcdcdacdcababccdbdbbdccdcdcdaacdbddcbcddbcadbddabacdadcccbabdcbadddababddcaccacadddcaccaaccdbdacddaddbaccddddcaacacadcacdbbdbaddcabbccbcbabdbbadbacbacacbdbcbdccbcaccccbdcdbcdaabbcdcdcaabdadadccbbaacbddddadaaddbcabbababbcbddaaddcaabbacdddbdabcadabdaddbbbdbcbdadbdccbcbaddcadaacbdbcaacbdccaddcdddacdcbbbcabbcccbbdaadcadbcbbcaaddbcdadabcbaabbacaddccabbacadbbbcddacabdcbddabbcbadabbbcbbbcabcddcdabdbccbdbaadbbcbbabbdaaccdaadaaacacdcaacbadacbcaccdddbbcdbaddbadbdcaddbbbcabacccabcbccaabbbadcbddadbcaaadccabaaddbbaaabbccbbcbabcaddbccaaadacabaacdcdccdcccdaadabcbacdcaaabdabadaabbbbdcdccbcbaccadaaacdbadbacabadaababddabcbcbaacbdccabaacaacbacadaaaaaacccabcbcbccbaddcabaccadabdadccaaadddaaaaaadcbddabdacbcdbdbdbaaaddabdaaabcaabdbbcbdbbadbbbccadabbbadadaacdabbcbacddcddccbaabacdacdbbdadadcbdbbbcdcccdcbdaaaaaadcdacabbcaabacadaabbdbadcbbadaaacbbcdcddbadcddbcddbdbbbddadacbabddbabccbcbbbdddbadabbcbaabbdbccacadabcacdaacdddccacaddbcbcacdbacabcdcdbdbbdbbbcbcdccaadddddaadadaacbdaabbcaababddcdcbadcbccdacbaadbdbdaadddabcbdddacadadbdcdbddaabcacbdcdcdaadacbacddadcbdbadcbdcbaccbdccdcbcddbabbcbdcdddbbcbadcacaccabaadacabaaacabacbdbbbdcccbddddbaacabaddadbbcabdaacdbacccdabcbbbbcbdccddadabbbbccaaacdabbdcbdcaadcddcddaadabddbcadbadddbacdadddcccdbcdddbcabaabbaacacccbbadabdcdaccccbbbbcbdcbcdabcaccaadbbdbaacddcadadbccbccdcabbcdadaddccdbbcabbddcdbcdadbcbcdcdabaddcddadabbbcdbdaadadcbdaabaddabacbbccaabccdadbbbabdbadacdcadcbadcccdcbdaadcabaacbdacddabaddccbaaddcaababcbccaabcdbbcdccddcccacdccbdccacccdcddcaacbbbcddcaabbbadadbaccabbaaadabcbdcccdccdaabaaabdddbcdaaaaadbcbaaabadccabacbcbdcabababccacbdcdccdacaddadbcdcabdaaccdaccdadbbccabdadddabacacddaababbcccaadcabcaccdddcbcdbddcbdacddabccacdbaccbcacbccbbdcbccadcdbacbaaaababbcaabcbbccacddabcdbdbbcbaacaaabcbadccadbdccbbaacaabcdabbbbbbbdcbdbcacaadbadbcbbdbddcdbdccdbaadccdddbabbabbdbadabaabbabacdabcdabcbbaccbaaadccbcddcaabdabaacaacaaacacdbabcdcbdaabbdcbadaabaacbabadacdbaaaadcdbbaadaabdadbabdabbccdbcbddabbcdcabdbabdabdbadbdcaaabdacdcddcbccadbcaaabdacdbbbabbbddcbadbbabcdacaadadacaadcabadbbbbbaddadcacadbbdabbbcbbadbdddcdadcbbabbacabcccaadbaacacbcdabadabdbabbdadabdcbadbdcabcaaccbbdabbbbcdbadadacddcadadbbbbddbcbcabadbdbbdbcabcccaababacccdbadccbccaadabbcbdadddbabaddbbccddcbbdcdadabbccdacdcaddbaaacdabbbcdabbbdcdccdbcaabaacbcbdbdbaababcabbdddbaddccbdccbbcbccacbadbaacabaabcaabadcbcbcbcddbccadcabaabdaacaadabbadccbcaacbddcbbdadbdbacdbccccdadcaabdaccbcccccbccacddbdadadccddaaacbaacbcacdbcdabcddbdddcdcdcdcaaacadaabdccccaacadbcaddcacabbbacbaddacbbabcbbccababacdbcbadadcbaadccbabadabddcaacaaacaacbcabbdcbcccaabcbbacccdaadacbaccbadacaaacaaabbaddbdbcadbbadadcbaabbdacddabbccacccbdcdbdcbcddbdacacabcdaadddcdddbbcdacaddbacdbdddbcadbabacccdbcbacaadccbbaacabcdddbccacadaabaacbdcbaddbabdbcacabdccdadbaacbdcddcaddcdadcadabadbccbbcdacbdbaccddaadadcdabccdadacadadcbccaacdbbccabcddcccdaaadcadaaababcbadcaddbcaadbdaabadcacccabdbcadccdbdcdbbdcaccbbacdcdabbcbcccccccbbacadabdddbaaaadbbcabddbbabcddccaadcccacacacdbcdadcaadaddabdcacdbddadbacdddccdacdabbbbcacdbdbdbacddbdbddaddabaadbdabdbdadddaaaaaaaacbacabdcbaddbddddbcccaadcccaccdcacddadcaabbacadadcdbcabcbddcdccdabcaacddcbddbadbaadaaddcbcacacbcdcaabbabaacadabcbbddbaacbbbbbaccaabddcabaadacbabaacbdbdbccacbaadbdbabadbcbbcdddcabddbdadcdcdcdddcbdaacddbccddbcadaacdbdadabdaaddabdcbcddadbdccbdcbdcbcabbcdabdbadacabbdbabddacadaabbcadadddadbadaadaccadbaadacbcbaaacaccabdcdbccccdbbdacbabcbcabbbdbccabcbacacbbababaccccbcabdcddcaccadadacbabcaabbcadbdbacddbdcaccdadcddcddccddddbddcdbcbbbbddcabbdddbccadcabdaabcadddcdccdaaacccbcadbddacbdcbababbdbcbcdcdcbcbccabcbccccacbddccabdcdaadcdacaccbdcabcabcbdaacadbbaacadbdbddaacadddddaccbacaddbcddaacdddaabdacddaddbacadcacbaabdbabdddbddbaccbbccbccdcaaabbcabbddbacabacbbacbddbcbcdacdccacdcbbadddaacabccccbcbdccdbcdaaabcbddcccdacbdcaddddcabcbdbccbddcabaabbdccbccbccaadcbbdaabacbcadabdcdddccbdbabcbcbcdcbcbaaccaaabacbadaddbadabcaaacddbcdcbbbccadcaddddcdcbdcadbcccdddbbbbababcbdcacabaadcabdadbddbbcdabdaadbadaddbacbdbbcdcddadacabcdddaabadababaccbcccbcbacbbccaddacbdaabbadaabdddadbbbdcbabdabcbcadaccddcbbcbbdbadcadabbdbaccdabcdcaacbdcdbacbdcdbdcaaababbacccbcabcdaaccbdbbcaddabacdbbcccbcbacaaadbcabdbcbdcdbcdccccbbbbbbbdbbdbcdcdbbabbcababbccbbcbcbccddbaabdbadaddabddcdbbacbbccaabdcbaabbaccdcaddbbbbcadabbcdcdbcaacbadccdccbbbdccdaddddcddbadbbcdcacadccadcadabacdddcdcaddbabbcbaaccdbcccbcccbccbaadbdcbdbccbcddcdbabcabaadabaccbcdbcdacdcccdbdcacbcbcdbbbcbccbaacbbcbdddaaabcbdccdbabdbbaaddcbcddcabbcbcbccbabdcdcdcbcabccabbbcbcdccbcbdccbcdcadbadacacdbacdccdbabaababbaaadcabaabacbdbaadabcccdbdbdaccbdaacdacbccbdcabacaaccbbcbcabcaacaadbdcaddcdccddabcbccbdbcaadbcddcbabdcdccbadddbcbddacbbbbddaddaccaabbacbdbdacdaddccaabcabbacabbabddcdbccdccadddccadcbbbabcdbcdcddaddacdcdadcaddaadbbdaccaacddbacbddcaaccadaabaaccdbbbcabbadaaddcaaddbdddbcbcccdbaccabbbabbcbcbccdadacdcccdbacacbcbdadabcadaabcabbcababbcdbbdddabadbccdbccdcacdacacddddcbdcdcacbacacbbabdcdbbdaadbdbacdbdccbbdbbdccbcdaccdcbacacdcdadcdcabbaddccbcbbbadaaaaccbbdcabcabbadcabbddbccacbbbdcbbdaabbdadbcababacbdbaabbcabaadadbdddcabadddcaddbaabdcbacbcaacbdacdcccaabccbbaaaacdbdbcadddadbdddaabadcaabccbcdbccacccacabcacdcdcbbbcbbbbaacbacdaabcdcccbcbdbbabcbbaabcbbcacadbdddcdcadaacbdbacdcdbaabbadadacdbbcdbccadbbcdcaabbdadcbbadcacaacdcdaddbbbcacadaddaadcaadddddcaacdabaddbabccbcbdbbcbcccccbadcbdaadabbaabbdacdabdcbdcbaddcbddcdacaacaaaccdababdcbdabacbdaadcdaaddcddaabadbaddcbcbcbdbbbcbdbcbaaccddbcbbcaadbcbddcdabbbadbdbcdcbadbadbbddaddbcdaacaabdaabccbabcbbbabbddcabdddcaaddccbadcdbabcabbaccddacbdccbaaaabadaaccbdbbcaaaadcdabdaccdcccdcbcbdcadcaadccbddddcdaddbddcaccbacbacbadaadddabaaddbdabbdbaabcdbbabaccacdbcadabccbbbbbcacbbdcdcacccbbaccddabacacbdddcbabaccaacdaaacadcbbdacbdabacddbcdbdabbccadbaddddabbddbcdccbdcddbbadbcbaaaacdbcdbdbbccdabcbddcddccccbcbcbdbcbcabcaccbaaaaabaccbbaddaaadadbdbcdbddbdabbbdccbdbdababddcbccddadbcbddbcdcbcdbbaddadabbcdddcabbbcbbabcbddabcbabbcacdbadabcabbcaddabbcdacabaabbbccaaccdcdccbbdcadbbdddcaacdcccbaaccdababacbdbbaacbdadbccccbadabaaadaacdabacbbbbccdcbaaadcadbdbcddbaccaaabdcdaabdbbcdcacaacbdbccbabdcdcbbcdcbabbccadbabbadcaaccddcadadacccdaaadddaacadbaddbdcdbdcbcacabadacaabccdccdadadaacbadbcbabcccbbcabbdbabadccccaddbcbccadaabbddcbcabcbdccbbdbbabcbcaacadbbcbcdddcabdddcccbdacdbdbbabdcaacdbcdbbabacaabccacadccdaacdacbadddcddcbdbbbaacabdabbbaccbadacbacccdccddcbdddcdcabbabddcdbbdaacaddccbdbcddaabbdcdacbdccbcdcaacccdaacdacdacabccddadacbbabccdabaadaaaddbadbbbcacbdaccccaccaaabbbabacdccbcddabbadcbddcabacddbbdddcadddbdccbcddcdaddadcbacddddbaabbbcadbaacaadbdcddcdaadbbccacbcacdbbdacadcbbcadddbabdabbdbdddaddaaabdcbcbdbccddcadccdbaccddaaacdadbcbacbbabbbaacabbdbcabdcaabcbbcdaccdcaccbcdccdccbcdaabdcccdabbadacbcdccccaacaaaaaddccbacacdcabdbcabcbcadbdadddbddbcabcacaadcabdadccccccddaaadccddabccaadbcadadbdccabbdccddabbbcabcbaaaaadbdadcaaabdbaadbadcaaaadbbdcddbabaacccdcdacdcbddaabdacdabaaddcddaabddaaddcdbcabaadaccaadcbbddacdabddaddabbcdabbbabaabbcbdcddbadacddcadaaabbbdcbdbcbddacadcbbcadcbdcdabacdaaaabcdddddadcdbdcddcdcdddcbcbcccddadcbcbdddaaadbaaabdcdcccdabcacdacccbccbdbabdcbbacadcacbacabccbdacbbddcbbcaabddbaddaddcbbdabbaadbbabcaaadbdcbdaadbcbababccbdcccbdadcccadbabdabddcbbaaddcbadcddbccdbaadbdcaddbacbabddbaddbabdacabcddabdaabcbaabcacbaddcabbabacbcdbdbbbaddcbdbdcdcbabbbbdcbaabcddbbaddadcdccbccbbadcdbababadaacabdcdaccdddabbcdcbcbaddcbaaddabbdababbbaccbbdddcbacccccdbddbdaddbdabdcbdaddbbddacccddbabcdccdadadbccbdcdacdcdbabdcdbbcacaaccdcbaabcbabcbbbddccddccdacbcadaccadbbaaadcddbdcacbbdddacdbaacdaabbcbbcbdadbbabaddacababbcacbdabdbcacbbccacdcdcbacacacddaccdaabdadcddacabdaddadbcacdaaaacbcacdadbdbbcdbcbabaadcdadbaabdcacbabcdaacadaabdadcddcdccaaaaadbcdbdddacdacdbcdabbdadbbbacdaadcbdbaddacaacccdbabdcbdbcdabcadddcbdbdaabddcdcccbbcbcdccdbccdaabdbcaddbaacdcdbbcdadaaabdcdaddbbdbbaaddbdbaddddabaacdccbbdadbdbaddbcaccddcbababcaaadadacabbadccdcdbdcdacbbcddcadddcdbbabdaadbdbcadddabaadabbdbbdabadabadadbccbccaaaabaabdccbcdbdbbbbbbbbccbaaaabbbbdbbbcadbacbcdbdbbbddacbbdbbbccddbcabcdbcddbccdcdbacccbcbcbabdacbacaccbbbbaacddaabaabdaabdcbabaadcadcbdcbbdadabbabdcdbbcdcbcbbbbdddacdaddccccbabcdadbcbccbdbdbdddcbcbbccaddcadbacbacbbdacbaccacdbddcaaccaadbcbcbbdcabdcabcadbbadacbbbdabbacaaabcabddacacbaabdbccbdaaadabadabaabdabadaacbaabcdcbbdddbadaaaccbcccddcddcdbaaabbadbadcabdbcaabacbbbccbcdbcaacdbbcddbcdcdcddcbabaabbbdcddcabcbdbdabadcdcacbbccccdaccbcdcdbcdcacadcbabcddbbbababcbddaadccdaddacdbbcbbcbdcbbabcbbbbccbdaabbbbdccbdcadccacdbcababdbdaaacbccbbcdbdaaddccddbabdabbacbbccdbbcaccdaddbcbbaadcadbacabdbabdcabddddaaababdbbdcaacbdbadabacbaadbdcdcdccaaacdbabacadaadbaddccaadddcbbdcccccddacacaabbbdbaaaaacaccdbddddcbdccdddbcacbdcdacbcacbbadaccbbbadcdcdcbcdbdcbabadadccccddbbabbabdabbdaaabaccdbbabaacbcdcaabacabdbdbacdbccdbcadbaadabaccdbccadacbbccbbcaddbadbbabaacdccddaabcacdacbbccbadbdddcdaabddbdcacacdadbbcbdbaabaadadbcddbbbacbbcdbddaaddddbacdddbacadbcdcabcbcccddcbaacbbbddbcaabddabbadbcdaaabcacddccaacdcadcdddabcbbbbadddccbacaaddacbbbddbadcbdcdbbddcbdabaccbbdcaacabccdbadcaababddddcddcbaadbbaddcddbbddbaaaadbacadaababddcbaacdaccdaadabbcddddadbddaccdddbbbbbdcacbaddcabdddcbbcacabbdbacddcbbaaabbdcdbacdacdcaadbdadcbbbcabcbadbaaadcaacabdaddcabbdcbccbcbcbdccacacdbaabdcbdddbcddadadbcbbaddabccaccaddacabcbbabddcdbbbcddcdbddddcabaacabcbdccadddcccbcdcdaabdbdccddcdcaccdcdbbdbabcbdbccbaadcdacbdcabadddcbdabbcaaacdbbbdabbbaadcbbcdcadccadacccdccddbababcacaddcddcdbccdaccdabcdcbccdaaacbaaddabaabbadcdddbcccbbbcdcbcacbdaabbabccabdabcbdbcdbcbabcccdbabdadbddddaabbbbaabdbaaaaddaccddcaccdbdbcaacdbabbabbadaabdababcaccaaaaaddbacaaddccabbdcbdcdabdccabdbbabdabcacbbbdbdacbbabcdcbacdddcddaaabccdbacacaccbcbdbbaabbadccabccacbdaaddccbcddacbdddddbabadcbcddcadddcabddbbadacdbbcaddabcabcbbccbbacddddccdbbacadacaaccdccdacababdabaadbcccaaadcadcbcbcaacccbccccbcabccacbaabacacdcddbbccbdcccdcbbcdabcaabdbcadbccaacbdcdccdcdbbacccacbbaabbacdcdcacbcbaaabacdddcddacadbaccdaadccdacdddbaddbbddbdcdbaaacaacddcaacdbbddcdadcaaaaacbdaaacacabcbdcaaaddcddaaccccacdbbdbacdbdbdabdaccbabbbbdbbcddddbbcdabcdbdcbdbddbbabccbbacdbbbdaddbdabbbadabaccadbbbbabcddbbddbddaccbaddbbccbaaaaaaaaddcbdcdbdddccbabdcddcacdbdccacacbadcccbcbccdcddcbccbdbbcccbababbdbaccdcabaddaccdacccdcabbcaaaabdbdcccdccaccdabdababbcdadcaccbdcbabbcddadacccdddbbabadaabadacdaabdcabadddcccbcacabdabaaadcccddacbddaccdabcbcabdbabacdbbbccbbdcddcdbbdccddabaccddadabbdddaadddbaabbcaccbccbaccaabcddabddddcacccdbdaddbbbbddaacbbcddbdcdabbbabcbbddcbbdcbaddabcadaadadaadbbcdcdacaaccbcccccbbccadbcccdbdadddbcbcdadadcdacadbbdbaadcbbaaddcaabccbbbabddabbbdcdadaabdbbcbdbccaacabbbcddbcaabaabcbcbcddadacaadccdaaddabcddbdbdabbabbdccbcacadccaccdcaaababcaabaadddccbdabddbcdbaccddbcbccbdbbccbcbdcdabccccbbdcdaaacaaccadcbcbbcbaccbcbbaacabcadaaabdddacabcbcdcbadacbaadbcbaabcabccdccbadbaadddabdacdadcaaccdcbbbdbccaaadacbdddacdcdcdadadbbccdccacacbdabdccbadcacbdaadbbbcbcadbbcbaacdbcaaadbccadcbdaaadbadcddddddacbdbcdddccbbcacaadddcaaadbcbcbcdbbabdadaabbbddabdbbaabacdcdabdddddcaccbdccacdadadaaacdbdacbdacdbbccdcabbbcdbdabbbdcddcbadbdcacdcaadbdaabdbbabbcbaccabaadcdcdbaddbbcbddcdbcabddbaccaddacababbdbabcdcacbccccadbddbbcdbcabdccadcddddcbacdbcccbabcdcbbacbdccadccaccccbcbdbcaabbdcddddacbdacdbdaaccbcadaccbbbaabaadbbacddddbcddacdadadabbdaccdacabcaaadcddddbaccacbcadbabcaabcddddcaddcdcdacbccbddcbadccbaccadcdbdcbcbbbbdadadbdbccdcdbcdaaaaadaabdadcdadabbaddddcaddbaabbabccabccbdbadcdbcdcdadccbabaabdbdcbadabbbdbaddbacbacbabddbbbccddabcadcbddcdaddbbacbaacaddaabdcaddbbaabcacabdbbadcddbdbcacdcacadaaccacdccdbdbdbbdbcbacdcdadacdadbdcaaccdcabbdaadcddabbcababdcdcdbacbaabaccdadcdbccddcdbbdcddcbccbacdaabbabdadbbdccaadcbcccbbbddadbdacdadaddacacaadddabdcbacaabbbdcbdbccaadbdbbccaadadccdbcacbbbadcbdcddddbdcbdcccabbddcccaddcddcaadcccbbadbcdcaadbaaaadbdcbdcdaabcbdbdcabacbcbacaddbdcbbddcabccbaadbbddccdbdcbcadbcbcdabacdabbdbcbcdbabcabcbcabbdbabadabdcabbbadccddddcddbbdaccacdbdcddabacacadadcaccbbcaddcdcadbdbcaccbcdbdcccdddcaccccadbddcdaaaaadadcbaadbbaaabdadaccbacdccaaccbaaabcddcdaddabacaacbcbacdcaaabdacabdddaadabbabbbdcaccacadbcddcabddcbccdbdbabaaadcaabbdcdbdccccdbaddcadcccaaddcdadbcaccdababacadcaaacbbddbdabcaaaddbbdcdcbdaaccbbdabbcbcabddcccaabccbcdbabcccaabcdcdadcdcbdabccddcdaaddcabaddabbaadbaccbddababbdbbbccbaabcbcdbbabbddbabcdbabdcbbabdcdcbccccdcbcddbaddbcccaabcdabdabcdccdbabccadbcddbdcbcbcccddbbddaccdbcacbbdaabdcabacdbbdbdbadddabacabccddbdadcbdccbbbcccbbacbacdcddbcacbaadbdccaddcbdbacbdacababbcdaadbbdacdbbcbcdaadbdcadcabcccadbdbbbdabbcccbbbccdddbcababdccccabcadddbabcccdcbaacccaabcbcdcbbcbddbacbcddccdaccbcbbadacacbdbbcabaaccacbccabcddbbddbddcbbbdcdaaacdadccabbaccadbbdbdbcbcbbddccdabdcaddbbbcdbdbcabdadcbaabcdbbdcaabdccddbbabadbbbcdccdaabcccddacbbcacddcadbadaccacabdaaaabbadcbabbcaacdababcbbaccaabdadcbabaaddacabcdbcddccdabadcacadccbadcbbcbaaadccdcabdbccaacbadcdddbaaaaddabaddcdabcdbbdcbbadcacacbdddcbdaadbdbaccadaddcadcbabdcaacddcdaadcddbadcbdbabcdcdcaadbacdadccdbdcdcacabbbcbcddaadccdacbacaacdcddbadbbbbcdbaddabdcdbdadadddababadcdcdcbdadaabdbbbdaacdbdcbdcbcdbcdbbbdbbdcadbdbddaadbcacdbdcbaadcbaabbdcaccdaacbbcaaabccabccacdcbcacaccabadccdabbdbcdadbbdcbcaaccbbbbddbbdbabccdcbbdccccbbabadaddcbddcbcbcdcbbaddabdcacbabccdadddcabcadcbcabbacaadcccbadababbbdbadbdadbddadcddcabaabcbacadddabdaaacdbbdaaacadbabddaadbdadabbbdbdddcdbbcccccabaaddaabdcdacddcdbccddaabbacbadcacdaabbbdbcaacabccddccdabababbbabaddacacacaadadaaacddbbababbccbaadddcabdbccbbdbbbcaaacddaddaaddbaabaaddacbccacbddcbabdaaacdadbbcddabcdabbbdccbaccdcabcccabccaaaaabbdddbdbccbcbccdaadadbbaddbbaadbdbabadadbbbcbcdbddcaddcccacdcbdcddccadcaaababacdadcacacaddbdbdbabadbccdadaaaccbbcaaccabacddaddbcabdadaccdadcbadbddddbcaacbbbdcddcbadaabccdaadcbbcdbbaccbabdbdbbbcccbabadaacadababdbbaddababbcdccacddbbbbdbdadcdacbbcbadabadbadaacbabdddcbbddcdcbccaacbdcddbabcccbdccdadcbcddcbdbdcacddcdcacddcddbcabadddcccaacadbcdacbbbddaaacdbcabddacbcabccbdbcbbaabdaabbacbbaadccdbbabbdbcadcbbadabacdabcdaaacbbbaabbbcddadbdddbbdcbbcaaaddddcdbbcbbdcadcaacbbbddbdcddbdbbdcdaadccddbbddcddbbcccbabdbccadbcdbaddddbabdadabcdadcdccadddbddcadddbcaabcaaabcbbcbadadcdddcddacccccabdbcdcccbbbbcccbcbdcbbbdabaadcbbbbaaabdaaddddaccdcaacadbbcaadaaacbdacdddccdadaccbcbaccbabaadabbaaaaccabbdcbdcbbaaddcdaabcdbbbbabcabcaabcbbdcabdbaadccacbdbdcccddbcdbdddacbcdaabcacbabbdbadbbdadacacaadabcaadcbbadcccaabccdcabbaadbcadbcdacaaadcaccaaacbdaacbabdacacbcbbcdacdbbbcbbbbbdbdccbbcabbbddcadbbcbaacdadaccadadcbacaacdcdaabacdbdbcbccbdbbaaddcddbbadaddadddbccdbccbadbdcccccbcdcacacaddcbdaccadccbddccaabdabddbdbcabcddccacadabcadbadcadaccccaaadcababdabdcdcdccaabcbaccdadcaaabbcadbdabaacbbdabbdaddcacbdcbabbdcbabdcbdbdcadccccaddabcbbbaacbbbdddcabbcdaacbbdbdcddcdadcccdcbabccdaddbbacaacdadbddbadadccabaacdcadcdbbbacdbcabbbbbbbcdadccabcccdcccddbaaadcccaabccaacaaaaadbdbdbcdcddadbcbcdaacbbccacbddcddcbddabcadcabbaaaadddabddbbbdaacabaaadbbbdbaddcaabbdbaddcbbcdbaadaabccbabdbcddacaccacdbabaddbdabdaccdccacbccbdcbcdabbdadaadbcdbdbadbacdbabbbbcaabadadcaccbbcdabdbaacbdbcdacaacaccbbcaccdcabbadcbadcddbdaaaacdaabbbaaccacdaabaabbcdbcbbdaacccccaabaddddaaacbaadabdcdbbadcbdabaaacdbbcadaccbabadcccaabadccdbacaaadaddddddbcaaddcbcdbdadbacadcdbddbcdacdbddbaabdbbcaaaaabbccddbdaacdaabcccdddbccbccaadbcbbddbbcacbbabdabbcdcdcdbacdbaabdabadddddcbcacdddbcbbdcdccaadbdbabbcdcacbbcadcdabbabbcdaababccbdbbbbdbbddaaaccababcaadadaaddabbcccacdcdadcacddcbdacbcccbbbbcabcbccdbcbabcbbabbdbdabadcccbdaaccacccddabcdddcdbbabaabbabaacdacdcdacdbcddacaccabdccacdbdabdbacddadbbaccbddbdccababbddcdbdbbdbcbbbadcbacbaddacbccaabadddbbaccdbbabbdcacbabcbdbcacbbbdbadcaccbaaabdbaccbdaaccbdcbdadbadccaacabcadcdbacbdbbcdcddbdaaaaddddabacabdaadaccdbaabcbdcdcacaddddbddbbbcbbaaaaacbcdbcdcacdadbcdcbacbdbcbcddbaaaccbcbaccbcbdccadbbcbcaadadbbabbdbbbbcbaabbccbdddddcbaccacdacddaabcbcdcacdbbdbdadddabbbbadddbdcdbaaadacabadadcdbdbcbacaaddbbbbaadbbdabbdadabddccccdbcdccddadacabaaaaccdabcbcaabcbadbdcccbcdbbaccabdcdacccabcabdadbdabdabcdcccabadcdcabaacddddcaadbbbdbbbcdabcdbbbdcdcbcbcddbabbbadadabcddcacdcccbadddcacacabdcdabcdadbcadbadabacdccabadacbccdccaadbbbccccdaabccccbaaacaaacbcbbabadcaabadbaadccddcbbccababbcbcabcdbdbadabadcbadccacbdbabbcbaaacacdbcbabdcdccadcababacbcbbdcbabbdccccdbdbbbcbbbdddbcabddccaccddcbcccacbcacbbbcdaccbbcadcbbddcbdaccaaadcacddcacbbdbacabdacabbcabcacbccbdcbabdadbcababacbacbaabaaccdcbcdadbcbbdabdcabdcdbdbddbbbcbcaabdbbbaddbcdbadcdaddcbdbcdaddaddbbadcdacbaaadcdcccbacdabaadddaaabbaddddbcaacdcbbbbbbbbdacdacaccbbbddcbacbacddcbaabdadddacbcabcccbcacbadbbccdcdabdbbddabaadbbaababcbdaababacdacccdaddbddbaaccbbbadbbdcddaaaadcccbacabdabaaaabadacbdaaacabdcdcaadaababcdbcaadabaacdddbdddabcbbacaccdddadabdacaddbcdabdddacccdaabbdbbbdddcdccddbcbbbdbcddbdcbccbbddbdabbbccbdaccdddcaacddbaccccacddbaaadddababaaacbccdbbbadbddbbcbccbdabcbadcabacccacadaaddacdabcdaccdcbbddbabddcbddbabadbbbdabacdbcabcdbbbabcaddcddbaaaaadcccddbbccdacbbcbbacccacdbcacbdcbaccbbadbbbbbcdcbddadddccdcbaacaaabcddabbadcdbbcaabccaabbcacacccbccdbabdabdcacbcbcacddaddbbcbdcaccddababdacbdcacaadcabaacbbcdcccaaadbddbcdbadacacaacabacaccdcbabdbbabbadababcacddcdbadabddbbbbcbcadddcaddcaddbabaccadcdcdbdacdaacaccaadddbbdbdbccdbadabddbddccdabcdcdacdbcbaaabacbbcbdbddaccabdbcdaccaabbddaacbbbccabccccabdbdbbcaabdcaccbddcbdcdbaabdabdbaabdcdbccbbcaddbbbdaabdcbcbccadacccdabdcdbdccbbbbabbbacabadbcdacabdabbcdccdababacdcaaaddbdbccbdcdaccdcbdcbdddcbbdbaaccbacccbbbdcbbdbabbcbadcabccbaadadddcacbcbcbbaadaadbaabdbcdadbcbcbbbaccccadabdaabbbdacdccaccdaabccadaabbdbcddddbbbababbadcbcacadccbacdaadcdaccbcbddbbbaaddcabcaccccdacaaaadabbddbaaddcdcccdcbdcbacdbcdabdbccdacccacdbbaadcdbabdbcabddccbbcdabbccbbdcccdbbdbddbdaacbddbdccdddabdbbbbdabcbacbddcddcbdbdaabdadabbbadabdcdbacbcbcbdbcabcaccdbcbbabcbccadcbbcccdbcaccaadaccbcabbbbccacabddabbdccbbaacdbaddbacccccdcdadbaabdcdadbbbcbbdbadcacbdadabaacadbbbddbaaabaadcbaadabcadcbcbcaacddccabdaaaccacacaddacbcbcbbcdadbabcabaddcddacbdabcdbaddccacccdbcdddbacdbaacdbbbbaabcdbcbbccaabcdbdbcabdccdcddaccbbabacaaaccaadbaabcbbccaacadddcaaadcaadbaabddcbaddbdcccabdabcadbccacbdaaadababcdcaccbadddddcbcadaddcbcccabdabcaaadddacdbabacdddbaabbbacdcccabcdadbbcaabbcddabcbbadbadaacccbddccbbaabdaaacaaacacbdcbcdcdccbdaadbdababcbadaabccdcdbbabcddacbbddbadbdabacadcacacbadacabadcdbaaaaaadddcdbddcaaaacacbdcbcccbbdcbaddabbdbddadacdacdacacbbadcdcbbcadacbadaadcdcdcdbdcdccccaacadbcacdbaddbddbbbcaadbcddbabcddbaddcadabbcaddabababccbadaabccacbacddcacccdbdbcbddcadaddcabcdddaacbbbcdddabddbabbcbcababcbcdccacddcddadddbacbdacacdaccaabccdddbcbbabbddcbccbbaadadaaccbdaabddddcbbababababbdcdcddaadcddcbcaabbdaadbdaddcadcbdaadabcdbdacbacdacdaadbcdcaddaacabbabbbacacadbdabbdbcbbacdbaaccdddacacacabbcabdddbcdbbdaabaabcacbaaccbbbbddcaabcdbaacaabbddcbbacacabcadadccdaddcbdbcddcccdabbbbabcddddbdbadabcdcccabaacbbcbcabbcdbcbbbbacdbabcaaacddbbdbaacadccababcccddcaddbdbcdbcbbaaddccccdadccadabaacdccccdabadaabdbcbcdccbbdccdaabcbddcacadabbccadacbdaaabcadbccbbdcdbbdccbbcabcbadabadbdccdcccabcdbaddbbabdcaddcccacccacaabdbbdbbcdadbddcddadddcbbbdadabcabbcdcccbbccadbccaaadaddcabdcdcdbdcacbbcacddadddcabadabbcbabbaccdaccbbbdbbdaaacdbddcaddbdcbdadcbccdccadbabccaddbabadadbdaaccdacbadacacacdaddcccbcbdaaababaddcbbbbcdacbdcacbdcdddcdbcbcaabbcadddbadbaadcadbaccbcdabcccabddddaacccdacddaabddbdaccaaaaacbbdbadadcbdbdbababddaaacaaabdcbdacdaccabdccaaacbcbcdadbaacbcaaababdddcdadccbacccccbbddbdcbdbcdaddddbbaacbbcacadcaccdcbabcdbaddddacbacbdadcacbbdcadddacbacbbccaadcdaddccccdbccdbbbccbbaaddacbbbdcddcaccccdddabdbabbbdcdaacaddcaadcdaccaddccdadcdcbddacdcbbcbcbbdbbacadacabdbabbcdcdadcbadcaadcdabadcdcbadaacbddabbbdcbbcccdacbbcbabbcdaaccbcbacaddbaddbbbabddaaabcbabcdccabcbddabcbadbbabdbacababadddbadbaddaabdadcacddadcbcddaadcabacacacdccdcbabccdbdcbbacaaabbccdbbdaccbddddcaacaaadbcbddbddbbacbddabdcbcabccdabbbacdbcaddabdadbbdbdcccdabcbcdccdccabadaababcbcdcaabaabbbcdcbdbdacaaabdcaccacaacdbdcdadcaccaacddadaadbaaadbbdcdcabacdddaaabccdabbbdbadabccabccacbccbcadabccdbcdcbabbdbdacbcabcacbbbddaacccbcdcdbaddbbdbaababbbcdcabbdadabddcacbbaaccdaddbdbabcdaabacabddbdadcbdcccbbacadaadbddccbbbbdaaddabbcaabadcacbbbcaddccabddacccdabcabadcbcababbbdccbdaabbcabbbdccdddabcbaabaaadbcddbbdccbcabcddcabadddbbadbcdabbcbcdccdcbabbcbbdccbdcccbbabadcdcdaadccddbbddcdbadcdaabdabbbbddbbccccabacacdcbabacdbabacccddcabcdcdadbdaacbbcadabcbbbbdcbabadadadaaaccbaaddcaadcaaacacdcabbddcbcacaacdbaddcbadbabddadddcaadbccadbdadddcccadabacbdcabacbdcdadcbdacbcbabdcabcdaabddbdaadabdcabbddbabdddaccdbcddcdaadcbddbddbdbadbddbdcbdbbadbdadbddddaddcbcaccbdddcaabaaddaddadcbbacdcadbdcbdaddabbbdaddbbcbddcddddbdbbccdbcddcdadcdddcbbacbacdddbabddddaacdbccdadaabdcccadabdbbcbcbaaaccbccacdabaadbbbcdbdacbaadcbbbbcadbdcabcadcadbacdcacbaddcddbcbacbbbbabdcacadadaacbdddabaaddddddacdcbddabdddccdbddbadaddacbcbccdddbdcddbbacbbabaaccdcdcaadcadacbdddabccdbacaccddcbacbbdbbdcbcacddbabddabbabcdbcaaacbaccaddbcbadcddbcdbdaccbbbcddaabaadbaacdadcccadbdbbabcbcccadcdaaddaacdacacddbdcccdbaabaadadbdccdddccbcccacabbccbacacbdbcabdbbbdbbdbccaaccbccdacabcccadcacccbdcbcbacaadbbabccddcbcdaaddaccbbdcdaadcabcadcdbbbaccccbdbccdbbbcccbdddbaddcbabcdaadbbddbccddbcbddcadbadbbbddcadccccbbddccddccbbbcdaabacbdbacdbabbbaadacbdcbdadadbddacccbcddcdcccacbbacacbdadcbabaabaaaabbcbcaadcacbbcaccbdcbdaabcdccdccabcccdbdcdbaaddbaaaccdccddbcddccaccbccdccccbdcadcabdacbaadadbbadccbadbbbaddbaddcacddabadbabacabbcbddddcbbcbccdaabaddbaaadcbdccbabadcadbcadcdbaacdbbbcaccdcbcdcbbbadcbacddadbdbcddaaccdddacaaddccacabbcbaaccdadcdbbcacacacaacbbdcdcbcbbcbaadbbdbcaabccbcdaacdaabdbbacbcdcaccbacdaacbbabbadddaadaadcdadcdcacdcbccddaadbbccdbdbbccbdccddbdaaacdbacbddcddddbbdddabdcccdbdbaadcbacdaddbcbcbbaddaddacdacabbdcaddbdcccddcdbacdcdbdababbdacaaaabcabcacacbbdcccdbdcdaddadcabdddadcdaddacbabdbbacdacdccdcccdbbdcbcdaaddcdaadbadbdbacdadbbbdbacacacbdbbadbdaddacabbcbccdadcdadcddbbabbdcbcabaabdcacbbcccacdcddaababbacdaaabddddcacdbabddabbabaacaabaddddcccdbcdaabdbaacaabdbbcbcaadabbdaaaaadcaccbcbadabbbadcacdaacbacbbdbadbacabaccdacdccacaababccdbbbaccabddadbdabdbaaddccabbdbcbcccaacabbccacdcadcadbbbcbcdcbcacbadababcacabaddaabbbbbabacadbaadbbdbaaadccdbdbcbacdcdaaaacdccdcbddacdcdbabbabcaaaaaaadbdbdddcbcdacaacaccbcacbbbacabdbdcbbaacdbcdddbdaacababaccdbdcabbacadabcbbddbccdddbdabbbbdbbbbdccabdbbcddddddaaaccabcbcdbadbdcbdaabdaaaababacabdbbabacaabcbbadcbacadccbcdbccccdddbccbadccacccdbdabbacbdacdbacbbacdbbbbbdcdcdbdaddacccdcbbdaabdbaadbdabddbcadcadcaaaadadbccacdbccbabdddbccbbcadbbdaddadbdadbbbbaabdaddddcdccdcbcdaabdcccddcacbcddaaaabbdccccddbabaabbccadcbbacddbcbbcaadccbadcbbacddaaadbababaabdbddadbaaddaddbdbcbdaadbabadaadccdbbbadaabadadcabadcabcdaddabdcdddacababccacbcbcdcbcbddcabbccdbcdcbccadaaacaababcbccdaaabdabbaacdbababcbbcccadccdcbbcbaaaaddbddaccbddddadaababbdabcbddcdcacbccccdbacbadbbacbbabddbdcbccbabbcabcddabdabcbccbbacbbdaabccbaccdbdcbcdccdacaaddcaddccdaabadccbbacaaaaccbbdcbdaccccacdccbaccaccccbabbbbddddccacddacbcbcabaddbdbbbacbdbabaaacadbaabdbabdcbdbbbaacdabccabaaaaddddccbddacbabdcbabbccabbdaaacbabdddbcccacaacaacdcddccacbdcdbbbbadadcbdcbdbbaabbbcdbabbbcacbbababcabcaabccccdadaddbcacbaabbdcadbabbccddcdbccddbdbacddaabcbabcaccdbadaadcdbbbcdddaadcaadddacdbacdcadddaddddcacccbddadabddccbdbbcdbbcbcabccababdcaccadbabcdaccdcaaadaaddbbcddacdcddccdcbbdbababcbaacdabdcccdaaacdbbacacddbaccabaabbdcadacbabbdbadddddcbcadaabbbadbdadbbdddbcbdcdabcddcabaccbcadbddabdabbddcadaaccbabbbcbbdccaadbddbdadddbcdcdcbcdccdddbacbaaccabaddcdddcbbcacddadddadbdaccbdcdbacbcaadddcdddbaaccbaadbbcbabcaddccbccaccbabbdbbbdbbbbadbdbacbcadcbcbbdcdaddddddcadbcbbddaaccccdbcddcdbddcdcbcbaabcbcdcadbaacbdbcadaacccaababdadaadbacabbddaacbaadcddbbabbaaabccbcbbcbdbcadddbbcddcdbaaddcdcadcbcaaccbcaabdbaccadddccaacbabbbdcbcbcabbbabdbbcaccbaaddadabcaddbabddcbacbadccbbabccbabcacadabcacaddbbaabcbdacbdbbccdaacdcbbaadadadccadcddddbbcadbcacdbacbbbcbadccadadaaadbdaaabbdcaccdaacbabbdabcacabdcbdcbcaddcaabdcacabababaaadadddcdbdaabdaabbcdcdaaddbbbaaccdcbabbdadabcbbdbccadbcbcbcbddbddabadcbbbcbbbbbcdacbbaabcdcbcadbabbbdbdadcaabaddcbbddcbdbddddddadcdabccdbabbcdbabdbbcaaddbcdaabbbbddcadaaaccaddcbccdacddaacbaabcbdcaddadddbdcabbacdcacacabddacaabbadacdaabbdaaaddbcccadabbbcccdcaacdabdbaabbdcbcaacbdbadaccbbaccbcdbaadbdbcccbbacbcbaacbaccdcdcbdccdaaabacdcddaabbdadddcbbcddbadcbbdabbdccdacccabcdbddcdacdcddaddadccddcbaddccabcaddabaacaaddcaaddcdcbbbbdabbddbcaaaccdccdacbdbbbbabaacacaaabaddadabaccddabcbccbbdcdcaaccaaabaaddbbcdcacdcbaadcaacabccacbcbadcdaaabcaaccbddcdabbddddbaadcabdbcdaaaacdabbbbaacdadbabcbddcaccdccaaacacddadbcdabaddabdbcdabbbdbaccabcddaaaacccaddbdbbcbabccdbacacabbaadbadbdccdbdcdbddbabcddbbccaacbabccbdbabbdacddbbcdcbdabcccbbdaccbdbabacdbcdadbaadcbdaddaacccbabcbdacbccdcdaadddbbbaababcaccbbcdacddcbabacbbcadbcddcdcadadcadbbcdcbaccacbdcacacbdadcdacadcccabadbdacdaccacdbbabbcdbdbdabbdbabcaadbbaabddaadaadccbdbdddadbdcadacbcadabcdcbdabbcbddcacdbdaddaaadaabdbddaccacaaaaccabadbcbcabaddadbcdadaadcaddacbdaddcaadbdccdbaaadbccacaddcdbbbacbccdbbaaaccccdacdaabbbdddcbbcaabaabddcacaddacddcabbbdcadcabbccdcadabdadaadccdcbabbabdbaacacbdddbcccaabadacdcababbbbbaacbaccdbcdbcaaabccdababacbaddbaaabdacdbdadbacdcccdbbbbdcdccbabacdbaddaabcbdacdabccdacdbccacbbcaaacdbdacbcbabbaddccaddccddbaddaaadaaccaabbaddaaacdbbdabacdbddbbbbcbbbcdbdccbbbadabcdbdcbcbbcbbbbabbcbddaddcdcdbadaadabadbbadbdbaaaaacdcaacddbaacbdcabddbcdabcddcbccbdbacbcbcbcacabbaadbadabdaaddbabcadbcaaddcdcddbccdbbcadbdccccbaaaacdaddbabdcbdaabadabdcddcddcbbacadcddcaccdbdadccbcccddcdbcbabbbbabaadacaddabbdadddbbcdabdadcdbaabbdddacabbcadddddcdaaadcddbbccbbbdaabbccdcddddaccdbbaabdbbcadaadbbabbdcbdddbccbddcbbbdacbdbbcdbacdccaaabacddcdacbaadacadbccccdcbbababccddabdccdbbcabaadcbacbadbcababdcbcdcccacaaaccbccdccadccbbbbcbcdbaadbdddbdbbcbbccbcbccccccabcbbdcddadcacbddcccccddbcccaadaacadcccaabaaacbdadbdbcdbbcbbaacbacccbbacaabcbcdcddcbacacbccbcddddabdddddcccacddcdbabacdbdabaabaddbadbbabdbcccccdaddabadcbbbbacdaddcdccbbaddabdabccadabadacddbabbadbddcdcabcdaccababbcdcdbcdbbabdaddaaabaddbcdcbadddddadbbaadcccbcdccbabddcdaacdadcdcdccdddaaabbabcbbbacbdbbacacbbdcbaacbdabdcbcbcdccabdbaccaccadacdadabdbdccbccaddcadcabbadcddbdabdbaccccdbcacbbbdbdacbdbbbccdcbbddddcbacbdbcabdccbabdbbbbcadbdbacdcdacadbcdaacdcccaddacbcccbcbcdcbbcdddaccadadaabacdacadcdadadcccbddaabacdacacdbabcbbbaabccabacbddacacbdbdacddbdacbdabbdcacbbcadcddbccdadaccdbbcdbaaddaccabbbccaaacbadaabacccdcbaabaddbdbdadccbcaabacdacdadbadaadbacbcdcbcbdabcdbbdcaddcabacaacdcbcbccdaaccbdadaccacaabadbaaaddcddbdabcabdbabdbcadbcaddabdadaccbcaddadbbdaacacbcdccbbbcbdccdaaabccbaadabddcbadaadddcbaccaabbbcdbacadccbabdcbbdcaadbccccaacbbdccdadcaaabaacbbdaadddabccdaadcadaabbcdbcaccaadddbbccaddcbbcddaaacdbabbabdaaccbcaaabccaccbccdbdccdabbcbbddaccdaccdaaacdabbcabaccadccccaababccbacbaacdacdccbdcdcdcdbacbcdbcacadcccaadcadbcbdcaadaddddcbdaddaacdccabbcddcadbcbbddcbdadcabaadcdbdadabcaaccabcbbbabdaabababcdbccdbbadbdcbcccdacdbbabbdddabdddcbddddcccbbadcacadcdbcbbccddbacdbddabdcbbadacacddabddaddbbbdccbbddabcadbcbddcdaadbbcbdbbcbabdcbacdcbacbcadaddbbbbadbacdcddadaabacaadacdaaddbbcdbcabdccaadcccabcdbbabdcdaadaaadbdbbbcaaacccbabdbadbacbdcddbbcdddbcccdbcccddaacaabacadcadaaccbcdbcdacabcddadddbcadbbbbaccdcdcadbaaadcaacaaabbdccdabccbaddcdcdcbdbaaddcbacbbabcabadacbadcdbdddcddcbdadcdaacabbacdabbbbdabadddabbdaabdbddbbcdaacccaaccddcbaadcdccddbcbdbcdcbabaabacdaadbddaacaacadbbccbacdcbcbbdccbcaacbacacbadbaabacdbbccbabbaddacabcdaaaccadddbaddbadaddcacddaadcaabbcdcdabaccdccbacaadbdacacbabbadcabcabdacbcddbacabbbdaabcbbcabaadddacaacdcadcdcbbcaaaccbcacdacdcccabcccdbcbbabdbcacbcdbccaacaddbbcbacbcaaabadbabaabbbbbccbbddcadacacddaaabaddbbcdbbdabcddcddbdbaccdbbaabacabcdcacccaadccdbbcbbaaadadaddacccbacbbcddcdadcdaccadabcdadcbddcdadcaaaacbcdaccddbcbbddcdbacadbbadadcdbccddabbdaddcdaacdbcacbcdbacabbcbdacbcccdacddcddbbadddaabddddaccdaadbbabcbbacabcdcdbbacbbbdbdcbaabdcbbbdaadbcaddcbdadaddcbabbbcdcbddbcdacccadcadbcdcbddaddaadbdadabcdcbaccdccbdccbcccbcbcbabbdacbdcddcbaadcddacdbcdbbababcadabacacddacacdbcacaabbdadadbaacbcbdcacbbcaacdddbdcdacdbabbacccdcdcdaaaabdcbaadccccabdaaccbcdbcadcaccdaaabdabacccdbadccdccabadabdccbadadbbbaccdcabcbbbcbadcdbaabadcbdacdacdcccbbcbaaaaaccddbbadddbdabbddcddadcacdaaabbbbadbbadbdacacbbbbdccaadacddbbbddbbbaabddbaccabacabdcacbdddbddbdcdbbccaddbdcbdabccaccacdcddaabbcddabcaddddcdbbabcbbbadddcdacbbaccccbcdcdbdbdaabdbbcdccabbdacabccdabaaabdaadadbdbbaaacbdaddcadccacbbbcababddccdbbdddcdbcdcdadbabdccacbcdcbdcdcbdacbdabdaacdddbaacabbcdadcdcadcdcddcbdabccbccddccccbdcabcddbcdbdddcaddccccbadbdabccdaabddbbdbacbaababaadacbcabbcdbacabbbbadadbbcbdabcaabcbabdbbddadaaaacadadadcdccccbcdccaabdbcabdadbcbadccdadaddacabdadddcbadaccbcdabadaadaaaaddcabdbacaacccddacddcadaadabddddcdbbbdbaabbcdbcbacccccadbaaccbcabcacaccbaccabdbdbbacdbbdccaadcaacaccddabacaaccacacccabdadbcccbcbbdcbadcadbdbacbbbbccadcaccabbbabbaddbadabccbbaabbcdabbdbbddadabbcddbacddbbaabadbbbbadaaabadcaabacaadbbdabadaabdaabcddabbdddbacaabcdadcaaaacbaabbddddcdcbacbadbabbacbbcbdddbacbdcdbbaaddbdabdcbdadaabababcddccdddacacdaacacdbbdabaccadaadcbaacabddccccccbabdccacacbdcdcbcadbcddbbbdcbaccbbababbbadcdaabcbdcbcabbcdbdcdaddccdcdcdabcbbdadacdcabcbbdccabcabbbcaddadbaabadbddddadbadcddbdccbddddabaccaaaadbddaccadccbaaddbbcbacadababbdacadbaaabcadbdcaaacbcdcdbabdddbbdaabaccbcbddbccadcacbdcadcdbcaccdcdddddacdaabcabcbbabaaddbadabdcadbccdaadabcadacddbccabbcbdaacdbbcbdaaddbcaaccbaabdbdcadcaddcbbdcdcbdacbdaabcbdaadaabacdabacadabacabadbdcbaccdbdccccddaddadddcdacbaccaccdbbabbadcadcadccacdcacbdbdbcdcbadbdacacdbddaacadcdacbdcbccdbdbadbdbdccdcdbaabddbdbacdadacdaccbdbacacadabbbccbabdcdcabbadcabadacbcabdabddacaaabddbcbbabacadbdaadabbdbaacddddcbbbbbcbbcbdaacddacabdccaabcaccddadbdaddadbbcaddddccbcdcbdddbacbdcbcbdddaddddadadbbcccdcdbdcacbcdccdcbbbbdadabcaadcacbcdaaabbcabbacbcbddddcdbcdaaadccccdcaaadabdcbadacabbadcaaaccddcbcdbdacadcbaccabbcdbaaddbbddbdccccabdbaadbcdddaaadadcbdaaddabcbbbcbbabadbcbdccadaabadacdddcaabdcadaacbdcadaacaddccbadadbcbadbbcaaacccbdcadbaaddbbbaabacabadaccbcbcbddcacccbddcabdbcabaccbaabbaaadcabdcaccdbcadbabdbaaabccbddadabaaadbdcbdaddcdabacabdbdbbccdacbbadcaacdbcaabdadadaadaabcaaccbccabaacddabcdabcabdaadabcacaccdacbcaadacbabbcdccbbcbcdcbbcbcddadbababaaccbbcaabbbabbdbbcdacdbbcbdabcccbddbddabbabccdaaabbdcaaacdababcdddadccaadcadbbcbdaabcacacccbcddcbdbacacacaacbadaaaaadbcacdaacdbdaaacccbcbdadcbbabdacaaaabaddadcbbbccbbaabcbcbcdabcdbbbdaddadaddbbcacbdaacbccbadadddcdbcbdccdcddcbcbbdbbcdbdddacbbacabaaccbaaadaabcddbccddadadbdcabccaabcabdbcdccddbdaabdbdaadbbcbdcccabaabdadaabddcabbadbbdbbacdcaccccdcbcccbdabaabbbcabbcccaaccdbdccddaaaddbadbacaccacaabcddaddacbdccacaaddacaccbbaaadadbbdbaacbbacdaddbddddaddcaaaababaadcdcddadbacbbdaaacbcdddadbadaacbcdbbcadcdaacdbdaadadacadbcabacbcaccabcbaabbcdbcbaadcadbbbcabbacdcdabbccccdddbababbacacdbaaddcdabdbaaacaacacbacabdcbacdbbcababcbddbbcbddbcabddbaaaacdbddbdcbdcacabbcbccddadadbdadacbdabbbcabbddbadbcaabcdbacacddddadaacaaabcbbabbbcbbcbcaaacaabbabbacabcbddcbdbacabadcacccdaccbabaaabddaadaacadadaadbacdddcaccdaacdadddddbaacbabcaccdabdaaddabaabbbcabddacddbdadbdcdcddbdcdccaddacadcacbabddddcdbdccacdbbabcdcaccddacbdaadaabdaaabddccbcccadacccabcbdbcdddbddbaabadcacccbdcdabaabbddaacbadbadddddddbcabcbcbabacbccaaaaabbaadcbbcdcdacaacbadccadbcdbbabadabadabbaaabcccabdcddcbaddcbdcbdcabcabadaaccaadaabddabaccaadbbdbabbbacadbdbcccbaacbdaaadcbbacaccbbbcccabdaabcbbcaadacbcbaadccacaccdbccacdaadaadccaccdaabccbdbdbcccdcddbcbcabddcabadbccbbbbdbdaadaddcbacdacbaaabbbacbaccadacbbdddcbcdcbadbccdccdcacdddacaddaadcccccddcccabbaadbaaaddbdbbcaadbaadaadaacdbacacdccdaabadbbcdddbbbaacbadcbcdcdadbcddbccdabacaabadacbcaccadcbddabadaabdddacdbbdacddccccaccddcbcdddabcdcdacaadccabcdbaacdadadcdbbbacbccaaaaacbbdccabcbadacdaabbaabacccbaacdbcdaddccbdcbaddcaadadbddccabbbbaacbbddbddbbadcdaabccbbdaddddabbabdcbabddacadcdbbcbbaabcbbcccbacbaabcaaaaaccacdcdbdcadacccccbbdbccbadabbdabdababcddabdcdabcadcbdaaddddabddddabcbcddcbaaccadcdbbddbccdbddaabdbddabadacbcddbdaadcddabcbaaddbcddcccdddccacadadbdcbbacccccadaccdaddbcbbbabddaddccabdaacbcaaadbbbdcdaacbcbacbcdbacaabbcbdcbabacabccbacddbbcdbdaadddbbadbaacddcbbaacbbabdbdadbacbbaacabbaccabdacbaddabbccdccccccbdddbacbaacdcaacbcbbcadbdaaccaddabdcccddaabadacacdbdcbbcbbccbababddbdadbbbdbcaabbbdaddcddaadacdcdbdbcdbdadabdaadcdcadbcabcdbaaabdcaddcbbaccdacbbdbacadadcbabdacacccacadccabdcdadcbbcadadbcdcadbccbbccbbbcccbddccdccabaccabbdabbbddabdadddadcdddbbcddacdbabdbcaabbababacaaabcbdbdacbccdbadacbbdabddbbbaaddbaccaddddcdabaabcccbcdaabdcdaccaaadacabbbcacabadaabcbcbcccadacaadbacdbbccccbdddddcbaadcabadcccbbdbacbdcdbababcaaccadbcdabdacbacdacaaaadcccadbbaabbdddcdbcaaabbdcdadcadbbbadcddaadabcbbbadabcbadadbdacdbcbacadbdbcaacacabcaaabdccadaabacabcabdcbdbbdcccaabdccbadddcabddaccbadadbdcdabaabbdbddabbccbaccaabcbabdadcdbacacaabbbcaddcaadcbbbdacabcbbbababdadabcaddbabbacdbcbdcdaacddabccaadbbdcbccaccccdbdaadbccdabcaaaddbccbbbbdccdcbbdacaadcdbdbcadbbcabbddaddabbbcaddbcddcaccbddcdcbadacdaddbbbcaaabcddabaabbbbdaabcabacabaaadaddddaabbbaacdcddddadcbdcbccacaaacaddbacbabbabcdbbccbcdbbcdbcbcacbabddbcdbabddcbcabbacabdbdacabdcbacbbacaddcddcbdbcaabaddadbdbbadcadcabaadcbcaabacdcddacabadabcdbbabdbdcdcbcaccccacacccccbcbdccccbdbadadcbdacdacbadccdcbbdaaccaabbcddbcacbccdabbbadcbdccaaaaddcbbdaaabaddbbbcbbdbcbbbdabdbbcbbdaccacccdccdbbcaadabadcadbbabcbaacdbacdccbdadccbadbddbbdbdcddddbbacabacdabcdcabdccacbadccacabaacacddabdaaaccdcbdcaccbabcccccaabcacbcdaabdccdcbbadadbcdadbabbbbcaabbcdbbacaccbdccaabcbccdcabbdaacababbcabcdbdabccadbdccaadabdacbccccaddbbcacdcdbabaadbcaadaccbdcdaddddbbcbaaacabdbcdbcbbcddbcaaacdababdcbaacbcbbbcaaaddbbbcbabbcacbcbaacccccbdadabdcddccddcbdbcbdbacbaaadbbbdbbddcdbaddcccdacadddbbcdbbcddbbcaccbadcdaaacbbcbaacadacdbcaaddbcdbdcaccabcbdadddcddddcbccbbbdbabdcadabdbdbbadbaccaddddcdabddadaadbaaccbbbaadccdacdbabdcbaababaaacacdbbacadacabcacbbcabdddabccccdbcbdacbcabdccbdbdbbbbadbabddccaaccadcacabbdaacabbacbcdaacbddbcabbdaccddbabaddcadbcdddccdaacdabaacacbbdacbacdbcabcadabbbdcadaddbcdacacaddbdabcbaaddbcbdaccddcdbaaaccbbbaddcabacaacdbbcccadcddaaccdcbaaadbddaaccddcdddaadbcdaadabdaacacdcdbcbbbcbacaacdacdcaccddabbbdbbdbbcbbcacbdbcabbcdaddababccdcdbdbddcbaaacbbcacccadaccdacdddadbbdddabcadbcdbcbacacccaadbcacaddcbcacbdababacbbbddcbaccbbdccacccdadadcbadaabaabbdacaaabccabdacdbaabdcacaaaaacccdadcdadcccdcdbadacacabdccdcadbddbbcabacbbdbaadcbbddcddaaabbbdbbcdddbacbcaabdcdccacbbaacddacbdbbdaacddbdcabdddcdbbbcdcabdbababdcabddddcbcdacdccdaaccbbabadcdbacbaadcbcdbadcccbbcaacadddbbccddbdbaccadcaaaabddbdcdbaccaabbbabbdddcabdbccccadcdabcbdbbcbdcaabaabcbccadbdcccaaadacbcacadabbdacababdcccbcaabadccddbccacbcabdbbacadacadbcbddbabbabbacddbccccaddbcdcadbddabcbdbadddbcdcbbaaabbaddddaccabccaccaadddabcbacbcdabbaacadcbabdbdddcbbacccbdddddacabacabbbdbcadcabccbdaaccccacbcabbcdaacabaddaccddbdcdbccddcbbccbcabdcaadbbcdbabacaadabcdbaccdabcdccdabcdaddcbadcddbbbadadbcabdcdaacdbabddcbacbcaccbacdddddbdcdacdadbccbacbaaacbbbddbbbaabcaddcaacabaadcaabddadbaddbddcbdbbcbcbaabbaadadaabbddbbdbccdcddddcbabbbbaabbcdbcdbcaababbdddadbdbabbdbadaaabacbacacbccbddaccadbababdcadcbbabbbccccbbddccdbccdcbacaaadabccadcacbdbadcdbdaadddcacabbcbcadabadacaabbdcacccbbbadaddbdaabbbbddaacdcdccbadabccbaaabcdadcbdacbddcdaacadadacdcbbcbbabdbcdacbbdbabcbcddccbcdddccccddcbccddacbadcbadabcbdddbcdbdadcaddadaaadddaaaabdccccacdddddacccddaaacaddacccadddcacdcabdadcdabcadbdadbdadddbcdaadadaadacdacaccabcadbdbacbddaddaadaadaccadbaaabbccdacdacbbaccbabacbdbcbdaaabdadccdcddabdcabadaabaadbcdbbabbbccacacaccacbcbbddbdbcacccbddcacaadcbabcadbdadadbcddcaccabccbadcbdbaaddabcbcdbdcbbadbabbdcddadbdaddbabbdabbcaddaabcddbabdbbaadcbdaccbbaadadabdcbadbbdacbcdbababcbbdbcacadbdccccbadcdabbdcacdaccbccdccdaddabbcabccbcdbabbcaccbaaccbaababcbadacaaacdcdbddcaaddcbbabddcdccdcdddbdaadcaaccdbadbcbdbbbadbabbdccaabcdcdabdddabddbabbacbadcaaddddccccccdacccdddbcaddcbaaccadcdaacaadddadaaddabcdbddcbacabcabbdbdcaaadccaaaaaacbccccccbdbcdabdcbaaaabccaadababbdbcacaadcaabcdadadddaabbdddcacdcabccdbcbabbdabbdaababcbbcadadaabbaadcabdaabbdadcacabacccbaacbbdcabdccdacacccabacbdbbcdbadadbdaadcaabcbdddaccabaaaccacaabcdabcbdbaacbaaaccadbdaaabdacaaadaaabcbadcadaacbbbdddabbabccddabbccabbacddbbddbbccaddbbddcadcadabdababcaadacdbdbdaaaddacdabbaacbdcdbddaaaaacacaccadbcdabdabcaabadbcccbbaddbdadabaababaaadddbdcabbcbdbcaddacdddddacdacaabbdcbcabdcbabbaacccbdadddccbadacadabaddaabcababaaadbdadbabdcacbdcbaadaadabbbadbbacdbbcacaadccdcccbdaabddacbcdaabadbbdacbabadbaaccdbadaabbadbdcadcbbddbacabdbbadadcabddccbbbabdbccababcaccbbbdacaaacbcbacbbccacacbccaabacbabccbbdbcacbacccccccdadabcbddbbddbcdbbccbbacadbabbaaddabcadbccbaaccdcbacbbcbdcdbccbdbbbabbdbccdadbaddcbdbdabcbbadcbdcccacdabddddddbcdccabaaaadacdaabacadcccdaaadbadbbacabcaaaacbbcdcdbdbacddccbadcdaadabdcdbccddbbcdbbccdaddbacbcdbcbaccdaadbcdadbbbcccbdbabdabdacccbdbbbaaddbccdcbabdbaaddabccbbacdbdccccdcaddadcaaddcdadbbaccbcbdbcaacddbbcacdbcacacdcdbbcdacbdcbcdadaaaabbbdadbbaccdadbcaaaccdcdabacadccdbbcaddabcbdcccbabaadbddabcddcdcdcccdddbbcaadddaabbdccdabddacddcabbbabdaccadcadcbdbabcdbdcbccbabacacdabcccabccccbabcaaddbcaaabadbbcbcbcacbcbdadadaabccbcbadcddccababcbacccacabdbcbccadbdcbcbadcaacadbdaacddcbdbaddcbdccacdddabdbaddbccdddcbdaccbcadaadcdadaaaadbcabdabbddaddddbdaddbbdbbabbacbdaadddbdadbbbbcbcacaaabbdbdddcccadccbcadcdbcbbbaabbdabccaddddddccdcdccadcadbdcaddbcdaacdbdbbcdacdddacbcbbaabbdadbdbacddbbdbdaadabddccdbdadcabacccbbbcbaaddcdcddcccaaccdcbddcbaacdbddacadacacbcbaccccbdadabdabcaacccacbaccdccddbdcabbcccccbadbdaaaadacbddadccbadcbddadbbcbadddcaacadbddcbbcabdacccdddddbdacdacdccbaddacccbcbddadadaadabcbacdbcdcbdabddadcdacadacdacdbbcadccbacbcaabdaaaabdbdcbcbccdcadcbaccdcadaaacdaadbcdcdabbbacbcddcdaaabcadcbbdadcaabbdddcdaabdcaacbcdcbcbdbadbdbadddcadadbdbbcdbcbbcdabdadacbaccdabbbaacadabdddacbdbdaadcaabbbbdcacbbbadddcccdabadddaccdabacaabcacacadbdbddbadbbbbcbcbabcbbccccaadbacababcbcabbaccbacacccabbdbaadbadcacbbddcacdbbbccabccdadabdaaabcacdacadddaadbcaadacacbabdaaccadababdadbabdccdbbcabbbdbccccdddaabcabacbaabddaaccbccbdabcccaacccddccdcabacdabbddccabbacdcacddccdcadabadbbbbdbcadadcddbbaadaccbdbdacddbacbcdacdcdabdbccabddaadbabdcacaacbbdcaddddddcaaadcbddabbcdbbccbaadadbbbcacbcabacddbcbcaadbbdcdccccbacababdcabcaadbdaccbdbadacbabcaaddbccdbaacdabbddacadddbccdcaacababbbcababcbdccbdbadaaabcdabaaaaddbcaabbdcccdadadacdccacddbbaddcabbdcdbdacacbdaadababcbddbdabdaaadabdacdcdadacbdabcadbbdacdaacababddacdadcdbbbcdddacadbdadbcbddbababcbcbcbbaaccaacbabdcdcbccadcdabdbacbddbccbacbadddcbacdadbcddaccbcdccabaccabcdbbbaaccaddbdbdddacccdddaaabbadbdcddaaadabdaaacbbcbbddcdabaabdddddbcccbacdaabacbcbbcddcbadccbddbacbddaccacbcbcccabacdadacaacbacbcbdcdddacadcdbcacddcbdbbbabdbdaadbdbbdbacadadadcadacbddbaadcdabbcaddddaccbdcbacabbbcbcbbcddbdbcbbbacbbaacdbdbadbbbbcbdcadcddadacdcbbccdcabaaacaadaaaacabdbbccdbbaadccdcdddbcbccabdacacccacaacccbdbdaddcdcbccbaddacbddcbdacadbddabbccbdcaaabadbcadadccaaadaadacdcdcbdaccddcabbcbdabacdacddabddaaccacdddcbbddbcbcdcccbcdcabcdbdaddadbccdddbddbddacbdcdbcdaccabdcaaabdbdaaddddabbbbcacdbdbdbdddaaaaadadbdddbdcdccdcbbcaacdaaddaadcaabdbcaacadacadddcdcbbbcdcbabdcdcdabdabbadaddcbbdabaacdacabdabaddbccbbadaaadadacabbcaaaaccdddcdbcccbdcacaacdcacbdaddddbcaccdcdaacdbaabbdaadaadbbccaccabdcdadbcbadcadaacabcacbbbcaacaaacddbdbccbbacbdcabdbcdacdaaacbbaaadcdaddbdadccdaadaacbcacdbccdabdbcadbdcddaaadbddaaccdcdcaaddabbdbdaadaacdccdcadbdabbdcdacabddbadbdcadddbddccadcaccdabadcbadbaadaaadbcaabcbdbcbcacbbcbbbdbbcaaabdbbdabcacbacbcaaabbcbbbaccbcacdabbdaaaadaadbcabacdbddcccbabdaccbaababdcbccabdaccdbddcaccabdabdadcbcbcacaadcdaccdcdacbaadbabbcabbbabaacbbadcadcdbbcdbcddaccddaacdbbdbbcabdbccbbbdbdadacccddcbdacaadbbcbdabcdcacdadbcaabbcdcdcaddddddcdbcbacaccbcbcadacbdbacdddbcbbcabbacaabccdadccbdaabacbdddadbdddbcccbdbdbbdddaddcccbdcabdcbbcbacaacbcbbddbaadaadaadbdacacadaccabbcabaadbbcbababcdadbaaadacaccabcaddccbaadabddddbdabccaaadbcacccadbbadaaadbddbabccbcdcdadddabbabcdbcbdabcbcbdaaccccbddadccbcdabadccddcbdbcdbdbbaadaccbcabddabacbdbbddbddcacadbdbbbaadddcdbaabccaaadddcbaddbdaccddbaabcdadbdbbcdcccccbaaaabcbcabaacccccadcddddbcddbcaddadcbcdbabddbbbaababbabdcbcdccabbccadccacdbcbadadbbaabbcabcaabacadadddddcbacabacbbabbdbbdccaabdbbdccacdaccbddbbccacccbddadbaaddadcadcccbaddbacdbabbbdcabdaadcbbadacdcccddaccdccdddbddacbaddbcccadcdcadbaabacbbadcbdabbcdcabcabccbdccbddaaadaccdccadacdbbbddabaabdcdddacaadadbcbdadccaddddacdacbcbabcaabbadbacbbcdaadadcbcdbababdccbbcacaddcbbadbbdcbdbabadabdbdbadaddcabbbbadcbcbaccdabdbdabcbbabbcbdcaaaccbcdadbcbdbaadcaaadcbdcdcbcadaddadacbcdbdadbbbdcdabcbadcdbdabaddddccbcbcbacabddcacbdaadbbdddbddcbdcacaacdbadacadbcaabdcabcbabaacbbcdbbbdbaddabaadadbdbbcaadbbccacbbdaacbccdbdcdbcddbdbabbbaaabbdcadacbdccdbabadabaabcaabdadddbaaddddbacbdababddaabddbcbbdcbabacbbbbbaacddbadcbbbadcacdbbabbaabddbbadadbdcbaccdbabcdccadcbdbcdaaaaacdcddbbdcaabbbcddaccbcbddaadbcaaadabbaaadbcaaabdbaadbbdbdbbacbdcbadadcacdcbadbdababcabdccddcdadadabdbbccdacacadacdbacaaadaccccbaccadbacbaadbbcbddcdaadbbabbabccaaacadccbbadbdadcbdadbaddbacbdabcbdbbdcdcadaabddddbccdcabcadbcbbacbdbdabbcccaadbdcacaaabdacaadccbadbdaacbdcdddbacbdbbdbaddacdddbcdcbadccadbabbdcabbbbcadcddabbddbcdadcccbadcdbacbdadaaabcadbdbadcdbdbbadabdacacbbbaccdccbcdaacbbacbdccbccccabadadcbcccdbadcdacacdbbcadabdaddbdbdaadbababaabaaddcadccaddcbababbdcabdacbcdbcaaacdddbccdababdaadccbadbcccdcaabbadbdcdbccdccbbcdacadbdabbdbdbadbacccbdadaabcaddaddaaccccadbdacccbcaaccdbbadbbcbdabbcabcddcbdccdcadcabbacdbadccacadadbbdbcddaaaaabaaaccdbcdbbcbaadcdacabdcdacddbbbddacddaadbccaddadcbadbddbadadcdaaadaaabadddbcbcdacabcaabddddcbdcadcdadcdbddaadaacbcbcabadccddbaccdcbbdcbadbdcdbaabddabcdccbbbbbccaabdbdaadacccccadbacddddcbbccaddbcdddbcacbcdcaddaccacbbbdbacbbcadbaabdbbcbcbcbadaacdabdabcadcbddbcccacbdcabbdcdddabbdabdcdbaabddabcdaccaabccbcbcacababdcbacabbdcbacaccddabbbcddccbaccbbaddaddcabbdcccdbacddddcbbdccbbaadadadbadaadbabcbaaaccabdbbcabacabbdbbddcacbacbdadaadbbdbdacbbdcdcaddbddccacaabbdcbccaaddbadbacaaacacdcbdbcdcacdcbadcbcbadcadaccbaacabadaccbcabbadccbcccaababcbadbcdbbadabcbdcddbcaddbdacdcbbbbdabcdccaacdbacccbdbabcdcddbbcdaaaabadbcddccbbcdbaacaccabcaabccaaccacbddadbdcacdcacabbcdbaadcdcdbdccdabcbaabaabacbdbbbbcbcdacbdbaddabaabdbabbdbadccbbabcbabcbbdcdbcddadcaacdcdcaddcdcddadcbadacdaddcbbcbbdaabdddccbcdbaddacbbdccdbaddadabbbaabbddbbcbbcbcdddbdcadbbdddbcadbccacdcdbdcddccdaadddabddcbcbaccdabaaabaccbcccabcaacacaddbdbdaddddccccadbbaababdcdacbcaacabbdcacdadbaaabaaaadcddcdcccbddbaaaddaaadcaababbdbcbadaddddbbaadacbbaaaaaccccacadadbadbadbbdbbcdbdababdadddbbabbdcdccdbcbdcdccbdddacdaaabdbddcdadbccacccbcaabdbdbaccaabddbcaddddbdadccaababdbdbcddbbbccadbcbbccadddabacabdbdbbacdccdbbccdddadabaabcbcacaadbdcdbddddcaaaddaddddaddbcbdadbbcdaccbaddccaaacbbacbcadaaddddabddcddacabdddbcabbdaadbdbaddaaccbcbaadabbcbcdcddaacbbacaccaadbcdabadadddaaddcccaaacdacddcccdcbccbaacbdcbbacacdabcbcadcbcbcccddadddacdbbdadccddbbcbbdacddddcbdbdcabbdbcabbdcbbaadddbbacccacaaaadcdabdaccdcbbdddbdacbbcaaccbabbaccddcdccbdaddabadadbdaddcbbacabdbdabaaabaabbcbcaadabbcddbaccaabadabababbdcbbbdbbcabdacbcaccdbbdddddcdaabbcbbdbabdcbdbaacdcabdbccaadbbbabadbcabdaccaaadacdccaacbcbbaccbdcbacddadccabdacbcbcbabacbddabcddacbbccbabbcdcdddacbbbdbcbbdaaddcaddacbcacacbcadacdbdbcbcbadcdacbadaccbbbadbacacabcccadcbcbabdbcbbddcbbcaccbbbcaaacccbcdbcaccbbbacdccddbaadbccdadcccdadadacddccdcbacdccdbaddadbaccddabadbbddcadbbcbbbbaabbdcadccbabcabaadacbcaaadcabbadbadddddcccccbabaaabcccadcddcadbcabacbcddbdddacdbadbbdbbddbaadddaacacacdcbcddddadadcddccccddacbdddbbababbdabddcadccacdaccdcabbabcddbdacaddbdbbaccbabdacbbbddcbbbaaadcddaacaaddcbcdbbacabadcbbacdcdacbcbdbdbacbdbcbabdabaaccadadbacbbccaccbabaaacdabadddbaacdbaccacadbaaacdaaaacbadbdabbacadbcaacdccdbbcdbbcbaabbccdaaaaaacbbadcdbcacdbcadcdbdabddcddddabddccbabccadccabdababddadabbcacbaaddbbcabbbdddbaaddcdbadadccdbadcdadddccdaadabbdcbabbbdcdbadddbdbbbadbccbacbbcabdbbddacdcabcdbbbaacdcccdacadacaddcbdbddaccbcabadbcdbdbadbcacdbdddccbbbbbadacdbbdcbbbddaddcababdbbcaadaabdaaacbdbadacbdccbcaabcacdbdbcadbabdabaaaaacdddbccdbcccdaadbdadaabaccabdabbdbadbbaddcbbddacdcbcbddbadadbccdbabbdababadbdbcabadcabcbaaabccbdcbddbddddcacbdcdcddccaadaaacdacdbbaaabdcbbbcacabdccacadcbdccdcdccbaccbddababbbacdcacddaabcccacbbddcaaadbcbabcbababbdccdcaacaadbddbdbdaccaacdbcdabcbcccbddcbccccacbcaccadccdbdcdbbbacadbdbdccaacaacdaddbcbacdbadcccaacadcdaadcbddaabcbaabdcdccbcabcacadbdacddaacdcbdcbdcabcadcddaabacbcadccbbbbccdbcabddabccabcaddbcbabadbdabbdddbabdcaaddbdbcbccacadccabacbcadbadbcdbdddabdbddcbbdcaaacbabacbcdababbadcacacbcadbadcdbbcacbdcbaddbcbdddadacdacccbcdbcdcaacbcbabcbbcadcdcdbdccdadadabcdcdbbabcaacbdabbcaddadcacdaabccabccadddbcbccbcaaabdccadacbacabaaccddadcddbcbdcdadbddddcdcabaacbbcdcbaddadabbbaccbcdcdacaddbadcacbbcacadaddddabadbbbacbaabbacacdddacdbbccabdbacbcaccdcccbdbdbcabdccbbabbbdbbccddaabaacdabddabddcccbdcdccaddacaabadbdddccadabdabadadbdddbbbbdcbdbbcadcbcccdaacccacacbbdbdbdbbacabaadccbcccdbbcdadcaccbadacdbabcdcdcbbacdbacddbbbaccdacbaabdddbcddacdbaacabdcbacddbcccbdaaddbdbabdcccdbbbaaaccabcccdabdacbbcbcaadaadaadabdccbaaaaabcbddccbadcdacdbdccdcdcbddddbcbcbbacdabcccdababcdcbacbdbabbdcaacddcdcdcdbcadcdadcccbdbdcaaadbbacddcbcdcbbbbdccccabddacbcacbadcbdaaaacbbadbcdadddbbaadbcbbcaadcdcdabadaabacbdcdcdabcbbddaaaadcbbcdbbbbadabbdbdbbccdbbbacbaccccacbcadbbcdcbbdadcddcbaacbbadadbcaaadacacbadbcabaadabcabbabbcbdbdcccdabaabcdbababdacbdcdcdadcccbabdaccbcddadbbcacabbbadbbdcdbaacdabaccdbddaaadcaddcbdcbbbbddacdadddbaacccbaccbbddadccccbaaddabccadacbccbababddcdacabdaacaadccbbddcdabbccbacdaacbbaccbdabaabdbaabbcbcddacdbdcabbbbbbaaaddbacacaadbbdcaabccaabbaddbbdcdabcdbddccdbdaabbbdcbaabddddacbdcccdbcaaadcdddcdcaadddcbaacbbcadcabcacbdabbbcdcbdbabacaadbbcdcbcdbdaaaddbbdbbbbbbbdaaccaccccbcdcdbdbadcccdcabacbbabcdababddacdacbcdacbbcbacbcdadaacccbcadbcbabccbcddbabddbaadccdbcddbadcbcbdcadbaddaddccbbdbbababdcbacbddcadcccababaacbcdcadddaabbbbbdadbdbaaadcbaccddbbaaccaacdbcdbcdbcbdcdddacdcbddaaaccadcbddadccbcbbcaabcbacadddaacddabcdcadcbcddcaaabcdaccbcbcddbccbcdcdddaadbcdcddbcccbadccccdacacaaccbadaacbcdccdcacdaaaccdddddbaaadcdcbcdbacabddacccbbccddbbdcbcbbccaaccbcaccbdaaddccdacbadacabdbccddbbdcbbbacaacbacaccdbbabcddadaddccadbdcbbabadacbacdbadcdbabdcadaaccdbabcdbcdadcddcaccccbadbcabddbdadbdccbbbcddccadcdabbaacbcaacddabcdacdddaadabdadcabbcdabbaaccdcadabbcddccdadaadbbbddbdadcbddcdbddcccabbbadaaaacddddabcabdaaccddbcbcdbbcbcdcdaaaaaadddabbddcbbcaddbddbdbbaadbabaccddbabcbdbbbccdcbacbaaaadccbbdcaabbdaabbddabdbbaadcdbabadaccaaaccbbaaddabdddcaaacbaaacbbcdbddcdcbbbcddaabddbcbbababbbcdacbbdaccdbaaadccdbdcbcccdcabcbdcbacadcabcbbacaacdaabcbacbbddcacdbbcdbabadbdabdcbdbadcbbcbcadacacadacddcddbbdcdcacbcbddbacbcdaaaddbabbddcbabddbcadadabbcbadbddbdcdadacbcccabcbbaaccaddabbbcdbacabadbcbbddbcccaaddcdabbdcdbccdbddacdbcadcddcaadddbdcdbbbcbbbababdcdacdababccbdaabbcaacabbdcacbcbcdaadbcdbcaddcbcccddcacbcabdaaaadcaabcdcbcddcddbcaaabdaabcbabdbaadccbbdcbcbddbdcccdabdddaaadaaabcbbbbbbcbcacdddacdccaadaaadbaaacaacccbaadcdbcadbbdabaabaabddaadcccccbccccddabbddaccbbabdcdcbabacbcbcdbdcaaaadaabadcdbbabbaacdbdbcdaadadadadbdabaaaacbdaccabdbabdccbaadaaccadcaaabbbacbdbcdcabdabaaddbcdabadcaabdcaadbdaabcbdcabdbcddadccdcbddbccbaccdbbcdabadacdabbcadbdbbdaddbbbddabcaccbaabbcdcdcacbcacdadcbbbdaddbaaadaacdaadaccbadacdcdbdddccaaccbacaaaacbaabcbdbadbdabddbabcbbdcccbaabacdaacabbbdbadccabcbabdbbdbddacabaabdcdcccdaddadbbcbbaabccddcaaaacabaddacddcadcaadddccabbbdaaccbcaaaccccbacddbaacaadcaacbddddddacbbabcdcdbccaadcbdbbadcaccabbcbcaaccdcdadaaddcbbcaaccaaadacbbddaccbbbabccdbbadbdcbaddbaccbacccdbbbabcdabaadbdadbaaabbacdcdbabccacbccdddccaaddcbcbcdbbabcbbcdcccacaaccbdaccdbaadcbabbababdccabdbbacaadcacdcbbbcbbcbbcaaddacddbaddcdbacdcaaabdddbcdbdbaddcbcaaadbbdbcadaabdccabcacacddaacbcdabbbbcdbcacdbdbdacdcdbdbdabdbcacdadcaabcdbddbbbdbadaaacccaacdabadbbcbcdcbbdaaaadccdabcdcabdcaccaabaaaddcccdccbdaadccdabdbbcdbcaadcbcbdabdabbadbaabaaababcaddbadadbcbdcdabaabcacdbacccdddababdacbbbaaabaabbdbacdddaaabbbbabacdccbdaadacccaaaadddabcabaadadbbdbdddadddcbbbdbcddccabcabadabdacbcdaaacaddbddbdcbdbbbbaacaaaaadaaccbbcdaacdabcdbbcacabcdaadcdadcdddaadcdaccbacbbbcaddcadbadddabcacdbbbacdcabbabccbaababacacaccadbcdcaccdcabaaabcaaabcbdaadddbcacbaaabdcbcddbdcaacbdacbacaaccbbccbdcbabcbabdbcbcbbbdadaadbdcdbaacabccbcacddadadbaabdaabbcaaadabcabddaadbbcacbacabacaacacbdbadbaccabbcdbacbacdabaccdbbbccaacabadadadccbcdacddabbadbbdadbdabdbdccdcbccacadccbdccdabacacbabbbbcacddaaccdcaaadbaabcddaabcbadabadcddabcbcccabbbdbbdcababacdccbbcdcbcccbcdbbcbdcacccacadbdcbdaabbacbaacbbbcdcbadbbbbcabacacdaadcbabcaaaabdcddcbcabddddadbacdacbadbbdaddbdcadaddbabdbbaadcabbaadaaddbbadddcbcbcdbdacdbbdabaccbcbcccdaabaaacccadbbcdddbdccabcbcbddadbcaaccabbabbccdcbccbcdcdbcaaadcadbcdcbcaacdaaacdcbdbdddcbadcabbdacbadaaacddcccbcdabcdbbadadaadcaaccacbdcccccbaaddbcbcacccdddbdacbdbaddacbaddaaacbbaddcbcbdccabbbbaddacdbadbbbbabcccccccccdaccbcbbcacaaadbbdcddcacaaacdabdaaaaabdbaadaabbdcadbbbbdccddaadbcadaaccdcbbacbdbccdddadbdccdacaabbdacdbdacddbcdbbabcadaababccaaacbbadddbdbdaacadcacbabccbddcbdbcdcccbabdcacbdbccbdbdbbdbdaaddbadadcbcdcdbaadbdadcadddacbabaabdbbdaccbcababcabdaacccacdabbadcbdaaabacabaccaaccdbdbaabbaabdcbccbaccdbbbbdcbccdadaddadddabacaabadaddabdcdcdddcdccccbbaabdbaaababaacbadabcadbdadabdcdccacbaaadbacacacaadadbbcbdccaaaccaaaabdabccbbaabccbdbdbaabcbaadabddcdcadcdbcdaaabbaccbcdadacdbdbadaddbbaddcbdbddaadbccccaddcaccdbdbddddcddbccbadacbbadabaaacacacadbdbbcbbbacbdaddcbadadacccbccbddbbcadccccbbaccabdbdacaadcadbdbccacdcdabcabccbcbccbbadaaadadaaddaabadcabbcbdcddadddcaccbdadcaddbbcabcddbcbdabadabbdddababbcadbbddcbaccdbdacbccbbaccdcccddcabdcaddddcddcaaabcbbcbbdbdddacabcdddcadddbbabddcccacbdbdacabddadbcacadacbcadaababcdbbdcabdcaaddabacaadcdcbbbcaccddcbcbccddddaacaacadcdadaacdacbaccadccbbdaccddadabbcbcddacbccbaccbcbbbdccaacdaaccdcddacddddabbbacdcbdbccaadbacbdacbcacccbacadbdcdadbbdabaaaaabaaaabaabbdcadbdacddaddadabbaabdbadcccdcdccacccacacaacabacbcdabccadcaabbccacaabddaaaacdcbcddccdcabccbabccddbcdcbadbbcbbdbadccdaccbcbadbddbcacbcccdbaacbdadaadaccabdbabddbcadddbaaaadcbabbcbadabdbdbdcbbcdacaddadbdcadccbdcacdabbadaaadbcbdbadadacdddddbbadcccddbcbccacabdbaacbdaccdccbcacaccbcabbbcdbbcccacbbabdcaacaabbdcddacddbddccacbbdccdadabddddaddaacdbccaadbbbbabcdddbdaccbabbcaadcccdbabccadbbccccadbcadaaadbcaaacbdddbcaccbadcdabdabdcccdcbdcacabbabdcbcdcabdccaabdabcbaaabadababbdbcccdcbbddbbbdbdabbddbddadddabadcddccddacbbcdaadacbacbdbcaacdbdbbdacdcdcacddcccbbdbcbbcaaddabaabbdbabdbaadaaaadcabcdcdcccbcbdabcaaadddabdccdcdbccdcdbdcacbaaadbcabbbcabbacdcddcbbaacbcdbbcddbadbbbcabdaaabcbcdbcadadbbabcbaabcbbcbaabcdcaaddbdbbddddddaaaadddbaddbcaadddbbdccadcbdadcbbbaaaaacbbaadadddcbcadddccccabbadcacdcccacccaabcaabdabcbadaabdabcbdbbccccdacaadbbbbbbdbcbaabbbbcacaacccacdcabdadcbdbcbdccbdcbbadddabbdabbacbcdbdabbdcbccdcabdacdcbadaadadacadadbacbcacbabacbaaabbbddababddbddbadcdcdcaadbccbddddaccbaaadbccabbabcadcabcbcdbacbbdcaaacdbaccbbdcacbdbccbbcdccacdbadbddadabdcbcacdbadaadbbddccbcbccddadabddaccbcabaaddadbdadaabbaadadabacddcddcccbdbcdccabcbcdcabaabdcbbbdbdabdcdbbadacbbaddbddaacabaaddcaaaddbaacbcabcaaadadcacdacabbaccbbdcbbacbbbaaddbbcadcaddcacddcccbbcadaadbdcbbcbbddadbdaaadccadddddadbacbcdcabcbcbccacdbbbdaacdabcadabcabbaaabadcdbbdadccddbcbcdddcbcdcbdbcdbadbaacadadccbbddaddcacacacdccabacacaabcacbadabbabbcdcccddbbcbdcadccadcdcdaaabbacabaacbbcdcccdacccbcbcbdcdcaddbcbcbcabdbaaddbbaabcaababdccbabcabcdbcabbadccacdcdbcbcdcdacbdbddadcbbdbbdaacaacabdbaaaadbcaacaacadcadcbbddccacddcaabcdcdddbbbddaacbccdcbdcbddcccbcbdbbcccdbcdcdaabacaaccbcacddddacbdddbaacdccacbdabdacdbdacdbdcbaabaddbbbdbbabdababcacabaabdbccababcdbcacdadddbbbcbdacbacabdbaabbbddddcccacadadcbccaaabcbbcabdadacbcdccbdbbbcaadddbdaddadcadacccbccadabadaddadbddcbcddabbaacbbcbbddbdaaadddabbadabcbcddacabbdbacdbddbbcbdcdbdbadadaaaaadbddbcbddacbcbbddbcabadbacddbbdcadbbbcacdcbdcbadacddddcdbbabddccbcbdacbadbacdcbdadbdabccadccbaaaadcaabaacadddcdbdaccbcdaddcccdaabdcbdbcbbbcadcadaabacdadccdabddabaabbcbdaaccdacbbbdbbdcddcabadaadacdccccaacaccabcbabcadcaddaacaccbbabbaadddccbbacbcaadddaacdcbdabcbbadcabcabccbdabcaabccbdbbddcdbaddcadbababdacaadaccddbddaabdcdadadbcaacbdadbcabccbbccddcddcdbacbcdddadddbadbadbabdadaadaddcacddbcccbdabcabdcaaaddaccabbdabacbcdadcadbdcdcbabbdaccdbabbaccdcaccaaadbddccaadcaadcdabaccacdccaababaabbbbadbcabdcbdadabbaabadaccddbbcacbadbabdacdcababadddccaccbcabbabccbcadcccccdcbadccddddbabcbacbadcbabaddadbcbcccddbaccbbdacadcbadaaaadabaccdbbdacbbaacdbdbcaabddabaccbddbcbacabcbacdbdddcaaaadcdadaccdabcddcbdccabdcbdcdbbbabddadcaccacdacbcbcdaabccccccaaaddbddbaabcbbacbadaddcdcdbabbbdbdddbdbccadbbdddaccbcdbdadbaddbbbdadbcbaacaadbbaadbcbaabdadabddddbdbdabbbbbacaddcddacccdbbdaddbddacdcacdcbcdbacadbddbcdbabdaccbcbcbcaabaaaadbcadbbcaddaaabddbcdadaaadbbbabbbcdcbbcbbcbdbacadaadbdddcdcbbcbacbccbcdacdabbccadccdccaacaabaccddcaadabbaacaaccdabbcddabbdacadcdaacacabdabdbbaabbdcbcabdaadcacbccbabadacddddacdabbdabbacaddadccbccdadbbcaccddadadbaadbcbcddcbaabcddabdccbaccdabaabaabdbdcaaddbbccbbadbbdcbbadbaddabacbbacabbccaaacccababdadacbcdacbcddbbcadbddcbdddcbddcddbcbaccbbcbdbcabbbabaaadbdcbaccbcccddaaabccccdbbbabcbcbdbabbcabccbbabdcdbbacdbcbbaaabdadabaaabddcbaccbcbddadbdddacbaaabbdadbccdcdcadcbdacaddddbbdbdacbcadbdbccbcbdbacbacadbadcacadaaacbbbaddccdddabcbbddbbdbaadacacdaccdbcaacaacdccdcbdddbbdcbdcdcbacaddabcbcdcdacbcdbbaccbabbccabbabbcabcbacbcbadbddabadacdabbdbbddbbbbdcbcbbbabbbacadbbcacaacadabcddabbdcabcbcacaacbbacdacabdacbcbbbcbdadadbaababddcbbdbdabdadadddacddbacdcddcbdcaabbcabcabcbbdbcaacbddbaadcabbaaaaddadaabbaaacbbaccdcacdddabaaddbcdaddabdbdccaabbdcacdabcbcacdbddababbacbdcdccccaabbdbddcbdbccbcabcdadbadcbbaadbdcdcacadccddddaabddadcdddbbdddaccabadbabbbcadcadbbccccacdbbdadcabaabcacdabdcabaccadbaabdbddbaacbdbbdbcacabdcbbddddccdaadcbccabddcacdccbcbdccbdcabccccaaddaabbacbacaabcbdacaababacadbcadacabaaadcaacaacdadbcdcbddadcbaddbddbdbddcbaabaabbdbdbbaaadaaddaabdbbbcbcbaaaadacdddbdcabccacbcabdcdacabcbbbababbadbacabbddaabacbdbacbdbbccabccbdcbcadccdadaabaaaccacbbaacadccaadcbdcdaadcaddaacaddbbbcbbcdabcbbacbacabcacdbddadbcdaabbbcdabdbdcccabbdcbddbaacbdabdbcbaaccbbcbcccdcdcbbdcbdcbadddbcbcbdabdcbdcabacabbcbcdbcbdcaccadacdabbbdadcacbcddcbdcbbaccdabdcadddddbbcabdcdcccbcaaacddbccabddcabbccddacdcbaacddbdcbcaadddcbbdccdbcdbccdbbccdddbcaabaddabdcdccbcadddbacdcabcadddbccbdaccccbbaacddddbaddcdcacbbdacbbdacaaaacabcbbdaddcbccccccbcadacbdadcdcdcdcaabcbbadcacaabbcbcadbccccbbcdbabaabacbddacccbcbcccaadbdbdbdddaabcbabbddbccbccacdcbdadcaccabccbcabbcadbabccbababcdbbaaabadacabbcacdabcadbaadbbacabbbbbcbcaadaacdbdaaddcddcbcdbcaabbabbbaabccbcabcccacacbaabcdbdbcbadbdabaaacaadabcdacbdccbacdadbcbdcabadbdccadbaadcdaccacbacdcddabdadcbdacbaabaaaddacadbcbcaaaabbaadcdcadabcaccdabbbcacbadacdacbcadcddaddabbbadadaddcaadcbdcdbbdabacbaccaabcdcdccbdbccdbdbdddabababdcbaacddaacdabbbdaabcbbbcdacdcdbcccbaaaacdaabadccacdddcbdbbcaabdabcdacabccddacbbbcaaddaddabbbdcabcbabbddcdaabccaadcbddadbdbabacadbabbaaabdabdddccbabacdabaccabcbaadcdacddbdadcacdbbcacbdcbbddaadaaadbdbbdababadacabcccdaaccabdcbabaabbbbaabbbddabcccbbcdbbacacdcbbbaccbcdabcdbdabbbaacaddcaddbdbdbdddcddbaabddadbcacbaaddbbcccaccabdccccccaccbcbbbdaacabddacddcacbddddbbbbddcabcaabbcddcadaabbdddcbbaabdcaaabbaacbdcbbcacadacacabbabdcaaccbccbcbadaababbaaddbccaaacabcaaacdcbbdcdcbdcbbbcbbcaddbacabddbdddcbacacbdbcccdadaaaadbcaaddccbdaaaddccdbccbdcdaabbdbaddabcacdabbbdcdbbbbbaccbabcdbbabccdccaddabbdcbdcbdcccccadddbddddaababcbbbcdbdbabcbaccdccdbccdaaaadbccacdbdadddadabbdadcddbbdcccbdcbdbccdaddcaacddadccbbbcadcdbaacdbcbaadddccbadcbdadaaabcbccbcdabdbacddcbdaabcacddaddddadbbddacbbbabddcbcdaacdcbdbdadcacbdbccdcdbdcdabaddacadadabbbdadbbcaadcacacaddccdcbdaddbccddababdaabacacabaabddcadcbbcbddadcdbbbaacadcacabdbdccadcaddcdaccbddabdcacddbdbabccbccacdbaccadabddbdbbbcabbdcddbddccacaadbdbbbcaddbbaacbdccccdaaccababdbbdabccdabcadcacdbaaaccbdbadbbbabbcaccbbddcbadacaddabccadcdaaddadcadaacaabacaccaddcadcaddbdaabbdbcddcccadcdcadbadccbaaadcbdcccdcacbaddbbaccbaaabbdbbddabcccadccaaabbcbadddabddcbbcbddbbccbcdaaacddbcadaacbdcaabbacbcdbcdcaadddadbbaccdddbbadbcdcddabcabadbadddccbdbcbcdddbadbcdbdbccdacadddcdcabccddcadcadbdbcdcabddabbdcbabdbaaadcbbdaccbcdabdbcadcccbbdcacbddbdbbadadcbabddcbbdcabbacacaabbccbddaccacccccabcabadbbbaacacadbcadadcbbcccbcbcdcacbcdadadddacbacbdccabdabdbcaaacbddddcccccacddbbbbaadabcacbbbcacddcaaaadaaccabcbabaddacdcaddcdbddcdbdaabbdbdadcadcadbdabbdbbaabbcdcbbcdccdcddcbdcdccabcadccbdabddddcbcbbbbadbaddaccbddacbcabbcacddccacccbaacabcbadcbbddbbcdadacddacacdbdbdccdddbacbaadabbcaabcacaaccbdaadabadbbdaccdcdbadbabbbbdbcbcbacdbdbadcdadacacacadcbddaaaaacaabccdadabbcaadcacaccaadaadddcdaababbaaddcabcbbbbddabdadddadbccccaaaaaabcbdacbabcbccbbdcbcdacdcdcdaababdcbbacdbcbadabcbcbadbbabddaaccbdbdcbbdcbbccacabbbacbcadcddbddbbadcdcbaddcdbaabbccccacbdddbadbbcdbbaadbdadbccbdaddccaaacaaaddddcacabbcaddbaccabdcabaabbabcbbcdbdbbdcdbcbbcaadcabcadaaaabbdcaadabacbbcdcdbaabbdcaccbbccbcabbbadcbcdbbcbbcdcdbbdbcdabcccaaabcbbcacbdbcadcbdccababbadcdbabbcbacaaccbcacdadbbabcabdbcdbabdddaadcbbbdccadbdabbabdaadaabcbbcbdddccbccbcabaabcaababcabacadddcbbcdbaacaccbbaddaaaaccdadddbaccbdcbaaabbcccbcbcbbdaaabcdacbbcbcaccabcabdcdbaadadbcaabbbadcdbbccbdcbcddbbdadccddcddbadcbaaabcabaccbdbddabcccacdbbdcbcbbadcababcaadabbddbbdbadcbabacdbdaacccdbadcbabbbcadadcbacadcdcabbabddbdcadcdaabdcdbcccccbdcddabcabbdacddadaaaaccbcbddacacbbacbccdadcbddcadcdcdadbbaddcabbdcbaccdbbbbccdbdaccadaabbccaccdddbdccacaccadddcbcddbcbcabdacdbadadadbacdadbbbcccadccbabbbcaaccbcaadddadbddaadcadaadcabddbcbadbccdcaabcdcdabcdaabaaaabbccbdabbadabbddbdadadbbbcaaccddbcbbaacaaabdbbdcabadaacbbbdbdaabaddaacaacbbccaccacadadbdcdaaacdccbdddbdcddcaaccadabbbabdcdabaaacdcdcdccacabddacabcbdacaccadbbbcdaaddabcdcacaddaaabaacddcadccbdcbbddbabdadacddbcbddbcdbdacaaddbacacbcacabadbacacdddccdadcdcbcacbdbabaccbbaaabccdbbacbbdddacadbbaddcacabdcbbaabcabbddacdbbababddbdcaddbbcbcbbddcbadcadabdaccbcdcdacacabdabbadccabbaccaadbcddddddabbaadacaacbbbadbbbbddbbbaaabaabdcbcaacadabababbacbabbcbdbabcdbaadabacbbbcdbaadabaaabccdaccaaaaaabaabdbaadabcbcbcbbacbdbdcaacacadbabadadbdcbcdbaadcdcbadabadcadddbaabddcacbacbaadababadabaaddadccacdbadbababdadbcdaabdcdbdaccdcbbabcdbabbbacbcaabddccddcdbabbaabbbdaadacacdcbbcccabcdcaaccbccbdbbbadbcabbcccccdacbbbaddbaccbaacccbacccbacdcddbddcadadaaadababaddccaabcabbbcacbaacdaccaabbccabdcdabbbcacbbaaadabbbabdcabbabcaabbbcacdbbccdbadddabacddaabdddbdccaabaabbacaadbdaaacabbcdacccdbaaccbcaaccddaacbbdbcbcdbcaccdccdadcbddcddcbdabababdbcaaccccadacbadbccdcbdddaadaaacaccbbbadadabcdcdbcacdbabbabacdbdcbbcdddacbadabbdacdcdcadddcdcdacdbcddcbbcbbdbbdabbdbdddcdbdbabacbabbbbdaddbacbbadabadbdadacacdcdcababddcdddddacddccacaadbaddccadcdbbaccdbcccbbbbbcdcbdcdaacddaccaadacbdcdbaaadacbbccbddadcddaddbcdcdcdddbaacdbdacacbaacdcccdbabbbbbadccaaccdcdacacbbbdddddababababdaabccbdabdabacabaaadacdbdaccaadbadacbacdccdcdacadbdcacbccbbaccdbcddadddcdabbddadcddcbaacbacbcbdacabddcccccddccdadcadadccbbddcccadbabaccbaaccaddabccabdccbbacaadcacdcbbacbccbabacdcabdaadbadbaaaabdccabcdbcbcbddabddaccaabcacdbdddcdcabbcbdaaacccbdacccdcdcbadbcdbbcadabababcbccacaaccadcdadaabbbccddaacbbcdcdacdaabcacbcabcdaadbdaccabaccccdabbdcbacaddacdbddbbbacabbbaaddcaadaadbcaaaccacdbcaadcbdbaaaaadcdcaacdbdcadbddddabbdbdbccaccdbaabcdacccadadccccabaabbadabbdcdbcdddabacdccdccadbcdcbcdbddacbbcbaabbbcabbdbacbcdcabbadabcbaadaddbbacaccbdaabbbcadcababadaabbaddddaddbbccdaccadbdbacccccbdacdbadbcadddddbcaabdddcadbcacacbbbbabbbaadaacbadcdccaaaacdddddcdadddbccbadcbcacbdddcddbcdacacdaadacbabacaccdddbbbbacaddddaccbbbaddcbcabcdbcdbdaabcbadbccaabacbbcbcdcccaaacddaddccacbbcddbcdabddaabdbbddabdcaabdbabaddddbbccbadadadbbcbdccbcccbdccccddabdddbcaadcaacbddcbacaabdcdccdacccaacdabbbbdaccbdacadddcbacdddababacbccadbbcdaccaabacbbdbabacaaaadddccbcdcadcaabaddddaddddaccbdabbaaabdddaddbbadcbaaacddbbadccbaadcbbdbddddbacbcabadabcccbbcbbababbdacabacaabcbbdaabcddadcccdaaaacbaabcdcdbbcccbccdaacacccacadadbddadddadaaaaccbbbbbddaadbdcbacddbabdadccbcbbcbaabbcccdddadbadbaaddaaadcadcadaadcbcacccbaddcbdbcdabbadccaaaaadbddbcccdabbaccbdbbcdcbacbbbacbcabaaaaccacbcdbabddadcdaaadaacabcaabdcdcccabcdadaacacbddabbccdcadcdbdaddcacbaabddcccbaadacbbdacbcadcacabacddccbdaddbdbccdaacdadccdaddaddbbacdacdbacaadcdddcaaddaababbcbcbbbbdbdcbbdcddbbdcbcabcacdaddcddabbdcaaddcaaddadbdcacadbbbaababdbaaddcbaabdaddbcbddaacddadaabbabacabdcbdacdabdddaabbbdbbcccddaddddabdbccbddbcacbcbbdddacdccdcbdbcbcababdbcacddbccbabacbccaaadbbdcacbbacadaacadcddccccdddbdacdbcdcaddcacbacabddbdcabbabbbdccdcbcdabbbacaaabdccbddaccabadccbcbdcaddbbadbccbdabbbbbccbcadaadaabcbdddcdbadbbbcabaadbadbabcbaadbdddbddaabaccbbddbccdaddcaabbaccbbbdbcdbcabbdcdabadbbacbdaabcbdddddbaacbbbaacadcdbdaabacabbcbdbbcddddcbdcaaccdbcccacbbbaabddbdbcdcccddccdccbbcbddcadbdbddccabacdadacbddaaaccbdccdccadaaccbbabbdbcbcbbaabdbbaaaabacacdbabadaabbdadbcabdaadccbbcbabcacbacbdcbddddbbadcacabddcbdacbdbdcbbcccbcabaadbccbcbdcacaddbccbaddaadcbcbaaddabbabbdbabddcbcdbccaadaabbbaddbbcabddabbadadadddcbbcdcccdbcabcdddadbcddadacbbbbcdbdababbdcbabacbcdcacaccbddabbdabcadbddcabdbccdaaaaaabacbccaccddbdbaababaabcdcaddbaccbbaddabbadbabcdcaabbdcbdcdddbdcbdabccddbbbdbddadcbcaadacaaaadcccabcdcddccaaaccaaaacabdbccdccdcbdddbabbcdbddaddadbbccacccdcbdbbbcabdaccabdbbcaccadccabccdadacaddbcaababacadddaccacdddbdabbdbcbcdbcbbacabcababacadcdbbcbdbacababdbbbcbdcbadadbabdadaaadaaadadadddcdbbccbcdbbbccdddbdadadbdccacadbdcbcabdddaacddabbabccaddbaaacdaaaccadbcaddbcbccadcbadcabdcbdaddddbaaccaaacbcaccabcdbadddcbdbcbdcdcccaaacdcdacaaabaccadbdaddbbdbbdcabdcbaccbcabadcbacbdbdbddacdbbddadaccaccdcdcbacdddcbcabbacaacdcdacdaabaadbdacbbbdbbadcdcdcaabcbdbbbccbbacaaacdcabcdddbccbbbddcaaadadacdacdaabdbadbaaabaddbabcdcdadcccabaaacccaacddcdbabcdccacbccacbabbbbdbcdacdadaacdcdcdcaadcbcbdbdccdcdbabaddccdaaddbbdcddcabbbcdccacbcdbccabbaccaaacdabcdcccccbdacbcbaababacdacbdabdddacbbbabbdbaadaababdbcbcabcbbccbaacabcbdddabbbbcdbbdcddbcbcdccbddbabaaaadadbbaddcdddabdcdbabdcdbdbcdcdbdacbddcacaacaaaacbbbddaccdacdddccbcbdddddcddabcdaaccbabdacdbcddcadccdcaacccbdccaabdcbaacccacdabdbabadcbdacbbddcbaaabdbcbaddacdacbdbacdbdababcccddacbbbdbdbddabcccacacaacdddcbcdcacbaddccbadabaaddbcbbcdbadccccbdcaabcdccbdcaacaddacacdbdcbaaaddbcaaacabbabcdbadacbaccdbcdbaddcddbbabbbbdabbaabadbcdddbaacaaadcddcaacadbbacabcdcacabbddcbccdaaaadbdccbabcacaddaabdccbdbdaacdcdcaadddadbacdacdbabaabbccbabadcccacbadbadabdcbacccbaccdcbabaddbcbabbacbdbbbcaabbccbccbaacbdbbbabcdbbdbcbcbcbdbdbbcacbddaddabddddddbcbbbddacddbdddccbdbbbdcbcbcdccbbacacdcbdadabcabcccddbdbcaacdbbcdcabaaaccdcbbdcbaadcdcacddabcdbcbcbbcdddbbbcabcbbcccbcddcaabacddbbabccdaabbaabbdcdbcddbdbacacdbddbabddbadcdcaccdaabbddbcbccdcccadcbcabcddddaaadcbcabccbcdaddbcaabcbbdbdaddadacdcddbaadddbcccadcbcaabdbbacbbdabaaaddbacbacababdbacbbbabdaacdcdcacdcaaaadaaadcbabdcadacadddabcdbcbccbadccaaabbaaddabababacbcdcccdadbddbccdbaadacabbddaadadabcbbcbcdccbabddabcdbbbbbbdabbdbbdaadaaaabaabaddcdbdddabcabadccbbdbcddbadccdbabadcadccbddaacbabddaabdabdcabddddbcbcddabaacacadddcccbbdcccdaaaddbacdadbddccacdbabacadadcacdccdbccadbcdbadabbabccbdacaadcdcadabcdbdbddacacdadaacdcaadccacbbbaacaccacbbbacbdbdaaaddcaabadddaaacbdcaadbddabbcdadcdabdacbddbabcdbbabadcaaddbdbbaabcbacabddccbbcaaccadbddabbacdabbaaabbbdbdcccbdbadbbbaadaadadcadabbdddaddcbcaddddccbcabaabdcaadaadbdbbadaadbbbdddcbccaddcaaacaadcbbdacadabddcbcdcdcddaacddabbbccbccbacbbdcdcabccdccdabbcbdbdcaccdaaacbadcbadbacbdccccdbbbbbddcccccccbdddcbcaadbddddcbdcdabcbddbbabcdadadaaddcdbaaabcbbbbddccdcaccacdbcaaddaccbdbabbaabcddcdaccaddbabdaaabbbdbbdcbbacdaccdabacadcbbbbaabdcbdcdbbbabbacacddbadcadabddacddcaacbddaccccaddcbdbcbacacdcdbbddacadccacabcdadcaddbadacdbabbcacdacdaadadcbacaaacdaaacbabcbadccdcaccbdddbbcdbdbccaddaccdddbbccdbddbbbcbbaaadbcdaddbbccdcdbccbcbadbcbaacaaadbdaabdbdcbdccaabbcabbbbaacdaaabcdbddbbaacdbddbbcddaabbdacbadccdccabcacbdacabcabdddabdbcbcaadcbbadcbabcaadcbaaccbdbcdcbdbcdcdcbcccaddbadcbaaaacddaccbddcdacaacaccdcddcacdccbbbdbdacddddcaadcacadbacdababbbacddcbbacbbbcdcbacaccddbdabbaabccccdcccabccdcabbaabbddddbbcadcdbcaacadcbaacddcbdbacccabbadadaabdbbdbabcddbcabadcaaddcaccbcdaabbdbadaabbcbaddaadbaaadbbbacbacdbdbbcacdccdacdcabdbcbabbddbcaaddaabadbcccccdccccdcdddbbbcbbbdaccabdbbdadddbacadbaadcadbdbaabbbccbbbddadabbbabbbdddcddbacdbbacdbbdccbddaadbcbcbcabcccabbcbccddcdcbaaaddddbcdadbdbcbbbabcccdbacdadccacadaabdacbadccdcdbccccbccdbacbdadccabacddbcccdcbdddcddbcabcddcbddadbcddddaaddcadcadbdaabcdbaccbdaabcbddacccaaaabacdacdcabdbcabcbaccdbdccacccbdacdbbccbcddbadaacabaaadcbbaddcddcbadbdaabaabdccaadbbacadbbdbccbabcbabaabdadbbcdcabccdaddcbdbbadcabcbcbbbdacbcadcdbadadadcbaaaddabbdabbdbbcbaabdccaacbbdbccdbaddcaaaddaadcbbbdabbaddcaabaccccabccbabdacbadaacacdcdbacbbcaabbbdcdacdcdbbccadacacbaaadbccacbbcbbaaabcdbabcbcbdaabbbcbacbbbadcbdadacdddccbbddabcdbdbdabdbcadddcbcdbbdbbadacdbbdbaccdcaadbdbbbbcaaabcbdcddaadbdbbdbcddaaccabcbbbdddbbbddadbaadcddaadcacdcdbaaaacbaabadbdcadbddacbcddabccadaacdbbadccbcbcddabaaaddbadcadddbdabcaabdbdbbbcdcbaacaaadabadddbcdcdddaabbdadbbbaacbaadbaadbadddccbbbdaaccccacbbadabbcddaddbccccdbabdddcbddbccdcccbdddddcbbbbabdccadaaaccaabccddaadbccddcbbbbaccaaaaaacbdcccadabadcabcbdbddbccdbcdabdcacdadcbabccacabddbdcbaacbbdbbdabbdaddadabadadbbdaacdcddbbadbdcdbabccbbbdddbaadccbbcbbdcddbbdcadccddabcdabbbbcacdcabdadadaaddcaccabbdabdcbabaacabbcdadabcbbdbddbadaaaacbbdbcbaabaaabbbdcbdcbaaaaabdacbdbdabdddcdccdacccdccccacbaadbabaabbdabdabcbcddbcbdbbbddcdcaddbddddbadbbcdaddbbbabcbcbcaaabaabcbcacbcddddcbcaacdbccadacbddbddcadcdadbaccddddbcccadbbaabbdcadddbabbbadbaadccbaacdaacacdcaaadbcccbaccbbcbcbdddddbdadaadbcbcdbcdbbdbacabbbddcadbdaddbacdccdababbbcddddaccbacabaacabbdbccbadacdcabbcccacccdbacbdcbbdbcccbaadaabdbbdcdaadcabccbdbabbbbbccbccbcbaaabdaaccbccbaccdaadbddaddaaacbccdadddcadddbdaccdbdaaaccbbdadbddcabddaadabbcbabaccbadbcbcccccccbddddcccbdccaaacbcdacaaadbbacdddacbccdcadddcabcbadddbcdccbbddaccadbaacacadccaadcabbbcabcbccddbcdddabababcaccddbbcdababddbddcabcdaaccacbcbadabdcbccaaddadcbdcabbdcdbcdcbdddbbbbccccbdcadabcacbbdadbadcdccbbddbddccabbbabbbdbcddcddbcbcadcacbcdcadbdccbbdabccddcadcbdddbbbcddacbccbaadbdcbcddbaacacdbacddaccdccdbdadadbcaccdbccbbdbdbcbcddbcbbbdcadabaadabbdaabbaaacacbcdbacdabdadacccacaaddacccdcbcccadabcdbcaacbbcdbacdadcbaaadcbacddbbadcbabaaccabccadbdabcccdaaabbccabacdbccdbbdbbdacaadabcbcbdbddaabbdbaaabdbbacbbbdcdcbdabbbbdacdaddddabdccbdbccaacacaddbbcdadbaaabbdbaddaacbcbbcdaddcdbadaaaacbdbbadbbadcbdaacbcdaccdddbaccbdbadcbccbcbdbbbdcbaabdbbacbbdaabbcadcaabbabaadabaacdabbcacbddabacbbdddbcbcccdbbaddbdadaaccadaacbcaadbabaddabbddadcdcadabdcadccbbcaaaaabcabacdbdbacacbbabbbdbacbdbcdacbcbccbdcaadbddbabcbbbadbcbbccbdadddadcacbdbdcabdcbcdaaabadddacabaccdcccbcbbdbbcdbcacbabbdaddbdccbdddbcdddcbbdbbdacbdaaadcbcbcbabcacddacdadbccadcdabcbbacadbdcbdbabbcdbadbddcdaabcbdadccdadaccdccdbdcadcccdaacdcdbdcaddcabcdbaabcacdcacddbdbcbbacbdacbcacbdaaabacbccccadbcaaaabadadccabddcbcddcadacacaaaddbadcdcdabaaadaaaaaddbcdcbcbbdabdcdbcccccdadcccacbbadcbddddddbbcccaccdcccaccddadadcbabdcaddbcaacadcbbdccdadbdddbabcbaadaaacacdaabdaaaccbbacdddbabdaaddbdbdacdbcaadbbbdcdabccddbcacaadcaddbdccacccbbbadadcbbbddcccbaccdcbaabcbcabaaadadccdbaadbdccacabdcbdbabcbbdabcbbcabdbdbbbabbdcaccacddadadcbcbaccbabcabaadddaaacdbdacaacbbcabdaacbccbdabaccdcdddddcccbcbbaddcbadababbbadcddaabbcabdbccabacabaabbdaadadcbadadadcaacadaabaacadcaaadadbbcdaccadcabacbdaacdabdaabcbbddbddbdbbaacdaadcacadbbbddcadddcdddadcadadbbccbadaabdcbbcbbdcdbdadbbaabdddadaaacdcdcababcbbcdbddadadaaaccbaacddbabcaadcacdcabdcbdbddbaabcdbcbcadbabcdadaccadddccddccbccdbcdbbccadbdacbaabccbbbcacdadbdcadbcbbcadaaddadcaddbbddbccaccadcacababcbdddadccbacbabbacbdaadccbccbabaacbaddcdbcdddbdcdacbacdadccbacadccdcadbcdddbdddacbacbdaadddadcaddcbcdbaabdbacbdbdddbddcadaadaaccbbacabdbddddddaadcccccbbdabdbcbbbdcadaccacddabadcdbaabaabccdbadaddaacddbbbcdaccdddcbbdbddddbddbadabbdbdabcacddcacdaadbacaccacbcddbdbdbdcabdbcbadadbcacaddadaaabcacbcaaacbadbdcddbcbcbdacdccaacaadcdaddbbbbbcbdbdacbdccdddbdadbbbdcccabdbddadacbacbccbddbbaadbbdcbdadcbacbbdacbacccdbddbbcbcdaaccdcbabacbadacbaccbcabbaadcdcbabbdaabbadadbbddbaacddddccabbbabaacadcbbadaccdcbcacdcacbdbdbbaddaddccaccdaddcaabacbbadbaddaabcdaddbbadbccabadccaaccdaacbcabadcdaaddbddbbdcbdbbaaabbcacacbcdbddbcdbdddaacccabdbbbadcbcdddcbccaabbcdbbbcbbcacbcbacaccaaacbcddbdccbdbddcbcadbcccbcdbaabdcdacbccddbdbdacaaadbcbaadcdacbdbdaabdbcccddccaaaaccacdcbcbbccbbbabbbdcabcbaccaadcccccbabbacdcbccacdddadbadbcacddccddbcacabacadbdcbacbdcdbaccabdcbcaccbacaacdabdaaabbcbddcbaccbdbcccdbddbbdddbdbbacdaaabcbcbbdadbdbcadcbacddadbcdbcccccaaccbcaaaddccddbddccaadbdadcadacddcabcdbbabccacbbddbaaadcbbdaaccbaabbabbdcbbbdcdbbbdbcabbbabbbcdccbaccdcadbcbcdaaaddcbddabccdaddcdbcbadbccdacdaddadbaaadccadbbabddcacbcdcabadaaaccdbcbbbbcabddabbaaccdcbbdacadbdbcbcbccadbdacbcbbdcbadcbacaadacbdaadaacbbcdbabcadacdccdbdabcccbbdddbcdbbdcacabaadcabdbbcdcacacbabbcddaacabbaadadacbabbcdcbadcdccbacbcdaacabddbbbcdcacddcbddcccdadaccbcbaacbdaaddcbcabbdbbcacdabacdccadbabbdbbcddcdcccaddcaaadbbccdcaacbcdaacddaddcacaccadbdbbcadcadddcacbaacdaaaabaacddacbdacccadbdbaadcaaacbbbcabbcbddcdaababaacaadcaabacbbacabddbcdaaacaabbacccbbadaaccddbbaadcabdcabacbaadabdaaacadadccababacdacbdbdbcaccbcabbdcdbdcccdadccbcbbadcdabbbbaabacbdacdddadaaabcaddacaababddcaddaadbdbcccabcadbbaabdcdaacabaabcdcdcccddaaacccaabcdbccbcbccbccdbaddcaacacdcdbcdaabcdccacbbdcadaaaaadabdcbccaaaadbdaccbacdbaaacadbdcaaccabcacadccacaddadbdcdbaccdcaaadacbbdcacbdacabaddbbcdadbbcddddddcdabccbcccdabbbbcbbabacadbcbcccccbaabccbcdcdadcdbcacddbaccccbccbabdbaddcbddbbcccbdaabacbacadbcccbaacdccabdcccbbcabdcbabadaddbcaadbbaaccadccddabcbaaaaaabdabdcccabcdbbdacccbaddbabcdacdcbadbbcbadacbbdbbddcacdcdcdcadabddcaccdaaccccbcdcaababaccbccccddbaababcabcbbdbabccddbcdccddacacadabbacabbacbcbcaaacddbabdcaabbcaaccdbaddcabbbbcdaabadaabadaddbadbdcbcdacbccddbbdabdbdcacddacdbddbcbbbdaabaabcdacadccbcacaddacaaacababadbbcbadbcdadbcabbadddbbcabdcacbbcdddbddabbbcdcbbbdbdabdbbbdcaddbcbbccbbaadddcbcaaaccccbbbaaacabcdaaddbdbcddadabdababccababbcdbaaccddacabccadbdbbbcdadcbabadadcccdbcbbaadadacbdbbaacbbbcbbbcacbccdbcbbacbadbcadbdcdaacdbabcbacadcbdcdacbbacbabdadddacbcacbcccccacbcaaaaccacdacdcdacddccdddadcaaadaddbddadccddababbccbddbcbdbdaaadbadabbbbbccccbddababacdcdbdaaccbadadccdcaadaccddbcacdabbadcccccdbcaddcdcddcbbacadbbccdcaabdcdadbdabaccdbbcbabbcabcbbbbacdbaccaacabbddaacbbabcbdbbdbaccabbbbdaddabcdbbacdddbddbdccbcbacdbcbacdccacddacdcddbadcabddaccaaddbdcaabbccbbbadbbdccbbacbcccbbbddaabddcbcabbbbbbabdcdbdcddbccadbdcbbbaacacaaabcbbacaacdbabddbbbabcddcbcacbdddabcdcbbbccadbaaadabdcdcbaccccaccadbadbabaddadadaabccbbbdbddaacbdbacddbcbbacbdcddaaadddadaccabccdabbcdbdabccbbacbcbbdababdaaaabbdbdbdcbccdcaaccabcccbaaccdcadaaadcaddcbaababbdbdddbcbdaaddcaccbdcaddddbbcbcbbccbdcccaadabdcbddaddbaabcddbdbccacadaaccdcacddacdddcccccdddcadabcccddadcabcddbddcaaddcbcbcabcbbcbadbbdabcbbadabbdcbbdcdcdcddccdadcbbdaadcccdadacdbbaaccaaacacbddabcbbddbdcdbacbbcdaaacaadcaaaaabaacacadcddbbdcddbaadacccdbdbddcadddadcdcbdbdcabcdbdbadbddaabbcdadbdadadacbacaaacccccdcdcadbddcbbbacdddabcddabbaddbacccdabdbcbcbacbbbbaadadabcaabcacadadbdccdaabdabcccccacbdccbdbcbddccbbbbcdaaaddbcdcdddadcabbcbdccaacdbdbbddddcaddccababdcdcdacabaddabdbcacabcadcdbcbaaacbdaadcbdacacccadbcdaaddbaabddadbbccacddccdaadacccdbdddbcdbcbbcacbacacdbbdbbcbddcbbdbbcaccaacabadcbccadddadddacbcacccdcbccbdcabbbdddacabddbadcbadccbdddcadbccacdadcbbbdcdadadaaddcdcbcccdbacadbbccaabcaaddcddcdddbcacccabdbabbcdacdbbddaddcacadcbbcdbcccccbbabdaddcacccdbaaacbcbcbbabcbadbccaaabcabbccbaabbbbbcbabbccadbbdabcaaddcbcbbbdcaaaccbacabdddbccdcbdcdaadcbddcccaddbcbbddacdcbbabcabaddadbbcbcbcdabcadcccdddccabddbdadcbaabcacabbaaddadcdbcabdbbcbadcadcbadddabbbadcadadbbbaddabddabadcacbabbabcdaddbdcbbcdbabcdbcabdacdcbdadbdbdaadcaccacbdddccbbacaadacbbdcaadcabcdcbbddbcccbdddaaababdccacacdabaacdbdbdaddcdcadcbdaddaaaccabbdddcddaaccbcdbabcdcadbabdccdbccadbddcdbcdbcbccdcbcdbbbacccbaadbacbababbbbbaabbaccacabcdbbdbcabacabbcabbbccdcadbdcbbaaacbcbcaadabbdaaabacacdabccaacabcaccbadcbccbdbddbcccbcacbddacaadcdabacadbcddcaacaababddcaccdabaccaaaabaccabbcadcddacccdbaccbcacddadcdaaacadacabdcccbbddaddbcddaaadcdaccbaddabaabdcacbcccaddccddccadcabdbabacbddbaaccaabcbbbbdadbbbbdcadaccccabddaddbbadcccbaadadccacdbaadaaabdacaaccbabaacbdcbcadacacadbbbcaadcaadddcadaabbdccabbbaddddacaabbcabbbaaaabbccbdddacdcbdbcadaadacbcdbddaccbddadabbbcdadddcabaccbabbacccdabbabcbdcccacddaabdadcdbabdcbccdcbcbacbaaccdcadaddbcbacabbdcadbcddbbaccbbddaaaccbacddcddbadddadaaaddbbbadaaccbabccbaadcaacbbbdcccddcdcccacadbdcaccabcbbadbacdcbbacadbbccbbdbbaadbccdbcadbabdacdcdbadccddbcbcacccbbcbaddabbbdabaacbadaaabbbacbabcabcbabccbcbbbacbaaabdbadcabadcbdcdabbaadcaccbbaacacbccabbcbbbabcbcaaacdaacdaccbbbbcdccbcaaddbcacbacbaadbaacccddbdbdaaddbccadadaacdaaadaadddcbccdaacdadddcccabcbbcabdaabcabbdacccdcccababdddacaaadddaadcbdbbdaddcadbcdaaadccbbbabbcbdcaaaadbbbbacaadbbbcbabdcdcaacacababababcdaccbcdcbcbcbabcabbcbcdcbbadaddccabcdbddcbbcbcadcdccbdbbbaabbcaaccbddacbcccbbcbdcdcbadcbbcbacbacdddbddcbadbadabadbbcddabaddbbbbdacbddccadbddabbcdcdbaacbcbbbdaadccabaacbdbcbcbcdcbcdbaadbcbbabdcabbdbdbadcdcddcacddacacabacdbdddcddbddbcbbadbaccabdabddcdcccdccbdadcabcbbacbcccccdcbdcbcbabdacaddcabcccdccccbbcdccbcbaaaacaacabdbbabddabbbabddcdbccbbacdbbbbdbacbccbcadccbdababcdabcbdccccbbbbaccaacbbddacbccbabdcdddadacbdbcdaccdbcbacdcdbbacdadcacbdcdbdddcadcbaaabbabaadcddbcbdccaadaacdccccdccddccdabbddbdbabcabcddbbbabcbacdaabbbacdbddbbdaabbbcbdddadbcdccaababbcddaccccbdbdbaaabdbcbacccbbcbcacdaababacbbaabcbbdbcabbabbccabcbdaaccacddccbbdcabaabaccdabacdbdcbaaccdddbdcdabadbbbabdbbcbaacbcdacbbdabbbbdcccacdadabbbcbcdabaccddcdcbccbacbccbbcbbabaadcbcccabbadcddbadcacdcddabadadbdacdcaababbdcdbcbcdddddababdcdcbddddbabaaadbabccdbbcacbdbccdbdaabcacbbbcbcdabbbbbddbbdcacadcdbcaccbbbadccbbccbcbacccabaabcdccbcdabddcddabbaaacccdbdabcbdddbabadbbddaacdbdbbccacadddaabaadcbdcbdbdacbbcbdaaabbbacbccaaacadbccdacadaacababbccdbbdbbbacdbbdadadbcbbbbdaabcccccdacadcbdacacccddbcabdbaaacbcbccadaddbabacadabbdbcdcadcdbccbbbbaaabcabdbdcbbccaaaabcccddbdacccbaccbdddccccdacdbccddddaacbdbcdacdbbaccbdccadbbdabdccbdcccbdcdbbccdcbabbababbccbcbbbbcdacbcbadcbaacbbaddaadacabacadadacbaccdbcdcbdbbbaacabcbdacbdbdbdcbdcdcaabcdcbaddabbabdacdccbaddbdcdbccbcbbcacdbbbbcbdbddcbdbbcdcbbdcadbaccbbdacbbadadacabdabcbcbbacbdaabbbcbddbaccadcdbcacdcdcababacbcdbbbcadddbdcdcccadbcdaacacbaabdccdcdccbbcabadaaaaacbddcdcdacaaccdaabdabccddcabbbadbcbabdbabdbbcbdabadabcbdbdabdccdacabdbcdcdbcaccbdaaaacddadddadcadcaabcdccdccccbacbdbcdbacbcdddbbbcccdabcdabbcabcddbabbccababbacbcbcdcadbacdcacaabccaacadaaddbbacaadbabdcbabbcacbdadcdcbcbdcdcdcbdcbddbdbcdaabdadcbbdcbbabaccadbdcdbcdaacbcabbadadbbcdddbdcdbabbccbcdacdcaadbaddccbbdbaddaadbcacdbcbbdddccdadcbdcdbdbaccdbbcbccdcaabbabcaaaabdadddccdbabbbbaaccbddcacadcbddcdbcccabdaadcadaddacdabacdbccbabbcddcdbaabbddacbbddcabbbcaccadddaacacacbcdabcccbdbbddbaacabbcadccbdacaaabacdbdbdbcdcbdddacddadbcddccccdaddcdbdbbdabaddacbcbadcacbdadbbdcacbabbaabbcaddaccadbbacbaaddcccadbdcbdaddaacbdbcdbbccbbbaadcbdcdbcacdaccbbadcdabbccccabccdacdcbccdbbccdacbacdbdacbabdcdcbddacbdababbbddbbabdcaadaddadbcdbabacabcbacaaadcdbccdcdcdbdcddabbcbbabadabbbaadbcddbaabbdbaccbbcdaacbbadaddbbdcbbdbddcabcbabaccccabcadcdacadbcccbdcabadbbcabccdcdabdddadabaccabcdabaabcbbabcbcbdadbdbddadcaaaaaccccdadddbbaacbddabaaadacbbcabbbbdcacadcbddccddaacddbcddbbacdcdccdccddaddadbacabbaacacdbdbbcdacacabadbdbadbaadabbbbdaaabddbdbcadbdabbdbddacadccddbaaccbcabcbddbbdbdddbacccbabdbbcabbbddcbaccdddcabccbbabcbdabddccdaccdccdccabcdcaaddbdbbabddabccddbabacdaaddaaccabcababbdcbdcccccdccdbbcccaaabaccbdcbbbadbdddadbbcbcdcdababcbdacbdabcadbcabcdbdcdaddbcabbddbaccbddbadadbcbadbddcadccbbdadcabcbdaaaadbadbdadcbacaccccbabacadcaacbdcaadabccadcccabdbbbadbadbbcabacabaabdbbcdabbbdaaccacddcaccdcabcaadaacddbcadddccdcdabdadcaddddddbdaccddccddacccadbacdbdcabccbdcadcdbbaadcdbcbdacdaddbaaadcbacaaacdabbbcbbbddadaccaddccdbdddbbadcaacddcaccacbaacdacaddbcaddaccddadbabacabccdbacbaccccdccbdbbaacbccdcaccdbabbcaaadcaaadadabdcddcdccbcdbabdacccabdbcddabdcacbdabcacabccbcbacbdccaccbcadbcdacdcccbcababddabaacacbbdcacdccddbdbdddcdbdbcbacdacbbcbaadccccbbdcaabdcbbabdabdadcdbbbbaccaaaacbbacddacabddcadabaadbbdaaaadadbdddccaacdaadcbadbaacabdbaadbdddacbdadabbdcccbddbccbdaddacbcbdbddcabacaacadbcadddccaadaaacbaddcbcabdbdaabddcdcbaaadcdbadbdaadddabccacdbdacabcbddacddbdddacccdccdcaadcddabcaadaabcdbbcddccbddcbdcdcbbccdccdddcacadaababcbdbabcacddabbcdddadaddbbabadbccdbdabbbaccdcadbbaccbadbddadbacbaaabbbbacaddccacbbdcdbcbddccdabdbcacaddccadbbcabbcabaccaabaabdbaccadbaadbbcdcddcabccaadaaddbacabccaabdcdcdadbbdbcadacccaaaababbabcbacdccbdaaddcdcadbbcbacdcdabcbcaddbbacddccbdddddbccaabdcbbbadadabbcbcacddccddccddbcdddcaddacbbcdabddbbbdcdbccabadacbbbaabcdccbabcaaaaadcdbbdbadddabacabdbdbcababcaddaaccbdbcdddbdcbdbadcdadddcdbddbabccbddacaccccbbdbadcdcdabbbadccbcbaadbdcaacaddadaaadacbdccabbbcdacbcdbbdbbcacdddbabbacaaddbccabbcdcdbdcdabdacdbadabaaddabcbacbcccdbcdcaccbdadbbccaabdccbaaacbcbabacaccccdbcccddcaccabcdcddbcdadacdaadccbacdcbaccacddcacaccadacdacbabacbbabdcbdcabbdadabdbdbdcbdbdddadbddbddacbcbcbcbdbddaabadbccbdcdbacadddacbacccabcdaacdaaccbdabbadbdcacaacbdbcaacabccbdabacbbbcccbdddabcbddddcadccdcacabbdcdacbcbddaaaccbccaaddadadcdcaabdaaabbaacacbacaabdabbccbcaabdcaccaaadcdbbdacbddaddcddccdabdbcdcbbbdccbbbbbdbaaadacbbacdcacaaabdcaccaadbccbaaccbbcaddcbdbbdcacddcbaccabccccacbdbbadbcddbabacbdccbbadadcddccccadbdadcbdabdcdaadcbaddbbbcacdccbaddcbdacaadabbaadccddbacadacbbbaababacabaadddcdcbacbcacababbaaabbbbaddddddcbcbbacbacbbdccdadacbdabcbcaccdbddacbdcacdcdccaacbccbdabccabdcdabbccddbbaadcbcbcabccabdbabbbbcbbcababdcbbaacadbacdcdabadddcccbaccbdabddaacbaddbbbbcbbcaacddddbcccaadccbbbabdacbdbcccbcdccdcbdabcbddcddccddbbdcddcccbacccdcdbaadcacbcacdbdddddabcbcdcccabcbdaacbcaddbbdbaccbdcaadaacacbaaaccbcbbbcbbcadcaccbdcabadabcdbdaaacadbabcdbadadacaccdabbaddbaabddcaacaccccadbbdcacdddabddbcbdcbbbacaabacdaaddbcaacbcddcbdabbccacdbabbcdbbbdccbbbdcccadbaadbccababbabccbbddbbaaaacbaaddabadabcadacbabbdcccbacddcbbaccccdbabbdbddddcbabcccbddbcbddaacaacdbdcbdaadababdbbccaabdddbbaaccddccddacaababbacdccadbbcbcaddbaabcbaacaacaaddadabcdbabaaacbcadacdacaccccaacdbcccadabaadccdaacbaadbacdbccadcbdbbacbdcccbacbdbccaddaadcbdbdcbcbabbacbbbbcabaacbcbbbabbcbaaccdbdbdabdabbdbacbcbdcababcccbabdcbbadaabbdacabcdcacadcacdaaddcbadcdbdccadccabbaddadbcdddddababbacbcbadaacdaacbdddcdcadbabdcbaaacdcbabacdcdcdddaaddcddadbdcdbabddbcdcddccdbbdadbbdbbaaaabbacabdcabbcbdacdbdacdadbdbcabbbbabcacdbdbcdacacccdbbccdacdababadbbbcaaabbdcaccdaaccbbabdaabbaaacabdabddbbccdcaabbbaababacdaabdbcdbcbbaaabdbddcbabbcbbaddbdaadcdddddbbacccdcacbbabbabdaaabababddcadcbcdbcdadbdcaacdaacbcddcccaccdbccabccaacddbababadccabdbccbbbdcbbdcadbdacabddcddddaadddcdcdbdacdadabbadbbdddaccdcdcccccbcadccbadadbbacbcabadbdaabbccbdbdbddcbcddbdcbcaccaacbcdbbadbccbaaaacacaadbbbdcdbbabbbbbcabbacdbdadabcadabacdabdbaabcabaddccbdcaabcdddccabacbdbaaddadbaddaccdbddaaacdabbdcdaacbabdcdccdabdacaddabcbbadcbdccccabacdaabdacabdbacbcadcddabccbbcaaacadababccacccabbdaadddadddccabbdcabbabbcbaacbbabcabbacadacabcadcdababaaccddbcacddbdbaccabadabadbdbabcdbcccbacccbaddbaccadbadcbbccaaaacbcbddcddacbbbbaccbcaaaadaccadbbdddccbcdabccabcaacccaddaacdbaabddcbaaabababbbcbcabcbadbbaddaabbabbaabcacabadcbcacbcbcaaadaaccbcbddaccdccddbdaaadddcbbccbccbcdcdaadddddbcbbbcabbddcbcbdcaddadbcabaacbbdacacacccccdccbcddacbadbdaaadcccdadaddcccdacddbcddddaaaddaaaadbcabaacdddddaccdddcacadbcacdabccddcbaccabdcddbbdcbdccadbdaccbacbdccabdbdabddddbccbdcacdbacbbacaabaadaaacddcbcbadccbaacabbbaccacbcbbdbbbccaadabbdbdcdbcbdcdbccdcabbcadddaabaddbcbcccbaadadbbcbbabcddaabbdbaadacdcdbacccbdbdcddbdddbbdadbbcaacabaddabbaabbabbcdacbbadbbdbaabcccacadcaacdaabbccdddcabbbabccabaacdbaaccbbcbaabddcabacabcacccccbbbddbabddacdcccadacbcbbddcccbcbdbdbabdddcaddcccdccbdddaadccabbabccaaabccdbaadababdddacdaadcaabcdacdddbddcaabcdbaccbdababbaacdbddbdcaaabaccaddccbcbdaddbbccaadaabaabacaadbacdabcddcbdadaaabadbdadcdddabadcdbadbbcdadcccacabdadabbccadddabdadbddbacdacdbadbbccadcccdcdadbbccaabadcddaaacabacbabdcbaaccaaabadcdcbbabdadccaababddabbcabbbadaccabbdbdcccaadcdcacdcadbcadcccdbdaaadcdbcdacbbbaaddbacbbbbaadcaadccabccdbcdcbcdabcdddaddddcbadddaaddaaababdcdbacaabdcaabacdccdccdbaccccacaabbbdaddbbdddaccccacaaaddcbccadbabbbcbabdadadcdadddbcdcdcadacadbbbbaaabcadabdcabddbaaadccccabdcaaaabdcddcdaacbbcacccadadbaaadcdcaabddcbbbaadcdaacadbcdcccaccddcbdbabaadaaadccddccddbaaccaaabdadaacaaaadcabbdbbabccdaaccaaddddabcdbcddbaaaadbdcbacbabdcaacbdacccdbddccdcddaacdaabaaadcdabbddacbddabbacbaabacdbbdbbacaccbadcabcabddcdddbbaabdcaccdadaccaacaccaadcadcdabcdbddacccbbdbbcaacbcadbbdabcbacdcdbabdbccccdbccaadabbbdcbddbabcaadcdccbbddbadabdaaccddaaaadcadcbdbdaaacaabacadbbaccddaccbacbdbaadaaddccdbbdbadacadcbbaacbdcadabbaddadacdadcadaddcdbcddbdbacccdbcdaababbbcacaadbdaddbcacaccbadbbbcacdbcbbdcbadbbddcacbbcaabaacaabaabccbadadcdacbccbbabcacaaccadccccdcbcaadcccdaaddacabcacbdbadacacbdaaddbdbccbdaadbadddaabdcabadbabddccbcbaccdbbbcaabaabaabbcadbaddccbbbdbbbcdddadbcbbbaabcaabbadabddadccdddbacbdbcbccccdbbdaaadcdaaabdacdbdddbbcddbddbccbbcacadbbbaaccbaaddaabbadaddacdacdbcccdcaabbababaabbddcdcbbabbdaaaadbacdcbacdaccacabddbbbdabdacbbdaccbcdcadacbdbadbbaaacccaaddabbdcabadcabddccadcabbddbaacbbaacabdbbddcdccaacddaacdbbaacbbcacdacaacadbbcbaccdbaabaddabccbbdaaddbabbbccadabddbdbdaaacbaabcddcbadccaccbcacdcccacdababcaddadcbaccaddbdcdbdcdbdccbbcbbbdbdcaadddccadcacccbcdaabcbcaddadccdbddcbcdbbdbbbddcdcbddaacbacdbbdbbdbadbbabcdbbddddcdaccdddddccbddcbdbbcddcbadbccbaaddcbacdcabdcacccdddcbaadbbdccaddbdaccbddaaddcadcdacdcdcdcdabbbbdadbbbaadaaddacddcbdabacdcabcccdbcbcdbbabaddcacadcbcdcaadabbdbbabbadbcabbacccbbbaadcbdabdcacddbdabccdbccacccabcabccbbdcbbadadbabaadbcccddaaccabaadababdcabcbdaccacbbabcbcbccaabcbabbacccbcdababcaaccdacccaabdbabdabdbcdaccacaaadadddbdcadbddcbcadbdaddbdaaddacbdbdaacddadbdaabccbabcbabbdcaaabdccbacddcdaabbcabcadddabbbcbcacccaccadabbdccbadbbaddbdbbacccdcaccaacccacbcabbacdaddabdaadbcadbcdbcbaccdcbcdcabdadbbabdbddbdadcdabcacbcdccbcbaabbdbaabbdadbcbccbcbacaccdacbccabcadaaadddbdcdaacdcdcddbbccdcadcaadbababdddbddbadaabbaabbdcbcdabddadadcdbbcacacdbbdcbaaacddaabacdabcabccbbaccaacabaadabacdacaadaaccdadcccadabaadaabcbbdcadadccadbcbaadddcccbcdbdbcabcadbbadaccadbdcdcccaacdaabbdacdbdccbacddaabbabdcdacadccbccdcaddadddccddabcbabdcdabbdcaadbabbcadadaacacabdbadacdccdbacdbabbcdcdadcbcdbdddcccccbdbcaddadcbccadcbcbacccacdbbbaadccdacbdbbabcbbcabaabbdbabddbcbabdaaadbbcbbcdabcbdabadcbcbaacdbdbacadbcbaacbaadddcaccabadbadadcadcbadcabbdababbcbcdacbdcbcbadbcbcbdadadcabcddbabcdadbdcbabbdcbbdaaddbbbbbcaaadccaabaddcbcdcccadbcdcbdadccbadcbcadadadadabccbbdabbbcbaabadddacccccddddaddacbcdcaacbccaabdccaadabdccdcaaabdcdacdcdcaabbcaabdbdcbcadacbdcadcdbacbcccccdaadabbaccaccdbdbdadcacbacdbdaccdadbadbccdbadbabddbcaadccccddddbcbcdcaaaddadbccdcaaadcabbaddcaaddbccacccaddddbbbdcbcbaaadabcabbdcbdcbcdbababddbbcccbcccabdabcdcbbbacbacbbbdabbcbacabbccaddddcbbdabddcbaabccbabbcdbabdbbabccaaddbcdaacccabddcbadbdbabbabcacabbaaddacdddabdddddbccbacadbcdbcdddaadcdcdadbdbcabaaabdcbbcdadcdabdcddacaccccbaaddbddbccbcccabbabcccddbaddbdcbddddadbdbabdcdcacdcbcadcacccdbbdcdabcacbaacdaddcabccddbcaddcabbcbdcadadcadbcacdbadccabbcdccdddbbbdcdbdcaacdcbabadaaacbbacccdcbadcbcbcbbbbbcadcbbccacbbccdbccbaadcdbcaabadabcdabdcaacaabcdaddcadacddaccbdcbacdbacadaacddbbaaddbcadbdbbdccaccbbddaadddcbadaccbbbdbbbaaaabdcaadaabbbabddaaadbaddbccbbaabaaddabacbcbdbbabaaddbcaaaaacacacabaaaccdcabbabddbdadccddcadcdcccaaacdbbabbaacdccaadabbadabdccbbabcaacdcddcccaccdcbcaadddccaaacabccbaaccbdcbdbacccbabbaaaababdcbbcdbcaaadaccdbdcaabaabdadbbbbdadcabdaacdcbcabbdacdccccbbadbcdbbdbbbaaaadcdcdcbadadbdbdbdbbadabdcdcacccabcccabcdabcadbdaadccbabbbbbdadbccbcdbcaddcabcdbacdbcdcaacabbdcaacacdbcdcaccdbbcbdaaacbaaccababdadcdbdcacbbacdbacabdbcdadacbabdcabdcccdadaaddacbacaccaabdbdadabbdddacaaccdadcddcbbadabbabbaaaddddcbcdcbccbdcdbcabdabcabccaadbddaccbccadbabddbbcabadcabacbcbadaccabadcdabcaadabdbbbbcddabbbabbdbbcdbbabbcaaddddadbaabdbacdbdbcadacdbcdbabcdbccbbdadadacbbdcbcadbbacdaddabaadaadadcaaddddaddbcaaadcaaaccacbcaaccdbaccccaddbbdccbbbdcadabcbdbadabadccdaaaddbbcbdcaccabadbaacbacaabbdcdccbccdaccdabcaccacabdbbbccccdadbccdabbbacdbdbcdacdcbcdbaaccdcdddababaccdcdbbdbbaccbdaadcaaacadcabcadccddcbdcbcadabdcdcbabccbacbabdbbaaabdccbaaccadacbabcadadaaddbccdabbdddcbcddacdbddccbbabbcddbdcacdaabbbbdbbcadcbbdddccbbabbbbcddccbcacacdaaabacbabaddcbbaadabbdabddcadadddcacacdbadccbcbacaacbabddbddabcbdadbbcddcddbaacdbcabbcbbdabcbbbacdcdaaccaabbdbdbddccaddccbcdbcacddabaaabcbabacbbbdaabadcaaababdaabcaabbdbabddcddcbdcbbdbdbdaacbbacbddacbcadcdcbbaacaadcadcccabababcddcccabccbdcbcacbdadcadacabbbaddbbadbccdcacbccbbdbaaacdcddadaddaaaaccddcddbdaddbaadacbdacccabdbdbbaccdccadabbddbddddbcaabdddbabdccbcccdaadadbccbddadddcdcabadacbbdacaabccbbabacdaabaabccbcccabccccbadddbddcbdaacacacadaadbabacacdabadcbcbadabcdcbaaadaaccadacccbacdcdcdbbddbaddbacdaccbdbcdcddadabadadbdaaacbdbdaddbdbbbbccabcbcadabbcaaabdbddbaaadcdcdaacabddacbbaadbdbadcdabaccabacaaaccaaddccdbdaaccadcccccddbaaabdacdbddbccdcaabdbacbcbcbadcddbbadaadddbbabddbcbcccbbccabcadcabdacaccdbddbdbabbacdcdbabacddcdabdcccbbcabbaaaaabbbbacabbdabbbaadcadbbcbdbcccbbacadbdbcabbbcddadadcdbbcdccbbbcadadbaddcbabadbaccaabbddddadadbbbbcddbcdadcdbddbaccdddcccadcddcabbbaccbaacbdadccacdbdacbabcdcccabacbdcccbcadccbcaadabaabdabbcbabccabcddbdaadbbdddacaaddabdcacabcddcbdabbaaaadccabdbaddcddbddaadcdcbacdabbbacadcddaaaaabacaabcabbbdcbcbbbabcdcacdacbbcccadacbbdcdccadaddaddcdaaadccdbdadcadbbaadcdbbcaacbbddbabcbacbbadcbdbccaadcccacddddbdbddcbabccabdcbbcbabcbcbcadbcabdacaddbbcbacabdbdcbacdddbbcdbadadacccdbdddddbbdddcabdadbacbabcaccdbddddcadbaccacdbbbbcadaabbcdacdbbbabdccabbcadcadcddbaddadccabdacadddbdaabddbcbacbdcabcaaddcbddacccbbbbacacbbdabaadbddabaabccadbcbdbdbddddabacadccdccdddcbbbadddccabdbcaababbaaaabdaddbcdacbcaccdcaccdabbccccaacdbacdaabdbddddbbacbbbdbcbbacbbbbaccdbdbcddacdaaabbacaabbdddccdbbcadddcbdbbcabccbabbbdddbaabcdbbbddbdacddadbccbbbbcbcdaabbbbdbddbbbcaccaacaadcaccadddbbaadaaaacacccdcdbddadbcddcbabdaabbcaadcdcddccbaccbdbcddbcdcbdcbccbddccdbddaaaadccbcccdcbcacccadbbcbabcacbadacbbcbacbddcdbbadddbdbdccbbcbbcacabcabcdcdcabbdaaacdbcbdbddacdaaacaacdbcdaacaaabccbbbccdbacbdacbbddabbcbddccddccdbaaadadabbadacdccbcddbabcbbdaabaacdddcabbbbbbcccbadbcbdbbdddbaccbbbdddbaccdccabddbcadccddaaacacacbbbdddccdcddbbabaabadddcdbbdbcaabbccacdabbdccccabdcbcbcaccabbdabbdbdcddbdaabbaacaadbabaadbdacbbdcddabacaacbbdbcccbcbccdbdadbbbbdabaacaadbacbcadcdddbcabbdacdddbbacbcaaaccddcbabadaabdbbcbbdcbcdccdbbacbdadabbcaddcdaacbcabccdcdbccbcdabbdcdcccbabaadacacdcddddbacdbdcdbbaaaaabacbaddbabdcbddcacdadacdacababcacbbdbdccaacddbdcbddddccdadababcccbadddcaabbdddbcbbcbdbccaddbbcbdadadcccbabaaccbcadcccddaacbcbdbdacdbcccaabdcabdbdcdabbdcdbdddbbcbaadccbbdbdcaadddaccaabdbdbddaabbcccbadbdbaacbbcdabcdabadaaaddccdcdcdaacbbacbabdbaacddbdcbacaccadbcccdaaccdddcbccadcaabcdaccaadadcacdcadabdaacbcbbbbbcacaadcaddbccdaabdbbbaaabccddaabbcabbaccbcbbbcddbaadacdaacdbbaacdbaacbdccbcbbaabbaaacbbbacabbaacdbbdcabcaadccbcbadbccdadbadaccbacbbcbabbddcbaadbcadcadabbbabdaadabbbbacccbdccaccbcdbcbbbabdbbabababcdbaddcdbacdddcbbcddaddccbccbdadbcbbbbacbdcbccdbcbabadbdccdbadbcaddaaabcdbdadbbdddacdbdabbdbdcdaccbabbbdaabcabdddbbcdbadcaacccddbcccacddaadbbccbaaabdbdbdabbabdccbabbbbaacacbcabbbccaddadcaddddacabcbddbbcacddbacbbcddbacacbbabddcbccdabbaddadadccdccccccdbbcbcccbaddadacabacdccbdbbdcacabbdcbaabdcadbcbcdcabbbdaadbcddaadbdaaaaaadacbddcdabbdcaabdddcdbccdacaddbcaccacacaaaddbabacaabbcbdadbaaadbccdbaccdcbaadaaabcbccbcbdbcaaabadccabacbabcadabbbdcdbabbcbdaddcccdcbaccdcdcaccaabcdabcdaadcabcdabccccdbddcdcadaccddcbdcddbbdbcabbdbbbdaabbaaccccaacdbdddadacccdbddaacccccaaddaddccbaaaacdbcccddcbdbdbaadcdaaaabbbcaaabbdbcabbcdbbadcccacabddbbbabcdccdabadacdcbaddcbbcbccbbcdbbbdcacccddccccbbbacaadccdbbadccadcbcbcccbddbcdaccbdaaadccabbaadbdacababbcacaaddcbbabcdacaabdcaaaddcdaccbcbbcaccddccdadcdbddaaccadcabcbbbcdadbbcacaaadcadbabddaadcabbcabcbdcdaabccddaabdacbaababbddabadddaabacdcccccbaccacdbcddcdddcccddddccaccaabcaacbcbddbdcacbdbccabcbbdcadaddaadaaadacccaaaaaabbdcdddddacbdbadcbaaddbddccdbddbcdcdcbdbcbddcbbccbbdcdaccbddcdaddddabacddaccbbdabcabdbdcacbcaaddacbcbdcccdadcbcccaaacbbcdadccadddacbcbdbcdbddbbbcccccbbdbadcccaaabdaddcccdddcbbbddbdcbdccabcbbaabdcbabbadbcccdacbcdabaddcabbaaabcdddcbdaddcccaadacdcbabdddccaddaaacdaccaadcbabccbbdbcdababdcdcdaccdcacbaaccccbbacbadccddabaaabbdbaacaaadcbbdddccabddadbbacbabbabcddcdbdabbddcbcddddccdcacaddcbbacbbddbcaaccbddbcdbcddadcdbacadccbdcdacdccdbcdccadbaabbbbabbabcddaadddaadddcbdadbccdbbdddccacaabddbaacabcdaddadcacabdbdcdbcadbabaacdacbbdddacdaddcccbccdaddcdbccdbadcdbccaacbccccadddaadcbcaabcddcbacdddbaddabacabddbbdcdcdcbbdacadcaaacbbbbcbadccbdbbdbbcbdbacaacabcacbbbaddcbcbcccbccccdcdacddcbdddbbccadbdbdbbabdadacbdaccaacbdadabcdaadbcccaacdaacdacabccadbabacdccadcddaaacabbaacccbacaacddddabcdaacbdcdbcddacbadbccabccabcdacaccbcbbadddcdbbdcdacadaadcaaddabbcabddccaaabbbacdcaadabbbdbadaddddbcbcddaaddbbadcaaacabcaabcbbaaadddbbdbccadcbdcaabdbccaaccadcadbadbcaacbcbcdaadadabbcabdadbcdaddbbcbadcdcdcccdcadbacadbabbdccdbbdaddccadcdbbdacacdccddcccbddaccdbacaddacbabccbcadbcbbdbdbbbdcdcaabcabaccaddcadaccdbdcbabdbddcaddabcacbaadbbdaabcadacaaaccacadcacabaacdcbdbbbcccabcddbaaaacccbdbaaaaaacbcbdbcbdcdcbadcaadcdbcccacdaabbcdccbdbadcbdbcddabbcbbbcbcaabddddcccaabaaabadababbcbbacbdaacabadcbddbaccdbdaaaaccadccdddbdcddacadaabdcdcaadbaccbdcabacbdabddddcaabaaadbadddbacacdcddcccaaadbacacdccacbcbbadabcabaacbbbcccaacdaabaabdadddaccacacbaddaadbcdbccbdbabbbccdaabdbbdbdccbcadabcbabcccdabadccddadbcaacaabaddcbabadcbbbcacdcdabccbbbbacdaaabdadddadcdbaccdcbcdaacbbdbbbadccdcbdacbbbbadccacbbacabdbcccdbbdabbbbabcdccbdbcdccdccacacdbaccacabcdaddbcdacdcbdbadcabcdabbbcdadddbadabddcacacddbbcacdcdbccabbcaaccaddadccdccdbcdaacaaabbbcacaacdccabbaabbaadabbbddccdbadddbaddacddddddcdcccaacdbabdbbcababaadcaaddcbaabbcadaababbdabbdbcbabacbdbbcaccbaaacbdaacaacbdcbbcacabcabdcadddcbbbdddacbbdacdbaabcbbcccbddccaacddbbccabacadbaccdcaaabdcaacbbddbaccdcabdbaccccadcdaaccbbaacaccbbcbbbabcdaabddcadbbabbddccdaadbadadbbdadccccadcadddccaddcababcaccbbddbdacbccaabdbcbcabbabdbbdbdaabddbcbaddaabbcbddbaccdccbcbddbbbaaccdbadcdaaaddaacdbbcbabcaadbbbbcbacdddbccdcbbcbdbbcadbccdabbcadacbbabbabcccbabbdcccdadbbbabbbcbdddabcdbddcbcccdadbcbdccccdbdcccddcdadabadbabdaccbdbcbdabbbdbadccbabcddddcbacbccaabaaddcdddcdbccbccdaccbbcbbabbccdabbbccabaccbbdbabbbadccdacdaababadadcddadbdcabbcbcbbbbbcadadcbadaddbcdacabacadacacbddbdcabddcbddcdbbdddcadbbacdbaddadccadccddbbdabadcdcadbbcbdcbcacabcbbbdcacaaabaddacdcabacbbcdbbacabdbcadbddaccadabacdadbdaabdbccacacbccbadaabcddbccaccdcabaabbbadbaabbbbbaccdbcddaaacbadddbbacbaaccbaaadbdabacccbacacaabbccccdcbaabababcdacccbadacdaccbcdcaccaadcbacbbcdabbcdaaaaaabaddabbdacbdddabcbbbdadcdddaddccdcabcdabcaacccadaaabaddaccbcdddacabdbcbaadabaabdaddcbacdcaacabdbcaaccabcddcbccacabacaadcbdbadcbbcdccbdcdbdaddccdcccadbbdccacccdababcdacccaacbabdcdadbdabbdcccbdbdddbccdaabdbdbacbabdccbcdbacbcddbbaaddbbdcddaaabbaadbbdbccdaaabbcaadbbcadaadbcccbbadbbcccabddaadbbcdcbbcbdccacccddabccdcdbddbdbadbacdadbdbabacccaaaadcdabddabdbcccdbacabbadbbdacbaddcabaadbdbbdbcadddcbbcdcaaddcddcabdabaddcdbabaccacbcaabcbdddbcccdaacacbcbabbdddcaabddadddbadcdcabbabbdcbbcadcdcdccacdbcdbacabbddbabbbcddcdcacddcdabbabbdbacdabcbacdcbabdbcbcccdcdcacaacacbabdcdbcdcbacacdacbaaacbbaadaddaabcccbdadaddabbacabccddccddcccdbacabcbdccbdaabdcbbcacbbdddadbdabbccdacdbcdcdbbbbcaabaacccdabbdbacdcdcccabaccccdaacddabbddddabddacdcbaddbcddddddaaaacabdbddcbcddbcdaccdddabbcaadbdddccabccaddddacbbcdaacbcddacadabadbddbacdaaaaddbcbbdbbcacbabdcabddbaacbcdcbddbbadcbbddbabdbbadcaaabacddbcdcbcbbccaabaaababcacbabbbbbbbdbbdcdcaddddaccbbdadbaaadadabdccbdcdbbadccbacccbbadabbbcaddaaaadacabcbbcddbddadbabcaabbccaaadcdcdcddcbbcbbaacaaacbbcccbcbaacdaaddbddcdcdaccccaabdadcdbcddacdbbdbbcaadadacdddbbbababbbbdbdcbbadacadbaddcacccdadbcabaacabcccacddddbddaddbaccbdaababbcdbdbddcdbccddbdddbadbdcbcccdcabddbdbdbdcbbccadcadbddabacababccacadacaacdccbdabcdccbadacaccabaccacadbdacdabcbdddbcccdbbbddacaacdcbabccabdbaabadcbbababbbaccbbcbdcacdddddddbdbbdcbcabacaabdadccbcbccaaabdbdbcdbccddddddcacbccacabbccdacdbddbcbacaddcdaadcbbbadbadcbacadbdbbcbacaccbddddaaadccabadbcacbdbccddddcaccbaadbbbaccdbdbcbcdcacdccadabaaadadadaccaabccacbbbdbbccbcdbcaaacdabcdacbcbcabccbcbabccadadbdddbbcbacbcabaaabaddcdddabdcddbbbaacdcbdcadcdcaddaaaadbcbcdbdbdcacdabbcaadcdccaaaabadabcdbdacdbcdccabaacbcbcadcabcddcaccaaadcccdadbabdabdcacccbaaabaccccacbcbdbbbdcbddbccccaaacbadaadacdbbccdcadbabbacbdccacccabacbdaddccdacadadbdadadabababcbbaabbbacdccbdbcaddbcbabcdcacbddbdddbdaddbbbbbcadcbbdcacdbddbdcaabcdcddabcabdddbcbdaacdaacaddccdadaddadbcbbdcadabcdbbcccaabdaaddbdcacbddbbdcdacdacbdadcddacdddacbacbcddcaaadbdcacacabcbaadbaccccbddbcdcdbabadbcadbcbcccadbccdaadcdaababcbcabddccacbbbddddcaddabbadcbdaddcaddcdacabcbcdcbcddadddaccdacdddacadadcabdbaccdaccccccddaabbbdcbdabbdcdacccaccbbcacbbbcacaddaadbbdbddbaacacccdaddabacdbbccacbaadabcbccbbbdbbcbaddacccadbbcabacdaadabcbcdbbacadccaadbbacbcdacbddcdaccbdadddcabbabcbddcbdacdaabccdbdadcdbbcbacdaaaacdacddcdcbcddbabbacddcdcbbdcdcbcadcaaaccdcdbdddaddabaadddbaacabdabddadacaddadddcdbacacdcbdcbccbdbcadcdaddaacdbcdcdcabacddccdbdcaadababaccabbcadbbacbcabdcadadadcabcbccdccaacadccacdccdbcbbddcdaabccabdacdadcadaacbdcaacdcbaabbddbbccddadabccbdbdcabacaaacddcaadcccabdccdabbbbcbbddcbccccabababbdabddbbbacbdcaaadabdcbcacacdacbadacdcbdddacaaabdacbbcabccdadbaccddcaaaadbccbbdadcadcadadccaddcadabacabdadbdcdaaacccaabadacdcadadbccbabbabacaccbaddbadcaaabbcacdaabaabadddaaacddaababddcbacbdbbcdbabcdabcbcabadbacaddaaddaddadaabbbbdaaaaadbddacccadddbdbcddddaabcbbccbaaddaadcadbdaadbbdacadcccdbdbaddccbdddaabbadcbddddaacdaaddaacdabdadcaacbcabbdddcdccddadcbcddbcccabbcbbcddacaabaccccabdbdbcbdaacdadcdccdaaaabcdbcabbbbabdcddbbddcabccbaccbbbdcdddcbcbdbdbbcddcccdacdcacabdbcaaadabcbcbdbbddcadaddbbbdcaadbcabbacbbacaaddabcdadbcbdccacbddbcacbcdcbabacbcddcbaabbdbbcddadabbbbbaacbabbabdbaacbbcdabbbadbbdccbaadcabdabcbccbbdbaccaddbbacaccdbcabcdccaddddaccabdbacabaddadabaabcacabcadcdcdcdccbaccbcbcbdbcbbabccdacbbcddadcacbbaaadcbbdccbcaddccddadbcbbdacaccbaacdacbbcbdbbbaacbdbbabddcbdacbcabbdbcbdbdcbcadbdabcdabdbdcadccdabdadddcdbdabbdccacccdbcbaadadcbabbbcbddcadbddcdbddbcabcbacdccbdcdcdbcdbccacbdbaacbbaccaaaccacdbadaacdaadbbbdbcdcccacbdacbbcddbcaccacbdcbbcdccaabbaabaccadcabccdccabbdabacaccdabcabcbdbadaaaadcddccbdadabbbcbbbcccbbbddacbdddbbbdbdcdbcdbcbcacccccaddabadcacabbabbbbbbdddbcbdcabcbbabcdcdcadccccadbadbadbdddbcddddbdddcccdbbaaddcaadadaddacadacdcbcdbbdddbcbadbbcabcabbdbdaaaadaccdbccbadccbddbbbcadbbbbadbacdbbaccddbacbadcaccccbbbcbddddcbaaabaaabdccbdddbabdadadcabdcdbaabdcdcababbdaabccbdacbdbbacadcabaaacdbcccdaababacbaaaaadcbcacadcdcbcbdadcbccacababadbdbacaabdaaabbaabaaccbcabcacabdbaddbbaddcbbbdbaaabdaddbdcccbdaccbdcddacddadbdbacdacacccdccdbdddcbddbccdbdbcddddacadadddbbbabbcdbbccaccdaccadcbddbadcccbcbdadaaabcbbccbdddaacdcabbcbccccdbcabcadcadcdbccbaadaabaacdcaacdbccdcbdcacddbcbcaddbaadbaadbccaadcdddcaaddaaacbaadacadacabdcbbadadabbbacaaaadadbadcbdbabdcadcccadbdbcabdaaabbbaaccbcacbacdabbabcdddaddaabcbacababdbacbcdcbbbdaabdcbdcabadbdabdbacdbaddccbaabbdccadbddbbaaddaaddddaacbbadaacaddbddbbdcacaabaddbbaaccdaadacabbbadbcbcabddadcbbccabacaacdcdbbcdbdbaacdaddcdbcaaabccacccadbddacbcccaccaabacddbbadcabdbabcbccdccacdcdcbbbcdadbbcadbbacbddaccbbcabbdbbaacbbabcbdacdcacaccdcbbadacddcabdbdcbabcbbadddddbddaaccbdcbcbdacbaababccbbbcddcabcdcbcdabbbbdcbaabdacddbaacbdddbaddaddcaaccabbabdaaacaabacccddadbdccbbdccabdcbbaccbbacddaccbbaddcccddacddcacbabadcdddcaabcbccbaadacadbcdcddddddbaddadacccacbdbbdbbadddcdbbacadaaacbbabbcdcabbdcbaadadacabbadddbdccdcabddadababbccbcdabdcdbacbbbadbddaabdaddbbcdadcccbdcbcababdcacbddabcbcccbddcdcacadaccdddbbcbabababcaaabcddadadbaacbbacacbdddcabdbddcbdcddbdaccaddddadbacbccbbccdaaacbcdaadcaddabcdabbbaaaadddadbadaaaabbcaadccbdcdbcadbbcbbdbcadcaabdccadaaddbbddabadacabcddddddcdaaaabbabbcdbcccccaccdcdddcdccdddcdadabbbcdbaddbbcdcadcdaadcbabacdbccdddacdddcbcdddcdcbdaabacdababcdaadbababddccbdaacbccbbdbabcdcabdddcbaccabbbdccacdcbabbccbacbcdabdaaacddcabacdbaaaabbdaacddabccadbbcbbcacabdacabbdadbadbcdadadaababcdcdaabaaacbbbdcdadcaadbdacdadcdbcbaaabcdcbdbcdddaacdbaabcccaabcbdbbbcbbdcdddddaccacccccbbadacbdcbbbabbbadabbbbaddaddddbccaaaddbddbcddcacabacacacddbddabbbcaddcbdcdcccdccdccacbcaaabcabbdacdabdcdaaaaddbdcbbbddbcbaabcbbcbdcbcaacbbaabddcdcbabdcbdabcbaaddacbddcbbbbaddadbcadbcdadabaaababdbcbbdadaaacdabadadddaddddddbbbcbaadddbddccbadcadaabbccddddcbdabcaacacadcabccdabddddcbccdabdbacbddbcabadbabbbdadaddbdadcbdadbdacaddabaacdddccddcbcaadababbbaabdccbbcccbbbaadbabaccbabbcdcadacaadbdabacddadadbcaacdaaaacbdaabdbbbabdcadbdbbcdcccccddaacbacacbccaaabccacbbcbcbddccccbbbbaacadbbdddbacdbbbdddcbccbdabcdcdbdbbbbcdcbccbaccdbbcbcacdcbbbcddccdbcabdbbddadcacdabaabdaaadcbdbdbdbabbbaabcbdbdaacaddabcddacdabbdcacbcdcddbdaadcdaaadcacaccbcdccdcaccbdacacdadabdbabcbbddaccadcccbddcbabcbbaabadbdbbaaccbbbbabaaaaaaabdbbdabccadcccbccaacaaaccabbadcdbaaacbcbdbbdcbcbccbdbbcdcdacacbaabbbbabdcccbdbcdcabbdcdadabcdcabccccbadacabbabdababccacbacbbababbbccdbbcbaaabcabaddccdaddaddadaccabccacdbdbacdbbddddddcbdbdbaddccaabaadbbddbcddccddbbdcabcacadccbbadacdabcacbdbccdbdbdddccaaccdabcadcdbbaaddabcacbbcbdccabcdcbcdcdcdaccdbbccbdccbdbabbbcdccacbbacdccaabcaadbcbdcaacdddcdccbadbddccaacdcabadacabaccdabbbadcdcadbccbabbcdbdbabcbcdaaacddcbacddbdacabaddcdacdcbccdaaabbabbbaccababdddbddacbbaccbbcabcbbcacabcbbaccabcaabcccbdbbabddaaaadbdadacbddacadcacddacccabbcabbdbdcaaababacbcbddcdcdacadbbcabbbadbadcbadbdcbaaacdaaabcdcbdbddbbdcbaaaacabadbbdbcddcdddbccdcdcdbacbbbcdadbdadaaaaadcbabbcddaadbcbbabcabcacaabcdaddcbabddcacbcbdaddddbcabbadcdbbaadcaadbaccdbccdbbddacddbcbcccdadacadcbaacddcadbdacadcacbabdccabdaaaddcadaccbdbdacdaddbcdcacdabcdacadcbdabcabcabcabcadabcccbdbbbdabdbdcdcaacdcbabcacddabddcdbaabcdaadbbbdcdddcacdabbcabcbcdbbddcddbbdaddaddbaccbcbbabacaabaacbbcdccaccbabadbbdcddcbabcbababcdabdaaabaabbbbdadddccdaaadadacbdbcdbadabcddcadddbcaaabbccdccacddbcbdccdabcabdaccabbddcdccccbcaabbaaddbabaabcccdbbccacbbdadadcbaddbdabddacdcabccdcddaddaacbaddabacdbcbcacbbdcabcadadcbabdabcaccbccbddcccaaddccdcccbcdaadacccbabccdddbadbadcbaabbbadbaccacbaaddaacbbacaacaabbbccdcdaccbabdddccccdababaadcddacbdddacaabdaaabccdaacbacadbcdaadcddbadbabcbabdadccbdabdbdbadcbcbbababddbccbcbccdacdaacbcbdababdbbaaccbacacacaaaccdacdbaaabdddadbbabddcacdcbcbaaacbccdabbaababccdaccdacbccacacdacabbcbabdbbbdcccccabccbdabaacabcbcdadccbbaacacbdaacaddabbabdbbdbacaacacbaacbbcdcacbccaadbdcaaaabbaabbabbdcccbcdcabacdabaddbbbcdddbdacdccdadadbcbccbdbdaccdbcbcdbdcaadcbdadcdaccbcdcdbcbdaccadcacdcaaaaccbbdddaaadbdcadbcdadabaccbdcbbcaaaaaddbccbacccadbbcbcccabdbddacbbbbddacbcdaabbddccdcabdbdbababccacdcbaaadacddcacaacddcbdaccacbadbdbbdbbbaccddababcbbdbddcabbdaadcdacccbaccbcdcaccacbcbbbccacbacaabcccbddacabbcdcccaabdaadbbdabcdbdbbbaddbcbcccccdbacaaccaacbabcbaccacaacddddaaccaadadbaaabdbcaadcdcbbdbdacaccdcdabbbadcdcacabbabdcaacadbaddcaaadcbcadabdcbcacdbdcabdbcdcabadcdaabbbbdccddbbadddcbdcddbcdcdaabadcbabcdcbbbbccabbcbcaadadbbcaaadcbdabacdaadbdcddadddcbdacaabdbddaabababdcdadacbcaadadaadddabcccdaaccbdacabbddcbcacccbdbdacdcbbaaadcddbbdbbcaaddbcaacaaacbacbdaddabacacaddbbacaababcabbabacccddabcccbacabacadddcbbbbaccbbbabcacbbbbaaddacbbaaadbcbaacdddcbaaccdaddcdbccdddaacdcdadcbbbabdddddbccbabdcdcabdbbcacddacbccdaddbacbbaaadbcababddddbaacabacaabdddcdbddcdbccddbddbcbcdbcbcbadabdcbccdabcacddacddcddcacdcaacabacadcbdabaadbdbbccbadbaacbcadaaddbcdacadacabcdbaccaaadbabdbdbacdacbcdcbbdcadbbbdbcdcadbdcbbbcdbbcddddbdaddabcdbbdcbddcccabadcdbdbaabdcadadcadbabcadabddcacbabbdbbdcbadcdddbdcbcbcbbdcbcadcdaaaccdcccdcbdddddabcbabaacabbdcbcccadacbcaabbcccdbdbdcbaacccccbbcbbbcdbdacaccaadabbacabddaadbcdcbdbccbcdcdbacccaadcadbdddacababacbcbcbadddbbdbdacbdbccdabcbcbadabccccabbaccadaababbbadabccbcaabadcdacdbcaccaaacbbaadbddabbcbccbbdabadbdddbbaccacdbcbbaccaccacdcdacbabbcdcccaaddcbaaddacdabbdbbabbaacbddcdcbbaaacdccddcccdadbdabacacdadabaabbdddccbdcddabdcabaadadbabacaaaacdadabddaaacdacacabccccacbdaaabcdbbaaabbdcbadbbdbddcacacaabbbddccbdcbabccadbaabcdbaacbcbacdcabbbcdadbabdbddcabbacbadcbadbbbcbcdcbaaabbbdbdbcddcaabccabcdbaaaaaaadddaaadaabaabdaacdcdbcbbcdaacddcccdadddbadccaadcbcacacbacdbbcbdcddabdccddbccdcbdddddaabadbcdcdacbbabaaddbcddbcccbdcaacbaaaaaabddbbdcbcdccabcaacaadbacbabaddadbaaacbcddadcdbdbcaccbbabdbaabdcdabbbacbacdcdaccabcabbcabdadbabbabdbcaacbccdcbdccbccbcdcabdcdbcdbbcaddaddcadabbbbbbaacdbdccccccdbbcdbbccbbcbcbadbdbdaddabbdcbadccdaabbaaddcdacdadcbdaadbddbbddddccdbbabacbdbcdbacbcaabbbbdaccccdbbcabdaaadcdadacccddcdbbdaaadddcacdaccdcabaaccaccdaaabdcdbaabbabaaaddbdbcabcdccabddccddbbdacabdbbabbdcdcdbbcbcbabacddddaacbaacbadacdaacbccdcdbcbbabcdbccdcbabacdaaaccaabbbddbacbdcdcccdabaaaabccababcacbaabbbdbacacabbacdaabbcddbaabdddbdbbcdbcdbcacbbdddaaddacbaadbdbcdabadbdcddbdbcdacdcbaaaaaaaddabaccdbbabddacddcadabdcdacbdbaabcdcaccbdbaabbddadccaaabbcbadddcadccccacbaabcddbdccaaddabdcbcadbcdcbbbbcacaabddbdddbbbccaadcbacaaacadbcacbcccbbbaadcabaacbbddababaacadbbbbddbbabcdbcbcaaddbbbbacacabdccddcbcdadddddcbccddabdcaadcaccadacaacdcdbdacdbccabcbbacddacbabbddcbbacdcbaccbcdbabadbaddbacddaabdadabacbdbcbbbadcdbbdcbadaddbacbbbcdbadcbbdbcddddcaaacdabbdccddcabccdcdbdbbcabccdadadccbcaacbcabbbddbbcacdadbcbacbdddbdcbbcddacdbabadbaabacabdacbddcdbabdbdcdabbdbbbcdbddaccdcdaccbacbcddacdbcbbcdabbbcdbdbdbdbdaaacdcabadccadadddcbcbdccdcbdcdcabaccbaadaacdccaabbabaaddbbcdcbcdbdbadcaccbdcabaadadadacbddcddcddccbcbbdbadccbbccbaddcccadccdbddcabbddbbaaccdadadaaddbabcacbaadbdbccdcddcddcdadabadaaccdbaabdadcddabcaddbcdadcbbacadacbbbdaadacdbcadbbdaacbbabacadcadacadcdbddbbdbcccaacbabdbdaccbabcbdacdacadcbadabddccbadbadaababcbdacaacacdcabacdbbccbbbabaaaaaccaaabaabaabbbbadbcddadaddccdbabbccccabccdcacbabcccacbbcdddbddccadabaabdcddbccbbcccbdbddcbbbddcabbbccacaacdbbbdbdacbcddddbadbacbbcaadbaadcdaccbbabdadacbccdcbaabdbbbdcbabddbbaccdddcbbadaddddcbadbdbbdcdccabaccccdcbbccbdcabbbadabbbdbbccabbddbadccbbacbbbbbcabcddacccbaddbddaabbdddcbabcaaaaccaadddddaabcbccddcccabdbdbdcbcdcaadadddcbadadbcbcdcabbdadbcbccdabbdbccacdadbcdddddaadbcdcdbddabbdabcbcabdcbadacccadcadacbcadaabaabdcbbdbdadacdbbbacdbcacccadbaddccaccdcdadacacdcacabbbbabcdcbbdabcbbdcddccbccbbabacccbcadcbbbdbbbdbaccdcbccbbabbcaaabbcdbddbaaaadadddcacbccaabbaccababaabbcdcdddbdccbbbcbbadadbacabcacacbdadcaabdbacbaabdccabcacddbdbdccaddbdddcbbddbaadbbaabcdaddacdabbccdbaddbcbdbbbbbdbabcabaddccdbaaaaabbacdbdbbacbaaabdcaaddabaddddadbcbbdcaaadadacaddadbcddbddcccbbbdcdcacaadacdaacbdabbbddbcbadaabcbdabdaacbbddddcdbadccbccbbcdbccdddabcbdaccacccaadaaaaaabbdcbdabdcbbbddcabbadcbdcccbcbcbbbdcbaaacabdbdaabbabcbddbdbddaabbcdcdbabadbcdaccbbbcbcddabdadbdacdccbadadddaadcbcaadabccbddadcdcbdcbdcaddddaaabaabbddddbadcbabcadbcdbdddacbcbcbdcadcdacadbccaaabbacaadcdddbbbdcbccacacbcbbcabcbabdbabccdcdacdaabbbdaadcddbbdaaaccbbbdcacddadbcbaacabcaadbbdbcaabdbadbacccdbaaacdcadcbadaabddcbcacddacbdbcbdbbbdabcdbcacbbbcbabbdccdbbcabadcdbbcdccbcdbcaabdcadbbcadbcdaabdcbdabcccaddaccaabcdbbccdcaaadccdbcacccacbcdcbdddaccabaccaaacaaaabcddcbcabdcdcadabdaccdbadcabbcabdbcdbababcaacdcdabacaadcdbacacdaabbddabacdbabdcbcbabbbdaddcbabccdaddcacabcdaabaddddbaadadbdbdbcbcddaadbabbcdaddacbacdbddbabdcdacdadcbacccccdadbacadbcdacabdadbddcddaacbbccadbdbdcabcccadacbbabcdbaaddacdbcacaacbcabacbbcbbaadcdbabcdbdaabdbbdcdccbaccacabbcddbadcadbabcacacbdaacbbbacbdaacccddbacbdcccdbdabcdcbaadabbacabcbdbabdacaccddcbaadbbbbdcbdcddbacaadddabbaadbbdaddbccdbabbccaccccbaaabacacaadcdbbbcbcbcadccacbbadcddbdbaaddcbddbbcdbdabdbcbcabdbcbbadaccbbacbbddaacadabaaaacacabaacaddacabacbdacaacbaccdcacacadcdcdabcabcabacbdacbdcccdadcadcadacababdabbbcdacadbcbdcbddcbccabcaccaadcbdbbbcbbcabadbbbdcddbcababbcdbadccabbbddbcddddddbadadbaccccaacbacbbcbdbbcadadababcdbbccbcadccabbaacacaababaaacbadcdcadbbadcdcbdaacbcdaddccaababaabadccdadddaccccadcabcbbcabaacdbdadabbcacbdacbbdaddddacbdaabacadabacbabcabdccacbbddccbbcdcabccbbbbbbdbdbcadcdbdbcbcadcdaababdaaaddabdbbabcddbcddddaacddcaabbacabddabacabbbbaadbaadddabbacdabcacdbcaaabbbbcadadbcdddcadcdcbbbdbbbabcccaadccddbaddccccbbcbabacdddbabaaaabdaddccabadcbdccdbdbbbbddaacbaadddacbdbacccaadbcaabdacbdabccbbbbdcbbdddccbcdcbcbcbbaacdccddabdbdbcdbbbbdabaacaddaccbccddbbdccbbddcdadaaaaddadadaacbdbcbadbddbdbadaacbdcbdabcbcadccbbcbbcabcbdacccacaababaabcccaadcccddcbbacdcccbbbdabdcbacdaaccbccdacdcaddbbdbdacddaccdbccabdcdbccbdabdcddaabcbadbaabbccddadcacadbcbbbbdbbacdcaadacdcbddadbcabbcdacbbbdadbdbbdcbaddadaadcdbbaaaddbdcabdddbcaacdcdccddadbbbccccdcbabcdadacacaddcddcaaadddaadcadbacbbabbbbdbcbbddcabadcccbcbbaaaadcdccbcbaadacbddbdacddabccdbabbadbbccbcdbcdacadbcdbbbbbaadbcdaabaaccbcaabbdaabacccbadbaddcbbccdcacbbccdaadcadddbadaddcbdacabbcbdbcabddabbbcdadccbbcaadcbccaadabaadcbbbbdacbdbbcabbbaabaccacdcdbddbbbccdcaaadcdbadccdabdcdbadcadccacbcccaadadacadbdabcdbaadcbbcbabdabacbcadcdcdacaadbdaddabccdadcddacccbcbadcadbcacabbcccaccdbbbacdbaaddacccdbcdabadcdbcddbabacacccccbbcccabbabaddbddcbacdcddddbbbaaaabbcbdccdadbcddccbabadbbbddbaddcdddbdbdcdbcdabdcaddbdcabccacabccbbaccbaddbddcbcadaacdabbbdbccdccbcdbabadbbdbacddcdbdbbdbadccacddaddbcbcdbcacacddcbadcddddccddbaadabadabcaabcadaaabdbbaabacbbbccdbdcbddadccadcbbbcdbcdcdcbcdabcaabccaccdbcbbdaacccabbcbbcadbccacdbcadbcdcbbcacaaadabcdbbdbaccadddddcccadbdcbcddddcaabdccabbdadbdbcadabadcbbaaadaccdadccccccbbcccaacbcadccaddacdcdaadbcbccbaccbbbccdcadcbccccdcabdacddabcadaccdaaccbcadacbcddaddbacdaccccbabccccdababcabacdccbcdcabadcccddabdaabaddddadbdacddbadaacccbbdabcbcdadbcbdabdbdcacdcaacddcabbdadaacaaaacccadbbdcddcaadccbdabdaaacadbccccbdddbcdbcaccabbbbbacdcdcccdcccaabbbbbdbbcdbcbbccacaadbcbddcdcaddcbddacdbdabacadddbbcabccccdbddbbaccccddcdbdbdbddcbbcbaccbabcdbcdcaaaadccbacbabccaabcacbcbadaaadbacbdabbbadddaacaabdbbccbdadbadbbbdbdbadacaabbbbaabbbbdbbddabbccaaccbbdccbdddcddbcbdcadacdaadcadbabaacabadbbbcdbdcdbbbccccadcbcbadbccaccdcababdcababbdbddbbddbaddddcbaabccbbccaddcdadbcdddbbdadabadbdcbbadbcbdcdaabbabdabbadadbaaaacdacadbdacdcbbbbadacbcbbaccddbcadcaadaadadaddabcbabcdbbbdddaacadbdcdaddbbcccaddadacdbdcbbbcbcabddbbcaccbcadcbbccaabdbdccdddadaaaacbbbadddccdaaccabcddaadcaaabbacabdbdbbcabdbababaaaadcbbbddcadbdbbdccbdabadaaaabdbcbcddbccdbcddbbbcbcccdbddbcbdadadadcacbaabcadbcbcdbaccaaddbcbaabdbbdbddcdabbbdbbcdcabcdaaaacbabcacaabcbbbadcdcdbdaccdaaacdacacbacaacdcddddbbacdbccdabccccddcadbbbcacbccdacdbcaacdddddacdaacadcddcbcbddbabcdcaaddaaaadbacaabdcdbccdaacabaabccdbbbcabdabbbcaadddbcbbcabcdadbaabdacbcbacbcaadacadcdbccadaabcbaacbcbacadbccbdddcccabbcdbdacbaccbccaccbaccaadddadaaddccaddcbadcdbbbcccddabbcddbdaabcbbacdcdbbbbaacbcbdabbdbaadbbbbcdabcdddaaacaacccbbdbbdcbabccadddbaccdbbdbaddccdcaddcabdccaaaacbbbadadaccbcbbdabbdbbdcdccbcbbcaabdbacabaaaaabbcdcccdcadadcdadacbdaacdcaccbdbbbbbacdaabaabaddccadcacdbddadabaddcddabccaaccacbdcabdabdaaacbbddddbaabccadbcbabddddadabdcbacdcabccddcaabacbdcacbbccccdddccdbcadbbaddbddbacbabacdbdbbaaabcbdaccbbdacbccbaadcccbdbdbbaabdcdcbdbcabcacadaaddaddbcdaaaddcbaaadcdbcaabddaaccbbadddcabacaadbcbdcadddbdcbdabcdacdabbcdbcbadbacccaaadadabcaacababdcaababdccbdcccbddbccbcaaadaacadadcbaddaaaacbbcacababbcabdcbdbcacbbbcddbddbcddddcabdcacabdbddacdcbddadccabcccabdcbbccbcddbcadcacadddbbbaacdbddcddacabbcacaadbddcccccdcaabdbabaaabdacbaabbdabccbbdabadbacbdacaabccaccdcddaccaddcadbbddadabcbabcaddadbbcdccabadacdbbbbccabcacbbacacdabcbaddaadcbdaccddbdaaccabaddadbaadaaaccdbbcbddcaaababcacbddcaabbbdbccdadaccabcbccbdbacaacbbbdbacddccddddabbacdaadbabcdaddcddbddbbdbccacaddabccbacadcacdbbcbaabcdbaacdadbccabbcccdcaabcbcdbbcbccaabaadbcddcccbdccababadccbcccbabbbbbddbbaabaccacaddaacbdaddbdbcabbbadcabdbdadacacacdbcdadabcdddacbdbadccbabdbcbddcccababaacaddcadbcaabcadddadadaadaacbbacadbaacdcddbbbdcdcabcdaabbacdbadadccdbcdcbdbbbdcbdcccabcbbacaacaccdbdaccccdaabbbbbaabcbcacdbddcaacaaabdbcdddbaadddacdaacbddacbccaabaacbbbcbacadbdbbaddcdaccccadbcabaadacdcbcbbabcbcabcbaadccabbcaadccddacdadbcbbabaccdbbabcdcadbccdcbcbcabcbbadddacdbbcaabbacbccdaccdccacbddcbccacdadadbcacabadccdabcbddbabccbcbaadcdbcdbdccbbaccaadbaccbcbbcdcabdcadbcdaacacdabcaccbabbababdacbcadbcddbbaadbcbdbadabaabbaabcdbbbaccaabacaccbdbcccacbdacbdcaadcddbaaddadcaccccdabdcddccbbaaadcababbcacadbdbbddaccaabbddcbadbcddbdbbdcacaacdbdbdbccadaccbdbaaabdcbdacbdcdcdacaacbbcbbbcbaabdacbcacbbbcacddcbbabbcdcbabadbcaddcbbbcdadcaddcbdcabbdbdbaabdbdccbcabaaddadcdbcdddccbcdaaaadbaccacdbcdacbcadaccacbcbddbbcaccdbadccbabcabbabcadacacbdaaabdcdbbadbdcabababbcbbcddddaccccadbcdcbadbbdcdadcccbaddcdaadcbbdcaadccdbadcadadbdbdbabbdcbcaababcdbadaabaacddcbbcdcabcaaaaadababdbadbacaaaacdaadcabdcdccbdbabbadbcbaabcccbadaabcdddcadddaadcaabdbbbcbadabbcbdbcbcbbdacdccbcdddcbdbaccdbdbabdacadbcabcddccbadacbcbbdcdcdddaabdddbbccbdbbbdcccbaaaccbddbdcadcdadbadadbdbbcaabddabbbdbaadcdadbccddadcdbcbdcadcaadccabbdadbcadcaaacaccddbdcbbbcaadbdaabbdcbaaabccaccccbccacbddbdaddcbaaacdddcbbdcacccdaacbbcacdddcbccdacaddcaaaccdcdbaabcdcbaaddbaacaadccbbaadadacbdaaabbacdcaccadbccbcabaacadccddcbcdabbacdabacbaabcdddbcccbacbaddbbadccadbdbcdaabcbaaccccabacbbcdabbabdcaccbbadcdccbbbadaccdacddbadaadbcbbdcbccbacdacacbcbabddcadbacdcacdbbcddddcddcbbdabbdacbdccbccababccadbaabbabdcaacdbccbcacabccddcccccbacbabdaaddbdaadbccaddbbdbccdbadaddadcbccdbacdcbddabaadaaaadccbdbaadbbbaacadaabbbdbbcabccdbdcdbcaaacddabcdacbbdababdbbaabccaddcddcaadbcaddbbabdddcacdadbddaadacabbbcadaaaacddbcabddddaabdadabbdcababcbccccdbbcbcaaabdbdddbcbabccbbadcaccbcaacdcacccbadcddabdaaccacdbbbbdcbdccbddbacbaadaaabdbabcbdbddbbdcacacacdaacbdddbdcbbaadbccccaadbddaabcbcccbbadbdddbdabbaaabbacddbaaaaadabaaccbbbcabbdddbbabbcbaadcbdbbcdbbbacababcaaabdcbdddbbddbbbccddcddbbdcbbbcdddadbcacddcccacddadbbbadddadbcddabbccbbbbbccbcdacdcdaacdbccabcadbbcacacdacabbbaccdcbbabcbbbcdbacdddbcdbaacddddccbdcccacddbccadcbccabbbcccabbaacadccbbadbaabbdddccccddbdacbcdddcccbdccaccaccaabcbdcbbbadddbcccaadaadbdccdadcadcabcacdcbbbcbbbdcadaaddbbaacdabaaddbdaaaaaddaccabcaabdabdabccadccbcbbccbbadbcacacbcaadbdaddcdabbaadabdbdbbaababaabddababdbadcabcdbbddaadbcaadccadabcdddcdaaddbdcbbbccdddbabdadbaccbdcbbbdcaadcbcbdababcbbbdbacacbccbbbcccdcabcdbabdaabaabbdaabcddcbdddcbcbaddbdcddbbcdabdacdcccbdbdacaddbcbaabaddacacdabccddddbcacaacaaaaddcbbdcbbddaaacdccdabbdcdbdbbdcdbdccaadbccbadcadcdbadcbbadacdaaccabbcbdcaccbbabbbcacdadccbccccadddcdbccacacbddbbacddacddbdcbdaacdbdadcbbbdbbbcbadbdbcbaccbddcdabcccbddcabddddaaccbaddbaccdaccccaccbdddcdabdadbccccddbadbddcabcaaddbbaccdabbacdcabbcdcdaadcdbbdaccbcbaabccddbddbdacdabcccdaadbacdaaaddccbdadbdaabddaaadcbbdcabcddccbdadbbaadddbaabdbdabababccddbccabbbdbbdbdabbccabddbcbdabcddccadbbccddbcbbddbcccccdbbccccddccabcdbccacbadcbbbdccbaaddadadaddacbbcaabbbccbbbbbaccbbbbbcacdddbdabacbbacbabbabcbcdddabcbbcccabadcdddbabadccccbcbbbbbabdbdaabacaaddcbcaadbaaacdcddadccdbaadddbbcabadccccaccdddcbbabbdaddabcaacdcbddadcdbacddcacddcaccacdcdccababcadcabddaadcaadddbdbacdadddaaddaddabacddbbbcbccddcbabcddbcabbcdbccdaccadadccbdcdcadbccdbaddddbaabaccbacadccdcacbcdcacaddaacdaddaabddbbadbabddbbdbaadacaadbbddbdbaadbabdbccdabcddbacccdcdbbadddcacbbdccbddbcbcaabadcadcbcbdbcabbaabaadbacdadcbacacadaaabdabdcacacccbcaddddccdbbadbcdcadbcabccadabbabccbccdbcddbcbbdbdcdadaabdcbacbdaaaaaccaabbdccadaccbbcbbacaccddbdddddcacbbaccdcdbddcddbcddbdcabbcdddababbbddacaabbabbbadcadccbaaadcccbaaabcdabdadbddabadcbbbabdacdbdbaaaadacaadcacccdccaaccddbbbdcbddabbcbbaaccaacdadcbacdbbdbbbadbcdddaababcdacabaddccbddadcddddccabacbcadddcdbbbcdbdbcbcacbabbacdbdabbcdcbaabddcdccccbcacaaaadccbbaddbdcbcadbbbbbddadbbcddaadaaccabaccaaacbcbbddcbccbbdddaaabcaccabadbdccdddcbccdbddbabdbbbbccddaabbbcabbacaadaaacbbbbbbadccaabbcdbbbcabbccbdbdadabcbcbabadbcccabcbdbcbdaddacdddccccbbbcbcdaaacaaacbacdccbadbdaadcaabcbddacbbbbcacccaacddbaccaccaccdacdaaadbbadccbdcddbacaacddddaaaabbddaddbdabbccaacabcadbdccdddbbdcaddaccaaabbbadcbdaabdddbbdabbbbbccccaacccaccdabdccaddccddbbddcadcbdbdbabdadbdcccbabcdadddcdccaaacccdaabdbcbaccbabbdbcacabcaaacccdaddacdaabacacccbabbbbcddcccaacbccaadaaadbaadcdcbcdcdcbcdababcbbaccdbabccccddaaacacdcabbaacdabcccdcabbadcccadcbabacbcdcadadbbccbcddbcaabdaddbadacbbddccabdbdabacdabdaacabdbcbadacdbccacbdccadaadccdbcacabacbdbcbacdcbaccacadaabccadddadbcdcbbccbcadcbdbbbaddbaddbbaddaacaabbbddacabccdbdaaabaaacbcdabdbaccaadadddcbdaaacdacacdbbbacdaacaccabdcadadcadcbbbdaddabadbdbbbdabbabdacccdbcddadcbababcaacaddbbdcbbaaaddaacbaabbaacbabbdadaddcdacdbcbcddaacaccadcaabcccccdcabbcdbaadabacddbcabdaddaabcdcadaccccaadadccbcddddddbacadaaacaddbddcdacdacadbaabadbdddbbcbdcdcbbadabacabcaaaadabdbcccbacaacaacdbbdcabdadaabccbcdbdddbadbdadbaacbbbaccddddaccbabdabbdcbddbddaccacadbcdbcadcdcccbdbcdcabdadcbadbdcdabccdbadddbbaaaabdaabacaadababcbddadabcddaaacddcbddaabaccddcbdacdbadcdccabdadcaddabdcbddbadcaabadcbaabdccddcbabddacbcdbcddcdbdaaccabdbdcbdacabddacdcacddbcdadbadacbcddccbcccabdabcdcdacbbdacbabbcacabbdbdccbdcdacbddbcbcdadcacbbdbcccdbbacdaacabcbabbabaaccbdabbcbadacabcdacaddcabddaadbbdaaadaccbaabacbcbbcabcddcaadccabbcaacdbbdacdcacaabcddccbbcbdacdddabadacddddabdbcacdadbbadbbddaaaaddaaaddbdaadaadbbacbabdabacdbbacdbaadbcbdbbbccccbbadcdadbaddbbdccbdaacacadabcbdccdbdcbcacadcbbbcadbddcdbaccbdcabcbaaabbacbdabcccdabadabaaddacabbabbabdbddadaccdccacdbcdabdababdaabbbcddcabdacadddbbdcbacdccbabcdbabbdbdbbaddddabdddbaadcdaabacbbaacddbdaaaccabaabddccacbcacdddbdabdcaacbadaaacaadaaddbadbbbadbbcdddadacbbbdbcdaabdbdbbaacabaddacaaddaaccacabcdababddbccccccbccdcdacdbaadbcbdcaaadbbadbacdcaacccccaaabacdacacddbcbdccdacddcacbbdcaddacaadccadabddaabaddabbcbadadbaadbdbdddbcabbcdbcdcdbbacbacabcabbbcccbbabaabadaaddbabcdccacbcddababbccbaacacccbdddaacbdddabdcbaddbdbbaddccdccdacbdbdcbbacbadcdcdadcabcccbcddcdbaddcabcbaadcdcacccbcaacccbdbabcaabcacdcaccdcdbaadcbbdddbcadbbabbcddaacaadadbdcaacdacddcacbaacccccddddcadbacbdbcbadaadcaddbbadcaddaccccdccdabcdaadabdccababcaadbbaddbbacaddccaadbbaddcbbadaacddacaaadcaabacdddcdcacaddbcbcdddccbcdbbabbaabdbbdbccdcdaadcababacadaadaadcbacdccbdbbbbbdabbbcdbbabbcdccbbbcdacbcdccdbabddaddadaacbadbaddabccdabbacbdcbbdbacaababcdcdccacdcadadbdabaccbccbcacbbdccdbdcadaaababcddacdadabaaabbbdccabbabddbdacbbbbcdcdadbadcdaddcbdaaabbcabdbabdaabcaabdabbadcabbcbbbcdbdcacccabdbadabdabdbadabcbdccbdbcddadcdbdbddcbbadababdbbcddacccdcdadbaaaabbaabddadcdaaadabbaadbcacacbdcdcbadabcdadcadcabbacbaadaacabbbcaacdabbdcdbadccdbbdccccabbccaadccdcdbcbbdccabbadbacccdcbddaaaddbbbacbccccacddabcdabcbcddacabbaabccababdadacdcddaacccdbcbdddacbcbdccacdbcacadaddcccaacccbbaddccddccdbcdbdcdbadbdadbdcdcdbdcababaddaabddbcccbdccbdbabcbcbbbcadcdcbddbbcdbdcacdbcbbcabbcbcbbacccdddaadabddaabdacabcaacdcabdddcacbcadcadbdbbdbcaacdbbdddaaccdababdacbacdbddddadadbdaabbdddbabdbbbdabadcdcbddbcddccbdbbbccabcbbdbcdcbdddaccbbcdcaabdbacbbccdcbddacbbcdbbaaccabddabbaaacddddaccbbdadaabdaaadaddaddacdbbbdadcbbccaaabdbbdaadbddccadccddaddacbccddccbddccacabdadacabacbcbbcdddccdaddccabdddbacaddcbacccbcbabdbbaadaccbbcdabdcbdbbabcaaabdcbbdbacacabaadabccbacdbdbbbbacdadbcdbdbcdbcbbcbacacdaaacabadadaaddbaccbdbddcdadbcbbbdacdbcbbddaacdbabaddccbdbccbbcdaccbcabcbcddcbdccbbbadbddbbcdabbdbcbbadaccccdbbccddadcbccccdbcdcdadadcbadaadacabcbaabbabcccdabbabdbbbabacadcacaccbabbbbabacccbbdcbabbaccabbdbcacaadcabaddaabadcdcadabbacbcddccacabcaadbcdabbccddddccabbbccbdcddbcdcccbdaacddaaddacdcccaabbaccbddcdccbbbbabbaddcbaaaaddababccadbabcdcbdbacbbbaadbcbcdabdbdcadaccddccbcccbadabaabbcdddaddabdaaddaabcbbbbadcaacdbcaddddaabacbacbbbcdcbdbaccddabbccbabccbabcbcddcdabbbadacdbccaacccaaabdcadabdcdabaabbbabbcddcddccbacdccbcaddbcdbdbbaaacccbabaadcdbabbdbcbbbadbacddbdaaddbbddddbacaacdbddbcaacbdcbdbdcaccdadacbdbdccdddcacaaddaddddcaabbdccacbabaddbcdcbbacbcbcdcaaabdcbbaadacdcbbdddcadbdbcaabaabadcdbcbbabbabbcdccdabbcdabacaadbdddbdddccadbababbabadddbaccbcddbabddabcacadbdcacadddcaabcddacbdabbdaadcbccaabbcabcbccbcbacdcdabdabadbdbaadadcacabbaddcdbcadbcbbdbcdadbbaddbddabccababaabaaabaaadcbcbcbadccbabccdcbdbddaddbdadcacbccdbbdcabcdaadcccdbadcacbacaccccabccccbccaddcbdbdbbbddaaadaddbdcacadcdaaaabdaccccbbdcdadabcbdccabababbbcacaabcacddcddabdccdbddcbddbbaccbdccdcbbaddbcdddacdaaabccabbbddcadcdbbdcadcdcbcaabbadccdabacbbcbdbaacbacdbdbddbbbddbbabadadddbcdbadbdcdbddaadbaccbddddbaacbdbdcaaadbabdcbdbbbdbcabbadbdbcdcbbdabcdcbacadbdaacadbacbaddddbccdadcdbcadadaaccdddaacadbdbbaaccadddbaaaccdcaacdbbccaabddabbdbdabbaaabbcbcccbaacacbcdbacadccddacabadbdacbddbdcbcccbaddddaddcadbdbcaadcabbbcaabbadbddbbbcccdacaaddbcaddabaddbcabcdbdbdbdbcbbcbaabddcbbbbacccddacbbdbcbadbccbbaccaadccbabddcdcdcabcadabaaadacabbaccaababbdacdbddadbcbccddccacbadbcdbdccdcccabbbcbbdcaccddbdaddbccbdbadddbcbdbbddaaadddcbdacbddcccbadcbccdadddabcbadddacdddaabcabcaccccdacaadabcabdbcddacaccacdccddbcdbaacccbdbadaabcdadcbbdcbbddbcacbdbccccdcdccbcdaddbccdabccadcabbabcdaaabcabdabdbcabbcbacabaccdcabccdbbaccddadabbbcbddadbabacbbcccccddcbdccbaabcbbbdadbcbaaccabacdaccadaadbcbabaddcdacbdaaaabdcdddcbbcacbdddbcabcaadbaacddcacaaddcdddaabcdabccdaddbbcdbbccccdaacababdddacdbcddbdaddddacddcdbbbcccccbcccbabaadcabaddbabdbbbdbbbdabaddaaccbbaadbddadabbdbaabbddaabddaacacabbaccccdbdabdbbdaaaabbbcdbcdababdbbabcbaabbaacacccccadbcdccbbaadbbdabcbbcdadaabcccbaaddbdcbaddccbdbaaadadddcdcbcadbddbcbdabcbdabdcacdbbadabcadcccbadccbdcbaddccdbbbadbdddaaacdbcdbcbdccddcabbbccacdccbddcddbcadaacbbabbabccabdcadcaddccbcbcbbbddccabdbaacbdcbcabdddccddaddabcdbddbacdbbcabdbcbccadbcabdcadababbbdabbdbacdddabcaddadcbaadddcacdbbdadadaadbadacdcdabaddabbdadbaadddabdcccaaddaddbdaaddaaaaaabbcbbcdcacabddbdaabddaaadcadabddbcabaacdddcccccbbccddbbccddbbcaaccbbaabbdccabbcbddabaacbdddddcacccbcbdbbadddacbcacacbdaaacddcbdcaabcbabaccaddbbadcdabddbdccbccaaaacaacaddcbcacbadbadccdbadaacbdddddaaccdadaaacddbcddacdcbccbabdbabaddbadcabbaaadddbdadcadddbadbdcbccaddcaabbdcbbcbabbbbdcdcaaadababadddccabcbbdccadaaadcbacbbaacbabcdcddccbddbcdaccbdcbdaddabcabcacaadbccdbacccdbdbdbbbaddadcbdbddbbbdccbccddbdccbaaccacdacabaacdadbaccadbddcdbadbbdccdacaababdbabcabdbccadbabdcdbccaacbbcbaabcabbccbbadbdbdbbaddaddbcdddccddcadaaacdddbcbbadacaadbbcbbbcabbcaabcbcbcdbacdacdaaacddccbbccdadcbdcddddacadbdbcdacbdacdcddbcdcbcdbdcbddcdbddbddcacdbadbbabddabbbbddcacddcaaaaaaacabbaabbccbcdcbbabcabbcacacbabdddbabccdccabccdaadbcaaccdbcaaaabdbbaaaccabddadbabcdaabdbaacabdddcaaaaaabbdaccbdccbbcabacaabaddcabaabccdbaacaabababaaabaaaacdbdcababccbabadabdcdddadaddbdbbbddadbbabbcadbbdaadddbcbddadbbadddcdcabcccacaacadacdbbaacccbcbaacacdcbacbbbdaccabaaaddbcdaccccadddcbcaaacbacdcdaadcacddcdbcacadaadbaaabcacccbddacddcbaabcdcacccbaabcadaabadccacbcacbcdabccbbacadcaacbacbabaccbcadbbbbacdbdbabdcddadddcaddddacadaadcadadbbdbacbcdccaabccacddacddaabdadbbcddcdcbacdbcaacddabccbcabacdabaaabcccbbadccccabcccacacddccbdcdaacbbbdcdbaaadbcdcbdcacddbbcbaccdccaaccadcdbdcbaadccbbdabacbdccccaadcdbbdcadcdbacccabddadbdbbcbddabcabababacdbbccacacabbadcdcdbaccbdbaadbcdddcdcbaaabdccbaddbdadabdcaaccccbadbdabbbacacbdadbbbdcbcdbddabddbdbacddbabdbdabccbbcadcddcbdbaabbabdabaddcdbacbcdacbadadbcddadbcaadbcacdabbbdbcaabaaccdaabdabcbccadbccaccdacbddbbddbbcdcadadadacbbabdcbbbacdaaabdabbcbacdcbccaccbaaabbddbaddbaadccadbdccdadbdbcdabaaaddaccabacdbddccaccdacbcdcaccaacdbdbbaacadaccaabbdcdbabcbaabccccaddbddcbcabdbabdddacacacdccabdaddadadadaddaccdcdaabaccbbdbdadadcaabadbddccaccbdcdbbacaddcbdccccbdccbadcddaccdbccddbabdaabaabcdcaabdbbdcbbbbbcaaaacdcddbabaddcbccacbddaacabaddbccdbdcabaabbabbcccaddaccdbcbbbbabdddababdacbcbddbcacacbacbaaccaadcccbaddbbbbbadcdbadabdabcdcbadcacbdcaabcacadbabbdbddabbcdbbaacbbddbadabcaccdaacbcbaaccddacabcadcabcccdaccbbaddadcddccdbcbdacabbcabdbadddddabcdcacddadcdbabbbbcaaccbbdcbaadbcaabcabcbcaadcbbdccccdadaacbbccacacddcbddbdbacbabbadacdaaccbcccaacccbabbcdbccdacbcbadcbcabdddcddddbaaabbcdaddadcdaadcbdbbcbcaadabdcbdcdaddcddaccbdaabcddddbbbabcabbbcddaccbbacdcabacbbacdddbdbbcbadadacbacbcacdcbcbdcccccabacbbcbcbbddbadabccbaccacdccbcaacdabbacbcddabdbcabdbcabdbbddccddbbddcaaaddadcbacbccbacccbcbdddaacccddbbbcdbcadbbcddcbabddccdadbbdadbcbbbacbdaddbaaacabdddcadddaccdacbdabadccbbdbbdbddaccbcbdbabdaacdbabadabaddbbabdabddacbccccccbbcbdadcddbbbbdcdcaddcdcccdccdabdcccdcdbddbdcbabccddcbdacddbcdbaccbaccabccdccddadbababdbdccbbabbaabacdbbddddabbdbaaddbbccbbcdaacadcbbaaccbcadadbbaaacdbadbbcdcdcdbcacdbbddbbacaaccdadccabbbacbabdaaabacaadccbaacbccccbcdcbbcddcadbddcacacadddcdaaaaccddccdadcbbbcccdbbaacabdacabbbdddadabadacddbbccaabbbacaccdddcbbcabacabcadcdaaabbadbcdbadcdabdbbadbcdabaaddbbbabddccdcddadacdccddabbdcbdcbccbbcdcbddbcbddaadacaacbbacacdbbddabcacacacdcdadbbbdcbdbdccdcccdacabdddcbdddddcdbacdbacdbbaccacdbdbbacbbbbaabaaaabcaacadcdbbdadddbacadabaabdcbacbcbbdbdadabaaaadadbacdcdddcbcccacadbcdccbdddcbcaacacacbbbcadadbbcbddababaddaaddbdbdcbbaddcdabbccacbaaaadbaadcbdadbbccaaccbaacdccbbdddaaacdbbcbdbddccdbbbbbdbacbdadcdcabdbbdaacdbbcacdbcabdabadbbdcdbabbbdabdacbcaaadccbcddcdbdbcabccbdcabdbbababdbabccaacdcbbbabadaacdcbabbcacbddbcdddabcacbabbaccdcdcabbbccdaadbbbcdcadaaaddcdbcddbcabcbddaadccbbdacbbdbdbcaccdddaadcbdddddcdcabbdccdabaabdbbcbabddbdbaadbcacadaadddcccccdbbbdcbabdacdaacdbdcadbbadbdbcbdbbbbdcaaccaccccbccbcaaddbccacabcacdcdbabaadabacabacbdddcbdbababdcbcadddccaccdcccbadacdbcadcdacdbaaaddbccdbbcaadacadbacccbbaabdddcccccbcdbbbbbdadcbcadccdcdcbccbcbbccbaabbbdbdccbbccdbabacbadabcdbbbbbddaaddcccdcdbdadacaadbdbdabdbcbbcabbacdacbdccbddbdbadcbdbbaabbcaaaddbcdccdcdbbadaabdabdcdcbdddaddbdadbbadbcdabacaadaaddcaaccbcdaccbaccdcbcbbdbdbbcabacbbcbbdbacdccaddbbaabcbbbbcabaabddcbdddcaabccbcbaaccbbabaddcbadccbcdaacdabcbabbcadccbadaddcadbddccbccbcadbcbccccabccbdbbcbdbabbcccdadcbadcddcdadabbbccdcacdcdabcaabdaabbbccdddaadccddccdaadcccddcbdddcccaadabaadacabdcaccbcadbcbaadbadcddbaaddacabacccaaccbddbadbdcccdddabbdccbabbbadccbadbdaabddaaababccaabcbdbdbddbbabaabbcbabcabcbdcdcaaadcbdbaaadacbdababbbbcbaacbaaccdddbaacaddaabcdcabdaaabcddcbbdcacaadabccaacbddbcbbdcdbbbaadcbbbcbacbddcaadbcdcabadacbccdddcddddcdbabbbadccbbdcdacdcbdaadbcaaacdaadbdaaccdcccabbbbdcdcaacacccbdabcbacddbcacdacbdbcbcdbbccccacbbabdadbccbdacdabccddacdbaaddcaacaaadaddcabdbbaddbccddbacbadcdccabcdccaabcabaaacadbcbacaadacdbacccabadbbdadbabdccaaacdcacbaaacdccddabcccbabdabbcadbbcdabadabaddbdadbcdacaabdacdcbadcdacbccbcdaaccdcccdbdbbccddacdaccdbcdddcddadaaaabdcbbccaacccadbbcdbcbbacaddaadadcbdbbcddbbaccbbdacaabbdbabcddbbdaaddbdbdbdcbaaadbbcdbccdabcababadacccdcdcddaabbbdddcbadaaaaabbabdaaabdccdabadbbadcbcdbcbbbaacbcdaaacbdcabcbabccddabdbdddccdbddccadcabcbacbddcddbbdaadccadcbaddacdadbaccbdbcbddbccbaacbadcccbddbbccdacdcacccddbabcabdbbabadcacccdcacbbdbbdbccbacdcacbdbbbbbdbaabbabccaabbabdbdaaaabccbdddcddacccabacbacbdbbbbaccccbddccaacbbcabaaaacababcddacdcaddaddddcccbbbcaccbdcbadcbdbccdcddcbcaabbdccbbbddbbbcdccdaccbbabbbabdadadbaddabdbdccbbcaaacbdbdcdcacdbcbddbdaddabcbacdbccaddcaacaddcbbdaacaadbcbcdadbcbbaddbbdccbbddcddddbbbbbcddccbdcabbdabbcccaccacacbddbaccdaaadcaacccaaacbabadcadacaddbaabcaababbddcbcacbdaaccbaadaddbdcdabccdcdacadcaccbcaaaaabddcdddbbbcbbdcdcabacdccdbcaabbcdadbacddbbadcccccbacaabcbbcbcabccabacccdadcadadcbdaadccbdaacbddabbacbddddcacaabaabdcbbcbcbbcabccddbcddbccbdbcaacabdcbcdbdbabbbdacacbbddcdbcbbcdbaadcbaccbdcabbcbcdabccdbadcbaddaabdaaabdadbaadccaacbadddcadadddccccdccaadacdccaddbbaacabbdcacdbdddadccbcbdbbcabbcabbacdbdddddbcbbddcdaaccdcbdcdacaadcbddddacbcdcdbddabcbdbdddcdabacddaddabcaacbdcbbddaabbacabbbcdadaababcacbbccdadccaccbdaabacdbbcbacbabcbccdabddaaacddcacddcdacabababbdbcacaabcdadcabdaabcbaadaabdadaddcbbadacacdabadaccdbbccadbdacdccadcbcaccadabdadabdabbdaaababcdddbacbdacbacbbabdbdcdacddacaabcdaccddababcbdbcacbaadbabdddbadccaddadddbabbbaaddcbaacabaaaccdbdabcdbdcbadaacbcbbaaabdbdacaaaadaddbdccaccdddaacadccbddcdaabdaacabdadcaaaccdddbdbcaccbdcccaaabcaccabbacddccddbaabcbdbaadbaaadbcdcaababcdbbcdcacadbbacbbccdcbdbcabbabdaadcccdaabdddadcdbbabbdabadcbddcbacbbbccddcbacadccbdaacbdcaacccdbadccbdbcbcadaaaadaddbdcdabdbccbcbdaddadbbccbbdadccdaacabbbbaabbcbaabbdacccbdadbbcbaacaddacbbddbcbadbbcdbcbccdbddadabcdccabbcdcbaabccacdbbaadadbbadcbcdddddaccdbbbbcddcbcacabcbddcdabaacbbadabdbcdddcdaccbabcbbcdaddddbdacddacddcaacbbdccbbbabaabccadbabaddbbdaaadbdbddcccbdcdccabbdbcdabdaddbaaadbbbbdabdaddbbbbcbbdcbacacbbccccbaaacbdadabbddbddcbcdcabccdcdbcbbadabdcdbcddcdbbddbbddddcaabddbdacbddddacbdcbbbddcddaccbabcdadcdbbacaadaaaadccdbbbccdadadcdcbabaabaccbdbbbbdaabbccacddddcdcbdbacbbcbbcbddcdcdaccbabadbdbcacabadbdbaaccdbbcbabaccaabaadbbbdddbaddbbbcbabddbacccddacbaaababddcacaabdcdbcbdcdccbbdbaddcdbddbdcbbbbcdaaaccabbcdcdcbbababcdbbacacdddabdcccbcddddacdadcaaccaabcbacadcabcaccdaccdcbbddccabaddcaccaaabdabcccccdaadaadbbbdcbddaaabbdccabcabbcbaddddcbcbdaaddbbabcacdbbcabacdbabcbcadaaccbbcdbdccabcadbdbacadaaaddcbcabccdcdbbbaaaddcaacccaaddcaccdaacbaddbcacdaadacabaccaddbaadbbccddaaaabacbcbdbcbcadccabbcccdabbdbbabbbcbdcadaaabccaadaadcabadcdcacdadacbdbdcaaddbddccadaaacadddddbabbccdacadaccadccbadcdbabaacabccabcdbdaaddaaaadbbbbdadacdcaaaabccacccbaaddaabbbbabdbcbdcabbaddbdbaaadcabcdbcbcbacdcccdadbaacbdcbadabdbddbcdcddaccdddbacbbbbdbbdabccaddcbcbaabbddcadcbaccccccbbbaddcbabddaadbabcbcadcccabdacdcaaabdacbacdccbbbbddacadacbacddadcccddcdbcccdcacccdcdbaabaaababaaaadcdadcbbdbcbddddbcddaaaacbddbdabdddadbddcdbbdcbbaddbcddadddadabbdcdddcdaabccccdcdacaccadcdcabcbdcdbbcbadddaadcdddadbacbaabcdcbdaadadabcdcddcbcddbddadcbdcbbbbdcbdabcdabdbacaaaacdbbdabdacbdaadbccddccbaadabbcacbabdaaabddcdbcddadbdccccdabdaabbbcabdbccaaccddbcaadbacbacacadddadadacabaacacadddaaadabddbbacbadbababcdcbdaabcbaabbaabbbacadaacabdccadcdbdabbddbabddaccacbdabbbcccbcdcbdaccddbacadadabcdcdabdbcccddccdbbdacaabcbbabacccddacaddcacdadadbdcabdcbbbdbdabcbbbdabddaaaccacdabcbdaaccdabbadbaaaadabccadcdcaaabbadaccbadaccaadbbddbabbdcbaadcccbdcccbbdccbaaddcdddbccddcddcbaaccdcbbcddbcbabcccaadabbdccabbbbbaaacbcbabcdacbbdddcddabbbacccccbcdbbddcdcabadabadddaaabdabadbdaacddadbcacddccaccccadccdbabdaaadcbccdbdabbbddababaccbaacccdaabcbcbaccccabcdbabbbcaccabbdaaabdddcddbbadbbdbcbdabbaaddcadbdbdddcdaddbbbdcabbcadbccbbbbcabdabbbbbcdcbbcdbcadbbaaccaabcacaaddabaacdabaabdaaabcdabbbcccaaacacabcdacbcdcacdacdcdbcddcabccdadbcbdbcabbdaddccbadadbabacdccaacdbbcdcccaccacadbacadbadbbadadbbccccabdbaddbcdcbccddbcdddacabccdbbadcaccbbdcbcaddcdcbcddbcbbcccdccbdbacdabbabcddabbdbacadbcdadbdcccacacdccacbadacdabdbacabaaccbccaccdabbaaaaacddcdbbdddbaaddcbbaabbcdbbbbbacbaaacddccaacdcdbdbbadbbcbcbdabaccaaacddaaadbdbbbdbbdbdccbbababcddbdacaadadaaacbaaaccbcbadbaacbdbbbadcacdcbaaacbadadcbcaccbcdabddbcddcbbcacabdcdcdddbcbdaccacccaadaddadadbbabdaddaaacbdccdcadddcaaccaaaadbabbbbaabddbbdbabddbcdbbddbaabbdadcaabdcccbababddbbddcbdaadccdacbacadcaddbbcbcbcbddccbaaaacbbccccdcadbdabaccbabbccaaaadaccbadbdbadbaddcddadcaccacbaacccaacbdcaaacbbdbdcdccdbcaaddccddbbcacdbcbbbaaccdbadacadbbbcbdbabdbcbccbaaaabbadbdbbdbcacacbbdbaccdaccdbdacddbcbcadadcbdacbcdbddaaabbababcbdaccbbadacccabbcdadbdccccdbcadbdcdcadbcbbcdddcaaaddddaabaaddbcccbbcaaddddddcbbbbbcdbaddabbbacdccbcbdbbddbbbddaaddcdbadadbaabbbabdbddcabbcacdcadadbcbababbbcaccbddadcdacaaaabbdadaddddcccabbacacbbabdddaddaccbaadaddcdabdcbcadacbccddaacddacddabbdabadcbabbdcdadbdabcbdadbddbcacbacabdcdaadaaacdbdaacbabcddbcddabaccbababdddbbcbbbbabacacdbbaccacccadcacbbabcbdababcdaaadacddccdcaabbdbbccddacdbdcbbcbbdbbbdaabdacacbdccbcaadbbdddadcbacbcbdbadcdabdbbdbdcccbcbddabdcaabddcddaddddabbcdbcdddbcaadaacaabccabbabbbdcadaaddaacbcabadababddcaaacbbdcabaadddaacaabcbdadcaddcaadbbbcbbcdaaacaddcbbcabdccabacabcabbcbbddbcbbdbddcbcbddaddadbcdcaabbdaabbbadcdacabdabbdbbcaaacbbdccddccaacacaabacaabcdadccdbddacdbdbdccbbcccaaadacdccaacccbcdaddcabcbcccacdabccbdcabbcdbaccbacdbcbdabdddaaabccdcbccdcbacdcadcabcbbcbdacaabccabdaadcbdacccbabcbbddacacbbbdddcaaadccbdbcbaacbcdbabdbacdbbdbaddbccbdccdddaaaadcababccbadcacaacdbacbadbbcbcadddccabcdcdccddcbcdccbaddacabacbdddcaddcbbcabddbcccdcacababcbcadaaabcbcaccbddbcbbaacaacbdcccadabbaaabbdbaacbadccabaacbbddabcbabaabacaddbacaadaccdadddaddddcadcbcabdbcabacdcbabcdaabddcccdccbacbcccabddaaaccadcbbdbccbbbdcccdcbabddcdbccdaabcbccaadccaadcbacbdccbbabaabdaaccddcadadacdccbacaadcbdbadddcdcadbadadabcacbabcdddabcbdccccbaccbdcbbbdddccdabddacaabaadaaaabaccabbdbbacdaccdcbaabddbcadbddbbdbadaaadcbbdadcbdbcabdbacdbcbcbccbcaadbabdaacdccbdddddabcdaddbbadcbacbbbcbaabcbdbbcccbcabdbcacacababdcdadcdbacadbdcdacdcbacbddbbbcbbcccabdbbccabcadcddcbbbaabdabbddcdbbbacaaaddbbabaccadbcbdbbcdbcacaaacddbbabaabdbcaacbddbddbcbbddcacacddabcbcdbdcbadbbbcdcbdbccaddcbbdaabdbaddbcdcccabbbbacdcccccbbdbacbcdbaabaaaadccddcbbbdabbbbccddcaccaabdbdbbbbcbcddadcbdacdacbabbbbaadabbdacddadabddbcbabcbdddcdbacccdcdbaaacbcacdccaacacbcdbbacacddbbdbbcabaabaaccaadadbdadddaabdbcbcbdababdbbcdacbcbdcddcabdcdaacddcbacbdbdbbbbbbdadbacbbaddbcbbabdbdacbbcacbabbadcdacddbabbbabcbacbdaadcbaadcaabcbbdbdabdcbccbccbbdbdcbcbdbdbbddddccddaabddbdaddcadacbdbbcddbaccadbaaaacddaaabaabdaaccdcaacbbaddaccdcabdbaaabcdabcccbccabbbbdbbcadcbbbbcdaccacdccbdbbadacdddaaabbcadcbcaccdbacdbaaacaccdcbaadbdbdbadabadcddbcbabbdbccdbdaddcdadaccdabbaddbacbdcadaabacccacadbddcbabccdbcdacbbdabbbbbadcdbdcbcccabcabbbbcdddabbaccddadaabaacccbbadaadaccbdacaccadaacccabadbdbddcccbbbbdabcdadcbbbdbbadcdddabcccdbbdadcacbabcacdbaadaabdddccbaaadddaadbccdbbdbbbcaadbacadbacddcddbdcbadbccdabdaccdcddbaadcbdadcadbaadacbcdcbabbbacccddaaadcccbcbddaccaacbdabadccaadadbddbabcadabaddbbccabddddbdbcdcdbcbadbcbabbdaaacdccbbbadcbddbbcccbadbaaaacaddabccbabccdcbbcbcabdbbbbbbbcbbccbaadbcabbcadddabacaacddadccccbdaacddaaacbdaddccbbbcdbaabaaccaddabddcbbbbdbcabcbacaccbbdbababbbdbdbbddcbdacddadbaabdcbccbcacaaacccccacbcbccbbbcdababbadbcdddadcccdaadccbbcacddbacabbbbddbbbbaadddbbcdcbcaaacdaccadaabcbdbcbbadccbbbcadcdbcbdaaabdabcacdbbcccadddcbbbbdddbaacdccbbacddbccaaccddcbbcccaaddcbcdcadbdcbacdcadacbbadaacacabcdcbcbbcddcacaaaaabcbcdbdabcdadcabbdddbbbbcadabcbdcdcdddcbcbaadaccaadbbdbcdbdbcdbbdbcadbdbbbcddcbcbbaacdddcdbdadabbdcbbabcddddccaccbbdaadabcaaaabcbcbacabdaddcccbbdbdbabcdcccbddbbcabadbaddccbcdacabbaaadcaabaacacaaccbbabcddadbbdbcdddbdcadcddacdcaabaaadcdcadabdbbbccabbccaaddddabcdaccbabdbcbcbaaadaacdabcaaddbbdccadbacccddaddadcaccdbcddcaccbadbbdbddbcdaabddbdbdbcdccbbdaabadaacdbbdbaadadddbddcbabccacaacaadbbbbbbaacababdcaadababdbcbdcacbbdbadccdcabdcdcadaabbdbcbadbcaadaacbdbcddcdadddddddacaaddbbbabcddbabcbbdbdbdcdbabccadccdbdcdabdbacbdcccaacdbbadcdbcacbbbdadbddcdabdabcaadacabbdbdbbcdabdbacbddcadbaccdbdbdcbcdcacbbcddabbdaaabdaddadbbbddbcddbacbcdbdbdbcaaccdcccdbdcbdaaaadacbabcbdabddbaadbaacbbcaabcbadbdcadcdabcacdbccdaadddcdbdaddbdccacabcbadcdbcacbbaaadddcbaaacccaabbbdadbaddccbbdcdbbddabcdacadcbbbdcbbbaadaacddabdbcdbbcdbbdadcbccbcbbbacabcbbadccbadacbbabacbaddbdbcdbbcbaabcbacbdbdbbdbcbddaddacbcaaadcabcacadaccdcdcdabddcbcbccbbccbdccacdadbdabdddcaaadbabdacbacbbcbcdbbdcbdbbaadadaabbcccbdcdbdbdddacdbcdccbcccabadcdcdbcaddaacddaacacbaaabdaadbaaddbbacbdaabccbddbaaaddaaadbdbdbadcbcadccddadcbdaacbbabdadbdccbaacadaaaddddacaacccbcbcbdacbacaadccbdaaccdddacbcdbcbcdabdcdcddbdbdbbdcbadbadccddbbbdddccadccdcbcdacaacbdaddaaabdccbcdbdbdcacdcdabbacabcdcaccaacdbadbaacddaadbdcdbadabacbbbccbdbbbddddacbdadccdbbbbdbbcbdcddcbccdaddbcbaabdaddbcddadbabccbcccbdbcadadcbdaccbbaaccdacdadabcbcbddaacdbbabbdccdabcdbdcaccaadbababbacbaaccaacbbbdbacbcdbdbbdacabddccbcaaacddbdcabbaacbdabbacacbcdccbdcabcdadacdcadbdcabcacacadaddbcbdbddcaadbabaadcbbcbcdbacdbbcadcacaddcbabadcccddbbaadabbdabdacaaabbaaabaaadbaaddadcdbbbcbaaacccccdccddbdaabbcbaaccbdcddaccadccbabbbacbabdaabaadadbabacccbbdaaadcacaaacbbdbdbdbaccabdaabbacbcddabdbadcabbdacabcbadbccdabdacabbbcdbacdadddcacdbabddbbbaaddbdbbbabacadbdcacacbaccbaabbcdcaccbbcccadadbccdcdbcbdbabcabbbbacacdddaadcadccccacddadddbdbdbbdbbbbddcacdaababccbcbcbbdacadbdcdaaddbdcaddbcaccbcacbbabbdacdbbddadccacdadadbcdacbdbcabacbbadbcadbbbbcabcbcadbdcdddbdaaacddacdcbddabbaabbabdaccdabdbcbbcddcdaddbbccdbaddbddbcaabdbcdbaccbbdcaaccccdddccbbbaadabdabbdcbccbbdcabaaaadabcabccccbaacdbcdbaaabadcbdddcbdaaadbabcdbabbcadbdabccbcadddaaadcbaacadbdcccbabaadccdabaacccababdcdadccacdcaaacbcacccbdbddadcabaaaadaddadaadcbdbdcabcabbdaaaaaaaaccacbbdaadbcadabddcdcabbcbaadbadbdcaadcaadbcaadabdaaabcbbadaaaadaabbacbbdddbcdaacbcacbacccdbdbacdadadbaccbabcdbaaaccccabbbdabdadacbbdcbdadbbddababcdacabdabaacbdcbbaddbbadbdaccaaccaddaabdcdbdbbbcdbacacdbadbbbbcccbadcddccdccbddddbbdcaccaaaabbcaabcbdbaabcbabacaadcabddacacdaaccccccbacbddddaacabadaadadddcbababdbacbadacdbadaadaddbbccbbdadadddbcaccaddcdbdbbbdbdbdadbcbaaaacaaacdbdcbaaccbaabcdbbadcabbbbbcbdaccbbcadbcddbabdaadcdccdbcbadddccdcddbadcbaaddccbbaacadcbbdadcabcaaaccabbdbaaddaabcbcbaaccccbbadaddccbbbbdcdcdabcdbdbbadcbadaddbcaacccdabbaddaabdabbccddadadacabccbbcddacdcbdcdabcadbaabddabbbabcaaadadabddcdbbaddccadcbadacbbaddbbbcabbccdddadbabbccccdacdccadbaaccbbababcdbcdacdaabccdbabaddbbdbdcdcaaddbdaabbacccaccacdbdadadacbcbacbdbbddbdcabcdacdcbcbdcdbdccbdbabbadbdaaaccdcccddacabdcddbbddbddaddadcaddbacaabadbcacacdaddaadcdcccdaabadaabaadbabcacccbbdbaadcbadabdcacdccddddbbaadbcbdcbbdabbcbadbccdacdcdddaadcacadabbaadbacabcadbaacddbcbccccbdbbabcbccacbdabddddadcddabaaadabbabacabbcdacdacbaadddbaccdbdccdaddbdabdadacdaacccbcabaaadabdbdbccbabdbcbdbadcaccbbadadbaacdcbddaacadddccadbbaabaacacaabbcadaccbbdbdabbcbdddadcabbabdcdcdbaadcbdaaddaaabacbddcadbabcaabbbaadaaadaabadbaaaacaadbdaccbbdbdccccaaccbbadcabcdddddcdcabddbbcdabacdbbcadbccbcabbbcbccbcdbcccdadabddaccdaddccdbabadaaabcbbbaadbbcbcdaaaaacdbbdbcdacdadbcdbccdaaabbcacbaabaadccbddddcbbcabbadbaacababbcbbdccccbadadbbacdbdbdbbbacdbbdbabdaccaabdaddaddbaddaadbaaadcbcddabddbccadddacdcaadbbdbcbcadadccddbbadbddbdbcdbbdcacbccccccbbccacdbdbbabcaaddbabcbbbacdacccbacddcddbcdcddadcadabbdbcadabcdbdabdcddcdcbadcbdabbbdbdacccdbabccbdcccbccdbbcbdddcdbcdaaadcadabcdddadaacaccaadbddacabcabbbabccadddcdddcbbaddddbdcbbddacacdbbbccccddadbbcdccbbbcbdaacabcdacbbcbcdabbbccdccbbdadcdaaacbaadabbaddbaabcbaaaadbcadcaaadabacabddcacbcaaabbadbdabbdacbcaaaadbdbaaccababcdadabacbbcababbccdbbdcaadcdbccdccbcbaaccccdbaddbaddabcdbccacbaaacdabdcbcdbbbbacdbaadcdcbbabcdabcadccdbbbdabadcabdbcbbbdcbcbbaacaddbcccbbcddbdababddcdccbcddcbaacdbaadddadabdaaddadbdbdabacadcdacddbadcdacbddabccbaabcaadaadbcabaabaadacbcbbaccbbdddcdcadaacadcbdbabccabcdddaadacabccadabdaadadcaaaccbcbacddbbcadbdbbbbddddcdccacdcacbcddcbbcdababcbbabcdacacdbcacadabadcaaccdbdadcadcdcabcbbbcdbdbcbadccddcccbacdcdbdbdbacbdaaababaaddcbbdababaccababddbdabbaacbabdcaaacbccacbddadbacdadaaabccddcdbacabdadbbabdcbbadbbcccaadcaddbacbddbbcbccbdbbdbbaacabdcdcdcbddcdabadcbaadbdcabbdbbbcdcddbadbdccccddbddabdcccdbcddaaacacdadabbabcacadadacaddbbadadbccdcdddbcadcbbbcdcdcbcbbbbdaaccaccbdccdcdacddacaabbdcdacadcddcdbdbbaabcdccddabdbdabbcacaacdacbaaacccbdddddbacddcbadaadbddcbbbdadbbdddabcccabbcadbbbcdadbacbaabbaacaddcdadddabcbcbdcabccdabcacbbccbbdacbccdcdbcbabcdacbdcbbacaacdddaddbbadbdabddcbbbccbbdabbcbcbacbbdbdbcaacadabbbcccdbabccccdddcccccbabcccabddccddddcadddaadaababddbddadacbcabdddbcaadcbacabdbdccccaabaddaadbcccacbccccacdbabdcddbbccdaccdbcdacadaddcccbbccbacdaccbbdbbcbabbacaadcacdbcdbabcaddbdcaaadcabaabbbadabcaadbaadacccbaacbbadacdacbadacddcdbdadbbacbcbccddcaababbddcacbdcadaaaddacbabaddbabcccccaabcadcbadddbcbbccadbadcddcdccbdacdccbdbabacccdacdbaccdaccdddccdcacdadabbdbccdadccccabcddaaabacbcbaaccaaddcdcbcddacacbcacabbcdcbaacabcdcbacbdcbbcbcaadcabdcbbcaaaabdaabbddaccdabdabaadbaaccacabbcdacddbccaaabdadbbbacddcdbcaddcddaaccdddbaacadabdcdccbacdacdaaaddbbdcdbdabdadddadaaaddbabbdbdbbadcbdbdcdbabbabcaaacdccccbccbdccadaadbaaaabdcbbcbdddaddcdadbbacabcdddadcdaddadbcddbbbbddacadacdcbbabbabccbdaddbbdbdccdbcbbddadbcdacaccbbdbbdddcddcddcaacddbcadcdaaadbaddbbbabddaaacccdaaccabdbbababbdbbcaabdccbacdabdbdaaddddcaaacddbaccbccbaadbaadcbaabbcbbcbbadbddbddbcbdcccdaacdbdbbbbadccbadababaacaaddbcbcacabbabbdbacccacabdcdbccdddcccdddbbabadacadcdddbbcddacccbbcbadacabcaabbaacbcccabbdccacbdccbbdddbdaadbaabacbbaddddacddcabcaddcbbdabddababcbdbccaccabccdabbccadbabbaabdacdcadcbdcdbcbddbacbdadcdabbcdccaadcddbcccbbdaaacaddddadcbdbcabbacbbaadaadcabdcbddababbdbbbbadcccdcbdccdbacbcbddcbbcbccabdccdddbddddbbbacdabadbbdcbcdabadacddbadabaacadcbaadbcdbbdadacbddcaccaadccbddccccbbdcccadaabacaabbdddcacacbdcccbabbccddbacddcdbadadcbdbbdcbacbbcdadacbbdbbddbaddddacbcaaaddbbcaccadcddaddbbdcddabdacdaddddacacdbbcdadbacccabbdcdcbcaacadacabaaaacdabbcbdbcdddcacddabdcbaddcbacbaabccbcdbdaabbcadbbdbcbbbcdcbbccccadbcbddbaaddaaaaddcbdbdadbadcdddcccbcdbcabacdbcccdbdbcbdddaddbbccadabababcddbcbbbcbbcdcaccbbadcacbccdacbdabcadcdcbdadacaccbaabbadcdabbbaabacdcccbbbcdadacdddcbdcdcbcdccccbbadaaaaadbbcbadbadaacbcaaacdbadcaaaddcdbdbdcbbacdccacdcbdbaccbcaccbbcbcbcaabcaaaccdaabbddbbdcabadaaccabadabccbbbcdabbaaddcdaacbdccccbadcacddddabdacabdccacdbdbacddbbdcaddcbdbccacadacacbbacbccdcdcdbbadcdddbcacabbdaddacabbcddbdacacacdadadcbddccdcaddcabdddbcacdcbdbddcdbadcbacdabddcddcbcdabcbcbbadbcbaabadbacadbbddbddaaaabdababcdccacabaddaabaaccccbddbbbadaacabdabdaabbcbaccdbcbbacacddbbacaaababaadbdbaddbacbabadcdcacdbcbdaadcababbccbdaadabbdcbaacbbabacadddbbadccdbadaccbdbcaabaadbaabaadbcdddadaaddadcdcccccdccbaaabadabbcaaadbccdaccbaddcddbaaaadacdcacccbadaaabbbbacbaaacabadbadcbaacadccccbcbbdacdddabadacdbacddbabcdcaaccbdaddadbdccbaaccadbcbcbddaaddbdaabdcddabbcabcbcacbacdcdcaccdbcbdbccdcdbcbabbaacacbabdbdcddaccdcbcccdccdaadcdcaabccdaaaccbbdccddcdddddababbaddadccdacadbadcaabdddabaaccbadadddcaaacccbdcadbbaccbcadaaadbbdcccaccabbbcdbddbadadaabbcdbdaccdcadcdadbcaacdcbbbcbdbdacdddcbaaaddcbaabbdcbbccbbabdccbcbccccdaacbcddacadadcddababaabcbdcacdadabddbdcccbbcbdbabdcccaacbdaccdaabbcacadddbdddadabababbdabaddabbbcbdcdbcdabddbbdcccbccaaabddabbdccdabaabdadabcccdcbbaaaadbcdaddacddbdcbcbcabbdbabcdddbdbaacbabaccccbdabadbdddddddcbdcdaacbdacccbbcbbbbabbaddcadcabdbabbccbaddadcddadacddbbdcaabadabcdabbcabcdabcbcaadcadabdbbcdbadaabaddcbdcbaacbacdbcddbdadbdaacadabbdddcabcabacadbabbbccdbbdbdadbddbcbccbbabddbabddcdaaacbccbdbbcdbaccccccdaadbdaaadcadbaaabaacddbbbbdcdddbabbbaccdcbcadcdbdddbbadaccadccccdbbbcdaddbabaabbcddadbadcababbbdbcacbdddbcccdcccbcacbbcdadbcddbbddcbadbbbbabbcdacacbadbaabadbabdcaabbacccaddaadbdaacbacacbbddacbcaaccbaacdadccccaddabddbdcbbdcdcddacaddbacccaacdbaabcacadaaabbbccdcbbdaabbbababaadbabdccdddbcddbbcdcdccccabdbcacbccdbdbabbbcbbacbbacabdcbaabddaadbbccddcccdcaddcdbdbdbbcacddbddbabcccbadbdbcdcabbcbdaaababbdadbbbcdcddaabdadbdbacabadbcabcadcaaadbabdbbacbcadabacdabbcabbdcaacabcbcadabcdaaaabdcbdbddcabccbddcdcdbccadcccddcbbcdacbbacccddbdcddbdddadcacbdaaddccbddaaaccbdaaddabccbbadabbdacdaabacdbdabacdcbdcacbdccabdaaabaaadacabcabadddddcbddbacbaabbcabccacddbcddddbddbbdbbcdccaddddaddbdbcdbccbaddbddaddabbdaacdabcadcacdccabaacddbbbdacdcccdabacdabdbbdbdcbadabccdcbcadbacadcdcdbcbdbdbcbbadabbbcbbdabaaddbbdbacabcccdccbbccccddadcccacaaddcbdcccdacdddadabbdcadaaaaaccbadacacababaacddbadaacddbaccaccaddaadbddaccdacabbbcaaaaddbaacabdadabbcaadbbadacadbbbcbcacbcbaabddabcadbabbdaddcccccddcccdbdaaaddcbccdbdbddcdaaaabbbbdaddcddcadbdcdcbcaabcacacccdbdbaadabdddccccbaaacabddcdcdccddabcacccccbbccddabadddcaccdcdaadcddcddbaaadbbcdcdbdaadadcbdcacaacdabdcbdcbdcbdcbaccdabcacacaddbbadbabbadbacaacdccaddddbdbaabcacccadcdcaaacbcaacddbdbbcaabccdbaabdaabdabcaddaadcacdabdbdcadabccbbadcddacbdbbcdadcaadacdcadddcbbcdcdccbaaabaaddcdbbdbbbbbdcbccdcbcbcdbcabcbccabbbdbbbbdccbddabadcbacaadbdbaddcdccdacacaabdacadcdbcdcbacdaccabddbdbaaccababbddcbcbccadbdcabaadacbdddaadccdddcabaadaacaabaddccbcdabbcadbddadcadcbbcadbcabcadddadcdabcddaddadddadcdbbbdadacdbddbaaccccbdbabadaccbbddadabcaabccbdacadaadacdcbddcadddbacdbabbbdccccdddcccdbaabbcbcbdbaaacaaaacbbbccbcbaabcacacbbddacabbabbcacbccdadacbcadbdbcdbcaddddbbacbadccbcabccaddcdbccabaaadbabacaaadaccaccbbcccbcaacaaacddcbaaaaadbdbcadabaaabdcbcdaacadaaddcbabcadababbddddbddbdaaccdadadbabbddcddbdadcbaacdddadbdbbadacdcaaacbddcbbacddbaacdccaadbdcadbabdadaaacdcadcdbddabbaacddbcadcaaacbbacaabacadcbddcdacacabbcccaaadbdbbdbbcaccdcaaddababbcdcacdbcaacbcdbaacdbdbbadcbbcbdcbdbaacbddbadddbdcdaaaaddadbabbbddcbdcabcdaaaacccbaabacddbdcdbcddaabadcdcadcbdacdccbdaddcbbaaadaabdabbacdcbdccdaddcdcbccaadbcaabdcbbbaaccccdbcdddcaddbbaabaacadcababaadbcbcbdaacdcbcdadacdddabcdacddcbbbdcbbbabcbbdadbbdabdcccbcbcadbbcacdacdcdddcbadcacacbadacaadadaaacaccbcaacbdbcbcdadbacbdadaccdadcccdaabaadcabbbadacabcdbaccabaccbabdacdbacdabacaaddcadaaaddbdbcdabbaacaadbbbdadcdadaaaabccaddbdddacdadccdadccbdaacbaddacdcbdaacbcadbdbbbbbacbacbcbdaccdadcacabdaacbdbabbccddbbdcaabdbddbdbcaabbbcdcbdbacaacdbaaccbcabcbdbcdcabccdbbcadadabbabcdddcdccccdbbdbccdacaacacadbaaadcbcdbddaabcbacddadaaacbadddbddcccccddccdcbcbccdacdbacbcdbdbadbcccccbcbbbacddcacbbccbacabadcbbcadbacdccbabddabcdcccdabdaabcabbcbcaddbabbbcadddbadcaaaccdbadbacbbdadacaadabaaabcaaddbcccacbdaaadbdadabddcadcddcaddbcdaadbcabadaaccbdbddcaabacabaabcdcbdcccccabbbadcddcbaaaddcbccdaadbdbddbdcbdbabdbacbadbdbaccacccdddaadbbadacccdbcdacccacacccdcdddacddcdadacaaaacccabbacdbbbbababcbabdcccbacacbcacabbaddccbddaaacbaaaaadaadababbbcdcdbcdcccadaabbcddcdaadaaaddbcbbcbadcabbdcbcbbdabbbaacdccbaddcaadacababacbaacddcdabdadabacbdccdbcddcbbacbcdaaccccddccbacccdcabaabccbcbcddbcbbcbdcabacababbdccadccdbcbcbbabaaccaadcaccbaaacdbddbccdaaaccbadbacdccbdbbdddbaaaaaaadcddbcbccbdbdaccdbdbcacbcdbdabbddccbaaaabacababdaabddcccddbbbadacdabaadadabcabadbddacdabccdcdbbbccdbdcdaaddbcdddbdddbdbbdccdcadabacdaacabbaacbbbabddaacccbadcbcdbbbbcddcdcbcacaabdbcbbcbdcbacabdaccbabdbcdbdbcbbaaaabadabcdaddcadccdddadbdbacbbddbadaaaddbbddcbbaadacbbadccdaaaacaacccadcadcbccbbbdababadbddccbbacaabdaddacdcabaaadabcbbbabbbdcbcabcdacccaaaabadbdcadabbabbbbdcbcbabbbdbcacacabcaaadcccdcbbacdaccdddddaaaadddcbbccacaaccdcacdddccbcdcbcbaaadcbaddaaccbbabccdcbddadbbcadaaadbabcdbcdbcabdbbdbdcbcbaddaddababdacbbbcdbdcccbbbabdbbbadbacdccdddbcaaacbccdabaabdabddaadbccbadabbbcbbdcaacaacdcaccccdbcdaadbcdaaaccbaabbabdddcaadbddadaaadbdbcdcddcdabbabcddabbcdddbcabacdcacbacadbadbddcadbbdcdadabbbaabdbadaccddbbcadcaadbcadbccdcbcdccbccddbbcacbbdacdaacdacabcadaddadbbcddbbabaadbdcadcaccacbbddcccdaaccbdcabcaaacaabccccdcacacabdbabdbbdccdcadaddddbcbdbcabbacadadcbdccdcbccddaddadbaaacacbccbbcddbddccadacadaddccbcabadcbaccababadbcddccdaabaababaddcabadaabdbbbbbccddadbccdabdaabbdbcbcabbdcbadcadcabacbbcbaacbccdbddabdbdaddacdccdabbaaabddaabcadbaccccaaccccaaadacabcbbdbaacdbcdbddddaaaaababdccbdcacaadbcdaaccbaccabcaaacddcdcaaddabdddbadbcbbcbbbdcdcbcadadcbdbaaacdbbaabdcdcbdaaaaaacdaddaaccbcbcbadaaabcaccdcdaccbcdcacdadcbbddbdabcbddbcdcaadcabcbdcdacaccdbdaddccbbcdbaaccaabddcacacbaadddaadbbdabcbddadbdacccaaacdaaacabbbaccccadbadbdbbacbabbaccdbaccabdabbacacabdcbdccbddacacddbbbacdaacadbbabdbcadbacccccbbcacbbacaacccdcaacccdbdacaaaabcddabcaaccbcddbaadadcaddccdbadddbdabbdcddaccdabbccbcdcbadbdcdcddbddaddbdcabdaadbbdddbabbadacbbdadbbaddccbddcddcacbcaacccacdcddadccaddbadbadbcbcabdcbbddbdadaadbcdbbaabbbaabadaabadaaaabcbbccabcbcaacabccdddadcdbcadaaaaaccacbdccdabdcbcbcadcdbcddaabacbbccdcbccbdcdcccdcddbbcddadcbaaccdcbacaacdddacadcbcbaaadbdadcadcadbbbcdccadabadbaddcaccbbabadccdaadcccddacbcdaabcbdcbaccdccadabcabadcbdbbaaddadcaddcbbabdaacaadbbbabbabcddbbdacabccaaabaaacbdcbbcbcdbdcdbaabccaadaaacbacbbdbdabbaddbbdcbcdccccdbaadcacadcacadccaacadbcbdabddbaaadddbdcadbaaabbabdcbadcbcbdccacaadaddcbdadbcbabdbdacabbbababcccbaddbcdbcabcdaabbadbbaacdabaabdbdcbddcbabdcaacbaadccdabaddbdaabddbacbdbdacccddacdaaadcdcbccdcdbaccdadccdbccadadbdddcbabcacaacddabadbadbbbaaccccbcacdcadaadcdaadacddadcbdcdaababddadcbcdccaabdbdaacbbabbdabacbadcbdcdbbccccabcbbdbbdadcccacbccddcbaccdaadcadcbdaadcddddadadcaabbdaaadcabacacdddaabccadadbbcdbbdccbdcaddadbabbacbcbccddcadbddccccaaadddccbcccacacbaccaaabdbccadabcadacbdbacbddaaadcabdadccaacdaccdadadbdbbaabcaddbdcdddbaccdcbbdccdddbbbcbacacddcaabddaabadcddbdcdbdbaabddbaaacacbdaccdaabadcdadddaaaabaccaddbccbccdcabdddbccdacbbaddddddbcacacdaabbabaaddbbcbccdccaadccdaacbaaabacbaaccbadbbcadbdcdadabcaaccdddabbbbdbbbdccbcdbaacddcacccbccbbabbccaabdcbcbbcabaabacdbcbacbbdcaababddaabadabacbabaccadbcbacbbacadbabbbcddbcacddbddcbbacbabbdadbcddbccacacbaabbadacabacddbacaccbddbddcbccccbadcdcdbccbacbccbcbdcabbabbdaddbdabdcddbbbbacacdccbcdaccbbdcbcbabdcdcdddddabbbadcdaaccbdbcdbcaacbdcdabbcaacccbaaaddcdddcbadccdbbbacabbdbbadadccccdbbcdddcdcadaddbadbcbcaccccbcaccdbacdacadddcbddbaadbaabcddbcccabacdcbcdadaddcccdbccbdcbddbaababccbbaabbdbcabcbacbbaccddabcadcbacadbcdddbadbdcdcdacbaabaadadbcdbcacbbaabcaaddcbdcdbdbbbddddbbdbbbcdbccbbddaccbcbaccbbdaaacacbbadccabbdcaacadccbcadbadcabbcbacddadbabadccaaaadadbaaabccdcddaacdbaaababccdbbaacaddcdbacbdccabcddabddddcaddcccbddcadaadbbcdbbdcddbbbbdcdbcbbbaaccbcdadddccabbaadbdcddbbccacbdaddcdbbccacadcbacacbddbaaabbdcbcabdddabbdadbcbbcddcddbccbccbbbdabddaccdacacacaaaadbdcbacdcbaaacbdddbbcdbadddbbccdaaddcbdaccdbccdcdbcccbcccdaccdbcaacdbbaddddbbdbccaddbacccdbbccabccddadbcbbabbdacbdabccbabdcbaaabcabccbabadcdcaacabbaacdaacbdcdcccabdcaaacacbdcaaacdcabbdaaaccbabaacdcccdabcccaaacccbbacdaacdcdcbbdaabbdbdadcbcbdbaddcdbaabdaaaccccdcdacdacacabcddacabcdabacddbadabdbacacbbbbccaccbccbabaabdcbcbbbbdbcabacbbbcaadcbabcacbabddcabdabbbbadadabaadccdbcbcccddbaddbaacaaddcdaaaccccbadbdacbdababadacdcbabbbdddbddaacdacacdbdcaccbbcacdbcbdbcccdbadbbaccacbdcbacbbccdadbccbcddcdbaadcbaacabdaaacddcdacadbcabbdbbbccccbddbcabccaacaacacadcabacccaabcccbabbddcddbabadaabcbbddaabcadaccabdacbcddbdaaacdabdaacdbbcbcdbccdbcbdbdbccdbdbbbcabadabcdbbbdcbaaabaddbadbcdaacbbdccbcbaaadaacbbbdddccddaaabcdabcdccdcbddbcbbcdaadacacdaadddaaabddabacdabaacbcbabaacacddbacdaaabbcabababaacdbbabcbabcabcaddacbdcacaabccdbcabdcabaaacdbcadaadccdcbadbdbbabacabacdabdccdbcddaaddcbdcabbacdccbbaaddcddbdbdcadbdcdbbcbdaddcbbbcccbddcdabbcacdbccbbabdcaaddbbaacccdcbcacbcabdcbacbadacccdbbcbbdbbdbcdaabcddbcaabdddabaacdbdadcaadbabaaaaaddbcdaddaccadbbdcdacbccadbcddacabbabbbccddbbdcacbcdbacabaaadbbadacdadcdcdccccbacbababbacaccbdadadcbbdbdabdaccaccdcadacbddabdabaaccaaccdaaddcbbcdddcdbccdccdadcccacacccabddbbdadbbabbdabcdbcaccccbddbddaccabbcbdbadcdbaadcdbcabdcacbbbdacbacdbcdbabbdcbccbcbbabbaacbccadcdbadcbbcbdaacdabbcadadcadacbcdaacabaccabdcabbaaabbdcddbcdcbdcdadaddbccccbdcdaaaaadccdaacbacddadbbbddccbcbcbdbcaccbbddadacadcbabbbaacaaabcdbaabdbbdbdadbbdbadaddaaaabbdaadcbdacaddddacaaaacdbcccdabdaaabcbacccbababacabdabbcaabaadaddabacccddcddcadcacacdbacabccdcaadbaccadadcabddbabaacaacdcabcacbabbbcddadcdccbcaabbbdcbdababbaacdccbdcdcdacaabbccbdccadabbcbbaccccaaababdcdbbadccbcdccdbbcbababbdcdabcbbabdbcbcccacbcdddbcaddccbdbcbacbaccccdddcddbbdaadcdacbbcccdddacbbbdadbcdaddacdddbcddbaccbadbcbcadaaddbcbadabcbdabbcacbacbcbcabdbcbcccbccdcbaacddddbcbaaaaacaddcabdcdbadbbabcaabadbdbbcddcbacaccbcaaddbbaacbcdcdaabdcabaccaadaaadbdbadcdaadcbaddbdbddddcbaaddaddadbbcaaccabbddbdcccbdbddbcbdabaddbacaabcbbacdcadaaacdaaaababbdacaccdcabbdbbdadbbdcccddbcabbbbbdbcccdbcccbaddcbaadbacaaabddaabbaddbaacdcbaacdaabaababbbcbaddaccbabdcdbaaaacbbabdabcadbbdbcbabaadccdadadadcaadabdbcbbccddbcdddbadddcdcbcbdcdaabcdbbdcacbcdbddacbbbddadacaabdacbaabacdcdaaaddbcaadccccaddacdbccadbccbdbccacbbdccddbcddbccbbccddbcccddbbccbbddcabbabcdbccdaacdbbcadbbdaaccbcccaccacbaddcccbdbbbcadbabcadabbbbbadcacbbdccacaacaabdadaccbbabcaaacdbbddacdcaaddbcbbbddcabcbddabcbabacadacbadccaddadcabddccddaccbdacadcbbdcabcaaccbacaaadaacddbcabbaddbccabdaacbbdaddbdbaaacaaabaacdcaabccabdcccccabccabcaacabcbabcbbcddcadacdaccbaadadcbbcabcdbdbadbbababbaccbabcacaadbcdbdbcddddbbcccdbdaaaadacbbcbbacdbdabbccabdbbdbdabbcbbddbaabdcbacddddbcaacadbdcddcbddcabbdcddbacaaadcabdcadcbbcaddabaadcdacdabbabababbcccddcccacdadbbdcbdcaadccdbdbcabcbacbdabcbbadadcdabbaaaaccccccacadbcabadddbccdcacdacabdbbccbcadabaabbbcccacccaadabcbbcdabacdacadccabaadccdddaadacdadbaccbcdaccabcabcaaaccddbcbcbaabdaaababdddaacdcdaddbbadaddbdabacbdbacbdabbbdadcadccabbdbaaabbdddccacddccccbabdaddbabbadaabcdcdccabcaccbbbcddbddaaaccdbbbddcbdccdbaccbcaccdcdbddbbabbacccdcbaaadcbcddbcdccaccdcbcdbbcbacadadcaabddcbdcaccabbbcbdaddcbcdadbdcaacadaccacacabaabaaacddbdccaadcbabbdcbddcbbdbbaabdbadacdcacbcdcdcabbbdbcbccccbdbabcdaccdbacdddcacdcdbbacdabcaadcbbbacacccabbbabdccdbabaaabacdbbacddacbcbdacadadbaadbbcacbcaddcdbdcabcdacbccbcbadbbabaacddcbdcccbbdcbdaddddaadabdbdccacdabcccbcabdacbdbcdaaccdcadbaaaddadcadddddbcccadbcdcbdcdaccccdddbdadcdacdddacdbcacdcbbaabbacabadcdacbcccadddcacaacabadcbddcbacacbaabdacaabacbcbbbbabdbccccbcdbbaccbacbabbbccdbbacddddbdbabdaaadabcadbcbcacdaaaacbcbdddccdacdbbdcdddaadcdbacaabcbbaabbadbdcbcbbcddbcacbabadcccabacbcbbbbcadbaabaacbaaaabbacaaadcaccabadbacbbdaaddbacccdcbacccbdcaababdbccdcabbcacdbdadcacdcbaadcadddddbdcccdbadcaacaacddccdccbaacccbaaacabcccdddccbdcaccddcaaacbdbabddbdbadbdcadbbdbabccdacbbbcaacddabccbccabcdadbdbcaababdcbadaddcccdbdcddcbacdcbbbbadbddcddaadcaddacbbccadddbcadabaddabddbacabadddbbdabccdbdaaacacabddcbbddcdddcaccddababccbbabadadcddcbdcaadbdaadddbcbdbcdccbccaadacbddddbadcbdbaacccccbdcabbbddaaaadddacbbbcdbdbbbdbaaddabababdbaccabbdabcbddccdadadcacacccccbbbddbbaccdbdcdddcaaccbbbadadcaadcccacccdadacdcdacddacacaabcbdbddcbcbbadcbabbbdcaadbccbadcabdcacacddccaadadbdccaddabcdcdababcbbdabccdabbcadacddaddacaadcbcabaabdbabbcbdabaddcdaabbbbabcdadcabbcdadbbbabdcbcbcabcaadadbbbadddcdccbcacabdbcbdbacadabdbdabaacdcddbbdcabdbddabdddbadbcbbdcbddcbcacbbddcbccacdcddabbddabacbbcbcaddccaaccdbcbddadbbaabacadcabdabdcddcbaacaadacbdacbccacddbcbbddddcddabcacbadbccbabdaaabaabdbcbbbbbdcbcddbcabddcadccacbacdcbccccdadbbbadccbcbdcabdadcccaadabbaacbaaabcdcbcbaadcaacaaadbddddaadccaabaadbadbaabddbdaaacccdbadbcbadbaddbdbaaccacabcabadbcbdbccbbbdcbbbccbadaacabbdcdcdbcaddadaaaccdcbbcadadddddadbcccdaabcdbbccbabbbcbcdbdbbcacbacbaaabbccaacbdbcbbcadbaacacababbcaacccdcddabddcdabddbacabaacbddccadbdabcdddddccbbdcbaccbdbbbbaacaaadaacccacbbdcbbdaadbacacddaabddacdbbcadadbabddccbadbdbaddabbaaababaaaadddbbcbdacdccbbaaddccabbabcaaabaccbddabaadcaccccaacccdcbbccdddbddcdcdcbcadbaadadbbbaacdddbcbbabbdbcbbcacabdabcaaccacbdadbdcbcdbbdbbcdaadddbbbdbbcbdcbadccdcbcccdbabdcbdbcbaacaabcabaacdacdacbcdadadadcabddacaadcdabbdaabdbdaabcdbcaccdbdbaabddbcbbabadbdcdcabddbaddabdacdadabcabacdbbdbdaaaacabdadcabcdabddbcabaabdbcadbccadcbbbcddbddacabcadaadcdddddbabaccdccacbaaccdcbcbcdaaadbbabcdccadcccccdadcdaccacbabdadcabddccbdbbacccdabadccccdcbdacbbaadccacbbbbcdbdcbcdbcbdbccddddabbbdbddcddadcaddbbbbacdbcabdbacacbbccadbdabdbacdcaacddabdbdbdaccdcaabcccddaacaddbccbabdbbcacadcccabbdcadacddacccbcacdccdddcdbbcbdcdbbabbcabcdbccdcbaaabccabbcdccabddbbaccbacccbabdacadcbaccbabbadbbbabcccccbbdbdccbdbccbdcbdccccabaddbcccabdcbaabacbdbaaadbadcdabaaaccbbbdcacdaaabaddbbbccdccabdcddacababbaacaaccdaccbbacdddcaadadbbbaccdcabbbdabaccaaacabddbadbaadacdbbdcaaddabbbdacaddadbdcddbddcbdbdcdbddbcbbdabdddcaaabadcadacdcbcbcbdacddcdbcadacbcdaacabcaaabaaaaacabbcbbdccadacdddbdbadacaacdcabaddbccccbcaabaacccacccbddabadadaccbdcddcaabbbabdbcbdbddddbbacccbcadcbbbbdbaaccaacdcabbddcdbbcbabddbababdbdcadccdbbaaabcbcdabbbdaaababddbcbddcdaabdcccaaaccbaaacbcdbbadadccccbdacacaaabbdbbaaaadcdabbabcdcaacacbdbddcddcacccabaabbbbbbdacbdaadbbaacddacacccdabacbcbbdcadcdadbdccbdbbdbddcdabbcaacbdbadaccdddcdadddcbbacbaacbbbdacadcdbabcbcbcabaddddcadbaccccbbdbbbbdcbcabbcaabcdcabddbbbccadcaaabdcacbcdccabdabdbcadabaaddcdbaacddacacddcbbccbdbabbbbbdcddabccbdadbdddccadaacabcddaddddabbabdaabaabdaccaccccdcbcdcdcbbccaccaadcaadacadaccbcccadbdbbbddbccdababbbaacadccacdabdcddaaccdbcccdbbccdaabdabadadadcdaccbcdabbadbcbbcccaacabdcdcabddbabbccbaadcdacbbacdaccacbbabacbdadcaddcbdddadaddabbdcacaccccbdcbcabcabdcdaddadaaacacadabdacccdaabcbdbaccdcaacaacdadabadacadbacccbaddbcccabdadddacaaddbddbbbaabacaddbcacbcbdddcadbacdbcbbabdacabdadcbbdadbbabdacbbcccdcaddbbcdccdbaaddcadddadcabcbcdbbabcdbdcaccbbbbadcdbddacabdbccbcdcadbabcbaabcdddbdcbbbdabadacbadacdbbcabdaddddbccdbcbbbbaaddbddcbcbdabdadbcdabaaccaaaaacbdbdacbbcdaaaaccdbdacaabbaccddccaabbcddaddbcacdcbaaddbbcadcbbbbbddcbbdadadbacdbcaddcbbcabcbdcdbacddabbdcadacdcacaccacdadbabadadbbcacaaddbdbddadccbdbccbaabcadddcdaccbdcccdcbccbaadbcccccdadaacbaddbdddbacabcccadcacadaabbbcaabadbcdbbdaaaadaabbaacdadbbbbaacbcbcbcdbbdbadbacdadabaacbababadcdcdadccadcaaacbdacccccbddbdbbccddbdcddabcabaaccdddbbdbaacaaaccbdcdcadcbbadddcdbaabdbbcdabcbcdddcaddcddcabaacccaadbababbcdadadbcdcdcaadaabbcbbbcdbbbadbaaacdcacabbcdcaaddbbcadabcbbbddcbddabaaadacdcbcddbaabdbdcadccabddcdaddadccaadacaabacbbcccdcadaddbadddabdcccddbbdcaaddbdacacadaddbbbdbdacdcdcdadbcadbddccbbdddcaadaabdbadcacacdccaacaaaddaccbadaaabbccbcadacbccabaccaadadadaddacabdadaadadbcaacaacbcaddbcbadbdbbdadcbaacbcdbcacccaaaddacdacabbaacbdcbbcbccdcadababdddcdcdcccabcbdbccaaddcdbdbdccdaddadbcaacaddddbdbabcccdaddaccbcdbddbaddddabcadcabadacbcadcbadcddbbbacbcdcdcddbabbbdcbcbdcddabbcacbdddcdbdcacbccadddccdbadcddddaddabbadcdacbccbccddabadccabaacaddbabdaaadcbdcddadbdcbddbcaadbbddddcacbdbabbdbdbcadddaddadbbaacbccccddddbbbcaaacdacaccabdcababaabadabdcdaadcbdacaaacccbccdcaacbbbcacabacaacdbcaabccddbcdacaacdacbacabbaaacccbddcdddadcbdccadcbaacddabcdadbabacabaddcaabdbbcbddbdcbadddbbdbcbabdccdcbcbbabdbcdbdcbacdbabccbbaaadbacacbabccabaabaabcaacacacaaabcaabbaabbbbddbdddbbbcddccabddcdbabaaccbadcdbcadbcabcdcbbdcdcbbcaacbbbbdcbbddddcbadbbdbaddaabcacbccdcacbabaaacdabdbdddadbbddcdddbadcbddacaccbaabcadbaacdabcadacbcbcbcdcabadcddbcdadbbbcbbcddaabddcdcadcadccddccdaaddbccbabbcdabadadcbdaacbbdbbcdaacabbdbdccbbaabcadadcccacadbdbcaddaaaccdcbdaaccacbbdadaadbcaabcddabdaadcbbcdcdcbadbccbacbcdabcdbabcaadbacaaabccdccbbbdaddaccbacdcdbcdaaacdadaccbcacbbabdaaaadddaacbabaadbbdaaccadddaadacddadcaadcdbccdbdbcdddcabdcbcddbababdaaaccbdbdbdcbaccabdbddbaaccccdaacadadabadbacccadbcdddbcdbddaabbadcabbbcddadcbcdcbbacdbdddcbdacccabdadcdddbddcaddbdddccbacdcdcdbddcddddbbdacbdcccdaacabcbacddbddcadbaabaaccdbdabbbccababddaadabdbacdadbdabdddaabbbcdbddbdadbcbbcdaaaadbbcacdaacadcabadddcdadbcbddbbbccabdcddcacdcacdcadaccdccadddccbdbaabdadddcadddbadbaabbccaacbdbdcbbbcbcaddccdaabddacdcacaccbbbbaababbadcdcabcccddbababbaacacabbdddcbccddcdbbcdbdbcaaccbacbbbdbcadabacdacdaccaddabacaddbaaadadadcadcadacabbaadccdacaddddcdcbcaddbbdcbdcaadacabcdccbdadbaacbdadbddddbbdacadcbccadaddbdcccddbcccacccacaaccddadcdbdaccbccacdbacaabcaaabcdabbadcdcdcccdacacabbcadbccbcaabbcadcaaddaddacaabdbcbcbdddccbcbbdaddcbcddcdcbdaddccdbbabbddbabcadcdddabdabbbacdbbddcdaccdbabaddbcabadcaadbacbdcaccbbcacccccaabbcccdcbbbacdaacadbbccbbadaaadcabacaabacbbdbdcdddbaaccdcaaccadcbcddaddabbcdbcadbcbdcadcdccdbabccbacccaccbbabadbbacdacbcbbababcaadbbbaabbacaacbacccddaddacdbbddabbcbdaddcbbabaadcdcddcbdacbcdcbabadccabcababdcabbadbaadddaabacaadcbdbcdacccababccdcdbccdcbcdcadbcccadcccadbbbaccbcadcaabaadabadacabbaddddbbcabbccdbbbcabddddaacaadccbbddcabcbacdcacbddbabcddabbddbabcacaccabdabbabdadcccdcbdbcdcdaaacadcabbdaabaabaccccdaccdbddadccccbacdbdacccacbddcaabcabcbdadbcbadcbdcdaaaaaadddacbaddcacbbcdbddcdbdadbbacdbcacbdabdbbdbccacbbbaaabbdbacacadabcbcdddacdaaaabbddaabccbabdcdbbbdbccadadbdbabadcbbabdacdaaaddaaababbcbaccddaacbcbaaacacaaaaabbbbcacbcbdbcbdadbcbbaddccabbbdbcadccdbbacbbaaabcdcbaaaabbaadcccbddddbccdbddadccccabdbbadcdababdccaaaababdaccaacabddabcbdacadaddcdaaabbbcaccddcbdccbacdbdacadbdbbdcaabbcadbcdcadcbacadabcbdbadadbbacabbdbcddbdadacccbbcabccdbadcbbacddbacbdbaddaacacdcbdcbaaaccdbddbadcdacbabbbdbabbccbdccddcabdaacbbaacdcbacdacddadbcccaaaccdbcccbacbbbddcbbabbbbaddbdbbdbbadbaddccdaaccddbddbbbaababcdcbdaacdaaaaddbdaabbdcbcadcdaabcbdcbbbccbabddddbbddbdcacdbcbcccddbddcaddaacddcabcdcbbdaddccaadbddabcbdabacacbadbadbdbbbabbbabddbbbdbdaabbddadccdbcacbbbdbbaacadcabbadbccdccdbccddcbaadaaaabaabcbddbcadbdbccdaccdbcaadabaadcdaacacddccdcddaaaabdbdacccdbcdbdaddcddbbddbcccbcbaddccaacccbdcacbdbbbddccbddbbbdbcdacdcbdddcdbaabdcadcbdcaacaacddadacacdacdadddcaaabdbbdcdcbbadcdbcadababdcabaacbcaaccdcaadcdddaddaaaabaaddaccbccacdbcdacacdcbbdbbbcdacdbadbdccddcacacccacabadacdbbcdcbddadabdcdcdaabcbccdabdbbdddbdcccccdabdabdddcbbcbbcbbcaddbaddadbacddabddccdbbabbcdcccbaacacdadabdaadadcaacbaabcbdcccaaaabaadacbbadbcddbaabbddcbacdbaaabbbddbbbaddbaddbcdcbadddaadadabdabbcbadccbbdaaaababbbacccabcbbbcadbcabbcccadbddbabcaccaaadaacaacdabdcabaddabddbcccbdbbadcaabbbdccbdcbacbcbcdcbadcbdaadbabcccdbacdcbabbdaacbdabadaaaabdcdcbcabddbcccdbdadbacacadacbccbdccaaaddddacdadccdcddadbaaddcadbbbbabacccdbcdaacdadaabddcbcdadbabcadccccbdbbabdcadbcdbbcbcdbdcdcdbadaadaabacaabbaccdccbcbbbadcbcbddacdcbdcbbcabaabccdcadccbbdadccccbbcbddcbdccacbbaabaabddccadaaabaccaaabcdadbdcadccddddaddcbdbcaabdabbbccddcdddbaacddcabdbbdcaaabddcabaabdcadabaaaacadaacbcbdbacdbcadbbccccbbcaddcaadbabaaacddaacaaccddacadccbbdbabacbddbdacabbaaadacdcccccdcdcbbaccddacaabadbaadcbccacdacccadbccddbcbadccacacbdacadccbddaccaccbacdddaccdbddaadbdadbddbcdbcdbbbcbddadaccdbacbbaaddcbdcbcbabcbbbacacabaaadbadbcbabcddbcdddbdabaccdaabacaabdddbaaabacaddbcbbadacddcdcbccbcdbbdbcccdabacbbdbdccbacbabdaadccbdabcbcccbbaaaadbbcbcccacbddaabbaddaddcbbdccbaadbabadacbccdcbdbadabcbdbccadbadbbbcddbbcdcacdddadccdcadaccbbccdccbacadbcbcdcabdbdcbdaabdbbaaaabbbcbcacdddddccddaacabdbbaaabcbbaadcbaadcdaaddccbabddabcdaacdaacbabbdcbdbbddaabdabcbcaccddaabdbdbcadabbbcddaddbbbdddcbadccccbddcddbdccacddcadcbbcddcbabdbcacbaabbbaadcbabdddaddbcbdbbbccaadbdcdbacbabbccbcbdcdcbddadcccbbaccbcbdbdccacdaddbcdbcbaadacccdcaadaddbbdddaadbdbadcdccbcadacdaaccacdddbccabcabdacbcdacaaacacacbcaaadcabccdbdcbdabdaacbabbdabdcccbcdddbadddcacadbbadcadbacdbababbabbabbcacccabcddaaddcaabbabbcbcacbacadadddcbddaabbadcdacbdaccdbcbcbacddbabdbcdacacaabbcadddcdbbdbcbbaacbbabcabddcbcdbdadbdbbcddddbabddadbcababddbbacdcabdacaabcdbbacbabcabcdacbbaadddbaadccccbbabadbcdaabcccccabddadcdbddcabaaadaadbccaacbdadbdaacbbdbccabdacabdbdcaadbcbcccdaaaaacaccbbaaadddddcaabdaabadbcddacacaaaabdcdcbdcbacdcbcacbaabcaabadbdbabbbbbbababdbbdaaadaabddbbacdbacaaddaccdbabdabaddaabadaaddcdddddcadccddbcbacacddcbaadcccacbabadbadacbccdbdccdbdbdbaabdcbdcadbdaddacadcdcccbcddcaddacadcdbcddccccbaccacaaabbbcdaabbcdcaacdbadddbdadcdcadbddccbcdacbdbdccdbdaddddabddcddbcbcabdcccadcbaacbaaaaaccdaaabcbbaccdddcbcabaaccadbbadccabcccbcaccddcdddbadddabbacbcdbdabcbcdcabbbdccccaacaddcbdadcccbbdaabdcabdccaaabdacbbbcbbacccabadacdacbaacacbdbdccbddbdcdadcbbdcaacdcbbcdbdcccabbdbbbbabdccdddcaacdcaaddadbddcdcababbaccdababcdcddaacbcacdacdbacddadaaaabbbdbdbbbbadccbdddadcbbbdabbaddbddbacbbbacabbdabdbadbcabbacccaccdbdcaaddccacabdbdccdcdbabdbbcbadbabaadcdbaaccaadccbdcbadddddcccbdbdbbbddadaadcdbccdbacdadddcdccadbabdcdcdbddbbbdacacbadacaccbadbbdcaabbcdbdbcddbccaabdacbbdcddaadcadcacdbaadacddcdaccdabdbbdcdbbdddbaaabcaccccddadaaaccacdcdbacdcbbccbacccdaabbdbdbcbdbccbdbbcdddacbbdccddaddcbaddcccdbdbaaadcccaccddcbccbbbaadacabccbcacbbdbcbbbcadcdbddacacaddcddcdbbbaabaadbaaccdddaddccbcacdcbddcadadcdaaaabbbbbdccddcaddaccddbbaadacbcdcddacbcddaccbcdbdccbdcacdacabdabccddaabccdaabcbadcdabbbdaccbbbabbbcbddcaadabadddbbcacdcdbaacbcbbbddccddbbccbbdcdbbbdccbdbaddaaaadbdcbdcbacdbbddbccccddbcbbcdddacbbddadadcdddddbdcdbbababaaccddbdadcccbdacacdcccacdaadbdabdcdddbcbdacacbababacbaadabbcbccdacdacabcccbccaddbbdabccadbbbcdacacccabcacadbbcdacacaabdabcdcccddbbddacabbabbddcdcccadcacddaaddaddcadabaacbbbbdbbbdaddcdddcbabcbabacbcbdbdcaccccabccadacaadddadbdaacbaadccbabbdccdddbbbabcdbbcbdbbddaadaddbbababdabddacccddddacdadcbddbbadcbbaddbbdadbdadcddccbadbdddddbaacdcccadcccddbcdbbabddabbdadbcdccaabdabdcddddcaccddbbcacaddcbbdcddacaddadbaaddbccdbccdcbabcbaabbdaadbbddbdadaadbdaaabdabdcddaaadaddaabacccadbdadbbbdbabdabddcbadabdddcbbbcaaddbaadcbaacccababcbdbabdabbbcdcccaacbadbdcbcdaabacdacabccbdaccccccdcabcddadccdccacdbddcdbbbdbbaaaddcdbcddbbcacddbbaabcdddacdbbdbaccddbbcbdbcbdaadaaacadcbadbbccbdbccaabdaddadcbcdbccbdcbabbdccaccdddabacdcccdcdaacabbcaccbdadacbcccdacacddbbddddcdacbacdcadcaadddacdacbdaddbbcdbcdadabbbbadbdcaddccbadddbadcdbdabcaaccabbcdbdaddaabcccdcadddaadaadbacadabddabacaaabbbdabcaabdadacaccabddcbcbbbdcdcbadaaadcbcbcbbbbbbababbcacbbaadaccdddbbbaddcdaadcacbccaabdddaabcccbdddacaccaaabdadcabdbcbbaccccbaccbcdcaacdaadcbbaaaaabbadaacdadadccbcaaadbbbbbdaacacdaabbbbbdabccccdcbbcbdacadbccbacdacdaacddddbadcaacadcdddccadcacabcdbbdcdbcddbbadbcddbdccacbccccabccbbadbbbdbcdbddccbbdbbbbabdccbddcccddcccdddddbacabbbdcaddbabdccacaddaaddddccbdadddcaabaaabaccbcbbbccbabcdcacbdabdacbadbddacbbccadbdadacadcaabccbaacbdadaccbacabaaabdbacacbacbdddcaadccadcdaddbadcbcbaadddddabaccbdccaacdacdccbccbcadbacababcbaaaddbcaadcdcdbacdbacabaacdacbdbdbadddadddbdbcdcbbbbbabcdcdddaccdcbccdaadccaaccdadcadcbbadcdaadadbbadbddaabacdbacaddbdbbacdbcbaddccadadbaadddcababaabdbbdaccbbdcddddbabbadddabbbdccbccbabaabbdaabcdbcacccdadcadacddaaabcdbbbddbcaaaababbadcddccbbdbdbbcccdccbacbccbccadcbcbdbcbdbbaacbbbcaaadaccdcdaccccababbbcbddbdcaccdcaabbbbdcacdaaadbbbcbabcbdcdbbcdbbdcccbcdcdadcdbbcbabaaabaccbcdaacacadbadbcddaaccababccabacaabdbcdcdbddbbcbcdbbabccccdcddcabdadabbcbbabaaadddadabdabadbbbbccbcbdaaacbabdacddaaadddaacbacbdacdcbcbcddbaddbbccdccbabdbbbaaaccdbaababccadbacbdacdccaccaaadbbabadaadcbdbabaaadcacdccbacadcbcdddbbcdcdbddccbcdbbdadaadabcdddbdbaacdaabbdbaabadbbccddbbdacddcbcddaabaacddddbacbbacccaadacbaaaccddcbbbcadadbdcadabbacaaabddaabdddbdadcaaabdbcabdddcadbcdcacbbbbddccbdccdaacbccbadacabbbbdbcdaaaaaddaabababcbbcbbdbabdccccbdbbdaddbccbbacabddddacddabcbbbcdbcbbccdcdcdbccdbdaabcdabcaaaddbcacbcbdcdaacdacbcabdbdbcbbcaccaadcbbbbabdcdddadbabbacaddccbcdcbaddddbabdbabaacddddbaddbabbdbababcabcbddcbadcbdbbdabddcdcabadaadcbdddaddcbcbcbdcbdbacbabbbccdacadbabbacddccbdcbdcacccdabcbcbabdadbcbcddcdcbcbdaabadcacbcdbaababdddaabcabbbbcdcdaacaababbdaadbadbccadbcacbdadcaabbabccdadcbbbdbdcdaabcbadbddadadddbbaaaabddddbaddadadbbbcdaddcaabdddbbdcadbddddcabcacaccbddacbbbacdcbadbcbbcdadbdaabaadbbddbaacddcbadbbaaadddcbdabdcbabddcdbdbbbdbddbaddbcddbdabdcbbdbcbabaabaddcccabbabadbabcacacdccddbbdcdacbacabaaccacdcccaacbdbccabbcbdbbbbdddaccddbddadabaaccbcccadcdadbccadbabcbbbdabcdaacccddaacbbbdbddcaccdbbdcdddddccdadcaabbdbaabcaccaddddbbabdbcaabcdcdbcbdadbdcdacbbbbdbcabcbcabddbbbbcdcbdbaadddacddcbcbbcdbadbbbbadaadbcccadaddbbabacbdaababbcdbcaaaccbcbdddaaacabaabacbcbbbcacadbcaabcdbdacccaacacabcddaaaabbaaaddcbabdaabbdaacdccabcadabdcbbdacbabddcadadbcacccdbbdaabbcaddabccaaababaaabcadaaadadbacbdabbcbbdaccccccaddcdcdacccaadabadadabadcaabdaaaadddbddbabbbcacadbdccdcbdcccbaadbaadbdbbbaccdbaaadbcddcbcbdbcacadbbbdcababacddbaaccacddccdbbaddacbbcadaaccbddcbcadcdccdbcbaaadadbdbccbdacacaaddcbdddcbddbaadcdbacccdbcbcccccbaddccabcccbcadaacdbbccbbbabcdcbabcbcdccbcbbbbbbdbbcaadbaaabaaadcbbbbbdbcbacccbddbbcacacbccaaccdabbaabcaccdadacbbdbbdbcbbcbdadcbcadbdcbddcababadccbaaadaabccbcacdaaadacbddbabaaadbddadddaccbadbadaaaacddcbdaaabaddcdcbcbdbbbdbcbcabdcccadadcbbdcccdbacadaacdadaccddcacdaabadcacbbddccdabcacdadbcdcbbdddbabbbdacbcdddacdcbbccccbbaddbbabbdcabadcbacbbdacaaacbbacbcbdabbcadcccbdabbcabaccbcccddcbbcdbdbcdcbddacbbdabbdbcbdacccbbbacccbacacabaadacdaadddaabcddbcbaadbaadcccbacbbcddccbaabcacbcbdbbbdacddccbbcdabbccacddbacbaddacaadcadadaaadacabadcccbacabdbcccacdbddbdcdadbbabbbbadbacdbcaadbcababbdbbdacccabbbacabddaabbbcabcdabddbdbaadaaacccbacbaaaadcabaacbbccabbbadcbbcbacccbacdacdccaabcddadbdcdaacccacbaddaaccbbaabdbabacabbacccccbddddadcccaadcbaaddaadbdcbbccaadabbaabdcdbaaaabbcdddbddcdacbadcddacdcdbcadbbdbcacddaccbcbabcdabdccccababadbaccdbacacabbbcdddbdaacbbdbdbccacdabcbdcddcacbaddbdddbbdcddadababccbdcbdacbddabbdbaaacddcbdcaadcbdddccabbddaaabadcddabadaadaabcdcbdabcbacbbdbbacabcdababbaccdbbdccdcbdcdadbbdbdccabdcbdcaaadcaccbbdbddcacaaacdaabcdacbcbadbcbcacbdbbadcdacadcbddaabadccbdddcdcdbdadcbdaddacadacdcbacacaddcabbdcdcdbddcbdcccdddacdbccbbdcdcdccdcddbabcabdbaccccbcbbbdcadcaaadccbccddcdcddabbbacaaddbddcadbdbbdbacbbbabbdacabcbcabbabdabdbababbaabdbaccabacdbabcabbadbdddcbcdaaaabadbaaaaddbcddbdcabbaabccbbcacbbdccddcbabdcaadaadacacccbbaccbdadcabccbcbadbddcdcbabacabcddddddcdccbbddcbaddacbabccbdbbbbddbdbbdacbcdabaccadadccbcadadddbadbadbdaccacbcccdbcaabbabadaccaacbadbabaddbaccabadbabcbdddcaddcabbcbbacdbbcccdbcbadcabccdbabdaababaaadcabdcccccadddbadcbaadabccdcabdabccdbdbccbbcdaaccbcbbdbdaadcbcbdbdcaacccccbadabbaaaaccbbbadabbcdddadbabbbbabcbddacaacacabcabacdcadbbadbdabdbcbacacbcbcabcbbdbbaabddbaccbcacbdcbaaddadabbdabbdaddaabadabbcdcbbcdbdcccdcaadbaaadcabcdcbdcacadcbaabbccccbacddacbabaaadcaaaabbcbccbdddbdcbcdbadccbbadacbaddcababdaaadddcddbcddbdcdbbdccdbcbbbaaababddabdccabababbcbcaacabcabdddbcbcdaccadddbddcadbdccddbbddcdbaccabadabacbaddaacbdbdccdddcadacccbcabbcccdaacbbbcdddabbddadbbdcacddcaddccbbbaadbbdbcabcaabbdcbaccddbccbadccadcbaccbccdbcabcbcbccddbcdacaaaaddcdcaaadacabbbcaabbccbbbbcadbdcbccdbdbaacacbbbdadcadcbcdacdcacddabcdcccccdddbabaabcddabdaccadbcaacbdbcbccbdbdbaadcacdabcbcbddabbbbccbcabadbdccbbcdbabaacababdacddbbdcbaddcadbbbcddbbcdbaaaccbbaddcdddadcdbcbabccadbccdcaacacdacdbbbbbdcaabbddddabcddcdccccccbdabddddcabcddcaddacbbbacddcdaaabbdaabbcdbdaadcbbdccdacbdcadbbdcabacdbddcababcaadbabdcdabcbcacacbaabcdcdddadaadaababcadaaacdaabdbcbccabcbacaaacacddacdccbbdbacbbdacbaddccdccddaccddddacdadaadaadabbdaaccbddaacbcbdbacdaaabaacbbcdbdaaaaddabbbdccdddaaabaaddabcdbccbbddcacadcaabdaadaaccaddaccbbdacdcbdabaaaabbccacbabdbaabccdbcbacccbadadbcddccacabbbdccabacaccdbabccdddaacaccbcbbdcddccddcaddadabccdbcdddccdcacbadbdabcbcbbbbdbbaaaaacabdcddabbadaabdccbaacbdccbcdbddcabaadbaadaadcbdadcdbaddbcbdacbbccadcbccaaccbdadacbbbdccabacacbcccbdcacbadcccabbddcccdaddcdcddcaadcbacbdbddcdcdbaabcbdbdddbccaabacdbccccbdacdddadbabaadadbadbcaccaabbbbcdbddadcbaabddacbaabcdccbcadbdbdbdaaadccbabbbdcbcaaddbcabddacddcadddbdddbdacacdccdcdbdcbbabadcdddaabcbddcddbbbcabcbddcabbadcdaccdcbbccdacdaccbdddddbaacbcabdbacadabcddacabcdbbbccabdbdabcacccdbccddbabcdddccbadbbcabacbdcccbdabddcccacaaacbbcabadcddccdbbbbdcaddacdaaaadaddbbcccbdbbdbbcbaabbcdabcaccddaddabcabcbbaaabddbbaaccacbddaaaaddccabadcdbaaaaccbcdcdbcaccaabcabdddbaddbdbcdbbbbcdcdbddcccdabccbdababcddcbddcbaaddadadbbcacacaddabaabdbbbccbaaacbcadbbbbbcaaacdaddbdcbbbdacdacaddbbdaaddbdbbdacbbaccccdcbdcccddbdbdcabaabdcdadcccaacbacbcbbadcccabccdbcccdacadbaccccdcaddbddaccbbbcbcbdbadbaaadcbdbdabdbcbadcbacdadbdccbbaccacbacdaabaccabbaadcddbaaddadaacdbacabaabacdaabaddbdcacdcacabcbddcddbaadadaacaadbbcbcccbbcddbdaabaaaccbacbbbddcbadbbccaadaadcbaccacbacbddababcbcabcdacccbcdddbcacbdbbbaddaddddaacadcbcddcbdbabadbbbadadccbacbdacccbccbbaccddbdccadaababbdddcaabcbddabbdccdcdadccbdbdacbacadadbbcdbdddabccbcccbdcbdbadacdddcbdacbdcbdcccbdadddbaaacdaadddbcdcaccaccabcacdbddaaaddadadccdacaddacdcdcaabcdcacddbabaadcdcbcbccacdcbdaacacdcbdadcdbaddcdcacbaaccbdadcdaccdacdbcbdcdbbaddcdcdbccdbcccdccdccddababaccadbbbaccccbabdcacaabbccccddadacbcbbacdbaadbbacbcadcbdbbbdcdccdabcddcaabbddbbdbdadcdaccddbdabdbbbaccdadddddcdadadacdcacdcdabcaddaabcbdcdccabcadcbabbaaacbadbbabdcbbacadbaccbabcbccdacccccbaaccbcbcdabddacbbbcdbdaddcacadcbccdaaabbddcabaaadbbbbacadcccdcaacabcbcacdadccbbccdadbccddccdcbdbbcbccacdcbdccabdcdbcdbaddcbadccbdbbcdacacaabdccaaabbbcdbddaadbccdcccdbaadabdcabbccccabbdbcccdbcdbaaabdbbaacacdddacbdbdcabbcaadaaacdcdadadcddabccaadabbbddbbabdbabcddcaaddcabccccbcdacddcbaacdccaacccccccbbcaccabdbbcdadbacbcabddddbbbcaccdacbdabbbdccdcbbccadcbaddacadaccdccacccdadabbcdccccbaccccaabbddaabbdbdbddaabcdccdddbaadaddbdacacdabbcdaadadbacbddabdaadaadaaaaaaddbaadccdcbaacbacaadacccdccbdcdcddbaabcacdacddbbdcaaaaddacbdcbcbbdacdbccbbacdcdbddcdbbbcddbadadcbcabcbaadbabaabdadcbdacbbcadacaaccbdcccdacbadaddbacaacabcdcbbdbcabdcddaabccbbbcaabccbaadaaacadaaabbccbbdaadbcadcccaaacccaabddaadaacadabcaaadcccaaddbbcbabdbacdcacdaddaccbdbcbabcbbdddacbcbacbaaaacadadbadcdcdbdaabbbababbdbbcdcdaabbabadaaadadadadccadadbcdbccbdddcadbbccddabdacbabcabcdadababbbdcddbbdabddcbbdaacbdacbacaaadaacadadcdbddbccbdacbcbdaaadbaabdaddbacdbddcbcbdddcbabdccddadbbbdddcdaccaaacbdcddcbabbdcbbbdadcbabcbbbddbbbcabcabbbacbadcdcdabcdacdadcadcddcbbabbaaccddbcbaabcabcbdbdcdababacabccaacdcbccbcabcbaaddbdadbaadadbcacdcbdddcbacdbbdcddacbbabaccbbadacbbcdabcccdadaccacacddccdcabbdaaccaaabcabdddbdcaabccacdbbdacabadcccbbdccbbbdbdcdbdbdbccbdaaaabcccadddaccdaaabacdbcacddddcbddcacabaacbbaddcbbdbdbccdadaabcddbaababddaadbabbbadbbdcbbcbdacdbadadbcbbbaadcbcbbadaacadbccabcabddacbbdcbdcabbababbdbaadcbbbdabdacabdcbbaddccdbbddcaaccdbbbbacacabbdcaddbcbdadbccccbcdbbdaadbddbddaacdabbdbbbcaabbdcbdbbddbdbddbbadddadcdabacdbbaddcaaadcacacaadcadbddbcbddbdacabcadcddddcaccaacdaccccbacbadabdcaacbcdcbdaacdadddccaadccacdccbbdcbbbbacddbcbacbbbaccacdadabdccddbdcdbbcaadabccccbadcccdddcaddbaabcdcbcddcbbcdcdacbaaccdccadcbaadbbbdabbacacbcdacdbacbdbbadadadcccbcdadbbdabdbccabacabcbdaaacbdbcdaccdbcacaacdabdbcaddddbaaaadcabdccdabdbdcadbadabbcacaadccadbbadcacdbcacbcaadcabbaccbbcdcaaacaaaabcbbdcbbbacdadacbcaacacbaccbbaaadacdddaccbdcabadcbabdddbaabaccbbbabdddacddaaaddaadbcddcdcabccccbdbcbabbdabbdbdaccbacdcbdacbcbcbddccacbcbadcdbcdbcbabadaaccaddcaabadbddbadaadadacdcaadcdcabbbdabcdccdadbbcdbadbcacbabcbddacddacaacdbbadcbbbbabadabbdbdbcbbdcbddbacbacaccacbcadbdbabbbbbbddbdbaccdacdbbabcabdbaaadcbbbaaabccbadcbacdadccbacdbccdbdbbdcacbcabcaddbcbcadbabbcaddaabbbcaddacadbcddddcbcddacadaabdbadacdbbcbddcdabddddbbdccbcdabadbdbaccccbdacabdbcbdbadbcbacaaacaabdcbbabdcdcdcacabacddbddacbdadcaaaddddcabccaaaddbcddaabddacabcbddcdaaaaabccabacdcdcbcabdcadddbabbabaddbbbddcbcddbdadddbccbddccdcabadbcbbcdbbddbbbdcdacbdaabbcabbadcbcddbaaacaabdcbdccccdbbdbdcadcdcbccbbabcaddccbaaaacaccbddcdaacacbbbcabbddbccbabccacbdabcbbadddbcabccaaacdbabadadbdcacdbaadbbadbccdadcddacabdacaabbdbdcbabaabddaabbababcbaadccadabdbcacccddcacdddccddabddcadbbbdcbdbcbbadccbbbcabbdbcddcbadadbbcdcabcbadacadbcccbbccaddbcbaacbcbdbbcdcbdaadcbdaacaccbbcaaabbabacdbbabdabcbcccaaabaccbddaabacabdccdabbcbdcaccccccadabbccacdcbacacabbabbcbdcdbdbcacbddabacbccaccadaabbcbdcabaaddaddcdadbbddcbabdcaaddacbcbcbdabddddadbadaddddaacaadabababbbbcbdccbdbacbbbbbbaaabcbadccaaddabdbdbdddbaddbccccbbbabacbbddccdabdccbbbaadbbabcababcdcdabdadadccdbadbbbddccbaabcbdcbcdbdaddadbcaacdcccaabacbabbaddbdcdbabaccdbccdadccdacdccdcaadadacbbbbddababaacaadbcbdbbaabaccddddcdcccbabadaababbaadcdacbacadcccdbdbccbacadddacacbdacdaddbabdcddcdacacccadddbacbdcdcacabbbdbdcbcacaabcccbacbaacaccddacbcdabbbaddccaacacccbcddcddddcbdbbabadadacbdccadbcabbdbbcbbcbabacbcddcacccbbddabbcaaacdbbcdbbdaadcbcadadddadccccbbcbabbccccdabcdcbbacbbbcbbadbcdcdbcbacacbacaabacdbdbcaddddaabacccadcccadbccbbabdbddbdabbadcbccabadbacbbddcdcccbbbdbabdcddaaacddccdcaaabbadcdaadabbbabcaacddbbbaaaabcbcaddcbbbacabacdcaabbadacbccabcdddbccaadaddadbdbccdbabdbcadcabadacbdddaaaccdbcdacddabbacbacdbabcbdcabaddddbcccabbdadcbddccdbbabdcaadccdcbcacaabbcbccddbbaabdbdcbbbdcbdbbaaabbadcaacbbdcaacacdbcbdbcbbbbaaddcccbdbcbcdadbddcbabbccadbaadcbdcccaacccadadadcbabadabddadcddbbaaddcbbdaaddabaccacaabcadacdcbdadcdbbcdccadcdaadbbbbaccbadacbbcaabddddddddbdabcdacbdbdcbaddacbccabcbacddccadadabbbcdcccdaccbabbacdcbacbacdabdcbbbcaacbbaaddaaacdabbacbacbcddddaabbbbcababaccabadaaaadbcbdabcabbabbacccababaacdacbabaddaccbdabdaacccdcbbcdcbaadabddcbdbababcaabcaaabbbbbdaaacabaddaacbbbbbbaaadaaaadddcadadcbaacbbdbcabaaabcbbccacabdddadccbdbddabbdbdbcdbbdbaacdbbddbcddaaababcbacbdacccaaddadccdacacabccbadcdddcbdacbccdcdabcbcaaddacbdadccbcabcbddabdccbadabdbcdabbdcabcaaacadbddcdaaadcccacbbdddcbcddaacbbacdbddcbbbbcccdbabbbddcbcabdbacaccbacbcdabcbaadbadbadabdcaadbabaaaddbacdcddadcddcbcdaaacaabcbbacbacbcaccbcddbdcadcdbdacbbabbdccdbabcbcaabacddccacbccadaabdacbccaabccdbbcacabccdbabccaddbadbdddcabadcdddccaacadaabdcdbdcaddbcdccbcaddaaabccacbbcaabaccabcbccdaddcabbcbacdbbcabdcbdcbbbadddcdbcbdcbdcddadcdbcdccdccacdcadbdabadaacdccacbcbbdbcbcccdcbddbddcbabbabcadcaacdbcacbdbadadcccadcacadbabdbbcabdcdddadcbbbcdcdddadacbbcccacadbacaaababbcadbbcbbcadbbbcaabbcdbdccacbacdacbbbadcbacbccbbaadcaabaaaaccccbbbbcbcbcadbabadbddbacbbdaadbdbdbcdbccacdacbadabbacadbdbbaaabdbddaccdbbaacbbdacdddadbbbbaabbddabccadcabddbdadadadaadbdcbaaacddababdcddadaacadcddbaccddabddacadaaabdcdbacbddbadacaabdabccadbddacccacddababcbcbaabcddbbbcaccbadbbbdcdbcdacbdbaadbaabadbdddcddbbabcdddcdcbdcaccabbacbbcccacbdabbddddbcdaddcadbdccccadcbcdacbddcbcbbdbabcdaaadddacbabbbdcccddadbacbcadccbcbbddcaccbacbbbdbadbadadcabcbcabaaaadcacdbacbbcadbdbdaadbaaacdcaddbddabbbdaccbddabbdacbddcddbbbabdbddddadabadcaadbbadabbddadacddddaacbbdbaadcaaddaadaaaabcacccdcbcbdabacaacdbdccacdaaadadcababaacabcbbdadabddabbbdddadcbaccdbdcbddbcdcddddacccccbbaddaddcaaadbdabbbcbddcabdcccbbdcdabbabcdbcdddabcacbbacacbbacbbccadcdaaaadbbcaddbbaacbbcdcccbbacdbcacccbbbabcadbbdadcbccdacbbcacacddccabcdbaddcacaabaaadbaaaddaddcbabacdcddcbaabcabbcddccadcbcabdacdadabdbaddbbcabccdcbdaacdabbcabccdabddcbdccbabbbbadbabcbdaadbdbcbabaabcbdadabbabcaabdacaaacdddcbabddddcbbcdcabdbbcbcdbabdbadbaabbcabbdabcbbcbbdbdaacccdcbddbbdbbbbcbcabbadcabddacabdaadbdabcdccbcaabdadbddbcdcabbabacdabcdaabbbacbbcccdccbbcbbbbaddacaddcdabaaaacdccdcdacaddaacdcccbcaadbacddddbaacbddbdbccddacaaddcccaaaaadaaccbaabddcdaabdbcbbcadcbcdbacdbbadccbdbbadacbbabcccacaccddadabadabcbcdcccaccaddbbabcaddcdccabadbacabddbbcbaccdbbabdabdcbddbbcaabdabcdbddbabbaabbacdadbcdbaadcadacbcbcbcaddbccdbddddadcbbadccabacbbcbbaadcbdbdcbbbddadcdccabbccacdcdccdbbadbbbaabbbcbcbcbaddbdbbcbdcddbdababdabaaacbbcbdddcacbacccdabadabcbabaddacbddaabdcaabccacabccabbcdbbcdaaddaacbccbdbcddaabaaabdcdcddccdbbadbbdaaaabcdbabbbdcaabbddadbcbdbccddbadcabaabcdcdaabcdcabdbcaadcaddbbbaddccbabbcbbcbadadddbbbbbdddaddabbcbaabdddcaccabdaacbccdadbacbabbccbaccaaccccbabaddcabbabbbbcacdcbacacbccccbdcddbbdabbcddbcbbcbdbabaddddabdabdacaabddababcdbcccbcbbaaaabbcbdaabbaacdbdccbadcddccbcbccdbdacbddccbdcaddadadabbabbdbacccbcccabbbcdcdabddcbbacadbcbddccabddcbacbaabddadcbbbbadbbabddbabbadbaddaaabdcbacacdbcbcaabddaaaacaaabbdcccdcdcbcddaaabbdadacacbcbccccacbbbacacadcdbadbccdbdcabddccdcbdcdcddcbadccabdcdcabdddaccaaccaccaddaadabcbadabdbdcdbacbaccdbbdaaacacbdbbccdcaaacbbbbcdacabdacbacbcdddcacdaaacddacccbbddcdaccdabbcaaacdbcacbbdbdadbabbdcadbbcbdddccacacbabdcbdddcabaaabbadbcaaabaadabbcccccadbaccdcdabcbdabbcacadacbcaacccdbadaadddadcacbadbcccdadaabdaccdbdababdabdabcacbdabcadbddbaacbbaacddcbcbbbbdaccbbcdbbbcaddcaaabbdaacdddddacdbddbbaabccaaaabcacbddcabadbbdacabadddadadcddbccccdadcabcdbdacdacbadbaabdabadcbdcbabdaabbcadcacdbbbbbdccbddbcbbdddbddadcdcdbccdacddbcbaccadcbcaabdcabaccddcadabacdccbdcddcbccdbccdcddaababcaacbccacbcdadadccdddddcababacbdcdacdbdaaacbacdabcbadcadddadbcaadcbdaadccdcabbdddbddbabbcdddaddbdcbbccbbccacaccabdddcdacbddabadadaccbddaddbdabdaddaccddcadbcaabdcbcbcababadadbcbdcbddadbdcacbbaabcbabdbabcbbbccddbccccbcacaabaddadcacdcdaababaccbdabdcddcbcbaacaacdbbdbccdcbbbbcadccaadbdcdbbaabaddaccddccccbcdcabdaaccacbbcdcdaddbbdabddcbbcbcccdbcdaabbdaaadbcbdbabdcadccacabbdbaaadbdbabaadcbccdccdbaaadabbcdcadccdcdbccccddbdcdacacdcdddcaaabbcdadbcaabcbdddbbcccdaaabdbcccbaabdcdddbddabdcdbbacdacbdcaadacbadbcadcbacbdacbadbdcdcadcbcbcdacdddbcbdbbacaacdadbbabaadccbbaaabbbabcdabddbbadbbbbcccdbaabdbacbdadbcaacbbbdbdbcbdddadbddddadacccbdbdbbcdbddcabacbbdadbbddbddbadabdadacadadcbcabcdacdaddcbddccbabaccdbadbdabbaddaabdaadadcaabbcbdabcbcacabddacacdadaacaabdadbbabddccdacbacacbddbcbdbcccccccbcabaaaccdbdaadcacabacbbcbaaccccbdaaabaacacdbbdbddbbcdbbabbcababdcadadbbbbbacddcbccbbdcbddcbcbadbadacddddcaacababadccdbddbbbcccabdbbddbdaabcbdaddcbacddacdbdaddbdabaddaadacbcbccccadccaaacbdcadcbabaacabdadabbdbadddbdacabdadaaadcdaacdabbbbcadcadbbbaddaabdacaabbacabbdbacddbdccbadacbbbbcacdcacacabdbdcaddcdbabbcdadabcbbbdacbddddcdbdbabddcaabaaaabcbddabdabcaacbbabbdcabdcabddbbbcadbacccbdbdcbccaacdaddccccadcbdacbdbbabbcddcbbaabccabacacbbadabdcaabcbaaacdaaddbdddcdddbaadaddcaabdbbbacddabcaabbdcbdabdbbababcbcbbaadadbdbdcadbccdcbdbabbabcddabdbbbaaadaddababcccddbcacdcaabacdacacacadcdddaabaadcbbbbccdcccabadbcbaaccaaaccdbbdaaddcbaaccdabdcdacbabadadbaadbcdbdaabcadbcdbaddbbdbccadbcabdddcbdabddddacbaccdacaacbcaabbcbabbdaddabdcbabcbaababcbbbbdbcadadabdbadddaddcbcbadddcbbcdbdbadbadabdcccabbaaaccbbbacbdbccacbdbacaaacdbabbbcaaaddccabdbdcacbabcddacaaadaabdacbdcabdbaaaccdbcbdbddbaccdaacbadbaddcadaaadccbcbaacddbddabbcbbcdbcdcdadddccaabaaddddcdbdadaaadbcdcddabadacacdbcbcccabddabacacccbacdcaabddbbadabcbdcbbccaacbcadadabaddddaddabddaabdaadbcbcacaccabcdadbbbbbbddbcdbdcadbcaaadccdddaabbcbbaabdccbabbbbbcdbaaddcbbaaacdadaacdabddddbacbbbdbdcdbbdadabdaabdcbabdaacdcdcdcccbbdcbcbdcadbadbdddddaadabdaddaacccdbdcadbdacbdcabdcaaadbbdddadaacbcdccadbbbdcadaddabdabdbaadbacacacbcabdcdacbcacdcdaccbcdbaacaabcbabddcabbabacbcddcdaccabadaacdbcdaaaaccdacdacacdbdcddaabbcbcacadcdbbddddcaaaacddcdcddddadaddaacddaddaaaacaabccdbdcaacbdcddbcbbccddaccacadbcadddcacddacabdbbcdbbbbbacdcdcaabcadcadcdbacccdbbbbbcdadaadbacabcbdaabadcacddadcdcaadddbbbcadaacbbaacdbddbddcaadbabadaddcbcdbbdccaadcabdaacbdbdaaddaaacccacddccbabadaccbbabcaddaccdcabaaacacddccaaacbddcccbcbbccddabbcbdbcdacbadacdabddddbdbdbcccdacabaaddccacbadabcccbcbbbccabadbbddbccadabdbbabbcdddcddbacabaacdbccbaabaaccbaaabcdbbbbdbaabdccbdcbcddabdbadaaadccdacbbbdbbcbddbdadbbcccdbccddbbdcadbcacaaacccccacadaabacabbdddbabadacbcdcbcadcdcdbbaacdbbacbdabcacbabbacbaccabbdbcdacbddcbbccabdaddddbbbadccaaadcaadacbbddbaaacbdcabcbbdbcbbccbccbbbdcaaddcabacdbbcabacdbbabcccaadbdbbcccbcbcddadaddacddbacbbaadbdbdcbabdccdcacbddcacddcbdbcacdcadbbddbcdcaadddcbcaacbaacccbccadbcabbcbcbddcabddcbbdddaccdaabdbbcbbadadbbadaabccdabadcacadabcbbdabcadbccadcbcbccdcabbbddcbadbbaabdadbbbabbdddaaacacbdabaaabdcccaadbdcadaaaabddbdbaaadcdcdbcdcbaaadaabbddcabaddadbddcdbcdababdccdddbaacbcbbdbcaaaccbbbcbdbbddacdaddbacccabbaaacbaabdccabcdcaccbbabbccdcacbbccccddddaddcaaadbcbccabddbcddddbccaccacdaddcbcddbcdadcbaacadbcbbbbadccbbacbdcdccdbbaacdadbbbaacadaabbadbababdccdadadaddaacbcacaaddaccbdabddcddbbcaddcadaadacbbdacdcbcbaababbdcacbabacaaadbdcbabcaadadcaadcaacddcdccdbcbaaddbdbbacabadacbbdadcdcccadcbdabcddcaabdccacbaddbcabbbabcbbaaaccddbdbabcdaadbaabdacadacbbacbaddddaddcabdcccdbaaababdbcdadadcdbddbcadacbaccaccbccbcabcadccbccdbdabbcdbbccbbcacbcbdabdbcddadccdaddcabbbcdbacccbdacbdadbcababaaaadbadcadadddbbbcdacccabadbaccdabadcdcdbddaabdbbdccdbdbdbbbcbbccaadaaacbcbccdcdbacbadcbbdabdadcaaacbccccaaaadbaacadadbabaabddbcdcbaaabaadccabbabccbbddbadddbbccbcabadbabcdcddcbababddbcdcccdddbcbddccdddaabcbccbdbadbdbdcbaababadbbbbacbabaaacccdbaadbdcdbcabbbbacbbdcdcaaaaaccccaadbcaadbcdcdcbbbadadbadcddcbcbcdcdadcdbaabbccddcdbdcbbcacadccaadbcacdcdcabbcdbadcbcbdcdabbbcdcccdddbcbbacddbddbcbbbabbdbabaccdbaaccbcabbbdaaaacdabcddcbabcaabadcdadcbcbadcaaadcbbddcabdccaacadadbcabbabddccbacbacccddcbddbdcabbacdacdcbcbcadbaddbbacddcbcbdcbcadadcdddcdcccbbcdcaabaccdbabdcdcabbcababdaaccddbcdcdcdbcbbbabbcadcbdadcaaaadcacacadadccbcbdadcdacacccadadbdaacdcabdabaccddcbdadaddcddcbdabdbabaccabccbbaaaadbdddabdbcbcddadaaccbababdbccabbbbdcbdadabdbddccaaddadbdbdadbdcabcccdcddccddcbcccaacdcdacbcaaadbcbaddbdccbcbcbadabdaadcddcdcdaaaacadaaaaaccabbbdadcbddbddbdbcadbbcabdbdddcbcacadcbcbdaddacbacadcbaddbbccadaabdbcdbaddddcbbcacacadadacddcbacabdbadbacbbadbbcabdadcbacbbdbcbadbbcbcbdabadaccacdadcccdbcbddccbdbbbdabcbccaaccbadbcdacbacbaadabdaaccccbcacaaaadaaadbdaccdaadccbbbaacadbbccbbacdabaadcddcadccacbdcbbdbbabaadcdaaaaabadaadaadcdbdacbddaabaadccbcdbdcddabdacccccbcabbbababdddaacbdabdddddacbdbaddacdbabababddddadacaaabdbcbddababcdcabaabbdcbadbbadcccdddacbcccbcaaadabadcbddbaacaddbdcccabaabdaaadcddaabcdbbbddbabddcbbcabbabbcdadbcdacaaadcaacaacaaaaccbacdaaabdbdbabcbbabcadbcccbbcbbbdaaddadbcabdcccddabcdadbaacaaddcaccdcdbcbbcbdcaddcddbdcdacacaddbcabaacddccacabdccadccbccbbabbddaccdabbcbbbdcbabaaadcbbcadcbbdadadbdabbaadddcbbcdaddddbdaaaddcdbdcadbcdacddaccbdccdbcbcbdcbcdccadadcadaccbdacacccadabdbcadaabaabcbabbcddccdaabadacabcaccbaacacbcddcaabbdabdaccabaabadaccbbabbaaaddaccccdaaccadcbcbbcccbbdcacdbadaddbabcbbaaaccdcbaacbddbacabcccdbccbddadadcdbdbbbdbdabacdcbbbdcadaaacaaaaadcddabbdbbadcabdacdabcdacaadddcadcdbdacbdbdcaaaacdaddaacacaabbaaabbcaabddabdbabcbbdcdaaaadbbcabdcdacbccdcdcdbbcdbaaaacdccadbbaacdbbababaccbcbdccbacabaabaaaaccaccbbadabddadaaaddbddadabddcaacadaaadadccbadcadbaaadacaabdaababdcabaccccbbdbcdabbbccbdcbdcdcccabcbdbbabbbdcbacccadaabcbcabdbadaaaaacdbbacbdccbabccdcbbbcacbbbcaccbcbcbbbbbccdcbdbcbdccbcdbdcbdbddbadcabdbccddbaacbbacdacccdbcaadbcaddccdcddadbacaaabcdbddacbadbaacddbabcaddacccbdbcadbbbcaccddcabbcaabdccdbdadcbcdacacadabbbbddbbcaccabcdccbccaadabbabdaccaabbddcbabbdcbadaddbbababccabdbcacdbdaccdaacdbaaaccabcdcdddccdbabdddadabdaadabdbdbadbcddaccaccbbdcbbccdcbbcddddbacbbbbadcdbacbbaddbadddabbbcdbcccdaccccbccdccadcddbabdbaccbbdbaaacaadbdcabbcdcddbccddddddbddcadccbdbbdddacaabcabcadacbcbacbcdcbbddaadabcbbcadccadadddacaabbddcabacaaaddcabacbdbddddacaababaddbadacddbcadcbbbaaadaacddbcacaabbdacdacaccacabcbddacbcddaadabbbcaaacacdbcbcbccddcccbaaadbdbdddcddbbbaabbbbdcdbbccbaaababacabadaddadacbcbcdaacddaccabadcacabdcaaabaadbcdaaccddddccabdaadccdcacccddbbaccbddbaddcaabaadabcbabbbdddbdaaccdbbabddabdabcbbbddbdaabbddcbaaaadbcaaacdacabccdbbdacbcddbddbacbcdcdbcaadcaacbbbabadcacdbdbbcbcdbbadcbbcddabbacacddabbddaaaccaaaabacbabdddabaadacbbadccabaabdccbabcacbdacdbcaadbabbbccbacaabcadbcddbcbbabbddcdddaccabcbcdddcbccddcbcaddcbcbbaccabbadddbbdabbdccbaabddcdbbbccccbcdcaddbdcccacbdcbdcbdbccaccabdcacbcddcccbcdcbdddcbbdccdbbbdcbacadaddcabcccacacbaaadbbbcbbcbcdcbbadbcbbabcdaacacabdaaabbcadababddcaadabcdcbbcaaddadacbccdcabccccaabaacbddccacbabcacabdbaddbbaabccbbadbababddbbddcccbacdacbdbadcbdaadbbdcccccbadccbbbcaacbbcadcdaccbdbadbbcbaaacbbbcabddbcdccbabcbdacaabcdcdcccddbcccaccabccdaaaaaccbabaccababbbcacdcdbcacdcadbcaabdcdcadbaabcbabcbdaacbbabccdadccccaadbbbcccddbdaabbdadbdcbdbcdbaaaaddcbdcbcdbbadbdddccbadadbdcdbaaabbdbdcbbccbccdcdaabadaaabddadddbddbcbcbabcdacdaadbbbbdaacbcaddbadaadcabbddaaddcbcdabcdaaccccdcdccbdcacbbdcaabddcbbddaadbbacbdcdccccbbbdadccacdbabdddabbbaccbabdaccaaddcccbbacdbbddccadbbcccabdccddbcadcccbbcbcdacccbbbbcddbbadbddcacdbacdcaabaddcabaabbaaadcbbbadaddaaadaadcacaccaaccdbacdaccdcadcdcdbbbadacbacbacdccdcaccdbccaccbcddbacbadbbbddbcbbcabccacbcadaddaacdcbdbdddccabbdbdbdababcbcacadacbacbbccbaddbadaccaadacaadacbbaaabdadabcdaddbaadcbcccbacabccaddcabbcbacbbcaaacddcdadadcababadcadbdaccbacaadcbdcbdbdcbaddaddcdbdabdbdabccdbbcccbaddaccabddccaabbcdcaacabcdbccbbddccbcdaaadcabcdccbdcbcbcbbdcabdabdbabbcbbabcccdacbdcbdcadaaadacdadaccdbccdbababaddddddabccadbaabdabaddddbbbacaabaadbdcbbdbaddccbcbbbabcddaacbbdcdbacabbdcbcccdbdbaaddaccbccbccadadccdbaacabcdabbdabbddbccaabccdacabdcabcdabdddadadbbbcddbcbbabaacadbcbdabcdbacaaccdaddadcabdbdccadbbcdabcdbadbbbabcabcbaadcddadacdcdbadddddaabadaddccacdbdcdcbabcbdbcbcbabcabacacacadadbcccbaddacaccadaaacdcaaddabdcbcadccdbcdbdcbbdacbbcbdbbbdbdcaaacdaacbadaabccdcdddabdbcddbcacdcadcbdbdccdccdcdccabaccaddddcdbdbadabaccccaacccabbdbabaccccbbbbacddcabaabaddaccbcbabaababaaddcccdbdccddcabbcbcbdcdbdacdaccddacbadccbcccddbcaccccdcacadaaaaaaabcaaaccdbdcddddbdabcacabbaadbcdadbccddbdccaccabcadbbaacdcdaaaadcadbaadbcdbcbdcdbbbccadbcbdbdacdaddbbcbadbcbcdbabadcccbbbdbacbddaccadbbdcdccbbadccdbdbbbbdbdabccccdabbabdddcbcababaaabdcbcdddaabdcbbabbbcccdcdadaaabadadccdcccaadbcbdccabbcacadacbacddccbabacaaabdbddcdcbdbbdbdbacdbcdbabccddbcbdcbbcccccccbaddabadddddcaddbdacccdbadabbbbbbcdbccdccadbccbacbbbccabdaccbbcbbababbcabacdbabbbbdaddabadcbabdaabcbdbdadcdaabddabbacdbccaaddbaccaabaaacbcbabbddabcadbddabbddccadbadbcddbabaacbdccdaaccbddaabaccdadadbcccbcbbccbdcbdcabcabcdcdaaddcabcbdcaaabdddabccabbaddbcaacdadbcaadcbacccccadddaddabcdddbaaddadbcbdacdccabcbdbbadcabbacbbbabcddabaaddbabccadcdcbdaacbadcadcbbababcdbdbabdddcadcdcdbadbddbadcbaacdacadbbabdadccbcbdadaabbdccddcbcccabddbcabcdcdddcdbbcaaadcabadbacacbcdcbadadcabaccadcdacbcacdbacbcabdbaddbcadbdbdcdabbcbbaabbabdaaabdadcadaabacdbaadddbabbbabaacbdbddbdaabccababadbcdcdcbddbdbccdccacabdacccadbdabcaccaadaadaabdbdbaaadddbdaccbcbaadacddcacbaadaccadadbcbaaaabccbaababbcdbdaacbdabacbbbcacdacabcbccccdaddbbccbcadaacbcadcccadbcdcdabcabdbdbdcadadbbacaabdbcbbdcccaddcdaacadaabbbccbbaabcbadaccccbdcacadcbddbacbdbbbdabbcdaccdabcdbabcdbcabacaaccddccddbcdccdbaaaaaabcacdccacdcbdbaaacbdbdadbccabcddaabbbcaaaddccbbbdbcbcdadccadbabddbaddaddaacdbabbbabadcaaccbdbbcddbabbdadadabdcababbcbcbdbbbcaaabcccaddcbbacccdaccaddaadacdaabbdcdbdcddbbdadadcbcdcdabbdcbcdbddadcddaabcacccacbabdbdbbdddbcabdcccacbacadbddacddacbdabcabbabcdcbaccdcaaaadccbcabbcabacbbbcbaabddadbbaabdabadcaaadbabaacaddbccbaaacbcbadbdabbdccccdabdbbbbcacaacadcccdacadbbadbdaaabaabbbdbdcdcdbbdaabbcddcaccbabbcbaddadaacadacadaccddcdbcdcbacaddccdcadadcbbbabccbbabacddddcaccdabbbdadadabdbabdaadcadbcdcdacddbbadcaadaaddcccdabbcddbaddaacadcdccbadbbcadcaabdabbaacbbcbcbaccccbdcddabadccddcdcaadbadbdcabdbbcaaaacdbdcdaacabdddadbadababdccdbcdaaabbcbcccadbadacbbbcbadacdaacdbcbddbdbdabbcdddabdccbccbaabbbbbabcdcdcacbcdcdaadabdbaaaaacacdaacbabdbdcdcbddcbbccababdacbdbaacddbadbaccbbcbccaabccbbabccaabaabbcadcacbbadbdbadbcdbbabadbdcbadcabdccabdbdacabddcabadbddadbdccabdccdccbbbdcbdcdababcadcbcaadcbbcbcadbbcdbcabbddaabbcacbbddcbdbccdbcdbbdabacdabbbccdbddbdbaadadbdddaaabaaacbdbbcbaddcbdbbbdaabdbaddacccbcadcadccbddcdbbbddaadaaabbdccdbaaabaacdccdaaabaacbbdaadddcdacadcbcbcdbbdcbdddadcddaacccbadabbddaccddbbbbbbddcbaaccbabcdaababbcaccbaabbacaddaccdbbbdbddbbcddcccdbaacbdaadddcdccaaddabcbadabbadcdbdccdacddcdbbbdaaababaadcaaaaadbabacdcaddddcbcbdbcbdcbdaaaddbccddcdacddbcccbadcbccadcadbcdcbddcdbcadabcbbdbacbbbadddbdaadbbabdbcabaaaacadabcadaccddabdaaddcaabbdddaccbcaabccacdcacabccbdddbbbbcdabcbbbdadcbccbadddacdcaaabbccbdadadabddabbdacbadcdbddbdbabbdbcacdbcbabcacbbbdadaccddbcdccbddbcadacabdcbbddcddddaabccdcccdcdbccbbdcdbcadccdabdabcacbcbbbcbbcacacdbabacadccdabccbbabdddccbacabadbacbddabcdabbcdcbdaacaacaacbcaccaacaadbbdbbbbbcddbadadaacaccbcbddccadabcdcbadabcadaaccdaabaddbaccbbbabaacaaddbcccbbbcbcaccbdcbdacaddaddbaabcdaddcabaabadabbbcdbdadaaabdbccbdcdacdaaaabdcababdcdbcabbcddbbdccdbdacaabbabccbdccbdbcbacabcccadbdcbcbbbbdcabcdbdcacddcaddddaccabbcadadbddacaddaadaacdbaccdabacbbdbcbcadbbdbccbddcdabccbabbbbaccbbcbbaabcbadcbcadbddddaaadddadaacaadbbacddcbdbbbccaadbdcbbbbbbbbbdaccddbdbbbabbcbcdadababdadaaaddcdcbbabacabadccbabcbaaacaadacbccddcbaacbcdacdcccbcbbdaddbaabbdcccbababdbdbbdadbdadbddacbdbbaabcacbadcdbacdddcdcabcbccbadbbbbcbcccdaaddbbccacdccbabcdadcbbbcbdcbcbcdacbcabbaabddbabbcdbbbacddacbcbbacdcabcddabcccccdadcbbcaddbbabcaadcdaabdcadbcdcdcadaddbbbdaccbcadbacbcbcacabcdbcbbabaccabbbcbdbbcacddbbcabcbababdaaaddadbadbdadbbababdbdcadcabdbaadabaaacdcccaabdadbabddacdbadccbcaabacaabddbbaadcdadbacabddccaddbdbccccdbcacbdcdbdcdccccacdddccbbddcadaacbcaadbccacabbbacdbdddbbcdccbacaaaccdacbcbcbbacacbcbddaabbadbddcddcdbadddabbbabadccacdaddabcacaaadadbaadbdacdbbcaacadbabdadabcdbaabbccdbbdcacacbcdcbadddbcbbadcccbaccadddbddaaabbcdcdbaddddbcaddaccdccbcddbbdbdcddbcadadadcbdbadccbcdbdbaccbddaaacbadcacabbdbcdbbccdbdddbcbdccdccddabcacdbbacdaadabbbacbbdbdaadadbcbcabbcbbcdbacccdbcdbacaadbddadacbbdaadcdabababacaaacbbaccaacbbdcbddcddbaaadabacddbbccaddbaadcdbccbcaccabbdcadcbacaddccacdcccddcbadccaddbdaadacbddcaabbccacccbbcdcabacbadcabddcbaaddaacbdababcadacddbdcdbabaacaaabadacacccdbcbbabdacbdadcddbadbddddacbaaacdbbbbbbbddcbacdabcdcdaddacdbbacadcddababadbddacdbaacdbbbaccaaabcccabccdccbdcdbcabdbddcbcaccddaddbcacddaabdcdacbddcaaddaacdaccabcddabbabcbddbdbcdbddbbaaacdacaabdbacdabcaccdcacbdbcadbbdabdabbbaccdaabaddcadbaabbdccacabdadddcbddcdbaaabbddddaabaddacadcbdabdbcbbcdbdacbccbcbabbdccdaadbbcadadbbdacbacbaabaccbcbbacdcaaabacdaabcbcddaadbbbabaacacaddabaaabcdaabcbabbdabcccacdaddbcdaabccaadabacacacddddcbdaadabdbdddbdddacddbdcacbdddcddaacdbdccbbabcbbdaddccdbbabcdaacdccbcccaadcadbdcabbbbbdccbcdaabdcabdacddadccdbcbcadcabdabacbcacaabbdbbbddbadcccaacdacadcddddbcbbcbaacccbbabcaccbbcbdadaacbbabbcccaccadccdbdddccbadbcdbdbabcaacadddadddddccadabdbcbcbcddbdacabcdccdcabdcdbcbabaabbbddcacacdcbacbddcdbcdadcdcaacddddbdddcbbbababbdadcbadabbbcbcaaadabbbbdccbbdcbdaabcdacacbdbdcaadacdacbaaaccbabbcdcaabcadcadddddbbdccbcabadbcdadababbabcacadacccddabdcaddbbadbcddadcccddacabddcccbcacdbdbacdcdacddbbdacdbddacddcbadacdacdaabbcbcbdaccdaacddbcbaadcaddabccbaaaddaacaacaaaaacaacccbadaccddabdbbacbbdcaacacdcadbcdcadbabcbacabdabadadcdbbbabcccabbbaadabacddbbcbdabbbadbaadadddccabcacbaaaacbacadbabcaacbbcbabaccdabdbbacaaaadcacbddbaaabaaaacdcbdababcdabaabddcdcdadbbbcbcdcacbbcbdacadddaccaccbddaccbbbdabdadcbbdacaaadcdaaccbcddabdbadaddcaacbbbccbbacbbabcbbbbcddcdcacdccaadadcbdacdabcadcadccacccacadabbaddcdcddbdcadaadbcccabddcddddcacabbcdadddbcaddcbacdbcdbbabdbabcaccaddbcdbdbcabdddabbaaaaddcbcbcaddcacaabbabdcddadacbcaacababdbadccbdcbbddbdcddabdacbdaaaabbcbbccadadcddbddbacdccacdadbcdacbdababacccdbabdabadcaddbccccacdbbacdcdcdbbbdabcbbbbdcdddadabacbacdddbbbaddacccacdadacbabbddadcdabbcadaaadddbbadcdacbbbbaddabdcabbcaadbadadaacddcbcbcaadddaacdaddcddcdcbbbcddbbccdadccbadcaccabdcbaabdadcdaddaabbcdbabbdddadddcbaaadccddbdbcdabdbbdabadbcbbaccbcbacbdacadccaabcbbacdabaadabadcccbcbaccccbddbaadaabaddcdadcdadacaddddcdbdaadabbcbbbbbcbabbcdbbdaacbcbbdddbbabcdbbaabaaacdcddabbaccaaadbabacdadaccdaacabdddbdbcabbbcacadcbccbddabdbdadacabbddaddbccbbaababdcccbcbadbbbbadaacaaddbbcbabbddbabddbdddddbddcacdcbccddcbacaccaadadadacaaaaadbddcabaaabddacaccbcaddcadaddbabbcaccbaabdbbaacbdcbacdaabdcaccabadddddbbabcbcdadadbdbadccacbacdacdaaddaadcbacabdcaccbcaaadcbcdacbabbbdbacddcaaadadccddacbdaaacbbdcccbdccbdbcbbcddadbbcbadbbabdccddddadaadccbaababbaaabcbdddabacddabcbdddcbcbaaabdcaadbadccbcaadbddcacdbbabacccaadbbcacadcbdabacdddbbddbccdaddcbaaabadbccbdabbcdcaddbadadcaacabcabbbcccadcbcabacdabaabaddccbbddbcacbcdadbbbcabcdaadadccabbdcaadacddbbbabcadbadccbacabaacbabdcdadabccabccbcbccdbccdcbcaacccccdbbacbdcdaddacdcacdcbbcaaddcaccacbcccdcdbdaaabcbcdaccdccbaaaddccababddcccaaabcacbaccdbacdacaaabaadbccdbdbbcccaadbdbabcddbcbbdabdbbaaaacbadcacbccdaddbacabddcbccbdbaacdabdcdcbbdcabccdcbadcbcbaacabcbbacdacadabbadccddcdaabdbbdbabcadccbaacbbdadadbaabdcbaccddbddcdbdcadccbbdcaccadadabddbcdaaccadaaadbcaaccbbdbdabbacbccdbcaaacacacabbcdcddccbabdbcdbcbababbaccbdaabdccbaabbcdcbbacccdacdcbccdbabaababccaddcdcaaaccbcabccdcbccdabcddadcaadcdbacaaabaabbaadbccbaaabaddaaaabbacbbbdcdccddbccdbaabdbcaabdbabacdaaaadbbdbbbdbacaadbcbdbcacbdbabdbbbccdbcacbbccacabbddcbaccdcdbccabddcddabddacbbbdbdcdbdbddbdaadcacccadbbddacdaaaacaacadbcdbdcbbadbdaabdbadaddcbbbaacbdaadaaadaacbaaadbdcabcddcacddcbcacbaabaccaadacbcdbcbbdbccdccbabaacaaaaaacdbcdccdddddcdbcabddaddabcddaabadbbbdacdcdababddbabbbbdabaababbbddbdaaaacbacacbbcadbcdddaabdddbcadcabaadbaabdabaccdacbbaaddcbbccbcbcdcadbaacabbbbabdbaacdcadbacbdcddbcacbbabdbadbcaabddaadcdddbbcbbacaabaaccbaddddcbaaccbcacadaddddbbbcdaaaddcaacadbdddbbbcdddbdbcdddaddbddcccaadbacdabcccdddadacacabbccacdadbcabddacbdacccbdabcadbdbaabaccbacdbdbcadbdccddcccdadcbdbdaccabcdccdbabddbbbbcdcdddaadccaaabbcaccaacdbdddbdcbbdbdddddddacbaddcdcdbccbbbbbadadcdcdbbccbccbadbdaccabcaabacbcacdbccdcbcabddccccbcdbdaaacacdbdaddabccbdbbaccaccccdbbcbaddbbcdcdddbddadbbbaddcdbdcddbddacbabdbddddcbabdcbddabcdbdcabadabbbcddcdaadbdabdbccdbcccddacbcabcdabbadbccaabcabcbdcabdcaccdbbaccaadbdbaadacaaaddcccdcbabcdacdbdabcaccbbccddadcdcaaacadcbdbdcacbdbdacddaaaddadaaddcbddcaccadbbaabbbdcbdbcbacbadccbbccbbbccababaddbaccbaacabcabcccaaaadcbccbdbcdbadbbcccabbcaadccccdbacdbcbcddabbabcbabdbacabccdbbabbdabccdcaaaabcdcbcccacbbdadcaabbdcccbacccbdbdbacaddcccdaddbcbcbccacacdcdbbadacdccaadabccdcacabadbbabdacdadcbbbaabbccbbddbbcabaaddbddbababdacabddbcbbabddacaacbbadddcbabcadbaacbaabddbcadddbbcbcbddcabbabdbbddabadaadbbdbabbcacddddcabbbdaabaadbadadbdbddaadcaacacbcbbadcddacddccdddbacbabaddbdbabbdadaaccccdcadcacbabcdababaabcdbaacadacadddaadaccdbdadbabcaacdcdaddcbdaaacdcdaabacdcdcacccccccbbcbdbbdadacdddccaaaaaadcdaabcbbbbcbabdcddbdacdcddddbccbddabcbdacdbadaabbabbccbacdcbdadbcaaaaadcadbbbccbbacbdccbbddaaddccabbabbddbcbccabdacabcaddbaaadacdbbaaccddabbccccbcbbccccbbacabdaddacaadabdcdadcddcbabdcaaccaadbacddddccabbcddacbcbcacccbcdccabddacbcdcdaaaacbddbacbbbbdddacbbbbacaacddadcaadbdaacdadbdbaccdbaccdaacaddaadabcdccadadabcaaaadabbccccabdccdccdbbabbdcadbbddbdcaccaadbbbaccdcadaadabbadbcacbbabddbcdbadbcbabdabddabcbabbbadaddbcdacbcacadbbcbdadcddcccacaaddcdadbbbadbbbabaaaacccaabdcbbbcdacccacacbbadabbdddabbbccbccabbdcddcaadcbdbabccbdadabbcabdccbbdccdbccdaddbbbaaadcbaddaaacbabacdcbaccadbddbaacddacddbacdbcbbdadcdadadcbccaccccdadbadcabccbdcddbcbbcacabcbbccddcddccddadbdadcdabcdcdbcdadadddbaccccbcbabbadcddddcdbdddbcaacbdaacccabadaaddabdcaccacdbddcabdcccdbcabcbbdbaabadabbbcbcdaccabbaaadddacddababdbbdabdddbacdadaaddbacddadbaaccbdaabaccbcaaadddccdabdbbcccdcacbbadacdcbdbccddbabbdaadcdbdccddbbbdadddcabbacabbbbcdbbcaacdacdbdbaaabacdbdaaaaaadbacbcbabdacbcdaddbcdbdbcbcbacbbbdcbadbadcbddaaaadabbcdcaadbddbaddbcbadcbbbddabbadcadadbdadabdcadccbbcddacdbdbadcadcabaaacabbcacabcbdbabdcddcdddbcbbccabcbdbbbcccacdadbbadddbbdaccadbaccddacdaaacbadcabbccdabaaacbadaccddccbbdaadbdccadbdcdaacdabcdddbcbbcccadbbdbaaaadadcccdaddcbcbccccddbaccbacaabccdabcbbcabbdbddbdccbbaaccccaaccbbadcacbdcbdababcababcbbbabdaaaaacadbccababdcccbddccddddbcbcaadbacacbadcdcbdbdaadacadccacacabcbcdcdccccccbdccabdbbccbdbbabdbaabcaaaaadadadbdcadddccbbacaccbbdddbddbdbbbcdcbdccbdabadcccbcadbcbacaacccdaacdbbcacbddacaaaadcbccacbcadbaaccccbbdbaaaadbacddbcadacbccbbacdddbaccabbdcadccabdabbbabcbbccabbbdbcdacbcdbcdbddbcbacdcddddddabcbccdbdabcadacccaabdcbaccabdbacbbddddadbaabacdaddddadaaadadcdadaddbbaabbdcaddbdbadcbaaaadbacbdadbbacbbbddbbcaaddadccabacdcacccccabcddddcbbacbbaadadcbbddacacbcbdacdbacccdccbdbbcacabcdbbcccaaadddbddaadabdbccccccbcbccbaaaadcacdbcdadbcaaccabcabbcbcbbaabcdcadadcbddabbcabbdacbdcacacdbdabcaaacbcbabaddaabdddaddaadccbbdddacdbcaddacadcaccbdabcbbadbbdbacbaacbdbacadbdbbcbdbbbbabcabddadcaaddbcdcbbccddbaaadbcddccbaababadccdbbbacbcdaabbccbdadaabdccacdbcbacbaadcddaaccbdaadcaacbbcbcdabdaacbbdccbaaddcaacdacbdcacabccddcbcdcbcbbbcadccbabccddbbbcbddabacadccccadababdbccacbcaacbcccbccbdcbcbbcbcbdacabacbadbdadbdbdcacbadcdbcddcaccadbbcadcdadddabaaaaadbbccbcddacdbcccbddcddadccbcaacbddccabaaaaaccdbdcbbbdccabdcbdaadcababdddbaaccdababbcacadbcdbacbdbbcddcacbdbcbbdacbcdacbbaaaccbddaadccaabdaabcdacabcadbaabbdaccacbbaccacccbccabbddccbbaccacaabaaaddacabbcaacddabababbbacadcbdddbbbcbdaadbcbbbcdcacbcccdaabcbcabadbababadcdacdadcbabcaccdbcccdabcabaaddabdccddbccbdcdbcbdbbcddadbaccdadaccaaddaacaabdcdcbdbabdaddabaaabadcaaaabcbddadbacaaaabddabcadacbacbaccdbdcbcdaabaacadbacaddbabdacdbadbcdacdcdbbddaabbadbacabcbcbaadbcacdcddbcdbddcddaabadaccbbaaaccbbcddbcbcdcadbcbdbacddaabdbbaddbabcdcadccdcccabacaaadbdaccdaddcdbabbdbaacddabddcbddbccaadcacadbcabdbbcaadbaaacbcadaabbcdaadcbdcdddbbccacdacbabadbdcbdddcaabacdaabadbdaaadbbcaaadcdbbabbdaaddbcbbddadbdbdcbbdabaaaaabbccaabdadaaadcdbbdbbbaabbabadcabcdadcdaabbabcadacdabcbbacaabdbdbdadadbdaabbacaddcaabdbadcbdadaaaaccdddaabaaddbacacdcddccccbdbbbabddaadbdbaadbbcabaabcdadadabbdbddbabcbddadcaaabbcaaabddccdabcdadacdcaadaddcabdaacbdaabccdccccdabddacbbbbbadabddccbaaaadaddabdccabddcacadbcddbdbaabcabaccacbdbdadbaabcbcaaddabcacbccbcbacdbdcbbdbdbbbccbaddcdccadddcddcdacaaacdddaccaabcbaaababdddabdbbdbcbadddcbabbcaaccccacacbabddccbadbccdbaaacdcabaadbaabdcdbaabacaadbcdcabbbdcabacccbdcdcabcbccdcbdadbbdacdacdbdbbbcaaddaabcbdbdaccbdcadcdbbabddcacaddabdddddbcddcabacdcddbabbbcbdacdbbbbabbbdcbcbcbdabcbaabdadcdbaadcddaabddcbccbddaadcdcadbcadbcddbaabddcbacaacccddbbcddabaccddbaaccddccccadabaaddddbccddccabdabaacbdbbdaabbbabdaaaacacbdcabadbcddcadbcdacaaaabcadbbbbdccccdbbaabbdcaaacacbdbbabacadcdbdbcddbcabcabbabcdacbbcbbdadbbacdabcdaacccdbccadabdcaabacaacddbbccaccabdacdccacaadadccabcadacbdacaacaddccabdbcbbcaabaccbdadcbdbcbdaadcdcacabbdbccbcaabcdccadbaddabaccbdbbbadcaccbddabdcdacddabbccacabcadadaabbbabcbcadcdcaddbdcbacacdbaadcdbdcbddcdaaacacddabbcbdbcbbccdabbbccdcaacabadcdbaccbadcbddddccdaadbdabdccbbaabccbbbcbcaaaabccbacbddcaaaaaddcdcbbbccbbadcdddbbddabbacaccacbcddbdbdbabdaaddbdbccaacaadabaddccbcabacaabcdaadccaccdbcabddbbbdddadcdcbadabaddbbcdcacbdbcdcbdddccbcdccaadaddaaadbccdacccadabbcacaadcabbcbbdbabcddaddccacdcddccdaccabadbaaaaacbbddbbccdbbcdcdcbdddaccdaddbbcdccaaddcbbccacdaddcadbdbddbccabdaddbbaccdbdbbdacabcdcbdcaaacdcddbcdbdbdabaabbccdcadcbcbbccbccaccbcdbdbddcadcddbdacbaadaabaacdaccabdccbaacdcaacbbabddadccaaacddadbbccddbdbdcccdaadbabdcdaaadaaaadcdadccbaabcdbbbcdddbcacacacadcdccdccaccadbaaacadbbbbddcdadcbdcdaadcbaddcbdbccbbbcacbbcbbbbaacbbbacdcdaabaabcbacddcabddaddbacccbccaaacddbcbbcdaaadcabccadbcbcdccaccbbbbcbadbdacdcdacabbddbbbacabbdbcbacddababcdddbbadcccaacbbcbcacdbccccacddcaabdaaaccddadbcbbbcdaacabbaddcabdddcaabacccdbacbdacddbcdbcbddcdaddaadadbcccdbbcccbcbadcaabdcbbcbabcacadddbdacddcbcacbdcccbadcbabbcbaabdccddbdbdadadbcaddbaadcbbadabbbabcbaadcbccadccdcacabcbaabbdcaabaabaaabdbdddcbccbbbdcadcdcaabaaccddbbdccdbbcddcaacbdbdccbacbdadbbccdabbbaccbcbcbcbbbcaccbcddabcbcdadddbbccacabccacbacddacaadbadbabbcaabcbccabcccddbbdaacaddababaabcdddbddcaabdbbcdcddbadcdadccbbdbdcadaaaaaaaabbbbcaabaacaddcacbbdadbdaadddcdddcccbcaabdbcdabbaccdbadcbcabddccbbdbbbabbdaacbddcdacadabaaaddbaccdaabababacdcbddaadaaabcdbbdbadcbdbddbdaccbcdddbdccabbdcbaadcaaccdcdbdabccdacaacdaaacdddbcdaaacaaacdddbdcbcabddabccadcdacabcadbabbbaacacaadadbbdbbbcdaadcccbcbccaacadddbdabaaaaddbccadcdadacdbdcaccdabdbdacbaccbabddbcbaacbddcdadccbaaccccbadadcdcdcbddadddddcbaabadbcddcbabdcbbdabdbbdbbabcdbbaddcdcaacdddaadbbbbacdacdccddaaccdacaadcaddcccaaccdccaabcdcacbdcaadaddaaddabccbbcbcaccadbadbacaaacaddbbbbadbaaacbadbbddabdaaabcaacdcbdbcdacaadcaaacdbbccdbacbccdbabadddbcdcccabcddaaddcbdabbdabbcdcaabbacddccbcdaddcbcddcccddabadddadbdcdacdbbdddcaccbdcadcbbbbdcbaddddababcaadbdadabbaadcdccdcabdcbdcbcacddccadbadbbbcdabdddadcdbcbabacdbbacdaaadadaddcbbbdbcdcbbdbbccdcccbdabaabaccaaabdbddabddabdcddcbdbaabbaaddcdaacdcbaddaadddbbdbdadbdbddcbdbdadaddadccdadcadcababddccccdcaccddcdcbbbadcaaaacdcbbdcccbadcbacdacaacbbadcdcccdbdcbdcbbcaadddacbdbbbadbcbbcdbadacbdbaaababdcabcabdbbbbadbacdacdaaaadbbbbdbcbdacccaaddccadaabbccaadccbaabbcdbdabcbacabdcdddcbdacdddcbdadbdaababaddbdbcacababdcccbadabacdcdbcbcaadbdabbbaadbdccdccdaabccbddaabbdbbcdadadbccbacdaddadcaaaabddaccdbabcacaaacaddbbdccbbdabaadcbacaabbdabbcccddcaababcbadabdadacdabaacabbadbacdcdacbddacbddabccbbcaaccabbcacaaccbaaddaabdcbccbadcbabdbaacabdddcadaabbdbabbdcaabdacdcbbccbabbcbbabadadadbdcadccccacdcaadbbcbabccabcccddadbbbccbabaabbbaaabcbbdbaabbddadabdcbbbcbadbcacacdaccdadcdbcdcdaadccbcbacaaaaccbddabdabcdccbdbadbccbccbcbacabacbbdcaabaddcdbcadabaabbaacaadccdccacdaaabcbcbabcddddbbdacaddbdaacbbdbcbcbdaadccbaccbdbbddbacaabbbabcdcbcaccabccdddcaddcbcdcbdbccdcccccbcddddcbcbdaaccbbcaccbacaddbabbabacdbabbbbdaddbcbbbbdcddcacabbaddabcbdadcabccaccadbdcccbacbbbddcdaabbbbadbbbdbcbccbcbcbbcdcbcdccaadcdabccdacbcdcdbcbcabddcaadcdcbadcacbaccbaaadccbdcbbbbbadaabaaaaaaccabcacdcdcacccccaaabaddaccababacdabacabcaaddadcddadbcdbaaacadddbaccabbacccbbcdccdaddcbabcdcdadcbbccaaaaabcccccbbcadaadcaadcdbcbabcabccbddbcdcbdbbbbbbaabccdbbbbabdcbcdcaacbabaadaaaccbdddbddcbcdcbdbadaaadbcabbbabddbdaadbdacadddacbddbdabbbaabbadabbcbddbbdaacadddbadcccccccbadacaabbacadacdcdcbcaaccdbdabdaabdddadcddbaccbcddbbacacddcbdbccacbabbbaadddaadadddbcbcdabbbbdaaadccaaadcbadadacbdbdbddcaabdbddccdaadadbddddbadbddaccdcbbbbcccbcdcbddccbdccabdcadabcacababcbbbddcdbabbabaddbcbbaddadaccddddcdbabaadccbccaccacdcbcabdcbdcdabdbaaccdcadbcbbcaababdbbadadcbabaabbddcdcabccaaacbaddbddacdbdaaddcaaabaacddadaadabacdcdcaaaadcabbacdcaacbccdcdcbcabadcdddbcdaaabdacbaccccbacabbcbaacbddbccabadcbdddadbbcbaadacbdbbaddbcdbadaccdcacaaaadbddbccabccaaacadaacbbbcabccdbdadbddbbdbdadaabdbdcdbccbddddcaaacbadabcccdbbdadcdacdbcbbddcdcbaddbbbacabddcadcaabcbbdbcabccddaccaddaacaccdaccaddddaacdcbcadbdabccaabaaaaabdcadacabdaacababdcddbdcccadadcbacaabddbbaadbadddacdaddcbdccaabadbcaacbddccacddcddadcccacddddcbacdccaadcbdddaacabcdbdcaabcadcddddacacbdcabcbddddabddaaabdabadddabaccbdbbabacacabbadccaaaacbdbbbccaaccabadaddcdbcaacbccddbbbbaacbbddcdbcdcadacdbaaddddacbcbcadcbdaddcacadbdadbbcacdacadbccbcdbbcccccabcbddddcdccaccaabcaccacbcbbcdadddbdadabbacadadaacdccdcdbdbdcdcdbbdadcbcbabdddadaacbdaacddbbcbadbdbbbadddbccadaaacbdaaabddccdddcccdcdbbdddaccdaddabdcddbaccbabdabbbcddcaaaabdcdbadadccbbcdccacabcbaabddcdabcbcddcdbadcbbdcaaccdcabcccbbcbaacabbabccdcccabdbabdcdbccabacbbbbcdcbddccbccacccbaccbcdaacadcadcbcbbcacccaadacbabcabacdabaccdcccdbacbbbabcbcbacdadabcdcccadacdbadddbacabacadacdbbdabbabaadacbcbdbbdbdcadbddaaaabbbdaaccabacdaccbabcdcbcbdbdbadbcdadbccabbdbadcabcdccacbbcbcccacdbabdbcbdccbbcabbbaaabcdcaddcaaddabdaabbddabdbccccdcbcbccbabadaababadcaaabddddcaaccccaadbaaccbdaddcccbbbbaacbccbaabdbbdadcddabbccdbdbadccadccccdcbbccbacbbbaabacdababbcdabacbcbbddcadaaabbacdaccaddcacadbcdcbcaaabbcdadadcbcdcdcddaadbddbdadccddcbabcddbcdbcdbbaccdcacbcbbaabaccccaabbdacccbbbacaccadababaacddcacddcacbdacdcddcbacbadaacbacdbcdcddbabaabaaaaabadaaacddccbdddbbdbcdcbbcccdaacbbdadacbbadcaabaacbdbadbdcbcddcdcdcbbbdbcabcdcadbbdcdabdadadcabddbcddbbdddcadbaacbbcdaabcbbcbadddcddaddcaaacabccdbddddbcaabadcbadbbaabdabbdcacadcabdcbdaaaaabdcbbdaacacbacdabacacccbdaccdccabadadcabbdacdbdaaadabaabbabddadacccdbcbcacadbacdddcbbcbcadaadcbbbcccdbcddbccbbcaabcaabadbdbbbabdbddaabaaaacbbbdabcdcdacccddaddbcdacadabbadbbbccaabbacacaddadcaadbcdbaddcccbbaaccaddcbbadcadacccdacbddabbdccaacccbabacdcbbcdacbaddabccdddadcadaacbabccacaabcdaddcdabadbdccacccbdadcdccdacabddaabbcccabcabaaaabbccababbbaccabbbdabcdaabaccccadccadcdddcdbccadabcbddcdbddcaaabdadaacaddbbddbcbacadaabcbbaddbbcacdbcbabbdbbdcbacabbddbcaaabdbcbccabaddbcbddcddbbdcbcacaabdacabccdabaccdcdcbcdacdddccbaadddbbbdabbadabaddbbbbcbbbdbabcdadabcbddcadadbbcbdbcbdddacdbaabadbdcaccdcdcbabdbbadcbcbdcbcacababbccdbaadbdadaccdbbbdacdaacdccdbaddbbbaddccccbaabcddabbbbcaadaabdacaccdacacacdbadccacaadabaaadcbcccbdbcabcbbbbdbaaabdcabcbacbbaaacabddcbdbaabdaccbdabbcddabbcbccbdcbbdbccacaddbbdbcdcaaacdcdacdbcabddcccbdadcbdddbcaaaabdcdbacdadbccdbaaabddbadcbbbbcbdcabdacbdaddbaadcabcbaadadbbdcddaabaccddbbadbadccaacccbbaaabcabbbaabcdcdadbadaddacdbbbaabacabadddcaadbaddccbcddcdaaccaccabdcadadcbdaccdadddbbcdabacddcaddbdbdbadbbbcdabacdcdbddbbcbcdabdbdcabdabddcaabbaaadcbdbdccdcdddccdbddadbddacaacdbbcdbbcbdccdbbdbaaabbdbdcddcdacccbaabbababbaadbbbdaddcadcbcacacbdaadccbcacacccdbddabdddbbbcbbbdcbaddabaadabdcbcbbcccabadbdabccccddcbddcadbadcacdbdddaabddccbbccdacdbaaaabbbdccbdbdbabbddacadabdbabdbcddababcacdddbdbbcacabbddccbacbddcddacdbccaccbcacacbcbcdbdcaaaccabdbcddacacbbdcbcbddacccdddbdcaaacbbccacadcacdccbbdcaadddabdacdddcadadddbdddcbdbdddbdddacbdbdcbcadbaabacddbaacacaaaaabcbabccaabcdacdcbdcbcdcbadddcbababbdbcdcbaacaaabdcbdcccdcaddaccadcaaabcbccbabbccbbbcddbbcaadaacabcaaccbcdcbcacaacbbcadbbbdaacddcbabdaccbaaabbbbbccbcbcdcbabdbdbdacdcbabacddcbaddcacbbdabbbacbdcaddaadaababbcccbbaddccbcbcbdbaabdddaadbaadbdcaddaccbdcdddddbcccadaddcabbabaddacbabbbaddcabddaadaccdadccdcabbbbbaaddaccbabcadbadcbcbaaddadcbbbddddcabcdadaccabcdddddcdcbcdcadccabcbbdcddbaabbabaacdadadcaabcaadabbbbabcadcdddaccbbbbaacdcbadbbbbdbbbabbdcccccacddddbbaadbcdacddabdbdccaadacdbcccdccabcacaaabaabcdabdbaddccbadcddabdccbcaabcaadccaacdadcaadddaaccabddccacbcdcdabbabbbcaabbacbaaadacbbdcdadcdabadacabcddcdcdcabbbaabdabbccdadcabdcadbbbbbbbaddcdabbdaaadcdbccadcddaaccbacadadcaddabdaccabcbcabaccdcbdacbcbacdbacaacbabacccddbaadccccdcbabadaadbaddbdadbcaabadddaabcbddacddadcdaabbadcdbabacbbabccabcbbbbcadcdddbabcaadbdddbdacbdabdbaaadcadaabccddadaccbdbdacbcabacbadcbacabbdddbaaaaaaadbbdbdccdbcbbbaabdbccbcbbabdcdbadbaabadcacabdcbaccaacbbdbddbdbcadacdabbacddcdcdbabaacababbababbbaacbbcbbdaadddcbcbadcbbccbaaabdbdabcccbbcccacbdbabddcdbcdcadadabadaddbcdbcabbbdaabacdccbdcacddbaddabdcbcadabccdddddbcaadddbdddadaaddbdbccbdddcacabbcdadcdcaadbbababcabcaaaddcaddacdaadabacaaadddbddacadbadcbcadbccccdddccbbbccbddbdacddcabcaccbbacbccaddcbabbaddbaddcbcbbadcaddddbdcbbdabccccaadadcdccbbdaddacdaddccbbccdcdbddbadccddbdbaadcdccbcdbbadabadbbcccccbbabdbcbdadabcbacdcccdadcbcddbabaaddbcdddccabbbbbcadbaacdbddbdbbcccabbacbaacabaddabdcdcabccccdbdcdcabbdddcdbadcbbcdabcaaadcccaadacaaaacccccbdccdaabccbaabddcbddbccdababdacdcdabdbdddbaabbaabadccacdcddacbaabbbdbacbaddaacbacdbcbabaacabdcdbadbdcaabddcabcaaadddaaabddcdbbccabaabcbacdbddbcadccbdbcbbabdcabacadcbcabdbbdabcdcddddadccadbdbcacccbbbccacadacdcdabbbbdcbdbbcccbbacabddcbcadddcaccbaabdcdbdaadcbdccacaadccdbbcdaaddcadaadbddbaaabacadabdcbdaabadcdddbcccacdaddabcaaddddccbcacacbdabcbcccacbcadcdbbbabbbbccdadcccdccbacdaabcbbbbdcddcbddbbddadddcbbddcadbacacbbbbbdcbbacdacdcdabbcdddbbaaaaddcabbbbbdcacdbcdbbbddabacbdcacabdacadbabadaddbbdcdcaddabcacccacabcaaacabdbbadbacdadbbabcbadbbdccbdddacbccbaabbaadbacabcbabdcbbadacdaadddacaababcbbabcacbcbddaacacbdbcbacdbcadddcadacbaaddbccaddcbbbbbbbcdbbccbcbcaaabbbaabccacdabcdabcabaabbcbdadabcdcdadbbbdabbdacacbbbdcccdcddcbbaadcdbbbcabdbcdcabcbbabadccbcbacbbbcabaabbcadaabdbdaccbdcaabadbbbbbcbbcaadccdcabadabaadddddbadaccdbabbbcbadaadddabdccbcaaadbaaadbdbbdbacadbacbaadaacbdddaacadcddacaddbdadbadaacdabadcbcddcabbadcaccaaadcbabcadacdcacaadbbdbddacdbccabcbdbdadcaaccdabaaaddabdadabaccbcddbdccbcbaaacddbadbcdababdbbdbdddbdadbcaacccbdaadacadcdbdcababbaadbcdcaccdaddbabaaaacccadaccdddccadbaabadadddcacacdddcbbdbbddccddabcddcbabdcacacddcbbdababaaabbaacacddddabadabdbcddbdcabcaabaabdddcabadaadcbdbbbadaabacbabbbcdacdcaaacdacbdaadcaadcacbcaabdadbacbdaccacacaddcdadbddcccdabcacaddbbadbccdcaaadcaacaadcdbdcabbaaababadcdbdcbdddbdadacbababcaaabdccbdcabcdcadbcdadbabbddcbcdbdbcddacdcbdddbdbaaddbddcaddbcdcbdacbaddcaababbdadddcbdccdbcccabbccbacabbccbcccdccdbddacadcdcdcbcdcbabadaabccbacbdbcbacbdaccbcacdbbddbaaaaabccbddcbdabadbcbcadbbdaabbacaddbaacabdbcbaacbacdbccbdabddadacddbbccaadaccaddbcaacddaacadabadbababcbacabbdcacacadddddaacbabbdbabaadaddcdcbcacaadaaaaaccabadcabcbbdcbccdabdddaaaaddbadbdbdadbaacdaaaaaacccccbbdbbcabbddabbcabbdbdaabbacbbdcdbbbaabadadcbdaaadddcbcacbbbacbaddcadadbddabcbabdbacabddccadccccccdddaaddcdaacdbbcddcadbddbaddcbcdbbcbbbabdccbbbdcdbbccaadadbccaacacbccbcbcbdcdcddcbbcaadcdbbdcbdcbcddddcbbcdacadcbabcacdcabbdcbcdacaadbccacccccacdbbcbcdadbcadadbbdbcbcbbbddabadabbcadacaccabbccdddcbbdddbcadbccdcdadccbbaadbcbbaabdcdcbaccbaacdbbcbcccdcbdddbcbdadcaabbacdadbadaddddddaabadbdcdadaddadbdbcbadcbdddddccaacbbcabccabddccdbdaadabcabacddacbccaddbadbbacacbaabdbccabbbccccbcbbdbacbbabddcdaccbdaddccdbbaaabababacddcbccabbbdbacbddcbdaadabcadbaabbbdabdcacaaabcdbcccacdaacdbcacbbdddbdcacdbbcdbdcbcdaaddacbdbbacbbdcccccbdddcdbbacadacbaadbcbdcdabdddbbcbddaacbdcaacaacaccacbcbbdddddcbadbabccdbcbddbaaadcbbaabdbbbcdbabcbbaabccdaabdaaddcddadbccdbdbcbdbadcbcaaddacbbccbccdcbbdccbacacabdcaaaabdabdabccbabaccabdcccccdaabbdabcadbdddbaccbddaaaadbbdccbaaccaaacbccdcdccdccbccacdbbbdaaaaacbcddddabcbabadbdbbcdacaccbdcacccdccabcadababaadacabdacadbbdcbacdabdaaaddbcaabaacbccbacdbaddcdadcddcbbaddbbaabdcbcddaadbcccdbaabbdadddcdcccabadcbdcdaaabcaaaccdbbccbdadadcbbacdbcaccbbbbaabcbbcbdbdadabdacaddaabdbdbdbaccabdabdcbcdabbabcccdaccaaaabdadabcdaadabddcdabddcacddcbacbbdddaabcaadadbabdddaababccccddcdaaddcbddbadaccbaadabdabcbdbadccaddbdbacabcacdbaddbbacdddddcdbcbdacabadcbbbddcbcdddbbdcccbaaddcddbaadbcbccacabbcbcdbddbaadabacaaadbadabdddcaacabccaababbbacaabcaaccaacdacbddbccdcacabcabddccdcdcaddbbbbabbdccbcaccacbbdabbcabbacaaddadccbabcbcccdcacbbabbbdabacaadacacababbdcdcdcabbcbccccddcbbccaacaadadbacbbadbdaacbdaadaccbddbcccabccbacbdaaababcdaadacccbaacbbadcdbdaadaaaacaacddbbcdabbabbdacccbccddccbbaaabadaabacdaadcbbdbaaacdabbababdccccdabdcbcabbdbcabddcbdcccababcddadaccbcccbcdcdcaaaadadcdacbcccdbccadabcdccbaacdcbcabccbcdccaddbcccadbacdbdcaddacabbcadcbabbdcabadcdaacdcbbacadadbccbcdcddbbccbaddabdddacdcabcbacccbbdbaaadacccabdaabacbccddcabcaddabadcabaabcbbabcdbacbaddbddbcdbabddacbcacbbcabaddcddcdaabcdbaaddbddbaadababbbbaaacadbdbbacabcbabcbdacacdabbcdbddbadcaacbaaccadccaacbcaddbdccdabcaaacbbdbbcadaacacddadbdaaaaddcbcdddadbadbdaddbaddbbacddcacbdbbcddabbbabacdaabbdabadbcddddbdcddbaccddcadabddaadaacbaddbcdaccbbdaccacdabbacacaddaddaccbbbccdcdcdaadaddbabcadbaddacbadcdaacbdbaabddbabbabcddacdabdaaaaaaccaadddacadddadcabdabdadbddcaddcacdcdcbbaabddcabcabbdaabbcbcbdbadbddcbcbcaacadcdccbdddadabbbdacabcbabababcaadcacccccbccbdbbacadbdbcbccdbbdabcaabddadcbbddaacbdaaaacdcbcdbaadabaaacbdbadbadadccdabababacddbcdcacdddabdaaadbbacacbadbdbbddabdbbcaabdddabccaaccbcbbadabccaadbccdbdacadaaaaaabbcbadbbcabddaaaaacbaccbcdbdccbabdaaccbbdcacabdbadbdbaadddabbdbcddabdabbdccdccbdbbaacabdbaaccdbbcaddbadccccddbdcddaabadaddcdcacabcdccbccadaacaaadbacdbddaaadaaccaccbccbdccbaadabcddadbdcbbdbccabbdaababadbdddadbcccaacddaaacccaccaaddadbbcdaadacabcbdbcbbdcddccddacaaabdacbacacdabbddcbcbbaddbdbcbadbdddaadbbcbadbcdadcdbbbababcbabacaabdabdcaccbdbadcabdaaacaddbbdbbddbdacbbbddadcdaabaccdacddddacddadcbadacdbcabddcdbacadcadcbaababdbbbacbabbddaacdbacbbbcdabbccbbddaaadabcbddddadbcdbababadcbdcdbcccbaacdcdcaadcdbbabbdbaadcbdaddabacabccddbabbdbccdcabdcbcdcddcadddcdacaddaaaaacaaababdcbabccdbdbcbdccdaacbbaaaabbacbaabbcabbbacdccccabddbbaddbdbcaacbaabcbbbdbcccbdcbdccbcbddaaadcdcbbcdaaaadaacccdccbadddbdccdaacdcbabdccaacaaaaccaaacbcaccaaccccbbcbbcccadacbddabcbcadcaadbcdddbbdcabbbdacddbaccabadcaaadadaacacbccabcaddabbaaccaddddbaaccdcdbbadbcabcabcbdbbdbddaadadccbadaaadabccdaaaacadcaadccdcdcccbddcddcccbababddcaadcadabbcacdcadaadaddcdcaadcccabcaadbcdcaadcdbdbbcddbccdbbbdddddcbaadaaadcbabcaddbabbccaaadbbaacbbbdcacbdacddabcabdbbbdcacdcdbacaaccbcbdbacdbdaaabbcdadcbabacbdccbbddcbdbbbbbbbcabdbdadcbbadcdcdcdcbabbcbbacdcccbbbabdaacabaadabcdbdbbbcbcaabdbdaabdacddddcddabcdaadcdabbddbdaaadbbaaaaaabaddbaacaaccddabacbaacadaacabaabdcccdbbbbaccbbaccbbccdbbadcdddbcdbacacbabaccdddbadcacacabdbacdbbccabdadcbaccabcdcbabbadadadddcacddabdbaaaccabccbcddbbabbabcbaabdabccaabddaacabacbaaddaabbddaaddbcddbdaaadaaaadabdabbabbabddadbddabaccaddccdcccacbddbcabaacbbbabdcddacbacdbcacdbaadabdadcbaccaadbddcdadbdcbcadababccccaaabcdddbddccdaaaddbdaadcbaabacdcaadddcdacadcdbabdabacadddaddbcbcbbcdcdaabaacdacbaacbcabbdabdbacbaaadbccbbdccadcddaccbabcbcbcdddbbccccbcdbbdddbdbddacbcaacabcccacaaccbbdaccaacdcdcbbcabaabcccaddccbaddcdcbbcaadcccccacabccbdababdcdcdbdbbccdcdbcadcdabdcbcbcbabdbcbcddbddabdcbbbcadcacbdbcccacbdbbddaaaabddabcacbcddacabcbddbdccacbccbbbadabbcbbbbddbdccdadccbadacccccacdddbbcaddddacdadbdadddbadbcdcddbdddcaccdcdbbcddadacdcbcabcbdaccaddcdcbbbdacddabbcbaddcdccccadcacacddaddccacabbdbdaadccabaaabaaaaaabbcbdcbabcbaccbdbdacbbbcccabddacadbdacdaaaddaacbaddbdbdbababbdbaabdbbaaddcabacbabbcbaaabdaadabdbddabbbbcacccaadcaacddabddcdcbdbacacbbaacbbcaccbccbbdbbdddcbcdaddbadbdbcacdaccacacccadcbbbbdbbdabaaacbbbcadbcdccdabbdbdacbbcdbadcabbadadcdddcdbcababbaccabbbddadbdaadbcbccdbadbbabdaddcbdddacaadbbaaabdbaddcccbabadaccddabcbaaadcdadcabbadabaabbddddacaddccbcbaaaccaddbbcbcccdcdabdadcbcccdabdcaccddbbcddbbcdbcbcacdaadadddbcaaadbbccabcdacdbadabccbbdbbbbdadbabbcddcdbdabcbadbabdabcdcdacbcccdbadbaabdcadcdaadcababddcbbdbdaadaadabbbbcbacabcabbddbccaccdbdccbbacbbcbadabbaabbdacdcddcbbcbcacbbacddbdccaccbadbbaababbdaacdbcdbdcbacbaaddddbadbdcbddadabcbcabcdaddabcbaaaababbcdddbcddcdddacdccbbcdcbccdbdabccddcabdabbcdcacadaacddbbddbdacddddabdbbdcdbbbbaaaccccdaabddddacaccadcbbbacbcdbcbcaacdaacdaaabdbdbbdddadbaadcbcdbcbbbdaabadbcddbddcbbddcbababbbcdccabbcbaacddadacdabbaabcccaacdbddbcdbcdcccbdccdaadaaaadbdbbcccdaaacaaddbbbcdcbbacacddbaccdbabccadccdcacbaddcacddbadabccadbdcdaaabbdccdbcaacdcaaaddbadaacdabdcdaadcaaddaadcdbaccaddbccdbdcacaabcdcadcdbbbcacdcbcdbdcaccdbbdaabdcaabdddccdbcbdccbbbbaabdcbdcabbabcadbccccadbdbdcdccbdcacaadbcbbbcbcddbacbdbbbaacbcdbadcadcabdadcbdaccbcbbacaacacaacabdadadaaadcbdaabbcbdadcbabbababdacbacabcadabcbddbdabdacbbcdbcbadbaadcacdbacdabcccdbabccbdbaccacabcbadcbdadabacdcddcdacbbadbdcadbccbbdabbcdbbbcadbbbdbadbabbcadddcbcdaaadacaaaaacabbdbdbcbabbbccdbadcbabcbcbdcacacbcddabacadcccbabbbbcdbaacdaaadaacabdcbdcbcbdcbacaddbcbadcbabacddcacaddddbdbdbbddcdcbaabdddbbadcbbdbdbddcbcdaadbbbddbdacdccdcaaadbaccbacadbdaddbdbcaaaacacbbbbddbaabccdabdbbbcbbdbbaacaabcabadbdbcbddbcbccaccdacbbbbbbcddbbbcbbbbcbddadcdabdbddbabcadddbdcbcaccabaaaccbaccbcbcbabcaaaccbdccbdcccdcbcacdbaaaadcdacbcddcbaddcbaaadcddcbaaabdbbdabcbdadaddddbbcaccbdcddcadccacbdbdcddbdcdccdbaaacdaaddbcbabaadcaccacaddabdcdbdcadcdadcaccccaadbbdcaddcabdadbbadbabbbbcadabdbaaacbcdbcddaddacadbadabbcccdbaaacccadacccdacbaddabbdabccadcbbabdaccdbdccdadbbbdbdbabcbdaabacabadacccddddbbcaaabdccabadadcdadccccddacadaaaadbdbbbdaccaddcdccbbddbdaabccccdacccbbbccddabdddcbcdadddcbcadbbcbdbbdacadadadbcddcddbcbddbdadbacbabbddbdccbdcddbabcaacbbababadbaabdaddabddbcddbbaaadcbdbddcccbdaacbbddbdacddccabadabbbdbbbcdbbddbbccadbabdccdacbbaabacaadddcbddcbadbbaabcabcacabbccdcbbcbbdbddcabaddadbaadaccbdbdbbbbbdccaaddabbdbaaabbdbaaddcbbccccabcbaadcccadaadadadababdcccaaddaddbbdbadacbbcabbabbdabbacdbcdaacaaacdccdbbadbaaaddddadbdbdbcbaaddbcbcbdbbddadddabbbcacbbdcbbbdccaaabaddbcadacbbcdbbabdaacaaacddabdaacabdbadbcdadbaabdccdcaadcabcbbdadddadcabccadaacbacdcacbdbaacdabccccbdcdaddcbbbcaaccddcacabdcacbabdddabbcdcabbdbbbbcbbbbccbbccacddbcbdcdabbbcccababcbccbddcddbddabccbaaaccbcccacaddcababcddadadacccddcccbdbdcddbbdaddbbaadbbbabcbddbdabcddbadaabaaabcddabbcdddbaadbcdacbcdadaccbdddaadbdadbbdcbcacbddcdbabdaababddbabbbddacbddaadcaacdadccaaaccbdcdacadbacccdccdbbdabdddbdacbbdbdaccaabdbabdccabaccdaacacccdbacbcddcdaadbddbabcdadbbcabadbbcdabbabdbadddbdddcabbdcbbcdabdaacaaccbcaacadddabacbdcdacbdbcbcacdcbbbdccbabcdcbadbcbabadbcababbdcbddadbbdbbaaacddadbdddccddaabccdcdbcdaccabddabbcaddddcabcdacbdbcaaaaadbdbcaabcdabadcabdbabcbaccaabaacacbdcdbcddcbdcccccacbddcdaacbabcabcabdcdcadbbccacbbbaccddbcaacabbbcabbdbbbddacdcaadcaadaabdacdccbbdcbbbdcddadbdababaacbaabccddaccbabbbaadabbdacbbabdbcdcbdbadabadddaddbcdddaacabdccdcbabaababcadabdaddaccdcaadccddaddabbaaacabbbccaadcababadbdccaccbabcbcbbabcbcabddabbaacdcbccbacabbcccaaadcbbbcdbbdbcccacbbbbbdabadbbabbaadcacbbcbaddbbbdaacdaaabcaddaaaadabdabcaadbddbddbbacdaddbddabbacdbbdadcaaacdddcbbbccacdaabacbdcdadcbcbacccadaabbdccacaccaccacabdabbccdcacadbdcbdcbddcbaabbabbccabcaaabccacccbbdbcadbbaddddaadcbaccdacddbbccbcbbadccdbacabddcabddbaacabcbcadadbcbbdcbcbccadacddaacbaacccdbbcdcdadcbdcdcccabddbdabcabcdbdbdacddacddddababbcbdacddbccdcddbbcaabbbcccdcdbccbdbdabbadcaadbbdbbacdcdcaababccccdbaabcababdcbdcdddccaadbcbaadadbadddaccaaaabcbcaddabdcbdcaadbdbadaccbcaadcdbdbdadddabacaddadbaccbdaaccabddccaadabacbacdaddbacdabacbcbaddaabbdcbdcbbcddccadccbbdabacbcccaadcbdbdbaacbcbbcdccadaccbdadccccddcbcadbdbdabacabcbaddbbcbbacacdbaddbabbcdbcacbbadcbbcbbaadcdacbabbadbdaaaabdaddcdaddaacbacddbaacdcabadadabcaccccdcadcdcbcacabcdbabcababdbbccdbabbcbccccccddababcbbcddcbacbacbabdaaaabacbbdcabdbabababdabddcdbdbaddcadcdccdababccbbaabbdbbacacacbbabaadcaabcdbcabcccabdacabaabcbcdcbadccabcddbdbbbacbbabaadaabddcdaababddacbaaddbaaabddbcbbdbcbcdccaacaccccaaabbdbdcdbbbababcbddbadacacbdabccbadbcdccdabaadadaadaaacaaaddccdadbcbcbddbbacadccabcbddaabdcbdababaaaaaacbccdbbdadbcbbbaccaaaaaadabcadccdbadbcadadcaacacdddabadabdacbacacbadddbcabbdadcbaabaccaabdacaddddddcdaaabacccaccaddadccadbdbbdadcdbcdabbdbaddddbccdcadbacddddbdaaaddcbbbaacbabacddccdabbcacbbaadcbdcdcbddbacacdbbdcccdccbcddbdcccdddbcdaccbabddacbcbdaddddacacbcbcacdbaabccbdbacbbcacdcbddcbcaddcdadadcdbaaabdbddbadcdaddcdcddabcdcbcbccdacdccbbbbaabcbdaabbdcbbcabcbaccbbbabbcacbcaadcddccdcbcdabaccccabcdadcadacdddaacdbabdccdcbadbbdbbbacbadabadabddaabdccbdbacaadbbdcdccdbbbaacaddcabcdcbcdabbadcbaaacabcbcabbcaadaadcdbbdbdbbcbccababbcdbccbdaddcdabbcdcadacadcbdaaaddcaadbcdcddbdcdababddbdaadacbbacacccaaabbdaaddbcacbccbcdbaddbdddbccaddbdbbcdcacaddaaaddaccdaabddcbbcdbdbcdcacbbccbcbcbbdddcbcbabcbbacaddbaacaabdabdccbbacabdbddbadbbbbddabaabdbacabadbdaadcbabddbcbddcaadabdddcdaaaccacacbbccaaaabdbbcbdadcbdcbcdabaadabcdabbdbccccaddaddbccdbacdbdabacbcdcabdacbbddbbcacabadcbccdaabcbbbabdadcddaccadadadddbabbddddbbbdbbdbbbcbddbccaadababadddbdbaabbbacdbaacbdbdaaabcbaddcbcbbcddcadcabdbaacbcccdddadbcbdcddabbacacdddbbbadaacdcdcacbacbdbccacdabadcababcdbbdabadbdcabdbdadacaabddabddbbdddbaacdacadadbcacbacbabddaadadbcdbdbbccbdbdadaabdcaabcdbdbbabaacadcbdaabddcaaacadacbdbbcdaadacbbdcddbcbdcadbbddddddabbbadbbddcbbdacdaaddacbcbacaaacccccddabadaabbbabbddbdcaacadccaddadddcbdcccaaaadcbbdcabdbdacadddcdcddbaabdbcabcbdbbdbcbadbcbdbbaaddcdbdcaacdbbddbacdcadaabcabcaadbddadadadddddccabbcbddddabcdcbcdaacbcbcadadbbbdccccbdddccdbadddaaabaacddabcadacdcddcdacadccccaabbbbbacaddcaaccaacdcdccadbddaadacabbbdccbacbbabcbbcacdccabbdbddadbdabadaddadbaccbcabbcacabbccabadbcbcacbdddbccbacbcacadbababbabbdbbdcabddabcbdcbbbcabcdabbadbdbbbbdddcbacdcdddbbdcacbcdddabbdadcccdddbdbabcddcddbacccdcdccdbdccdbacbacdbbbbdbbdadacddcbcccbabaaadadbbcbbcddcddbcbdcaacccdabcbbbddbdaaabdacaaadbacdaccadadcdbcbbcdbadcacbaabdcddbcdccdcabccccbcdadcccbcbdbcddacbdcbacccabccbbdcaadaaaabacbabbbccaadcbdbddddccacdccabdcdcdddbdbbbcbaabcabddacbbcaddadbccdaabbdbacaacabdcadbddddaabacaadabcdcdabdcccdbbadadcbadacaadcaaaccdddddadbdcbccccbcbdccbcaaddcdccdcaabcdbbbabcabbccdacdbaacddbcccbbdcbcababcdddccccdbcbdababacddbcacdcccdbbabddccdbbdabdcccaaabcadccdbabdcadaacaadbdcbbbbbbddabbbbcdaabaddcbcdddcbacdaaddabdcdbcbdbbbbdbcacddccccabccbcccbaddccddbadadccaaabbdcdaadbcadbaddbccccccddaaacdcaaccabdacdcbdbbabaddbdbcabbabcaddddccccacbcddbbcdddacadbadccdaadbcbaabcbccabbbabaacccddbababdbaaabadccdccdabbaaabbddadcbdabbacaaaccadbacacbaadcbcbccadaabaaadbbbbacddcdbacdbbbbcaadabddbcdaadbcddbdacaadaaccccadcadbcbcccaaadddaabdcdaacbbcbbcbbbdbaccbaccdcccdbadaccbddacdadcadcacaddbccdcbcaccacdcccbaadadbcaddccdadddbcbcbcdabacadddacdcdaddabacbccdbbabdaddaacddacddabdbcccdbaaddcbcbbacddaaddadcbbbbccdcdbdbcbbacbdbabddbcaddbacdaddbacdcadacccbadcbdbcccdccdccbcaacaccccadcbbbdcccbbccabbadcbdcdbcbbadabbabcbddcdbbabdbaaabcdcadbcabbdaddbcadadcbcadadcdcadabcaddbdddadadaddcaadbbcdcbbdbcabbbbddbbbcdacdacdaccbdddcaddcbcddadbadddbabbddddacbccdcdbdcccbcbbcbadcdcddddadaccbabbdaacbbcaaaacadbdcccdbcdbdbbbaacccdaddddabdbcbbdbdcacdaaddccaaabadcdcdacacccabcbddacccaadadacdddabbaddadccdbbbcdcccbcccacdbcddccbacbcbacdaaddadbbccdaadcbcbacabbdabddccbbcaacacaddcdaabaddccbdcdaaaaaacdacbbdbddbadadbbddcbbdbbcabbcbbdcbcaaababbccdacddcdddabbbdddbacacbcddcbdddbdcaadcbdcdabccaccdbbdcdaabcabdcdcadddbcacdacbbacaaddcacccbbdccabbdbabbbdbbbccadaddbdcaddbbadaaaabbccccaacbbdabaababcbdbdbdcabbddaddcbddadabbabbbaadccbaaccdaccdbaaadccdbbcacacddbacbacabaaacddcaccaddadaaaabaccdbcdbdaaaadabcbcbcadcbdcdbbccbddbdbdadabccaccaccccaccaaacbbcacbcddaaacdaaaabccccdddcadcadccdaddddaddccbacdcbbbccbcadcdacabcbbadbcbbaabddaadcbadddaaaaacbcccccaabdbcdaaadbacdbddaacadbadbbabcccccacbdddaaabdbaaadabdbdabbcdccdbdaaacdcabaaacdbaddabbddbaadaabcacddabdbddbaaddcabcadcaacccadacabcadccaaadccccabcadacbaddcdcadcabadccbcdacacadadabddaacbbdbdcccdbadacddbabcacabbddcddbadaabdccdbdaabbbdcbddbadbaabdddcbbabcdadbacbdbddcdaccabdbccdcdcdcccbccbacabaadcddcccaaddacbadcdcabaabbbcdbaabcacdacbdcaddccadccbcbccbabccbbbacdbddbcdaddbddbcbabdddcdabbbacccabcbbbccaacdaaddabccabacabadabddcccbaccadabbbbacaaacbaadcbadbacdddbbbcbbdacdddccbabaadddbbcbdcbdbcdabbcbbaaadbcdcbccdcdbdbbabcdccabdadbabadddbcbcdccddbbbcbbbcbdcddbddcbdaccadcbabdbaaabbcdbcbdacbbbdcdcdbadbabbdbcabcdaabdbbbcabcbacadddcdabcddbdbbbdabdacbcbcdbbbbbcabdddadcddddbdadacabddbaadbcbdcdbddbcbdaaababdbbbdbabbcdacdaabcaacccdddbbacdcdccccbaccdddcdcdaabaddcdccbddbccbcadbacbcccbcbabdcdabccaadbddbdddcdcdcbbbddacdcbcacdaadaaccdacbccdccdcdcbcbcbbadcdabddbddbbdcdbabbdcccabbacddccaacccaddadadcbabdddabddbddacdacbacadbbbbacbbcbbbbcacdaadddddabbacdccbdddcabcabbbcbccaabbacdaccaddaacdacdbcdbccadbadcdcddaabdacbdccddaadbcadaaddbdadbcbadcbbcacaabaccbacddbdacdccdabdadccdacacbcacddcdcddacbbacdddcacbbddbcbdadaabdccdbcccbdadbbadbccbabbacacdddcacdaddacabcbccdadcbbbddcbcbccdcbcccbadbbbbdccbbabbcbcdbabbcabaadaabcabcdbaacbdbdabaaadddaadcaabbdbaadbbbaddcadbcdacbcddcaabacbddbadcdcddaccadbacadbaadacdabccdcdccbccccdabdcbcdccadbcacdbbcacaccbdddbacccaacccbccdabbbacbbcacbaaabdbdbaaaacdacccbaacabacaaadccbdbaabadacbabaaccccbdbaccadadaaaaccabdcdddbabcdbbbbdbabadcbdadbcbccdbaaaaccbdcdbbbbbacddcadabdacaacdddbcddbacbccbabbbcbccccaaabadcaabddbdccacaacaaabdcdadddbddababcadbdddcbaaccccabbbcdabcbcbccdcbcbdbabcdcdbcbdccccbcaccbbdddabdcadcbdbcbaaaabccadddaacccabbdababdbacdbdaadabbcaccabccaaadaddabdcaaccdbdbaccaabdaabacbbbdadcbabbcabaccadbdbadcccccbadbdcdaddcbaccbbdacadbcddcdcdccdbcbbaaaadbccbabbccdcadcbddaccadbcbdcdbbbdcbcdabdbbcbcacdccbbcdbdcdddbdaaaaccdabccaadcadbdccbaddcbbadbcaadbbbacbadcdbdbbbdcbbbbaddbbddbccadadbcdcadcbadccddacbccbbcdabababcabbabdacbbdcccbccbbddaccdbdccbbcbaaccccbccdcbcccdbddccaabbbdabccdcadbaacabaaabbddbdbbadabaabccbababdbbdbacdaccaddcccdbaccbcacbdcbccbcacbdabdabcdabdbddbdbcbcbadabbbbabcbacacbccddadacdaadcadaddaaacdaddbdbbbccddcbbddcddbdbbcdcbdbdcaabbdcbabbdcbbcaacdbbadbaaaaaadadbabdcdbacbabbbbcbddabadcdbdbbddbcdcbdccccccccbcabbdadcdbbddcddbcbadcaccddadabdabbcabdadcdcacaccdbdbccdaaccccbbbdbcaacabaaaabcbbcadacdcdcccbddbdcaddbcbbdbcabdacddcdaddcbbbcabdddacbdabcccdaccadbbbdcacdbdbabbabcbabddadbddabcbddaaddacddadbadbadacbabadadacacbdadacbdabadddcbabbabadaddcccddcdacbddcbadbbadaacbbcabacaabbbdddacdcbcadddaddadaadcbacaddacaddacadbcdbbbcabccdadcdcacdbacbdddccbdcbabbbdbdcaccbccdbcbaadcdcdadabdcdbcbcbabddbcaadcddbdacbdbbabbbcabbdcbdaabcaccbadabddcccbcbdddabaadbbdaacabadaacdcadcabdbcbacabaccccddaccabaddaadcabbbdaddddcdcabcabbbadbddabbabbdbdaabbcdaccbbaaaabbbdcdababcdcadaabdacbbbacdacdaddadccddcdacbbbdbbbcbcabaaaabacaadbbdcacdaadcacccadaccdcaacccbccdaccaaadadabbdbaacdcccccddaccbaaadcdbbbdcabcaacdbadbaacdaaacdaddcbcdabbdccabaacdbcbacabccdcdcbdaacabbbaddcaccbcadadbcdacdaccacbcbbabcbdbbacaaacbcbbaaccdacdcccdbdbcbaaaaadabbcabbadacddadcbcddcadbcbaabadbddcdbaddaadcaddcadcdbaacbadccaddcabbddaabacbbddccdcaabbdccaadaabaccbcacabdbcaaaddcbaddbccddadbbbdbbdcadacddacddaababcdabcbbcccaacbadabcacdaccbbbdccccccdbdbaaadcddbacabacabaddaabacddbccccaacdbdaabdcccbccdccacbadbbdcddbdabddabbddadaddbacaabadbacadadbcbabdadddcbcddbcbcbbcabadacbbccdbaabbbadbcdacbdcaacdcdcadabdbaddbbbbacaacccbcdccdcbaddadbcdbdacdacbcbcdccabdbaaddbcdcdaccbdadcabcdbadacacbdcaadbdccaaaabdddbbddccdaddbacaccdacbbcabdcddabaccbdcaaaabccbadbcdbddbcbbdadaadcdbbacdcccddacadcabadbdabbdaabbccdcdbabccaccccbccabbcdcacabbabcbdbcadcbddccdaaccadabccadabaacdccaabaabcdcadcacdcdacadccdddbbdbbbcacbaabadcbadccaaacbaddbcbbddccbacdaabaccddbdadcbbccdbcbababaaababdadbaacbcaacdcdaccbccbddcccbabbdadbcbcabdbcdabdcdbcabdacacaddaccbbdacdcccdcddddbaaacccbdcccdacdcabdbaddbbcaaccddaadaadaacbaccdadbddbdbcdbccdbaddbcaddbddbdacdaaaacdbaadadaabbdacdccabdcdbababbaababdddcdbcdcccbbddadabacabdaccbcccbcaacadbabdabbbdddcdcdcbcccddabadbccbcbadadadddbdbabbbaacbacbddabbddbbbadaaacdddbbcdcbcbacbdcaaabbbdcddddabdcaadccdcadccbddbcddaabdbadcdacdcabbddddacaabadadcddbcdbadcdbbbbbabdaabdcddcaabcacdacaccaacdbabddabbbaddacdacbcabcbaccbcddbbabbbbabdaabdcbadccaccbddcdabdddbaacdacdccdddcbbbdadacabbccddacdbdcddddccdabbdabcbdcaaadaccccdbbbdaaaddadbaccbbccbcacaacdaacbccbbadaacababbcdbddbbcccddacbdcdcbdcabbabdacaccbdbdcbdaadcacbcbbdcaacbdacccddbbbdadcdbbbabdddaabcddaacdabdbddabbccbbcbddacbddccdabccdbbcabdaaccddddcddbdabdabbaddbcdbacbbdaccdbbcabacdccaacabacadcccbccadbcdbdcdaaaadbdaccabcaaadbcdcdccdbcadbbabacadcdccbaaabcdacadadabccbddcdbddaadacbbabbddcbadbaacaccbbaadadcdbcbbbbcbbdbdaaacabdadcdbdadddccdbbaaaacaacbbaaddccaaaaaabcdddcaaddbbabcabbddccbdbbadddcadcbacbabdbcbcbdaddabcbacddaaccbdbabddaaabddccdcbabbdbaabbbccbcdcbdbdcbdcbbdcbddcbdaddddcddccddaccabcddaccbbdbbacdabbadbdabdabbabdcaabddcdcadcaaadbdcccacdbccbaadcadbaadbaaaacbabcdcbccdddaabbddadacdadddbdabadccbdcdddccbcbddadabccadcadccdbbcddacbbcbdcbdadbcdabccddbcbccdcdaabbddcaadaabaabccbcbccbbabdacbaddaadacacadcabdcdaccdabcacaaaccacddcccccddacabadcaacaabbccdbcbadadbcbccccccdcbbabacbadddddbbaccaabbacdbbbaccaccdbdbbabddabbcabdcaaabbdbcbacbdbaaaabdbaaacbbcbcbcabcbbcddddddacaacccbcdcbccbbdcbbdbbcbdcbcbadadddacdcdcbaadccacbdacbbbaabdcdbbbddbdabcaabadbcdababadabcaadccadbccabdcdbddacdcdccbbddcbacddcbcdcdaadddcccbabbbcadacdbdabddabccdbdbdbadbcbbacddcdbdcdacabacddaddbbbddcdccdbdbdbadcdcdaddbccdbaddbddadccbccdbbdbaacabcdbadbccbdacdcadcccdadcddcdcabddabdbdcadbdaabbddaddcaacaddbddbaababdbdacdaccbcbbbcacdbabcaddcdcdcbccabcccaacdbbcdbddbacdbcddbcbbcdcadcbddaddcdddbbacaacabbdaacacdaaddcccccbbcdabccacabcbbacadcccbddacbaadcadacddcdabbadbdacdddbbbbdddbccdddccddbcabcdabacbaaacadacdababddbdababacaacbabdbbaabdbaaadcaacccdcbdbddddbbcadadbbabbdccddcdadcdcacacacaacaccaacdbcdbabcabdddaaccabdbbaadcbdbaaaccdaaddacbbacaaddddaddabbdcbaccdbbacdbaddacabbbddaacddcadddcdbdacdaaadaaccbacbcacdccababdacaacbccbdddccdbcbabdcccbbbbcddbcdaaccbdddabcdcbdbacddaaccbbbaaddbbdadbacaadbaaadcbdbababcddcccaddcababcbdccbdcaadcbdbaccbadbcbcacddabcbbdbadcbcadcbcdbaadaacdddccbadcbdacaabdbacbcccbcbdbcacbdadcdbcdbdcccdaacabccddddbdbccdaacccadacdddaaddcdcbdbcdbcabbabbddcbdabbdbbacccaaaccaccacccccacbbbbdabcbaacddbbccbacbbbaadbbadaddbabaddaaacaabdbbabaabddaabaabcacbabcddadaccadbdbbadacacadbdcadababaaacaaccbbaadaadbccdcabdbdadcabdbbacddaddddabcddabcbbaaaabbdbbbcbabaaadacdcbcccdbdbcddbcacbdbadaccddbdbcaacddadcabddbbddaaaaacdaadcdcbaddaddbdbacbdabacabbadcaccddabdbcdcbcbbcaacdbcabbbcaddccacccccbdcdaacabdcdcabdddbbbdccdcabacbcaabbacbdcdbbacdadddadcbdbabdbbabbcdaccaabdbddcdbcbcadacabdadcdbbabddccaadbdddccaabcacddcbabbbbccbcdacdbaabcacdbddaadcbbbbdcaddbabacbaaaadaabaaccbbaaddabdbbbcbcbbcccdcddbccbdbccabbbaaabaadbaabdcabadcdaddbcacbbcabdaccdcbcbbbdaadbcaadaabdbbccbdcadaddcccaabbccdddcdabcccdadddbbbbbddaadaacacbaaaacabbdcbdddddbbadabcbdaaaccaddadcbadbacdaccbacdbbcbdccacddbdadcdcaccbbcadccbbbaacddccabacdacacdaaaddadbdabcdaababbadcdbbaadcdacaaddcdaccbbdbadcccbcbabcdbaacaacdcaabcccacdaddccccddbbacdccbbbacdbdadbbcbbbaaaacbcabddbbbcbdcbbccdbdbcaabcbabbabcaacbacdddaabbccccdbdccddadbadcddcdbcaadbabdccbdcdabdccadbbbbbabbcbacccaabbbcbcabddddbdbbbdaccacccdaadccacbcacaabbbaccdbcdddaddbbdccbdacdaacddabadddbcaddcbddcbbbbbadcaadbcddcccdbaabaaabbcddbccadbdccbccaaddadbaaabcddcddaacaabcdbadaccbcacddadddccbcbdaadaabbbcbaccbacadddddaadcccbcadcdcacbcccbddcccbdadccdccccaaaccddcbadadcbbaccaaccadacbbbbaddaddbbaaabdcbbcccaaaabadaaccddccbddddadcdcdabcdbaccddccadbabddbaaabbbbbadddcbdabbbcacdcccadacdbccaadaacabdcaacaacaabcbddbdddaddbaabbaccaaaadbbdcbcdccadccacbbdbcadbdaabcddadaabbacbdcaadcadddccbabcdddccdaabcbbdaadbcdaadcabadbcddbbbddcabaacddaccbddccbbddabdbcbcaabbaabdcddbdcbaccdbdbbabdddaabdcacbabaacddacbaccddadadaddadacdddbdbccacaccbabcbcdcddaddcdadadddcbadaddcbcabbadcadbadbdbadadcdabddcddadcdbdbdddaacbbbdbddaddcbabdadbbabbdccccdccadacadccbacddbcabadcdaaaabaabaacbacdadbdbaabaaadbbbbaadacacdddabcaaadccbadcbbaabbdcccaadcaabccbdbbcddbbccdaddbaabbcdcccaddcaadadcadabbbdccacdbacccdbbacddcdadcaaadbbaaaaccbbadddddaddcabcdbacaccaaabbccababcdbdccaacbbdbaabdaaabdbbcaadddaabbcddbbaacbcbcacccdbdcdbcacccadcdcdbbadcacdaddadbdbcdbddbbaacacdabcbbbaacdbabdabdcbadaadccddaadadbdddacacdbdbdcbccaacdcadabbdcacdaccacacbbcdadcaccdcabdcdaadccaacdddcabbaadbcddbbdcbcaaabcdbbaacaddabdbcccddccdbcdaadbdcddcabbcdbcbddcbcabaccacbaacadcabccbdbbbcbccdaadcbbadaacadcacbabacabdbcaddaddcabbacddabaddcdaadcccdbbddccabacbccccbacaccddbcbbbddbbdbdcbaaccaaacbcbabbaaaadcdadbbacacadbacdbcbcbcccabadbcccddbadabdbcdacabccababdadcacadcdccadccadbccbdbcddddbdbdbdbabaccccdadbdacdbadabbdaabcacddcdbbbddbcddbdcbdddcbabbdcbbcadacadbacbddbbbddaacadcdcdbaacadcabcbdadbddcbcdbabcdbccccdddddcbaadaadaabdbabcdbcbbcabdbdcbaabaadbdbaacbcabbbcdaccadacbccccacacdcaddddbadddacdbcbaaaaccbacaddcabbacbbbaabcccddbaaabbcdbbbabbabcbaaadcdbabaccccdbdabaadcdddbccdbbabdbcbbddaaddacbbbacdbdbcddccbbcbdaccdcdccaabbbddcdcabbcdabcabbaadbbdcaacbadacddbcdbbcdccacdabdccdcadbadbacaabcbbdabdbbbbbddbcacbcddcdabbcddacccaddddaacbcabbddabbbdadddadababcccdabbaabdacabdddaddcbdccbadcbbbbccbdbbbdbdcbdddbbbdcabaaddcccbbcdaabdbbbddaaaacacadadcdbcabdadadcacaddabacbddcdcabcddbaacddcbddcadbcdcdcaacacadddbadadaddcccadbddcdabdccddbdccbbacdbabbbccbccdcdcbbdabdabdcadacddbccdcadbbadddbababadcbabbaaadcbbdbacdaacddccaaaabcbabddabbaddbaabccbdaaacaccdbbaacdcbbbabacdcdcaaaddbbbaaaddcccabddbdddbcadaccdcbbdaddccaaacadbcbcdabcaaddcbcbaadbbcdaabbbdbddccbaccbabbcbbdaaccaadcbaddbbbaadbdbbdabdadbdacadabaddbbbddbdbdcbcdddcaadabaddaddcdccdccdbbbdccaaadbbdbdcadadbdbdaddabaabacddbcddbcdbadacddcbddacdbddcdcaaadccadcbbdcbcbccbcacbbbddcaccbdaacbdcaddbcabcbbbccdcaadaaababbcabcdcbddadadcaacbcbcdabaaadacbdbbdaaaccacdabcddaabcbbdbdcacabacaadcadaabbdbdbaaabaddddacccaccdbbacabcaacaabaccaccbddaacadadabbdaddadaabdcabbbbabcacdccdcdcdaadccddcbcaadcdaacaacccbcacdbaabaacddcbabaccddddbbbcabcddccddabbddaccdacdddbacdbaaccbaaabacccaccdbdbccabbdbbaadbcbbdbacacddaaccbdabaadcccabdbccccaaacbbacbababcadcdbcbbaadbaababbbbabdabadadccbdacbbbbcacccaabdcabdaddabdccbccbacabbacabacaacdaccadaacbdacaddadddabccccbcadacabddabdacababbdaaaaadbdaccdadbaaccbaacccacddcdaaaaddcdbddbabdcdbcdbaccddabadaacddacdbaaacbdaccccadcabbdbbbddbaccdabcbcabadbbcccbdbcdacacbdbacdcbabcbdadbcdddacccbacdacccadacabbddcadaacbdacbbbcabadbabbdaaababdccabbcbdbcccccdabcbbcbcdcbabdcdbaaddcabacbbbddbacdcadadbddcdcbcbadcacbdcbdbcadbddacacbbbcbdbabbbcbadbbacbcbacadbbabacbaccddcccdacbccdcccdaacacdcaccccddcaacadacccbabcdacdadaabcdccadbddaacaabdaacbbdbacabddbcdacabadbabdbccdddbcdbddbadcdbcaddddccbbbddbdbdabbdbcabddbcacbdbaacaccbbacddbaddcbcbaddabaadbbcbcbbabcbabddbbcbdbddadcbbbaabaacbbbbcbcbdacbdbbbbbadbbcddbacaacdabdaccbabadddaccaccdabbcbdddcbcbbcbbbcabdbcaaddbcbdbcacbbbdbdbdcababdbcdbddadddacdbadcbddaddcccbccdbddcbbadbbdddbaabaaabcddbabdadadcdddaacbbcdbcbbddddbaabadddcbbdabbbaacaabcacbdcbbbcdcbcdadacbabcdbbbccdcbdaacbcaaacccdddccbadcbcccdbddcbbdabcdaccadcbabdacdbddacbdddbcdccaadbbcbdbcddddcddcbbdaaadbaddbadadbaaacdcddddadacddacdbbbcdcbcabadadbaaacbabdbdcdabaccdaacabadddaacddacabdbcddabbbabbbcddddbdbdbbbcabaccdcddbddbccccddcbcabdadbbdcacdbdbdadabaadcbcdcddacbaccdaccdddbdcbcdbacbbccddbbbcaaabccdbcbdcabdaabcccdbcbbccbcaaaddbaadcabdcbccccdbbdbbbaaaddcbacddcabbacdaaabcbcdcccbccbcacbbddbaadcbcaaadddddbccadadccacbbbaabcccbbbbbbdcbaccdccbdbbccbbadcbcbaccddcaddccccddcadaabddbcdbdbcdabccacabbbddddcadbcacdbcbdbacaacbaaabddbbdddbcccadacaadaacacbbcbabdbabdacaaccaacddbaadcaaaddcbdabdcbbbdddbcdddaadddabacdbdadcaccbbbbcbaccadddbccccbccbddaccccacbbcdcddbabaccbccddcccdcaadcbbabdcbdcccdcdcbdccdbddcdcdcbddabdccbddcbccdbdacbbcbdabaacabacbbbbcbcbccccbabacabdaabddabddbaadbcdccbcadcdccbacbdacddcddddbcbcbcadbaccaacbbadaacbacdcbdadcdbbbabaacbaaaaccaaaabdaaaaccbcabdcbaccdabdadaacbbabaaaacdbadddcdaaccabdbbcbababbaccbbcbadbabddabadabcbbbaaacbbbddcddabddaddddabcadbdcdbddacccacccaaacbdaacdbcbbbcbbcacbbdcbdccbdabcacabcddbdaadadcbdddaabddacdddcddccbdddcaabcabbcaabaadcaadbcdcbbdbaadaacdabadacabcbbdcbdbabcbaccbaadbdabaccdbcdacbcbdaccaddbdaabaaccddaabbdadcdcdddccbadbababbbbbbcbaaaacddccaaacaddbabbddbabbaddbcacdddcbccababadabaacdbbbbdcacbdcccadbbdcddaccabbddbdbcbcdaccdcaccbcbabdbacccdbaccadacccadddadbaabacadbcabccabadaccddbabcbdbdbabbdacbcbbacaaabdaccdcdbcadccddbdaabcdccbadaaacacbdabbabbdababcaddbbcacdcbabbdddaadbbcaadababcadbbbccbdacabacbaacdcdcbaacbccabbbacaaddbcdbcccdabbcaaaddbdbabaaacdbbddccdadddccbddcbdbbcccbbcddbccdacccaabbcdbdbcdbbcacadbadcccabdcdbaabdcbcabcddbbcbccbdcdbbbdadbacaacaacdddcbcbbcbabddbcbdaadbdbdaabccbbdddbbaaabbadbdbdbadaacabcaaccbaccbdbbcdcabbabdadddbaaadcadabddbbddaaabcababdcdbbbdcdddcddccaddbadbddcdcaaaccacdadbabbbaadbbcadcccadbcccacadcdacadabddbdbabbacdcdcaadbcdbbdbdcbaddaacaccbdadddbccbbbacbcabbbcddcadabbbcdbccdcddddbcbadcccaaabadcddbadcacdddadbdbbbcdbccbcbabdcacbdccabddcbcbaabbcbbbdddddbdbdbdaacdddcacaccdaddaadcccbcabcadbdaccacdababdcbbbadbbcbbbcaaaadcbbbbaaacbcdcdcbadcdbaacdcdacbcadadcdaaacbbddabdddabddbcbbdaaacaccdddadbbbbbdbbadcddcbbbdaadcccbdbbcbaccbbcbbadcdcdadcccdacbadbcdbdadbbcddaabdcadadbbdccbdbcdcacbcacacbddddaabccdcbbddaccbdbdcbbdcabadadbacadbcbdaadbdcbcabbcdcbaccccdbcbdbbdbabbcaccaacabbabddbcdabcbcdcadbaadcaaababbcbdbcbadadcbccdacbdbdabaadadcddccbacdcaadcadbadcaddaabaccbdcabcdcbdadddabcdaddacccaaaddabbacdcbaccccaccbbcbabcdaccabcbaaacbdbdddccccbacabbadabaacabaabcadbddababbbcadcdaccabaccccdbdccdadbcaaadabcdbaadcbcdbbbcccbaadcddddaaddbaadbbcaddadabadbbabbddabdadbdcdbbadccbcaadacbdacddcccbcacabcdcdaadddaddccccbabaabdbdbbcacadbbdbaabbccbadbbdbadbcadaaacadcabbccbcaaadcbbbcdabcacabcdcacaddddacbdacabccbcacaabdbcbdbdcbccadaaacccbbcbbbcdaabdbdbccccbadcdadbbaaadcacaabddddbabadabdbcbcbbbdcbcdcbbabbaccbbaccbaabdabbcacdccbdbabdcbddabdbbdababccdddadcbadaddbdbbbabdcaabbadbcbdddadadbbaabaabbabacaccdbadcbacdbcccbbcbacacaccaacccdcddcdabdddcdcdacbcdcccaacbdcaadacddbddbdcbbdabacbdadacaaaddabbadcdaadbdcababdbbababaabbcddcdccbaaadccaabbcbdabcbccddddabdbacaaadccbcaabdadababdabacbcbacaacbdabcabddadcdadcadbbcdccbbcabcadbadadabbcbcbcabdcbbcbdacacbbadccbdaabdaabcbacddabdcbbcacdbcdcaadcddadaabbdaccbcbdbbaabbbbcaacbdbbbabbdcdadccddbbcbcbdacbbbacbbcadabdadcbcacccdbdadabcdbbdabcaaacbdcdcababdaabbddaadcacddbabbcacbbdcdaacccacdcacdbdacbaabbacdaacbbddccdacbacbcdbadaccbaacbbcbcddddaaabbbbdabdacadbbdbbdcadbaaaccdcdadbcabacbadadabcabdccbadbbccdcbdacdbdbcabadbccdbdababcbdabcdccadacadbaadddbbdaaaddcaadcbbdcaccbaccabcacbdcdbdbcccbcbdcbcbbbbacdcaadcaadbacabbabccddaddbaabacabdbccdaacdbbccaacabcdaacdabacbcaaaccadcaadcaddddcccddaccbcadbbddddaababdbbcddacbaacabababdbaccbadcadbabdacdbcabadabaccbdabccadcadabaacaadaabbbbbabccacabddabdbacaddccdcdabbcaadbdbdbcbcacaabbcddddcbcdbbdaabbdcaaacdbabdabdbccdcababaddcdbdabbccccabdadcadcbcddcbaabbddbbcddddaaabcaabbaacbccdabcdbababddcaacbbcbacdccddcdcbcabddcdabbdbbbabbcbabcbacadbdcbabacbcacdababcdacdcadcbcbcabdcbabcccaabbdbcdbdadcddcaacdcabdddbbdcaabbabbccabcadcacabaddcabaabadbbdaaabbdbdcacdacbbbbaaabdbcdcacaabddcabbdabacbdddcddcdaabbcadabdbaabbbadcbbcccdcacaddcaabaacbdabccacdbabdcaacadddccbcabccacbbbbbacdcbabdddbddbbaaacacaddddacabccbcaacddadbcccddddbdabbcdcadcdcabadcdbcddadcbaaabcaadaaaabacbdabbdaacbdaadcadbacaddabcbbababdadbdcaccbdacccccabaabcbccbdcdabcdabbcdbccbbbcacaddccddcbddaccaddaccdcdbadabcccabbbcbbbdadadacbdcaaacbacaaabccdcaaadbccaddacdbbaaacadcaacbadcadacccdcbbbcbcbbbdbcddcbaadddbaacdabbaadcddccaaabaaccdabadcbcdcccbabacddbcdcadadbddcadddcabcbababdaabbbcbcbcacabdbdddacdacaabaabacbbdbaabdbdbbcaccabcbaacadaabcddccbdcddccdacdbdbbdbcabacadaaababaabbcbdcdbaddbcaaccbddaadaaaabdabbaadacabddddbddbbcbcbbcabadbddabcdabacaabacbaadbbcdddbcdbdcadccdccbcacbcddaabdcbbaadcbaaaaacccdabdbdbcdcbbadcbddadadacbccccdbcbccddabdaabdbbdbacadbcbccbcdcaaaabaddadcabdcdcbadddccbbdbddbdabccdaaddbaaabdbabaccddddddadbadccdcdaabddcabbcbdcaabaaabccbdadbddadacddbdabbabdbcacdbcdccbddbacdccbbddbbdaabdcdbbdbdcbddaddbadcccbbdbaaacabcbbabadccbbadcadaaaabcaccabccaddabacaaaddbdbbcadbdadccbccabcdcbadbdaaabcccabbbadddcbbdcaadbcaaaccbdbdddbbbdccdbdbdddaacabcbbaddcadbaddbcadccdaacbcdbaaadabcaadccaaaaadadacccbbbcbcbacdbcbbdacddcdababccdbccdbbadcdacdbbccaadbddbbbaabccbcbbdcacbabcbbcbbcbcdcdaabaacdcadabdcdaddbddcbdbcadbcddacadacadcbcddbbcbadbbbbccababaacadddacbdcccbcaddcbaacdbabdbacaadbbddabaaacbcbbccbdbbbaaadbcbcabdddddadcadddcbaadacbdabccacccdddbbbcbacbbdcbcdcaacabadbacdbdbababdcdacbdcadbcbcaadadcacdaaacaadcaacdbcacddadbbaccdcdabbabbbabaaacacdbcdacdaaaadcccdccbddbdbadbbbcccccdcddbcbccccbdbcaabdbbacbcccdbadbdbcbacadcabaaaacbadaccdaaddbbccbdddcccddccbdbabbaaaacdbacbbbbdbbcabadabcdbadacddbabaaaabcbabaaadbababbbdccadbacacbadabbbdcccabcdbdadddcbacbadbbdccaaaaabcadbcdccacbbabdddbacdcdddaadcacddddbdcbdddacacaddddcbbacdcddbbddddcabcbbbbdadadcdddcdacbcbadddbcabbbbadaaaacccbabcacccbbcbabaadccdcbdbbabbbdbddccbbcddccaabdcdccdbacbccbcaddabddbbddbbbdcbbbdddbdcdadbaadaaaaaabacacdcadddbacaabadccbadbdcccddacbabdbdcdcdbcbbcaccbacdaaccbacadbabdcdddacbcbcababacacadccddadddbddaaaabddbdddddbdbdaddacbbdaddabdbcdccacabcacaaabdcadbcacdcadddbabaadadbdcabaaddbdcbdcaaadbabbcbbdadbccabdbdbcccdcdbbabbbccdbaaddabbacddaabaacabaddbbdbdaaadaacbadadadbbbcccdbdabcabbdbdabdbcccabaccaacbdadbccabbdcddacabcdaccdcccdadadabcaaabbabdcddcbbdaacabdaacbcdcdaacaaabaaabddbdcccbdabcbcabdcccadadcbaaaabadaabcdcdcccbacbcdddbabaadcbcacccbddbcddadabcbccacbcdbbcddddbbabbadcacdbaabaaddcacdadacbdbcabacabacaadcddddbcdddbbcdaabdcdcbcdbbccddadbdbcdbdddabddabbcaacdbdbdbddbcddabadbbbcdaabcacdddcaaaaddccbcbdccdbacaadaccdaabdabaccdabaabccccdbacacaccbbdccdbbdbbaabbdbcbdacbdadcbbaabacdabbbcdacdddddbdcaddbddaacaccabcabdddbaaccaddcadabbbdcabbadbdaaaddbbaabdababcacddddabcacadddccabadabdacbbddcbdabdbaabbcbccadbbccbbcbdcabddbcabdddcbdacbabbaccbddccccbccabcbdaccabddcbdddadadaaadddaddadbbadbbbbdaaaccbdbbddccaccdbbcbaabddcdccccbcacdcaccbbacbbbabdbacabbcbacacabddddbcbacaccaabbaaadbccbbcabbcccdddbdcbaabcddcdbaacdddbdccbdbddcdccbaddccabcaacacbcaddccbdcdcdabbbbbaaaadcbcadbaccadadcbacbbbcbbccdbacbbcdbdbccccccaadaadddccccabdadbdccdcdcdabbcbadccacbcdbbcbdaacdcbbacbbbcacabbddcbcdbbbbaacdaaabbddaaadcdbcdabbaabbaddccaaccccaccadbcacbcaadbccaabaaadbabcabdbdcdccdcccbacbcdadcccbccbdcabadbbdabaabccaabbdaccadaabbaddadddbdcccdacbcdbacdbbbcdbbaccabacacbbcddbadddcdbcbdbabbabcaacbabcbdbabcadacaaadabcaccadcaabcdaadbbdcbadddbccccdaacbcaadcddcccccdabdaadaddbacdddbcdbcaaddcabcbabdbdbaacdadadbcaddadbdbadacdcbbcbcaccbdabcdcddacbbdcbbbcddbdbbdcaadbdbdcdccdbcdcabdcbbabdcbddacdcdacbaddccbcdbdabaacacaabbadccbbbbccbbbcbacccadabacbccdabbdcdcdbadcddbdccaccabbbbcbbcaddddacdbaaccbcdbabcabadabbdabdddababdaadccbdaaabcdddaadaacccdcdbbaaaababbcbdcbdbcaaaaadabaccaccddbaacdabbbbdcbccdcdaaadbbdaccbcaabdaddbbbcdacaaaaacdbabcddccadacbcbabcdccddcdccccbcbacabcaddabdabadbcbddaddcbbccddbbcccaadbbdbbcbddcdcdbbadccbadabcbcadaacddcbddaadbaaaaadcbaacabaaabacdcacbacabadccaccaaadcbcdbbcbbdabcaccaabbcdacabadaacbadcadccbcdaccbcdbdadccadcbdcadccdccdaccdbdccacdabdabddaaaadbcdbccbbdcbccccccbdccdcdbcadabadcbcbabcdcdbaacddccbbcbcddaabacdbdabcbddcbcdbdbcccdcdccbcbccaacbadcdabdccaacaccbdbbcbcdcacbcdaabcadddacabdcaddddcaaadaababdaacbcdacadbbbacaaccadadbacdbacbdcdcccdcacdbbdaadcbacccdabdcccdbbccdddacdcaadaabdcaaacbcacdcabaacadbbbaaabdbadabdbadcacddbacdbcadcbdabbdadcddadcabaadbdcdbbbcdcccbababbacbabaabdacbcbbadbdcbdbabbdddcacdabdccbacdbaacbdadbccaacdaadccbccacdbdacbcbbbcdbbcabbaddadbcbdbbbabccaacadcaddbcbacdadadacbddcadabdacabababdaddccadcdabcdccaadacddcaacddbbbcaaaaadbabbbcaacbdabaabdbdaadddddddbcdcaadcababbcaacabcdabaacabadabaadabbaacabdccaadbaadaabdcabacdcaccaadbaddcdcacbcadabdcbcbcacaddcdbaabbadbdbccdadbbcacacbdcdbdbbadcccacdaaacccaaabbdbbaacdbccaadbdbbaacbbdaddcccdabaabaccadccadbcdcbbbcdcacdbbdcbacdbdddaddacacbccdbdccbacccbadaddbbbcadcbdacaacacddcdbbcdbccbcbbbcddacaccadddbbacaaabcddbacdcdaccabbbaabbdaabcdaaabcddbcaddcabdcbbbcddbdabcbbcbadccadadbadabacdbdabaaabcacacccadadbadddddcdaacbcbababdbacadcaadbdbcdddaddcdbcbddacacdadcccdabaddbddcacacbddabdcacbcdcaaaccdccdddbbacabccbddbbdddcbdadaabbbcdccaadbdcbdbabdccdaddccbcdacdccaaaaaadaacadddbccdbccdbcddccbbabcdabcbbabdcaacbadbcbcccbcdadccbdbdabbdcbbdddaddddcddbaabbccbabcccaacddcadbdcaccbbcbdadcdbabadbdacddbccabdcacdacbaaadbaddbdddcbdbaddcaabcaabbbbbbbbcadbabcddcaadbdabbcabcdabadcabbaccdbbbadccdddbbbaccadbdddcaacaccacdaacdbbbdcaacadccdabcddbadcccdbbbaaabdacaaacdabdaaabbbdbbdcadbabbccccddacdabadbcaddaddcbbcaaacabadacbadbcacdaddaccddcadbcbddddbcdababbbaddaccaccbbbaabbddabdbbbdacdbbdacdaaacbcdbdaccbdbbacbbaacabadcabcabddbcddcbbbdacaaacbadcdaadcadbdbddcaddcdacccaaabddcccabddbdcaabddaddbccadcdbdcbabacdabbbbddcdddacbcaacadadccbcccdabcdacabdcdddbccddbccacdbbbdabdbbddbbcadbbbdcbbddcadcbdcaaadaadbccbabaacacbdbdbaccddaddddcccbdbcbcdddaddcdcadccbbbcaacacdabbdcaaccaddaccadddbdcbccbbcbdbaabdabcddcacbdbccadbcdccbbbcdbcbacbdbbdadcbbbbdbdaabdccdaadaddddabddbcbcdbabdbaddbacadcccadbbbabdddcdbcbcbaaddaacabbaabcbbdaabacabadaccddccaccccbddbddaadbcbbaaadcdbbabcbdabaddcddcccaabaabbdbbabdcadbdabdabcacdadabdcabaabdccdaddababadcbacacdbdddadbdbcabaacdcacddabcabdbabbbdaabcdcaabbdaacdddbdacdacbcdddddacabdabaadacddbcccbbccdbdcddcabadcbbddbababddaacacdaabacaabdbbadccbcbdccdbacaabcdddcdbbdacbbbdaccdadacaddcbaccbbdbadcaaddaaaaacdcabbbdcaddcccabddbbbbcbdabbaccdbcbbddbdcbcddbdcabaaaabacaabbcdcdacbbbbcccadcbbabccdcbbabbcbadadaddddadcacabbcdbadadadbcddaccccaadbcbacddcbabadcdadddadbbdbacbacdadbddddaaddacddbdababdbbdddddbdaadccddbcdcaaabbcdccdbdddadadbccdacbddbdaaaabddccdcbaddddcaabaacadddcadcdbaacdccccacababddbcadcbcddabacbadcaacdabdbbdabacacbbacbcadbabccbbbaabacacbcbcacbbabbabaacbdabcdaacbbdbadcbdcaadddbcacacbadbacaddbadbcbaacbdacacbaddbbbaadaabcacacdacacadbcbcddaabdadddccaaaddbbbacddacbacbdaaabacdbbdcaccdabdbacaccbdddbdcaabbbcbddadccacdcaaccbadbbabcabaabdaacbaccbaddccbadccaddbadbbcdbddcbadbababdddcccbcaaccabbbdaacbbdaaddddcabaaadcaacaacccdcbcabbabccadcaaaddccbcbbcadaadcdbacaabbaccdbdcabaccdbcdacdcddabdabacdbddccddadbdcbcbcabbcddabcccabbddabbdcdcbdbddcbbcccdaccdadbbabdddbcbaadaaacacddbccaabaabddbbbaccddcbdccaccaddabddbddcacdccbcbbbbaabbcbddbcdbbcabcadacadababdbdabccbbacbcbcaaccacaacadbaabbdbcddcbccacdabdadbddaabcdaddccacdadacaadddccdbcccaacccdbbadcbccaabaddcccdcbdddcdbbaaadbbacaaabdcacdcdadcddddbbcbabadacbadcdbcbccacdbccdcbabdbdbddbdaaacabaacadbddbaccbcaccdabaaabbcbbaaabbcdcdaddbababacddadaaadadabaadaddbdbacdcaddbbdadcdaaaadaacbdcccddabcdbbbddddbabbcabbacbaadccbbbdddbcbcdbbadaddacadbdaaddcccaadbccbacbdddbcdbdacdccdddacacbcccbdaaaacadbcddbbadbcacaaddccbcbadabcdbdbbbcababcaabcdcdcbcbdaabbddddadbcaaddbdbadabdddabdbaabddcdbacdbcabadcdaaccdbbdcdddbdcbdcadcdbbddabdaaaabbdcabadacbbcdadddabacdbdcacbdaacdddcacbbabcabdcabdbbcababaddbaaccdabcbdcacacbbbdccccaabaadacdcdcddbaabbcdacacbcabbcdcbbddbbdccbbdacddccbbddbcbaacbdabcccadbadbacaaccdcbbdccbbdabccadaabdddcbcabcaabbcabcdcabaddacabaccbdabcadcdbddbadddaacbbbddbbbdcadbabbacdcabdccabdaabcbadbcaabbbabbdadaadbbacbcdadddbabacbbbbadcaadbbabccbbabacbcaaddcccccadbbacdcabbdcdaaadddaabcaddabdabcbababdcbcbcbbdbcbdcaddcababdcddacdabddddbbcadcaaaaacddaadadcaaccaaacbdaddaadaabdcccdbcdaccbcbdddcccbddbccdadbacdccbcdddbaacccdccaaaacaddabdcccacbaddddcdbbaccaccdcbcdaaadbddabcdbabdcadbccacbcbbdaabcabdadbadaabcccdcddaabbcdbddbbbbbbabbaacbaddabccdbbbdcaadbcadcdbacabccddacccccaacabcabbaccbbdabdcbbbadbbabccbaababccdccdbababbdddbaadbdbaaadbabcabdcadccdcacadacbacbdddbacabcaccbaaccbdcdcacdcabcdddacbccadbaadbcadcdcacaddddadcddbbdabcccacaccbcbcdaacbbccaadccdaddadddacadcabccaacdadbdddadabbaccbddbdcaaadddbddbcabaaaddadadcbaadcacbcdbadcdbcdcaabbccaacdccabbacacdadddcddddadccabcdddbaadbcdabbadaadbbaadabaaabdddaddcaaaaabbbadcaaacbcaabbdaaacdadadcadbbadaaadaacbdaadbdbccabddaddbaaaadadccccbbadadcdabccbcadcabbadcadcbbdbcdbaaadadbdddcdacbbdadbcbbaacacbdcabdcaabaadcbaaabbbcbaddadadadaabcaabcddddbdbbaabcdaccccadbbdaddadbbdacadcbbddacbdbbadacbbcabaaaaacaaddcdbbadbcaaccdbbcccadcabbcdddbbadcbbaacaaccdbdccbcccadcacbdaaadbaabddbcadbbbacbcbddbdacadbdbdbadbbdcadcbadcdbbadcdabaabdcbdcccbcacbadabbadcdddcbcbbcadbbbcdabbacdaaadbbcaaaaddacbbccdbbdaabdcbdacabddbbabaaabcadacaccdabdbddbcbbaccabddbbdbdcdcdbccbbcbcccbacbdbdccbacacdabbccacadabbadbaddcdaaacdbcbaddcbabcddbcaaadaccaadcdabdadcbbdbabbababaccbaadddbaabacdaaabcdbddbbdcdacdcdbcbdabdcdddcdbbbaaadbabddbbddadcadabdbbaccaacdccaadbabdaabcdaddcdbcddbbadaddcbaabacddabcaadcbabdbbabdcbdbacaadddcadaaaccdbabcadbdbbacbabdbbdcdbdaccbaabcbdbddbbacdbbdbadabcaaccbadcbacaaabbcbdcccbacaccbcadcbbcbddddcdcbbcdadaccccabcbccbbbacccbbbcbdaaccdbaaabaaaaaddaaccddbbdaaaaccbcbabababddacdbabdaaacbcdacbaccaadccccdcaaddddbaadacbbabcdadbbabcadbbcdccdbadcbaaacbadabaacdbddacacbbcdcaabaacbdbdbabbdcbbddbaabbabbbbdcccabacaccdcbcdcbdabcbdbbcbbcbabcddadbcddacbbcddabcbbdadbddcdaadabddbadddbbcddbcddaacbbacbbcadcbbabdbbabdccdbbddcbbcadaacbbbadbcabccbabdaaadcddcadcaccccacabdacacdccbbccdddddcbbbbaabbdcdccbaabaddaabbbcbbcccacbbddaaadbbabacacdaaaaacbdcccacbcbccbddbdbccaabdbddcddbdababcaadcccaddbddbccccbaaaabbddbdddbcaadabcbccaaadcbbadaaabddadabcddbddabbbdbcacbdadaddbbcbbbccaaadcdadbdbddaaddcbacbccadacccdcacdbcdbbdbcabbcdcdaacdadadbdcdaadcadbcddcdccaababdabbbabacbacdbacaabacabcdabcaacbbdaabdaabbcabaababdcadcaddacddadaadabcadcbccccddcbdadbcaacdbddbcaccaaacaadbaccabcdcadabcdacddcbacbcacdabcdbdbdcaaccbbacdbcdbdabdadcbcacdbcdcdcaabaaaddccccddaadaabbdbcbdcbacbaaccbaccaabdcaabbbcbcdadacddbcdddacddaccacbcdacdabbbbaabbabdbdcbdaccddbcadccdadccbaabcddabcdcdabaccabbaccbdcbaabbabbcaaacdaadbdddbbabcdcdcadccdcbbaabacdcaadaccccbbdaabbbbaabbdbaaadcdcdccbcacabaabdbacacbdabcabcdbbdcbccdccccbdcbbdcccddcbcdbaacdbdacdcaabbaaadbccaccbcbdbdbddacdacbbcdabbdabccabccdbbbabccbcdddcaacccdabbaddaccdbddbdaadaadabdcccadbcdabdbccdcbbdddddcdaabbbcddcdcbacbaaacaabaadcbddcabacdbbbbabacbbccddcdaabcbbcaadadbdbdaacadaadddcbaabbddccbbcbbcdcbccbdbacdcdbbcbaaaaabbcbbacdabbdbbbbdbddbbdccdcaadcaddcdadabdbbdbabaabdacabbccbcccadbbbddcaadbabcabccddbaacdabadbdadbcaddbcdabdbcbdddbacddcdbadbdcddcddcdacdbddaaabddadbdbddbbbbbcbaadccdcbbbbadbcabadacaddbbddabaadcbaabcdcbcadbbddcbaadbddbbcbcbdbdddabccaadabdaaaaabbacacbaabcbcbacadbcabaaaacdddbcbcbbccdabaddaababbbddcbbdabcdcddcaddcbababadcdbdbccccbddabbbadcbddcddcacadccdbcbdcadddcdccbacddbcccaccaccabadacaddaabddbdbabcaccbadccacabdabcadcbabbadbcddabdddadaddcdcdaacdadcacbcacbbdbdadcbdcdccccbdaadcabadcaddbdbbacdbbabccccbdcddcbaabaccadadcbbbdadbababbcbaccdbcbabcdabaadaadddadbabdbaadbddcdadabbcbaabbcdcadcadabdaadabdbadcbbcabbccbabdcbdddabdacacbabaaddaacaadcdbbbbccdbcacadbbcbdbbcaacdcaaccdadcbaacadbaadabcccdddbacaaacdbdbbddddbddabbcacdabdaaaabcccdaabbdcaadabbaabccabaaadbdabccbdbddcaadccddaddccdbbccdacbdbcbadbcbdaaddcccacadaaacabbaacbacdbdabbcaabcacbcaabacbcddbdcbbdaabdabddbaddbbadcacbcdcadcbccbcaabbdccaadaabcddaaccaacdccddabbbaacccbadcaabcbcdabbbaddccbaccbbdcbcbcdcdabddacccabacbbddcacdcdcdadbabccdaadacbddcbbbdaaaadcacdcaccacbacacacbcdacdaadaaddaccababcbcbdadaccbdcbcaabaadadbddaacbaaccbabcddbbbbdcdabccbabdbddacbacacbbcbcbbaadabccdbbcadccbbbdbcdaabdbdccbadddaadbadcdabbcdabcdcabdcddbadcccbbbbddcbddbddabbabbcbaddcbcaaadbccabdcadcbabacabccadcbbbcbacbadcacadbddaabbadadbbcdbdbdbdbbaaacdcccbcbdccdbbbaaabbcbddcadbdacadbccccbcddccbdbdcabbbaacbcbcaccddbddcbcdbbcccbbdabcbbcbbdaaababbaaadabdaabbcbaaccdacdadacaacdabbaadabdbcbcababccbbdcabdbcbdbadddbbaadbbcbbaaacadbcddacbabdaaabccaddbcdccdacadbbaacdaacdcabbcacadccbcccabcaadbdbabbdcdbbbdcadaabdabaddbbacdbdcacaccdbdbbadcbbaaaacbacbddadddabbbadadbaaddddcdaadcdbcacaddbdaccddcabbabdcdddccbadbcbbcbbbbbbcbcccdadcbdbccbaabbcbcbbbdddbacddcccdccabcbabaaddaaccbccaaaabdbbdbbbabbdaddcbcbdcddcbbdaccbdabbddcbcccccacbbcddacaaccacaabaabddabdbccdcbbdcbabbdabbcbadaddaddbaacdccdbaddbdaacbcdacdacdaddacccadcbadabbadbabcbbabbcaccbdbbdcdacabdbacadbbbdaddaaaaccccccddddbcbbdbcabbaaabbbbadbaccccabbcaaadbbbabadaccdbdcdcbbbdbbbaddbddbcdadcacbaacdbdddacaccdaadcbcdcdbbdbaaabdccbddddbcbbccdcabcabbccbcacbbdddbdabbbdcdbaddbbaddabcdbcadcadbdacaadbdabcbbbbcadaabbbabcbdbcaaacabbbbddabbccbcacdadbadbdbcabcdbbadadaadbccacbabbaadbbbbccccabadcacbbcdbbdbcbdbdcddcabcdbddbadabbdacccacabdbbddaaadacbcadcddddccacaabadcbbbbcaaddaddbbdddcbcaadadbbbcaddcddcdbadcbcadcbccccbbcbccabbdbdaacbcdcbcbacbacdcaaabbdbbbddbbacbbabbcdccddbdaacbcdddbdbbadbbcabdcaacccbddcacdadcadbbbbbddccccacdabccbcbdbaddcddaccbdabdcbcdddabacdbdbadaaddbddabdaaaaaadacacadaabdccdccadabacddcacaadbcabbaaccaadbbacbcdcacbacbcdaddccbbbdddccbdabccccaddbcbaccaaddbbdcbdadccbcdcbdccbbdcadbbcaacbddbcabccaaadccdacbacbcdbdaadbcaaacacbbdacccbadbcaacdaccbbcaaabacaabdddbbbaddcababbdbdbcdccbdabcdccddddcbbcdcdddaaaacbcdcbcdddcaccdaccccdbcdcdbacddccbbcabaaabaddcdadbcdbcbbcbdccdbabccbaabccbacbacaaddddbaadbcadabdbdccabdbacbbdcadbdddadadccccbadccdccddbdbadddcdcbddcdcadcbccdaaccbacbcadccdaccccdacadbcdccdbaaddbdacabddcbddabcbcbadcbcdcccaadaaacdabacadbbcddabbcabdaabbdbdbcbbabddcacbabdcaccadbabcadcdacddabbaddbbbbcadbdacdcbcaaaaaadddabaaadddcababdbabadcadacdbababbabcbbbbcdcdcdcacccbaabccbbdcaacbbdaaaabbaadabbbbbccdaadcadcadacababcccaccaacabdcaadadabdbdaabcaccacdaacbcbdcbdbdbabcadcaabcabbcbcaddcdbdadbcadcccdbdcaccaaaacdadbdcaabcddbdcbcddcbddccaabdccdbbcaddbcddabbbcccadccacdccacdbabccdbaadbdbbcdacbaacbcbaabbbbccaabcadaadbcbddcdaacccbcdbcdcbdbdacdddcaccadcdcacdcdbaadadabdcdbbdcacacacdddcacdcabdaddbdbabbdbadadcddaadddacaacbadccbadcbacadcbadadaddacaacdcadbcabaacccabadabdddcbbaadbbacabcbbdabbcbddacddaacaacccaddbdaadacdbdbdbccbdbbdaacddddaddbcbadaddcdbccbbddddcdcdcacdaddcbbdcddbdadbcbdacdadbaacbdabcdbabccbbaddabcacbdbabcdcdcdddcabcddabccdcacadbcdcddddbcadbacacbdcdacabdbbbcbabdacbabcbcabdacccbacddddbdaaccdbbdabcaabababbddcbdbabcacdadbadaaabcdbbdccdbccdcdccacddcbaccdabcbacacbbcdbadaacbbaaccbaccababbbcccdbccddaaaabbacdbaabccbdbdbdcdabbadaabddcabacdbbababbddcdcabddbaddadcdbddcaccdcadaadbcaaabccaaccacdbbaccdabaaacddcddadcacacacadcbdaccbddadaaaabadabccaccdccbccdcadaaaccbaccddcbdacbabcccbcbcdbddbbbbccaaabccadcbdadbdaabcabcbbbbbcaaaabbcdbbbddadabacabdbddacacdaaacdccddabbcaddcdcaccaabcbcccdcacbdccacacddacddaddccddccdbbbbabbccbcabcbbccabaaaadbabcacaccbaaaddaacdbbdaccdbcabddbcdbdaccbaabbbaababcbcdbaaacdbcaaadaadccadbbcacbdbaddbbcacadadabdaaccbdbadadcaadadbbcabccbacbadcccccadbcbbbdcaabbbbbccddddacbddcddaadabddadccadaccdccabbadbadcabcccdacabdbdddccdbcccabacbabcadabcbabbdaddabacacaabdadddabcddbaccabcacddcbcabbcbaabdbccbabdabdcadccddcadbbcbbabbacbdcbbcdcdaddacbbdbcaddcbcaacbbcbcdcdbdabbbbacbbabcbbabacadddbbccddcdcbadcddbdcbbadcbadabcbddadcbbadaddddcdccbbacccacbbbbbdaaaadbddadaddacbdabdaaabdaadbbdaacddcababbcdbadcdbbcbcdabbcbabdacbdbacaabbdbbdbddadacbddadcdabcadbdcdaacdacbcbdccdbdbbcbcbaaaadadabdcbbabbccabbbdddcbcbbbacbdddacbbadccdaddaabcdbbddacccbacbaaabccbbabbbcacadaadcaabbdcbbaddbacddaccccddabdaabaadddddbcbbcbadaddcaaccbbcbcbacacabdcccccaabaccdacaabcdbbdacaaddadcadcbbcdddabbbacadcbbdddadacaabcccdbbadbdbdbddbbdcaacdbcbbcddcdcaccadcccbddadadddbcbaadcacbadddabdaaabadccbccdcddabcdbbcbcdaddacaabbadabaaadabbbcbaddcbabaadaddaacbabbdcacbabbdbbcbdacbcacbbadcdccaccdcdccbcdddccbbbdbacdcadbbdbdabcccdaaaccbacbdacbbdcaacbcbdbacdcacaadaadaabaadddccbbbbacacdacccbbbaaaaddbbccdcbadbabadcaaabddbbdcaabdabcbcddaadccadbabbacdaacdcdaabbcdcaddbacaddcccbbadaaccabdbadaaccbdcaaadcddcacaccabdadddbabbbabcbccdbcbdbacaadaaaacaaacaddbdadbaddccbdacabdcababcaddbaddcbbbdcccaaacddcbbabaaccdbdbccbccdcaadbdaadcbdcddcacdacbdcdcccdbabdcadcadbdccaacbbcadcbbabcaaadabaddcbbdcbdcabacdaacbbcacabcdddbcdddcbdddbbddddcbcddcacdacdaaccabdadaacadabdaddcbcabcadbcaddbbcbabbabdacdaaaccdcacadcaacdcbccadcadbaccdcbbcdcdbcadccabdccacaddacabcdbccbcbaacbbabaacdbabcbbbccddddadcbbbbdadbccddddcbcdcdababddbcdcddcdabbcbcdbabcddbabbdccaacbdabbbacbdcabcdcbbcdadbbbbdbdbaccccdabddadbdddaacabccbadacbdcaadcdabcbbaaaddbcccddacabacdaacdaababbccbaacaadbddcabdacadbbbabdbdcdcadbdcdbcddccdcccabcacaccacaadbbddddaaabdabdccbbdcabcbbdacbcbbccdbdbcbcaabbdababbaccaaaaccdaadaaaddcbdcddbdaaaacbcbabdabaaaaadcacaabacaccbaabdccdaddddadbbccbbdddcbdbaabbaaacbbbabacaaddbcdaccadbcaadabcbaccdabbddbcccdcdbbbbbccabdccbdadcdbbccabcbadcaadccadacbbdcdcadbcaadcddadcabacdddbbbcdabdcbccdbbcbcccdddaaabbbacadcbddbdcbdbbbbdbcbadabadcbacaabcdddddabbbbaddaacadbdcaaabdcccbbcadaabdacdbcbaababdcdbdbadacccacadaabbcadcccdacbabbaacddbbbaaacaddaabcbacadbabbabaddbaacabdbcdabdcdccaabddccbcbbacabccaadabdbaadbbacdddcdbaadadddadbdddddaabbadadcdabaddccbdcdbacdadbcbbdabdaaddcbdbadbdaccbbbcdacacadadddcaacbcabcdabbccacdddabcabaaabbcdcabaabbdcdaabacdaaababbdababcacbbbaaddcacacdacbabbacddcbcbabacaccadbdadcbdccdbdacbccadcdcbdcdccccaaadbddacccccacbcddabacbacddbaadacadcccabbaadbcdcdcbdbadadbbacdcccddabbbcacddabcdcddccababbbbdcaaccdbacbcbdcdbbbcbcbbdabdbcbbbccaabdaabbbbcaabcbdcdacbdddabdacabaadaadcbbcaaabdbccdbabccdbbbacbbacbcaadbcdddbabaaccacabaaccaaccbbdadbbababaaccdcaaddaddcaacccbdbdddbbccddbaacabababcaabbddabaccbdcbbdabadaaaccbcbcccbbccacacdcdbbaccdadbdcbbcccaddadaaaacdcbbbcacdcccaadaddddbbdbadccdbccbbdadbcbbdbcccdabbccadaccbdcdcbcccabdacacdacbcbddaadbcbaadcddacdabddadcbcdcadabccbcbddadbdaadadaabdbcbddbccdadbabaaacbcdddbdadacddbadbbdaabcabdaadaadcddadaddabcdcbcddacdbccdabccbdbaabdcaccbdaaccbabacacaaccdcadaabcbadbdbcaaddadbdbbdcbaabbccdacadbcabaabbbdaccabcbbcbabcacccbbccadbbbbdbddbbaddbbacadadbcacccdcbbbacbbcaaadcbcaaaabddadcaaaacdbacdbcccacccdcadabbaadadabcbaaabbcbabaacbcadabaacccabbadcdadadaaacaadbbdcaddbabcbcccbbdcbccdaaaabdcabcdccbdabcbadbadacaccdcdbcdbbdbbdadadabcbdabaabdbccbcdcaacdcacdbdaabdbdbbaacbaacaaccdbabdbcaddcbbbaacccbdacadcbadbdacbcccddcbccbbccacdcddcabcddccadcabaddcdccbbacccaaccacbaaabcbcbcbbbbacdbcababbdcabaadbbbdbadcabbbdadcdbcaaaaaccbbadbcbcacdcbbadbacdbadbacaddddcadbbcaabdddcbdbaaadbacdcaadbacbcaabccccadcbdaddbabdbadababbdadccbbccabbbccaccddaabdbbbacbdbccccdbadaabdccbbddcbccadbaadbbbdbddacbccbcbcaabccdcccbddcdbdbcddcdcaabdcddbbcdabaddcdacccdaacdcbcadcbddaccaaabdddcdcacacaccacbcdcaacacdbbdbccddaaabcddcbdcdcbcbadccbcdbbcdddbddbacbcadaacbbadadbbccdaaaadaccbdddacbcadadccdaddbacadbdcdadcacdabccdbbabcbaacadaababbbdcdacbbbaddcaaddbcbbcaaadadbbcabadbcbdccbdcbccaacbbbcaddbcaaddccabdcacbcbaaadbaddbbcbbaddbadbdbbacbddaddabcaacbcdbbcaacbbdbdcdcababacaabacccbbbbddbcdbddccddaabbcdaddccabcaaacdcddbbdabcbacbaddccdaabdcdbbdddcbadaaccdbdadbccdccddcabcbcdccbcacabbaaadcadcbacaccbddcdbabacdbddbadcbdbaccacdcbbcbdddbdbccccdcdcccdaabdcdabacacacccccaaddcddbddadbbbccaadccaaacddbcacccdadbdabacbcdacbbcaaadadcabacdbcadddbbdbcaabdbadcbcccaadbdbdbcabdcadaaabdbdadbabacdbccbccdddcacaadacdacdddcbddcdbdcbacdbaaccaccabaabdccabadacacbccadabbcaddcabadbdabbcbbbacbcdaacdacddccdbcbacabdaadddbdaacaaacdcadaaddbcbbdbcbdcadbcbbdddaddbbbcacdbcaccdacdcbdbcbaccacdbbdbbdbccbdbacdbbbbcaadbbdcaddaabcdabbaddcbbcacacdabaaddabdcbbbbccaccadbabcdbbbbbcbccdaabcdccccacdabdcbddabcdddcbdaadccacdbccadaaabcbaddbdabcdddadabadacaabcbddcabdcaddccadbcccdadaaaccbbdccdcdcbcddcbadacbcdaacbdbbbcbdcccadcbddaabccaabacadccddadadbaaddaacadddbccacbcdacdddbccbdccbabdabcbaddaadabbcdbacddbdbcddcaddaccdbababdacaaccccbdbdddcacbcdbcbbccacdacabaaaccbabcbccdadcbaccaccbbdcababcbadcbdcdccabcbdbcccdcdbcbdcddbdacbdcaabcbacddbbbcdccaabddbdcbbdddccdddcdddaabcadbbabbdabaabbddccabcdacdcdcaabdcacabddcbadabadbdaaadcbdcaaaabacdacbaadcdcaaabdbbcddabdbbaabbccdbbcdbbadcacbdccbdcbbcddcbcdccdccbacbaccdcccccccdcbcadabcbdbacababbcdcbabdadcdaabacdbdbcccbcbacaccbccbababdbbdbcbacacaddbbdadcdadddcadbbcdddabaacbaaddadadabacacaadabdbdbdcaadbcdaaaaabddaabacacadcddcaaabdaadbabacdccadacdbbbbcbadcdbdbdabaaaacdaabcacbbadaadadacadaaabcdaacbbaadbdadcbcbbbaccabadbbadccdacdccbadcbcadbbcbbccdcadaabdbcbcbacbdbbaaadbbcaddbdbcbbcaddaaacccdcddbdbdabdcacdaddacdddcbcbcadccaccdcbbddacbcbccbddddcacbdabbbddddbadaadbcdaccddbadbabacbacbddccccdcdcacdcdbabaaadcbdbbddddbcdcacadaacbcdabadbcacacaacabdadaaddbadacddacdbcaccbddcbbaddabcdaaccdcaddcacacbcbcabcddcbcdcabbdacdabddcdbdbbcabcbddaaddcbabcdbcbadadddaaacabdaddabadcdcabdcadacbbddbdabdcbcddaccdbcbdcccdcaccacdadadbdcaacbbabaaaaabcbacbaabcdaccdbbbdbaddcbdadcdcdbbddbdbadcbabbcdaddbdadbddbbabcabbdaccbddcbaacbcbcdcccddbcdcddbdbaddbcdbcccacbadbdabbbbadcaabacbabaabcddacbbdaddddaacccbadccdbcddcddbcabaabbcabccbbbbaaaaabcadadabbddaabadbacdaacaabdcdadaddbbdbdddabadbcbabddadbbbdccccabbacbadcdbabdaddabaabcbddcbaddddadbacbbacbdcbcdaadccdbbaabccdadaccabacabdabcaddbaccdadddaaccbdacbabddaabdcdadcccdbbccdaacaaacdbbaacdbcaadcbdadcaacbccacbbadcaccaacbaacdadaaccbaccbadbbaccddcddcddbddaaaccbabbbaadcaaacdadcabcbadbdaddbdaaabbbacbccbcdccacbdcccdcccdbadbbcccdcbcaabaccadbcadadcabdacaaaadddddcaacaccddabcaddbbdddcbbadddcbdbadadcdbbbdacaadbacbaabccbcaccddbadccabdbbbbadcddabbcddddcabbcddddadabcddccbdacbdbdcacddacdadadccaabacbbbcabbbdaaaccddcddbcacddaacbddccadcadcdaacbcabadddacbbadadaacddcbabbcccdaababdbadbcabbcadacbddabdadbcccabbaaacbadcaaddaaacdcadabdbadadbdcbbdddddaabbbdccddcadbcabcaacbdcbccdcacbdbbcdbdcddcdcadacccabbbabccadaabcdbbccddcbbadaaaacdbcccdbcbcddcbbbabcdcabadadbadbddbccacdadbbaabbabcabcababbadcbdaaacdabddbbdbabacabadcabacadaabbaacdaddabbbdbacbccadcbcadcbdcdbdbdbaccbbcadcdaabbaaaaaaaacabaaabdcbbbabcbdbbcabcabcbbcadbccbdbadabbababbaccbcdbdabcbaabacadadbddaabcdbacaddccbbccdddbdacabcbcdacddbcdcadcdbdddaaacdbbcbdccdbadbbaadabdaadcbbcdccdbccccaacaaabdbddaccddcababcdcbaaaaacbabacacccbabcdcaadbabcdddbddcdbcaabcdbbdbadbaadddabcdbbdbccbbdbabdbbdabcacaaaddddcaabdacadbbacdbdaabcabacababdcdcbdbccbdbbaabddddcdaadccdcaccbdcddabbabdddadbccbbbadbcbdbbbccaadadaccadbdbbbacabbcbccaccbabbbbbccaaabaccabcacbccdcaadacdbcaacdadcddbaaaacacabccbccaacbabbaddcbbcccbddabdcbabcbdbacabcbcddadacddddbdacddacabaadddaababaadbbabbbdadbccadbadbbddbcbdadbdddbbbbabdacaddacadaccbaccbcabacdcbcbddbaaacccbbcdcccadabbababacddcadbdcbbacadbcccbacdbadbcdbcdbbbbbbdadbcddacccdccbcadcabcaabbdbbddbcbcaccbbdaacadcccbbddcabbcbacadaaadacddacbbdcdabbdcccccaadbcbaaaaaabaccdddbbccbdabcbcddcdaadbbaaabbaabcacdcbddbadaccdcbaabbbacbcbcaaccddadcbabababbcccdccabcccbadccacbbbaacdaaadddcddddbcaddbbbbbccbcbaadcbdacacbdbbcdbacddcaacadaadccddcddcbaccaccabddbacaabccdcaadccbdadcdbccadbccddcbbbaccddbdabaccaaabdcbcbdabcbbcddadcabaacaacbbdadbacbbbacdcbdbcccdadadbabbddbddbbcabbcbdadaabcabcbdbdaccdbbbcbabdddadaabbbdcaabbbcdcddbddcdadcdcddaabccbccabdabdadaaddddaaddacaccbcacabdbbbccbddcabacacbbddbcbdddbdccbadacdadcdabaababacdbccbbdbdcbabbbadcbadadccdbcbccbdbdcdcbcacbabcbbdcbccbbcddbddddaccbaacbdacbddbdcacdbadbbacbdbcdaabbabdcacdaadaddaccdcbcadabadcbabbdddcccddabcadbdaccddcacacddddadbcdbdcabbaccdbaadcdbccdabccbdcdbaccbddbddcadcbcdabdddbcdcdbbbbadbcadacbcbdabcbbabaabddbadaacadcdcabbddbdccabcbcabacdbddacaaaacbbddccdadacccabbdbbaacdbdbabacbcccadcdbcdcbdaabdacaababccacdaaadaabdcbdccababbcabbddbdacadddccaccdaadcacbcbbdcbbaaacbdbdaccabaaadcddccdaccdbbdbaacdbdaaaadaadbcaacdbccddbbacddbbddcddabcbabdadbbdadbbbcacbabbcababacdacddbbdadbbdaddbcccbddddabcabacccaacdbbdbbcbcbdadadbbddadddaabcadbdccddcaacbcacbacaaddaccdccbdcdbdcccdaaabaacaabcaadccbdbbdddccddbdabbcdcdadcbbcaabbbccaabbbbbaaaaacbaccaccbcbabdcbdadabaabaaadaccacbacdbbccdbbcdabcdaddadaacdaabbcbdbdddabdbcdacabddbaddbcdcbadaabcdbcbcdcbaddbabbaaaaccabbddcdcdbbcdadcbbcbbdacbdcbbdccdbdccdbbbcbadbcadcdcdacaddddacbbcdccaccadadcdabbabaccaaacadcbbcbdbbcacdcbbcdbcabdddadacbddadaacbabbcabddabdcbabccddabdcbbdddabcbadbdbbcaaccabadbcaabacddcabbcadaaccadbacccacbaaaadcacbcaacabcdabcbbddcdddcbababbbdbbbbacabdaadbccdcbabbcabcacaccddcdaddacadbcccbbbdbacbaadcbcadabcbdddacccaddcbabbbdcdcbccacbcabddbaabaccccbabbbdaddbadaaadbadcadbbbaddccdcbbabcdaaaadaacdacbccabaddbcaacbaadbbbccadbddadbdbbbbccdbdbbbbbcbdcdcdcadbdccbcdbaacdddddcddcadccacddcadbdaadcdbdadbdbacdbcbcdcbbaacddbdacbddacbbbdcbbdaaccacadbadababcadcaaabdbabcabcababdddbbddbabbcabaaddbccacdababadabaabaccbccccaaaacadbdcadddccccbcdddddbbcbccbbbccadaaccdaacdcbdaadccbbccbdbbcbdadbdbacdcdcbdcaaccddcbacadbaddccaabaaccccbaaaabcddbcbbbdabcabdcdcaccdacddadbacaadbdcdadcbabbcbcadcbbdacdbaccadadcaaccddddabcbbdaaadccccaddcaddbaadabbdcbdcaddbadbcabcccddddacbcabaaccdacaacccacaaddbccccdbacaadddbaaaabdbccacbbcccacdcdabcacbccadabcacbdbbcaadacdcbbdbbbcadcbcbdababbccadcdacdbcdddadcdddbdcbabacabababcaacdcabadcabcbcccdcabacbddcbbbbaaadcbbabacddbcbdadcbcbaaacbbabddabdbadcabcaabacccdcaaddabccdacbcbabaaababddabbbbbdcbbdbbaccdacaccccbbccaddddcaabaddababbbacbabaaadabbacccbabaabaadaabbadaabcdabccddbdcdddbcddccbdcbacbbcbabbddcccdbabadcbccdcaaccdddcbaddbababcbabbdcdcdcdbacdccaacabdcbabcbdbcadcbabaababbccabbaacbbdcaacbaabbcadabbdadddaabdbbdbadacaccabccadbddaabbabdadcdcdaaaababdabdcaaacdbaccbbabaccabccdaaabcaabbaadaadccdbcacbcbccacacaddadbbbcbdcbddbdbddacdcaccbaaacccdbbaabdcacbdbaddddbbabdacaadbbbbadbabbdacabcddbadabcdcdbdcdcabcbcbddadbacbabbdaadacdcddabddbdcddbdacabddddddcbabdbcddbdabcdcbcbdddbdbcabbcbccddddabbcddadadadadcdcaacdcadddddabdccadcaccacdbbdacccdddbaaabdcdcadcdcddbdbdacdbbdbcdcaddcdcccddaaabccbabbdcccbbaadcacbccdccabcacadbccbbdddbdbbaddddaadbbcbdcacdadbbbcbddddbdccbabcacbddcbdcbaacbdadaddbadbcadaaaddacacccabcdbdbdaadcdbbbaacbbaaaddbdcdccadbbcaaaaaaddadcaccacaddcdcaccdddbcabdcdcacccaaccbdbbdccddbbaabaccabadccccbdbbadaadaddabaacccdbcdcacddddaadaabdcbdbdcacaccdddabcabbdbbbcbccbcabdaadabdccbcbcdadbcacdcdbdacaaacdaacbcbccadbadcbddcaddaddcaaddbbcacdacccdaacdadbbdbccbdcaadcbccdbadbaadcbdabdddbaaabdbadcbbcbccddbaaaccadadadddbdddbdaaabdcdcadddadababdabdcbddcdbaacdbdbacdccbbdaacbbdbcbcbdbccbccbccaaaaaadccbaacaaadacabcdababbaadbdaddadadcaaabbdabcaaaaddaabcddabcadababacabaccddcbcbaccbdaaccdbccbaaacdaacacaabbcbbdbacbadbdbdddaaccbabbbcdcbbacdadddbdadcaacabdcbdbdadbbadddadddadbadcabcabcdcbdbddbcdacbcdddcacdbddcbabdbbbcbbabdcdcdadbdccbdbccdcbcbacbdbabaacdcadacaaacaaacdabdccdbdcdbddcadcbaaddccbbcaddabbdaabaaccbbabcabdbdbbababccaaccabcbaacadaabddaddbcdcdcbbbbbbaddadbbacbadabcbdbdacbcdcdcaddadcdcbbccbabaacacdbadbaadaaabbabdcaacaaaccbaabbbdddabccccaabcdcbdbcdbccadbadcdbbadbccacccddacdcbdcabadadcbdabacccabdaabbdcabdbbbabbdddbacbcbdbabdcccadbccacabdddbccabbbacbdabcabbaaadcbddddcbabdcbcccabbbdadabadbaabccdccdbdabacadbdabdaacbbaaacbbcaadccaacadaabcccccbccdaddddcabdbdacbdaccdbccbbcbdbcacaddbdadabcbcbadddcdaddbccadbcccddcdddcbdbdbadbbddbcbcdbbaadcacbbbacacdcabddcbdcdbbbcbddcbddcbcaadbdabaaababbadcbccccccbbbcbcbbcaaababacdcdbbacbacdddcddbddcaacbdacbbbaccbcbddacdbddaaacaaadccdcdaaddabbaabaaddddaadbcbccabdadcaccabbcabbabbbaaabacccdbddcdbcdaddadcdcaccbdaadddadabbbdaddadcaacdcadcdcbaacbbbcbcdcbbaacbcabcdbabdbbadccacaadcaaabadccabdcadaccdbdbcbdbdbbdacddabaccccabddaababaddcbcbbdadaaccbacdbdcacababdaacddabbbcddddcaababcccbacccdaccbdcadbccdbbabddadaddbdaacdbcacccbdcdbdbccdcdbdabbdbacdbddccabdabaddabbdddabbdaadbabcabbaadccdccddacadcbdbdabaabcbadbbbbdddadcdababadccadabdacbdababddddabaadcadcccaacbcbcabbbcdccbdbdbabdbbcccadaccaadadccbbacabdccadacaadbcdcadbbdadcacacdcddbbbabadaddddcbcacaaadabdcadbdcdccdbcaddacdcbcbdbddabcddacdbcabbccbacbdababaaccdcacbabcddbcbbbbbdcdcadccaabacadddddccbaadadabbdadacadcaaddacbacdbbbacccacdbcccacaacaaaadbcccdaaddaadddcaadbddaaadddcbbacbbdbddbbdadddaabcccdaabdccdddcdcbdbdacbbbcbaaaabcdcbcbcacdddcbcacabdcadbdabaaaddbadbcdccaaddbdddadacabaaaddabccadbdbbbaccdbdadddbcbbddcddddcaadacadbbbabdbbabdcdacdbcbcdcdabadbdcbbbaacabadacbabdbccacdaaaadbdbcdcbcadcbbdabbddcbacbbaccabbdbbccccdabdaaaaaddddbcbaaddcdbaccacaaccccbcdacadddcdabbcbcacdcdaddacdaddcdcaaabbaccaddbacaccbcccdbbaddbccdbbacbcaaccdddbdadbcbcdcdbdbbdadbdbbbdddaacaacccbdcbdcccadcadcaabcdddcbbccdcbdddcbddccadbdcccabccbcaaddabadccdbacbccacabbcccdcbcccaaacbdcbcadacbbabdbabcaddcbacbbaaabaabbadaababdbbabdbcbadbdabacbbdacbabbbbdacbaacbadbadcbdbbcbdabbabbdcccaaaadcdcdbcaaccccddcdacdddadddadcccacacbdcbbcdaabddbaacbabdadbcddacadcabbdbcbddaccabcdcabbbdcaaaaabacacaaacabadcbaaadddddbbcdaadbacddcccdbbdbadacadbadddbdbddbcbababbbcbadbdbbdabccdcddaabdbbdaacccbaaabcccddbccbbacdacbabbcbabacbddcdacacadbbaabcbdaddbadcdccabacdaaabdadccabadcaabaadacbbdcacdbcaddcddddaadcdaabbbdcabbdccaabbbaccbdabaacabdcbababcacbccbddbdbdaabcadabbcbbdabdbdaadbbaabdcacdccccdddccacabbabcbcadddacacbbdbdaaddbbaccdddcddbabdbcbddacadcbbcadbdcbddaaadddbaccaabcbddbcbabcaacabddbbcdcaccbbbabcddccddcabbbaadcabccbdbdbbaaadadcdddaadbacbaaacdccbdaadbdaadadbbabbaaaabdabdcaaadacabcabcabdddadbdbbacbabacdcdaacaabddcdcbbcbcabcddbaadcdaddcdabcbbacbacdcbcaacddcddbbbbcacbababbacccaaadbdbcaccbdbabacadbdbbdbdcdbddbccadcbbabcabdbbdaadbacadbaaabccaabdbddbbdbabacaabddddccbccddccccdbcbaccccbcaddbbacabaaaabccbbcbdababdddccabaaacdaaccbcbccdacbdccddcaacaadddabbbbdcccbcdcadbadddacabdaccbdcccadaddabddabdcbcccddcbdabaabdbbadcabbccabcdbadcbbccdbbcdcadaccbbbdadaaacaadbdcbaddbcacbaadbbadcbbbaadaabbbbadadbbadccdbddbddddcadaabbbbacaaddbadddbddaccbabadacdaddbaaacbdcadddabaddcbcaaccbbacdbcadadbaaabdcbdcdbcdabbcadddbdcdcadacaaacaacbbaccbdddcddbcabccdcacbbbadcadbdbbbdcabdbddaddbdabdabbcdcbbddddabdacbcdbacacdcdccccbcbbbbbaabbbbdaccadbbaadddddbbcbbddaaaadbbddaabcacacccbccacabddadcbbcccbacaccddddbacbdadddccdabdbbdcbbaacccaaabdbaaaadbdccccdccddaaaacaddcabaaaaacbcbcccaddcbbacdbcbaabdcdaabbaaddbdbaaadcaacabcbdddcdbbcbcacdcdabbdaacaaabdaaadcbbadabdabdcdaaaccbaadccabbadbccbbcccabaaacaccaadacbbddacdbdaddacdcbcadcabaacdadadddbaccaccdadbdbcccdabbaccabcacbaccddcdcadcadddcbdcadbccdcaddbbbbabaabadbbddddcbabbbcabdbcbdabadbaababbdbccdaddcbdaabcbacaaadababcbaddcdccbdbabbbabdbaccdcbbbbcccabcdaddcbdbddacdcaddbabdabdacddbbcdccdbcbcdabbadabbbdcbbaabddbadcadccabdcbdaacbbadbccbcdbddcaaccaddccddbdbcabaccbaacbabccaadacddbbadccdcaaabbacadaadaaacadbabcddababdbbddddddacbabdddcbabbdbcaadadccdbbdaabcbcaaaabadaccdccaadcadcaaaccbbdabbaaddabcbadbbbbdbcbcacdbaadcacaacadbdbbaccaccdcbcacbdccccbccaacddccbcdbdcdaaabbacbddbcdadcacaabccbccdcaabccdbdcacdcaabcbddacbdbdaadddcbbbaccbbbcbcabcbacddadadcdacacaacbcdaabbdcdcabdaaadccacdbcbdacdccdbbadbccddcaddbdccdaabdddcacdcbbaacbdaabcccaddbdcabdbdbaaaabacbbbbaabbcdbbabddcaadcabbddbbbabcadbbddbaacadbbbbcabbcdcbbbacacbabdcaaccabbcacbbcccddbcbadbabcdbadadbcbbdaacbcbabccbdcbdcdbdacdaddddbacaaddbdadadddbddababbaccdaadddcbcddbccccdaccbbabcadababbccddabadaabbabbbcbcccbadabacbcccddaddcdcbbaddaaaadcaabadacbabbbabcbddddaccaacdcddbbdbcdbacadcbcaaccbabdaacbdcccdabbccaccbbbbccbabdbcddaaacbdcaabcbbcbddadadbbcbbdcbcabddacbddccadcaabbadaddcbadcadcbdbcabbabdddddbdbcdcbdabbddbdcdbaaaaaabcdcacccbddcadbdcbcabdccdbababdcbacacabbbbdbccabacdacbdccadbbcdabdbdcbacbabcbcdacddcaddadaddcdbcccbcbcacdaccdbadbcbdbcdabcbbdaaabddddbdbddccacdbccdaabbccaddabbadbdcbaccdccacbbbdbcccccacbcddbccdbaacdbabbcbaaabdaabcbcbbcbcbbaaddcdacbdaaaacbcdccacadbaadbbdbbacaabacbbdcabaadcccaacabadbabccdccababdcdcbddddbadaaabbbdaccbdcaaabaacaddacbdcaddacbbbcabbbaacdbdcdcdccaaccadbadbbadadaccacbadabadbdaccbbcbdbbdbcdbdbadaacdbbcdbdacaaacddccddcdcaadadbbaabaaaaabcdbddcababaaacadbdccccbbcdcbbacbdaabadacabcddaaccadbcbbabaaccbbbddcbcbabdcdccddcaccdaadccdadddcaddbcdbacbbddddbdccddbcddcbccabadbabbdcdbbdcaadbdacddbaddcccdbbdaababccbdbbdabbdbbbbcdcbdcacdddcabacccdddccccdbdbbdadcdccbaddcbbddbbabcdbbdabdbabcdbccdcabdcbbdacbdcbadbaccdcbbcddabacdddcbbabdbdaddadadcbbcbbbbcacccacaacaabcdabbcbcbbccaccdddcddcaaacaabdbcbbcaaccbdbbaaccabbaabdcbdbdcbabacdccdbbaddcaabcaabcacabccbcaddbddcaadbcddaadddaacdacadbdcbadaabadccacacdacbbcbbddaaddbdcdcdcaabaaacdbcbacdbdddcbbdbbabadcacbccbacccbaaadcbcacacbcbcbddccdadacbccacdbbcaadcddaddbbbdcbddddddbcdababbccabddbdcadbddacbcbcbaccddaccddcbbcdaaadcbbacbdbbacadcadcbcddddcddcdcddcccacdcdbbdaccadcadcaccaabcdcdbbaaaddcdbcbbcdddadbccbccddacddddcbadaadacdacaccadccbcdaaadcdacbcddcacdcccdddcaaadcdbacaacdbaccaddddacdaaadbbdacacabcdcbbacdbcaaaacaabaacbcdccdababaacaaaabcddcbacdbcdbbabacbcddbdddddbbadccabcacabbdcdcbbcbbdaabdcdcdccbdbdcdaadadddbbddbdadbdadadddcbbcdddbaddaacbadbaddadadaabbccabddbcaccdadddacaabaddcaabbbacdbaabaadccacbacbadbdddbacbbabaacaadadcdcdcbcbcbabbbcdbbccdbccbbbdaaabcdbacbdddddaabdadabcccbcdcccaddccdabddaaabdddbacbaaccbaaddbddaaddbbdabbcccadcabcdacaccabaadaccaccbbccdaabdcbdbbabdcbabbbddcbcaabbcaadbbbdcdbcbcbadcdbbbddacabccbddbbbcdbaccadabadbdacaaccdbbbbdadadabdbaccabdcaaaababcabcbdccbcdcdaabaccdbdddbbadccdacbcdbabdaadcdbccaccadcbcdccbdcddadadccbdcdacabbbbdabccddbcacaddaaabbdcbcbabaadcdbadaccbcdbaddbdbccacddcadbbadaadbaccadddaaabaaacccdbaaccddbcaccacdcaaacbbdbbaaacbddadaaaabcdadabbccaadcdabcdcbadccdcbacbcbcacacaaacddbddcadaaaaabcbccadaccacabbcadacbdddddabadaddabbdccbcdacabbaccbdabacddddcbcaaacbcaaccbcdbdabcdabdbabddbddbdcdddabddacadcdbaabbbcbcdadbbcbbdddaccadbaaabdbacdbbadcddcdccbccdaccbbcccaaddcbabbbbdcdadbbdcbcdccdccbbdaadbbddabccbcadbcdacbbbbccdbadddcdbcdaaaadadccbaccadbdbdbaccbbbbdccbdbbdcabaabcdaaaccdbdbddaaadcccbbaadadabbadbdadddadcaacacabbdadbbdcdbdbbbbbbcbdaabcacccadddbcadaabcbdaddcaddbddbdabbbaddbbddaacbcdbabbcdcdadabaabcdbdcabcdbccabacabbcbdacccacabaaaadcbacaaaaadbcbcacabacbcccadccddabbdadddcbccadaaadccbddbbdbdcacdcadcdabaaaccadbdcbacbddadcdacaadbccdadddcbdbdadbcbbbaadbddcdcdcdacccbcadcbbdabadabccacccbdabbbabcbaddcbaddcacbaddcabcaaddbbbdaddbaabbabaaddaabdaddcbccbcbabadabcdddcaaaaccbcbdcaadcddadccdacbcccabbcbabdccbbdcccdccccddacdbcadaabbdbabbbabbbdcabbbdacacbddacbddcaccbabcaaaaaadbccaacbacadddaadccdccabbdddaacdaddacabacbddabcddacbcabdbbcbdddccadcbbadbbbadbbbadcadadddacadadabccadcdcadadbccdcdbabdacccbabdcdccdaadbcdaadabbbabbaabacacaaaddcdaacbacbdcdccdcbbabbbcddcabcbdbdcacdbccbccbaadbcaccdacacbcbcabdadbacbdaabdccabbbcacbbddccbadadcbadaddbbccadabcbcabdbbacdbdddddcabacdcabdabacaddbccacadcdabbabbcdbccbabaaddabcbdcccbdccbdddbcbdcabcddbdaaadbcbdcdadaccdbcadbdcbccabccaccabdbcdcbacbcaabbaaabacacaacbacbadccbdcabcabacaacacdcddbacacccdadabbdacbcbcdadabccaccdddcbaacdbcccaabababddbbabddbccbddbbdbdbcdaabaacbbadddbbabdcdadaababadccccdcbdcbbdcdcabaddcdcadddcddddacaabcccdccabddbadbbabdadbbcbaaadadcacadcdcddaadbccccbaacbcdbacdcabadabbcbcdabdcdadccdddabcacaccdcbcacaccadcbdbcdbdbbcbbcdaacccaddccdbbcbacacbbcbaaccadaccbccaaadddbadbbdaabbababdcaabdbcdbbaacbcdcdaadbbbaacbcdcdacacddbbbcdbcbbbcbbdadbbaddacaccaaaaaddadcddbdccacadbadcdbddbdabcbdccdabcabddddcbabacabdcdddddcaadcbdaacbcbbaabbbccbccdaacabcbbbcdccdaddaacadaadbbdbdcccdbabcaacccbaddccbddccadddcdbcaddddbaaddabbccacdadaaaddadddaadacdbddcaddbbcbbbabbacdaaaccdbcdbaabbbdbaacbacaaaabbaddcaaccabcdcdbabdaaabacdaabbdaabddbaabcddaaccaaabccdddbaddcabcdbaaabdbadcbbaccbcaccdaddbbcdccbadbbaabbcbdcadcbbcdabbddbdcabdcbcdbdadbcbdadbbaaddabbccbbdcdbcbabaccdcdddacdcccbcdcbcbddbcddbdddaacdaabddbadbdacdcbbcbabdcccdacbbbdcdabbbbacccbcccadddadcccddbcaacccadabddddacdcacbccdcdcbcbdcbbdabbddcabaccacccbcdaddccacbbcadbddbdbcdbbbabdbbbdaadabaaabdabcacbddbaadcadcacbddabbdacbacdacddaaddcbaaadddcdcaababcccbbdbbabaaddadbcadaaaadbadabddaabbbcaaccbcadbbcdabdacadbabdacabbcdaddbacaaacababcdbcdaddbbddcdabdacacacacdaabaacbcbacdccacdbbcdbbdaadadccbcccaadcbaababcaabccbdcacdadabaabccaaabaaabacdbdbcacacaaaaadcabbcacbadcadacdbcdbbddbbadacaacbbdacbadccbccddadadacccabcbcdcaabbbdaadddabcccaabcbddddacadcabdababadbdbabccbadadabdccbcdaacdacdbabdadbcbcdbcbadaaddbdbccabbaddbbbabbbcbdbbadbabacaacdadcabbbdbaabaaaadcbbcaaaaacdbbddbacadbcbcbbdcacdabcabccbcaabbaaccadbbaabdbcdaabaddccbdbaaddcacbaacacdbaccadadbaaabdbdcadcbccccddbaccdcaabdcacdadcbadacbdadbddbdacccbcccdccbadcbdcadbbdbacaddaccbbbbcddadcdacbabbababcadcbcdaccaadcdcbdadcacdbcbcdbbbcbbabacaddbbbccbabdbbaadcbddaacbbdccacbdbdbdcccbbbdcbdcabdbaccdcdadadbbbabcbdbbababbacddbbccabccabccaaaaabacadacddacadaabbdddcaadbbccdcadaddddccdbcdddbcadbadcdccbdcbbdacbacbccdcbaaacbdccbabcabbdbcdaaddccdcdcdbddbaacccaacadcddaadabbbabaaccbadddbcacbbcabaccaadcbbcdcdabccccdadbaddbdabbdccbbbcccbdbbbabdbadaadadabadcadbaadcbabbddaabbbaaaccbcdbadbccadbcbbabbcdbbaacbccbbbadbdbdbcbcbcabbbdcbdcabbdabcbbbbadddddacbcbbdcaabccabaabadcdaabdcbdaacbabadcabacccaddcadcdcdacbddbadcdbcbaaabdadbbbabbcdacddddababaadbacdadbbddbbcabbaddccabdaabacbcabddddcccaaacccddbbcdbabccdadcdcbdbdadacbdbadccdbbbdbadcdaadcbdaadbdcddddcabbddcbccdccdccdacadaddbaddababaacdbcbddaccbccacacbcdbbbccbccddaacccbddaddddbbcaccdbadcaaadcccbcaddacbacbcdabdddddadcbcadabbadbcbcaadaccccadddbccbcccdcccdcbccbddddcdaadadccbdcccddcdddacadccacacdbddbdbcdbcccbadabdadcdcacbbaddbdbbaaaadddabbdccabbcabbcdabdadadbdbbbdbcddbcbdacbbbabaaacbcbdcbbacddbdcdadcaaaddadddcbcddabbaddbaadcdcdcdacbcaadbcdcdcaddbcbcdaaadccdbdbbdbdacbbaaadbbccacdabdcbdddbacdacacaadcacadbaaccdadddadddbbabbacbaddabcdbbbdbbdcddbdacacdcadbcdaccbcbdaabdcdbbacabccccddbccbbcbacccbacdcbdbbcbacdcbaabcacacdcbbbbcadcbbdbcdccdacdccdaadddbccbaaabbbcaadbcccccbabaabbbdaccadccdaaaddbbcaadaaadcadccbbcbddabccaaacacdbadabbabbabcdbcbaabcdcdcaacdabcbbbcbdcddcaddcdddabccbaccbbdaaabdaccccdbcdbdcacacdbaaaadcccacbaacdabccadbaaddcdcccacddbbbbcabbcbcbddabddbcbccddadadbbbcbaaabdcddbbcadcbddbadaadbbabbbcacadbbadaaaddcaadbadccbccaaabcccccddccaadcdbdaabdbacdaaccaabcdaccbbaadbaddbdabdbdaaccddadacadcabacdabbdbabcaaadbbccaaabbbacabadbbabbdcdaccdcacdacdddaabcbddabdcddbbdcbbdbaddbaccbccbacbcbacbaddddbddaadacadadcbdabdadabdbdbaaabdaadddbdcaacdaacbbadccababaccbbccbdaaacadddbacbccaabdcaccaaabbdbcbbdbaadaddcaaaaaccddacddcdddabbdcadacddcacbcabbddbcdcabdaddadcdcaacbcdadaadaadadbcbabacdcdaccdbabbaacdcdbddcbdcdcabcbcbabbbdcabcddcdaccaadaaddbcbcdcdadabadabccccdcbaddcdbadcbcadcccbaacdcaddcddaddbcdacbccccaadadabdccdaddcdabdaddccabdddbddbbbcccacdbbdcccbaaadbbacaabcbbbccbcbccbabccbcacbbcdbcaadabdbcabcddcaacadbdadbdaabbaccaaccbbadabcadacccdccdadcdbdccbdabbdcaadbabcaacadbdacdabbadbdcdbbaabdabadccdabbccacdabcaccadcbdbbbdbdcaccdacaacbacddbbdbdadbccddaadccdcababbccadaccacdaccbbaacddaaccbbbbcaaaccbccddbbcddcbcbaaabcdccbadcdddcbbcddacacddbabddadcbdccbdabbbbbacadccaccddcbdbbcaabaaabdcdbabddbbbddccadbdddcddbcaadabbdcdacbcdbcbabbdcbdbddcabddabbcccdcabaacbbbbddbbbdabddaddbbddacdaccbcdadbdcdbbcddbbacdddbcbddbbaaabbddccdccbabddadddbbcdcddadbbddaddcddcdccbabbacdcacccadcacccaacdbacabaadbbccbabcbcabacdadcdddabbcaccacccbcaacabaddcccacbccdcbbabdadcdabdacaccaaadcaadaddbaccbcadbbdbacdaadcbcbcbbdabdadaaaddbccaabcadaadcdbcadbcddcdbaaddabadacdadadcddcddabdddcbcdcaaaaacdcadababbccaaabcccabdcdcadaddabcdcbbdbdbcbdbaacabcddbddddbddaaaacabbdadbacadbaabbabcabbbabaadddaaddaaddbbdcbcccddaabbddacdcadbcababcaccadbbbbdbacdcddabacaabbbbadbcadddcbbcdbbddddcdccaaaabcabdbbbdaaddddabbdaadbacabaabdcbacbdcbcbdbbddccdcdacbbababadadcbababadcacdbacdacccabcdbcccbbbdacbcddbbbdcddbdcabdabcbdaaabdbadbaddacbcbcddbbccdddbcbabdbaabbdcbcbdaacaadddabcdcdcacccaacabdbaccbdadcdabadcadccbbbdcdbcabaccaccababdacaccdadbdbccdaaccadadddacbaadadcdadcbbbbdbcbdcabccdbaabadccbcaadacbabdddcbcbbcbbcbaccdddadcdcbccccabccddabcadddcdbaabdcdbbcaaacbababadbcdcbabcbccbbabcdbcbccccaadbacbbdbacbacbbcbaacccbdddbadaacccdddabdbbcdabcccabcdbbadadccaddbadccbbdbcdbcbacaabaabdbadbdcdacabacbdacacaabccbcbaaacccbaaabbbdadddadcababddcababcdbdaaadcaadddacbddcabadbdbadbbabddddacccbdcdcadcacddcdaacbcbabbabbbbcabdcaacbdcbbbbcbdacbcdcbcbbdacaabcbbacdbcdbbdccabddbbbbabdcccdcbdcdbcdcbdacdadaabbaadbdaaaaacddbdbccbccbdcbcbbbdccdcdbadadbdabccabaaccaabbbdadcaaabaaabbbaacddcbcbcbbdbccbacdddcdbdabdbdadccbdbbdadaabadcdbdabacdcbbcadbdbabadcccbcabacbabcaccbadcabdcbbccabcbddacbabcdbababdbbdccdaccbcdcbccaaddcbccacdacbadcaddcbcbbddadbabdbcabbbcdbaddacacbcdacccaabbbababbadcbaaddaaadccbbcacbabbadaadaababaccadcdbbccdadaadacccbdacdaddbdacccdccbacadbbcbbdadbbacbbccbdbadbcdacbaabbadcacbdbadcaadbaddcddcbbacdddacaaaccabcbaaaccdcccbacbdabbcdcdcaadbacbcdddbdccadbabcacccbdddacccccdadacbdabdccbadcbbaabbbbbcbacaddbaccadbdddcbbbccaadabcbaabcbcbbccdccaadcaaaccaaabcdbadaccbddbdbbdbddbcbddbbdccadbdacaaacaacbbbdcbccdbcbbdaaccccccadbbaccacbdaaddabccbdaacdcdcaaacbdcbbcacbdaaddabbacaddadcabdaacaadacbbbcbddcccabbbcdabdbcccbaacabcdddbaacacaccbdacaacacacbdcdcacaaaabadbcabccbcdcdbbddabadccbaaaaabcabaadaaacaabcbdabaddaadcaabccdcccaccadbcdadddcdbcbcbabadaacadcbaccaabddccacdccadbdcccdacbbabddbdbdcdbacbacbdddaacaabdbdddabddbcddbabadcddaadbbbcbcaccdddcbdbdcdbbaccccbabcccabbadacabbddbcdcbdbbbdadbbacbbccdcacdbadbabdbaaabccddcaaaabcdcbacdacbbcbdccaaadddaacbdababdddccccaccbabaadccabaabdddcadbddbcbdbcbacdcbcddacddcccccbdccadbdddbbcabbcbbbdbbbbcddbbccaaacdcacdaaccddbcdbbcdcacaabdabaaabbaacacaabaabdcccdcddbbbbaadcaddaabbbcbbccbcdcdbaadcddddaccdcddccbcbadcdcbddbdbbcdcaccbbacdadbabdacddcdbdbcdbdcabdbddcbaadbcbbcacbadcacaadcaababbccdabdaaccdddbbbdcbdcddacdbbcababcbbbbbcdbbbcccddaccdccdccccdcbbaddcbcadaabcaabbdbbdbbdbadcdabbabbbdcdccabbabcbaabdbdbbadbbbcddbccabcdbaddcbbcccccaaadabaaaaaaaacdcaccbaaacbacccdabdbbcaddbbcaacaabccbdddcdaaacddbbdbdabbbbaddbaabdddbbaaacababcaccbabccbdaacccadccddbdbdaabdaaaadacdbdcddbcccacdbadbcbdacdababcdacacadddadabdccabdccdabaadaddcdcbbabaddabcdccababadccdacdbcbaadcbbcbcdacbdadccdbbdadaadbbcbdbcaaccabcbbcadbccbacdcdabacaadaadacbdabcaaddbacbdbccccbabdaacbacaccccdabbcbccbdaacdbbacbaddcdcdcdcdbdbdadbbaadadcaadbbbbdbcbcbbaacabcaaaddaaaccbbcccdbbaacadcaacdacabdadaadddbbbbccaddbbbbbaddddbccbbcbbadcdcdcdbaccdcccbacbacacccbbdadddcbbbbbcdcbadbacaaabbbdabcdacbcaaddbadbabdcbbcbaaadaacaabcdcdacdacbcbacdaaaaabcabbdddaccdbcbbcbabbabbdacdacdddcbbcadcdbdbbdbaaccdacbbcadcbadbbcbbacddaaaaadacdaaddaadabcbabbcbaabadadacdacacbaddbccaaaccbaddadcbccdaddbccccccbaababdadddccdabadbacddadccaaddddbaaadacdcbacbcdadadabbcdbddababcbcbacadbcbacbcbbddbabadddbccbdaabdadabdadbbbddddacccabacdcabbdbbddadcdbaadbdcacdcacddadbaadcccbbaacdbacbabaddaaadabcddbbacadcdaaaabbcccdbcaacbccbccdadcbabbdcbacbdabbabbabdaabacbdcddabbdbdbdddabdbbdddcbdadcaabcdbdcdddbadbccbbaaadacbadcaacdbbabacdbdddbdbdbbdadadaddadabbccadbccbaddacabaddcddacabadddacdacabacacacadbaadbbcbbabbacdddbcacdccbccabcdcaadacccccadbadabacadabdccdabbabdacbbabadbcadbbdadadbccdadabdcabdbdadacdcbdcdadaccabddcaacddabdcccacdbdaabaccabaadacabaaababbbcbbcddcbadbddbcccbdbabcbbcdddabbcbabadadccbbadbdddddacdaddbdbdcdcbdacaaabbcbaacbdcdbbddadadbbacdcbdbcbdbdabbdaccbabdbdbdadbbaaaaabdbdcccccbacdacaaacbaddaacacbabaabbdccacccccbaaabbaacbaabdbcdcdccdabadcdddbdadbbacdcbcacbacbccbbdbdaaadaddddbbcccdacdcaddddccdbadbcaddaddcabcacdcdcaadbdabcaaccaccccbcbdddacbdcccdddaadbddddaddcdacdadbddcabaaddbdaaabadbccdbaccdbbcacdbbdabadaabddcbdacabacadaddbccadbbcbdbaaaccdbbbcaabaaabadbdcadbddddcabacadbdbddbcaaadacadcdcaacabccbbadabababbbcabdcdcadcbdccacdcdaaddbdccacaadbabbaaabccddccaabbccbdcacbbbbabbccbdccabaddadacccbbdbcddacbdabcbccacddbbbaadabbcccaccbdaddcbbaddbcbdadbbcaaddccdbacccaaccdcbbcbbbcddadabbcccdabcccbcacbdaaacbbddabdbdbacacddabacbbbcabaaccbcdbacaaccbbbddbcbbbababcbddbdcadbcbbcccdcdcbabcddcbacdcdbcbcccdcacdadcadadbddcbaddcbcacacccdcadbdbadaaadaaddacbcbabccbdbbdccaaacaaadaacbadcbadcdcdcbcbdddabcadaacdccdbcdbccbbbbacdccbccdaaccddddccdaddaacdaddddccbaddccdabacaddacbbdbbdcccbaadcdbbccdcaacbdaadbccdadaaabbadccbabcabdcddcbabdbacdaccdddbccadcadaddacbbbdddcbdaacbdaadaabdabadacbbcbabcacabbdccbaaadbdabbcdbddccdbabdadcacbbccbcdcadabddcbadbbcbddbaacadcaaababaccdaccbacdddabccacccdacdadcdcadabbddddaabdcdbacbbbdaadabadbcdbacabaabcdbbdabbdcdabcbadadadbadabdacbccadaabddddbabaddddcbdabcbdddbdddbcdacabacabddaadabbbadbbadadbbccdbbcbadadabaccccbbbdcccdcabdbacbbccdadbadbadbadccbdccddbacdccbdacbcadbdaacbacaadaacbdbabcdacaacdbbdbaddacbbadaabbaddbadbadccabccaabbbabcaadbbbcdcdddcddabdcdaaccadddcdbcabdbcbacbcdcaadcdddbbbaababcbaccbdcadcddbdabacabacaaabcdadaaadccbacadbcbdcdbbdcccbacaacdbacaccdaaddbcdcbabacbbcccbccaaddbbbbcbdadcaaccdcadddbbbbcabbcbacccbbdbdcddbdaccdacbddcdbbababcccdcccdaadccbddddcddababbccbbccadbdadbdcccccaddaddbcabaacdccbbcbdccbbadabcddcbcbcdaadcaacbcbdcadbccaccbcccbdddbddabaacdbddbdddddcbacacabaccadcbbbcbadaacddadcaccaccdccbdacddcaabbcbabbddddddbaaaaadddbbacbbddcbbdadbbdbdddcaacdabddbcdbaaabaddbccdaabcbdadcbddadadbaaaabaddccadcdcdbbdbdbaaacabddaacdddadbcbbbcdabdcbabdacbabdbdbcbadccbccbccbccacdddbbaccbabbcbbbaabcaddbcbadcddadaabdbdaacbadbadbddbbbabcabdccdcbababbaaddbcbbbabdddddabbddbadcbbcaacdadcbaabaacadaacddacbaddadadbaaadbbbbbadadadcccaadabddcdacbcbbdacdcaddcbacdbcccaaddbacbdcaadddaadbdbbbcccbaddacdcccdaddcaabccadddabbacdaabbcbccddadaacdcdcbabbbbbcbacdbacdaaccccbabaacbabcbdcbddbbadbdcabcaccbdadbbbbcdcddccbcaadabcaaddddacadaaabddcdccbacccadbbabcaaccbdccbadbdabddcdadbbbcdcabbaaadcabddbddabadadaaabadbabbabaaacdcaacdaccbcbabcabddadddbcdaacdabaadbdbdbdbcdbccaddabcccdcbbcbbababbbaaadabcdccababacddccbababababbddbcabcabbadacbaabaddacabaacccbccababbbdcbbaaaddcddcdbdbacdcddccdbcdbdbbcbddacbabdcaadddabbbacbabcbccacddbabdaadccacccbcabaadbcacdbccbabbcbaddbaaccacbdadcbbbddbacdbcdbdabcabaadaaddcdccabbbcaccaaacbbabaacccadbbadaabcdcddcabcddbbdabacbbdcaacbdaccddbbbbaabccadcacbcbcadbcabbaddbbcdbdbadacbaadbbbdadcadcbbdaadaacbababdabacabdbacdabbbddbbadabbdcccbbbcaccacaadbadddcccdccdadcacdbdacdbcccddcbcabddaddbadccabcddcaabbddacbcabcbabccdcccdaabaadcacdcdcababdacacdababccdcdacaacadaaccdbbddcdcbcbccddadcddaabccabcdcbbadaccccacaadbdbcacadabcbcadbcdabbdddabcdcddddcddcaadaadbbdabacadcabbcabadccaadcbdbbcaddbcdcadbadadcdbcddddaccabbcbacdbcaacaabbdababbbccaddacddacbccbbcbbcdcdddbdcdbaaaddcdbabdccdccbbdacbdbacadcbdbbccbddcaacacbacdcadcbbbbbbbadccbadadccaabaccbabbbadbbcadbdbbcabbbdbddcbdbbddbcdadcbcddbbabcccaacaaabdbbbcddbdbbadabddcccabbdcdbcabdacadcbcdcadbdbccdbcbbacddddbcbbbbaddddbbcddbbccbaaadbcadadadbaacbacbaaddaaacaddaadbdcabcbbaaadaadccaaadcdbdccbcacddabaaddcacdaaddddcaccdacabdabacddcaccdddabcdaaddbdbaaddcccbacadddcccdabddbbaaccbdcdaddaabdbbabaccabacdacdbcddddcaabdabacbdddbdddcccabcadbaaaaadbdbbcdccaddadbbdbcbcdcbdbccacadcdcbccaabbacbbdaaabdccadcdddbddaaabbdcdbcbdcacabddaabdaacdadabdadbddbadaacabcaacabaddcacddbabbcabdababcbdbbccbbcaabadcdadbadadcdcbaaabccabcabcabbbcdaaccacbdcdbccadacbadbcbbcccbdcadcacbbcbbccbaadbcbbadabaacadaabaaacaccddcdbdabbacbacdacdbbbddaccccccaacaaacaaacdcbbdbcaccacdcbbacbcccacbcababaaacdcdbcabbabcabdbcccbaabdbddbaacddacdbdcccabdcabdbdbddccbccdbcbabbbddabbdcdbcaadbccbcbdddcbdbdbbaddadaabcdcabcdababccbcdcbcdaadababadccadbdaabccaaccdbccddbdadabacdbcddcccdbaddbdbbcccbbadaaccdabcbaadcacbbbacbcacacccbbacdccdcadbbdddccbbbbbbbaddddcddcdbddddcbddbbacbabbddcabdcaddabadadaccaadacdadadadbdacdccdbdcdcdbaccdcbdabcaadadaadbbabaadabcbbacbbbcdbddcdbcddcbbdcddbdcbcccbcdbbcbbdccddabacdabdcbaaacccadadccbbaaacccbccdabcccdbcabadbbdcbcdabcbabaacddbccadaadccacbbbdaacabaaddacbcacccccdbcbccdbbaccbcbbdaacabdbadbadccccadbdaaccacddaaadddabaadadbadabddbcbdcadcbbaccbccdbbbdcaacccacbdadcadaddccbbddbdcccbddcacaadbacbabcaacccbccaddbacaddbaaabaabaaaccbccbbdbcaabdacaabcccbacbbabaacadbddbcbaccdddabcdaccbbccdaaaadbbbbdabccdacbdabbdaaccdbcbbddddccbacaabbdacacadbbcadddccccbbccdacaadbcbcbcadcabbdcaacdabbbddadbacdddddadbabdacbdaccabcbbaabccaccaaaadddaaaacacdbdbcbcdddccbabbdaadaadbacbadaacdabdddbabdabacbcbadbbbbbdcdbccbabcaaaacdacdbbccbdaabccbbdcdddccaabdbcabacbaabdbbbabdacdbddcbdadadbbcdcddcaccddddaccabdcdddbadbabcaaacddddcddbaaaccbcbdcbdcabcdaabcccdcadcbbbbcacaaaababcbbdcacbddaccacbccaabcccbcbabdbabdacadaccbaaaaccbbaaccdccbddbbaabccbcbbbdbdbcbdacbaacccaadcacdbddcdbaddbdaabbdcdadccaccdddaccdcbaadabbcdcbddbaaddcdbbacdbdacabadbbddbdbcadcbdbcdddddacbaaccaccabaacbcacbabbdbcbadbbacdddabababdddacbccccbbbccbbbbdddaaadaacdbaadbabacbdaddbccabdcdacabaccaaabaccdbccbdcabdbadcdddbcadddcabbdacadadbbddbbabcddbdbaabaaabccacdaaadcdbdccddbbababacabaabdbbbaadaccbbbdadcbcbcbbadbccbaabcbcbdcbaddacdddbdcdbaaabccbdbadbacccbadcccacccbcdbbbddbcdccdbdadbcdaccbaccabdddbdcdcaadccdcacbbdacacdaccbbbbdcbbdbcbdabbdbaddbbcbbdcaaadaddaaabdcbabbbcdabbdcdadcaacddcbcccabadddadcacbbdbbcddabbcabbbcdbcdabcddbaddbddacddbdaaddcbbdcdbdadaacbdddabaadcabbdddcbdbddaccbbcaaaadbbdcbdcdaaabdcdaacbcdbadbbbabaacbcbcdccddacabbdbbdbaabbaadcadabdbcaddacdbddcbacdcccddcaaddabdcbdcbabbcdcbacdcdbcdcbbbdaadbbacaaadcaadadbacdbbdadbcdadabcdabbadcbadcdcadcacadacbacccbccbddaaddadbbddddbcabbccdbaddaddddcabdabacddbacdcabddddcbadddcadacdcbcadacadabcaddacbcdcccabadddbbaacccaccddaaadbadcdcdaabadcdaacbbbcdbaababdaabbdcddabdbdddddbdaddacbaadbcabbcbbccbbbacbaabbaaadcdadabbaacccabbadaadcbdcaddbcaaccddcbdbaccdadcccccdcdcacbabdcdaaccccccdbbacddadabcbbbacdbddbdcacdabdbdcadccbaccdbddddbdaadacababdaabaadccdcbdbacabaddccbacccacabcaacdcbbaabbadcdaddabdabaadadaaddabcbcaccdabaccbabbbdcaadddadadcbcdcdaadcbddbbdaaabdddccdabbabdcdabdddaacbadbbdbcbadcadccdbaabaaabdbddcacdcdbcdaaaacaaabcccaccacabacdaddcccaabbbbdcdadaadadcdbdaccbadadbcbcddaccdbbdcdbaacddbcbcbaacacabbbdcaacccccbaaddcdaacdcdcdbdccadcacbacadbaccbcdabdadadaacbbdcddbaaccdcbdccbbbaabddbcdaaabadadcdbdccacdbadbddcdcccbcbaaacbcacbdcdcbccbdcdaaddaacccdddbbaddabdaaaaacdbdaabdbbccdddcccadbacabbdbbaadbbabaacaddadbdddcddadbdcadaaadbdbabddbddcaccbadddcdaacaddadcbddccdabcabbdbdbcbbdbcaaabdbbddcdcbbaadaddcabdcacdadabbdbaccaacbacddaabbbdaababdbbdaacbdbcbcdbdcabcaacbacdbbccabbdaabdccaaaadccbdbdabdbddcaaabbdcacaccdbbdacacdcaddcbbaadaaaaaddcbacadaaaddcbbdbccbccdcddaaccdadadaaaccbacaaadcabdcdacbdaccdbcaacadbabbdacbbdddbdddcbabbcdbcdacbaacddbbbbacdaacbbdbdbbbcaacbdadddbcbabcadbabbbaddcdacdcbbacdbcdbbdcbdabbddabcbdcdcdddbdacaabadaadaccabdbccacbdadcbbacdaccbdbaaabbcbcccabdccdbbdbcadcabbaaddbbadabcbdbcdbdbbdadddaabbcbcbddcaabdcacaccdbabcdaacccabcbaabbbdbaacbcadadaaacadaacabddbccccdaabcbdcadbbadbaddcadcbddcddadbdcabdcbbcabadddadbcdababaacbadadbddccadbbcdaadddddbdccbddcabdacccccaccabdbdbbabbcdaadababbddcaccadddccccbabbacdcdbddaacdbabcbdbcbbcdcdbdbacdbbaacbdddabccbbbacbaabcdddabacacdacbbdaaabcabcacbbcaabcbcdddbccacccdbdddbabcaccabdaccadcaacadbdbadaadddddaadababbdcdbabacbacbdbbcdcaaaacbaddcbcddcbddadaaddaabbbaaaabddddacadcabcbbcacddcdbccbaacbadcdaaaadadbbdaaabdabacbbbbcbabdbdaccabdcdcadddbcbbcbbdbddbccdcccdabdbddcbbabddbbcbbcbabbcbbccdcaacaccbdabbdcabbdacdbdadcccdcdcaddadacabbcbdadcdaabacdcbbcdacdacbcdabacacbcbcbbcccbdaabddabaddcbcdabddddadaccdbdacccbddbccbbbcdabdcabcaddcbcbaddacdcbbabaacdcbcbbbcbabdbdbdbddadaadddddbaadabaaacdddadabbabbdccdaaaddccabcdcdbcbdaacccbdcbdcddcabadaacabacabcdadabccaadaacddbccbaaadbadadddcacdcdbcdaddccccdabddaadcbcbbabcdcabcbccbaaccbdddabcadbddbacbadcdccadadddddadcacbbdbbdaababbbaabaaccbbdabcaaadacdcbbdccdcbadccccddbdbadbcaacdccbdcbcaaaaaadddcadabdaacbdcdbcbbbccbccbcdbcbdbdbcdcabdaacaadddababcdbadaabaaaddcabcdbbbaacddbccadbbcacdbbbcbcddbcdbcddaaddccadadbbabcdaacbdcccaacbcccbadabdacacadddbbbdbcbadaccdcabaddcaddabbdabcdcbcbacbdcdbddbcccaddccbaabbbababadcacacaddbdbdcaaabaacbadbaccaacbaaacacaddbdabbcdaababbbadaadadcddcbccbcdbabaacaacccabcabcddccaaabdbcaaacccccbabdcdcdbaadccabcbdbddabccdabbddabdadddbabbcadbdaabcbdaaccabbcdaccbdabcdbdddccbbdcccdcabaddacccadbbcaadcaccbdbddabadcaabbdaacadddacbbabcbdabcdbdbddccabcdcddadbccacbcbdccdadccbcbaabdaddbcbdbcdabcdabdddcccbddcccbabbccbadddccbbcbbbccdcddbbdbbdacbabbbacdbddaadccaacdddaddcbaccccbccabbbddccabadbadddbddadbaabcdadaadcadaaccbccccacaddababdbbbccabcaacccbccbbcaabcbcbbdacbdbacabcddcccbadbcabacabdcccdaabdddaccaabcadbacaaaddcdabdbababacdccbcaaadbcbbbbdcadcccbdbcbabbccccbabcbacadacbacbddabacadadadcccaadbddcadaabbbdaabacbdcccdddabdcccabdcabcdaabcccbbdaabccacbdccadccdbacaaacccddddacadacdadbacacddaabbabbcdbcabdabbbabbcbcdccdbbaabdbabbdadbaadabcadaadabbcddcccacdbcdccccadabacabaacacbaccbbdbaacdcbdddbdcaadbbccdbdcbcdcdcababcaabdcacdbadaddddcdadabcacbccbcabaaddccdbcdabcccdadbbdcadbdddcdbdbbdbbcbadadadcbbbaccbbdcabdcbabbaacdacbdaacbbcaaddccdcacacbbaddbbdbcbcbcacbddccdbdaadbcaddccccdbcbbdbabdababaabdcabcaacccddbabcbbccbbbadaacaabacdddcbddddbdaabcaadbcaccaacbcbabcbaaacbcbacbbacbddacaadcbcaaaccdacdbcdadbccdaaabccabcdaabbdbacacdaabbabcadababbdababdaccdcbcdadcbabcdccccaabbbbcdbbcaccdcdbddbacabadaaaabdcbcddbbadccaadaddaadaadcdccaabbbcddadbacaaaabdacbcacabcbbbdbcbbdcbccccabdbcbacbdddcbdcabaacccbaacbdcaacbbbddbccabdaaacdaaabcacadbbdbddadddddbbadacccabbddbadbabbdbccdbabbcbaaccccdabbddacddbcccbddcbbcddcacccdaaddcbabaacdabddbabcaaaadcbbdaacbbbdcbdabcbdbcbaddbdbcabccbdadabadcabdddbadabddcaaaacccbbcadcdaabccacdccadcabcaccacddcdcbbacbdddadcadcbdbdaabbcccacbccbaabdaabdccddacdadacaadaaabdacacaabaabbcbbacccccbdddbdadccabaaabbacdcaabdcadddcabcdbcdadaaaaddbccadcdbcdcbbacddabdccbdddadcccbdbccabadbddcddbccdddbcbdbbbadbccbaccacabcdabbdaadbcaadbcbccbdcbcdcbdaccccccadabdbbdcacabadadadbadbaddccaaccdcccddbcdacaacccdcccbadcbaddccbacddcdaccbaaacbdbcaabcdccbcadacaadcaaabaacaadcddcbacabaacbaadacbccbdacccddadbbdccdbacccdcaaabbdbcdcadacabdcddaddbdbdcaadcaaabacbababdbdadcacaacbddbcbdabadcadacadbadcbbacbacaadccabcbdbbcddacaaabcbdadacbabdabbdadddabbbccccbcdadbcbbabcdbdccbbabdabadabcaadcbaaaababdacbdcacddcacbadbbbcaadbddaaddabacbaaccbadbaabcaddaabcbcdcccbbacacbdcacdbbcaabddcaccacacdcbaadbaccabbcbdbdbccbbcaddcbcbddccdcdcacbaacaaabbdaacabaaabccbdabaddaacdccdcbdbcabcbdccacbcdaadbcadccaacddcaaccabdcddddbdcaaccdcdddaddbccdcbcacdbdcaabccdaabbaccbabadadacdbaacdccbdcaaadcaacbbadaabdaddbcdbbdcbaaabcaadbbabbbabddaaadbcbbababdddadcccbbadacaacacccabaaddbaccbcdabbccdbdabdccacaacabcdcdaaddabdcabbddcadccbddacacadcccacbaaacdcbbdbbadbdabadcdbabdbbbcaadcddaadcdabcdbbcabdbadabaaccabaaccadaaabacdbbcccabaaabbddcbcdcabcacdcbdcdbcccaacdcdcadcccbdbaaacdabcccacaacaddaddbdabaacddabcdcaacdacabdabadacaabbdbcbddcccbdcacbacadacbabdccdcabddbadaccacabcbbcbddbdcaddbccbcdbbadbdcdbccdcdbacbaababccadbcccbcccbcbccddaaabdcaaadccbaccddbaaaaacbbdccaaabdbbccddadaccddabdaaabddaaacdcaaabccdcbaddaabcbbddaddddcadadcbaaaddcbdbdcccbdbdcbddaccabdaccabcbcbabbadcccdcadacaccbacdbadacbdccaabcdacbadabcbadadabacbbcaabcacdcdbcbcbcdbaccdbcdbabdbbbbbbddcaaacbbdbbbbdacdbddbacadddaaaabacacdddddadababbcdcdbcbcabdcabdbdccaadbbaadbcadbccdbcdccbadadaddbabcddcdabcbccdcdaddadccdcbdbdcddaadddccddaaccabcbcbaaabaacbbdcdbcbdaaaaaabadcddbbdabaadcabbcbbcbdaddcccbabccaccacbddbbadbccddcaacadadaaddcdadddaadcadabdcadcaacbddbbbacacabccbdbbacacbcbcdaacdcbaaccbbdabaacdbacdaddacddcacaabbbcaadccdacdbbaadddddababacaacddacdbaaacbabccacaddbadccacaaadacdbdbabdaacbbdbdabbbcbdacaddbbdddadcdbbaadacaddcccbbcbcddabbbddacdbbdcadbaddbbdcbdbbaddaddccbbcabaddacddbcbadacbdcaacbabcddcacaccaabddabcbdbdcddaabbdddbbbcbddaabddadcbcbbbcacbbcdacdabdccbdcabdcbdddcddabbabdadabcdcabadbadaaabdbbcbbcccbaabccdddddbadbbdcbcdbcacbbcdbbabddadcdadbcdbaababadabcdaadacbabbcdbdcacaddcccbabadbdabbddabaabcbdbcbccbcbcadcbdbdbcccdcbbaddcccdaccddbbbbccbcbadbbadcabcbcdaaccabaddcddbbcabcaaacdcbbccadddcbaadcdddddabbdbacdddcbbadaaaabcaadcbbcabaddbdcbbccbbcdccdabcaacdabbbbabcabdcabadcacacdcbadcabdabddcbcacaadadacabbcadddacbdcddabdabcabdccdcbbccdcdcbdcdadcdcabbdddaabadbadacbbabdbbcdadbdbbbccdbccbdddbddbbccbcbcbaadcdcbbbbadbcdacbbccbdbaabbbbccbddbabdbbaabcbadadadcbdddacccddbabbbaccdbcbccabcddbcbcccdbcdadbdbdcdcccdbbdcbaddaddccacdcabbddaacbdbaddddbddacdacdcccbdbbadbbabacababaccaadbddaabdcddcbdcccbbcadabaabddabccccdbadacaadadbccdbbcbaccabdbbccbacdbbdcbcbbbacabacadaaddadcacaddbacdacbdadabadaccadbaacaccaabdcdddaacbdddcbbdcdaaaaddcaadbdbdccbcdacacdccbaaccddcbbcdadaccaaadccdbcdbccddccdcbaabdcccbcdacaaddabcccbacdbdaadcaaccbcbbbbacbccdcabacbaaabbddabccabcabcbadbdcabacddcddbcbcbacabaccdddbcabbdcdddccdbcbccdcbcbcdcaaaabacadabddbaaddcdbabcacacdbcbacabccbbccddaaacbadccdbbbbcaddacdacabdadbaabdaabbdbdcabccacdbbbcbbadaacdadacbaaccbbabddcbdcacaadcacbbbcadcddccbbccbcadbacadcbdcabbaacbcabdcadaccaccaddcababddbbdbaccdaaacdaddaaddbcbdbccbbbbdddbbbbadccdbacadbadcadcdcbbccabbcbddcacbcaadbabcabacdcbaabcbbdaccaccabdbadccabcbcddbacbbbcbadcbdddbabaabdbdbdcccbdbcadbddbccbacddcadbdabbcadabdcddacbccadbbbbbccbcacabdabdcddccccabaccbbaadabbccbadadabadbadbabddbcaaccbbcbbbabcdbbbaddcdcdaaaaabbcaddabbabbbbcdaadadacdacacbadbcbaadbcbaaabcddabcbdacdbbbdbbdccbcdcbabddccabddbbacbccdabccbabdbdcccaabdccaaccdbaccbaddacccaabddbabccabaddacaadadaadcbcdcbcaaaabcbcaabbddabdbadccacbccaadbaddbbbaccdabbcddbbdaaadcbadbaccbacbbccdcacbabdcadaccabbdaadbababadcddcadcacdcdaacabcbbdabacabbdccbbcdacddadabcdbccdbdcccaddddbbdbbbbaaadddbccdabdbddaabcdcaccbabacbbcdcdaadcaaadbdadacacdbbdadabcccccdaacadccbaccdcddddbcdabbadcdbccaacadaaaccacbbadbdcbabadbcadbadcbcadaadcdccaacbbbcadbacccabbbdddbaaccdddcbbcaaaaabbacbdcadbccdacbdaacccaaaaaadcadbddabcabcbdccddbcacaccabaaacdaababcacdddddabccababadbbabacaadbaacdadbbbcbbbddadcbbabddbadaadcdccdabdccbbcccbdcbacbaaadddddbbaacaccbdadbbcbcaddbcabaccaaccddbbadabcbddaaddaccadcbcbbdbbbccbcabdabbabadbacbbaabcbddabccabbddcabbbcddbabdabacbabccddccddcbcdccdaacacdbadabccabbcdbcaadcdcadbcaaacbccaaccddacbaabdbbabdcaadddbcbbbddaaabddcaccabacbbcbbaaacbccbcaccacbbdcdabcaaaacbdbdbacabcdcdabcbcbcdbcbccbadabadddcdddbbadccbaddaddbacdccbcdcccddaaddcacadbdddbcacbddddddcdacaabbadabaaabbbccbbcdccabadcdabaccbaaccdacdadddadaddbdaccddddcbdabcbaacadcbbbddcabcdbdbbaaaababdbcbccabadbbbbacbaabcddcdbcdcabbbacbcbcbadcbbdccccbcadcaccdbcabdcdddbbabdcaabdcbadcbaadbdbdbadccdddbdbccdcaaabaddbbacbaaadadbcdcaacbaacadbadbbacddbabacdadbcdbcbcdbadaaabdbbaababadbbdcbccabbcadbcddaabbbabbcddabbbacdbdbbbbdaacaaaabccbccdabadcaadcabdbcabcabdddabaaabcadbccdccdcbaacacdaacdacddcdbbbccdddbdacbdcacaaaccdcdbddddcdacdcdbbcbcdcbccaaacdbacbdcccaddcddcbcdddddaabdddddcdadadbdbaabdaabbbccdacbcbcccdccdcacbbbcbdabcaacadaabdaaabbddaaadcccdadbdddcabacadcbcadbbbaacdbabaddaaadbacddabdddbccbaccdabbbddaaadcabccbcaabbdbcbadadbddabdabbdcbbabcbddcdccaadddbcadacadadbbacccbcdaabdbbcacacdbdcbabccadcaaaddcacdcdbcbddbdbccabbbbbabbdbcbaaabbabcdcbdabcadbdbcbdbbbaccddaacdcddabbacbbdaacddabbadacadbbccdbcaccbaddcddcadbdadacdaaaabcccbbbdddabbdadbdacdadbacbbbcdcbcacddcadcdccacbbadcbdacdabccbbcdabbdcbcacbbddcdaddabdadbcdcbabdcabdbcabcaaacdcdbacbdaaabbcdddaddcdaadbadbddbcddbdbacbbabcabbcbcbaadaacccccdbbcddcacdbbbadaaabddabbbacacbdabaadbddbbbbaaccaadcaddadacdbccddcccbbdbdcbacdbdccaabcaaddcbdadbcdbbcbddbdcdbcdcaaacccdbdaabcabaaacacaacadbabdccabccccaccadacaabdcdaaaaacaccbdbbadbadadcbabbdacaabbdbbcabaabaacbcaccbcbbbdddbccadbcdbadbddccddaccacabcddbacacabbbdaadcdcdbacdaddbcdacdccaaaaabbbbadbcbbdacbbdcadbadcbccabaaabadaabcaacabdccbdbbabbabbcbcbacbcdcdcbabccbabcdcacdcdddcdadaaddcdaaacabbdbdbcacababbadcaacaacdbadbccddacddcbadccbddabccaccddacddadaccbacadcdcacbcbdabcacbadcacabcaabdbcadcadbadaadbacabddddaadbdaddbacbbbcadacbdcbadabdaaddabddabbdcbdadccdcbdddacbaabbdbabcdbcbadabaadadcabadcaddcdcbcdadbaccabcadababaaadacabcadaadbcccdadcbdbbdddadcdbdacccbbcbccbdadabadaddaccaaacadcabbacacddbccaaccddabddbddcbdcbbcaabcbbbbbbdaacababdbaccaacabaaaacaccaddaaccabbacaddbadbaaacaaacaccacacccddbadcbbccddbdcdbccaabccdaaacbacdcabcbddddaadbdbbbccdddcbaddcaabcaccadabdbdcdadbabadbcaacacabbaddabdaaabadbdddddadaabcccddcccadcdcbacaccbddbdabbcabdbaccdbdbdadacbadbacdaacdacacadaabaabcacabcdccdcddddcabaddabdaaaaaddbcccbacacddcbacdcccbbaaccbdbddcaaaaacccacaaadbbbdbadbcbbaadbddbabbdabbacbacbccaddadddbcbdbbaacaaccbdcbcdddaddbadacbacaadadbaadabcdabcccaccbcbabbabcaabbcbaaaadcbaaaaacbdadbacdbadaddcdccdcaacdbabdacccaacaccaccacddaadccadccbdcbdbacdbbbaadaaacadcbabbdbaaadbbbabadbccabaaabaacbaaaccabccbaabdabbacacbdaabbbabbcbaddaabccbbbccabdabbacbabbddaddacbccdacddabdabdbbbdabbddcbbcbddbddaacbcaacaddcbbcbcbabdabcaaaacaccabccdddddbcccabccaacbbdccdbaddcdacbccbccdddcaabdbdadbcbaaacadccccadacccdbbabccabacbddbddddcadbcdccadddaaddcbbddabcaccabbdcdbddcccacdcdaaaccccacaacdcdddadbcdcdcccbacaaaaadcdbdcdbaddabadabbddadaccacabbbadaaddabbacbdbccabdbbcbaacddabacddcccbcddaadddddaababbbbcadbccccacadcdacadbbcbcccbdbbabbabddcdbdbbcbbbddabcdcccbcdbdcddabdddbdbabacbdaadccdaccbadbbdbcbdbadbccbbbdccdbabaabbbaadaabddcadabcacaababccdaabbcbbdbdcccdbdcdccdccdacaabdddcbacbbdcadbccdbbccbdccdabccbbddcdacbdcadadbacadbadabccacbadadbabbdaacdcdcdcaadbdcbaabbbbdcbabdbcbcdcaabbabacadddbbadadabcccbabcacbccbdcbbccbddbacbabcbbdaaacbbdcadcdacdddbcacccabcdddbadbccdbadabcdddabdcdaaaacbabcabacababbcdbccbcdcdaccbdcadccaabaaddddbbdbaabbcbdabbcacdddacbdbabddbacbacacabbdbcbcaacadccaabcacdacabdcddcabcdbaaacabbabccacdbcbcabacadabadddaccadabbcabcbbcdabcdcaaaddacdbccddabbbccdacabddcdbbbbbabacababcababdbdccdcadababbacbcacdcabaaaaaccdaccddbdcbcaacddccdcdcabaaaacdaaccddacbccaccadcddbdbbbadddbbbdbdbcdbacabcaacbaaaccdbbbdcaabddddccacbadabdaddabddcabdccbbcadbadbaccacaccaabdbcadaadbadcaaaccdbcabbdbdcdabcbaddadccaaadaddbdbccabbdadbabdbdbacdabccabcdabddcbacdcdaabacacccacbabaccdbabcbaaddcdcdbdaccaadabbdcaacdcccbcabbadacaabddddcbbacbdccccaddbbbaabbbaddaaccbdaacadabbdddacccbabcdcdcdcdcbabbbdaaacaadadadcbcbdccdadbcabdccddadabdadbacabaabcbbbbadaccbbcddcdaabdadcccdabcabcbaaddccadbabdccdabdcddaccbcbdbcbdcabaabddcbbddccdadaadccccabbbbaaccbbbbcbdadbcccbcbcdcbaaccbbccccbdbacabbdcdddbcdbabbacabaacadddbdcababcacacbbccccaaddabdcbbabaaddcdaabcbbdbddbaabbcdcbcbabaadbbbddaadbccadcbcdcbccaadabcabbcddcbdabdcddaddddabaabaabcabddcbdbbbaddbdcccbbcbcacadddcabdabddccacdadbdccabcabcbcdcdbabbaddabaacbdacaddbcbdabacbdacbbadbdddddddabcbbcbcccbcdddacadbabcdddbdabdcbcddacbccbbcbbbbbabddbabcacadadcdaddbbccbcabcadddcbabdcbdbdacbbdccdcdbacabbdcacbbdcadbcdabbbccddabacaccbbbaabcbbcdaabacabbdbaacdbcaddcdadacccbdddcacbcababdccabaabbcbddccaddcbddabbbaacbbccddccdbadbacdbcdddcdabbadaccbbaaabcddddbadcdcbacbbadccdbccbccabaabdbcbccbdbbadcdaacbcddbcadadbcbcbcbbcdcccbcbbdadacddcacaadbcbdcdddddddbbbadabbcadbadbddabcbbdcacbaccaacabdcbbadbbccbdcddabaabdcaacbdccacbcbbcaaadcddbcaabdcddbabbbbbbddccdcdaacddccdcccbbadcdbcdaddcacbacccdcccbadbdbabbdddbbcbbcaadcaaddbabcbbdabcbdbdcaacbbadcdabaabbcddddcbddccccadbabbdbaadcbdcdbccacbabaaadabbaadbbddddaddabddddbabbddbbbccccddabddcbbbdbdbcbacacbaacbccadbdaaabdaadbdcbdbcacaacadbddbbdadccacbcdcdccdbaaddaacbaaabaadbaaadabaacdbcbccdadacadaacdacabbacbcabcdadbdddbbcdcbcdccabcbbbabbdabdaccabdcabdbbbdadccccdbccabcacdadabdbbdadcdbcaadddaddbdcdcdacdbbdcdddaccdaadaccaccbccabacbbacbbdcdcaacaabacdcabdcdadbcbbacbddcabdaacddbbcbcdbcbcaaabcbcbdcbcbabbbdbadcdaadddbacbcbcaaadcaadbddbacadadbcdacabdbdabddccccddcabbbbbdbcbddbadcadaddabbdddccdbadacdabdaddabbddadbddccacabbddabdcbccbabaddabccabdcbdcccdcbcaacddacdbbcbcccbbdabdcdcccbacbbabdbcaccdaacaccbbdbcadbdcccdbdaddcbcdccbbaccaabdacdddcdbbccbabbaccbbbbbcadacddbccacdbbcbdcdadadabdbbaddccccddacdbcbcacdaabdaaabbccbbcadadaadcacdacaaabcacdabcabbadbbacabbccbdbadbdbccdaccbaadcddbcdcdabcbbaccaadadcacdadaabbcaddcbcbbbbbbcbcbdcbdcdcdccdabdaacbbbbadbabbbcdcaaaadbcbcdaadaacdbcbbbcbaadddcdcadacbdcbacdabcddadbbdbccaaaaabddccdacbcdbabbbddcadacddbadbdadbcdcadbdbbacbcacbadadbaccadcaaccbccbbaaacadddadadbbbbddbaddbbdaacbcaddadbcdbbacbbdabbaccbcccddcaddbadcbcabdccabddbbdcabcadbbccddbcccdbdabcabcbbacbddadbccdbbabcddcbaccabbaacbaabdddcccacdcabbbdaacccddadaaadaacaddcbdbabbdcaaacadcccbdbddbbbdddbaaddadcacbddbccbcdcbdcbbcacdaacbacbabcddbdcdbcdcdbbacbabcdddbdcaaaaabacadccdaacbbcaaacabacdddababcbbbbabccccaadabdcddcabcacabcbbcdcbadadcddacbadadddadcabbccccadcdddacdddacadccddacbadbcccadcacdbcddaddcdbbddcddcacbdbcbcdccabdbbddaddddcaaadbddadccacbdcacbbdcdcddbbdccbcbabccaaddbcccacbadbcdccccdbdcbaadcbaadccadbbddadcacbdbbaccddacadcbabcbdadcdbbccccdcccbbdaabbcccdcdcabbaaabaacacaddbdcdacddabdabacaddccaaababaccbddcbcdccddadadccbcbdcccdcdcacaaacccbdddbdaaaccacdbdbddabdcadacbcabdaaccabbacbdcbaabcdbdbcbcddacaccadcdcdcbcbaacdbaabdaaabadcababbbdacadbdcdadbdadddaccdbcdabbbccbdccdcaadaabbdcacadaaccdbcbadbccbbacacccdbbbcaacacdbacbdbcdacaabbadbbbcdacddaaacdcacddcbbacaaccdaccabcabdddbcbaccbcabadcacadbdbaddccadcccbcbadadddbacaaaaccbadabbddaccdacdabcbdabdadadacbbbaadbdadaabaaadbcbbcbabbdccdcdcadbccbadbabbabaccbbacdbdcacdccdcbcbcaaaddcbcdabcabaadddabbddbaacacbdadcccccacbcabaaaabbbcdbddddcbcacbadacbcaacdaccbbccddddacbabcadbacdbcabbabdbbcbddbccbdbabddbbbdcbdaadbbacabacdcbaddadbcacacbdcacbacdbcccdddcdccbbdddaaccdbccaaabddbdbcdcacaccdcbcdbcbcababbbcccabccadddadcaddabcbabdcaccdcaacbadbddbcbbbdcbcaadccbdcdcabbddccddadbbcbbbaabcbcccccbadbccbdcbadcccdcbdbdacadcdcdcdcddbbdaabcdcdccccbcdcbdddabdddddcabcbbdaadddbadcaabcbbacbbcbddbcddbadbbabacddcccdbabcbbddcbddddbbccddccbacaddbcddbaadbcbdcdddccdbbaadbcaacdababadddbcaadaaaabbaddcadcbcaaaacadadccabbdbdbcadbacaabbccdddacdbdadbdbaadbbabdaaaabdbbdaddcbbbbbdaadccccccccababbddbdaabddabcbdabdddbbdddbacdadbbadbdcdacbabdaddadababdacdbccacdbdddcdddadccaaaababcddadabdcccccbcbbbbccabcbaccbbbdcdaaccadddadadaabcdaaaabaccbccbacadaccabcccccbcadbbddbddcbdbadadbdccbbcddbcbadadbbcbbcbbddcaabbdcdbdccccacdcbbdccacacbcbbbbbddccabcdacddbdcabacdacbccdcddacdcaccdcaadcbabacdcaddbbdcccbadccabbcbdccddbcadcbadbaaaccdcaaddaabbbdbcbccbbadaacbbadcaadbcdcabbbccdbdacdcbcaabdcadaaacdbbdddabcabbddbaabcddacabaccbcacbdcbcdcdbaccadaabddcdcccbcbdbcdabcabdadaabcbabdcbdabcbabdacbcbbdcacadddabbdcdbdacadddacaabaabdbdcbcbcbdbdcaacabdbccdcacbdcdccccddaaacccbbdabdabccdbbaaddaadaacbbcabacdabccaadcaaabcddcadaddcbbbcacaccdddcbdccbdbbcbacbdbbdcbbcdaaaccccbdcbacdcbacbbabcdbcbcccdaaabbbddbdaccaadababbacacbcdbacddbadcbdccbcbcbdddbbbcccaadbbcdddbbbabbbabbbcbaddddcbcadabbddbbccaacbccbddaabbcbadbbaabcaacccdaabdadccbaabbcbcddabcdddaabaaaadbbcdabdbdadbbaadadcdccbbbdbabacbadddddcbacdabacbbdbcbbcadbbadcbcdcbbcbcbbabcdccbdcbddddddcaaddadabcdddadbdbabdabacddaddcbddbbaaaccdccabdccddcbbbaddcdaaabcbbbcdaadacaaaacdabbabaadabcacaabcbbaaccbdbbadcdadbcdcaaaadddbdcdbbacdadccdadbdddbabcaaaaaadbbdadbccbaadbcacbbabaddbcccddaccacabcdddabbbdcacbbbbbbdaabccbaaabddabdbaaaadbbaabccadbdbccbdddbcdbbabbddaadbcbcacabdaabcdbcbcdcbbadaadddbdaabddaabadbdbdcbdcbacbdcdbdbabcadbacbddabaaaadddbcadccbbaaadccdaabcdccdaadadacbdacdaaaabccabbbadacdcbdabbcbddacaadadbadddacbabababdbabddaacbbabbddbbacbaddadccaccdcdbbaccccdcbbbbadadbbaadddddadaacbdcdabcdcdbaddbbabccabcbdddddabddcdcddaadbddcbbddbcdcbbcadcbdbbbbbcdcabaddabbbcbbbcacacaacdcdbdbabdbaaaadcadbacccaadbaddadcacbabbcacdaaacbcaaadbdaddadbdccccccdbdabcbadcdbdbccccdddbbadbbbdcacabddcaccdaaddbdbabbbdcbdbacbbdadacacadcdccabbbdccadbcabbbadbdddbdbcadbbcddcabdacdacbabbcbcdbbabdaadaccadbbbacadbbddacabdccddadbaccccbbdcbdbddacacbacabcccbaddacddbddddcaddddccbcbbcdcabdbddbbbabbaacbcababaabddcababbbcdcacbaacabacacadcccbadcbaadccadcbbbbaacaabdacbabdbcdcabaabbcccaabaaabaddaccacddcdbadbccbdcacababcaccaaacbbdbbdbcccabaacccaddaacddadacbadbbdbacbaddaddccbdddbcabcddcaccbbdaabadaabbcdcacdaddccaaccdcbaadcbccbbbdcdcbbccdcbacddbaadacbbdabdabacabdbdadbabddbccdcadabadbbdddbdcbdbbbcbccddbcabadbcdacadcbcacbaabcdbddbbaabdadacdbdddadadadbbdadcbacddccbabdaaabbdcddabccacdcbbdbbcacaddbcdaddbbababccaababdbbadddbaccababdbacbaccddcaaacbcdbbddababdbaddcaccccbcbddbcdcdbdadcdbcddddbbdbcdaabdcbbbbcccabcbaccadcaaaabcbababddbabddcdbaabdddddbdbddacbdcbcccbaccdcabbadadccdbcddabbaddcdcbacdccccbaabccdacaaacbccbcaaacdaddaacbddacbabddbbacabadadbdabdaddbbbcccbccacdaccddcaddccadbdaaddacbbbcbabaacdbdcaabbaabdcaaaaaacddbadbcaaaabccabdccaaacaadbabadbcdcdbdbdbbcbaccabcdcdaaacbbacbbabcacadcbdadadcbcdbbbbbcdbbacdaddbacdabbdbbbbbacabdbadcbbabdabadacdcbdacddccacbddbbddadbbcdacddcadacbaacbbccbadcbcaccbabbcdbddbcbbcdcadcaddbbadbbacbbcbbabddbbdccbbaccddcdcddddacdaccaddbbabbcaaadcbdbaaabdacdacdbababacbabacdabcaddbaababbdadcaaadcabbdcdacccbbcccbbbcddbbbacddacbbdabacaddcbaaccbabaccbcbbbcaacaabadcbdaadcdaaacbddadadbcadbabbcaccabaddbdacabddbbdadcccabacbaadddccddbaabbddabbbaddbdbbcbcdbbbbdacbcbcacacbbbdddcbcdbcccbdbbdcccadcbcbbcadadcdccabbcaabcdcaddccbdacdddddccaacbaddcdacaabdbccbadcadbcdbccdbabbbadbacdccdddcbbdacabddbddadadddcabcdaacbbcabbddccdacacaaabaabcbdacbbbabdcdcbccbdcdbcccbbabbdadcddbabcabbbdcdcabcdbddcdbbabdabbdcdcddbdddbaddddacbdadadbdcbbbbcadcbdccadabadbcadcdacadcadbacaaaaaabacdbdddcabadcbcbcdddcacbbdabdccdbdbccbbbcabacacddcbdddacbccbbdddacacbbddbabadaacdbadcdddaaadcccaaaabcbbacbacdccdbabdccadaabbadaccdcdabdadacbcdadaacbbbcaaaccdccdaacbcdbaabbdcddcdddbcbdbbccbaadbbccbadccaddabcaaaacdcddbadccdcabdacacbcdccccadaabcccbacdbccbcacccacabacdbbacbbdaadcdcbdaacaaddcccccdacaabbddbcbdadddabccbacdddcaabadaaccdbddadbbdcbabddbcadbaaacadcdaccdcaddabdadbcacdaccaaadbacddadbaadbdacadbbadaadbcadaccaccacdaabdcbbcbacccabacabacbacdccbbddadcbbddbbcddbdadacadadbbbadbaacbdcdcaaaaadbaccdbacbcbbdaabdadabcdadabcdcbcdcbbbdccdcbdccddaadddbddaaccddaccacababaccddbabbbaccddccbaacbaddbbababacdcdcabdcddaabbcbaadaacbcaddbabdaaaaaddaaacbccaadaacdcbbbbcccaadbbabdddcbbcadaabbcdaabbcccdadabaaabadcaabbadbcacadabbbbbcdbcbbbdacdbcbcdacbcdcadbdddbddbcaabbdaabdbaaddccddbdadabaccdccddbbbaaabcccaacaabcbacabcbddcabdacdcbaaacdabcddbaabcabdccadabbacdbaaadacccabcddcbabbcdcdcddbddcadacbcadadcdbabbcccdccadbacbdddcaccabbbcddddbcccbbabcaabacbbcbcadacbabddcbbcccacdcabddaabbcbabacbccbbadcbbbdcacbdadbcbbccdbcdaadbccbbadbabbadaaaccdbdbcdaaaabbdbddbbdbccddcacdadabbdacbbabcccdcabddbbcccdadbbcdabbcddcbbdcdcdbacbdcdcaacabaddcdddadcabcbababbdbddbadcaaacbdccbabcdcdbcbcaabcbaccbccddcccdadcdbaddccddccdbadccadbdcdbbbccdacacadbbbacdabcbdbdcdcdabdabdbadbdbcbabacdabacdcdbadbdcddacbbccbcbddddadbdbabbcbdbcdbbabcaaddadacbbaccccabadbabbcdbdccbdbabcacbbadaaabddcdcbbcacdcaddcaccdbcdbbdcdcdccaacbcabcbacbbabdbadadbbcdcdccccbdbbbdadbcbabbbddaccccddaacbaccccdbcdaddccadbdaccbdcabbbabdacabbababaacacbdcadcbcabacdabacacaacbccbdbcababcbbddcdbcaadcaaabaacdbaabdcacccccacacbaadbddcdacbddcbaabbcabbadbadbccdaaddcaadabccadcdcdabacbaacbdcbcbbdabcdacbcacbcaccdbbcbaccaccddaddcacddaacddbdaaaabadbacabaadbbdadddcdacbacbddacabdaaddbdabdbbbcbbdbdaacadaddcbababcadddbcbcbacbcdcdadcdaaabacbacabaabccbdbdccdcbcadcdbbdddbdbdbdcdcaaabcdbadbcaadacdddccbcaabbccadadcdaabcacbabbdbcbbcaaaadcbcbcdabcababbbbcbdcabcbdbcacdbabccadbcdddbcabcabaacccbabbaacbcdabcbdabdddbdacaacbacdcdccdaccbaacbaccdbddacdabadcbdbcaccabddbdbabddadaabadcaaadddaaabdbbdbacaacbadcaddacadcdabcbbbdadccbcdbbadccaacdbacaabaddbddbcbbdcadadddbcadaccccbbbdcdbdbaadbccbadbddbaadbdababacaacbcbdcdcddbddaadabcccbcbacdbddcbcdacabaadacbbcbdcdccabddcadcbdacbadcaaddbabddabbcaacdaccbbabacddcdcddbadbbdacbbcbcbbcbcdaddbadabcbbdcadbbbadaccabcbbcddcaadbcdddcbbbcbdcabccdbbbacacabbdcddbdccbbdcbcbcadccabdcccbacabcdccaaadbcdbadaaadbbbbcdddcdaaccddadccbdbaccdbabcbcbcdbbbaacadddabbccbdbcbabcdacdacdabddbdabdccabacdaacdcccdacbbcdbccaccbdbbbbbdcbbbdcdbcdbbdaabaabddbbabbabbbbacdbddbbddacabbdccacbccabadbbbcddccbacaddadbdadddaddccbdcbcbbacddadabbbddcabccadacadccaddcadbbaddbbabcdadcbacdaaacddbbbbacddaaaaabbcbbdbbcabcaddbbccbbdbbcacdacdcacbdbcbccaccbbbbbbacdbbdcdaabbdacacbbcadaadabaadadcaccdcdacaaadbacdddcdbbaadaacbcacacaccdddbadddacdabbadcadabccacacdabdcdcababdbadacbcbbddabbaadabcccbbdbccaacacddbcdbbbbaddcbacddbbcaccdaacdccbbacaadbadaabcaadacddcdbddbadbdcbaadcbddccaaacaaaaaaadaacadbddbdddccbacccadbbdcbbbadaadbbcaaadcdabbacbcdbadacabbadbdccbdccbdbbbbdcbabbbabccbaccddbbddadaaacbbbdcabbcbdcdbacadabdbcbcccadacddaadbddabcdccaabbbbddcadaabbbbbcbbcddbcdacbadbacabbbcdbababbcabbbdcbdaccdacadadacacabdcaaacabdaabbbbcbcabdcdcaacacdacbccdbccbdbdbbddbcbbacbacbdacbdbbaabbcbdadbadbadccbabaaaadccaaccbadddabaabaaadbcbababacabacbacddbabbbdaacccbcbbbbadacbadcbccacababcdcbabaabbaacddbcbcdacdadaababbdbcbaaccbdddababccbdcabcccccddbdddcadabcadbabccaaaacadabcccddbbbddcbabbaddbbdbcbabacacddbcdbdccddbacdacccdabdaacaaaababbcddbbdcabbaaaccaabdcdaabadaacbbdbcadcbcbdcbacacaabdbaaabdcdcaadccdabbdccbcadbbccbdbaadcbdaacabadcddccddaacadaadcddbcaddbaddacabdbbbdccdadddbdadadbddccdcccabdbdcbcbbdcaccaabaadadccdccadacccbbcdbcabcadbaadadddadbaadaacbaccbacbdaadadaccccdcbcdcbcaaacbcccababbbdcdcabcbbbaddccccccadddcbdbcabbacabaadaacaadcbacbaddcbccdbcdbcaadaaacaccccadbabacdcdaabcabcbaadadaddbbdcaaabaccdaddccdabdadddcbcadcaccddbaddadbdcaabaaadbbadadadacabdccdaadcdbbcdaadbddcabadcccbbbcbdbaccbbcabdaddbaccbbacdbbabdaaddbababacacddacdcacacabbaaddbcdcddbacadddbabdcccbcbaadcaaabcddabcaaacbbcadaccaacacabdcccdbdddaabddcadacacccccaaadacccdbdcbababcaabbdcabdbdcbdccdbbaaccbbbcbaaacbadcaacbcbacabdabdccbddcbdddcdbacccaabbbcacdcadcaddbbbbbabbcddbbcbcaccccccdddcadcacadadcddddccaccdbcdabdaccccbacbaccaddaddcbcbcaadbadabbddbdadcbcdcbacaadcdbbbbccdccdcabccabbaacdaccdddcddadddcbcbabccbabdcbadbadaabbbdbaacabadaaaabbadcaadbcdccddcbaccccaaccadbdbcdacbadbadabbbacbacddbdbcacccbdaaaddccbbdacddcddcbbbbadbbabbdcbabdaadbbcbabdcacbbccaabccbaccdbbdbdbdacababddbdbbdadcbaadabccccbcaaadacaabadadbadbcccabaaaabbaaaabbcaaabaacbaaaaddbdababdaddaacdbaadaadacbaccbccbdbcbdccbbbadaccdddddadabccdabaddbddddaabcabacdcbacdcacacacbdccbcabdbbbcaabaabbaddcccccdbaadbaadbbcdcdaadcbcdbddcacbadbcabcdbcddcccdabbbbcbababcbabdcaccaacbbcbdaddaaabcbcccadaabdabdacdbcaabdaaccdbccaabddddbcbabdabacdcdabbbdaaaaaabacbbcbaacacdbcbcaacbdabadccdacbcbbbccbaabdacbaaccabacabdadaadcdbcbdbcacadccdbdacdabcbdcababdcaccdbaacdbdcbdbccccdcacbacbcbdaccbaabaddbabcbabaababadcdbcabcccdcccccddbcbabddddbbbabacaacaabbdbbccadcbdcdcccadaccbdadbdacabbdcababbaccccbbccdcbdccbdcbabbbaaadccbdddbdcddbaccdcadcdcacacbaadcbbcdabaacbaaaadadbadbddaabcaabaacaaabbbcbbcbaadbddcbbabcacabddaadadcddccbdacdbbbdcdbcbdcbdcacbcdcaddcacbacaaaacbdccdcaccddccadbddaabacbbdcbababacbddcdcadaacddcdababcaadaabcbddaadbbdcdcaadadbacacbbabaccdaabcbdcddcaccdcdccddbbdabdacbacacccbbcabacbabbcdbcbdcdbbaccaccdbaacddaacaacdaaccbacccbdbdbabbdbadacbdacdcacdadcdacbcdbdabcbaadbbdabbbcbccddacdabbacbadbcbaccccdaadbcdbddbbabdcdbbaaacdbbaadacdaaaaaacbadbcdbbcaaaaacbcbdabcddcaacddadbbccddacabbdcaccbddacccdaabdabddaaabccbcddadbcadadbacddcacdcabcbabacdcadbbdaaabacbdbbdadccdacaaadddadcbdabddacbbddcbabdbbacdbdaabcbdbaaaddcadcbaadacacddbdddccabbacdacddddacbbdadccdaacdbdbbcbcccbdbdcccacabaaddbccacbaddabbcacbddaaacaccbacacbcdbccbddaacbdaacacacbaaabdacdcabcadacbaacddacdcaddadccabaaccadbdabadbcbccbbcbddcdbbacabcccabcbaaaaabadabcadbbcadbbaabdcabcddcaaaaccadadadadccccddbabaaaccbabbcabdcdddcdadcaacacbdcaadcacabddbaaaddbdabadaddaaaaaaaccccdccaacaddaaacbabcbadcaadcaaadabcdabdcbbcdbaacdacadadacaabbbabadaaccbbbabbdccaadbbbbbbddabbaccddbdcbcabdcddccdaacbcbdddbbaacaabcbdcccccacccbcaddabbccbdcbdacccacbdbccbccdacbbdcadbcbbbbccabdbdcdaaacadcaacccaacdcdcbcaacdcbacbababcbabdaadabcdcbaaadacccacabcdacbdbdcbddcbbadbadcbcdbcccbdbdcbacddbbacddbbbbcddaadcbbdcdbbddabdcaaaabaaaaaccaaadddbdacadabbacdaddbabcdbcbdaaddcababaadcadbdbcccadbdabadadcdcddcccaabbdbacbbbaaabcbaadbbcdddddaabdcaddbaaacdcccbcbcbbbdcbbdbbdcabddcbbdccddbadbaadbadbabdccacbaabccacabbabdabcaaaadbdcdccaaacbadaabaaaaddabcbcbbcbddbbbbcaabddbabadcbbbdbbdbbcdbaaadbcbaabdcbdcbdaadcbadbccabcbabbdcdbcbacdcdbadccdabbcaaccdaabadcccadbccaabbcddbccacbdabdaabdccdadcbacbabdaaadcbcaacbadddabcbacbbccdbcdccdcdcbdaabadadcdbdddcbdcddadaddbcbbacabbdaddcbaccdcabdabaaddabccdcddabcbaadaaabbbddadabbcbdcbcdbcdabbdbccabdbdadaaccddabaccccacacbbabbccaccbdbdcccabdabbddcdcabdcbdbdbdbabbaacacdbadaaadaabccdcdbccddcdcaaccacadbcdcaddbbddcddccddcbbcbdbbbbacaacacdaadbdaabacabbbdbbcdacbccadccbaaadcdcbbccdcbdcccbbcdcbaabdbabdddabccdcccddcaaaabbcbbccdcddcdbabdadccbbcaaaccabbdaaadaaaaaaddabcccbdadcbcddbacbacadcbbdcbacccbdcdabdabdcacbccbdaadacddaadabdabaaccddccbdcbcdbbcdbdcbbbbcdbccbddcbddaabdacdbddabdcbdcbcadaddadaaccadcaabacbbadbbdbdddddbcbacdcadaadbcbaccbaacadabddcbadabaaaddcdbaccbaaadccbcbdccdbbbadadcaddaabaacaccbcacddaabddabddacccacabcabccacbcddadcababbcdacaccbcccaaacdddbbdcdbcbbbadcbbcbbcbacbdddbdbbcbadcdadacaabdcbbadbcbbabcabbcccbaccdcbcbabbadaabdbcabacabbdabccbbbaadddadcadccacccdbabbbdddbbbadbbaccbbbabaaabdbbddbbbcdaabbdabaadcddacdacddcdbabdacaacaaacdbcadabccadcdaadbdaabcbcbdbbcdbbdcacbdadbbcbcdcadadaaacbcbdbbcbcdabbdaddcbabdbbdcadcbcaacccbbdadcbbabdaaccbbcbabbbcddcbddacbcdbdabdaabdcabcddccbccaaddababbdcbcabccdbbddadcdbbdbadcbaabacccbdddddbddbadacbcdabbbcbcdaadcabcccacddbcbcdbdbcbaddcadbaccbddcbdbdbdacabccddacccbddcaadddcbacdcdadcacaccbbbacacadcacbcbddbbdacbadccbccdbddabadcaccadbaddaccdcabbdbbbbbcbbaddaaddccbddaadbbbaddbbcbdcbdbbbdcabbbdbbccadcabaaadddbddaadbcbdcdcbcdaddddccbdddaadaadadaaababaccdbbcabcdbbabdcbaacbaabaddcacccabcadcaacabbbacdadbabccdbbdcbdcdaaacdaaabadaccabdddacbabcbadbccabcccdcdccdadaaaabbdbacbbbcaaacdadaadbabdccdddcadcaadcaaddcadccacdabbbacbdbbddbcccdccaaadbdbbdbbbacadccaccbbacdadcccbabbcbdacccccbaacadcdadbcdcabdbbbccaabcbacdcaabdadadbbbbcbdbbadbabbcacccbbcccbaccadbdabaabdbabbdacdcbccbccbbccabbaacdddcdbccaaabdcabacbbcacbaddadbdbcddcadcabcccccabdcbcdadaaaacbdbacdcdaddbdcbdbcadbdccacccddbdddbbabbaadbdacbbdccddbbcccbaccbcaccadccaaccbcbabcddddbaaacccababaadccadaabcbcbaddcbcaaddbccdbbdbcbcacaddcdabdabaccdddcdbabdadacabdccbaadadcbadcdaaaaabdacbdcdacbbbbdcabdbadcbcbbcddbcbabcbabdddcbadabdcacdcaccbbabbbddaabccddacddaabccaadbdbadcabddbdddadddcbccaccdacbdbdbbbcdcdadabbcabacccdaadccbccdaaddbddcacbcacbacdaddcdcbaacccdbcdbabbadbcabddbbccdaccdabaddccdbcadbddcbcbcccdbadcdabddcdcaaddcdaccccabcbcddaddbccbcaabcbbdabdcaaccddddcadaadbacdaacacacdcbbbbadccdbcdadbadacbaaaaacbbbaadcaaabdcccbcdbbbbbbabbddccdccbdbabaadcbbbcdbccababcdabdcbacaadaadddbcbcabdbbcacbdcbaadacdcbddccbdbdcddacadddbcdddcbaacaadbbadcdbbbdbdcbcdbbaaabcaadbaacadddabaacbccdbcbcddbccdabaadcaccdbaddadacbbcbdacbacbaacbacdbccccdacddddbbaabccacaadccadcaacbcddccdaacbcacdddcbddcaccddabcbabbbdcdbdabccadcacbbbdaabdaadddadcbbbadcbdcaadbbdcbddcdabaaddbacdbacccdacdcaccbcdadddbbdaabbabdbacacdbdabccbabcdcacdcbddbaccbbbccadcbababdbcdccaabccdbdacccdbbccbcdcabddbddacdcaccaacbcaaabdacacbccddccabaaadcbdbdbcaddcbcbdccdddacddadbcabaccccdbcabacacadcdabacbcbaccbddadbbccbddcaacdddddaadadadcdbdcdabbcbabadbcddcdbdabcdddcdddadbbcabaaccddbbadccacacdacdcccbcadbaabbacbbdadbaadcbcdbdcdbdacacbaaaabaabcdcaabcacbabccccadcbcbccabddbbbcccbabdbdbaddaacaadbabaaaadadbbbbabcbadaaaadbdcbdbddbddcadddacdaaabcccaccacddbdcbdadababaadaccbbbdbbcccadcdcadbadbaddbbcadabccaccdcccbacdabcbdcbcbdcbdcbdadaaddbcabdacaaabcacdacccacbabadabddcadacadbadacbbccbbbcaaacdbacacbbbdcbbadbbccadbbbbdccdacbcadacdaabacbbcddaabcccbdbabacbadcdacaccddbcadaccadacdccabcadacbcabddbdaabbdddbababbcaabbcdbccdabbcbcadcbcccdacbdcdbdddabdbdaacddadabaddbaccbdbdbcbcccbdcccbadaccadbdadbadcabdbccacbbaddaabdbbbdbdbbcbcaccdcbdbdcbdbdbcadcddacbccadaaaaaaabcaabddcbddabdbadababbddaccbbabdacbbcbaccadabbaaddaddddbdbacbdabdadbcacddaddbdcabadabddbbdccabdaddabbabbbdbbabaadbcabcabcccdccbcdbbabcccddcbcdbaddcbcbdaaccbccabcddacdaddbcbcaddcbbabaadcbbbdcabdaadbdadabbbdcacbaacabcccddcccdbabdbdcdbaddccacacdadcbdbbcccaaaaacadcdabcddcabadddcdcbabbadabccdaadbdaddbadbabddacccbdccbdddbcdcdacabbabbaccddacdccdddcbbdaabcabdcabcadcdaaabbadccdadbcaddacbaaccccddbcaacbbabdadacacabdccabccbabdaabcaddbcbdbccabadcabbcddabccddbddcadcbbdabaaddadadbbddcbcbdbdabccacbccbccabcaacbcbabacdaadbbabaacdaaaabcadbcdbdbabaaadcdbcadaacbadacabcccbbdabdaaadbbbdbdcbccdbbbcabccdadcababbcaccdbbbccdbaccbcddaccbdcadccaddaccbcbdadadbccdcdadccbadbcccaadcdcdbbaabbadcaadaaabdbbdbccdbddcdaaabadabddbcbbccadaabcaabadcbbdbdddcadcdbbdddcdbbcaadbdcdcccaaadddbdbadaabbddbaaddbbaabcabacddaacdddccadacdabdccbdbaccaaadacddcdbccaccababcadccbdddbcacddabccbccdbbcdabcacdcaddddccdadaacacccdccdaccbaabadaddadbbabcbaabdcbcbcdccaadabbcabadbbcdacdbccaacaccdccdabdddbabbaccbadadadcccbabdcdcabadadaddaabaaddbddbdabbaabdbcadadaabbaacbbdacccccaabbcbaacbbdbcdcdbbccdbbbacbcddaaacabbbdbcbaadcbadbdddbcbcdcaccbcccaadcbaadcddbbdccbbccdbcdbacbdbabadbccbbaddacaaaadddbbabcdcadcadbdbdcdabbdbccacadbaacccadcbacbaaccddcacdaacbdbdbdacbbabbdcacbbccbcaaddbccbbaddbacbbcadbcbcaabddaabccadcabaaaddbbdaddbbdabbcccbcccbdcbadacbdbddadddccdabdacdadcabaddaabbaadcbdaaccddbdababbbdbbcbadcacaadcbbbbbcbbdbcacbbccbaacdcbcdcdabcbaacaaaacbbddddbcadbcbddcddbdccdcaddccabbadacadddaabcbdaadcbddddadaacaadaabbdccdbccacdbbbcacbadddddbdbddbddcbdaabaddcdccdcddacadcdcdbcbbcdacdcadbcaccaccabbdcacbadbacadcacdcdbddcbcdcbcdcdacbdbbaddbbddcddbabbccabbacbcbcaacbcaadacdacbaccdacdacaadbbabdcabcdcacddbbaabbaddcbcabcdbadddddbddabdadadddccbdadcbbcacccddaccdbcccddabddabdbdaaacdcbcddabbaabbdacdadbcabddcdaabcaacadabccabaccdaaacdacddccddaacbacaccbbadcdacbdabdddcaaddaaaabadddbabacbacaaccaddadacdcdbaccddcbdcbdbcdacccaabdcbbbbddbcaccdacaaaacabcdbbaccbbaddddaabcaadcdcadccacdbccacccaabbbcaddbbaddcabababccbbbaaccabadbccdbddcabcddddaacaaacaacccddbcdadcddbbcacadddcccddabddacabccccbacdccdacbbabcdcdcdacddbdbbabcbacccacaddddaacbadcbcbbaddadccbabaccbabdaadcaaaadbaaacdbccbaaaddbaaddaaddcbdcccdadbacddadaccbcddbcbcbacaabcbaaaccdbbcadccabbadbabdadcddcdbcadacbbcccddbdbcbbdaddbbabdcbbbcaaddabcbabcdcccaabacdbadaccadbbbcbdaabbaabbcddcaadacddbbcaadcaaaadcaddbdbcadcbcddcbbbadadacbdbabcbabbdaddbdcbbccbcacadabccdaacbcbbcacdbcbcacdbbdaabdcdbcabaaccbdbcdacbbaddbadadaccaaccbbaacadbbcccdaabbcadcdaacbabdabddbdbbcbbccddabbdcabbabaccacddcdbbdcdbabdacbbacacddcadadcbbbbadaddccbbbdbbaddcaccaaacdbaaadbaddbddbbadaddaaababbccadaaddaacdbcbcadaadbabaabdacbdbcdaaabaccdbaccccbbacbccadbacdcadccacdbbadabaccaccacbabdccdaaadbbdbdabaacbbabaaccbbdddaaaacddaddbbbaccbadbdcbdcbbdcccacaaccbacdabadaddbbacbddccadbbccabcdbabaccaabccbbcddbdcabbddbcaccdabacbbccdcacbadbcddabdcbacdaadcdbadbbcddddddccbbdcbbbabbdcbbcbbccbcbabddcabaaabbdbcbbadaccacbddaddabdcccccbcbdaaabadaaabcaddadabccadcdaabaadbbbdbbacccaacdbdbdcdabccdbbdbbbadcdddccdabbbccbcbdcdadccddacacbcddacdabccaadcbabdbabbacccdbabbcadabacacddbbcacaaacbdbbacddaddcddcddabdcdabaaababcabacaadaadcacbdaddaacadaaaabdcbdabdcbcbbabdbcbadcdbaadcbbcdbacbdadbaabcacaaddcbababdcbaabbdcbbacdbadabcaacaccdabacdbdbadddbaabcbbdddcdaabcaddbaaaaccdacbbbcdbbbaddbbbbaacadaaabbbbdbdcbdbaacabbbddaacbcddaaddcacabcccdbdaadccdadccacccddabcbdabbcaadcdcdcbabcadadcabdccdddccaababaacdbdbcbdcccacbbcddbdaabcbcaababcbabddbbbaddbbcabbbbbddbaaaabcdacccccdcdbadbbadbdbddcacaccdabdccbbdbaccbdbadaabbbcbacacaadbccbddadadcbccbbdaddbabdadbacaacbcbbbdcbdcdbcbbacbcbcbccbbbcabccbdabbaacaddbcadaaddaadcbcadaabdacbdddccdddcabdacacdcbaabbdbcbaccbccbabacbaaacdccccbdcaccbacaaadaaaddbbbcdbccadbcdbacdbaaacccbbdbbccccbcabcdccadcadbccabcbabbcddabdadbadbdabcbaccccacccddbbbacadabacccccdbdbcdbddacccddaabaaabbbadaccbcdccacdacbdcbddabdaabaadbbcbccdcddcdacabcadabadaadddbccdaabccaacdaabdbbadcadcdcbdcddabbdcbccdbacddbcdbaabbacbdbbbcccbccccbddbbaadaccabacacddddacbcabaaccbcdcbbbaaddbdcdadacddabdddbccbbabacccccbbdadbbbbcaabdadcbddbaddbbaddabcbcaaccdbdacdcbcbbbcaacdacddbcdcdacaccadddbdabdadabacacbcabcabcbccccaddcccaaaaabdadabdcbdcabacacddbbaaccadccaccaaaaaabdaddabdbcdacbbacbddcaddcaccacabbcbaccbdbbadbcdbdbcddbacbdbaadccddccabcadcaaaddacdcbcbbcdcacdcabadbabddbaadddadcabcaaacbdcdaaccabadacbcbbbabaabacdaadccdcbccbbacddbaadbcbabcaaadccbcdaddadcbddbbbcabaabacabcdadbaccadbbcbcddddcbaaaaaccbbcaddadbdadcbdabcdbbbacccccbdacbcbacaadabbdccdbdbdddcbdbcdaabcccacdbbbacdcaccccbcdbabddddbdbcbdcddcbdbbdabadddaadccdcccbbaaacdccddbdbdadaabccaaadbcadcccbabdadcaddcababdbdbacdadbabbbbdadacdcccacccbaadaacbcadccababbdacaabadabcbaddccaaaccddbadbaccdaddabbcaaccbbaacaddabbabacddaacadbadbccadadbadbbcdcacdbabadbababdcaaaaccadbadacbcdccadadbabaacadbbbdabddcdabdbcaaaadadbbdadbbabdcbbabddbcbddbadbcdabcaacdcadcaadacddcbccdbadcbbbddbbadcdbdaacbaddbdddbaccdbacbadbadabccbcacccddbddcdddcddbbcadcddbcdacdccbcabbcacccccdaaaccddddcbbccbacdcddddacaccbdbadccdbabddcbdadaacbcdbbddabdcacadaadbdbabbccddaddbbcbabaacdcabddbdcbabcddddadbcdbdbadcaabcbadbbbdccdababbbacdccbabadabcdbdbcadaaacbdcacabaccdddbaabbbabbdcddbadcbaccbbabcdcdabadbbabbccbcddcbccbccadcabbccddadcbcddadcabbddccbadadddcaadaacacbbdccdaaaaccbadaabbbcbbabbadcbdddadaacabbccaabdcbadcabcaacbcdcbadcbdccbaccacbcbccdabdbaadddccbabbacaaaaadbdaadbcccaabbdabddabcadcbbabcdbbadcbaccdbcbdddbcdbcdcddbdabdbcabadbdaaadabddcacaabbbacabdbabcbdcaaaaddbbdcaaccaddcbbbbcabbabababddaabbadbbccbababdbddcddacabdcadddcdbdadcbccabcccacadababcdcbddbbabdbdccabbdaadbbdbbccdacbaccbacacaadaabbbacccdccbcccddaaaaaaaacadaaadcbdcdcdacacbcdccaccdaadbccbddbacdabdbdbbacadcabddbbccddcaddcaaabdbcccaaacccbccbadcacdccbbbdddabcaabacabcbaacdcabaacaabbdddabbaaddccbbccdbcccaacdddbddcaabcabadabababddbdbccbcbdabbbaabacddbcaaaaabbcacaaababdacdcdbabcbdcbcadccbdabcaaaabdcacaacdabcdbaddccccbdddaacddabadaaacacadaadbcababdcdacdccacaaaaddbccdbacadaddcadbbcdaccddbddcdcabbcccdaacadbdacbaaadacabaaadaccbbdbdaadaccabbabbbdcabacbcbcbabbddbddbdbbcbddabbbcddcddcabcacacdbcbbdbbbadbddcddbabadaaaaaaabbbdcbcaaaaccaaacdbaccaadabacbbaaccbcbdddddcacdcbbcccbcddccdaaddccadbdccddbcadacadcddbadcbdadcaabdbccbbbccdbaccadbcaababcdcbcdbcbddbdadbccbbccacabdcabaddabbbcacdbcabbcbacabdbccbbccaaadadbddbabcbdbbddbdbdbccadaadccacabdaabddbabbddabdddddbadadacbdadacabcbdadbbaadcbcaaccadcbabdacbbdcbaadacbdabbcdccaddbaaacdadcddcccdbbcabbbbadacabaccccadacbcadbdbdacddbabbbdccadbddcdbccbbdddcccccadccbbbcaadddbccacbdbaccabbbbabbcbccdcaaccaadcbcbadacccaadbbdbaabaabccacacbbabdcbddddaabacbaabbcaadabadabaddcdaaddbacbdbaadddaabacacbabacaabccbdbccbbbbbdbacbbdbbabbdadcdddbcabdcdbcaccaaadaabacbdbdbccadacdcbbadcbbacabddddaaddabcaccbaccbcccabbacddbbabadbcbcbcdbccacbdcacabaaaccacddddabdbadcddcaaaddbcadabbddbcabddccabbcdbcababbcabacbacbaaacaabbbcaabdbdcbdccbbbdbbaacdbdbdcadbcbdbbbcbcbabbbcbbcdaddbabccccaadcbcbaacabbabdaacbbaccaabddcdcbdcdabbadbadbaabbabdcacdbbbdbcacabccdccadcacdbdbbdcdbcbccddacbacdcabdbbaacadccdbdaaacdabbcdbcbcdbaaddbcbdcbcdcdbdcadabdaacbabccbcdcbbcbbaadabbddcacabacdbcadcaabaaaacbadddccbccbdbabdccccaaddacabcddccdbdbcbbcccdbadbacccddbadbccbadbcdcbadaaddbcbcdaddcdccaaaabccabddbbcdbbcdabdbbaadbcabcdcbdaaabddbbddcbadccaddddcbcadbbbbabdddcdccdadcdacbcdcbddcdabaabdacdcbadbaabaacdbdbbdacadbcdcbbacadbdcdbdadbaaaacdaaaccccbabddccdcaaacbacddadbdcdbbdcbadadacbdacbbacaadcdccdbcaddbcdcdadcdddcaaddbadacaabdaddbdaabdabdacccdaacabdcccbdbadbbcdcadbcdbbdacdbbbacdccddaccdabcbdaaddcbbcbddabacbddadadbdbababddbbadaacddbaddadaddccabbbcbbacbbabcbacaddcbdbdcdddddccbccbcaabbbbbbbcccbabddaddbcdbdbabcabbbcccbdcabbcbbabdcddddcdaacdbcbcccadbbdbcadbcadbcddbdccdccddacaacaaccdccaccbdbccaabaccaabdcbccacccaccddaadaadabdbbcabcadcbbaadcaaacbcddaabccacacaddddbddadbbaabbdcadbdacbaacdadbbddacdbdcadcdabbdbdbcbbbabcdcbbcdcbcabaaccbadabdddabcabdabaacdbccbdbdcaacccbcbcbbbcbbbccacbbcdaaccbbdbdccaaccbdadcbdbdcababcaadaccccdbcddbdbbccbbbccbdbaacdddcbccbbabbcbbbcbbabdccaabdbadbbabcacadaadabcaccdbacdbcdcacdabaacdcabaabbdbadbcbbbacbaabcddabdbbadbbaacbcddadadaaadaaadaababdbabdbacaabacabdcacaddacbbbcaddaaddbdcbcdcacbdccbacdabccdddabbdcbabaddddacaddabadbbcadbadcdbcbcddccccacbaabacdcabbccaaadcacbcacaadbabddacccbaacdbbccbdcaaccbbacbdcbddbccdabbcbabdacadccaabccdbabddccacdabcaddbbcbaacdbdcaaddbccdbcacbdacbdbbdabddcbddaaddadabcaadaddabcadacbcdacadbabcacaabbdacccccadccdcdbabcabdadabbcaadbcdbcbdcababcddccadbcdcabbdacbdbbcbbbdbbcabbbabccbacccabbbdacbacaddbaaccbacadbabdbbddacdccbadcbcbdcdcdcaaddabcccaaccdccbbcccbaadaccbcdcdbbdcaddbaacabbdaaddababcaccdbdbcabcdaaaadbcaacdbcaaacdbaccaccaddcbcbbdaabbadcccaadadcbdbbdbbcbcdccdaacaabadbaccbdaabadcddabaadaddcacdacccbbabdbbabaaaaacbbdbaddbdbdaacbdabbcaaacbcbaadbdadbccdccaabacabcbcbbcbbddcacdbcdccdcdbdadcadddaacabcacbacbbdbacdcbdbddaadccddcdcabbcbccddbabbbdbbcadacdaddacdacbbcbaaddacbcbcdadcbdbaabaaadccddabdcbacabbcadabccbabcddbbaddbcccbdadbdaaadbabbbaacaddcaccbbcbdbddaaadbcbaddaabcdcbbcccccdbbdaabccaccdaabbdddcbaaabcbcdaaacddcbdddaacbabbccabbccdacddccbaaacdacdddacbcadbadcdcddcddbddcccddaabdbdbccccccdadcaacdbdddaabbaddadadccadddabdbabaacccadabbabaaadbddabaacadaddbbaddbcdcabdbcdcdccbbabbcaccdacbabccbcbdbaddaddddbabdcbcdaaaaccacbbddbcbbbadcaaaddbcacbddcacacbdbbabaabaadcadbcdcaaaddddbbbcbcccdccaccaabbcbdcddbcabcdbadbddacbdcbccdbcdddbdbcccbbabadacaadaccdadcdbbacbaccdaabccdbaaccaaddbbdbbddadadacddacdadbbcbbaadababdbcddbacabdddbcabaadaadbccacdddbaaacbbacbbdcdddaaddacabcadddcdcddacbaacaadcbacdccddcadbbdabcdcddcbaabdddcccaadcadcbbbaaddddcaaaccaaddcacacbabdabdbdccbdbcacabddabcdacabbdbabcdadbadabaaabbcbaccaacdcabcbbddbdadacbabddcaacdabbbbddabaddabcbbcbdcddaababababadcbcababddccacbbcabacadbcadabaabbdcbcdacaccbdabbcdbacbabbddcddccdcbcccabbbaaaaacbdcabbbcacaabccaccbcbcdbcddcbcbbdcddaabdacbacbcbacdcabcdbaaabbadbdbdbbdadcdcbbcbacdcbdcabdabaaabddabdccbacddcdcbdbddccdcdbbcaccddccdadcbcdccbbdcabdcdbdaccbddabcccbacacbbbaababcbbacdddbccdaaadaabadcaaabcadbadcbcbbbbdbbaabacaabcdacdbdcacbbccabcbaabccccaccdcbcacbaadbcddaaaaccdaadcddccbcadaabdcadcacadbcaccbbdcbdbdcadbbabddccbbbbbbdbadcaacbacaaabcaabadabacacbdbadbacbcbddabcabacaddbddaddbdcbcccbabdadcdbbabcababaacabddccccabaadcbacaccaabbcbbdbccdbaddaccbababaadbcdcacbcbcaccbbbbbccccacdbcbbbdbdaccbcbdddbcddbadbbadbacabdbdabaacabbcabdddcdbbaacbdadadbcadadacaacbbadbdcbdbddbdbbbbaacbcbccbbaabaabdcaaddbbdbbdaabadadaccdcbacadbdcdadcacccccabcabadddbcdaabbcdbdbbaddaaacbaacbacccbddddacbdbabdacaccbadbccbcbbbcddcccbbaddccbcddcadcbdcabbdbdcaaabbcdccddcbbdcaccdcacaacdadccdacddbdcbabcbbcdcaadcbbdcabbbabdcdabbdabaacbbaacddbabccbbadbcbdaccddbaddbdcbcaadbcadbdbaadddccbaadcacaddbacadbcbcacdbddabbbdccdcabdcdcccdbcdcdddcbacdddbaabccacacdcacaabababccbccdcdadbacccdccdcdcbcabcdccdbdbcbdcbcaadbcbaabcbadbababbabcabdcabcbaadbbbbcbbabdccdccdbbbacbaacccaaddcabaaacbbbbcbcbdcacdbaaaacddbddcbccbdadaabddcabdabcdadccbbcbbcbcbcbbbabacdbdcddcbbcbcdcdacbcdabccaddbabdbddcdadcdacddbadacaaadbcadbbccadbcccadaccccaaaccadbdbabadbccadaddbdbcbdabbdbaadabcabccbcdcaddbcbddacadcdddabdbbdadcddaaacbbcacdaacbbbdacddbbcdabcabbcddaddcdaacabdcdbcbdacccaadcacdacdcacdcdcbadabcbcbbbabaacbcdcadcddbcabdaacabccaddddbdddbaadaacccccdcbadddaaccaddadabbcbabcddbcacddbdcabbcdcaabadacdbacdababacbdcdaccabddbccbdcddccaddbcccdcddcbdcdcbdcaabaaacadadbabaccbabbaabbbaacdacacabcabddcadddbdccbacacaadadbacbccccacdcbcabcdbdbabbcbadaadccbadacacbbbaddcaacacbcaaaabbdacbabbaaabbcbacdcddbcabccabcddbbbacdadacbaaacccaacdddabaacddaacbadaabcdadbbabddaaddaaddcddacdcdabbbbccdcdcabbbaccdcbcdbadcabcddcacdbbbccbcddbaccdacadbbddbacbadbcadcdcaddbbddaabadcabcbacdbbdbbdbbcdcbdadcdbdbcccdddbaddacdcadbbaccdaabcdadbcddadccaaccccadacaaabddbccccddcaabbadccdbababcadaccbadcbddbcdcaddbbbbdadbddcbaadaddccaddcbcdbdbccbcbbcdccbbbbcacbcdabcadacabdabbdcadbcbbbdbaddddabdcaaabccdbbaccdbcabbadccabbdccabdbccccbbdcbccbbbdcabdcbaadbcbdacddbdbcdaacabccdaaadcdbcccbaaadbcbbbdabcababddcbbadabdcddccadabaadabcddbbbacbdabccbadcddbdcbabdcdbaccbccdbaacaddccadcdbaaaccbbcbaaadadacacbcabbdbccacbdbbdbbdaabddbccabdbadccccdcbbcdcadcbcabbabbaabbbddbacadabbcbdcaabddcdcabcbcaccaabcdaacdcadbabcabddaaacddaddcadacccdddcdcadbbddadcaabbdaaadaaabbcbaaaaacaccbcaabbdbadbbbbdccdddccccbabbbcbdacddaaccbdcdbaacadaadddbccababddbbcdcbcdbacbddddadacddddaaccbabaccacdddcccdcbccddccadaddccabdccdbdccbdadddbcaacdcdbbdddcaadabdcbacaaacbbddbcabbcbbbccddcbcadbccdbbdcaadccddbcdaacaaaacaadbacabbdacdcaabbddaabdcdbdaabcbacdccdddbabbcabaadbaccaacdacbcabdacbdcadabcdbaadaccdccaacdbacacbaccddabdbddabccaccabaabccccccbaacdbdcbbbadababadaaabdaddbbbdddaccacbbcaccbdaadbbccccccdbabbcdccacdbaccadabcdcdaddadbccadbbdddabaccdcadacdadcddbbcdcadabacacabaadccbcbbddbbccdbadaabcadcdbbacdcaddbdcaadcdabdabbadcccbabccabadabddbcbdbbdcdbcabaacdbcdabcbcbaaabaacdddacbacdbcadbdaabccddccbccdacbdbdcddadcccacadcbcddabcbabdbddddabaccaaccdcbaddbcacdbaacaacccaacdaaddbbbccacddbcdddbcbccadcbcbbdccbcdbcbccabaccabcbcdaaabbbcabacadaacabbcabacaccadcabccbadcacdcbacdccbddddadbcdadcbcbacadcbddddacddaadcdccbadbbbccaaaccacdcbbdbaabadbbbbbadcbacbabddddddcbccddadacbdbccdddbbccabddcbabdcccbaacbcacadcdccddbccadacbddddaddbddadadbbcdadbadcabcdbbddcddccadcdadddcbabddcabdbacbadbddcbcddaaddbdcbdddadcabbadbdadacddaccdaddbdbccdacabbccbcdaaacadadbdcccbddccaabccbbccbaddddbcdccdabbaacbabacccadacdccbdddaacbdaabaaddbdacdcabdbccabacccddabacddbddacbdbdabbcbaaaddaddbddacacacbbbbcaccddcadccbbadddcdbbcdcbddbaacddbccabdddabcdbccbcdbcddaaacaacabcdbaaddabdbdbccacdbddcddbcabbabaaabcdcbccacddbcbcdbbbacababbcddcdbacabbcdcaddbbcabddbdddadccabcbabadaaadcaabccadcbccbdbbcccaddacacdbbdcbaadcdbbbbcadddbadaccdcccadaadaacbabcadbdcbbaacbccdccaaaabababddabaacbcbaaaaadccdbcbaabbdbcaadbdcdcbadacbddddaaaccadbbdaddddcbcaddcdddaadaadbdabadbacdcbbcabdacbdbdccdbcddaaccdacbbadacdaabaacbbbdabcacaddbccbcacbcddaacabdcaabdddaddcaababbccdadbabbdcdbbbbcccddccdbabccacddcabaadddadbadcdccccabbbcaddbbdabbddaddbcddcababddccddadccdcdddddbcccbdccbabacdbabdbadadbacabdcdbcbaabacdcdaabdcdcadacddaddcaadbcacbcdcccddbadaaccbadcabbaadbbacccacdabbbadbcacdbdbcbdbbbaccbcdacdcdbbcddcbddaaadbdbccbabacabddbdddacdcdccccadbcdccbdabbaacadcdcbaddcccbdbbabcbdbacccbddbdaadadaadcabcbcddcccabcacabacddaacdbbaaacbadabcbdaaaddaacadbccadddbbaadbdbcabddcdbbdcaaaddddbccbdaadbccdccdccbabdcbaabbcbcaccbbbbacbcdabbaabcdadaadcdbcacaccdbabdbdaccbcdbddddbdcdcbcbcddcaabccabddddbbdccbbcbcbdabdcadbabcdababbbbdcacaabbbbaadcaaddacbabdabdcddacdcdbccaabdcdbaaadcacbcddcacbbdcbdaccacdaadddcbbcdadddddbcdcbacdabdcdbbabbacddbabaaddbcdacacaaacbdcacddbdbbcaddadbaacaaacbbaabdacccbbbaccbaaabadccababddcbbdadbbaabdcacdcdaabbdadcbdcdbbcbacaddcbdbdacbaaabbdbbcdccadbdadacbcbbaaccbbcbabdcdaacbaccbdcddbbaacaaadcdbaaacccacadddaccacabddabcbbcabccaccdacbdabcabdabaadaccbcdadadcacaacbbbcabcbccbabdadbbdbbbabbcbbdbbcadbbdbacadccdcbcdabbaddbcdaacaacbbbdbabdcccdbbbbcdddaccadbadbbcccadcacccaccdacbcdbaabaababcadbacdbacbccddcbaabacbcacaacbbaaadddcadcbaaccabcadcabcddcdcbbaadddcdcbdbdbabbcdcadacbdddabbccdaacdbddaddcdbcadaacbbdccdcaccabcddcdcaaaacabbbaaaadbbcaccdbabbcccdacacbcbacbccbabadababaccdabacbbdacaacaabddaaacabcbbaacbadbacbcdcacdcddaabdabdcddbcacaccdcbbcdcddaaaadbabadadbccbcaccdcaaaabadbcbbadcacccbbbccdacbabaacdaddaccadbdacdaacdaacacdacccdbccabbdccdbabbcddbdcbbaaabddbbaabbddacabdbacbdaddacbcbcdbaddcaaadbaabbdcbcaddadbccacaccbddadcdcdbbacaabdabcaacccadbcdcabaadcdaabcdbdabddabadadcbcbcbabaadbaaacadbcddaddabbcbcbcbdbdcdbabdabdcdbbadaadcdddcacbacbcdbaddbaaddccccbbbccaaaaaccdccadabbcddcbdcbaaabdadacbdbcdbdbbdabbdbacacbbababddcaabbacaadbddaaaccbabababccdcbaddbadbccaabbcbbadddbbbcadadabcbddcbcdcddbdabdcabbdccbddcbabbbaabdddbaaadacbadbbabaaacadababddaabaaacdccbdcdbaaadcbcbccbaadacadabcddcbcadcbcbdacacddbcbaaccabddcaddbabcbdcdabbbdcaddcacbbcbdbbdcdddaadadbddbcadbdaacabdbdbacbaadcadadddcdabcbddadccccadccdcccdabbcadabbbaccbccabcbdcadbdbdbacaddcdabddbdadcbacccdbccabcbadabaadbbcdadbabdbbdbabcbdaccbaabcbababaaabbbcaddaaadddcbcdadadcccabcaaddcdbccabbbbaaabcbbcdcbbabdcaccdcbdbbcddbddddabbddabbbaacdccabbcdbbdcddadaadccbccdcbdcabaacdcbbdcadcdadcabcbbbbacddccbaaabbadbbdbacdabdccbccdabacbbcdddccbcdddcdaaabbbcdcaaadacbdcccadacbdddbbdbcacadddbddbcdbabdcbdacbaddbddaadadbdbbdbbacbbccccbaaacaadcbacdcbbccdacadaddacaccacddacddbcdcbdcbaaaddcaccbbdadabbbbcaccbccadcbddbabdbacccabdbdcadddacddcdcdbdcddcbacdacbabdcadbcaaabcbdddcaabcaccddcacddbbcababbccabcaacbdbbdccadabddabaadbdbcaddbcababccdaccaccbcdbdacddddadbbdbdcaadbcdaabddacdadbabddabccdccdcbcadbaacaccacdabcdbccdacabdbdcdcabddccadbdbcbdcaabdbdddaaccdcbbddbdddcacabcdbddbbcdcbbabdcaacabbabccaaccbadbbacccbcdaadbabadaaaddbccbccabdcccabcbdbcacbbdbbdccbcadcdcbabadbcacbcbbbcaccdacaccacacbaddbccbacadaabbcccbdbaccccbabbadcbdddcdcbddcabbdbccababddadabdcbacdabaacaddcbaadcbabdbbbcbdbcbddcbbdcbbbacbacbadaddcdbcaadddbdccbdbbcdcddcbaddaaddcdaacdabcbbccabbadababbbcddddbdddabccccbbbcaddccdbcdcbabbaacdbbdcaaadcdabdccacaacddacadabdccbabdcabcbcdabbaaddaaacacdcbccccbdcabcbddbdbdccbcaccddcaabaaccccdbbcababcabbbdbccccabdbcaacbddbdaccabadacccbadaadddbbcadcdcbdcdbabddaccdacdaacdbcbbdbadbcbdbbdabacdcacdbdacccbbaccbdcaacddcccbbddbbcdacbaaddddcdcbdbdbccbabaacadacdabcacbbdcddbbdaddadabdbabacaccccbdcdbdacdcaacbdabcacdaaccadcadaacbcabdbacaacbaccdcddaacbcaaccbdabacadbbdddbababdccdbadabbcbccccaccbabbaaabccdaccdaabbacbcabbbbcaadcacbaacbbcdcbddabdbacabbbaacccbcbcdcbaabddbcbabcdddabccaddbaaadbdabcdbdbddcddccacaaabacbcddddddbdcbcdcdacadacbbccadabcdbdbadbccbbdbdccbcbabcdbdddbcaaacacdbbccadbbabbaacdddadbbcacddadbccdaacccbdacdabdbddacacdddccabdccddadbcbbadadadcbbacaabbcbadacdbabcdcbbacdbcadccccdbbccdcbacabadabacdbdcdbbadbadcacccbabcbbdccdddbcdaccddabacadcbdbadbbcabbccdbbabadcababdbcaadbbaaaadbadddcaadcbaaadbabbbdcdbdabdddacdaabcbdcabcddaadbbbdbdbdcdcccbbbbdacbbcdccdbacccdbcccdadcdabcabacbdabdcabbddcaadbdabbbbdcdadadacdcacbabdadbdbbbdacdbbbacbcccabdaadbabaadbdcbdbaaabbdcdaccacbbaacddccdbdbabcccacbadcbbacdddadccadabaddbbcaacbbaacddcadbabddbaddbbadbcccdcdcbcdaccbbaddbabbaddddbbbaaacccaadaacaccbaacabcccbbcdadcccccadcddbbdbddcbbcbbdcadaadbdacabacdcbcdbdcbdbdddddcccdaaacdddbaacacdcdbcccacbbabadbbbacbbbacdbdacaccdddbadbccdcdcbdbbaaccdccbdbddbdccdaabdcabaaaabdcdcbaccbcdabaadbdaacdacbbddaccbbaacbddcdbabccacdabbabdddccbdcbbdcdbcdcacdcacbbbcddbbaabbdccdbacacccabdaccadcaddbcbcdccadaaddabdcddbabbcbbdcdaadbaabcdbaabcacdbbacddddbabcbdadbadbbbdbcbcdcadaadbbaacbacbddbcbdcdccdddadccadaaaabddddcdcbcaaaaccabcdabdacccccdddbbccbbcbcdaccaacbdcddbacaddcdbbdccdbcaaacdbbaabddbbdcbcaaacadabbcdababacdcbbdbdaacdbadccbcbccccadadabaabbaababbbbdbcaaadaabdaaadbdabcacaadccbdcddcbadbaccdbdbbcadcdacacaacacddddbaacbabbadabddcdbbbabcbaddccdacaadbacbcccaddbbbdcdcddacbcabdbdaabdacadbdacadaacbccabbdbccbccabaaadabdcbaccbbbaaaaacccabccdccdcdabadbdbbcddcabdddcccbbdbbcdcacaabcbbaadcbbbadccccaaddabddddcabdcacabbddcadcdcbbabbdaaabcbadbbcabdccdabacbacdcadbbbcddddcdcbdcddcbcdcccccadabdbcdcacbddcacccdaadacbabadddbdbdacaaacccdaadadcadccacdcacbabbaddaaacabaadbdaabbaadbcdabababbdbbbbaacacabdcdbbdcbcbcbdabbadccbaccbadbcadacbcacabddbbbabbdbbbcbaaacbaccbbcccdccaabdadcdaadcddaacbaccadbddabccadacbbbccdcdddadabdaacadcddcbbdcabbbaacdbadcabacbaabbbddadaddaabcdddccbdddaccadddcaccddacabcccdabbcddccbbcabdadbaabbcbcbaabbaccccbacddaadacbcbdadbbaaaccbbcddaacadbadbdbbbabbdaadababcdaacbbdbdcdabdabaacddbccbcaaacbacdbdaadadbdbadabaabadbdbaccccddbdbccabbdddcaacdaacbbccdacadcbaabaadcdbbdbbcabdbdccbbabbbdcdcbdaacdadccbdacccbbaaadbaaccbbbbddaabcccccdbaacddabbcdcacbdacbdccccdaabddccbccdbaddbcddabdcccadbbdabdcbbabbdacddbacbbabddcaabcdadcbaaccacddadacbbdababbcccbcddcdcbbabbccadbbabaccbaddbbaddabdcbbccbaabcbbbadddadddaadccbadadaccadadcdbccaccbbaacbdcacabdaadbbdcacbcadcdbdbaddabaabbcacbbabacabbdccbadaccaccbccdccabcddbcacacadcacbbcbdacbbbbdcbabddcbddccdbdcbccddcbcccdcaaaccbbbcbccdaabccccdbabbbdcadbcdbbcbaabdddcaddcdadcccbdccdbddddcddccabcdbcacbccccbaacacdacdbcdaddaadbccabddaacaddcdbbdbbdbddaababcbcddbdddacddbaadaacbccdacacdabbccbacdbcacadabbcdacbbcacdacadabcdcbcccacbcacbabbcbddbaaadbaabaadbabaccadadadbddabacbbacbdcddbbbdccaabdababdabcbccbcbbbcabcdcbaabcbbbccacdbdbcadcdaacbaccdacbacbadabaadaacdbaaadcacdcdcabbdcdccabaccbbdcaabddcdbbabbbdcbddadbdadbdacabdccaccbbaabaabbcadaddccabdbddaadbdbdcabcadcacbaaaabdbaacbacbbabdacaaddcdccadbacbbbababaddddcbbdacbcdacbcbdacbccdcbddbacbdcbbdbaacdbadcbbacccbbdcbcbaccadacdbcacdbcaadaacdaddccbaabbdcdaddddcabacaaccdbbbbccaabbddbabbdbbabdcdaabbddccbbbbcccdabbbcbcdaaacddcccacaabbdbabaccabcbcacaadcbbcbdccddcbabadddbcbadcbcccadabadabccccccddbbdccbacdbdacdbbddcdccadbdababddbdbbacabdbdacdddbcddbabadccadcdccabbcdbcbdcbbdddcaabbddbaaccbbbcbcabacbacbcaabbcccccbbaccabcccdbadabacbaacddcbbdccbbddcacaacacabaddcaccdddadccacabbcabaacddcababaaddadadbabdcbbcdbbcddaccccabbcccabacbaccabaacbabdaccdbcbdbccadaaabdbcbabddcadaccababdccbababdccadddacbbcaadcaadacbcaaaacabaddcddabdcbaadaddaadcbdcbdabdcadddbadadddbcddaabdabcdbdaccabddbcbdcdbbdcbbcadcbdbbccbbcdabbddbbaddcdadbcabdbbdddcddcdbcdaccbccdacaadbacbbcbcddddbcaaabdcdbabdcaabcdbddaaaddaacdddabccccabacadcaaaacdcbadcadddadbdbbccdbdadbbabdababdcabdcdaacadbdacaccacdcaccacdbbaacbaacaddbdcbcdadbdaacbacccacccaabbcadacccddccdddcabcbabaabdddabcccccdabcacdccaccaaacddbacdbdbbcbcbbcbcdaaaadaddccbadbdacbdcddcbcdbddcddcaabbdcbbabdcbabdacbadbbcdadcddddcdcadbcdabbdcdabcbbcdccbbdaddadaacbcbcbaddcccdbcababdcacdbcdacaccaacbbbdbdacacbbbcabcbcdbdcbcdadcbccdcbcbbcabbbbadccacaadaccaaaabbbaddbdaacdcddcabcaaccdccbbaaccadcabdbdccacaabbcdabccabbccbadbbdaadcbaabbcbdbbccbacbaadcdbdddcdaaadbaddcbcbacccdadbbcdcaaccbdcccaadcbcacddcccdaacbabaaccadbdddbaabdccbcdcacbbdbabaccbdccacbacbbbbdcbdcbdbbbacaccacabaacdccadcadcadcbcbadbabdbdcaabcabadaaccdaadcbbcabbccccaaadcaabcadadcbdbbccdddaadcadacdcccddcaacbdcaabaddacbaadbabbaabacbbdcadbbbdcdccdbdaadabcbbcbbccbdabbdbabaadabcdcdbbabdcbdaddcacddcadbdcbdcadcbabaccdaadabddccbabbdcaadaaabdbcdbcdcdabdbddbbdbcbbbbcdbbbcabcbaabdddddabacddbbbcabacdadaccbcacdbacdccdccbddbbbcbadbbbcbadabdddcdcddbbcbcbacbdbaaabbadbbacdbcaccaaddcbabbddbdabbbacccaaacbcbcddaddaabbcbaaacbdbcdccadaacacaccdaabcccdadadcbbbbacaabacadddbcbacbcccdbbacddbbdccccadcbccadabcdcdaaabdcbbcbdaacadaddabddaaddcabaaadbdbddabaabbabdadcbdcdbbbabbaadcdabdbcdaacbdbacdcdabadadbacbdadbdbdcacddabdbadddbdaabbabbddbbcabccdabddcccbdccbacbbcccababbacaccaadcadbcbaabbccdbabddadadbdddbbdabdcadddcbdbabdbcdcaacdacddddcbbccbddaddadbccaacbdbadbccddacacbdcbdbdcbdbcaddacdbbacbbadbddcacbaddacacddaacadbdccacdbccddbdbccdabcdcbdbbbaaddcdcdbcbcbaabdaccdabaabccacabacdabaacbacddddbbaadbacbbdcbddaadabcdacbabcacabbbddabddbbaaddcccdddbcbddddddbaccdadddcbbcddabdbddcbcbacacdbcabcaaddaacdacbdcacbcaccdbdbbdbaaabaaadbcbaaccabadddbaadaccddadadcbadbcccdacbbabdacdbddaabacbbddaaadbdacbacbcbbbbbacdadaadbbaaacacddbcacdcbaaccbadcdbbcabacaabacaccdccbcbcdbdbbcddbccdbadcdaaabdbccaccacbbaddcdbcddbaabbabacbccccaccbaccaddddcbacaabadcdbddacbabcdddabdaaadacbbadaacdddccbdbbbccabcdbbbccdbadbcaaacdabcdcabbbcccccaacadbdadbcacabccabbbcdabddccdbbaddaccabcdcddbcdbccbbcacccdbadadabaaacbabbdccbaddbdbabccbdcbcdbaaddabcbcbccdabcbbaabbcbcabadadaabcbdbcbbbaaccacaddcabadacddddddbcbcdacabbabacbbdbbcacacbdbdddbccacdbbccdbdcbaccdbbdcbbcaadabddccddbbabdcabcbaacdabdbdbbbbddbbaacdbbdbbdcdbddbbbaccbdadccbbacbbdbaccaddadabddacddbddcbcbbbdabacbcabaabacdbdabcadbdadbbbdccabbaccccdbacaacbdabbbdabcbaddadcadbdadadbccccacbbcaaccacccbddcbaddbadcaabdddcaaccdaaaccadabadaaddcdbcadabaadaaacddddabcdabbccdaadacddbccdacdbadbcabcbabdbbddbcccbbccbcddaccaacbaaaacbadccccadaaccaabadbbbbcbbbcdbbcbacabdcabdbbacddddddbdabcdacbacccbbcacddabcaacbaddbcdacacdcbabaaddbdbcaacbbbbaabcbbdbbbaaaababbdcaacbddccaccdbcbcbddbbdaccccccadddabccbdbdcbdacbaaaabaddaddacbacdbdbadcdadbbdbabdcbbcacddbabaacdbdddadabbdcabcdccdacabaccabddaadbbdacbdadcbcbccbbdbdddbadacbcbacbddcdcdaacaacabbbadadcbaccadbabbdbcddacdcacdcdcbdbcabdbcbbdcbadadcbbcaccdaaaddbbabcabdabddaabacbcabcaccbababdabbcbbadabdbdbacbdadccbdcdaccdcabdcbadacdcdbdacbacdddccbccdbaacddaaaadddddcaababbcdcaccdbdccaabcadbbdacdddcdaddaaccdaccbabbbcbacacbdaaabacccaddaaacaacadcbdbcbdaacaaabdcadacaddcdcdccdbcbcdcabcaccdcdccccabcbadaadbcabacbcaaacacdddcbdbdadcbacbbccbddcdadadccdbbaabcccbadcdadddadbbdbbcacdacdcdaacacabccbdddccbaabddbdcbcbcbbcabbabbabbbabddabadcbbadcddaccbacdbcddacdccaccdccdaccbcdcadcabcbdbccacdadccbdcdcadabbbdcbbbbcdddcabcbacbaccaddbddcabbcddcbcdadbdcbbcaddadaabddabadcbadddcbcacddbcadaaccbadacacdaabcacdccdbbcbdadbbabcaccacbcaccdbaccabacbccbccaddcaacccdddbdbdcbccabddbabbbbbbacdbdaddccbccdabbdaacbcddaacaaaaaaadacbbbcacdbdcbaddccacccbcbaddcdcdcdcaaabbcccbdcabcdabdbcaaccccdcdccadacbbacadcddabdbaccdabccadadcabdbabaddbbdacdbadccdabadbdcbbbcdadacdabddccbdaadccbcbcbaacacdbbbdbccdbaaadadbbdbdacaabcbbcccbbbadaacbbdbddbddddacabbbccbbcbdccaddbdddcbdddaccaadcbbadbcdcabcaaccacbbdbbdaacdddaabdaaaabdcbcdbdacdcdccdcbccbaabadacbcdcccabcbcdccccccbddbadbbabaabcbbbbbdbacddaaabddccdbdddddbacbacbbadddbacbbadddbccadcaadadcbdbcbabcbddddacccbddacaddcbcaacbcadcbcbcbaadabbdbcbaaddabdabbaacdddabccbdbbbbacadbadadbacabaacabbaadbbbdaaadaaaaddbbbcccdbbbdcbaccbacddaccdcdddbcdbabbcadddadbdabacdbaccddbbbdcaabaaacdbaacccbaacadcbaadbaddacccacacbbabdcbccabadcadddaaddcadcdbabaddabdcdaadacdcbaaacbccccbdccadbdccdabbaddabbbaccadbcabdbbbccccbccbcbccdbabcbcaabcadcdabccaabaaaadcbccbaadabcaddaccbbacbabdadadcadcbabcdbcaccaccdcbdcaddbbadcabbbddaacaacaddabdaccddabdbaacbcbaddbbbccdcbaadccbddbdcadcdbbabbbcacdacdacccbdccdbdcbccdadbdbbcbcdbbccdbaddacacbdcdaacbbdccdbbddbccddcccdcaddbbbbababcaaccaccaabaaabacabdadabdaaacccddacbcdcdcccbacabbcccabbbaacbacbdbdcdddacabcbaccdbbadadbbbbacadabdadbbbbaadadcbbbacabdbdabbdaccdcbdabdbdcbaddbdbbaddbdbccccbbdcbdcbabbbcbdabcbcccbccbaddcaadcbadbaabbbbddbcdcacacbdcbacbcbdbaccddbbbdbadccbbbcaddcbbacccbddaadadacdddbaabdbdbbbbcccacdacdadcaadbbacccbacbaddcbdcadbadccdbcccaaccdadcbdbbddbdcabbcddbcbcbbaacadcbbdacabcbdbabcbdadbddadcadabdcabdaaadbcabbcccabcabadbcccbdaddcaddbaababbcddbbcdcbaadbcbabcbadacdcacbbbabbadbaccbaacacdadcaaadbcbacaacbcddbbcabaaadbdccacaaaccdaaabcbdddbabbacdcdacaaabacdadbbaabdbcdccbccabbaaddbdddaabccacdcdaccbaaccddccdbbbbaccdabaabdabccdabcdbdcbcbbbdcbaddbdbaccddbaaaabadcdbbdbbbdccabdcaadababddbbccbaacdabcddccbddbbbcbdbbbbccbdabcbccdbabbaabdbcbcddbaddcbbabdddaaaaddcaabbdcccdccbcaccacbbaacbcdbbcbdddccccaaddadbbdbccaaddbddcccabcdabaadaddcdaaabcbbadabbacbbdddccbcbccabccaaaaccabcabbdadbddacabacadacccbdbaabcdbcbabcaaccaacbccaadbcdacadddcabaaaaacddbaddccbaabadacdcaccdacbaadaaabbcdcbaacdcaacbbccaacccadddabdaaabbbdadbddddcabadccbbccbddbcacccbaddbdcdcddbaabadcbcbdbdddbaaacbcbdbbbdddbcccaaadabacbbadaabdbcdbaddacacbbcddcdbcacacaadddabcbdaaabadbadbbcaaaadddcacccbdcccddbbbddadbddbdacdabdcadcabaddadadcddbbcadbbaddbbadbdcbcdacbcdacaaacbccbacaccbdacbddadacddbbadcbcadbabdacabacabadbdcbdabbbbcdbcacbcccbadcbcdbabacccacdcdabaacaaddcddbdadaddcccdddddadcdbadcbcbccbdacaccccdabbcccdbdddbcdacddcbadacdaadbcbaadcacaadcbcacdcadcdacbcbadccdaadbcabaaddbcbbacdcdccbcabadbddbddacbbdbcdbdaaaaabdabcccddcbcabacdadcdbcabbaccbaabcadcbdbcdbdaabdbadcbbcdcccabdcaccdbbabcacaadccacbccaaaaddbddaadadccaccadbcabccddbccbcdababcacadadbacbbcccdcbaddacaddadbaccaaddbbdaabaabdbbdccbcbdaadabbdabbdbbdcaddcdcbdccbddaadcdbadcdcddcabccaabbcbbdbadabadcbbddadcddcbccaaaaaaaabdbdcdddddcddccbbbbdbcadddbbdbcbddbdcdaddabbacdddbdcbaaadbdaacbcaaadbbddccbbaacbbbccdadbcbcaacdddbadadbdccdcdcdbdbcddbdabddccbdcbcdcadccadcaaddccabbcbbdbbccaabaaccabccababdbdbdcbabcddaadcbcbbcddabdbbdddacddcaaaddadcbbcaccaacddbabacdaddaadaaaaddcdbaccbbdcccbaadcccadddadccdadbccbaabdadbbaacacccdbcbdbcaadcbbcbccbdbaddbaddcacbbbcbdcabacdcaddbbcabcdccdabddbdccbbababdaabcbdddcacabbdadbdbdbcddbbbcaccccbbadbcadabcbbbdddacbbadccaccbdbaaadabbbbbcbaadabcbdbbacbadabaccbbddabcbcdcdbddcdabbbdbdadbbcdcdddacdcbacaadbacccadcdccabacdbbccccabcaddcdaabbcdddbdcccccbdbadacdaabaccadbdbcbcadacbcbdcbaaaccadbbdbacaabccdccacbcdbdaddbbdcbccbddbbdaaadddccacdaaaaacaadabbdcdaabbadababbaabcdbcdacbdcdbdabbddaccbccbabddacddcdbbacadacadadccbbcbaaabcabadcadcdbaacdaddcdbabdcaacbcbbcdcabbbccbbaabcbaaaacbccacbaddaddcaacaabcddccddadddbddbccbdbdabcaababdddbcadbbadaadcccdbdbbcadaadcdbbabdabacccbcdbccbcddcabbbbcbdbccddbdbcaacbbddcaddcbbcdbbdadccadddabccbadbccbdaadcdabacacacdadbbadbdaaabbcddbcdaabaabbbdbbdbdaaacdaabddbbbbcbbabdbccbaadbacccbbddccbddcbdacccacbdcabadbbbdcdbaddbbacaaacacccabaddadbcaddabdcddccdcdccabcddbbcaabdadabdbbdddcddcddbcdcbddcbaabddccaddadcdbadaabbbcacdcdcacadbdcbdbbcdacbdacadbcbadcbacbdaacccdccdbabcaacaabadccdcadacdcadddbadcadddadcccddccccacbaddadbcabbacaadadcccdcddbcdbdbcadaadbdbbaacbcbcdadcdcabdaacaaacdadcaaccaacbdaadddabdcaadaaccacbdbdcdccabbcdacadaccbdbcacdddcccacdaccbdababcaaadcdbbabbcdbaaadacbbddadaabadcccccaddabcdcbabddcaccaadadacdbabcbddcbdddaababcacdaabbdbbadbadcbbbabdbababaabdaacdbadbacbddabccbbccbcbdbcdccbbbbcdbadaccbbcaabcdaddbccdcacdcaccacbdcccacacbadcaadbcaaabbbcbcbcaadaadccadcbbddcdbbdcdddacbabcccccaccdccdaaadcdaabbbaadabbbbbabbaabaaaadcdcddcbdccbadbdccdaabaabdbddcabaaadbacccacaabbaabcccbdbbbccbdadcbcdabccacdcabdbddaaaddabbdacdcdacdcbcdccdbbaaacdabbbdacdddddddcaacddabddadbbabcdcbcaadbadaaacadccdcddbacddadaaccdaccdbadddbdcdabcdcdaadabacabacacbbadabdbdabbcadbbdbcddbdadcdaabaadbabddabcbdbbaabbbcbbabcdacadcaabaabdbcacdcadacbcdccdbadabbadcbcacccdaaadcdadababbbbcbdacbacdabdcdbcbccadcddbaabcacdbbcacccddbababbdcaababadddcdcbaccbdbccaacbdadbcbbabddbddccdccdacabcbdabcaccabbbbacddbbbaacaccaccaaadcbbacbbccdaabcadbcababcdbbbcdcabadbbcaaacdacdcccabadbddbbcaadcbcdbbcbbadadbbdbadccdadddadbdadcaadbcadcaddabdbaaddcccdddcabbabcacaccaaccddbaccaaadccbddcbddcacbdbbbbcaddbddbabcabcdbbcababcccbbcbacabccbcdddddcdbcdbacbcaadccabbbbabcaaadcdbbabaacdaabddcacdddcaabbadbbcdcdadacddaadbcdcdcdbcacddacdacabdbcacacaddabddbbbccababadcccdadbacbcbbcbcdcababcccdcdcadbadadbbacbdbbbcaacaccddcdcbacbbbbdabbbbcadbdccdccaadacddabbdddcabcdabbbbabdaacdabbcdaaaadcdccccccabdabaaacddbbabcadadbbbbacdbbcababcbddbbbbcabdbaabcababdbbaabdbbbdaaabadcdcccdacdacbcdbcdabcabbacbbadbadcabbccdddadaaabbcddbaddccbbacbdcbcdacadadcdbbacdcaaddaabdddbdbcbdbcbbcabcbbccdcacaaddcbaacacbbaddcbbcdcabbbdbdaaaacccabbadcdcbdacdbdcaddaaadaabddacdcdadbacdcdcbaccdccdadbccdbacdbccaaccbacaadaaddcabbadccacbabbdcaabbdadacbcbcdcdbaaaacdcccbcbaacbbbddddcdccadadaadccadcacaadbcbbdcaccacbdcadabbccddaaababbcbaacabaccdbcdcdacaadbaccdabbdaabbabdaadaaabbdadbbcadccccdaccddadcaaabdaacaccddbdbcdbcdadadcdabbbdbbddbcabacccabbacbddcbbcabbabcdadabaaaddbaabbacacbdbbcdcaacdcdcbbacabdbadababcaacdccddcbccccddbbdcacaacbdccdacdacbdcdbcacccdbcbadbcbacdcacdcacdccacdcdbacdbcaaabdbbbcbbcaacdbaccdabbbdaccadabbdadccddddbbccdbaddcbaccddbbdbcabbcdcacbabdaababdcddbcbdbdaacadbaccaccbacbcaaabaaadddcbddbbdacdacdbaacadcccbaabbababdabddbbdbbdcadcbadbbaabbcbddbbdcdbadcbadacbadaaddcbaadcbaddcadacaddcbaddadbbcabbbabdcacaadaabbabcacdacbdbbdbdacbcdaaabddbcdacdabbdcddbccaacaacaadbbddabbddddadbdaaaaddabdadabaddbabdbbbdddbacdadadbccbadacddcabaadbbbbdacdbacbabdcadadddabbdbabdcbadcdaddcdcccbdccccabdabcddccaadaaccdacabbbddaadcbacabaabdaabbcabbdadaddabacbababbcbaadbccaabbcadbcabddbddadaaadbcaaabddcaccbddaddadbacabccddddddcdbcabcabccadabadacaabccbcadbaabdbaabbcdbabcbabdcdadbadadcbacabcdcbbdbbcacdacddabddacaadacbcddbcabaadaadbdbddcacadaacadbccabbddacbabadccdcdcccbaadcbcabcabdbcccccabacbdacddaacbbdcbddaacabccdcaddccbabadabacabdcabbbcdbddcdcabdacabdbadcbccbbadadcbccddaacaacbbadacacdcbacbbccaaabcbcdcaddcacaadddbddcbccbcbcccdaaccbaacdcdbcdccadcbcbaabcdbbaddabcacdddcbbbadaabaacddcabcbcaabbabcabccccddcabcdbccdcbbcbabbdaddccbcaaddaccbcbdabbcdbbdbbabcacccdccccdbacccbccdbacaccdcacdccaccdacadbacbaddccbbbbdccdaabacbbcbdcddcabaabcdaadbcbcbbabdcccbcbadcbaabcaccacadcaaababccdaccbccdbcadaddddcbdbbbadcbbcaddcadcaccbacaddcaddcbdaaccdaaabadcadcdcbabcbdbbbadddccbabadcbddabcdadcabdadabaaaacccaaabaccbdacbcbbbbbbbdcdbbbbdcdbbaabddddcccddabcdcbbcdcddcabcaabaaddadbbbdadbbbdacdbdbbabdcddccadabccbbbdccdbcbdcbbcabdabaadcacdbbddbbcbdbdddcaabacbdabdbddaaadcaadccbdbddabdacbdddadaaadbbcbacdcbacaddbcaadcbdabbaddcadbbcbadcdcbbdbaacbcdbdcbcdcbbaaacbacadbdaadaccccdacbccbccccbabbbaadcbcdbabaababbdcbdcbbdbcbbcbaddbbaabcbaccddcdbdcaadddbccdccadcdbbbdbabdcababcabbddcaacccadcbbcbabbadabbddcdaacaabbcabdadababdaddcdadbcddbacacdbcadcaadbddbbddabdcdaddbaabcdadbccaabaadadcdbbbaaddbcdcaaadbacaabadabcdbcbcddbbdabbacdaacbdcccdddbccbbbaaabbbbddbadcdbadabbabcaadacbdaaacbaaadcdcdbdacdcdcacadcacdccbdcdbbbcddbddbbcbcddaadaadddaacacbddbdbbbbdaaddcdddaaddccbaaaccacadbacbbbdaccdbbbccbbcaadadbbdbbabcddccadaabdababaabcabdaccaddccaabaacdbdccabdcbbccaaadadbbbdcddccdcbacdaadadadcdcacbaacdabdbdddadbacdaaddabbbbaadccbbcccbadcccbdbdbbcaddaccbcddacdacdbcbcabbccbdddcbdddddbcdabdccdcbacdcbcbdcacccdaaadbcabdadadabdaadbaadddcabcbadaaadabaaacbdacbccddbcdccdaccadaddaddabadbaacdcdabdbdcbdaabccdabacddbccdbabdbccacaadccccaabdcbbdaaadbbacbdbbabdccadccaadcccaccdbdcbaaacbdddcaacacabdbcabcbcaaaabcaddbcdacdbaddcbcaadbcbdcccacccdaacbbdbabacaabccccaaddbccacdbdcbcdcddcbaacaadcdcbdbadbcdcadbabadcdadccacbcbbaaaddcddabccbbaccabcaaaabccccbdccbcdccbbcaddcdbcaabbdcdabcbdcaadbbcaaaaddddcccbddbacbbddcdaacdadbddaaadadbcbcdbccddbbdabdddbccbdcaacdbbaaacdabcbbddddbcbdadabbcbcbccacadaaacdcabdcbabdbbcbacdbccdcccbadadbdddadbaccdacdbddbddbcbbbbbddacbccdaadcbbbcdcccddadbbbbccdbbccdcbbbddadbacadcccbdcdbcadbbccbbaccddaddcbbbdcaabcdcdcbabacbaddbccdaadcbdbadbababcaaacdcbbddabdacacadbdabddbbcdaadbbdcddccbdabccacacadcabbccdbbaacbddacbabacbbdbccacaaaaaccacdbdaabbddcbcaacbabbbaaabcbcbcbabcaddbbadbaabcdaddbabaacadcddcbbdddcbcbdadbdbcaddaaabcbaacdacbcaccaaddcaccbcdcbbcabcdbbdbaaccbcdbbadcbbcdacdaabdddbcdccdacbdababdaddbababacbdbacabdabadbdabcddccbacadbdbaccbbcbbaadcdcbdbcbcbdcadadabbddaacbabbbddbaaaaabccddbbccdbbcdccdacdbadbbdbcdacddbbddcdbabcbbdcaddaabbddabbabddbbcacabbdbbaccdccacdcdbccbdddcddbddcadbbcababdddaacdcbadadabdccbbbbbcbdcaabbacabdbdcbadcbabddbbabbccbdddbdccaabcbaacaccdbaaababdaaaccccccccbdabcadbcacbaabcdbbbdccccbdbacbbbcdbdbacacacaadbbabcbdcbacaabdbcccabdcadbbcccccddadbadacbdacbaabadcbbadbaadcdddccbabaccacccccabdaaabdbddbccaddbbdadcacabcaddcccbcdcaaabdadbcccaacccaaaabddcacaacbabbdddadaabaaaabdabadcbdaabbbadadccadbadacacbbbcacccbcacddacabdddabababababdccccadccdcacbdbbbbdabccbbabacbabbcddcddacccacadacdcdccccacacdbbbdbadadcdcacdabcbdbdccdcdcabacbacccbbdabaadddccbccbcbbbcaaddbcabbbdcaacbbaabdbdaacddccabddbacabdabaacbdcbccdcabcadbbddadbddcdddcddbabddccbaccbcaabdabadccbdbdacbdbadbddbdbcaaacccdcaddaaadbbdccbadcacdbbacacadcdbacbadccccabcbbadddaacbccdabbabcccdcaabddbaabadcbbadabccadadcacaabbadcbbbacbbdcaccbcddccaabdadabcadaccbbaddcbbccadcabbdabdbcccbdadaacbdcacaaaadcbadcccbababbcddbaddbccdcdbddbccabbacdcabdcdcddcdacbabbdccaacdaabbbaacbbcbbabcdadbbcdcddadbdbddadcbcbcccddccdbcbaacbddbdcaacdbcacadacbacaadbbbdbbcbccbacddcccdddccabcdbadabddcbcdaabadbcbdacbabcbaadadbaadaaacadbbccccbacabdccccbbaabcbacbccdbcddcbbdccbaaccaccaccaabaaddbdcadddcbaacbdccbabddcbcadaccabccdddcaabaacaddbddaaadccbdbbadaddabdacdbcdcdadababcbaabacccdbdbabdcdbccbadbbacddacddcddcadbacdcdcbdccdcbabbdabbccaabdcbccbddacbaaacadaaabdddbbcccaddcccaacacbadadbdbacdbacaabdbbbbadcdbaadbaaddaacdadddcacaabaabbbcdcdaaaaaddbdcacdadaaadadabaadadcbccaaddcaccaccbaddcbbcddcdccdbadabcbdadbcbdaababcbcbcaccddcbccaabbdcaccbccabbbcabbbcbdbaccabdbdabbabddbabcbcdccbcbbaaaadcbcdccbabcbcadcbddbcdbdabadcbbccaddcdccbcddacdcbaccabdcbdcacddacbbbbacbabdccddaaccdbcacdabcbcadadacdaaacacdbaabcbaacbbdbacbabddababccbbcabdaaaadbbdcbbaaadccccbcddbabadacaacdbacdbcbcddcddbabcbccdbcabbdabbdbdabacdcccbcccdcbbadbddddaacabdbbccaaddcacacadaccbbadddcdaaaaaabaaabccccbdddbdcccaabcccdacbababdcaccaccdacdcddacccababdabbdacdddbacacbddbddacababdddaaddccdcadbabcadabcccddcdcbabbccdaccaccabdcbacaadbabbbdaaacddcbadcdbbadacbddddcbcdadbccababaabcbbdccdabbdabcccbdbbcbcbccdadacbdcabbbacbcbccbbadbccbbdbcabddaabacabdaaaabacadadbddcdbbdddcbdbaadddcdccadbbbaaaadbadacbdaadccacacbaabbddccabcbddbdacccdcabbdcccdcacdaabccdbdacccccbacdabdcbbcbabdbbbcbbcadbbbcbbddcdacadacbacbbbcccabbacabcdbaccbbbabbadcccabadbcbbabdcdcccbcbbbacdcdaabcddccababccdabaaaadbbdabdbdddbabcdcabccaacdbbdccabddbadcbcdadcbadccbdcdababbacbddadcbcadabaccddacddbcbcaacabadbddabbcddbabadcdbcbddabbcbcadddddadbabbcbdccbbdcdbdaadcdbaabbcaacbbbabccaaabacccdaabbcddacddacadbcaadcddcbbdccbbcbbbdcadbddcddadbdbbddbdabbacaddababcaabcdccadbaccabcadbddbcdaabccbdadadbbddbabdddcacdddadcadcbccbbcabbcaadadccaaadabbddacbadcabbcacdcdbabcbacabbcbbcaaddcabdbcddcabddacbddbcbabbbcaddaababbcabbacbdcacdadaaacdcaaddabbdddaacdbcabbcbadbbabdbabdabcbdccddcbdcabdaacacabdbbabdbbbbcddabbbdcccaaaaadcbbcdccdaddbccdcdcdbccddcddbbbbaddbddcdddaabacddaadbbbcbdcdcbbcacbbbdabbaacadabadcbdcbcdbdbbbacdbdcddaccdbabbdcbdcabacbbbbacbbcaaabbcbdcdcbbaccaddacdbbaaddcdccdbabacbdccdccdbadbacdadadacaaadcddabbacbdcdaadaadbcdbddcbabaabcdabadbdbcdccaabccbacccbbbbcbabcdadbddcdbcdbbabbaababbcababcddcbaabdddaccaddbdddaddbbacbbddbaccdccaaacadcccbcadbaabadddcdccccabbbdadcbdabcabbbacdabcbcccdcacabadddabbcacdcabbbcbbdccccadabadbbcacbcbdadbbabbbdadcabacbadbadabddbaaddbdddacbddbbcccbcbbaddcbdbaddadbacbaccdcaccdbddaadcaacbdcddddcbcbdacbbcbbdddcbcbaaabddbdbadadddbbaaaccabbabbbbddaddbdaccccaccdabaccbabacaadbcbcacbacbbbacadbbdcbbabcdcaaadcadadabcbcbbbbddbbdbdbcacdbbdababccdcbcccbaadddccdabadbacacbaacbcabaccdcbccdcdbcabcadadbcaccbdcdadaabbcdabadacdabbbaacdbdddbbdcbddcdddbadabbbddbcbbdccdcddcdcdccaabacaadddaacacacdabcdacbaabdabccaaabddabaadcbbacbcbbaaaadcbabcaacdddbbbbdddcbabdcacbcdaddccbdbaccdadbdbbbcacccbaadbdbdbddbabbcddbcbadbadddbbcacbaaaacdadcabddadddbadacadcdcbddddaaccdcdaaacdccadacdadbccaddcbaaddbdcbbddcdbbcbbaacccbcbdbdbdadabbdcbcadbcdabbacaccdbabbbbbabbdbbddadbdabdbdddabcbaadbbdcaabbdbcbddddaacacdaabbabcbbadcbdcacbbababdccaabbdaabdcdabaadbabbccbbcadbcdaddcbacbaababaabaddcccccddabddcabcbcaaaacdbadddbadccccccbdaabcdcccaddcbdcacdaccadbabcabbadddbcabdadbaacadbdbcdbcccdabadbccbcaacbbcbacdabcbcdbdbadcdaddbdaddcdbcaacbaacccdcdcdaddbbbdaacbadbbbddccdcddbbbdcbbdbbcddbaacdadbaaddbcadccaacadbacaddaccbcddbbbbbdcccdbcdcbacddbcdcddbcbaadbacbaaabadabccbbdbabbddddbbcddcadabddcccbcddbbaddabbcdccbbbacdacadcadbbbcccaaaabddadabcdabddbcaccbcdabadbaacaabcbcddaaddcaddcbbcbdaabcacccaacbabbbaadacddbbbdbbabccdbddabbadacccdddbcaaccbdaacbdcdccbaccbaabcbaaaaadadbcdadbbbaddbacacdbbaaaadbcddaaabadbbccadbbbddbdbbdaaaaddcabbcbccccabdccccbacbcabacbcbdbbbaaadcacdaddaccbacacbcacbdcacbaadbadbbcaaababacaabacddabdbabacdcbaaddbaccbaabbdbaabcbabdcddccbccccacbddbaddcbccbbadcaaccddacacabdcbdccadbaaabaddbbbcddccacdccddbdbcbaddabaabadabdbacccdaacbdbadabcadadadcadabacacabbdccbdcbdcccbadbbccbaacaaacabcbadcdcbbbbdddabbabcdadaaababadabcadddabdadbcdbdacdadadacdcacbabbdabcabccacaccbaddabccbabacddadacadccabdddcacacbabbdbdcbcdddaabdcccdababadbdcacdaccddcdabccabcadacacaaaacadbabacddcbbaccabbbadbadbdbdbaadadbbdbdcaccacaacacdcdcbbcbdccdadabcabcacbdadadcdcccbbdcbabbcbcdbddcbcddbabbadbdaccbcaacacacbdcbacaaadbcbcaaadacdcbbcacaacddcbdccbddccadadaaaccdddaaddcbbadadbadabadbadaaabbcabcacccdccdcdddacbccbdcbdcdabddcdccbbddcdbdadbadcaaccaaddcbdacbdbcabdbaaccdbcccbcbacbccaaaccbddabbcbddcbbbdbdbdddbadcaabcbabdabdaaabcdcbcabccdbcdcccdadcaddbbadaddabadaadbbadaabddcdabbbabadaccdddaddbacaccbbdcdbcbdcbabacdbadcddcdbadaaacdcdaaddabcddcaacccacbcbbbccbcadaccdccaabbddcaaacaadcbbaabdbdccdadcaabcdbcdacbadaabdaaacacbbacdddabcacbababdabaabdababbcbcdbcbcdbccbdaddcdadbccaabcbcbaaabbdaadbdcddcccccbbbbcbbacaddadbbacddcdcadbcbddabdcbabccdbabaabacbbaccbbbcddbdbaabacccbbdbbbabcbccadaaacaccdacdbacbcadaddbddcbdbdddcadbdcdbbcdddaaccdaddcaadcddcbbdbdadabdccdbbcadaabdcbbbcbcabacdabcdadaadcaccabbdddbcdbdaddababdaaaabbadadbabbdddbacaaaaddcddacaddaaccbadcbbcbdcacccdaacddbcbcdbacbadccbcbcbaacdbdbacccccbcdbbaddbdcdbdccaacdcabdadbddbcdccdaccdcacadcabcbcdaddcadbabcdbdacabaddbbbccdbaabbdaaaacdcaadccccaaacbdccdbcaddbbbaacccaddadccbcbbaddccaaaccabdbadaaaabddbdbcbbaaacdabdddccddbaddddbdadccadcadddbcabcccbcbcbbdaadddddaaadaaaddcddccaadcbdcdbdbcbcccbbadbcadcbcbdadaccddccaddbcdbbdabcbcacacbcddbcdadbddbabdacdcababdbbbacccabaacbdaccaabddaaadcbcbdbdcdabbcadbdabdcdbcacbabbdbcbccdabbcaaabbabdbaddaccababdadacccadcdccddbdcdbbbcadabcbdcacdcdddddaabbcbadaaddbcaaddccccbabcdbabbcbdcdbddadcdacacddcdbbbdbdcdaabdcabaaccdcdbcbababccdadbccbcadaccabaccbdddbbcdcdacdaccbcbbabcdbcaccdabcadbddcaacdbdaadcccbddbabddbcacdacdbdcabddcbcbddacdcbcbadcbbbccabcbcbcbbbdcbbbccbdbbcbdcccaaabacadabdaabdaaabbcdbcbcaccbaddbababcaabcdbbddcdccdcccdabadcbacccddadabccadcccbabcbcbddccbdcdaacddbabdbdaadcacbbcbbaccddbcdcdcaccbdadadadbbaaaddcdacdddaaccddaccbbcddbaddbccdaaabbaacbddbdaaccbdbacbabcaddbcccacbbdaddcccadaaaabbccdbdabbbbaccbbbcadcacddbabbccaacaabccbabacdbbcadcbacadcdbddabdcbdbbddcabdbbaaaaaabbbadbbbabdbbccacbbddcddabccdbdcacadcacaabcbaaabcbccacbaaadcdbbddacbaaaabccadbbbababcbcaaddcbbabbcbcbadaaabaddcadccccaccadbcdbdabbcbdcdadbcaccccdcdaddbaadabadabdbbdadadcbcadddcbadddbcbacdbaacadcdcacbdaddabaccdcdacacbbbabacbbcbadacbdcbaaacbdbaabbabaddccdccdcbaaaccdabacdcdaccdbaadbbabdbbbaacddddcdcacbabccadacbccdbdabddabcdcaabccabbacbaaaccdcccadbbadcaddabcddcbccbbddbbbaaacbabaddbbcdccbbccaaacdbcabadaabddcaaaadbbababccbbcdbcbccadccaddccbacbaacdbabbcdcbdadcabbbdacbcdacccdcccdbddbbbcbadaccbaacdcbaccbcacaddbdabbcbabaaaaadadbdcabbddddcbaddbdabaaddabcbabadaddcadaaacaccacbbdacabbbdcdaabcaaccdbacaddbdbddcccbdaabaddbbcbbadbbaacacbabaddaaadabdadddacdaaadcaccbdbccadbcccccacbaddbdbadcdbdddadbadcbdacabaadcccadbabcbcbdacaaaabaaccbdcbcddcdbcabdcacdccddcbcbabdcadacdbcbddbccccdbccaaddababcacaccacbbcbacbcccaadabaabbdbcbbccaaabaadacbaddbbadbddacacbbdbcdddcdbccccadcdaabcccdadddbbbcaddcdbdbacdbdbadaddbbddcbdaccbdcbabbbbddcdbbcabadbbcdddddbbaaddbadacdabddbcddcaadccbbbbbbbdbadbacbbdadbdadbcbcbbaacbccdadacacddccddaabdabadbaacacbbacbacacbaacaadaaadddbbbdccdbdabcbbdbabadbabaacbabcabdaacaadcdadaabbcaabdbbbddbcdaaddccdcbaacbbdbddcdcbacadabaaccdcbdabddcabcbbdcbcaadcddbddabcbdbacadbcdacbdddaaddbddaddadcaacadabacdcbbaaccdadcdbadbabbcacdcbbdaaaccaccadbbaaddabadbccacbabdbabbccabadbaacdddbaadababbcadbaddabbbabbddaababdddbabaccabbbbddbaddcdababbbcbdbdaddadbbcbdcdcdcccbbbcccadbabbcdbbbacdbbcaacbaccdcbddbdbbcddbaccbddbdcdacabaabbcbcadcbdcccdcdadaadcdbbaacdaaacbacaadaddbcaadbbaaaaadbabcccdadbabddcdbdcabbbddbdaadddbaabdbbdbcabdacbabcbbadbaadbbddcabacdcaddcacacccbdabdcdaababdcdaacaaddccdbabdabcacdcdabbacbabacddcbadccbcccdddacbaddabdbccadcaaaacaadcbbbcbcbbaddacabacddbcdacccbbacabaadabccbddacacadcccabccbbcadcbaaddaaddbabddddbcaddabbcbcddbbddbaaaccbdcadbdaabdacbacacadcbbcdbabcbaabaadddcadaaccdbdcbabcccbaccadddacacdaacbdcdcaaddcdaaccdabcbbcdabcdddcccbabbbcabbacbdadacddcacbcbcadadacdbcabbbbbbaabadbbbaaaadbcbdadacadaadcbdbdbdbddbaacabcbddaadcaabcabcadbdcdabbaababddaadabbbdddcddbcaadacacaacdbdddbcdadbdcdcacdcbadaadaacbaabcdcdcbcdddadaaddbddddbbccbbccadbdcadcadbaaccdacbcbbdbaabbcbbbcbbdbdacddbabbcaccccaddabccdcadabacdabbbaacbabcaabcabdcbddcabacaacbbcabbaccbcccdbcdacdbaababbcbdcddcbdcccadcdbdabbbacaccbacabcaddcdabccbccddbdccdaadbcbdbdcdbbbdbbdcacdacdbbaacdaadaabbdddcdddddbababcddbdcaaaccadbccacadcdbddddcdbcddddbcdbaaadacbcbaaaabbbdcdadcadcadcabdbdadccbbcddaadcadadccdbcbdddacaddddbbbdbdaaccddaaabacbadccbaccadcdacbcdcdcddbcccdbdbcddabcaaccdadabbcbbcbaadbdcaabacdcdcdcbddaddcbdaaabdddbbacdabddabcddbbadbbacaabcbacbbdadcbdccaccdbaacacbbacacbdaccdaccddcbaadaaadacaddcbcaaadcaacadbadabcddbcaaddcaaadbcdbdcadbbdbcacbbcbddabdccaaacbdbdabccdbcbddacdddbbabbdbdcabddcaadacdddacddcccacdaacdababacccadabadcbdcbcbabaaadbcbcaaadcbcbcbadaabcbbcddcddbacadaabdbcacddddadcdccbcbdcadcadbbddbbcbdcaacacbcddbcdacbdcdadbdaaadabbbbdacaabdabcadbbaaddcacdadbdcbdacadaacdaacbaacdccbcaccdbaaabccdbbbccbbababdacbcbaddadcdabcdcccccddaabcbadadaccadabcadbadacbabadbbbdcabddbbcacabddaadcbacdbaabaabbccabdababdabbddbbccaaacccccdcddcadbdcdcacdcbbadbbcdbdbcbdacbccbaddbcaaabccdbaadbdcbbbbdacacadddcdababbcaacbbaaadacbbcacabbaadbdbdbccbbddbcaacdaadbddcbddaaacbddaddbabcdddadcbddcbdcdddddbcdbbdcdcadbdabdbcacabbcaabbcbaacddbacbcbdbacacbdccbdbdcbcadabbbdbaadacbdcadbdaacaaaaacacccdbbdacdccbcaddcccdcabddaabbcbdbadcaacccaacacadcbdbdcddaadaacaaacadcbadbcacbdbdccaabcddadabbdcbbdaddaacccddddcddcccbcbcdbabacbabadabbdacddbdddacbbbbbccbcbaadaaabbaaacbcacbdabdbbcbdcabaadbdcbaabcdcddcacadccadcbacbaccdacbddacdabbbacacaaacbadadbcbaacaadacddcbaacdacadbdabcdbbcdccddbaddbaddbdbcbccababbbccbcaddbaaacbdcccdabcbcaddcbdaaacbaccbcaabdabbcdbccbabbbaaabbdbaccdaadacbabbbbdcadbbddbbdadaabbbbdbbcaddcbaadcbbbddcacaaccbdbaadddcaddadaabdcccbddbcbcbcadbbccdbbbacbadbbbadbbbbcbabdbdbabbdbadaddaadcbccdcbccaacaddbabbdcdbabbcbdabbdccaccbadadcdddbaabdaddbcaddcdbcccccaabddcacddaaabbdbcdabdcbbdabdaadbabddbcaacddacabbcaaabbaccbbcbdaccbacbacccbcddadadbdddcbbaccabcabcbadbcbdccabbdacdbddbabaaddcdcbbccacddbbdbdcccbdcccbcadccddabdbcdbdaabdccdaccbbdbcccbcdbdccadddcdccddabbbbaabaddaddbcbdccccbbcdbccbddccabaaabbabaaabbadbcdbdaccaddacccbbbbbbdbcbbaaabbbabbcaadcddcacbaddcbdbdcdaaadabbcdccdabacdbdbdbcbccaccdccdaacadcbdcdabcdabbdadcbcabbdaddadcacddccbbdaccbcaddbdbddbbddbcacdaacadcbbdbcdcaabdcdddbbcdcabdabaccbdcabddabdccdabacaadabdacbdaddcbbbdaadabaadaccccdcdbbdbabcacaadcabaddcbbaaddbdaaadaaaddaadbbacbcaddaadbacbabbaacccccacaaabcdbcccbbbdaddadadadadcddabbacdcabaccadcdcbdcbaabaccbaddcadabcdabdbdaaadcddbacbcdaabdacaadaabdaabaddbbabacdbdcadcadcbabdbdccbaabddcccacbddcabbbaabbdcbaabadcabbabdcdbcdaadacdadbcdccbcaaddbdbbbdabcddccabdabaddabbbdcadcacaddcadcdcddacdabacdbaacccabcccbbcddbddbddadaadcccddddcadcdcdcdabadbcbabcdcbdccbcbdccbbcbbbbcbabbcdcacadccdcdababbbcabdaabbabddaabbdadbdaddcbcbabbbbcadbbaabbaadddccaddbaddadccdccdcabbbdccddcbabddbadcbadabcdadcbbabdaaddcbbabacdadddadcbcbbdbbbcabcdbbbdbddcacbccabcdabccbbcbcabcbacdcbabdacbadaabadaaaabacbababdbdabbaccdbdabdccacccdbabcacdcdaccbcadaacdcbbbccdbcdcbaddacdbcabbaccbdbdbdadbdacbcdcbbbcbbcbbdccdacdcddcadbaabdcbcdacadacdddbbaddacbaccadcbbcbaaabbddddacbbaabcbcabdacaddddbaabdbddabaabbabbcccdbcaadabcbcacbccbcbabadccadbbadbccbacdddddcdbdbadbabcddbddadcbdccaadbdcdbbdcadbdbdbcddbddcddbbcdbdbbbbcadcbcbadaacddacaabdbbdbabadaaddcabcacabaacbcabcdccddcabcdbdbabdacadbaddddadbdcdabadcbddbcbbbcacacdacddcaaccdabbdbacddddadadbcacdacacadaacbbcbddbabcccdbaaddabdadcaabccbbccacaacbbcabcdddacdbbdbabcbaddacdcdcddaababacaaddabdacccbacabcadbacabbccccabbbcbaaadcddbdddaaaacbbabadbdcbdccbabadcccaaccdadbabddbbcdbaaaababbddcadbdddacdddddadbbdacbcdcbdabdcdddbdcdbaadadbdbcbdbdaaabbcccaabdbbccdbbccccccacdbbdabadddbadbbabbdccbbdccbacacddbabaadbbbccdcabcacbcabaabcabdbddbcdcdadaaccadbccbaddcbcdccbadcbcdabcabcdbcbdcbcbabbccddabbdbcadaacbbcdacacbacbbaaaadbacaccdbbaabbccbcdbbbddaabbbaacdcaaadcaddbbcaadaabadbbcdcadbadabcbadcdcdcbdccbbaabbbdaddbbbbbadbcabadddadcaabaccaccdacaddbdadaadabbbbcaadcaaabbcabcabdaaccddcadcbadacadccdadabcaadbbbabdddaadaddcaacccdccccdcbaccdbdbadacbadacaacbccccdaacbccbbdacadbdbcbddccbbaadccccbbaddcbcabbbcccaadbbbcbadabcadabbcbadcdcadbacacddabcbbdbabdbbcdadabdaacbbbdbbabcadcdbaccdcdbdbabdaabcadcddccbbcddaaaccadaaaaddddccbdcbbdccdcabddabbcdabcdcbadcbadcadcccdbddabcdbccdaacccdabcbddbaccaacdbadadbcacababbadcaadcaaddccbbbacabccacdcacbacdddbbadadbbcdcccacdadbcadaddbcaccccbdbaababaddcadaccddddccbdadbcbbdccacbcbcdbbccaacbbbaacdbdaaccacaadccddbbbbbaddbcaaadacbdccdabcbbacdaacaccadaaaaaabccccddbcacacadcdbbaaabdaacbadddaacddabcdbcddbbddadacbcddacddbbcdbdadcbaccabddaabdcaabbaaaabadbcaccbbcdcdbdabbcbbcabcccbccbaadccaabaadbddabbadcacbdbbdcaaaabbbadcbbddbbbddbccbbacdabdcacdccbacccacbaaabcbaadcdcbdddcdaabaacbbccddcddcbbaacdbdadbbbcacdaaaddddbcddddcabcdabcadacbdaaadcdabadcddccaccaaabbabcdcbbcbcddbddacbbacccaabaaabdcdccdcacccbdaaddacccaadabbdcccbbabdbdbddaacaacbbbbabbdabdbbdaabcaadcdabacdddcbadacbcbdccdababdacdccddbcdbbcdabbadaddaaadddadcdcbacbddcbddccddadbdaaacaacccbacddcadcdaadccbacbbaadcbbcbbdcadcbbabadbccbdcacabbbaccccbcacbadcdacdcadadacdaabcbddcbdddbdaacbccadbbdcadcdcbdccbabbdaaddcabbacdbdbcaddbdddbbcbddabddcbdadabadddbdabbabbcbbbbdabdabcbdabcbadbacadbbdaadccbadcdbacdadcbcacdcdcbadddacdcdcdbbdddccddbccbbdccdadccdbccdaddadcadabdbabcbdaddcccbaaaccbabdadbcdbccddcdbadaaddcdddbddbdcbaabadcbcaaadcccaabdbdadcaabbdabdcabcdcdcadaadaccccaadacdbadbbcdbdbbcacaaacdbcdcdaabcdbcadcabbabbcdcaccbddcbdcdcaacdbdadbcdaaccdaacddcdccbbabdaaababdacbdbbadadbcdcccbaccbababbdcccbbabbdacdaddabadddaaababccbbccddcdacadacabaccacbccdcababbadbcacadbbaadbdacbdbadbddabddadccbcdacbdbdcdadbbdbdccbacbcdbdbbbcbbbcbddadabcdbbccbdacdbcaacabbaccbdaadbdbbadcacccabbcbddbacacbbdaaddcaaacacaacbccadbaabaabcdacaccabdcbacdadadccabadcbbbbbbbcadbabdcdbacacacbbddcbbcadbdcdaabbbaaaddaacdabcdddcacdbccdbcbdbdaabacadbdabadcddbadcbcbdbcccccabddcaabbbbaababbccbdcbccdcabddacddcaccbaddbabdcbbbadaadbdbcbadabaddbdccbaddbacdbabdcabbdabdbdbbbdabadcccbdbaaccddcdaccdccbdcbaabaaddbbdccaacbabbaadddddddaabcdbbcacaccddbbcaabadddbdbccccccabbdbdaaaaadbbaadbaaddcccaddbccaddbcbccdccdcadadbdaabcacbbcaddddcbbabacbbbabcacbadbddbdcddbdcbdababccaddbbcabbbdbadcbcbbcdcacbaacdbbbadcdbdbcaccabaccdabbddddcdcadbbdadbabacdbbcabcacbbbdbaaabdccdbdabdbadcaacaccdcacaacabdadcbbdcaaddbaccabdbddaabbdabdacdccabbddbcadcbaadbcdbcbdbbcbcbdcacacabccadaddcccabbdbdbccaabacbabdaddadbcbddbbbdabaaccdabcbcdcbaccbddbacbddabbbcbbdbdaadaaccbcccbabbcadbbcaddcccdaaacbabcabaabdaabdacccdcabcdaabccbcabbcdcccaacbabaccdbcabacdabbbcbdcccdddbddbbdcabdbcadacabcbcbaacbcdadccaabbdadcbcbcbacccdcadbddbcaadddbdaddabdaacaaacacdacacbdbacabbaccbddcadbdbcacbccdabcbddbaddbabbaaaadbbdbccdcdacddddcbabdabbaabccdacbadcbcdddababcacadddabddadbdbbbdbdacadbddadcbcdadaababaabbcdcdbbbdabdbddcbbdadbaadddbcabcbbdcaddbcccbbdaddabdbcbdcdaabccbcdadbdadbcbacbcbbdccaabacacccddddbddabcaabaddccddbdabbcbcdadbbcbabbbadadbcadcadcdccdadcbcaabdcacdcdbcabbcbdddacdccbccdbdbacdcddccccaccdccccbdbacbacddadcbbbdcdbcbdddcddcadcdccbaaccdaaaabcddacaccaacbdbdabbbcdadbdbdcabdaaddbaadabababdccbbaccbcabacabdbaccaacdaaacbdddcbdbacdacbdbddacacdddbcadbbccdadbdadcbabbcabcaadaccbdcbacdcdadbadaacdddadadccdcaddcbbdacbbcaacbaabadcacbbcbbdbbbcadcdbbbdabbacadbabdcdbbdbdbbbdbbacdcddbcbcdbcddaadbacacacdbabbdcbdadbaaddacaadbdbcdadccddaabacdbdaadbababaabbadcbadcccbaddbabaaccddcaacadcadbcaadbabccbbacbdcaccbcadaddbcdacadaaabbbcdbbcdddddaabcccbaadbccbcdabacbbbcadccbbcacadbdbaaacdabdddcddbabdcabcccabdacadadbcddaaddcdcdacdaaaddbcaabbdabbbdabacbdcddbccbaacdacdcadbddccddcbbbadaccaaacbcbcbacccccbdddbbaabbaaabbabdbddccbacdadcaddbbbacbccacdddbcabaaaccaaccdaccacdaddcabadddbacbddcccbadcbaacbdaacaaddabacbccbabccdadbdaadacbccbdaaaadccdacbcbbcbdadbbdacaabaabbadbbbababcdacbdcaaadacaaacdbdbccdcaacaacaabccabbabbdbdcbaccbabccaddbddccabbadcabdccdbdacdacbabccdaddbdccacdccbcdbdaacbccbbccbacbcddcdcadbabadccddccaaabcadcadadbabacadbdadddcaabbabcdbbcbdbbbcddbbcadbdaaccccdaaabdbddbbbdcaaccbccaadcddcabccbbabbadcddaccdabcdabbaacdaaddcacccdbccacbbadbbbdcddcbbaddbdaddadabaddaddddbaabcaaadaacdbbcddbbaabaaaccccdabddcdcabdcbbccdaccddcadbbcaacaabadadcdbdbadddcaccbadcbdaabdcdcddacdbabccbcccdadccbdaccbababdbbbcdcadcccabbbbacabbdbcacadddbacdcacbdbcccddddaccbaaabcadadbbbdcacbcccacdbdddccccadddabbcaccbbbcdbdbaccdcdbaacacccdaaaaaacdccbaaccadabbccccabcbbacdaddbcdaccadbdcdcbdacdccdcdcadbcaacccdadcbbddbdddbbcbaaadbcbcbcadbdabdaadacdcbdddabacdcdcbaaacddadcdbbadaaababcbaccbddacabbdbbaaabbdbcdcacdadcacccbdbbbbdadbbbabbdaabaabcdbbcbbcadcaccbacdcbacbddccccbddbbadbbddcabbccbdddadcdcaadcabcadcddcacdabccccbcdbdbaddbaabdadcdaaabcdbdcddcadabbbccbddadacbadaadbbbdcbdcdbddbdbbddbdddbcbdcbacadaaadbdbdcbbbdcdcbaaaccbccaccddccdbbdadbdcbcdcaccabcdbdbadabbbacdcacccdbcbdacdcaacaaaacdabbbdbdbbaacbbbcabacdcccacdabbccbbbbbccacbcddbaddabccbcdbccacbcccccbbcbcaaacddbadbbcdcdbccbcaabccdbdbbacabaabdabcaccadcdaabcadcabbabaadcdddcbdacdcaacbadbbaaaaadccbdccdbdbadcacdadabcaddcabaadcbacabcbbabddaaddadbdbaccdcbbdbaacdcdccacbadcbdabbccdbbbbacacbbbbbdddacdbcadabcbddaacbaccbddcbcaababadabbbcadaabcbdbbccddbabbdabccdbcdbaadbcccbcbbbdcdcccbcaaadbbdacabacbdbbbbadbbbcabdbaccccaddccdccdbbddcbcdacddadaabbcadbdcacddbbdaababbbcbcadddcdbbabdcbcaadcccbadbbccacdaadbadcacbdbbadcacdcbbbabcbbccddcbacadbdcdaacbabacdcdaabcdaaaaaabccdddccdbdbbbbbaaccaccabcbddbccbdbccddadaccaddbadddbbccdcabbcbbdadbdbaaddddcdcaccbdbbcbabaddadbbcdbabbcbccadbadaddaccaacdaacbdddbbdbbbcccbabcadaddbbdaabbdaacacdbbadbdaacdcbdaddbdcacabdbcabaccadabdaabadcdadabbbcddababbdbdbaaacacddacabbbcbbadcccbbcdbdbccaaabbdbbcbbdbacbdcabaacbadbdbbadbaabdbdcddccbcdbdbdaaadddcdbaccddcbdadbbbbaabdbdccaaddbadbaacacbddacdaacabacccaabcdddbbbccbcbbaabccdcaacbaddacadddbbcddbbdbbbcbaddcadcbaadabcbcbbcaababbadbdbadcdacbcacdcbcaabdbabcacacabccacdacdcccbcaddcddbdddcbacddacdabbaabcddcccacccaddacdbbabdcdacadaddbbbddccddbcdaabbdcddacadbbcbdbadbcabbddbabcdacbcabbaccddcaddbccdabbabadcabcadabdddcbbccbbadcbbbbabbdcbdadbaddacabaacbdbadacbcaddaddcabcbbbccabccdcbbadcddcbbadaaddaaabbdcbbcbabdddbbacaabdacbdcddbadcdabdcacadaccaabcaacbdcbcbdbaadbbbbcdacbcbddaacdbacbbbdbaccabcbadbbbbbacabdcabcaccddcbbcadbbbbcbcbbdadadddbdaddabddcbacbdbbddcaaccbcdbbdcacbbcbcbbccdccbbdacdbdbdccccbacbaaabbacdcbddbbacccbddcaacccdbcbabcddcadacaaaaaaddccadcdcadcdbcdddaacdabdbabbdabdaaddabdbdacbbbabbaddcabddccbbabaabccabcdbbdaaacddddbcbcdcadbaddadbddcabdddcaacddacaacbaacadcccabdbaaaaacbcdbdddcbbababcccdacddcbaccdcbdcccaacdcadaccaddbabdbacbaaaaddbbdcaacababcbbaacacadccbbcbaaadcbdcabadbdcddccdbdabccdcccacdbbadabbdaaadaadddaadbdadccbadbbabacbabdbcddbaccbbadbbccadadccaacdaacbcbbdbbbdacccbadcdabacdcbccbcdcbdcdbacddcddaabcccadbcbccccadaacaacbbbadbccadaccdcadacbcbaababbcabcabaccacadcbbabcababacdcccddadddbdcdddaadbcadbaadbcddaaadddaacbdacadbdcbaaaadabbacdccaacdcbdccdbabadbbcbaccaccddcbcdcaadbbddcbdccaccccaacbddbbdddcccddbdddcbcbbbbdaddcdabadcaacdbcaaccabbdcbbadbcdccbcadbdbbbbadcdcbddaaacbcbddaabbbcdaaddbddabcdddbacbbbdabcddacacbdacadacacdbddcaccdcabacbdaaccabaabdbbccdccdcdaccabdaddbccabadabbcbbaadabddbbaadcbaacdaddddacaacdcdccaaccacaabbccbaacabcccddbbdaddbdcbabbbcadbccbaaaabcdadaacbaabdccbdaacaccddcbddbabdcadcdcabdacabbbcbacbadcddbdadaaddcbcdabacdddabcaaccdadacadadacdaabcdadcaaaabdddcdbddcdaccdabcabcaaccbacccaddaddccbabcbdddabdcdbcdcbcdddbcabbabcccbdddbbdcbbacbccbddcddbccddacccaccaabacbcbbbddcddaaadabbcbdcabadbbccddaabbababcbbbcbdcadccbbdabcdcbbccbababaccdabcdcdbcbdcdabbdabababdbbccbaccbbdcdaabaaaabccbdbdadbaddcdbcabdbcbaadbbdabcdbbbdddcdbbcccbccddbcadcdbcbabddbacbbddaaccbabaaabbbddcdacadbccaadbcdcdcdcccbabaccbdcadcadabddcbbbcbbbdacbcbcbbcbbbddaabacaacaabadbaacddbccbcbaacbcbbcdabbaabbdcaaadccadadcdcbabdccdadacddacbbbdbcabbcdbbaacdbcaadbdcdcbcacbddcbdbaacdddacddcbddbbbdbdaccaabbcbcbddbadbbaadcdbadaadabcdadbacbacccccabaaccdbcdddddcccdadadacbccdddbbdcbbdacbcadcdcccabbbccddccbababcddccddaddaccdddbaccccbcaabaadacdacdbadcabacdbbbacbaacbbadcbddcabaccdcbacddbcbddcbcbbcaababbdbcddcadccbcaabbacabbcccddadcbaddaddcddbddbdbbcdbdccdbabbddccdbabdcadbbdaaddddbacadabcbdadadccadbaccdaaadccadaaacdadddcccdacdcdcabddadabccccdcdaacbcbccdbaaccadcbcdbbbaaacddcbaacacbcababcacccccddbbbabdbccbddbdbddbacdadcbcdacdccbadabaacadcacdcdabbaddddbcbdccacdbbbbabaddbabbbbabdbaaabaccdabbcdcacdcabacadbadacaacacbadbabcdadcccddcaaddadcaadbaacaaccabbbbdbcadbaabdccdbbbaddaadccbaaacacacdacaadbacbcccddadcddccbccdcdcaacbaddabcbcbddbbdcadcbbaccacacbcacdabaccbcccbcaccccbacdadbabddbabdabdcaccbdcbdddaddaacbadbadabbcbaaabbaddbacdabadbcddbbbccccbcbacdacccdbdcbcaadbacadaaacbaddaccccdccbddbdccbbccbdbbbbbbcdbadccabbdcbdbcccdbadcbddbbaabababbdbdccdbbdbbaabdaccaacacdacacdcacbbcdbbccdcbaabcbcdcbcaabbccbccdbdddabccddccdbbccdabbadccadbdbdcaccdbabcccaadabadbcbcadadadcabbdadacabbdbdaacabadbdbddbbdaaddbccacdcdcacdaccddbbacbcdbbdcaddbabbcddddddcddbacdbadbadadadacbacdabbddadabccccbacbddcddbddbbbbacddcacbdadadabcaaabbcbabbcaacaaacdaaadadabdbbbadbaacadbbbbcbcccacaaaacbdbcabaadbbddacacacadcdadaabbbdccadadbdddcbcaddacbadcabadbbcdbbbabcacabdadabbabdcbbbcabbbdbdccacbddcbcdabacdcdadbcddcdacdcadcabbddbbcdcaccbacbadddcbbaabbcbdaabcaaddbdaabdaccccadcaaababacbbdcccabdcacabbcaabbdbbbacabdabbdaabdbadadbbdcacadcdaacbabdbbdbdddbaadbcdbbcdbcbdcddbbdcabbdcbdbbdbbdbbaadbcccbdcbdbccbbadabdcdccadbbdccddcdbacbaabcacaccadadbacaddbbbbadbdccdabbdcdbddcabddbbbcbcbabacbcbacccdaabbdddadbcaccaabdbdbbbdbbbccbaabcadbdbdbdcdccdbabcacccadcccbcdcdbadbcadadcbbabcbddbdcdacabdabcdcdabbbccccacbcbaaacbccbdabbcabbddddcdaadaddcdcadabccdbadadbbcbcdbdcccabcccdaddcddaaabbacdbbadcbadcdabbcdddbbdbaabcbccbbdadacdcdcabdccddccaacdbdbdbdcbbcddcbbacbbcdadacccbcddbdacadaaaabbdbaabcaacbabcabbcacadabcdabbdacacdccddcaacdabcdabbddcaaddabdbabdbcdcdacabcdaaadbcbbadbaccabbccadccadbabaddacacbbdcbaddbabaaadababbbcdbbcbbdbdddddaadccbcbddbcdddbbbdaaacabddbcdbabcbbacadabcbdaaabaadaaaadccbdccdaccaaacbbbcbbbcccccacaccbcccddaccbdcbbcbddbccaacccababbabddacadccaccdbbcdadcddcacadcbcbddaabdddccbcdaabcdbccbbcbdbddbacdbcbddcdacaabaadbbadccabdaddacdbbbdcdabbaacdbdbccbcacddacdbabcbaacaccbaaaacbddbcbbacbddadaabdbcddbacbbcbcbacbccdaccddaaaacccdcabcabaaabdcdadabbdadcadbcdbdcdacbdbcbaabbcbcdcdbdaccaadddabadabcabbdabdddabdbabcaaabddabcbbdadbbddabbcadcdbcabbcabbacddaacbdabacaabcaacababbadaabcdccbaddcbcdddbbcbbddcabccadbccaababcdcccadaabaddbcbaabbcdbbadadbcdcdcbdcadcadabbdabaaabcdcbccdadddcbddadcbbcacaacaacabaaaccbdbcbcaabdbacdbcdcbbabacdcadbcbdaaccddbdadbbcddcabcaacbadcabdaabbbddadcdadbbadabcddaccaabdabbccdadbbbcbcbcbabccabbdabadcdcbdabccdbacddadacabadcacdadbcbbcdabdcbbbccbdbabdacacddbccbbbabcdbcdcaadadcdcdcbcbacaccabddadccddcdcdbcdbbbcbbbadbbdbcddacabcbdaabcacabbcbddabbddabccadaadbcbbccbcdcbaabdcbdbbadabbcacadccaadbbacadcbcbadadbadaacbbdcbddadbaaacbcbabadbbbabcdbababbcdbcabbdddcaddcdbccbcccaccdaabdaacacdcabbdbddcccacadcbdcacbcabcbcdaddccccbacccccccbdbaabaccccdaacaccadbacccaaadbdacabcacbcdbcabddabcbdcbbaaadaccbaaacbbdbcdbaccdaccaacbacbabaadabaadcaaddddbcddbcdbccadbbcbbdbdddcddcbbdbabacbaccccccbccbacbadbcbaabaaddcbccccddaadbbacccbdbbccbcdcbadccaabbcaabccddbbadaddcacdcbabadbbabcbbccbbadbdcbccaddbdacabccacccadbdbcaaaabbaaaddcdbadbcccacdddccbcaddaccdababdcbcbdbccdaaccadaabadcdbcddaacaadaccccddcddcddcaaacadbbdbcbabccdccdacabbdacaacbbdadbdcadbbcdbaddabbaaddcbcaaadcccadabccadadcdbdaadabbcbdadadacdcddbddbdbadbcdbbadcadacacdbbcccdaabaadaacbcddbcbbcdbaaaabdadcacacbbcbacabaddabcadbbcbbaabbdcdcaacbdcaddccdcdadcdadddaddabcbabaccacadbccddddbcdbbdcaccbbaaccbdbbdbdaaaccdbccddcddacbabdbdbabbcadbbbbddbcbcdadadcadabacdbdcaccddbdbbcdabccaaaccbbbaddcaadaadbbaddccacaaaaabadddbacaaddcbdbbdddbcbccbcdcabbbdbbccaccdccbbddcbbdcdcdbbcbbdaababaadbadaaacdbbacbdcccbadcdaadcbdabcababdbcbcbaddadbdbbbbcdaddcbdbaacdcabcacadbbaccbacaabcbcdaaccadbcddcbacbcbabbdaadbdbbdabbabbccbbbdbccdcbbacdcdbddababcdbbcbdbccbdbabcbddcccbdadcabcbcadabcbbacbabbadbcaccaaddaacbddbcdbadbdbacbdbbbccdccbcccacaacadddbdccaacdcacbaccbbabccccabbbddcaddbdabdbbaddddbacdcadcbdbcaabdaddabddaccdbdacabbcaccccbdacacbcdaaaadbbcdbabbcdcdcdbbcaabbdadddcdbdcababacbccbbdaabbabdbddababccdbcaaadccdaccbcadacbaccbadddccbddbaddaddabbbdbcccababdccaabaabdbdbcadabdcadddbaadaadadadcccbbdbdbdcacdbcbaccabdaacdabddbdabcbbbaccbcadbadaaaadbbbddbbbbabbcbcaddadcbdbdbbdbacdbacbcaaaabcbdacddadcaaacbdadcbdbbdbdaacaaccaabacaabbbbcadbbdaadcbdadccbbbccbdabdacaccbdcdccadbccdbbbbbdcbbccbcaacbbcdabadadbbcbaaacacbdcdcbbccbdacdaaaadbbdbdabdcaadbdbbdccacbbbbccbcaabddadaddcdbccdccadcbbadabbaacbbdbcababbcdbcdcadaacdaabbbbccadbabbccbcddbdaacadbccabdddbddcbdbadbdabaadcbcdbdcbaaacddbcdcacdcacbbcdbadbdddcdacaddcbacdbcabaddacacdabcdccccdcbdacacccdbaadabbbbbdabaabaddcadbadccaababcbdcadacdbbdbcdbcaaadaabadccbbdcdbaaddbcababdbcbdbbbcdddabdaadbaabbcadcadacaaaccbcdcbbadcdcaacaabacabbbabacbcdbbaacbdaadcdbacdaabcbdccbbaadcaccbddcacdbaddbaddaabcacccdadabbbdbbbccbcdadcaddacacccbbdbdbaddbcababbdcadaddadbbbdcadacbcddaadccbbdddbccbdaddadabcaadcaddbcbbaabadcabdcacdbadcdcbcadcababdddddbcdbcddbccddccdddacbaaadbbabddbccbdcddddccdadacbcbaadbbdbbbdcbbbacdacaadddbdcdcbadaaabcabdbbaabccacddacbcbcabdccdbbdddbbacbcddcbbcbaccaadccbbcbcdadbadabcbdcccaaddacbadaacbbbaabdadacdbacaccabcdbcdddcdadcbbcdaccbadadddaccdccbbababddbddbdbddcaacddbdbaaccadaaacbcbdcdbabdabcdccbddaddcbbacddcdbdabbbcdbdacbaacdaccdadcddabcbcdbcacddcdacaddcbddcacdbbadadadbaadbdbbcdcacdaccdcabccbdadcdbdccddaabaccdcaaaabdbabbaccaddcadbdcddcabcaaaccaabcaacbabccaababbddaabadbcbabaddccdacdccdbbaabdccadbbccaadadabdccadabdadabacbabddccddbbbdaccaacbaaadaadaadcbbbbcdbabadccdcadacbddcdbbaacaccccaacbbcdabbccddbbdddbcadabcdccbaacdbcaaacabdaadadcdbdbccabacccbcbcccabbbdddbccbcdcbddccbddaccdcadbddbdbabababccaacbadcbaadbdadbbdbbabaddcbddcacacdcdbaccddddcccbccddddaadddbbbbbacaabdaaaddcdcdccddabacbbacaacacaabdbbabdcdcddbcbbdadadcccdaadbcdabbaabdcbdbbacbaaddbccabcacbadbccbbdbbdbdbdbcbddddaaccdadddacaabbcbacaadaabbdbdddababadcabcbddaddacbddcbabcbacabdbdabdaddcddbaabcdcdbdaccddbadbdcbcadacdacccaacaaabacdadcacdacacdcdccbdbadaccdbcaaabccacabccbaaadccdcacadbabdbabaadcaadacaaadaabdacaadacadbddcaacdbddabdbbcdaddacdabacbdbabccbccabcdabddcbbdcaccabdabcddbacddcaddcabcaccabcbdabdddbcbdbacabdabdabdcbcaaaaacadcdcbacadccabaabcadbdcabcdcdacbddbcbbaadddcbbbcaabddaabacadabdccdbbcadbaccaacccaadcccababbcdcdccadcbdaccccbddbabcbadbbddbdcacdaaacbadbdbcaccdbabcacacdbaddaacbadbbbdddbcdcdbddcdbcaaccddacabbbddddcdbbdadbdccaccccbaaddddbacddccdccddcbdcdbabbccdaddbbbdbbbcddccbdbdacababdbddabacbaddcddacbdcdcdbcbbdbcbccbcccdbacbcdbdddcdcaacaacbbdbadddbabdbbcaaaddcbdcadbacbadbaaababdbbdbdbdabcbccdacbbbaadddbcaacadbcbdddaabdcdbddcccdcccdacaaacdadcbdaaaabbadacacaaadcbabcdbddbdaaacdabaacbaccdcdabcbbcabbccdabdcdacdbaadbdcabdcbabaaaabbabbdddabcaddbbaadacbadbabbabcdaaadccbdcddcbddcdcccddccdcbbacbacbadaabaadbbbbbdbbaacabccadbbdcaacbccaddcacabaccaadbccabadbabdacadccbaddbcdddcbacbabdbacadbaadcbcabaaadabbbdabadbcdaadadaacddcdcaabbbbaababacbdbdadddddbdcbcacbcdcdbbcdbdbbaddbdacbadccacbbaaacadbdbdcdddadbccdaabcdbccbdbcacbacbdcdccaacdacaddbdaaacadabcddbaadadcbaccdddcdbbacabaaccddbccbdbcddbbbadbccaaadacdacbbcaddddcdaccdccbbabdcaaddccadaccbdaaacddbcddcadccdcaabacddcccdcbcbadcdbadbbcdccabadbaaadcccdacadcaabdbadacacdcbdbdbabbdcbcbaaddcdcacaaadaabcdbacbacbdcadbacdddddabaadbbdacdbdbadadcaaabacbbbcbccccaddbcddcccbaadccbddccdbdcbddbdcbccbadcaadbaacdaacdccbbaddcdaababccccddaadaddcdddcaabaacdddbcbcdddccbaaaaacbcccacccaacabbbaacdbcdbdccabccdbcaadabcabdaddbbdbdbbccaadbacbaaaddacacbbddddbbbcaaabbbddaadbbacbadddaccabdbcbdacbddaccccbdaadbadacbabaccdddadacaaaaadddbabdaacacdbcbbbccbddddcdbbcacdaaabadbbcacadadbbcbcbdbdcdbbaabcdcbbcbdabdacbacbdadabdacaadabddbbddbbcdbdbddbdcaadbcaaddadcadccbcbbcaaaccbdcbdacaaabcbdccdcbddbdaabccbaacccacadbabccabbabbccaacbdccadbcbacbcbabadcacdbddcddbadbcbbaadcaaddbabbacbcbabaccdadbaabccbbcabcbacaacaababcdbdcaddbccdccddcaccddabdbabcbbaddaaccdabccbbdacbaccbdcacdbcadacbccdbabcdcbaadcaadacaaddaaabdbbcddbbcaadaacdcaccddcccabacaaaaaacbbdacbbcccabaaccdabacdcacdadcbabaadacddbddcbabadaccbcccdbbcbcaccbabdbddcadaadaabaddaccadbbccadbbbdabcdaccbddddbacaadbdadbdcbabcccbbdddccbcdabcdadacbcdbbcadbabaadadcdadbddaccdbbcaaadddbbacabcabccacbccabddaddbaadbacbcbabdadcddcbaddcaaabdcbdadbdcacbbccbacbbaccacadbbadddbcbadcabdcbddcbaaabbaadbddaabdcbbdcbdcdaacaabcaabcdbdbbbbadaddbbbcbbbbcdcbdcbcdabcddbadaccdcbcbdcadbbbcddbddcbcbcadbadbdcccbcccadbababddddcdacaddaddbaacbadaacbccadcbccdcbbcdacaabccccbacaaaddcccccdbdcbbcccbddcdcadbabbbbddcddbdbcccaababdbcacaccccbcdddabbcabaaccabdccadcdacacbdbbbbbdabcbbdcbaaababaabbbaadbbbcddacacaaccadddcddcbcbaddcaccbabdbddcacdbcdbadccdcbbdbbcacddabcacbddabbaaddcbcdbcddddccddcabccccdaacdaccddaddddbadadabadadabaabccddbcacbbaacdccadbcbdddabbacbdddbacbacabcbbddcadbbcdaabdabdcdaabcdcabddabcdacabbadcddbdbdcbdccbbdcaccdacaacbabbcbbddaabbbbdcadcadcacbaabdadbaadacdaacabccdbcacdccadaccbccdaaabdcabbbaabbcadcbaabdaccdacbbcdccdbabcdbdcacbcddcbcdbaabdadbcbcdacbaccbdaadcdcadadbadcdbbacdcbabadbabcaaaddccdcaadbbcbbdbdcccdaacbccabbdcbcccbccdbaaacdabbbdbdaccbbcbbaaabacbdbbaddcbddbabdadddcacddcbacbbdcbbadabddadcddbcabacbcdbcdbdacaadcaddadadadabdcadcbccbbddccbccbdaddadcadaacbbadccbbdcabcdadabbabcccadbaaabadabbadbcabcadccacddaacaccdbdbbdcbadbcacbbabaaddabcbababbaaabdcadaddbbacbabaccaabbadcddbbccadacdaccdddbdadabcacbcbccdcbdddcbddccaaddadabbdabdddbbaccbcbdbdcccaaaccdcacccbcaaccbaadcbdadccbbbadcccbdadbbdadbbcabbdbcddbdccccccaccdbdaadbbacdddddacdcdbcbcbabdacdbbcaddacacabbbbcdadaddacbbbabdbcbdcabcaaaccddcdddcaabbcbdbddbaaadbcbdccdbcddcbbcbcabacdaaaaabaacdcbdbadbddbabacdabcaabbbaabaadbcdbdbcbcdccbacacdbccadcabdaccacdcdccddabaadbcbdcdbabdbadbdcbcbdacdbdbbbaadbbcdadccacaaabcadcbcbbcabaabbcbbcdabdcbadbacddbdaacabdccbacbdbbdccadcbddcaddcaaabcdcdccacddddcdbddbdddacaabbdcadaccdbddcccddbdbcbddbaddcbadbddaabcaddbbaccdbbbcadccccabcddccdaabcbcbbcbcdcbdbadddabbdddddadcbadaadcabcadddadabccabadccbdcabbdaabbbcccbabcaccdcbbddbadaabadcadccaddbbbddbacaddacaaaabcbcdddbbcdbbbaabcdccbbdbbaadaabcbbaabcacbdaccaddbcbabdcbdccbbdadbaabdbcbddaabacddadddddbbadadcadaadccccbdcdbbabaddbaccdcccaccaddbcddcdbbcbacdccddcaaaccabddcdddddccacbbdbddccdbbacddbbabdaaccddaadabaccccbdddddcbccdbaaabdadcaabdadcadcabcdcabaaabcdccddddcdcdacdaacdacbaaacacdcadcdbacbacadcdbdbdabbbbbbabddbaaacbdcbbcddadbbbacbadbbadadbbcbbbcbcabdacacaddbacbbdbbdcbdbddccbdcacdabdacccaaacaddddcbaadbdccccddcaacddddccbabdbbdcbdcacacabdcaaacaacbaaaadbaacbddcdababaacaadbbbdcaaadabdccacddcbadbddadcbbccacbdcaaddcbaadabacbccddabddccdcdcdacdcbacccbdadddccdbaccbdbdbdcbadbcbdaadcbbdbdddccadbadcaaadbdcbcddbbdcdbdbbdbbcadcabaabbbacbadbcccbbcadccadcaaddadbabacdcadbdbdcbbabbaccccbbddadcdbcadabbdacbaaadbadbccdccabddbdccdcbbcacabaadbaadccdbabdbbaabcbbdddcbcabacaddcaadbdcaacccbadaabadcabbdddccadcdcbdddacaabacccbbbdadbccbbcababbcdaccbabbbddbacbdbddbbccbcacaccbacacbbcdaadccaaadcdadcaddcdcaccbbabcccdaabadcbbabadacdbbcccddcdacccacaaadcbbaadaccadadcdbbdaaabddacddbbbcbabccbccdacdcacdcaaccaacbdccddbbdcaabdddbcbddaabdbadbcdabbcdacadccbacdddabbcbdaccccadbaddddddcadbbadcbbcbddcccdcbadcdccaadaacaabcadbdddabbbaddaccabccdddabdbdadaadccbbcdcbabcaacbdaaabbdbacaabdcbcaaddcbbdbccdcbbbbbccbabdbcccadcbcabcaadbabdabddcddbbdbcadaabcacdcdbdcbcddcabddbbdccaddccabaacabdabacddccdbbacbcdadaacdaabbadbdadbdcddbdccdbbdbbdbbdbbdcdcdaccbadacacadbdabcbadabcdcbacbcbadabcbcbddbbbaabbbdbabddbabaddacddcdbcdccbbcdbababacbbdddcccababaaacdaddbdbbacacdddddadddadaaababbcdabacadaddbcaacaabadbaaadabcbabdbccdadcdccdcbaabacabacdbdababccdcabacdcaaaaabbdcaaabcdccdcbababdacdaabcaaddabddbbbbcaadddcdbbcbbadddacdbddcccdaddabdccbdcdcaabccaadacddddbacdbbacdcbbcbddbacbccddcdcdcaddaabbcccbcddbbbbccaabcbaaaadddccdbbaabacbadcaadbcccaddcbadddcacbacdbbdbcbddcdbbbaaaddcccacdaaddbcdcdcddbacaddcbbbdccddddcadadddadccbccaadcaccddaccdaadbcdcbcdbdbabaabcababdddcabbccadcdbbcaccbdbdacddcdaacdbaddcbbbbdbbccabcccbcddabddbdcbcaddcacdccaadaaadddcddbbccabcaaabbbccadcabdaaddaaddbaaddadbbdadbddababacdaadddcaddcbbabdccabaadcbdcbddddbdcccccaddadbccbddadbcaacaddabbcbbddbcbaabddddccbdbbccbbdaabaacacbbadbadbbacccabbbbcdbcbdbbabdaacdcaadcdccadadcdbcacaaddcdcccbbddcbbbbadcaaaabcdaacdbccacbadcaccadbcabdccddcbbabdabccaddcabbcbddcabbdbadcbcbbabacbaddaaccacddcdacddabcdacdcadbdddbcddbbadabdddabdbddacaaacdcbddccbbbdccbaddadbcaadcbabcccdcabcdbccbbdddbbcddcbadccaababddddcaaccbcbbacabccddbcdbacaacaabcacccbacdbbadbbacdadcbadbdddabaaccddccdbbdcabaddbccbcddccaddcbbbbcccdcbdddccababcdccdbdadbddaacabbadaccddacdccdbcdcaabcbabcbdcbdacadbbcdcddcabdaadacbdcbbcdcacacabdddbaabbadabbdccdbdcdbddddbadccacdbacbadadcacbcabcdddccddbdcbacbcdcddcabbbdbabbcdabaabcacddbaaadbdbbabbdcccbcbadbadbbaacbdacbbcadddccdaccdcbcbdadacbbaabbdcddbcbbdccacacdbcdaddbdaaabbcbdbcbdaaaaaacccadabbcacaaadbbacaadacbccbdadaccdbcdabcbaabdbbabbcbbadccaddbdbdddbbaacbccacccdabccaacddccacdcadaccdccdbacbdbbabcdacbcbbdddaccdacdaadbddcaaababccababbdacbcdaccbaabbdaccbaccbbcdadcbbabddbcbccbaadbabdaadcaadccdccaddcbbbdcddaaabcbbccacbdaccdcbcacdadddaccbbbcaaadbadbababaadddaadaabaacdcbaccddccaaaacddbaadaddbabcbdbcbcccdabdacdcdbcddbdacdbaababaccacddacbccadcbdacacacbaadbbcdaccdacbccbcdaabbadaadbaadbaaacbbdbabbadcbdacadaccdcadcbcabdddcdcadddcddbbcbdcbbddacbdbdababdbbabadddcbbbbaccbaaacaadbbbadbcbddbdaddbddcddacdaacbdddbcddddbababaaddcdcbbcbdacbaabcbccaaaccabadacccbccdacbdcbaadcabdacbabddacbaadabaaadddbbbcccacacacaccacbbaaaaabaddccdadaaaccdbbddddcacabbcacbcccdddcbbdaaddadcbdbbcbcdbcadcdddadabaccbabdcccaaaddaabdbcabcccbdbbbabccacabcadaddbcbdcadbabbccacbabbacadadbadbbcbbbdaabadddadcadddabbbbbacaaaacaabdcadbcbaaccdddccaabdabbbbbdacdababdabddbdcacbbabdccdcbbbbdbcbccadaaddbaacbcaaacdaaaccadadabacdaaccdddbacddaabdbbaccabdcddabcaacdaddaddddacddbdbaaabcadcdbdcdcbdcbaddddbccadcabbbabddccdacdabddabadbbbdaaadabbaaddaddbaaccacaccddbdadddbbdaccbdadaaacdaababbdcddaddabdddcacbdaddacabbabdbabbabbaabaabcaabaccdbdbdacadbccadcbaabccbabaabdcabcbcabaddabcabbadccdaaddadccaccacaaccaabaddbbcdddbcbbdacdbcbcccbcdddcdabcbccaddcbbaccadacaacdadcbbdcbddbdbdbdcbbdcacbbdbabcbcbdcbacabcccabbddbcddbadacdbccdadcdcbcdaacadacdadbdacdbacadcbaaacdadabacadabadddcdabcbbacbbdcccdaaadbbdcacdddbdbbdabcababcaccbdabbadaabadacaadcdaccdacbaadddbbcdbabacbddaccabdbdacddddcdacaaadbccabcabbbdcaaacabcbdcccbbaacdbcdcaddaadbbaadaabdbadcaadcbbbbdbbddccdacbaadbacddbdbcbbcadaabbacadbdabbdbbdabadccaaddcbddbcabadddadabccaabbcbdaddbbbdcabccdbacadcabbdbbcddbaacaabaadbdcbdaddddbccbaccccbdbcadccbcbbccabcbdcbaddccddabbdcddabbcbbdcdabdcdbcbbbacaadbcdbbccacacddadbbcaaaaadbbcdcccacadbbdaaddaabadaadcabcdddcdacbcadccbdbdacbbadcacbcbdabdbcccdcadccacbbdbbbabacdacdbddaaccabdbbcdbbddacccaacbacdcacddcddadabbcadcbcdbbdddbbbccacbaaaddaddbdccbacaddcdbbcddacbbdadddccccaddcbcdbdacabcdabcbdbbacacadbbaccaccabccacbbcbcbcbbdbcaddbaddabaadcbdcaccbcadbdbdddbaaddccaacdaddbdcbdacbbcbbdccccbccbdcbdadbaadbdddcdadcaaccdcbaddddaacbcbbbcaddadccbbcdaccbccadabdbcaabbdddbdbacadbdccbababddbcccbcbdbcabcdacbdaacacdadaacbdbbcdddcdaccabddcbbdabbacabcabbbdcdbbccdcdbccaacbbaddacadaabcdbcddbdbadbbdadbacabaddbdccabcdadbadbcadbbdaacaaddbcbcacdccaabdbaadcbccbdacbabbcdbaabcacbddcabcacccbdaadddcbdccdccdadaacacdabaccababdcbbcbbdbbdabdbccbbdcccadacadacdcbbddbddaacacbdaddbbacadcacccacabbccadaaaaabdbbcbdaacbcadcbddabbdcaadabcddddaccbaabccbcdddaddbdbacacccadcbbcddaaaaccbbcaacccbacccdbaccbbddaadcaadadccadbbabbddcaacbbcdccdbcaabbabbdccdabadadbadbacccbacbabbbdbaaabdcaacbdacbcbadcbaaaadcaccdcdcddbabccbaccccbcddbdbbbadbddadbbaaacddbcdbaacdbacdaadaacdbacabadacbbbacdaaadaabbcbabbcabaacddcbcdaadacacdbdcbdbbababbaaccbbcccdcbcccbbadbdcabccbdadaddcdbbaccdaadbbdbabdddacccbdcbddbaadbbbadcacccccaccccbbdaadaacbaddbbbaacaacdcbbaaabaacdbcdcabacaabcbbabcadcacddbccadcaadaacdbddcdbdbbcdbbacaddabbccbbcccccdcaccbcacaabaddbbaabcbaaaadddcadcaabbcdbacacabddacddbcccdbccdbaaaadccbaaddaccbdaddddaadbaddccaacbadbadbbcbddbbbbdbdbbcdbdbdababaadacdbdbccaadcdccdadbbcadbbbdcaaddacdcdbcddbbcadcbadddddacbaaddbaccadbcaacdacbbabcccccddbadabccbbbbbbcbdaaacbbadbcdacbbdacaacdbdadabccbaabcabdbdbdddbbbbacdbcbbdabbacbcadccdadcbbbcdbdacadbabbccacdacbbbacdbccccbaddbbccbcdbdadbdcbdcbadbbacdddbbbbbbdbcbddbdcccdbccddadbaacdbcbbccdabcaddcdbadbbdcdbbcdbdbbacdadbdabcabaaaacdddbcddcababbcbcaacbcacaaadcbbdabcbabdcdaadbdabbaacddbbcdaacadaaadabbdcacdddbcbccabdcdcbdadbcbbdddbcdabdcbcddaacbbaaacccddbbddbddcdcacbbddcdaadbacdcacbcbbabddaaddddaccbdbaadcdcddabdadcbbbaabdbdbaccabacccaddbaaaacbccbdcddbbbddacaadbdacaaccdbdcacbbcbccdbbcabbcaccbcdcbbaddabbdcabdaaccddcdabdbaaddbdadacbdbaaabcddadcdadcbadcddcdadaacdaacdaadbccccbdddbbdbbcbbbccccddadbdcddaacdddaccbdadbcddcdcaddabdbdabccaaddbcabdaacadabdbabcdadaccddabcaaaccbcbabbdbdcbadddaadbdbbbddabacdbabbdababcbbdcabcbbdcaadaaccbcbcaccbbacbaadbcddbadbcddbbdcdcdbcbbbcbbbaadccbdbacccdabaaddddcccbcdcbdbadabbaacdcbaacbcddbabcbdcdbbcaccdcbacabcabacabdbbadabaababcadbaadaacacbdddbbadbcbadcbabbdddaacbddababbbdaaccbaccdabdddabcdbaaabadccdbdbccbcbdcbbcbabcaabbcdbccacbdbadbaddbbabcbdcaabdcadbdbcbadaabbabadcbdbddacadaabcdbadcabbbcabbabbbbcbadacdbcccccdcdaabbaaacaadbbaccdadadbdcadbbcacbcbdbcdbcadbdbdcacabacaaccdabaaacadcbcddaddacbccccddbbcacdbdbbccbbbbabdbbaaccbcadccddbbdbdabacdbddacdabddccddbaadbdbdcdbddabbbbcabddbdacbacaccaabbdcbbdcdbcdadbabbaaddbbddaaccbacbaabaacbccdaababcbbbcaabacbbbacbcbcbbbbaddaaccdaaadbcbabbabdcabcbadadadaadabbbbdbcbaddbdbdcdbddbbcdbcaabdcdabdcaaabcacbcabcbddadbbcacdbbcadcbbadcdaccddbccccbaddbadaaddaadcbaaabadadaddccdcdabacbcaabccbaccbbddbbdacacbaccadcdadaaddbccdccbaacdbdcbadddbdbabaddcbddddbbbcabcdbbbacdbcaadadadccdbcacbbdddbdcbdcdddccccbabcbacaabcbacdcadbdcacdddbdccadcbcddaaddbdbabaaacddbbdddadcccadcacdcbbbbddadcbccadcbabaabbbbbbccabbaacbcdbdcaabcadccabdddaadbabbbbadcdccacaddcadcdcbcbcbbcabbadbacddbdbdcccadcdbdadcbddcaaaaaccaadcacadcbabdaccabddbbadbaacdaccbcddabbcbccbdcbbcdbdadabbbabdbdbdadddacdbbddddacccdadaaabacaadcbaddbabadbcddabdaadcbaccddcdabbddcacbacccbdbddcdddccaabcacbcbddbbccdaaacccbaaccabdcdcbbcdbdcbdddcaadccdccdbbbbabbddaccaaaadaddcbbbdaddccbbbbcaddabcbbdbbbacaccabdcbbcdbdbcdbadabcddbccdcbaaabaaddadadcccddadccccdccccdacdaadddaadcbacccabbadaaccacdbcbaaacbdddaaacbaaacddcdaddaabddadbbccbdcdcbccbbbbccbcccddcbcbbbcdccbddabacccbcdadcdacaadcddaadcaaabbbdbabbdbdcbcdaacdadaacaabacddcbdbbaccdbcdbdabbbcadbbdcccbdcbcaccdbaddccbaddbdbcbdbdacbbacabacccccaacbcdacdcdbabcccbcccccdbbbcddcddccaaaacdbabadabdbabaabddbabcacddcbadabbddcbccdccaadcdbbdacaacdabbcdcdbbabaaacdccabdcccdcbaddddacbcbadcbddbadadaaaaddaaaabbcccbcbaaaccbbcdccaddaddbbddaacdaabacbabdcadacdabbdacadaabbccbbbdccbbaaabddaddacbddabcbaadadadabacabcaacddbadbdadbaabacbbbadbbcbbcbbabbcdabdcaccbddaaccccbddbcbdababacdbacabcdccccaddbbdaddabbcaddacdddbbbcadcbacacbccacbcaaabdcadabcdcdccaaccadccdcbacbbaccbabbacdacccccbbdccabaabbbcbdcbddabcbcccdabbdabcdbbcaaacdbbcabcdbbdaccddddbbaadcddbcdadcbcabcadadccadacdbcdcdbdaaabcccddaacbbcccbaabdbddcddccbcaadabacdaccaabbcbcddacdabccabbbdbdbdbacbaaadcaaccdaaccacbcacdbcbadabacbdddcccbacabaacbbbacabaadddbbabaacaabdddbadadcbbcadbbaaaccdcdddddbbccaaaccbcdcbccbaabcaaccdcdaaccccbcbdcbdcddbcdddaacacdddaadabdccabddadaabdbaacbccadbadababbcbdddbdacdabddaadbcbdcccadbcbccccaccbddadbacdbddbacababdbccdadcababccabbaadccbdabbddccbaacdcadabbbbbbdbcaaddcccccdcaacdadaadaaadabcccbdcccacbccdbcadbcadbbaadadcbaacbcdddbccdcdacdacccdaaacabcabbcbacbcdbacacdabadaabcbdbcbadabdabcdddaaaaaaadcacbabdacabbabddcbcccbdddcdbcdbdaaccbdbbcbbacdbddbcadbacbdadabbcdcdbbabdcdaccdacbbcbdbbdbdccabbcbaacdcdcdbdcaddbcaadaaadaacdcddadcabddbdcbacabaadababcbabcabbccdbbbdbacbadcbdadbcccbaaaabccabcdaadcadcdbbaaaddbbadbdbadcababcaddbbcbbadcdabbbbddcabdaadcacaabdbcadcccdacacdddbcbacabcddcbcbcdbcbbcccbbdcdccacbbadcdbaaccabadcddaaddbdaaaccbabcdcdccccbbdcbadacbccdaccddbdadddbbdbadabdadbabbdadddccdcadcdbccbadaacaccdbccbacdddddacdabadddcddadbadcccabdabcdcaabdddbcddcaddacddbdbbdcdaaabbdcdbaaaacddccabaacbcdabdbdbbdbbbcddcaabaccdbdccbadadbcaadaccbdcdbcdbddcccabadcdbdacccbacdbbadabcddcabdbaaddadbadddcbdbaacdbcadccdabbddddbdacdbccadbaaacdacbcccacbdbccdccdaaacaadacbcbcbdbbddbbccadcdddaababbcddbacdbabaccccbcbacbbdbbccbbbbbacabbdbccdbadcddaabdacbcabbaabaccdccbdcadcddbacdaccaaacbaaabaaabdcaaaaacdaabdabaabdbccbbdcdabbadccaabdccbbccabcdccdaadbabdddcccbddccdcaddbbabacacddbbbcbddbccdbaadbbcccdcbddbacabcdbddcabcdbaddadddcdaabcbddaccbbddbaacaaabbcdadcaaddacaadbccadddabdaaaccddccadcbbaaadabddabcaaacddaadddadacabddbdbbdbdaacabdadbbcbaabddacbadabdadddddcdcaadbcdabbcdccacbdacbacdcacadddddbacacdcdcbbcaababababbbdbcddadacccbdadaadddbcdadcabdbcbbbacdcbccccbccdacccbacacbbbdbaddcbdbcbdcacddaadbdbdddaccbdcbdbcbbcaaabcbaadbdaacdcbdbdadadcddbbacdacddabacbbccdbdddbababdddcacddccddcbbadbabbcbacdcbcbcaacacdabcdabcddcdadcbdbbcbdbbbccbddddcabcdcddbaadddaacdaccbbcbbbadcbdbacdcbaacddbccbdcabcccdadaddadaaacaddbddbcddcbcbadbcdcddddddcdccadcdbccaccaacabcccadccdbddacdbccadcaddcbcdccacbacdacacaddcdbccdababdcbcccbaccaaddbaccdacaabcabdbbaacaccbaacbbacbabcdcacdbaacdcdbdbbcdbbadbdbbaacbacdadbcbbcbbbadbabbdbcdcdbcbacbbcdcddbbcacaabcbcccacbdccaccbcdabdacddcdcdddaaddddadacdcbddccabbbaabaccabbacdddddddbbcbaaacabbcccbddbdbdacdddbcdacacdccddcccbdbddbabdabcbcacbcbbbbbcbcacaaddaccdabdaddbcddbabccdaababbacbcabdcddbaadbccdaabbaaacacdcacbcbdadaabdabddadddabdabccbdcdaccdbbaaadbaddbbdbabcdbbcaacbbbacbcadaacdaaaabaddadadcbbacaacbddddacacdcacaadcabadadcdadabaaabccadacbdbcdcddbaaadaacdabdabdacccbdccdccdaddbddbabadcdccbaccdbcaadcdbcacdddcddccdbdcbbbcdbbccaabbcddcabbdbccddaabdbdbdcdbbdcdcbbcbacabddadccbcccdbdbababccdbbdccacdbdbacbbadcabdacdbaadbbbdcbbacacdcdaacdadddcdcaadcccadddddbaaadbbbcbaccdaccccdacdbbcbbcddcbbccbbccddbabbbaddbccaddccbdadbaccbacdbdbcdddddccbddcdaaacaabdcdabdbcdbbaaadccbbdaacbcccdabcabdbddbcacacbddbaaacaacaabbddddcddbbdddbbadabdcabddaddabaccdbdddbdccbabccaccbbcaaadddcbabcacaadacaaccbaddcccbddaabbcbdbcaaaaabdddacccacadbcadbbbcabadabdadddddaddaadcbbccdbdacdbacdbaabbbdbbbcbaabdcabadaabbacbcddbccdaacbbaaddbdcbddcbdbdcdcabdcbbccddabdabddcdbccbbaabbddbabddbbcadaabdcdacbbaaaabbabbcabcdaaaadbdcbbacbabbbcabcaaabddadbcbdabccbadbcdbaababacdbaacddaccdbddddcacbadbacddcabcbdbcccbcdcccdaacbaaaadaacdadbacaaabaddcdbdbabdabdaadbbdcbdcbdbabdbccdbacbaacbccacadbdabacdacccbdbbdbbaccaacbdcacbdcdbdbbcdaadbbccdcbddbaacaccdddbdcdcdaadbdbddbdadddadccabdcccacbcababdcbbdbdddabdcadbbbdaddccabcaaacbaddaddcbcbbdaacccdaddccaadcabbaacdacaddcdbcbbaddbbabccccbcabdbbbbdacdbbddaddbcbaddcdbcbdacabddcbbaacdcdabcdcbaddabcbaddcadbcadadacacdbcabdbabcaadcabccbdadaccdccbdddbabadbccaccbabadccccadacbbbaadbdacaabcacbddcbaabababcdbdcbcddcddbacdcdaaddccaacdbdccbaaadccdcdcabcbbdbadccbaadddbcccdaaccabcdbcbbcbcadabdbbbadbbacbaaddbddbddbdcbacadaacdbadccacdaacacbdacddcbcdbacdaddadcdbdabcbdbcdddabdccbdcadcdabaabadbaabdbadaadcddaaaaccdbcadddbbcdbbbcddbadcabccddaaadccbbcbdbbbdaaabaddbccbbdbaacbdbcaadcabdcbdacadabadccdaaccddbacbbabaabcdcbcddbdddcdbcdcabbcbbabbcbbbabadbadbabddcbdaaccccddddacdccabdcbdccbcccabdbddbabacdddaabddbcaaadccaccbacdacabdadbddcbbbbcacaababbabbcabdcbddcbadacddabcdacdbdaacacbdadacaddadcdcaaabcabdbdadcaadadcbacdbbcabcabaddcaddcaacdddacbaadbcabcdcabaabaaccabbbbccdabbbcccdaccdbcabdabcababcbbcabbbbcbcdbbbacbdccaddcdbdaaabcacaaababcccccbbbdadadccbdccbccacadabbdabccabdbbbabaabddccccacdbddddacbddaabaddacddcdbaaadcaabaacbdbdbdbabcacdcadacaddcaaadadacaaccbdcbdbbcccaccdbddcddcdbbabcaacdacbdadbdbacbdcbbbdabaacbaabadadccbcadbccbadbcbcccadbacccccadbcbdccbaccadccadcbcbbbbcdccddccbddacaaacadccccdbcbbccbbbdbcaddacadcddbabdbccacaaccddcdacbdbbbbcbbbcccbdcccbdcccababbcdabbdcdccddaccdccdcbbdabaddbbcdabdaccacccddcbccdcababbdddcabdaabbadbcdadbaadabbadcbdabcababcdbaccdacddddbabdbdddccaabcaddaddaacdaaabbbddacbddabdcbacacbabcdcaaaaadabaadbccdbcdaaadbacdbdcabdbbaddbabdaabbacaaccacaabcdcccdddccabbccdadccdccaacdadadbcaabdacdcabadbadbaccdddccacdddccadabacbcbbaacdadcddbdbacacabdcddaadbabdbaddbbccadddcaccddcccdbcdbdabcbcdbcaabbbccbdbdacbbdcaaabdbaddbdabcadbadbdadaadcdabdacadbabccbbbcccbcadaabbadbaccacddddcdcbccddcbcaaadbaaabdddacbaddbdbdccbcaacbaabadaacacddbcdbadcccdaacddbddcbcdaaacccbdbabddbbaacbbcddacabacdddbdbcacaaccabdaaaddbadaddddabcabdcbbccdcccdccaccdcadcdbdbaaabacabdcdcdbccaabaacbdccccbabbbabcddadabababdadabcadcabbdcaaccaaadbcacbccdaccdbacdbbbcacdcbbddcdacddbcbbcaccddccccabdadbbaacadaddcbcdddcabddcccbccbaadaadbcddabacdadbdddabadccabbbdbbaaddaccdbbdcdbcccaaddbaaccbacbccdcabddbdaddcababaaabddccabaabadccdccbbbdbcaddcabaabccbaccababcaaccdcadccaddaadaaddccbcddcbbdcbccaccddacbbdcdbdaacbcbaabbdcacbcacbdbdcbaaddbabdbbbcaadddabbdaccaacbdccbcbaddbccabcdddcbdcdcadabddcaabdadadbdbdcdbbcdbaabbdaadbdbadcabbadddacadbdabbcbddcaccdaddccdacbcbccdbbbbdaacaacacdcccabbdbcabcabbdcadabaadcabadabbbcdddcadcbccbcbabcddbbaacdbbdbabcbbcdcbadabaddcbbbdcbbcccbcdbdcccaccbdbcbbadccbbbabbcbdbdaabdbbddbdbdadaaadcaccbcbababcdacadcdaacddabbbdadabbaadbdadaabbcbddacdaccdcaaadababdabbcbaabdbdddbbdcbbcabdcbbbccadcdbabbddabccacbcddcaddddabacdcacdcadabbadccdabaaccbdadccbacacadbabdaabcaaaddbcdcbbdadddcacaabdccbadcdadbddbdbdacbacaddacacacbacbadaddcacabacbdccdccdbbccacdcbbcababddbaadccaddaaadbbbababbbbcaadcdcaabbdddabdcbdbabbaacaccdbddcdacbbddcaabbddddaadbccabdbcaaabcbbddaadddddabbbcbbdabaabdbdaacaacbadcbbcdadbccaabdbccccccbbbcbbbbdbbabababcbdbabcdbbcccbcadabccadbcdcabccbbbdbdcabcdbbcbcbdbcbcdbaddccbacdcbcdbcccddabddcadbbdadabbbcbcaaacabdadaabbbcbacaaaddbbcddadaccbcaaadaacdabdaacabadddbbaababcbccdcbcdddababddddbbaacdddabbcbdbcdaacbccbcdddbaacccacbdaacbaccaabcdbbabdddbcccdbbcbbcacbdcbccaaabdddadcbdbdcdcaabbdaaacabacddbabdaacbdccabdccdbdabcaabddbcaaccddababcbbadddbdadccbbccaadcbbddadbdbcbccddbaabcbabccbacbcbadacaacdcccdbacccbdccdddbdaaaddabaccacdbabdaadddbbbaaaaddbbdbcdaabcbbadcadcaaadbdbbddbdaccddccdacdcdcbacbbdbcdcbbbcabcacdbcbdcabddbbdbbcaacdccdaabdbacbaabcadaadcccbdbdbcdddbbcdabbaddccdbccddcbaccaabbcabddccddbdbcadcacdbbcadbdbdacccbbddcdbddbacbacbabdabccbcccdabdcabcccadccbdcaaaadcaabdbcaabdccaaabcbbcdcadcaaaddcacbaabdcabaabbbbddacdcbacacdabdabdbabccbcbdbbacbccdbcdcbcccccccdddbccdcbcbcaacdacabcbaccaddcdcddbbcdacddddcdbdadadaaccdaabdbbdaaccadcacbadacbddbdaacaabbabcdaccddcdababccabbdbaacbccabddcbdbdbbaddaccacbdccbaddccdaabaabcacababbdaddbbcbcdabdccbccbdacbadadaacbbbbbcabbbdcbcdaaddabddbacccbcdcbbacbdbcddabacadbcddbabbdcdbdbaacbaddbcabadddcddadcacbddbabdaccabadadabdbbaadaccadbbaabacccacacadbcbbcdcddaabbbddbdcbdbbbdccbaabccbdcabdadccdccaaccdababdadcdbbdacbaaccbddbadacabbdacabdbadcbbaddaaacadcbbdddbccbcbbbbdabdbaacccdccbcabccbadabcadcaadbdbccacdddcbdbabdbaddbabcdcabaadbcbdddadcabdadcacbcacaaaacbbcaaaaacbdabdddcdaaccdbbdcdbbbdbcaabccbcddabbbddaccacbadcdaabcbdacddcbadacabbabdbddcbabdacdbcbadccbdbcccadadcadcaacbbcdcaabddcabdaaddabbbdcbaabdbadadaaccdbbdabbdaabccdbadbcaaabdcadccbddaaadbabbdabcbcbababbabcacdcbbdaccdccdbdcdcaabcdbdbbbabdaccaadcddbacabbbbddcaacbaddacaaccbadbaaddbacdadaddaccbaabdbcccdbadbddababbdaabaccbbbbadacddabcbadaabccaddaccabbadbabcaacacbccadddcbbabaadbbbadbcacdbddcccbdcdbbadccdcbacaaaddbcdddcaaaaddacbcbacdabddbdcdcacaacccdccbdbdbcbccdddcccdbaadcbdcbbcadaabdbdbcabccdcbcbbbdbbccbabbbddcaaaabbdcbdbaabdbbdabbcabcabacdbbabbccadabbdabadddddcddbbdcaccabcadbdbbbaaddacaaadccddcdaddaccadcbadcdbdaabcccdddbbaaadcccdbbcdcdacabccbbbbadcdbcccbdabdabcbbbcdcbcdcadabaabdbcccbcbbccddadcaccadcccababbacbabbdcdccccaabdbdddadaaaacacbbbccadbaccbbdddbdcacabaadbacbcccdbbcaabdbadaddaabdcdaddcbaddbaccacccabdadcdadadabbabdbddcbcabacabbbbdbbbbbcdaaadadaaaaadbaaccbcbdcaaaababaccacaaabbaccdccbbaaaabbabbdaadbacaacaaabbccbbcaaabdadcdcbdddccbddaaaadacdbbddccdaddaddbdabaadbbbcdddcbddbccacccdabbdadabbcbdcbdbadaccdcbbddaabcbacbcbcdbacaabcacccaddabaaacdcadbcdaabccdbaadcbadabaabbddcabbbabbbaddacdaabcdbadbcdadccbdbdcbbdbcadabadddabdcbcdaddccaadbadaacbacddaabdcaaddbcdabadddbcbcacaadbdcbdddcdbdbdaabacbacaddddadadbbcbadacbdbcaaadacbaccbccbccddcdbabbcdbadbaddcdaaaaaadcaadabbdaaabcbddababacdbcbbdacbddcbccaabaccbacbaaaadcaadadbbadddacdccabbbaabddcacadcdcdbbbbcccbabbcdaacadbbdaadccadcbcdacbcdccdbdccdccbbaddbdabcbbdaaaaccddcbcacbddadcccdadcbddacbccbbccbbcaaadcbdbbbccacacbbcdcbddcabdaadbbbccbdabcdadbbbadcbdadcbacbbcdbbddacbdddcbccbcbaddccdbcbdbdabdddacbcccccaabaacadaabccdccabddabccddbabbdbcdddbcdabbacbdbbcbabaccaadcdcdcaddcbdadcbdbdbdddaddbcddbcbbbddacdddaaaaabcbaccdcbbaabcdaddbbbacbddacdcbbbbdddcbacbaabaaccbdbdacdbacdbaddddbadcbcddbabcdadddadbdacbbdacbddddbcbccdcadabadcdddbabdaadadadaabdcadcbcadbdddaaaabaabbbdadcaaadacacdcbbadacacbdbdbcbdbcacacbbbdccbdcacdbdccabcabbdbbbacccbbcddadcababbdadcbaaabddbbcacdcdddbbdbaddcdbbbcabccbdcdcbadcddbdbcaccadccccbbdaccdbadcabcdcaabdcdbabdabcabbccacadcabddbabcbcbccbdadaddcdcacbcbccdacdbcacdbdaabbbcdcaccbdcaccaaaaacdaddcbdacadcacbacaaaacabdccabacaabdcdbccadcddcadbbaaadddbdcbbcbacdaadadacaabcbacbdabbcbbdaabdaaaabccabdbdbcccadbddabbddadccaccdbacdabcddcbcbbaaacbbbddaabcdbcbacccccaabddbcaadbcadccabaaccbcaacbaaddbadaabbcbbbdacbaabacaabdcccdabcbbabbaabdbbcacccbcadacadabdbadbadcaadbbcccccbddbaddbaababccbbababdcbaaadcdcbdbbcbabddbcdaccdcabacdcacdbccbcbcabadaadcbcacbaabcbbcaddcadcabddccadcabaccdcbadcbbbbbbcabbbdddcadccddbdcdaddcdcacbbdbdcdcadcbbabcbcbcbdccddccaadbadacbbccdddbddcacdbbddcbaddbddbdadddbbcbacbacccdcadcdccdbabaabdadacdcdccabdabbbdcbaccadaddccacabbcdbaaabadcbcabbcbacacbdddaadcdbbcccbcddacadacaccbcacdbcdcdaccabaacccdbddbaccbbdcdbbadcbbabadcbbbdbcbbccddadabcbccddacadcdcdcbdccabdbdaaacdcbbddcccbdccdcdccbdcdbbcaabacabcbadaadbacbcbabadbcbabbbbbcbacadbabdbbabccdacbaabdaabdccddbaabadddddddbccdbdbbcdaabdadaccdaadaaabcdcadaddcddddabaadddababbbcbddacdadbdabbccadacdabcccbbcccdbcdbbddcbbbaacdccbcbddacaabacbaddbbccbdcbcadcdacdcdaabdbdacbddabaaabaabbbaccabbaaaabadbaadadbaaabadababbcbbadbbbaababdabadbbbacbabcadccdbadaaabdbcccddbcadacdbdbdadabcdcadcbddbbaabdddbbdcbcabddcbcbaabaabbdaabadacdabddcbbcdccaacbbdabddbdadadbabcaacdcaadcbbcddbbaacdcbdadcbcdcbcbabbbbadcaaccdbccbbdcdbccbbababacaabdccdbacbccacdaacdababdaaacacdaadcbcadadaaadbadadbabcdccdbbacdacdaaddcadaddddcddacdcbbbdbbddbadbbbbbbaccaddbacbddcbabbacabaccadbcbaddbacbcbbbacadddcdbdcdadcdbbbcaaabadcbddaaadaabcaaddcdbbabbadbcddbdbcbaaacddadcdaabcacdaaacaccddcadacbabaccccacabbbbdadabacbaccccaabbccacdbacdaadbaaddcbdabdcdbbadbdbcbbcbadbbabcddbccccdbbbcaaabdddaabbcbcccdcdabadccabaaabdddcbaacaadaccdcbcbbadbabbcdaaacbddbcabdbdbdbdadcdcbddbaadbcddaaaabadbccccdbbdcacaacdadcabbacddacaaaacbbacbbaaaabccdabddcbadcdacbbdcacacabdaabbbbdbbdcaccacbbbbccacbcdcaaadcbdbadabddabcddddadcbbccbbbccbdcbdcbabcabcdbcbabddbbdbaccdcbabacbdbbbbadabbabdcabdabcbaabdbacaddcdbabccaaddbbcbcbabaabdcddcbabdcacbbabdaaacddcdcdcdbdbcabadccbcaabddacdbddbccacdaacbbacaaabacbacaadbcabbdbddabcdcacaababccadbdccaccddcabcdbbdbadbdccdadccbbdcabcbaababadadbbaababcbbccabcdcbbdcbddbdcbcbcbabdccdcddadaabcbbbcbaacacddcbadcacbabbdaccababbaabacdabadcaabbcabcabddbbacdddcaabcbbbbddacdddbbdadcbaadadaaccdccbacbaadbadaacbccdacaababadddacddbcbdaacacbbcaaaaaadacbcdaacccdadadabcadccabbbcbdbdaccdaaabcccdccdcdcbcdacdabbabcdddbbccccccdbdabacddddaaabbccdbaaabdccddaabbabdcdbabdccddcbdcbdbdcaacdbdbbcdddcddcbaabcddaacaacbcaadaaadbdbdbaddccbaadcccdadccabbbdadcbbbcacccdabcbdbbcdbdbaaccbddbaccdaabbbddcbbdddbdcacadbdaadbcdadabdcdaaccdccabcdcdddcddcdddaaadaaaccdbaccbddaddcbdacacaaaaccdbccbabbdcdbcaadddbddaabdadcddbcbcadbbcdccdbdadacaabaacbcabdabdcabaacdcbcaabdabadcbdbadccdbabdabdcbabcbaddcacbbdccaaabbcacddcbaabcbbcabddbcdcaabbcaddabdddaadbbcdacdbdacacabbabcddcbbacbccbadbcdaaadaabbabaaddcabdbaddbccbaabaddbbccaadcdacbcbbaddacbdcacaaabcdadcdddddbddbdaaccdaccbcdcacaddbdaabadaabcabdacabacbadcdbcdcbbdbbbabdbcaabccbdcabbacddabcacbbbcadbcabbcddcdbaaaaaabaddaaaccbaddbcacddbcddcbcddbbabdadbbabbcabcaacdbcbbcbbaabbcddbaaaccdcaddacacbbadbcbddacdccbbaccacccddbaddaddcaccdcbdbacbaddcacbaccbabdaadababdbddacddcdbbabcbaabdbacaaacbbdaddddadaaaadcababdabccdacbcccabccbbccbdaacacbdbbbcbddadddbcaadbcabbaccbdbdabcbddaadaccadadcbaacbcbcbdcbdbcacdabdbcacdbaacdaabbcbdccbddbbdadacdbadbdbbcdccadabbbbcccabbbadcabaaabaadbcbacdbacdaadbaccddaaadccaddddcdaacdcadacacdabacdbdbababadddabdbdcaadbcaccadbbbbbcbcddcbadddcdbbdcbccaddaacaaacadddbdcaacdbdadccaaabcdcccadcacacddcddbddacbbbccbbacccdacdddaacdaccdacddacdadbabaacbddcbccbaacdccddabccccabbadbdcdabbbcbbcccdacdcaaccddcbdbcbbdddadabcccdacbbbcaccdcdcddbaddccccdbdbcddbbdbaacadadabbadbcccddaadbaacabbddbbbccdcdcbbabddacdbaddbcdabdcdaaccaadcbbadcbdbabaddbddacbaabddcdddddbabbdcddacaacacddddaddaabcddddbcaacabbcdcbcbdcdbcacbcdbcbbacccccdcddbcabcaadbbddacaddbcdddcadacbdddacccdcbdabcacdbdacbcaccbdbaccdddcdbbabcbdcbbcdbadaacdbacbbdcbddcabccdcbbacaadbcaccadaddcdccccdbdbdcbcbbaaccdbccbccbdcaddcdbaccabccccccbbaaabcdbadcddcabcbaaaaccbcddacdddccdddbbbdaddccadaadabdbbacddacddabaaddcddbbdccbcdbcaccbdcbbddcbcacdaaabcadbdadbbbccaadddbcddbadbaccdabbbdacaccbcaaabdbacdbbbcadabdadbbccccbdadccbadadcbdddababbcccbbcbbadbaacbdccbaacbbddadddaadbdddcdadabdccdadadbdbbdcbcbbcbacbadabbcdcbdcdccdbdbbbbdcddcdabccdabaacbbaabdbdcbbadaadaabbabcaacdbdbddcbaaadbbadcacacaaadabbdadcdbbddddccbdbdbdcaabadadddaccaddddbbbcdcabdcadabacbccdacdcbdcaacbcaabcdddabaadcbddbbbbaaaaadaadcdccaacacacccadcabadbbbcabcccbabcbcdaaddcdbdcdabbcabcaddadaacaabcadbdcbcacbdbdcdacdddcdaddcaacdcbbdcdbcaaacbdbddccaddaacbddaabdbbacddbacadbdbbbacabddcdaabcdbcccaddbdbbbacdaaadddadaddbadbdacbddbccbcadbaddbacaccababddbabccbaabbadcdccbaadbaacaaccaadabcbadbcbaddabddbaadcadbddbdbacddbcabacdabdbbdbccbacbbcbabcddaddddaabcaccadddcadccbcccdcabccaccccaabdccddacddbdaacdabbaadabccacaadbbadbcdccbcdadbcadacaadaabadcaacadcadcccbbbcbdabacabdadbdbdcbaacaddddaadabaddcacdaadccbbbbccccbddaaacdcbbccbaacadddccbdcabbabbdaadbccdacddcabcbbddacaadccbbcccacabbdabdabdcbcdbbcaaaaaabddbccdcbcaccdbcccadcbcdacbdbacddcadcbddcabbaddbbccbcacdabcbaacddbbbcdaacbcbdbadccbdddbccaaddccdadbacdcdddacddacbdbccacddabacacaacdaccadcdabbdcccdbccbaaddcddbcadbcadbcdddaacdbabacabccccdacbbbddadadacbbabbccbabdcaccdbddcacacbabcccbbdacabdbddcdcdbddddbbcddbcaccbacdabddbabdaacaaacbcacbadabdddadcbbbcaadadcabbccddbdcaaaabdadcccccaadcccaadbbabcababdabaadbacdccbdddbbdbaabbcdbabacbadbbccdbbadcdcddccbbabcabcbbaabdddbddbcadbccdcadbabcccbdaaadbadcccddacccddacdabdabbaccabdaaadadcbaccdacbcdbbbaadabcdcdbbacbacccdcbccdbdbaddcadcccccdacadaccadcdbabcaddadcccbcdadccbacbcdcaaacbccaacbbaabacbcbbbdabddbcddcbdbcadbdcdcdbdbcbbbabdbbcccdaddbbbaccdbccaccbcbccdbababbaaacbbadccadccbccbbddcbbaacbbdbcdccbdaadccbcbacaabbdbaabcbdcbadddcacabdbbdcacbacadacbdcdcdcbababdcdbaaddccdbbbbadccadacdbaabcbbcbdcdccadbcddccacbadadbbcaaadbbdccabbcacacabbddbabcdadacaabccaaddabaacbbbbcbccbcddbdcacbdadcaacccbabbcdbbaaabacbcbbbbaabbbadccacbcabcadbabcaccdcbcbbcadccdadadbcbbbdbcaddddddbccdacaddbdcccbbbbcaaddbbcabaacbaaccdaccccbdbbdbcaacbacbbbcbcacaadcbcbdbbaaaccacddddaccbaaccadddccccccbdccdddcdaaabaaacadbbacdbcaaacddcdccbddccbdabdbcddadcadccdabadbdbddcbaadbddadcacdccdbaadcccacacddcdaabaddaadbabdbccdaccddabbcbbdaabdaaccdcbdddbdbbcbbcddcadaadabccbbbacddabaccbcddbdcabcdabaaabbdcabcabbacadaddddbdbcbccdacacbccdddcabbccacdddacbdcaadbdbccddbcbababddcabddcbdcbdbdcddccdbdbcbaaccabaabdbcbccdaabccacaaabdcaacadbbcbabcaacbdbbdbabbbbcacdabcabadbcbaddcccabbcdbdccdaabdcbdbabdbcbabbdacbdaddcbbbcddddbccaaaadbaabaccadbbcccddccdaaacccbbacdbbcabbabcabbdcdcabddbabaabacbcddddbcbabcbaabaabcacbbdddcabcccddcabacddccdacbbbcacabcbdaddaaabdbcacbddbddacbddbcaabdccccadcdbddacdaadbadbabaddbbbbadcdbabbbbddddcbaabdcbcbddacddcdabdbbcabadcbdacaabcbaadbddcaaaacbdabbbdcbcdccddddcbddbbcacaaaaddaaccbcacaaadbacaaacdbdbbbadbdbcbbcbaabcbbccbcacabaccaacbcdabddcccadbcdcbbdccdbabacadacdcbabddddddccbaacdbaabdddddbccaaadabaccbccabacaabcbabbadabaadbdbdabcacababdadbbdcdcbcadacdddbcddccabdddbbccabcaaddadbbcdadbdbbddbbaccbcaacacabaddbcbbabcddbbcccbbbababdcacccdbabbbdaaacddbaabcadcdadcaaaddcbdccaadabbccdbbcccccbcccbdbdbabcaddbcabbbdbdbabdbbcbcacdadcddddaadcabcacaccddddbdbcccbacabccdaaadaddaacabdbcbcbcbbaacdcdbbcacacdadbaccacbabbdcbaacbbdacaaadaaaabdcacdbdadacadbbbbdcbcbdadcbcdbdccdbaaadaababcbbadcacbdbbbaddcabccbdbbadddabcacaddabdbccabccdccdabaddaaabbadcaacdbbcccdddaadcbbacdbccbacacbaddcaddcadccdaabccaddaaabbcdbbbdaaaaadccdbcabaacdbaccaaaccadcacabaadcaddcdaddadbcdacacaddddcdccbabcbdcadcbdcadadbcdcccacaabbdcddcadaaababdcacdacdbcbadcbbadaaaadbdccbaadbbcaacbadabcbccdbbccddcbdcbcbcdccaaabcdcccdddbdcdaccbadaabccdaddabbcdbcdacbcddcdbbbcadaabcbcbbdccaadddaccbcbdccabccccbdcbdadbcccbcacbdcbbcadccaccdcbccdccbcabcdccccaaacadabbababcaadcaaadccdbbcaddbbaaadacacbcddcaddadcbbbdcbddacadddddadcdcbdbdacbaccccabcababcdaccbabcaabccbdacdcddbcadacabcbabadcddcaadbaabbdccabdbcacdbdbadbddabdacbbdbbddcccbbdbccbcbbcdabbcdddabccadaacdcddabbcaabbdaadaccbcdbcdadadccbbccbdacabaccdccadcddadabcccbcdadabbacaadcbbcdadbbacdadccacdaabcdadaabddcccbcdbcbabdcccbadadbaadddcabbdcaccabbcbddbacddbaaabcadccabcbcaacdcadcbccddcadbabcaacabdaddcbaaadddcbbbdbdcabbdbddbaabbcdbdabdcdbaccaadaadddaddcdcabdbdbcbccacddddaaddcacbbcbdcaabdddbadaacbadadacdabbdabdbbccbaaadccbbbdbaccaccdbdadccddcadddcdbcdbbadabcdcdcdcaaacbdacddbabadcbbdbaccadddacdcabcaddbbaccaccbddcbadbbbdbbbaddabdcbabcbbcdcacacaddacabbdbcadcbbadbdddbbcabdbbbbabcbdaddabaaababaacbccdbbcbdacbaabddcdcdabbbccacacbbbdcccbadcaddcaaccbaccddccbbaddcbdbdbabbbcbbbaadcdddaccdbbdbabbcdbbcbcccbbbaccadcdcaaabddaadccbdbadabddacdcbacbdcbcaaacdcaccbcccacacdddacabacbdcacbabdaacbcdacacdcabbdacbdacadabacdbbcdbacbccbacababbcdbbacabaadcbbdadbdaddcdaadacacdcacbbbbadccbadcdddcadbcbcbdddbddadbcbbddbadddaaabdaddcabadddacdcabbbacadbccacabdadabddbbcbcbdbddaccdbbdccabaccddbdabbabcbadcbdabaacadcddbadbbacdcbdadcadcaabbcdaaaabcacacbbabaaadcbbaadabadcbbaddcaabdabcdccddcdbddabacaaccacbdbcbacabaadadcdddccaaaaccccbbdbccbdaddcddbacaaddbcadaccdaccabbaacccbaddbccacbaaaaccbbbcbcadccdcbddbaadddbbbaadbcdbdaaacdccdaaadbbcdadadcdcbcabaadcaaaadbdadaccbdbaaadacbbdabadbcccadcbaacacbccaaacdcbcabdddbdcbbcaaabbbaacbddbdcbdbcaaabbabbddbbdacbccbdcadddcdbdbaccbabcdaabdaabdcaacddbaddaaadbbacaddbabddcddbacbbbccacadbbbaacabdadcddbdcaadaddddcbcddaabbabaabacacaddcdcadadbbabbcddacddddccaacbaabccbdacccadaddabbddcdbdaabcbdacdbdadaababdcbbdbdacaacdacbdbcdbcdbbaadadccdbaadaddccadcadcbcbcdabcadabaaadbaddaaabbddbdcadaabccbdcaacbdabcaaacabaccadbaacdddbbbcabcaacbdcccbdccbabcbcbdcddbbdbdbacabbcaacabadddcadcbdbbcccdaabddcdabcbcadabbacccaddbcadaddadadbbcbacbcabadddddcbcadbbbdcabbdbbadbabbdbdbcaadbcbbcadbacaccbcdabdcaacababaacbacbbdacabdacddbcbcdcccccaacbacbcdaacaaabaacbabddaaabdbcaadcaccdaadcdadacacdaccccdbdbcbabbbbbdcadabbdcadacacacbddbacbdcadcdbbccbabacdcaabaccbaacbccdccbaaccacbcdacaaaacbcbcbaadccdaaadbbdacdbbbddcccaacacbdbacadddaaacabccadddcbdcbddbdabccdcbcaacacbbbcabccabbddaaadbccccaddbcddcdbdbcaaaccccaabdbcdcbcdcbacccaacadbadbacadcccacdacaacdddbdaddccadcabdccabcbbcdbaccaaaadbbbbbccccccbccabdbcadcacbadbadccdccadbbbacadbcbbbcadaacdbddacdccacadbdbadbdbdbbacddabaacbcacbbadbddcbcdacbbccaccbadbdbcacabbdddddddccbbaacbdbcdccbabcbdcddabddacabbdacbadddbbadccbbcbcadbacbbcdaddacdbccddccacdccdaccadaccbdadaaabcbdaddcdcdadabbdcaadbdadabbcddccdcccabcacbabdcdacdbacadadccbaccacccbbcaabcabbbcdadbdbdabccbdbdcdbcbacddbbaddbbadccccbcacaaadcbcddcbadcdbadccddabdcbcdcabbacabbdcabbcbddbdabbddbdbdcccadaaabdabbadbcaadbcaabbcbcdacdbabbaccbbbbddcdddbccdccacaccdbdaccbdbaaddabddaddbaabdaacabbddcabbacbabbbccbaacadaaadbddacbaaddbadaadcaacccabddbadacdbbdabbbddbcbccbcdcbadddacabcabddaaddbdddacdcbbadabbcbaddaddccdbcabdabaaddcbacaaddbcdabdddacbcaccbcccdacccccacabdbddbcadadabddcaaaaccccdddcdaaabaabbbdcddcbcddaaadddababccadcdddbbabbabcbcaabdadcccccaddaaaaddcddbaabddaabadcacbddddacacdacbbbdbbabbaaadcdbcdcbbccaadaaadaaaadaaccdaabadacadcbdbbabcaccabdcbbcddacdcdadaacabadddbddacabacbbccccaacbdbadcabacacddabdbcdbcbcbcbdaaddcccbbaaadbcdbaabacbbddadacadaacbdacbcdaaabcadbccbccccdcddbadadaadabbcccadacdababcdddddcdadbabdcdabbbbdadbbcbdbacdcbddcbbacdcbabacdbdcdddcbddccbbdbbbdddbaccdabadddbdcddbddacdadbdbaddcabcbdadbbdcbbcbbcdcaabdbddbcdaddbaddcbdaacddacbaccdbaacadbcdbcaddcadbdcddccdacdbabccaddbcdcbbbcacdbabddbaccdadccbaacbcabbdbbdbadbdbdcccbdaaaacacbaddbddbccdddbbacbbadcddddccccccddacdcbbcdccbccddccccbabdcacdabccabdbbbcbdccdbddcbcdaaabadaddcdbbaaabdcaddcabcbbdacdadbcbcabbaaadcacabdcbbaabcdabbbadaadacaacaabddcdbdccccddbadbdbbadcdbadaacbcbabbdcdaacddabadadadcaddacababdcacdbcacdcbdadddbcdababcacbacadaaddaddcddbaaaaacabcbddccdccacaaacabcdcbdbdccdbcaadacdcbbabacbabacbdbabbbbbbdbabacbcddabbcabdbacaabcabcccddbdcbdddabccacabbdabaacabdbccdabcadabdcdadbdadbbabbcaddcdccacdbccbaccaacdcadaccbdbaaaccbabacbcbcddcbbcdcddaaacaaaabdaabcaaacdddcadbdbddbbbababcacbacdbbdcabbcadbccbbcbcddbabdbacbcdcaabdadcadcccdddcacbbccaadccaadabbdabcdaccbddcdcacbdbcabdbcbbabbdbbdbcadabaacbbddabbdddacacabcbcbdcaccdcddacaadabdbaabaaaadccccdbacdabaaccddabdcaacddaaabcccdbccbdacbacbcabbddcbbddaaababdaadbbcdbabdacbddadcbadcbdddddccbccbbcdbabbbacdadaabacacbabababadcbcabdcbabccacbdbdbddbdccdbaaabacbbbdaabdacabaaccbcdccbaddcccdbbbbaacaabaadddabaabbcddbdbbccabcabdabaabadcababddacbbaabaabcacbccbbddabbdcaabcbcdcdbcaccbaddcabcbcacdcbaaaccaaaddadbdcdcaabcddaaaddddacccbaaddcbcacbccbbcbcdddbcdcddaaadddccdbbaabaabdbdcacbdabacbcdbcddacbcadbbbbbabbdabbdddbaaadccdccaabbbdbcbbccbdbcaabbabadccdbbabddcccbcabbccadcddaadacbccacdcddbcacdadcdbdbcbcdcdcbbcdccababbbbaabcbdabbadaabadddcbdbcccbadbaaababccbbadddcbddacddbacddddabdbbbbadcbcccbdacdbcbdcaaddaaaddbddbccacbdbcbbaabdcadababbdbdcccdcdacdcddbcbcbccbcabcaadddaabbcbabdabdbabbbabcdccbdcdbdbcaddaaddcddbdbbaaccabbddacbbabbbccdcbacabbdddccdbdaadddaccacabdbbbcddbcdbaaabbdcbcaadaabdccdbdccccdabcdbabccbbacbabbbddabaddbddcbdacccabcbacaddbbdcacdadcddbbcadcdcdaabbbccaccbabacdbbccacaccadcdddacdbccdbcdbdcacddcdacbabdccddacbadcddbacccbbbdacdadbcdadddddcbdcddbbbaddacadcddbddbaaaaaccbdabbccbdcdaabbaccdacdcaacbdbadabdbcabadabcbabcaccadcccdbbdadcabbcabccbaaaaadacaaaaadcbacabdacbbddacddadbbcdcccdcbbbdcaaaaabadababbbcadaaaaadcdcddbccdbcbdadcccbdbdddcadcbabadaabcdadabdbcacbcdbabbccccabdbabcaaabcccdaddcdbbcaccdbbdbbcacdacacccacbcddbccccddbbcdccdbccbadabcdbaaabbcaddbdabacbcaccbcdadbbbcbccaaddcdaadcabddbbadcddadaabcaabdabdcbacdbbacdcacbbadbbdaaabbdbbdcaccdcccdbaabadcddaccddcccdaaadddcaddddbcdcbbccdaddaabadcbacbbabacabacacacadaadaadbcbbdbcbdacacacccdabadcbdaddbcbaaacadacbdccacaacaabddaddbbdbcababcbccbcacacbdcdadcabddbcaddaddddbbbcabbbadacdbaccdbcdbcccdcbdbcbbdccdcbacdbbabcbbcddbcbcbadddbbcbcbbddddabbabdcadcadbbbbcbaddcddbcacbbbbbcddbccdbcabaabdccabbbcbddbddaaddbdbdccacabcbcdaaabbbbaccadacbcdcabbdbdcacabdcaadcdcacccacbddccdbbbbcddcabbaccbcdccacadcbdbcababcacbbaacccabdabdadcdacacabcccaacdacadbcadcacaadaadcababacdcabdabddaaddbaaabacadcacdbdcadddaabaadbaaccdcccadaadbdbaddaacabcabaacbbdbbbdcdadbcbbacbdadabdccadbdcbddddadbcabbaccacbddababbddddbcaacdbacdbcbdabaabadcdcababbacdcaccccbdabadcaaddcaaadbdccddadbddcacbbddcccddaabcbcadacabacabacbcadbbdcaadaabbaaccadbcacadcaddbaaaacbadcabbaccdcabdbbacbdaabdccccabdadcaaadccccaaabdddddbbbdbdacbbdccbcdccddbcdbdbaaaddccdbbdabbabbbbcabbcbaabcbbcdcdcabbdbdbbbdaaddabcccbadadadbbaacbcbbbacccbbdadadaccbababcdacbbbdcdbaaabbccccadaacaaaaaabdbcdbbdcbaddccbdcbbcbdacbdbcadbcaaaddbdccacdddbbbbdbdaadaddaaaaaccdbccdccddcbcadacdbbbbbcbdbacadddbcaadbcbcbacccbbcbacacdbcdcabdaccdcacacdbcbbaaaaddaacabbaccacacbcdbbddcbadddadabdcabaacbcccdbccbcaccaadacbbadccaccbacccccabbddbdcbdcdddbbaaadaadadccdcbadbabaccdaccdbadcdbdbbaccbcbbababccbdbddcadadbbdcbbaabaaddbbabddbbaddbdaadabaadddccaaadcbabadbcaabcdcaacaacdaacdccddacbaadcccbcaaadaccadacccddbcdccabbdabbccbdacdddccccadcbacddadaddabcccaddbcccbbbadccacbaaccdddbbadabcadadadbbbcccccbacacdbcabccccdaccacdaadacdbaabccbcadbdbbbadccdcadabaacbbbabaddaddcbbcadacbbabcdbdbcbcdbaabbcdcbddcbdacadadabbbcabcdbcbabcbdcbaabababcdcdbdddaccadacccaaacbadbbacdaccaaaaddacadadbabcadddcdcaadbddcaaddaccbbcbcdcadadddcbdbbdcbdcbaaabbadadbbbababcaaddccaadaacddabacccdcacabcbabbbabaacabbdcbbbaabddbadadacdaadcbbaaaacaaabdccadbdbcbabcbacadadccadccadbccadaadddbaaddabadcdbacdbbcdcddacadaacbcacbcaadccbdddcbacbdbaaabbcdccddbcdcbddacbcddccdcabcbdcbdbcbbadcdabbccdadbdacaadcbcdcdbbccbcccccdbabcbddcddbadbbaaaddbdcbcbddababcaaacaabddaabbdacdbbbdbcaaacbaabcddcbaddcbddbaaddccccbadccbaaacabddbddddaababdcbbbbdbbccaacbddbbcacacadaadbbaccadbccbbcdbbcabcccbaabdaabdbcddbaaaacbcbbcaabcacbabadaadbcbdbddbcdbabdccbdbbbbbbccadacabacbdcdddddbbccbbccaacbbaaacdaaadcacdddbabcccdcbbabacadbbbcbacdadbbacadacdbbbdcacbacccabcbbadbbcdacacadaccadaaaacadccaddcbabcdabacccbccbbbbbbddddcbdabacaabdcacacdcdbdaabaddbccacdaaaaadacdabcbccbbcbadadcbdbdacdccacbcdbcdcabbcabddadcdddaadabbbbacdccbaccdadacddddaaddbaabdbbaaabcaabdabdabbdcdddacbcbdbbbbbcaaabbaddbdaacaadbabaaccbcddbaccaccbcdbbbdabbbbdbbacbbacbdabcbcdbcccbcdaaaacccabacbacacbbbdaadacbcaadbdccbacadccbabcabcbbcddabbbddcaaddbbccdabbacdccdddaaddbaaaadcbdabccddbddcdbacddabbaabddacddaccbdadbbaababdbccbabcbcbcdadbdcddcdcadddbacadbacbdbcdbdbddbccdaaddbacbdabacbaabcabbcbdcdbacdbadaacbbabdcdddcacddaaaddabbdcccbacdabdaabdcbaabdbcdcccdabbaaccbcbabccddcdccaacabbbcdcdbbddbacacaabdbadababdccacaccbbdcbcabaabcccabaaccaacdcdaccbddcdccaccdadccbccaaabdacdbcddbbdbbacdbacadcacdcabadbdbadccbcdbcdadaddcdbcacaaadcadcddadadadadcddccdcbcaabdcdbcbdcbbccbcaadbdbccccdbccbdabdbcdadbcbacdccaaaddbcaccbddaaaddcdcdbcdacdcccbdbdaccccdbcddadbdbcddaadabadccdacabaabcccadddbacdbacbdadccccbaddabbadbdabdbabadaddbabdcaabcbbcbacddddbcdddadadcdcaccbadadbaccccadcabbdbcbaadcdcdbdbdddacbcdacadbcccacccaadddaadcabdccddbdbdabdcbdcccdbccabcdbacdbcbdccacaacadbaaddacbabcbbdddcdabdabbddbaccdbaddcdaacbadcdcbbbdabdabdabcabbcdbdcdddbcbddacaadbababbaadaddbaacdbcdddcacadbcaadbcbcacccbcbbbdbaccaacabdddadccdddabcdcaabcadcbacbbaabbcdabbcdaacdbdcbcbcdbaacbbccdcadbdabacdabcddbadadbbdadabdccaaaabbacdbccbcdddaaabdaacddddbdddcadbdddacdabcbaaaddbccccdbdccddcbdbdcccbdaddacdcbcccaddcddcbddddbaacbcbbdcddcccdbcdbbdbccdbccaacbaacbbdabbbadbabdaaadcbbdacccccdbacccbacddbdbdddbddbadcbbbbbbcaabddccadaacccdacbccacbccdcdacaabbaabcbbabadbcccbccccacdacbdaaddbbcacbcbacbcdbbddbbdddbdbbbabdccaacddacaabacaaabcbbaccdbbddbacdabddcdcdcbdbddaddadaddaaadcabcabadddaacabadddacdbdbcbcccbbabdadcaabbabcbddbcddbcacbbbdbbcbccaabccdddcdbcadadccaddbaaddccaccdbacccbdbbbbdacbccccdabccaddddcdcdcdbbadacbcccbcbdcadcddbbcbcdcbcaddaaddbccdcbdaabdabbdbbdabbbaacddcccbadccbcabccdaddabccdbaabbbbacccdcccdcdadbcbdbdbadcaabaccdbaabddcbdbcabbadabbccaacdbcdadbcbbcacadddacdbcbabacccbbdbcbdddddbadbddacbdcaddadbddbbaccaabdbcdcadcbcaadcbacdcadaadcacaacbcaccadcdbddaddbdaadcdaadcbbcbddccdcbaadcbcabadaaaacdaacbaabdcccbdaadbbaaadcccddaaadaccccbbcaddddcdbbdcdcaadbcdadbaaabacddaacbadcdccdbbccadbaaacaccaaadabcacaaaacdaabacadcbabdacbcabdbdcdaccabcdabcdbababbbbdaacdcaadbdcbbddbdbaabaabddadaddbcdacdcdadcbbaccccadabbdcdaaddddbddaccdbccacdbacccadbacdcbccbddcdabdbddadaccacbdcbbbaddaaadbbaadbddcbbbacdabbaabdacaccdbbacdcdddddbdddadccdaabccaaabbbacbadbabcdcacdabcaaccddabcbdccbabbddaccbbcaaabadabdbcdadaaddbbdcabbbddaabcdbaabdbbbdccbcaadaaabbaddbbcdaddbacacddaddcbbaddcadbbdddbbdadcbbacdadcbbaaadcacbdcdbbbcdadcacbbabbcddacabddcbacabcabcbbdabbcbadbcaccdaadaddcacabbaadaaaaadadaaacdbacdbccccddcdcadadaddaacbaadcbcbdaacddddbdcbdabbcbbdcbcaacddbcaaccbbdaaaabddbccaacbcdbbbcbbdbdacdbcbbbddadbcdaccdaaccbdcadcbdaccbdcacacacbdcdcadcccaabbcdcbbbacbadadbadcabbccbcacbbdbbadaababbbcccbabcbcacaaacccbbacddcdcaddacaadccbaadbcddcdcbaacbcccadbcddadbbdaaabbcbbaaadadcdcbbcabdacbcdcdcdabdadbdbcbbbbacbccddbaabdbadddbccbbbaccabcdabbaccbaabacabdbbbdcbcdabbcddababcadcbcbdcbdddaadbdacabccdadbdaacbacbbdcacddcacccbbcbbdbccabacdadaabacdddccaaaddbaddbdabddcdccddbacadabcdadadbaddbabcddcacbbddaadacddbabcacadbabcdcdbbbcbcdbaadcbdaadbdbbbccbddbdcadaadadccccaacdaacaaaacbbabdcbbddabdbabcbddcbdbbddbccaadadccaacdcccccdbbaccdbdcaccbabbabdcdacddcccacbbbaaacccbabbadbbacdcddddcacbcbbcbbcadbddacccbdbcadaacaaabdbadbbbbbcaaccbabacdadacdacadbbcabbddbbbbdddbaabcacaacccdbccbaabaccadaaacdabbdbcbddbcaaabdaccaddbcccddbcaaaaacdaacddbbccccabadcbcbaacdadaaccbcaaaadbdcddbdabdbbbbadacbacbadaccadcccbadadbacdcabcdcbacbacbacdbcdddcbddaccbcbccddabccacdaabcdaacbcbdcadbdccbacbdcdcdcdbbbacdaabcaaabadbbadaacdacbabbaaabcbaabdbcbccacaccdcdadccbbdabaaabbcdacccdbaabcddcacacbaadbbabcaaccbdcacabaacbcaacacdacacbcddbccbccdcadbbacbcadcaddcccbddbbdbabdbccaabdcaaaddaaabacdabcdbddcbcaadcdbdababdcdcdacbdcdacdabdbbdadabdcccbbcabaddcabcbcbcabcddaaaabbabbbddabbabcdcbbacbdacdcdccabbddacbabadcaaddcbadadcabaddabdcabadaccccaaddbddcdcabdbddacaabadacdccbabbdccbbddabaccabdadcdbaadbbcbdbdcaadcbdadbacadadcdbcbdcbcbacbddccddbbcdbacaabadcaddbbdcdbdcaccbacdcacdaaddcdcdbcdcbccaccdbbbbbccdbbcaccbabbcaadcbcdcadacdabcabadaabcaabcdccbbaacdbcdadbdbcccabbabdbdcdddbbaaadaddcbbdcbbdbdbccaabbaabaadcdbccdadacacbbababaccbcdbdbacddddccbcacabddbddaabcdadcdbaacbcdcbcccadabdccadbbbccbcbaacbacadabcbcccdaaadaccdacddcadcadbcabbccbccaabcadaccdbcacbaaabdaabacadbaddccdcbcddadddcdcdbdbdbdcacbdcbcdbadbababacdaabcdacdabdbbabcbabcdcdbaaacdccadadabdadacaaabdcbdbaadcacbbabddacdadabacacbdbadcacbaddcbcccdcbddcdadbbacdabadbcdacdadbbcbdcddddaddddcabacccabbdddadccabdacacbdddcdbbbcbadcbaaadabbbccbbdbbadaaccbaccbcddccbcbaaaddcabcaddbcdbbacacaaadcadccadcdccdcbdbdadaabaacbaaaccdbdaaacdbdabcaddccdcbccccacdaabaddcdbaccbbabcadacaaabcdbdabcaabdaccdbbbbccacbabdcddddbabddcdcdbddacaaababacbcbbcdacdabaaacbaabcdbbcbbbdcdaacdcacbccadbbcbbddababbdaacddbabcccadaabbbadaaacccdcddccadddbbbcabcaaaabbbbdacabcaddaaabcccadaccadcdbcadcbbdbccabbccbbbcbddaaaaabdcbaccbbaababdcdcabadaaaabbbaddbcaadadbccbcccaaacdccddcbacbaadaccdcabdabcaacdcdcdaacaacbcbcbdddbbddbcdbbadccacccbacbadcdabdcbacbdbadabbcabdccbbcaabccaaacaababcbaabbbabbccdccbdbcbacddbbccddacdcbabddacabbdbbcdcaacbdbcbacdbdadaccbdccdcbdadcbabbabdcbcdcddccbbbcdbbbabdabaababcbdabbacdabcdbbcbaadbbdbcbccbbdcabbdbabcddaddbcabbacacbcacaddcdabcbcbbbcadadddcbccdbbdbbcdccaaabbaadcdcadabdcdbbbbcbbbdbcacccbadaabbcccbcbdcbbdacbdaaccbdcddacccabbbdabdacaadaccaabcdcbcbdddbdbdccbaccdbdccccbabdaaadbabdbcaaaddcabddcdbbbccddcbadcdbabaccdccbddabcdccacccbbdaddbadcdaadcadbabadbdcddbabdddaaddcbabddacdbcbbadabcdaacaadbbdcdcdadabbbcdbcdadcbcadbbdbaadccbcacabbddaacacdcdabbaaacdaccabdaacadbbdcdbacdbaccccbbbaaabcdacaabcdcbababadbcdabddacdcbcbbdaacbbbbccbdaccbbdccabcdaaccadabcdbbbbbcaccbdddadbbdccdbbdcdbbcbdadabdcacddcacbbdbacbbadccbdccdacbaadcadccaddcccbbcbbdbbddcccbdbcbbdbdcbcdbaaccbcdbccbbbaadcbacdaaadbcadcacaadabccabaaaacacdaadbbcdabaaabdcabbadaacbbdcaccaabacbabaacbbacbdbddbccbdaaaabaaacbcacabdcccadbdbbbbabcbbcaabcabaacbdacaddccdabdaddccccacbdaddcbdababddbbddcacbdccdbbdddbaacadbcbcdccacdacbbdcbdcddccadabdccdcdcdabcdbdbbdccdcbdcaddaddddadcbbbaaaababcbacccdaddddddbbabaacacdaabcacdabcabdccdaacadacdcddbdbbababdbbcabbadbaddcabaccaabaabbabdaadaddbdddbaaaccbcdbcddddbaadaadddbbcdadaccbacbcccdcbbdadddcabccbcbaaadacccbababbbcdddaadadaaadaccadccaadddddabddbaadcddcdadcbcccdcbacdacbadbcaccbaccacdbbcacadddbdabcdbbaccacdcdacaadaabcddaccdcbddbbdbbdcdbddcaacdbcbccdacbcccccadadbbdbcddbacdadbcaabacdbaadadcbccbaaaacdbdaadcbabbdcdcaddcdaaccdbacbdbddbccacdbccadabcbbadbcbcabccdabbddcbabbdaddcbadacdcacbdaadcbcdddcbbabdbbadabdcddbbadadccdcbcdddddbcaadacdbddbdcababadbdbcdabdabddbcacadabdaaabdcccaadbcbbdaacdddccadadababadbaccbdcbcdbdbcdaadacbdcbcaddcbacbbadddacaddcddaacaaaccabadaaccdabddbabbbacbdbaacacbdcaaacbdcdabdcdacdbdddaadcbaccddbbbbbaccbacabdcabadadbdbdbccaaabbdbbabdaacddadadadabadcbcbacddacabbcbcbaddbdccddbdcbaadccaaddabcdcbdbcdacbbbaaaaacbcaabcbbbabdbdaddadddaccacacccacacccaddcadadcddacbabdabbbabcaccddacddcdabcabcabbbccbdcbdbbdcbacaddcaddadddbcbddaccccbdbacbbcdabbcbbbadaabaadaccbdddcdaaaaabbccabbbacccadabcbabdcdbbadbacccbacbddcdbcbdadaabdaadabbdbcdadccacdbdbbbdcdcbddaacacbacdcaddddabdaadbbbdabababcdbdbbbdcacacddddcaadbbacccdcaacdabaabadccbaacacbdabdcdabdadadaccadabcadacddbdcccaacddcbaaddccdbbcdacddbbdddbacaadcbaacacacdacddacdacbcdcdddabdbcadbcdccacdbbbcdaadabdbaacdbbacbabadcbcaddbddabbbaaaaacabccddcabdccbbdcdaccdcabdcdcbdabcccaabcbcbadcacdcddbaddaaaccbadadccabcbddadadcaddbddbcabdcbbabdcaabcbbcaacabcdbaadbcbbcbcacaabbcddadccadcccaaddbbadbcbabcdddcacbbdadcddabcaddbdbddadbbacdbdaacbaabdcbbcdbacdcbccadaaddcdbabadabcbbaaaaccbdcdadbabcdabbabdababdcbddcbacbbabdabbaacabddbdadabaadbabadacdbaacaaabcbdcbbadbacdbddacaabbccccbdbdaaacdbacacccdbbbcdaacdbbcadacadcddbbdadbdcacddadccbbdcbbcccbddcacbabcbccadddaadcbdababacbbacbcccabccdcccbdabddccbccddbcbbabaddbddcdbccacccbccbbbcdddccdabdbbdbddaaacdddccdcdcbcbbbbdcbcbcacbbabccccddbacaadbddcabcbbaabaacaadabbadbaaabdaccdcdcaacdcbabcacbcbabcabdbbaccccbbcbbdbcdadbabcacdbadacccaabcdddddabbbbbcbadcaddccbcdccdadacbcbddddbbdaabddcdbddbcdddccadccbacdcdbdddcbabdaadadadcdacbdbabbaadbcacbdadababacabbddbdacadaacaadabaaacbaacccdacdbbddbdaacccaccabccdcddcdcabadbaccbbccbbbbdcdcabdabdbdcbccbdadadbdcdccbccaccacabaadbcacdadaaddcabdcaabcccacbadadcaccadaaaaadbaccbbabcdabcbcbcbaaabbdbddddbdddbcabbdcbddabbbacdbddcbbdbdcdabbdcbabddccbacdaacdaddddaaacacddcddbacacbacbabdbaababdbccabcaaaadbacbbcccbddadcaacbbbbccadcacabcdbaddaaaabcdcdcccccbcdacaacadbdcdaababcccdbccaacdccddbdccddacadbaadbbaccbbaaaccbcbabddadbdadcabbaaabacdacdadbbcabccbdddacaabcdbcdbddbabccacdcbcdbadcccbbadbbbcdabbbbacbdddadcbbddacaadcaccbabcbdacbaadadbabcdcdcdcddabaaaccbcaacbadbbbabcaaabdcacbbccbdcadcbccbbbcbadaadaddccbdabacddacadccbacbaaadcbcbccdbccdaabbdbcabbdbaaddddcddacadcbbccdadccbbdbddaabadadaccdaaaddbcddbbcdadcccccdcdbcccbcdddbaaaccccbaddadccdabbcaccacccbdddcbdadcaaabcddccddcdcdbddadadbbabdbdabbdbbacaabcddbbaadacdadccbaddadddbaaabdbadbbbadcbbbadbccdbabcaabcdcdddcccdaaabcaaacaadcddacacccbccdabaadddabbdbadbbcabddcabbbbdaccbabbcacaabcdcddabdaddadccaacdaaddbcacbdcbddbabbdbcacbbcadbddcdcababadcbcddaabcccccdcabadcbdabcabdabcddddccacbdccbdbbbaaacdcbaddaddcddcddbbcbcdaccabdabbdbabaadddbabdabddaadccdacdbccdbbdcacccccabcccbcccbcdabddadabaadabcaaabacccddccccbdcadddcdaccbcbddadbadacccddacabcaddbdbbccbbabcbbddbadbcbbbaaccacdbdadcbdccadcdcdbadbacbcbbdbccbaabdbdcdaadbcdccadbcacdcccaacaddaaabcbadaaddccbddbdddcacbadacadcadbbaddddacccacdcacabcdbccbdcdddcdbddbcabaccdbbcddaccaaccaccbdaccabcaacbcbcdbcbcdcbaaabacdddbddcbcbcddcaaaadbbaadcdcacacaddddcbdcbacccbcddaaabcabbdcadddccabbadbbcaadddbadacabacabbcadcbccbaaaabcdacbabddaddcddccabddddbbbcdbadabccccdbccbabdbadacccbaaddaacddadacdcbcccdaabbdcdabaddbcbdbdacaadadcddcabbbacaadcbcddcdbaddabcabbcdadadabbdbbbccbaacccbbabddcdbcacbbcacbaabbaaaacbcccdaadaaadcbacabdbcdbddaacdabacdbaddcacbdaacbbbbdbdcddbaaddacdabaddbcdccdddcabbdbccaadbbcdabcbccacdbccbcaabbaaabbdabaaaacbbcaccaddbacdccddbbbcdddddbcacaaacacbdddabcbbdabcbdcadddcbdbcabbabccbcaaaabdaaabbcdccadadbbbddacbabbbbcacadcbbcaacbccabbddbbaccddabaabccccbabcdbabbdadccabcbabdbabbbcadcbdabadcbcaadadcabbbdaddcaddaccabdcaaaddbdaccbdadccbcbbbcdcadcbbcbabdcddbacccbdcdcabcdbbdcbadbdbaacacadaabdddacbcdcbdbddcdaadabcadcacdcdabccadadbcaacddddadacbcdccbcddadacdcdaabdaaccdcbabccbbcdcddabbcbbbbcdbbbddacaddbcbcdaabdbadccbbccdcdcdbaadacdcbacbbacaaabcbddbdaccdcdbdacadcbabcacacabddabbddacccacbabdcccddadaabacbabdaabdabaabacdaadcdcabadadaddbdabdacdbadadbbdbbabcaddbaaababdacbaabddccabdbcbadacbbcaaddcddddbabaadaddccbbbdacaadbdbbaabcadbdcbbbddcdbcddbdcabcdbabbbdcdaacbdcbadaacbccbacddaddaccadabdcbcbabaccabbacabaadcbadbabbaadcbbdddbdadccadaccdabaacadaaacbcdbccddcacdbbddaaaabddbbbdddbccabddddbdaadabaadcacddbbbcaccdadddcbadacbddabacbbaaaaddbbdcddaddccdddcbcbcccdcacbaadbdcacaaddcddcdccbdbdadddbadabdacbcbbbbadbcadcabbccccaacaaaaacbacacdaddabbbdbcbcbbaccbcccadaabdddacddabaccaaabdcdbbaadddabcbbdacbdcabacbdbccbacdabccdcabbcadddbbddccbddaabbbbbdbccccbcccbaaacbadcaadcbbabcabdaacadddcbdcbcacdbdbccbbaabbbddbcccbabddcbdbcdcbddbaabdcbbcbccaddcdbcbbbbbccdccbaabddbabcaabbbadcbbdbadcaaadacdcbdcdcaaaabcacddbdccaadcdaccddddddaaaabbaccacbcaacdcdcbaccbbabaccadcbaabadcdadaaabcbacbdacdbaaadbcabadccacbdbdbdbabadacadcdcbdaaddcdabadadddcccbdcacccbabdcdbcbdbbccdcdabbacabaddcdaddbcbdbccbccdbdabcaddcdddbbbbdacdaccccccacdcdddaabbdabdcbdcdadaccccdacccddaadaccbdcaddaacaccdadbadccdbadcdaacdaabbdbddbbcbacbbbdabddacddbcbcbabcddaabaadcddaccbdcaaccbdadbbbcddbbbccdcccdcabacbdbcddccdbdbccbcdbbccdbddabccacdbcdbdbbaddbacdbccdcdcabdbdcbdcdcadcbdaabbbcbddddbadbdcdccababcbabdcdddbabcdbdcbbaaddaaaabacbadcbcabacdccaccccaaaccbadbcaaaabaaccadbccabbcabcddaaddcabbbadbabcacadcbdacdcbddcbdddadccbbacaacdcdbddcbaadbcbaccddadacabbdbbdccdaacdabdddaaabcdddcbdabcbacaacddcdaadaddddbdddbacdacbbbaabbbdccadcddabdaacaabcddaadccdbcabadbccdcadcabbaccbdacdbdddbabaadadbccdaccdacbbcbacbacbbcaadbdacbdbabbadcddabcaccadccadabdcddaccdcdcaaaaddbcbddabaadbcbadbdbddaddbbbbbaccbaaddcbcddbcbdcdbcabacaabcdcaccdddcabbdbbbadacbcacacbabbaaaabccabdbaacababcaaaadbbaabcdccdabdaacaddaadbcccccbdcbababaadcdddaddcdddadcbcdcbdadcaaddcabaccbacadcbccddcadabdcdaaaacaadbbacadcdcdcaacbbdadaccdddccddcaddcbcabddbbbaccdacabaddadbbbacaacdcaaabddbbdccadacabddcaacdcbcdcddcbdbddcabbbadcacddccaabcdaaadbbdbcddabccddaddaabaccddccddadbccdbabccccbbdbdbadaddaabddbdaabbbccdcbbbadabbaacacdabadabcdcddaabcacdbaccbddcabcbacddaabccddadacdacdddacbddabdbcddbaabdcdcabadccdbbbdbbcaccbccbbaacbccdcadacbdcacadccadbdccdcaaacdccacddcacbadcddbbcbbbddaaccadabbdbdcddcdbbbcbdbdbddacaaaadabadbcadaabbdabdcacaddbacbdbabdddaccbbabdabbdacaddddbbaaadbbcdcdcdaaaacbbbccaadcadcadbaaddddaadabcdbaaaaabcadccbdbdcddcbdabcdbdbabaddcbbdcdaaddacadcbacccbdaaccbbccbacdcacbcddbcbdabbcaddccaadcbbdaacadbaabbdbcdbcbaccdadcccaabacbdabaddaccbccabdcbdacadbcabbddcbdabbbdcbbaaccccbbbbbcbbcbbcbadddcbcaacdaddbbbcbdbcadabdcadadcadbaadacabdaadbbbadadcccbddabdaacccbbbcbbcdbcdbacaaaabddddccabccacaccbbdabacadadbabcdaaaaaabbaadaaccdbabcacdaccaccdadcbaabdcbcbbaadcdbcaddbccdaadabbbdaaabcdaacbcdaadabdbaabaddcdcdcdbcdddbddcacadbbbcccdbbacadddbabdcdabaaacdddbddcccccaadaaacadcdccaabbbbbbbbdaccccdccdbbdaadcacdbbbbbccdbddddacdabdcccdcccaccdacadaabacbdcaacaaaccdccbbdadcddbcdcdacbacabdaacdcdcccdcdbccacdadbdacddcdbcaabacdccaddcbbbbddcadccabbdccbaccdbbacdadadcddcbcbadcabdbdddccacbacdcabbddcaddabdacadaabadbdccbccbbaddbadcccbaacaaabbdadbbdcbccdadcdcaacbcdbabcaaaaabcdddadabdadbbaaabcabddcbabbcbdcadccabdcaadcbaccabcbbbdcacacdcddcabccbbbccbdabbddbacaccaddaaabadcadcaaabbddababbaaaaccdabacddbcbcccaacccabaadddbdadcdbbbdcadcacaccbddabbcaadbccbbbbaaaddaacbdcdaacccbdaabbadccadaabdcbdcabccaabdaddddaddcbbdaddaabccabaccaaadcbcabcdababdabcdadcbcbadacbabdcadabcdadccbaddccdaadbdbbcabbdcccdccbdcdbaccadabcdacadbaddaaadcbcbabcacdccdabcddcddacaddbcbaabdadaddddcbcaaabccdbadcdccaccabbacbababdbccaccbcdddadbbaacdaadbcdaababadbcabbbdbcaddcccacabdabbbcbbbbbacaaabaacdbcacbbbdbdbbdaaabcabdcddaabcaaaccbcbdaccabbdbbbbdbdaddbddccaadaacbdadcdabdaacacccdabacbddcaabbabcbacaabdccacababbcacdbcaccddcbdabbacacbacacddaddccabcdadaddcccbdbdaaccdbbbcacccbdcadbbaabdddbbbacdbcadcddaccbaababbdccdbddddcdbbcabddadaadddbdbddbdbbbcdcaddadcdbdaacdacabadbacddcaacabdccdbabcaacacbabbcbddcbaddddbddcadcdccccacdddaccdcddcdcdacddcdbbbabcaabddbaabbcbcbcdcbacabcdabdaadcaaaddcbbdbbcccdddbabbbdddaacbdabbdddadccaacddcbbccdbcdbaaaccadbacbbbbcccbbbddccbcadbbadacaccccdbdcbdcbbbcbbdccbbdbdbccacacababdcbbcdbabbaccbccccbccaccbbdcdbbdaaaadaddbbbdbbaabaabccbacacbabdcacabbdcbbadcbcbbbcbdcaddbbbaccdcdaccdcacdbccbccdbbcccdcabdacbbdaacaccaacaacbbdbbcbdcacadacdcdacbdabbddccacaddaccacddbbcbbcccddcddcbadabacaadbdcbcaccabdcdcaaadaccacbbbdbbacdbbcdbadbdacadbdadbaadbabcdacababdabbdaadabbacbabacbcbcbdcdacaccbacbbabdbbcccbdcdadbaddabbdcacbccbaddbcddbcacccbdaaaababdadabbaacbdadaaabadabddddbcbdcaadcabcbdcdddadccdbccbcaacdcaaddaaddaabbcdbabcacabdbabaacdabcbcbccbacbddbbddaaaaccdcbccdaaccdabdcddddacacbbdbbcccbabcccdaddbabbaaaccddadadacacbcdaabdacdcbcbadbbdacddacacbddcddcdbddadcabcaacbbcbdadaabbbdabcddadacccbcdbcdcbcbccdddbdbdbbbbcdccaadbddbcabdbabcabbdddadaaabbddbadccbdcbabbaacddacbbaabaaabdacbaccbbababdcabaadbccacbdddacadcbaddabbcaddaddcaaacdbcbabaabcddbbabcccaaaccddcabadbdbacbddbbcdacdacdbdddcddbbcdbdabcbbbbacadcdccdbaaabddadcdbcaadacccbbcbcabbabdabdacbcbabcddabcbbddcaaacaaacaabccbbbaadacabddcadbdcbdacdbddabcaaaabadbabdcadddbbddcdccaddcccbcbbabdcbbbcbabcddcbccdabdbdaaaabdbcdbcbdbabababcddcddabaaddabbbbdbabcadddbdbacbccbabdcaaadbadcaacddbbabbcbabccbccacabaabbaaddcbcdbdbaacababadabbacdbacbcaacddacbdaaacadbbacdcdabdabaabcacccccbbaacabccccaadaabcabccaddcaadaaabcdddbcddcabdcbdcbbbdbdaccddaaacabcdaddadadabbabcdbbaabacbadccdbcccdccccbbddccbdbcbcaccbdcdcdcdcdddcadbbbabddddaadbbcdacbbcaadbcddcdbcddadaddbcddcaaabcdbcbdbabddbdddacbdcaadbbccddcbbbccccabdddbaadbbcdbdbabdbaccdaacbadababcbbdcdcccbbcaadcabbcabacaddacbbacbbbbcaadcabcacaccbadddcaacabaccabdbdbdddbdaacbdcddaadcdbbbabdaadcacadadbcacacdaacdbbccabbbbbbddaabddbbdabdaabcccbcbadddbbbddbcddccdcddacacdacabbbdaccccdbcdddbadbbaacbbbcadbdbddbbacbddddaccdddbbbadccacdcaadcdcbddbbbbacdabacbbdcccacaacdddaabcaaccacbbdadabccadcbdcaadbbcbbcabcbcbcdbabcacdbbaaadcbaaccdacbabdddacddbcaaadbdaadadbaabbbabdabccbcbdbdddabcaabbdbbccdcbbcccddccbacdbcdbdadcbbdacccbabadcbdbcabbbadbbcbcdcdcbabdddaabababbdacaacdbbadabbdcddcadacbbacadacbdddddaccdcbddadbcdadbadcddadacdbcdbcdcdcddccdbbaacdccddddddabacccdaccaabbbaacccddcbadbabcaccdacdbadcaadbdccdddadbcdadbbddacdcbdabcccabcbbdbbcbbbcccbdcccbcbaaabdabcbacdbadcddadacccadccbcdadabcdacacdbbabcbdbaaabadaddcabbdddbcddcacdbabcbadaabadbdadababdbdcbdadcbcabdbbbbdaabdbdcacdacaccadbcababaaccbabbaacdabbacdcaddaddcccbccbcdcbdbddbaabddabdaadbadbbccbbabccdcddbcbadcbdcababbbabbccddaaddcdbbacdabbcacbdcbbcdbacddcbdabbcdbcddcccbcacddbccdbdccadabbddccbabaadcabcadbccbdacdbdcabbddbdddbbbdabbbcccbcdaabcaadbcbbadddbacbaadcddbcbcdbadbccbaabaacbbacaccdcaddcbdaaabdbbbdcddbacaaccbbacaccabcccbccccabacbccbacccaacbcaddccddcadacadcaacaacbcacbcdabadcabdcdbddadadbccdcabbdadaddcadcdcabcdadaaacccbcdbcbccbdcbbcdacbdabaddbccbcdccdacadbbbadabcdbddcdcccdbdcadbaddaabdcacbacdcccbdcdbbddcdbcccbaadddadacbddaccbdcbacacddbbacacbaadbaabbcadaaacbddadcbddcdbcccadccddcdadabdcdcbadaacddcaadccaacdcabacbddcacddacccdbbabcaddccadbddccabbbdbdaadcbbbbabbadaddcaddbddbaabdcaadadccdbabcbcbbbabcddaadccbcbadbbabbbabacbcbaaabacdbabbcbccabbcaadadccacabdcabadaccdddaddcabacbdcdbabdcdbcbbddbdbcaabcbabcbdbaddccdbbabadacbdccbdcdababcaaddbcdcbcbbabcbdbbcaaadbdbbdcbdbaabddbdbdbdddbbbaabbddbcadddadccbcdcbaadccbaaadbbdbabdcacadacbdbbbaccdcbbccccacccdbbaabbcdaaaddbabbcabbdcbbdaaacdadbbdbbcacdacacaccdcadabdacddbaaddaddbbdabbcabbdacadacaacdbdddddccbdaccacabadabcbacabcbdbdcbadbcdaccbdadddbcbaaccdbcbacdacbdacdbccbbadbbcbaccccbdaabdbbddbaabdbdcbacbcbbcaaacadbbdaddbbdbaaaccbcaddcccbabaaaccccabcdbcabacbddddddadbdbdabbdddcbbaddabcaaacabcbcccadabadbcbbbcdcccacdacbdcabdcbdcbaddbdcacabcddbddbbdbabbccbabcacdaaadcbbabccdadbcabadccbddbbbdddaaddaacabcbdbaaabacdaddaabaabddcbcdaccadadbddcacdcddccabdddacabcdcddaabbcbacdcdcadcaaaabbcadcdcaacaaddabbcadbdbcbbaddbbaabcbbbdaddbdcdddacbacdbbdaddccbddaadabccdaddcbcdaabcbddabadcccbcacbcabbdcdaadadaccaabbdddbbaadaaddbdbdddacdbdbaaccacbbaddcabcbcdaacdbaadbbaaacbcabaddbccdcbbbacdcdadcccdabdccadcdbadcccbcdbccccabccdccdcbbadabaccadcbcbaddadbccdaaacbaabcadbcdbaadbaddbbcacbaabadaadadcdbdbcbdbabccacdbcbdccacacddcaacabcbcddcaddcadcbccaadabbbabcdcadacbadbcddbcadbdcaddcccbdacbbcaddcdccdbccaadcbbaadadabbaabcadcdcbadbcbadcbbcbabccdcadcdbbbcadddcbbadcbaacabccbcdbdbcabcbddabbcabdacdaacdcbdabcdccabbcbbabccaabadadbcdcbcbcddddddadcbdabccdcacdccbbbdccadbbacbdacaadcccdddaadcaccaaabdccccdaddbcadabbddcabbadcbcadccacaadddacaadaadbbccdddbccbcddabaccadbbbdbbbddaccadcccbbcabbbdabbbbacaaadccaacdaddbbccbdcddbaabbaadcdaccbcdadcbabddcccbabaccddbcdcbdcdabdcbaddccadcdcdadaacaadbdcaaabbaaabacbaadbbcdddbcbbaccacabacadcccbbdbbabaaadddadcddcbdbbccbaacdcbcabbaabacbbccdccdbcdbadddcdddddabcdbcbccbdadccbcabdaaccbbbdbcdabddbcbabddcbcbdadcaaacbdcbbabdababadddabdbddcacacdacdbbdabbbbccccddcababdcbbcbabbbcacbbdbbbdddabdcadbcddcbcabdcacdbdaddccbcddacdcbbadbaacbbdbaabcacbbcbcabcddbcbccdbcbbadccbbcbddabcdbcdbacbabbdacadbabcaacabacbddcbbccadabcdbadbcbabcddabaacadcdaabbcbdaabcddbdbbabbaccdacdcabacddbccbdbccbdcacccbbcbbccaddccbcabaadcdcdcccadbabdddadbcdadbbdbaadacbbbcccabdbcaccdcaccaaadbbbbcadbdbcdaaadacbcdbdabcaddabadbcadccacacadaabdadcbbbdbccdbdacacdddabccbdcbaaddabdacaabbcddacaddadbcaadbccadccbacaccbacdaaacbcdbabcacaccbaacabdcabbaaccadbadbcbbbdddddacabbccabdbcacdcabaabcacddddabaddcbccbacabadcdbaabbbbcadcbdbadaaccbdbcadadaadcacdbccadbcabdbbcaaaaacacddddbbcdbcccdbbcaacccacbdccddadccdddbbcacdaaabcbbacccbabccdbdcbadbbadbcdbbbddabddbcabdbdacbbabdcacbadbdaccdccacbcabdaddaaabadddabddcbdcadbdcdccaabbbacdaddadcccbacdbacadbdacccabcacaabcadddacccbaaddbcadadabddcbaacadbdbaabbbdaaadacbbbccbdccabaadaabddacabadcdbdaabbdabcbbdadbccccabcabaabaccbdcddacdcbbdcacacbcdacddbcbbdacabdcacdcaacbadacdaaddacdcddacbdbbbbbacacadcbdccacaaabcacaabcddcadbccbabcabcdddaaacbabdbcadadbbabdbcdccbcbaaabbcddabcaacdccaacdcbdbacadcabbadcbcdccbabdcacccbddaaabcbbdccddcdcccbcdbdbabbdbabaaacddbbcdbdbdabddcddccdbbbbddbcaccdaadaddadbcaddccaccaadccabccabbabaacccddbaaabcdcabdbddddcdbadbbbbcdcabbcbdbdbcbbdbcbdabadbdddacadaccccaddccabaacbaadbaaadcbbcdaabccbcdbaaacbdaddaabcbabbadcbaddddaccbcaadacaaabcbbcbbcddaabcbcbdbddaacddccddaacaadbacbbbaacaddbbcbccaabbcdddddbcdabcaaaabcccaadadacdbcbbaacddbdcddaaccbacddcadccdacaaabdbaddbaacccaadaccabbbdcaaadbbabbbbacbacccbabcbacdcbcaaacacdcdbbcaabbccabdccdbccaddaabbcadabbccacdccddadbbbdabbbadaaadbccdccddcaccbbadcccbdaaddabddbdcdbbacabbcbadccacdbacaaacdacdababdbddbbdaddbabbacadddcdaaddccadadcddccbdaccababaabababddaccdacbcddcdaadaddcadbccbcdcbcacaaaaadbcccbbbbcbbadcccdbbbcccacbcdadccdbdcdbddbaaddccabcabbacddadabcbcbcaddcaddcacabddcbccccdccaaaccaaabcaadabbaabbccddaacbcaaabaaabdaabdadaadbbbacadbddadacdddbbcbadddbdaacdcbccaababdabbdbbbcaaabdcdcaaaddbadccddddbccacbabacacbdabcaccabbbccbcaadbccbcdcbadabcdbcbbcdcddbaddadadbcddbcabbccbabbbcddbbbdcadacadcbbbdccdadbbccddccaccbccdcdbacbdcdabadbbcbddbabcbddddcabbddaaaccbaaadbbbaadaccdcdcacaddbadcbbdcbadddadaccbbcaabdaabcbaabaaddcdabcbbbcdddcdccccaddbddcdcdbdbdbacddcacacdbdadcbcdbbbddbcbbbbacbcadabdbbcbdbcbabbbcbbdddbbabbacccacbbdddcccbbdbacbdcbdbcdcdddadbdbcccbdbbcdaccccbbbcbbabdccddabbdbcabbcadbdcbacdadadbcadabcdcadbadacdbdddbbdacadccdbcdbadbbbaccdadcadcbdcadbacaddcbcdbdaacbddabccabbdadaabccaccdbcadbcabaaabddbbbcdadbcadabaccadcbcacbddabbbcccbbccccdacdcdbbccdcbacabdacddcdaacbcbabaaabbadcaabddbaccacbbadcdabababdbbacccbbaabbacddababaccdaddbcaabdddbcbaaccddbdcadcbddccadcadacdcbdccabcaddddacdcbcaaaabcdadccdadddaccaccadaddacbbbbacdaaaddbccdadadaddaaadaacbabcdddccdaaccbdabcdacdaadbbbadccaddcdcccabcddcdadcbcaadddbdaacaacbccabbdbbbdaccbbabbaadaccccacacdbbaaaddacbbddbbdbcbbdadcacaccdcbbcaaabbabbabbdaaacddadbdcdddbdbadbbbdadabcdaacaddccabdcddabdcaccbdbcdbddbbacabddbadacdacbadaacccbddabdccadacbdbabbacabadbddbbdbbcacabddacbadadcbcbbbcccaddabccdbbcbaadbdbbdddbdbbabdbaaadcdcadddbbcbdbbdbdddbcdbdcbcadbbcbaabdbdcbbcccbbaacbacadaabbbcccbcbbbbbdbbbcddccdcaabccadddbbaaccccbccdaadabaaadbaacddbbddabbcddbbbcdbdadcabbaabcddaababbbbcbaadaddcdacdbaccdacdcbacdbacbcccacdaacdddaaabbdccddcbabddbcaaadabacbbdbcaccbcbddbbacacbbdbdbdcadbdbddccadccbcddbbabcbdacdaaaabcbbbbdbbbbaddacdddccddbabbabcccccacacabccacacabbbacbacccadacaabccdbbccddbcbabbbaddddcabcbaacddacdccadaccbbadbdccbdabbaccbbcadccaaddaabddbddbdbaaccccacdacaadaaadacdbcbaccbcaccbabaddccacaaddcabcaaabbcaccddbabadbbacababcbaddcbaabcaadaddbdbaadbaadacdbdcdcdbadabcdabaaacccabbdaabccbdbbdcbcabdbbcdbdcaaababbcccdbabcdbcddaccacbccdbddcbabaccdcddbdbaabaaccdcbdbdbbcdbbccccdabacaaadcccddabcacbbcbddddddbcbcbcddadcbadabacdabbbdadbbadbcbadbcabdbdaabadadddcbadadadbcccbdbdaccccccdbbabdccbaaababdcbddaadbcdcadccccacbcbcbbbadcdacddacdccaaacccaacacbbddbddbbcdcbbcabddbbaabcbcbaacbbdbaabbaaadadbcacbcddacccdccbdcabcdcacaabacabcddbcbabcdadacbbabbbcbabdbadbccbccacbcbddaacdbcccccbadddddadbaadcbdcbbdcdbadbddadcaabbddcdcadbdcccbbcddbddacddadaaadaaacdcddcdccbcdcdacaadabbdaabdbbdabccaacbcadbadcaabcdcdbbddcdbdbbbdbcabdbbbacdbbddcacbbdbbdccdbbdccaabcaddaaacacbabccdbadcaddcaabdbadaaddcccbddcdbcdddaabcadddacdbaccdddcbabcaacabbcbcbadabaabccbbcbcccbdaddbaacdcdabdddbdbbbcdacdbacadacdbcccdaaccdbcccadadcdcaabcbadabbdabbdabbcbaadcaaacdcddcdaadaaadbcccbbcbdcadbcdadbdbccdacdcaddbcbaadaaaadabdacdbabdcbccdbccaaccbbcacdcdaaccbbbddbbccdbdccacbdacdccbbccdaaddccbbcddaddcdcdabadbabcacabddccbccbbbdaccabcabadabbdcbbdddcbaadbdbbccabbddaabddabcaccaccdcaabdaabaabdcdacdbbbaccdbabccccdccbcdbcabccadcdcdaabccbcdacbcccabbbabdcabdddbbbcadcadbdbbbccacadcbadcdcbcdbbddccaadcdbaaccadaadcbccaabddbbacbdddabcbacbccbcdabadadccddacabcdcbabaaadbbadcbaaabccacdddbbccdacdddaaaaaaadbdaaabcdaacccacdcdacabdddcbbbddaadbbcdacbbcbbbdbcbbdcbdbdcbdcdacbbccbbccadbbbbdcbbddbdccdabaddadccbabdaabdccddcbdcaddbcbbccbbbbcdcdaacdccbcbccbcdabdbdbddabcdbcdadbdcaadddcbadbcdbbbbdddbbdcabccdbbdbdadbdbbcbdbaaacbbaaadacbcbdaddbdbcdaddbaaddadbcaacdacdccdacdccdadbccadcdacbdddcacccbcaddddadadcadccdcbdbdcccacbbcbdacaddcaabcadacccbccbbacbbacdbcdbbddbdaacadaacbbdbacbccabaacddcdbbdadaacaacccccacdcddacabaaabaaabbdbbacdbbddabacbcaaddcddcccbcdaaadaddcabbbdddbdbbadbcbdcccbccbabdacbacaabaddadcacccbddbacbdbdbccdaaaadaaddbddbcdaabadaacbbcadacbccdbccbdaabacabbdabaabbbbabbbdaacaacdadbdadddbaccddbaacbdddcadaabbaccacddcdaddbbcdabbdccaaabdccbacdacaddcadaabcacdcdbadadbcaddacbcbaddcddbbcaacbbcadbdccabdaacbdaaaacbcbcaddcbbddbbbcccbdcdabcbbabacdbcbbcbacdccdddbcbbaabcccbcdbabacdccbdaacdccaabdbcacdccbbbbdccdbabdaabbcabacaacbdbaaaddcbcbddcbabadbccdcaddbbdccbbdabbdbdcdccbccdbddabbbddacacbcbaccdabdcdccaacadbbadbbdcabdbbcacdcbacaaacddbdccdcdbdcbaccddcdbacdddddcaaddcbaadbddddbaabacaadbcabcdbdbcddbdaddcbbbdcdddaaabbdbdcbdddccadbccbbccccadbdaccbbbabcbbcbddbaccbcaadaabbdcbcdbbbddbcdaabcbbbdddcbccdaaccdcbcadcbcddcadddccbccabdbdbdbccdaaabbddccaaddcaddcabddbdbbaababbabbbcaccabddadbaaacbbbbaaaaddaccaacbbbbcaadadbaadbbbdaadcabbcdbcbabacabdbcabcdddcccdcbacdabaaacaacdbcbabdbdacbdcbbcacaacadccdccacdcabccaabdaabdbcabdabcadcdadcabadbdadcddcbbbbaabdbcbabadccccdccccabbcbaddccdaacabaaabdaaddacbabacdaacbcbcabbcaaaaadacdbaaaccadbcdbaabbdacabbaddbacabcdbcbdcccbbbabadacbabbdbbaadddabbbdddbabdccbacbcdcacdcacdddbacdabdbdcaddaaaddadabbddbabbddacddaacdbdccdbadadcbcbcadbccdbdaaccbacadabadbdcdacdccbcbdbccbddbcbbbbbbdbaddacbcadabcaddbbaacdbbdcbcdcadadccccaccccdbcbaacccabbbddbcdbdadcbcdabccbaadabadcacddaccbcddbbdcdabbacdbcbbbbdadbdacdadaabcacbdbcccddbbbaacaaacbbdcacdacdccbacaccaabbababbccbdcacdddbdbbbacddaabbbacadbbaabcdcacacabacabacbcbccaaabdbcdadbddbacacdcbcadcabcbbcadadcbcbaddbcbbaaabcacabccbbdbddbbcabddbbdcabdbbbabdbbaaaabddcdbdbbddcaddbaabaaabccaccdbcddbbbacddacabbdbdcdcbbbcaccadabbbbddbddcaabcbbabdabdbbbbddacadabbcdcbabdddcbcababbbddacdabadbabdaacbadbbdacdabdabbdbdbaabccbbbdcdbcaabcdcdbaabadcbdcbcdbbbbbabdbcbbabdacadadadaaaddaddcaadadbcbcbcabdabcbbaaaabadabddadbacbddcbbbdaacabbdacbababdbdaddaababababbbaabbdcabaaddcdcabdadccbabbdadacabdabbdcbccacdacdddbbcdaddcbcabacdadcbdbcdadaddabdddbdaacabccaaaddacacaacacdbacabababbaabccbddaabdbddbcaabdacaddabccdbddadbcadbacbbdcdabdddaadbacdaaacdbdcdadbabcbdcbbcaccdaddabdcbbdaccbbcabbbaabdbdabcaadcdacdaddcccaaaccaddabdddcbabacbdcadcadccddbdbbacdbdcdadddcccbadbccbdcbdbbacbdbdaabddcaaccbcbcaddbbdcdbddbdddcdcadaadcabaadcbacdadcccbdbbdabddcdadaababacdbbadccccadbaaadddbccdcbdccaabccbadabcbccacbbaaabcdcabcdadadcbccddadbbacaccdbcacbcddbbbdcaacdacddadcbcbbdbacacdabdabcbdcbcdadcccccbbbbcccddddbcddbababbddaababaddcdaaacabbbccdbbcaccdabdadbcabdcdadbdbdacbadddacbdaabbcaadcccaabacabddcbadbabcbbadbdbaddddcabbddbbdaccaabbbbabdcddbcccbddacdbadbacdadcaccababccdbcddaadacaddbccdbbbbdbcadaabdaadcabbaccabadccaaccdcddacacddcccaadcaacaaddadcbbdbbbbbabcddaccdddcdacbbacbadabddcdabadaddbdcbdbcdcabadaaaddbbccdbcbbabcabaacabacbbbcdcdbddabcabcbbddcabadccabbabdadadddaddacbaaddbaddbbcddbbdbaccbdcbdaaddbaaacbaccccccccdaccdbaaccdacdcbbadacbdcadabcbcaddacabcaabbdaacbbbbcabbdcadbbddcadbdddbabdbbaabdbaadbbcbbaabbddcdaddcacadabddddaccaadabbbdbbcbabbcdbcbbbccdaaccabdaaabcacadbbddadaadcaccabcdacdcacdbcdcaadbccdcbadcadcdbdacdacacadbaccacbbaaacdadcbbdabbacadaacadcccdabaddcbbabbaaabdddacaaabdddaabcdddddaaadabacccabddcdbdcacacdbaaabccbdbbdcbbdcddddbcadadacddabbacccdbdaababaaaadcdccbadabdcbbddbbcdcdaaaadaddbaabdaadaccddbcccbdcddcbcbaccabcbabbabacbacadbaabaaaabdccaaacdbaaacbdccaabdacbbabbbacbcabdccbadbdcdadaaacdaaadccdbcaabbcacbddcccdabadabdabdddbaccbcddcaddbdcacadcacdccbcbcbadddacbdbdccaacabdcacaddabacacbbaaddaacddcbbddbbcdcbadacbbcbbcbcaaaddbdbadaabccbccdddabaccaaaddcdaccaddbdcbdacdcddcccdcbbbcaabaabcccccccdabcaccddcdaacabaaadbddaaabcdcbababccdbbaadadccabdacbbbdbbdbcbadcabaddbbbcbabddbddbdbdadaadaadbcdbbcadbbadaadbbddbbbaaddbabbcbcaddcddcdcdbdddababacbbbccadacaddbaabcdacbbabddbadbcdbdcadaaabddcbcabcaacadbbcbdbbbdbcaccdaabddbbddbdbddcadddaabddddbcbccabddddabbdcddddbbaaccdacdcaacdadcbcdccabbddccddacbbbcaaddccbcababdbabbbbcadcdacdaaacdaaaccadacdabccabbbdcbbbcdbdcccbabcdadcbadcbccdcbbabbcbbdcadbdbabdbdcacbccdadcaabcddcccbbaaddcaadbdacbddaaaddcdcdbdcacdaaabbcbbbacbbabbabdacaadabcbacdcdadbdccdabddcddabccaacabdaaaacabacabacdaabaccdccbddbdbdcadbbbcadaadbacabcccccadaaaadbdbddabbacbaabcadadacdddaacabbbaabdcbaabdbaacddcccaddadabdddaabdbdcadbccdbdddabbdabdbcbabaadcdcdacaddbaadbbcddbcbbcacddccdbcccaadbaccbdabdcbdbabddbdbadaacdccabccdddbbacabbdaddcdcbdbbaccababbccacdbaccacdbbcbcbbdbbbacdacdcdbadddaaddcccacabdacaddbcdcdbcaddbbcaaabacbdbabccadbabdcccadacbccdbabbadcdababcdcdbbdbdbabacabaddaacacabdaaaaacaaddbcdaccdbccaaabdcbcabcdbcaacaadcbccbcaadcbdabacdadadbbbabbbcdcdabababbdadbbadaacadcacaccbabaddbbcdcdddbddbbbadabaaaccdacdbbcddabdbbbabbbdccaadccdacdbdababddaadbdddcbdadbdbcaccbcdbbacdacbcbbbbacaaadaccdcbadcadcbabadccbaaddacabcbcabccabccacdadccccaaaaccddbdcbacbcbdbaaccccdbccdbddbcadcccbbbdabdbadaccbdbdbcbdcaddcccbdcbcdcdadcabdadacbdbbdbdbcdabcdadadaaccabddacbddabcaadabaabcdbdbaaaddabbcdcdbbbbcdbbcdcacaccdbdcabbbcbccabcacbbdbddadacbcbcacdacacadcccdbbacaaaacabdbcdbcbcdaabcbdcbbdcadcbdccdbacdcaacbcbcadacbdcaddacadcbdbcccdabacccbddcbbdcbdbcabdddbdbdaabcbdbcdcabddbacbcdcdccaccddbddccbbdddbdcabcccdddadaabbdaaddabcbdcbadddcdbccdcbadbaacdbbccbcacccdcadcabbcbbdcbaaaaccdbaabccbddadddadcbbdcbbadcbcccabadddcccadaccacdacccbdcabaccdccabcdddacddcdcdbbddaadacddccccbbcacabbdcbaadcbaabadccbbcacabcacccdaccadbbcbcdaabdbadaaddcaabcabbbcacadaadadccbbaddbddbdadcaacbbcacadbcdbbcccbcabbabacbdababdabcddaabcabbcdbcadacbcddcccabccbbdcddadcdbacdcccccaaadcaabaaaddadababbbcbaaadadacaddabbaddaabcbcdacddabcaacabbaadcabdcadbaadbdcccbccadbcddbabaabbdbcdbdacadcdbdcbadcdbbcbdbcdbbabcddbbcddcddbbbdbdacdcbdcdccaaddadddaadddcdbdadacadbabbcbbcbdadacccdddcbabaccbdadadadbdcbbabaaabadaacbdbcdbbabadbdbbddcdadbccbcbdbcadddbdbcbddccbccbbddddaacdcadbabacaacadbddabbcdcbbbbbadaaabacdbdcbdaddaacbabcdabcbdbccbabacddcbaaddcbdcbbddbbdbbddccaaddddcbcaaccdacacccdddbcbbdacadbadabaddbcadadadccaadcaacbdadcccbdbbbccbdadbdabababdddaadcdadbcdadddabcaabacabcaabbbdcbabbcbabccdaacaadbababaddaababbbcaccccadacacabababcbbbbcddbbdcdacbdddbadddccacacbdbdabcacbcdacccccaaadbadbbccdddccdcacbaadcbcdbdcabadaaccaddadbbadbaccabddcdaddacdcaabcbabdbdacdcadbbabcdcdcccccbbbdcdadbdbaccdccdcddcabccacdbbacbcaacaaccbbdbaccdaccbbacbbddbaaccbaddcdcbaadcbaaacbaabadccccaabcdbbbbdbddccadbcadbacbdaccadbabbccdabdaabdcadcbbddbacdddbdcabdbabcddacbcbbbbdaabaacbdbaaaddddacdbadccccbcadddbadaabcbbcbbdaadcbbcdaccacaaccadddccbaaaaabdcccabbbadabbbcabdddcabaabcbbcaccbadbcdddcccbacbabaacaababacdaadcbacbdddaabdabbbdbcdbddacbdcdcddcccacabbbcbacbcacabcdcbccbbdaabbcdadbdbcbacccdacdbadadbacdadbdcdbbaddcacbcccbcbdbbbabdcaadadadababbdbbadccbaddaaacaabbbdccbdbbdababdcbdaaaccdaadadbbbdacabdacadbcdcdadccccacbbabddbcdcbbadadcacacddbbbadddaddbbdddaddcabbacbdcdcabccccaccdaadbabdcddcddabbacabcbcabacdaddbdadbaaaacbaaccdbddddadbbcdcdbbadabbbdcaaccadbbcabbbdccccadbcdabcacdaadcbcddbabaabacbcddaddabcabcccbdddbbcdbbbbdadbacccdacdcaddbadbbbdbbcadcbcbbbdbacdabbbcbadcacdbdaadacbaddbbbabbcbcaccabcbacdaabadcaacadaccaacbbbacaadccadcdadcabbdadacccdaddabdccbcdddaccbbcbaadbddbaaacbcddbcdabbabddbacaabbdcaddaddbcdcaabcbddaadcdcccaddbacdaccdbadbbcbcadbccaababbaacdcbbddbbdaababdbbabdcbaccddadbccccbbacdaaabbcbcccccbdabdcaddbcbcbadbabdadabddbbdbbcbddcccaccbccbcbdcdddddbabacaddcbaddbacadddbcbcdcaacacdadbacdbcaaaccbccacdbdbadabdaddbdcdbbabbdbcddbbdbadbcaabbdbaddcbccaaaacdbbbbddadacacadcacadcaacdcabacadbbadabbcabbcacdcabacbaadcadcbbdddbdbacacbbdbcdcccddadcabdddabbcaabcbcbcbabcbacbdbabaabacabbaabbacbbacbcddadbcbbbdbdbbadabcdcccbcddcddccbaaaccdbbbbacabbdcacbdcdadcadabcdaadbadbbbaaabdaaaabaacababbccbdbcadcbdadbadaabcdbabccdaddcbbdcbdbbdcaccbccbcbcaccdaacadcdabcbacbdcddbdbbcdbbcdbaaccbbdccbcbbbabbadbbddcdaaaddacdabadbadbcdbbdadbaddcbdaabadbbaaadadddadbcdcbaaaabbcaaddcdbcaadddadccbcdddbdadbdbbcbadcbbcdacaaaaddcbcbbbddcaabaaccddccdcacddaaaadaabbcbbaaccaababbcddbaaabbadcbadadaaddbccbdcdadacdbaadcacadbdcabbddbddcccdcbddccdbaccdabbcdaabdaddcbbcaaccaaacdbccabcbdadbbdadcbcacaddaccaacaabaacbcadcccdaabdacbbcddabdabdbdababccccdccabccccdbcbccaabdaddabbacadcdaaddbadbacddbbbddbbacadabbcbddcdbbbaaaaabbddcdddbbaddbbcaaaddacdbdaadccdbbdcdabbbccbadcbccaaddbdaaaaaabbdcaadddabcbbadbdddcdbddbabdcadaaddcbdbccddaadbbbcabbbccdaccbabcabddcddcdaaccbdbacccaccddaadbaaaccddaabadcaabdcdbbdacbdbabaabaadbcdbcdcdbddcbdbbbbbcbdccaaacdcdddacddddbbaaccdcababbbdacbdacbbaabddbaabccbccacbdababdcabbadbdcdcbabcbbcccdabaacddadbbadbccbcbdbdadbbcabcababdbbacdaacabcccdcbaacdcaaacbaadcbbdacbdcbdacddaaaccbddcbddabaaaccdadacabdadbccaabccaaddcdbbbdabddbabdccbcddadbaacacdaccbdbcacadcbaabbbcacbaadbdcdbdaadbcaaaacabacbbcbcdbbbddcdbdbdbddddbabbdbccaccaccadcabbadcacdabdadbccbaccbdbdadacdcbbabaccbdccadbccdbcbadddccbcadacdbababbacbadaaccbcabbbbacdabbbcbddacdccbdbcdabbbadcdccaabdabbabdadddddaacbdcaacdcbcbcdcbbaccbdacacbcdddbabdbcdbaddcacbcbdaababcaaadcabaadadaacbbcdbcbbbaabdcaaabbcdcdadbbbdaadcdbcccddbbcaaacabcdacdcadcaabbcabdabcacbbcadccbbdcddadcacbcacacddaddddddcdbcabdbbabcccabbadcdbbbcabbcabcdcaacbbbdcbaadccdadacccabddcdcddacbddbbdabcbaaddcddcdabacacbaaacdbbcdbdbbddabbdddbddcdbadddadaacdbbbdccddacadbccaccddbaadababdccbdbbaadcbcdbabcbbccdcddaccdbabaadcdcdccdbbcbccbbccddbacabbaabbadcaacbbdbcccbcacddaaaddbabdcacbbcaaacdcbcdabbccdaadadaadbdacccbdccaddcbbdadaaadcddbccbaabddcbcadbcabbcdabdaabcabbbaabaabccbaaaccadbbdaddcaabdcddccaaaabcdaadbdcabdbdaaaaacbbbcbbdcadbaaacdbabacbcabcadbbaadccbbbbdcadccabccacbadcccccacbadbcadacacbbdaadcddbabbcdcdddbcdddbddabdccbcdbcdabcdabbaddcccabcdaaaaddaabbbdabbccdcdaddbaabadcbcaddbbccdbbacbdaadbacaddcadcdbcabccccbadcbdbdddadbbbccbbdbaaadcbdaabcbacabcccdbbbcacbcdcdbbbdaaabbccbcaabbccadaddbdadaccbbacddabaddbdcbacbabcabacaddcabbcbaaadcdcdcbddbdabdacbadcdbdcbbabccabcdabdcdabccabcdacacbcdaaabbbdddbbaddcddaaccdddbacdddcaaadddaababccdaacbbccaddbaddcddbadaddddcccadbacadaddcdcbccbbbbbabbbddcaddbcdbccdadabaacdaacbdacabbabddbcdbbcdaccbaaccccbcbbbadbbbdcaabdacbcdbacccdadcaccbabddcdaabadbacbdcabdaaaadcaccbddaaccdbaacbcdbaddcbcaacaadaddbcdaddcbdbdccaddcbddaddabddacbbbabacdccaacbcacaddddcbddccdcbcddabdcacbcdccabdbccdccacccbdbdadabccaacaadddbcbdbbdbbddabaabdcdacaacbdddddbbccbbabcaadbabbabbdadcbcbcaabdbcacccbbacdaaccacccddccdacccddabddcaadabdbababcdbaabdaddabbacdbbcdcbadcdbaaacadbddddcbdcaaddbcacbbbabcabccbbdbcddacbdbccaaabcbbdcdcacccacbbacaabccbadaddddbcacccccddbdccdddbdbbcddcadbccdabddbbcdcadacccbbabcadddabcdcacbddcdaccdcaadadbadcaabdaccadbdcddbbadbcacdabcabcadaddcbdddbbdcddddbdcbdcacadbbbbbdbcddcdccacbacccccbbccccbbdbcaacadbcacdccbbcddcaddbaacdadbccabbcbccabacbaabcbddabdddcabccadcbdcadcccdbcabdcbbcaddcddaccdcdabbdbcbbacdbdaaccbbddaadacddbcddcdcbbcacbbaabcddaabaacaadbcacbaacdccccaabdddacabbddccadacaaadcccdcdcaaacdcbcaacbbaacbccbcdbaccccbbdbcddcdadabcbddabcccdcaacccaabaccdabacacccaabadcbabcaaadddcbddcdadccdabbdaacbcbaaadbbbcdcccdabbcbbcccacadbdddbaacccdaadaddaadddcadbdabdaaadaabdddaddddabbaddccbcacbdabddbaadabdaadcccaddaaacddbbcaaddcbacaabcdccaabdadbdbdbacaaabbccaadcbbdccabaddacaccaddcdaddbbaddddcdadddcdabaadaddbcdcacbbdbcbacddcbbabcadbdddcaccabbbadaaccadabdbacbacaccdbcabdaccbcdbcdbdababbcadaccccbbdbccdccbcbcbbbbbdcdbaaccababdcabdaaccbcdcbddddbcdbdabcbbbddbcdddcccbdacbbcccdbdccacaabdcccdaabbabaddccaaaabddcdcadbddaccdcddabbcddcddbdadbabbbdcddadcbbabdccbbdcbabaccabdddbdbcbbddaccacdbabddbdbbcaaddddabcbbadddbbbbccccbaaccccaadcbdadcadbaacdcbbabbbbbdaabbcaaccbccacbcabbdadbcbdbbddbdddbdbccdddbdacbadbdcaaabbacacaacbcbbbbccddcbcbbcbbbcbbcbadaddbabcaddcadcddaabaadbdbbdddcddadbdbbaccbcbbbdcacbbdcabbdaccabacdcbbaabbcbbabdcbbbbcbcdbbbbbdbcabdcbcdccbacabdbdddbbddbacbdaadbdbddaacdbdbaacdbcabbbddabdaaababdcdcbadbacddbaddcbbcdbdabbcaadddcccdcbaaddadcacbbdcdccddbdaabadccabdaaaaabcadbcaadadbdaadddbbadaddbaacdaabcbaadbcaabbdaadaaabddcdddaccacadbaacbabcacdddadbbdaacdbddaacadccbbdcaacabbbabbadbabcaaaaadcbbdcbccaaabccdbcbabadccbdbbbcabbdccdddcbcdaabdbdbbccdaabcdcaddadcadcdaacdadcbadbdacdbbbddbaacaddbaacbcacbbdcdddacabdccbdbdddbacbccbadcdbdacbbccacbcdacaadccbdbadcdaadbadaacbcbbdadbbdaabdbbdbaacbcccdaacacdabcccbddcdccacddcdadabbdddbbacddabadcaddcddddcdbddaddcabaadbdadbcdaabddbbaacabcdbdbdbddbbcbdacbccdbbacadaadddbaccbaadbdccadbabaddcadabbbdacdacbbccaabbbadbbabaddadbbccbacbcccbdbbbdacdbacadacadcdbcabaaabacddabddcabccacdbdabdbddacbbcdbbdbbcddbcbdacacabaadbaccacabadabdbddbadcddccbcacacbbcacabbbbdcbbdcccaccababbababadbcccccbdacdcadbbbbbdcdcccaabaddbdcabbacadbabcddcccbbddbabaacdcdbacbccabdaacaadddaddcddacaadbccbadcbbbdbcdabbcabbbabcbccabcaaabbabbdbdbdbbdbcccaaddbaccccdacbcabbddacdabcddbdbccaaacacdaccbdcdcbccdaacdccccdddbacdaacaadbddbbacdcdccabcdabbcddbabaadcbccbadbaadaaabcccddabdddcaaccbcadddcadcddaccdbcddacdbcbbdbacaadcbcacdacdaadbbbabcabadcbadddaadbbadabbbcddbdaadabcdddaccabaacacdbdaaadccdbbbababdacdbaccdbbdababbddacadbabcdadbabbddcbccdcddddabbcddddddabddbcaaabaadbddcbaaabccbacadbabdcacdddacaacdaddaccbbacdcdaccbbccddbadbadbdadaacbdadbabbdaccdddcadbabcbccdcdcdcccdcbdbaddbabccadcbbacdccbdcbdcacdaccccbddbababdbcacacdcbaabbbacaacbcccdacacbcaadabbbcccdaabcaccadcbdbbbbcacadcaccabdcccccbddbdcabababdcabdbdbababbbacccaaddbdbcddbdadabdacacdcdbadacdaadccccbddcacbddbdbacbdbcacbcccaadddadcabbbadbacbacdadaaacbabaccaaddccacacccabbbdacdadcadbbabaabbddbabdcadbbaddaaccaadabacacdbacbdadcbbcbaacdccdcdcabacbacacdbddbccaccccaacbaababdcbbdbcdbdccbcdacdbdacddbdbaccbddbcaddcaadcbbddbbadccaaacbcdabdbbddcbabccbaadcbbdbaacdaacdddbdbdabadadcdccadbcaadbddcabbdddbdcadcddddbccabcbbbcbbabaabdddcdbbdcabbcadddadaabcbcbbaabbddbcdabdabccbacdccadadcaddbcacbbadbcbdcabccababaaddacadcbcddbabcaaccbbbacdcababccbdacacdbabdabccddbbcdbbcabaaaaaabacddbddbddadabdbbdaccdcaaaaaddaaaccaabbcaaacadcaadbabaaddacbbcdbabcbdccbdaddcacbacbdbdaaddddddacaacbbdaacacbcbbcddbacdabddadaacbdddbbabaadabcbdcbaccaadcbdbdcdabacccdcabbdddcbccbcabcacaabbbadcdcbacadadddbdbbaadbcababcaabaaccbbabbcddccbacbbbcaccdaccbdaaccbbbabdaaddcaaaaccdcdcbabbcdbccabbccbbdcacabccababacdcbbbadcaccaddbccbaccbccdacacbacdbcddcdbcbbbbaadccbacdbdcbdbbcbbddadcaadcaccccadbddcbaacbbcbbdcdacbdbdcaccdaacabdcabbcdbdcacdbcbdadcbadcaabaccbdadabaacdcbabcadddaccadaabdacaccbccaddcacbaccccdbbdacbccdccdacaabadcddbdcddbbbbdcadaaabdaacadababcbdbbbbddbdadbabbdabcbccdbaadccbdddcadabbdbcabbabddcadcadaacdbabdddaddaacabbadcbcbaabadbbadbacdbabadddbdcaddbabbdacdacdbdadcabdaadcbbadcbccbcddbddaadbccdadcddacbcadaaababbdcdbdbbbaaadabbbdddadaacadbdadddadadacbdacddbdddbdccbaacdcbdcccdacbcbabbaaddaccbabcdbbbbcdcabcdaaccacbcddbdbabdbbbacaabbababdaabacddadabdadbdbcbbbbdacdccdaaadcdacacdcacbcaadbabdcabbccbbdcdbddbbbbbdabbadddbbcabbacabaccbcdccbcadcbddbcdcbccbccbaaaaacdbcdadabadacaddabbbbacabbaaaadcbacccacadccbcbcaccbbdbddbadcaaaabcdbbaddddccabaccbbbbaadccdabadcabadcaabdaabbcadabaadcadccbdbddccabdbbbbababbcdbacbcdcdcdcbdbccacdcbaacdcdbbabbcadddcddddaacccdbabcbabdcbdadbcaabbbcaccdbabddabbcaacccabbaabcddabccddbadaaaccbadcdbddbbbdcadaaccbacacdbcbdcdabbbcbbaccaddbaabdccddaccdbaacddbabdacbcdcdcbaaacbbbdabbabaaabcbbcabaabcaaccaddcddcbbaaadcabadacbadaddaddabdddaadbcabddcadabdbcdacaaaadcbaadbbbcddccddbaccdacdabdaabacccabdccbcaaacdddbbbddcdadadadbdacdddbcaabaadbaabbcccaddddaaaacbbaaaabadadccddbabcabbcadcbbdbddcccbcbdcdbdccdaadbdbddcdcccccdccddcaddbdcdcbbcacddaccbaadcdbcabbaaccdabdbddabcbddaddbdccbbcbbccdbaabcbcbdbaacdcacabbdbacbaadcbcdbdbcddabcddadbcdbcdbadccccdadcaaabdbcddbaccdaadcbccbdaccaccaacbdbabdbbaacbcadbcccabcbacbbbcbacdcbcdcbadacabdaaaccadbbdaaaaadcccbabbdbcccbaccdadadaccaddccabdcbcbddddbadbdcacbddbccacdabbbabbabdbddbccbddaadbccbadcbacadcadbcddabbbbabddcdabbcbaabacddcddaacaaddddadccabdddddbaabcbdcdbcdaabbadcbadaadcddbaabcddacdbdbbcccaadcddadbdababddcaccbcbdbcdcdcddadcbabdbdcbaadabdaddabbaaddbbbdcbabbbaaabdabcbdbcbbcbdbbadbcbdbbaddcbdadbbbbbbdacccabdbbaacbbcbaaaacbbaaabdcdbcddbcccddacddbbdbdddcbaabcbcbccacddabbdbabcdbbcbcbbbbabdcdddaaaaacadcbacababacadbbaaabdbdddcdcbdddbabbbaabdbddccbbccbabcbcdddaccadadbaabbdbdcbdbaccdabdcdccaddddbcdabbccbcbccdacbcbbcdcdcacaacbcadbdcacbddbbabdbaadababcdbabcbcdaacacadaaddcbccdacaccbdcbabbbcbddbdccdddacacaacbdcacbcbdddbdcadccdbbaccbbbcdbddadccadadaacadadbbaacaacabbddbdddabaacbcdcbddbbbcbacdadcbbabbacacccadaddcaadbdbaadbaddcbaadccacacdcabcbddcdcaacdbabadccdcdcbbabacaddacdbbdabdbbcabdabababcaacbcbdcacacdddcdbbdaddccdcccabcccbaacbaadcbcabdbdbddabbccbdadbddbaccddbddaaabaabcdcacddbbdccbabadaabddcbaaabbcdbbacdbbddddbdccdcadbccadacbcdddadcccbbccdccadccdcdaaaddbbbcadddccdbcdbacdcaddbbcdddcbbaaabdcdcbadbbcbabccacdacdddabaaccabbbbababaabaccccddcaabaabdbcdbadcbdbddcccbabbbcadbddcdbbbbcbabddbbbacccdbcccdcaaaaabccacdadbaccbaabcddcdbdddcccbcbdcdddacbaacdbbcddbaaacdddbbccbccadbadbacdbcabdbdcbdaabcdabccbaabbcbccbbbbcdbabcdccdcadddccbdbdcacacaabccdbbcdccbdabbbabadcabaabbadcdddaddaddcaababaddaaccacbcabdbccbdabcccaaadcdabaaadddbadcbddabdadddbaacbcaabdaaaccbdcadddcdcbccbdabbcdbbddcacbcddcddbbcbdadcbbbadccbbdbbdcccadddcdbbbcbbcddbbbdbbddabadbbbbaabcbabbabcbcdcacacdadadbacaadbbccdaadbcbcbddcadcaccbbbdbcbbddbddadbcbcbdddcbbcacdbbabbaabadcdbbcbdadabbcbbbddcdbdbdcabdbdcddabababbdadbaabbbbdbabdbcccacabadcdbdbbdacabdbbbcaaccdbaaaacbacbcdbccbabababcbcddbadbbabcaaacddadbacbadbcabbdbcddacbbdddacbcdcaccdbddddacdccabbbccdbbadbadaaacbcbaadddacabddccdaabadcdccdcbaccdaaacdcbccacbabcaacdbabccababacabddbabdbccbacdcdbbacdbcaaaaaacabdbdbacbbdbaacbccbdabbdbdcbcacaadbadbdbacdabbddacbcdddcadbcdbdaabcaccbcccbcdcdbbddacbaadbacabacccdaadcdabbabaaccacdcbcccabbcbbdbbadbbbdacdacbaddbcdabddadcdbbcbcdbadcbbccacddaddcacddcdbdcbbbcadccacdaacadbddcaddcbdccaddcdcadabdbbcbacddcddccaacbbbdacbbaddabcadcaacbcbdbcbbbabbdcaddccbdbacccdcbcabdbaddbdbaadcbddbdaaadcaaacbcdbbcdabdcccdaaddbbaadbabbcbcaddccbddbacdbadccbdcdacdbcdaccaacaaadbbbbbdbabcccbcabbbacccaabcdcadbbbdbbdbbdbacdddcaddababdaacabccddcbcccbbddcdabaddbbcccaccddcadbaacacdacdadccdbbcdbccddbdbbbaabacacbbacbdbababdacaacbabdbbcadacddbaacdadcdcaaccdcccaaadabcbbbdaccccddabcaddadcbdcdcdbabdcccdbdcbbbadaaabcbccadadcbacdddbddbbbbcddaddcdabbcbbcddcbccaddbdbbabcbcacacdabaaabbcbcbacdddbbcdaaadbbcadbaabccdccaacadcdbabdbabbcdbbdcbcddcabddaccdcdaaabcbacadbcccdacbdcacdbaccaccbdcbadccbdcabadbadbaaddadcbbdbbbadbdcbdcabdaaaadcaaacccbcabadbcbaccadacababcbcbbbccbdcbbddcdadadbdcacbabcbdccccaaddadbbbdccdbccccdabddcaabcccadcdcdbbccacabacaabaaabcdbaddcbbadbcccbcaccdadbdadbbcadabcbbddadabdaddcdbcababacbaddabbbddcabcaabbbbbbdbcdcbbdabdbbaddacadabaadccacabbacbbdcdacabaaccaabcadccaabbddcdabbbcccddcbaddcbcabcaccbbabcabdadabacabacddbadccdbbacbabdcaccbdadbabcdaaddbbccbbccaaadadbaabaaabaacbabbacdcdcadddbddcdbbbdbcdbaaccbaadacabcccacccdadbbdbdbacbbaddbddcddadcdbcdbccdbdaacbacbabbadcdaaabcdbbddadacccaddccccbdbcbadcddaacbcddbddccaabdcbcaadaaccadabaadcadacdbcddcbbdcabcbdcaddcbadbbddbcbccbbcbaaddbdbabdaddddccbbbcdcbcddaaccbbdbcaddbbcacbaccababcaaabdcbaddccaabcccaadaabdabbbcccbcbdaabddcbbcdcbbcadcadadcdbadbcacaacdaaccacbdcadadacbaaadcaabddaaadccaacdabbcccabccbccaaaabddddabaddcdcbadadbcdcccbcbbabccbbcaaadaabcabacabddcbaccaabacbdbccacccaddbbbabadcbccbbabaaddaacabdbcbbdcdbcdbdccacdccbaadcadabccddcbaacdabdbcdddacdddbcccbcdbbbbadbcabbdddaddcccbddaaaccdbdbcacbddbcdadbbddccddaaddcbcddbaaaadcccabadcaaaaacbbbaabadbbabdccbbcbdaaccbcbbacbdccbabdcadacaddaadabcaadddcbadadbadabdaabcbcabccadabdabcabbaadbaabaabddacaacbdcdccbabdcadadadbacccdacabbadddbbabcdcdaaddcdabaccdbdcaacbcccdcdaadbadabaabbbaabccabcddbbaabadcabdcddbcaaabdaadcbacadadcabbcdbcaccbbdaccbbbcaddbacbcbbdbbddcbcbaccbdadcabcddcdaccacccabadaacccdbaddaddbacccdccccbdbcccdcddddccacbddacbccaaddbbdacbdbcaacadccbaaddbdbaadcaacbccaacaccdcbdadaadbaadadbabccbbaacaacdabddaabdccbcdcbbbbababdcbcbacaddccbaaacdaaacbdbbbacbbbdacbbbcccbdacbbddcadacddbcbbbbdabaacdbcaaddcbdddddcabcddbcaaabacdcdbbbdcbbaadacdaddaddcaaaaaaabbaaaabadabbdcdbcaabadcdcddbdcdddadadbbddaaadaadaccccdddbcadabdbaddcabdcaaaabaccaccbacbaaaadbbbdadcccdbadbbababdadaaabdddcbbabdcccddabddbbcbbaabdbbbcccdbcbcbabbcaadcddbdaaadbbdbbadcddadddacbabbbaaaabbcccdccccabcadcaddbccdabccddcdaccddcababccaddcdacddbbdbccabccaccbddccdadcdaacdbbbbdbadcbddaabdddaadacabcacdadaddcbababcdbdbbddbbaacadbbcadbaadcddcbcbbbdacdabbcbdbcabcaabaacdbccbacddbdccbcdaacabdcbaaccdcddccabbbdbddabdbabddcbddaaaabddcbbadacadbaadadbdcdbacababdbdddabdacdcbbbcdcccadcaacbdbcaaababcbbcccdbcabbbcbbdacacabdacbcadcaddbbccbadabdbadccbadcccdbcbbbdabcdcaccdabdbdddcccadbcacdcddbabcdcbddbddbbbacabaacbbbacdabcdcddbccbdbbcacaadcabdadcdaababbbdacdbdccbccdabbabacbadcdcaddbcbacbaddcdbaadbbbaadaaabbdbdddbaddbcaccbcccbacabddcdadccccbcbcadcbdbaaddaabdbabacdbcddbbadadbddcadbcdcdbbccbdabdadadccddddbbccbbacccaacbbdbcccababdddcbcdbacbbccbcbbcadadcadaacadddbcbadabacdaaacbdcaccbcdddcdcbaaddbcdbdbcbbdbbbcbdbbcaddaaacdccbacccbdaddcdacadddcbacbbacdbbaccbbacbaddbcbcdababbacbbccbacaabbccabaaccddadcaadbbddddacbbdbddabbdabdcadcbadddcdaabbaccacbbabddcdbadbbbaadddccdddcbbaaaccddcaddccabcbcbcbdcccdcccbaaadbbccdbddddbdcbabdcbccaacccbcbcdcdbadcbccaabbcabddcdcdababbaabadcbbadbbabcadddaaaccdbdacccdabdccdccadaaddddabdcadabcacccacdabadacdadadaccbbbbbbacaddddbcbbbaccadacbddcabdbcbdbdabaabaacbacacbccaacdcbaacabbbbccabacdddcdddccccdcabbccbbccabacddcbddcdbabcdcccbcbabbccdbbddbccacdadabcaaacdabaaaaaacdaaaabdaacccbccbbdccccdbaccbabbbabdcbcbbacdbdaabdabcabcccaadabadbaaccacbdddbbdcbddacdcdbbdbccccdcdabcabccadcaacdcbddbabbbdaccccaadaddcbabadcbbaabaadcbcbdadbbbddbcabbadacbaddbaadbddacbbaccdbbccbabadacdaaaccaabaabcbabdddabbbbdacccdbaaaacdbccddaccbaccacbcbacabcddbdbaacbdacacddccacbdcababbaabdcacdacbbacdadaabcbcccbadabccddbadbdbaacbdabdbbcabcbbcacabcadaddcccddadacacdcbcababbadbdcaabbdcbbacccaaabbcbaccaaacaddabdabdacdcacabcabdacdadccdbadabdddcbdbddbaabddbcacdcbbbccbccdccbcaccbccbbbdcbabcaccccccaaadddcbaabdcaccddcdddbdaadcccbcdabbdcbcccbdabbcddcacabdccbadadadaccdcdabdcdaccdacaacacdbdabdaadadbccdbabbabbbbcdcbbbcadadcbbababcadcddadccbbbabbaaaacbbcccaadaabdddbcabdbbaadbadadcadacbbabaaddbcdabdccdcabbcbbaddababadbbbacdaaabcdacdcbdbaacbbccdbbbaccaaccddccbadbdadcacccaaadbbbabbcbbdaadadddcdbabccdaabbcacddaaddcbbaddaccdbdbdbbbccddbbdbccbbcabddaaaadcddadcaadcccadccdcacddabbbbccacaabddabccaacaabdbdbbadabccbbaabababdcacaccbacbdccabbabcccccdbaaddcdbbadbbcddcdadabdadaadbbccbaaadbddabbdbcadcbbcdccdbcacbcddbacbcbdaacacaadbdbbbcadcbbbcdaaaacbdbcaacbababcdbbbaabdcdccaaaaacccacbdcbbccddccbcdcddbdcabbbcdbdcddacadbbbbaacddcdcddbbdbcdbcbcabacaadcdaccdcddddaadbddaadbbbcbadbbcacaddcaaabdbcaaaabababdadabcdcbcdbdabbabbcbddabdbacdbabbdbdbacabacaaddbdaddbdcddbaabcddbbdcabadbacbcbcbbdddbbaaaddaccbdbdcdbaaaacdddcdcaaddcdbddaabbdcddcaacbabbacaaadcaabbacdccbdcabddcdbcddccbacdacdbbbddcdbbbbdbaabcbdbcadaccccbcadacdadddbdcdbaabaddaacdabcdabaaccbccacdccccacddbaaacbccaddcdcaababbabadbdbcbcbdadadcddccbcaabaacdbbcabcbbbdbbbbbdaabcbbbccddaadccbbbcdabdacdaaaababddbbddaaabadddcdbccbcacdadacbdabdcbddcaadcddddcddbbacbaaaddcbaaadabcccbadbaddcccaccbdbdadbbdcbabbccbabacadcdaccbabdcdadcccabbcdccaaadaddabbbaaccddbacdddabdbbdabcbaccdaabbdbbccaddacaccadcabdacdddacaaaacbcddcacaaacbbacdcaddabaddbaababaabbabbdccbcaaabddbddcaccbcacaadbbccbbdcbcabdbbaaaabdbaacccabbdadbcbbbcaabaacbbcdbcaacbccaadbbccbdcbdcadccccacbaabbadbcacbcabadbdbbcbcabbacbdaadcbdbbdacbdcdcbbadcdbadddacaccdddddddcacdcaddaacdcbabacbcbaaaacaadcabcabbadacdaadccabbbbaaddcaaadbaadcddddccbbccadbadabadadaddadacaacbbdbadaadccddabcbdcadaccbdcbdcacaadacdadbccacabbbaadabbcaddacbdcbbbcabdbababbbdcddcaadccbacddcbdbbaabdaaadddbacbddddbcbacdcbcadcddaabbddcadacdcbbaaacdbdddbadabcaacdccccbcaccddabaaaaabcccdcbbcacdcaaccccbcccbbbccdbccababaaccdbdbdaccdacbdcbcddcccbcbcdbdbddbabcbcbcccdaabadbbcdcdcbaddcadbcdbacaaababddcbaacdcbaddaabcdcaadaaaadbccdddcabdbcaddbcbbddaddccabdddcdababadcbacbbbdbcbcbbcbaaabccbaadabdcbcdacdbaabbdbaaccdbcdbcbdbcbaccddddaabbaadddcdaabbaadbbacaaaadadcabbdbccacabdcbbcabccbddcbcbbbaaccbdaddadadbabbccacddbccbdadadaacbcadbbddcdddaabaddbdcbdddabdbcdbcbaaddbdacddaabaadaacdcadabddacdcbabddcadcbbdbdbabdcaacaaadcbaacbbcdaddabcbccbaadbaabaddaccccbcdbbcbddbaaacdcccdbabaadbdbbcabddbcbccbacadcbbddcbdcabbcbacdccbbabccbdadcbccbabddbacdacabadbdbcbbababacccbacaacdaccbcbdaabbbcdbabbcabcaddbacadbbdcdbdcabdcaccabbcddbcdbbbbaadbcbbdaabdaaccdbbbbccdbcddbdabcdabbccadbabbadcdccaabcababbabdbddcdcdcddcdadadcaacdddccdbbababbdcadbdadcdcdaaabaabdcadaddcabadbcbbabbcbbacbbabadabbbccbcbdbcbcadcbacabdaabcdbabdccddbabadcdacbaadbadabcadbbcddbccbddcddcbaadccbdbcaacddddbadbccbbdabbbaadcababcccdacadababbaabddcabbbbabaabbbdcbbccbbbabdcdababcdccabdbbadabadabdcadbcacaabbcaaacdcacdacaadabaacabaabddcccdbdcdbccddbcdaabbbdbdbdacdaacbbaababcacdccacbcaadadaacbcddabacadddbcaabcabbbaddabdbccbcdaacdbccdaabcaababcaacacbbbbbbaadddbcdbddccdddddcbaddbacbbabcccabbcabdbdbcacdbaddcbbdcacaaaddaccaddccbabcdbdadddacbccccbddcbbccccacccdadaabbbbbdbacbdcddcacbadbdcdbdcbbdabcbccbaadccddddccacabbbddcacaaadaaaacbcbcccaddcbdccbddcaacddadbdcbcdacdbccbcaccdcabbcdaabddcabccbbadddccdacabdcccdbcdcddbdcdaabbbaccdbcddcaacccaccdddacacbccbaaabbbbbaccadbbdacacbacbbccdabdcbaddcdbacbaddcdbbbdbdadcdabacddcbcadbdbcdabbcdbaaabbacbddcdcbacddbccdabacbabccdacddcddaabcadbccdcbbbbaaadabadbdacdbcacadddcccddddccbadcaddcbcccabbaaddabbcdadaacddbcaaaabcabbacacbdabacaddadaaddaddccabccabadbcbddcdbcccdcabdcbabbbbcccbbbcbdccbdddbccdcaadbaddccdccdcbccddccdccdcbaadddbddbdadbbaabdabadaccbcbbcabaddacbbdcadccbcbabdcacdcdababcaaccbbaccbcbabbdbbaabccbbbccccddaacbaabacaccddbdbddddadcbbbbabcaaaadcddbcdacbcbabcdbdaaacacbbdacccaddbbdcbabbdacadcaaababadccdcdabcdbdcdabcccccccbcaaaddabbbbabcbcaaccbcabadaddbdbddacdbcbcbdaaadbcccabccabbaabdbdaabdabccdccbcbcdbbdddbcccabbcdbbbcabbdaadbdcdaccbdbcacaaccbdddaacccaccdbcddccbdcbabdadbbaabcdadbbcbcaadcbabdddcacdcabdaccaaddcaacdcbdadcadaccdbbbacbadcddccbacdadbdcdadabbbdccdbddabadaabdbaacbbdcbcdcadaddddddbdcdaadcabcabddcbacccbabccabaacabcbbabdcadcabbaaabddcccdcdddccbcdadcdabacdbbddbcabbcbddaccbabbddcadaadacdbdcbadcdddbcabaabcbaddbdcdbcdbcbdaaaadadbcbdddbbdbbbbbaabbbcbdadbdbbdababdcdbbddccadabccaadabbaabdbaadcadbdbbbadadbcadabbabaccbddbcddddbbdbcdadbaaaacabccdbacabcbabdadadacbdbadaccaacadacccbdbbdbdddbbaddccaccdaaccbcbbccabbbacbbcbacabbddbdaaabaacbcdccdacccaaddccdbadcdbacccaccccddbddacddacabdaaabddcbccdbaadabcbbcbddacadcddbacbcaacccaccbdbdbbcaadbdacaaababdccacbcdbbdabcaacbcdcdbcccdddbaadabddbbdaabcdcabbcbcddddacacbdcbdcbabbadaabcccaadabaaabcacccbbaaadaabbbcccdbdabddbbcaccabbdbcbabbbcadbbbdabbbaacddcccbcccacadacddabcbccbacbccabbcdcccccbcccacadbbdbdbddaccdbdadacdcccbdccabcbdddabbabdabadabcaabbadadcbbdadcdddbadaabdbcbdacdbdadccbbcaaacbdbadbbbcbbcbaacabdadcdadccadacaddbdacbbbdddacaaddcdcdadcbcdcbdbbccbdcbdbbdcabbcdcddcacacabcaddacabaabacbdcadabcbcdbbccbccdcacccccaacadccaabdcddadabadcccdddbcaaabdcbddadaabaacdbbacdadaacccdbccccdbadabbcabcccbbdcabbabcddbaaaccdbdaacababcbdabcdabaabbacdddcdadbddbabcdbadadbbcdcbbcaabbddaadaaacddbcbadadaaabcbbdddbcbbdbddacddaaacacbbaccdbbadbcdbaadabcaacbccbddbcccbbbadcacbdabcdccdcccbbbcbabbddbbbaadcdbaaddddbbacbdddaaabacbddbadddcadccaabaabbbcdaaacdcbbbdacccaabcddccbbabadcacdbbbbaacacbcbbbdaabbbdaccdadbcbccabbbacabbdcdaadbbadbcbaaddbdbabcdbdacaabcddbddaaccccababcccadcddccddcbdabbdccacacdadcdcdadadbccaacabccbbdadddadbccbcddcdbddaddbdaabcabdaaadcbaaaabbbcccabbbcacdcdddbcdbacbcdcddcdcdbbcbaccbbcaccbbacabaaabbadccddabdbcbcddbbcaddaccdddbddbddaacdcadcdabaddbcbccbdbbdaccdbabaccbcbcacccadccadccbabccbcacbabadaadadbdbdbcdaddadccdabadbadcacabddbcdcdadcaabbcaacdaddadcdbbadaabbbdcdaaddabccbacbbdddcdbabcdcadcdbadbaccaacaaccdabdcaabadcccdbddcacbcddcdbbcbbdacabdaabadacabcbdbcaabadacbcbbdddadcabcaabbdcaadcaaadaacddbbddcadcdabadadbabaacaadbdcccbdaaaaabdbdbdbcaacdbdcddaadbadbdbddaacbdacccacaabbbacdaddcacdacdbbccbcdbcaacdccddacbcddbddbbdbdccadcbcadbdbabdabcaaabaabbabbdbaabadcbdaaccbaacdcbddbdcacbcdadddcdaabadadacddaacdbcabbacdaacbacaccbacadabdadaddacadaabbdcacbacaccaccccbbdbbacbabdabbcabcabccbabacadcdbcbdcbabdbbddbacbddaddaabddccdabdcdabbacaaaacdbaddacabaadbbaabdccddbccbccabbcabdbddbcabccbadabbbacaabbdacdcdddcabdddaadaccbaabdaadccddcaaccdbbcbdbcdbbadcadbcdcbbdadcacdbaacbbcbcdddbdadabbadabaccddadcabdbbabcbdcdcacaabdbaabccadddbacbdadbcbabbabddacbbaabadacdaccddbbbbbbdabbabcddcbcdaccdaabacaaccacbbbacadddabdbbbcaaaccbdcdccacaadbdabbbadbcbdbbdbcdcdadbbacbbacccbaccbabbccacdbadababbdacbadbdbadaabbbdaadacccdbdbcbcaaaaadbcacaccaacaabadcacccbbcccbcddbcdadacdbcadacdacbdbdbcbaddccdadacdaadddbccbadcddcadaddbdbbabddccdbcabcbccdbbdbadbdaaaacaacccaaddbdadacbbaddacabadbcccacdbacccdbdcccabbabbdbccaabcaacdccdbcbcbbbbccbacaaadddcacbaddababcdaacdcbcdbdccdbdcaaddddaaabbbddddadaccacbacbdcbcddadbadbbccdaadcddbbbaabbabddccdaabcdacbbaacbccababccbbcacccbbaabdbbaacdccbacbdcdabcdcdabbcbbdbcaccaaadbaacddbbcdbccdaadabadbacccbaacaaadadddabdbabacaaacbbdcdcbccbabadcdadaccabadcabcdcacbcdabaddbacabadaacacacaacbacbbabaaadccbcddadacdcbddacdaccccbbababdacdcdbbadbcdcaadcabbdcddabacabcaacbabcbdcddabbaadccbdccbadacaabdadcadabadadccbcaaaabadadabdadbcdccccbdbdcaacaaddacbbdaabbadbabdbcadddbbcbbddabcdcbcbddbbdbcddbccababbdbbbdddcdcccbcacaddccbbbccbcdaaccbabccadcbacabcdccbaacbddbbdcbcaccaddcbadbaccdabacadcddbdadabcddbbdaaaaaadcacadabbadacaddcabdacdcadcacddcddcdbbcdbadabdacdbbcdbbccddbabddbdccaabacbdddddabaaccdcbdbcbbbbaaacbbbbaddccdadabddcbacadacdabbcccbdbadbcdbdbbbddddabaaadcaaabcdbaaabdbdccadcccbbadcbadcddbbbddcadaccdbcacdbbccdbdcbdcbbddcdcdbcbbbdbabbbccccaadacccbcbdbbdaddcabbdbaccccbacbaddaabdbdccccacbcaacccddadacadcabddbbbccbbaacdccdcaadabaadbaccddababcdcaaddddbbdadadcaabccbbabdadadaaddcccbdaadabdaddaabacbdccacadacaabdbdccbdaaddaaaabccbaddcccabababaccadcaaabadbbbbbcdbcbabcbccddbdcccbbcadcaacabbdaacbbbabaacbbcddcacdaababbadadbcddbcaddabbcbbcabcadbcacbdcdabbcadaaabbbcccbddcbcbcddcbddbbacaaadacdbabddbcdbdcbdabddbadabaabdaccaccdbdccdbdaaccabadbcaacccbdccadcdabccaadbddcbbbcbbcbdaddcaddbabaaaacbdcdcbddbaaccbcdbdddbaccadcddadacadbddacdadadabddcbdcaacadcdcccdacbcdaccabbbcdbbabbdbcadadbcdabcacbcdbbbddbcbccbbdbbcabccdadabdcbadbaaddaabdcdbabccdbdccadcbbadbbdbcaabdacbbccdccbcddbbdcadcdbbdbdabdbcbdacdcbaccdcbbbbbabbdbdddcddbcbddbabadcbbbbddbdcbdcdbcbddcaacbacbbbddccddcabcbbbdcdadacacdbdcaadcbcabcadacbbcaacbbccacbcdddbcadaababacccddcbacabbdddabbcbcdbcdddddcadbcdcdccbccabaddccaacaadccbcbdabbacddcadbcbabcabdadacdacbbcdadbbbbadcabcdbabadcabcabcacddddcdbdbbaaadadaacbbbcddcbcbcaadcabccdccdcbdbaaabdaaacadbbbccbadcbacbdcccdbbdaacbccdacadcdccaddabccdaaabdcbcbaacabdacbbbbabaaaadadbcdacdbcdadaabbbdaadadcacbccdbdbcacaaddcaaddbaaaacabdadabdbaabaddabbabccacacbdbdbaadddbcabdbaaaddcbccabaccdacbdccacccbcdabaabdbbdcbdcaaabbcdbbabbdccdccdadaacaacdbadccdbbcbbdbabaadcaccbcdccccdcadaadcdbbbcaccccdbacdaacabaacccbddbdccddbccccbddcdbababdaacacdbabcbbbcbcaabcabcddababbacdcddddbcbdddcaabbcadcadbaccddccdcbabdbaabaaacddbdddaacdaaccdbbbbddbcbddabcddddbcdbadabbdbdccdaccdaccacdadabcdddacbbbbdaabcdbbbbccacdccbddbddadabbbacbbccabadaddcaccacdcacdddbdcabdcbaccbdaddbadcddcacaacddbadabdacaaaaddbddacabbdcdacacbdacbadadcbbbaadbccabdbddadddaabdabcbccdbacbbbcdddacbdbadcdacbbdaaadcdbacbadcbdccdacacddbbdaddddabbadcdabcbaccbbbadadcdbabcacdbdbbbabcccbcdcabddcdadcaaaddbbabcdcaacaddaacdddaacbbbddcaaaaaaabdaacabccdbbadbbaabccacccaaabaabcbababcabadabdddabdcbddbcddbdabaadbcccccaacbcdbaadccaacadabcacbacccaabdadaadacbdbcdabbdcdaabcbdaacbadddaccdcdcbbcaccbdcdbaaaccbcdbabadcdbabacabbdacbbdcacdbcbdacdccccdadbbdaaabccadaacccadbcbbadbacbddcbabaadadbabcabdddddcbbddacacacabbdccdacaaadbabadacdbcbaddcbbaddadbacccdcabaaacddbbccaaccabacbbdbbbbaabcbbdcdaaacbdddacadcdbbcbdbdcccbccbddcccccbbacbaadabbdcbadddbaacdbbadacbabadbdacbdaaaadccacbcaccabcacccdbbddcbcdcadbdbabacadbdbcaabdccbbbddcabbcadbdadcaabccccacddcabcdbccbddbdbcaacbbddaabbbdbaaaabcbadabacccbdadaddbabaabbdabdbdbcacbddbdbcbcccaddbdbdddddadaaddccdabdbcadbcbabcdabdbacdcabcadbddcbdbdabcadcbbbcabacdccdaccdabaadbbaccbbbdbbbdcadbbcbcdbcbbdbdbbabcabbbdbddbabddbbbcbaadccabacaaaccbcdcbcbbdabdaddbacdcadcdbbadcccdbbaccabacddccaaabcccbacacaccadccdcbadbacaacadcbabdabbbddaabbdddbdadccbaddbaadaacdabaaabaabdcdaabcccdbdcdbcdcdbaabdbcacdaadcaccbddbbbbddccbaccadbcbabcccabaababadbbacaccddcbbcdbdcaddabdaaaabccadabdcdadcacdadcdacddabdcaacaddcabbcbcadacdbcdddaccadacbcdbadcdbbbdbddcddcaaacbdbcacdcdacbdcaaababddbbbcbababbbdabcdbbabbdbdcacdcbacaadabddbcbdcdcbbcbdddcbcbaddcbadccacbcadbbbababacddabdcdacdbcacdbadabcdccabaccbcbddbbacdbadcabadcddcbabaddadccaddcbaabaadcbbacacacbcccbdbacbcddcdabdddbcbdccaaababdbdbbdcddabbddcadaacabddbaaaddbbbaadadabcdccbadabbabbabbacabdddabdacbcdddbdbdbcacacadcbccdacdcbdcadbcdcaaacddadbaacabcdcdcdbcbdbabbbadcdbbacdcddcdbadddbdaddddbaacabddcdcccaddbcaabdacaabcaaddccaacdabdbdbddaadadccddbbcbdcddbdccddbbadcaabdccbbabbaadcbaacccbabbddccbbbadadbaabacadcbabbaababdcccbdaadbcdcabcabcddbcadbabdaadbccbacddbdbcbbcaccccbdcddbdddccababbcacacbddacbcdbadddcbcddbaacccdcdbabccdcdaaadbcdadbdaabdabddcabcddbccabbbcdbccdbdadbccdbccdcddadacacdabacbaccbababaababdbdddacabbaaaaddaabbcaddcabaacdddcacdbdbdcababccddbdabcbdbcaacbacbacccbbcbabaadacabcbdabcbdabccbcddbbcbddadbaaadbadadcddcaaddddaaabdddbcbdccdcaaacdcdacabdbdabddcdaacacdcacadbcbcaaaccadcabddaadbadbcbbbdbcabdbaddcacdbdababdcbcbccabbdabcbccdadbdbcbcadaabaacadcabdababbcccddcadcdbacccdacbcadaacbaacacddaadcdddccbcbbabcbddbdadbcababaaadbaabdabccccaccbaaabbcbdddabddbdbcdcbabdcbcaccacccbaabcddaddcdbdcacbabaaacbaadddcdbbddaaadbcccbbbbbdcabddbddabbbacbdcccbdcbcdbdbcadbdbdcaadbcccabacabacbbcaadadabddcaccadcdbbbdbadddabbdcbacaabaacbccccdaaccbaaaddccdbbcabccaaaddaabbcdcbdbbabbbbbcdbdccddcaccaaacbadbacdcdcadcddacdacdddaacddcccdbdcbdbdaccbccbcbcbbccdadbcdcbadccbaaccdadcbbadcbabacdcbcddaabdbdaacdcbbcdddbdcbccaabdbbaadddcddbdaadaaccddcdbcbcacdadcaaaabbdadbbccccdccabddbccadacabacddcccabdaacabdddbddcddcabcbbbbdccabaabdbcaaadbaadbccbbcadcbcdbbdcdcddcdabbbdccaacbddadbadaaabcabbabddddcbdbadcdbacbdbdddcbbbcdbbaacacbcabcdadbbcabcbaacdacadbccbabbdadaacabcddabbbbcaacbbcdbbbcbaaddcdaaaccabcddacacbaacaadabddbccaaddacccacbababbcaccdabccbbbbbbaaabaadcbbdccadaaadaabaababdbbdabaadacbbcadcdabcabaaacdabbcdcccdadbabcabdbdcbdbdbcaccdbdddaaaabdcadacaaddccdbcccdbacbcdacaacdbadbcbddabdcabbccabddadbdbaccbbbbadbdaadbbaccbdabaccdabdbdadabddbcaaccaaadcaabbbbccabcbbabdaddbcaaadcdacccbaccdadaaacaabbdddcacdaacbdcaabacbbcadacacabbbbdcdbbdcadcbcabddacbddadcdabdacdbbdbabddaaadabddcdbccbcbddadbbddddaddbcbbcbbbdccaaddcbcbacabcddbcadacdcccbabbcbaadbabddbadbaaabbdbacacadabbcaacabdcccbdcbcbdaddcaccbacaddbdbabdbbbccaccabdbbdddbddccbbccdabddcccdadcdddccccabbccbdabbadcbbdcbbccbdacdadbadaddbabdcaddbcbdbcaadadcbdcadccbbbcaaacaaadaacdbacacdcacdbbacaddcabcbbdcdcbcbcbaadacabcabcddbbcbbbccabccaccbcabcdacdadabddcbccbdcabcbabbbbaddcabdddcbabdbadcdadaddadcabcabbccbdbccacddbdcbbadccadcacabbbddacccaddacabcccdcccbbcdcbbcbbabaccbbaacabbdabaccaddcbdadcbbbcbbcdaaadaabdadcddbdddcaadabddbbbadbaacbcbadcdabababdadbdbcaaacdaaadcbaaaaaaddbdbbdccabbacbbcacddadcddbabcdddcdcadacdaadcccbdbcdcdaaaddabbccbcbacabdcabcbdccbcabdddaccdadbcaccabccdbadcaadbaadccadcabcbaacabbbcdadcdccbbbadadcccdbbbaacabadddaababbaccadddccdcacbbdaabddddabcaccaabcaaaaccaadcdbadadaabdcdcbbbddccdabcadcabbbdaccbbdccbdbacdbbaabadacaaddaabadccbdbabbabaddcdaabcbdbaccabbadaaddbaaaaaadbddaababbaaacddbddcdcbbdadaabadcbbdddbcababcbaccddbaacadbcacbaaaaaaacdbbdaaacbcdcbbadbccdbdabbacacabdcbadcabbacbdabbdccddbbddacadddccbabdcaabdbdacabddbbaaaaaacdaabacddaaddabcaadadccdadaadcddbcccbccaaababbaabddbdcdbaadabadaadaaabcbbdcbadcbbbccbbacabbadcdcdcabcbddadcccddbadbcbbbacdcabaaadaaddaccdcdcadbcbacccdabcbccdddaabaaabacdcccbcbbddcbbbdaabdabbddaadbdcbbcbcdbcbbaadbbaddbacbadddaabadbcabaabdcbdaaddaaccabdcccabdadddbdbddacbccccbacddabcaddbddcbdacddaadaadddbdbcbdcaadbabdaadbababbcdaaaccdbcacbbccdcaccaddcadcbcbdbdabbcbdbccbccbaacaadcadbadbbacbbcdcbccbccdcbbacbccbdcccbbdbddaddccaacbbadacccbaaaddbbcdcabbaccbabcaccddcbcccddbabdbdcbbccccbcdacbbbdacbadcacbbdacbbbdacddbbcdcbdddbcdbdabbdcaaababadaaddccbdaaddacabcbbadabdbadcdcdabcddaacccccdcbabadabbdaadbcaaaddaabbbacbabaabdabbaddbddbbbbdacbdaadcbbabccddbabcabbccbdccdabbccbabccabccccbbcbdcbccaccadabdacacbccaaaacdbdcdddbababdadaaabaabcbcabcabccdaaddcabaadaddbaaddcbcbcbdbadadbaacacaacdacaaabbbdcdbaabcacbaacdbccccabcdcbbbbddbacccddacdcadbddabbdaaabaaaadddbcadcdddbbddbaacdacabbaaccaadacdcbbcdacaabbcbbcbbacbadcaaaddbcdcccdcddabaddccbdcadddcaaacbcaddbdbdbddbbdddaccdabacadbaacbcdcddbccabbadababdbcdcdccbadabbbdcbdbdcaabbddbdabbcdacbbbcdbaddaacabcbdadadadbbcdccccbdcbabcbcabcabbbbddbbdbadcacaabacbbdaabacccdbbadbcaacacbbcdddbdbdcadddabaabccdabcbdaaaacaaadcaadbbbaaacdaddbcaababcbcbbcbdbdcdddaabaacbcdabacabbcacadbccbbabbcdddacbcaabcdbadcbdbcacdbadddbbdbccabadddbadaabdbacacaaadbccacacdddadbcdaccaccdadddaddaacdcbadbadcccbdadacadccdbddcccbdcdbaadaaaadaddaaccddbacaaddcccdbcabcbaabcbbcddbddadaddaddddddbbadadacacacadcababdcbddbcdaadaaaadaaadcdcbacabbcbccadbcdddbdbbcdcadbdbdcabaaaaccdacacabcdacdbcbababcbadacbcaacdbbbaaccdccbccacdcacdbaddcdadaadbdbccaaaadcbcccabcbbdabdbaabbababcbccacbdbdbbbcbacacddcbbbdbbaabaccbcccdadcccdcaabdbbbbabccdbbdacaccbcabbcdbdcddcaacbabaadcbbdbadaacdaaacdbbddbccadbbbdabdcddbcdcdadbdcdbcdbcdaadcbbddbcabbaaccaccccbbaacbbadacadacbbabbabdaddbabadccbccbbadcdcdcbbcadcbdcacadcacbadabbdcdcbabcabccddcabcddababcdcaabbcbdadddbccadabddddbadccdcabcacbaaddaddadadcbbdcacdaaacdcddabaddbcdddaadbbabbbbcdbaccadbcbbbacaccbcccdaabcabaadddaaddacccbccacddcbadacadacbbcabcaccdaacdaababccaabaddccadcdbadbdddabbcdadabdccdcbddcbccbacacdcaabaccbabbdbdabbbcbabdcccbaaaabdcdadcbcadcbaadddccbadcbdbacdaacbbdccdbccddbbddcdbddabdddccdabadbddbdadbcabcdcbcacaadddbccaabadbabddcbbddaaaddbbccddabcbaacdccacbcacabadcdddcbcabacdbcabcbacdcdbaaadbbabcbdcbadbbadbaadaaaabcaddaadadbcbdacccddaaacddbabbbdaaaadcbacbcbdcbdbbcbadbccbadbcbbcdaaacdddaacdbacabbddcdabdadacbdadbbcadbbaabbcaacbdbdcbbaadabddcaaddbdcbdabaaaddcaacadccbababbdbadabaacaacadcabdbcbabdbaabaccbdaddadcaabadcaaacbadbcddaacacddaaabadccdaaabbabccddbcadbaacdacaaddabaddcabdbcbaccdcdcdbaaabbcadbaddbdaddbdddbcbbadacdbabdbadcdcdaaabbccccbaaddaabbabddadbccbcdbabccccacaaaaccbccbcdbacdbaddacddaabcbcdcccadbacdcddabaabcbccbbcddcabdcdabcbdccabcaaacdcdcccdbdccabdcbadabcbccaddcaccdccadacbaabbbbdaabaddcdcbabdbadcdcdddcbcdcbcdcccbdadcbcaacbaddddbcbbdccdbbbbaaabddabcdaabbadccbadcdabbcbdddbdcbcbbcacccbcbbcbcaabdadcaacaaccdbcabccbacabbadbddcbbcaddcbdbbbadadabbdaacacbabccdadcbbcbccbacabdacacdaccccbddabaadbdbabbbabaadabacadbadbaadddcacaabbcbbcdabdacbcbbbbbdadadabbbdabbbddbbbdbccadcdadccbcdcdcadcdbacbadaabdaaaabdcbbabaabbdcbdccdcbacdddcdabdbccbdbbbabbabaacaadccbbacdacbbccdcadddaccdbaddddabdaddbccacaadbabbcacdcbccaacacabbbbbaddbdbbabdccbbadcdddbcddcddbbccbcbdbcabcdcbdddbbbdcbccbabbaacbbcaccdacaababaccaadddcbbcacbbdacacbcbdbbbadadaadacaadbccbaadddabdbcbdcaddcaacddcacdddaadaadabbcdccabacdbbdccbcaddabcbbacaaccacccbcdcdabcddbbcbacdadcbabcacddcacabdaadbddbbbabdbccccbdaddccbddccaccadaddbbcbbdcdaadadacababbaabbddabaccbcdacbbdadccbaabdbaaabbcbabdbacdbdbbabbbddacadcadcbccbddcadbbbbccbddabcdabbdbdbcdbdacbbaaaaacbdccadddadaaabaccdbcdcbdccbdcbaaacbdbbabddaabcbcdcbbcabccdaccdcbacdcadcbaadcacadaaacbbccdddcddbcbdadbcadbcbcaddbaadddccaaaacbadaacdcabcccdbdcccdcdaadcdaddbbddabddcbcadbbbddddbdcaadddbaccbccacdbcdbbcbdabcdddcabdccbdbcdabaadcccddaaddbccacdccdddacaddbcccbbcabaddbdbcbbccbddaaacddcaccacddaabccdaccccabbaaccdbcaadcadbddbbbacdbdadbddcaadbbddaaabdbdcadcadcabcbcdbbaaabcbdbcbaabbbbadabcbbddcdababccdbadcabcbabccbababbbbcaadcadbbdddcdaadacbadbdadbadbabaaccccabdcbadaaaccdcbadaaababaaabacdacddadbccbbcaaddcccdadacaabdbaadddcbcaddcbaadadccdcbcbdaacbaaaaccabbdaadccababbabccdbbdbddacacbababcddcddcaadbbcdaccbcbdcabbbdcccdacccaabcdacdcbdabdbddabcdddcbcddabcdadbbcbcbacbbddbbcbbacddbacdaacbbdbadcdaaadcbdddbdcdacdbcaadbbaddadaabababadddcadcccaddccddacddbbccbcccccdcadabaaddbbadcddbdbbdbdbcabbacbacdbbcadcbcaabccdbacdccbababadbadcabbcacacccbcdddbcbdaddbccbabbccdacaccabbdadcbbcdbbaccaaadababbcdaacadbccccbdacabdbcdcacabbdcbbbbbcdaddddaaacadcdddbadabbabacccbcbadbacdaccbacdcaccadbdadabddddcddaaaddbccbcdacddadaccbacbbbcdaabdaddddbdcdaaabcdabccdadbbcdacbccadacadbddbcbddbdcccacddddadcdcddbdccbbbabadcbddabcaddcacaabdcbbcbddbbcdaabaadabaccbbcdbabbbcbbdbabbdcccbacdbcbbcbbbbbbdbabcbaaddbcbabcadadaddbabbdadbdabcbabdbcddaddcbccbccbcccbadcaabacccabcdcadcbbaaacbcbcbccacdbddbaddbbdcdbadcbdadcdadccacddbacddbadacdcadcadbdcbbdcbcbcabdababaabaddcbdadbacbbacbdcadaadaaddcadacaabbbdbdcaadcaaabcdcacddaddaadadbbccdbdbcbaddbcadbbbcacdbaaabcccdcaddddbddcabddcdcdbbbcccddbdaadcadbdbbcadcdcddcbbcbbbccbaaadcbccbbdddcbbbcbcbdbcdaddbbbccccdccadccccbccaccdcddabcabaddcccbcdcabadcbccccaabaadcdacbabbdbddadabdbccdccabccbcabdaddadbadabdcaccdcdcbadbdbbacdbbbdbddcdadbddbbabdbccdaadaabdacbadabbcbcbcddddadcacabaaaadcdcadcccbcbdcabcbddaacbbacbcdbcbdbabccaccbcdbbacdcbaadbbbdcdbcdaccaacdaacccadbbdadcddaabccdacbaacddddccadbcbddcdbaddcbccadbdddcabdcdabcdbacdbddaaacbcabbccbcaadacacdaacdcbabdaaadcddcddbcdcabccdaccdacbabdbcbbddddbcccdcabbcccdbaccabcdcaacdcdaadbbacacdbacbaacbaaadadcddacaddacbdcddadccbabbcbdacdcdccaddaaaaddbdddcdddbcbcadabbcbabaadaddccdadbdaccabdccadaabbcbabbbcbaababdcdddcadbbdcbcbbddddacccacbcdcbcbbacbcdcaacdcbbcbbbabbcbdadabcadabaaaccacaccbcccadbbddbcaccbdbabbcdcbcbcaabccbaacababbbaddaccddaddaccaddccaddcacacdbbbcdaadcacccadadddacacaddadcdbbaddcadccadacaacbbbadbbddaccbbbccacbabbcccdcabdadbcdcdbbaadccdddbdcbcddbaaadcccbcdabdcdacddddabbabdbbdadaddcbbccdddcbbabdacbacddbcadacbbcbdacbddabbbddbbacabdbcdaaadbbdbbbdbadaccacacbddaadadababacdbbbcdccdbabcddbdaabbdddaacbadaddaaaaccdccbacadabdadabacdcacbaacbadaddadadcbcadaddbbdccaadcbadacdaddddbcddbacabdcadcdbdbacbbccccaacbaadaaacaaccbcbdbdcbddcbbadddcbdaacdbdcdbbcbcdbdabadabddbddcdaacccddcadacbcbdaaccbbddbaacbdbbddcbaccdcaccdcbdddbddccbdacabdbaadccdbcbdbaaccbbcdddcdacaabccddbabcdabdcacbabdbdbacbbccaddcadbcccdcccddaadcbddcaacbdcacaabbcccbadccdbdcdcccbbabdddadcaaaddbbaaabcdcbbdadcbcdddaababbddaacbdcabcbcaacbddcdbcaadbcaabdabccacacadccbbbdbbacadadcdabdcdcbabcdaaddbdbcaacbacaacaacaacababdcddcabdacdbabaabacaccabadacadacacadddcdcacbccadbdbadcdacdccadaacacbadababbbdcaddbbdcdccaaacacdbccddcaaacabbbbbacbbbbccbcbaaabbcddbcdcbbaddcdcddddbacdacdaccbdcabccacabbdacbcdcbdbccdaacabcacbdcbbddcbbaccbbbcbccdccbbdcaadaaaadacadbacddbcabccbadcbccadccdaadbdddcbdddbccbabbccdbdbbbacddbddadadbcbccbddaacbccabbbdccdbadbaccaadadbbdbdadcacdcbcbddcbcdacaacdddbcbcbdcaabdabacbacbbbbcbaaccabdbbbccccacacaaabccdabbbdaabdcdadbcddadbacabddcbaccacccacbddacdccadddabdbdbabbcccabcbdbabbacbdcadbddcdddcababbcbddcaabcbbbbbdbbbdcacadbbcbacccadccacccaddaddbcaabaadcabadbaabcdbccbabbdcdaccbcabbaabbadbabdabacdddcacccabbdcabbccbdbbdaadadacdbbcbbccadacbccaaacbbcbbccbdacacadabcaddbcdcaddcadcbcbddacbdbdcaabaabbdcccbcadbdcacbdbbbcaccccccbacbccdbdcbbdcacdbcdbadcdabbbbbcdbcdaadadbcbaccaccbbabaadcbdcbccdabccbbcabadaccdbbcdcbdaaabadcbdbdcbcbcaacdddadbdaddbcabcadaddaaadaabbbbcbbababacacbacbcdaadbdcaddbddacdbabbcbaddbbbdacbdadcddbbdaddbdcbadbcccbdbbdccdacacbbaccbacacdadbdacbcabcabadcadadcaabdcddaabbacccaacbdccdcbdabdbbabdbdaabccabddaaccaddbcdbdbbbdcbdcdbdaddabaddccdccbcacbacadaddadbcbadcddaacdaaccbaadcacabddccddaddcdaaadaccbddbbcdabbdddaaaadadaaccaccbbdbdbcacaccacdacacadadaacdbdadbdbbbbbccdaddabbbdccbdcbdccdbcadddcbbadddabbcbadbdacdcabbcdcdcabaccadbcaccdccabbadbaccdcbaddbdaabaadabddabddbacaaaccddaabdacaddacbcbacccacbacaabcbbccddabbddcccaabdbbacbdcbcdbabadbdabaabdcddadbabddaaddccdbdadccddaadabaacdcacacbbddacdaabddadbbaccccbdbaabaadaccacbbdbabdcaccbbcaaddbcbaacaccdcdadcdbddabcacbcbdadcbabaddbddaacbddbaaacadabcbabcdbdbdacdbbcbadcbcbdccacaabbdabbcacbadbaddbaacaacaddcdcaaadaadbdadaabddccdcdaabaaacbbbdadbdcdbdcddcddabdbcadabaccdcbddccdabaccdaaaabdbcdaaadcacbbcdddbbdccdaaabaddcbdbbadadacadbadcddccdbccdbccabcbbbbddbcaccdbbbbbbdadadaccaacdcaaabddbbbcccbcdbccabbadaccbbcccbdbbadbcacdcadcaacddaacbbbbabaddbcbabcdddbbcbccdbacadcbcbddbbacaaabababbcbbaddadcddbccaababbbddbcabbbcccabbbccbddaadccddcadccdcbdbadccaadabbabbcccbcdcabaddcdbbbbcabdbaaabbcadaadcdadbbbadcbadaaddbaadadababdcdbdbacbbcdbabacdcaabccbbaacbdabcbdcacdcddcddadccadabbbabcdadacbadaddacbdaccdbcdcddccadadddccdbbdaddbadbdcadaddbaddaacaaacbbbacccbbabacabcccabadcccdcdbbbabacccdcbcabaccaadbaaaacbddbcdbcbddbdbdbdacbaacdccbdcaddbbddacdcbcbadddcabddcbcabaddaccbdccbabddcaadcaccdbcbdcbdabbbdccdabbacdaaabcdbbccbbddbadbcbcbdbbacdcbbccbaabaacdccbbaddbbddbbcacaadbbbbbbbddbbdacaccacdcabbbaccacdddcbabaaaddbcdbccbbbcaddbaacdabbcbdbcaccacabacdcbbdbabdadbacbbbddbaadddbdbbbddccdddbaadababcbaddbbcdbaadaadccdaabdacdbbcbdbcbcddbabcadabbaacbdbaabaadccaddacbaadcbabdcaccddabbaabaadadddbbabcacbdcabbcbacbaabccabadddaccbddaacdabcbcacbdcccacbadaaccbccadbddaaacdaababcacacdcadadbbcdcabacabcdbbbaabccbdbbbdcddddcbcdcdabcdadacccdcbcccaccbbdcaadcdddcaacccacbbadadcdabdcbdcaaabddbbdbdbacabaabdbcadabaccdcbddbccdcacadbcaddddbabaccccabbcaccdabddbccccdcadbdbbadbdbadadaaaacdadbdacabaccdcbdcccbbcbaaabbdddbcdcabbdcabaacddbbdadbdcccdbcabbbadaadcbcccacadaacaaaabcbcdbdaaacbbdcdbbbacdababbbcbcbaacdbaadadacdabbcbccbaadcadaadcabcbdadbadcddacbcbdbdcbbccbdcadcdcabdcabbbadcbbcaaaaddcdaaaadbbaabccadbaadcccddcaacadcadacddbbcccabddddabbcddcbbcaaccdbaabdabadadbbdabdcdddcdccbcabddbbbbdcdacadaabddaabadcaccacdaaaaaabaddbbbcbcdccdabccdbbadaabcabdcadccacbacdcdaadbcbaabcccdbbababbabddadddddbddcabcccbbabbbccaabdccdbbaaadbdabaddcaccdbbdabccdcdddbabddbcacaabdbdabdccbcdddcccbbdaaabcbddaaabdbacaaacdccbaccddacbccbdcddbdcabcdcbdddadbcabcbbdaadacdaadcdbbbcdaacabbacddabcadadaabcccbdbbbdaadbcdcadcabbdcacaccabdccddcadcabdbbbdcbcbaabcadcdccdcdccddaddaccddabdbdacccdcabaddaccccbcacdccaaccccdbcbdcbdbdcadbcddbbdbddadccdddadccacdbbbbdcdbcabdbaccdabbcdaddaccdadbbcbddcdaacbdbddcaabdaadcbdbbbdaacdddadbcdadcbcaabcbacbaacabccdcbabadaadcbddbabccccadddadbcdababcbcaccacbcaaadbdbbacbbbacbbcbccbddaaaabcbdcbabdcabadabbbabdbcaccadbadbbccbddddddcabdbcabcaabbabbdbaddbbdddcbbadacccdabbcbddcddbbaacddaaadbaaadcbdbdbdcbadbaaabcabdabcbddcdbccbbbcacddacccbdccabbdbcaabccdcdbdbccaaacddbdbbddabbbdccaabadbdcbdccaaabacdaadbcdaaaacaccbcbdadbabcaddbadbaadcdbaccdbabbcbdbadbdcadcccccdaaccdcadccacbcdccbdadcbacdccdaccbacadadadbdcbccbdababcabadbabbbbddabddabaadbccabdddcdcaadddadccdbdbbaadcbabccdbbcdaabdabdacacdccbadabadabbcabbcbbddbcdbdcdbcaadaabcbdcccbaabdddaccbcabaaaadaacadbcbadaddbcaabacccdbdcddacdcbddacaaacbcaacbbcbdaaacbcaadcddbaddcccacbabacdacacbcaaaaaccdaddccddabccdbacddccdbdadccadbdbdbdaacaccddcaaccdbdcaccdddcdcaabdaadacbdadcbdabbbbdabdbbdcadcdbddbdcacdbcabcbdbbbabcdbbcdabacbdcabccadaabcdbacadcdbcdbbbcdbdbbacacacbbddadccdadcdcdadcadbdbcddbdabcdcbababcccdbabccdddccdcaacccdcbdcacababcacadccdccbdbdbbdbbbbbdbbdbaacdbabdbcbbccabbcbccadbdbbdddcbcbbaabbbcbcaddacdcddccddcbcddddaaaccbcdadaadccaddbdccdadcabaddacbdadbdaaccccbaddccbbaddccdbccbccadcbaacbabbdbabbcbbbcdcdccbdbccacaaadbaadbdabbbcbbdacddbacbddadddbbcbdbcccbbbaacaaddbbdabaaabdbcddbbacabbaccdbcaabddbaabcbabaccacdbaaddccaadccddbcdbcacacbbadcacbcabbddddcddbdabccbcbcadbcdcbcbaddbaadcbaaadcbbcacbdbdbcadaaadabbdbcdbabdbbddbadcccbdaacaccdadadcdbddcabbdaaadcdcbdcddabcabbbdadccdcddccdaaadbaacccdcdbcbccdcbbdccbcccdcdbcbcbdbabaccdabdccbcbcabccaacaaaabddabdcbadbacdbaabbdccaabccaaadcacbbadbbabadcbadbaadbdcccbabbabcaaccaabdcacdbdaabcadbbcdbccbdbbbacdadaadbaacdccdccccbcdbbbabacadbccacdcabccababbcdabdababcabcaadcbbadccdccbdbbccdccacbdcdaaabddaabbbacdddbbccccabdcadcacdcbbbbcbacbcbbacadcddaadabbcadbcabdaaccdbbcdaabadcabcdababacbbadcbcaadbdbcbbcbcdaddddadadaadbbcdbddcabcbbacbaadabbcabddbbbcacdaaacbbcdadcaabaadbadabadbcbaddbccdaddbbbdcbdaaccccadabcccbbdbbccbaababbddaaabddcabcadcdaaaaadaddbbbcdadbbbdadcbcaccaadbccccdbcdcbadccbbadbcddaaccbaccccbacbbaaddbbcdddcdbacacaadcadbdcabaccdaddaaccdbdbabadcacabdbdccaaadabdcddaddacbddacadcabddacbdcaccccaaabdaaccbddcdcbaabbadbdbaccbcbbadadcaacaaccbaaadbabbdccddadbbdaacbbdcadddbdbdbcdaccbadccbbcccbcdbabbaaddccbadcadaaddabbadaaabdbadcdaddaadcbcbaaabbcdccdcbbcdcbdabcdabdbacaaaabcbbabacbddcabdabcdaacdbaaaccbbaacbbcabbacdbdddcabddcddbbdacddcadacbaacadccaabcabaaddbaabbadbacbcddbbcbcbddcdababbacdacabdaabbaaacdbbadacacccaadacddaabbddbbdcaaddbbabdddcbbbadcbaacdabcadbadbbbcdbbbcddbcbcabdbdcddcdcdadbacbccbaaccaadbdbdabcaddcacadbcadcdaacccdccdbdbcdacabdcabadbadbcbabdbbbcdabbbdadaaabddbabacdccbbdbacbcddddbddabddacbadddcaaabddcadabaddbccdaaddcbddccbbbdcbcddddabdacacdbdaaccabcaccaaddaddadcbdadccaddabbcbbadaccbabdaadbcbadaabcdcacdddbddcdadbadacdcccacabadddddbbbbdaaaabbdabaabbadcdddcbbbdbbcccaaddabadddadacbbaddacbdccccccbcaadcdddcbbbaccbccbdcdbbdcbccbcaaabddacacaacabdcadccddddbcadcacbdbbdbcdabcbbbbcbccddadbcccbdccacaddacdcacdbabbdbccbadaaaddbbadcccdaabbabadddaadacdacacaabdadbdbadcabadabbdbaadbaacbaddcccaddbcadacccbbdcaaccaccbbacbbabdbbcdbbbcababbdcdddadcbcbbbdcadbdcccdbacdddaadabcdcdcbaadbaccaadadbbadbcabddacacadcddadbabdccaaaabcccbcaacaddbdbaaaacaabcacbdabadcdaadcddacaaaddbcbaaadccaabbdadaaaacbaabdccdcbacbcbbcbbddbbcbbadcbbadbdddcbaacbdacdaacabbabcdcbbcdcaaddccdbbbbddcdadcddcabccdcabbbbcaacbdcccdbadbcaacbabbabddccabbbaaccddaddadbccbdccacaccaadaddacadcdbabbdacddbbdacacaabdccbcbbcbdbbbdcadcacbbdcaaadccaadccacbdccababacaacabdbaaaadbbdcaccccaacacbaacdcbdbdaccdadcdaaaccabbccabadabdcbbcdbabbbbaacacdabcdabacbccbaddbadabadcddbbadaadcddabdcacbddcbabaadbbbdbbdbcbcdcbaddadcbadadbdbcaabdbccaaaaacacadcabdbcbaaccbbccabcaccadabdabdbaadbdabacbcaabddaadbabbabaccccdabbabbcccaabcdcccdddabbbaadbccdcbcdddbcadcbdcaaddcccdbbdcdcadcacccbddcbbcadbcddbbdbabdcaabbaabdccbbdabbcacbbbbcaccabbaabacbdbdddcccacadddcbcbdaaabdcbbacddcabdabaddcadbacdddbbdaacaadcadcdddabbbabcadcacabbdbbddddcbddaddadccccbaaaabadbbbaccdcbbadcdabddaadbbaadbcacbabbcdbcbcaccbdaaadadcadcdcabbcacbaadbcbaadabcbbbcccdbadbbabdcaccbcddddadcacaaacbcbacbbdbbbabccbbadcbadabbacacddcdccdcdabdbddccdacdccdaacbcbccbadcdcadbbbcacbaadcaccccccaaddcaddbcacdcdbbacbdaabcaaabdcdccdbdaaadddbacaaacdcacddbcaabdadcabbbbcaabcbbdacaaddbbbaccdabdcdddbdabdcbacdbcdbdcabdccdadbccbcaddcbdbddadcacdccbdcdccdcdaaccccdbbccaddbcdbbccadbcbacbbcdcbbdbbcdcdabcabbcaaabccabbadbcaaaacbdbdbadcbbccaabbbacdaabdcbccddcbabdabcaadddabcbcaadaabbcbbadbcabdcdadadbbbdadbbccbdbddbcaadcdcaccacdacdabbccbcbddccbbcddccdacbcbdabbadcaddddddbbdccdaaddaddbcdcdbccddcddcdddadbbbbcddbaddbdddaccddbaddccccbccbaabaaabacbddbccddbdbbacacbbdaccbbcbccbabddabaaadccabacdbbdccbaddccdcccdcbdabcbdbbbbddcaddcacdbaaacdccaccbaaccbbcbdabdaadbcaaddbbadacbaacadbadcaacdabdcbaaddddbcddbcacddadadcddddbaaacdcadbabddccccbaabdddbddacbdbcaaabadcdbaaadacbadbcbaaaabcdddddacacbdcdbaccbdddbdbcdcdbacacaccaadcadbcbcbddabdacbbdadacbddadbbaccdcdbbcbbdabdbbbdaaadbbcccacadbcbbadacdbaaaddacabadcbbbbcdbbbaaabcadcdddcdbccddcccdbdadadddccdabbcaabbcadcdbbbbcbcabccacdadcadcdcacbbaddaacddbaacacbbadbcaabadacaaaaddabbababcdcdccadbacbdddccaddadcbdddbcabbdcddddbcabcbcabcadcbdadaddcbacdccbdddcbaabcbcaaadcbdaabdcdcddcbcabbcbbcbcbbcaccabcaadbcacdaaababbacacbdaadaddbdccadacdaaddabddcabbacacdaddbdcaabbddddabbdddcdbbbcacbccdabbddcbddadbacbbddbadcbdbcaddbdaccacbabccdccbbcccdbbaacddddcbbbdcdaddaaabbabdcdddcdbdbbbcbadaabaaaccccccabadbabcdcdaccccbbbcaddbdccdcbcaaabcaaacdacbabcacbdbdbaadbcabbcdbbdadbbdacadcdababaabbccdabbcaadaddcbbdabbbcbaabbaabadadbacdcdadbbdbbadaddcdaabcdaaddbacacaaacbbbacbccaabdadcadbaccabadadabdcdbccadacabcbdbdcbadabaccabdcabcbdbbddaddabaccbabccadaaccbaabdbcbabddcdcaccdcaccdcbbacabdadbabbdababcdccbacabbcbcccacccdbacddbabcaabcdcadccaccdaaccacdacabdcdcccbccadbcaabaccbbacdabbacdbccbcdbcdaaababbbaacbaccdacadcbbcacbcccbcbcdcbaadccadbdaacdccdbdddcacacaddcbdcbaaabbbcdbbbcdddaccccbaaacaddbaaccdaaccdaaabdcbcddbbbacabcadadbaddbdccdcdbdaadbadaccdbdccdbaddbbabcddabbcdcbdcaddabccbdbcadacddbcabcbbadddbacbaabbcddabbadbdcddbadbcdacdbcbcdddabddccdcddbacbabbddaccbabaacdaacbdaabaadbdbcdddacbacaabdbcacabdbdddbcccaaaaaadcaabdddbbdcabbdaaddadddddcacaacdcbaabbbaaddabcdcccbdbcaaacddbcbdccbddabbdaaaabbdaacdddcbcdcddcdbcabcbdaacdacaacccdbbccbaadcbadbdacdabadddbbddbbabdcbdadccaaddddcaccaabadccddbcdcddabdaaaddcbabddcccdaddbdacadaadcbbcdddbccdaaccbadcacdbbbcbdcabbcdbabcadacbbcdbdccdbaaabbcccdbdcabcaadbdaccdbacbacbdbcdbadbccdddabdadaaacbbddacdaacdcbbdcaaddcbdaabdcccdacdacbdbabadcbccccdcabbacddbaaddbdcadbddabbdbaaacabdbbcdbdacddadbbcccbcdbbcccbdcacdcaacadbdccabbccdcabddacbdccbcbbcdbcdddcddaadacccbacbdbcbccbccabdaddcbddbcbdccbabaccabbcacacdbcabcdcbaadadbabcacbdddbbabdaccdaadbbcdaccdababbdbdcbacdcdaaabdabcbdbdbacddddcbabaccccadadacbdcdaadbbadbdccaadaabacbbabdcbadaadabdccdadaddadccccccddbcccddcbadccacdbdddbddaccabcaabdbaabddcadccdbccbcbabccdcadaddaddadbdacbaadaaacbabccddcaddbacdacbabdaaadcdbaccbdacddcaaadbcadaaccccaaaddcdbaccadacabdabddadbddcababdbbbbbbcbbdbddacaadcbddadbcbaccbacccdcdcccacdbbcaddbbaaddcaccbddaaaacccdaabddbddbaacdadbddcababcbdcbdcdcdbddcbacbccbdabdbdcacbcbacaaaddccbbdaacacddbdcbbdcbdabcbbccdbdaabaabdbdaabbccdcbbbdabbadabdcbadcacdccacaabdadbbdaaddddaaadcacccddcdddcdbccddbaccbaaacccbacbadbbaaacbcdbddcbdabacaccadcadbddcabdaaacdadbbacabaacbddcdabddbdddbbddabacdccbbdcdbddaadabcbccbacdbcbabcabdabdbbcccddcbbbcaaacabcabdbbabddccbdcbbdababbabccdcbacdbdaabbdcacbadabdcabaadcacadddbbccdabcaacdddbbadddbaaabaadabdbaabadaacabacdaabdbadcdabcaacacdccabadddbbabbccddcadabacaaacbbcacdbbcaccadcdabbdaccdaabdbccccbdababccbbbcdbdcacadacacbbcbaaacbbbcbccbacccddbaaabdbabddddabaabcbabcbacabdcdaadaccdcbbbcaccadbbccaddabbddddbcddbdbabdbbddacbbaccdbcdcdcabddccababbccabaddcddbbaacbbabdcaddddccbbdbcddbdbccccbacbcdcababaddacdadbcddcabacbaaabdbdcbcabacddaaadcccbcadcddcaddcabdcaccaacabdbaacdaaacdacddadccddbcabcbdadadaaccdacbbccbacacaccdbddbbdbbcacadcaabadacdccdaddcaacbacdadddbadccbcadccdcbbcdaadddcdaccadbddbdddbaadcddbcbbbcccbcaabdbdbadbbbadbdacdbbddaaadbdbcbcdccbbcadcdaadcccbcdbabdddadaddbbbbbcbbcddddccccbaaaaabccacdbbccabcbcbdccbaccbabaaddadcbdaabbcaaacabdcaabacabcdcacbbaacccddccbdbabbdddbdcdcdaaccdcbbacccadcacacacaaacacbaccacbbadccdccdcabaaccdcabdcdaaacdbcdcbdbaaccbadaccbdabcaabcaadabdabcbdaddccdddbdccdcdbbbbbdccdbcbdbcdbdccddbbbcbbacadccacccabaadcadacaccadbdcaccdcbddadcbaabdbbdacadadadadbaadcdcddbdddcdcbdcdcdccacadbdaadbdadcdbbcacbaabacdacbdacaaabbaddbaaadbccdaabbcccddbbbdacddababdcdddbcbcdbabdbcccccbbdcbdbaccbcabddbadcbdaabaacdacdbcddaadaacabcbbbbabdbbcbbcbcdbadcddcbbcdbaadadddcabaddcddbbdaacbcccbaacdddaaaacacbacbcbdbdbadbdadbbddaaccbbcbdacbbdcddacbdbcaaccdcbdcbddddcbbddcacdbbaccacaccdbcbdcbbbddacabbdabacabacabdcbddacbbdabaacdcacabccaacccdccdbbbcddcbbdadccacadaacaccbadccadbcddcdbadadcabbbdbcdaacbcdbdbdadcbaabbdcbcdddbddaccdcbbbdbdacdccacaacbbbadddddccbccccccddcddabcbdbddddcbcbcddbabccbdcbcdabbbccdccdcbbbcabbdabcdaddbadcaaccdabdccbbadddbcbcbadadccdaddcadcbcbadaacbbbcdccabbbddddcbccbabbddcbcbcdbdaacbadbbdbdabdcdadccbbabadabbabcbddddcbdccadddccddddbcdddacdccadcacdbcbdcccccbccbddbbacbccadddcdbbaaddccccbbdccdcdabadbabdbaaabacabdbddcddbdbcbdcdcbcbcdddaaddbadaababdccabbcacbbcaadcbddcbccbcdaaaacbabaaacbcdbcdbabdabbdbcddbcadacbbddbbbddaddbbbabaaaabaccddacbcdcbbbddcbbcaadabadaadddaccadbabccbdccbaabdcbdcbacbbaabbcdbadaabdccbadbdaabcbcbcaddbdbbcbdcdcdcddccbcbacadcdbdddddbdcaaacbdbdcdccccadbbdcacabdabaddbcaddaaaadacbaabbacccdcbddcadabdbbaaabbdbddbcbabaccdaddbcbacbdccbbdadcdbddabdaaaddcdadcdddaaacaddaaaccbaccddbccdbdabbcbbdbbdbdddabdbdcadbcdababbcccdcbdcbbacddcbbdbbaabbbdcbdbdddcbdbbdcbdcccbbadaabaabdbbaacccdabbbadaacdcdbcdbaddcbddadddcdbbabddcbcddbcbbbdddcdaacdbadccacddcdcdcabccabdcaddbadcbcbbbddcbcacdaddbcdcdacdcdbbdcaddcdcabadabcdbcabdcaaaabdcddabdabbbdddcbbdbcadacbbcdddadbcdaaccddcbacbacbabbdbcadddccbcdabacdcbaabcccddddddaacbabbcbccacdbcadcbdddacdbababcabaabdacdcddaabdbbbbbdbbabdaddabcbbabdadcaaaddccbabbdbccdcaccbcccdcacdadabddaddacdacdacdcdcaabbdadadcbdabdbbdaaccadcaccdcbadcadbddcabcbacccbbcaddcccbabdbcbdbdaacddbccddcdaddbabbcbbbbaadbddcbccdcbaabcaddbbcacdcccadddcacabbcddbabaacdacaaaabbccdbabcddbdabbbaadcabbdabddaaaaadadddcdcdcbcbbdadacbabcbbabbabcbdabdcabccccbdbdcdcbdadcbdcdacbdbcbcacccadbdbaabbbddbcbddbdbcbddbadcadbbbbbccddbcbbaabbbaaddbdaddbbdaddcadabaddbdbcddbbabbbbbdadbcbdbccdbaccdbadcdbdabdabdcddbbaddaabacccaabcbcbdcbddaddaacaddbddbbbddcdccbbcdccbacbcbdbababbccbaadddbabccdadbbdbbbbcbcccbdbbddadbdaabcacbaddabcaadbcbbacaaadacbdcaaaaabaccbcbdbbdccacbcdaabcabddbabbbadbadccbbcdcccddababadcddacdadadabbadadbbccddcdccdbaddcbcddbbcdbcbbbdabcdcdacabdadbccbadbdcdcccbddcdccdcccddacbaaabccaddbacdcbabbcbbdcacdabbdbbabccccdcbcbcacdcbcddabacbbaaabadcbcdbaddbbacabdcdabbbcddbaaddbbccdbdccacabcbbdcacbbbbcabdcbbcbabbdcdaacdddccbdddbbbdaacbdabdbccccabbcbbacdccdbdddccadadbdddddbacadbcbadbbbbdacdbacddbacbbaadacadcadbadbdabddbdddbddbcdddadacabbddddabbaadcbdddbbdabadbddaacdcdccccbcbacadabdabcbbbaaccccbbaaadbbdbcdccddcbbdddadbcbaddacbcbbacddbbabcbbcdbcdbcbdccbcbddacbcdacacacabaadddcbcbdabdcbdcccaabbcbbcacbcbacadcdddbcacaaddddcccbddcdddcbbbdabcabcaaacbdbbdcbbdbdacddcadaaddccacbbbdaddbdbabbbdbbddabcbbcbabbbdddcaacaaabbcccadddcdbdbcaaddccbdbadbcdacdadabbdcbccaaacadbdbbcdccdccaabdbcadbdbbcdcccccdccbbbdaaabcabadcaddbdacbcdaadcdabbdbbbcbbdcbdaccccbcbdadbbabacdcdccccdaacadbbbabadbaddabccacbdcadbddbcdaddbbdbdbccacbaccdbdbbdadabadbcabdcaadadbbcbbdabbaacbcbbbcdbccaddcadbadbbccaabddcbccdccbadbbdabadaadadddaaaaaddddbcbabcdcacabbcdbcadabcadddcaaacbacadddddccbacddccabdbaccbccabbbdabddbadbcdccdcccccaaccccaabdcbcccdbdabadcbbbbaadbdcdbdbccbcabaacdadbddbbabdadaabbbcdaccbdcbbbbacbcacacdbcacbadcdbcdbdcaabaaacdbcbdddcabcdaddcccdbcdacabccccaacdccdcadbccaaddcaaacdbcbbcadcdbbbbbcdbdbcdbaccdcabdabdcdaabaadcdaccbccdabbbcbcbbabbbdbdaababbcbcdcdaccdbacdbdddccbbcbaccbbcdbacadcabcbcabcdadacaccccccbacaaddabbcaccadadadbdacbaabaabdcdcbbddaadabcddccddaabdccbcdddbaacbabbaddccbbddaaddadcccdbdccaadbbcaabcddcabbabcddcddbcbcabccbcbcdabdaabcbbddbbcccadacdbcaadccaabbbbbacbccdbcbdddcdcccdaaabbbcccbcaacaadbcbddcadcaacacadccaacdcabbbccbddbadbdcdccdadddaabddbddcabaabadaacbdcddabbdcccdcdbbaaacdacbdbabdbcdddcccddcccaabbadcdaacaddacccaddddabcbaabddbbbbbcdbbaadadacdcadcabdaccbdabbcacbbccbaaacdcabdbcbbbaaadbdcdddcbbdbadabbcbdddabcabaaadcdbcbbdbaaacdcccadaacbcbbcabcccadbdbaddaaccbadbbacadddbbcdcdbdacddacddddacbccdbabbaccccbadddaaddccacadbabcbcbddaacadbaababddbccbcbdaddcaabdddccddbbadbaadbcdadbdabacbadacddacabcdbacddbdacdcbddbdcbaabccdaaaddcabdbdccaccbabacdbcadbccaaccacabdbacccaccdbcacddccaccadbdaacbaccbacbbacccadbbbadabcbdabdbbccccccbbbabddccbdbbacbbdabcdbbbacaccdcbadccdbdadcabbabcbccabcbaaaabadcacdddaccdbbcddbadbddccbbdcdddaddbcdcadbbddcbacacdddddcaddbdbcbdaabddaccbacaadadcabcaabdbcbdbdadcbcaddadadbccdcbbcadbdcdbaabcacddabcdbacbddbddcaabdbcdccaaacbdaddbbbcbcccabaaadbadcddabdbbadadadabccbcddbbbcdcdbbbddabaaadabbaaddbadbacbcacadcdcacbacababddacabcababcdddccbaadcbcaccabacbbbdabdcbcabadcbcbdcccacaabcabcbdabccaabbccbbaaaadbdcaacadbabcdbdadbadacccbbaaadbcdbdbcbccadbbdbccdccddabccbaddccacbccaaacadcdbcaaaddbbaddabccaddcabdabbaacbcbbdbdaabdcdbcbdadbacbdcbccbabbdccbdbabacbbacbbdadbdbadbabbccbababddcbabcdbdadabdaaaabaabaaabbcbcbcbaabdabbbababcadccacdabbabdbbcdcacbacdbcaccbccacdcbdbccbacadadabbbbdbcdbaaabcbbbbbacdcbbdbcdadacbddddbbaddabccbcaadccbbdacdabcddbcaccccccadbaaaaabcdbbbcaaadddcabdcdccbdaaddbbbdcbbccacddacaadcaaabdbccabcdaabbdabcdccadccccbaaaaadabbbaadcbdbabdbacdccbddcbddddadbaacaaaadddadadddacaaaadabccdbbbacacccdbabdbadbbdbbbabbbdcaabddaddbaacabdcdcaaabbbbbabcacccacddbaaadbaadccdaccddacaacadabcdabccbdbababbcabdbdcddddaadbaacaaaabadcbaaacbdacbdaccdaadccdcbbbabbcdabdbabdbaaddaababacababaaacabcabddddabdaaabdabdcbbcdcaacbadbdacbdcacddcdadacaaddacadbaabcddbcaabcdababbbdcaddcdddabaacbcdccaddbadbcadbbcccdaacbdbcdadacaaabaadcaabcdddabccdcdbcccdcbaddbbbaaabddbbdcaabaabcaaaaccbcdccdcccdddbdbcacbccaacdbcbccdbdcbababcaadbdddabacbcacabcaabcddcbcdaabaacbdabcbbaddadddddbacddaaabddcccdabdcadadddaabbcbbbaaaaabccbdabacabdacccdccccddcddbbacbbaaddbdadddaaabdcbbbdaabdadaabbcbcccaacabbcdbbcdddaacbcdccdcacaccbdddbcaabbbacabbcaabaaacbcbbdaadbbddbccadcbcbaabbadddbadcadcdcbbbcbcccccddaddababddbcbaabccaddccbaacadcadaaacdbcabacdbadbdbdbcbdacacdcaabaccdbbbacddadaabbdbdbddccdaaabddacdbaaddddcaacdcabacdbdbbcbaaccacdacadcbccadccbbddcadccccabaadcacbacdcabaaadbdbabbddddccccdccdabacbaccdbdaddaddbdcabdcbabaccacdcccbddbabdabdbabacadbcbaacdbddabdcdadcabadcadaaccacdcbcadddbccdcbadbddcdcababcbbbcbadddaddbdbdbabdacddcabbbccabddcdabadadbdbdcabadbbdcdabccbcccccccdbcaccaccbdbbacdbbaacadbacdbaabcacaacaacddadbcacddaacbdcabbbcdacadadcdbcaadadadaadcaddbadbadcadbcbabbcdbdddbaadabddaccbbcbaddcdabcdbbabbdbbbcacaacadbadccbaaccbbbdddbabdbbbcccdbccbbbbbddcddacdcadcabddadbaadddbcdccbacaccdccbbacdacdbaababdabccbacbbcdbdbddccdcdcbbadbcbbaacbdabbacbbacdcbaccdbcbcbbbdcdbbdcadaacdbdbccabbaacdcbdcaaccaaabcabcacacacadcacbbcbdcbbcdaddcddcbccbdcbbcadbbaacbbaadabcabbaacaacbddcdcbaddbdacdddbcdcdccabbccbdbabdaaaacabbcbccadaabdbcddbdddabccbbcdcacbbbdabcbdacabdbacaacaddcdccccddcabcccdadbcdadcccdaaabbbbdadcccdaccabaddacacbcdbdaacddccbabcdbbddcbbcdadbcacadacccccaaacacadcbccdcbabbddbcaaaabcdcacbdadaadcdacbadbaaacccaadcbacccdbddbdabcacbcacdbdcdadacdbbcccbbdcacdbcacbaaddaaaaddbbdaadaccddbdabccbccbcacbcdcddddadabdaaadcaadcadcdacacabdcbabaaadbdcdabdacddabadddccababcadcbbbadaaabcacaaabddccaaacbabcdcbcccaaacddbdbaccdbbdababbbacaaaacdcdbdacddaacddadaabccdcbcadaaadbbcccdbacdadddddbdadcbbbcdcddccadbcdabaadcdaadbbaddcddabbdaaadaccbacdbdadbccdcbadbddbccddbaadcadcdacdcccddadcdbadbdadaadaacdcccabaddcdbddaccbdccbaadddbdcdaadabdcdabccccbabcbacbabadaabccaacacbbbaacabddcabaadacabdbdcdaddacccbbbbcabdbddbbcacdbabcaadbcbbbcbbdccbaacbbcdabbdcacccbbacbdbabdadddbddadababbadbdabccbbccccbddbbddbdaacbddcdadccbbabccdbbaadbdbcadcdadbcdbbccdbdbadabdacbcdbcaccccacdccddaccbabadbabdbcbbbadcbdcddaddadaacdabaaccaaaccbacbdabddabdaacdccadcdaabbaddbacbcbdcdcbbddaaaacbddccabcdddaacbadcccabbadcabdabdccbbcbccbbddcccbbaadaabcdbcabbcdbbdaddcbacdbdcbccdcbbaabdcbcbdabdabadaddacbdccccbabdacdcdacdadadddacdadaababaccbcbbcbadcbadcdaddadacadddadaccbbadcdcddcbababdcbaddabdbddadddccbbddadbbddadbbdbacccdcdabacabcaabcbcdacdacdbbdbddabadcabdaccbbaabdbacddadadcaabdaaabdcbccccdbbdcccbbcccccdadddabbcdadddabbdcccbabbabcacabbcbcaddabcacbdbadbdbccabcbaccadcccbdcbdbcadacddaacadbbcacaaabadbaabccddaabaccaabccdcbcadddbbbbdbddcdcbdadbbbcabadacdcadddbbabbbcbddbacabcddabdddacaadaadcbbacaabbbdbbcdbaccdabbacdbdbddaaacbcadadabbbcadcbadcabbcdbbbdacdbdbabbcbcdaabdbcbcddadacbacccdabacabaccbcacbcabaabbccabbbcccacbdcddabacdccbddbacabdabccbccdccbccbcddbbbddaabcacbaddcabbabaddadcabbdddcbcbbdbacdbbabbdabbccbdcdccbcdcabdbdcadccbaabbccbcbadcdccdcbbabdcacaaddcaacbacbdbabadbdcadacbdcaacdbabbcccccdbcaacdddcdddacabdcaabbabdbabddaccbabddbcabcccacbdbdaddbbdccbcbacabdddccaaaddccadacaccdcdaaaaabdadccadccacabddccddcbbbabdbccccaaaddaadccacdcccbdabbbdbcdcddcabdbcadadbcadcacddcbbbcdcccbbaadabddcbcdadcbcdddccdaddccabbdcaadcadadaccbdacaccdcdbccdddaddcabbcaddcbbddaaadbbaadcabdccdcbadbaabddbbacacbadaaadacbddcaccacdbbddcbbbccabaacdcddbaccaaadaaccbcaabbdaaccdbdadcbadcacdacbcaacabcaaabaaccdacbcbadbccdbdbaddcdbcccbcbddadbccdcadcbcbdacdcbddddbbaccdcdbaadcbbdcbbbbadcdcccdaacaabdcadcadccbcacddacbbdadbdbabbadbbcbccddddadabbcadcbdabdabbcdddbbdbacbdcadbcabddbdcaccabcddbdbbbadcaccdbddbacbbbbbccdcadbaadaddbadabcbcbcddbdacdaacbbdcbaabaddabbabdbbcbbbbadcaadaacdcbaddbabdccbbbbbbbaaaccdbacdbaaaaacbbaddabbcabbbbbaaaabdaddddaacacddccdccdacdadccdcccadadccbacaaccbaaccdbacabbacbcadbaaddbdbcadbbdaacdaadadaadadbadacabdbbaddadadbbacbcabadaaacbcdbcbccdbbdbcbabcbadbcaaabcaabadbdccdbbaccbdcabcadcbcacdddbbddacaabccbcbcbbcbbcadcddbdcdbbccdbdbbcbcabacbadbbaacdbaacabbccbbdcabbbadccbababcabdcadcdddacbdcacdcabbdacbaacadaabdbcccacabddcaacadcdbacacdaabcdaadcaacdacbdadcaaacbbdbdcdcacccbcccdbabaabcdcacbaddbdbbcbbbadddcbacadadaaaccdabbbcabaadbacddaabaaabacaaaaadabcadbdaccbbcaccdbbcccbbabddbacbabbcaccbbbcddcacbbaabcdadcbcabcccddcdbccdcacccabdddcacabbcbbcaddbdacabcaabdddddbdbcdcaacbabbcaddcaabdcccdcdcbcacdabaaabbbddddabbcbcabacbdccaaaaababdbddcbbbbadddcdbcacdbaccbdbcccbbccddcdabbaccccbccddaccddcadbdbbcbbddabdabaadcacdbbdbcbcacaaaacddacaddabaacbadddababccccbdbaacbaadabbdadccbdccbdcddcdbaddaacbcabdbcabbddcdbaabdbdbdacbbbbccbcdbadacbcccabccbbdaddcdbcdadccdccabdcacbddbcdbacddabdcbbddadacbbdbacbddbdaaaabbdaccdadcaabadabdcadbbbacdacabddbbbcccbacacdcccdcccaaccbabbacdbdcabdbadddcbaabccacaaaccbbbdcdaccadbccaddccaccddccbcabdcabdddccaabbdacadbbcaaadabbbbcbbabcacdbaacaccddadddcdddcdaaacadaacbdadbcdbaabbbbbbbbcccdacabadddbaabbadcdcbaadbabaccacdabdcaaadbcbcccdcadabdccddacacadcddaaabacdbbbaddabadbdcbbbacaaabccdaabbccccaccccdacbbbddbcccccadbbccbdbccbcddadbccaaddacadccdaddaaabdcccdcdaaccccbbccdacdccbcccbbdcadaabcbddaddabbcddcccbabdccddccbdaacbddbddbbabbcbdcdaababddabcbcdaccaccbadaddbbcbbadbbbdcacacbbbbcababcddcdcdabbaaddcabbadacdabbdcbcacdbbbdaaacbcbcdbdabaaadaaaaabbbcacbdadaacdccdbbdbaabbaacbcddacbaccdcbcaaaadbcbabbcdacccaadcbcdcdddccaabaaaabbdbcadcdaadacdcaabbbbccbcdcaccbbabadaddaadddddcdddbdbcbdddbbcdabccbbbcdcadcbbcbcdaccccaabdbcbdbadaabbabbdbaacabdcbabbbdaddbaccdcbbadbbcabdbbccbdcbccdcccbaadadbcbbbccdabdccacdbbdcabaccbbdcadcabdcbadbaddacdacbaddabbdccbacdadcaddbdcacaadccbccbccdcdadaaaccdabdccaaacaaaccbccabdcacbadbccabcbdacbababcabcabdcacbcbddbbacbdbbaaadacddbdbdacdaabcccdccbcbdadcdcddbcbaaccdadbdcbaaaadcbbcbacbbabbacdcadbbadcccdbcdaaaabaccddcaabbaaadbaabdadcdaacbcdacddcdcdaadcdccdbdbbdcbddbccbbacdadaacaddaacdacbdbaacabadcadbcbbbaddbbddbccbcabababdacbbdcabaabacacdcdbdbacdbacaabadacdaccaccdaacddaaccbabdbddccbabcbcbdccbcddaccbcbcbddccaacbdbcbabdcddbdcbdcdbaccbbcdcbcddccbdaddadabbbbbacbdcaacbccdbbcbbcacabdcaacbcbacbadaccdddadbccbcccddabbacabadcdacbcbccdabbbadbcaaacdbabcbddddbbbbdadcacaabcacacaaccdcccbaabccbdcaadcaddddbdaaddccbddbdcaddacacbdaabaccbabbbaabaabbdcdcdaddbbbbbcbcadcbaabbdcddbdacbadadcccbbbcddbbbbbcbdbadcacadabdddcbcacdbdddddcbacdccbbcbbabddaaaddcdaaadacbddbbadaccbbaaabddabaccdbaacdbdaccddcbccbdaccbddccbbbdabbababdcaddaadcdcaccaaaddbdaaddcdbccdbddcbbcdbbdccbacbaaabbbddbbcacaaadccaaadcdcbacccaadccacbacdbbdcbabdbcacabadcbacabdddcbccbccbccadcdbdcdbadcabcbddbaccbdddabacdbbbdbcbbbcccdbccaddbabdbaccaabbaaabcdddbcaacbdddcadcbaabbdabcaaddbacddccdcaabccadadbbdbbbcbbabdadaccdccbaacddbdadcbadcabcbbdddaacdacbcdbdababacddaaaaacdacbadbdcbbdaabdddcadacbbddccabbdcbbbbabdadcbbcaddcababadcdabbbdcddcdaacdaacccdcbbbdcabbddabbdaccaccbdacbbbbcaaaaaababcccabbbcdbbddcdcbbbadadccbcbdbacaaccdcaddddcdcadcbabbadcbacadbbadbbbabcbbbcccbdddcbccbdddcccbdababcbdacbabdccadccaacccbcabdddabaaaccbcbbbccabdbbdabcabbbdbccadabccabaaabcbdaaaadababaadcababddacdbdddacdaaddccacdbabacdbbadcddbcdaaaabdadcadccaadcbcbccaacabcacbccdbaccddcdccdddcdaadcbddababbddccddbbdddadacbcccdbbbabadbcabcbadabbabdcacabdcbbcbaabdaabbdddbbaadbadddaabbbadaaacadacdcbcbbdcddabacabdacabccdababccaadcdacaadacdaaababdbacacdccabdbbdbacadaacdddbbabdcccccbddaaacddcbbbccbccbdcdcdacdccacccbccbcacdaccbcbdbcbadaacccaabddcacdbcddbcbcdaccdabcdbcbbbcbdddccbdcabcabaddcdcdcaccadbccccaccaabcddcddadbddbcbcdcacdbbadadcacbbcbbdcccdcddabdcbbacdbccdccabbdcbcdcdbcadadadabbddadaabdbddabdadbcaacdbbbdcccdcdcbbbdadddacbdaacdbcccdddacabcbadbcadbdccdaddbadbcdcdcbcaadbbdacbccbabacbacddabbbaaadababaaabdcbaacddbdacdaddcdbdaaacdcaadbaaadddbbaddcacaddbddbbdbdbcbbdcaddacaddabdbcdcddacdacbdaadbcbabaaacacdbacaaaaccaabbddaacbcccddbbdaabddbdbcaaabcdaccbcdbddcddadcdaaadaabbbcbbcdcddaacccdcbdcadbbbdcbbcdaacdabcccabddddabbbabbbbccddbacbbbcaabacdcaddcdbdcccdcdccccddddaaacbacabacadbdbcaaddaddddbbbddbccccdacaaaabdcccdaacddcdbddccaccccbdbddcabcbcacddbbaabcccbbcbacabcabbacdbddbbabcddbbbdbabbdcdbbcdbaccbdcadbdcbbbcbdcbbbbdcaacdaabadbaabddaacbbcadbccbdadcabbbcdbadadbcadbaacaacbccacdabddccabbcaccadddcbbdcbaacbdabbcbdacadbcaaaaabaacbaadbdadddbdacbcaaaaababcbbabdacdadcaaabcaccadbdaaaaadabdbbbbddbccaaddbbdbcccbacdccaccadbbdabbbccabccadbadbcccadcabccdaccdccbbddabddcccbadccabcacddaadccbbcddbbcadaadcdddbadddcdabcaabbadbcacbbcbdaadcdcabaddbbdbddbadaabcababccbdcaddbdaadabadbbbadcbbdabdacdbdddabbabadbcaababcdaaaddddbdcdadacadbbccabdacccaaabdcdadcbadcccdccccddabacdbadcdcdddbacbcdddbcdddbaccaaabcdaacabdcbbcbdbcadcbbbbaaaacaaacbadbbdabbcbaaddbbbdabdbcacaddaadbabbbacdcaadabbddbbaddadbbacbdddbbddaaddcacadaabbdbccabddbdbaddcbdbcbdbcbccadacbbdcdcbbbbdbbabbbbaaaacbbacdabbcbcbdbaddaaacaaadabbabdadadadadaaddbbddccdbcbcbcaddccadbbacaabdcabdcabdcdadbdddaadcaccadcbdbcdbdcbadaacddadbcaabbcdacbbccbccbacbbbddcaddabaaadadadbaaccbaaacdcabbbbcacbabbbbaaaddbbdddacbccccddbbdbdddbbdbccdcabbcdaabaabadaacbbdadddbcbddbccbcbacdccccccbbcbabadddadacdabadccaadaacabdccbdaddabaaadadabdbbcabccacdcdcadbdadcababcdadbaabacaadaadabcccdcdcadacaddbcddccaadddadabacadbdcdbcccaabbcbcadacadbaddacdadcdbbaddcadaccabcadbbbaaadccddccdccdcdccacbdabdabcdccaacacdcddaaaabddaccaacacdcddcdccadacaaccdccbbabbdabbbabacaddcccadcbbdbaddababbccacacaababdcddbadbaabaadbccacdabccdccddccdbdddcbcddcccaaddaccddbbbacabcaadbaaacaacdbadbacadacbcadddbbcacacacaaccbdcddddabdaddabddcdbbdbaddbadcddbaadbacbadddddddddbbddcbccddaabdcbbccdcbdabccdbbbbaccdcbcaaabbcbccdcbacdddcbacbabdcabdbadcacbdadbddccbbdbdcbbacdaabbbdacbbabcadaabdadbbacadddcaabdaadbadcbaddacaabccbcbacbdcbbdcdbdbadddcbdcbbabbcdaacaccacaacbcbbabaaddbacaabdccaaaadcbacacddbdccbbbadccdbdbacabcacdccdaacdddcdddacdcacccdddcdccaddabbbacaccaabcdcacbaddccdddcabbaccdadadabacccdabbdcdbddbdacadcdabcaccdccdddacbcddbaaddabdaaabdbcacadbadbacadadbccbbcabcbcacdbdbbaccdacdddddcadbcddabdcdaacdcbcccbcddbbaabdbbdabcbaccbadcbadcdadbdddbaadccacacadbdadadddddcabdccdabdbbadabbadbaadcabadcaadaccdbbdaacaaaabdabcbcdbdbbdabdbbcbbacddaadacdcaaddcdacdcbbbdacbdabddaababdacbdcbdcbdcdbbddccaacdddbdacbbbddcadccaabcbccbccdbabcddcbdcdcaadaddcabcabccbcddbdcabbdcbcbbdacdcccabcaadcdbadbaaacdbcbccadcdbacbcdbdbbdadbdbddbdcdcacbbaddddcddcadaddccbcddbadaaccbbccdaacacabdbcdabcacacdcadaaabbdaaabcbbbcaaadababacdddcadcdbdbaabbdcacababbbdddcccbbabccbbcdaabbabadacacbbbcbdabbdccccdabccddadbbbabdbbabcdbdbbabbdcbaccacddbbabacaddbbcbabbbdddbbaacabaadcabddccaadacdbddbcbcddbdadbcdaaadcbabcaddbbdcbcbcadbbddabbcbcadddbbdddccadbdcbcccdadcddbbaaacddaaadcdabbaacacdabccacdaabbcbaccbccdacaddaabdaaddcdccadbaabbbaccddbcdcbbcbaccacdadabcdbcabcdacbbcaddcddacbdbabdccbdbbbcddcaadaaddbbbaacdbcadbdbcdcadddccdddacdbcdbbababcccdccababcbcbcddbcdcabdabbdcdbacccbbdbdccbcbdbbbcbbabaaaaddcdadadadbacacbaaacbaadcdbcbcdaadcbaddcdcdcacbadbabaacadbdcbdddaabdacabcdabcabdcccdbbddabdccdacabbcacadcbcbcbbadcbbbaccbcbddacbbabddacbacbdccbccbbcbddccacbabbcabdbadbdcadacbdababdbbacbacbddccbdcdcbbadacbcdcdbcbbaddbbbdbdaddabdabcaddabddccdadacddbdcabbbdacbbccdcddbcbacabcaaabbcbcacbbadbaccccddcdddadcbdbbdcccdbdcaccddacaccbababbdddbabcdcdccbadbbddcdcbbcaaadacdaccabcbccbbbcaabcadbbddbbdbdaccdbbabbdabdcdbdddaabdacaaadddbdaaddbadbacdadddbaabccccadbcbcdbdadccdadbbcddcbdcbabcbbdacaddadccbababbdcddbabdcbbbcdbbdcdcdaaccbbabcbcdbdbbaadccacdabccadcaadadabcbcaddbbdbbbdacbdccacbbbcacdcddbaabbabcbddcccbcaaaaabadabbccaacbacbbacbdabaadbbdbaadcabdcdaabadbaacdcbddbbbcaacccdbaadcbdaadaaaaaadaabaabacadaddbaddabaccbdccaaabcdbbcaccabaaaaddabcddbdbdadbbacababbcbdbbbdcbccbaccabdddabccaddaaacadbacacdcaadcabddcdddcbcdadcbadbbbdcdadbdddcaabcbddabdcaaabacbbdcccbaacabbcdacaaabababbcadaddbadaadaadabcccbbaaababbacbdcabcaadcabddcbcbbacbdbadabaccddcddbcdabaadccddcdcaacaabbcaddabdccdcdccdcbbbcaddacabbaaabcacbdcaddabccacccaccadacdbdacdbbbcdabbabaccdbacbbbccbcdcddcdcacbbcbdaccddbcaacaddbaccdabbcdddccaabcddbdbcabbcdacbdbcdcaaddbdacbcddaaccaccccdddbccbcdbbdbdbadbdddacabddcaccdcbbdacdcacbbccbbdacccbccbbdbbcbdaaadcacadddbccdabacbccaddbabbdadacbbbcabdaccdabbcabacaddbccddbadcdcbadbacbccbcadbdcbcbaddaabcdbbaadbacdabaaaacbdbddbbabbcadddaccadaddbacdaadaacdaadbbacabcdaccddacbbbbcadbbbaacbcbbbadbddddadaacdbbaccacaacababdbbabcddabbbdabbcbacccaaabccccddcbbcdaabbbaacbbcdcbabbdcacbcccdbccccdddddacdabaacbbddaddbaadddcddbacbdbccabbbbcbadcbcddcdcadabbbcbdadcbabadbdbaabdcaaaadbcdcbddbdcbbdbcbdcdababcacbcdaacbadcdbbccbbbcdccadddbaccddddacbaccdcaddbccdcbbbbcdadaccdbaaabddacdbdadcccccaddcbacdbaacbacdabbbacdbbcbccdccddaaaacdadcccccbdacbbdcdbaaadaaadabcabddbdadabaabdcbcbaccbcbdcccbbbdadbaddaccadbddcabbccaadcbddcbddddacabcbadbccaacbdaaaccdadcabdbdaccdbbcdaabcaacdcdaadccaacdddbdbaacaaabdaadacacdcddddadbbaccccbaacdacccdcccaaaddbcdddadbdcdddddbcbddabaabcaabbbdaddacdacabddccdcaabacccbbcbaddaacbbadcaaccdcabbccbabcccaccaddcbaadcbacbdcbccdcbbbaaadaadbbbccdcbcccbbcdbcddbbabdcbcbbaccabaadccbccacdbdccdbdbdaaddbbadbaadaaaacadcccdadcbccccbbbcdbccaadbccadbdcbbcaaabdddbddadbdddaacdbbdbaddaaacddadadbccddcadddacabbadaaccdddbdaadcbdbddbabdcccbabdacbaccccaccabbacbdadccadabcbabaccaaabdbccdbadcdbbdbbdbdadcaaccacdaccdbabcbbcdbaaacdadcddbdbadcabdcbadcababcdbaacdbacddbadcbdabdaabbccdbbbbdacdcdabdddbbcbcccacacccdacaaaabdbbbccaabcacaccbbdcbdbcadbbbabbbbcdcdcbccaccdcadaaaacabbdbbdbbcbbabdbcbbabdbbcacbdbabdbacbababbdadadaadbdaccaddcdaabdbaababbcdbadcbcccddacccdbaaaccdcaacdadbbdcdcadbaacadcddbdaabbcdcdbdddcddbacdbddddcbccdbcdaccbcdbabcbdcaabaaddddbddbccabaacdbdbaacaaaaaacdcccabcdbdcaaccdbacccccbcbccbcdcdbdcddcaaaaaacdbbdadbdccbbbdcccdbaccbcacddaddadccaabaacdbbcbdcaccdadbbacadadcbdbbccdbaaaacabdaadbaacbddccabbdddccbccadaccaadddbcccdaaaabacdcbccacacdabcddaddcdcdbabbccbbdbcacbccbddabadbacbdacbbbbbdbdadccdadbddbcbcacacbcdbcbcadddbbbbacccdcaabbaabadbcbbdbbabdadcbdddcaabbacaacadddabdadccbdbbcabcaacabbbdcabdbbccbabdaacdcabcbdcadababadadcdbcbadadbaaccddacaaaacabddcabbabcbbbcbabdbcdaddddadaccbdacbabcbccbbbcabcddccadbdbbddcadbdcdadaddcdacadbacdbdaccabdcdcccdddccccdabcabcbdccacccdbacaadaaddccdbbaaaaccacdccbcacaabdcbcaaaaccbdccbcbcdbadcccbdcdbdcabdddaccbabbdadaaadbabbbabcaccdbbdaccababbbcabaddddacddacbbcacddabcbbbdbbadccaabcaabdaccddbdaabcddccdbbbccabdcadbbacbddbccccbcaaccbbacbaaadbbcddcabbaadbbacabddaddaaddaaddbacaabbdabbcacabbcabdabbddbbbaddbaccbcacabcbdbddcaabbdccbcaddddbdabbaacddadbdaccbddbabbdbaacbbccbbbdcadadabadacaaacaddddbaacbbbdbccbdddcabdbdadadbcdcbbacddaaccbaaabbcadacaddbcaaccdbddcbbcabadbaccbabbbdcbbaddccbcdaadbcbcdbcabcdbcaccdcdcbddbaccdbadababbbadcacddbbdcacdabdbdaacdbabadacaadddabbcdadadddbdadbabdbcbacdcbaacacbdbbabdaabcdabbdbdadbdbdcdbdddaddbabbaacdcacddaabcbdbcaadcabbdddddaabcabdaddddbbdcdccddabdbcccabbdcdcabdcadbabddcccbcdacbcbacddcbaaabccbbcadabbbdcdcdddcacacbcaaccbabcdcacdbacbdbacdccdbbccbaabadbbcdcaccaaadcbacababcddadacbbccbabaaacdcddcbcdbdcadcbcaacbccdaadcbbcaddabbcadbcbdcaddcccbbadbcabaaaabadddadbddabddcccddadbdcddaddaddbcdadadbcbbdcaadabadddaaddadacaddddcdcdbddacbacacbdddcdcadcdcddbdbabcabaabccdadaabadabcdcabbbddccabbaaabadaadbcdcbcacbacbcccdbadbabdacdaddcdcdadccbadcbacaaabcadcbbadbbccbbbacbcbccddbcccbbaacacbbacdcaaabbaabcbcddabacbaaabadccbdadacdbcbdcacdacdddbdcadaacaacccddddcaadaaccdbabbcbcacdbadcdabccacbaabbbddbabcbabadcddccdadadddcbcdbbadcabbcddcbaababbbbccabccbcaacbaadbaddaaadabaabcdcdabbbdddaadaabaacdcabcbbcabdccccbbddbcaadcbbbdcadaadbaabcbcbddbaaaadddadbdabddccbdcaaddbaacddaaaaddaccbbcaccdbadabcbacbcabdbddcbcbcbcdbbcaabbdccacdacaacabdbbbcddbbdcbdddccdbaaddbbbdbacbdccaaddbdbdcdbbcddbbcbdddbacbbbaccbcccbbaccbcdaccabdcdcbdacadbcdcbababdcababcdcdcacabdcbdbaccacddcaddaddabdadaacdcadcbbabbdddddaadcadabccabdbababbaaccbaddcdbbdadcdcdadaadbcadabdadddcbaccbbcadaaabcacaacaabbdbcdacdabdaddaabcdbbabaababcaaaaabbacbcbcacacaccbabcabbbbdcabddbbdcbbbabbaaacbaadabcacbdccdcdbadbddabcabbdbddadcbbbcadacbdcdbcbbbaddcdcddbdbdabcabbcdcaabdcdbcdabbccbdabddddbccdcdbbdaaccdcaccbcddaddcacbdbbadbdcadaccbdbabcbbacadcdcbdcaaddabbbabcddcbcaccbabbbbadbacbdbdbbcabdddcbaaacaacacadcdaddbcccabdacabcdbbbadbbcbacdbccccdaabbabbbcdadbdcbbbccdcbdbddabcbcbaacbcacddddccdbadadcbcadccbabbdccbdacadabbccdcbacdbcabcacdaddcccdccacdccdabacccabbaccbabcaadbbbdbccbbababbddbdbacccddccacbdaabcddabbddbbdbdaabcdadcbaddcaaddcabcdaadbccabdcccdcbbaacdbaaabcbaacdcdcaddaaddcdabcddbabdcddbddabadcabcddaadaaabacabdbdccacbcadddbcdaccaaccbcbabcabccdbaaddabbdbddddbbbdcdcdbcddaccbcccaaaccdcbabccdbbbcbabacadccacdcdbbaadaadadcadcdaccbbadbccaacccacdbbcbacdbcabadcbdabdcccccabbdadbaabbbcddacbbbaccacbcbcdbdadbddbadbbaabcdcdbbcdcdbccdddcbdcabdadabddaddbbbbcacddabaaccabbcbddabacadcddbcdbbdcccabaacabbabcccadaadcacccacddaabdaadcdccaddddbccbdcdcbaabcdcdddcbbdaacbaaddbaadacadccbbcabbcbdbaaccbdbcbddabbaccbdbdcbccbadddbabcababadacacacacdddcbddccdabcaaadbabcccdcdadbacaccbbbddacadcaadbcccabddbdadcddacbdcaddcccdbbaddbcdaabdcccbcabaaaabbdcababcacbbbcaacbcddabdcaddcbbdcdcadbcdbabbbdddccdbabcaddacddcccbcdaacbbccadcdcddadcdbbddcacbcdccdadcdaababdcdbcadaabdccbaccbbcaabbdbcbaabcbdbadcbcbacdadbddccacbadbcacadaadbdbcabcdccdccdcccdbccdddaacdcdacbdbabbaabbbaccaccbdacbdbbacdbdaaaccaddadcddbdbbacaabdbcdbcccbacddaaadbbbadaddcadadcbadcddbbbddbdabccddbcbccdbbadccdaddaccbcacbbdccdadaabababcdacbcdccabdabdbbdddabccaccccbbdaabddababcdbddbabbbaadcdcdcacdddcdcabaadaabddadcbdddbdcccacbdcabbdbcdbaaccadbccacacabacdbbcbbabdcddbcbdbcadbdbbdbcdbadccadacbbcdbbcccbadadbaccaadcdcaacbaccbcdbdbcacbccdaadccbddbbdcadaaaaaddbcabdacccdbcdaaaaadbbdbbcbcdbabbbdcabcbaccaaccabbbadcdcdddbcaabdadcdacdcbccadbdccadcbcddcbabcdaacddbcbcaddccacdbacbddbcbccccddcdddcbccbcdaabdbdddbcabdbbaaaddcabccccccccbbbddcbadacccaadacaddaaaabcdcdddaddbcdcdccdcdcdcdadbdbaaaabccccdcdaddccadcbdbacdcacabbccbadbbcacddbaacadccacadddccbbdacbbcbbacbadcbdacddaaadbaababcacbabdabbcaacacaaaaaccbdaaacdccbdccabaabddbbbbdddabdbacdcbdacacbbccbcdcdbcbbbcbcbcaacdcaacbbdbcabdaddaadcacccccdbbacacdabcbcdaabdbbddabdbacdbaabbadaaaaddcbbdabadaacdacaabcaddbbddabbdadaadaddcbaccbbcadaacbaadbacddacbbccddddddbddaacadcddbcadbdcadbcaacacabccbcddbaadcabccaaadcbabdcaccbbdccbaccccbbadcaccdbcaaaccaadadabdbaaacaaddbaacdabcbdbbbbbdbddaaacddcadbaaccbbccdbabbaaccbbacacacabdbdbbdbbaadcbbdabbdabaaddcaaccacadcacdbdbdcaccddbcccdcbacaabaacacccdcccbbbabdabbcaaadbacbddbacdccdaccbcbaadacabcddccacbacdbadcaaacadddacdacadaadbaacbadbdbddaaadabddaaadacccaacbdaaaaabddcdacacddaaddbadadbddcdacdcbdddbbbcabaccbbacdcbbabbbbbacaaddbbbbbbbabbcaabaaabbcdccdcdcadcddcdbdddabcacadadaabbadcbaabdabaabcacdddddbadddacacacdbdccbccdbccacbcccdbbdbacddcddbcbdacdcadacdbbcccaccbababdcbdbabbcbdbdabdcdcadaacdccbadbcaddcaccbabddbabcdbcabbadbdbaadbbdcaabcaadabddadbdcdbadbdbcdbcdbcbccadbadbbcabbcabbadbbcdabbbbccadaabbcccbabdcbaccddcccadddabcbbaaadccadaadcddcbbabcdddbccdabaddcabdbdcacbbdcadabaacbddbacbcdddcdadcacbdcbbbaaaacaacaacdcaaccddbbdbadadbaabaadbdacadcbaddadcadcddbbcadacaabaacdbbdbabccdaddaaddbbdbbcbbaccababbcbcbadaaabddcdccaaddaacaabdbaacbcdadccabaaaababddbdbbddbdabbddcdacdddcbacccbcdbcabaccddbccddcaadcbddbcaddbbaaaadbccadabcaaccabdcdccbbaaddbabbccabccbbbadbccdbaccacbbbdccddcbabadcbdadcdbababcacbdbccdaddbbddabacddbadcabaaabdcdbddbcdccdcdabccdaacdabadbcdcdbdbbcdddcbbaabcdbdcddddbddccbbbddcadbbaaddabcadccabdabcbbabdbddcccabcabbdacdbaccdbdaddccbdaabcdacabdbbabbbbbaadddaadbacabbbcaaacccddbcadccaccddacdacdcadcbcccacdcbaddcdbdbddbcaacabbccadadacbcadbacabbbcdddbaddaacdbabdbacbcabaadbacacddcbaddcacdcdcbbdadadbcddccbabcbdcdcadbaaabccdcdddbabcadcbcbaadbaabccdcddacddbddacbdaacaabbaabcadaddbcaadaadaddadbdbdbaaacadbbbcddadbcccddcaadbabddadbbbbdabdddbdabadcbdbddbdbabbcddcdbdbdbccbadcaaaddacdbadaddacabbadccbbccbbaadddccbbbaccbabbabadadcccbdbacabbacbacaddbddbddaacccbddcaacdabcbcddabdbdabdbadbcdabdbaaaddcbacbadccaddbcaacddadbbacdcbbcabcaabdaacdaccacbbaadaddaaacbcbbcdabbccdacabbddbcacbcdbaabbcacababdccaabbcbaaadacbbbabdbbdddcddbaaaacacbccccdacbdbcdcdccdacabbdbbaadbacdbcacbacbbbdbbdacccbaabdcbacbcdaccbdbaddaadacaccadddcdaaabadadadbcdbbbbcdaccbacddbbbabdddddbdbdddaadaadaadcbdcbabaddcccdcdacbcbbccbdaaabbbacaacacaccccadbccbdddbddacaacdbbdaabccaadadcabdadadbbddbbcadddbaccacaadbaacbbbdcadabddcdabcbacdbbdbdccaaadcacaaabdbadbccdbbaabacbdaacdcbcbdaaaaaabbadccbcbbdbbcbdadbdcbbcdbaaabbadbcccbbaccbabacabacdbbddddacbbdbcadaaacaccccddccdcadcdbbcbccbbacacbdcbcdbbbdabdbbbdbacbbbbdabbcadccbbcaaaacabaaccccaddbabdbcbaacccabdcdddcadbdbabcaccaabbbacadacdabbbabbadbcbddadcdaabcdcabdacadbadcdbddbbcbbdabacbdabcaacabddccbbaadacdcdcaabcccdabadbcababdadccbcbbdabbbddacbdacabdadcdbbaacadcbadddbddcaccacdccccaababdcabbbbbddabbcaaacddaddbcddccdbcddacbacdbdcacacbddcbcabcdbabdaddacdcadcaabcdabadcdaadabcbdbcbccdcabdacbdbcbbccacdbabcacadbcacbcddbcbcbacbbddbdcacbcabcbddddaccbbbcbdadcbabdacdbcdbbaacbcbccacadcacdcbcaacacacaacccbdbbcadbbddabacabccdccdaddcdbaacbcdadddaacdcaccadcdddacadaddbaaaaaadabbccbcaccdadcdccacdbccbaccbcadcdccadbdbcaaababbcabdbccbbdbcacabcabddccaccacdccbabbddbbacdadbdbcbcbacdacacabcbcbdbcdbdadbdbbbcdbdcbbcaaacddacccadabaddcacbcdaddacdbabbdbdcbddacbdacabbbcbcbaaccddcddaabbcbcacdccbbcbaacdadacbddbcbaccdacdacadccddabadadbaadbdccdbbdcbcbcadccdbdbdbdbbcadbddbabdcabdcdcaabaaaadbabacabcccbbadadabcaadbcadbbdaccbdcdababddacdadacdcbabadacaaccaaddcabbdababcccabcdacbaabddcbbddccdddcabcbbcbcddaacacbcababaadbbbaaccabdaacbaabadbdbaadbbccabbbbcdbddbabcabddccbcabbacbdcccbdbcdacbaddbdcdbcccabcdbbaaaacbabadbcccccdbcaaaadcabbdadbdabbdaddadcacdccbbdabaacaccccacbadbacddcbccdcdcadbacbbcbabdcdcbbbcdccddaadaaaabcbdabadbccddcbdbabdabdaadbaacbabbdbddaaacdbacaabcdcddbdbdacbcaddbdaccbbaddcaddbbcddcdcadbbdbdbdddccbdadbcaacbcccbcaaadbacdcabdbdadaadddadacdaaacbdcccbbacbbbaddbdcaddcbbadcbdccbabaabcdddadbacdbbbdbdbdabcdcaddadddbbdcbbccbabdaabcaddcdababccadbbcdcdcbdddadaccdbdccdababaccadbaccddcdacbdcdccddbacccdbabcdadbdacbdaabccdcabbdbbacacaaddaabbaabdcdcbbadacadcdaacaaabcddbbbbcccdabddbabadbbddcbdadbcbccbddddbdabbbabadcbadbcacaadbccbcbddbbbadddbbcdaacdbbdadbaddcdbabacddbbcbcdacbdcaadccccbdcddbcabdcdbdddbcbcbbabbbabbcdcaadabcdccbaadbbddcdccacaadbcacababcddaaabcdcbdbdddbbbacbabaabadbdbcaddcdcbdadbcdacdadabbcddadaddcbbcbdbabdaabacaaddddcabdcbbdccbcdadcaabcaabacccabdbabbbaccccbdcaaaddbdabbbadbabddcdbdcccdcadbadbbdddbdddcbdadbbacddacaacbbdcbdbaadaadbdbbcacddbcdbcdcbadcdddddaadbbdcddaadcacdcbbadcaaabcacdccbbbbaccdcccabcdcadbadaaddbbcdcaaabdaabdcdddacacddbcbaabdccaaaacddaaaaaaadaddbababcdbdadabdadcddcdbdbddcbdcbadacddcdbcbbbdbdcbcdddadacaaadcacacccdaaddddddbdccdacadabbbbcbcacaccdacbbcbdaccaaabaacbdcbabbcccdaabaaacabbcdaddddbaaababdcbbabdbddcbdaacbcbcbccdadaabaadcaccbbaddcbabbbdbadcaacccdcdcddacacbdcbaadaabbcdbbdbdacdbaddbdacdadaccabdbccbbcaaaaddbbcabcdcbbbbdcdabcabdcccaabdaadcbbdbacbddbbbcacbbaccbbacaaabaabcdbdbaadbbccbabaaddccacdccccbabcdabcbaccaaaccabbdadbadadcdaabccdbaccbaabcbbadcdcccdccbbbdbcadbdbcccdddccbcddaabbdbccdbccddbcddaaccadbcacbccddddccdbacbadbdddacccaccdcbcaabbcacbdadcacbcdbcdbcdbccbaacbbbcddbcdbdcddacbcdccaacbddcdbacbcbabdbcabacacaaccccccccbbdbccddbcdaddbabdaaccbcabacaabdcadbdccdddacadbcabaaaccabacbdccadacabbccaabbacaacbdaaabbadacaddbcdcbcaadddabdaccabaccdbaaddbaadddacbbacbbdbdaccbaababdcbacabcccaccdabccdddcbcaadaddbaccbcbdbaacccbadcbdcbbcdccabdcaabbbacdadcbabccbccabddbdacadacaacbbcabbaccddaaadddccaaccbaaacbcbccdacbdabdcdadbadcacdcccadaddbaddabccbdddbbacacaabdccdadbcadbacadabddbbddcdcdccbccbdcbbabaaaadcadbaabbaddabbcaaddcadddbdbbdddcabdcadbbaddbcaabbbcbbaccdbbccaabbcbcbabcbcaadbbdabadbabcccdcabbcadbacdaaccccaadbababcabdbccaddcdcacdbdabccabaddccaaaaddbbccaaddcdbccdddaadddabcdbcdcddaabcacaaccdaaabbaaacadadbabadbadbcdbbdcdbbacbabbabadaddbcadbdadabbddacabddabccdccccabadcaccadabcdbaccbabdcaddcddcbcccaaaaabddcbcacadccaacaabadddbabbccdcdacdacdabbcdcbacbccddcbaabdbdaabdbbdadbcdbbcbbdbadddaccbadaaccaabbcbcdbddadcabadbabccacdcabdbbbbaddbbdccbdbdbcabbbccbdbbadacadcccccccdbcbaaaadbdabbccacdcdbdaccaacbacbdcbbaaddddbabaaddbcdadbdccabdabbdcccadbaabcbaadccdbcbdbccddbcacacadddcbdbbbdbadccacccccadbccbbccccbcdbbbbacdbbbdacabcbcaddcbbddbcdcbabdabbbdbccacccdbbdbbdcadacaadbcacbbdbcbddccbdaacacdcccabadddbddcdddccabaaadddbbbcdddccadddcddcdadabaadbadcdabadadbdabcdbcababdbcdbdbaadabccaabdbbaccaadcdcdaacbddbbdddbbbbdcaaddbddddacabbdcddacadacbababdccbaacadabadcdccbcbaddcbadadbaaabccdbbccccaaadcabbadabbcabacddcddabbdaacbddddacaaacacddddbccdbbaabaddccacababbbcbcabdcdccddbdadccbcdbbddbbccdbabacbddcacdbdaaddacacccbcaabddcdddbcdddacbdacdbcccacaabccacabaccaccdaaabbdcabddabdbbdcacbaacdbcbddcbbbddabbbdbcdbbdcdbdaacaaacdadcdaddcddacabaacdddbdcaacdacbadddadddcbddccadabdcbadadabdbcbbddaabbbacddaacbdccaacaaabbcdbdaccddcccddabccdacdcbacaaacadbadcabddbcddadbbcbabdccadacadddcdbcdcadbdaccabcdaddbdcaaadddbcdbbabccacdbdcbbaabdbcadbbcabcbbabdccbdccacadcdaddbbbcbdccbcbcabdaaadacaaadccdccccaacadccaaddcababaccbbddbabbdddccccdcdccbaacddadbdabccaddcbbaaadabdbaadccbacadcddcccbcddaaacadcbccccdcabcaadabddadadbcbacbaaccadbbbdabbaccabcdccabdbccbcdaaddddaacddbcdcdaacbaabdddbcccdccdcdbacacbcabdbabbdbbbcccdbcbabacccdcadbddbdddcbcbdaaaccccacddaccaaddacacdcbbacdcaabaaccdbbacacbabbbbcaccabadbdadbdddadbdadacaabcddaddcbdbbbdbcbdcdaacbbbaabcdaddddacacabdbcadcccbadbdcccdacdcccbdadcdaaaaabcbbaababbadaaabcdcdcbdcbacddccbcacacbccbdaddccabadcabaddabcddbcaadddccccddcdbbbdbbcdabdbcbaadadcdbdbdbacdcadbcddbbddcadbadacddacddcbcbaaccccdcabdabcadadacbbbbbddbdadccaaacacdcbddcbcbdabaaddaadccaddbadbdaabddaddbcdcbadbaddabbdddcccadbbdddcbcaccccabdcadbabdbdddbbcdccdbadbabcccdabcacbbaaacdaccbddddbdbdccdcbdcdddccccdbcbccbaccabdbbabcddccbcddddbcbbdcdabcdcdacacbcbdbababdcadbcbbddbaccbdaadacddacbbabbcbbacbbccdadbcccdcbddcccdaadbcadbdbcdccabcdbddddacdcbdbcababaaaadacbbcdacacaaddaccababdcdbbbbbcddaabdcadaaabcddcacdccdccccbddcaddcbbcacdadbacdbcbaababdccaccccddaaaacacacacbbcdcaddcdaddbbcacbccacacaaaacaccaabccdcdcadcabddbbccbbaaabcbdccabccdadbcddddbdcdbbdadaacaaccdbbadabaabbaddacdcadabdbbacdbddacbbadbddaadbcddbdacbccddaccdddaadddcaaadbbaaacdcabdbcbbddbacbcbabdabddbaccbbadcadbcdbbcdddcddcdcdcacabbadbddcacbccacbabdaadabcdaaadcdddbabaaacdbccabcdccabccacccccccbbadbacdcbdbcdadacdbdbaabacbaacdbaaaaadadacdbadcdaaccdddadbdcbbadccdcadbcbcccdbbcbabaaddaaadddbdddcbcdbccabccdcdccbbbdcbcadaaabbadabdacbacdddabdabdabbbaadbbdaabcbdcdbcbaabbcbaddacccbadaacccaadcbddcaacacdbbdddcbcccdccbccbcadcdaadbaccbbabbbcbdcdddcadbbbddcdbcbccccbdacbcdabbcbbabaacaccdccdbbbbbbddadccbcdcadccaacacbadcbdccabddbaccbacbdcddbacbdacabbaddadbcddddbccabdcbbcabddadaaadbddcabcabaacccdbabadbbcaacdacbacbaadcdbddcdcaaddabcdbdcccbbcbbbcbccddbdaaaddcadcadcbbdaacddbdabcccbccacadbacbdadbbaabaabbbbabcccdbbbdabdbcadadaaaddaddddbabaddddbbaddaabadbdbcbbaabcdaaacadcbaaabcbccbdcbcacdaaadcbccaaccbadcbbdbaddbaccdccacbdadcdbcadccdddcbdadcdddbadcabaacbcccaaabbbdabaccbcdabbdbcccdcbbacdbbdbadbcdacbbdbdbdbbddccaccabadaabddcbcbdcccaaadccbcaacbbbbbabdbdbdbbbaadbaccaadbcadabdcbabbcabdbabbbaccadaaabadbddaadcaccabbbdcccbabcbcdcaccccbccabdcdbbcbcababcdabccdadadbdacbddcabacdacbddabddbdaaaacbabaadbbabdabbabcdaacbbcaaaabacdbbdcbdddaacabcbbdcabbcacabbaaabccabadabacbbdaddcadabacbdbcdcbdbcbbabbdcabcaaabcaaaaacbbadadcddbdaaccdbcaacdbcdadbccadaddcaddabdccaddbbdabbdacdadabccdddcbbbbdcabbdabbadcdacdcdabdcaadcabaccbbdaabacddbdddddaabbbdbbcadcbbdbbbdaacacdabdcbcdcbbdabdadcaababccddcbcccadddbbcbacdcaababbacdbddadbddacadbbcacbcdaacdccacbcadbbadbbcabadbbdddbcaabdcdadcddbacbabcaabbaccaaaacaabdbdadcacbbbdacbbacbcacabccdabcabbbaaddddaabbaaaaabaccacddbccabcabadcccdabbbdbcbcaaddaaddbdccbddcccabcabcdaddcacbcabacacacdadbdcbccaddaabdbdcadaaabccdddcbcbbdbacaacdbcccdcdbaadaddccddccadbadccaddadbcdacbdaacaaabadcddbcdcdababbddbcaddabcbbccbaadbbbbbbcbbbbbbcdcbabbccbadadcacbcaaccddccdabdcdcdcbbbbbcbaaaaddcbacccdaddbcddcadcdcbaacabbdcddbdbadcabacadcccacbdbdcaabacdbccbbdbbdccbdbcdddaaddbbdddbbdcadabddcacabbcabaacbddcaabddcdadacbdbccaacccbbaabdaaacadabddaadbdacbaaadaabbbccddababcccccacdaaacdacadaacccdaddbcaaaadcaccaadaddabdbbaaaabacbdcddbaaaaacdbabdcbbadcaaadabdcdabacaadacbabaddbaddbcadbbcdacdadbaacbbccaabaacacdaacaadbadbbdacadccccaaacdbacabcccdbadcccaadcadaccaacdcbaadbaddabacababcdcadabbacbabddccbdabbaadacbadccbaaacdbcdcdbbbbdabbddacdaacdbabbdaadabaccdbbdbcccdaaccdbdabcdcadcdadbacbccaaddbaccddaaadadaacbdddddadcccdacadadaccdcdbcbaccbaaccadcacddbbcbaadcccaadabdcbbacaadcddbcdacacdabdbcbabcccdcddcdbbbcdbddaacbccccccdabcacadaadddccaccddacaccadaabccddabbccdbcbabdaadcbdbaaaacbabcababdcaabadabadaddccddcdcddbcacdccddacacaacbbacddbaacddadcacdcdabbbbbcbccdadbaaadddaddaccadcddabbdcabbcdaacbbcdccdaaaccabdbabbdaaddaccdddadcdcdbbbbdbbbdaddcacbadabcacabbcbcdacdacdddbbbbcbdcacbcacdbdcbbadcccbdaaacabcbadbddacbccdbccaaabdabbacabcacbadbdddabacdbadcdbbaaddaacababcbdbcdbcbcabbadcbdccdcdccaaabdccbcdacdbbaccccaacabbcadaacdddcbbacbdbcabbacbbabbacdadbdbabaacbadaacbaaacaaccdbbcbabdccdcdbaabdbbdccccdbaccbdbcdbaddabddcbccdacadbdabcbaaddbdabdacccdcbaabbadcaddabbcacdcccbbacbdcadbbcaacadbdaaabacbdbbdcabaddabcbbbdcbaccbcbabacbdccbcdacdbcadabdcabcaadbaddbbdddddbbadbbaabddbddbdddddbcdbdccdabddbdbcacadccbabcbddcddbbdbccbacbddbadadacbccdadaaddddbcdcbadaadccdcaaacdbbadccdaadabcbdadcacaadbbbabaddcaacdbcabccbddbbabaccbdbbdcacacddaaccadadacacaacabbdabcbbccbcdbddaababcdacbcdbabbccaadddbdacbbcdbcbcddacacbabbdadbaabccaddcccddcaabaddbcccaddddaabacacbdbddccacdcaabdbaddcdbcccdcbaddacdabcaabbaaabababdbdbbcbacacadbacbacacaabbdabbbacddabddbbcbaddcdcdcdcbadcdbcacccdbdcaddddbdadaadccdbdcaccaabbacaccbbaadaddbccacdaaaaddddcdddaaaaaddcbbbaabbcbaccbbabdccddbcddcbbbbbdddcadbdabbbaaddacdddbdcccdacdbccaaadcabdcdbdcbdbccdcbcacdcdacbcdcdcbbccccdcadccdaabacdddbddcbbdbddacbdccabdcbccbbdbaabcbdbcacbbacabbcbddcdaddccdcddbadbbcdaccbcbacbdaaaddcbcadccddbbabcacbdacacdbdbacdaaddddbbbdcdccbcdbbdbdacdcbbcbbacbcdbdababacdccdcbdcbabcadabaacbccaadbcbddadcbdacadbbbbdcadddcdaaaccbbbdaabdccbbcccbdccababdddacacacbabbcdcdddbbdabcbdaacbcadcdcadbbbddcdabacdacdbdcdbbcdccdbaccdbbadbbdbaacbbdaadadbbcaaadbcdabadbbacdbabdabcbacacacddcbbcbdcbcbabdbaddcbacaaccaabbdbcccddaabaacdcbaccbaddababcdcbbcdcbcdcbcbbabdcadbccabcdbcaccbbaccadacacbbbbcbbcbbdddacccadabadccbdcbccdacbcbbcadabddbcaddaaacdbaadcdacbdaacdaabadcdbccadaddaabbcbdddbcbdadbdacbadbbbbcbdbcbddcddbcdbacaabdbadbdbcbcaddcddbaaacdbdbcabbdacadbdadacbddacbbabcdacccbddbbdbccccddbaddcdbbbbdbbaabcdacacbdcbbadcacccaccbabbdbdcabddcdbbbdaaacabcccbcabddadcbcbbcacdccabbabaacbcdbcabbaaabaabbdddacddbbbddbdaccbdaabdddabccbdbabcddcadbcacdbbbdcccadcdabdcdddcacbdabccbccdaadccdbaadbbbcbdcdbbbabcdabbaddabdbcbdbbbdcbcabacbbaabcddaabbbcbddadcbaabadabbbcddabbaababbbdaabbdabbbdbadcadbcbdbbadababcdacaacbaadbccddbacaabcbdddbdcacbcaaccbdacacdbbbaccdcbdddadacbcaaadddaaddddbbdaddcdddbdccdcbddabacbdccdbbcccddacadbabdddacbcbdbbccbaaabcbbabbdcdcbdaddadcdcddcdbddaccdcbaadaadbabbbcddabaaccacabcdcaaaaddacdbccbacdaadabccabcbdbcadcabcbbbaabbdccadbbcbcbbcdababbadbbcbbbbabcccbcacabaaadccaacbaadbcabbdcdbdbbcdabadabdcbdbcddbadbbdbcbbcdcacdacdcaddbcacaaddcabdcdcaccbbddccbdaabccbccbcbdddcbbdbdbaadcdcabdadcbcbababbbdbdbaacbdcabbaacbbbbdcdcabbacabaaddbdabbbbdcabdcbcaabbdddadbabacacdddbdbbadcdccddacddcccbddaacbddddacbaadddbacadacaacdbadcdcdaabbbadcacaaadcdbdacbdcbaddcccacdcaaddcdbaaaaaaaabccabddabccadcaabdacdadccddbcabbacadabbacaacddbaaccdcadbcabdcdadccdadcabbaaabbacccdcdccdcbcdaddabdcdccdbccbbabbbbdbcaaabdbbbcaabddcbaccdddcaabacaadcccccdaaacbbbbdaaddbaaadddbacdbcdaabcdaabaaacbdaababddcacaddcdcabaadbaadcbabcadcddddabbaccbdcabdcbdabbddbbbbacdddacddbdbbcadcadbbcddbcabaddaccdbbaccbcacacacdbddacadcbdadbddcdccbdadccbbdddcaccacaadccbabdbaabcdacdbdaadcbccabbadcdacdabcbcbcabcbbcbabaccbccdbddbcdadbbacbdcbdccbcddaccababcababbbaccbbbcacbababbddbcaccccdbddddcabcbdcdcdcabccbbdccbdcadcdccbbacdabcddacdbcabaccccbbccdbdcaaacbbdabacccdcdcbbbbdccadcbbbcbdddadcadbddcbccdbbaaabcdbdabaaaaadbdacbdbddcaaadbbaacabbbcbcccabdcadadbdacdadcbcccadcaacbbbaabccaacacbacdacdbdabdaccabbdcccadbacdbacdcbcbcbcbcddbcaaadddccddbadcbabadacaadcacdcabaacccaaaadbcccddddddcdccabdccdaaadddcbdcaacbdbcabbcacbbccddbccddcccdbdaaaaabbddaabadacaacabaadbcdccdaabdacacaccbbdadaddaadccbdbaaadadbcddbddcdcdcaabdbdaaddccbabbabacaabdcdbbbdabcccadcaacbbcbdcccabacadaddacabacdaddcbbbabbbdccbcccbbbcaacbbddbcddbcaabdbbcaaabdaccbcdddcaacdabacbcbcabddabbbddccbacaacdbcaaddddcddbbddbddcbabccaaaccaaaccddbcddcdbdcaddacadcbbacaaabdacadabdbcadccccdbdbaddbbbabbdcbbdaadccaaacdcbabddbbbabadacbbcdbdbdbacbcaadabbcdcaadcbadaccaddbadbddccdbdadbcbccaccadacadabadbdaddbdacccadaddbddddabbadadbcacccdbaadbccbdcdcdaacabdaabcababbcccdcdacbdabdddcbbcccabadcdbabaddababcdcbdbaccdccbadbabbaacdcdccaacabdcdccdbcbccdabbbababdcdaaabddabdccaaabcacacacbddbbdaadcdbbbcaadbbdbdbbccdcacdcddcbbdcdddccadbdadcddbcabadcabcbdcadaadbbbccddcdbaddbabbdddbdcbdcabcababaabaccdcdadabcbcbdbdddcccbaddadbcabcaddbaadadcbcbddaaacdacdddccdabcacaacbbbaadbdddbacaabababadddbadccdcbadaacdbddcdabdcdcbcaadbaabbaacbdcbabcaabdabdccccbdbadccabcccacacacdbabadaddababaddcacdddcccdccdcadbbbbbaddabadddabddcaaacaabbdbcbbcdbabadbcbcaaaccaadbbbadcacbaabcbdbcdacdbaddbaccddbddcaadbaaabcacccabdbbccaccaabcbcdadcaadadadaabacbbababcacaddbbbabdddbdbcabcccdbaaacbbcdbdbbbdbccababcbccbbdcdcabdbacddcbcabccbbabbbbbdadccbadcacdcbcbddbccdcbddadcdcbcadddcadabbbcabbcdbddaacdacabbcccbdbdcbbabababddbdddcdcaabbdaccdcdaaadcaadabcacbdbbacddabbcdbbbacbbabbadccbadbbacaaccddcdabbdbadaabacbaddcadadcadcdbadcbacbddcdacbacaddacbcbcdccbdddbccdcccdcddbdbbccccaadcabadbbdabddadbbaddabdaadbabaadaabdabcbcddbdaaccbcdaaacaabcbbaababbcacdbdbcddbababacdbcbbbbdacbdcabdbccccccbabdbdcabbabbdddbcbabbbdbaaddcbbadcabbbaabababcacdabddddddbaadbadadadccddcababdddbccbadccadaaababdcdcdbacabcdaadbaddcccbccbbddddbddaacccdabacabaddaaabcabcbddaadcdaddbbaccdcbbddddaddcbcddbdacbbbcdbccaacaadbbbcdcbbcbdaddbbcacddcdbccbaaaddbcdbdcdaddbcddddbcdcbdacdbdbbdcbbdddcbbaddbbdadbdbabdaabadbcccbbbcddcddacbccbbcbbcbcddaddbbdabdcadaadddbabadcbddcbddbccbaaabdabdbaaacddccbbdaddaccdbbdccdcbcadccdbdaccdabbbbdcccdddbcdddaaabbadcdcacacadbbadcadaccdadbabdbadddbbbbcdccadadbdaacabbddcadadccabbbbbadcbdccdccbddcaaddccdcbdcdcacabcbdddcdbbdaaaabdcddcacbbaabcccbacaaabbbcdbccbacbdabdbbbcabdddbcadbaaddccdabbcdbbdbdbcbbccadbadabddbdbbccbbcbdbcadcabcbaaadbbbabdaddccdbadcadcddcabbbdaaccdcdbbbaaccbcabadbdbcbbadcacbddccddbcbbdcadaabadbbcdddacbcadabcbbbbdcacdccacadcaadacdacdabcabdcbdcbaaacaacbadddcdcabcddadbacccaadbcddbabbbaaaaccdbccaddcbacddaddbdbadbcabbbccddacdbadadabbacbabaacbcbbbcdccadbbcdcdccbcdcccaadbaaaadbddbddcdcbcabdbddbbcaddcbcddaaacaadaabacacababcabcdcccbcdbbcadadccabcbdbbbdcabcbbbbbcaaabbabaddacdcdbdbabcbdacabddbabdcccbdaacdcbccacaddcacbcccdddabacdabaddcbbaabaadaaabddddacdaddbdcbcdbbcccdcaddaaaabcbaabbcddacaaccccacbcbabdcadcddacbbcabcaabcacbcddaccaabddadbdbbcdcdcccdbcaadcbdcdcadddddacbadbaaabdaabcdabdbadddbdcabbadbcbbcbcadadcaddaaaadcccadddbbbdaaccbdbcadcccaccddadccbbccdcdacdbdacbaaaadaaacddababcaddbdcccabbbacadccbbcbddcddccbcbadaddcacadbcddbcadadbdddabdcbdcdaccccabcaabcbacdaabadcbbadbbabadabddcbcdbbaacdadcaccaccbbdacdbccbbcddbacacaabcbaadabaaaabacdcabcaddcdcdcabddabaadabdaabcacdddcdababacdbaadaadaabbdbdadbbdaacaabacbddacadbbdddbdcacdaccaabcbbdabbbabbbaaaccbaddbadddabadcdddcbdbabcdbddddcaabdacbbbbdaacaaacdcdbcddabacdcccadadcdcababacdacdcbadbacbdddbdacdbbbddcdbbccbabbbaadccdadacaddacacbbdddacdaacddcddaaacccbdbccabddcbaadcbaaadaaddcbabccadcaabdadcbbaacbadabbaddbcdbdbadbacdbcaccbabbabdddabdcccadcdcdcdcdcbadccbccacadddddbdcaacccbbddbaacdaadaacdcdcbadbddadbaaacdccdacacdcdacbdcabcdcdcaacbadaaadabdaddcddcabcbaccbbcadbacdabcdabadbccccdaabccabccddbacdabbadbcabddacdddbdccaddaabadcadaaddbddbbbdcadccadaabbccadbdaaaaaacabdbbbbccabdaaadcbccaacbcdcbbadccbcbddaacdaabdadcdaaacabbacabdacccacdcbccdcaaaabacbabcabdcbaccabdbdbbcbdabdbbbacbcbacbacddabdabbabdacaaaaadacbadbcdcccddccadbddaccbaacaadadbdddacddacbbcbdcacdaaddadabcdbcbdccbcccaccdacbbcbaaadbbddbadbcadbdddddadbcdbabbabdaaddbdccbbccbdadbdbbaabcbddabcdcdddbaddcaaabbdbabccaaccdadaccbacbbbcdaacdbbcacbcadddbcabcdbbddaadbcdaadabbbdaacbabcacbbcdddccddcdccbdacbbbacabcbaacbcbabdbddadcbdacbdcabcbdbddabaacabaaabcdbadabbabcdcbccbbdcaccadbbdddbaadabccbcbdbbdbcccbdcdddcdaadcdbbdcdcadddbabdbdaabcbdccaabccdcbadcabcacbbcdcdccccaddcccdcabccbbadaccdcdadcdbbbacbcddbbdacbccddbacaacaabaddcdcdddcbbbbabbdcbbcbcdacddbcdbbdcbdabdbaddaacdcaabbdcadcaabdbbaacbadbcaadddbccdbbcbbbccbdbabcbcddddcadaadbdbababcaadcbcbabdbdabdabbbdbccbbaddbbcbaabddcbccdabaddccbacccddddbcdabddabbbcbbcdbdacaddbdaccbbdbbcbbdaacdababbbbcbcbcdaacccabbbbbadcdaabdbddadabacbadaccdbcadaabcbddcdbadccabcdaddbbddaddcccbaabcbcbadcbdcacabadbcdccccaaadcbacbcdbddbcbdaccdaacbaacadddbdbadadbbbccbdddbccabacddcadbcdacaaaadacbdbcdcccdcdbaabbdccadbdaddaadbdcbabddaddbddccdababcadbbcdcbcddbdcbbdcadaddbbbdacabdadbcaddadcaaaaadcabbdbcbdddbacababccaccdbdacbdcdccaaddcdadbdbbcadacdcaacaddbbcdcdcababbdcdbdadcbdacbdabbdddaadbdacabaacdccbbbacdbacccdcbaccdaccbaddcdabcbadabadcccbbcbadbbdabdbcccbabcdbddbddcbdaaaadacbcbcabccdbcaacabddcbccdcbdbdadcdbadbaaadbccbbcaacbcdccbaacbcdadcdbadbadcccadcaddbcbaddababbcdaacacdcbddbbaccacbbbabbddaacddccaaddbccbcacbddbaccddbbcabbbdcddbcaccdbdadcadbdacdccdbdbccccddabbdbabcbadbcddccbbdcacbdbbbdbcdcbcacacabcbccbbbdaaccccbcacaacbbabbadbaacbbddcbcdaaacbdbbaadbadaccbccdbaaadddcacbadcdcbabdcdcadaabddbddcbcdcdcddcdbccadbcacdcbdadcbdcbdabadadaaddcdadcbcadddddccbacabdbbbccacbacdaddccbdacaaabccabbbdbabdadcabbcbdcbddcdbccccdaccdcadccbbbbbbbcbcbbacaadcbcbcadbccbcaaabadcbaacbdbacbbdcbcabbbbbcbacdddaadcababcbacabbaadbadcbdadbacaababaacdcaaabcddaccbcdaddccbdbdcaabcadcacadadccbdcdcddbccbbccdbbbdccaacbdacbdcdbcddaadddadccccbcdcbadadadddbbcacaacaaabcbccaaddcdbcdacbcdabbcdbbcbbcccaacdbaddadbbcacdaddabbaddbbddbdbccbdddcacdbacccbbdaaaadbdbbbbcccbdacbdbddccadadbbdadcabbbabcdbdaccddadbdcadcaababccbbbbdaacccbbbbbcdbdacdadcdcaabdacbccbadaccbdddbcabdaaaaabdabdbdaadcdcdacbacaadbdbcdbacabddbcbadbabdbbdbaddcdbbddcdcbcaaadccbbbadcccaacadcdbbddcccbadcdaaadddcdcaaacdcdaabddcaccccabbcbadcdcbccaadabcadbcdbbbbdbacbcdddaaababaddcabccbdbcbcbacbcbcdbcbcbaddaababdbdaacadbccbcdcdbccdcabbdabbdbdaacaccccabbacddbbdbadcacadcccbacdbdcbcdbddbbdadbbcccbabcccadabacdacddcaadccabbdcbdbcbddcbbabacaaabbbcaccadcdacdcdbcddbabcbccaacabbcddcacddccbddadaadcbbdbcdbcccbaddbacccbddbcccbcbbbadaddbdbdabddacccbdbddcbdbbcbabacaddabdbcdbadccccbdbbdbbddcbbbdcbcdcabdacdddbcacbabaaabccdbdbadcddaaabaabdbadacaaaccacddbcdcdaacaadacccbabaabbdabbacabaabcdadacbbbcbbdacbdadaacbdddababaadbacdcabdcdbccacddbbdbcaaaaddacacdddbbcdcdcaadcadcdddaadddddcddbccdbccbccdadccddcdaccaddddddcdbdacdcdbdadddcdbaabdcdaadaaabcbabcdcbbbbdcbdbdbacdccbcbbbcddbaaaadadcbbcccaaacbbbdbcbdabdcccacadacacbdbaccdaaaabacbdadadcaaaabbaccdbabbddadbabbabbdbdbaccbaddbdbaabbccbacdaacabaabdbccbaacbcaccbdacadbccdadcbabcaccacdbdabbdabbacdacbdcdccbbdcddbcbcccabacaadccabaabdaddadbaddabbdbaacbcdcacbcdddcbbdbbdcacdbadcbddccdcabbacdcdbabdbcbbbcabdccdcaaacaaaaddcaccbadbacbdbccadcbbacdccdaadaabcdddacacbacadbabcacbabdaacdccdcbcaaccadddabaccadcdbdccbabccbaacccacacccdcaacdcacbdadddcdcbbddbbbbdcdbbddbddbcbcaacdccadaccbdaabcabaaabaadcbaaddcabccaadccbbddadcddaabcacddcdcbbabcddbabcccdabdbacbdaacacdcddbccddddcbdcaaaddbdbcbdddddacccbdaaaadcaacbdcddbbaacbabcdcdbcbadaddbddbacddcccacdacbbbbdabbbcddbbbaddabcadacccbdaadabbdcdbdacdababbcbcaacaabcbabbdcccacadaabdbbbdcdcdaabaacaccbcbbddabaabbcbcdbdcbddcbacbbbadaaacdccbdbdacaddcbcbdcaaddabbcddabacbacdacdbdcbddabcacbdbacadbdaacbacadcacccabcdabcccdbabccbadacddabdaaabcdbcdccbccbbcbaccbbcccbbdadbbbcacbbadddacdbbacdabacbabcdbaaadcdccbcaddcabbcabdcbadbcccbbbabdcaddaabbcbbdcaaddbccbbdccdbacacabddddddcadbaadcadbccbcccacdccdbdcdbdababccddacbaabccdbcdabbbbddddbacaadccdbbccabbddaabacbbaabbababbaccbddacbcdadbccdcbadccbacdaccabdbdbcaaccccaaddacabbbdaadacaccbddccadcaacdbdabaccbadacabbacdbdbbaacaabdaccaccdaadccdcbdcacacddbcaddaacbcccdaddbaccaadcbcbcabdbaaaaabddbbccdbbbadcadaadadcaabcbcdadcaadadacbadcadacbbcdddbdaacabdaadcbccacccbaabdbccddaadaadadbdabbabdbdbdcaacadbdcdacaddbaabddababcdbbdadbbccaccbbdabdacccbdbdbcddbcdbbabcbccbdcabadaddbbbbdcdbdbababccadacbbdcdabadbbbcaaaacadbbdccddbcbadbabcbbcdbdaaabbbbdaaaaaabcacdaddababcbcdcbabbdaaadcdbbdaddabacbabdbdabbcaacddccdcacbabcbccaddcabdbcbbcbbbdbbabdadbcbdbabcadbbbbdcbcdbaccaaaaadadbcbcdaddbdcbadbababdbbcbbddabadbadbcbadcccddddcccccdcaddcbaaadcdadbabccbccaacbbdcadcacadadabbabcbcdaaabacacbaddbadaabbbbacdddcddbdbbcaacbadacdadcdcdabdbddcbaacbcbddcdbacccaddccbbbcdccbdbbccdaaddcdaddaaccaddccdccdaabcddabadbbbbaadcadbadddcccddcabbcdbbdaacacccdbbabbcdcbcdadcddadcacbadbdcdbdbacadddbabbdabcbcbbabcdbdcadccbdbadabcdcacddcbcbbdacadcdacabababcabdbbbaacbbaabadadbcdaabbdadcdccdbdddddabadbabadbbdbdcccadcdaccdbadbacddddbdadaabdabbdbcaadbccbccdbdbbabdcdbccadddaaadbddbdabbbaadddaddcdcbcbbcddbdcbccaaadbbcbcccadadbdbcdbcbdbbbbabcccdbdaabbdabaacbcdaaacdcbbdacabadbadccbdcabcacdbdbcbcdcaadbbbcbaacaabbbcacdbaacabacbabcbcabaadaadbccddacadaddcaacadbbcbaacacbadacccdaccdbaacdcbacbbaddabdadaadbcabbccdbdbaddccaaabbdcdcaabddababbadcdadcbabbbbabaccdadaaccdababcaabbdabadadacaddaadadaaddbabababcadbabbdddcaacbcaddbcaaaacadbbcaaddccbaadacdcacbdbcdbbdadaaadbdccccacdadbdbbabacbcdadbaacbadccdadccabddbabbccbacaadcabadbcddbaddbdaadbcdcccccaaccacbcbacbacdaadcdddcabcddbcadabaabdddcdacaabbcdcbddadccadbacdbbacbabbbdaaaabccdddabacddbdbbbbaacaddabdcbbaccadacddabdbdaccdadadbcccbcaccbccdcadaddcdcbbbaabadaccdcddcacadccaadbcdaddbcddcbdcbaaaabccbbaacabcdcdaaaccadcacbabbbdddddcacabcdbcdaadaaabdddbddccbcbcdbbcbacbbdbacbdbccdbdacadaababacabdcabdbdababdaadaddbcdbabccbacdbadddabbbdacccdcdbcbdcdcbcdbdaadccdbccaddbbcbaaababbdbbcacbabbddbbadabcddcabdccdbadcacdbabdbabdadabcbdcaaaacabbdbcddddbccdaadddbbdddbdbcbaacdadbbcbdcbcaadbadddddbdabcabacacdcdacabbbbababcdabbacddccbcdbdccccbaaccacbdcadadacabdaabccadbacdcacadbdabbadcbbbcdcacdbabbbbacdabcadbabdbaccbbdccaacbcddadbccadddbcadddbbaddbcadacbccdabccbccbbcdbdbcddadabddbcaadbdbacadaaaaaacbbaaabccbdbddabbdaadaccbcbddaaacaaaacbcbbaaccbdbbcbdccdddccbbacddcbbbcadacbadabbcbcbbdcacbcaabcbaabdbaacdbadbccabccddaaaaaabaadcdbccbcadddbabaddbdbbabcbadadacadcbabdbbbacdccaaadacdbbabddddddccbaadabacdcdbbcadcbaaddbbbbdbccddcbbcdbaabccbdacccabcadbdaaadbddbabadbdabaaadabdcbbdbbbbcbbaabaacbccddbbdabccbccdaccccdcadbdadcdbbdadaadcbdadabdabadacdbbbddcdbcdcaccbcaabdbaadbacbdaccdbacdcabbadccdcbdcbabcbcbccaaabcccbdddabbbbdcdacbcadcabbdacbcdadbddadaadcccabdbcaccadbbcdadddcacaccaddaabddddcdcdcdcbbcdbadcddcabcdbabaadbdddbdaacaacbdccdacddcddcabccabadcbabddbdadccaabdcadacbcacabdabcaddadaddbbabddccbbbcbcccbdadddaddacdbacacdbaaacbaaacaacaacaaabbacdbcbcdbacccbbbddbacadaaaccdcddadbdacbcdaaabdabcbcdacadcdbabacdbaadcbabdbbdbabddabbdbbcadcadaaccdbcdcccacdbaaaadcccbdbdabaadcccdababdacdcccbbcaddbaaaabcbbcbbbbdcdbdabcdabacddbdbcdbabadacdaaabaaddababdcddddbdcbdbaaacdbddcbacdadddbbccbcdabbbdaaaabcccabacacddaabbcaacbacbdacadaddabadbbcbcaacbcdbacaabbcaacddbcaaadcbdadddaccdbbdbacdabacdbcbaadaddbdbdadbccdcadcdcabbbadbbcacddcddcacddabbbbddacbcadabbdcddddcacbccadbddddcbadaccdddabdadbcaaddacccadaddcddbcddcacadbcbdcdddbdacacaaaddcbaaaabacabdadbcdbccbddacccbbdcbbaadddcaadbcbabacddccbabdcbbabdbcabdaccbcddcddcaacccbdbdaccbabcbdbbdbdaacbdaccabccacadabbdcabcbdaacbccdcbbbbcdabcbbdababbccdccbcaaacaaabbdabbacbcbbbbdcbcdcbacbcbcaaaaaaddbbadabcbcbbbdcbbaccabdaabbaccdbbdcbbbcadbbdbadadcaadddbabbabbbcaabcdacacbcccaaabbaccbbabcadddcdbacabcbaabbacacdcaccaddddaaaadabccdcdcddbaccbdbdadbabbbddbbadaccbaddcdaaaadbbbdaaabaabadccabcdddabdbbaadabcabbbacbdaabcbbbddbdcdbdadcccbcbacaaccddacbdaddaccadaccdabbacdbbbabcacabdadccdaaaacddcdcdadbdcdbdbddaaabdbbbcaadbdcbdadcdcbbbcccdccdbbcccababaaaaadcdbdcacbabadacdaaaabbdccdcadaacbdbcbcbbccbdaddacdadccbddbcadadbbccccbdddbccdcddcbdacdbcdbabcbdabbaadcaddaabbcdacddbcbbddacacbadbdcbbdcabdadbacadcaabdcaaccaaadacaadccaaacbaaccbccdaaadccadcddacdadcdcdcddddaccbbbdadbaccddccdccbdaacbdcbbacaabbbbabbbacbdcdddaddcbbcaababbdddbcaabcacbbaddadcdabbaddbbcdbbcdacdbbcbddbbdadccbbcaccdbdbbdabcccaaddacddcaadbcbcddbbddbcbbaadabcbacacdddddcaccbbdbcbddcaabcccaaabbabacbaaaabdcdaadaccbadcbaccadbbcbbaabdddbbadbbadaaadcdbbdcdcacbccccdbdccbbdddbdcbcadbdabccdcadbbdaaadabaccbdbbacdcacbaadbdcddaaacacdcbbbcddaaaccdbaadbddcdbbcddaadaabacabbbcbbbadcadccdddaaddbbdcbdbcaacdddbddddabaccdaacbbacbcaabddcbdbadaaaadcbdbddcbbbdbbaddaacbcbdddddcbccddbbcaadcdaabcadcbaccadbdbadcbcacbbabccdaccabdbaaddadaacbacaaadbbbdcabbadbbdccacdddddbcbbdcacaacdcdcccbcccaaaacdbccccdcaaccaddbabbbdcdabaaabdadbcbbdbbcaadaadacbaaccbdabdadcbbbcaccacdbcccdbaaddcbcbdbacabddacbbcddcbaabaccabdaaddabddbdababacdacacbbdabccdddddabcbccdbcacdccacdbacabbdbcdbdbbdbbaccaaddadbadbcbbbddbabccacbbbcaaaaccbdbbdaabdabdccdcbbabbabaccddaabaaabccbadadaaababcccadcccbcbdddcdcdadacaccdaccccbdbcbbaadabcdbaddbbdbbccbacacdbcbcacdcaaccdcccbcaacbcdaaddbabaadccabccacbcadcaadccbbaddabccdadbcbdacadbbdbcddbacdbdcbcbaabdcacabcdbcdbcbdbddcdabddbbcbbcdbbcbdbcbcdccdcdccdbdbddcbabbccddcdcbbbcdaadcbdccccdbbcbcccabbadcadcadaddababbccbbcdbccbaccbcdccbbddbbdbcbdcaaaaccabbacabcaccabdaabddddabbcabbaddbbbbacaabbbaaaaccdaacdaccbbdadcbbbcbddbddcacdadacdbbbcccbbbaacabaccadacddcbbbcdbcaccbbccabdbabdccaaabdcabddcbaddbadbdbdddadbabaccbcbcaddbbcabccbcdddadccccbbadcaaabdbddbbaadbbbcdadabdcbccacadbdaabdccdaaaaadcadacbddababbdbbddcdccdacdbcddadadcccbcdbddcbddbdabdbbadacabaacddbdbbbbcddcbdabccdcbbaaaaccdbdcbbdcbaccadadabbdadcddcdcababdbaaddcadadabccacadccddacadbcaddaddbbbdbddccaaababcabbdbdaabaaacaacccdcdaadaabcaaabbdadddbcbbabddbadbacaacbcacbbacbacccadcacdbbbbbaaaaadbddbdcaccdaabccaabcdbaacdddcbbcdbbcbacbbcccdadaabbabbdaabbbccababaaadcbddcbababcaacdbcacbdabaabcdbcaacccadbbcdbbbbbbcbdbaaccddbdcbcdccccbbabbbbdbcdcabbbddbbdbdbcacdbdcddabbbbdcabcccdddcdabbddccbbadcaabcdadaabdbabaabbacaadbdbbdaacbaabcadcdbaddcadccaadacdccbdbdbcddccbabadbabdabddaacaccccddbabbdacadbcabadcdbadbcaddbadacddcdacbbacdbadcaaacadbbaabadbcbddccadbdbbdaadccbdcdcbccacbccbababcbdddbcabaabbcdacbddcdaaadaaaacbacbabccbdbaaabaddbdacabbaaccadcadbdcdbaacadbbabdbbdadaacdccdaccadbbcdacbaaabaccdcadadbdbacbadddabcabddacdbcbddacbbabcadbdcccdccabdacacdcadcbcdbdcdbddbcdaacbdbdbcacdabcbddccbabdcbdbdcabbbacadddccadcacdaaaabaacdcdccbbabcdddcababcbcdacdcbadbaacacddaddddaaaccaabacccdbaddabdacddbbccacbbdabdbadacaaabaaabcdabdbcdadacddacbccdabbbabbdaddbbadccaccadaabcadbaaccdbddadcbdbccacbcaccbaaadddcbccbbdacbacdbaccabbabddcdaddddcacadadaaacccccbaccdbccabdabdaadbcdcddcadcbbdacdbccadccbbcdcacccabcbdaaabdadadacccdaddcaddbaddaacdcddcababddddadcccdcaadadddacbdadbbdbbbcdaddbaabccbbbcdbcccdbabadcadddcbcdbaaacbbacdabaadacdcaaaaadabdabdcbbdddcbbdddcdaabcabbcbbdcaacccaadbbbabaccacbabdacaabcbcabbadacccbbbdacdadcbccdcacaadbcaacbdbcbdabbacababadbabbacbbbbbcbcbbcdaadcdadadbbbbdabacdabbbabccbccdddccadbcdacbccadaadddbbaabaabbdcbddadbbccacaadabdcabaadadbbcdbbbacaccdbabacaaabbcddaacdccdaaabdccbccccbddcaaccaadbcbaddcdddaadcadabdbbbcddddbccbddabbcdbaabbccadccaaabaaadbbccdbadabcadcaacacccbbcaccddcbbaaaabdcbbdaccaadadbdbaccdbcdbcbcccacacaadabcaabdcbaadbaacacbccaaacabdcbadadcacbcbdacadacdbaaacbbbdcbdabdddbdcbaaaaacbdcacdbddcdbdbdbccdbddadcacdcbcbdbdbabbaacacbcdacccbbcddacddbdcacabccaddcccdccdbadbcaadcdbdbdcbabdbbbbcdbadadbcdcdcdaabdbcabaaddbaccdccdaaddbcbccbbcbdbcdcccdadadacbddbacadaacbaabbdababcbcdbcabbaddabddbbddcbadbadcbdbdbdbaccbccabdbcaddbcdccaabbbbaaaaadadbaaacbcccadbddadccddddaadbdbacabcadbcbabadbcdddbdbbdbbadbdbcccbbcbbbcdcddbbdcbbbbaadccbbbdbddbcaadacbddabbbacacbbccdcabbabcabaabdaaddcdbcbabcdbaabbdcccaacbdbdbacadacbabbaaccbcbbadbddbbaccdbadbabcdbacdccaadabcbcabddddcddadddbbbccdbcbabcabaccaadbbacadaadcbcaaabaaccaddcdacbbdcadcddadcdbbcbcabdbaacbcbbaacdcdbbabcdacabacaddcadcdbcaacbccbbdcaacdddccbbadcbcddabbbaacacbcdcbadbdbcbabbcadaacddbdcacaabccbacbbdbdacabcdcdcdabbabccbdbbbbbcabcdbdddbcdacccbdbcaccabcdadbdddcabaaccdcdddccdccacdbaadacddcacbcddadcabdbbbcccdadcdbccddcabcadabbdccbcabbcadcaadcdbaacdddaddbaccdbddbcdbcaddacbadddabbccabcbdadcdbdacabcbccacdcbbccdbcdcaaaacacbaadbadbbacbcdbcdcdbcbdcbccbcdbbcaddbdbdccdbcdbbbaddaadabadcaacaabcbdbdbadbbadacbbdcccdbabbaddadacadaabadaccccdbdacaddaaddbabbcdbbcccbbaacbadaabbbdbcabdcacdcddbcccadbcdaadacdbdbbbacadadabcabdcbdbdbcbbbacaddcabbcdaadbbdccdacdacbdcacbbaaccbccaabddbccbababbbaabdcbcdacdcccbacabdbaacaacadcacadbbbadcccccbabcddababcaacabbdcddabbcbabcbccbdaaaabdbaccbdddaaaadcddbdddbabbbacbcbccdcadccddcdddbdccccdabdcddbaccbabbdaddbbcdbaddacadaddaaabbbcabaddcadabdbbacbddabacbcbbbdbdaadcbdcaaaacacadcabdbacaabbbaaabccddaccbacbcaddadadacacdbdbbdbdabcabddbaccaccaaaddccbbbabaabbbaddddbdbaaabbcbacbacacacaaaddcaaaacaabacdacaabdabbaabbaccadcbbbabcbaddbdcbbbaadcbbdbaacddcabdadcbcbcbaccddbbdcadbbadbbbddacddadacbbdcbcccbabcbcbddacbbccccdbaabbcdbcadaaaccbcbcaccbabddbccbdddabdddabcadddabcbdbbdcaacdbabddbbdbcbddccbbbbcacabdcdcdbadbdaaacbdbdabcdcacbbcbdaacdadaaddcbaabdadcddcbbaadbddaddcbcadddcaacbcbbbabbdcbababddbcdcaccadddcadadaaacdbcdabbaaacdcbaddbaaaadcdcbccdadccadcaccabcdbdcadcdaadcbaabadcbabdabcbcadcdcdbbaddbcbddabdacdcabacaacbbdacbdababbbbdcadccadacaccbbcacabaccbccabccbbbbacdacadadccadaaaabdbbdccbbbddbdbdabcccdbbbdccababbbcbdddaaacbdcbcaccdbabdbbbcadcdddbcadcadadbddacaacccccdacacdbbcbdadbadbabdaccaaaacbdadaaaaaddbdacacccbaacdbcacaaabaadabdcabbbabdcdcacdcdcbbddbadcbadaabccdbcbcbaccddabbccdaccbbabdbdcdabdbdbdcdcdbbacdcacdaaabadccaadbabbcbadbcbbaabdbaabaacaadabdddccacaadaabcbacbddcbdbddbdcbbbccacbcbcccababbccccbbbcccaacccdbdbacaccaaaaadadcbcabcabaaadabaaaabcacabaadbbcbbcdacccabbdabbaddabcadcbadaacbbddaadcccbbddccbaddaaacbabdaddddbadbcccabdcadacdbccbaadabcbdcdacdacabbbdbdcbddadbbcacdaadddcbdccbadacbacbbccddbdcbccdbdcadbcacbdcccaabcbbbbccadbadbadbabbabdccbacadbdbcbbbbdcbcdbdcdbcadbcbdbdbadbdcbdaabbcbcdccdbcccadcbdabcadadcadcbbcbbccabcabcbccbdaccdcabcbcbabbaccdcacddaaacbbbabbdbcbcbcccbbdddcbddcbaadabbbadcbabadccabccdbcaccddbccbbcabcdcacbabdbccbbcadbcacabaacadcbbcbaacbdccaccdaddcdadbbddbddbccacccaddcabcacaaadadabcccbdbbabcabaadaaacdcdabbbadabbaaacacdbcdabbbcdbdaccdacdaabbcabbaccdabcdaddaddacdcdcbadabbaddccbcddcdabbdddadddbdbcbcadadacdcdabccacdabaaaadbbbbbaaddddcbbaaccbdcdddcdbdaaccbbcaabdbcccbcdbcbabbcddbbbbbaadaabdabbcbcacddbbadabacabccddacbdcdcadaacccabccbaccaacbabdddbaaccccacdaacddcadacadcdcacbadbaaddbcccaacdbcbbadcdadbbcbbbdccadcbdbddcbacdbadcaabaabacaacbcccaaaadbacaddabacbbcccbdbbbcaadcdcddadaacbabccababcbbdbacabddadbbdaacacdbcbabadaabdacaaabcddbddbddccbaccbabcccbccdbcacaaabbbcbaddadababccdbccbdcdabcbaccbcadaacaadaaaadddbbdadcccddbacabaabccdaccbbcdabbbadbcbdaddccabaacbaaddccbccbccddaadddcdbaccaddbcadcdcadcccbcdddabaadbbdacbdcbccbdddbcbadbbdcdcdddaacbacdaccacbdabdcadabdaadccddccbcbcadcdbdbbccbaddbdcdacdaabbbabccdbbadcadaddbbddbcdddddadabcaccacccdcddabccdbdcaaadcdcccdacdcadacadcabcadcaadacbdcaddcbdcbaabbabbbabbdabcbbaadbdddcbdcdabaadcbdcddadacdabbacacacbcdababbabbbaaaacbdadabadcadcaaabbaadaccdddbaadbbbbabbbacacadcdcdbdacaccaadcaaddbddaadaaddcbaccdcddbbddabcaccbbbadcdaacdcbcabaaabbdcddcbbcdcdbabddbcddcdddcadbccacbaccaccbcdbdccbcbdbadbadcabbccbdbacbdddcdbaacaccdcaccbccabbcddbcbbcdcdabbbbacbcbbabbaadbbcbaaadcabddbbdabccacbabadaabcacabcbbaaccabdbcccaabcdbbadbbdbdccbadcbcdadbacadcadadbbbdbddacdcacabaccabbdcaccbddddadabcacbabbcbccaabcbbaddadbadbcadcdbdcacddaaadcdcbbcaacbdaccddcdddddcacdaddcaadddbbcbdcbdcdabaddccdcacaaaacdbcbbdcbaadbacdadaacdbbdbcbabdaabbaadbbdccbcdabcdcbcdbcadcdddbcdbddbdbabdbbbdcdcddacccbbbbdcdbabdaadcdbadcdcbddddbbacccbaacbbcdababdcbcadcdcabbcbabbdbcdcdaadacadbbadacdacaaadccadccdcdddcaddcadcdaacbdccdbdaaaacadbdaaadddddbbabdacacbaadccbaaaacaacdcbbbadacadcccaaccaddccdabdcddbbddadaabdbddadabccbaaacbcbabcdbbbbabbdbaacccdbaaddabbdbabbbbbbbccdaabbcdbaddaabbddbdbbaddbaacbccddbbacdbcacbaaadcdccdcaddaabaabdadabcbccaddbbbbadbcadbabadcccbcababbddacbaaddddaaddcdacbabbdcbbbcaacddadbadaabbabdbbbdbaabbbcdbbdadaadbdbcddbbaacaaddcaaabbddaabcacababcaaadbdcdccbaadbdbcacdbdbcbababcdcccbcabdddbcccbdcbbaabcabddcccdbbaccccaadaabcdadabbcacdcdcdbadabddcbbadbbbbaddcaadcbaccbcdbdccccbbdaacbdbbccaccbaadabcadaddbbcabcdccabcadccbaabaddcbdcbddcbcdbbdcbdddbbbbbcbbdadbbadccaaacaadaddbbdcdccdccbbcbbbcabbabccbbcdbbabddcabddabbddddbadbcddcdcbdadcaacbdccbcadcbadbcddaacbcdaadacbdddabccbcbadbdbccdadaaabdcbdccbdaacaabdcbbdbdaacaabddddddccbbdadbbabbcccdadbaadbaddbcccdccbaddccbdbdddabccdbacdabbccbbcaabaacbabdaaacdaddbbbabbbbcdcadbbabaadbacbdaaaabdbcbacbcbccccaaaacbbcbbdacdcacddaaadcddbcdaadacadccadcdbbbcdababacabdacacbccbaadacdacddbadcbcbadcacdccdaacdcbcccddbcbdbbacacbbcaacdcdbacccbdcbcccdcbdabbbdadcacdcaacababbacdbcaadcccdacacacccdcdaadcdbcaaabdccdcddcdccdccabdcacacacdbbdddbbadddabdacdababdbbbadcbdbabcbdbbcacdabcdaabadbcdabdacccbdabdcdcaccbbcbbacbcaccadddacababccbadaabdcadcbdaddacbbccdababaabcbaaaccddddbdcbcbdcaaddcddcccbccdbddbcaddcaaaacabdadbcdcdabccaacbddbaddddddabcbccaaabbcccccbbbabbadbadbccaabccabaaddaacbdccbbabdaaccccdabcaddbdbaadbacbcddbbddbcbacdabcdacdbbcadbdbcccadabcabcabccabdababacaadaadbbbbddccbccbcbdcbbaacbbacdbadcabbccbccdbdbacaaabcaaadcacdacadaaddccacdabcbbaaacbdabacacadbabdcaaacdbbacbdcaabdbcdbbddabdbdacdbaccaacbbabaaccbbacadccbbabbbbbcdcbbdaabcbbcbcbabcccdaabdccbbadabcacddcdadbdddcbbdcdcdcdbbbcacabbbadccdabcbcddadaacdbbdbaabdccccadcbcabccccabdabdcbbddddcbcbddaaabbddabdccabbabcbdcbbcdbdadcaaacbddbabbcdddddbcadadbcbdadadbadbadcbbacdacbbaaddaadcbccbcdacbbbcbcbadcddabcdadaababccccaddcccacadabdddcaabbacadbacadbdbbcbdccdacabaaacbbddacbacdbbbcbcabacbbbcbcbbdbbccdbcaadabbcdbdabdaacadccdbcacacbadbadabbadcddccbacacbcdbacaaaaddbdcacaddcbdcbbabababaabbdacccadddddbdadbdddacdbdcddabdbbbbabdddbdadbcbacaddcdabddbddddcaccacabbbbdcdaddcaaddcaacadcadadadadaadcacbabbcdbcbcccbdddacbbacddadcdbbbbcdbabaaabddacbcbaababbccbabbaadabbdbdbaccbcaadadcdbdaddacaddaccbcaacbdcaababadbabcbbbcddbbbabaccbaddcbdacadcadbddcbbbdbabbbccacbdcbccbbabbbdaaabbcbabbcbdbbdbdddabdcbdabbbabbdbdabccadacabccaddbadacaaaadbbcbdbcbadbbdacbcaadbbbcdcbbbacadcbabbbcaccdcabbbcabadddbcccdcadbbcbabcccccbcbcbdcdccaddddcddbbcbacccbddaccaaddaddbcdbddcbdbbaaaddaacacbbdaaabcabdabbdbdadbcadaddcdbcdbcacdbbabdabdddddcddaadbabbddcaaabacdddabbdccddadbdbbbbabaabccddbdbcabbbdbccbaadbccdbdddbdcaacaaaadbababdaacdadadcccbcdcacbacdccdaabaadacacccbdbdcabdbccdcbabadbdcbccdddbdcbbbabbdbbccbddcadbaccbaabbcbbcacadccdabdbcbaadadcabaadbdbabaacbdcaccadbdccbbaabccabcadbbcbcabcaadadcacbbcaaaadcbbadddabcdbbddabbdabdaddcddcaabaccddabadbabcabbcdadddbadbcabdbcbbddaadbcbbddddddbbbbcabdbacbcacdaddcabcdaabcbbccbcabbcbbbddbddacbbacacacadbcaccdddcbcbdcdaacbcdcdcddcdbccadddbdcabacbbacdaaaadaacccadcbdbbabadcdbdbbbbdcacacddaabcbbdcbcdcdcccdabbdadcadcacadbabbbaacaabbdbaadbcbadaaaacbbaaabcccaacccacbccdaaddcacacabddbccdcbdcabcacbbacdaaabdbdbadbcbbddbdccdbcdbbabadddccbaacabcddcbababcccbbbabadbacdcdccbaabcccdacadaabaaabaabaccadbdcbdbccdbcdcaacacccbbddadbcbbcdaccadccdbdcdccababbcaddadbaccaddcacabbdbbbcbcaababcddddcabdabbdccbbcbcadacabadaddbcdcccccabcbadbbbcadcaacbabababacdccbacccbcbabcccdbcddbcddaaddbabbbadaccbacdaddddabcaaadaabadabaadddbabbcaaabdbaadabaccdccdcddcbddacabcbbacdcadacccabdcdbcbcdcbdaddcbaaccbdbadbdcaccccdacbcaccbcdacdbccbbbdcaadccadaabbcacaddbcdacdabcdccadbabadbccdbbdcababaacccdddcbddddbabcddccacbbcabdbbaaabaacbdbbbacbdaadcdacdbbbbaddbcbbdcaadaadbdcbbcccdaaabacbbcbacbabacababccccbaaacaaacdcbacabadddabbbababcadbdbadcbabbbdbdddaccdddaadbdcdcacdcbacbcbaccccccadbddccbdabbbccabbdbdacdcaddadbdaaaabbadcbdabcddddbccbbcaadabdbddbcbdcbacbcaadacdcbacadabbddaccbcbaabbabdbdacdcabdcdacdaaddaaccbdbadcccbdddadddcbcccbcadcaddbbddaabacdaabddbaaacbdcbdcabadcdadccadacadcdcbbdaaacaabcabcdacbabdccdcacbaacddcadabbbcdbbdbacdadadacaccddcabaadcdccbdbaddbbbdbbbdcaaadbdaddacccaaadddbaaddddabaddcccadcddbdadccbbdabbabcacdabaacaaaaddbbdccabccbcaaccbacaaadadabacaccaabccbdcbcadabdaaddbabcbbccacadccaadaccabacbdddcabdccadbbdaabdbcbdabaaadccbaaaacddaabccbbbcabccdbadaccbaadbabbcacbcaccddbaddccbcdabaacddabacbcbbcccddaddbcaadbddbcddaacacccbaddbdcaaccddcdbdabdccdcaadacbcdbbbaadcbaadbbacbddcbbdbadccdbcdaddcabacbbcaddddbbadadcbccbbcabccbcccbaddddbadabdaadbbcdadcbbbaadadabdddaacccdabcdbaddbbdadaabbdbcdcdadbcbbaaccadbdccdcadcbcbaabacbabbdacdabcbbbabcbcaddadbbabccabbdcbcaddcdbadcadcadcaacbdcccbcbdabaacdcbccacaacdaaacabbbdcddcdccbabdcaadbbcadacdbbcabbcaaadcdcddbcbccbcbadaacadccbaaaadbaaacacbcbcabbccdcccdbbdaaaaddcacddabdbddcdbcbaadddbcacaacbdcdddcbdcddbccaccabdcccbcddbdbdcbcaabdacbdcbcbbdddbbabacddcdcbabdcdcdcddcdccccdcabbbbddcacdbdcbbbbbadabbaadaabaabcacbdcbddbadddcccbbbcbadadcabbdcdadabbbaccccddcbccdaccdadbdbbbdacacbaadccabaabbbbddbabdbddcdcdddabcacaababccdbccbacaacaddabbbbcbccdaacddcccaccabbcbbcaddaadbddbddbddbbbbcbcbbcabdbdabdaaadbbdaddddbcbaddaddbddaccccdddcccaaadaddaddadbddccbcbacbdcaaaccbcdaacbcbaccdacdbaaddacabbbadbdaabdaaddccabdaacbbbbbcdaadaabbdbcdccdabbcbacddcacabcbccaddcddbbdbacbbccccdbdaabcddadacaacdaaccdbacbddddcbdccccbaccabababbacddcbbcdbbcabbddabbcadacccbdbcbddcbdbddacacdcbbaccbcdbccbdcadabacaaadbdbdcadaddacdcbadcbcaaddcadbaaaaadcbcdcccbbdabdbaaddcdbbdbcbcbdabdaccaabbcccbdccbaaacacbbcddacdbcdcaaccacccabacdbaaaaaddbaabccdababbacaddcddcbacabbaaadadcaaadcccbadabbddddacbddccabbbcdcdadddbcabccadddacdacaddbcccacadadbcbacbbbbbbdcdacacbcccbacbaadbbdccbbadbbdddbbbddbbacabdabcdaabcbddbdbaddbdbddbbcddcbbddcabdcaccdaacddbbadcdcddccddaaaccdbdaacbbbaacddaddcaddcdabbacbccdacbdaddbaabcacbcbadccbbddddbadbccbccaddbaacbaccbbdacddbdbbaccdbddbcccbadadddcbccbcbbcbbaccbcaddbbabbabcbcdacbaaabadcadbcddcccadadacaccaccbbcdbbcbcddbdbccbdadccdbbccddaaabcbacbdcbbcaadbabcdcadaacacdbddbaccccdcdbabcaadcabcdbdbacbddcabcdbdbbcccdcdcddddbaaddcaadadcbbcdbdbaacabcaddcabbdacdacbdcdccdcdcbbbccabcccaadcdccdaacbdcbbdabdaabcdcadccbacdcbcaddccbacddccddcdcaccddbdcabadabacdadaccabddbbddddbcdadcbcbabdbacacdbcccababdbbbdddacbacaabcaaaadadbdcdcdcdccadbcbcdabaddacbcacbacbabbdbbcacaaccabcdadcddacdcddaccbaabbaadbcacbacaddbaadbaccabbcdadddbdaacdacbdcabcadacabadddaaddcaacbacbbdcdcbcacdacbcddcdccbcdacbdacbccaaadbadbbbbdcaccbcddaaccbbccbabaabcccbcabdaccaccdcdcccbaacbccaadbadbacabdaacaabcaaacaadddbabcdaabdbbdbbbdcbaaccdabdbdccbaadaaaadbaaadabadbbbbcbcddaacbcbcbdbccaabaadccddacbdaccbbdcaaaccbadcbcddcabcbadbcddddccdaacbaabbadccbaacadadcccdabcbbddadcbacdaaddccabdbbddcaaadabbcaaaddbbaddbbbacdbcaacadbacdbccbaacbcbbacaccbbcccdacbadbcdabbcacabdacdcbdcddcbcccbaddbadbdcabadbddaadcbddddbacdcddbabcaadabdaadbdbabdbaadcccdcabaadababdbcbcccddbabbbbdbbcdababcdbcbcbdbbbcaaacdcbdabcdadccbabbbcdccbbdacbbcbcddababcbaabbaabdcddbccbaaccbddbddbaddcdcbddaaadabddbccacaddaaadcabdaadddbdabadcbbcacbadcdcccabcbcbddaacaacabcdcccbbaabbacdbcbaadccbabacbbaacbadcadccbbadbdcacdbddaccadbdabadbbccbadcbccdabbcdcbbaccadcddddacabdcadacbaabaabddbdacaacdcbadabbbcbadddbacaaaabdabdbcadbcdddbbdbdbdaadcddacaadcdcaadadcdcacddbaabdcbbdcccdcacbcdddccbcdccbaaddbcbadadaddddbbbacacdddccbddccbccadbadadbbbadbababdaccbcccccbbbbacdbcbcddcdccabbddbdcabdbcabaddbcdcadaccdbbaacbccaadcaccaddaccabbccabbaaaadacbdbaacabaacdcdbbdbdaaaabababaabdccdacaadccadbbbdaaddadaadacdbbdcbaddabaaccdbababcbdddbcbcadaacacbaddbabbddbcbacdacabcbdacbcbcbcdbcdabbdbdadaabddcbcdccbcccbdbbccdabcdbdadcadaabcdbbccdabaabdcdbbdabdddbcaaadddadacdaadabbcbbcdacbacacbdbbcddadbdadacdaccdbddccdbcdbddadacdcbadddacdbadadbcdacbdacbacaabddbbabbcdccdaccdcabbdbcdccccacdddccbbbbbbcdaccbddcabbdcaddddbbddcdccaaddaacbbabdbdbccdbdbdcdacabcdabcbaddbaaadaddbcdcacdaabcdaadbdbcdabddcbaaccdbcdaabdccccdcabcdddbadbacbbccdbcaacdcaddadbcbdabaddacdcdbbbdbbdcacbaacccdcdacbdbccdbcbdddababbcddadadcdbdacaaddaacdbabdaabadbcdbaccacbddcacdbbbcdccbcddbaaaddacbddddbbbcddbccdabdbdabaaadcbdaddddccbadccbcbcbbdbcacdbbaacdaaaabacbdacccdcdbddcaaababbdabcbadbdcddcdacbbaadcbcaaddcbadbdcbdabcadabddadacbdcdaabcdababacbbbabcbaddcdbdbabbdadacbaabdaacbbddbcbcdaddaadcdccdcadccacbdbcdaccbacdcbbcbcdadccdabcabadbcdbbcaddacccdcbccdadcbbaaddbdccacaacccbcbaadadbddcdcdadcdbbdadaacccdaaaccacddacaabddbdcbbabbaaddcdbdbddbbdddaaadbacdaadabbbdcdacdaadaabaacbaadacacabbacdbbdbcaaaaaabaccaddbabaadcdcccdbcccacdbdcdcbcbbbbbdacdcaaaaaccdbabdcbcccdddbdbcabcdbdaacbdccbddabbcbdbacddbcaaadbacbbaaddcabdabdcdcaabcdcbcdbbcdbababaacacbacdaaadbdddcdaaddbdddddaaaabddbcbcdadbaacbbdbbdadbadcbbaacdcdcaaaadcbaaabaccbdacdbaaccdbbbaabcadbcdbcabddacaaccbacddcbadcdaaaaadbbdaaccbbbaaaabdbbccddbaabacadccadaabcdcabbdbddbadbcbbdbacabcbcdcbbbcaabaaadddbcbcacdcacaaacddadcbbbbbdacbcdcddcbccdacadbbbabaabdbacbbdacabdbdbdacbbcbbdacbdbccacdbdbdcbadabcbadacbcdbdaccbcdabdaaddaddadaadbacdbacddcbdadacddddcbdcbbbabacbcccacaaabadcdbdbabbcabdaabbbdbbbdcdbdbdaddacacbacdbbcaddbccbacdacbaddcadcbcdcacccdbabbdabadbbcbaaaaccdbbcbcdbdabdcccabcaaccccbbdcbaaabcdabbcbdbbbcdccddcddbdcaddabdbdabdabadbccaaaacbbaccccbbdcbccdbaddcaabbcadddbbcdccadababcbccaacbbacbbddcabbbbdbcddcadbbaadcbdddcaaddddadabaaccdcbddbaccaadddaddbcabccacaacdaabacbdcabcacddddcbabcbddaccbbabbbbddaccacdabcddbbdbbccdbbcddbbdbbdabccbbdccbbaaacaccddbbbcdadbdbadbacccdcbdaccbbddaddbddbdbbbdcabdabacbcddccabddabccbcbcdbddadbbcddbdadcbbbbdddcbddcabaaccaaacdadcdabcdaaadbbbbbdbbccabccdadbddbdbbabadaddbccabbaccddaabddbdbbcabdccdaaaddaababddbaabdbdcacdbbbbbadbdabcabcdbccaaacbdaababddabadcddaacbbdbcdcbcbabdabbddadcdabcadacbaadcbbcddbbbddddbbbbdbcddcddbaabacadbadccbdaaadbbddbacccabadaacbcaabdbdbacbbbcdddacadbacbcdddbaadcddadddabdccaabacdbccdbcacdbcdbcacbddadddcacbddadbbbaccccbcbaaccddbcddadaabcdcbdbbcdccddbdcccaacccaacbdaaaabacbcbbddacbaccbcbdcdbcdacacbddcacdbadbadbaddbacdadacdcdcdbaccdacbdaacbacacccdbccacbdacabddddacdbdbdcacaddcaababcdcdbadabaccacdcdabdddacaddcdcdbadcccaabcaaabacbddbbaabcdddbcdcbabaacadbcbacaabcbdbaabcaddabdcbdddcccacddbddbdaacbdbbccddacbdcdbccadbcbadacaaaddcdacadbbdaddaaadaaaadddacbdddacadbbcdacddbbabbdabdddaccdaacbcbdcabaacdbcdcbdadcbbdacbddcddcdcdbbccdcbbccdbcbccccbbaaacddabbdbdabccacbdaacaadcbcccccabdbacaacaabcabdbbcadabbcbbacbccabbcaabdbcabbdcbdcdbbdbdccadddccacdabaacdabcababdadbdcbcbccccbcbbdaccadaaccbddacdbcddcabddaaadadabaaababaccbdacdaacddaaadddbdbbacdddbabbdcdcaacccabcccdddadaabcbcbccdaaaccadabdcaaadcbbccbdbdccaccddcbdcbabdcccacdacdcaadbbbddabdbdcacbdabdbabdaadbbadcbbcacbaddbcabdccccbddadadacadcabdddbcacbaabcacaaadbbacaaaadcbbcdcbdaccacdddadcaccaaadccbaadbcddadadbbdabbbcaddabadcadcbbbbddbbadddcadcdbaddbcbbccabddabbbdcbcacaadaccbdbddabcadbbcaaaacbaacaaaaacdadacbdaaabaadaaabcccacddabdcdadbacbbddbabbadbcacbdaabcaacdaccbaacdcdaabaddbbcbcbdddccddabacdddabacacacadccbaadaadcccdcabacddbccdabaccaaddabddbcdadccddcdddccbbbacabacbdddaacadadbcccabdbdbaacdacddaddabbbdcbbccccbbadaaaacaaddbbdaccabdbacbdbabdccccddcbbbcdccbadbbacbdcdddababccccbddcdadabcacadcbccadbcbcacbbbbdddbaadabacbbcbbcbddadadbbdcbacbbbacbaccbadcbacccacbdadacbbadcbdbdddcdaabbdbacccddddaccbabdaabbcbabddaddabbcccbabaabbddbddddddcccbadaacdcbdadccbaabbadbaadcabbadbdacbbaacacbaabcdcdddaacdddbdcacbdbcdcaacdbacadabacccccadbdcdbccbbcbbdcaabbaaaabbbdbdadacbbdcadbbbbbcabcaadabdcbbcacaccabddcccaccbccddbaaacadbccdabdcdbddabbacbbaddaabbbdcacdaddadbcbdaacddcabccbacccadccccabadbacbdccbdcaddccbbddbabaacccbddadcbadaadbadddbbaacdbaabdbdbcccdbddcabbdbdbdbbccdadbbcbabbaabcbdcbdcadbdcbddccadaaddacdcaddcdbdabaddbbcdaaccaacacacddadbdddacbaabcdddddccaddcadcadcdbaddccbcbccbaaababbcbccddabbccdabdadcadaadcccacccbbbcddcbcbbacdcdcbbbdcbcdcccabddddccbbdaabaaaadacaadadbdcccdbbaabaaccdcccdddabdbbadabbbccbbbcddaaddcaaabbbcbadaaddcddadacadaaabbacadaabacdbaadabbadbaacaaddbacdacacccabbcacccaacaabdcddcdcbacdcbbbdcacbcdacddbbaacbbbabaddcdbbcdccddbbdcbdadadcacaadabdadbaaaadbddbadadcacbdcbcbcaadaadddbabdbdabbddaaadbcdaacdaddbbdddcddddcacbddaadadcdcbaadaccbcbbdcddaccadcaddccdcbabaadaacccbcbdccbaaaaaccddcbdaacbabbdcbadcddbbcdbbabcbdddacabddaadbabcdbadabdbdabacdbadcadcaaadbbabcadcbbaacddcabccbdccbdacaccbaddadccbddaaaabaaaaababbacdbcbbbccabbaacbcaaccdabdadbacdacaddbdcbabccdabbcddbbdbcabbbbbbccddcccaaadabdcabcdaabdbcbacaaabdccdaacaabcaaacbdbaadccbcbabdcbcaccacaccadbacbdadddbbcddbabbacadacaaacdbaabccbdaccdabcdadbdaccbccddabcbccabdaaabadaaadcbaddbbadcddcccadaddbddcddadddbddaabbcdaabbbadddcddacbccdacadcabddcadddcccdcbdbacbadaaddddccbbccdabacadacbdbacddcdcaacababbddcdaadcdbbbbbccdaccabddacacaaaadbaaadbdababddadbdbacdbdddccabdcadabacccccbdbdbcabcdcdaadcaaccdacdbdbdbaaadcccabbcdaaabacadabbbacaabbadbbdacaadccbadddbbdabaacbcbadcbcdbadcacaddcadbdbbdddcabcaabadcadbcdbcdbccccacdacadccdadccadccbadadddbbdaddddddcccbbdcacdbbbdbbcbbdcccaadbcbccdddabacbddcadacabcdadcbabbddccacbdacbadcdbddbadcbbddccaccdbbcbdddaaabdbadcbcaaaddccdbadadcadcbbcdcbaacdabbabddcbccbadaabcabadcbbcabdccbaddccccbdcdacaacabbcabadcdacbdabddcdbbbcbbbcaadcacacdbabbdbcacdaaaabcdcdbbbbaddacbdaacadbdddacdcddcdddbabccbcbabbcddbbccaadbdacddacabbcaaacabbccddddabacdcccaadadcabdabaccdbbbdbaacbbdaccdabddbdcabddddccbabbdacabacaccddcbadaabbbcdcdccaddbcadddcbbcadcadadabdcdadcadddadbadbbcdddacddbbacacaacccdaaddbacddacddaaacdaaabddadbbdbcdbababbcaddbbadddcbcddadbdaadbacdadcddadabbdacbccdadacadcdadcbaadcddaaaaabbadbdbbabcdaabdabacdddadbbdbcdcacddccccbacdcbdcdcbcbddcaaabbdccddddaadaddbbddcbdaacbcacbbdacaddccddbbabbcabbadcbcdddbcccbdbbcadbddcccaaacbcadccbbdcbacbdcabcddbacaddbbbbbcdcbbaacbcadcacacbbdcbbccbbbacadddbddaddcbbcbbbacacaccadcaaaccdddbdaadcadddbbdcbdabaadcdbcccddcdbbbbcdcbbddbdcdacddcacadabadcbbaaacadccaabcdaaadcbbbcaabdbbbaabbacdcdaaccddddcbbaacbaccdccdbdbbccdbdacacdaabddbbbabcabcbcacccbdabdabbcbadcdacddaabcdbbcccdcbddcacddcdbadddbabcddcaaabadbaadbdaaabbcdbddaccbbdccadbcbadbbabbdcacdbacbaadcccbdbadcccbdccccbccbdddbcadcabacbccbbcbbabdacbccbabcccbdaccdbcdabbdaabacaabadbdbaaaabadbabcacbabcddddcabcaaadcdabdabbaabdbdcdbaddbaaabbadbdccccababdbcdbcacddaabbbcabbbbcbccddbdacbcdbbabaacddacbacbbcbddddacdaadaacbdbaaaaaaaaadcdcbcccddddbdbabccdaccadccbacdcdabbcdbacbcdadaacadabcabdbdbddbaabaddccdabbbcbcdaddaabbdcacbbbaadbcacdaccddabccbdbaabaddbcacdabbdabdaddddaccbdadaccbdadbbcabaaaaababaacdbbddbbaacdbccdbcbdabdabcaacddabacacbcdcabadbbabcadaaddbbbcdbacaddbacbacccdcbaaabaacdcabbbbdbaaaadadbddaacadadacaddbbdaacddabacccdcaacddccbbbbddbdbcbdcdbaccdcbaadacdcdcdbcbacdcaadbdbbbdbddaabcadbcbcbdcdaaaabdddadbcbdacdccacbabbccbbadbdbabacabbbadccbbacccbbdcabbdadadbcdabaddaddaddbcbcaabdaacacaadbdbdcadabdbdacdcacbbabbccdaccbbbbcbbcbbdbaabcddabcddaacaabdbddddcabbccdcddcdcadbabcababdcacadbbcaabacdbacacacdbcdbadacdadbadadcbdbadcdcbdbaadddddcabcbbdacbdbcdbbaabaacddccacbcbadaaccacacdbcaccaaadaabcaaadbdbbabcdddbcacadccbcaaacbaaaaaaaabcbbddbdcadabcbbdccddcddabadcdbddacabaabbadcbdacddadacbcbdcccdcadcadcadabadbdbbcbbbcdddaacdabbcadccbaaccbbbdcadcaabbdabbadacbadbcadcccdabdccbdddaaddabdbaacbacdbbcdaccdacacbadbaacdddcaabcccaaacccadcbcdbcccbdaccacbcacdbdbddbabcbadaacbdccdacabbabbccccababdbdbdbcddcccdcbaaacdbabcbddbcbaadcbbdbbaccadbaacdcdcadbccadbacbcabddcbccacdabaaadbcbabdcaccbbccdccacaabccabdbccaadaddcbccbbbcbbcbdccbbababadcbcdcbaccadaaacdabdbbbaaaabbdbcaadbcaadcccbdcadccdcdbaddbccdadddaabdbbcaadccbacbaadccadccdcccdacaaabaabaddacddadbddcdbbbcdabccacaaccaabcdaddaaccacdcabbddcbaacdcdaadbcbbaddbacbbdcccddcdaacabbabcdcbabcaccaaaaccbbcbaaacdacbacaacdbcdbbbbdbccabcdbdbdddbabbddcddcdadbbadcbdbbdbbbcddcacdbacadcccaadabaccacdabaacbaddadaadbbabdbacdcbbccdcdbbacadbcbdbdcadaacabcaadaaccdadbcccbdacddcadccbbcccbbbbdddbddcaccdbdabcbcbddcdcbbdcacbdaddadbdbbababaccdcdbcadcadcdcccaabbdbdbccacaccadcaabbdabbdaacacbcabbbadbccbcdaadcabcbacbaccabcbaadaccaabacdabbacccaaaacdbcabaddcbaacbcdacbdccbcbcabcaccdacbadccaacdbadacacbdcaddcdbacbcbccadccdbbdaccdbdacdbadcbabdaccdcdbabdbcbcdabbdbdaaadddbcdacbadcccadbadabcdddaacadabdbbdaadabcbbdbbdddabaaacabdbcdbdababadccdcdadddbdcabadabccabaccbddaccdcaadababacdcdccbcaccacbadcbdccddbbacbcddbaaadaddcaabcaddaaaddbbcdbdddababddbcdbacabbaddbdadaabbdbbaddbabcacaccabcdaddabdcabbaabbaaddcbacbadcacddbcdccdbabdbadababbdbadbdddbabadbdbbaddaadcabdbaaadadbbabbbbcaddddadabcdbcbdddadaacbdcbdbaaddcadaadabdcaadbddbbcbaaacdddabbaccbbaccdcaadbcddddbabdbacbbcbabdcdcbadddaacacabbcbcbdbdcccbabdabbabccdbaabacaccaacabdddcdbcabaccdaabbdbabdaccdcadabccadbbaacddabbbcabdcabcbaacdaadacdabbabbbbcdaccabacacaddaddccaabccbcbcbdcddcbbabcdcaabaddbbcbcabcacccbabaacabababddadabaadabdbccddcdcabacbdbadcaaacbcbabddbddadbadcbdcdcddddcacadacbdadaddabbdabcaabdaddaaccacccddccdddcdaddbcbbadcdadcdbaacbcaabccbaabaabacddddcbadcbaccdbbdbabbddcabddabaabbbbadbcadddccbbbcbdcbacabcbadacbaccbcabbadcabcdddbabdcbadcbccdcddbcbbdaaabcaaddcbdadcbbcbbacddadaacadcdddbcdacbbcabdbcdaabacbbbbcbdabbdadabccbdaaacccbaaacadbbcbabbadbdbadadbcbbacbaadaddcabdadabcaccbcaddacbbcacdcddcdcdbcbcbdaaacabcddcbadabbcabaddcbcdcdcdabdbddcbbbadccbbccbdddadccbcbaaccddccddadacdbdaddbdbaaaacbcbdabcdcbbdcdbaaaddcccbbaabccbbdcddabcdbdaccdcacbbabdaaddbcbcbdbcbaaabdccadcadaadddbbcdccaadcdaadcadbabcbddcbaaccbacbdcacddccddcbaaacddbbcaacdbbcdddaaddbdadbbcbcdadcdbacbdcaabdadbdbaadbccbcabadbdaacbaaccccbccdbcaddcdabacccbbcabcbaadddcadbaacbaddacdaadddbdbbddababcacaabbccacdccddbdadcabcdcacdbdccddcbcdacbadbaccaaadabcdadbbcacadaddacbbdcbcbbadbbdaababcdbdccaaddcababcabcaacccaaaaababbdcdacbcaacdccabadaaadbaddcadccdabbbcaaabacacbabacddddaaccaaccbdadddddcdcddccbdbddcaacccdcdadddbdacaaaabbbbbccabdadaccabccbdbaacaddbabdaddabaabdddbacabccabcadcbcaddacddccaadcccabbacdddaccbdcabdbdcbccbccbdbcccbadabaddabdbadccacbcbbbbdabaccdcbccbcdbbcaaddabbdddbcdcaadcaccddbdcbcdbcdccddbabdbdbdadcdcbdbbdacccccbdccdbaaacddaccaaaccbdbdbbddaddddcadcbcaabbdbbdcbabadbbddacabbcbdcdbcabbcbaddbddcbadddcadccacbaabcbadcccaadabaaccbcddacbccaccaaabbcbcbcbdcacaccaddadbbbcdddabbaadbdacbcdbcacacbccbacccdbbbadaadddcaabadcbddbcabbbddbaddbbbddaabdbcbcabdcbadadaccdbbbadabacbaadaaabdcddcaabcddcdbdccaacbbcbcadaabccacbabdbdadbcaaaddadddacbaaaabdadcababaaccaaaccadbaddbccaadaabadcacdbadbddbcbdcbbabcdaabdbbadcccaabdadaabcccdbbddbbaadcadcddbacabbdcdaadddccccabbbabdddbccdcadbdabcaaccadbbdaddbcdacddabbcadcbbbacbcbadabbdaaacbabbdbabbddbccdabdccadaacdbdaadbcdcdbaccacbcbdbadbbcddddcadcabcabddabbaadccbbcccacdbcaaccbbaddbdcbbacdddcacddddacaaaddccabacdbbaabbbadcbcbbddacadbababccadadcbbbccaccadcadbcabadaaacddacbdaddbdccdcababdcdbbdcdbdaccdddacaabcadddacdcabcdcbcbccbdabacdaddbcbabbabddacabdbdabaacbdaccdcbacdccbddadbccdcdaddcddcccaadbabdcdbcabdaccabcdabaaadccccbaabbadabbadbdacadbccdadabcbdddabbdcddaccabbbcbdbbadadccbcccaadcaddccbdccbacdbdbdbbbddcababacadabcccbbaccddcbdccadacbcdcadbbadadcaacabbcadddccdcdacacadaccacacabacbcccaccbcaaaaddbddacdccababcbddbbdabaaacadaccdbadbdbcbcbcdcbbcdbcccabdddbabcbccdbaccdabaadcdcbabcaacbabaccaacccccbadcddadddbdcabdbdadaacacacccdcbbabdcbbadcbcabbdadabcacddcbdcdbbdaaaddbccdcdddadadcabcccdbbdcaacbdacccacbadcdabddcbcaacaaabccbdacddcdcbaaadbdcaabadadbaaccbdabdadadabdbbcbcdddddaddcadabbbdddadaaaaacdcccacaaabbcddcacaddbcabdbdadcbddbbabaadaccdcbcbcbbddaccdbcbcbcdcbcdacccadcddddccacdabbcbdacbdbaabdabdccacaadabbbdbcdacaccdaccccbcccbcbcbdccabbbcbaaccaacddaaccabcbdcdcdcccbbdddaaccbbccadccbbadbbbaaddbdcccbabbcaccaadbcbbabdcbaacddbdbcbdaccbcacddddddacdbacbdddddacdacbbbcdaacbaccbcdccbacaabdbadcbcbccddabbcabbdcccdcbbaacdcadabbddcdddcaabdababadaaccabdbbdaadabaaaadbbccbacdabcbdbdaaacacaadbddaaaacaaddcbbccdbbcddbdddbddcadadbcbbcbaaadabddcdaccacbacdbaacbbbaddccadadbcabbbcbaadacaaddddabcddbcdaadbcacdbabbbdbcddbcacbcadcbdabcaadbacdbbabddbadaaaadbaaccbabacbddbdcdccacdbcbcdbcdcccaabdbdabdadbbaddbccbaaaabbbbabbddcdcabadddabdbbaabbacdccadcddcdbdbdbacaccdbcbabbbabdccabcdcabcaacacbccbcdabaabddbaaadaabbacacbababcaadccdcbaccddbacdbcacddacccbabdccdababbadbcdccddaddbaaacbdbadcdadaacddbdbcbcaccdabbacdcdaacaaacccddbbbbaddbcacadaabdbdacdccbbcaaddcabacbdbddaabbdcdbcdbbaaadcaadbcddcacabcdcccacbccaaacdcaaadccbacdbdddbabbdbbbbbbabaadbacaccddcbddcaaabcaccaacbaddabbdcbacbabdbbbbdcbbabdacaaadadabaadddcbabddbbdbaacdbcdcdbdcbbbccdccbbdcddcbdacadbdacccaaccdadabdcbccaccacbdbaaccbcdcbaabcccbaabddccbccdaaccabdcdccbcbbacbcdcddcccbbbcaabaabaccbadabdbccdcdbadccababddbbaccbccbcbdbbcdacacccabddbacacdcddbdacdadadcdbccdbdadacddcccccdacdbdcbbcccbbdabbbddaacbbababcaabadcdbdaaddbbdcabcbbcacadaddaddbccbdbdbcbbaaabacbbaaaabdabadbcaabbcbbaddccacdcbbadbdcadcccdabcabadcccddbbdbacacbadccdddabbdbdbbacabbccbdcccbbabacccccccccdbbacabbdcccbbdaccaacaaacdcbbdaadcacaadcbccccbcdaccdaadddbbccbddcaacccbacacbbaddbbbbdabaaacadcadbdcccddcccbbabdbadddcdcaacbcaccddcbaacaacadcbababcdbacdccbdbbcbddcccabaabdcdbbaddadbabbdadbbabdaddbcacaabbdabdadbdddbddbdbbbdbdcbdaddbaaaccaacacababbbbcbbdaaddcacbccabacdbcdbdbcccbdcadcadadbdcbabbccadccbbaccbcdddabddbcaadbcadbbbacccdabcadabddacccabacdbccadcaaaacddddadcccaacacdddddcbaddaaabbacbdccadcccddcdbacadcaabcdadddabcbbbdabdbbcccdbacdddccddccabddabcddccabadbaddbabdaccaadadaacddadddcdcccdbbaccdcccbacabbdadbadbaadaadadaadccbadcdaccccdabccdccdcbbdcbacdcdbbbcacccbddabdabddabdaddcbbccdbccbcdaccddacadcdddcaabadadbabccabbabbdadddcdbdabdaacaacbdadaccbdbacacdcdcaaaacbbddcbddcdadbaadbcdabbddbaacaccadacaddaddbabcdccdaadaacddcdadcccaabbcccdcdadcbccaaabdadddbbcdddaaabbabdadbdcbdcacdddccbbabbbdbdddabbccbccbbadbcdcbbcabcdacdbcccdbbabddabccacbbdcdccbabbabccaabaaadbbcadcadcbbbbacabdbabccddbacbbabdaabcddcadbcabbabbcbaacdddaaadbdbdabdcbdcaaaacabdcabadcdcdcdcbacdccdcbabcadcccabaddbbbcddcaccdacabcbcccbdbacaaacacdcdcabcdbdacacbaddccaddbdbcddacdbddcdabcacbcaaccccadababddadabbbabadabadacdabdcbaaacdddabbaadbcadaccbbdacacaaddccaaacbcacaacacaddbbacdcbbacadcddacacadcbcacbbcdaddcadddcaaddbabbaaddbcadcaddabccbdaaadcdbaccddcccdbacdacacdbaccdddbdbdacdadcacacbcdadbbdcadaddabdbbcadddabdcbbdadbbbcccaaddaadbbbdcaabbdddacbccdbaccbdcbbcbdccaaddbacbabacdacbacbdaccbcdadadcadcacbcbdaacadcabddacababbcbacbdbddbcaadadcaaddaccbabbcdccdacdadbdaabacbcaddaccbaadbdadbbcdbbccbbccccdcbcddcaccbbcbaaaacbabccddcddbdcbdcdcaabdacccadcdddbaabacdbdacccddcacacbdaacbacadccdcbadcbddcacbacaccabadbaaaccbbdbccdddcbabacbadccdbbccbadabcdcdabaacbadbdaaacdbdcddbcbbbdabbdaaddddaaaabbccabcdacccdacbbddacdbbdccdbccaacadcacbcddabaaacaaabbadadbdaacacaadacccbdddddbabcdcadbbdaaacadbadbabdacbddcabddaabddbaacdbccbcdacdadddbbddcacdbabcacddaccbdcbdcababccaaaccdcbcbdbcaabdcadddbdbadcddacdcdabcaaccbaabccdcababdcccaaabdcacbbdadabaaddcadccaccbddbcbacacddbccbccababbddccbcccdcdcdacabcdbcaabdaacaabddbdcbadbabbacdbbddbbabaaabaccddbcaccabcbaadbcababccbacbcadcddbcadcaccbcaccbbbcbabbdcbbacddbcaacddcddcbbddaadadbcbadcbcabadbdacccacdcdcabbdaaadcdbddcbabbcccaccacbbcdacdbcdabbbdcccbdddcbbaaaaccbdbcdbdbbbbddcbcccabdadcaddccdadabbadaabdbcdccabbbccacdbacacaddbccbadcddbdcbcdbabacbcbbabbaacadbaccabcccaddaddbcaccaabaacddbcbabcdacbbaacacbaccccdcdcdddacdbbcdacbdacbcdbbccaaddbcdbdbbddbaaaacbbccaaadcbbbbacbdbccaccbdaddbcacddcaccdcadddcdcbabbcccdabddadacbaccdaaadcbdccaaccadabdddddcabbcbaaabddccbdbdcabacdacddcabcbadccdbbbbdaadbcaadacbdbcacbdbbbdabacdabaacdccbaddcacbcdabacbdcaacdabaddbdabdcbcabbbbacccdddcababcabbdbbadbaabdcbabadbcdabcdaaaddccaddcdcdbacbbbbacccddcacabbccbccabbbccbbadaacbbbabcdaabadccddccddcacdacbadbadcbdcdcdbacdbacbccbbbbbdddddaddaadabadccbaadbbaacbacbccaadddbacddacbaaabcdbaddaacdbbacababaaabbdddddbcddbbabacdbbacdaabddbcaccaaabbaaaccdacbacbddddbabcdbccdccaddbdaadbbdababaccaacaaaaaaaaacbccabacbdaacbacabcccbcdcbdddbcbdacccccddcadbcadbbddddbdbcdccccacdddaddabcacadcddcdcbbabaaabaacddccabbcdadcdaacdbdbcdbbdcaaccbbaaadaddacccdbccacaabccaababbcabbdddacbacaadaaacaabcdcaccbbacdddaaabcbacbcabbacbddaaadaabcaaabcdcadcdadbbaacdccabdabbdadbacdcdacdcadadbcbcbcaabadadbdacdcadbaddcbbbdbdabadddcbacccabadccaddcabbaacacadbdddcaddbbdabccdbdcaddcdbcdbdbacdccdacdabaadaaabcbabbabccaabcadcdbbddaddccbaaaadccababccdbccaabadbbacadaaccadbdddadcdccbabadaaddcadbadbbabadadadcdbbdadcadbbcdcddcbabaaaadadbaaaccbabaccbbccdcbddabcadbdbccbbcdbabccabcabdcacabdadaaaccddcbcdbcccddccddbddabcbadbacbaadadbaccdcdddbdacdabddabaddaabbaaabcabbcacbbcacdcdcdbbaadaadbdadcaddadcdbdbaaabdcdcdbddbcacbccacaacdcdacdcacddcdcddbcadbbabadbcbbdbcdcdaadabddbaddadbadabcbbcadabcbdabccdbadbbcdacacdccbcaacaddcddaabacababbcaabbbbcdddaccccabbccaadadbbdadbabcdbdcbddcbdadcacbdcccababddbdcddbbbbcaaabbbaddaacbbbdcbbccabbdacdadadcdbdcabdadbdccbacdadbaadcdbaadbdcaacaabcdddabcbbddbaccdadacdacaadccbacbcddcdcaccbbabcddacdaccdcbcaabdabcccdacaadaabbcabbbadabdccabbcbadcbacccddccacddcdddadcacccdcabdcbcbabaccdcdaacbbdcadadccadbcbcdbcabddadbdcabadbccadbdbdcdaaaacacdadddcbaacabbdbadcddcdadcabdcdadcdbcacddddadddddcbacbdbdababbabddabbadbcaadbabadbacaadaddbabcccbbdcbadddaabcbcbddddacddbcbadbacaaccbaaccbcdcbcbdddadbdbbcbaaacbbbbbacdabacbacababdddbacccdbaaccccbcddadddcbdccbddbdbabbdbddbbdadbccdacaabaddccaccabcdacbdbaacccadadbcbdcacaaabcbdcacddccddcbcddbcbcdaacababccaddbbdaabaacbacaadaabddacbcbbdaacbaddccddbbabadcdbaabacdbcaccaaccacadaacdcbbcbdadaccbcacaddcaaabadbcbcbbdcbcbdbadbabdacabaacbadaabacabaddadbcdbbacbdbbcbdcbbbdbdaccadccdcbcdaadbadcdbbcdbdadbbccdbdabbcadbddcdcadddcddcabadddcacabcddccdabbcacacdbadacbdadddddddbacdddbbadaaacccbcdcadcddcabdbaddbbbbccbbdcdcabdbabcaaacdddbdbdbabbdbabdddaabdcdabcccbbcbbaaacdbadacbcbcdcdddadcdcabaccaabcdbaabcaadbbbabddabbcdccbdabccdcbacdbdcacbcbbdbbadabcccccdbcaacccacdabcdadadbadabbdcdabaaccbdacbbdbcadcdbdddcbbdcadbabccdaaacacadadcbdddbccdcdccccacaabdaadcbbcdcbacacdbacdbdddadacbbbabbadbdacacaccdbbacbdbdbbdbcdcbddacbaacabacbcabadaaacdaddddbabaddcdacacbcbddbaabcadcaabbcdcddbdbabbccdbdccabaccbdbabbbcacbacabdcdbbcbdacbcbabccaddadcadddcbbcabdbaacbaccacacbadcbcbabdcdbcacbbbdccccbdbddbaabbcaabdbadcbcccaabcbcacccdbdbabbdddcccbaddbdacbdcadadaaabcdbadddabbddcbadcabbcdbbacccdbcabadaadbcccbbcbabbaccdddcbbcccbdcbdccacdcbacaabcccdddbddbbcadcdcbbdcacadbcdddcdcbcbacacdbcdabacadcddbcdccddbdcbdaccbabccbcdcacccddaaaddaacdacdbddcdcbabdccbaccddbdbdbcdbbaadcbcaaabbbcadadbabbcddcbbabddccaccaacccddbdbcabddbbbcacbaadbcccdcbaacbaddbbabbbcadaccdadbbdbadcdacbbcaaaacacdbaddabdbcdadabcdcbcbdcdcddbbababcbaacbbdccaabdcdbdbbacdbaddadbddacbaabcadacadadbcbdcccdadcccadbddbddccbccaaddbccdbbdbaccadcabbcddccaddacbdbaadabaaacadccdcaacddaadaabbcacaddddbdadcacaccadbdcdcbbcbdcabdcababbdabcdddbcbcbabbdbabbbbadaddcbaaaadbacacaccbbdbdbdbaadcdbdadaadcbbabbaacadccdddadbadcadddcaacdabacdcccdabdccbaababcabaadbccaddddbcdbcdbabbbbbcbcabbcaddacaccccddcaadaaacbdbdcddbbbabbbcabbdaddbbdbaaadacadadaaccbdcdbcbcbaadadacbcaddbcabbbcdcccbdababaadcbccacbcaccdbcccbddadcbabbcbacbadbbbbbcddcadbabdddcdadbabccdccacdbccaabddbdbadaacdacdddbcbcdddcccddaabbdbbccaaadbadbbbbcaacbcabcbcabdcccbdddbcbdaddadbcabaadcadccadcdcacadaddbadacbcbdcaccdbddacacccdabddcadbbdddbcccadadbdabddcdbddbacccadbcbacbbcbcdbdbdcacddbcaaaacdbcddbcacaccbcbdacaabcbdbddbcccbaccaccdbbacacbbccabaaddaddcaabdadadadcaacbccdccdcacdcadcddaaadaabbcadaadcbabbaacbccbdddddacbaaacccabbcdababcaaacddadadbbaddcdbbdcabbaddcbacaabbcaabbdaddcdbddccccdbbbbadbbdcdacbcdccbaddcbccbbdbadcdabadbdaccbcdcccaabcdcdacacdcbdaadadbbbaacbcdbacabdbcabcbabbbbaabbaacbbacbbbabaadbbdbbcbbbdcadddbcdcccdacbacbdabbdddaabaacddaaaccadcadaabdccadcbcaacbaabdadccccabcdcdcdbaaabbdcbbcdcdabcdadcbbabaabdbaadbcbaabbdadcbccbdbadaadcdadbadbaccbcdbacbcdabbcaccadababcbcdcddbcbcacbbbaddbbbcabadcaabbdaaaaaabbbacaddcdcadacacbabddcacdddabdcdbaaadddbadcccbccdbddabddabacdccaddddcbddbbddccddaacbdccccabccaaacabbbaccacabbbdadcdaacbabacdaadbccdddabdaaddaddcaddcccdbddddcdabdddcbdbbcccdbbbacadbcadacdcdddaccdcadaabddadcbabcabbadcadabdccdbdbcbcccdbbbbddbbbdadcccadbdbbddccdbbdbcbdbaacdadddcacccbabcabcdabcdbaaadaaabbcdcdabddbcbddabbbccbcacdcaaadbdbcdcccdcdcdabcaccbcbaabdbddbadcabbcdabcbddcdccdaaaacacdaddcbcbacbcdcdddabbaadaddcbcccdaabacaacabdadbbbdcadbdbcddadaaaccccabaaabdddaccdcdccddacdbcdbbdaccbdbcabcacdcbdbbdbdbdaadaaddaacabbacccbbacbbdbdccbcbbacaabbbacbcacdcbbadaaabbddacaacccacacdbcdbdaadcababaaacdbabdbaaababbcbabbbbcabbbcdbcacaacddabdbccdadaabbbdabddbaacbdbdbbaaadddbcaadaddccbdbaacdddbbbbdccaaacbcccbdcccadbbbdaaccaabdccdccbcadbccaccbbaccaabbdcaabcbcdabaabaabbaadccdcbdbdaabddcdacdcdddabadccbdbcbcacbbbcabccaabdcabcaccaadcccaacadadddaddcdbdbbaadbcdbabcddaaaaaadddbccdcddacbcdcbbbadcbbaacccdaccaabdbbbabbcabcbccbcabacddddaacbccbdbccdcdcbdcbbaddcbaadcadaccddadaadbcdcacdbdbaabcbbbdcadbbcbdaabcdcbcbcdacdaaaddacdbddcacdbcdaaadabdabcbcbdbdbacdadcbbcdcbadcacbbddabcbbddddbbdaddabcaaadddbbdccdadbbaabccbcdaadcdbcadbccdbabbbdcdbddcadcacacdbcbcdcddddbadcaccbdacdddcaccdddbabdaabbbbcdbadccaddbcbdcbccdcbcbadabdbacdabdccabcacaacccbdcdcbacbbbdbdacdbaaadbccbaacbabacbacbacbacaabaddbaadaabbaadaabccdadcbadadaabbddbbcbdbcdccbcacccacccbadbaccbaccbcadaccdcdaaabbccbcbcccbbbabcadbccbcabdbdadbcbabacacdcbdddabcccbbabbaacbbddcaadabdacbcabcaabdbcdababdccdddddaadaaaccadbcbcbaadddbcbcdabbadcaaaccdbdbddacaadaadaaabaabbdbabaacacdaaaccdcbddccadadcbcccabbbbabdaadcbdddcaaabadaaadbacababaccbdaaddcdbbdaadcaabddcacaaddddbdbabdbdcccbdabbaabadbcbcdbbabcdbacddcdbdccaaddadbdbbacdbacadacbababdbcbbaaacbcbbcdddacddccaabbcadcaaadcabbddababaaddcacbdcacacbdccbcabcdadcdabbdbbcdbcdcaabcbbbcabbcacdbadcaacdcacdcaaacaacbdcaaadcccdbdcdaccbaaaacadddbdacbdabbdbdaaddcdaacbddbcbdcccdbcdbccdadbdddadacaddccbdcccddcbbdccacdcdcacaabcdaacbdacacdcabcbcdcaadddadccaddbbbccaadccadcaaacbcabbccccbcddcbdbcdbcdbbdabadddddcbbcdadcaabcccbbaaccabbdbccbdaaadbdbcbbdbcaaadabcdabbbbdccbbdabbbddcbadccbbbbcccabcbaadacdabcdbaaccbbcbdaaadbcaadbccdcbccacdbbddbbcdaacdcbcabaacaabbacbccbcdbdabacbccadccaacdcbbbdbadbaadbacbdcaddbcbaacccaddabaabbaaddabbbcdcdaabddaccbdadddcbdcacbaccbdccbabadccacdbbcadbdbcdcbbdbdcbbddbbcbadbcbddcbdaadbbababbdbacbddddaabbadaabbdbbcbcdcadbaacbacdbababbadacdcbcbcbdadacdabdbcbacadbbddaaabcddacadbdccbdabcadaacadabaaddabdbabccdbadcadabddabcdbdabdbcaacbcaacbbbbaacbadcbdcdabdcdbaccacbdbbccbccbddbaadddadcbbcbbacdbdbdbdccbdbdddababbddbaddadadcdbadbadaabdbdccbcbcbdcbcadadadcdcccdcccccdaacbdbaabcbabdbbbdccacaacdabbdbcccdbcacccadcbcaaadaabcbbbabbabdcdbccccdccbacdbcbcadacccbdbaacdbaaddccacbdbcdbcabacdaaddbddbaabcccbbdadbbacaaacabbdabcbdababcabcdbbacadabdcacddcdddabbcbdddddbaabcddadaacdddacdadadabccdccacdbcdccadabbddbdbabccdbbbddacccadcddbccaacaabbdccbbdccbdcdbbdcaaccdabbaaaccadaacdabbcacabdbadadbcaccdccbabcbabadcdddbdddbccadddcaccaccbadcabaaaaddacdabcaacabcdbccaddacbacbcadbcaadbbdcacdddccdbcdaaadaadabdbabdcddaabbdccdcacbbbbabbdaddbdcbacdbbccbbbcaabadbbdcdbbbaadcddcbacbdcccbbcbaccbabbcccdcbcddbbddaaacbacaadbbbcadababbdaaadaadcbbcbccabbadadcccbdbdcbabaaddddcbacbadccdccbaabcdbbcbdbbadcdcacdaddcbdbdcbacdcdbcadaadcacadddaadcadcbdbdacabaddddcdccbcbaabdacbcbdadbdbabdcaccbbaddcdaabcacdcdcadbbdbbdbcabaaaacabccaddbcccbbaacabaaddbdcaddccacaaadbccbcbaccbacaddabbcddbabbbacbdbdcbaaddddcbadabccadbbdadabbbabdcabcaabcadabdccbbcdcadbbcadbbaadabcbaaaaccbcdbaaabacaaadabcdaabcabbdbbccddccaaadddbcbddcdbcbcaaacbcbccbaadbdbbbaadbabcbbdddadddbccdbcddadacabadcbaccabdbbbdcddadcacababdbcaccccbbdcddddcaacbadbcbbacdcacbadbbdadcbdcdddccbbabbdbcaabacbbcabacdaacbdcbaacbadadbdcccddcacadbaadabbdcaaccadccacbcbacacdadabbcbacbccadbcacdddccddabacadbccbccaccacabcdadbadaadcdaddadbdaadccddacbcacadcdabdbcaadbdcdcdaacbbddcddabbcddbcbbbaadcaacddbbbdcbccdbadddcaadccaaacdcdcccabbdbcbcbbcbbccdcdbaddcdbbccacccdcbaacdcabcdaadcadbbabdcbdbbacbbdaadacacababbdccbdbdacadddabbcdbdadbbaaddabccdaacbdadcbbcdcacabdbadadddadaacacdbdacadaccaabddcdcbbbacbccacccacbdaccabcbcaccbcaaacadabaababdaadbbdbdcabcddadbdbccabcacabccbdababdbcdabcabacbadcadbbdbccaccccadbaddadcbdabdbabbddbdcdbcdcaccddadaacabbbdaaddbbabdbcadcbcabbcdcddabdbacdbbaadaaadccdcdbcbbccabbbadbcdbbbcaaabbcdabadcbbdaacddbdcdbacbdabccdaadabaabddcacabdacdddddadccabacbbcbadddcabacacddccbacacdacaddaccbdbabcbacadabbbbbdddbbbbadbabaccabbddbaabbbaccbcdccbcaacdbabbbbdcaacdddcaccadcddaddcbacdacbbbbcbccbbaccacddbcbdbadabbadccddcdbbddabccdcbbcbadacadbdcbdbbbcbbbacababdbbcbccdccddbabdbacbbcabdddddcddcabbcddabbbcababcdadacacdabcabbddaadcddbcddaddcdaaacabddcdbcacaadbadbcccadbbbacabdabadcdabdcdbdcbadabcddcbbcdadcabbbcbabdbbcbccddcbabcbaccabbcddcaccabcadccadbccadbcdbbcabaccdbcaccdcdddccbaaadabcacbbbdadcbbcdadabdbcadbbbdbaaadaaabadaaadbcaddccaaabaadddbcacdaaabaddcabacbdcdabccaccaddcccdbcabcabccaaadcdcdacadcbcbdcdcadadacacddbabadaccbbbbdacacbbbcbbbaaaddaacaaabcacdaaadddbdadbaddacabbbdaabadccaadbccbabbadddbaaddcdcdacacbadcddcaacddbcdddbaaababbcbdaddabcbbadbdbadccbcbadabccadddcaccaaabbbaaaccbacdbbcadadaadaadcabcabbacdbcaabbddddadabcbadbbdcacbbbbdadacbadaddacdddacdbcddddadbcaaaabaaddaccabccdddbaaacdbadaabacccacadaccbbacbaacadbabdaaaddbbbaaacbabbacabbabccbcbddaccaadadbabaccabadbbcbddbcabaaddcdcadcdababcddcaabcadadcdadbcddcbdabddbdbdccbcbccddcacccbdbccdbbdaccbbdabacacbcbaaadabbdcddcacddbccbdcbdddadbaabbcabcddadccbcbadbbdaacdcdccbaadbdcbadbaaddcbccaabccbdddaacdabcacdadaabccbbdaadacccaabcabcbccdddbaabacbacdcaccaacbabacaababdcdbcbbaccccabccacbcdadaabbcdadbbbbbdbbcaaabacbabaaddcddaacbdcbaacbbadccbdbbbdcccacacdddacbaacbaadcbacadabdddbdcbaaccbdccaccdbaaddddddccccacdbadcdabbaccdaabcdadaccccdcadacbbdccbdcbcdaddbabaaacbabbdbaabcbbcaddbaddacbbbaacbbbcbccbdbcabacbbcbaaddccadcbaabaadcdabccaabdcdcdcbabbbadbdabbacdbcbddbdccdbbbabdcadccabaabdcdbacabcaacdcccaadacddbbabcaaabadbcabdddbabcacdbdaaccbcbbdbaddacadbccddadccccbcbbcddbcadcdaddddcccbddddcdcbadaacddbddbaacabcacababcbdcccacbabbbbbdbbdbdbcbcbbddbbacabbcbaabdcddcbbabcaaabbbccbaabcdacbcbadacdbaadaababdccccdcbadcaabcdddbbbccbacbaccdcbccbabaaabdddddadcbbbacccbaacbbcacacaadccaacbcbddcdbbacacddcadbbacccbbbdcbbcdaadcdccaaacddacadcdbabbcddaabdcdbccaaabdcdbabbcdadcadabadbdadcddddbdcdcacacdddaccdbaccddddcabaabdddcdaadcddcadbdcccdaaaaaccaadddbbdaaaabcddaadadbbcdadcdccadaacacdaccaddbabcbbbaabbccacadbcbbacbdacacdbcdaddcbaaaddbdcbbccccbdddcbbcddcacaccbacbccdbdbccdbabbbdbabdbdbcaccccbdcdccbacabcaddbbbdbcaadcacbcbcbabaababbadbdbadadbdacacabdbaaacddccccabacdcdacbaccdcbdbaccdcadabadbbccababcdddbdcbacdaadaddcdbbdcacacdbaadbdcacbbbacbcdaaaaaccdabadcbcbbcaabababdddbcdccbabadcbcaaabcdbaaddcdcbbaccbcdaccbdccbdddbcbaaccacdacbaadbacabcacbadaaacbbcbbbdcaabacdcabaccbcabdacbbdacccbbbcbbdbaaacacbaccdbbcdcdaadabaabcbcccdacabadbbbdddbccbadabaccbabacdcbcabdbabbdbdcbabbccccccbdcabbcbbbacabcdccdbcdddbbbcbbdbddbbdadcdacbdccdadaaadaccbabbbdccabadccdcdbdaabadbacaabadaddbdabbbcbcbaacacddcadcccdbacabddcbaabcbaabdbdcdddaddaccdcacaaddabadcbacacacdcbbabccddadaacbadbbdaaddccccbcbddbabcbbcdabdddcccbddcbcbdcadcbbddddbdbcccacdcbbdbbcbdbabcdcadaddbcbaccadaddcccccacaaaadaaababadbadbccdbbdadbbcbcddcbabdcdaaaadccacdbcaadbcdaaadcdbcbabaaacdcbdacbbdbcbbcabbaccdcbbaacabdbdaacccacdaccddbbdbbabbddccdcabcdaaabdacadaabadbaacbbcccdbdddbbcadbbdcbcddddccddcdacbbdcaabaccddbaacbcabccbdacddadddacdddcdacdbdadddbbbbbbadabdcbacdcbabdbddcdcbdabbdacbddaadcbaadacadaddaaccabdbddcabbbadbcbaaddaadcaddadbadbaddbcbbcacbbdcbaacadbcadbdbdaabdddbcabcbcbdccbacbdcbdbbcabbabcddcdabcaccacabaddacdbaabcccbdaabcbaababdabacadcdcdcddaaaadadadadccbcaddcabaaacdbadabcacacaccccccadbababbbbdbbadabbabaacbacbdbddcbbadccbdcadcbdddbdacabdbabacdbdacbcdbcdccbdcdbdaadbadbdbbcdbcdbdbcbadadacccbcdcadddbcbbcdadbacdccdacdbaaccbbbaaadddbadcaddbbddaccabdbbdaddacacbabbdbcdaddbbbcccddddcabdabbdabddbcaacbbddcaccdbdddacbadadbaccaccddbdaddcbcdbccbadccadcdccadcabaaaabcdabbcbbdcdbabcabbdcbcdbdbaadcdabbddbdaaaabcabbcabacabbcbdadabbaacaddccdcdbabdaadacaddddcccacaccdaacaaadaccdabcaccaadcbcddcccdbdcaacbadaccccaadaacaaacccbdcacccabdadaadbbcdbdbddcabaadccdadcbbbdcbacaaabbabcaaaddcabcdcbdbcbdbcdacadcbbbbadaacacdadccbddaaaabcabaadbccdbbcabddabcacabaacbdcccdabcdccdbcacdccabbbcbacaddacadabbaababcccbdacbcabbbbaccdbacdabccddccbabaaadbdcbdbddbbadcccbabbbdaaadbbbccbabadcaacdbdaccdcdadbcaaccdbcdacdbadcabdbcacbaabbdcaccdcdbcbdcbaacacacddbaddcddbcbacddabacccacdbbbacbbccddabdabdaabcadbdcbcaadbddabccddbdaacbbdacdaadadcbcabcbcdacccbcbddaacdabdbabbddaccaaadabaddaacbdacabdaaccdcaabcadabbbbddabccadacabcbdbacbbadaacbbbbadcbbadddacdbbacdcdacdbabbbaabcdbadbadbaaabaccdcaccaabacbbdbadddaaadbbadddadbddddcddbdccccbcdaacadcbccaacbadcaddcbcdddbdbcaacbddbcbcbdcdbdacacbdbdcaddbdcdcaddaccccdabcccaddbdaddbbacacbbcabaccdcdbcacdbcddbaabccbadcadddcabaaacbcbcbbdbbddaabcaadddbaddccbdadcdbcacaadbcaccbcdcacbabdcbdbdbcccdacddbaaddbcbdcdbddccbaddbcdabacaccdcdabcacdbcddcbaabacaaacadddbdbbdacbddddccccacddadddcdbcbdcbbdccbdcaddcddbcaccacbbacdcadbcbaaaabaabdddabaabcbdadadadbcabbaccacdaddcaaacdcbccdcdcbbaaacacaccdcaddbbcaccbbcbccdbacabbacbcacddbcbcaccaaaadcbaaabdcaaacaaadabbbdbcddbdbaccbcbadcaddbcdccdcabdcdbccabbdcacbcaadddbabcdcabddcaadacaadabdcbdcbdacbaccdadcaaaddadddbddaacaaccbdbbdbadcbcbccaacbbcdccdabadabcbacaccacccbdddbbdacbaaabdaaccbdababaccbcddaaaccbccbbacdabbcccdcaabbbbbccabadcccbbcbdccaaddcbdcbaabdcdcccdccabaadcdbcadddbbadccabbcbbcbbbadaddbdddccbbdbbccabdabaaddddacabdcdbabdcbbaacdcabdcdbabdcaaacdddddcbccdcddcbccaadddcaccbbaacbbdbbbccabdcbcdaddbabdaccbdbacabdccbacacdcadddbbcbaddcacccdaddcdaaadaaaaabaabbbccbbbababacacdacabbcacabaabaaaacdbbbcabdcbadbcaacabbbbaddadbdbbdcdbcaadbddccdcaabdbbcdbadbcaccaadcccbacbdcbcdbadddabdbacdaccdabbabdaadcbcababcddddadcbccbabddbdccdacbbdbaaaacccdcdcbabadacbbbbcdcabaabbadcdcabcbdbacccbdcdcbacadcabbccaaccdccadbddbcdbabcbbaaadcccbbcaccbbadadaccabaadddcbaddbdabccadbdcdbabaacbbcdbdcbaacaddddcdaaaabdadacbcaacddbbddbcadacdbdbbcddaabcbbcadbdaabbbaadacbabdbbcbddbacaabddadadcabdcbbcdbcccdddbbacbbcaaaaaaacadbdacabbdaadccbcbcbabdcbabbcababbdcbcbbbdbdbaaccacdabaadabdcadbddabbadabcdcadbdadacdbdbddcccadcbbadcdadadccbacccddbaacccdddadbadbdaadababddcabacbdbccadadabdddbdbcaabddccacbdcadccbcacabaabcbdbaccbbdcbbbdddbdabcaabaddddcaabaadbbaaacacadaadcdddccccacadbaddcaaadbddbdacbbdbbdccaacbbcbdcddaacaaccadddbacbbbadacbcbcbcbcbdcdaaabacadccadaddddabcdaacbcdbdcdbbcbdcccaabdadacabccbbbbbdbbadbccbcdcbcdcbcdbdccddbadbdddbbbdbdcdabbcaddbaccbbadbbcbaaacbbdcacdabccdcbcdcbaacdbdddbddcbdbaaabdcbabacbaadbccbbbdcbcaadbcaaabddcbaddbadbdcaaccabccacbbcdacabddcabbcdbbcadbbbbaadadbdbabaaccaccbcabcadbbabadacbcbbdbabcbbadcccabdabaccdcbcdabdabbdcaadcaadcdddbcbcadccabbddcaadbcccccdcacbdccabcbdacbdadacabdddbcbacaabddbdcdcbdcbbccbcdaadadacbdcbbdbabcccdbaacccaddccdcbaadcaddbcbddcdbccbdbcabddbccbacccccabdbbdabbbbcbaaddbddbabccccacaabdbbbcdddbabccdcdbcaacccdbaadddccdacbdccbcddcbaadddccdddacdbcbdcaccdbccdcaacaacbbabdbdacbcbabdbddccadabddbadcacbdacbdbcdbdcbdcddcaabcbaaadcccbbccaddaccddaccadbdccddbbcdacdadbdabccacadbaadbaddbdbbabdcadabcbcacabdabbdddaddbadadcaaaccbdacbaaadaabbbaacacccadbaccabbaacdcdaddabdabaddacdddcbbdbdadabdaccaabbcabdcbadcddcbcaaccbccaacabddbcaabdbdcdddcbbbcbbbdcdcdcddbbbacccacbdccabcbaabdaabcadabcccaaccdcacdbdbbaabbcbbdbbbadadaadbdcddcbdbaababbbbcacaabdbaadcdbaabcbcdcbbcaabdaaabcacddcdaccaddaabaccbccdccaccadabbcadcdcabbcdaacbdccbcbcdcdacdccacacacddbbbdddadbdadddaadacccddadaabaabaabdaabcbabcbacccbbddabbcadccdacaaabbbddddbddbbcbcbbdaadbbabbbadabdcaabbbadcabcbdbadababcccaaccddbbdcbadcbbdabdccddcdcdbddaccabaacdbddacdacdcaacadbbcddadcbbcaaaaccbbdaaacccbdaccaddaccdabbbadccbaabbaabbddcdaacadbcbbbdaddadbccdcacdbaacaacacaaadddcbddaddabdaaabcabcbabdddddbcbdddcbbbdcadbacbabcbababdcbdbcbdacacacdacaaadbbaabcbdaadcdbaadbdabbcbcabbcbaaddbcadadbdbadbabaaadabdccbaacacdbacddaccbdcdaaaadbbddcddbbdbdbdacdcdbccadbdaccdabacccdbacdbdbcabdcbbcccbbdaabdcbabdcbddacdbbdaabddcdbcabadaadccaacadaacbbdcccddcccddbbcddbaaccdaddbcbaacdcdccaababbaaaabdaaccccdacbdaccbbbaaddbdbdcdccbddacddaddbcabcaacdcbcacaddbadbabcbacbdbbddbbcdcabdcbdccdacbbbcdcaaaaddaaabbbbcdbdccbaaccddabccaddddcddbdcbcbdabadcbcbdacdccccddccaaaddcbdccbaacbdccaaadacddaadcdcbcabcbcccccbdcacdbcdbcbcaacabcbaacddcbbbaaadccdababacacddaccabdbabbdbcdbbcbbcbbbabbabdddbcadaccbaddbdabcdbcccacbaccccaabdbcaaabaacadaacbabdbdbaacadabdcbadcccbadbbcbabadaccadccdaadccbacbccbabcdaabcbabbcdbabdacddbacaddbcaabdadbbacbabbaaaadbbdbabcdcaacaddbadcdabbbbaaaabcddabcadbccbcaacbcbdccadbcdbaddcacadabdbccaacdabbacabcbaabcddaacdacbdbadababbbbcdbcdacccaacaccccadccaddbbcadcbbbddcaccabdcbcddaccaacdcdabdabdddcbacadccddcbdacabdaddbcbdcbcaacacaadacdacacccdacdbcabbdbddbcaacdadaadbbacbcabdcbccbbddcddbcdccabdabbbcbdabadbcdcacbacabdaacababcbbacabaadacadbcaadbacddbdccacbdaaadabdaaacaabccdadadcbcccddadabddcdddccdcaccbcdbacadcdcbccdaddccdaabdacbdbabdbcbabdbcbdacbacbaadcbcbbcdabbdabacdbabaadddbbbdcaacbabcacbbadadabcdcacababadcacaabbcdaadaadbbbbbddadccadabdbdaddcbacdcadadbddccacdcbcbcadcaccadbccdadcddadddaabadbccbddbccaabaaccbbdaaaaddccbcaadacdbaabcbdbaabbabcbbdaddbcdaabcbbaabcccacdcacadcbdbbcdcbadbbbbbaadcabdddcbdcabdbddbbccacdaadbbccbdadadadaadadbbabcdddccabddcabcbcddadbbdbccccaabbcdabdacccbbcbcaabccabcdabdcbaabdbddabcdcbbdabdbdcbccaddcadabbadaddaabcacbdabddadbabdcbbccdacacadadbcdbbdaaacabbcccadbbdabbccdabaaabadcddbbcaaabcbdaaaaaaaaabbabbbdccdcbccdddadabdacababdcbbbabbaccddbcaadbddcbacbcaddbddcbddaadbcdbbdaaccdcadcaacabbbacddbcbbbbbbbbaaacbbdbdbdacdddbadabcaaadcdddbabdddacbbdbcbaaacbcadaaacbaaabbabcacbdccddccabdddccbdcacbbccddcddcbacbbaaabbdabdcabbbbbcabcbcbcacbcaabdbdaaadddcbbbcacbaccaaddadbabdbabbcddccaacbcbbddcaccdbacdbcccbccacdbdbadacbbcadbaaacbbcdcbdbbabbcdbbccabcdabcaadddaccabdbadcddbbaaaabadcbbdaabddcddadcabdbddccadadadccbdddadcbdbddccbdbddaadbcbbcabccbbabadadbaadadcccacacacbcaccabcaabadbdccbdaaaadabdcdbaadbbdcbdccbbaadabababaadbccaacdbcbbacadbacdadaccacdabadbbcbbdabbaaccbccbddbbccbacbcbacdabcadbabadbacdbcdcbdcaabcdcbdbdcdbccbabcddcdcdbadcdbabadbaddcdcaddbabdabaadbdabbcbddcdbcaaaacbbdcbadbbdaabccccabbbccacacbbaacbacccadcbabbcaacbdcddbdbccacdaadabcddbdaacaccdbcbbdbbdbccdcdaaacbccddbcbcaccbadbaddadbdcbdcaacaabcabcbcdabdaddbabcbdcdaacddbdcbdcbaccbcbdcddbabdcabcccbbbdbbbdccbcbdaadbcdaddbbdcbaddadccbcbccbdccabbcbadabddadadadacbcabaacddcbcdcdacbadbdacbbddabddbadbcddbdbcbabdbddbacdbdcbaabdddbbdcddacbbbcdcbbcacbbdbaaaddaaccaaaabcaaaddaaaddcaacaccbcacabacacadddbcabccdbdbbcbbacaacbaacdcdddcaabdbdababababbdbadabbcaadaaadbcccccddaaadbbdadacdccaadddcbbcacababbbaabdabdbaadbdaddbbddbcddbccaddabacdadbdcbbacdbccdaabadcbbbcbbddccbbdbcdcccaddadddccdbacabaaadcbaddbbacbccccdaaddbcabddcadbdcddbcdcaddbbcdcdabcacaaaaddbbbdccdadaadcadcddabbcdbcdbacccbbbdbbcdcadbcabbacccaccacccacbcaddbbdabcdababdcbbdabbbacbddacdabbadacadcaddcbabddbcccbbdacbbdabadddacabdabcbbcdbdddbabbdacdbdddcdbacaacdacdabbbbdddddbaacddcddbdcacbabcbddcadbddadaabbaccbbadacdaadcbbabcabacacaccbadbabaabacadbcdbbadabcbbddabacbaadaacbaaddcbccbccaadcdaccdcadcdbdbccbabadaaaabbddcaabdccbbcbaddbcdacbcdccbbaadcadcdccbddabbdaacacbcdcccabababbdbcbcdaabbbcccadcbccdaacccccbbbbcbbaddaccdbadbdaacccabaaaacbbcbbaabcbcacacaaccccbdbcbbcddbabdbcbdadabddddbbdcdbbbbdddbbaadaccbacdaadaadbbcdcbddadacbbdadbbaabddddadaadbddacaaaabccadcdbcbbcdbdbaccdbdaddcbdacacadbadbcdcdccbcbaababdbddabbbaddddcabddbbcbabbdcaadaaaaaaaccccaddbbbbcadcddadcdcbccabdbdadcddbaabcbabcbcadabdccdccdddbcdaabbaaaccadabbbccbcaacaadabbadaaaacbaaabbdbddcccbadadabccbbabbadddcccdcdccbbbadacdcccacbabbacbdcdaddacabbacdabcbcdadbabcdacccbddbcabcbdacbdbbdcacbaccdcabdabbadddcdcbcadbccbbcccaaadcbcdacdabaaddbdcabdbcdcdabdcbdacdaddcbdabbcccaabdddbcabdadddccdbccdbbbcddcbcdddbbaddbccdadcbacbadacccddcbbcccdbdacdaddcdccadacddabcabbbdbabdcaadaddcbdcdcdccadcddbdacaddbbcacdbcbbacbbabcacadddbadabadadaaaadbcdbcbacaaddbdbacdacbabacdcddcddabccdcddbbdbbaccadcbdddddcccdcdcdbaaaabbdcdccddddabbdcccbdadbdddaadbacbabdaddcdcbbacacaccdccdccadccadcbabdcabddadccbddcbacdccdcbccabbacbcadaddcddabbcbcbdddcadccdbadbbacbcacdcdacbdbaaadccdabcbdcbddabccccabbdcbbbaaadbcbcacdcbdcbbcabdadbcdbacdcbaaaccdaccaaccabcabddbabbdcaadbcbbcbaacbcdaadbcacddacdcdabcbadabcdacacbccdadcaaaccadaabbccaaaacaaadabacaccddbdbabcaccbbddbaaddbadaabbdadacbdcaccdabccbbbadcabbcbcddacadbaddaaacddbdaddbbaabccbbbaccdcacadabbccccbabdcdccccbdbbcbbdcddcaccdcacbdbbcaadddbdcaacbbcccacadcbabcabbbcddcccaabadacdabcbacdaccbbdaddbadccaabbbbcaadcccbbdcaacabdbcbbbbbabcdbadbdaddbbabddbabbbbbdacacdacdaddcddabcbbdbbdaccaadbccaccbbdaccabcbdcbbccdbcacbaabddbbdaccbbbdbcaaadbdbdacbbabadddccacbcdbccdcbcbcbcabbadabdddaddaddbcabccbbabaabcaadcbbbbbbcbdbaadbadbbdbcbbdadbcadbcbcdaccbbdcdddbcbcdabaccbacaadabaabbbcbacddacbccaddbcabddcbdcdcabddbcbaaddacddbccaacaacbcdbbaaccdadbbbdcbbabcdaccccbcadabbddbdbacbdaabadcccdcbdddddcbdbacadbdddaaacbbdcbcaaaabbabcadcadcbcaddbaaacdacbbacbcaccbbddbdcbbddacaaaabbbadbcbaadcbabbddcccbccbbbbdbbacccbadcaaddbdbcdccbabcadcacacaadbdccadbcdbabcddddccadbcbcdabdadcbbdbcaddddcdccdbacacbdbdbadaaaccadcccdcbbcdcabdcdbcbdbbdcadbadaccccaddacabddaaccbdccabaadabdabcbdbdbadbcbaccdbcccadddbcbdcdaacdaabaccdaaddcbdaadcccacabadbccdbbacdcbbcaaadbbbbacabbbdaadcaccaccdcbababababdabacbbbdbbababddbbcaddccbaacbbdbdcccdbadbcabdcdcdbdbdbdbcdcccbddcabdbddccacbccaacdcbbddcdcacbacddddbdabdddabccdbacaadaacdccbacbacbdaaccaadbccbcbcdbbbbdaddcacbddddaadbadbbbbacacbabbdbcaaadddbabbcdbbaadbdbdcbbccdcbdbddaddccdcdadcdcdaaddddbdcddabadbcdbddccaccdcbbdacccbcbcaadbbadbabbcbddccbdababdacabaaabcdbdbccbdcbdbbdaaccbddadaadbabcadbdcddbdcbdabadadacbacadbadbcadddaaddccdacaaaabbdbdbbaadbacababbbddadaabccabaadacccdccaabbbdaddcdbdaacaccbadbbdaadbcbdaabccacbbacabdadabdacacbabcabbccabaaadbdcbacadbbcacbcbcdcdbabdcdaacbdcacccaabddbdabadbdbabccaaabbddccadaddcadbcdbcbacdbdddbcdcaaacaabaaadcdabcdbacdbaadbdadbadcbbdaacbbdddcddacdbdbdaaadacbcdbacdacddbcdccabbaacbaddbcbdabbdccddbacabddddbaabbbdcaacacdaaabacbaaabccadabdbacdcaccaaabdcabbdacdbcadacccccdbccacbccbbcbdaaadbcbbdcdadcbdaadcbddccaacdbcbccbdcbbccaacdbadbddcbdcbccbcbcccbcabbbacdddcddccbcdccaaabadababcbbbadaddcbbccbbcabbabcadbbcdbbbbdcacbccbbabcbdabccaccdbcbcaacbbaddbddabdbbddbccbabbdccbdbcbbaadcccbdcbdcbbdabbdcccaabaddbbadabddaddbdababccacdabdcddabdabccdcddaaaccbaabbbcccbbacdcabddbcddbdcacdbcdccdcdcbddcbbddcaddcadcdbdbaadbdaccdbbcbcdbdbadbddadddccadcbcabbcbdbcadcdadbabbdaaacdababadabaccddcdccbabdcdabdccdbbccdabdacbcdaadadbcdaaadcddcddbaabbcacaddadccccdcadadabddadadddbcbbaadcccbcbbacdbcabbacccdcbbddadadbcadbddcbdacbdcbcdbcdbbdabaabdadadcdcbbbbcbcbddcbdccdabdbddaaadbbadcddbbbddccdaacbdcbadbadacdabdddadcaaddbbdcaaabcbdbabdacbcadcddbbbcccdcadabcbcdcacaabdadcaccccaddbdddcaccabbcaadacacccabcddbadbbaccdbabdabdcbbcaababdbcdadbccdacabbcaccaaabdbbcadababbabaacaabddbcabcacaabdaadbdbcbcadaaaadbcbbaabcdcaccdaccdabaaadbccabaabbdbcacccbdacacabdcbbabcaaaaabaddabadcdbcbccbbacbdcdaadcdabbccbbdbbdadacbcacdcddabbbabaabbcdbbadacdcdabcdcccadbbcdacccabddaabcbcdcddcabdccccccbcbacdddbdabadbcccadbdcadccbcaabccddacdabbbdcadddbacdbadaaaaccddcbbabcabdadbbdabcacccdcddbbaccaadbaddaddaccccbbddbbacacdbccbaddacaadcadabdbcdbddbabcbadbbaacbbdbbabdaccaddabaaacdbaaacbaabdbbbdacbdbbadcdbdccbacdccddacacdaccccccdcadbddddccccbdcabcdacbbcdbcbaddabaadacabcdbbdcdaaaaadaacdaddcbddacdadcbbdacddaccaaabaacdddcdaabbbbdbcbadcabcdccdadaaccccbbcdbbaadccdacddccbbccbabacdcbcbabadcaccadacbbbcbbbbabbaddabdbadadcdcbbcaadabddbdbdbabcdadcaaccdddacbabaaaacbccccbddadcbccdcddcaaacbcdccbadaacbababcadbadbabadacdcdddaacacabadccbacdcaccbbabdbaaaabccaabbcadabddbcddcdcadaadcbdcbaacacddbdbdaddccdcddbcdabaacaaadcbddbacbdbccadcdbcbabcdadcbdacdbcacaaacbdbbccccdccbabcbdcbbcddddcddbbddabcbaaaadadbdabcacdcbddbaabcabbcdcdcdabbbacccaabcbccaabdbbbdcccaddbccccdcddbdcdcdcdaadabbadccdbabccbbcaccaaaabbcabddccbadabdcccdccadbbabcdcdbbbccdadbcabbbaadcabacdaaccaddadabaddaababdcbcadbbcbabcddbaaacccccccccaabcdcddcdbddbabaabacbdaccbbabadbacbccbdccadbcbbadaddadcdcbadcdbcabaccabadcbccdcccbbcbdcdddbdbaddaadcdadddadabdcbcccccdcddabacbbdddbbaadcbccabddadcdacbbadcdaacdccccbdacdbcadcacbaccddbbaddbbcbaabbdcbaacaacdcbdcbccdadddbaccddbaabcdbdbbaacdaacabaddddddddbbadcbcabaaaabcbabcccbaccbacbbadddbdddbaddccabbacacbdabdccadcdbbaaabdcbabcacabddbdddddbcdacbbcacdcbabaaabaccdcddbbbbbbdbdbbbbaddaaddcdaaaddbaaadccbadbcaacbcbdbaaabdabbcbabbdbcdacccadbdbcbbccccdaaddadccbaaabdbbdcbddbbcbdcbccdadadcadbbccdacdbacdabcbabbcccaccbcbbacddddacaaabbaadbccddbbaccddcadbabbdcbbbadacbcdbcddacbdcbdcbbddbaacdbaaccacbaccbbcabadadadbddbacccadcdacabbdadddccbbbacccabbcccaddbcdaaccdadaadaadcccbbadaadacaccbbdcccdcaaaacddccabcbcdcdbaaccbbdacbcbdbcdccabdbbaddbdaadcacdcdbcbcbdcaabcbabcacbdaaaccdbadccddbbcacacdddacaccbcabdcbbcddddadaaabadddbbcadaacdbdbbdaabacbabbbaaabdbbbadaddcaadcbcaddababadbadaddddbdaabbdaddccbcccacdbdddcdcdaadccdadacacaababaddcbdddabbcaaaadcdccbccbdccbccbabdcdcccbcabcdcbbacabdbdcdaadcdccbcaddbcabbcbabcccaccdbcaadabccbbccdcdabdccdaccbabdadaacdbdbbcbcbddabbcbcdbabcbdccbdcdababbdcccddaddbcbbcdbdacdcccbaccdcaccbdddcacbdddcdbbcacadbbdaabbbaababbbbaabaacbcbccabbdacdbccbcacccbabccaabbdbaadcbdacbdbadbcddccacbdbdcacaadbddbdbaaadcadbacdcdcdaadbddcaabbacdcccaaacdcacbdadbdbdbdadabbdacadddcaccddbddcddaacdaccaabacacababbcbacadcbaacbaabcbbbddcddcacacbcdadbaabddbbbdcdabcdbacacabbdbcdacadcadabbaacbaabdbbcacbddbacadddaddadadaccadbcbcacddcacccbcdbcabdbacbdddbabdcdcdccccccbcbddbbbcccadcadacbcbaacbacbdcdacccbcdcaadbacdacabdddddaddabdbaabcdcaadcaccdbabaccabbbbddbbaabdbaaccacacaabbdcdbbadcaacbdacbabcdcdcbdbbdbcccadabbaacdcdaabbdbdcaddabacdaacabcabcbbbcdcabdbcbcccdacdacdbdaabbdbdabbabdcdbcbbdbaadbcdbaacbcbbadbbddbbbbadddaadbbdabcbabbbdcdccdaadaccaccbaabaaacddcdadbacadaaabbcdaacaaacdbdaacbdbabacadbbbcccaabcadbccbdbbcbbcbcbabddccaacccdcbbbccbbcddadbaaddbcccdacdbddcacadbbbcccccbccddcbabaabcabdddddcbdcdaabdadcdcaabacbadaabaaadbcaadccccddbdbbddbcaddccadaadaabaabddcdcbababcccaabdbdacdbcdbcbacaaaabdbdbaddddbccaacbbdcccbcbdbaadcbbdacbdbacccaaabbadbdbcbaddaabbaadddccaaabccacbdadacacbacdbdabdcdcdaccadbcdbbdaaacadacdccdadbaaccaadcbbdcbcaccbaaabcccdabdcbbbdbabbccddacbcdcbbaccabababadabcaabbadbbcbaddbdadbccaddbbaabacdbabdccbbaacbcbcadbacabbdcddcadbcadbcbaacbccaacdbcdbbbbcbacbbbcddcddbcdabdccdabacbabbababbadcabbbdcbbdbcabbdadcdadbaacbddbccaacdabaacdbbabbadbdacaaadbbabbbcddcdbbbcdacdcadccddbccdbacdabbbdbdddcabdacbadcdbcdbbcbbaadcadcaadbbcbaacbccabbadabbabacbadcaabdbccdabababcadacaabbbaddbcbbdbbbbadbbddddbbdbcbddbbcabdacaddbdabacdbabdbbcaaddaccbdacddacbbcddbcccbdcbcbbdabcddacaabdddbdcdbcadcadcabbadbcbaaadabcbcabaacaacacbbdccaadcccbbcddbcdabccaddbdddbacddbadbddaaadbbdcacddacadaccbdadaccdccacaadaababaabccabacadadaddddbabcdccbaacadacaaadbababcbbadbaaaaaaaaccdbadabaadbdbbdddaddaccabcdadaaacbaddbcdccdcaacabbdadbcdccacbadcdcdccacdbcabdabbbabccccdadccabcdbcccaabccadbdcdbaababcabdbbdabcbaabdbbdcdbcdbddbdbcbcababbcacbdaaaccadbaaabcbacbbdccddbdddbabdaabbccbaaadcbcbabccdcabbdaadaabadbdbcddcadaabcbabdccbabaaadcbbbdaacccdddddcddbdcddcbdadcdcaadcbcdcbdadcadbdddcdccaabdbcdbaddbbbacdadbccbdcdcdadaacbaacdaabdacacdbbcdbcccadabdcbadddbccdcabaacdacddcddbbccbaaddacbdacdacbbabcadbcabcdbabdddabdacdbcaacabdcdbabacdbccdddbbcbbcbaabbabadaaadadcdaaccbdacabacabbccbddbadccccdadbaddadaaacbccacccddbaaddbdbadcdbdcbbbaacbcbcdbccdddabddbcaccbdbdcbdcaccdbdbddbdbacdddabdaacbbbadbcbaaacabaabccdbbdbbbdcdbacdacdcbdadcdddbbbbcbaccdadacdbbdcbaccddaaccddcabdbcababbbccdbcacdaccabbabbaabdbbbdbabacdbaabcdaabbccdaacdddcbbbdddbdcdadbaaaaabbcbacaadbbabadabaddcabacccaddaabacccdacdadbccacbcadabbcdcddddbbaddbddcdcaccaacaabaabdabaabddddddabbdbcbbbbcadaadbddbcccacdccbccbcbdbcbccbccbcccacccadacbcaccdacdcbadbdadcbdbdccadaddccaacdaacddabddaaaddaadccdcbcdbddbbdacbbcbccdadadddcacacdbadbabdabdcbaabdbbbddacaaddccdbcbabdccbbbdaaddbcdcccbbcaccbbdcbdbbddcaabbccaababbccacaabbcaabaaacabbdbadcababdacaacdcddbdbdbdcabaccbdaadadabdbaaabadacdacdcabdddacbddaaddbdbccadccbdcbcdbacbaaddcadbaadcbdacabbdabccdbbdbaadddbcbcbbcadbbadcbdcdcdabbbbbacbbdbbdbbcaaaccaaaaacddaabcdbbcdbddbccdbcbdabdbbaabaabaaddabddacbcabbabbdabbcaacadbdccbadbbcadabcccdbbaadbbbddaaababbadbdababbddbccadbdaadbbbaadbbabccdadcbacbadbcbdaabdbaacadbaddbcdbbcdbcdddaadbcbdbccccacdcdbacdccbbbaabbcbccdbcacbabadcbaacacbdabdacaddaabcdcbadbcdcdaaabdbddadadbaacacdaaccbdcabdaadcbbbbbabdddbbbcbdccaddddccdcdcbabcdcbdbbcdaccdcdbcdaaaabdccaaccdbdaabbcccdacadcbcbddcdaacbbabaccccacddbacadbaabacbadaddbcddcdaddaacdaadaaaaadcbadddbaaaadbcbddddcaacdbaddaabadccdbbbcbbbbddddaccbabcbddadaabbdacccddabdaddadbadcbcacbbbacbcdacdcdbcadddcbdbdcbabbbccdbcbcdadbddbadcddadcadcdbabdacdbbdbbbbdcdadcbbdababddddddbaadcbcbabcabddcdaabaaababddbbaaacaaccbaadbcbabaaadbbdccbcacbabaddbadccbdacaacdcabddbdcdbdaadcbddabdadabdadbcddbbbbabbbccbbbacdabbbadddadaababcdbcdcbdacdbcddbaabaacaccbacbaccdddbbababacdcdbadadbdddcccadbabcbdbddcadabacdbdbdaadcbadacabcccbabacbbdaaabcbacadbddabbbadcbabbcbcdcccdccadacdadaadacdbbbbcacaddabbaadbdcddcbbbdbbbbabaacaaadaaabdacaacdcbbdccdcdbcddaccaaaabcdcccbccadcdccbbbdcacacbbbabbbccabbaddadcabddbccddcccaaabdddddcaabcbbaabcdddacdbddcbaaddcabaaaccbdddacbbbcdadbabdbdacbaccbbabadcadbadbacbbbdacddddcbdacaacbdabacbdbcababcdacaddddccccdcaaaaddcbabaabaabcccbabbadabbacdcabacabcdaadcbdadaaacacacabdbbdcdbbbbdcdaacbbdbaddcaaabcbbddcdadccbbccbdbdddbaabdcddacdaadacadcddcdacbcdccbcbcacadcdccaabcdbcccaddcaccccccdaadcbdcaccbdbaaddbbacdcdabcadcccddbdadcdddaccccbbbbcccacbaddbbbdbadbabccdcccacbaaccdcdadcbbaccacbbccdaaccbbadcbddbcdcbcbaadbacdbbbacaaabddbdddbadacbadabcadabbadaadbbcdbcdbbbbabcbaacacddcbabadabcccbacaadcaacbbcbccdddbccddbabaabbdbcdbaaddbdcaabbbddadccbddcbacdaacaccddccdbacbdabbccdbaccdcbdbddaddccccbccdcacacaddacaacbcacbbdbcbdcaadcbacacabbddaacbbdbddccdcaacdbdbbdaccdacaaccbbcadbcddadcbdcacabddbbcdbacbbdbbcbdaadddccdadbdddaabddabacdadabddbcaccddbbbdbbdddacbcabaddbcccdcadbcccaadcadabaddbcadbcbdacbabbdbbcadccbdbccabbddaadaddcaabcaacadcddccaacdabcacddaabbcdcbdaadbbbcbbdbdadbdcdbddcbcaacabbdbbadccbadaadadbaaabdddcacddbabcddbbbcabaddabbcbabadccadcdbdadabaacdbaaabdbcbbccacdadabbbaddcdccadaacdbccabcacbcbdadcadccbbccadcdbccabbcabbdaabcaaddcabababdddddcccbcbabcaababacadcbdccadcaccbddadbacdadbbaadbdadbdddcddccbbdadddccccabadadadabaabbbbaaaadcddccbabcaddadbbccaadbbadabbacabadcbcdbcbadabccaccbaacadcadddbcdbdbadbccccabadabacdaaadddadacababaabbdadbbbdbddbdbcaddbbbbabaadacdaadbcbcdaadbcccbacdbbdbdcaaadcdbdabcadbdbcccbccabdbcdadbdbbccdbabcabaddddcaaaabbddbdabaadadcbacdcaacdadadbabcaaccdcbcacdcbdcddacdccaaddcdbddcdcaabcabddbaccdbdccacbcbcdcabdbcaadbcccddcdaccccbbbdbdbdcbbaaaacbbadcddbbdacbabacacdcddbcdbaabbacbdcbdabdcbdaccaabaddcadcccbabcdcdaddaaccddabbddadabdbacdcacbbcaaadddcbadddcacdacdbcdadacbbdcbaaaddccaadaaabcddacdacabbadbccabddbcddbccaaabcdbadadcaadcbdbabcdcdddaddbcbaacacbcdbacdcddcdbcccbcdbcacddadcbdabadaababbaaccdbabbdbbadcdabbcbbdcaacddadacbdddcdcccbbbbddddcabbdacbcdabccaacbacdadbbbccdbbcddbacbaabaadbccdcbdaadabdbcbacbabbbcabbbbdaabbcbadadcdaabddcbdadbbcabdbbbbadaaaadcdbdcaabdcbdddddcdacbcdacacddbacacbbcbacabdcccbdadbddddddacbddaaccdadadccabcdccaaabbaabcddbbcadbddbdaabbccaadccabacddcbacdadabdaadbbdcabcddddcddcdabbcbdabddabaacadbbbcbcbbacadabadbccdbdbcddbaaadbbcddccaaaddcabcdcdcdaacdbdddddacabcccccddaabcabdbdbaaacdcbdadadbbbbdcdddaccdcaabdcabccaacacccabbdbdcbdcabbbbcbaacdaabcaacdbababdbcbccddbacbdbbbdcadcbbdbaaabdbbbddddcdbdcdbbcddcdaadbddaaaaddbbdcdcaacdccbaddbababbacdbbbbccaababcbdbbddaaacaccdddbadcabbbcccbbbbcadcbccddbbddcdacacbaddbcbdaccdcadcbaaddaaaabaacaabcbccbcbbcdaacbbbbcacdddcbacccbdcdcbdbaaabccbbdacccbccbcbcccbdabcdadcccccdbbaccbabdddbdccdbcbbabacddbacddcdbcbbaaddbcdbdadcbccdadbcacbadcbdcdabcabdbabadaddcabcdaadccbcbbdaddcbddcadbcdacddabacccbccbcabdbaabdcdcdadacabccaacccbbbadbbaddbdbdcddabdacadcdcbcdccbdbcaddaaabbabbbaddcbabaaabbaaabaaabdabcacdccddaaadaabcbbbdbbcbccadadadcbacdabdbabbcabdbdbbbcddaaadaadcbbaadabdbcadcdcaaddacabadcccbacaddcbbdcbdacaacddcaccddaaabaddcccbadacaddbccbbbcbdbacbcabdaccddcbdccccaabbbadaddaddaababdbacccaacbaaddbdccdbcdcacacabbadabdccbaadbcdabaabaaadbbdacbddcbbcbcdaaaadcdadbadabcdcbdcbdddddbcdddbdaabcabbdadddcbcdcacdbdbcdbdadacaacabdccdaaddabdaacddbaadcdabdcadbacbcbddbcddaabaccabaaacdabcbcbbcbcddcbbdbadaaadabaaaaacbbbdbcacbbbbcbdaacdcdaaddcabbabddbcdadcbbacbadbccaacbdabcbaabbcaadddbacaaaccaccacdccbddcbddbcbbaaabdbdbcabcbdbdabaaaadaabbabcccdbcabaabbbaaaacdcabdcadbbdbdbbacbdbcddbbdbbccadacadcbdbccbcbbbbddccdcaadaacabbcadcbbaaadcabcadbabaddbbbcddacbdbcacdbaddbbacacbdbabacbcbadcdabcbcdbbadacccaccaddadababddbcdcbcadacbddcabbccadbacbdcdaddcdabbdcaddddbaaabbcabbadcbaaccaabccaccddbbcbddadbadcabcdaabdcdddacddddcbbbcbdddcabbaacabacaccabbaadbababadaddddcbacbbabaabadbbaacdcabbcabdccabaddadcdcdcccdacdaccadddbcbaddcddbcbcbbdadbbaddadbdddbbcacacacccaccbbcdbabacdaaccdadcaaabdcccbccbbcacbdaccdbcdadacbdccccaddbaccdcdbddacacadaaadaabdcbcbaabddcdbbbdabaacadddcbbcccbaaadbdbdcbbaccacabbcaddadcbdabcbccaaadacddcbcabbabcdcdabcdbaadacbdddbacacccabdbccbcddcdaacbbbaacadcddadcbbbcadcbdaadbcbdccbadadbbaddcdcccadbcddbcdadaabbabaaabcbadbdaaadbadccbbadddcdbdcdbcadcdadddcbbddcacbacabbbbdacbbadcdcdcddcdddcacbbcddcbabadbadbcbaadaddcaaddddbbcacbddbcccbcddabcdacccbdcdddadabdccadbccdaacaccaadbbcaacbdadbbbbbaaaadcbdcddabcdcabadadbdadcdaacbcbbaaabbdcbccdbcbbdcbadccaadcbaddccbdcaddbdccddcccbbcbacdaacccacbddaddcbaacacabdddccadddadacabadadcddbdacddacdaabcacdabbbcdddabbbaacdcaabbbcaabdacbbdbddadbaaadbadbbaaddadbadbbcaabddbbbbbadababbdacccbddaddcaabccbabcaaabdaabbdaabbcbdacccbdbabcbaccadabaadbbcabddddabaccdcbadabbbadccbcbcccdbabdbbccdcdabdbaadabdaabcccabddaadcdcbbbadadbbadddbdcdcbccabbcacbdabcdabbaabbcbbcdccaabdaddbccbccdbadbabddacaddbacbadabdaabbcbcdbabdacbcbcdbbdacacbaacdbbabaccbdaaddbcbbcbaaccdbddacacddccabacbdacddddcabdaaadbabacbbcbdacdaccbaacaddbddadacbdbdbcbacdbdaaacabacbddccdccdcabccbdaadccabcbaabbbabbababddabdbdacadcbcdadacdcdacdacddadabdbbabacacaabcbcbcbbabacbadcabbdcaabbccccacdbbaddacddbbbccabdccbbcdbabdccbaadccbccadaccdbbcabbbbdcbbbdbcabdcdaadbcbadbbccccdacabbcdaaaaacaddddbabbbcacbbbcdaadbcbabbbcbdbbacadaacdbdaacddbddabdccaacadbbcddddaacacccbbbacddbccdddacabadbcababbdcabacaacbdcbaabbaddbaccdaabcccaabaccdcadddbacadbccdabaaaddbcbdcadbacabccdcacbcbbdbcdbcacadbaaacdacabaccadcacbdbcbcdaddcbddcabbcaaccabcbbccdcaaccaabdddbcdcbbbbbcaabdbcdaccabcbabcacbadacbdacadddcdcdccbabdbccdadccdcdadcdabadddbacabbcbbccddadaaaabcbaddbdacacdbcdbdbabaaddcdbbdcbdcaccbcddaaccdaabaabacdbbddbcbabaddbdddbcbccbccadadadababcbaadbaaaccdddccdcbdcaddbcbcacadcdaccdbababacbbcbdcccdbcabcdcacddbaccabbbcadbacaccdaadbbaabbbdbbbadcdbbdcccaaababccbcaccdacddabdcdbdbdaadcbaadccdccdccdabbbbbccdbcccdbddaacdbadaaddacbaaccbabbdaacacaabccddabcbcdcaccccadbacddbdbbbbabbccaacacacdcdbadbdaadbdaabadbdadacabacaacacbbacabdcbcabdaabdabadcdababbbddcbabdabadbccabbdcdcbcdddccbdcaddccccbdbbbdaadacddbcbbcdbbcaaabbdccacdbaacccdacdbcccdbbbcdabdabdbbdccadbcabcdadbaccdadcddbccabadaadcadbaadcbbdcbddabaddcbcbacddabcdadbbdbddddddaacddccbbadcddadaaddbcdaccdcaaabbbabaacaadbdccaccbcdbbddddadcacdcdcbbcaaaadaadacddbbbccabcacdbdadbdadaacbddacbaacbdbcabdacbcbdadadadbadbbdcabbccbcbbcbcbadadaadbccddabdbbadcbbcacbabcdccdadadcbcbcaccbbabcbcdccdabcadabbabddadabadbddbacbbaddddbdaccacdbaccccbccadbcbdadccccadbabbdabddacbdbdadcdbcabcbccddadaacaabdaabacbcaddabbcdacadbcadbddadbdbcaaacbdbaaabcaadcbabccbdccddacccaabdbbbbdaccaabcbabdcbccbbbbacaacbadbadbabbbbbdbbacdacbdbbaddcddbcbcccdccdaaccccbcbaccabdbbbcabbadbcadbaddddaadadaccccaddcdbdcccadbddbdaabbabdcbccbadacadbbbdbbdaacccadbadacddcadbcdabacbbdabdabbbbbdacabcdaaddbbcadccabaabbdcdcbcccabbddcacdaababcaaabdbdaadccdaacbacabdcccbcbbcbcabbbbcdacbadbbaddcbcbdcbacabadddbabdbccdbbcdadcaacacddcdabdcdaadacabbdbdddcacaadbbcbbdcccddbbbbaabdcdacaabdbbccdbcdcbaaddbcaddcaacaddddadabccdacdabacddcdbcabcaddbdaabbccdbaabaacbcdaaadabcccbbccabbbddbddbbaccbcdccddaaaaadadcbbaccacadccbdcacbbbcaaaccccccdbacaaccdadcabbbccdabcddbababcaabddcbaaddbcdcdbdcdbcbdbdcccaadabbbcbcdbccbdbbabaaadabdcababaddcddcdccacdbaccdaadbdabcaccbddadbbadabaacdddbbdababcdccccddacaadbdbdbabbddcdabdbcbaddcbcabdcccbdcdbacacddabcbcadadbccabadaccbadbdbbaaaaccbbadadcdabcdaaacaddcbdbddbabacdaccbbddbdbbbbccddbaacdcbbcdbbabdacbbcabcdbdabcbaddbbdbccbdacbdbbcadcdcdaddbbbbbbdacdcbdaabbdbddaadbbcdbcadabaccaccddbdbcbabadbcddabaccbaddcbabbdacbbbcbddaabdcbbabbbadaaddabdbdccdadacdcccacbcddbdcddbbdbbaacbcbbaddcddaabcabaddadadbbbcccddabbddbaddaabccbbdcbbbabcdbdacdaacccaaadcddadbbdddbdccbacbabbdcacabdcadbccdcbdbacbbacddccddbadddacadbdbddbacaddcdacabaaadbbadaaccdbcacddccbaccbdcacbcdaabdbabacdbaddddcbbcadadcaadbabaaabcdbbbdbabdcabccccddaaabdbddddacbacbbcabcbcdadcaccdaaabbbabbacbcddcbdcacbbcdbabcaabbccbaabdcaadbadbbacbbcdaddadbdacdacabcdacbdbbcbddddaacddbbacbadcbccccdbdabbacbaacacacbdbcdcddaadadbabdcacadbaadbdbdddacacbbdaabcbbbcbbcbddbbaadbdabddcdaabdaddccdcbddaadcddccbbacbacccbdbccddbadddccdbcbbabbadbbadabaaabcbaaacddaabdacdaabbccdadcdcbadbaccdbdbcbbcbddccacdadadccbbcdacbdbcacdabaddcbaadbbdbbccddbcddbdcaaacdbbaddaadbbcbdbdcadcabdabbbcbcbdbbaacbabdcadddcbcdaddabcddddddcabaaaddcabcccabaccddbcaadaadabdcadabacdadbcdadddbccdcbdbdccabccddcdbccdbcccaacbaaabcdcdaddbbabadbadbbdbdccbdddacacabbbbdaddbadcdacccdcabddbcdbdbcbdaddaaccbbcbbbdcacdabcdcdadabbbdccdaacdddccbaddcdcbbacbbdcacdbbdbbdcdddddabdababdbbbbcbcccdbdddbbcdccdcbdaddddaabacaababadcacbddcaadbddadccbddaaaacdabcaabdbbadbcaabacbcdcbbdbccdcbccaacbaacabadadaadcdbacadbddabddbacbdcdcaabacadbdbddcadbbbcaddbbacaaddacccddbbcccabadbbdacdbbdbbaddcbadcbaaadadbbabcdcacacdcabadbbdabbdaaddcdbbcbacdacccaccadcbdabccbdacabacabdbcbadaabcbacdadbacacacccabbccdcccbadddbadcadccabdcccabcaddbbbadabbccaacaabddadcccbdaaaacccbaabbcbbdddaaaccbddbbdcacaadabadacbabdaadccabcadbccdddcadbbbdaddbbdcadaabcccaddccaadcaadcabacabccddaaddacddcbdbcbabcccabdbacbbcdbdadbbbcbcbdadbbcdcdadbabbcdadbbccddacbddbadcbbadccbcacbccbaccdccdddbdddcbdddcbddcbcaaaaabdadddcaaaaccabacccbccbdabbabdaddbdbaaaabddaadbabddababacdabadddccbaabcccabbbacabdbcddbcdbdbdbadacbdddccadcbcbbbbddbccbaacbadbaccbbacddabdaababbcddcbcdbaaadddadaccdbbbdaaadbbdabadbcacabbddbbcccabadcacaabdaddaccdddbbdbdbccddcadbaccccdacdbabcdcdbaaabaadbababaadbbbdbbadabbdbdcccbaaddbbbdccbbacbcacadbbcadababbddaddcadcaaabbdccdbcbdddbcddddcbcacddbcddcbdbdadcacadcadacadacabdaadabcdaadccabdbbbcbacacddbbdbabdbbdabbccaaabdddcbdbbcdcdcccddabdddccbbababbddbdcbaaadbbcabdaabbbaaddadcacccccdaadcdaddbcdcacdacddaaaacabacccacdaddddbbbcadbdaccadbdabccdcccacbaddccbdbacdbcccdaccabddbdadcadcdccadbbabcbdcadbadbcaabbaddbabbcdabbdcbcccadaacacadcccbabbcbcabcabccddaccaacdaacbadbccbddddcdbbccccdbaaacabcbbadbaaccdddccaaacaaccacacbdaaadddbdbbbacdabdddaddabbbdbdacaaddababbbcadbabcddcacddddbdbadacbdbccbbdadaccaccdacabadacaaaddcbccccbbdabcbabdbbcdccbabbbcbcbcbbaabdbdaaaadabdacbcadacaaccbbacdabcaabcaacdaacdaacaaccdacbbabaadacbcdbbaadccacbdcabadabdaaabcccdcbcaadcbbbbcdcaadcbcadadbbcadcbabbddbdcccbbdcababcacdacddbacdcbabaddbcbabbbacadbbbbaabbabacaadbacddaabbbadcdacddbdcdbbddcdabccacdcaaccaddbdcadadccbcbdcadaacbcdcbcaddcbbbcbcdbccdddbdaadddccbcbacadadbbddbddbbdcbccbadccbaadadacbdbbbdbbabdddacbcbbbcaabdddadaccaaabcccddbddaddcbdbbcbccccbddaccabcddabdcdbabdaccbcddddabbdbdcdbbcdcaccdddbdadbccbccbbcbbacdcadcaddcabbdcdbbdbdcadbbdcbbdadcbabdbbacacaaaababadbaddbdbbbbdabdabbbbbbddaabaaddddbcbcdcbcaacabdcdcbdbdddaacdadaabbbdadbbaacbcabadcbaaabcaadabbadabbcadcddacdcbbdccddcbaaacddbcacdcdcdabdbbcbbbacccdbdcabccbaccddcbcaddbadacdbcbddbbcdaccaabbbbaaddbbdcabbccbbbacbacdcadbdcdddbbdbdadacbadaddcccbaacdbdcaabbcdcdbaaacbbdacddacddbbbbabbbaadbcbabacacbcdbddadcbdabcdcccbacaccbdddcddcaaadadbcadbbacaabddaacbcaadbdaaabdaccdbddaacacacbbdbbcdcadbcbdcababdcccdbacaccdbdbaddccbcabcddcbbbacbdaaddaababdbbcacdaddcaaabcadcaacbbdabcbdadcdbcadbaadbcbdababbbbcdbadbcbadbccadaaddacccabaacbaaccdbbbccadbdcbacacddabbcbdddaacacdcdabdadcbaaadaaadaabbddadabcdacbbacbacbdacaaababbddbddbddcacadadbacdbcbcabdddcdbacdaccaaadbabddcbbaabbadbddbbaabddddbabaabbbdbabacbbabddbcddaacccccddcabbcbbbacddcddcccaacdcdddbadddbacdacdcddcbbdbbcdadcdbcadbaaabbbccbadbccbaccddbdcddcacddadcacbdaacdcdcbdaddccabdbbddbacadccacaacbdddabbdccbdcacdaabccaabbcbddadddcdaadcdaccdbbabccacbaadabbacccadaadbddcabdcbaacdcbcbaadddcdddadbacbcdadbadcbadbaadcdccdbbbacbbbddcbddccddaadadabddbcbcbcbcbdcabdccacaddaccabcdaacccdbcddacacbcdaaccdccbaadacbcddccabdcbbbabaadbbadbddcabdcaadbddbaadcdddaddbaaabaadcbcbdcdbbdbdbcdcdaaddcdbaadbddabaaaaabbcccaaaaccabaabcaadbabdaabbdddaabcddabacaabcddcdcdbddbcdbdbbdbbcbcaacdcbadabdacdbcbadabcadaddbadacccdbadaabadcdcbdcbcbbacdcaacaddabbaacacbcbacadcdadbbdccaaccabdadbadaccdbdcabacbbacacacadcbbddaddccdccbaacbcaaadacadbaabbabbcbbacbddcacbabbbbbaccaabbacadbcacdbcbbbacbddadacaadbcadaddabddabbcddbbddbdddbaadbdcbbdbacdbacbdadacbdcddcdaccccaadbddbcbbdaadaadbdaadadbccbcbcdbdcadbabddabdabbccaddaccadabbaddaaaacdbcddccaaccdcdacccacbddcdcccdacddadadbcdcccdcaccdddaccbcdcddcdadcaaccbcdbabcccddbbdbbdbbaabcddcdaddcadcbbdbdadcbcdadaacdbdccabcdbbaddcdcdadcbbddbadadaaacbbaddcdcacbababcbdcacdcabacababbaaacadcabcdcbcbbbbaabcabcacaaadcbaadaddcbbdadbddcbcddabdcabaaabbdccbadbcbdccdbdbcadaaacdcddcdcdabccdcdbdabdddabccbdbbcabdcbbcdadccdcbdbdbbcaabacaacbbcadbbdaaacaaccdcaadccbdcbbacdbbcdaadaadaadadccbcbadbbababbcdacadaddbdbcccaacabbbdcbdababbdcadbcddbbdbdcddcdbbcbacbadcdabbccabcbcdbaaaadbcbdbdabcabbaaddabccbbdcbacaacbdcabcabdddadcdcacadbddcdbbcabaadbddcdddbdcabcdcaaccbdbbadadacadbddbdabdabdbbbababbddddcbcacacadccdddbadbcaacdbcdabdbaccbdaabbdaaacbcbabcbbcdbcbbcabbadacbcaccaccbadcaacbabaabbcabaaacddbcacdcddaabdccadddbbcbbddcadddbcccababbccdbabbbbabdabdadbbdadbadbaacdabcbacadacccdadbaadbbbcadbbccbcacdadccbbcdcdacdbdacabadbbddccadbdbcbbcdcaaaddabdcdacaaaabacacbddabbbcacdbbbdabcdddbbdcacbbacdcbbccaacccabbbadcaddaddbabccadbcacdadbdabcdbcdbdadcdcbababcaacaccbbbacdbdbadcccdbcbcdccaadcdcdbabababcbbacdacddccdccdbbbbbaabbcdcdcdbdcccdbbbbbadcaacaaaacacaabcbdcbdacccbbbcbbabbcccaccbcbcbccbbadacdabbcdaddcbdcdaacdacaadcbbdbcdbdbacbdbdbcbbadddbddcbcadbaaccdaabdabccdbcabcaaddbdcaccdcdabacbcbbdbcbcdbadcaadacccbbbddbadabcbdddddaaddddbbabdcaadccabccccadabadcaacaacdbccbdacbccabcccbdddabbcdbcababaabadabdcbbacbdabbddacabcccbdbaabacdbccabcbacadacccbdabaccadbbbbdccccbbdacdbdcbdbadabbcaccccabddabadbcacbbbadadcbcbcacaabbadadcbdccacdcaaadcaccaadabcccaacbaaadddadcadbaabaccadbbcadcccddcddbdbddcccbdcaddaccabbbdccacbddabadcbcabcbcdabcaddddaabaaddcaacbdddbcadabdacdccbcbdadbdcdcaddacdabbbbbbabbdaadbadadaabbbcddcdabaaaaacabcdcdbbacacccababaadadbbddcaddcbabdaadcaacacccaababdddcccadbddcdcadacadadccdadbcdababdabbdbaaddcbcbdbddadcbabadcdbbdddbcbbabcdcddcdbaadccdcdadcadbdccbacaccadaaddadcbaadbacdcadabdcaaaabbacccabdabacaaaacddadcddcbbbabcdaddadabaccadbcacaadddcdabddbbacbcbdaacdaaaadbddacbdadbadcdacadcbbbccdadcbccbbbcdaaddacadcbdabbcdacacccdbbbddddccabbcabbddaaacdddacdbabcbbadbacdcaaaabdccbadbaaadcdcbccaadccddaacbbccbaabcaddcaacbcbccdcddcacdbdbcaabdbaadadcaacadabacdaddcaccbbdacbdbcdbccccdbccaacacbabdbdbcaaddbdabddabaacddcbdbcbacbbcdccdbcdccaccaaaaabcdcddccadddadabcadadaccbbbddabcbbbbbaadaccbcbdddbdadddcccccdcbccadbcaabadbdadcbbcdccadaacabbddbbdbdaabdadaacdbacccadbcabbccdbdcbaddbaaddacaaaaadcdabbccadbcccbbaabbdaccbcbdcaddcadcabacdbbabbbacdacaabdbcbacbbbbbdaddddddbdbacdadbbddabdabdbacbabccbadcdcbaaaddabcacaddbdbddcacadbcadcadadaccbbdbcbbaaddbcbdcbdabcbacdcbcdbdcbaddbdcbbcdaccaccbadbdbbcadbcdddcbdbcddabbdaaaacbbdcccbcbbbbbcbadbcabddbbbddcbdccdcdbcdcdacdddcdaaabcdbabddbbaacdcdccddadcdcddddcdcaccdbdcacadaddcadbbbabaacbabcaacbcbaadcaabadacbccdbcccbbddddbbbbcabddddaaacbdabaadbbdabccbbabbdbcaaacdabdbdcadbbccddbdbaccaadbdddccadbdadbbabcbabaaabcacdadacaacdadcddaccbbacdbaddbddbcddcabdbddbddadaaccdbbdcbcdadbdbabdadbbcdbabcabadaacdaaddcaaaadbaabbbbdccbaddcbabccaaaacddacccbaadbccabbcacdcbaddcbaccdddddbccccdacbbccbacbbdcddabdddcdddbddcddcacbdaaacdddbcdbabbdabdadddbabbccdaadbbbcdaacbbadcddbbdcbaadbaaadcbbcbbdababccabaabdbbbbcbcbdbbdabdbdabdacdabdabccddcbadbcaccbdbcbabdabddcbddbdadcbbccddabadacacdaddbccdaaacbcbddddbadbccadbaabddabaabbddddbddababddacdbcbaccbacadabbbdbbcccddaddbacbdcbcdbdbbdcbacacdaddadcbbcabcdcdbacbcddcabcabcaddbcbbbaabcabaadcddccbbcadadbdbccadbdabacabddcdcaacccbdacddbadadcdbcabcbbccdacdcbcdbbcadbcccdbbddbdadcbcbcdbcdbabdadcbaababdabcccccdbccddcaabacadaabbdbcbcabcaccaaacadaacbbbdcdcabacacccdbababcaabcabbbcbdbccbcaaddbcdccbadadaccdbbccbacbadbddbbbcdcaaacbdaaccdaaaccacdacdbbbabaadccbadcabdabdaccdacccabdabaaadadddbcdddacbcadadcdddcdbcdbbdbbdbcabdcdbcbcdddbdbccddbccbbcdcbcbdbbccdadddaaabcbdbaabcbbabaddabcbdcaddadbcdacbadaaadadbcbbaaddaacaabcacbccacdabbaacabdbdbadaabdbcbbbabbabacbabdcdabbdadbcaccdddbcbaaccacabaabdbcbcbbadbbcdaaccbcbabbbaccaaadcccaababcbaacdaaacadabbbbbbabaddadbdbcbaaccdddaabaddcbcbbccaccbbaddccaaaacaaaabadbabbbbaadacdccbcdaaaaccbddccbddabbabdcdabdabaddaaacbbcdadbcdddadddbadbdbcbaacbbaabcbbbbbbcadabdbaccdcdaacaabccbbbcdddbddaabcbcaacddcbddadbbddacbbbabddbdcabbccdbccaaddbacadbacaadbbccdccababcaddddaadcbaadcddddcbaabacaaadddbdcbbadabdbcacaacbadacbbdccacbabbcccbcbcddaaacadcbbcacdcaacccadbaacadbabaccccabdccdbdcaaabbabadcddbdccbddbdadcbdabccbabcadaacccaadadbbddcdacbbccaabdcbbaabddcbcdcccabaabcabaacdbdadddacbbcdabaccabcaabadddadcbabaabddacbacbddaccbabdcabbaccdbdabacccddcddabbaccacabdacdbdddddddadcacbacadcbaddbcbddccdcbabbdcddcdadacabacdcdaccaacddacbccbabacbaaddababaddddcbdbbcadbbcbbdcddccbabbabdcdbbcbbdddccdbdbcbaaabddddacadcbbdacbadbdbbbbabcabbacababdbaccbbabcabaacdccabcdbcdbacbddabacccbcdbabbcdaabbbacbccadcabbacbdabbacaacccaddbbbacdbacbbdadabdadbcaccbddbcadaadabcaddbbdabcadbddbdacdccccdadbcccabbadbdaaaabddbbadbabcbabbcdcabcdacbcdccbdbdacbcacabacdababbcbdabbaddddcdcacbbdbaddbadcabbddaabbbbddbccbbabcaadbbabdcabccddaacabadccccbadacdbbbcdbbadcaadbdccacdcccaabbcddbdacdbacbccbcaabbcdabaabdccbaaacaddccdcdaccbbbddabadcccadcbbaccdbadbaddcaabddaccdbddbbbbbaccaddccddbaaddcaacabdabccbcbddacccdbcbaacbadbcbccabaadbaabdddcabccbdbbddacbadaabbcddcdbdabcdbbaaacdbaddcaaddbbabaabbdcaabdaddbbbbcdcbdabccaacdacdaababdccdacccddcacccbbadcacdacacaacdcdadcaaaaaddbbadcdccdaccdabccacdddcacacaddadcbcbddbbabadabbdabdddbaadaddbacdababdbcbbacdbddcbadaadddaddacdcadaadaabcacadcdbabbcbccaadcbddbbbbbbbacdddacbbdbbccbddbbbaaabdbadbacacabcdabacccdbdddaaadcdbacaddaccdcccacdcbaaaabbcbdaacaacadaadbadbdbbabbcbccadbbdbcdadddddcaddabcaddcaddaacdaccbcdbbaadddcdadbabdddaaabcadadbdbbaccdbadddccddcddbbaccaabdaadaaacadbcbaacbdabccbadbcadbcbcabbbbccacdbdbdddddddaadadbdbcaaadaadbdacdbdccdbaaabdacddbdbbddbbbccbabcdbcdbccdddaaaadbbbbabdaccdccacccdabdddabaabdcbbdcaddcbadaabaccbcdccbadbadbacbabcccdbcbdcdbcbdbdaacdcabcadaccdadabbbbbdbdacbcdacacccacdabacbdbccccbdcdadcdaacbcaaaccbabddcacabdcdaacbcabdacdbcdadcbabddcbbddbdddcbdccccdaddbbbaabcdcdadcccbcbbaaaababcbbdaabcbbaccabaccbadcaadcacbbbabaabadaadddddadddacccdcccabddcbdbdbbdbdbccbcaaddccbbdbadacdabbbbcbcbccbbdcaccddacdddddcdbbdccacadabbdbdadbdcbdabcbaccaddbbdbcacddcdcabbabbccbcddbbadaccadacabcddaacbadbadcccdadacbabacabaadbccdbdaadbbcbadccbaabdcdabcaadbddddcacdcaabbbcdaccccccbcbcaabccddbcdbcbbcbbabadabbdcabcbbacdbadabdcaaaddccacdbddcddbaadabdaadadaacbadadabcdcabcbcdadcdabbdbdaababdcbadcadccdbcccdddcabacaadbaaccbcbcbabbbaabcbbdbdadcdcbcbcaaccadbdabdcdcddcdabbacdcbdccddaacaccbacccbabbcbcdbdcabdcbaadbbcccdcaacacdcdbcccdbcabacbbcaaabcbdddcabacbdbddccabcbabdabdbcadbababaaacacdacddbacbbccaabcbacbdbcdabbabccadbbbcdabbaaadcaccacaaabdbdabddadbbbdcbaccbcadbabacdaaccabaddacbbbcdbddbaaddaabccaadbbbddbadadbacbcbcccdcaadbdbcadbcccbdbccaadbdbcababdcddbcbbdcacdbdaabbaabcbdadcbbbaabdcaadcaabbdacbbaddcbbababdbacabacabbaacbbdaadddcaadccbabdddccbbdcaddddaaacacacdcdcbbcbdcbcbacdbcddbbbdadabdcddcbbadaacadabdadbaadcdabccdccbccbabbabbbaacbbaccbbdddcbbdcdcccdacaabcbdacabbbbaddacddbbbcdaacdcdabccabdddcbabbaabddcacabdaccbcdcadbdacadaadabddddbabccbcaabbbbbdcacaabdadddddcddccadacdbccdccaaabadbddcabcbdcabddbbadbbaacbcabdaaaadbddbadddcbbbcabcdbbdaaabcdcdbaddbacacccbccaddadbbbbabbacaaccbbaccdccbabdbcbdbadaddacdacbcbacababcddaabbdbdcbccaabbbbdbacaadbbabbcdbacddcdddaadbddbaabcabcbbbbcaaccbcaacdcddbbbdacdddbbaadbabccdabdbadcadaaccadacdacaaddccdcdcbbabdcaabdcaababcbddbbbdbbaccacccbcbbdcabacccbccadddbbcaabbcddddcbcdadbcdacdccaccbcadbbcdbddaaacaacbbbabcdaabdddcccddacbabdcaccbaabcdbddccddcbbcbadcbbcdcbbcddccdbbcdddccddabddaaaaddcdddcbbadcddcdcabbaccaccdacdadddbcdcbbbddcddccadbccbabcdabdabdbbdcccdcbbcadaaabddcbcbaccbcddabbccbdbddccbbaaaacbbcdcbaabbbccccdbadadcbbcaddbccdccdadbaddaadbbbbdccadddabddabcdbcbcaccbcadcccbacdbccdbcbcbbabddddcbcbcbdcccbbbacaccbbbcabbcaadbaadaadcbaacddbcadbadaddbdbdbcddddbdcbaaabcdadcbcabbdcdccdddabaddbbbcaddbbcbcabcabbcdccacbbaacbbbbddadbdbaabdacdaaaacbddbadddcabdbbddacbdddbbaaacbbcdbabcdbbbdbbddbcccddcddbdbdbcccddbbacbbaccdbbcdaaadbacbbdbcdaddabcdbaadbcccacbcbbdaaaaabcdabbbbcdcdcccbcaaabccbbacbaaaaadddccacbdcccdddaacbbbaadaabadaaaaadbdbbdccccdcbabbaccaadaccdccabcddcacaccbdcdcbadbcaaabcaababccabdcbdccdcbbdacbdddddcbacbadbcabbcbcbadadadccdbabadddaacbadcbabbcaddcaacccddcddbcbadabcabbddccccabccdcabdacabadbacdccbbbdbadaabadbcdccdabcdabdddcdbccbaacbcbdaccbadccddcdbcadccbacadbacbcdcddcdadbadaadbbccadaddadacdbbbaaacaccaabbdcdaacdcaacbadcadadbdbccdbbcddbaacaccbddccdaabbbabbaadaabcdbcdabaabbcbdbabbcaaddadaabdaccdbcbccbccadbacadddbcabaccacaaddbacbddaccccbdaccdabbdaabcbbcadbaddcdabddbaacdccddaddabcabbdcdcacbbcddabbddbdccabbdadbcbddbacaadcbcabacddbdbdcbcdcbcbadcabaabcaddbcddddbcbcdccdacbbbaaaddaabdbabcdbaaadacaddacbabaacdddaccabbacdbcbddbdabacccadbdcddcbddaaabbdaaccdabbcacbcbadbdbaddbdbcadbcadccacacbdcacbbcacacacbcccdcacaccacbcccacdddcbbbacdcbacccacdbddcddadbdddaabbccccbccbaddcaadddcabbacdcdaddadabdaaaadacbccbbdabadbbddadbaccbbbccbbddaaccdbcaabddaaaadadabadcdabbabdbdddbbbcdbccddbaaacbddbbbabdbcbbcbaabaadcabadcaccbbabdabbcbbabcdaadabccbdbdbabccabcddbaddcbabbcddbbdbdbaacacbbcdacdaabbcdbabbaaabbdaccbcdaaadbbcacccadacadcdbdabdddadbabaaaaccccdccbbdcacadcdcdbcbdadcaabdbccdaacadddbccaadacbdbdcccaacccbcadacbddbbbbadabcdbbcabccbcaddbddbbacdbbaacbababcbbdcbcaccaadbcbbbaddddddccaadaacbadadbdbdcdacbcddbaabbbdddcbccbcbabdddcbdacdccddcbcbcbaabaadcdadbcbbcdbbcaacbcdbadddddaadbddbddabdaabdbbcaccdacaacdacaccdcbaaddbdbcccaaacdcccbbcddcdbaddcccccadbdbbaccbdaadadddbcddddcdcdcacccaaabdacabbdadaddccabddaadaccbbabadcdbabdcbcbdadbdaadaccadcddcbbcdccdbbbcbbdcbbbaaddddcccccbbdcccbbcbbbdaadbdadcacbcaabdaabdabaddabdcacbacccadbdbabaddddbdcbcdaacbddddcabcdaccdaaddcbdcdbdaabcbccbcddddbabdadacbbdcdacdbabbddbadddbabdbabdaccdbdbdaaaabcacaabddbdbddaccdbcacadcdcaacdaabdbdddcabaddaabcbcabbadbddbdbdddcaadcacadbbbaaccdbbabbdccddaaacdacbacdbacdcbcddbaaaadbbcccaacddabaacdccdddccbaccdcaaddcccbbaadbaabddaaddcabbdbaddcaacbddccdadabcbdacdaababccabcdcbabdccccdadbccdaaaddaabcdadabadcbcdaabaddcdabcbbbacdabdaccbbbdadcbaaaababaacaacabbabcdbbdaabdcdbcbaddddabdbbbddadddbacbbbaaabcdbddaaabadbcdccddcbdbaddabbbbdddabccbadaaadcbcbdcadaabcbbcadbabaddcabbbccaddacbabccaacdabdabcadbdabdbbadbccacabdbcadccdcddbccbddccbabaabdacbcbacccacdccbababcdcbcbbabcbdccbbdbbabcbdbabbdcdaacbaabbddccddaacacdbacabacbbdbaaddbaacdaabcabddcaacbccbddcbaabadbbdccbabbdbdbacabbddbbbbcccbdccadabcdcdddaaabcdbcaacbabaacdacdbbbbbcbdcdacabbcabbbabbdadccacdcbadcbdccabdaadcdccccbdcccdabddddadbacabdcaddadacaccadacdbaadbbbdaadcbabbcbbbbbdccbdacbacdbddacbabbacdabdcbbcdbcdaacbccdcaddadabcadcdbadcbcadbbdddbcaccaabcbaaaadcbcaabcabbcbdaccccbcaaadcdbcabaccdcbabbacbdaccbaabbcacdbcdcbbdcaadbddbcbccaaaadccbaddcbaaaccdadbdcadaddbccaababaaabcdbaabddbaaabbcabacdcddcdcbcaddcaddbbdadddabaabadddcbcbcbabdbddbaddbaadacdbcabccaaaabcdbddccdabddacdddcbcdbaccdaaaddadaddaaaaadaabcbddbcaabacbdcdcbacadbcaccbcbdabbdadbbbbdcabbdcaddcdaaadaabccbabcccdadcddcdbcaadbdcbaaacbccaccacbadcdadaccdacbccccdccadccbcdacbadbbbccdbaddabdbdcbabcbccacbdbacdacddcdddbaabbcddcbadbbcbdcaccdbabccacadcadddacbbddddccacdccccccdaaabbcdacbcddcbddabaabbbdbbbbcddcdccccabaddabdadccacccbbdaadccacbaaabddadcaddaabbdaccdadacbbbaadabbbacdcbadabaaaacadcaadbbbbabbbbadccbcadacdaddabdabddaaddaddabdadbabbdddabadbdccabcdabcbbacccdabbadcabacdbadadaadbcaaccaacbcbdddbdadbccccbbdccbcbdaaabccaccccdbbbbbdcdbddaadccadaccaaadcbcddbacddbccdcdabccdacaadcaccbdacabdabcadbdcbabcbaadcdadddbbabbaadcbbdacdabbaaabacdcdbbbbbcdbccbaccabdadadbbbdcbdaddabbacdabddcdbdadcdbaaccdccdcbdadacdabddbbcaadaddabddacdcaaaddcadaaaaadabddccaacbdabdaabbacddccdcaddcacccacdbaddcacbbadaddcdabaababddbbbdbdcadbccadaacbdacbddbbdbcadbbbccdddacabdaabdcacddddadadaabddadcaddbcbacbcdaacabdbbabdcabbabacaababbcdbdccacbaddacbdcacacddbbcbcbddbbaaacaacaadcaccbbabdddaaddbddbdcdcabcccdcaaacbdddabbbccbacdbadbaaddcddbbdacaacdbacdbaadacdcbdbcdaaadabdbbdbaccccdbddbadbccaaaaabadabcabcacdadbbabcccbacbbaddabbccacbbbdbccdbbaadccacccbadbbabcaccdadcabdabccbbcacaaaaabcdcadbabdbcdbbbbccacdcddacccbcaaddbddaabbcbbbcdccccbcdbabacbbacbdbcddabbdccacccbcdbdcbbcbccdbaadabbacbbaacddcabbcdaacdaacdaddacdaddadbaddbbdbccbbdaccbcbaaddbddcddbddcdbacdaabbcbdbbadbbdcbcbadcddccbacadbccdbccbcbcbcdcaabbbbbaacddbbcdccbcdbddabddcdcbbcbdacdaadabcbdabdabdbdaacdbaabadddbabbbdadcbcacdaddacccdbccabdbccbcbbabacbaddbbdadbdaddcdabdddccabbcaacbbcdacdcdddbbaddadcbabdddcaccddadbbddaacdabbbbabcacbbaacccdbbdddbddbcbbbbbcababdccdaaddbacbddabddacdbadbabcbcdcadcccddabaabaacbabbbabdbabddbdaccccddadbaadccbacbacacccdbccabcbbbacdadddcbcadabbbdcbdbabccbcddcbdadddaacaabbcacccbccbbbdccdbdccacbcadcdbcaccabcabbcbacbaacbcdcccdcddcaccabbbbbdcbcdaabcabbbdbbabdccdcbcdddccdabcbabcbccabcaddbbdacddaaabcdcbdadabbbdbadbdccadabbaacabacdadbaabdcbdbbabbcbaaabdcadadaccddcbbacaacbdddcbccbaaacddbdcbbdccbcbbdbbdaaddccdbcdbadabaaadbadcadabdcacabbcaccbcaaacdbbcacbbcabccbdaadbdcdddacaddaddddcaaaaccadadcdcbcbacadabdadabacdbcdacabddbbdcddbcddadbaccdacdbbddcdbdcbdbdbccaccbaabbbbadcbdcbacdacbbccaacaadbbaaaadabacbbbadbacaaccbddabdbcaadadaacadadcbaaadbbabdbbbaacaddaaabbddaabcaabcccacbbabadbdcdbdaacbbcdbbbdadbcbdadaacdddccbddbbbdcccddaccadccbacadcdbabdcbabcdcbaadddabcbaacdcdcccbdccacddbbbdddacbdadaddddbabcddacacabddcbcbdddabdcdbabcbdabbbaaaaacccabccdadadbbaabaddbbacdaaaabbcbdaaababbdbccabacdbdbbbdccdacacbaccddcadcdadbcdcbcbaddadacddddcaccbcbbdddbbbaadcccbcdccadcdccadbaaacbdaabcaabccaaadbdcbdaacabdacdababdbbbaacdcaaadddcdbbaccaaddadbbcacadaaabaccbccbcddacaacabacdcbaaabdbbaccdcabdcbcabddccddbcdbcabdaabcbddbddcdcdcdddcdddccbbdacaabddbadccbadcddcbcaccdddcaadacbacbcbabacbadaaadacdcbdacbbacbcdacdcdbabbbdcdcccdadbcdacddcaadcdbcbdbcbcbdcbbcdacdcdcaaaacbababadbddbdcdddbbdbbcbdaccbdabcacdabbccbdacaccbacbbadacaacaddddbdbccdbdbbaabdbdabdcddabbdbdadcabacaddbbcbbbdcdcaadcbadabbcdadcbaaaadcacbcdbcaababcacdaadcdddcacccdaddcdaddbbabaaacdccdccadccbbcaaaacdabdcaabdacadddabddbdabddcacddabcddabbdbdaabdacdaabdbccdcacbaacdbbababdcccbccbbdbcbdbbcbaccdacdcdcdcbadbbccdccccbdbbddbcbaddccbbcaaadbbcbcbabdabddccacccaaabdadaacdcbcaadacacadbdadaabcbbdcdbbbacabcbbaaaddaaaaaabcccdbdddcbbcabbbcbccbdaacbdcddacdcbdaabadacdaccaddabdabddccdadcdbbaddacacdcadacccbacaabbcabbaabddbdbdddddacbadbacabcddaabcbdbaadbdaaddbaaaccdbcbcccbaaadbbdbccdbdadbbdcaddccbdaccdaacaaddbcdbcdcdbccabbcdbbbbcaddbdccadcdbbabbabcbadcadbdcdbbabcdbbbcababacdaccadaddbddcdaccaadcdadbddccaadcbbbadbbcccbbccdddbdddcabcbccbaabadbcbcbdbbabdbadaaabaaaabddccdcdcddacbadbdbacbddcbdcaabacccdaccaddacbcadcaaccbdbabaaadadaadcdaacbaadadddcccbbbcbcdbcdbadbaccbbbdaabbcbcbabcdcdbbcbacccabadcddcacdbaabddcdaaddccdccacbbbbcadccacbbddabbbcbddacdcbdbdccddaabdbcbcaaccabdcdbdddabdbccccdbbdbdbbdbccbcbdbcbdbbbbdabbcccaccbabaddaadadcabcbbdbdabbacdddcbccaccbcaacbdddcabbdaababadcdcdabbcbdbdcdbacbbdbdcaaadddddccaccacaabbcddcaadbacddcbcccadbaacddbdcdadabaabcbcdcbddadcbabdacbcbbdbddadcacbdbbbaacbbbdcddcaacbbbcbcaadbdbddbaabbbaadbbcccbdcdbdcdaacbaccbdbaabcadbbdbdbaddbacbbcbbadbcbddbdbcbbcbdccbcbadcaababaadccccccacdaacbcbacabcbaacdaacdbabdbabbadcaacdacbbccacacdcbaadacdacdddacdcbaacdcacacbdcbaacadaaacccccddbababcccadaacdddbcbacdccabddbccddaccccbadbbbbdabcbbabdabbaacddcbcacbaadbcaadacbadaadbcdbbcabbaaaadbaacdcddcdbbaddadcaaaaccdadccbdccbdabbddbacaccbbcdaadabddcbdadcddcddcbbbdacbcaddbddbddcccdcddaacdabddabdcbdcddadbddabdcbababaabcbacdbadcdacaadaddbbcbaaddccbdbacbabbbbabadccaacbbbbcdcaaaaacdcbbcaadcbabadaaabaccbccadccdbbbcaaccbdcbbdacbddbabacaacccbcccdabcaadccbbcaccbacbcccdbacabaccadbdcbbbaaddacdacbbbdcddcbbbddabdababccabdddadaaacaccccbabcacccabacbdbaccccaabddbbacdadbdabddcbdcddcccddcdbcddbcbddbdcbdbabcbbdccdddbccbaabbdbcabcababbabdaabaaabbbcabdcdadbccdadbbabbccdbdccadbcadcccdbdbbbbbcaaacbacabacbbcacbbcaabccdabbaadadccacbccdbcdbdccadbbcccadaabbbcbbcacbdaacadbbdddabababcacdaaddddcdacdccbbbbddbaabacdaacaabababdcdabacdbdadcdabccbcacdbcaadbdadbcddcddccdcbaabbaadcdcaccaacbdaadcbaabcdabbbdaabcccdbbdbdbadaaddabbbadccdbcbdbbddcabbbcbbdbacadbcadacdaabbbdcbaddadcbcbbcbcbcabbcbcabbdbaabbdbddaabbcabbaaabbcacdacdbbacbcacdadbcbcccacacaadaacacdaacabbbbabcbaaabbdbabbcdcbcdcbadbccccbcbbcbabbcccdddabdaddcaabdddcddababcadbcccbadacadadadbacadddcdbcbbcdaabadbaacbccccbbcdbdbbcbdcbbdbaaadcdaacccbbcadbcbdddbddbabcccbdadacbdcacccdcbddadbacccbbaabcbdababdcaabbbbacbddbcbbacadcdbacdaaabddcacddcdcabbcaacdcabbcdabcacdabadcddcaccbccaddbdcbadaadbabababdaddacaaaadbbbadccddaddcdcdbbaabbbaccbaabbcdcbdcdcabcccaccdaaddbbaadcccabcdcbbaadbdbdbcabaabdcdbdbdacabbdbacccdbccadcbcddbcdaaaaadcddbacabcdabddacaabbcaabacdccbacdbcacacabcdbccaaadccbcbcdacbcdcdcbdbbdacacbaaccbbdaaabdbbdadbdacaacbcdacddaddbddbaacadabdbdbcddacaaaaccbdbdbbdbdadaacbaadbbaacbabdcdbcdcdddcbddcaaaabcbbabaadbbcadbbcabaaddbbabbadbbcbbdabccadcaacddaacdadcdcbcabbdaaddabbbbcdcdbbadbcabddccbdbddbcddabcaabbabdabddcbdcbbcdcbddbcbaccccbddaacabccdcdbbddaccbdbbddbadbcbccbdbbaccadcdcdcacaddaacdccabdadcddaadabddddcbdacbbadcadcdadadaddcdcbbdcaadbdccbbbcbaacbadbdcacaccdbcacabcdbcccbadbabdabaaabaabdbcbaddacbbdabbdcddacbbbddcdccdabcdcdadcabbbababddadccdbcbcbadadcbddcdcaabcccdddbabadcaccaacdcabcacccdddbcadbbadbaadbcabcbdabddddcbdcabcdbccdbadabdabadabccdaaddbbddcabbbcadbdcbcaaabaddcdbdcdbabadcbbaccacdaabcabaabacbcbcaaddcaabdbaddccabdcbdbcaabccbabbbcbaadaacacdabdbdbccbdacccbcbddbbdabaaaccddadcbddccdcdddabdaabcddcbdabbbcbacdccddbdbcbaaaddbbdbcaaabdcdcdacacbbbaaaaccadabcbccbabddddbbcabbccdcacbcacdaddcccdacadbabaaadcbaabcaaaaadabccadbcdadcaadbccdcaacdaadbaaaadaabaccaddcababbadacacdbbccccbdacbaadbdacbcbdabdbcbccaabcdacccacabbbcdcdbcbacdbcdccdbdadcdbbadaadaacccadaccbdcbbddcddccadddabdbbcdaddcdcbabacbacccccdcdbccccddacdccbadbcabdbadabbcacdcabaabcdcdabdbdbadbcbccabccbdaacbcdaababbaddcadcbaadbcbcaddbabacbddcadadcbaaabacddccdabbadbddacdcbabbbcacdaaadbaadccbbbdcbccbcdbadbcaabcacdddabadabcaabbabacacccbdcbdcbdacdaccdcacddabccdabcadbabacdbaacabccdcadbbdadcbbdcdcbadbccacabbaddcdbcbbaaddbdcccbbaabdccaaddcdcbbddccbaddbaccdbbdbbdcaccbbdaddbaddbaaccaacbbdccacccaadaaabacbdacdadaaddcbcbbdbddcbbccaaabbabbddbbbccabbdbdbbaabdddcabddaadccaadbabbcdcdddadaaccdbabaadabbabaaabcdddadcacccbadbbabcbbdbacddababbbbabcbddacaddbdddadcaadadadcbdbcbacacaccdbacabbcacbccdcbddbcbcacdacaadccbbaadabadbbadbccbcadcaacdcdbddcddaacddadbcdcccbbaacacbdbcbbbcabccbbbbcbbcdbdbaccadcacabcbccdadcacbcdcbdcbbdddbcbbcbaaaddcabaabcbcbcabbbcdabbdddcadadccaacddaadbacbbbabbbdbaddbcdacaaaadababbadddcabccdbddaacbaacaabaddddbdcacaacadbacccbdbcddcbbcdbbbadcddbbbaccbabbdbddbcabcccdacabdadbbdaacbacdcddbcdddcdbdbbabadaaddcdbddabacbccabcaaaccacacabdcbacdddddccaabaadbcdccacabadcaabddabdccadcdccdbbbabddbbcbbdadacaddddbbcbdbddcbccdcbcbcbadbccadbbaccdabadabccccadbadbacacbbddcdacdacbbccbcbadacdccdbdacbaabdccddbdbbcccbbddcabdbbcbaccbbabcdcbccbbaddaccbdccbacaabbbbaaaddabadabbccbcbdbaacddaabdaadbabbbbdbaabddaabacccdbadabcdacbccbdddcbdabcdabdcccdcccaaddbadabbbdddddcdcccccbdcbadbadaaadbcbcccaabacabaaabdbdacbabbaaaddddabbbacadacabaabababccdadacabadabccaacaaabdaacbddddadbbaacadcccbbbccdbcaaadacbcbbbcadccadabcbbaaaaacdbaacdadacbcdacadcdcbacdaaabdaababbdaabcccadabccabcbaaaddaaddcdbcdbcbacaabaadcbbbbddaaddacabdababbcccaaaddcadadcabddacdbadccddacacdcabcaacccbbbdbddcaaccdcdbdabdcdccccdbcbaabddddadbcdacbbbdcababcbaccbdbbaaaadccddaaddccbcdbccdcbdbcdacacbcdabcaacbcbabdacbadcadcabcbacbabbcccdbdadddbacbcdcaaddcccbcacbdaaaabaccadabdbcdabddacbabdddaabdabaacaabdddbaccbdaccbcadcddacaadacbddaacbcdcadbddacaacbacbadaacbdabccbacccbcbabbbcadbbbabbaabacabaabdaccbcdadcabdbddcccaaaaadbdadbcacddcacaacbcdbbddcbdcdbbccadcdaccabdcbbccbdbccddcaaadbcacacbbbdbacbbacddbdbcdbdddcbdaaddbccccabcaacabacacdddaadddddbbabdbbadbbcadccddadabaccabdcaaddcdccccbcddacdddaaccdabbbcdbaaacdddbcbdbccbbdaddcdccbadbdbccbccbcbabaadbcacabdddbcadacdccbabdcdaabbdadbcbbddddcdadccdbbabbdcacbbdbbdbbbdddcccaaccbaccbdbdabddbbbbdcbbbacbcdcbddcbadccbacdcdbabadcdaddabaddbcacabddbaaddacaabbdbcbaacacdaddccaaabdcacaabdcbdaabbccaccccbacacccbbddccadbbabdcccbacacccacbbbadcbdccaabcbbbbdbdadbbbaaadbcccaccbddcabbdabbdadadcccdcdbcbbbacaabbacddcacdccccacacdbdcdbabbaacbcabaaacadadaacbacacbdaadccdbbccccabdbdddbbdbbacbcabaacbaadcaacbaacacbbcdbcdddddcbbaaabcdaaadbdcbcacaabaaabcccbdcdaadddacabbcdabacaadbdbaccbbaddcddacaccccccdadaabbbbcbdbbabadcaccabbbabbcbcdbdddbcdbaccbaabaadcabacacdbacbcccaacaddcdacdbdbbabacccbdcbcbcdbdaacdabaabbdbbbaccaadccbccdbdccbbdaabcbbaabddccdbbcddabbcdabbddcabaaadbdcadbcbdaddddacbbabdcdccdacbdcddcbddabaddaadabdaacbbadcdbdcacdbbbdbccbdcbddbccaaccbadddbcabadbbdcabbddbcbadaadcbcdbbbbcdccaddbcacbabcccccccabaabbacbbdcbdbacdaaaaccdcddbacdbcdddccdcdbacaaacbdbbaabdbbddccabacbdbabbdcabdcbaccbdaacabcacdbbacddddbdcadaddddbbdbdcacbdddcdcdbacabaadaacddcacccdccccbaaacbdccbdcabcdadabcdabbcdcadbcbadbcdabcccbabbaaaadcccccdadddbabcacbcaaacabbacdacbdcabcbccbbbaaaaacdaddcbacadcddacabddddbcadabccdddabbabcdcbabbcdcdcabdcdbbbbdbccabbaabaacabdbacaaacdcdacabbabdbcdacbcacdbaddaacbbcdadbaabdcbaaccbbddbdadcdadbdcbaacddcaadbbdbbdcadcacbcaacbcddddddcbdaabdbadcaddddcdbcdbcbcabcdabadbdbccbcdbdadaaabdcaadbbbabcbabdcaccabcdddbaabdccddbdaabdaccbacabbbddbcdcdbacbddcbaacddacdbccccaabbbccdcacbccbbddaccccadcccbbdacabadbccddbccbadcabacaabaabbcacbccadbcdcbcbbbbdaabbdcbdaaacabcababddcbccacabccaccbabaabdbdacdccddbbcdcbaaaacabdddbcddabdbdddccdcacbcdbbddcadbdabdccaccdadccadabdcddabbcdbdccccabadddbbccabadadcddcaaaadbdbcadcbbddccadddcbcdccddccabbcabbbbaadccacdbbbaadacabcdddbcddadbbbcdcadaccbdaacbbdacdbcadcdcbabdbbacdbacabdbabacdcddbabbbbcdbdcabbcbbdaacbabaadcccccbdbadccacbdcdaaabccdbcaaddbacbcaabbcadccbadcbdcababcbaddacddcaacaacbcadcddcabddbccdcdccbabcbddbddaacbbdbdcccddbcdacdcbcaaaaaacdcaabbcadcacddbdaaddccbcbbdadddbadbacaddaabcabccdbabaacaddddbccacadcdcbcccbdadcddccbbacabaababadabadccbabaaddbdcacccdcbbdcadbbaacbdcdcbdadabacdbdadadbbcdbcccdcadbcbbbbdabbadccbccdbcbdcdbcbcbcccadddaadadcddbcbdbbcccadddbcbacbbcbaacacdbcabcbbbabcddaacccbbdacbccdbdcaccdcddaaadddacaacddbddbcaabdabddbccccacccddcbddddaacdcbdadacaddcccacbbbcbabbcaaadacddbbaaccadcbbbcdbabdbbdbdabbadbdddaaababacdadabacacbdccbddcaacddbacadaddaddaadccaabcbdadabccccacdbadcbccdcbcdbadacdcdddcbaddbcacbddbdadbbccababbbcdadbbdadbdddbbaadcadacabdccdcdcabcdabbadbdabdacbaaaabcddacadadcbaabcaadbddcbcbddbdbabdbccccaacbcbbabcdaaabcddccabbdbadbbcbadcddbcaaabdcdcaacbcddaddadcabdbdbbbdbbabccaccdcbdbdbddcbbaaacdaddadbccabcbcdaaaaaadbcbacbcbbdbbababbaaacdddbbccdaabbbdcbdbccccdcdddddbdcbabaadaadbcdddbbabbaccdcbdaaddaddcaccbbdbcacacadcbbbacbcbcccbaccdaaadccbbbcbbaddcbcdabccdabaaabadbddcccdbccbbbabcbadcadacacabbcbdacdcbcbccdbacddbdbacbcadcdddbcadbdbdacbccaddbbccbacbabbbccabccadabcaaabcaaddcbcccbdaddaccdaaddbddbacaabdaaadcccccabbbbaacaddaaacddcdaacbddabadbdbacccbaaaaadcadccaacbcbaadacbbadadaacbacadacdcaadabacbcddcadbbbdaccaddcdadaaabccbacadabdbbbdccbcdaaaccbcccdabbbacccacbcdcacdaccdbbacbddbccbaccdbcdcabaaccbaccbcadaadaaabddadbccacaabaadcdbdabdacbaccbaaacacbddaabcaccacbcaccbbbdbcabddadcbacaabbdaabbaacdbcacadbbcccbcaaaaadbacccccdabccdccdcdcadadacccacadcacbddaacacbbcdcccbdddaacbbbbdcacacacbccbccdaddcbdabbbadcddbdcbadcaddaddbbccdcdcdabcbdcdcadadddaacbadabaccdabdacbacbcbdbbdbcbccbabdbbbbbccdabddbababbbdbcadadbbbdccaddacddabbbdbcabbcbddcbaabbdcacbcadaccddbbdbccddbbbdcbcdbaaaddaacadbbaaaddcbddacadacddaabadbbacadaddabdcccccadbbcaccbaabdacbabbabcaacbcaacdbddbbaccbbaaaddbcbcbdcaadbacbdbdccaccaaadddcdacbdcaabdbadbbbbbccdcbadbccbbcadcaaccbcbcdddaacdbaccdbbabbacdddadbabbddddbdcaadcccaadabcccdaacdbaaabdddbcddaaadcdccadbccaaddbcbcdcdaaddadcbbabaccabcacbdbbcbdcbbddaadaaadabddbcadcdcaaccadcbbcbbcabcadcbddbccdacbadcbaadaadacdabbaddbacacaddcaddacaaacbbddcccbbccadabcadbaacbcccadcbacadaadacbcaaddbababadddbbbdcbababcdadaabbddbbdbdaaaccddcbcabcacdcacdaabdbcababdcccdbcbdadcdddbdadadbbabdcdaabddbabdbbcbbcabcccbadbcdabbbcbdadbdabcaaadddbacadbbbaccdcacddcabacbcadcdbdbabccadbadbaddbbacbadaaacbbabdabccdabbaaddacaabddcbccabcadbabadcbabbabdaadbaddbaadacacddbadbcbcddccdccbabdbaacabacbaacadccadbdbaccaaaabdbdbdaabbbbcdcacaabbaddbcbabbadaccbcabdacacbbcbadddbaccaaddbbbccbbdabcccbbbddcbccabbdadaabaaddacddaacdaccacbabdbabcbdccbcadaabdddbcbccddcddddddaccaddababdbdababcacccbabbabdcdbccddabdccaddacbccacaccbdccbcdbcbdaacddcbdaacdddcbbccbabdadbbccccacbbaacdadcbccdcadcaaddaadbcdcbbdcbdccdcdbbccbbdddbdcdbddabdabcdddacddbadaaaaaccabcacacbbdcbdbcbcbabacaccaccbbdacdbbcdbccdbabadcdaadbdabddadcaacdacbacbddbbdabbccacaadcdccdbdcabbabacbacdabbacacdccadbabbcdadbbaacaaddaddaacadbaadddaccddcaddddbbabdcbcdbbdbabaabdcdddcbaccadddadcbdaccababadddbcdccadddcddbadcabaacdccdabdcbbdadadadacacbdbcbccbcbadcbdcddadbbabdbacbbddabdcacdcabbbaccbccbcadabbbddcbbbaabccaddaacbddddcdcbcccdadbdbcdcdcccbaccadccdaadcaccccbcbbddbbbbbacdaaccdcadbaddbddbbbdccbaabacaddcdbbbbccbdbccadaaddccacacbbbadcaadaddbabbbcccbbbbdddcbbbbddacbdbacacdacacacdadbcaccbddbacaaacdcddbadadcbaabbaccabcdcadcbccaddbadcaccdcdacdabaddccddcdadddddaadddacbcbdaadcdbadbddaccbdbababadabdbcaadaaacacbcdbbbdacacaabbddaaccabcbbddbcbdaacddccaddcdddbcbbaadacabcdbcdddccdbbababadbdbbdccaacacdcbbddbbcbabdcbdcbdbdaccacbdadcbdbadbabccadcabbcdbcbacccacbcbcccdbbddabacddcbbcdbbddcbbaddbdcbdcbabacaaaddbbcbbddcbcdcadcdbccbaacddbbaccdabbdccbbbabbbaaadaddddbdcccbadcdcacbdcdcacbacbddbabcdbddacccccbdddacdbcbadbcdddbaccacabdabddadbbdcddbcacdbddbcaabbdbcdbcdbbbddcdcbddaacccdbaacccccbdccabacabddbacabacddccbcdcbdaadbabbbabdadcdacacddccdccbddddbcabccddadcaabcbbdcbbcdcadbddadcccbacacbbcbaabadcdcbdbcdccaddbdacddccadcddddbcabdabccacdbadbaaadacbdcddababbbddbbcdaacddcdbccbbdddbdbdbdbcdddcbcaccababbddbcaacadbdcacdadaabbcdabbdbacbadabcaabbdaddddbdaadddcacccdacaabccabcabdccaaccadbccaabdbaddbccccaaccacdbdbbcbbcacaabbacbcaaababadcddabbaacbbbbdacbbacdadaacadcabdddcadacbdccdadcbbbdbcabcacacbbdddbbacdacbbaddbddddccbdccaabccaacadaddcabdcbabcbdadddcdcaaccbbacdabacbbabcbdbcdaacadcddcbbaaaacbdddbacddadddddacaddbbccccbcbdabddadbdabddbabddbbdbcbabcbdbdbbddcaabdcbdcaacdadbadadbcacdddcdddcbbbadabacabdbbbddabdbcccddcbadbadcdcacccabdaccdbdcdcbbcdcbcdbbabbdcadcbaadabbabcddbaaacacccaacdcabbcddddccdcaadddaabaacacbcdbacdabdbbbcdcdacabadddbcbcababcaacaddcbdaaabadcbaddcccabdabaaadabdcbcaadddcddbddcabdddaddabddbdcaddbbbdbcdbbdacdbabadcdacaccdaadabdaaabddbbcadbababdcadaabbacbdcbcaabbadccbdccbbcccbbbccabcbdadcdddbcdaccadbbddccaaacaddcddaadbadbccdabbabddcdaadaacadaabdbaababbcbbcbbcccbbddbcabddcadbcaacaaddbbacbdbabccdaacdbdaabaaaacbbdbcaaccabdadcaadbdcdbbcbddbabcadaacdbcdaaadbdbdbacacdcdacdcbdddacabadcccdcbdccdcdcbcaddbcdddcccbcbddacdcacacbcddadaabaaadcaabacaccccabacddcaacdbaaccdaadadbaacdcdcbbbccbcadbadadbcabbdcdadddacdcbbcdbabbdcbdacbbcdccaccdbbdbaaacaabccabaadacadccccddabcadccdcbccbccadbbbdbacabbabbccbdcdcdcbaaccbdaccbbaaacbdbadbcbcaabcababcdbcadbdcacdacbabbaccddccdaadcbcacaacdcdcbacbbdccdcdabaabacbcdaccaaaccbadabdabadabaccbabdadcdddbcbdbdadaadccaaaddaadadcddaccbaadbccbbdacccdcdaabbadcbcbcaacdacbcacbbaddcbccbcadbcccaaadadccdbdccddcadcbdaccbdcbbabcdcaadbbccbdbcadcacdaacdbbcdbbccbadcdcabdadbabaacaddbdabbaccbbcdcbbbcdccaacadcacbdadcacabcbbdcccabdaaacbdbbdcadbddcaacadcbcbabbabcdbabdacaaaaabdabcdadbbbcdcdccbacaadbddccbbcbacccbbacdddcdaacddddbbbcddaabdcccdbabccdcdbcdddbbabdbabcdaacdddabcbdbdcadcccdbccdcdddaccccbabadabacdcdacddcacdbabcaadaddbaadacdaabcabacadabbbcbcacddabdbaaabdadacabcbdcaadacdbbbacdbcdbbbbbacbabdcbcababccdacdbbcdaaadddbbcabcbcdcdcddbabdcbaaaabacbdbadacccbdadacbadddddadaccacdcdcacaacacababaadcccdaddcbccdbdcbbbacaadcddbcaddbdaabddaccdbaccbdccdadcaadccdccbcbaaabbdbaaabadcccccadbcdbbabcbddacbcaccdabacdcbacbcabaabccdccaaccbddbbadacbddccaadbaccbbccacbabcbbbdcbaddcbcabdaaaddbcbddbbbaacababcdbcccddacdccdaabddbbcaacbccaaadbbddcbddcccabadccaabbdbdbbbcdbccdbacdadbbbaaabdbccaddacabcaadbccbacdcadacdccaaabbcdacbcccdcdbacccdbddddcbbbadcaaabdaacdcaaddaddaaaabcdacbbbabacddadaadaaadbacbdbcbdadabccbdcaaabddbacbbccbbdcbdccbdadaaaacddbdbaaacacabdbddcddabcabdaaddbdcbcaacdcabcdacabccbabbcccdcbbcadccdbacaacddcdbbbaddabcdcaddccdbadabadbadccbdbaaadadbcbddcabbabcdddbbbdbbadbbacbcdbdbdbcdccccccaacacddbdbbddcbddadbbcbcabbbddbcbcabaacddcddddadddacacbddaababbcddadaaddbbacbadbdcbaadabdbbbbaabdcccabbbabddddabadacccbbadcdbcaadbcbddbbcdbbbaddbbcbbadcadbabdcccdadcbcbbdbbddbbaacadabcaacabbbabcccbadcdbcbccdbccdcdcccadcadabbbbdaabbccdbcbbadcaddcbdcbdcdddbdbaadacaacdabcabaadbacdcbabacddbdaaaaacdaccacdacbdadcdacdbdbaaabbbdbdcaabdcdaacacdcccdabacdbbcbbdcdcddacbabbcbbdadaadbbcdbbdbabdbacdbbcbbdbcbadbabbddcddbbdcccdababbcadadcadccaadadaaadbbcdacdbacccabcbdbcdaccdcbadccdacccbcdbbaaacbbaccddbacadbaddcdbbcbdbcadadcdcbbaddacdbabadcbbcdcdcbadbaaabcbdbcbaaaabbbbdccbdbbdbadcdabcbbbdaacccbaddabcabcdcdbaacbbddddcbcbabdacabdcdbdaabbdaddabccbacbdbbaadbdabcdabbdadadadaababcddabcbbabacbbabddabaabbcadadabaacddcbdcbbdccacdbdcbbdddacccbcbdcacbdddbccaacdadaaaddddadababbacacddaabacbdcbaaaccaddaadcacdccdaddbdbcdcddbcdbadddbacaacbccdacdddcdaddcbcdccbbcbbacacacbddcccbacddaccbdacddcabaacabccdbdccbddaaaaabacdadddaccdabcabdbcdcdaccccbdaabcaaddadbccadddcadccbbaccaddbcacdabbbdacababacdddcccbaccbdbbcccaccbaacccbacabcbbbdbcdcbbaacacdaacbdbabbbcdaccbabcdcccccaddcccddaccaacbbaabdababdcabdaaacdbcaacdbadbbddbdcdddcdccaddbcbbbdbdccbadccbbdddccbccbababaaadaacbcdcccbbcbbaaddbbaddcacdccdcbadcbabbdbdccbccddacacaabbadcbabcbbdbdcaabcbbdccdacddacddbbcdacdabadabbbdccabbbcadddbacccccaaacadaaadbdadbcbbbbcaccbdbaabddcbcbdbccdacaacaaaccaacdabdddbbccdbccbadbadcbccbbcdcaadabadccbbdcaacccbccdacdcbadcbdabdcdbdaabdcaddcabacbacdbadbbdababacadbbaacbcabcbddcccbbacbaaccaaacddccbbdacbbdbadddbadcadbdbcacddbaddadbcbbddadcbdccccbbcacbbcddcdadbbbdcccadbcddbcbbacbddbbddbcacbddddbadaaccaacbadcccdcbbcddcbaccdabbbcdcacadaabaacadabdacabdcddaccacaadcbcdcddcadabdadabcdccdcaabadbccdacabccbcdddcbaccdbbbbdcabadbcdcabbabbadaccadbadacccccddbdcdaccbcdabccaaaccddadcbbcddbcccbbacaaddcbccabbbabbdbaabcddcdbcadadaccbbadcdadcdccdaadcadcdbbccdbbabbbdbdbaacaaddabdbcaaaabbdcbadbcbabdaabbacbbabcdddcaccaacdcbbabdacdddcccacccbcbadcccbcbacbbbcbbdabbccabaaadaadacddaaddadcdbdddadacabdbbbbacbabcadbdbdbdbbbbcdbbcbdddccdccacdbdbaabdbccdbdadddbbacabdbdadccddddadcbbaaddcbddbdbadcabaabccdbdcdddddbaabbcbbbaccccdddbbadaddabcacbbdabbdcbbaacccdbdcdcaaddbdddbaadcbdaaaadcdabbadddcdcaabdaabdaaabdbadaccdbccacbbaccdbcacdcdcadbbaaabbccbabaaddadacbbdcbccbbadcabcaaacadcdabcbdbaabbcccbddbbccbadbcabacbacadbdbdadcdcbbcddbadadcdadabaabdacadaaadbdaddaaacbbbaabbbdcabaadcbaabaadbcbdcadddbbbadbcdadcadbacbaadcccabbdbcddccbabddbabbbbbcbbbcdadddcbabdbabcacdbcbddbaabbddabaacdaddbbcbaaacbadbddabddabaccdaccdccdccbdcbcbbabdcdcccdbddbaddbcaabdadddadabdacccbbbbddddddbdaabadbcddaabdbcbcaccdbcbbbdbcbccddacbddadabadacdbcbadbcaabbbccdcdccdcddcccdacaaccccacbdccadaaadbcddbbcadbdddaccbaadddbccdaccadaabbacabadadcccbaadbbcdabbddbbbbbabcbaddcdadddadbabacdbdcadcbaabaadbbadcbdbadddaaaadbaabcaacbcaabcadbcdddaaaacaccbacddcabcbdaacbbbcbdcdbbabbbcbaccdcbcbabbbbbdcdddbbcabbcabcbaabdbcbcaaccaacbabdccbbaabacbbabbdccacdccdccadddccddacacaaaaadbbacadcacbdbaacbdcdabcaaabbcbdabcbadddadddccdadbacdbcddcadcdacacdaaccdbbdabdaaadbcacabccccabdbbcbcbaaaddadacdcadddbcbaacccdcbbdababcbadcddaddbabacbaadbcddbadccbdddbcdadabadbcdbaadcbbdacbacdcbddabadddcccacbccbcbdbdbbbabbdbabccbcbcacbaadbbababdbbdbbbacbbddabbcccdadbddbdabadabbdadabacbbbabcdddabccbbbacbddddaadbbcabcaadbbbbdbdacdabacbcdbbbaaccbcdcbabccdabcdcdbacbaacbccacabaddbbdbcdbadbaaabdaabbbaddccabacbabcaabdabbaaabdcddcbcbacdddcbcdbdcacacdcdcddbdadccccbcdcaddddcdbdbbdcccdbaccbacadbbdbbadaddbcadbbddbddadcccdbaaacbbaadcbadabbbabddddadccaabdcacabbcddbacbcaaabbcdadbdaacabdcbddbbcacbddacdbbbbcdbbbabbbdbdaddbcdbbcbdcbabadabaaabbaaaaadbbbbcdabdbcdcabaaaccabbbbaccddaddbbcbbcadabccacdcacdbddbdddcbbbdcacbdacddadacddbddbaaccddbccdbcaacddcbacaaadddbbcaddbcbbccbbdbbdcabcaaacdbdaadaabddbdbdcacaddcccdddadcdddcbdacbdaacccccbbaaddbbbacbdbbacbcdddbccadaddbbcbdbdbdccbdadbdcdbdcdbcbacababddbdbbdaadbcbacddabccdcbbccdbdcbaabdabddcdbaccbbdcbabcddaacbbbbcbdbbcddcdaddadaadaccbbbdbcdbcbcdcbbbabcaabddadccbdabdacddbbcdaabbdbbcadbbabdadadbbccacbdaccbcddcdcbbbacdcbbcaabaaacdbcbadbcaacddcdaaabcccabbaaadbdddbbdacdbcddbbcadddcdabbbbacaaaddacbdbacddaccbdcbdbdccbbddadaadadadddabaabacdaabddabcbdbcaaaccbddddabacccdcdccbddbbcbccdccabbcdabbdccbdcadcbbaacadbacdadcaadcbcbcaccdadbbbdcababccabcdcaaadbddbccbadcabbbcaccacaadccddadcabbacdaadcaabcdabccdbdccabcdcaddaabbadcbdcdbaaddbaadadcbcacdadbbaddaabddcbbadacbbdcbccacaadaccdcdaabdaddcbbdadcbdccacdccaccdcbbbcccacdcbccbbddbabccdbadbddccaacaacbacadacbadbdbcabcabccbabbbbdaabaddcbabbcabcbdcadcaadbcaabdaaaccaaaaabbcacadbbddbcbadadbcbbbacdcbddcacbcbdbadbdcadadcbaaaadcabbbddacddcdcdcbbccacdcdcdbbdabdddcbcddcdbaaadcaacbbdbcbcdbcbccdaadaadccbabbcabddcabaacdcbdcccbbcbdacbdccdddaddadbabccaabcddcbccbcadbccdbaabaccdcaaccccadaacbcbdcdacddcdcdadcbdbcdddaacbddabbaddbdbddbbadabaaaacbaadcacaadddaaadcdcdaddaabcbdcadcaabbbadbabbbbbbacbcbddcdabcdbcdbbacddaaaaacbcbaaaacddbadbcccdadcbccdbdacbcababbadaacdabdbadcaadbacabacacdbcbcacbcdcbbbabbcabddaccbcadcdabbdbdaacbcaadbddadbcbbccabcccdcccaccdabddbccbcaccacabacabdabbaccacbbdaddbdbdcbbaabacbddbbbabbcccabacbcddddddbbabdacdbabbaabacaadcaaddaccdacbbbccbbcaacbacdbbabbbdadddbacddcbdbccdadbacaddccadbcbaadaacbcaccddcabdbdbdadbdbcbdcdbdddcddadcaddbaadabdcbbdbbabadcaaadddcbbbcdcbcacbbccbdacdccabdcabadbdccadbccabdcadaacddbcadbccdcacdabbdaaabccbbaaadcbaacbcdabadbdbaccacacacddcaacccbbaddadbbdccddbddaabbcacbcbbacbaddcadbaaaabacddbdcdbadddcbcbaddbdaaaabccdbcbadaadbadbdcbbbbdddaabadbbbbbcdbdbcbaddbabadadcbdacabccbabbabbbabdbadabbbcabdcacbcbbddbccccbdcaacddddcdcbcbbdbbccccbdbadabbbaaacbdbabdbcdcddacdaabbccabdbaaccdbbbdabaacaaddccdbbbaccadabbdababdccddbddbdbbdbdcbacbddababdbadddbcbcddbbabbbbbcaddddbadacbcdbbbaaaacaacdbacadbccdcbbdacbbbcabacbdacbbdaddbbbabdadbdbbcddbbcbddbcccdcaaadbbccadbdbddcadaabcdbbcacdcbbcdcadbbadcdacbcbddddcadacbdabbaaabbbacbadadddcbbaccdcdadaccacdbababcdcdaddbaaadcdcacbacabdddccabdaaddaadbddacccababaacabbddcabdbbcbaadadbcddacddcdaacdcdcbdcdcaabaaaaddbbabdbccdabbbdbbddaaccdcbadcaddbdddaacbabcbccdcbcbbcdaaddabaaaddcaddcbcadacdcdaabcbdabbcabbcddcbacddaddbdcccbdbcadbdbabcbddabacbbaddcdaacbdbadbaccdcdcbbddcbacaccdacaaaddbcdbcdcbddbabcadbddccddaddaaccdacccaabaabbcccdbbbddacdabadbbdcbabadbdbcddacbcaccbbcadccdabcddbddaacbdcccabddbccacdbbbbbabccbdadbaaadcdbababbcdabacdcbbcbadacdddcaabcdcbbcdbabbccdcadbdcbaacabcbadccdcdbcbcbadacdcaddbdcdbaaadcaaadabbdaaaabbcbcaaabbababcdbdcdddbabbaccbadbaddadddddbbcbadddbdbbcdccdaccacabdbdcdabcdaabcdaacdcddaaacacccbacdabdabacbabccaabccacaabacdcadcadbbddabcbbccaccbbbbaaaccaabdbdcbbcbbdbadbbaabaacccbabdcccbadcabddcadcbbabbbdbcaddbdbdcddcabcabacbcbbcbdbdadaacadbdaacabdddaccaababaccdddbbdbccadbddbccabcbdcabdadbddcbccdbabbcdacdcbbabdcdabdcaccdcabcadbcabaacdaddbdcbacdaabccbcadacdabbcbbddaaccbccbcacadbccddabaadbaccacbbdbcdccabbddccbcabdcbadaaabcdccbcccadbbdbaadbddadbccbdbbdabcdabcdddcabbbdbadacccbcdddbcddbcacbdddbbdaddcabbcdbccbcddaacbabbcdcdddabbccabbdabbacdcabbbdbbbbcbbbbaacbadbcdbacadccddbcccdbdbddbbdbdcadbbcabababbabacdbbacdaadacdaccbccdcaacdadbcadbcdadcbccdaadaaaabddbdaadcbcbadaddccbbdccdbcbbbcbacccbbcdbdacabcbbdddacbaccdaadacddbbddccddcbcbabcabdcababadacabbcdbcababbdbaacccbddaaababaacbacaacbcacdccaabadbdbcbdcacabaacbbdcddbcbcdaddbcdaddaaabadcbcadcaccaacdabdccdddabdcacdacabbabccdddbaaadadbbadbdbdaabaacdbaddcaacccdbdaadcdadcbdcdadcadbdccdbbadacacddcaadbaabadbcbdccbdcbcbaccbbdcbcaacbcbbbacacaadcbbcaadbabdbaccaaddadcaccaddabbcccaadaaaaaccbbcdcccaaccadcdbbccbaccccbdbcacaacacadcbdaaacaacccdbacdddaabdbcabadaacdbbdcdaadddadbcdcbaaaadbbaabadbddccaacbdbacdccdddcbcddcacddcbacbadabdcadabbccbabadbaaabbdcdbbbbbdcaddcacdddbdabaacbbddabaddaabdcdbacbbabcbcabbbcacdcbadcbbdbbccaadcbcbddbdabdaadacaadbabdbcbaaabdcddcbdcaabaccabcaaddbaacacddababdbdcbdbcdadaabcdccdcdcdcbcbcddbdbcdcaaaadbabcadcccdbdbaaaddcdbaaaaaabcdaabcabaaabcbbcdabdacbadbabbdaacbaccbcddcccadcccbbdddcdababcdbddabbbbbaabddcabdcaacdbcbbdcbbdcddcccbaccaaddabdaaaccdbdaaaabbdbdcadbacadbcbdaaddbcdacccaabbbdbabccbaaabaccdaabaaacddabdbbaccddbdcbcccaabbacabdccabbdbdaacaddbaaabdbbcdbccbccdbabababcdccdcbccacdcdccbbcdbdcbccbcbdcabbbcbbadbbaaacaaadbbcbaadcdccdcddcbcabdcaaaadbdabacdbbacabcddbbacbdaabcabbdcacacdaababddcddbdddccaabdaaadbbabadcdbddbcdccaacddbdabbbdcaadcbaccbbbaacdaccbbbccbacaaaaabadddddccddcaabdcadacaadaabddaccddbacdacbdababcdcddabdbcabdcdadcbbccbcddacaaaaccaacacaaabdcbcbcacccdaacadbcddcdacdcaabcbadaadacabdabccddbcdcbddabcbcbaaccbadddcccacddcdcbbbccccacbdddaabcaaddaabdcbdaccdabaccdbcdbadcabccabcbadcbbddacdbabaabdacbcdcaaaacabccacbbcaddbddcaaacbcabcddcbdbaacdabbbcaacacadcddbbaaaabadbcdbcdbaadccacacbddbaccdaaaaaaabcbdbcdbcccdabccacdcccaacbcdbbdcdcdcabaacadddbadcdcbcbbcddcdcbdddcdddccdaacdbdaaadbdbcdbaccbbadadddaddcaabbbdbbdbdabbddababacccdaddcbcbccdadbccaacacbdcbcdbacbbadadcdaadabbaddddaccaabbbdabbcacddbbcacacdbaabcddbccaaacbdbacadacbccddbcbadbdcbacbaacbcabbbbbaaacbddbaccbdcccccdbadbabdddaabdadcbdcdccdaabacddcabadacaadacabadbbddccbcccadadacbcacdbbdddadddbbabacdcdcadcadccdcbdabdadcabdccdbdbdacccdbdaaabcacacdbdbbcdabbabbcacbcdddccdbcabbbabbdccdbaadcaccbbcabacddadcadabacabbaddcadaadddccdbcabacabbcbdbbbaacddcabaaabdcdcdbacaaabbdcdbbacbcadabaaadddabcbdcbaacdbccbdbccbbccacdaacdabacdcbadcbbadddcaaadbbdbadccdbbdcdcbadabbacbccaadbadaccbccbdcbdbcbaddbadadcbbbddcadbcccccccddadbbbbdbbccbabbcddbbbababcacdadbdaaddaaadaaadbadadbdbaccbcdcaabcccbaabbdbccddcdcccdadbbbcdddcbbcddbbbbcabcdacdbccccbcaaabaccaadbdadcbaaddabddabdddddaabaacbbacdcabacbadccddcdcbacaadabddcadcadacacdccacaacbdcdbcbccaadbaccaaacbbbbabbaabdbdbbabbdaaaabdcadcbadddbbadacacadbbddacacabcabbbaacdabaddbacccdbdccdccbcbadcddbcacbbcbaaddddddbacbbcaaacdcdbcdcdcaabdbbddacdcdccaadddaadcddabaaddccaadddcabcbdddacbcccddacbdcaadbbaccabbbacbcdcacadbbccbbccacddcdacccdbbbcddbdcbdbcdbdccaaccbdbddaaaaabcbbdaacbdbbaabccaccabaddcdabdaabdbaddabccbacdbdadccbaccaccbbbbadbbddaaaacbdcabdaadbadccdcbcdbccadccbbbadaadbacbdbcaaccbbabbacbbabbdcaaddbadacccccbdbddbdcdaaadacdddbcdccabaccccddcabaddacbaadcdacbcbcacddcbcccbbaacacbdadaacbdccbadccbacddabccdbadccddbcccdbabdbdbacabdbdbcdaacbbdcbbdbaabcbcaabbbbbabacaaccacdcaacadbcadabdcccccabacdbaddbdcccccadbaacdacbaaaacdbccaddbabccbbdadbbccbabdaadbbdcdcddbacacdcdcaaaadcabaabbbacddbaccdacccddcbbbbaccdbccddaaabdcdbadbcdacccabccbddbbbaacbaacdcdaacdcddacadcdddcccbacaaadacdccbccddbbcdbadbcbadbcacadcabcadbcbdbbcbcbdcaacbcdcaabababcdabdabbcbaaacccccccaccddbdcbdcaddaaddcdcdbcaababdccccaabbcaaadcaadbacdbbadccbccbcadbcdbccdaacddbddaddadabccbdbabcddccbacbbddccddbacaadddaacacabbcbcdacaacacacbbdacbadbbabdcdabcbdbdbdcbddbaabadcbcccbcddbbabbbabccccdabcaacabbccbcdabccbbbdadccbabdcdaabbdbbdadcbabdbcacacabaaddbcbcdaaccadbbddbbbdcbbdabdcdcabddcbddbddcbdcbddbbccaadacadbbbbcdaacbdbbcadaabcbadacbddcdbdbbabddaddbaaabbbacbcbdbdabbabbabdcadcaacbaadbbdaddddcbbbbddddbacdcabbdadbacdacaabdbabdbccdabcccaddddcacbcbdacbbacbdbcbdcdbdccdaaadddacddcacacacddabaaadbbaadcdccbdacacbcabbdccddadcadbcdbddccdcabcaadbcbabcccdabbbcbbcaddabcacdabdccadbacbacbbdacdbcabaddddbdcccbbaadacccbdabdaddaadbbadcadaddcdbbbbaacaadcacdacdcadabdccdbdabcdbabcccbacadcdcbabacccdcdadcdacabbaabbadddbdccbaddaadabdbccdcbdabdbccccbadddbbbddaddabdbcaaababcaadcbabdbcbaccbaacaacadadbcbbccbcddadbadadddcbbbabccaccbadaaddbcbbdbbdadcbdacbdcacccbdabddcdcadbaddddcbddaabbcbbddbdabbdbdcacabbdccacbbaddddbcbcccbbcddababbdbcacbdcbbccacbaaadbcdaabdbccabcbdaaaabcbdbbdbbcdcbdaabbccdacabccdabbabaaabccbcdbcdcabcdbbadccdddacccbacdbdcdddcabdbaddabcdabddaddbbcccabbaadbbbdcbbdddcdbcbcdbcdadcaddcaacbdadadbbbddabadddbaabcdadcacaadaabcbcdadccbaddbbdbbcaddabccccdbaacdcbaabaadcdbcdaccaaacddddabadaadbdaaccdccddcdcccdbbcbbbbbddaacbabaabcdcacddadaabccacddcddcdbadbccbacabacccacabdbdddababdcadddbccbbcacdabcbcbdbabddbbcbcacbdddbdccadbcacdcabdddabacadbccbdabbcbdaddbbbdbcbccaaadacabcaccdcadacbaccdccddaadaddbbadbdacddaacddbaadddacdcbbbbdbcacabdbcbabdbdacabacacdbbacadadcddcbbaadbacccbdaddcbbbdcacbacaddbbcbcbdbbcbcbabacbccaddabbbacacdacdadadddabcaabddbcabbbbcddcadbbaaadccdcccacaacbcbdadbdbaacacbcaddbdaaadabbadabdaacbaaddddbbacbbdbcbdcacabbdbbbcabbacaababdbdcbbaacbdaadbacdbadbbddddbadbbdbcdadbbdaaabdacddaddccaaadbcdccdadcddababcdaddabaacbcbaadbaabbdcddccdabaaaadbcccadbaaabccadcaddaacbccbbbbccdadcccddabaaaacdacaddcdbdcddbbbcacdcbaabbdccbdbdacadcdbdcddddcbaacabccacdadbabdddcddcbacbbbdacccaadadcaadcbbdbadbbdadaaadcaaacddacdaccbddbbcbbcdbdcccadaddcddabddacbdaccccbcbaabaddcddabbacdddddccbbccbcddadcadbdabaccbbbccacbdacaaccbaacddabbcadddbcdcaaaddbcabdbbbbadcbcbdbbbbdaccacacdbcabacdcddbcbcbbdcaaadcabbbacbdabbbdddbdbcacbcbabcbbacabadaaadddaaddcabcaacccdadccbdcadacbcbccbbdbabdbcdabdadacbddcbbccadbbadcdbaccaacbbacddaadbcadadadcccacaddadcbaadbacdbbdccaadaaabbcbdcbcaaadbdadcabcdcadbdcbdbababcbabcdbaaababdbdaddbaadaaaaaaadacaccababdbddccadbddbdbcaacababdcaaabdbabdcdbbaabadaabbaaaddcacbcddbcaddbacdbbdbcaacadabbbcadadcaabdadacaaadcdacadcddcbbcccbacacbccbaabdaaaddaabaaadbdaddccddbcadbccddbadbcbbdcbddccbaaddbbbbabbbcbbcccacdcacdacddbcadabcacbcdbcabcbacbbbbdaabddabdcdbaabcdcbacabddcbbacdddcddcbabadbcbdabaadbdddbcdaaddacccbddacacdacbcacaaadaaddddabcaadcadbcabaaacdccdacddbcbdaddbacbacbdbcbdacabaacdadcbacbaacaaaadcaaddaacadcbbdbccbddaddddabadccbadccdaacbabacbaccdacaccbbcbbdbadbdcacbcbadbddbacbbcbccdddcbcadddcdcdcacdacbbbddccaadbacacbddacadadbaccbdadbccdbadadccbbbcbdbaccdaadcacadddcdbbadadddadcdccdcdabdbcabbddbbdbbdacdccabdcacaccacaabbacaadbdbdcabdcdacacdddbbacaddddaaaccdcbdcbadccbbacbcacaadcdaddacccccdddddadcbdaaaacbdbccbcaabdbacddbdcadcacdcbcabdadaaaacdbdccbcddadccbaccabcbabbcbabbdbdaabccabababdcbabdabdcccbbcacaccddadbaaaddadabdbdcaacbadaacdbabcdcdddcaaaaaaccaccbacacdabbbddadadaaacadacdacacdbcaabddaddddbbdcaabcbbbadbbbdbbcdbcbacabadddadddccdbacdadcbcccccabdcddbccaddabbaaccdddbcbdcdadcddcdbcdaacddadacddbcacbddbccbbbaadccdbcaabacbbcdaababadabcabdcabddaddcdaadadddccdddbdadcadcbaaaccccbdabacbbbacabbbcdcddaabcbbddcbabaadacbccdddcaacbcbabddbaaaadacbcbdcbbcbcbddcbaddcaacbbcccdbbbccdaacddcbbcbaddadbbbcaaacabcadbadaacbddcdabcccbbcabdaaabdadacacccadddaacdbacaaddbaacacadcddcadddccbbacadcaacbaddddcabadcaabababdccbbbbadaaaaaadabaaadbbbdcaadbbbcbddaadcbaadbbbbcbddbdbabcccbabcccdaccbbbcdcdaabbadbbddacbddddddadacddadabbbdbcabdcaadbdacbcdabdcabadddadcbdddcbccddcaccabbadabbdddcdbabbbdcbcaabbcabcbbadadacccadadcbcbddcacdadcbabcdbabdcdaacabbbdccdaacdbbcaaaddcdddbbbbcddababadcacdccabdcdccadbcbacccccdabdcbaadaccbbbabcdbbdcababcdbcddbbbdddbcadaaddbdcbcccddaacdbaddcddcdacbacccacccbaabdbdbbaadbbbbccaccbbdcdbcaccbabccabbcccccabdbdddaccdcaacacbcccdadcccdbadadccaadadbccabcabaccabcbdbabaadbabaabccbbcdbabbbabcdcababcdaaacaddbaadabdacdaabcaccbabaaacabadcadddacadababbaaaccbacbcbdbababddaabccbdaaccdcadaabcbbcdbbdaadccbadcdccbaacbdcddcbbbdbabcabdacdddcdcdadaccccdddcabdcdbbcacabdbbcbcdddcdccbbdacdbcabdccbccbdcddabdcdabccadbbcbbdccdabcbaadabdcbabbbadbbabcacddccbbdccbccacbaacdbbaacaccacbababbdddcabdcdadbbaadacddbbabdaccabacdbacbdcbadadaacbadaddbbcaabcaadddbbabbbcacdccabdbcccaabcbbcccbcaaaaaaddaabaccbccacacbdcbababdabcddcbdcbacdadaadbdcbdcccbcbbabddcbdcdcabbcbcdddccadbbacddbddcbbcbcdcbabcccbabacbaddbbcacddcbbabbcacccbbacbcadddcadadadcccdabbabdbacacaacbccccdddcbccdabdbbddbbddbbbccddbabdcaccbbbabbbbaabaaabcbddacdbaacbaadaabddddbabcadacacacdbdbacdadddcdbcccabdddbcddbdbbcddacbabcbcabcbaadadadcbcbdadacbabbbacddbbacbdcaabcbaabdbdaabcbdddacbcbaabcbbbcdbcaabdadaaaaccaddbbbaadccbdbbaccdbbcbbdaaddbcaabaccacdcaaddbdccdbadcaacaddddddadddaabaacdcbccadabaccccbcaccdbbccacbbadcdbacaadabaddcbcabcdccccbcbbcdbbbddcbadcaadaaddccdddaacaabbadaccbbbaaacbbbdadbaadbdcacdcdcadcddabbabdbabadcbdacacdbbddbabdacdcdababbaaaadcdcbaaccaabcbacdddaabadacdbacdcccacabaadcdddcdabacccacabaddccadcccacaadaabacabbcdabadccdaddabdcdabaabddbddabdcbcddabaddbabccddbcbbcccacddccacbabadddadaacdadaaaacccddbbccbacdadddcdbdccdadbcbcbadcbbddaabcbcbddcbaabacbcacbaacccbcbabbddbddccbababbccdaadaabdccbdaabbacabcdcabaadbcaaacddabacddcacabcbabbabacdbbbddabadabaddcbdcbadcacccabbacabdcdbbccdacdbcadacdcddcdbbcdabdbdcdddcbdbcbadddbbbbaadbadaacbdcdcbcddcbdcdbbadbdcdbbcdbdbbadcdcacccabbdabacbdaadbdcccdbaaaabacbadcccabbcabbbcdbbbbbbaccbcbcbbbcacbbbbacacadcbaabbdddcaddbddbcdacbadcbccbbaabdadcaadbadccbcbbbadabacddadbcbaabdbbdabcdbcabcddacbaacbbdabbcabbbcbabdcbbdbdabbacadbabadbbcadbbadcdbbcabbadacdaddcbbbdadadddbabcbdbdacbbababdaacccbadddccbdadabbbababacbbbcdcbccacdaddddddabcabccabbcabacabacabacdacadcddcabccddbcdcdddabdbccbaccaabcbdbdbacdadcdcbaccaadbadaabcaccbacabbdabdbbdadbbadcddbbdbabcaabaaadcbbabaccabababdbcddaadadccddbccdabcbbadabdbbaddcadadbaddcadaababdaddbcbbbccdbccbaaadbacbbacddabbdbdccccbdddddbabbaacadaabdcadcccdbbdcbbddcdbaabddddddaacbbdccdcddbabbbdcadbdbcdccccabacbaddababbacbcaabcdccddcddaacbcaccddaabbbccaaccacbaabddacacdaddadacbdbbdadcbddcbabbcabcccdcdacdabaccadcababbcdcbcabddcadbccbabcadcbcabbbcdbddabadccbabcabaacdddbcaddadbaacdcdaabbbccabadadcababcabddcabcbddccbaccaccdbcddddccdacbadddcbbbadbaaaaadccaaaddbcabcacabcbbdcdbbccbdbddbabadbdbddddadbababbbcdbaadaaaccddadaacdcaacaccbdacbddddddcdcbbcabaacabbcdcdacadaadcbccdcadadbdddbdaccdbabcabdddbbccabddaabdcadcdbdadcaabaddbdcabdacacdbbbababbbddbcacababccbdcccacbbbacabaacaaaddddbdcdcbbaacabcbadddabdddaddbbdabcbababbbcdbacacdcdaabbdbdacccbaadadddcabdcdbcdbadcadadbcbacacacbaacbbdbddaaccabbbddaaddcbcbcbbbcacdbcacacaddbdbdabddbdbdddcabdcbabadbcbdcddcddcadbbaaabcbdbadaddcbcdacddbdbcabccbcbcbbbcbcccabdadabbdbcadbbdcadbbbcbbcdcdbaacacdcabcbbbdcdabddbaadcbddaddabcbddabccabbaadadabaacabadccbcdbbabbbcdcabbabcaadbbdcacbbcbaddaabaababdbcdaaabdddaadcbbdacaabcaddcdcbdcbcbcbaacbdcaacacbbcbabaacdadbbdcbcccbbabaacdcaaccbcdbabdbdaadabddddcdccbadadddcdbbbcaaccbbbaddbdbcabcddcdadbbcbdacacababbcbbdaabbbccacbdcddbbabbbbabdbccbdbcababccaacdcaadbddbcdbddddbdaddbdbcbdcbccdcadbddbdcdaddddcbccabcaddabdaacdcaccddccbbcaacabadcdbbdaddababdddacaacadcbcbcdcdddddcbbbdcacdabdcddacddbcbccdaacccccbacdadcacbbbaaaddcbbbcadadabbababbaccdaacacacbbdaadbbddacdaabbbaabcbacccdadaaaadbcdddddacacdacdbbbabddccbaaadbbabcbadbddbaddcaaddcddccdabbbddadaaaccddbbdabbccaacbdabbdbddbdbdaacbbaadddaaaddbabadcadccdbaddaacdcccbabbbcbbdaadbbdadbbdadbbbadccacdbdcacabcbcaaaccdaaaabbaaabcdbddcbcdbacabcaacbdbdcabbcadddabbcddadbabdcbdbccccabdddaadddddccbbcdcbbaaabbdcdacaacbcbbbbcabaabcbdcaabbdaddaddccacadadbccacdaabaaacabbdccddaadabdaabcdabddabbbccbbaadaabdcdbbcbdddbdcbbbcbbdcbbabaacadabdbbcdabadcbccadabbacbddaabbcdddbcdccaacacdddbaccdbdbbdbdcdcbaddbccdcdcaaddcbbbdadbbaacbdbdbbdabdabdaaddbdbacacbcbabbaaddddcbbdbdaacbadcbcacabacbbbacbbccaccdcabccdaaaadbddadcaaadacabacdbdddddddccaaaaacaacaddcbbbbacdcbabcdcbdaaaddbddcdadcaaaacddaccbdbcdacacadacdacccbdcbbcababaaadddbcdbcabcacbaaabaddbcbcadddbaaaaccacabcdcbbbdcbbabadbcaddbddaddbbabbdcdccabaaadddddddbacbacccaaaadbaaadcdabdddabbbdbabbadabadacabbbdbdadddadddbdcbacccacabadcdddadbbbdacaaadcadbcaadbccbbaaaacdddcdcbcaadbbddaabbdababccdbaddbdbabacaddbcabadbcbadcadbcadbcddcbddbccbabdcdaaacdbdcbcbacaadbddbdabcdabdacdcccdcabaccbdbbdbdcdcccbaadccdcddaccddcbddaccbcaaadabaccdcbababbdcacbadbccaabbacaacabaaabadcdbbbbbdcaddddadccadbbbcdbaccbdbbddbaaaacdadbbbcaddbaccdbadaddcdbcccdcdcaabccababbcdabcdcbdccaaddaccbbadcaabcbdadabbabaacacbbdddbacadacaabcabaddadacacadbbbcddbdcdcbcdaccdddbcbbaacdcdbdddaabcbcdcbaaacadddbbadddadbdcccdbaddabcadaccccaccdbddcaabddbbdcccdbddccccaabaadacdbbabbadcbabababbaadbcdbabaadcddabdbbcdbbbbdaabbcbcabdccbaabcbdbdacadbdddcaacbdacaacccbdcbadabbbaacdbaaadacbacacacabccbbbcbcabbcaacbdccaacabadabdabdccddadabcaaccaaacdbbdacbccbbbbabbbdbaabacdddcbddbdcbbacdbbdddddcdbaacaaacbdbcddaddbccbdddccaaadabcacbdbcbccdadcdbccababbbbacdbcdaabccddadbabaadcccaadbdbdddacabaddccccdbcdaccccddacaadcdbabdabdaadadbaabdbaddbdcbcadcaddabddcbadbbcbbccdcdabaccaadacaaddbbcaabddbaadcccbacccbacbbdbacadadbacbadbccacdcbaaaccaaddcbdacbcdccadbabbabaabaaabaadcbdbcdccbdbdaddbbadaddbacaddabacdacccccbaddccadabadbddbcabdbaaacaabddacbaabadacdcddaabbdbcdbbbdddcabaaaddcbabdddacccddbdbdadddcdabdcbdacbabcddbdadccddadbababcdcdbddadcdcabdccaccadccabdbbbbadadabccbbdbbdccadcbcccadcacccbabdcdaacadbbadaddcdbbaacabbcbbaccdccadbcacccaccbaaabcaaaadcbdaddcaabdadbabcabbbbbdbddddcccdbbdbacddaddcbddaaadbbcbbbacacbcdcbdabccccddbccaacaabdaadbddccbcdacbadcacbdaccbcbbbbbabbcbbabdaacccadbbdbabdbaddddcadbcdaccbcabaaacbddcbaacccabddbdabcaadbadcbbdcacaabcbcbdddcdcccacacbbbacbdacabddcdadbaadadccccacadcbbddacbcabcdacadbdaadcacccbbaaabbcacdacbaabcadcbcbdbbdcdbbddbccbbaddbbccbcccbbcbacbbdcccaddaabdcdabcbcdadbcdccdbddcdcdbbcaadbabadbcbbdaccadcadbddacacbcadbcccabbaddabbbabaabdcabbbcbacccdcacbbbdddaccbaacabdbabdcaabdacbcddcbbdccaccccbbaddcadbdbbcddaccddcacaadaadcbbaacbcbbaadbabababcddbaacbbadddbcacbbbcbababcbdcacabbaccbabbbabdbadcbcdcbdbadadaaabbaddbdaabbcaaaccdcdadbcabccdaaccacbaaacdddbdbcabdcdbdabccddcbbbadbcacbacabccabacdcddaaacabbacddaacadcbcabcbaacccbcdbcdccbbbdccaabbbaadacbddadacbaccdddadbbbdbddcdcacbcdccbdcacccccdbbbdacbbbbdcaddbbccbddadccaacdaaacbcbadaabdddbcbadbcdabdbdcbcccbbdcbaaaccacdabcbcbabaabbccbdadbaddbcacdbadcadcccbacbcdbbaddbcddcdacbcbaababadccbbacdbbcdaacbbdbddccacabbdcccdbccabddbbdacdadaabddaaccddbacdcaaababadbdaadcaaaabbcadbaacccccacaaccbdcbbdaadbabccadadbcacdaddbcbbbdabbcbbbccacccdadaabdbdbdaccaccadccacbcacdcdccadabdcacbbabaadddbbcbbcacdcdccabdbbdddbcbcaabcbdbacaabcdccababbacdcddcdaadcbadadbbddbadabadccbdbcbccababcbabddddbbbacacddcaacdaaaabcadbdcdddccaacdacdbdbdadbbdaaacddccdacdccdacaccbadccccdcdabcbddbbbaacababbdcdbaaaabadcadcaddddbabdbccbcdddacdbacdbbcbbabcddbbddccccabccddddccccdcdaadaaaddadbbbdadbcacbdddbabbabaadbdcbccbbcacddccbdbcdadbdcccbcdcdccdaddbbccccabdccddacadcacdbaaddbcaadcdadacbccbaaaadbddacdbbbddbcdcbddbaddddcbbcbaccdcdabdccaccaccbcbccdddacabdbbcdddcaaaabdcbcbdaacabcbacdcccbcbaddadadbaddccbbccaacaaacbcadcaacbcccbacaabdcaabadcacbbccdcabadbbdbbaaabdaadcddbcbabcbccddbbbcddaddbddbcbdcdaabbbccbcbbddcaaadbcddbdbbadcbcabcbcacccabacacaaabdaabbacadcbddbaccccdacabcdbcdcbdbdcdcbdaccdbadaaabababdabbabdbcbaaabbbcabaabcdabbdbcbcaadaacadacdbbdacdbaaddaadbaadcddbcbdbbabacadabcabddccbbbacdbaddddbaaabdbabaadccabadcadccddbbadcbddacbaabbacdcbbaacbdacbdddabcddbadbdaccabccccacacdacabcccdcaccadbdaccdddbbbabccdcdcdbddbdbdcdaaaadababcadcadaaddddbacccdcacaacdbabdababbcabbbbbccaabbcacbdbcdcaadaccbaacabbcbcbdcadbbaaccdabbccbadbccaddbbadcbccdddccdabdbcbcadadcaacadddcbaadabbadadbacacaabddacbcbcbdbcbdcddcdcacbdbdbbaadabaadaabdabcadabdbbdabadadccdacabbdddbaaadbaabadadbcbcddbdacacbadcccddddccbcdbacdaabddddcdddbaacbaabccbdbddddabbdddcdcabccbabaaabdcdbcbadddbcbccdccbbddaabadddacacbcacbaddcbbaaabdbdabbbccdbbaabddaccccabdcdbbdbccaaccdcddaccdadbdabdbbacccbacaccdacbabdaccdaccccdacadacababdbacdccaddacabdbbaddcdddccbaddaddccccdbccddaadaaccabaadbcbbccbabcccadbacbdbddbaacbabcadbcabccbbbcbcbaaacacadacdbadcbcdddcbbbcbdbbdacddbdcaaccaccddbbabbbdabaadccbbadacbadacadddaccacabbbddadbcabaaaccaabaacaaaabcacabadbadacddcabdbbccdbbbcdbcabddccdadbddcbbcadccdacbbaaaacddcaaaaacbcdabcbabcdcdaaaaddbdaaccdbabccbacaadacdaabbbcbbabcbabdbccbaabacccbdbcbbbdacbdcbababddcccaadcbacbdbacaddaacdbcabcadbcadcadaadbabaddcabbdacccbcaababbdaadabadbadbcacddadcbbbbdcbabaaaaccbcadbbabddabbbaddddbacdccdabbcbaacabdaacadabbdabccadcddbcacdacdcdadaaadbbdbbacaadccdcbaadcddacbbcaccdacbbcdbccaaabdcdbcbbacdccbdcaacdabbcdacadbcbbdaadcccddddbbdcaabcccddacccaaaacbcabbbadbdccacadbcbaaacbbdbdbbbabcdbcdccaadbcbcbbdcddcabbdcbbdbdbcbaaabccdbcdacabcbccabadabbdccaadaabcbcdcdabbdaabbbdaaddacccdccacdbbaaaadbabcbcaccdbcabacabbddcdbdbcbbbacddbdaaccadbbbabccdadadccdacaabcadabddabaaccdcbcacddddcaddddbabcbbbaaccdccbdadcaccadcbaadbdbadbadccbcabcbabbdccacbbbcabdaabacdcdcdcbbbaddcbbabdabdabaaacdbdcdadbcdcdcdadbddddcddabdacabccacaadccddbacddbdbdbdbbcdcdcbacaccdcaabcbbcddcbbdbabcbcddaacbaccdbacdddccabdddddcdaddcdddcccdcbbacbbaddbadcdcacccbbdcadddacbcbcbddcdabaababcdbcbcdcccbabddcadcbadaacbaaabacbabbcbabacdddabddaaaacdbbacadcdcbcdbdcdbadcadadcadcdaaaabcbaddbdbdbaababadccdbabacadabbcacabdcbaabcccdddaccaadaaaacbacacabaabddcdcdbbdcdbaaccbbaccccadbcaabcabacabcddacddacddbcabcbaadcdcbabdbbacaaaccadccccdabcbcadabaabacdaaacdbbcccadbabcacbdadcababdbaccbbadaadbbaacdcbadcccacdbcddabaabacbbdcdadbcbacddbbbaccdaccbcdabdadddcbdddbaaaacbdccaaaddbcaddcbcdababadcbbaabdaacabdcddacbccdbabbbbaaaabccddacdaacbccbbbbabdbbaccddcbbabcbadcbcdcdbcccdcbadccdcabdccabbdbaadcbabdabcccaacbddbabbadddaaabbccbdbbcadaaaabdddaabdbcdbdadbdddabdccdcdbdcccbcaccdccbccdcbdbdcabdadddddbbcabbbbdcccabdbacbcdbbbacabcbadddccbcdcadccadabddadaaaabdddccddcbacdbcabacacddcdabccbcdabcdcccaabbccbddaabbacbcccadcaaabbabcbdbdbddcacdbdbbcbabcbccaadacbcdaaaccccbadacbabcddacbcadcbadbcddbbbbabdcaabdddccabccbbcabcdcaabdcdabcdbcaaadbbdbccbccccdcdbcadabcabbcbdacbaabbadaacadcbadccaabccaadbccbddbbaccabddabcabbbbccbacdcbbcabaadccdcccddbabaddcdccdbddaaacbaaaadcccbbdbcbbabcccbbdaccdbbdddacdadbacbcdacccdacbcdadabdadcdbbacadaacdcccbabbdacbbdcccaacbddddcadcddcabababdcacaacdabdddbccddacabbbbdbbaddddbdabdbbcbccdbcbbcdcacccacdabaaabbdacadadacbadcabbbdcbadbbaaadacdadaacdddbdcabcbddbbbcadcdabbdcdbdcbacbcbdcddbdaccbddabacacabbbbacbabbcadddbdaddabcbdbabcadbddbdcbbdbbabacddcabbccdcdacbaddcccbdccdddcddccabbcbbcdddadcbdcacadaacccbacaabcccabadacdbacdacdcabaccbbdbbaaacabccdaabaadaadababaccaccbbacbccddacbdcbbdcddaaabcaadabdbdcddadcacdcdcadcadaacdbbbcacbdddcddcbcadcccaabcaadbcbcdbdcbacccddbccbdbaccbacccbacdddacddbdccadadacabacbdddcabcbbdbabdcdddbbcacadbaabacaacdbdcbbdbcddbbbddbbabbcdccddbddacdccddcdcbdacabdcbacaaacdddbdcbcacbdadabcaccbdcabcacbbbccbbcddcccdcdbaadbbabdbbcbcdbbbaacddaccbbaccbbddaccabadbcdcbdbbcbbdcbbbacdddcddcadcdacdcbcabbadaadcbbbdbadbcbaaaaaaaabdbbdabaddddbacadcdacdccadbcdbbcdabccadabddcbdbacbababccbbcbdabadadcbabcbbbbaacbbcbcabcbdadcbcdbaabbadcaddacaddbadaddbcbadcacdadbbbadbdcbdccabbbacddacdcbcbbbaccbacabbcdcdcbdaccadaabbdddbccdbddcacddddccdccaacbbccbccaacbabbbdbdaaadccbaacdddbbbacadcbdaaadcadbdabbdbadddbddbcdbaaaccbbdabddaabaaaaddddbadcdaabcaadacdcccccbdaadbadaabcbcacdcaaaccabdcbadbabccddacababdbbabdcdacaabcccbcdaaddbbbdbcdccacbbbdacdaabcabbaaadcaadbdacbadccaabcbbcbdcdbcdaccbabdadaaaacdabdcababcaddbababadbbcbbbbcbbaadaccbbbacaddabaccabcabcdbbabdbccdcaccbbbdcbdbaabdaaaadbaababaacacdbcbcaacadbbccadaabcaaccccaabaadabaadbdbaaadaabdbcdbdbccaadacbdbabcccadbdabaccbbbaccaadbbaccadbcddccbbcabcabdddabdbbcbcbbcbcaaabddadcaadaaaaadbdbccacddacbbbcbacadbdadababbbcccccadacbdccaadaadadbcbadacbaaaaaddcbdadbbcbddaddccdadacbbbdacbacadbbddddaccbdddccddadcbbbabbaddbaccbaacbdbabddddaaaaadbcbdabdacbaadaccbabaccacbbbaaaabdabaccacaadadabbddbcbadcaddcdcddddacbdabccacadcdbabaacccbbbaabbdbbccaddaccaacadccadadbcbbacdccddbaacabcbbcbbccbbdbabdddbdcaacddbdbbabaacbcddcbdcacbabbbdbbbbaaacbadbaaacbdabbdddbdcdaadabcdaaabccbbabaacbdbcabbdbbbcccccaaadcdabadbabadaacdcdaddcbbbcabaabcacaaaddacacccadcdbddcadaadccbbcbacaaabbdbbbabcadbbddbaacbbdbdbbbbdbcdbcadaadcbdadbcaaabcaacbadadaddddacbaddccbdbabbaadbdabbabdcddbcbcdaacbaaabcdaadaadabdbbcdacbbbbbcdddcdbabbbdbcddbaacaabdccabacbabacdaaaddddbacdbacccddccdcacabdbbbdaaccabddcdcabaadbabdbbbadcacbabacbdcddaaabdcacbadcbaaabdbbdcaaccdadbbcabadddbaacdaabcbbdbddadccddcadcbcdbbdbcbdbaccbbbdadadacbcdbdacbadbcaccbdddcbaabbdadbcabbbcdbdacaddbdcbcaccdabdbdadcbbaddaddcbadbcaacaaddbacbdbcbccaccdbcabcdccacbcaccaadcbacccaddcaabccdcdacbacaacacbadababbbbccbddbccbcddcaaddbddcbcaaaacaabaddbccdbcbacbcddddbabcacdddbdcbcbcbdcbcdaabaaabbacbccabbbdcdabaaabdbaddcccbacaacddbbadccbbbaabaccbdcdaadccdcdabbdbcbbcbcaabbaaabbbadaadcbdacddbdddcddaadaddccaabaabdbddccccbcccccbcabcbccdcccdcaccddabaacbdbbcccddabbbababcbdcdabbdadacabbdbaabdcababcbbcdcdbacdbbbbaadddddadadcdadaccbadbcadcabccbbbacbacddcbbabcdccbddabbcaabacbccdcaabddacccaabbadbbbdaaccaaacbbcaabadabcdadbbacdbdbccdbddabdbdadaacbdcbcaacacaacadcadcbdbdcdbabaacdadcccbcbbbccabacabcbbbdadbbaaccacddcbcbbccabaaabbbcbcdadbabdbdacabbbaadcdbcdacabdddacccdacbbaaddccccddccbcdbbdbdcbdddccdcbabbdddacacbadaacdbdcadabcbdaacbdcccdddbcbbbccacbaacacdbdacdcdcdccaacbbdbaacddaacbaddaccdbcdabdbbdaddcadccdcaaccdcccbcaacacabdbbdcbdccbddaacbadaccbdaadabdbdaaaacdbdbaacacdadbabdbbccdccadcdcadbdabccdccccdbbaaacaadcdbabdaaaabdacaccaabdaababccdabacbabbbbbcddddaabccaddaabddaadaacddbacacabccacbbdccbaacbabacdcadacbcbccddaccaaabcbbddabbcabcccddbccacccadbacadaddbddacddbdbcbdcdccbaabacdadbadcadbdaccdadaacacddddcddbaddacdcabbcbaaabaaaabdacabdcbdcdadbbcdabaacacdcdcbbcbbacdadabdababccbcbcaacabadcdbacdacabcdbcbccddbbcdbccddbabbadaacbcdcaacacbddacdddbdcaadacccacbdaabcbbdadacbabadacddddddbaaaacacdacdbdbcdcdaccbacbabcbacdbcadbdddabcbbcabbabcadbbabdcbbbbdddabbaaccabacdccabdccbcddabadacbdbcdcaccacccdacdcbdcccdacadcdccacbbcddadcdcdbbcacccccdccdcbbdddcbabcdddcacadbbbabddbccacdabcadbaadddcaaaadabcdcbccabbbbccaaccaabbaccdbdcdccbdadbadbbbcdbbcadcdbbcccbacadadaabdbdacbdadaddddcdbdbcabcaddccbacadacadadaadbadddcabacdcdadadbabaacccdacdaabdbbdcddabadcccadadacabdcbbdadcabbabddddcadccdbccbcbccdbcdcadcdbcacabccacbbbcaaacbcbdabbbacdabbdbcdddcbcacdacbbddaddabacddcaacdaacdacddcdccaabacaacabddadacddadccdbcccbccabcdbcccaadddcaacbdbdbddabddbccddcccbccabadabbcabbdbbccbcddaaaaaaabcdaadcddddbccccbaabdacdccadbdaadcdbbadbbaaaddccaabadbcbcdadccaddcdcdbcdddabdbaccbddbbbdcabadcdadbdbcccadadcbacbbccabbbbabacbdbaaabddccaccdccacbcbbaccdbcbbbbbcdcdbccdbdbdbcaddacbdcbbbcabbbadbacdddbcdadadadddacbdabdaacacdbaadccbdadaccbadbaddcbddcadbdcaaabdccdaadbbcbabcccbddcdcbabbdcbbbcdaacaacbdbdbadbccbabdabcbbbacbaabbdabdabaaccdaabadaacabccbacddacccaccdcacbadacdcdbaabbbacddaddcdbcdaabbbaacbbddcaddcdcccabcddcbcabadbcadbbadabbbdadacddbbcdadcdaadbbdbcdabadaadbcababcbcccdcdbcacacddabacbbaaabddcdcacbcddbcdadbdbcbadddaacbadddccccbaaabbbddccbadacbddaadabdddcaccbccbddbbdaadaadabddbacddcbddbbdddcccdbdcaccdcdbaabbdddabbccbccdbcabcdbccbcbccdacabdbcbabdbccbcabbcdbabbbccdbabbdbabdbbbdbdddacabbddcabdbcccbcdbcbdcccdbdaccbbadbdaaadabbcbcdabaadaccbdbaabcbabbabacdbddddabbbdbcacacbacadbdbabddacadcddcaabddbcdadadacccbdbdcbdcbdddccccdadaaccaaaacbdcabbcccbbccdadbddbdaccbcabbcaddbddbdbadcddabaabbbcccbcacadcbdcbcaadabbbbcdabcbdabddccadcbddcccadacdabcdbcbaddaacaddbcaabdbdcaacbdabdabdacabdaacabbadadadddbdbdcdbbadddddbaccaacbcddbbdcdadcdcaaacdadbcbcdabadcaaadbdbadadcdacdcbcbabaabccabcadabdcccbdccccbaacccdcbbcaaacdcbbacdcaddddcdccbcbadcbcdcababbabbbdcbbbddcdbdacacbbdcbadabccabcbadaadbaddaaddddabccddacbdddadabcdddcdababaaacbcaadacccbcaaaddccbbcdbdabcbbdccbbbbcccbdbcabbdccadbcccdcccabacccdadbcaccccdacaccbdcacbabacaacbccbabdbbaabdbbbdaacbccbcbcdccadddacbbacacbbbcbabdcccdccddabcdcbabcddaaccbabcaccbcbacbadcbbccbbdccdaaabdaaccbbabdaadadacbbbccdbddcbdacacbdacbccbbdabcaccdbbdbdadabbcbccabddaccabbcdaddddbcadacaacbbaccdaadbdccaccbaacccdbcbcbabcacdbbdcadcbcddacaccbbcbcbabcbdcbdccdccbaacbababccabdaacbccadccbcabbaaaadabccbdddabaaddddabdbbabcaacdbccabdadccaacdadbbcdbcaabbdbcddccdbcbccbbccddcccdbdcacdbdccbbaaabacdbadbacdcdcabadacaadabbdcdbbccdbcdbaadccaabbabdcaabdbadacbddcccaaacdbdbaadddddbbadbcdcdbbccbcbbbcaaccdabadaaccddbcaaacaaacabccbdccadaddabacacddacdacaaddbbdcdccbcdbbcdbccdacdabadcabbbbabbbcdbbbbddcbcbcbdaaaababcdacdaaddbadcbcbcdbbdcdcddddcbbadbcdaadaaacccabbdccaaaccccdacdbcbbbccadabddaaddabdadaddcbccbcdadcccdbdbcdaacddbccaccabcaaccccdbcddccddcbdbbbbbbcabcdbddbbddcddaabccdbaccbcbdacaccaddabbcbadccabcddadccbddaadabbcddbcacdbaabdabbddcbabcdccabdacabcaacabdbcbcdbccaabbccbddacbbdaacaabdaccbcbaccdcaacacddbabbcbdcbadaadaabadbcaccbcdaccbdcdbbaadbdcdbabdbdbbdcbdaacbcaababbaacacbcbbbcbadddcacbddbcaadcadbbdabdcacbcccaccbbaadbbcdddabadbddadcddbaabcdaabababaccccbabbcddadbbdaabbbbcccdbbcaaaaccbadbddbaababcddcccbccaabbadadbdcadacadcddadddcbacdadcbadbcdcdcdbbcadbadacdbcddbccbdcaccbbbacbbaadaacabdaabcacdccdbbbcadbbcdccaccdcaccacbccbccaddbbccadbcdbabadadcadbaabdadabbdaadabdacbbacbccbcdcbddcaacdaddacdaaaccabaddcaaaadacaadbadbccaccacbabcdbaadccaababddaabdabacddaaaabbaaaacdadccabadbabbcdcabcbcccbaccdcaaaacdddadaaddabcaccdcaacdddddcbabaaaabdcbaaacabbdcacdacdadcbbbddcbbaaaddccbcdddddcdbcbbdddbacacabdcbccccbdbcdbdacdddcbbacbdcbbcdbdbaadbdcdacbcbbacbbaccadbaccbbbdbdccbbaabdadcaaadaadccddcbcabcbdcdbddabacbdabbcbddddaaacbaadcabbcaadaabaaacadcdaaddbbbdbdaadcaacaacabcbaabaacbaccabaaacdbabdccdcbadbabbaacccadccbbcddbabcdadcddbdabccccabacacbadcdcccdcbacddadaaacbbdaabbbbacaccddcabadbaccdabbcaabcbcdaaddcdbbdcbdcdbacacaadcabbacbcbcabcbdaacdadcababacbccddbaaaadbdcaaddcccabacacdaaccdcaadbcaaddcdaaccbaddbccbdaccadabdcababcabcbcadccbddddcbcbdadadacbaabdacbccbbadddcbdbccbdbcaacacdcabadbcbbcdcccbbdddbdbccaacccbaccadcccbacdccdbcdbdccbbcbbbdddcdbdacababadcadbdcddacdddcdbadabcbaddcdbabbadcaabaccadcddababadbbbaccacdabcdacbabcbdccacacbccabbdcdbacdbadaccdcddadabbcabbbbcbbdbadcbbddadccadcacdbbbbbccbacdcaaddbbbdddadcbdabbdddccaacbbacabbaccddaddbabdbaddadbddcdcccbacaccadccacabacdbddbdaccbaddadbbcaccaadbaddbbabcbcbbbcababddcdbbccddcbadbaacdcadacbcabbdbaabdcbddbbabbdcadabbcdddadabadbdcadccccddcabbdbccacadddbbaadaddcbddddccdbbdcbdbdbdbccdcccbdacaadcddadaadccdbbdacacdaacadcabbaddbbdcabccadabdcdadaadadadadbdaddbabbcdcdbacbdbcddcabccadabacbccbacbaccadbaddaabdadababadaaaacadbdaddbbabccabbbadbcbcbbaadccaabbcaddccacacdccbbadbaccaaaccacccabbabaccbdccdbaccdacbbcddaaababcdcbbccbdcdaddadbaabadcdaaabcadcdccbcabddbcaaccaddacbbbaddabcaadabbdbbbbbbdbbbddbadaacbadbcabdcabadbccbacddbbcbdbddbbcdacaccdddadbccdddbdccadbdabbcbcbbdbbcbdabaadaabbbcbacdaaacadcabaabccbdbbdccdbaaaabdacbdccbdaaccdacdbdacbbdbbbaacbdcccddadacaddabcdccdbcdcbadccdcadaaabcbbadaadcdbccddcbcabbccaccaacacbbcddaaabdbdaddcbbcadddbccdcdbdcddccabdcdcaddbbaaaaabadacbddaddcdbadbbbcdcdaadbcbcddcabbaacbbaaaccccacbbbbcdadaaabbcacdbbbdbddcadbbbcadcadaccbacdacaabadacdccabdcbaccaccbbdadcaadcacabbadaaabbcdcdaabbabdbcaacadcaaccddacdbddbaabcaadcadadacdbcbddbcdbacbdcabacaadbaacdbdbabadacbcdcabcbcabcdaacdbdbcbbdabdbbacacbdbdbbccbbdcbcdbdbddddbcaccbcbddbbccddcabdbcdbacdcdcbddcccbbbccbbaaabbdadcbddccabcaaaaddcadbbcdabbcabcacbadddadabcbbcbaabaaaddddcacddadaccbddacdcacaaadbccaddbcbbabbbadababbccddadabbbdcdabcaddabcdbcadacccbabddbaadcdcacbdbdcbcbaaacaabbbaacbbabbbcacaabddccdddbdacbccacdcbbdddadacdcbcbbbcabcbadabcbacaacacbcccbddabaaadbdadadccaaccdcaabdcdddadabaacdadbabddbdabdbdcacaabbcbacaabddabbcddddbacddabcbddccbacaadbababacaccadabaadcbaccacbdddbacbcdcbbbcbadcddabaacaacbbbadccdabadddcbdddadbbcdccbdbbcdcdcddcdbdaaaacdaaccdacdabacaabaadccdbabacdadadbbbacbcababcbaadbcccdcbcaaddcccbcbbccbbddaababbccccdaadbdaaaddbacddaddbacccddcbcdbcabdadaaaaddadabacbaddbaaaddbdacdbcccaacabcbddaacdaaabbabacdccddcbaaddbdbcddababacccbcdccccbbadbadddbaddcbaaccbbcccccddbdababaccbdcacdcccaacacdbbcccbcdacdaacbcdbdcccdcbbcabadcdaaccbccdabcdbbadccadbcdaaaaaabdcadddadbdadaddcccdcbbbdbbbdccbdbbbacaabdbbbacabbbbbacadddcbcabdddcddacaadbbdccdbadbabcdbbddbbabbbdbbcacbcbabdaddbbcccdddacbbaaadcdcdbdabaaabdbcbbaddbdcabddccaacdccdcbaaccaadccadccdadbaabdcdbcbdabacddaaadbbcadadaccacbdbbcdbaaaabcdaabdaaadccbdccbbccabcacbacaacaaabcabaddacccccdcddadbccdcaadadcabcdccaccaddcbcccbaadacbaacaacbaddcdcdbdcabbdbdbacbccdacaaaaabcbddacadbbdadbcbdcaabbbdcadccbbdcbcbccadadddbcbbcbcdcadaddcbbcbaadaccbbdaadbddacbcbababbccccccacbddccdacbdbddadcdccccacadaabbcbccdcabdbbccdadaccddddadbbacbbbcacaabacaadccdccadabadbadcbadddaacddcbccdabcabbbddbaabcddcddbbccbacdbbdbcddcdbdcddcbdbbabdbcdabbdbdabcaadcdbadbcaccacbacbaaccadbbbcdccbacbbccbaacbdabcabbabdbacabbbccdbddcbaabddbdadccabbbbdbbadadbbaccccbdbbbcdcbbbabbddbdcabdcdaadcbddbdaaddacbdddbddbacccbabacbbbccdccdbbdbcabbcddcdadacdcccacdacccdbaacdbddbaacbdbcaaaabacbcdbdbbbdadcabcdaccdccbcbbdaabbcdbaacdcabaacacbbaccbdcaccabdbacaccdcdbbbacddbcbbbaadbadcbabadcdbbcbcbddcdbccdbaadcadcdbdbcabccacddcaabcdacdabbabcddabbcdbdadabadbdcddacbbcddbdbbdcbcbaddcdbaaaaabadbddcdcccaccdcadbabdbcccadaacddddcbcccbacbadabbababdaaacbadccdaacaacdcbdacacccccdaccbabbadddabbbddcbaddcadcbbabcbbbcbdddaddbcbbdbababbbcdbbdddbadbacaacacadcbcdcdaddcaabbabdbdaadcdcadabacbbdcccaacacabcabcadddaacdbcbabbcacddbddcddadaabdcadcccdaaabcdbcccbccbcaaaabadbcccabbaabbdabccbbdccaabbdcbadcaacacbdaadbbcdbbbbadcdccbdababcdbbabbacbddbbaddabacadcabbbdaddcaadadbaddadacbdbdcdaadbcdccbbacaacbdbcaaddbdaabaacacabdaacbcacbcbdbdaacbbdacbdbdabbbbcddbbddbdcbdcdcaacccdbaacddcddbcbbadaabcadcdabddbcddadcaaabcacacbcdbaaadaaadaacaabdcacbbcdbbcbacbbcbadcccddcddadccccadcaddcaccaabdabbbbcbcaacacbcadadbdcbddcdabbabdbaadadcacdaddcdbbbccbcadaabdaccbdbacbdbdcaabdccadddbbdaaaaadaabacbcbcddddbcbddcadabccdccacabdaddbbaacbdddcabacddbbabcdcabbbbaaddcccdacbbcdcbdbcabdcacadcbdabdadccdaadaccdaaccaacccacdbbaacdbdccdddbabbbdbbddadcacacaccddcbdbbcbaacbabacccdaccddbacaddcbbcccdbdacaaccdcabbacddbcacddcbacacbddadddadbcbabddccddbcacacadcbacabcaddbbadcaadaacdbccdcccacdddcbcbcaccadcbabcabadbadabcaccdaacbcdcddcdccbddccdcdcabbacbacbdccbcabdaacbcbabccdcabbddaccbadcbbbdddababacabcbcacbbaaadbabcbdabcbacbabbddacaaccbbcdbddbdacbddcdcdaadacdabbbaabdcacdadddbdcdbabcddcdbcccccbddabdbdcbdbacbbabbadcbccdcbcdacbddacaddddaabcabcadaacdaaacbcccbbddddcbccdadccbacdcadabdddbbbbdcbcbcdaddacaabcdbbcbaabaabdababcbdacdbcaadcabccdabcdacaccabdccaaacabbadbdcacbaadcbdccdcadbbbbbbbacdbcdbbbdaddcdaabccbbdadaabcdcdcabbccbacbdaadbadccdbcaacbcdbddbccccdcdbaaacbddaaadbdaccbcdccdcabbbbbcdbabacddbdbcacddabddadbdcaadacadcdaaacabcbacaccacabcaadbcaabcbdddcbbaacdddbbbcccdaddabcdcacabbcadcabbaccbbdabcacaccdabcbaaaddcbddabbaabcdabbdbbcacbdddcacbabddbdcbbdaabcdcdbbbccaaaccbdbdaacadbcccdbbaddccdbaddccccdbcaaabdadaaccdbbbcbbddadbcaadbdadccacaaaaddacadabccbaadcaccabcccbacddccadaabbccdadaaddbaddbcccccabbcadcdbdbbadcdadbadabbbcaaabbbbacababacbaccdbbcddbcbcdabaaadabdbcabdcbdacbddcaacbababbabdcddbaddcacbaacccaacdabbadabcadbbcbbcbcacadcdbcbdccbbaccbcdbdddcdadccdabcddacbccacdbbdaaabdddcdadbaacdbcabcdacbcbcccaddaacbccccdbbbccdcbdadadbacbaaadddadcbdadbdcaaabacddabdccadabbacbbcbaadcddcbddbccdcdcabcdbaccabbbbaddcbcabcbbdaadddbcddaaadbcbdbacbacddcaadbcdbaaccbbbacbbdadcaddcdadcccadbdacbabaaaabcadbccbbdddacbaabbbdbbcbdccdbdadbbbccbcdbbbddcbabdbaacaaadbdbbddbaccccdabaaacbbccacbbdbaaaddcccaccdbcdbddcccbdbbbccaaccabdcabbabcbcddcdcadbccadbbccddcbdbcaaddbccddccccbcddadcacadcadcccbbcccbaababccbbacbddddadbaaddcbbbacbcadaaadaddccbbacbdaaacdbddcbdabdddaabacbcaccaabccbdbdbdcccbcbadaababbbbcacbdaacddbbddacdbadccacdddcdcdacaaaaaabaadadcddcbbaddccdabaaacadccabcdddddccdbaaaaccddccacddbbcadcaaacdbcbddbdcdabbdabbababddbbdccdddddbabccabcdcbdbcacbcbadacdacdcadcdaaabadbbdbbdabaaaccbdcaaaaaabcddddbdcbcdbaadaaaddabccacabcabbbadbadcccbcdcdcacadbcbaadabcbbbdbdbadbdcacbabacacccdbcacadbbcbcdbcbacddbbacbcaabbdababdbbcdbdadbcbacbcababdacdabcababdcccbccdabddcbddbbbddacccdabdcbdbcdbacacbcccbaaaddacdabdcaddacadbdbcbcaabbccdcbbdaabbccdabddaabddcaaacadabbbcadccacbabdbadbbabccaccdbbbbdbdacbadbaabddbacdabadadaaadccbcbbcbbbbcdbcddbaddcdddacaccdbadbbacacaddbdbddccdaddccaacdccaadacbdcbaacccdadaadcdabccccaccbaddacbdadcbbbcacdaaddcdadacacbdbdcbbbbcdcbbacdbcccadabcbcbcbaadbabacdbaaaccbcadcbacaddabdadbdbcccbbdcbbbdbbdbcdbabccccbbdddccbdaddacaddcabbcdaaabdcbbcbdbababcbacadcacaabaccdbddccdcbdbabccdbccbccababddddaabbbaddbccddaadacdabbaabcbdccbaadcacbccdbabcddbadbdbcdbcbacbbccbccbcddccdcdcdddaadbabddabbaccabbbcabcdccbddabdcccdcaababaaacbacddcaaabbddbcccabdacadbabdbbacdbbdadcdcdbcbdbaddbcadddadcaababbacadbabdbddddbcddadcdbbccbdcbcdcbacaaacaacbccdabcbcbbabbddbabcdadbdccccdcaadbdbbccbacbccaacddbacaaadccaccbbadcdaacaaaadacbadbadbcdcccbdcbcacdabaaaccbddddcccdadabaddccdabadacbabcbcaadbcbdcdcdddccddccaccddcdcabdbdadcdacdaccaabcacbdbcddcbaddcacbaaacacbbabdbbbbccddbddddcabcccaddadddcbcaccbdcbacbdacbcadbdbdbcbdbadbaaccdbdccadcddbadbcdbdcccbbbcbccdabbbddbccaddbdcbacaaddbacadacbcbacabdccbdcddabaacddcacacdabdbcccacdacababbbbbcbcacbacdbacbbaaadabadbbacdcacdcddbdcaabddacccccdccbcaaadcaccaadcabdabdccbdbaaddccdbccbaaabbdccddbdbbbabbcddbcaadbcddacacbacbbbadbccbdcbdcdbabcdbcabddacdccadbccabcbdddbabadcccbbbdbdbdccaabbbbbabdbbbbdbbacccaaacbbaccdccacbdbaaddbcdcadccbdcbcabaaaddaacabcdbcdcacabbbcbddabddbaddcbbbdbacacbbbddadbcdaacacbabcdbbbbbadddaddbddbbacaddbacdcaaadaacdbccaddabababcbdbbdbaabdcbbbacdcbacdddaaccbababaaccadcaaddcbcaacdaaacbbcbdddaaddcacaaaabbddcdbbbacbdcddaacdbccbadbdcaacacdaacbaacbaaaabdabaddcacdabdcbbbbbcbcabbcdaccabccabcbaabcdaadbccbdbcbaddaacccbbcbdccdbcbbdbbbbbbbcdaccccbadabacbadaabaadabcacccadbccbcbbaccbdcaccdbcbbbacdacbbdcbadacdcbccbdbcaacaabcadadccadccacbbbbacbdbbcdbbbaabdbccadacbdbddddbadacddcbacadbababdaabbcbbbdbbcbdcdddbdcaabaacaaddaabdccccadddabcbdddadcdaacbcdbbbdbcbaaccddbcbbbaaaadbddccababaabaabcabcaaccadbccbcbacddadbacdddcbcbbaaaaacabbacaaadbbdaabbdcbbcadccdbbdbabcdcddaddabcccbcacbadddabccaababbbaaddababbbcddabbcccccdbabbbabcbaaabdbacccdbdbbcdaaacccbababbbdbcbddabaaaabdccacaaaddaabcaacdddccdabaadabdadbbbcbbddabdddddbaabddbcdacbcbccabdcbdbbccbdbcabbaacbccadbcbdbcdbbaddadbcdcbcacadacaadbaddcabdadbbcaadabdabbcbbdccaadbddddbccbcbdaddabbabcbbddbbdcbaacadbabbbadcccccbacdcddadaacbbcdcaabcdaadcbbbabbddcbbcadbddcbabbadadaddbdaccbdabcdddcaddcdacbcbdbbaccbbaccccddaddcccccbcdbbbaaaabadcaccabdacdccdadccbaddcadaacadbccdcaaabdcdabcadddbaadcdcdbcabdcddaacdadaccaabcdddacccaacbcbdadacddcdacbabcadaacabddccdaaddddcdaacbcdcbbacbbabdbbbcbdcdddcdcaaabbbccbccadbcddababcaaaabcabaccbddbbddddbcdcaaabdacaacaabaadcbbbdbdaccaccdbcccdacdadcdcdababcccbdbbbcdddbbbacdaadadcbbdcbcdcbcbdadaaddbccbcabccdddacdbbcdbdccbaccbcccddbbccccbcacdbcddbbccbccddcdaadcacbcbdddadbddaccdcabacbbccbbddddcdabcbbccdcbabcbabadbacdbcbcadacaccdacbadbdcacabdcaadbacbddccbacbdbdaacadabdccaadbccddcbcdcbbbdbcdcbcdbccacabaacaccbbbdadbddcaddbabccbcbddbbaabaaadcbbadcdbdadbcaabbbcadbaddabbacdbaadbcddaabdcdcbddbcadcbadbdbdbadbcdddcbcbbdcdababaaabdbcccadddacbcddbbddabbcacccccdbbabcabadbabdcdbbbbbbdcaadddaadcabacbcaabcbbccadabbdadbdddbcabbbcdbbccabbabcabdccbcdcbcbabacabacbbdbbbcdbdadababcbdacbaccabaccabbcbddbcdbcccbaaddaacadbddbdcacaaccadaaadbbadabcccdcccbbbdcddabbacbbcabaabdadcacaabbacadddabcaaaadcdcccdbcdddbaabdcaaacacdbcbabbcaadbdadbabacbbddbdbcdbaaccbbababdcbaacbdcdacdaaabdbdadcdccdddacddabdccccadcdaacdcbdababadbbbccdaabaadadabbdabddaabcddddccabbdcdcbcacbcdadacadbcaddbadbabcccbcbcdbbdacaaaaddcbadddbccbdadbbcbadcdacdcdcdcbaddbcbdbaaccaaaddbcabdbbadadaccadaaddbcbabaadbbbddddcbbdcadcdabdbccbcdcaaaaaacacccacccadabdaaabcbbddcbdcccddbaccaaaacaccdddbbdadaccdcaadcaacbbdadacbcbdabccabbddbcddcdbadbcbabcbbabbdcdddacbcadbbcddcccccdbcacbaaaddaddaaacaccdcbbaddbabcdbdddcbcddabbbcdabababdddbdbaddacaabbbbdbbccdbcdbccdcddabcabbbbcbacddabdcbcdcdccdbbcadcbdbcbcbbbaaaacabbbaddcabcdbcbbabdddacbbdcbbabcbddcaaaaacbdcaacccbbbbddaacddddaababaaddaaccdbbdbabadddabdaaabbacbcaadbcbbccdacbcbcabccccbddabddadaccdddddacdaaadbbaddaddcbcaadbcabccadaadcbbcbbbcddacbbcbdacdabaddadbadabdbcacdabcbcadaddcdcdbbcacccbbbbcdacddaacadaababcbccbadcbbaacdbdcdaddcdbbdddcbacdccadcdcabdabdbaabcdadadcddadbcbabbabbadbdbdcccaddcadcdcacaaabaacdaaccabcbadcbadcbddbcbbddadacadaabdbdacbbacdbaaadadcabdcaaccdabdcccbdabaacdbbdcabddabdbdacbbdaddddccddbcbccbdaddbbcdadbdbaadcacabbcacdcdcbcbababacccaacabcdcbacdcbddcaccbacbbdcacaaacddbddbacdacaabbbdadabdbdcbabddbdbcabccbccacaddcdcbdaaddddbdaabcbcdaaacdcbbbcbddccdddcdbdccabcccaacccacabbbdbcbccacddcdcbaaadddbcdaaddcbccacbbcddddbadbadcbdbbdadbdadbdbbaddbbcbadaadddbcabcadbaabcccddcbaabcbbadbdcbcdbdadbdaddabdcdacaabbcdcadcabbcdbbcacdbddbaaccdcccdbcadacddadadcdbcbdacaccaddcaaddbdadabbcbcccbcdabdccdbdabdbbcaadadbcdcbcbccbbccdadcdcdaacdabababadcbacbabbcbdcdbbcaaccaddbccdadcbadbcbaccbdacdbcddddacadabaddccbcaddcccabadaccddbcabcbbdbacddcaccabdacadacbccbcdccdcdbcabcdcccddcbdcddddcdccdcdcdbabdcaccbdbdaddcaaddbccbddcbacdbcaddbcbadcdbbbabacdaaddccccddcccbdcdaacdbccdaaaaccbaabacbacbcddbabdccdccbdadcabbcabdabddbabadbdcacccabadacacccdbcdadadddbcbaacacbdcdacaaabcddacbabbbbcbbcaccbcbccadcbdaabaabbaccaadddabbcabbddccdcbbabbbbcddbbcdbdaaddbdcaabcbabaadcddbcbdacdacaacaabdcbadaacbbbaabcabdcbbcccdacccbaaacdacadadbabbabcbdabaacddcdbbadcaddaabaaabcdccabaadccccabcabdcdcaabdcdcbcbdaabbdaadbaddcbbbacdcacabcdcccdacabaccbaddccccbdcbccdccdbdbccbdabbbccadabbbbacdddcbcdcddaccbcbcdbcdadaddacaccbdcaddbbdcdbabbbadcbdbcabdcdbdcddbbddcdbccbdddccbddcbaadcacbaddadbbbcdadadabbcabddbbcdcabbcacbadbdddcacabdbcbdcadcacbbccabdcbadaabacabcbabcabbadcbcaaadcdbbdbadcaacbcbbcbdcacaaacaccbcacdbdbaaaddacbaadbdbdbbdddcccdbcbcadaacddbdbcdbaadbadcabaaaddacacbcddddcacbdddccbddbddababbcccbbdbcaaaabaadbdbdcccdacdadcacaabddadabccadbdcbcdcdcdaddcbabdbccbdcbacadabacddbadcbaccabbaaaabbbbcdcbcccadccdcabdccabaadbdbacbcdddacdcbbdddadddcbaababaaaabcdbccbacabdbdbabbbdbbacbbbaaacaaabbcbdbdbdbacbcddabaacaaaacacdadababbcbadcddddacddcddbdabdaacdadbaabacddcbbadbcadbdadbcbaadaadbdacdcacacbdbdaaabaccddbcacccbbacadcbacabbdbabbddcbdaabbddbccacbcbadccbacddcbcadabdbbdbabcbbbbdcadbbddadcddbcbaaacbccbababcdaaccbcbcbbcdabaaccaccacacacbaddcadbabbadcadbccadaaacdabdcbdccdbaabcddaadaddacbabbcbcdaabcdadccdcccbaaaccadbdcbababdddabdbcacbbabdacbdddabaabdbdaaddbbbaadbdadbbdadaabaccbbbcbdbdacabcbddccbabbbdccddabcddcddbccdcbcccaddbacabdabcadbacdcdccbdddabbcabbbdaadcdddcdaddaacbbbadbcccadabbbadaddadbdbbdbdbcdcadabdacacadcbbaadbdcacdaadcdabdbaadbdabccdaadacddbcadabdadadaabdcddaacadabcadcbcddaddabcdbbccdcbcbaabbbbcbcaaaabcadddbdadbddbabcacddddcdadcbdacbabaabdbdccdccadcdcbbbddadbcbcbacbbdbdddcdabadbbbdbbbccddcbccabcddcaaacdddccabbcbabbacbbbcdacdacddbdbcacbdddaaaddbaacbdbaccaacbbcbaddabbdbbaabbacdddbdbaacddcccadacadbddaaddadbacaaccccdbaddcadaacdccabbbacbddbdbabbdcdcbbccccbdaabcdacbddaddaadcdbcdacbbdababccacdababdbacaaaccbbbaaacacbdaaccbbbcdbcccabdcabbbcabacacdbbdadcaaaaddaaddbccacaabaaaadbdbddcdaacbdacbbbbbddabacddddcdacbdbbaabaddbadcbbdbddcdaccabbcdcbbddcaacbdbbdbaabcddbbacabaccadacaabaccacbbbacaacbbdcdaabadcbbadaaacbcabcaaaacadcbbccddccabdcdbdbaccbcccaacddbaacdbabacdaccbcdbabbdddccabcacdbacadadaaaccdddaacccabbaadbbcddbcddccaccabbcadacadcdbbacdccdbbadcbddccadcbcdbacadaabbbcaabcacabcddcbdbadabbbcccdbbabadaabdcdcbdbbaacacdbcabbbcabaacabcbbbcdadbdbddaddccdadcbbcbadbdccadbabadcbddbcdadaaabcabadaaddddcbdaabbdccdbbbbdcdccacacdcadcccbaabdacadbaddcccddbaaacbadcdcccaddaddbdbadcdcabdbdddcaddadcbaddbaadcbcbadbdacacbcaabaadcabbcbdcbcbbbadbaacccadbbababbbccdcbbcbabaddacabaabadbcadbbacbdbcbbbbccbaabacbdaaccadcabadbdcbddcddbdbcaddbaacbbcbacdbbcddaadbbbacabbdabdbbbacaadbaacadacdcbdbbdaabbdcbabdcbccbaaccadaaccdacbabbdbcabddcbbcabdbdaaadbccabdddddadacbcdddbcdcddbbddcaadabaddbdbcbaaadacbbabbdccbdcdaacbcabaadacadadbbdaadcddccccaddaccadadaacbdadcaacaddadcabdacbbdbcdcabbdacdaacdaadbcdcabbccaaaaadbbbbdbdbbcbabdddcbcccabbabbbabcdbbccacbadbbbbdcdcdddababacbdbdbbabbbbcabdbcdadccacabcccdcddcabccdcdcbccbcbbcacccbcabdacadaddcdddaccbdddabbabadbbbdddcdbaddadcccdbadbadbdacdcdaadabbcaadcdddcdacbbabcadccaaacabcdbacbcabcdcdaaacbadaddbbaabacbddcdddbdcdcbddbcccabccdbaddbcccdabdadbacddccadcacdbaadababacbdacddbcbbdaacbbacaadbcbdbddcaaabdccbcbdbcacddcddccbddddadcccaaadadaacdddadbdbddbcddbaabacaaaccaccdbbcdabbdccaadddcabadacaabbdbacccbcacdcacbcccccccdbdbbbcaadbcdbaddaabadcdbaadcdbbdaababdddadcdbcbdacadaacbaddabcacadcdabaaacccacadbcadbdaddacabbbdbbcdadcdbcddcadacddadabbdacaadbcdbbaaaddcbaabbcbaacdabaddcccddbaacaaacdabdbcdadcbbacbabddaccaabacabddacdbbbaacdbdcdddaacdbaccbcdbbcabbbaabddcbababbbcaacacbaddacdcadaabbbcdbaadcccadbaacabcbbcdcddbbdccdacacbabbadbacddcaaddccaadcbcddbdcbccdacbbbbbbaadaabbcdcdabdbdccdddcacdbaaccaabcabcadaccdcddadcdadacdaccabdddcbdcbdcdccbcccccaacbdaaccadabacddddcdabccdbbccdcaadcabdcbdabcdcadcbcbbbdbcbcadbccabcbbabaddacddcbdddcabdcbadacbcdbbdcacbcdadccabbabdddbcadddbcdacdddadaabdcadaddbcbbdaddcabdbdabdbcdbadaadbcdabcaabcabdbccabdcbabadbabdadadbacbcabbccaddbccccaacadaabaabcabdbcdbabbcdcdbaccabacdbcacdbcddcbccdbbadbadaabdcdaddacaddabdbdcddaabcccdbcabbdcddbbddadcadbbcdcbbcddcbcbbababadbdbdddaaaaadacccdbdccdbdbbdcdabbaddccddbccccdddadccdcdaacabddbccdacdbdbbbdbdacdbbdcdcbaabbaaccabbbaaacaacbdbcdcaaaddddbbddaacccccbbdaccdccabacbdaaaaddaddacdadddbdaacabcddbacbcaadbdddddcaadcdcdbcabdbddbcabbacdcbaddaadacaadddbddabbcdccaacaacdddcbddacaccacbabdccbabbccddbcbbacaccbaadbbdabbcdddcaaaaaaaacddaabadbabbcdadcbcaaacdaaccccaababdcabdaaadcccacaabbbbdbcbbcbcbadadcccaadcbaadccdbdcabaddcbdcbaaaddbbabcbacadacdbddddbcadacddcddddbaddcccabddabdacaaccbdbcdbccbbdbcbdbdabbacabbbadbbddacacbddcdbdadacadadbbadacbaabcaacddcabbaaadcabccabacacdbaaabcdcbadcdddaaaacccbdcdbdabaabcbacbcbbaaccccadbcbbdaaabcddbdcbcdcdabdbcbbacaaaaddddacaccababbabbdabdabdbcbaaddcaaaacbcdbcdabcddcddcacadddddbddbbcaadcddddadddbadcddbabbaddcddbcaabbaadbbbdcbabacdcaddabcdcbbaacbdbababbacbccdcdcbbbcbbabdcdabdbbbdcccacababcddcdbbdadbacbadbddcadaccabccaadaabccaabbaccccddbcbbdbdbaadcdddabdccadcdccbbaaccaadbdadaaabacaabaadacbbdbbdcabcdbddaddbbaacbbdccbcabcccbaddcaddcdaacbadbabccdddaadcbadbcbcabaccabdadacddccccbdcdadacacddcdabbacdcacdcacccbdbbcdbacdcbbbdaacbddbbccabcbcadbaabadbacabcbbccadccdabaacabddbdbddabacbadcacbdbdbdacabbdadaaaaadabcbdadbbdbbadabbbddbcdabbdabccddaccddadcdbcbadabddcbaccddccddabcaacdaacbbabdbbdbcdadaacbcaddcddaabcbdadcbccbbddadacdadcabbcddbddbadbbdbbacdcbaddaabdbccbcbcabbddcbabbcbcccabbddacdacdabbcacaccaaacdbcbdacbaddabdcaaddababbcbcaacaccccdcddcacccababbbabdbaccaadccbdbacbacbbcbdaadbbcadccbcbbcdcabaaddbbdacdccddbabbdacdadaccbcbdabaabbaacaaaabbdcccbdbdacdbacbcdabccbabddbabdacddbcbaaaadbddcababaabdbdbcacdcacddcbaaccbdddcbbbccabbdbbdabcbadcbbbbddcddaacdaacabbaccdbbabababbdadabaccbccbcabaadccccddaabbcaabbacabacdbbcdcaacaadccacbbabdaaadaaaddbddbcaadbdddaaadadbbbdcdaaaadacccaadabbcbdacadbaddcdbcdaaccddabcdcabbaaaadabaccbbabddbadddbbddbbddcacadcbadcadcbcbccccccbbaaccdcbaaddddabadabbddadccdbdbaaabacbcaaabadccaccbaddcacbcabbcacdcbbddaabbcccdbdacaaccacbdbabbcdaaadbaabdcaabbbbddacadbcaccacbdbbaaabdbaccaccbcadaabaabddbcabaaddcccdcabbccacdbcdcabbdbcdcdabbcacbcbbadaadcbaccdccacaddacadacdbaadddbcbaaddddbadcaadcabaddabbcbccaaddbcacdccccababbdbadddadcbaddcaccbbaaaacdcbacdcddaacaddaddbaccbbbbbdabbdddbbccaaadccabcbcdacbadbcbcdcbcbccdabadccbdbdbdbaacdaaacadacbabbcbbbaabadccbddacbbbcdbaccdabcdaacadaabbabbddabdcbbcdadddcbabdcabdbcdcaccacdbdcbbcacdcbdcabdcbddbbcdbccdcbcdcabdbdaccaaddcadbdbbdadddaadaccbbccaabddccbdcddbbdaaadcabbbbabbdacbbdaabcbcdadbbdbcccaccccaaacbabddabbacddcbabdacabdcbadbaaaacddbdadaaadddbcacadcdcacabcacbcacdcccddbdbabbcbcacbbbdcbbaabddcccbaadacadccddacbbddddccccdaaddbaaaacdacaaadcabbbacbbcbbbbdcbabbaaaabcbbcbddbbdcbcbbdcaaadbdadddbbbdcdcbcdbadbbcacdbcbdaccdcbbacdbbddcbdbdabadacbccdbaacdacdbadddbbccdadadcbaabcddcaabccbcddcadddacaacacddcddaacddbbcdacabcdbddabcacbdbbdcaacccccdababcadabddcdacddbacaaccdbdbabaaddacdcabcdbcdbdacbbabccdccbcdababdbaddabacbbcccadbdbbcdbdddabccdbbddcacdaaacadacddabdcbdaddbaadbcbcddcddbbdcababcbcdaaccdcdbcbacccdddabcddbccbdbcacbbccaabadaababcdbcaccbdabbaacdacddabcddcabaccbabaadaccdaaadbbcbbcadcdcdddaddcaadcbcabaaabbadabdadccacadbaadabbcbcddbbdcdcbadadbbdbdaacaabdbdcccabdacbacaaacabbdaddbcdddadadababaccbbcbaddcaccccbaccbbdbbacbaaddddbadbcbdadbcadddabccbaaaacbdcbabdcccdaacdccbbcbbcbadabdaccbbaccdbbdabcccdcddcbbcbbdaabdbbacbcadcbbccccabdacdacabcacdbbdaccbdcdaaabdcdcdccdacccbabbcabdcdcdadcadcbdcaacdcdbcbadaaacabaabdbcaaadacbdbbabcaaabdacdaaaacddcbccaccccdadcacbbabdabaddbdbbbacacdcaaccbaadbdaaacdbccdbcccdbdccdddcadacaacccdbbbaddcdadaababbbdbcddadbdddbaccddaadcaddabdcabaccaaacddbaddabcaaaacdcaacaacbdcdaadddcccbddadbabaddddcdadcdadadccbcddcadacaadcdbccdadddcdcdbaccaacaccdcbdcdbbdcdcdcbdbdbcabbacddacdaccccbdbabaaccdbbaccabdabbdbbdbabbcbbbcbadadddcacacababbcbacdabbbabcaddadbaabbbacbadbbaccddcbddbcadddcdccbbadcccbdaacaccbcdbcbdcdcdaaacabbadaabcddbcaadbdccbaadbdaaddbbabbaadbcdbacaabcdbbacccabbdaddcddbbdbcdaddbabcdbcaccdcdaabdbbadbcbdccdbaccbccdbdbdcdbbbcacbcbccaadbdccbaaaacbbabcdacacaddbbdcaacbbbbabaaaacaadcbcdccadbababcadbcadabbbcdbcdcbdccabbdbbaaaabaaadddbbdcaccbadcbcbcaabadcdadddacdbaddbccabdbadcadccacadbddadbcbcbdcbbbcdccdcddcaaaccaaaabacccbbddccbbddadbdacacdacacbcbbbabdddcadcdacddcdaddcdcdbbbdbdccccddcbcdaddddbbdcaacaccbbbaaacbaabbdbdbaadbaddadbbacbccbbcdadcbdacddbdddcbdababbccdbbcbbaaacddabbaadbddcbbccdccbbbabdcadcdcdccababacabbcdcaacbcaacabacadcddbadbdaaccaddbbbbcdacaccbabccbabdaababacbccbbcadcbcddaccbcddcacbcacadabdbaabbaccabcbddddccadbcbcbadddbcbdbbcabdbadbaccdbcdbabdbbaacddbddcdccdcbdbaadbbdbadcdbdbdbcacadbcbbbcaaabcabcabccdacbdbbddbcbdcbabaaadacdcbabccaadabdbccdbcddbabadacccdcaddccccbbaabadacadcbadbddaddbbaaddbabcabaacdabdccdbacbcadcdbbcdcaacbabadbcacbdcdcbdacabddbadddababccdbbccddacbbabddbcacbdadcdacccddcccaaaadbcdacaaaccabbaaaadcbcccbbdddddabbbddccacddcdaacdccdacbcbabbcbdcbbabacccdbadbcbdbdacdbabdbdddbbcdbbdbddacccbbacdabacadbbdbdababaabbcdaaadddaccbbadadabdcdbcbbddcaaccaaacacdccdbabbcbbaadaadaabbddddacdbdbdddcababdbaaaaadcadacababcbcdadcbbaccaabddcacbbaacbcddaadadbdddaccdacadaadcdddaabbbbacabdcbdaddacdddcdabacbccbbcaddccaacddabbababbcbacccdbacdcdbaccabdcacdabccdbbbbbcaaaaddadaaaccdaadcbaadaabbcddcacddabdbddbddcbaaddbbbccdcaccdcdcdbabcaabaddaddbccccacadacbcbadaddcabccacbddccacbdcabbdabbcbcdabdbddcabadcaccbbcdcddbbbcdaacbbbddcadaddacbddabdaacaccadcdbadacbadcadabbbbaaaaabdbbcbacbdddccadccadbbbbbcdccbdcdcadddacbddaaaaacddaacbaacbcdbbadbaabdaadcdbcacbdcbabbdacdcbdcdbabcabacbcaaccddbadabccacbabbcabbcbbbcbcbbdaaaaaaabddbbcdbabddddabdaacbdaabbdcadadccabccadabbdaadbaabadcbbddccaaadcccbddbcdbdadccadcadddccbababbcaccbbcdcaccbbddcdadcabcaccdccacaddcdaacddadddcadcddadcbbbddcaadbbacabddcddababcdabcacbbdacaccacbbabbbaccccababcccbbbddcaabbdcbcaddbbbdcdabaaacabddbddbababdddcbbcdaadaabcddbadcadaadaaacdcdabacdcbdbabacddbbdaababdbcbbbabddcbcbdbadcbddbaddbcbcaabdadabbaddbdbaaacadbddabcabacdacaccbadbcdabdacdbdbdbacaabaabcbbbccdccbadcbcabadbcddbaddcaccdccdcbdaddbbcdddcbdcbdcccdbaccdddbadaadcaacbbcbabacbadcbdbaddbbcabdcacdbacbdaabdbcadacdacaddbcbbabcdabaaadbcadbdbabbdbcadadcbbdadabbcddddddcabdbcdbddcbbddbcccaacbbcbdbddcbccabbabcdbdaaaccdbcaaaabbabacacbadaadbdbdccbbcaabddabbcbaacabdabdcbbddcdbccbcdbdcdddabaabbcaaadcacdaabcdbadbaabcacddabddbddaaadddbdbbabacacadcdccaaaacbcccadbcdcaccaddadcbcbdbcccaddaddaacdbabbbdccbccdaacdcdcdaacacccaadcabaccacccdaadcbcabbaaaccaccdcabbbbbbdddcaadadbcbdbbdcdaabccbcbcddadbddacbaddbacbadbcacbcbbccbabbacacabacdadcabbabacabaccacaabbabddabdcbcdcabbcbbacbbcdbaaaaccbbaaaddcaccbcacdddcdbcdadcdabbbbbcaabadacabaaddddbcdaaaabadaddcbacabdddcdbadbccddadcbacccddcbadbbdcabbbbacababcbbabdabadcabcbcbbdbbabdcdbcdbdcaaacadbaadcdbbbacdcccbcadaadacdbbddcddccacaccdadccccacacbacbcbadadaacaacdccbbbcbdbadbabbabbcbadaacabadadbbdddabccdaacacccbdbabbbaadbabbdcabdbdbdddbdadbbccdcadbbacdabddcbdadadddccbcbbaccbbbbaccabbcbdadacddabacddcbaadbcbbabaddbdcacbbacabaaadcbdacadbaabcbbacbabcddbaacdddbdddcacaacadabacdcccbbdddadcdcdaadcdacbdcdacabdcbcdccadaabacaabadccbddcbadbcccbddabccacdcaadacacbaaacbabbccdcacabbbabdbcbdbbbabcbcbbdddbdcaabcbcbddadbbacbbdaaaabdddabccccbdcbbbcddaacaddadcbbadcaddacccacdcbdacdcbcadadaccdabcdcbcbccbabdcbaabcdadaadccdddabaaddcaaaacabaccdcdbdbcccddadaddccaacbcdddbbbdbbcabaadabdbcbccaacddbcabdcbddcddbcbdbaaababdcacbaddbcbaabaadbcdbabcccddabdbccddbcabbbcdcdabdbadccbcdbbbcdddcdcdadcbadcdcaaaccadddcbaabdbdbcbadbbacabcdadddbdabaaaabbacdaadaacccdbbcdaaaabcaccbababaabccbdbbccbbbaadcbbdabcbbdcbacddcdbacabdcbdbdbcaabdcacdbabcbdcaacadcddacdbcbddddcacaacadbccacbaabaccabddadadbbdaabadcacabdbbcbbacabaadbbdbaacddcccbbbbaaadabcbbbccbaddcdcbdaaadcddbbbdbabdddaaddacbcacadbcddcdadbdcabadbcbdcdbacddbcbbadcbbbcccbbaabcaabcdbccaadaabaaacbabbdbbdbabbcaadbcdccbbdbcdcdddabaadbadcdacbadadccdcadbcaddcbdacdabadcdacbcbdbbdddcbacadbabdbcddbbcbbbbcccabdabccccdbbbbcddcaabcdbcacaaddbabbccddacdcbdcbdcabbbdcdddbbbacacdabaabaadabccacbdccaacbcbdcdacddbbbbababdddbcaacbbbabcbcdabadbcbabbddcabbdadbacabdaabddaddaabbcdbaccaadbdaddddbdbacabcabbbbaabddacabbbbcabbbccdcdabadadddabdbcbbadcaadabdacaabdabdabdbddacdbbbddacbddbdcabccbaddcbacaccccbccaaadbcbbacdabbaddbbbddacacabcabddbabadbadcdcadcbdbdbadbcdbbbcdbbadddaddbddaccccdbbcbccbbacdadcccabdbbcaabbbbabbbaacbccaabccabbacbcdcdbaabbdbdcaacdaacbcdbdcdadaabbdbadcbcdddbdbadcdabccbacacaabdabaabcdbcacdccbbaacdbcdbacdcdccbbbcdbddcbdcbbcbbbbcaccabcacbaadabadaccdcddadacdcaadbdbadcaabbbadbbbacbbaabdbaacbdbcdcbabccabababddcbacbcacddcaddaacddabdcbccbcabbadbdaddadadaabbcadaadabcbdbacdcdcccddcdddaaabbcdbdabccbabdaccacabaacbabacaddbaadcdbdabbccdaaccdcaacacdacbaabaadabbddbccaaacaddabcbddcbbbacdbbaaadbdbbaddbbabcccdbaadcbbddacdadaddaddccbcbaddbbdcddcddbbbdbbbcccdbabdaaabcbcabaaadcabddcdcdcbcccdbaadbadbcabdbdadbabacddbccacbcadcbabbbaccdabcacbaddaddcddcabdbabbbcdaddbdadbaabddacabdaadbaadaadcbabbdcbacacdcdbdadbcddabaccdabbdaabddbddcbaddcbdbadadbcbabcaccdbcddcdbbaacbdabadcdbbaccdddddbcdbdcbacaacacdabccdcddbdaccdbdbaadaaadbddaadacccabbdbdbabadbcabcdbcbccadcacbadddbdadbbaddcdbdcbcccbdadabccabcadbaaadddcbddbbdaddbdbcabbbccbaabbbcbaabdddcccdbabcbaaacbaacacdbbdacdbcbccddacaaabbcdcccbcddbbdcbdcdbccbbbddcaddbcddbacdbadddbacbcbabaccbcbbdbaabdcacbdccbbcabcccdbbdbadcadbcacbccbcaddbbadbcdbdddbbbaabcdaccbbacaccdadddacdadcdadcdddabcabcaacdbdacbcdcaddaaaccdabaddacbbccababdccdaabadbccdbaaccaadaaadacbcbacbacddabdcdbbdbdbdabcdbaacabdabbcbbcdbdccdbdaabddcdbccababaaadacabadccaacdbadaaadbcbdcbbbabdbbbdaccbabaddabbbdabbdbccabcdadadddadacdbbaaccbcaaadabbaccdbdddacddccdacbaaababbcddaddcddddbcadbcdbdcaadadbcabdccaadccbdcabbadbdbbaabbacbccdbdacbdcacbcadccdbdaabdbddbacaaadcbaddbcdccbbcbcdaccacdbadadcbdcbdaaabdcbabbaaabcadabbbdbdabbdadbdcccbddbbdcabcbdcabcbcbdacdcdcaccccadaadabbcbbcccbcbcacabcaadcacacddcbdbaccaddcdbacbacacccccaddcccababdbccccbdabbcadbcdcabccaadbabcddbbcdaaacbccdbbabcdadcaadbbabadcaaacdcdccdacddddbabccaadbabacbabbadcbddccccddcbbdbddbcddcbbdcadbcccbabaabccabbaabadbccdadcaccdadcdbbbacddbdbadcbcbbdbcabbbcbdbbdaabddddccddbbacbabdabaabadccdacbbccddbccddadcdbcbcbbbcbbbdbcadcbacacdbbbddddcdabdbbdcbabcdccdaddbbddcccbddccbaaccbacacadcaccdcbdbdaccadcdbdddcaabdcbcaadbcadcbcdbababdbcdbbdbadacdcacacbacdbbadcdddbddcbcdacabbbccbdddcccbcabaddcccdababbddadcdcbaccadaaabaabadcbcbdddbaadbdcbbaccbbaccdcbccaaabccccbcbbdcdbdaacabdcbccbbdbdccbbddaacbdbadbaadbbdcdbaadddabcdbabccadacdadaabcdbbdadddccdcbacbcabcdacadcdcabcacbacaadccccbbddcdbcccadccadcacbdabdacaadcaaabaaadbadbdbcdbabccddbccbaddcaccdabcbdbbabdddcdcbdadccddaccabacdbbacacdbbddcdcdbccaadabdbbabbccbbaabdcaadbadabacbadbabaacbdabcdcbbddbbdddaabdaabaccbbaabadadbbbcbcadacaacddbbccddadcbabbddaabdbcbcaabbabcabcddbaaccaabcbbdcdadcaabbbbcbaabadcbddddbccdabaddccbadddcbcddcdcdddddcabdcdbccdacdabcbacabcdadbcbadcdabddacdcaddcabaddcdadbdaccdbadbddbddbccacabdcbcccbbcccbbdcabbaabdbaadbccdcdcdcaaaaaabccabbbcaaaadaaacbabddacdaadaaabcaadbbbbaddadaaaacddcbacacacdaaadcaddbbcaaccacbbdbdccadadccdcaccdbadbbbcddadaabababbdbbabcaccaadabcaaaabbccbbcbadcabccdcdcbbaabdbdcbbcacdadcdbddccbbadbababdabaaddbadccaddaaaaaacbaabdcacdacacbbdcacdccacacaacbbacdacbbcaacdbbbccdbcdbcbbbcaadbaacaccbccdbaddbacdcacbaadaaabbbdadadbddbdbbdcaddcdcbbccccccdaacbabcbbcdcddccacacdaaadddbabccbaabbaccddcbacddbddacdccbdcbbbaacabddddcbcdbcacdaabbddbcdcdbacddbccdbbdabbcddbdbadabcddacdccbbcbaddbcbcaaadccbccbadadabdaddbcadaddddccbcbcbadacbbcdcccdacbdadadbacddccadbccddbbaccbbcbcacbdddadbdaccacadacabddcccdbcdcddabdabadacbccbbdacbcdcabbbcdccaacdbdaaccaabdccbcaddaacacbddbdccdabacbbbbdddbacaaddbabdbacaaadaddbacdcadcaccbdadbddbcdbacbdcadbcdcabcaddabcbdaaacddabbdbbadcdcbcdaacdadaddbadaddbccbbcbcababcbdbdbbbbcdcbcbabcbadbdbcdbcddcdcbbdacaacbdbdcdbbccbbbbdcdadbdabdcccbdddddbdbbdbbabccdcabaccbcbdddadcabbdcbcdcbabacaaaadddbabdaaadacbcbadcbdcdbddcacadbcabddccabccbbdbacaaacabbcdbbcbcbbcaddddcbabbccacbadaacbadadabddbbbbccdaaddbccbdcaccbccddacbabacaadbbddabaddbbdccdaddcbcabbbdbbabcdbdbdbcabccddbaacaccbcacdbdddcbdcdacbdbcdaabbbbdbcadcdabddaaaabcbaaadddddadaabcabcdcaacbadadbdcdccbadaabbacdabacdbaaaacdccdbaabdcbccadcdbdcdcbbcabbcdcbdacaddbaabaacdbdbbbcaabbcacaaddbdcdbdaddbbcaaaabdbabdabcabaacdadbacddbdbbdccacbdcbbcabdcaabcdccbcdcabbbcdbcadccbdcdadddbcbbaacdacbbcacacdcbdcdcaadcdaaaccacbbaaddaacddbddbbdaccbcbbddbababccbccabbaaabbdbabbdbccbacaaabacdabcadcadddadccababcbbddccdcdacdcccdabacdaaaabacbbcbacbcbdbddcddccbbbadddbadbbcdacadaacdcbcdccddbcacaacdddcdcdbadacacaadaddbcbacadacbacddbcbbaaabbaaabcbdbdbddbddbadabcaddbcdbaabccaabbbcbcccbcdcadbbdacacbbbaacbacbacdbaddcddcaabbbddababdcdbbacaaabcadaddddbdcdaccdbdddcbdbaaddbdcdbaadcdbcddabddccdbcbabbddaadcabdcadcbaaaaaacdaaaddcbbdddcdaddbbacdacdcaddcdcdccbccdbcbdddbaadabaaacbdcbadcdadadddcdddcccccddadcbadabcdcccadddbadbddacbcdcdabcbadabaadabbaaaadabccddbbbcbddbcaaabadddcbbbadddbcacbddddaacddcdbcbdbcbacdbaabacbbdaadcaaccbbadaddddacbabdcabadcaddbcaacbaadbcabbacccbcbcdddcbdabdcbcadbbabddaacbddadcddaadbccbddaaccbdbacdacbdddbbbbbacddadddaaddadabbdbaaaaabaddddbadbbbbbdbabbabdbdbbbccccabccabcaccdccdcbcbdaacbabdbcaaaabacacddcdadddbdcabadcacacdbbcdbdacbccdaabcbbdbcacbcdbdcbdbadcabaadcbcacbbccaacbcdabccaacaabcdaaccacbcbbcacdbccddcadadbccbdbddcddcdcbcadacccabcaaaaddacaabbababaaaaddbaccbcddddbaddbccabcabdadcddcaccdcacdbcadabddbcbbbcdbbaabbbbdaaaddcdcddabccdcaaadaaaacbdccacdcbdcdcbacbaccdadbcddaacbdabcbccabdacaadccbacbddcdbcdabbbbcbcbbccdaabcdabccdacbaacadcabcaacbcbddabcbcbcdccccaacdbdccbbaaaabccbcdabbdcdbcdbcaacdbdaabaacbcbbcdcadcbbcddcbccaccdcdbbcccccdcaaabdcdcccaabdbcdcadddcdacbaabdbadccdbacdbaabcbbcdddabdadccbbbaaadaabccdddcddacccabbbccdaabacabbbbcddbadbdababbcbaadabdddaccbdddcbcacdbaaadbabdbdccbdbcaddcbddccacdbacdbdacadcbcbabccbcadddabdbdbbbbdcaabdadccdcbbacbcccdaddcdabaaadbbaabbddbdacbbacdabadccddcdaccbaaacaadacbcdacbddbcdabacbccbdccadbdaabbabcabcdccbdddabbddaccdaccdbadbcdbddccdaadaadbbbbdbbbbbbacabdcbbbabdcbcbaddcbabdccdabdcddaaddcbbadcbcbacccdccdbacdbbbcbcdbcdcabddbaaddbbbbadbccbaccddbcabbcbacacdacbaaccabcdbdbbcdacdcddaacbccaabcabcdddbbdcbacbcabacddadcdccdadadddcbbcdbcbbbdddbabbadddcdbcbccadcbcdccdacbdabbccbbdacdcdcacabcbddacdbbabdadbabbdaabcbccbbadadabddcbcbbbddbbdddbcdacddcadaadadbcaaabcdddaaccddabbabcddcbadadccdcbbacadbdaccabcadabddcccdcbabbabbdbaddbcadacbdabcbcadbddcddbbdcacaccbaddbbcbcbacaacaacbabcabdbcdbbbbdadcbbabbadbabddbacbcdbabbbbdcaaaabcbabccbdcaabacbcadbaccdbadbdacaddcbabccbabdcadcbbdaccdacbdabddaccddcdbcbbacacaabcadddaadcdbbdabaaabcdbbccbdbcdadadcbbccbaaaadbaaccbddaadbccbcdcacddccbdbababdcdcbacddbaabdaaccaacaaaddabaadadaabbcabbbcbacabaaadadcaabcaaadddddacccadccbddbaabbacdbabccccdbabbbadabbacdbbbbdbaabdbaaaabcbaccaadaacbbdccdacbaacbabbcddcbbcabddbcbabdccdbbbddcaaadbbadcdcdbdbbddacabcbcdadddabdacacbdbaddcccaacdccdcaadbbcbaddbcddddccddcbcbbacacaabddaacdbacccccadaabddccbbddbaabcbbdbcaaaaddbbbabcadacababbbdacdbabddddcddcaacdbadcccbabccdbcaabaadbcbdaadbacaaadbacaabdbccaccadbbbdcdbdbdbbbdbccadadaaddbbbabaccabdbdccbcbbabdcbbdbdabaaacaaccbbabadbbcaaccbcddcaabbbcbbdcdabcadcdcbccccbbcbdbacbbbabcddbccabdbcacdaacaaadbaccdcbdcaababcdcbcbbbdccdaacccdbccacadadaabadbacccbaacccbddbddccbbcddcaccccababcbbcddbddccbdaaccddabacbacabaadaadbacbdbcccdcdccdaabadcdaaabdbbdabbaccddddcdadbdabdacdccbbbbacadcbdccbcaddddddaccccaadbaabccbccdcdabdadbdddddadacdcdddaabcadaaccabddddcbddbbdcacccbaddabbbbbbcabacdbbdcddadccbdacbbaabcdacdadbaadaacbcddccdbcdbaadcadaddaddabbadaddddaabbadacaacdccabdccdddbaaccbbadbdbbaaabbadacabbcaacbddaddacbcaddcacddbaaadacababadbaaacdbbcbcacbcabdbcaabddddbbbdadcbcaccbbcbbdbddcbcccbcbbccdddbaacadcdcacbcdddadcababddccdcdacaaddccaddaacddadccacddabbbbcdbbcacaddadbdcdadabadaccbabcdbacbaadbcccbbdbddbbadcabbaaadccdbcbbbdaccbccbbdcbcaacdbcdbdabbcbadadcbcdabdadddbabacbcbbdabdcabdcbacabbacbadcabdabacbacaaacbcccadabcddcaccbbcaddacccccdacabcbdbdbdaddcbdccccabbbcbabdaadbdabbdddbdcdbdacdcaddbbacbdcacaacabaacaaadcaabddaabadbcccaccdcababbcdaacaadbccadcbbbacbdabbdbcdbadcbdaddccabdadcbccadccdbdbaccdabbcaadcacbaddaaabdcccbbbacbbbbbdcbdadaacaccbdaddacbdaaaacddaabacddcccbadadccbcdbdaccadaccbdadcbcdbcddddbcabcbdddabbcacbcadacbdadadbbbcbddcccbbdddbdcadbbaabdcbbdbcacbdcbabdbabbadaabcccabddababcabbbcddbcabdcaccccdcddcbcaddaaddcbabcabbdcacdbabbddacabacccddbacaaacbdccdbdbdacdcaadcdcbdbcbbcdbbbddbadacbdbdbdacbcdcabaddabcaadccbddbdbacabddbdcbadcbaaaadbaddcdbbdcbcaaddccbbbbbdddbcdccbbdbcdccdaacacabbcadddabcdbcdbdadbcdabdbdbdabcdcdbdbddbddcdccadbdaabccdbbbaaddcabcdddbdabcddaabddabbbbbbadccadaaccbddcaaabcbccccacbabbddbbdcacbbadccacbbbbbadbbdbcbbddcdbcddaddbcbbdabadccacaadcddcbbcdcbdaccabbaacababcaabaabaccabccccdbbcbabacbbacbdacdaaadabaadcdacccdaacacbccbaadbcbdbcbdbaddcdcbdcbdaccbbabcabaccdcccdacacadcbcbbbabababddcdcdadcbcadcbabaacdcbdabcbcbadcacbddcacddbcdcdacccaabcadcbbdbbcbbccacddbddaccaadcddddbdbdacbbdbacaadbddbcdcddacdddddbdbabccbbabbddcadbcbaadbacabdbdbacdcdacabdbbcacccccbddabbdbabbbcbbdbabcaccbdabcddcbcbbadaddddabdcdccbabddddadcbbbddaacabcdbdaadabbdccdbccacbcdbdccbabacddbddaaaadabdababbcababbabdaadbbdacbaadbabbbddbaacdcdadbadaaddacadacdbbccaaaaddbbcddbdbbabbacbbccbaacbbcbbcdabdaccddaccaadabbcabcdbabaccdcbcbbbbbbcdcbdbbccabcccdcccddcdbdadccbdadbccdddcddacbbcaaaccbaabdddcddadddcaabddadbaaccaadacbbacdacbbaadadcbabadcbaacccbdbbcaacdbcbcacabcacbcccdadccdccaadaacaadaddadcdddbbddabaaabdacdcbbddcadaaaccbacbccbdccaadddbbbcddbbabbbdcbbcdccbadbbdbaadaaccddcddcbdabcbacaddbcaadbcdcaaccbcdcbbabcdadadbcadabdaadbcbdacbaadaabdaccaddcabccaacadbadaabcbcbbdadbabaddccacbcadcdadbcbbbabdcacccdacdcacdacddcccbcccadddbadcdaddbbadccbcdcaaacccdddcccbaaaabdbdcdcdacbcdbbdbcabcccaadcbcccccbcbabbdbccbaabadbdaadcccdccbbbcdacddccccadacacabdaccaccbdddadabddcdbaadcdbddaddbcbabbcccbcadbcbcadbdadbabdcacaadccccdccaabddcadddabcbbcaacddbaaaccddccacccddacacbdadabcaacbccabbcacadabacdccbdddcacabddcdacbcaddbdddaaaccdacdccbccbbcbcbacbdbaacaddbdabbcadcaacababbdaabdbbdacccbbddbddaaaadcbbcddbabacdbbdccdbcadcdadcbadbaddbdadbcbacdcabbaddaddabdabaadbdadddacbabbbacdddbddaacccdaadccabccabcddcbbcacdacbbabadcdababbababdbccacadcacaacabbacadbbdaccbccdbdaacadcabbabddcacdbbddbbbcdabdbbccbcdbdbbdbddddadbccacbdbdbaaaababdbcbbcacdcbbccbdadadbdcbacbcbdbdcbdcabbdcaddaadbdabcacdacabbbacaabadcbabbbbcdcccbbbbcdbacaacddccdadacbccabcdcdcdcadbcdaaacabaaddaabbcbacdddcbaccaababaaaddbabbcacddbddddbadaccbcadcbacaacaacbdcbcadcaaccbcadcbaccdaccbdabaadcdacbccabddbabbacbadbcbdacacbbabdaaababcbaaddabadccabbcdbacccadcdcacdacababbdbcdbabddabdcabdcaabababbabaccccbdbadaacbbcaddabaabdadbcabaadacbbbbaaabdcabddcacdbadcdbccbbabacdaaccacacbaddadbacddaccdcbbcaccbddcdaaccadddcbacdbaddbccaaddddcaddcccddcdbbcbbcacbbacbdbddcdcadacbbddbdacdaaaabbddacbccdccbcbdddaaabbddbdadbbdcabbbaaddcabaadbbaabcabbddcadbbbcadccbbcdccdaaabcacbcacddbddddddbbddacabdcaaabcddaabbaccbcadbcadbabaccbdbcddcdbaabaababbcdbadbdacbbbcbddccacacdcddddaddabacdacbbdbdcbaabadabcabdcacccdaddddabdcdabdbdcdcdbbcbaadcacaaabcacbacdbcbabaccaccbccdaacbcabdbcdaaaccdadadbbdcdbcddbcbcabbbdaaaccadabbcbabbdcddaaabcadacaabacddabbdababcccbdcbdcdabaaddcadbacabbbacbbcabdcbcccaaadcbddcbbbabadadbcbdcaadcbbdadcbbdacbcccccbbdccadbabaadcdbbbcaabbabbbbcdddcdcaaadabdababcabbaadcadadaacdbaaaaadcbccdcadddaddcccbccaddcbdacdbbbcdbadbddbcdbbadccdbadacddbdcccdbadcabacaacaadcdccdcbdbbdcbcbcdcdcaaabbcdccadbcccdcaaaacbdbaccaccdabadacddacabccabcaabbddbcbcbdcbababdabaacdabccdaacddbbcabbdbabbbaaaddbdbabcbcacdccbddacaaabdacbacddaaaabbadcdcbdbdcbcdcbcbaddbcdbacbaccaadcabdcaacddbaadacbadcaddccbccacdacbcdbaacddadcbacbacaaaabacbdbbdbdabcacbbcacdaacddbbbbdccbcabdcbaddbabcccdcaacdddbaadaadacadbcdbbdadacadccabdcadccccadbdbbdbcddcccabdcaaacacabbbacdbacdcdbaaccacccaaaaccccdbcabcddaabadbcbaaadbbcbbbbcdabaaaacbdcddbddcdcacddbdbaaacdadadccbcdcaacccbbaccbcaacacbbcacdadadabdbddaabdaabdccdcbabbbcdbdbaacdabaabcccbbacdabbbbbddaadadaabaccccaaabcadbcbadddcadcacaaaacbabccbabdabcccdadccbbdabbcacddbdcaccabbccbcdbdacaccadbcdacadbdbcdbdbcaaccddbaaacdadccdbbbcbadbabdcaccbabaadadacddbacadaaadadbbccaccadcaccaaaabbdaacbadcdbabaadcbabdbcbabddcdadbbdcbdaadcbbbcccaccdaaddaadccbacabdcbdcadacdcbaabcbcaadaccdddaabbddacabbacadcadabcaacadadcbaabbcbdbbaadaaacadbddaacbbddabdbbaccdbdcbaddccbaadacbdbcdaadbccdbcbbcddbcdbbababbddbbdddabbaaacadccccdbaddcadacddbcdaddacadcabadadacbccabbcbbdababcddadddabbdacdaaddadbbcaacccadbadddadcddacdcbcacccadbccdccaabdcdacbcddcabbbcacdaaacabacaacbacdbdadccddbaadbdcdbcacdcabbbccadccdbabaccbbdcbcabadababdabcbcdccadabacabbdcddaadcdcacadcaccabadcbcdcddbccbdacabacaaabcaacbbbccbdccccadcbcacacdbbcbcadbcbdadcacddaaabccadabddcbbacacaabbcdbbcdbbacadbccdcccbbdbbadbdbcdaababbbdbbddbdddcabdaabcdddaaabaaaabccccdbdccddccadbadaddabaddbabacddcbadcacdcabbadaadddacdabddbbcdabaacacbadadbaccbcbcbadbdcdbbabcdadddabadcdbadcacdbacadcadcdddbbcadabddacbdcadcdccbaccbdcdcbbadddbaabdabbbdbbcbadaacacaacadaaacbdbacdcccadaacdbabdccdbdcddabbaddbddcbdadbccdadccdbbcabacaaadcaacaadacdcdccaaaaccadbcaacdcbbddcccabbabcdbadaaadcacadbddddbaadadbdaddabdabdcacdabacabcbadadcaacbccdcdcdbbabaddbcadcdadcccaccdbbcdbaadcdbbbdcbccacdcabbddddaababddaabbcbdbcdcabaacbdcacabbccbaccabbbdbbacadbcdabdcacbbccadadddbcdcdcbcbddaaabcabbccadabdbadbddcdaacaccbaaadbcdbbcccdccdcabbacdccaadbbbaaddacbcdbaccdaabcccacbadddabadddacdcaddddbaaddccbccdcbacbacaccadaaccdadaabdbbcccbbcacabbcbbaadcadbcabdcadaccbbcccbbddaadcdaabbbdcadbdcbabcccadccdcdcaabcbaccddccccaaacacdcbdbadccdbaaadddddbabcbbaccabbbcbdacdbbbbdcbbacbbcdddbaabdbaaaadbaddcdcdaacbcdcddccdaddabddbdbadbbcaacbddbabdabbbcbcabaddcdadcdbcddadaddcdabdadacadbbdaadadbccddaddaacacbcbcdbcbdcdabccbaaabbbccdccbadacbbaabdbbdacbbbbbbbadacaacdabbbbdbbcaacdbbbcdbbcbbdddbbdacccbadcbaaadddacdddbccbbbcdcbaacacbcccdcbbbbcacdccbabcbbaddccbccbcbdaadbdabdcdccbccdbbacbdadcaddaddaadcadacbaaabccbdbcbbbadbacabdbddccdabbbcdaabbbbbccdbcaccdabcaddcdaabdcbabcadbaaaacbcadacabbabbcabbbbcabbadccbaabdbcccddcbdaadadbbccdbcaadbbacacaccabbccadbcacbbbdddcbccabcccaabaacccbbbdacdaadabbdaacacbdbdcdaaccacdadcbccdcdcbbbdcdccdcabbaaacbacdacbcadaabbdadcabcabadacdbabbbbbacccaaabacccacdabaadcadcbcabcddbaabcbcabaddbcbdbdbaacbddbaadcacbbcddcbbcbbaadcbacbcbbacdcdcadbadddbaaadcdcbdcbbabbcccbdbadaadccdadcacdaacdcddbdacdcaaabcccccadaaaddcaddaaabbabadabbdbadbdcaacbabdcdabdcdcaacabcaddbdcacbadaababddbadaacabddadccddbdabababcabcacdbccccaabacacdbbabdcacdcabdbabbcbcadaabdbaaadcbabcadddcdabbbcccaacbbbbcabbddbbabdbadaadbbdcdbcccbbddaddbcdadcbbadcddadbaadcbbabaaacdccbbccbcccadacbcbdaccacbbcbaacaaaaadddababadcccbadabccadcdddadabdcababdcdddcdcbddcdcabcaccbddcabacdbddbddbaccaaddbdddabbcacbccbcaddabcbdcacdddbdcaaccaacdaadccaadbaaddacbbacbaaacbaddbdddadbbabaacbccdbccacccbcaaadadabcabdcdbbaddaddbaddccdbdbadacbcabbbcddcdbdacdcbadbdddcadbdcaaccabdbbccddadaabbbacdccabacabaaddabddcaaacdadbaaaabcadcdccbccbcdcccacbdcbbabdacaadcbaaadbdcbcbbabccbaacdbdbbdbcabaadadbccaadaddccbdabdccddadcbcbaaabbbbddcbddcbdbabcbdaddcdddbbcbaaacbbbacbcdbcdcbddcacadcdcaaabadacdacbacbbbdbdddbcccbdbbbadacddadaddbbbbbcdddcbcdbcdcaacadbdcadbcabdbbcdddcbdbcbadabcbdbbcbbadaccccaadacddbdbbbcddacdadcdddbbbacddcbadbcdcccbbbbabcdbdabdcdbdcbbdababaabbabbabcdcdcaccdbdaadcbacaacdadbdcbcbbbaabcdacbcddbbcddacdccacdddcbdbdaaccbbdbacbbdacaadabbdbdcaaddcdccabaabbabddbaaabbdaccdbaddacbbaaacccdcdbdccacdaaabaabaaaddacdcdaabcadaacbdbabbadbaaddbacbbbcdbadccaccbaccdbbccdadaaabbadbbcbabbabdacddabbddccdccababcccdcabddcacaaaababaadadacacdbcccaacbbddaabcdabaccdcbabdcababbbbcaadcddcacadddddbdaddadbddacacccdccdcbddccdcddcabcdabdabbbbbcbcabdbddbbabaaacadddadbdaadccaadcabcdbaccadaccaccbaaddcbdbabacdaaddccacabdccbdadbdbccdddbcaacdabacbdacbcabbbbcacaaaddddbdabacacddcbbdacdcaabbabdacdcdadbddacdcdabadcdcbabacbddbababcdccaaacbdcbbdbdbdcbdbadabcbddbabaccbadcddccbbaacddcdddcbcbadabdbbbcaadccadcbacacbdbbcdbacbbddbaadcccadddbbdbacbddabaadabbadccdddbdaaacabdccbacdaababdbdccbdccadbacddbababcdcbaddddbddcbcbbadbcbdacadadcdcbabcaddbdcabcdadcaaddbccccacaddabaacdcabacccaccbbbdcddbdbaccddbaadbbdaaaaacaacbdbdaacacddcaddbdabaadcbcabbdbccbcbcabdddddbbaaddcccabdacddbbadaaabdbaccabacaadbcabbdacaadacccaaaabaacdabbbcaddcaaddcbcbaabcdbdbbcadbdcadccadadcccdabadcbdbbbaabcadccaacaacdccbbbddaddcbbcdddaaadacdcababacdadabacdcdbaabaadbaabdcdbcacccdcadccadbadabccacdbacdacaacdcacdabdbbcbcabcadbbbddcabdabcbbcddabadbdcababddbbccdadccbcdccdacbcbccdaaaddccdabbaccabbcbbabbbabdbbbddddadbcccdbdacadbadacccaaacccccdbbccdadbbdaacdbdbbbcacaadacbdccdaaaccbbbdbacccccaddcaccddbbccdddbbbcabdbaadacdcacdcadacdacbdcdabccdbadbdaaaabbbcbcbbdddbcbadbadbadabbddadcbbbacccbddccbbbddabaaaabaadcabcdccdabadadddaccbcbdcadadadaddcbbddccabbdcdadaadcbbcbcabdbbabccdcbaabdaabadbccbbbddbcabaacdacbacaccadbcbbdbabcdddddcacadbcacdacacaaacadadddcddbbdbabaddaddcacddbddcabccacbadacacdaccdcadcadaadcadbdddaccbdbabcbaaaabdcccabcadcccbdacbbcddbdbadbaacdababcdaccaadbabbbadbaacdaaccbbbcaaaddadadccbbbdddadcbdacaccdbcccbcddabcddacdbbdabdbaddddcdbacbbdbbdcdcbccdacaadcddcaacabbaddddaaacacdabcacdbccabaccbbdabbbcbdcdcccddadbcdadbcdcaddbcbdabbbbadaabdbdbaadaccddcdcdabbbbdbcaaddbccbcccdbabdcaaccdbccbdbccbcbacbcdadcacaacbabdaabcdadbcdaacabbcddbabacddcddadbbdadddadbabaabbabdddcbabaccbbaabbddcbbadcddbaccbbcaccdccddbbccaacabcadbacdabcdcdcabdaabbbaccaabdcbdbcdbbbaabcddbaccacbadcbcbbbcbdaaccccbdddabbdcbadbddadbdddcacccacbddddaadccabacadbbbbcdacaaabcbcbddadcbadbbadadcacddddbbbcaacdcdcbddcbcacbabadacbdccacdcbdbaabbbabccdcadddbdbaacbdddcdbdcdaadcabdacdccacdbddbbaaaaccbbcbddccdbaaddaacbbbadbadbaddddbdbccacbbcdacbccaaaabbcbcadaccabbadaddaabccddbdbdcabdaaacacaabccabddccccaaacccbcbdccaacdcabbbcdabdcaabdbcdadabbaddcccbcbcbcdbccacbbbadbcdacbcdbccbdabdacbacadabcaabbcdabcdcdacabdbdcdadbcacdddccdacbdaddcdbbcbbdbbdbbbaadbbddaaddabbddbabcdbcabcaaddcbbbdbbccabaddddabbcabdbbacddbcabddabdcacddcdbbbbccbddcbbbadadccbcbabcbbdbcccdcdaadbcababacbaddaaaddcdaadacddbcddbdababdcdadcacddbbdaaccdbbbaabbbbcabdbbabddbddaabdadbddcdbdbbcbaacbcaccdacdbabdddbdadaaaabbbbdcaaccbddbdcdbcdbbcacdacdacdacdbddaaccdacbaaadacaadbcbcbadcaaabadbdcdacaccccbcdadaddacdacbacabccbabbaaacdcabdbcdccbdadbdadaacddaadccacabbddaddddadbadacbcbddbacdcdcbcadbcdadbbccabdddbcabdcacaabdaddcdbadcbbabcccacbacdcbaabbabddccbdcbdcabaddbadbabbbaaddbdddadabdadbbdbcdaacbabcbddbccdcbacccabdddaccabbdccccdcbddbcbdccadccabbcddaadccbdacbdadadcbcbdbccddcaccbcdabbaadcbbccaddaadbdddbadabdbbbdddccaabbdcbadaaabbaddcdbddadddadaabbcabbdbaabdaabbdccddabaabccbcdabcccbccbdcdddbddabcbbccccadcbcaddbcadcdbcadadacdcdccaaccabcaddcaababbccadacddbaacdabbbdbadaacbddbabdcdbdcddbacbabbadacadbdaacbabccbccbabadabcbacabbacdbdacbcbacbabdbbabdbcbdbdabdddaccccabbdbdbddcccbcbadcbbdbcdbccdccdbdbbabdccacbcdcbcdbdcaaddddbbcabcddccabcbdcacdbdacdacadcaabacbdacbdcddaaaaadacddcbadacccdbddacbdbabbcabdcccbadccdddbdcbbdbbbabacbbcbbadbcdabacdaccabcbcabcdadbaddcbcdbddacdcddcddcadabbdaabbdabbacdaabdbcbcdcdcdcccccdbabdddccbabbabadbaacddbdcadbadaddcdcbaacaacaadbaadbbbbbcababadbbaaaccddbacbacccbdadaaccacccbdbbddbaacbabacdadddbdbaadbddbdcadbaccacaacbdcdabcbbdddbdaaabcbcabbbdaadccdadcadabbcbdccdccbbdbcadddcadadaccdccaccbbbdbbccbbddbcaccadbcccbbcbccdcccbbdcdccabadcdacbcbbbdcabcdadadcbbaaccabdcdcadbacbbacbaddaddbdbbbbcbbcbaadddbdbdabacddacddcdaadbdcccabdaddcdadddbbadccbbbcdbcaccbcbcdaadbddccdbcddcaddbbaabbaacccabcddadbcddabddbacbcbdbccbdabacdcaddaabdcbbddcbadbaacaccbbbbacadabbdbcacbcccdbacacababcddadadbabbbbbccdbbcddcbcbccaabadbcbdbbccdddbdaacdaccddabdadbbcadccabcccbcacabddcbacacdcabadaaabcbcaaaacaabcccbbcbcaccaccadbccbabbabaabddddbbbdacbbccaaacbcbdacbbadbaabdabbaabcbcbabbdbbbacadbdbdacdcdaabcbbadbdbccabcbdcdaadddacacbccbbbbccbcadabbbcdbdbccdbddcbcbbabbacddbcbadbcddcbaaabcdabacdbccbdabbacaacbaccaccadbddcdacabbdcaabdaaabbbbbaaabaddacabdcdcbbdbccaaacbaacddabcdbccaaacacaacddbbcdbadbdaddacdbbacddcccddbbbdaddcaababbdbcddbbbcccddbbacccbddabbabbcbbbcddbadaabbababbcbdcdcbcbdaadacdacaaaddaaabbcdbabacbbbbcddaadacbdabdaabbcdbdaacabdaaaacacaddccbcddbcacbbccdccacabdcdcccbbdbdadaacccddcbdaddabcdabbbcbabadbabaaacadbbaccadddadacdaacaddcddcddbadbbdbbbcbdddbbabbdbaddcaaccbdcdcdbcaadbcdcbbbdbcacdccaccdaadcadaabbdcbadddbabcbadbacddbdccbcabcabdcdcdcbddcbddbabddbbabababbbadbdccdadbcdbbccdbbaaaabccbdabaddacdcaaccaddbdcadbacdcadbcdcddbbaaccddcdaadcbcbccaaccccdaadadcdbcaddcccaabdaccbbbddccbadbbdbcddbddcbbcbcbdacdbcbdbaadbbbcacddabdcacadadbabdbbcbddaacccaccbcaddbaadcacdbbabcdbdbcdccdadbadcdabacadbacbdccaddabbaaccddccdabdbbccbccdadcaabdbcaabcbbddabaccadccdccdaaabacabbbbadbdbcabdadadcadbcaabdaacbbaccdcdaacbacaddbcabadddadaddabaacadbadabdcdbbcccbbadbccdcbdaaabcabdabbabddbbbdacbacdbdbbccbddacbbdddbccdddbddabdbaddddccacbcbddadabbbbbbbacdbcabdaabccdddaabcaaaaddbbacaacbcddaddacaccaaaacddccadbdcdccccbbabbdccdddabdcbbcaacabcabcabdbacbdddadacbbacdabbbcbbbdcbcdbcabcbaddbcbaacbabbbcddcacdadcaaaabbdbdbbccdcbdadcaddcaadccaddbabbbbacaaaddccbaaabbcccabacbdcccccacadbacabdbbabcbddcbdbcccabacccaacbcacabccacbbdbdaaadddbbabdadcbdcdccaaabacbadabbaaadbbbaccdadacdbdccbdddbdaabbbdacbcbdcccbdbddcbacbacccacdbacbbddaaacbabbabcadccdbbcbddbabdabbbacbbabddacbccaacccabcddcccdadddbbcabdcaaddabacadaddadacacddbabbcbaccabdcbdacabbbddddccddddddbdadacdbaaacbabcdccdbddbcaaaadcbbcabcaabdbdcdacbbacdddddcbdaccdcadcaabdcbaccadadabbacdccbabcddddbadbadddccaabccbaaadbcacdaacbbbdcbaadbcccdbacbadaacadccabcbdadbacacbadacbcccacdcacbabccaabbbdaabbddddbddabcddaadccdddddcbddadcabbccdbbdbabbcacaababbcaabddbcbdacdcaddccacdcbbbcbcdbbdbcabcadacbaabddcadcabdbbcaadcaaaaadaaccabaccdbcbaccccbacbdcbcbcaadaabcbbbaacabbadacbadbbaabdbdabcccabbcddcbaaadbcbbaabbaacccacadbbdacdbaaddacabadccccddccbadcacbaaaabccadcdcbadaabcddcbaabbdadacdcadaacaadbacaccdccbabbddabcddaddadbbcdacabdccccccdbddcccadcabcbcadcabbdcdabbabbaddcdadcbaaccdacdccccdcababacdddadbdcbddadadbbcbbacacbdaadbabadabbaaadbabcdbdcaababbabddcbbdbcbaccdadbdaaaaccbaccbdccacbacddcabaabbddccabbdbddcadbddbdbdadbdcdbcbdbdabacdadbdddcddadaadacbcdddacbaaaddcbdcddcdddbdbaadabbddabbbadcddccbaaccccbcbabcaabcbaddddaadbbbabbcaaadcdddbbccbdbbacadabbcabbabacdbbabbcddbcbadbcabbadadccdbbdccaddcdddabcacabaddacadcadcaacacaadbdcddbdbdabdabbbcadadcddaabdbbbddadbbcbddbdacadcbacaddabacdadccbdaacdddaacdcacbdcdcdddadccdbdabcacababdaacabdcdbdcdbddadddcadabcbbcaaddcaaddcaddbbddaccddddadccaabaadacadcdbbbaaabcaadbdaaddbcbbcddbbdbbcdcaacbddbbaddbadadbcbadabbdabaabbcaddacbcaadbdcdcdcbcdababddbbdbdaddcbcdadcddcaacddbbaadbcdcacabdccddbaadacbbbaabbdbacbadcbbdadabdbcbccabcacbbcbcaacdbcabbdacaaabcbadcdccddcbbcccccbaddbaddcdbccbddcccddddaabdbcaacbacddabbcccbbabbdbbdaddbcbccacbbdaadbcdababdcdcbdbcbaadbbbcabcaacacdbdcadbdddcabbabbdddbcdadbdccbbbacdbccbdddccadccbbbbcbbacdcbddaddbbcaaddcccdccdbcbbacaabacaaacbbdcaadabcacddbdadccdbcadddcbccacbbcbccddccccbcddaabbcabbdacbcbddaddaddccccbdcdacbbcbdcdcdcdbcbdbabbdddcbdbabbddccabbcbdabccaccabcbcdbdcbacdaaadaabacccbacbcdbabaacbbaabcbddcccccacbccdcbcbacdbaccdcaaaaacdbccddccacbcdaabaacbabdbbcacdaabdccdadabcddbabbdbdadddcdacaddbbcbbdbdaccccdbbadabaddacdaaabbbaaddccbabbacbcadcadddcadbccaccabcabdcdbcaccdababcbbabadccadaabbbacbdbcbdddabdddcadbaddbdbcdcddacaadbcbccbbbddabbcbcaccccbabbdbacdcdaccdcccdddabaaacbaadbadadacaadccaabddbaddccbcaadcaaabdbccdbdababcdddbcbddddbacbcacbdacabddacbaabccaddccbdbaabdbaddbdddcccbbadcacadaabacdccdacadbcbabcddcaaacdabdadadbdaddcaadaccdccabdcabcbdabbaadbaabcaaddbdaaddcaddcdbcdccbcaddbbccadccbbdabccbbbcacdcbcaaddcbcdadcdbabaaddbacccababbccccacdbcddbdcaaabdbbcdcabcdddddbddcdbcbdcdddadbbbcabccbcacddbabbddddbaabdaacbadaaddaddcaababaaabdcbccbbdcdcbcbdbbdbbbdbaaddbaaadacaacbbbdcaddcadddbbacddbbccbdabbbccccbabbdcdabbabcacdddbcabadbcabaddbbabbadbaabcbbddbcaabbcbaabbadcbabccbcbdaadccaaddadbcddaccdcbabbbbabbbbbbbbacbadccccbabcbbbdcbdadddbdabacdacabcbdbcccabcccadbbdbdbdbadacbbdbbccbcbdddcbcbdcbcabccccacbcdddaadddcbcacccadbacbcadbcdacbddbaddaabbaccdabbdbdbbbacbdbacbbadcccdcacaacccddacbdacadbdaddbdcaabbddcbbacddadaabcbccbdaacabccdcdaadbabcabddabaabbdabaacbccbbacacdccbccdccbdaaddbabbbdbcbbcbdcdabdccccddbcabacabbadccbbaaabcbbbcdaabbcbcabdcadbccaddcdbcddbcdbbbdcccdcacadacaaabcddabbcdabddcbdabcabadcccabbbcdcccaabaaddbddaacdcdddcbcabdbbcbcacacdcccbcdbbbbdaddaccbcdbbcbdbddabbaccbabbbacdcccbacddbadbcaadbcdddabcdbccbcdddcbcddadcdbcddcddbddaaabacbacacdbbddccbdcbdcddababacaccaacdcacabcbddadbbcbcaacdacdacccaddbccdbadacaadbcdccbbaabacbaaddabdbbadbaabcdaddbbabcdcbdaccdddddbcddddbdddbdcaaadabcdcabccababdbbbcccbdadabbdddcbcacdcccbbcdccdccbabbdbbbbcddbcbcaccdcbbdaaccadbbddcbabcccdbdbddbaddaabaacacaddddaadaddbdddcbbbbbdcdcddcacddddddddbcbbdabbdbabbbdbcddbacccacbddcaacbdbaadbbddcabcdabbdbdaabbdaddcdcbbbdddbdadbbccaccdbbdbbcabdbacaccbcdbbdaacdbdadbcdbaccccdcaadacbdddcabddaacdcdacaaabdacdbdcbcbbdbcccabccdbaccabdadbdadaaabacabaddadcccadbaadddadababaacdbdcacccaaddbdbbbcdaadcbccabdbbcadbdabaccadcabcbaaccacabbbbbcdbbacddcdbbbddbacadacddbabadcdaaccaaacbabdbcccaccbcdcacaabcbdabbaadbdcadbcbcacabbcdbcdbacaddaacdaabcdccccdccdacbbabcdcacbbbabcbaadbddbdbcbdcabacddbabcacacbcbddccadbbcccccdddadbaacadcdddbcadcabaadcbbbdcadabbbbacbdbdbbdcaabbcddbccddbbadddacddbcabdcccacacaddbbaadababbaabbbbccaccabaddaaddcbdccaadcccabdcbaaabbcbddabaccbaccaddaacbdbddaacdcbbadadbbabbaacaabccbaabcabbdcbcbcbbccadaacbddcdcbbbcbdcccdabcdddddcccacdbbddbbbdaacdcddabdabbaaabbbccdccbdaacabccbbccddcccacbcaaccbddcddadabbdbcddbdcacddbbdccaacabbcdaaaabbbbddadbcdcbccdbaddddcdcbadccccdbcbddccbcdcabbcbdcaccddbbdcbabbabcdabbdcdabdcabdabbcaaabdddaababaabccddacdbcccabaddaacabcdddcacadaccadcdcacbaadaccddccacadbbbddbcdabacbaddcbbadacdaacbdadbbabddbadbbcabdacbdbcbccadbbdddbbdddadadaccdbcbbcccacbbcbbcbccbddcabcccaaadbbaabbabcdabbdcdadadababaaaddbdbbaadbadbdcdacbddddadaabcdccabbdcccbacdcdcaadbcabbccdaccbabccabdcdacbaaacbabcacdddcdbcddabdbbcaddcdbddadaabbbbcdabadacaaabbcabacaadacbbabccdddaaabddcdbbbdcacbabadacbcddababadcdbbaaabadaddbdaacadadcdacdbbbbbadbcbdacccbbaaaaacaadccadacddacccddcdbdaabbccccbbacdacaabaababadddcdaabdcbcdcdbbdbdccbdadcbcadbbcacabbdcbaaaabacdbababbccdbdbbcbabaccdddbccadbacdabaacbbbdabdbbdbbcbaccdddcbdbbcdabaacabdcbbcbaabcdaadbddbacaabacbbaabcaddbaabdaadacadcdadbddbbaadcddccabbcadaccbaadbdbccdccdadbbacabbadabccbbbabddbdcacaabadaabbcadbbadbdaccaaccaabcaccacccbcbcdbabdcaddcacbbbbdbbcdbcaacabaddaaacbbdbabbcbccdcbcacdbdcbbdaaccaccaacacdbcbdccaccbabdcdddbbacbdbaaccbdcdcccaaabccabccbaccbbdbdaacacbdbbbcbacbdcddddcdddbcbdccbbdcbacabcdadcaaadaabdabbcadcbadcdbbdabaacbcbbadaddccccbacacbcdbacddcddaaacbbdbadaccbbcbbccaaadcbbbbdbdbcdbcdaddaabbccadacaaccdbbababdaddbcabbccadbbdcabacbbacaacddbcabcadcbabdaacbcadbbcbcbcabdcabbaccbbdadbbacabacabddaadcbacdbcddbcddbbcadadccbabddbcbbccbdbdcdaccdbbcbabddabbbdbaabbdbabcadadddaacbbacacabbdccbaccabadddbdcbdbddccdbdbbdddccacdbadcbdbdcadadadacdcadddacbaaabdcdddbadbcbdabbcbccdcbaacdcdbcdbbbcbbcbcbbadddddbdccababbcbbcbddbbdadadbdcbdaaabdbcbbcaaadabdcdddddbcbbbcbdadbbbccadbaadbdddacccbcdbcdbcbccbcdadaabccddacababbabbdcbcacdacbaaaacdadcdcbabccbacabadadcabddcdaacdcdbcddcadccdcbdbbdaacdaacdacadcccacdbacadacdabcdcdbdbddcbabcdaaadddbcadbcccbcbcbabaabdaddcbdabaccacccbcdcdacdaddbcddbcaabbacbcabdaabcddaccacbaccadddaddbbddbcaabbcccbbbccdadaadbadbcbdcaacbdaadbacadadcadbadbdabaccbccaaadcbbbbacacacadaaabccadbacdadccacbbcdacbddbbddcabcadaaccbbdcdbdbdcbbaacacbbbbdcbccbbbbbacaabacdbbdbcaacadbdaadbdcdcbbcbbabaabadaabcaccdddadbaacdaacbdbaaccddbbdacdaacdcacdacbdddccdadbaaadbabdadddaddaabddcabbdbccaaaddaababcbbbddcdaddcccbcdbdbddcddcdcbaaccacdcbcacbcbccbaaaddccbbdadaabcbbdbbddccabdadacbaaabbaadbacbdccccdaccbdbdaddbccbdbabbbbaacbbadcdaacbbccdcdcddcbdcacabaccdddcdbbdaabcdabcdbdccaaadbbcdccdacadcbdabdacabddabbadbdcbadcadabbbcdbdabccaaaabcbcabcbbacdcdcbbdccdcacaaccdbbccabcdbaadabbbbadcbdbabbbcbdcbcdaacdccbdcbaacdacbddcaccdddbcaadcaadcdbddcbbdbbabaccacadaaabccabaccacbbaaabdbadcbcaadabbbabcdbcaadcbdcabbbaccdbbcabbdbaccaccbdbcbadacddaaccdacddacacbcdcaadccddccccdacabdabcdddcbbdaccdabacbcccacababdddbdcbaabbcacdbbacbdabcabbbdbccacddbbadbbacdbcbaacddcdbdcadbccdcbdcdbadcdcabddbabdcbbcaadbbacbdddbcaccaabbabbacabcabcabcacacddccbcbcbbcdaddadddabcbbdbcbbaadadbacdcdcdbbaadcdaadacdadbdbdcbcabcacabcdbaaccdadbabaaabdddadbaccbdbbbbddaabbbabdbddbcbcacbbabaabcdbabdbadccadadabdacdcbdadbbdbddbccdcabbbaccabcbababbddabbaadbcbddcdddbadcbdbbbdadaccbbbaabbcdbaacabbcdcbcbcbcaadccaacdddbacbccdacabbdddaaadcbacdccbdbdcadbddbdacdadabadcacaacdccccdabacababaabbacdcccadbdacdbbbcdadcbdaacbdacbdabcdbccbcddabdabaabbdabbdbccbaccdaaabaddbddbcacbaacadcdbabbdbcbcbccadabaaabbdbdbcdabcbdcacdcdbaaacbaacdaccbdabbcddbbcaadaaacaaacdcadbdacaadcddabbddcccadcacacbbccbdacadabdbccabbcdbbddadaaccdaaddcabdcabaaaddacababbddacbddccbbcdabbcccdcdcaaabddcddcbaddaaccccdbdbddacaaddaadaddcaccdadabaadabcbdabbbabddcaababcccccddcdccdcbdaccdcbbddadaadadbdcbbabbdaaabbcbadbabddbcbcdadcddcbaabadacbacddddcbadbdbaaadccddaaacdbdcbdcbbbbcdbddcdabbabbbcaddadcbacbcbabccbcadccacbaadcccadbcadacabbadcaccdbbdbcbddacacdabcadaaacddbcabcabcacbcabbccddccddaddabdaadcbadaaaabaddddabddadcacdcabcbcccbcbcbccacdbddadccadabbdcbdcccdaacaacbbacdcabaccddcbcbbbbdaadccddbbcbcaccccddaabcdcdbdcadddcaabbacddabbbacccaadbbdbcddcbbbcbacaddccbdacdadccbdcdbbdbddccacdbbbaadabacdcbbbadbacaadddddbcdbdccabbcccabcbccddddacdcadbbcaddddaabbadadbadadcccdbbddadcbdbbbccabcdababddbbaaadbabddbbcdbadcaacdbdcadaadbcbaacbbbbacaacaabccabdddabddcbcababdadcbbddccaadbcadbabcbdcaadbcdbabaddbabbadbdbacabdbdacbacabcdcddbcbbdbaacbbcdbbbbdaddcadcababbcdbcadccdadbbabdaaadbdacacbbcaacdccabccbdcabccaadcdabdcddbbbccbdcdcacaabcdcdcacbbbcbabccacdbdbddbdbbddabbdacacabcdcdcaaabacaaccdadabcbdccacbdadabccbdbdddbcccaaababbaaccbaacdcbaabcaaccbbdcccddacdbdaddadbababddacddacbbbddbcadaaadabdaddcbbbadcbadabdcaaabacababccbaabbcccdaaacbaabcacbabcbacaddaabbdddccaaaddcabcadbbbbddacbddddadacdbbadcdbcdcaaabdacbbcbadabcbbddcbcadcbdcabccabbdbddbdabcccbabadacabadccacbbdabbbcbcbcaddacacabdccdbaaaadadcadbbccaacbaaabbcbbccbccdcacdbdabddacbbacadcbbaaccabbccdadbcacacbdcbcbbbaddbabddadaacdbbbaaabbbbcbccbcbadbbcababbbaccddadbabaabacaaaccddbdbabdddcdbcabddcdcdbadabcbcdabbdbabacaccbbbadccdbcbdacabbcadccdbabdbcabcdbabccabbcdbbdbcadabdbdcbdddcbcaadcbdcdccbcddcbccbaadccacdbcdabdbbccbdbddcdbabddbacddbdbacdccbbcccbcaaccbdbdddcbdccaadccbabcccddcccacabbdbbdcbdcdcadbbbbaacabdaaacbcadcddbadadacbcacdcaacddddcccdabccadccbbbdadbccdacaacacbdcaaddbabbbaadacdcbcbccacacccbbbccadabaddaccdadcbaadacbdddbddacbabacbcccdabadadacdccadbaacbdcbabbaacdbdccbacdbccdacbdabbddcccdbcdbcadbabbadababdbdbaacddbddbdbbbbbadcabbbbcbccaadccacacadaaadabddcddbabadcbbabaaddcdabdbabdbaccccacabaadabcaccbbcdccdabcbabcccdcbabcbccdcacacababadddabaaadacddddbdbbadbdcccacbbdbaddaacdbbabddbbaadddccddbccdbabbbbabccbbccaaacdbdcdbaabbcdaacbadaccddbaaacaadabbccdcbabdcbbbabcdccdcdbbadddaadbacbcdacaacadbadddccacaaaddcbcdcdcabaadcccbdaaccdbddbcdbbccdaabccdadacbabcdaccbdacdbbbcbcdddadcadcbbbabdcabcbcddcbcddacdaccdadcbbbcbdbdbcbabcdbacbcdbcccadaaadbcddcbdadccddabbdcdcacadbbbdcccbccacbcbabdccdaaaadaccbbdcdabbcbbbbbddbcbdcbcadbbdbabcaadcaababdbbddbbabadcbdadccabcacbaddbdcbdcdccdcaabccccdaccdbbadaabbbdcdcbcddadabbbdacdccbdababbcbabcdcadbcacbbbcababdbaccabdacadccdcdaacbdcdaacabbbadbcbcbcdacdcccbcbdccccbaaccbcdbccbaadcddbaddaabddbcdabcddcdcccbdcccccdbccabaaabdaacbddcdbaabbccdadcdbddcdccaadbbaacadcdadcdccaacaddddacccbccabbddacddcbbccccccbbcacabdababdcbdcdacbacdbcadadadacddcdabadccdddaddbbdacbbbaadadbbabdaaabddaaccbbabbdcbddaababbccccbdbddbacdcdcbdcbabaabdbbaadcbbbbaadacbdbdcdcbcccaacddacacbbdcccbacbaacbcbaabbadaaadaabbbbbddacbbcadbadbdacbbbcabcddbcaaabbddcccaddbdacadaccbbabacaaababbabcdccabbccbacbaddcacdaaabbbacdbddabbbbccbcbcdcbbbccccbadddaaadbddaaadcabdcabbcdaadbcbdadcacdbaccccdcaabdbacaddaadbdcbbcabdabbbccbcadadabaaddacbcbdbadbdddcdbcacaddaaabddbdbbdcbadcdcaccbbbbadaacccaaadbaabaaccabbbbcbabbdbdabcdcdaddcdbdddcddbcdddbdcbcccabbcbadacaaaabccddcccddabdcccddccbacddaccabcbaadbbcbbdcbaadbbdbcdaacccbdacdbbacbcaccdbadadadabbcaddbbbdbcdcbddadabacbcacddddadcccbdddaaddbaddcdabacccabcbcaaccccdaacdadbcabdbcccbdbababbdcbacbddbcdabcdbbbbcdcccdccddbdbbaaabbddbbacdbabadaddcadcdbdabbdadbcacdaacddcacbddbccabbdabaaddaccaaccbbcbcbbdaacadcaaacaacbcbbabcaccdaadbacacddabccbdacbbbcdbadaabcbbbaaabcbddcaacccbcacaddabcdcbbdcbcdabacdbbbabbdabcdcbccadaabccadaacaaddddadbabdbcbacbdbbbaddddddccddcaacdbdaadcdddbcdbabdcaabdbdbcccbadcdacdcbcabdccccaaaadbdbcadbdbbdccdabcbdcbdaadadacaaacccdbcdbacbbabcbccbdbaababcbddcbcbdabbbcdaccadcccdcaddbaabdcdbcdaaddddddaccccaddcccaaabaabbdccdaadcdbccdbdadbbcdacdacbcbabcabababbcdbbcddadbcdbddaacdbbdadbdacbcbcdbdcabdaacdbadbdcaacaababadaaacbabacacdadbaabbddbcaaadcacdadddccccbbbcbcaccdbcdccaacdbddcccbacadadbbbaabbabdcbcdccbabcdcbccacddaccacbaaacbdbadbbbdbdbdccaabbcdcdbbccacbcaddabbcbaccbabcbddcaacbcbddcaacacbcbaaacddcbaadabbdaddbaddcacabddddaccabdbccccaaacbbddaddacddaacbaccdcabbdbdcaabdcbdbdcbdaccbbcdcabdaadaddbcdbddbbbcddccddcdbdaabdaaccccbdcdbcbddcacadcbccabaacdadcbadbdbcabddcbdbbdacacbddcddabccbbcbbabbaccaabbaacddabacdccccddadbbbcccbdccaddcddadbdbcdccacdaddadbacbbcddbbcdabbdddcaccccdbabcacabcadddcbabcdccddabcdacabcccdaacabcbacdbbcbcbbcbabbacddbaccdadadbccdbadcdbbcaddacbaaacccaacadcbaacbcdabbddaacdababaccbdaabdcadccabcbadbacbbddcbadbdcbabcbdbcccaaabadcdcadbddcbdcccddddcadbdbcdbdbbcacbccaabbbbccdbccabbcaaaabbbcaddacaabcabadccbadbdbcbccaddbdbacdabdddacccabbabdacdcbcbaaabacdbcdabdacdadabdcbacabacaddcdabcadbbbcccbcdddcbbadabddadbbacabababaadcdbaabcbdddabdddabbabbdbdcbddaaadbdbbbacdbacbbddadccccbbabbdcbadabacaaabccdbdbcbbcbbcbdbaccaddccabccbccdbbdbbbacbdbbbcddbdacdbaacccdbaadbcabbaaadccddbdabcabbbdcaaddbaccbbcccdcdcadadadacbacacaaaabcaccabddcdadcabccccdbadbcabbbcdcdcaddcdabdcabdccccadbcdadcbbaaababccddaccccacbcbaaadbcabdcacaaacbccabdcdbcabcbdbaaababadcacbdaddbcdbdadbacbbcbdcaadcdcbdabaccaccdbadabbcddcddbdadaabdcbbbbdbbbadaabdcdacaadddbabdccdadaaddcbabccccbabaccabbaaadbbddbcbdababcadcbccbdcaaabdabbbaaabcaddabacbabdbbbbbbbddababaddbbcbbcaaabdadabdabdddaacadbbdcabbacbcbccdcadcdaacadcbcbbdacbccbcdddaaabdbbdabacaddddddbaddadcdcdbabaacdabdabadcdbdbbadcbcabbdbaabcbadbbdbcbddaadcdaabcccdcbcbbbcabbbcdbadabbabcbdbcacdcccadaadcacbbcddccddadababadddbdcabccaacdbacbabadcadabdcdacdbdcaadddbabadbcdcdbbdacabadbbbbdcbaaaaddcacbdbcbbadcaaabbdbdcabbdabcacdaacaddaabaacabbccadbcaaaaabaacdaacbdbcacadccadddbcadcbcbddbadbbccdadddbdcdbddcccbdabcbcccacadaacdcbcddddbccdddccaddaaabbcbaabcbadbbdbbcdadbcabbcdaacaaababbbaaadabaddccaccabddccbabacbddcdbaaadcbbcacdaadaddcdaaddaabaaabddbadacccdbdbbdaaabbdbbbbdbdcbaddabccbdabcccdcbcababaaaddbaabdbdaabddcabcdbdbdcabccbddbaacbadcdaabccdbbcadabcdaaddddcddadbdbbaaccbdbbdbbbcdbcabdcbbdcdabdaccbdbdcdbbcabbadadddbddbbaddadbadaababddaabcabaadcadcabcabcccabdbabdddcbbadbdcabacdaadcabbaccbddccbbcacdcbdccccccddcbdabdadbabcdbddbccaacbcdabdaaabcdccacbababbacdbdcbddaaacbdbadcbbbbaaaadaaddbcbcbccaadcbbddcacdbdbdbdabaadabbbadcacbaaddbdaadadcdaaadccddcdadabcbcdbdacbcbcdaadbbcdccababbbccbadbbdbabadcdabbbaadcbababdbdccddccbcbcbcbcdddaacccddacabaadacaddadabbcbcacaabccbdadcadbaccdbbcdadcdcaaaddcccacdddcddacdbbdcbccdbdbbcdadddcaddcaadbbacbabaabbdbaabdcaabbcdadcdacbcbdbabacddacacaccddbabbbcddbdadcdccabbbcabcdcadcdadccdbbbbdbbddcddbadaddbaccdbcccadcdacdbbccbbddcbdaaccbdbabcacaabaacbcabacaacaaddbdbdaaadbdbbcbcacaaaccccdbcddacbddccaadabbbdbbbdcacdaaadcacddccbdabccddbcadbcbbddbdaaddbddbcbbcaaabaabbcbabccbddcddbdbdbbabadadcdcadbaababdcccddaddcccbdbacdddcacaadbbbcaaddbcadadadabdcbbbdcabdaaaababdcdacdcbddbdbabbccbdcddcdcbaadbbdabcbcbbbbbbcaddcbccaddbdbbaddbbbdcddbaacacadccbbdbaacdddcdbacddcbcdacccddbadcdccbbccdcccadccaabbbbdbabdcddccdcbaddbdbacdabddcdbacacdddacccbbccbcacbbcbcaabaddbdcdabcadaaabbabddbddddbdacabdacdaabcacbdabcdbabddbbaddabddcddcbcddcddcdbcbdcababbcaaadaaabbaaabccadccaabaadabbabcaccdbdbcdddcabccabcadbcaaabddcbdbaacdbacadbbdcdaaabaadbdbaaaccbdbcbdbdadadadddccabbbacadccaaaabddcbccdbcacbbccaaabcacadcdacccdadabdaadbaacdcacdaccdacabbbdcbdbacdaaccbddbbbcbabbbdccadacdacacdabcbdbccdbcdbbdbbbdddcabbdbadacbcbccaddccbbacddcbdbbcbbbddabbaacabadcacbadccccbbcaacccbaaabadbaadaddbadddacbaccccbcbabcbbaabcdaddddaabbddabacdccddadacdcccbddbadbcccdacddddaabbababbabbcabcaabccbaababddadcdacdcadcabacdaaccbbacadcadadabcdaacaabbdcdcdaacddcbbbaadaadabadddbcbdacaaddddbbbacbadcabbacbdacadbcaabddaaacccbdbdabadcbddccdccdbaaddbbbbcadacbcbcaabaaccbabcdcbcdcdccaddbdadbdaabbcbdaacdcbbccabcacbabccbbcbbabdccbbbdbaabccbccbadacbbbcaddddcbbbdbddbdaccbadddcaaddccadaddbdcdaadcaadbbabbadadbaaccacddcbdddaacaadcddabcacdbcdaadbbdabdbadcbcacabdbbbdadbccbdabaaabccbcaabdbbaddbbcdbabbcdbdcbcbbaccbaabccdbccaaababababdabacccddabcccabcbdbdcbcbdabdabdadacaccdcbbcbaadaddacaadbddcdbbdcabacadaaacbbacbdddbbaaacddcbcaacaaabbcdccbacaacdcaaabbbdcbccdccdbcbddcbcddacddcdacdcaadcabcbcbbcaabaddcadddbaaaacaccdccdbabcbdbbaabbdccacacccadbcaaccabcabcaddbcaadacdabcbcacaddbcaacadacbaddcdacbbdcadccabccdbdbcbdaccabdbdabdcdbbccbacacaddaabbcccdcababdcccccbbcdccccbbdbcdcbabdbcadbcaaaaabdbdddacbbdbaadcaacdacaadcbbacdcdbcccabadabdbdabbbcbacabbdbcdbccccdccdbdcccdadddbdccbdbcaadbacabdbbbbaacbcddadcbdadcdadbbddabaababdcacddbbdcdbcddbccdcbbacdadabadadbdcdbaddbaadcdaacabbcaccddabdbbcbabbadcbdcbadbadaacdcdbdcaaababcdbbadbddbbdbaaabbdacdccaadbcdbbcaadabaacbdbcabcadccacacaaadbddacbdcccadcdcddcadcdbaacabaddcabdccbdccdcbcdaccdabccdcddbcdaaadababdccdccddbaadbdabdcbcdcdaabaacadddababdadaabbacdcccdbadadcdccabacbcbadaccccbddbcdcbaddcccacdbabdcadbddcbdabddbcccdacbadaabdcdbcabacdcdadbcadccabddccbcaddcbdddbddaadcaaadcabaabddcddcddddaaabdddbbbdccbbccdcbbacddbcaacdbdabdccaadbcdddccddabcbacdbabbaaadcdccbdbcdddaaacbdccababbacbdccdadccaadcacbadccbcbaabbddcbcdcbadcddabcdccccadbcddcacbadccbddccbdbdbbbabaddbacaddacdcbbcdbcabaccbccbbbcbdddcbbdcaaaabbadccbbbacdacbccccaabbddcabbadadddacbbadaadabcdcacbacdcddbccbaccdaddccdbbdaddadacabdacdaccabdbcbccbbcddccabddcbcacaadbbaddbdddbcbbdcddadaccbcccaccdaaacccbacddacbaaabcadddbaaabccdbdabcabaacdaaddcaccbcaccbacaadadbdccbdaadabadbabadaddcaddbaaacdbcaabcdabaddbbdabddabbdbccdaaabaddaacbcbabcdbdbdaaadcbabbbabcabaccdbabdaaacababaaabbdcccddabbdabcdcddcaadadcbcdaadacbcdaacdcdbadbabbcabadabcbacdacddcdbcaaacaabcbcdddcabacbcdaaaabcccabccbcacabaaaddbbcabbcaadaacbacdbaddabddbdddacadbdccdcccbcabbadbdccadbcdbaadcbbbaabbdddabbdddccddabdbdbdbacccdadcdaadbbdccabddcdccabddaacbdcdccdaddcddbadcbaccdbaaadacdbddbacdabacacbbaddbdbabbbabcbdbbbcddbacbccadacdacaabdcccbabaabcacddbbcbdbcdaabdbbcbadaddbcbdabbbbbddbabbbcbbbcddcbdacaadbdbcbcccacdbcbacccbbdadbcccbbdaacadcabacacbbadccadadacbbcbadbbdbacdaaacbabacbddcdccaadaddbabaddacdcaaaccdbcbcaadcabbccbdbdccbbbaaaacbbabcbdaaddcdcbbbabaaddabdcddbbdbdaaabcbbcacddccadacdadccddbadbaccbcdaaaacadbcbdcbbbacaaacabdccdcbbdbabcccddaaccccdadacaaadabbdbccbaccabcdabadacbdbddcbddccbdbcdbcbccbaabacbdbbcabdbaadbadbbaccaacddabcaccdaddddbabaaadccdddadcdbcacbdcbcdccdcdcadccbdcacbdbadcdbcadcbdabadacbbdcccbdcdbbcbacbcdcbdbbddccaacaccdbbdbdcabbdcdabacdbccbdacadcdbadcdaaaddbbcabdcdbadbbcbadacaaaddcbbccbabacdcdaadddbacacaadddcbcbccdddddabcadbaaadddabbccabcbbdddcbcbdabdadddbcadbaacabdcabdccdcbbabdaddaadabcbccccbaabbababaaadaacdbcabaabbcbbdbcbbbcbbacdcbbcdabddabcacdacdaacadbacccdbbbbadcccdbbabbbdccbbcbbdcbcadbbcbcacccadddbbbcddccbacdadbddbccabbdcbbbdbbdacbcdbdcdadbdbcbcdabacaddacdcdbbaccdaddcaccdddbaabacacddccdabccbcbdbaadabccbadaccbcbcbacabacbbcddabcbcadbbadbcadadccacaaadadcbababbcabbdbbdbddaacaabcddcbdbbcdadbaccdababdbaadddcdbdacccbadcdbbbccbaabcbdaccbcadcddcacbbdcddcdcabbcccabcbdcdbbbdbaadbdcaccaabdabadcabaccbaabddcdadcbdacadddacdcccaadcdcdcbcbcbddcbdaabaaacacadcdcdcdadababbacbdccdbcdcdbddaabdbcdddbdacbbdadaaadbccccbccbbdddbaabbdcadbacbcdcdbbcdbcacdadcbdbcbcabdacabbdcbaccaacbccabdcacccaaadbdcabcbcdbddcaacdbdcddbbccdbcabbcddaabadcabcaaacbbdcaabbdcbddacadcbabacbaadcccdddcccacabadbdcbbcbadcacacdbdaadddbccbadbbcddabaacaabbcddbbbcdbcdbcadbadddcdccbbbbaaaadcaaddbdcbacccdcddccaccabbbabdbdabadbaaccbddbcdccadbcbdbbbcbbbbaddcbdabdacadadacdbcdbdbdbabcacaadbdcccaabcbccdcbcbcabaadadcaabdbccddadaabbadacdbdabbcccbabddcddbccdbaccbbdadcccbccddbbddaacbcacddacdccdbbcadcabddcadaadabccbcdcadbdbbcabdcdcdccacadaaddadcabdbcadadcbbabbdcabdcbcbbddcbdccccabadbcbaaaaabbabdcdcabaadbaccadbaacdcdbcbaaaabccbddadbabdbbbabacbaccadacabaabbadacaadbabaccacbadabbdbdbbaabbdadcaadccdddcdbbabbdaabadabdaddddcdbadacdbaabcbadbbddcdbdaaadadacaabcadcbbadadacbabaaccababbcdacdadccdabadbbbbaabbbcbaddaaddcbcacdbccdbdbacdabdabdbdcbdadcdabbabbababdcbacbccbdaadcbbabddcadaadcaaadadddbaccdccdcbdabdaaadacdacccbcabaaacddbddcdbcaadaccacbdbbadacddabaddbbddadbbacbbcaaacdaccdabcbabcdacabbdcaadbdbbbbbdbbabdbccadddddddcbdcddcbcdcaabbbddccdbaaabbcadcdaaabadadacadaccdaddddacbdabddbabbcbdccacbcacacbcccdbbabdcbaddabbcdcadbcaddddaacadccdbacabbadcadbcbddcdddcabdacabbdbdbaadbadadcadbadadbbddbccddddaaddccdbacbcabccaacdabccabdcdbcbbbdcbadabdbdadcadabbaaddcabccbbbdadaacdbcacdddaadcdbddcadbbbcdabbacccacbadddbdcbcaabbbbbadcaabbdacadaccaadadbbdddabaddbbbacbdbcbbbadcacdccadadbccddaababccabbddbcadabddbaaaabaacacbadbcbbdddbddaacaabccaabadbdcdacbbcacbbcbddaacbabbacaddaccbdacadcddbbbdcdaccbcabbbabbadaaacabacbcbdbcbdbaccbacbcbcbdbaccdddbabccbbacbcbdcdadaaadcabcdadcccbaacdabcdbacaadabcdabadbcdacaacdbdddbaadaacbaccddaababbdbbbcacbdbabbdabdbbadbadccccdbaacdcbcdddcdacaacdabdbbaaccbbcbdcdabbacbbbcbaaddbdaccabaabbdaacadabbbdddbcccaacaadcdddacddcaabbabcdbccaaccacbcbdbaddabaccccdcccdbbcacdbcdddabddadcabbaaadcbcacdcaaccaddcbbaabaddbcaabdcdccdaabbabadaaaacddaadbcbbaacdaabddcaacaaaabbbadcdddaababababacdadadaadccabbbcbbdcbdaabcacababcaaabddbbcdcaacbdbdbcbcdbddacbacbadbddbaabcbdbdbcddaacadcdddacdabbcbcdadcdabcdacbbbcacbcbacdaaddcbbaadcacbbbacbdbacddcdabdbcdccdcbdcadcbbaaabbdadccadddabddaccadadddaadbdaabbdbbbdbcdabacdaaddaadcdaaaccdaaacbcbbccbbdcadcdcbabaaddaabacbaddbabdddbadbdbaabdcbbbbbbcaddcdaaccbaddbbaccaccadaabdabbcdcccaabbcdcadbbaadcdbcccaaddadacbcadcbbcbcdbddcbabcdaabcadbbabacdabacacaaaadbddbbabbdccbcbbcbabbadbddbdbcaccdaaabbabbababdbbdddaccbdcbdccbbddbaddbbddaddacabdcccdadaccaaacbcddcabccbdcadcccbdaabdcbdcbbbbacbdabbdcbbcddcdbdcbcdcbbdcadddcbadaddcbcabdbbacbbabadbcccadbcacbcbadaccdcbbaccddccbbaadcdccbbcddcabcbaacddacbccdbbbabcbcacbcdbcacbddacaacdccbcaaaddcddaacbcbccccaabdbcdbbdbababcdbcdcadbbdcacdddbccdaaaabaacdbaaabdadddbdbdcbbaacaaacbabdbcdccdcdbabacbadaaababaddabcbbaacccdcdbabadcbacdaddbcacaabdbdddcaaacadbbaababbcadddcbbdddbcbbcbcdadcbdbacccdccaadabbccdbdaaaddabaccbcacbdacadacdbabacdbcabddbdcaabccbdacbbbdbddbdabcdabbdaabbcaacbcdbdcddabdadbcdaddaabacbaccbcabdcacbdaaadbdbaaacabacdaabbbadccccbdaadadcbccabcacdccddbdaadbbadabdbbbaabaabdaaabdccdddbcbddaaccbcbcbabadbcdbdabacbbcdcbcbbcaaacabccbcddabaccccbcadadaddbcdcccbddaccbbccdbbbbcbacbdccdacabbdcccbbbdabccccaddcdbabbbbbabbadbbdcabaccabbddccdcbcdaaccbaadadbaabdbbbadcbcdcaaaacabdbdddddbdaabcdddacacdbbbcaaabdcdbcdbaabaccbccacddbcdaabdabcdbbdbdddbbbabacadbabccacddacdccbaabdcccadacbcccccadcacdccbadcaccbbabdbdcbabdaabddadcddaaaacaddadcaddcaddddaddccdbcdaddbacdaabbbaacdabaccddacabcbcbcbaaabbbbdbadacacdbcaacacdadcbcccabccadcbcdddccbadbbcdadbcadabbbcaccacbbbdabbbdcbbbabdbacccbbcdddcccdabbaaabdaacddadcccddbdcddbcbccbdcdddbbacbddabbcacaadcbccaabccbabcdcaadbdcdcbcacaaaadcdadbaccbdadbcdacaaabdbcbcaddccdabaddabbbadadababcadaccabcabadabdddbdacdccacdaacbddddbaaabdbacdaaddabbdbaababbcaadcababacbcaacbcacaccbbdbccbcaccabbdddbcbadbddbbacbcbbcdcabbdbcacddbccbdcbabbadbbacbdcdbcdaacbadbdcdddcddacacdbcaadbcdcdccccbcbdddcbccccdcabbccadcbddabaddababadcbdddcadccacddcadcadbbdccdddcabdcbbdabaddcbdccddbcccccbbccdaccdccaddcbcadcbcabdaabbbbccbababcadadccddcaaccabdcaddddaacbadcabddbabbccacddbcbdbbcacdbadccddcbbaccacbcbacbccacccabdaabaabcbbbdbcaaadbbacdbadcadbbcadcbccdbddbcabcaabaabcdbacacbaddbbdcdbbddacaacaccdbabccbacacddabdaccdabdddaababbbacbbdacbdaddaabcaddddacdabbcdaaddabddcdabccdacbddaccdbdbbbacacbabdbdaaacdabbdbdccbdbbbcbdcdbbdbaddadacdadcbaadbcaddcdcbabdaaabcabadbccddcadaaccbcbdcddaddcbaacddcdccccadccacadcdbacacdcbbbcccbdadcddabddcbcbdbacccbdacbbdadcbacaccaadcdbccbdbddcdcddccbcdcccbadadcabbbadddadbccacadbccbccbbbdcaacdbaaadadabaadbcbaacbcaacbcabbacdabadbbaabbdcbbbdbdadccabbcbdabdbddccadddbacdbdcddcabbdbabaaaccacccacdaddcadcdbadccdcbbaccabadbbbdbadccdaaddbabdadcbccbbccdacadbbabadabadbaccbabdaacacdbddcdbbaaddddbdabbaddcbbbbccddccdbbbdadcccaccaabcccbdbabdbbccdbacddcccaaaddcaabbcdcccdaadaaadaccdacacbbcdbdcddccdaccdabcdacbacbcadbcbdbdbcbcbdbcabdaababacbdbddccadbbcabdbbbaabbbcacbdccabddbcadcdbabcbbaccdbcdbcaacccbbcccdbdbcadbbdcadadbdcdccacbaaadcdaccdbaccccbabcdabcaccccdacaaddbdcccbcdcbbacddcdbadcacbcabababdbddcdcadddccdababacadbcddcbbbabadadadcbbcccbabcbbdaacdbdaaccabdccadaccdbadadbdcdaaacabccdcaadbbacadadbcabbacadbccdcaaaaddaddccddbadbbddadcacccdaaababddbadcbbcdcaacbdaadbcadbcaadbbbcccdbdccddabdaabdadaadcdaccdcdbacadbbacbabcccdbcdbcacdbabacbaabdbbccadacdabdbabddbaaaadaadcddcadccbddaaadcbdcdccadaacdaadbabbadcbcbdcdbdbcacddbabcdadbbabcdadcadacadcbddaddababccabababcddcadccddaaccaadadadacbadadcadbcaadcaadbacbccacabdddadbcbdbcbcaaaadaddddbbcbddcbbaabcbcadacbdcaabdacdccadcbbbdccaadcdcaadcabdbabdbcbcbcbabdbcbbdbbbcaccdcccdbacccbacbcaaacbdbaddbccdbcccccdcbadaacbbadccbbbabbdbacccaacaaacdcddcaadbbdddaaaddadcdadddcdddbdbaacdbccabaabcbbbdadbccbcadbdacadacdcdcdadcbdbcbcdaddcbbcdabbdbadbcbabbcbdbddaabcabcbcdcbcaadcdbbdbbcbacbcbddaadaacccacbdbcdcbdcccdaaddbaabadabddbdbccbcdddccbbdaaaacbcadbbcabadacbaaccaddadcbbcbacbbbbbcadcdaaaaccddcddbdaacdcbadbdacdbadcbcbadcbcbadcdadbaadbacaabaaacbdddaaacdacbacbbddcccbdcdcbabcdbaabdddadbadbbcdadadbbdbbacdbcadcddcdcdcabdbcdccadacbacabaaadaabbcccabbbadddacdcacbdadbccacbadcbddbbccacddbaaddbdadddbcadabbcbccdcacbccbabcddabcbcadaddacbddacdddadbbdbcddbdbdaaabddadbddcddaddbbadbbabbadbccdcbabdbdaccdaaabccbdbaaaddccbaabcddbcbdcbadabcdbbccdadbcbbabacdddaccddabccdccddadaacbccdccaaacdccdbcaccdcdcddccadbbaccacbabcabcccacacdbbdbcaacbcdcadbbcababcdcdccbaddaaadababbacbbbccddcbbccbbccbaadcccbdbddccddaddadcabbcddbdaddbccbdaadabbabbcbacdabaabacababccdbbabbababcaaaddcdcbcdcbacccabddddaaccacccddcbddbcaccdbccadcabdabcaaccbbababccdddbbbabacddcccbdcbddbabacacddcdadcbbdbadbddccdbabcaabbbadbdcbcdaadbbadaadbbadddbadaddbaabdcabdcbcdadabbcaacaaabadccbbaabcacddaacdabcdcddbcadaddddbdaaddcbbcbbcdadbdcaddcadbcaddcadacadbbbcdbadccdbcdbdcacbddabccdddbcaddacdbdcabdcaacdcbbcadbddbaaddddcccbdccadabcaccabdabcdbdbabbddbcbaabdccaaaccdbbbcacddcdcabcbcbacbababaddbaaaabdacaadbadbcabbdccababdbbadbacddbcbdadbaacccdbbacdaddaacabdbbbaaddacabdbbadababadbcdcbbbccccbcadddcbcbdccccaddcddcdabccdadadcbcbdbabaaddaaadddcabbaaddcaccbaaccddccdddbdaabbcdaaccbbdabdbcdcccdbdbaaacbdcbdabcabbbaaccacdcaadaacdcddcabdbdbdbaaadaccdacbcadabbabcdaaadabcbddbaaacddabbaacbcaaadccdbacabdbabbdbacdaaadaaaccdbbcdbcddaddddccacdcababdccccaddbddbbdddddcadabcdcbacbabacbdcabadbabbbccddacdbabccdccbadbbaabacabbadbbccbacbaaaaabccbddaadcaadcacccbbdbdbbabdacdadcdacccaabccdaadcaacaacdadcccdcacbacabadbdbaacabbdaadadddccaaadbaccaccaaccacadaddbbbcdcaaddbaadbdabadcadcddcaacadcdcccdbccdcbdbbbdccbcaacaadcdaccaaabcccdbcbadaccbddbbacbccacaccbddabdaccbabaacbccdadbaadabbbadccbdbcddacdcdbadcbddcdadcddaaadcbcbbacabcabcaaaccbcbabaabadbccadabdbadcdadababdaddcacdbcdadccabdcbdcdaacbaddbabbabdccbbbbdacbcdabbacddcdcabbcdbcbbcadcbbadbdadbcacdcaccdbcbcccdcdbdbcacaddccbacaccbbbdbdbbabdadbbdbbcbcdbcacdbbaabcccdbdbdaabdbbcbabaabdabcbcdaabbbbaaaccabbbdacdbcbdacdacbbcacbdaabcbcadcaddaccadaddabbabdcaacabbacccdadddccadbacabddabaaaddddcacdadcdaddbbbbcadcaddacadcbcaaacabacbddbccbdcabdadddddbdcdaabcdaddbabcacddbbbdaacddaabcbbbcabdddbbaabccabdcdcacacbacbbaabbadbcacbbabdccbcaabacccadaacabadbbdaacdabcbcbdabcdcadcaacdcacaacacbcbabcdabdbabcaccacdbddaadabbaaddbcddbadddccaacadcddddaadcabcbdbcdacdbdacabddbdbadddddacabdadcccdaacacbbabaacabcababbbbcbcccbccdaaaaadbddbbabdbbbabdacdccccdabbaadbdbbbddbbadccbddcbdaccdaacadaabbacbcbbbbabcbccbabbccbaabbddabbabacdbaaddbcdcbbcbdabbccbbddadcdbacabaacdaaccdddaadcdaaabbcdbaaadadbddaccbbdacacadadbaaabddccdcbcdcdbdaaaddabccdbaddbbbadacaacaaaccdadaaacdbdbdbcbbbdbdadabcbbddbcdabbcabcddabbbaaacbbaaddacdcadadccaaacbabdcacbadcdaabcdcddcadbabbdcdccdaccbadcbdddccdacbdccadcbcbadbadbcdcabbcadbcdccacccbdacbadccacacdcdbacaabcbaacdcdbaacddcdabbdaadcbabcdabcbcbacbcbbbbbbabdddddcddcdcacbaddddbacddbbddacdaaabdcdabdcadcdacdabddabbadbaabcacaadbddcddabdbcbcabbddcacdbcdddacdccdaabdcadcbaacdbbcabddddabdbccbaaabdccacacbbadcbadbadcbdbbabcbbbabcdbbbaadddadbbcbcdaabbbabbcdcbccabdbcccbacaabcccacacdbbcddbdbccacabdccaabddddbdbaaadabdcbbdcbccddacbaadadadadacddbdcbdbbbccaabbdbaccbcbacbabbdbbdbcddbbcddcadaadbbbaccbbbdccccbbadccbacddddccbdadabdbaaadbacadbdcdcacadacbcbdbaccddcbdcdaaddacdaacbbddbbabbaacaadadababccdbddcbddcbcddabcbbabdccddbccabbaccbadbabdcdcaaaabbabcacccacddabdcaaacbdcacbaddbccbbaddabbabbcbcbbcdbbabbcdabbbdbababdddacacddaabacadbdacdbcbadcddbcabbacadabdccddadddbcccaaabcacbccababdabddcaabaacdbaacdcbcabdccdaadacbdabcbdcacabbdbdcdcdbddcddcabbdcacbbababdacbcbcacaaddbacaacaaabbcaddcddbdcacddabdcdbdccdcbcdbdadbcacacacdcabccdcdbddabcabbccbbddacdacbcdbbcdcddaaabbcaaccabbaaaacbbabddcaddacdadabcdbddccbcdacdcadabcadabcdbbddcbbabdbccccbdbbdbbdaadbadaaabcacaacbccbcbadaacbcbbcabdbcabcdcccdbbdcbcbaacadcaaabddcdabdcdacccbcbacddbdbadaccadaacbdbdcacdcddbabadaaddbddddbaaddbcabdccabccbddbaacadcdcbbbadbdcbcaccdccaddabbbccadaddcbcbccdcbabadbddbdbbadcdcaaadccaddbdcacadbbbdcdcdbdbdaacaaccaadcdcaccdcaabddabddcbacdcaacaddaaabddadbcdcbbabcaaacaabddcbdaaacbbbaadcbbdaabdbbdbdcccacbdcdcbadddcbcdadccdcbdbddadaddcdcaacdacbaaadcdabbbdbaacddbcaabcccddbccdabbdbcbdbdadcccadccbdbddadcdbccdcdcdcbddcdadcddddacaaaccddbdcacdbcadcddbbbacbbabbdcddcbadaccdccbdbadbcdbacabdcdaabdcaaadcdccdcbadcaabbdcddadcacaccbdadbacdcacdddacbddbbbdbccdbdcabbbbacdcdbbcdadaddadbdcccbcbacacddbddddcbdddbdaaabbbabbdaddcdcbcbdacccbcdddadaacbcbacdacdbdadbbccacadaacbbccbbccbcbaadcaaaadcbaaadddccbbcbccbccbbaaabbacbadabaccabbbcbabbaaabadbadccbbdaccbcccbcbbcbaaccdcacabaadacdbabcaccdbbadaaaddaaaaadddbbbccadddddbaddaabcbadccbdcdcdddbddaadabcccddbcdcacbbdcbdbdcacddccccdabdabbcdabdcccbdaacdbdbdaddadaaccbbbaacbaaccdcaadddbabddaddabdbbcddacbcdcaddadabbdadcbacabccacbbabbddcabbaaabcdabdddccbadbacbaadccccbddcddbcadadbccdcbcbddaaadcbaabdccdcdbcababdddcdaddcdbacbcaccccccaaabcbcbcbbbcddbcbdbadaacaccacadcdbaabdabcdccdabadaacaaddbabbdcdcbcabbddbacdabbddbbabcaabdcbdcddccbcddddbdadcbcaaaaaabbdddababbdcaaccdcbbbbdbbaddddcbaabaabcbaddacbabbbabdabbdbbccbacccdabcccbdcbcdcbbbcaddadcdbacaaadaddbcdddaddbbdaaacabcdbabbbdacdacbccdbcdaddcbdbdbbabdadbddbbbacbcbcdacdccbdaacabbadccadbcbcabdcacbacbbadcbacabaadacabcaddcbddadcacbdbcbbccddcbccddbbbccbcbaadaacdacccacbbacacdbbaabbaaccadbccbadbdbaaddaabcaccdbdcbadaddbcbcabdddcbccbcddadcadacbadaaaabccccabbddccdbaadadbcbaabcbdbdcdcddccccdcdbccddccddccadbaababdaaddbcadabbbbbbdcbaddaabbddcbbccbddbdcacdabdcbddadbbcaacaccbcaaaddababcdadbadbdacbccccbcaababadbcbdabccbdacabcbbadabddadbbcdbacbbbbcbddbacbbdabadbdaadadacbcdcbcdaccdaadddbddbcadbdccadabccbbccbcbccdbaddaadbadacddddbadbcbbacbbacbdcdabdadbccbcdbdbdddbddddabacdbdbabbabadbcbbcddcbbbacbbbaabcdabcbccbbdbaaadbbbcdcabaadbbaddbcddcaccbddcacbbdaddcbbbabadcbbbccdcaaddcacadbababdbcbdbbbbadadadbabbbbdcbbcdaccdcdadabbdadcdbcbcbbcdbccabbdabaccacdbbcabcdcaaaadbbdcccdabcbadbbacbcbbadccdbdccaabdcbbcddbbacadcbaaaacdaacdcacddcdcccddbbbaccbbccdbdaddcdabddcddbabdccbbaadaadbccbdbaaabdbbdbdbcdbdaaadcbcbccbdccddcbdadbbadcadbbaacdcbcddbcdadbbbdbacdaaaccddbaddbaacbaddddaccdcccbabaaddaddabdddcbacbabdbdcabccacbadabccccbcadababddcbdbccdcabbbbabacbdbadaaadbddbbdadbbadbaacdabcaabbccadcadabcaaaccacacaadddbddaacbbcabdddacadccdbcdddbcdddccaabadddcdcdcbababcbdbbabcdccccddddddcaabddacabadabbcabcbdbbddbbcaddabdddcbdcabdadcbddcacaacddcdcdacdcdbadbcaadbbacacccccccdddbabcccdcddcddbadadbcdabdadacacaaaaaaabadbbdbbbddbcbbdaabdcddaabccbbacabdbbdbcdddcbaabddbcdacbcbacacbdddbdbcdabbcbbacbcddabaabbcdacbacacadcbbddbadabbbcbddbcdacabdaacacbdadccadaabcabdacdbaadcadadaabadbbaccaddcacdccaabcbbdabccdcbbaaddddbdcbdbcacdbddaabadbcbabbdbccabdcbababdbcadcabccdcbcbaaadaccbdbcacbcdbbdadddaadddbabccbbcdcbcdacdbcccacbacdbadcddacbdadbcdddbcdbabbadabcacccadbcacadcbddbdbdaccbbaccddcadacbddbcaaaccdadaacccdddabacbbaacbabcabaabcbdcbdcacbababcaadcbcdacddbaabdabdbbbababcadbdbbbaddbcdbbcbadccbdbddcbdadadbcbcdccbaabcddaacbccdccbcaaddacbcabbabcccbdcdbbcacdadacbacbddacbbcdacdacdbbdddcacbbabaaaddabddbcabbdcadaababdbcbadacaaabcbcabdccacccbaababcabdaccaddcccadcbbbabbaabbbbbaacbacbabbacbdadbdccbbcadcbcddabcaacddbcdbdcaddcaabaccaaaacacdcabbccbbaccdcacbdaabcccbdabcadccabdccbbdbcbaabcbdcacaccdcabcdaacbdbddcddaaaadcdadccbcccbcbadddadababbbadcdbbcdcccaadacdbdaaddacadcabaadcdbdcbdcdbcbadccbcbcaddbaddacbcddadbcbcbacdbaacdaadaacbdaaddacbbcdbbdbbaacdbbcddbdcbaccdbcadacabbbbaaacdbcbabbccdbaacaccaacbadcdcababbdbddbccccddbaccdbcdcddcbbaddcddbccadacadabdbadacbbaaabbcdacdcdaddacadcccbcaacabbabcabccdbccacccaadbddbadaaacdbbcacdcdbbbbcdddabbacbcdaddcaaacdcccadcbbdbbabdbcadacdcdcdddaadcbccdcbccdcbcdbadcabbbccbaadddcbccacadaabbadcaabcbdcdadcbbdddcbcccbdbaaaadbccdbdcacdcadbaddccdcadaccccabbcbcdbbbdaccabcaacbdddcdcbddccdccdbcadabdcaccdccdbbccccbabdadcbdcdbddbadcadadbacbdcbdabcccabbcbbabddaddbadaccddcbccbcabbabbdababbbdbacbccbddacaaaaaadddbacaabbddcdbddacbcdddbbabcadaabaababdbadcabccabaacbcbcaabcaaadbcdaabddbadacdccacddacabbdacbbbcbaabdbcdadcdadadabdccbdccdccababdacdddcdabdcccabacabcdadbbabdddbacacddabacacbadcbbdbabcbbbdbcacacadcbccbcbdbddadcacdaadabadccddbbbdbcdbcadbccdcabaabbdbcacbbbcbbabadbaabdcacddcbdadcccdbccaddcdcddcaadaccbbadabcbbbcdacccbababbaadccccaababcdbdadddcdabdbddabcaadadddbdadcabadcbccaadcdccaacbddbcaccababcccadbabcbacacbbbcaabbaccabbaadcaccbdadbccdcabbaddacacacaacccccccbcdabbccdcabccddadabcdbdbdbbddcaddcababbddbbadddccadccdcbbbcbacabdccdacdcbcacbcccababaccdcdbddcabbbbdabbbdcbbbccacdcacdbdaacdcbbbbdaddbdcbbbdacdabdadabaacbacbabddcabbcbdddadbacbddbbbbbcbbacdbddbacccddccbbcbdbcabadcaadcaabbccccdccbbdabacbacdadddcacdadaaacbccdcbcabdbbbbbcdbcccccdbdccadaaaaaabdddbabbaacdbcddacdcadbacdacccbbcaaadbcbcaacddbaaaadadbbabbcaaaaadbddcccabdbbbcdddcdbddcdbdcaccccdbdcaabcabcccbccaaccddaacaaccddadcabcbcabadbcbcdccccdaacbcbcaddbccddbcaddcbbdcddcbdaccdacbadcbdbcbdcadcdacaaababddbddabbabbdbdccaaadbacdccddadbbdaaacababbccabbaadacabdcdabcbccdadbabcdbccccacddaacdbacccbadcdbdaaccdbddcabaccabaddbaabdddcdaaaabacdbbbcabbbaaaabbabbcabacaaabbddccacbdddcbbaaaccbabcddcbcccdabccbddcdcdbaddbdccdccaccbcddddcbbbddbcdccacbdabdbaddbabddabcaabacbbccbbbbabbbddbcbccdacdabcacabcbabbaccdcaadadcbadbddddbddcbaccaddbbbababbbcddaacbaacaacadbcbacdcbcacabcdaddbcadcdcdabbbdbadabbabdcddcaccbcdbcbabdcabaaaadbabccdaddaabbcbaddaccdcabaaadcdbaaaadadcccaaadbdddbaababccaabaabcbbabddbdbdcdacdcbbacadcaadaaaaddcdacdabcddbdbcddbdbbbbdabddabbbaaaacccaaadcbabaabcdbddcccbdcdacccababdcacbdccdaabadacaddabccbacccdadbdabcacbdcbbddadaaabcdcddbdaaddbaabbadbbddaccbacdabcabdcdaabacbdabacacdadcaadacdcaaadaabdaccccdcdcdabcaaacdbdcdcdbaaddadcdddbddbcadabddadcaaaabdbbdcdaacccbaddadbbbbdbadddcddbcaacdccbdbabadacccbcdbbbcadbdcbdcddbbcbcbccacabdabccdabddcaccbbcaacdcccbddacdacabbaddddbbcdbdddadbacabbdddcdcdacbaccbddcacccdcdcbcaadcadadadcbcdaccabdacdcdcadddacdcabadbdabaddcbbdccdbacaaabcbacadacdbcbddbdbddccdccaaaabccbabbdabcbccbadbdcdcbdabddddbdbccdccdcaddbbdcdbdbaacdaccdacbcbabaabcbdbcdcbabcdcdaccdbdadccccdbddbdbaadbacdcdcbbacadccacddcbccaadaaacbaaacaadbcadcbdbcbadabdcabbcbbbaacbbbaccdabadcdabbdbcacbccaadaaaaacadcdbbcccdbdadbacbdabaaccbdbacdbcabacabcaddbacbdacccdcacbbbccbbcacdaadbaacdcbacaadacbcacdcbaccccadaccbcbbdbbdacaaabbadddabbdccdbbaadadacdcbdbcbbcadcbdbaaacacbbcbcbdbdbaacaddbdabbcaacadcbdcacabdacddbbbcbacacbaaccddbddbdbadabcabadbbaddaacadcbdddcacbdcaaaabdadbbbaaadaccddbaacabcbdbabdcddbdabccdbcbdadcdaccadbaccabacacccdccbdcabbcabacdbccddabbccbcbbcababcaabaabaadccdcacbabaaacadbccdbdbbbccbcdcddbdbbdbaddaccbcdbccaabddacdccabadbacddcaccbcacbcaadccddcabbdbdaacabcdbabcdcadacddbdcbbdbdbdbddabdbabcbadbcabcbbaadbaaabdacdcbacccccadcdbbbdcadabcbdbabdaaaaacbadaabaabcdadcdbbddacdaaadcbcbacabbcbcdbaaaabbccacdacacadddcccabbdcccdcacbbbcacccacacadbbadaabbccdbdcdddbbdbdbbcabacabcdddabcadabcbbdcdcddabaaabdadadddcdcadddddccbbbbabcbadacddccbddabdbcddbaabcdddcabcadccbabddccdacbadaaaaacddcdbdabbbdcacbaddacbabbcdcbdcbabccddbdadabaddabcaddacbdccbdbbbbdcdbcbadabcdbaacbcdaddabdbbdcdbacbadbddaabadcdbdbdcabccdccbdacbcadbddcadbccbbdcacdcdabdcdaaadbddaadabdcbdddcaadcaddbdbadcccbaadbccaaddbaacacadacdacaadddcdcbacbbcdbaaadadbacdccabdcabbabcadbdbddaadadcaaccccccadacbcdcdcdacbacbbddacaadddcdcbdaddadcdbbddaabbbadaabadcccccadbdcaadadaaabacdcaccdcdbbbdcbacbbcbacaadabaadaaddbdccaaadbdbadacadaacdbbbcccaddbdbaaabaaabbadadbdcdbbbcdaabcdddcaaccaaacbaabcdaabbddddbdabaacdabdcbbacdcacbbdcdddcbacbbbcbddabbdddabdadbaabcadcbdcacbbaaddbdaddcabccddabdbdbaddcaccaaadddcbdcbacaddadcabcdbbbdacbaacaaadadcddaadcbcdadbbbcabbbbaacdbaccdcdcdcddcabbbdcadcbccbcabbdcadccacddbdaabdaccaccccdccadcbddddbadbbaaccadccaabaabbdcacbaacbddaddbbbccdabcbaabcbdccccbdcccbabdabcdbddbcbacabcaacabadcdbbbddaccaccccdcdddddaaaabccddcadbbaddacbaadacadaadbaddaacbdcdbcacbbddadcaddcddbdbcddcaacacaccadbcdcacbbadcbacadbccacadbbcdabbdadddaddbaddbdbaacaadbabbbacaddccddacccbdccdcabbbdadbdaaaaabbbcaaacbddcdcaccbaaccbacabadadadbbbdcbddcddacadbbcdbdadbcacaaabbbdabddbddaddbaccacdbaaadcdabaccdccabcabaabbaabdbcabadadbaaacabacbddadcabacadccacbcbbcdcccacbdddcbbdbdbddbbddcabddcadbdcabcdcdbdbdccbcbbbcbbabccadcbaaadabdabdcdcbaaacbcacbbaabacdbdcaaadcdcabbabdcdcbdccccbacddaabaacacbcbbcccabcbbdccdbcdbcacacddcdabddcabbaaabbcadacadaadbadcadbcdbcddbcdaabcdaaadbbdcccbcadabdabcbccddcadbcaacacbdbbccbacdccbddadccbbbcbbabccabcbccbdadcacbbbdddcadcbcdbdcabdccbbcbbaaabbdacdbaaadaddbbddacaabaadaaaabcdbbdddcbaadcbabacbcabadbcacdaaccdbdbbddcadabdadbcabcacabdbabbaaadbddbcadccdaadbbbdcaddddddbadbabbcacbcdacbcbcccdbddbcaabcbbadadbdbaccbdbabbbaccdbacadcbabbdabdbabbacccdacbdbacabacdcdbaccbacabbcbbdbcacadbcadccbdabcacaadbabcdbbbdbbdbbcaddbcdaaddbadbcacadbaadcdabdcaaaadaabbdadabcccdabbaaaddacdacbcddadacdbbcaccbcababddbcbbacbbdadabcdabccdaacccdbccbcbbacaddacbaaabdaadadbaabdbddbbabdddacbcabadaddbbdcdddccdcaccbadcdddcccbaadcaaccddadacdacaaabccabaccabbdabddbabdadbabacdcccaadccbddbbaadcadcbdcacbadbdabbdadddadcdbdaaadaabdacddddaccddcadcdaadaaabcccacbbaaaacabdabcdccaabccddadabadcdcddcdcaaddcabbbcaccddbdddcdacbdbcacbadacdcbbcabdbbabacbdcaaadbbbbcabbccacaadabbacdacbdbbddbdcddddabaacccdbbadcccdbcbddcbccaaababdbccacaadbbbddadcaccbcaadcadcdbbdddbdbacbbdbaacccaabbaadbbbbadcbabbcaacccdacbbcdddccbbcdddcacdacbadcdbcbdaaccaacddccacadbcadccdbbcbbabbbbbcabcddaadaabbdbadcddbcacadbbaadabcdbdcabccddcadbdcddabbbaadccaaccbdaddcbdccddcacdbccdacbadbddbddcdbbdaddabcabbdcbcbacdcacdadaacdcacddaabbdadaacbbacdcdadabcdbdcddbdbcbcaccdbdaaacaacccdcdbdbccdabcddddbdbbdbacdddadaadcbaacadabadbadacdddcdcbcabdccdcbabccbbcbccbbaaccaaccdacaadcdaacbacdccdddbdcbddbabbcdabdddbacbdaaaddcdcbccbdcabcdcbacdddbaccabdbdccbcadaaabdadccabbddacbccaaccbddccddbadbcacccacadabbccadbddcaadbcbcdbcadcddcdacdbbaccacbbaaadcddbaddcdcccbaabcccbbcacbddaaaddabddacacdabcadbdbddaacccdbccccacbbbcbadadbacaddaccbdcccbdcabdddaadabbbbdaacccdaadaaadadccdaabacccbbadabadcdbbbaddbaaccbdcaddcbccadabbbdcdbdaacbabbbbdbcacbabbcbabbabbbdbcaacadaaccabaccbaddbcacbdbcdbaabdddccaaacccaadbdcbbbbddbaadbcaaacdacdcdaddccacabacaaabacdbbbaababcadbdabdbcaadbadbcbbdcabcadbaddcacabbbbaabbadcaadccdbaddbdddcaaabddcbbdbcbbbcbddbbaacdaadbdddccdbcdbadcaacaaccbbaccbbdacbacacbccbbbaadbddddcdbdbcbcbdcbadabbbcbcbcddccbabccbdadbaacdadaacdbddcbabadacaccccbacddddbabbaabadcbacbadbdbacddbdcaababcacdddbabdadacdcaddccabaccaacbddabbdbacbaabcccdbddbacccdabaabdaccbccdbdbcbbaabaacbcbadcbdbccbdbaabcdcbaddbbabbabdcacabbdbacadcbadcadcdcccdaaadcbccbdbcddcdbadcdabbdaccdaadddddbdbcdcbbbcbabaacadabbccbdabadcdbcabdbdaacabacabccddaacbbdbdacbacbdbdbdcabcaaddaddbdcdadbbababdbdddddcbdbddcaabccdbcacccbaaccddbddccabcaadbcacacddccbdbdadbbbcabadcdbaabdcabbbdccacaabbdbdcadcdcdcccbdcdbdbcaaaabddbcbcabadcdcbbccbdacdbccadadccdcbdabbbdbbdbcaaacabddccdbbddadcababcbabcbcdacdcdaaabccdbaabdbdddcbbadadbdccbcbdddcdbbccacdbcdcbddbabcadcbaaacbcddddadaadaaddbdcccaabbcbbdabbdbbcbcccdbddabaacabddbbccbbdcdbadbbcabadbdbdbacdabddddbbcadabccbdaaababddadadcaddcdbaabaddcbbacdcdabddbbddbacadccaadbccdddbdadcbcdcdadbcadcccdbbdcaddaccdbcbcbaddaacbbabbbdbbddddbdaaadcdbcbcaaccbccbbcccdacbcbbaddddbadbbcbdcaddcdbcddacdcbabbdaacbdbcbdbcbcadabcabccbdbddbaabdbadbbcdadccdddbcbddbaadbdbcbbdbccdddcbaacdcbabcbacdbaaaadaddcabddaabacacbcaaddbdccadcccdddbcabccaaccbacdbbccbddddbadadbddcacbcbdcacabbaaacdabccbbaacaabddccadcbaadaabcaaaddaddadbaaaacbbcabcaabdbdadcaadaacddcadcacdcddbdcdabbdcabddadbcdbcbcaabcaccadacadabdaabccbabbbbdbbcadbcdabbaadaddbcbbabcbabadddacddbcdcccaadbadcdcacddabaaaadbbbdbabddadcbcabdccaadddbdcbccdcbcddccabbbabacaddcbccaadcacdcdcbaddcadbdcbaacbccaaaacdbadabaccbbacaccaacbbdbccddaccacddccaddacbbcacacdadbccccbdbbaacaacacbdbcccdaccccddbbbbcdbdaadabbcdcacacabaadcadbdcddcdcadcbcbdabcdaabbaabbcbbbadcabdabcbcdaabdcdabdaaacadddccadccbbbbbbbbbaacbcdbcaaaddaabdacbbacbdcdaabaddaacabcdabcabcaaadabcbbacbabbbadbdcbaadbbaaddbbabddabbaccdddaaccddcbcdabddddddbcabdcdbddaacdbdddcbcbacacadbaaccabbccbbcbcdcdacdbdbdcacadcdcacddbbbdbcdbdbccbbabbcdaaaabddbabdbabcbaccdcbacccabdbbbbcbcadbadaccabddcdccbdacdbaabaccbcabcdcaddbbabbddcacccdcbcbbddcccbabbdbaabbbbaacadaadbcdcabdbdaababddaaddcccacbadcadddbbcdaaddaabdcbbcbbbaaaadcbbbaabccacbdaaccddbbcddcbbadacbccadcdbddaabdadbaabcbcbabcbcdcbbabddcacbcabaddacbcdbcbaddddacaddbaaccddbbccaccdddddaccbbacacbdacccdbabccdbdccacaacbaddabcbddbbdbbdccbddadaaabababaaccadbbdacaabbacdbcabcdaabbbabcbccdcccbbdbbdbcabcacabbaaccbdbadcddcddadcbacabbcadaddaacdaaccabaaabcddaaaabbcbadcaabccdadbabccccaccbbbbabbdbdbccaaaddbbddabbcacacddaadddaddcbddddbbcdadacaacadcaddbaabbbdbdcacbadcbacdcdaaadabaacbdcaaaaadddbbcbabaacadbbaacaaaaadcaaacbbbdcbbcdaacbdbaadadacbbcddbbccaacaabbcdaacaaacacddbdadbabcbdabbbabcbcabccabbacdbabcddaacddacdbdbbcbcddbdbabaadabaadbcaddbcaadcddddccadacdbabbaadaacccbcadcaddacaddcacbdbdabdabaccabdcbbbaadcbbdccddcddccdbadccdcaccababdcdcbdcddacadcacabbcaaaababbabdaaddcabbbbabbdcddbccdcccddcbcabacdddbccaddddcabdbadcacaabddbbcaadaacabbddbbaacccdadcaaddbaacddbaacdcdbdbbdabbbdbbaabdbdcdababbabdaabdddcdcbabccbdaacbcbbcaacbdaacbaadcdcdbccbabbcddbbbadabdaccadddbbcddbacacdcdbdddcbbddbccbaadbcdccccdcbdaddadaacbdccbbdbbdbabaabaabddcdcbabcbcaddaaddadcabdbdcabaddcdcddbacddcbcbbbcccaacccbdccdcacbccdaacccdbadbadbdbbcccbbdccccdbcaabcdbabdcbccaacccabccababbcdcadbbaaabadddbdadbbcdbadabadbaaabbdcaacdadaccdcbaadbcaccddbcbdbadcbddbcccccadbcdcdbcbabcabaabcacddcababcddbccbcccabcbbadadadbbbbcbdadcdbcdbadbdacaaddddbbddaabcdcbcbccbaaabacaddcabdcbadcaaabacddcbcdadaaddbcacbcddccddaadcccdbaaadacddabbcdbccbddaacccaaabadbdccbaacddbcbadaabdacacbdccdbccadcbdccddcbcdcbcbdaaadacbadaccddcabcababcaccacabbcaaddbacaccaabcaddacadbdacdcaacbbcaddccacddbcbdabbadcdbbbbaaaddaddbdbdacacdbccabdcacbcaacabdadbaacdbbabadaaabccbcbdbcddddaadbcddabddcacccbcdccdbaabbdccbbcdcbccccabddaacabbacadcdaddbcaaaddaddddbacdacbabdbaaaddcacbaccabbbbcabbbabbaadbdabbcacddacadadadadadbaacaabaccbccbdcccdddacbbddadaabcbbcadbaaccdbbcacacbcadcdbacaacabdcacadcbdbdadbddbcadbbbabcaadbaacadbbbbaaaabcccdbdabdbcaaabdcbabaddccdabbbbbdbccaccaddaaddcadaccdaacdbbbdcccbcadccaaccccaddccacdcbdbbcbbcbabdbddddccbadaadaddacbcdbdadcccaccddcbccadcdaaabcddacdcacacdaabddaaaadaaaadabdacadcddcadacabbdddabacadccbdcbcdbbaacdbdbcbbbbccaccbaaddaddbadcaadaddadccdcaddccaaaabccacdcddbddabcababddcbaddcdcbacbabdaccbbccdbddaadcbadacdaccdbaddcbadbcccaabbbddaadddcbcbccabaacccdbcbabccaacbdbdbbdaadddbdbadcadabcacbccbacababdbcccdabbcacabbaccacccbaadaacdddbdcbaddaacddbaccabccaacdbbabaaadaddbbabdbddadccdbdbdabcbcbabcddcbdbbaabbcabcbcbdaacddcdccbcdccddcbaddcdbbbbadbcccdaccccabcdccbbacbbbbccdbacdabdccdcadbaaaccdaaddbbadadcbbcaaabaabbccdbabcbcdacaacbbbaccababcaacddcdaccdbcbaadcdacbabadcbdccacddcbdabddbdcaadcbdbdcdaccdcddbadaccbdbdaacabacbccdcbddbdbdbdaccbabadbacbbcbbbaabaddbdaacaddcdbabbaabbacabdbbdccaabaddbccaabbadccddbdcbbadcaadcacbdcaddbcadddbbaabccabbdaadcacbdcbacbadddcddcadbbdddcbbdadbccabdbdaccbdddaaaabadbcbddbdcddabbccdaccdbbdbdbaccbdbdadabbddadbcbdbccdbaacbddbcabbadacaaccbbdccddcdbcdcadabdaadbbbdabdacdddccdadbcadadbbbabadcbccabdacadcdacaccdbdcbbdbbbcbdaabbddbdbbbcccabbacaccacaaabdbdddbbdbacdacdadbadaacaccadbacbcbadbaaabacbddcdcdaccaccbaddcaddaccdbddddabdddabbadddbadccdbbcadcbbcbbddbcdccacdccdddaaabbbbcdcdacbdcddabbdddbbdcdbccacbaaccdaabacabacbdabdddcacaadacdaadbaddccdabdadacccabbdcccadbbdacdddacacddaacadcddccdcccbcbddcdadcccbcccadbabaadbbbcbcdcdacdbdccdccdbdaccdcacbbbcbababacbadccbcaabcaaaadaccdcccbddddacbadaababbbbaabbdbdddcdbacbbdacdbadaacdddaaabbaddccdcadbbddbbacbcdbdacbcadabccdabcbdcbcaaacbcdbdcdccdcacbccaddddddbcccbdbdcacbabcadbbbbaadbaaccbaccdddbcdcbdababadacbacbdcddcacacdcbbbaacccdbdcbdccbcacadbbdbacadcbacbcbdbbabcbdacccbcbaabadbcdcbddcaddcbdbbbcbacbdddababaadcddbbadddbdddabddbacabacdabbcacddbcbbbbdabcbdbcccadbaaaacaacaabbbddbcbdbdaaccbdcdabcccadbcbdbdcbbcacdacccbcdcaccaaaccccbdaddcbddabaaaddacddadcadccaccdabacbbdcdaaabbdccbabbadbcccccaaccbccaddcbacdaccaddddbbacbcdabbbababacababdbdabdddbaacdcbbabdaaddddbbbdbacccaabbdaacabbdabccabdcdbcaadccdcbdabcbdbdcbcdbbdcbcabccccddaadcacdaabaadabdabbaddbabbbbdcdcddaabacbbccbdcadcbaddcaacabbcccdaacaadcaddbadcddbdbdcdcbbcdbbbccdabcdcdbdbcadbacddbdbbbbbadcadbdcbbbbdcbbdabdcbdcbdbdccadcccdabdcdbdbaccdbdabbcabcddabbbacadbabaacacdadacbbbcabdabbcddcaacabbbacadbaabaddccabadccabacdadcdacdabaaccbcdcdbcdadcbdadbcaaaadddcaababbdaacbabcdababbacbaaadbbdcdadbaaaadcdbdbbdcaddbdaabdabaacdacddbbcbcacabcdbbdacccddcbdabaabbbddcbadabccbcaaaacbabdcaadabdddbbbababcbdbbddabbdadaababbbcbdbdadaccbaabbcdaaadadadcccbaccdabcddcbcabaaddcdaaddbaababcbaaaabbbddcbbabccddadccbbcacddbbccdbbcbdcaabbccdaadbbbadbcccadcccabadadcacabbbacdcababbcdabdcaadacbbdaacabdcbbbcbcbcabdddbddcbbbcdbbdcabbddaaddbbdcdcacbdadaddbdcddbddbbcdadabbadbdbbabcaabdbadababbbcdddbbbcdccabbcacdcabcbcadddabaaaaaaaadabcdddcccaddccdbbaccaddbcccbdaaddbabccbbabbabbcadddbcddddcbaabdcbacaddbbdaabdcccaacaacbaacacccaaccabaaddbbdbbbdaacadbcbbadddbacccbdcabadbcbbcdaccadacddbcbbabbcaaadcaacacdcbdadaaaccccbacdbabdcbaacaacaaadcccddbcdbdaddbcaddaabbdabdabdaddbdccccbbcacaaabbcabbdcadabbcbbadcdacaadddbcbabddacddcaddadcbbaabbdccdcdbcabaddcabbbccadcbabbccccdddccabdcbbdaccccbcbacbdbcdddddccdbacdbdabdcabcbcdcadabaaabaaacbddaadbddbccbbaacbabbdbccabddbccddddbadaabdaaaabccabccdcbbdbdacacccbccbbbaddbbccbabdbcadaabcbcacadadccdabdbddabdcbbbcbbdbbabdabbbdadaabadcbbcaadbadcbcdadaadcbcddbbcabbbdcdcadabcbbcbdcaadadbdbcbcddcccdbaacdddbabbcadcdabdbcdcdcdbbbcbaabcaabaddddbdaaaacbcaaaacbcdcccaaacabcdcacbdcbdadcadbbddbabbbbbbadadcdbaaccacbdabcbacaaabcddccccabcaddacabdbcdcdbddbbbcadbbcdbbdabbbcdcbadcabdbabccbbaddcaaccbcbaacaacbcbddbabdbdbaddadaddadbcbdadcacbbbbabbadcabbcabcdaaacbabcdcdcdbadbbcdbadcddbbccadcbdaabaabdbbbdbbabdadcbdbcddccccbbdbcbaddaaabaaaabbdbcdbababdcbacacadbcaabacbddcdcacdabccdaadccdcdcbdcabaaabccdcbcdbccdcdcabcabbbdaaadbdaccdbadcccadbddcdddbccaddbcddabbbaddcabcabaabacbccdddbbdadccddabccdadaaaccadadadbbcbaaaadddcaaaddbccbaaccbabdbcbcbcbcccadbdbbabacdccbdcacbaddbbcdacddbdbbadbbdcaccbabbbcccbdaccabbaacdacaddbdbcadaabbdbbdbdbdcbcacbbaaadcdaadbddadddbbabcbbddaddccdbbddcdbbcbdaddabbdbbdccacdcdadccdaacddcbbaaddcdacddbbbcbcddbdcbcabddbdadbbbbcdaccaacbcdacaacadacabbdabacbbbbdbcaddccbdadbaabccbddbcaadccbbcbccbcdaadcccadccdbbdcaadacbbadcccbcdbcdbdbadcaabcadbdadaabddcabccabccbbddddbaaacbaaadbaddccabdcacdacdbaadcdaacbdbbdcccbbaadbadcabbccaadaabdbbbdabcdcabcbcccdbaacabbaaabdbcbaaaddbcbcaaabcccccbdbcbdaaabcaacddabcbbddbcadddcddcdbddabdbcbdbdbcddcaacaadbadcdadcdadacdddbacadbdadcdccccdabcdddbddacbdccadbabcccbcbdaccccbbdbbbcabbadddbbacbdccbbddddacdbcbcadcadadbcacbcbaddacabaabcbbdadbbdbadbaccbdbcadbbbcbababacccaccaacdbbdccbdcbdcdbbdaaaacbaccccdcdabbcdddcacbbdbcdacbadaccdaaaacaabccbcabbdbdaadacdbcdbdcabdbbccdabbabbdacbdabdbadcdcddadccdbbddcdddcdadbccabaaadcabddbcdbcbcbbddddcacaddcbbccdaabacdbdacaadcadbdbdbbabbbccdabdbcbcadcbbdabccbaccaaadbadcbbcdcacbddcdccadabcccbbbaccbacdcccaddcbcbbcccbdbcbcbadacbdcdaadcdcdcaaddcbcbdbacbcadcadacddbcddadccacadadddccbbcddbdbbdabbddaccacdbbbcabdbcacabadaabcdcbdbabaaababacbbcdacdaddbbcbbbcbbdbcbabcabdbcbaccdccdbdaadcccdccddbbdbaaacabbbcbacddadddcbdbdcddbcbdbbabacadcbbddaaaccdaaccbbbbdcbbdbaadaadaabcbbddaaacdcdbcbbcbaacaaabdacadacadccbabddabccbcaaddccadabbaadcccdbccbdbaaaccacdccbcbdbbccabcaadbbdaabddbcccacbbdbbcddacccccbacdcbccadbacddddaabbacdbbcdbcbbacdabadcbbbdbadabddbcdacaccbbadbcddabdbbbcaddcbaaddcbdddcacdbdaacbdbbaaaadcbbcadccabbacabbabdcadcabaddcbadaabccddaabcacbcbbcdcddadababdcbdcaacadddbaacdaddcdaabbaaadbbbdabcabcdcdcdacaadacacaacadcbaccbabdadccdabdbabcaabdcacdcccddabbdadbbcddadccdcaabdadaacbcacbccccdbdcbbcddbddbbbcddbbbacdccbddadaacddacbcaaddbadcddbddabaaabbcdcbbbacbcbdaabbbbcaacaadadbbcbacbdaddadcdbaccbaaaabccadacbbdcdbabbbcbddabaddaacbaaadaddbbbcdddacacabdccdacaadcdccdcbddbabbbdddcacdbbdadbcbcbadacaabdcadbcbdcdabbcbccbaabbcabccbaacaaadaaadcacddcbbbacaadacbabdbccbbababbdcacaabbbcdbcbbdbabbacbcbacdbdcbbaadadadcbcadbdbbaccbcccbdbacaddddaadbddaccadaacacbdccdaacaababbacbbdaacdbdbbcdaaacdcabaadaddadccaaaddccccbbcdddabacbaddccbbddccaabddbcdaccbacdbaacbddcdddacbbdbacccbbbbbacabddbdcdbbccccddcaadbbcddaccdababcabdaaacacbadccddabcdbadaacaacbbccbdbcbbbbaccddabcacbbbbaaaccbccacdccddbabacadccbacbddaccbccababcaaddbdbbaaddabdcbbbcdabbdddbcabacacaaacabadacbcddbdbaabdabaadcbabdbcccbbaabdcbbbbcccdbbcccdcdbddccdcddbbadbaaddbbdaadaccddbdaabadbcccbccbccdcbbccbcbadbadbdccabbcadabdaabdcbabcbbabaabcadcdccbaabbcbacaadccdbbacdcdcbdcbdadcaaaccaacaaabbcabcccdbcdbbaadbcddbdadddaacacdadccabccddacbcabcadccdbcaacdcaabadbddcacddcddcdaccdbcadaccacadacaaaaadbccddbdcaaaabdcddcadacddbcbdabbcbcbbdcbacddbbbbdadccadcbccbddaabbcdacadddcaabcdbccaabacdccbacbacddcdacdaacaacbaabccaaaddabccabccacddabdccabdbdacbaadbabdbcbaabcaaabcaaadadbadccbddacadaacbcbbdcccadacadbdbcddacccbabdddcacbbbbababbbbaddaadaacabddcaccbbcbdacacacbbaabcbcbbabaaddaaabbacaabddbadbccacbbbbcbccccaccbcbdddbbbdaababbabcbdacaaaadbccadbdbdbaadbbbccbddcaabaacdaadcccababbdcbdbbdadbbcccaadcadacdbccbdcddabbcddbaadcbdabbcabcbdbcdbcbdcdcbcccbbdabcbababbbaabbbabaaaabcdadbddbaadacdabdddcbacadbbacdbbdacdbcadcdbddbdddcaccbdaadcbdbdacabdcabcbcdbdaaccabdddabbadcbbcdacbbccadaabdccbbbdcbbaccbaddacdadbdbabddadcdddbbbbccbcaddbbddbbdaddadaccacbacdacbcdddcdbaaacdccbcaaaabaaabacdaabdcbdadbbacacaabdbaccdbccacccadcbbdcadacbbbbaadababcacabcdddbabacbacdccabbcdccdaddacacbbbdacdbbacdaccabbdccabbacdabcaaddcccabcddcdcccdbddcbbdcadccabdcdbdbdbdcbaacbadacbccadbdbccbdddbcdaadbacbccbcdacdadabbdacadcadabdcdacdacddccccabadaccbbacbaaabbabadbbddbdabcccaaccacacddcdaaaacbdabbdbbdccbcdbacbcdcdcacddcdbcbcacbcaadcbcacacbdbcdbdcdcadbbdcbbaaaccdcdbaacdbdcdddbbadbcddadddbdbaaaadaddbbccadbcdcdaddcaadaddbabbdaacabcbbbcabadcbccdaabdbdadcacabbccacadbcbdcadcbccabbcadccccccaddcadadcdacddbbbbbaddbbbbccdbbbbbacdbaccbcdbbabbcbaabdaabbdcdcdcaaadcacbacadadaaacbcddaaccbbacdacabccaaccadcdacdbabbaabddcbdccbccbbbbcbdbacbbdbdcacacbabdacdbcdddbcbabdacccabaccbcaabbbdccaabaabaadaccadbdcacdcdadbadbbdbcbcdbcaabadaacddcacbcdacaadccdabcccdbdddddabbcacbdacaabacdcddabcaaabbdbacbaabccdaddabadbbcdcabddccbcacbdcbdaabdddacdcbddbdbabdaddbabdcddcbccddcaddbbdddbdabbaddcdcdaabbcbdacdaaabaabacdddaabdabcdcabbbaccbdbdbddccbdcbcaddddbdabcbdbdbbcaacbcaadaacbdccaaaadcbbabccdaadadacbbddddbbdbcdacdcabacdbdacdcaddcabcbbcccbabaaacbcbaaccaabddabddabccbccbcacdbabdaddbddbadabaddcabaacccdcbccbccaabaadbdacbdabacdddcbdccddbbcdccaddadddaaddbbcdaadcbabbbbbcbabccabacabcdaabdbcbdcbcddcadddbabcdbabccddcdabbbddacbdccdcbaacadaacccadcbccdbabddccdbdadcdabccbdbdadabcbccaddcccdccdddccabcbccddbbdbccdbacdcccddadbdccaadaaaadaacababbdabadcaadccacbdbcabaaccccbcddcbdccbccabaadbadabdbdcbcbadaaddbcbbabbadacbadacdbaadacaabdcccccbcabbcbbccbcabcaccddaaaadacaaacbadaabcdcaadbbadaaccbbacdaacdbccaaccbbadbbacdcbbaddbbbdaabbddbcdcdbdaadaadaabcbbdbdbbcddaadbacaccbcacbbbcdbadcaabaaabcdcbcddacccbcacbdbbdaddcbbadacaadbbdacccddcbcbaacbabbddbdbccccbaacbacdabcdbdcacadbbdcddaadcdddcddacbdccbabaaabadbcdbcaabbdabaacacbcdabaadabcbcadbacdbcbbbccdddcdabdbbacadcddcbbcdbcbcacbdaddcddbbbdaaadcacacadbddbbdcdaadbdbdcaddbddccacadaabcbdcaabbdadccaaabaaabababacbddaaaadaaaaadacbbdaddcaaddcacddbbdaaddaaacccdadbaaabcbcbadbadbcbaaaabaabcbddadccbdacdbcbdadcaccaaacbbaaabcdddacccaccbcdacdaddccdcbcdccdbcdadddccdcadabcaaadaabdcabbcbdbdcacabbacacbbccbdddcdacacababccbaabdadccadbdccdbcbccdccadcacccccbcdbbdacbadcdababbccbabcadcabaccbcbdadbcdbabaaabbcabdaacadcbadcaacaddcbbdcaaaaccbdaddcccacadadaddbbacbdacdbbcaaadbbbdbcddcbbabddcdabcbdcaacccbbbbbddacdbccaaacaccbadccbcccadaccaacccbaababdaaabacacddccdbbdbdbcbbadacdbababbbccdcadbdbdcbcdacbabdbacbdcbddccbbbaaacababcddbbdbcbbdcaababcdddbbcbbbdadacadbdcbbdddadcbccddcddcbaacabdcdccdbbaabaacabacadcddbabdbabcababdcdcaabdbcabdbddaddaadcddbabccddbacabddaabbccbaaaacabbabadccaabbbacacdcdcaccdcdaccadcbdbcabacdddcbadcabcbccbdababaaabbdbbdbcdbdcbddaabbddacdadbdbbacddabdcaccacddadccbddbaabbddcbaaaabbaadcadaadcddddaddbcbadcdbccbccbcdcbdbcbbdcdaaadacdbbdccaabacbdbdddccccacddddbaccbcbaabbaaadddccabcaabaadabcadbbbdccaaaccbadbaadddadcdccddbbdbacbacacbdaaabcaddccdacdbdabdbccacdcacdcbdaddcabccaacabbbadbadbbbbcabddcaaadabcaaacdcdbcdccbcdcbacccdaccabdbbcabcddaccacdacadacadacdabacddacbbdbadcddaaabaacdbabdabbdbcdaccabdbdcbccddcbbababdcbcdcaaccadadcadaabbdcbadcdcbbacccacbacbbccdbaadbadddcaabcccddadadabdbbdbcacdabbacdcccdccaaadabcacaaadbccadccbdcaabcddbabbadcdbabbbcddaacbaababccdcaadadccbbcbacbaacbdccbccbacddddbbdcadbbadcdcbdbdaccaddacbacdabccdbcccaaabaadbdbabdccaacaacdcbbcacbabdbbadcabdcdbcdbaccaabdbcadccdccaadccbadbdcbccacaddbbacddababcbaabadbdcaaccabacbcadbdbddabbdabbcbdddcdcddcabbdbaaccaacaaadbbcbdabdbaabacdacddbaacccdacabcbaddbacddcbcadbcdcadccabbabdcaacbababcdcddacacdbccbdbaccdabdcadddaacaabcadccdaabbdbcbccbbadabcccbddaccbccabcdcbcbbbbccabddbcdadcdaadacaddcacdbbcabcaaacbddbcbcddabbdcbaaddbbdadcccdccabccbbcdadbccdadddccdbdbadcaadddabcbbaaddccadabbbdaacddaddbaaddcbbcccccdacabcdcddcbddbacbbcdcdaddcdbdddadbaadadcbbbcacccacbdbcccadaccddadcaababcbcbdddbccbdcdbaacbadcadccccaddbdddabbccdabccabdaccccbdcabbdddbbdbbabcbdacdbcdadbdcacaaacdabccabcdabdcdabdcbaddabcaccbcdbddccabdcdadbaacacdcabdcabbcccdcdbcbabaacdcdcbcdbabdaaababbdbadaabdcadccabbcabaccadbccddbaabcbdddddccaccdaaaadaddbacacacbadabababcdcbbacdbabcacbcaaacbbbddbaccddccdddacaadacdaabbbbddabbdbcbcbdcaddcddbdadadbabdaadddddacacacccadaabaaddcabdabadbdbacbccaaacabdbbccaaddddbaaadacbbdaabbbcdabadacddccccdddcabaaaaccbbacabbcccdbccdaabcbdcbabccaddcaccbcacbdaacdaddabdbcabbccaacdadcddbcacacccabdbaabddaaddbbaccbcbbcabaacbdbdbaaddcacaaaadabbdabddbbbbaacabdcccaaaaaacbbaabbbcbcadcbbcdadadaabaccbdcdbabbbbbadcdbaddcdacdbcbbbdadbcddcadbdbccaadaaadaddbdbddbadbabacdccddcbbadccdaddabcdcdadbabbbbcbaadaacdbcdbdaaadbdbdabadadaddccdcaccccddadacaabdabdcdcbaaddbadcbdadcabbcdcbdbdabaddccbbdccacbbaaaaababcabadbdccacacacdddabbdadadabcbcdcdbcadaccadcbbcddaadbacbadbacbccbccadacadcdbaaccdbaccdabcdcddddaccaabbacacbcdccacdadcadbabbddbbddabbdcdadaccdbdaabbacbcadbbbacccbbbdbbccaaaddbdabdddcacdaadaadbcabdacccadbdacbaacacacddcbaabdddabdcabccaddbababccccccdaaaabacbaaadabaacdccdabacadbacabadadabbbabdaadbcddddbaabcdccdcccbadbcdbcbcadcbadabaccdccbdcadaacdbababbcadcccbbbdcbdbbcbcaabadbddccabcacbccbacdaabbbabacacdabbcbaccbbdacddbcbaabcbbadbbbdacbcbccbbaaccbdadddaddbbbbbaadddabbcbbcaccbdbaaccaaadbdbcdbcccbbbddbcdabcbabababbdddcccababbbcabbaddaddcddbbccdcbdcaccacacbaccdbbdbbbcabcdbbbabbbaddbcccdbcabdbadabaaaabccacbdddcddabdbbdcbcbccadddccbdcbbbdbcccddccbbdaacdabacacadaadcabacbbbbcdaddbcbbacacadbdbbdabdcabccbbdcabbdddacdbacadacccadbbbddbbdbabcddcaabcabacbbbdbdbdcaaacababdbacaaacbbadbdcdbbadacbbabbbcdcadbaccabbdaabbbacddababcddddbacdccdacaddbaadacccdcaddacadbbdccddbdbdbbdcbabaddbbbadbadcaaddccbaacdcaaacbdcabdddcdbdaaccdccccbbddcddcbcadbccadcbacadabababbadacccbdccabbabccabcdaaabbabcdbbbdabbbbbaacdcbbacabbbaadaddbabaacbdacdcdccccdcaccbbaadabaccddaabaccdbdcbadadccbbadaacacdddabdcbcccacacddabadcbbbaadcadbdbccacbbcbdbcdbdaacdabbdbadddaacacadaddcacadbcaadbbbabbdacdabcadacbcdbadcaacabccdddcdddcddbaacddadcbcabbacbaacabbbcdaabaccbcadaddcaddaacabcbbbddcdaacacbdbdcacadcdcaaaaadabcbddcaddbcdbbbacddcddbbbacbabcbbbddbadabbaabaabaabdcaadcbcabdcaddccdabadcccabcbdbadbaddadcadabaddbdabcaabcdabdacdbbaaccddddbddabacaddbadadcbbdddabaaddcaddcdbbccbddcbcdcdaaacbbcccbaccbaaccaaccdaccaaccddcaadcccaaacbddbadddcbcccaacbbbdbdbabdcaabaabdbabbbcadacccccbbdbbbccbdaaadcaacdacdcbcbbcdccbbcddaddcadddcbbbdaaacbaccbcdcbdabbadaabcaabddbbcaddcdcaddabddaacddcbdbbdcdccdabccdadbbccbbbcacbdcbccbcbcadcddddcdacdcadcdbdaaddcccaddbacbbdcbdddcbdccddddaadabcdbdaacdbcaabcbbccabcbbbcabdaaacdddcaadcccddbcdaabcdbbbbdbabaddbbdcabbabbddbcbacbdbaacbacabcbabadccbcaadabddbacdddcdaaaaddbccaddaaabccbbdacdabcaacdddbcadbddbcbdbacddacbadcbbddddcabdcdbbcbdccadccbcccdabbadddaddcdbcadabdabbbacbcbbddbccdcdbbcddacabbaaadddbdcaadcbdcbdcdbdbabacbbdaacccbbaadccbdcdadcaabcddabddbbdbccdccdcbdddabbdbcbcbdcdaaccdbcdccabbbbcacaaacaddcdbcaabbaaabbdddabdbcbbabbbcbbdabbdaccaccdacabcacddccbdaabdccbbcbdcbbdabaaaadddaadbddaddddddbdcaacddddbdcabcbbacccababddbaacdcabbbacccadadbcbadadcdddcdaabccaacabacdaadccacaabadcacdccbadbddaccbbdadccbacdccbcabcbababdbdaabdbaaccccaacaadbdbcdddcaaccdbcabaabccdddccccdbaabdadbcbdcddbaacbcabcbdccdbabdbbdbccabdaaadccdbdcbbdabbbcdcdddaddacbcdbbcddcbadbabadabacadcbdccccbaababdbcddcaabdddcdcdbbdcdbbdcbcbbcdbddababaacaddbdbcacbcdbbddcbcbcbbbabbbdadbaaaddaaaccbbcacccccddcadcbcbcabbabdcdaddbdbadcbcaadcbdbabdadbdcbbbaccdbcdcacbbdcacdcdaaddaacabadbbdaccdbabcdbabcddbcaddcbbdcaccdbbddbddabbcbcdbadcbcaabccdbbcddabdbdacacadcdbdabbcdccddcccdacbccaccdbcccbbaddccdacaabbacadbddddbdccccdbdccbbdddcddaccacbbaabddcbddbaccdbdabccaabaaaddcbadccdbdbbacdbccbabbbbabcbdcbbaddbbbddcdbadddabdcccdccdccdabdabddcdaacacacbbbdbdcbbcdcaadbdddbbdacbabdddcbbdddbcccbacbcdaddacddadcababadacbcccabdcdbbddcdaabbbdaabdcdcacdddaacaddcbcbaddddbacabaddcabbabcbdaabbdacdcdadcbdbdaccaabbbcacddbbbdbcbaacddccaabcadabccccbcaabaccbcbdacabcadabbccbdabadccbbbddababacbadbaabaddbccdbadadbcbbcbbdccddacddbdadbadacbabbadbabccaacaacdabacbbaccbcccddccadddddbdbabcbbddbcadbbaadddabccacaadccbabdbbdbcbaabadcadbdbbdaddcadddcacabccbacbdaddaccddcbcddacaaaccbcbbcdcdadbabbaabdcadbbdddbbdbcaabbddbdcdadbdabadadcddbbdacdbcaacbaaddbdbcccabbcbdcadaaabadabcaadcdbcacdcaadaddddaabadabbbadbdadccaccccacdcdadabadbbdaaadbbbaadcdbdddcaaabdcabcdaadacaabbdbcaabaccbcbacbccddbcddadcdacccbbbbdbacabadcbbddaacacadbdadcdcbadcdbdbbadbabbccaddbcdbadadaacabdccaddacabdadcaaddacbdabccbbcccaacadddacbcdabcbdcbccaccabdacddadcdcdaacacdbdaabdcaadcccadaaadbaaccadbcdaadcdacbdbabcabbbcabbbbdbcdbcdcdcdccdaaddddaddbdcabddbdbaaccbbaaabbdbbccadbbdaccdcacdcbbbdbaaacdcdbcbaaddcdcddacccdabccbaadccdabbacbacbbcabdacbabcbcbacdcaabaddccadadcddbacadcbabdacabdacdccdacbaddabaabaadacbbbdcabbdbcdcababdaaadcbcadaabaddddbdacbaaaadbbaadddbbadcabbcabdbdbdbaacdcbcbddaacbbabadbcdacacbdcadbacdbdcdcabaddcdaacdbdbcccabcadcbccaadbdbdbbdbdbdccdcaddacaaddbcbdbddcdacdcddbababcbdadcbdddbdbaabdcbdccbbdcbcabdaabbaacbabdaaaddbbdbcccadbdcbaacbdbabdcbddddaddaadadaccbdabbadcdcaabddacaabddccbacbbccbabbbdccbaddccaacccbbbdddcdcaccaddcbcdadbcdcbbdbaabcaccbdbdcdcadcbabadadacddbcdbbccbabadbbbdcdadabcdbcbbcdddacbacbcbaabbbacbcadcccccdbbccababadbadccbaabaaadbcbbdcabcaadbdaadbaacaabaccdbbcacaadcccddbddcdcddbaacabbaaaabcbaaabbdddcbbbddbcdbacaadacbbdbcbcdddabcdbaccaadadddacddaaaccddbccdadddbdabaadaddcdaaacbdbdaccabbddaccbdbbadaaddbaaabaabcdccddabdcccaddadaadddaadddabcdcaacdbddcacddcacacdaabbdcacbdaddadbaaabaaccbacbdabbcabaaccbaaccbadadadacdbbcaddcddddadcdabbdcdcbbbdaccbaddbbacaaacabbdbbbdaabdbcdcaabaddddcccbcacdcbadccadbacccbbaccbdcddbbbcbccdcdacdcdacdaabaabddbbddddadaacbbcaabbdabbbbaaaaaaddaacccacbacacabaadbbbdabcdcdcababdacadcdaddddbbccdcbdabacaabdbdcdaaddadcdcacabbadaacbaacbacadbbacbbdccaaccdcdacbcaabbdbcdaabadbbadcbabaadccddaadaabcaadbbbcdabcdadacacdbdbadddacdabaaaabbbbbcdbcbcacdaadacaadddbbaacdccacddcaabdddbbabbadbabddbcabbcddcaadbdcaadbdabcbdbbbbccadcacdbdaddbdccccddaccdaddacaacccdabcbccdaababaacaaaaacddbccddbaacbcadcabbbdccccacdcaddcaccaabccbacdccaacdabdcacbaaccadacdbaacddddaccabaccabddcbcccabbcacacbbbccacdbdabdadbbbbaabcbbacddabbaadddcbbcdcdbccadabdbabdacbcccbdcaaddacdabbbcbbdbbdaddccbdbcadaabcccdbadaabbcdddcddabacdabdabbbcacbcdcaacabcacadccadbcabbcdcaabdbbabbdaddbcdacbbdaccabdddbabcbcdcccbbdaabdbaddaddbbaddccacddacabcccacdbdbbbcccbbdbcbaadbbdcccacacbbcabdaddbabbcdaadddbbcaccdbbabacaabcdbbbbcaaaacdcbabaadacaaadcabacabcbbddabdcbcaadacbdbdcbabadddccbaabdcacbccadadbddaaaacccdbbbaaddadabcbbacddbdcdaabdacbadcacacacdccacbcdadbcdcbaccadcaaccababcbccdddcdabaccccabdcdbdbcacacadbacdadacbdbbacabdcaacdcdddbacccadbcacbcdacbaccdcddcabcabdbadbbcccabdcdcbadbbcdabcbaaacadacdababbadccccbdaaaaddcaacdcaacaaadccaaccaddbddbdaacacddabcadabadaccdddcbcdcddcbddbaacbbabaddbacabcbcddddacbbbcbdcdbdbadbcaaccacbdacccbdddacdcbbcdbbcadddcacdadcddbdccabcddbddcdbaaacccccadadbdcacbbabdccbacaabbcabaadaddbdcbabdadbcadcdadaabcbcbcbbacbadcbccacddddbdcacdbbaacbbdcababddddccbbacbcdbabbbbacaabcccadccddbdcadbdbbabcaaaadbadcbcdbddcccaadddcbbdaddbbaabdacaacbacbcbbdcaaabbaadddccaadadbaccadadabbdbcccddcddbacddadcdddcaaaabaacdadbadcabbadabcdabddbbacbaddbcdcdcdaccbcdbadddaadbabbbddddabcaddcdbacdacbccbaadbcabaacbbabaaacdbabdbadacbbddacccadddcbcbabccccbdbcdaacddbaaabadbababcdbcbddcbbdbccacbabdddadaaabbbbbacabbbbbbcbbbbcbdcbbcddacbcbabbadddbdacabbdcdacdbbbbddabdbdcdbbccccbaaaabdcbbaabdacaddaacbcccbbdcdaadcadcbbbdbacbccaaccdcbcbcadacccbccccabcdbdadccacbcdacbddbdaadddbcaccbbcccbbcbdcabdbbbccaadbccddcccbdcdaccbbdaddacaacababcadbdacabcacdbbadcdcdbabbcddcccacdcdacccdbbabacadabdaddabbdccaabbcbaadcddccaadbabdcddbadcddcaabdcbbbdbacadcddbdadbddadcbbdbcacbcddbcddbabdbdaacadabbdadcbadcddbcbcadcbbcdccbdcaabccacbaacaacbacdbdbbcbaddcbacbacabcdddbbccabcdcbcadddabdabaacdddaacccaabbbbcdcadabacadadacbcabcccaabbbabdbdbbddcadcdcabbbadaccadcdccaaccbdccbdadcadcdabbdcbdcacabadccbacbcddacbcbcbbddadaaabdddbcacadbbabcbdbdcdaadcdaadcdabcdaacccdbbbbdadcbdcbccbacacbcddaaadaacddcadbdbcdccabcdacdcbdddbdcbbabdddcdadacabbadbcccadadcabbbabaaaacbdaadcbadadbbacbbbcbdccdacdcdabddaccacdddbddbddcbbbbbacbaacbddbcdcddbbdacdbdcaccaacabadbdcadcbacaacadababadbacabadbacbdcdadcccaaadbbbccbcbcabccacaddacdababdbbbabcaadcabdbdcacccdacacacbbdcbadabaabcdcbbcbbabcbaadcdddcbacaabddaabbbccdbbcccadabcabacdcbbbddadcdbdcdcdbdbaddcdbacaacabdbdddddccadcaddbbbbddbcabccacaccadacadadddcbacbcdaaddbddddadbdbbccadabdabbbadcabdaaaadbcbadcddbbdaabbaacdcdcadbdabdbbcabddadbdbdabacbbcbdccbddbdcdadccbbdbdaacdbccccdcdbccbcbdbbdddaabbdcadcccbddacddbbccaadcbdacdcbadabbcadcdbacbbcaccbcadcbadaabbcdbbbbacabbccbadaabdabdbaadcdccdbaabbcbbbdabcaccaacdabbadaadaacbabaddcdbdbccadcbcbdccbacdbadbdadccacaddaccbadadadadbababddbbaabdbbacbcacbcabbbabbbacbbdbacbabbbdcabbdbcbbbccbcacddcbbdbbdccdcbddddbdccdacdddccbcaddccbadcbbbccaadcabddacabbababdbbdddcdccccdddcacbbcbaccbbaabdbbcdcbddcdbdbcbdbadbcbbbbddcdccacaddabcdacdbccbbaacccddacaacdbcaaaacacbabbbbacdaaddcacaaccbaacacadcdccbdbbcdabcaaccddddaacdabccccdbaadbbbbdaaccdbdcccaddacadaccdddbdcaabaddabacbdabdcccbbadccaacbbcbaccabdadaaddddaacccadbadadbbaddddcbdacaaaccbdbbccbacaacacbbbcbccbcbbaadbdabadacccddbdbabbaacbcaaacdbbdabdaacaddcbbcddbbccbdbdbabcbacacdabdcbdddcaccdddcaadbdddcbdabbddacabdbddbbddabdaadaddcdadbdcadbbcbbcacabacadabdaabadabbdacccadbcbdacacababadcdacdbbdbcdcdbdabadddaabddadddcaaaadbbacddadaaababdabbbcddacdcdabcbadbbbcabaabaddcdbaabcbbacdcadadacdcadabddaddbdbdbaaaddbcbcdbabcacaadbdcaddbbccbbacabcbaccabbdcdabccaacdcbdcbcbcbbdbddcadcdbccaaabacdddddabdbaacdcacabbaddcddadbacdbadbccacbbdbbabbadacaddaabccabcbbddddbdacdccdbdbcdaacccbbcabdbacdbcbcdaccdcbdaaacbbdbccddbbcadbbdacdaadbabadbdabbccbbdabcbbacabdaddbbbadbbaadbcacbadddabcccaadbacdddadcabbddcacbabcacbbcddbdaacbacaddbbdddaccdbdcacdcbccadbdacacdabcbccaacdaabaaddacdcddbadbdacaacccbbdcccacabacbcaadadccbadabcccbaadbdbadddbcaddcacdbcacbcbdcbbdbabcddbcbcbacdbcadccabdbbabadcabbcbdaccdbdccaccdabaabaadbcdabbabbadbbbcdabcbbabbabdcaaadcdbcdccdbbcbbbbcdbdabdbaddbabaddddcacdcbadddadbbbcdcbcaadaadbcaacabddcdaaddcabcbcdbbcbdbcdabbaaddbabdbdcdcdcccddbccacababaabbacabcadaaaccbbbabbadacbbbcadadabcdbabaccbccaccabbdcdacabbdbaacdbdbcbdadccdcadcbdbaaacbdcaabcaabbabcbcbdacaabadbaaddaabbcbdbacdcccbcbacbddbbdbaadcddbbadbdcbaccdcbbbabdccaccccaccadacdacaddbccbcddcbdcdbdbbbaabdacaacbacccacbbcdcbcbbadbdbdababacaadcbaddabdccaccabbacbccacdbcdbbbdbbcacbbbbdcbadcdddacbbccddccabcacabacccabaaaadbdcdcaabcbbadabcbddaadbaabccbbbccbccbdbabdddbccabbccbcddbbbccdbaaadbacbdadaaabaacbbdaababadbbaddabcdabbacbdadccaadabdadacbaaabbcdccdbdccbaabcbbbcaaaabcabdaadbbabcbabbbadaabcaccbccaccdcbdbcabbdbcdaacbdcaadbcbcaddacacaacbbbabdacdbadcbdabaacbcdbbadbcbacaddababbabbbaccaddaaacdbcaccddcadcacaddaaaccbcbccacadaccdddbbdaaccbbacbdacdbbcbabbccacbccbdddbacdcdbbbbcacdddcdddcbccbbcdabddaaaaccbdcbccaddcadbdbaacabdcdbadacaccacbdaacadbccacddabcabcbbdbadacbadcddbcdbcadcaadccabaabbbaccaaabccadacababacbbabdbdbbbbacdaabadcddaacaccddabbcdadabcdabbadabacadcaccdcdcdcdbacdabbadcacbcbcdcbdadaddddcacbbbcdcbadbcddcaccabcddadbcbccabcadcccccaaabaaacdcaaadabcadddcbbdbccbbdddadbadadcdaaacbaacdacdabccaddbaadcdbcaacdaccadccabdaddcdbbacbdddababcbadbacdcabbbabaddaabcbaadbaddbcdaccdabdadabdacbcbccbdbbdabbdccaaccadbdbbabbccadccdbadbdcdacdabbcbbabcbdbadcdbcdbbacbadaccbaabdbaaadbdccddadbcaaabacdddbdabbdbaccacababdddcbbacacbbbbbbbbdbbcddcdababbcbccbcdcabbacbacdcbbbcabbaddaadacadcaabaadcacccddabacdcaaaacbbcbbbbdbcdbbcdcacbcbabbdccadbacaaabcacbbcabbbaaaaddccabdbabaaaabbbdbabdaadcbccbdabbbdcaccbcdbcabbdccdbabdabbacdbdaccbbddbbaccbcdaacbaddabdadabacacadabcaaadadcbbadcdddccbbbcddcaacddaadcadbcbccdbdadadbbcbbaccdadcbabcaccacccdabbdacddcbbccabaaccdbbbcabadcdbaacddccabddcaabcccdbbcdaadaaaaabddbbacaaaaddacbabbacacbccbcdababacdbdbddbabdbdaabbcdabdadddabddabcdaccbbcdabcaacbaaabddbbdbabcbddccacbddbcbacadaadccddbaddbccbdabcddbadcbaccaababadcbbddabdccbcdbcabacdbadaaadddbabddcddbcbbcdcdbccddaabdabaccacbdddabdacbbbabddcdabdaaddbbcbdccbcddbacdcbbbababdcbaddcaddddbbbdadabaabaaadddcdaacbcaababcdbdbdbadcaabcdaaadddbbbcbbabdbccccaccabacdccdbadcccabdbacbcdccaddcaccadbabbdbddacbbdccdbbbdbbccaccaddabccadbcabbcbcbacbbbbcaacbdcbadabddddacdccaacbbbbaadcbbbbadccaacbaddaadbdcadabbaddcbccccdccbabacdaacadabadadcbbcadabbbacaacbdacbabbcdbdbdbddbcddaccaaadbbbadddcbababcabaadcbbcdcabaadcaadcacdbdcaaacbddaddacdbdadcbacaacbdddbaaaccadcdcbabbccbdcbcdabccaccdbadbbdcbddbddbccbbbadbaabadcadbaccdbbdaaaadacabbdcbbabdbdadccbbdbccbcadcccdddbbaadccbadddcdccaacabadcdcaddcaadbdcaaabdcacbdcacbdbbcabadcdcadaccabbbbdaabdbacaddacbbbcbbbbcddbdbddddaabbabcccccdcadcaabadcaacdabaabcbadccccdaabcabdbadbccaddbbcbacabbcaabacaddacadaaacdcbcdccdacdcacabdcacdadcbbbdbdcaccbcacaacbaadcabdbbacdbacabcadaadcbadabddbdbccdcacbccbcbddaddcddabcbdcbcdacccccdbdacaabcbabcabccdddbcdadabaacabbadbadddddbcccdaccdbcccbdcaccdddabaabcdbccddcbabadbbcadcabbabdcadbdaddcababdaaadbdccbdccadcbcacddbbadbcbdabcccdaadddbbabcdbadbdcaabcddacadcdbdbbaabbbbcdcccacbbaaacaaaaabccacabcaadadbdaddbbdcadbbacccddccacabbabccbbbcdbbcdbaadabaddcacccabccdcccaacbbdbbccccaacccbcacabcbaacbdbcaccbcacabcaadbdbbbbccccbbabbacaaacdadbdaaacbbccdadbdbdadbadbdcccacacddbcdddbadadbddacdccdcccbccaadcdbddddcaacadbcbbabbccddbbabbddbbcccbcabcbcbbabbdcccabcbacbdddcbdcdaccbbddcbdbcbdddccddcbddbcccabbbbdbcabcdbbcabcacdcdcccabadcbcbdaaccbdabcbaabdbcbcbaacadbdbccddccbbcbbdbaacdbdddabccdadbccadabaccbddbdbbadabccddcbddccbcddcdcbbdbddbbadaabaaabcbcccbbbdaccbabdcccadbaadbdbabbdbabadcbbbbcaacbcababcbacaabdcbccaacaaaaabaccbcdababadbdadddcaddadcbddbcdcdcbadabcdacdacabdccbbddbcacccacddcdaaaddcadacaababaadcbabcdbcdcbbcbbaacbdaccbbcaccaadccdacbadbbbcddcbacdbbbcbdcdbdcdaaabdbaadbcbaaacccbddddbcbcbcaadcaaabdacabdacccddbccacbaddcbaacabbbcacbdadcccaacbbdbbdbcdbadabbcbaabbdabbccbacaaaacabcdaacccddaadabadbcbdacacbbdcdddbadbabbbaadbcacdabcdbbdcbdcdabbadabdcbdacaccbadcccbcbdcdabadadabddcddcdbdbbadcccbdccdbacaddccccdccbdccacddadcbabbcdbccabcadbdcaabcbcddbaabbbacbccadccddcdadabcacdccaddbabddddcaddacaaaabcaadabcccdcdaabbbabccdcdacaacddbdccadddbadcabbbcbcdadcbcdcbcabdcbcaadabadadbaadccdbcdbbdbdbaadaddcdbadcaaadcdddcbbacabddaddddaacdbaddbcbcdadbbddadbcaabcacbaccbdabbcbcdbacacacccbdcdaaaaccbdbdbdddaaaacbaaaaddbaddadbbdbccabdadcdaddaaacdbabababbcbdacabcdabbbbccbcdbdbcadacbdbdaabaacbbcddabaaacbcadbdacaacbbadaabcbcdddcbaacbdbbdcacaadaaaababdbcddbdbaacbbcadbbddacdaaccbdcbaadbbdabcabbbdadccbcdcdddbbbbdcdbbcabcacdbdbddbdcdaaadcdacabdbbccabdaccdbbdcdbbcdacbccccccacacbcdcddbacbcdbbccdcdabcdbcaaabcadcdbacbdcdaadccaccacddacdddccdbaacbabdcbcbcadcacdbdabaadbdbcddbabbcaaacaadcaddbabbbbdadddcbaaabbacaabbadadbaabaadadcdcacdcacaababcabdddbcbccaaddcaccacadccdbaabdadcdcbcddbadbcdcccaddcbbcadacccdbabdddbdbacaccabbbcdcbddadabdabadaadcaabadadcdccacabacdbcaaccdbbdbccdbccbbbaaababcaccbcddadadcbcccaabbacbbdaacbdadbbdcadcdbabdcdcadaccaddacdddacccbddcbcadcdcdaabcccdcccbaaccaabddbbabcbdabadbbdacabbccabdabacddcadcccdbdacbdadddbcadccdddbcddbcdcccdbbaacbbbbddacbdbdbcbdaababaadcdbcbaaadbdcbbcadbbbaaddbcddacbcdcddcacdcacabadaacacdddcabbbabcdccddbcbdcdccbaddacabccdbdbcccadddccbdbdbddbaaaaaaaccbcddcacddbbdbdcbbaadcdccabbdcdcbaabcacdacbdacdcbdcdbccadaacbbcdcaabaadadcabbbbaccbbabdcdcbabbcaaadbabbdbcdcdddcbbdcabccbabdcbacdaccacbbbaabaacabbcabcccbbbaddadddadccdbaaddddbcddabddbabcacbaabdabdadbbbcdbcdaabadcbdaccdacbbcdcccabdddbcaadccccaacdcbdbdbbabaadadaabbcdaccbcddacbcbaddcccabbaaacabbdbdcccbdaaadcbcbcbccbdbbcaccabbccbbddcadbaabacdadbadddcbdbbcacdbddcccbacdcccbdcbdbddbbccaaddccdaabadbadbcdbddbdadadcaccadacdccbcdbbdccbacacdbacacaacdbcdcbdaadbccaaadbcbdadabddababbbdacbcccaabcbcbbccdaabbdaabbbdaaccbdbbddcbcdadaaaddccaacdbddcbaddaddbaaadbaabcbccbaccdbdacbaadbbcadcbbbabcdbddddcdcacbdadccdccdbbbbddddbbacbadbdcaaaabdabacdbbbdbdcadcbdaabcbcaddbabcbaacddddcbbdbdbccccbadbabbbcbbddbccbdcdcbbaacdbcbcdcbdbcbcdddbbaccacbcddcabcdccdbbadabcbaaaaaaadbabbadabbbdcbaddabdcddbacabdabbccccaddaadddcdcddadbcdabccbdadbcdbddbcbcabcddacabdbccdcaddbcbdbbbcbdaaaadbacbaabadccdaabadcdbabdaacbcbddabcaaadaabcbaacaacbbdddcaacaadcdddacaacabbcabccbaaddbadcacbcaccaaaaddbcadbcbdaabdbaaabccdcdcaacbadacabbcbbddddcdbaabcdcbbabdbbdbbaacccbbababcddddbbaddcddabbcdccbaacdddcbabccdaadaaadadadbbaabbcbbacbcccacabccabdadccdabccddbbbaabccbccadacadddddaddccdaabbbbcbacabbcbabdbddcacbccaccbadccbabbdccabcdddddbabbbbdcabbbbcaacdddacadbcddbcbadaccaabbbccabacdbdaccccbcdcbcaabdbdaabbdaacbdcbadcbcadabcacaaabadbcccdddddaccbcacbdbdabcbbadbdbcbdbbcbdbaabcbbbdadcddccadaccaaabbccddccdbbbbbdabccadaddaadcdaccbccbabacacaaacbdcdcabddddccbabdbcdcbcbadbdaacccbdddbbbcbacbdcbbbdaaadbdcaacdcbdabdcaacdabcadbdcadddaadbadbaababbaacdaaadbcbabdbdbcabddabbccbccdcbdaccadaadbbcabacabddacbdcaabbbcdbcdcdabddccbccadccccdddaacaaaccabbcbbcbbdbddbcabdababbbcabaaaaabbbcadccbdcddcddcdcaabaadcadbbdcbcdbacaccdabcacbabbabbcbccbdddbbbbcbcabbdbcbcacbbbdcbbabccadaacbdbbadccaabcdcaaaababaaaddcbcaabdcacdcbaadcbbbcbccdbbabdbbdacbcadbbcccddcacdcbbdbbddaaadbbbbbacdccbadaaabccbcbbadadabbdddadcdabcdbcacaabcbaadccdadcdacdcdaaabaabdcdbabbdddaaabbdaacdabdcccaabbaddbdcbdadbacbadacadadbdaaadbbdcdacbadbabdbabaccddacccbbababbdbabdabbdbbbcbadbdddcabbbabdaccccdabbdcaccccabcbbddbddcbdcdbacccacddcbccdadbbcaabbbabbdccbaccadbcdccdabccbcdccdbbdacbdbcdbdcacadbabcdcccabbacdcddbbbacacdbccbdbbdbccadbcccabdbcadddcccdcabbdccccdcdaacaaaddbacbcdabcbcdcdbbdbdaaaddcddacbdcbbadcdaddbbcaadcddddabcbaccbbbdccacdddccccdaddcbccacddabbcdcadcdcaacbdbccccabdbcbabcdddbaacadbabbbbacbaaccaacdacbccabbbabdbacacaaacbdcabbccaabbaadadacbdabcbdcabbdadbdddbbddcdadadcdabadcacdaaccacddcdbaacbdbbbabdddcaccaadabbdadcccbcdabdddbaccdbabdbddccbaadcbaccdccbddcacbdcdcddddcabbcccdacdcccabcbacbcabbdabbadddadadddbdbbcbbcdcbabccddaccddccdcdabbbabadbbabcbacaddcdbcbcbdaaccabdbcddcdcabdddacbccaaacdbcccbdbdbbbdbabbaaabdabaddadabacbbcabcdbabdcdabcdbbbcbbaadcdcaaadcbbccdcaddabcadbabcccccabccabcddadaccbbabadcacdcbbbbdddcddabbdbbcacddaaadbbbbadddbcabccdadaacacbccbbcaccabaabbacccadbacbdbcdbdcbdaccccaaacbbcabbcbbcbcaddcdbbadcbbadadbabbbddbdbaccabbcabaadcdabcabccabbacdbcccbabcdaaabbcdbdccdcccddabaddcdabcdbcbcbcddabdadcddcdbdacbddadaabddabbdbdaacddcaddaaababbdaaddbddcbacdcdcdabbddbbaccbdddcdaadbcbbccaacaaaabbdbbbbabcbdabccbadcabccacdbaacdabcbbbddccbaccccdccdbccacaacacbbdbbccbdcccbdbaabddbccbabcacdbccadcbbbbddcdcbadbadbdacabcacabdbdcdaacaadcdbdcdbdacbcaccdccacdbababcacacdbacabbababdbbccdbcbcddccbdccdbcacaadadbdbacabdadcbaccaabaacacdcdadadcbbbcacbaacacaacadbaaadcaddabccbddaadcdddbdcaaaccdcabddcddaacacbbbdacbbaaddbdaddddacccadacdabcdabcbabcbdbccdcadaacadbbbdbdcdaddbccabbbacdcccdbdaccbaaccdaabbcbcdbcdaddbccbabcbbbddddabbbadbbbccaadcdddbdddaaadbcdadbdaaccdaddacaccdbaacddcdabbbcccbcdbdcabadadccadaacacccabbadcddddaccbcbbccdcdcbbcaaddcdabcadababcaccddbcdadcdaabccdbaadaccabbaaacadddbbdbbbadbcadcdcdadbddbacaccbacddaadbadbdcbbdbcdaabdbabbdddadbccdbacccddacacdbaaddcbdcbccbaaddaaaaddabdddcbbcadcbbdddddcbcccbccacbabcccbbdcbcacbbdcaddadbdadaacccdccadcabbadcbbbbdcabcbacdbbbdbccbcbcadbccdccbbdbdccddddcaacbcdbcaddacbdcadcaabacbbdccacddccbdaacbdbbbcacabbbacdcdddcdaaaabaadacbcdcbcadcdadcdbbcccdaaccaaaccaacbbdbbbddbdccbdcdaadadccccaaaabcbcccbdcccacdcaddacbbbdcdbdbacbdcacabbadcbdadcbaabbabadccbbddababbbbcdcadcbaadcdcbbacdcdaacdddccddcdadadaddaabbcccbbaadabcabadabbbcbabdbbcbadacccbcacabbabbadbdcbbccbabcbcbbcdbbcbbdcaaabdcacacbcbdddbcbdbdababddbaacddbcaadabcabcccacabaaccacaaacbcdcdcdbacdbbcddcacdbacadbdbbddcccaaccabcccbdcbbcdadaaaabadbabcbdcbdcddcdaacbdcdbaadadacbaddaccacadcaaccdccbdbaacbccbdacabaabbdccbdbddbddaddcbcbaadbdcaabcdcacddcbcdccababbcacbaddbbcbddbabdbddbddddcccaaaabcabccbaccbacbbcccdbbdabcdddbbaadbabccdabacaacbdacbbddbdbbbcdcabbbdbdcbabcccdcacacdbddacaacbcadcabdcdbbcbaaacbddabcccbddcadabbbabccdccbadaacaddcdbcdacbbcaaaabdcdacccdbdbdddcccccaacbaaccacccbacdadaccabdbadcddddbdcaccbbcbbbccdbdcdcbdbdacbdaadbcccccaddbabadcbbacbbaacdcadbcbbdcdaaddbdcbbbabccdadbcadcbacdababcacabcbbddadabbddcaaccbdacadcdcddbaccaacacdadadabcbacdadcabccdbadbdbabaacbdadcdbdbbaddddbddbbccdacdcccaabacbdcdaddddbaccbdbbdcddddcdbbaccaadddacddccaaccaadaabbbdccbbacacdabababccabdcbbdadacdbbbcdaacdacdddaacbddabddbbddcccbababaccacdbdcdbdacdacbabbaaadbbbbdcddabaabbaabdbcadcaccdcaaacdbbacdadcadadddacdaaccdabdcddabccbdcbabcbbdaadacdcccbadccbdadbaddccbaacbddacdbccaadaaddcbccbbddbcdddabacbaacbaacadbcccdadbcbbacbdbcdcddabadcbacdcccabdcddadddbbbdcaadcbddbbcaaacaabcaccbadccdaabbccaaaaccbbabdcabccbdcbaadcdcbccdbbcddabccdccaaadbcdabbddabdcdbabbcbaababadbdbccbacbacaaabcbcdddcdaaccddaadbacccdccddccbdabcabaabbacaccdddddadcccadddaabbcbabdcbadccdcdacdccddbbabdbbbdcdabddcdbacbaabcabdaaaccccdabaacaddccbabaddabcdcbaabcbdbcbcdcbbdcddadcbdddcddbbbbaaccaadbcacacddccadbdbdbcdbababbdcccacadcbadddbbdbabdabbcabcbdadabbbcdbbbcbccaddabcbbabbbddadcbddabcbabbaaadcaabaacbadbcacbdcccccdcabcdcacbaabbaabbdcaacaccbacdddccddbdcabbabcbacacbacbddbdbaddcadcdaabbcdadabdbcaccdcaabaabacdcbaaccddabbbaabcdbadcdaadcbccbcbbccacdaccbcdcccdcddcdccdaaaccbcdddaabdadcabbddbdbbabddbdaacadddacaccacbcbbcadabbdadccdadbbaadabbbcdbccbbdacdabddaacaacbbaaddadbbbbacacdbaadbadaddadcaccdcbcaaabcacbdaaadbcadaddbccaaacdbacdabdacbdadacbbdaaadbabcddcdcbccbcbbabccdaadbbcdcbaaccbdadacdddbbcbabbbdadcccdbcaddbbacaacbabbdcdbabaacbccdabdbdcbddcbbbddcdadaadadbadcbbbbabababccabdaaacccbddbaaaabababbcddaaadddccdcbabbabdaddbbbcbaacccaccabcaddcacaabddddcddbbcdcbdbcabcddacadcaaddcaacbcbbddcccabbcaaddcaacaccdcaabbbdcaaacbdccccddddbcdcccaaaddbbccaadddbdbacbdbdadcaabcacdabaacaccaaddcaacdcdabdacbbdbabbadbacdcadabadbaadbabbbadaaadabccacaccbabcdbabbaabdcabbdadabbaaacbbbdacaacdaabdddabadbddbacbacacccdabbdbabaccbbbbddbdddddbddbcccbabcacacdbbcadbbdccadcabcabcbabadadaddcadbcdbbbacacdbbbcaadddacbaaaddacbbbbabacccadbcdcacbdcacbdcbdbbcacbadcaccabaacdbcccbcbddcbbacaaddccbcabcbadbabdaddbcbacbacadbcbacadadbcabbbccbcabbbbbabdabccabcacddadbbadcabbdabbbccabddbccaacbbabcacdbdcdaddcbabdaacbbcdddabddcbbccdaaaabbcacdaabcbdbbbcbacabbbaadacbabcbabbcdaccadabacdcccdabdabddcadaabbbcccccdaabdbabaddbacbdaadadcdcadbcbccdabaabdaacbcddaaadbaaddadaabacdcbbccbbdddaddacadbabacabdbbcdcbbadcacddaaabdaaddacddacdabdbcbbadcbccdbbcdcdbacdbbbbdaaddbabcdcababbdbcddbdaddacdbaccbadaabacdbaccbcabcdaaaccacbacbcdcbbabbcacaadcbdccabaccbcdbcbbcacbbadcbdcdcdadcdbacbbdbcddbdcdcadccdddabadbcbadaadcabdcbacccbdddcadbcbabacbbdacccabbaadadbdacccbbbddacdbaadaccdabcbabadcbddcdacdddcccbdcabcaddabaadbccdccbcddccddacabaadadbdddcaadbdacaabccdabccbdcdbddccdcacdacaadbbccdcccddbbdbdaacbabdacccacccacabbbbdcbcbccabdbabcadcbcbbbbadadbcbacbcacbddabcddadabbadaadcdaddabdccbadbbbaaaadbccabbaababcadbaccaccdaaacdbbadccaccdbcccacbaccabaabcabcccdaacbadcabdbcdabadacddcbddddbaacacadcaaaccdaddadaabaacdbbdbdaccccadaadbabcadbbaaacabdcdbdcacbbcdddcdaaadccbcdaddadaadadbbcbbdadcdcbadccccadbacdcdbdbaabcabadbbcbbccdaccbadacaccaabccbbaabcdbaabbdbcbbbbdbcbbccdccdcbddbcdbbabdddadbcaaaadacabcddcccdabcbbaabbaacdacbaddbbbccdcaddbbdabdbaacaadddaccbccaddcdcbbcbbcdccbbdddcbdaddabdbdcdaaccadaddaaccdcacabbadacaaddaddbaabbbdabcdbcadcaacdabcddccdbdabccdcacaaadaadbddcbdcbccdbabcbbccbcbacaadddabbaabcdcadccddcdaccaddcdbabdaaddbabacddcacdbdbabccacdcdcdbbaacdcabcacabcabaadadccbababcabdcccaabaaddccaabdaaccdacbbddadddcdbaaadaddcdcbdcbabbdbdabccacbbddaccddbbbbaccbaacadddabcbdadadacddccddbaccdadaddddcbaadcbbbbabaccdcdadacdcbbccaddacadbadbbccaaacbcaadcbbdbcabacaddbccadadcaaccbbacbcabaddbcbdcddaabbabddbbaddcacbccdaacdaabccbbaadabdaacdaacacaccacaadccdaccddbccdabbcdcabbcabbbabadccdccbcccaaabcdabdbaadccddaaaddbaddbdcdcccdbadcbcbccacbddbbcbdcaabbcabcaacbadccbcabacddcdabcbcdbacacdbddaaaddbcbdbabdacdccbbcdbcdbbcaccaccdacabdbcdcabddabdccbbddcddccaabcacccddccaadbbdbcbcdcdaccbacbaadddbbdacdadabaaadbaddadddbdddbaabdddddabbdaacabcadbddbbdbdaccabdabacbadcbbddacadaaccadaccadacadbdbabddbdcbcaadbcacbcbdabcbcbacadbbdbadcdacbadacbdbacdbbcccaddddddabdcdbabcaacbddbdabddadbbbaaddcbdadbcbcdccacbcbbaadcddbbdabcbddacbdaddddccaaadcabbacdcaaacdabccbccacdaabdcacacbcabbacaacdabdbcbdccccdbaaccdacbccabcbbaacdbdbbcadabbaddabbdacbdcaccbbacddaaaadabdbbdbaaaadaccacccbcabbddcdaadcbdcaabcbbcabadbbbdbccccdacddacccacdbdcbbcddbabadaccbcddbacbcdbacdcbbcbddbdcbbcbbbacabddcaabcacdacadabbbacdbbadcaddbdacddacdcbdaadcbcbadbcacdbaddacaccbcbdbbaccddcddbddcdddcbabdbabcdacdbabadaaaddbbccbbcaabcacbcddacbcabcaaddcdcdddddacabdbcdcbaadbbacacdcdbcabacdacbacdbacacdacbabbcacdddabaacbdddacccdacbcddadbdadcacddbdacaccbbcdaadcadbabadbdddbddbabcbaddbdbcacbcacdbbddcccbcbbcdaccdbbbbcaaddbdbcdcbaaacccbabddcddaddaadddabacabcdddcbcabdddadcdbbdacbcaacdddcbacaaacdcbdabacabaacbdaabdaddcbdacdbcddccbacaadbabcbbacbabbdcaccabacabcdccdbababccdacbbddbddaadbadddaadabbdbbcdcddbbbbdcdbabcbbbccbdcdadbcbbdbcdabccddaaacadbdcaacdbcadabbdbccdadccacdcbcdaaccaccbadcababbbdddccacbcddababdbcbbadacaabccbadcabbcdabaaddadbbabdacdadcaacbcddcacacbbbbdccabacdbadddbbddbbaaddcddbbcdaccddbdcbbdbabdccbacdbdcbcdcbcdbbadddbacacabdaacabccabbbcccbcabddabdbbabcadcccccbdacdddbabccbadddcbccbacdddcdabaaaddadddcdbbccdaccdccabccdcabbabdadbabdbdbcdddcbadbcdddbabaaaaacbaacbcdbccbaddabaddbbddddddccadcbbbdbdddcbdaacbdbbcaabbdbabaccbdbbdddcdbacccbabddbacbccabadbaacdccaaacababccabddbadacbddbaccdbabaacaadbdcdadbdddbbbcdddadcaccdaaaaadbbccdacacbbdcbabbbcaccddccddbcbddcddcbcbdbddadbcccbcbadcbccbbdaaccdabcbaabdaaccbcccddbccabcbaccacdccbcbaacccbddbbbaccadbccadbcbaaccdbddaacdabacddcbbdbbccbacaaaacbabbdaacabaaabbadcccdcbbcddaabdacadcdaabdabbddbbadadcbcdddbbbaadddaacbbabcdacaccdcababcdaacacddcbadddbddacbadbbccdaadcdbddacbaacccccdbadcdaaadbdcacdddbaddbdacabddbccdcdacaabcdaadaccccacadbbbdcaadadcccaadabcabcbbdcaccbbbbacdbcaacacbbbcaaadaaadcdcbaaadddddcbdbbacaaacbdccbbcdaddadadbaadbdbabbaadbacdcacddbbccbbbcacddbbbbccbccdcddbdacccbdbdabbccdcdabccbadcbbdbdadacccddbaddddccdcddbdadadddbacbadddcbacbbccadadabbabcadbdccbcbbdaaaadaabbabaddcdadadacccdacbbdaacdcaadcdcabbdddbabcbdbcddbdbdddcacbcdbaaadbdbdccbaddbdbbdcdccdddccdbcbabdddddacdcdacabcbccbbadbbdabccbbdcccaaaccbcbcbdabccdbcddcdabbacabadbdadcdaabdbcbdacadbcdbadbdabcdabdcacbbdbdcabadcdcbabcdaccbdcbbcaccbbaaabbdcccadaadbdcadcbbbddcabbbcabdcaaadcbdccddddadcababacdbaaacdddaadaacaadcadaaacdcaabbcdaccbaccdbdbbdbaabaadbbdabdacbdddabbcaccdadcbccddbccdabdadbccbcadababcccdbcadbbdaacddaaddbccbaacdbcdbbdbaadccaddcdbcdabdcbdcbcccababacaccdbccdbdcaaacadbadabcdacbdacbadbaaabaabdabcdaaddababddadcbcaccdbabccdbdcbbbcccbcaccbddddaddacddccbbaabdabbdadccaccbdadddddcbcbdddabddccccabbcdcbabbbaacabdbdaabbbcbcacdbbbdacbdcbbcadaaabcbacdaabbbacddbaccbadadbbcbabdbdbaacbaddbacbbcbadccabbdbacbbdbcdbabccdbcddcbbacccabcaadbdcadadabadaacdcdcbdbddcacbccaaccbaaaacacbabddcccdcbcabdcabcaadcccbaabbdbbdadabccacdadacbccacdabbadddadcbbcbdddaabadbcadbccdaaabbaadaadbdbaacbcaaccccbbcbccbbbcbaabcdadbadbcddcdcbdbcadbbabaacbabcccbabadcaadacbbbadbaddbaaaddbaacbadbdbcdadbdbadacaddbbabdddcdccbdaadadcdbdccaaadccbccdddbbaaccacdbadbcbaacddcadbacaaadacccbcddabdaabdbbdadaabccbcababdadabddcdabaaaaadacbbadbddabddbacbddcacdddacadddcacababdaddcdddbaaadbbcbaabcadbadbdcadddaaaaddbbacaaaacbbccadbabbcaaaadccaabadaaababddbddacdbccabbccdbcdcccbdadddccdaacdddabcabbbddcbddacaabcbcbdcdbbacabbcccdccabcbcddbbbccdbabbbcdcdaddabbaadaadcacacacccdbccaadbacdbcdcaaccaccdacaadddbbbdaaddbbdcbadacdabcdaadccadbaabadacaadbbdabddcdadbbbccbcddcbbcccdbaabdaccbccdcadabdbdadabccdbbbbddaacaadbccbbcdcabacadcadcbbabdcacbbdddacabaadaacdcaacbdbdacbbaabcabacbdbadbccaccdaacacbadcdbdcbdcadabcccccdbdaacbdbadabadbcacdbccbcacadbabcaabcbccdacdbbcbcdcdabddccbaacbbababaacacccbdaabbaaddabaacddbccbacdcbdadadbbacdbbdbccdadcdbabdcddcccbbbaabbbdadaababcdbdcbdbabbcabccdcbbbbdcadcdcdbbaccacadbcdcadbbcaacbadcbdbbabcacaabddbbabccaabcddbababcdbdcbccddcaabbadabddbdbbbcddbadccacacacbabbdacadbcbcaaccdcbdcaccdacadcacabaaaadbddbddbdcdaaadaadbddbaddccddadddcdcccabaadcadadbccacdaddcaabddacbbadbcccddbcacaaacbccabadbddbbbdbdaadccbacdcbbdbbdbbccadadabdadcdcaccadbcbdcacbdddbcadabcbbdbccbcabbccbbabdacdbaddcbbbcddaccabdacdbcdbcacacbaccbccccabbcddcbdbcaacdaccccaabdcabaaccbcaabbaadbdaaaaacabbbddbdacbccdaccbbcabdacddabbccdccccabcacbdadaaacbdadddcacababcbaaaaabbababdabaadcbbaacbbaadaabbcbadbacbaadaaccbbbcadcaadacdbadcdaccabaabdddadbdbbbdcdddbdaacabaddabbbcadccddaaddcdbcddbacbbabadbdbadcacdddbcadbbcbaaabdabbcdddccbbdbaacddababcbadbcbdddacbadccbdbdccaacbcbdbccdbbacbccabbdabacdbbcbbabbbdcacddbddbbddabdababbdcbdcdadddcabbdaddcccbbbdbaacccbbcdaccabddddbbaaaacbaacaadabaccbddbdaabcdcdcbdbdcccadccccacabbabdcaddcbaccbadadcaaabdadbdaabdbbaddacadddddcbcbbbabdddccbbabcdbdcabdbdcdababadbbbdabbbabbcacaddddabdcbdbcbccdacabccbacbcadaadadbabdbcaabdabacccbcadbdbcbcdbbabadcabaadddabdbaddddcdccaabacdabcdbcbdbccbbdccaacbacaccbaacadadcdabcdbbdcacccdadcacaadadbababcdbccaaacaabaccddcaccaabbcbdcccccbcaadacdbaacbddbbcbdabaccccdbdcbdccbabaaddadbccbbdccbaadcddddabdababbddadbddcbbbcbdbbbdaaaaccabdadcbabbadbacdcaddaabcdabdadacbcbccacccaadcccdbcdcbbbacbbcacddbabbccdaadabdcdacaccbdbbccbbbdbaddbbbcadcacddcacaabadbbaacbcbccccddabdbaabbddddbdacadabcccbcbcdabacaddddccdcdcdadcbcaacadbaadbacdcdadcbbbbdcadaaddcddacdcbaddcdbcdcbbcbddaaccdabadbcccaaacdabbcccbbbbcdaccbcbaababaaaadddaacdcacadbdacddabcdddddbbcbccbbdccdbaabbbadbababdbacdcddaaddbdacbdcdbbdadccccbbcdccaacbbdbaacacaadccdcddcbddbaabbbccadcbdaddcbcacbbdaabdbdbaaaddddacacdccbdbdadadbacbaddbdcbccdaccddbbadcddbdbabcbccbbcbcdddbbdbcddbcacdccccacbbadbabddabacabcccdbbddcadddcdcdccdcbdabdadcbbcbbbadbbbaacadccbcaabcaccdbacaadbddcdacbdbdabddddadbadcbadbddcaabccacaddbdddcaccdbdcaaaadbcacadbcdbcdabaaaddccdbdaadcdbaabcacaddcdadbcdaabbaddabcaddacdddcbbabaaabbbacccbadccacadabcabddccaacdddccbbabdcabbadbcbccbbacdbbccacabddbdbaddcacbabaabbabbcddbdcaddacccbdddacddabadccccabdadccddccddddbaadcbbdadadbbbcccddbbbbabccdadbbbbbabbabbdbdcddddddbbbcacddbabcacdbacdcdbdcacbabbaddabbbcdddabdabccaaadcaddcdbdccdadabadbdbdabdbbacbbabbddabbacbcdcdabaaabcbdbcbbcdbcaaacdddaddadbbddabdddbdbaddaddbababacdcdaaaaacadbbacbcdcbbabdbdbcccccddbdcaaacadccaccdcabcdcbccaaadddcaabbbdccddcdbccddadbadbddabddacbbaccaacdbbdadcadcddabbdcbccdbdabadbdcacdbddadcdaccdacdbbdbbccccdbbbccadcddaccbdccdccaddacbabbddabdaacbbbcbabbddadbcbdacdbdcbbccdcbdcaaadbddbadabbdabaaaaacccdbbbadbcbdbcddcbdccdddadaaccbdabdabacbadaccddcabadcccadbaaaaddccbbabbacbabdabbabbddacbaabcdcccbcdccabcbabbbbccbcadbaadacacaacdcbccaacbaabbdcbbbbccdababcdadaddadbabdadcbcddadabaadaccacccbdacdcdddcbdcbaadcbaaacabbddbcbabdadacdbddacccbcaaccccbbcbaacabdaadccdbddcdaddbabdacaadcabccdaaaacdbbbbbddddbdccccbcbccdcabbdcddbdaccabbbbcabadcdccbbbdbcabbbddaadcacdbdbcbddabadacbcabdabcbcadddaabddaabdbdacbbacadbccadbccdaadbbbbcdbcdacddcccacbdbdacbababbaddcbdacdacbabaabcbadbcdcdccddbdbbdbabdcabdbbbccccababcbcdcbddabbccaabbddccbbaddadcdbddcccbaccbcbcabacdaacdaacdbaaadacbccdabaddbaccacbabddcdabacaadcdabacdaabcbacabcacbdcbdacadcaabdbbcadbbcdadccacbbbcaacdbbdacbddcddadddabaacdaaccdbaacccdaabbdcadacbcbbadcccadabdcbabddacddbcaadacddabccdbddbcddcccaacacdabdaaaacadbaacdcdccddbcaccaccadadccacbddcbccdcaaccddacbdaacdbacdacddddcdacbbacddccbaddaaabdbbbbdbbabbadbbdcbbdbcdaccaaacdddcadadaddbdabdcbdddabcacccbbdcbddbcdaadbaabbbcadccdadbacaccbaadbcabdddbbccadbcddbcaddcbbabadacacaadddbacaacdccbdbcdccccbbcbdcacdabbbdbcacdbadccacbbbabcabcddaabaddaddbdadbbccabdcddccdcabcdaccdddaddbcabadacdbddbdbaddbabddbcdbcadabbaddccabaaddbcbacabbcbddbabccacddcdbccadcbadabbaacbbdccdaacddcbbcddbdbdddcdaadadaccbadbbaadbccdbbbadacaacadbdddddbabdccdbbcaaaddacbcdacbbdcdccabadcadaaabddcddbcbbbbababdbcdbbbaccbadbbdbcaaadbbddbddbdaabdaadbcbadaccbddccbdccbcddcdcddbccccdcbcbdbbdadcbdadbdccaacadcadbdacdcacdccccdaacbccdacbddbddcacadddacdbacdcdcbbdcacbaaccaddadabdbacbcbaccabcadbabbaaacccacbbcdadbdadcbbbcddbcccbbabbadbdbdcbdcaaaabcabddbdbdbdcddddbbcbdcdbbccbcdabdddcbcbdbdcacabdbacddbcaadcbdbdbcccdcddbadacaddcdabacddcbdadddbdbbbccabacccadbacdcbbacddbbcbddbdaddaacccaddddaadbacdcbbccccabacdacbaccadbddaadcadaddccababbbabcdcacbdaccdcadbdcbcacccbdadbacbacbbdbabdaadacabbcdaccabdaccbcabbcdccaddbcacaaddbadddacbccabbcdabddcdcacddbbccdcbdaabcbcbbaaacbaabdcdbddcaccdbbbbccacaddcaaaddbcddcbcdaabbbdaacacadcbbadddabcbbbbddcdacbabdabdddbdadadadacdbacaabdacaacbbacbccabdddbdccbacdcacadcbdcdcbabdcdacabdaacdbcbbaacdabccbbadccbcddbddaaacaaaabacbddcbbabadcdaccaadbdacbaccdaacdbcadcbdaadccadadadcbbcaacaabbddbdabadadbadabcaccbdcadbbdbaaacbaaacdcccccbaddbbaacbbddadbcabdbbddcbaddbbbcdabaaaabbddaddabaccbddbabbabbababbacacbddacacbcdcaaacdcdbbbdccddbcdcbdcccddaddbdabcddcadbbbdbdacdcbabaddcbbadacbdcababdacadbbdbabdbcbdccdcabcadbbdabaaddcbbccccabbaccccadcbaaadcadbccdabdcbdcdaaadcbdaaaacbbdcddbbaadaaadcbaccdcdbdaaddadbcacacabaccacbbdcbaccdabcddcddabbbdcdaccabbcdbabaaddcadaadcbddacaadaaccbaadbbcdccbdbbbcbabaabbbbcbddabdacbdbaddcadababaabacbcccbbccdbadbbbdaabddacbcddabdaadadacabadcbcdddacccadacbabddacbadadcabbdbbcabbcdabddcdcadaaabadbabddcdaaaacbdddadbddabadaabbcbccccdbabcaccbdbcabbacbdacacbcacddddabbcaadbbdbdbadadddacadddcdbbaaddadcccaadaaddabcccdaacdaabbcacddcbdadcddaccbacdadbdddbbbaddbadbcbabcabcabcbccabbdbacdbadbbbcbcadcbdcbcdbcbbdcbcadbddacdbbbadbabcbddcaacbababadaccacaddbadababdcbcbbdabdaadabbccdbacabbdbbdabdddcacacbbddbacbabcacaccacacbbdbdcddcbbbaabbcbdbbabadabbadbcabbcbcbaaacabccaadaddaccbabccdbbaaccabddbdcbccadbabdabaabacdcddbaadbdbbbacbacaddcddbbacdcabbdbcddaacdcbabdacadabaabcccadccdddaccddadbbbdbccddcacabbabdadcbadaacdcddaaabcbabbcbbaaadaddcdadbabcbbccbdaaccdddaddcdbdcadbabdaccbcdcbdcdddcdbcdacbccaabcaacaddabababccbccbbcbbbbbbccbdcdabcbadaaccadcdbaccddbcccbcaacdbdcdbdccbdcccddcddaddccabbbcbbaccbaddabddbccbcaaccddbbdbbbbcdcaaaadddcacaaacbacaabdccccdbbbdddadaaddddbbbcdcabbbdbabddcacdbdcadcbabcacdbbcbbccddcbcbbbddbbdaccadbdabccbdccadddaaccadcdddacddadcadccacdccdacadccabbdcccccacadadaaddddbcbcdabddcaaabdcdcadcdbccbddccaacbcccabdabbaadadbcbaacbaccababddadababdbaabaddbcabaaaaabaddcacbabdbabccccdabbaacaddcdbbccaaccbbbacbbacbbcabbbbdbabcdddabcacbcbcadbabdadcbabadccdcddadddccdbbadbabdbdcbdadbbbadbaaadbcdacdbdbabbcddabdadcddcccdaaadcbbbacbbabdcabadcbadbbadbbdcdbbbcbbcbacdbdcbcdbbbbaadcddabcccaaccbcadadcbbcbbbaabdbdbbadbbacccaddbadacbcbcabbadcdbbbcadaabddabddbdcbacbcadaabbaccbdaabadbdbcbbbaabbbdabccccddaaadacadcbbbdbdaccaaabcbbdaabdbbdcdadadbdaadbcacbbdadcbacaabccacdccaaccbddbdcbbadaadbacaaccadbdccbaadcacacbbcbbdbdaddbbcadadbbabcdaadaaadcdabcdaacdcaaddbaacbbbddadcbcccdcaddddaaccabbababdbccaabcaddcabbcbddaabbbccadddcabcdaddaccadaacaadbbdbaadbaadbdcaaadbccaccdadaccbdadbdcdbcaaccbdbbdabaacbbddacaacccbddbddabdbbaaadcbadabbdabcbcbadbaacdcbadababdcdcdddcdcbbdcccabccbbbabbdbbadaabbabaacdbbbcbaccaaaccabaabbbbadbbddbaddcbddcaaacadabcaadabdaaadbdabbbaaccbdabdaacbdccbadcbdbabbcbcaadadbadcbcaaccdacbbbaddabdbccbddcaddbddddcbbdddcddbdacacbbbaddababdccbdcccccbdcdbbadcbaababbddcbbaabdcbabddabdaddbcabdbcdcabdbbdcdabdaacbaacccdbadaaabbcacdbbaaabcddbdadbbcdbccabbbaabbcacdadbcbbaabbdbcaccaadccddbdddabdbcbbcaacbaacadbcbacccdababddcbbcbbabadcddaaaaabdcbddcaddddacdaabbdcdccbcdcbcdbaccddaadbbbcccdbcabcdbabcddabddcabbcaacdcbadddbdddddaaddddbcabccbcadbbbdadbadbaddaabdddbabbacdacddcccacabcbadababbbacbcccdbccbdbbdcccdbdacadaabdbdddbbbddcccdbccbccbddccddddbdaabcbcbdddcccbbadacbadbbdddbcdaddbcadcbcbbcaccdaacacbadbdbccbdbdbbcdbadaadaccdcabdbddcdbdbbcadaacddaddccdddcccacbdcdcabcbadaaabdcdcadaccbcbdbbdaabcdaaabadccdcdcdcadcbdbbadabbcdadccbbbcccbbbbbaaddbccacababdabbddaddcaabcacabdabcbbbbabcccdacacddadbbbabbddabccdbbcbdcdcadadbccbcccbaacdcdbdababdbacdbddaddbdbbcdacadccaacddbbabbcddaabaabcccacdadcccddbadddacbcadabcddcbbdababcdaddcbbccaccccccdcaaaabcbbccadacbaddcabcbabcaacbbbdadcaaabbcaacbdcaccbaacdadadcbdadbcbbabaabbbcdbaadbabcdcdaaababbdadbbbcbdddadddabdddcbdcaadababadbcaccbabaabddadbcbaaddbcbacddbbdbccdbbcbadbccbccadaacddcbadddddabababbbbbdccabaadccbadabdaadcaacccbdadbdccacaababcabadabaabbbaacddcacdbcbcbddbddacacbaccaaddcbaccdaaadbbcaaccbcbddacaabdccddcaadcdbcaacbdcdcbbaababcbdbabbcdccbbcacacaabccdccdbabccbbbdddacbcdbbcaaabccddbbcbacabcdabdaabaabccdccaadbdbbddbbbabcacaacbccdabbdcbaccbbaddbdcabbcaacbadacaccbbacaacaadabdbbcaaaaadadbdcadbcbccbacdaddaabdbdbbdadcbbddcabadbcbcabaddcabaaddccbacaabcbcdbddbcdcdbadcaddcaaccddbcdaccaccbdacdacddabdcadccdadbadcdbaaccadbddbcccddacabcadcacbdcbdcabacbdbbccadbadbdabcdadbbccdabdbcadaacbbaaacdddaabaadcaadcbcadcccdbacdcadabbcbadcabadcaddbcaabacaadcdaccdacaaccaabdabbadbbaacccbaddbaccdacdccbdacdcadcacacbdbdddaccdcdbbcaaaadbcdcbabbdcbaacbbbaaddbcadbdddddcdacdccdadbabbbaacdcadaadcdcdbbddbcbbadcccdbccdaabaabbabbcccccbdcccbcdddadabdbbccddacccccccadbddddcaadcdccbbbdaaaddbbadadddbbcddcabcccbccbaccacdccddcadbaaabddbdbdaaddddddcbacdbcabcadacbddcdbcbddbcdadcbcadbcadacadbacdbdacccccbbaaadbbaaaaadadaddcbccadbcbcdcbbdddccdbcbbaacaccbcaccdcaabdaadaadcacdbcdadadccbccacbadcbdcddbbddbadabacbbcbaddcdbddcbddcaccaccbdadbbdaabccbdccdaddccccabadbaccabdcddcbcdbdaccadbabadbdabbcbbddccddddacaaacbdcaabadaccacdacbbdcdcbbdaccbcaddaadaacddcacccabbdddbadabcccddbadacdcbcbbddaaccdaadcdaddaddbbbbaababbcbcacccdacddabcbaddbddbacbbaccbcacbddcdcabcbddaacdbdbbaaabaacaccddaccbaddddabcbccdacbcacaccdddcadabdcbcabddabdbbcabababbdcccddadbacbabccabddaaadcbccbdbccdcddbcdaaadadacddcbddaaddcaacbdddccdbacbbbacdbdaadcdcddddabcbcbbdadcdacadbbdacdbddcbddbdacaddbaabcdcdacabbbddadccaadbdbcdacadabcbcbccdccabcbdcdcdaccbccaaabdacadbddaddbdbdaadbcbbacbacaabacbbdacbabcbbacccdcbbccadbabcdaacdbccdaddcddcacbdaccdccadaabbacdcbdccbdadbbbacadaadcccabcacbdddabdddbaaccbcccccaddccdccbccdcabbaddcacdabdddcbcabcdbcabdbacdcdcaddbabccacaddacdbdbcdbaddddcbddcdbbbdacaabdabdaddbdaccdccddadbbaccabbbcccaacdcdcdadcccbaacbaddabbbcaaccbbbbbddcadbcbdadadaadbcdcadcaabbdcaaaccbacaadabcaacbaccdbdacdacbdaacbbbabbbccabadbaadacaaaaacacccdbdacaccbabcbacdccdddcbadaadddcbdabacbaaddbbabbbdcacddcdccddccbddaadbbaddacdbccbaddbacbabbadcdbcadcaaccbcdaacbabdccdcbbbdcaddcdacbcbbdaaaadabcaccaacccadadbabacdadadccddaccdcdccadaacdacacbbdccbabdacccbcbabcbcdbabadabbbbabbbaddabbccaccaabaccbcbbcdbddcaccbbcbddadbcabdddbbbdbdbbbddcccacabadcdbdaaacabdacdbcddbbbdabcbaabbdccbaabbdcaaabbccabaaacbdabaabcacccbabbbadccdbaadbcbdbcbbaddabdbaaddccbdadccdacccacbdcbcbdacbdadbdddbccacbdcacaabbabdcadaaacabbcdbababdcccdacdaddcdccbbdaabaddcacaacbbbbbbddcbbdadcaadcdacbbcdcacddddbdbbadbbcbdccdbbbdaaddcccdcccadacacdcbdacbcaacdccbbabddaaadaaaaadbbdbaacacacaaaaacadaabadaacbcdbaadcbcdbddaaccbaabaacdcdaaacbcacabdacddbdcaabcabddcbacadbdbaadaabccdcaaddddacadbbbdabcbacccbcaacadaacdbcbbaabadabdaaaccdcabadadaddcabdcdbabadabadaaccabccddcaaadaddddcbcbadbdbbccbadbcdaacbcdbdbaacdbbdacaaadddacaaababdcaabbaaddddcabccabcdadcbacbdadacadcbbcaabccddbdbdbcdcddbbdbbadccbbabcbbcddacbaaabadbacaabcdcabbdaacaabaadadddddabcadcbcdbcbaadabcadbbbcbdacbcbadbdbadadaaddddcccdbcdabdabaaacadbdbababcaacbbcbacccbdbdacdacdabcccbddbdcabbcdbcacabcbccbadacdaabbcbddadaccbdcacdacbccbdcdbcdbdcdaabcdcdaacdbadcababccbbabaaaaaaddbaaaaddabcdddadabbdadabbdbdbdcaabcacdbbdabdcbcaadbdcaadbcaaccbbbbdacdbbcccabcaadacbcdcbcabccdcdbabbadabcddbbccabaaabdcacdaaabddddbbadddcbbbbbdbcadbacaaccbdbbcccccccbadadbcddbdacbcdcbaadaccdbdcccbcaacdbaaacdbdbcadbdacabdcacdaccddaacddababaaddcaaacaaaaaabbcccaaacacabdaadaadcdbadadabbacbbbcdcaddcbcaddbaccccbcdbdbabacadcbacbbaacabcdadcdbbbabadcbbaddaabccddcacbaaadccabaacbacabcabdcccbddcaacddccbbbdddbbbddbdcdcdbcdcbaacdabdbbbacddcdddaaabbccbdcbabbcdaaddbadaadaabcacaaccdabcdacabcdcbdacabacababbcaadcabcddddacbdbcddcbacccbdacdccabadacadabcbddddaaadcddbbbbbbcabdddbcdcdcccbbbccbbabbaabbaccbbbccacacaabbbdbdddbddabcdabbbbbbdadddccdaaaadacbcdaadaacbadadcbaacabdbbcdccbbbbadbdacddabcabcbccdadaccadcdcadaddcddcbaccadbddbdbabbaaddbcabbaaadabcddbddcdcacadbddacaaccadcdbacbdcbdbabcccddadaaacdaacdccabcaddbbcdcccabcbdcdbacaabbbacdadcbacdadaddccaddabadddcddbbcccbcadcacbcccdbbdbcaadcbbacdcaacbaadcacacbabacdaccdacbaacaabcdcabdcbdadddbbaadaaadbdbccaabaddababbadbcdaccbdccaaadabbaddabacabddacdaccddcaaacbadcddcbccccaadcaccbaabbccbbdabaaddabccabcbadbdaaaaadbdbcccadcadbcdaaabaccadcbbdbacaccbdaddcdcdbdaaddbdcdccdabaabbbbdcabdaacdbaddbbccaaddabdbdaaacabbbaacbaccbbcbdbddacdcbbacaccdcdabbacbbbadaddbbcbbbddcbbdbbcdabbacddbcbcacccdabacabcdbddbaacbdadadcddadbbdbcadcaccadddaabbdacdaabadadcbdccbdbcbdbdaaaddcbabbcadadcdacbbcdcddabcdccbdabaddbdbcdcccbdcadbdbdcddabdbaaccaadcaaddaabccadbcadaacdcbdbdbdcdbbddabbbaaaaddaccbcbbbcdbbaddcadccbcdddaaacbacdcbadacabbcbdadbcacdbccbbadcacdddddadabadcdacbbccdcbccbacbcbdcadcdccadaccabccbcbadaccdbdaccbbaadaddbacadbadadbdbcabacbdddacbcacbbabbbccabaddcdcacbdbbccbaddcdcdadcaabbaabdcdabdccddbbcbadadbbbdaaddabbcbbcddbbbdccdacddcbbdabaabccbacbacdbddbcadcacbbbdcacbcbdbdbbabddaabaabbbabccddacbbabcabccacdcddccddbddbadaddabadcccbccacdabbbbbaaacbdbadacadddabbbcbcabdcbccdbbcdacadddcdaaadcabacaabbcddabacbababcdbadadbabbbdcdcadddaacccdbadcbababacadbabcccadabcacbddbcdcccabcccbaaddcccadadbdacacaababbacbbcbabdccadabdcccbbcdcadcabbdadcbbaccbdadcbaaaadbaabaaaccabdcabcddbaddabcadbabcddcdadcddcbcadcdbaddadaddcabdbadcdcdabcdcadaadbbabbdadcacdbadaadbdcacbaadddbaabdaadddcadcbcbcaaccdbacbbaccbcbdcbbcddccbacbddddabababdaaadcbbbbbdccdccddbbcccacddbabbbbccbbaaadcccbbbbcbacdcdaaddbadbdbdbacbccaadacdaababbdbcbcdacdcacbccccbbaccbdacbabcabacaddcbbdbadbabddccbadbcdadbdbcadcdccacccdacbbcbbacccadccdbdabaddaccbbbdbadccbaaddaaacbcccbbcbccbdbdaaddacbcdddaaccbbdbdcabddabcdbdcadadbcadbbdbdaadddabbbcaccbcdddacbbaacbadcddcabccaddabcbbabbccdbdcdabadccaacaaabacadddcbdbaaaddadccaccacadbcbdcaacadaadccccdddbabccddcddbddadccbcaadcdcabddccbbabbdccdbdaaacbabcaddadcbbbdbcadcacddbcacdadcbacadbabdaaaccadcbadacaccbdcdddadbabdadbadbbaabacdcabbcdaacddccddcdcdcadcacacccdaacdcbddabadbdbdbcdcbbadcbbbaabcbdcbbbdaacbadcddbcbcbccacdbbdcbcabaaccbabbacbacbdbddbdcadbdbdccabddaaaaacbacadddbddcbabaabbdabaacdddcbcddccacbabbbabbbdcaddcabbbddbdcbdbbbbadbaddabcbdadcbdbbaacbddbdbddaccbaacdaadbacaacaaccccabcccdcbcdadbaabadbadcaddccddcdcbcdcbabbccddbbdccdddaacbccbdbacdadccdcaaaddbbdbbcccaddbcccdbaccaccdbdbcbaacccbbbcbadacbccaaabbcbabdddacacaccdaaaabaaaaadbacdaacaddcbaddadacbbdadcbdabcdacbcabacccbadbcdbcaddbdbdcdcabcadaacaadcbdbabdbcdbadbcddccababdbcadaadbdaabccbbcbddbaadacacbdcbaadaabbbbcaadacbdbabdcacadbbbbdbbbcdcabaccdbbacadbcdcbdbcbdbaaabcbddcdaddccdadbbcdaaaccaaccdccbaccccbdcbcddadabaacbaacacccdadddadcbdadddccbddcaaabacabbcabbbcdddbbcddccdbdbdbccbccdcbddccbacccbadcbcdadaaabaccacaadccdadbdabdcbacbcacbbdadcadabcadcbdbaccbccbcaadacaddcbabdcdcdacbbbbbcddddcadcabbcddbcccddcccbcdadabcadddbbdcadbdcdcadccaaddbdadaccdbdadbcbccabaacdbabadcabaddcdcabadabddbacbbbcacbaaccababcaabddccbacacaadacdaccbdabddccaaaaacbbbcaddcabadbbdccbbbccdcccabccddadcbdadcdbaacddbbadddcadbbdcbbdccdadabdbacdddcddbcacabbdcbaaccddcdccbddabdcdbdcbcdcddaddcdaccddcccdbcaddbdacdbdbacbaaacbdbbababaabbdaadaddbadbcbadcbcacdbaccacbbabbaacabccdbdcaddcacdbcbdcbbacddbbcabcadbdacaccabadcdddccdcdaccdcdaddabbbdadbbdcabbaaabadbccabadddbcdbacdabdabaacccadbddabcbbcbdadcbbbbdcccbdccdbacdacbdcbadadadbdcccbbcbdaccadacabbbccdbcababbdaaadbabddbdcacaacbbabaabcaccdcaddddacacaaabaabdbcbccbdddbabbcddbabccbaaccccccabaccabacaabccabcacbcdbadcddccbbddbaddcccbdbcbcadabdbccabadbabadddbdaaddbdcadbbbbdbdacccaadbcaabbddbacdddddcdbdbbdacacbacbccbccddbcbdcacbcbbdbbddcdaacbadcbbbdaaadcdbdaaddaddacbccacbcbdddbbcbadaacbcdacccdccbbacaccdcacbbaddbdaccdaaabdddbcdbdbccadcddcadcdacabadbbaabbbccbaacdbabbbccadbbdcdcbaadcccccbcddccdaddacbcbcddcccbacbcdbccbbcccccadddcbcaabddcbcabdddadaaadbadbdddddadbdabdcacabcacabbddbcbacbcabdcbddadaadadcbcadacaddbbdddbdbcbcdacbddaccdccdccadadbadbcbcdcdcbadacbbcbabdcabbcdddadbdcccaabcabddacbbabddaacacabbabdcaabbcbbdbbcccbbaacadcdbcbdcbdacbadaaaabbabaaadbcaacabbbdcdacacdbcabdbcbdadacccdbbbdbadcaaabdccbcbbcbdcacbdacdbdbbdaaccaadcadabbbbdcabcddaaadbcdadbacdbadaabcbabcaaaacacbcbbcaabcdaccbddddcadbbabadbdbdacacbcbddaadadacdddadddbabcdcadacbcddbacaaabdccbacacccaacabadacbbdccbaddccbadaaabbddabadddabccbbccdcdcbddaadbcddbcadcdbbddaaabadabbbccaabcdbbbcdcbcbddbdcbdddbdcabdbdcadcbccadbabbbdddcacdaddcadcbdcacadcdcccabbbabcbabadccaabbcadcbacaaaccbaacccaaabababcbdbaadabbbdbdbddadbcbdabddbbaaddabbcccabbbcdcadacdddadcddccddbccccdcdabcdbccdbdbdabcabcdcbabcabaddbbbbdbdcabdcaaddbabbdbaaccbbcabbaacabcacaddcaabbaacddcaccbccbbabdabdbadadccbccdcbadcbdabaddaaadadcccdaccccdcccdbddbbacdccabbcbcdabaabcaabbdcccdcdcdabdcdbbdcdbbcdcabbccbcbbddbdccddabdcbcadabbdbcdaccdcccdaaddcbbcbacdcbdcdcacdacbcbcdadaccdbccabbbbcbaaaaadbbabbbdbdabdadcdbadbdabbdddbcbcacbabccbcabccddacabdbababcabadacdadcaaaadcbddbabcccdddcdcdcbbabbdcdaaaababcaaacdccdbcdcccdacabacabccacbdcbdbccacddcbdccbadadabdcacacdabdbacdacaddbdcdcddbcbbbcdbddabcabdbbabccdaccdaaadadbbcaaaabadbbbcaadcbadaaadbcacdabcabaaacbacbbaacccaddbabdacbabbcbcbbdbadbcabdaddbdabbbdbdddadcddddaccbaaaddccdabddcdccacddacacaabdcdacddaddcaccabaddaadddbcdaabacabddcbacdcadcaaacbdcadcabbbcdccadbbbbacbaddabddbbabddbcddddacadaddadadcdbcddcdaabcdbdcbdbcadbdbdcbacccdddcaccabcdbacadacbaacccaaadcbabbacbbdabcdbcdbabdacdbcbdbcaacddcbbccacabdadcadcdbaacdbcabaaaaabccdaaabdabdaabcdbdbcbbcaadcaacdccddbadbacdddbaaccbbaabdcdcbadbdcbacabacbadacdaadbbcccdadcbdbaddbddcbcbaacbadbcdddccabbbbbbbaadcdabccaccbdadbcbdbdcdaabacdcccddbbcaabadaadddccdddbccdbcdccaadaacdcacaacccbdaadbaddbccaabdddadccacaabacacbabdbdcaacaccabcadbaccbdcdddccabcbcbcaabdbbbccccccdacddcbccbacdcaacbcdbbbcbbbacddbbcbbdaccabcdccdacaccdbacdbaccccbcbdbbcaddacadcabcddabdcdabbacbbdbbaabbbbddaabbaadcbcaaddadbbdcdadcabcadaabcaadabbccbacadcdabdadcccaccaabcddccbccacbcabdaaaaccddbdbbbbcbdddcabcdabcbdcddbdbaccaabccabbcdbabbbacaabdcaabbabdcdbbcaabddaccdaacacaabacbdcabcddccbbdbbdccdabcdbcacbddaadbadbaadbdcadadbcbcbbdcccaabadabddaadccacbbabbabaaacdbaadbbabdadcddbcdbaacaadddbabbcabaccacdbcadadcdccdbdadbcaabdccbccadcadddbcaddaacaaabbabcdbcadbcbaaaabccacbdcddccaaadadcabacdcdcdacdabdadccdbcaaaabcbdccbabdadcabddaaccabcabddacdccdabbdabdadcdbdacddbabdbcccbcbbddadbcdbdcdabbbbacbbcbdadbabcddaacdbbccdbbddbbdacaabbbcbbcbaaadbddadcabcbbbcdcbcddbbbabacdcadbdaddcbaccbdccbbcccdccdadcdacabbbdbdcdbdbdbbcdcdbdbcbabbddcdcabbcbcadbadadbbaadcacdccaabccbcbdbcccbbabcdcdabcdcbaadccbdacbbdddbdabccccabbadddbacaccdcaabbcdadbdabbddddcdcadccacaadaabddcdbcaaaadcabccbcdbbaaacabcddadaaacaabcdddbbbbbdbdcdcbcacbddcbaacddabbdbdaddabbdaababcaccabdccacabcdcdcacbadbabacdbbbccdcaadcbdbddabccddbbdbadacdadcabcabaadccdadbadbcbbbbdababacaaabddccaddbabdcdcbdabccccbbcbabacbdadadddddcdddacbccdcacbbdaabbacdcabacbbdaadbcadabbacdcbacdcadaacbdcdadaddcaccbdbdaabdbdcbdbabbabdcabccbacaababcdadbbdcacbadbdbaccdcbacabcaddddcbaacadbadcbdddabaabcddabddbcaccbccaddbbaabdddcbbbbcccbbbbdbdbcbcacaabdadddddccaaaaaadcdcccacbadddbcdddcccbbbcbcadcabbbbbbbbbdbcbdcddcbcaacdaadacaaadabcddaaaaaddacddcaddbcbabccbbbaabbbccbbccadddabcadabdaaaddbaccbcadacbacccdbcdacdcacccccabdbbaddbdddcaddaaabcbcdbbbabbaccbabbcadaaabbcbbaaaacbadbccbddbcbdaabcabdaaddcacbabdccaadcabdacdbddadacbaaadcdadcbabddbcdbcadcbabdbbaaabdadbddbccbcdddabbdcbbabbaabdadaadbababcacdcdaddbbcbccabadccdcbccadbbbcdbbadbcbcadbbbddcaaadcabbcadcdcbbbddaacacaabccdbacdabbcddcbcbdbdbdccdbdccbddbdcbaadcdbbdadacabddadbddbbcabdaacaaadbcdbacbddccabaccabbbaddababaacbacbacbaddabcddcbadbdddcbadccbadbdadcaddbacccdadbaaccdaaabbaadababbcbddcabdcacababbaacddcaacbcbacdababccaccaaddbbbccabcdbcabdddbabdaadbcbbaccccabcdbdbbbbcddccadccbbddbaaccbcbdbcbbbacdbbdaacabdbcaaaacbcdcdbbaabbddadcdbcddacddadcaccbabbbbbccbbcdbbcdccbbadcaacddddbcbdaddabccccccbdabccbdddbaaccddbcaddcccadddcddababbaacbcccdbbdcdbbdcbbcdddddacacababddbbbbaacacaddcacccbaabdbaccdbabbcbbdcaacbcbaaadcbcccabbdccadbcbbbbbacbdbbcabbcaaabcccdcddabbbadcdcdaccacbcbacaccadccaadbddbaabccabdcaaadaaaccdcbcccddbcdadbcbdcdaaacbaccdabbbadadbbadcbbaabdcadddbacbcbcabacababdddbdbadaddcaddcdbadbbcabdadaaadbbcbddacdddcacbccbabdcacbbacdbbbacbbdbdbdddcaacdbabccddaabaacbbbdcababacaaddaccdcdcdacaababdddcabccbbdacdcaadaddbcabadbdacdbcdadddcabddcaaddbabcddcbbbacadbcadabbbadbccbddcacdbbadcbcabbadabbbccacabdbabcadcbdaabdcbabbccdbddddacaacacdbaaadcaaabcdcaaaabccabacbcdcbbaccbbbdaacbccbdabdaccdaccadacddaacdacbdadddaaadbabddcabbcddcddbdacabccccbbdccdbbaababdbccdcdcbbcbdaacbcbbdcbddabbabbcbddabbcdbbbccbdabbcaadddabaadbadbbddcadbadaabaabbbccbdbabddaddcabaccdcbaddacddabaabdbadbcdccdaadadadddabbaacadddbcacccbbbccdcaaddbaddccdcdadaacaaaadbcbdaddabcaccccdadcbccacbddcacaaddbddcddbccadbdcbdbdaaddabaddbababbadbdddcaabdcaccdbddbcbbabadbaacaddcdaaaddbbbcdcbddadccccdcaaaabcbaccaadabbccabcdbcabccacbdabbcddcadbdadcbabbdacdcbadacacddabbbbdccddabcdbbbadbccdbaaccdbcbbdaabbcddacaadcddabbddbabbbdccababccaacacdbcdcabcaabcbabbabaabccccddbdcdbbadccbddbdabcadbbcbbdcaabccaaacccdddaabbcadccbdbdcdcbbaddaabbacdcaaddbaadbccddbadbdaadcabbdccabbdbadcacbbddadcdaacaddbacaddcbdbcccabbcacbbddaabbaadadcdcdacdbdcdcbcbaccabbdaacbaaadbdcbdbbcbbcdadadaabdaabbbabacaadaacabddbaacbaccacccdcadabacdbddacdddcddcacbcaaaacdbdadbccbdbbbadaabccbcbbdabcdbabdbcaaaaaacccbadcbdabacccdbbccddcabaabbbddbcbcabdbabdbaacdadcbbcdccabcbbddaacddadcdbdabcbbadabbbabcccdccadadbaacbcbacbdcadccbaccddaccaabbdadbbcaccbcccbaacabcadaccaababdadddcaaccccbddacdbbbbdcdbaadbaaddadbddbacdbbdddcbdaabdcbcdcddaccbdcdbddddacbacdadbabadbadcbbdbdacbabcabcccbaadbadaabbbdbddcbbaccbbddabcaddaabdcaccbbcacbdbcaabcbaddccbdbddadcbcacacbcbaacccbbcdbcdddcddbbbacdcdacdbccacbbbdcbacbbbcacccabacaccdcbdbacaccaccddacccacbdabacdcdcaccbabacaacdaaadacbbbaacbbabaacccbaaddacbbcdccccbcdcadddcbccabbabdbadcaabddbdcccabacbadbabcbbbacbddacaabcadccddbabacabccdaababdabddbbcdabddbddbcadbcacddcdacbbddaabacbcabcabcabacddbdddabcabbddbdcbaacdabddddcccbbdadcaadcccbaadbcaddddccdabcdbbccbdacadaaabddbdbbadcbabdaccddadcdbbddbbdddccbabbcdccaadbbcbbadbcccabdbccdcaccbaaadacaaccabacbabcbabcaccbdcaacacbddcccbaadaadabdcabaaccadabbdbabaabbddbabdcadccaccbbbcbdbabacabacbcabccababbccddbcdadadaddacbcabcdddaaccaccbacdadaddcdabdcaabbdaadcbcdadadbacaddbadadbbabddabcabccacaccddbccbcacaddacdbcdcacabddccbcadbdacdccadccbbcccdaacbbbbdadaddacdabcdbadbaaaaddbbaccdbbccddbbbaacaaccbdcbbccadacddbbdaaaaadcbbacbacdbddaacbabaccbadabbcdcdacbaccbcdbaabadccacbaccbcababdbabccacbbbabbdbdccbbabbbbcbcbaababbcbacbddbadacbbdadbdacdcbadaadccbdaabcdddddcacacbadadbddcaccadbcdbadacbaaabacdbcbcbdccaddbdcadcdadbddcbbcadbdbdcadbcbaacdbaaacbcdabadcdbbadbcdcdccdcabaadcbbacaaabcddaacacbcbaddccccccdacdcdabcdbbabadcddcdbaaabccdcabaabaaabcabdadbbaccabadaacddbdcbadbaadcbcaaaaacbabdabcbacabcbbdbdcdabbacbbddadbbdcbcabccdabcdacdaccacddbbdcbdbabacbadbccaacccaccbbdadddadaaaddaddadadcbadadcadddcbbdacccdabaadadddaadccbbcddbbdaabbcacdabaababcbcdbbdabbcbabbdababcbbdccdacccddaaaaacbccdacbccacdddcadaccbdacbdbaacacddcbcaadbabcabbabbadacdaacdbccdbccddaadacddbdbbdbbaaacddcdacadaacaaaddcabacadacbbabdbbdbcadcbaaabbbacbdddabbaaacbadcccbbabacbcddccacacbcaadbdbcbacddcaacdbbbadcbdabdaaaacdcdcbbababbcdabaacccbcdbabbddcdbddbbcbdddacbdacacdddadbbdbacdaddacdcabcddbaabbdaddcaaaaddbbdcadadacdddbdacbdacaccabcbdcabccbbaacbadbaaaadcbcbbdbbdccbcdaaadcbddbcbcbacbdcbcbbbacbdbcaddbbdadcadddddaabccdbdacaccddcccbdbdcaaadadcbbbccabaccbcbdaddbcabbbaddcdabbcbcaadcacbbcbdadbdbdacdbbdabbadcbdaabdaacdabbacaacdabdbcbccccdaddaacddbabaaabdaabacaddcdbbaddbcddddbabcaadaaacbbdacbacbbdbddccccabadcdcaaaccbdccdacaacbabccbadccdabddaddadbbbaadbcbadacbdbbccaaaaabbdcbcccbadddbbadddbbcbaadbbcbadbbccbbbadbbdbadcadcdacdccdccaadaaabcbccababddcacadcbbbababbbbabadcbcccadbdababacdaccdbcbcabadddadbcbbdbadbdcbdaabccdadbdcdadaaddbbdcbbcabbcaaacbdcccbbabbdbddacccbdaddacdcaccababdcbcdaaddacabdbdcbadbbaaddaaabcccdbacbcbdaaccdcdccabcdacddbcadbbadbbbdccbbbbddbcaabbbdabbcbadccbbbabcabbdbdbcbdccbbabdbbdabacadcdbbabddaaccadbcccdcdcacbbbadbcdabbbdcdbadacaadcccdddabcacacdbccaababacaddabacacbcaaacbdbbcddbadabcacdabacdabdcbdbbddbbccccbdcdbdbcadadbbbdabacdaddcbdbddaccabcadcdaabbbcacccddcbabaddabbdabcacadaabbcadbdbbdadababbbabaadcabdcadcabccdbdcddbdaadbbcbacdbdcacdaadabcbbbaabacccacdcdbdbcbdcbbcbbccddabddacbcbbccbabbdbaacbbbaabcbdadbcddaacabddccdcacaacbcdcdabcacddbaccccaadabbaddcbdcbbaadcddddccaacccbdabadbcbbbabddaadcadbddbcdddbadbdbabbaadabcdcccccbbdddbdcddbbbdacbbbdbddbacadbaddccadadacbbcddaccadccabcabacdaccdacdadcaaccbddbaaaadddcdbbbbabbabdccbbbabacdcaabbabcbadabdaacdacbdcdcadbaaabdbaddabadbdddabbaabcdcbaaacaadccdcbabdcaacbdcbcbaaccdccddbddacdaddbbdadbcadbcdaccabaccdcadcadaddbbdbccdcdcadcbccdabcbcbacacbddcabbadcabdccaacbcdddaaacdcadcadbbadcdaddddbaabaccbaadcdcacbdbcadbccbddaacabcdcdacdbbdbacdbcbbcccdabaabaaaaccbbdbddacddcaddccaddbbdacccbcbcabaabbdbbbddcabaaaaacbbabbabbbabadbcbabdbcdbdaddaadabbcadcbddabdbcdabdbccdccbdbcccaaaccdbbaddccbbddbadaccbacaacdcdcdadaaacdcdbcddddbcbdcbcaaddcddddbbccdabbdbbacbddbbcadbabaddccbbabadcadbdbcdaccdcabcccadadcaacbacddbacdcdcbdcabdabbcbbdcbdddaadabdccaddcbbcacddddcdbcadbddadbabadaabdadccdbbdabbacbadddbadccabcabbbdccbdcdccbaaabbbacdabadbcadbcbddddbbaaccdbbdcccccbdcdbcabcddccccacccbbcbdbbbbdadaddaddddaabddbbdcdbadbbdcbdccbdbdbbbddddbdacabcdbcaaddbdabdbaddbddbccbaaddbdbddabdababadbdbcbdbdcbabbbcbbdcaabbbabdaddbabcdbbbbadaacadbddbacdacddbbccabcdddaddadcacabacdbcaaddccbcdddcbadaacdabdbcacababaacacaddaabcadcccccdaadabbaddaadcbbcabbcbacdbbbadadbbbdadbababdcbacaacdadcdcdaadbbbadbabccdbbddbdadadccdcbbbcbbcadaddbaacdcdcacabdddddbcaccabcbcaddaaddddcccadbbccdbaacacadbdccdacabbacbaaadbbababbdbaccdcdbdacdbddbbcabcbdbcddacdcdadaabccbbbcbcbcdbdcbdcaababcdababdbabcdddcdacaddddadcbdaacbddcbbdcbbcddcdbddccacccbacbccbbdcccbdaccddddabdddacdaaadaddcdcabcdcddccdbdccddacbbadabcbbddcccbccdbdaaadbabcabcbbbcaaaacaccddacdddbdbdbdcbbbbacaaabcbabbbcdbdbcdcccaadccdacddddbacacdddbcddcacddaadccbcddabbbbcdacddbbdacaccddccbbadccbdcddccdbbbaacadbdcbdccbbdcdbbddbaabcaccdbbdbdcabddbaadbbadaaabddbbcbabdaaaccddcadaadbacdbcbbdacccadaaaccaabadccbaddacdcdaababaacadcdcdbbbdcbbdbbcdbdcbbadbadcacbddbddadbbdbbdaccddbcccdcdacdddcbdccbdccccbcabdddacbabdbacdcdbbaccacbabadcdccdcbdaacdbbabddbdccabaabdcdabddccbacdcbacacbacadcddbacbadbdcabdaabbdbdabcbabbbaacbaaadbdcaacadbbadcabacabcdababbcbcbddbbddcccdcacccdadbcbcaadbcabcbbabcaaadcccbccdcbdbdcbbaccdbbaddabcdddacabdacbbdbbabcadccdacbbdbdccdddbacddbcacacbbdaabbccabaaddcbacdcabdbddcbccbcbbcbbcdaaccadabacccababacacabddbbccdcdaaddadbabcacddcdbdaabdcacaadbadcabcbdbcbacdbadbdcabcaadabbbdacbabdacabbbbdccabddcbacdcbcaabadbbdadbdbccbcdbdbccacadcbcdddaadaabbccdbbbbcabccdbcaabacbcbdddcabdccdbacdadabbbdcadbdbacbcaccbdbadabbcdcdabbabbccabbadccbbbadcaabbbddaaadccdaacdabbcaacdcbdbbadbcaacdbaccaabbbbabaddcbdababababccadcaaccdcacabadcadddbcadbdadcdbaadcddcbcdbbbaadddadcdacbcdbabddacddabcaacadadcbabccaadbbaadacbadcddbbdcaabcdacccdacdccdcbaadccacbadbabbdbacccbccbbacccabddccabcbbbbbadddcbcddbadbbbadbaadaaccddcccacacbbdadbbadcbbccaacdbadaccbaaccbadcacabdcbaddccdbcababcbdccaddbadccabaadbcbdbbcddcbbddcbcaddadadabdcaabcdacbcdcaaaabacaacbdadbbcacbbdddbcccaaaadababccaccbdcacbcccaaacacaaaadcbbdaccbbaababaccbddcddbacababcdcdcbdbcbacbbaccdbccaccbbbaabadbbaabbcacccddccdbdabdaaacacacbdcdbdbadbbdccddbabdbacdaddaababbdacbcadddadcbabccadabaabbddadbdccbccccbabaacabdbdadadddbacbbddabdaddabacbbdbcaddadacccddcbdddadacaaacbbadddcddaadbcbbdaadcccdbcacdacddbbdddddadccbbaabdcbddcdcbbbabdbabdbaddcacacdadcccbabccbbacddabacdbcbaaabcdaabdacbcaabbbcabbcddabcababcccdaddbdadcaabdbcdcdadcbdbabbadccbbdabcbcbaacccdbcdccdcbbdddcbcabddcacbabddccacbcdcbdcbdddabaacbcbdcadabababcbacbdbbdbbbabadbadabbbcacbdcaadcddcabaddbdabcdcdadbccdccddbabbbdaacbabccaaacbdbadaaddcbdcdabaacaddbbcaabdbadacaddcddbabdbbdaaabddaadbbdbabccccadadddcaddbacddccaacbbacbbcadabdcdcadbccaadcbdadcabccababdbbabddcbadaadbcdcdcacaaddadabacbaabadbaccaddaadbababacddcacdbcdaddcaadbbabbaccbbdcadddccbaddbbcbdbdbdbdabbdbbdccdaaaaddadbbacdccdbcacbbadaaacdddcddddbccbddcacccddbbdccbdcaddaadcbbcbbbbbcddacdaddaddccddbbcccbcbcaadbcdcabbdbbcccdabaddadbaabdddcadcaccaacddabccdcbabbbdaddbbbccccbdabbbacdadccaaaaddabcaaaaccaabdccacaaccacbdbadbcaccdaaadcdaacdbddbcdcaabddaaaddccbddcbbaadcaaabddbbabbdbacdadbacbcbadbccadacbdcdababdbbadacbdaccdaadbacdbdbbcbbbccabdaacaccbbdacabdbccabcbbaccacddddbbaacacddabccadacbadadcddccbaccdabdcbbabccadadabcadddabbbbbbdddabbdcdbaabccdbdbbbbaabbaacbdcdcbbcddcbaddcbccdcccbcbcccccbdddcddccccdddbcbbbddbcabbbdbcbacacccabcacbabdcaddcbadbdbbdabcabddbabaadbcddcdbccaaaaacdbcddbcacababaadabdbacbdddaacbadbabddcdaaacbdbbdbcdaddabcbaacbadbcdabcdbacdacabaddaabdcaddbcbddcdbcddccbddcbdaaaddbcdbaadcdbbadddcbacacacbdbccbcccabdcbadbabcbacacbcbaabaabdbddaaadacbdbcdaadcababddabbdabdbccdbbaaabcbbcabbcdbbcdddcadaacccacbdcbaaadcadaddbbdaaabbaabdbadbccbddbacbdbdddcbbabacbbcacbdddaccbbbdccacacbcdcccadadbcbbbddbbbcadbddcbcbccacbbdbacdddcdacdbccbdacbdcabacbddcdcbabdadbbdcddabbcaddbabadaadbcdcadcdbacacabdddcbddcaddabaabbcbbdaabddabacbbcababddbacabcbacbcddbadbccddacdaacbdabcabdbdbcacacbccdacbbbcbbcbdcaabdabcdaaacbadabdbaccbcdacabdaadabcadabdbbadcabcccabababcaabdbdadcdcdccdbccdbacdcdbdddbacccddbbbbbcbdadbbcacbbaabababbbbcabcdacaccabddbbccadcdbacddaadbdababaadddbaadbcbdacdbadbdcadbdccdcacaaabbbdbdacaaaabccbddcbdbccacaabbabcabaaadcbadacdabdccddbbaadabbdcbcccbabcabaadbaadabaacdadbbaababcbbabacdabdcaacdddbabbaddbabdbdcdbaabaccacaaadcddddabbbaadadbbbdadcdbbdbcacdaabbbaaadbababbadbcdbabbaadadababdaabcdadacacabacdbdbdbccbcccdbbadabaaadbaacccdabcabcbadddaaaccdadcbdcdcaabdacdacdabbbcbbacddcaccdcbcbaccadaccbbbaccddaaaccccdcdaaacadcaaaccbcddccbccbabcdcdcabcdbdbbcbabbabdbadabdbddbabcacdcccdcdddbacdaddbbabbadbcdbcdddadcdbacbbbdcadcaaadddcccdbadcbdadbcadcbcadbdcaadcacdcabccbdccbddddaaccaddcabdadacdadbcddddabbdcccdaabbaabdbcbbcabbdcbbbacccaaabdababbabcbdaaabdbcbccdcdbbdacdcdcbcbcbbccaddadcdbddaaaaabcabbbdcbacdaababcdddaddabaacddbabacbbdaacaaabaadaabaadabcdcbadacbbcbacdccaaabdbaddcdbdadbdacccaaddbbdbbabdbbbbbdaadabaabcaaacacadabadacccbaddacacddaaacccbbdbccbcadcccdcccbbaadbcbbadccbbccbbcbdadcbdddccdccaaddbddbcadcdccbdbaaadcadadddcadbbdbcdcdccacccdbaacbadbcabcbbbcaccdaadadcbdbddcacbabdabddcbdcdacbcdcadbaababdccabbabbaabdabacdcbdcdadddabdccbdcdbabbbaaacdbbabdbabcbccccdaabbddacadcbaaccacbabaddcadadbaacbdbccaaddcdbcaadbbccbcacbddbadcababbddacdbaddaaabcbdcbbbadbdbbdbacdbdcdacacdbadcdbcbaccbdadccccdaacbcbaacccbcdaddcadacbddaddcbdbcccccbbacbdaadcbccacadddaccddaacbabbcaadcdaabcccdacabbcbdbbddadadbddcdcdcabcccadadddbacadababcbdcccadaaabaccdbbdbdccdbadaccdbaabbacdbaababdcaabadabcddadabdacaadaddbcacdaddbbabaccadbdbcdccabcbaaaabadaaadaaadaccbbcbacabacbaacdcbbadddacdbbbbadcdbbaccdadddabcabaaabdbabcbbccabbbadaddcabbddbadabbdcbcbdadbcdbdbcbadddbcdaacccaaddaacccddcabdbabcbaccabdcbababcbdddbdabbcccbcbaccccacccadbcdacccbadddadddbaaddcdbbbdbaaacacbadbbaacdadaacadabcccddbccabddacaabbaadcccabadcbbddacbdacddaaaabbaddaaadcbabbdcabbaadddcbdbaadaaddbdacbbbbdcddaadccbdbddacbcbabdaaaabcaaddcdcbccbaadcacbbabbdbaaddcbaaadcdbbbbadabbbbabcddddbcdbcdcbdabbaadaddaacbdadcdabadbdbdccaadbbcbcadacbdcabdbaabccaaabdabacabaaaabdbddcbccacdbcaaabaabbaabcabbdabcbaabaadccababddcadbdaabdabadbacbbbcbbdddabbcbbddacddcdddbbddacdaccddbddcbdacbddbddadacabdbdbdccbaabdbbacbcddabdcbbaccaacabddcddbbaabdacaaabddbaaaccbaccbdaccadbbaaccadadbbdadbdbadadcbcbdcbcaacbabbdadcddababbaadbadabcdbdbbbadcacddcbbdcdaddcadbcdddadccccbbbbcdbcbbaaadddabbadcddcbbdcbcadadbbccbcaabdccabcbcddcdadaadbdcbaabaddcbbacbaaddcaddcbcbacbbbadacbdbbdadbcdcdcabcabcbddbdacbbbadbacaddccdcbbdacabacbbbdccbdaacdcacabdccabdbdbcccbdbadaadcacddddaacbbdbdbacaabbbcbaacdcbccdccacabccaadaadbadacdcabaabbcacdccdadcbddbbaddabcaadbcdaadcbcbccddcacbbacccbaabbbaddababcabcbbbddbcddaaadbddbdddbdabbbaadcbacbaaaabaaaabcacacaddcdadacdbbcdcacbadddaabacddbaabcdbbbabddadcccbaabbabaabdcabacaadaabddbabbdcadbadacbbbcbdababacaabbcdcdacacbbadbdbbbdbddbbabdcdcccacbbbadccbcccdbccbcdcbadccadbcbcdcbabdcacbccadacabddacbddbadcccaacccabaaadabbddccdacbbbdbccdccaddbabdbbddcddadcaabbcacaaaabddcbbadccaaccddbadcdddbddddcaddaccadaacbaaccdacaddbdadacbadaadcddcabcbdcbcabcccabdcaabdccdaddbcadcabdabacbccbdccdaacacabddbccdcddccbbdcbcbdcdccdaabcdcadaaabbbccadddabccccdbbbaacdbcdccdbdbcdccccbdbcdcddcaddaabcdadaccbbaabbbcacdaccadbcabdcacbcabdadabdcbddbdacaadaccbccddcbadbdaabbbbcddbbccdcbdcbaccbaaabcbbabddaaccbaaccdaacdcabdacbbbbcaadbdddddcdbadacbadbdacdaaabbdaabcbaaaddcaacabccccbdaacdacaadbcdbacbabdbcacbbcadbdbcddacdabbcdbacacacdcdbacdaacdaaccddcdddbdaaadcbbcbdadbdcaccacdacacdcdcdacbdddadaccdbcacacbacdcbcddaadccbcccdccdbdddbddbacdcaccaabdbdaccdcadaadadbddbbbbcccccbaaaadddbdbcdbbaadbcdabacadacdacbccddbcdbcdddbacddcbabaabbbbadbcbdccccdabadbcddcabccdcdbbbaadcbacdcdaabdbcdadaadadcaabbddcdaadbddcddbbbabbaaabbaddbdbacabacbddcdabbdbcddacddbacadaabaddaaabdbaadacabdaacadadaddbacbabbbabcccadadbcbdacbddbbabcaabbaccbadacaddbbabcaaabacaadbcdcbadcaccabbabcccacdbbdbadbddbbaabcbcccccdbaaddcbcaaacaacbccccadaaccbbabaaddccabcadabbcccbbacbbcbaacdacaddadccadcdbcccbaabdbdcadacdbccbabcacdcbabcbcaddddcbadbcbbdcbbabcbaadbcaaadacabacbdbbabddcdaacddabcdcbbadccbabbcbabdcadbdcabaaabadacccdacbbacddcacdccbcaadbaaaadaabdaaabcadabaaacaabcdaadbaccccccbdddcbacbddaddadbaaddaadcdccbdaabdbbadcbddccacdaccdccdbccddbccacbdbbdbddcadbdabbaadacbdabadcaabaaacadcdbcdbbddaaccaacbdcaadcacbdcccdaddadaccdbbacddbbbabbdbbadbbacbabaaabacaaadcadbaaacaaccacdcccadbbbacaabcdabaabbbddbbbbaaccbaadbdacabacbacbacbbcaccccacaddacdaaabcacddcacadabcdbaaddbdcbaabddcbbddabaccabdacbabddcacaabdbbccaacdcaacbbcbdcdadaabbcccbbacddcdcddcabcbabdbcccabacdbdbaabaccdacddbbddbcdabbbbcbbbdbbaacdacaacbaccaadcddddcbddcccaaaadcabcdadcbbccbccadacddabcacdabababacbdcadbdbbcdcaccbcdbbabdcaaadadacacbabdaaacadcdacdaddbbdbacbaadbbbbaddccbbaacdacbababdacdbdddccbddabdddddcaaccdcbadccabacadddbdbadaabbcacddacacccbddcbbcbccdcadbaadbbccbdabdbddaabcadddbababadbbcdcabaaaabadbbcdadacbcabadbbabdddcccbcaaddcccdbdbaaadccaabdcbddacbdaaacadacaaddaaadcaccaddbccbccbddbcdbcccabbaaacaccaadaddbcccbddcaaabbaccacbcadbbabcdaadccaaabccddddabaabddaccbabbacdbdcacccbcccbbacdacdadccadbbcabbcdbbcdacbcadabbdacccddbdacbbdaccadadabdbdcbbadcbcbababadabcdcaacabcaadcbcdadbaccccdabdbaccdbccaadbaddcdbcabcbabacdccdadacbaaddaadbbdccbbadcabdcddbbbbbbaccaadcccaabdbcdbcdbbadcdadbadabaddcacddccddbdabccacababcbccaccabcddbcabadbadbcbdcdcdcdbcadbabcaaabddaccbcccaddabcdaaabbcddcaaccadaacadcbcbcbbacacaccbcddcdaddcacddcbbbaacaaccadbdccbdbdddbdaabdcdbaddcaadbcadddbbcaaacacbccaaadcdacdbaccdcbccdcddaabdcdcbbaaccddaacbdcbaabbadddddcacbcbccbbabbccbdbbbcbcbcdcbaccccbbbcacacdbdbdcaccdcddbaddacbbabbbaccbcbadbdbcddcdbabacacdccaadbcaaadadadaaaaadadadababccbbababbbdaacbcbadcdbcdabdbbccddacddabbadbaabbbcaddbacabadabccadcbbcddbaaaabcdddbcabccdcbbdacbbacbacdbbbacccccccacdddcaacbddccacdbbcacadaacabddcdaccbdcdcdabcbddcaadaddaacbdccdaccccccbddddaadabadbcbabadaabcbccdbbbdcddbacdccdddccbacaacacadbaaaadccadbdcdbcddcdbcccccbccbabaacadbcabcabcaddcaadaacdccddddcadbddabbdaddaabbdabadbabbdccbaccccdcdcacbbdcaacdcabddaaccaacacdbbcdaaadaacbdcacaabaccacaabdbdcdbdbcdbcdddcbbccbcaacdbbaadbcaddbdbcacaadbccabbacdaabdaddbacdcdccdcddcbddcddbccccbccbaacbcbddacccbcbaadcbacabdacaaadcaddbdacaccdaacbacbcbabcbabddaaabaaaccdadddacbaaacaabcccacdcbcccccbbabcdabdbdabadbdaabccababaccbdbdadacaadcdbbacdcddcbaaabbaccccbcdbdccccbdabdacdadabdaaaaacadcbadbadabddbbdcaccdbbcbbdbacababcccdcadabdadacddbdddcbdbbabbbbbabdbbdacbccaadacddbcdcdacbcddbcabdabbdaadcdbcadabbacacccacdcdaabdcbdbcadacccdbbcaaddaaaddddbccabbdadbddbcdabcbbadbddddabbcbccadcbbddbbaaacddbbdddcaabdcadbccaabbdadabdbdccacbcdbbcdbdcdcbdacdcacdddbccabdbcdddbbcdbbccbddcaadbbadccbabacbcaddadbcabbdadbbdabddddddbcbdabbddacccbaccaacbdbcaaccadcdabcbaddddcbabdbbaaaadabdbbdaddbcbaddaaabaaabacabbaaccdcdaaacccbbccdcdcbdbabbbaddaacaacabcbdcbadcdbbcaacaaacabcdccabcadaccddcdcbbcbcdbdaddbcaacadbaddbdbcdcbaadaaddbdcbbacbbabbadcaabbdddbcbbcbdadbddbcdddddbcabacaddddacdcdacdcbaadcaaabbdddcabddbddcdbcadadbbdcadacdcaaacacbcdbbdbadccabacadbdabdcdcbbddccbacdcdcdbcbdacdbbdcbbdccadaacaacaacaacdbcaaccbdddbaadddccccbdccacbadcbcccabadaabccabdabbadaddaabcabcdaccbabbdbbcadacabcaccddacdbacccbbacdabcbdabcabbdcbbdddadccaccbcbbabdcaaccadbddccaabbcabdddddbdddddddbbaccaddbdbaadabaabbddcdcbbcabcaacbabcdbadddbbdbdaabcccdccdaddddcacbdbddbbbabcdabdcbaabbaababacccbddaadcacdaccdaaabdcdaddcdbdbdabbaaadbbbddcacccdccabadbdacdabdaabdacdacabdcddbdcdaaaccacdccbaacdbdbdaccacabcdbbcadbbadccccabbadbcbdadacabcadcdcdcacbdcabccaacabacbccccadbccddbdcccadcabbdabcccdacbcdcbbccabbbbcadcbbddddcadcdadcdaddbdbdcbcbddcdaaaabacbadabbdcbadbbbdadbbdbdbccbccbdcabadbdcacadbaacadbbddccbcccabbacbaaababcaaacdacaddccccadcaabbadadacddbdbabaddcbbbdbaaaacaadacbcccddbbdcadaddabcbdaccabcbddadbaaccccaadbbddddacbaccdbbcaaaabbacddabcbdcabbbadccdbaaabadaabaadabcabcdbcabadcdddcbaabddaacbbcddadcbacaadbbddcbacbcaabbcacddbddbabbcbdcbdbcadcbdadbcbadaaccbbabcbccabbcabcbdbaddcbcbbcaabcbdabccacaccabddbbcbbddbacadbbaccdabbdbbdbbbdadbaddcbababbdcbcbabdabdccbdadbbaaacbbbcccadcdaddbcdbdacbabdbcbcdddddcbbadddaccabbcccbbdcacbdbbdccdcaaacdcdcacddccbdccabdaacdbcabacdcdadcddccdbbdcbaadacaadbdbccbadadbddbaaabbaaacaccdaabbadccdddaadadddcabbbcaccbdcbbbadaaadacddbbdbdaabadabbdaaaabdbdddbdbbcccdcababaaddbaaacadbbddcbaddddcadcdadcbcdcddabdabcabdaacbccaacadadacaddbbabbcccbccccaadcddabdcdcabbcdcdcbddadcdcbbcddddadaadccdbbaaabadccbacbdbbdcaaabddcaaabcdbbadaccdaddccbbcacbddabdcddcccaabdadbbaaaddcbbccabcdacabbabbabcbbcaaaacbbadbddbccacabddbdacdabacabdcccddbccbaabcdaaadbbcaaccccccdadacdddbdcaddbcdbacdbbbdaabdcbbccadaaccabdcdadbbcdaccaaccacdccaadbbabbacccbdacbadcadacddbccbdabcabdbabaacbcddcccccdbcbaacababbdabcacabcbbddbcdbcbcdbbdddbccaacdbacbdcadbbaacccccbbadbacbabbdabdcacacadbaccdddabaacdbcbcddcdcdadabbddccaacbbcdbcbadcbccdabbdcdbbaaacaadbdaacccaccdcdcadbbbadbbcdbbcadcacdabdcddddaacdaaadcddddcbacbacbcbddacacbaacbbbacbaadbdbddadddbababcaabccacccabdcdcaadccbcdaaacabababdaaabdadbdddbaadbbbdbadabbcbbabcadcababbbbddddacabadccdacaabaacdadacadaabbbcaadcdacbaaaaddabaacdccbbbaacbbbaacadbdddbcccccdbabdaacdcaabdbabbbdbdbcddbdbabaaabbccbdaacccbbdacadaccabaccaddbddadbbcccccabcbbcddacbadcaddaaddadadbaaabbbbcdbdcdcccbbcbabbdaddbadbadaaaacbaacdbbccaaababbbdbbcbbbdccddbdadddbdcabdbddaabbcbabcdaadcbbbadddcdbbcbbadcdaaabdbaccdcbddaadbaaddddccbddcbaabcacdabbaddbbbdcbadbaadadcdaadcabaccadbdcbbabdabaabbcccacacddbadccabaabcdddbddddcadaddcbbadbbdabdddbbababaaadadadddcddccdaaddadaabccbdcadbdbaabadacdcadcccaabaadbaacbdbbabaabadcdcbaaddbadcdbaabbcbcdcaadccbbdadadcaccaadadddacaccacdccddddabddcaccadbaaddccbacdacdddbcbdccdcdcabacbdbacccadcaaabccbadbbddcccabdbdbcddcbdabcaddddccdaabdaacbbaadabbaababcdccacacccdcdbdadbcaabbabcbbdddbabdabcbdadddcaadcabbaacbbbaddadbbacbbccaabddaaddacddcaddddbdbdcdcadaadccacddacdaccbacdadaaaaacadbcbbccdabbaccabccadbdcbacdbcbdaccadabdbcdadaacdaadbdccbdaddabadcbbdbcbccddbaccadcbcbabbbbccbdbacabbdbccdcababacdacacdbcbbabdabdaadaadbdbaacbddcdabadccabbbccadacaadbbcabbdddcdabdbcabddcbdcabdcbababaabacddccdabaddbcacacccdcbdcddbbddbcbcbacdbcdbaaadabbdddcdaacdacacdbbdbcacbbbabaccdddbabdbadaaacaadbdbdadbadcddddddcaacabcbbbaddbbcbaaaaacbbadcdcaaaccacabbcdbabdcaccabbaadadbddabacabadaddcbaacadaddaadcddccaabcddbbdbaacabcbcccaaacddacddcabbcabcbbdacadacbaccddaaacabacacddbdccddbbddcacbababdcbbbdabdbabaabaddcaadbbacaaccabddaddccbabcdbabbacdcccacaaabccbbbaabccacdcaaccbdaabdaccbcbdbddcdcabdabdccaddabdbccbabcacddcaccacdaddabccbdcbadbdbdbddccbcbcaabccadcccdbacccdddacacbcbcaacdbbbadacaadbcacadbdcdabacbddcbdddbabcdcdaacdbaabaaabdabbccabdadbadaabcabcddabbbbddabbdaddcbddadcdadcaadaaaacbbbdcabccdadacdcbdaadacdaddbcaddcdbdbdacbdcaacadabaabbdbcaaccaaccbcddbbcbaabaaddadbccdcccbcaaacacabccadaddadbbacacabddbcbadbabbbbcccdcacddbcaddabddaaaabacbdbabcbaddbbcdbaaaddabcaabbdcbbccbdcddaaaaaadbcbacbdaaadadabbbdccdabdcacdbccabdcdbccabdadaabdadadaddbadbdbcbaadcccdccabbbcaddcaacddbccbddcaadaddcdcadbcadbbaccbcaddcccddbbcbacbcbddbcdddbdacbddcbddbadcdaaddcaabccbbbbabccaabacdccbdbdcccabbcbcbcbacaacacabdaabcaacabbaadabcbbdadacdbbcccabaadacaddacdbcbacdcdbccbdccdbbdadcdddacabacddccbbaaaababcaabbcdbdcbdaabbdadcaaabbbccdccbacbaabadccabddccbbdbabbddabbddddcaacabbbdbcabcbacdaadccdddabcaadcddacdddcddabdabccbccdacbbaccccbdabcdccbbcbdacdaccbcdddacbddabbababcbbccddaabdbdbdadadbaaddbadcddddaabaabccdacbcacacabddbadcbaadcbdbdbbcdaacbbaabdbacdcbaddcdcaddcbaccdccacdddcabacaaddbabcbbbbbcadaddbbdbccddbadccbadccdcbccacccdbabbadddcbbbcdacdbcbddadaccdcabadbcdbaabcddaacacbbbcaccbadcddbbcdcaabbabbababcdacbaccdcbcdbdbbaccddabdacccbbdbcdabdddddadcaaaabaacacaddbdccccaadaccbbcdcaaddbcbababdbddcacdbddaaccadaaabbdabdbaadabbdbcddccdbaaaaacbbddccdbcdaccddbaadaaaccbabcbddbdbbcdcdbccddcabbddabdccbdaacaadadcbdaadabddcbdcbcbabcdcabadcbaaccaddacbacdcababdccdadccaabdddabbbbaaadbcbbdcccabcbbaddacbbcdcbbbadbddabccbbcadaacacbabcdbcdaabbbcaccbbbbddcacbccdbabaacdddcdadbadaacbcabdbdaccbbdcbcdbbacbdcaaabddcbbadcbbcbcdadabadabbddbbdadcbccacddaaadddbcaddabcacbabaacadbbdccdacccdcadcbcaacdddaacdbbcacbbbbddacbcbccdbddbbbbcddadadacbabbaccdaabddccdbabcbacdadcadcadacdadbccbdbcdaacbcdbcbbbdadcbabbddccddbabccadadcbcdadddcbbaadbdaddbbcadbaacbccdabcaaccbaaadaaccdcdabbcaacbddacadbacdaabbcdbbbbbbabbbdcabcbabbdbdaabcdcddacbcbacaadbbcdccabdbcdaadbddaacccbacbacbbbadaddccabababcbcadaaabcaddbabbabbcdaadacccdbabbccbcdbdbbcaaaaaacaddaaaaaaacccacbbccdddbcaacdcadcabbabccbdcccbbabdccacabcddcbbcacbdabbdacacbcadaadbdaadbadccacdacabdadcacbcbdacdadaddcbaacccabbaddccbccadbcdbaccbaddaccdcddbcdcaadabcacccbdbacbcddcacccaaaacadacaacacbbbdbabbcdacbabdbbbbdcccccdabbcdbbadcdaccabdcbbbdccdadcadaadbcdbacbabcabbabbbdcdabaabdbacbcdccadaddbcdbcbcbbdbadbdabcbcadcbadabdcdcddcdabbdcddcdadbbccdcbabdcabbccbadaabcbbccbcdcadaddbddccbacaabddcbcbdcaccbbcbcccababbcbdbcaacacbcdcbacdbdcacbbbddbababbdcbdddbadaadbbccdabdabcdcbccccbdccbaccaccdbbaccdccabbcccdaabbaaddbcdaddbcbacacabbbbdccadddaadbccdbccbbddcacbadcabdbcccbdcdaaccdddcaabbdbacabddaadcddcbabccbcddcadaaccdaccbadacadcaaaadbddaccbcbadbdbcaadcacdacaccbbacdaadbddadabdccdaadddaaacaacadcccbddddddbccaccbaadccbaaccbbbadbaabbabaaccccbdbcbbbbbcbcaadbcdbbabdcccbcadacdcaccabdbcdcdabcacdcdaadcaddcdcbbcacbdacdaddcdbadacdbcbaddcdbacabbababaddbbcccbaccbbadaaaaaadcbaaabccbdcaaabbbcacacbcdabcbccdbcdadadbacbdbcabdcdcccabaaabcbbccbddaccbbacdbdaaaddabaaaaacadddbdcdbccdcadbbabadccdbdcbbcdadaaccbadbabacddabcccccacdbccdbdbcaddbcaadbcbdccdbdbadacaaadbddddddddacdbabbddccbdababcaabcbabdddbcadaddbbcdcaabbdddadabacbcbaacbabdaaddbbcaabbababbbaabaadabbbabcddabdccbabcccdbaabdcdcdaaddcbdbdbbaccbddcaaaabbbdcadccdcdababbdadabcbdbbdbadcdababadcadcccaabcadbacdddacbcdbcaaacddbaabcdabcacacddcddadcacbddcccababccbcaccabbbacdbdabbccdaddbdcabbdccaacacbbabacaacbbbccddbcdaddadccdccacbcbcdaadbbcbacddaccdbcddcbaaccabccdbcdbdddccccabdbdddacddacadadbbcacdaaadbbabbdddadbadabcbabcbcacadadadcdddaacacaccdddddadddcbbdbbdaaacddbaccdbacdccddcdbababcdbcaccbcbddaabcdacbcbbbbbcacaccbcbacdbcbbbcdcabdbdbaddacddcaccabcaaddadbdadddaadadadcbbbaacccbacbbaddaaabbbcddcbdbcbbccbacbccacaaccadabbacccbddaaaadbddcdddacbaadacdbcdabcccdcbdaddabadaabdddbabbadcbcddcaddbaadcbaccbbacabbdaddddcadbaadaabbdbbacabbbdacadacbbcacbbbddccabccdbbacbbdddccaaaddddaadabaccaccaabddbacdaacacbaadcccabcdddccacbdadbadddabddcabcbadcbcdaabccbdacdcccdbddcddaccbccabbddacadbadbdccddbabbdccbbabaccbdbcccbdcabbccabbbccabcadcbbbcdbcacaaaccbdbcddbaadacdbbcbbbccacdcbbbbaacbcacabddcddccbacdacadbbdcaacdacacaacbbcdadccbddacdcabacbccdbaacaabcaacddbcdbabddabadbdbcdddaaccababdbdcbcbbbaddadbddbccabddaacbcdadaccaddcdcacacabadcbdadcdbdcbdcadbbadbdacbabbaccaaddcccaddadbbddaababbcaddabccbcbbcbcdabcabaaddacdbadcaadcbdbbddabccabcbbbabcbabdabdacadbccacaddbcaadddbdabbddadaaccaccdaaaadccababcabdbbccbbcbcaaabacbccdacadcccdbdbabdcbbbcabaccabcadcacbaadddbcccbcbbaabaacaabdadcbcbcddacdddadbabcdacbddabbcccaabddddaacaaadadbbabdbdaddcacdcaadbcbbcccaabcdccdbcbdacbadcbbcbbdadbcbbbccdcacdbbcaddcdccdccdcabdbddcbdbbcbcababbdbabdcaddacdddaadddcdadadadcdabacbdcdddbcdbdbbdcdcbabbbdddabcbccadccdbcbcabbdacaadaacbdccccabcbccdbbadddcaccccaccbddcbabdbabbaabdbbabbdbbadadbdbcaccbbbbccccbaadbcddccaacbdaabbdbdaaddccbabdbcbadadabbccaabbbaadabdaddacaaccacdbccbdbdbddaddbbdbccdaaabcdcadddccbbacadadbbccdaaacbabddbddcbccacaddbdacbaacccdbbcbaaaacdcdcbdccabbbcdcaaadbbbdbddbbcbdabdcbccbacbaaadacbbbcdacaadddbbacbcbcbdadcacaddabbbbabbbdbbbddbacbdadbcbcbdababcbaadbacbdbdddbacaabdcdaadccbddadddcbaaaccdcabacaaaabdcbcbbaccaaaabcabbbadbabacbcaaddbcacdbcddabaabcbbabababbccbabdcbbbccbacccbadcabbaabdabdadbaabdcabdccbbdbdbacabcddacacdbacbaabbbcdcbdaacaaccbbccddaacaabdadacbdaccddbcbcbbcbdbaaadcdddbcccdcbaabbabbaddabaaddddaadcaaddbbadcdcdacdabcbabaabbcbdbcccacbcaccbcccadbcbbbddcbdadaadaccbcbbaaababbbbacbdabddcdbdcbcacddbdcbccbcbbaaddacddbbcadbdbdccdbdddcadbddcaaccddacdcadbbbdadababcdcadccdaddbcbabaccdbadccdccaccadcdcdbddaddccdccbabaaccadddcbacccbccdcccdacbdbbabbabcadabdcdddcdcbbcbdaabbabaaacbacbbcbccaaccbcbcdabccdadaddaabdcaaabacdacddbbdaabcdaacbbcbaadddadbaaabaadacadccbaacddccbcaddacbbbadcbbbdbadbacdccaaddbbaaabbadabdbcbcdabbdbdbbddaadadaadbbddbddccbdcdadaccbdbbddddbcdaaccdaacaacabadbcbbcaabdbaddcdbadcccbaacbacbadacdcaaaaadddcbbcbbcaacbddbadbdbdaccdabcbadbdabdbdbaddbddabdbddabbdbabcdabbbdcdcacadcabacaccccabddbaccababdabbbbcbdbccbcbabdaddcccdabdddccbdadbaabdacaaabbbbdadccdcdabdaddadbbdccbbbdbabddccdcbcaaccbcccabbcabbdbccdbaabbbccdabacccaddabdbcbcababbdbaacbddbbabbbaacaccbddadcacdccccbdbccabbdcbadaaaddcabdababaadcbbbbcdababbccbccbdabbdacdbdbccbdccdcdbaccdcddccccccacbabcdcbdbbbbcddabcbdbcaaacbdddcddaaaacbccbbdcadccccdbdcbdbabaaadbbdccabcacbaadbccbbcbabcaaabcdbcdcacccdccadbaabdadabacadccaaabdaabccadbcdbaccaadcdbdccddacdadddddacadccbbcadadcadbbdaadbccdbbabbddcdcbdbacccbabbaadccabbadcdaaaccdccbcabcbdbdacdcbddccacbaddbacdabbdddcbcdddcdbdbaadabadbdbccbccabbcadccdddbdaaddddcccbccacdacabdccacccabdadbaddcadaabacbbdacbcbdddcdcdcbbccadbbcbaddcbbccddbcbdddbcabccaccaababacadcadddaddaaadcacdacdbaadcbccdadcbdbdcbabaddbcdbbcbcbdacbddcdbbacadaccbbababaccabacaddadbcdaaaaaacbdddbcacbacacbcdabaaccbcbaabbaabdaacdbbbbabbdccbadbdaacdbbbdcbcbddbacaadadacacbdbabaccadbacbabcaccabbaadbdcbbacdccbabcacbddadcadaaabdcccdcbcddaabadcdbbcabdbbbababdbbbadccaabcbadcbacdadcacababdaacbdabdadadbdcadcddacbcacdccddddcbcabbcdcbabadabddccabaabbadcbbdbbcddddadacababdadcddbdaabccaabadadbdbadbabcdcaaddbabbcacddcccdcbabaacacbbbccbcdddbdbcabcbcbbdacadccccbcbbcdbbcdbcccdbcbdacdddbdadcaccddbcdaaabbcbabbbaaccccbdbcaddcaaaaacdddbbdbbcdbbdadcdcbcbdbacadaabdadddccabbdbabcdddaacbbcdbabccaacccbbbbbaadcbdbddbcaccdccbbabdabadcbcababdacbbbbaabadaccaabdabcddccaccaaaddaadacbcccaccbcaadddabbadaaccaccdddabbcdcddbcbcabadbbbadaabbdcbdadbaabbacbcbbcddcccdcbcbccabbacccacabbdbdccddbabcbcabcbcdbaddbdccabbcaabcbbcabbbbbaabcdbdbccdbcababdcdbbcbabddcccdcaadddaaccdbaaddbcccabddbccabcbadbdcddabcccaaaabcbdcdbdbadacacadbcaddccaabcacabdbbbcadcddcccadaabcdbdccdcdaddddcddabaaabdcabccbacaaaabcacddddbbaddaabcacaccbabadccaddcbcdbacadcaaabccbcacabdadadbdcdbcbdabcddabaaabacdbcdcbdbaacaddaaabccbbbbdccbcacbcbdddcadddacccacbdadadbabcbcccaabacdcbddbabadccaccbcadbcdaadaaabbbbdcccdabadcadbcaccbbbdcbdcddcbcbdcccddcdbbadacaacacdcddadbbadccddbdcdcabbabaacbaabbbbdbdcdbcccccbdbadaddccbcbcccacdaccbabbbdbdbbdbacddcddbacadbabcdbbbaaabadccabbbcbcbbabcdddbbabbbdacbdacadbcbcabcbacaccacbdddaacabcaacbdabdbbbbdabddddcdbbaabbbddbbcaacdcaadcaabccddccdcbdddaaaccdaaddcbbcbcdbdcbcccddccbcacccbbcddacaadcbccacabdbdddbcccbadcbccbbdacdccbbdcaabccdadaccccdccbcabbddbcabcabbcbccbcbabbbccbdbaacadcabababddcddbbadcbcbacdcadbbbaaddacbdddcbbcbcacaccadccddbbbadccaadcddbdcdadaaccbcbdcbcabbbbcdcdbbabaddaabbdbbdbdddabbbdacccacdcaacaacbdbdbbaadcbaaadaaddcdcbcbdbaddccaadccbbdccbdaddabcbcbbccacdbcacccccadcaacdcbddadbbdbcbccccacbdddbdacacbbcbbacaccaadabaabbdcabacdccbbddaddaaaccdbbcdbbcbadacaadaccbabcacbdbdccaabcaabaaaddccdbaaabbdcabababacdaaacbcaabbabadacccdaaddbbbcdcddcaabdbaaddcaddbabcdbdcbabadccdabddbdcadcadbddadcadadadaabbadbbdbbacacbaabababacbdbccabaababddcababaadabdbcaadcccbdadbcccadcbadbdbdaacbabacbdaddbcdcbdadcbbcdcdcdbcaaaacdacaaadababcdadabdaccbdcbaddcbccabbaadaacccbcccbbcbabdcdbcabbbdccacdbaddbacdcbadbcbcaaaabcdabaabddcbcadadccccdcdbbcadcbcccaaddcabbcdadbccabdabdcdbacdabadcacabdbcbadcdbaccdcabdcbccabbdabdbacacacbbddadcbaccadcccaadcbbbcaaddcdcaacaadcbdbadbaaacddcbcccbaaabddbaddbabccccccbbcdddadcbdbadaddabbdbabcbdabbdcaaaaaaaabbdbddccacbbbcbabbbccdabdbcdbacccabcabaddababaabcbadacdddddaabdadccdccdbbabbbbcbbdcaaadadacaabbcacddbcacacbacdccbdbdcaacdabdaccdabcabdabbaacdaccdbcccdacabababaadacbdadbdadacbddccdbcccbbacddabdccbacbbdacababccdbadadacdbddaabdcbdbcddcdacabcdaadcaaabccdaccdbacdcddbabdadabbaaaaaadbcbcddaaccbccdddaadccdaacdbcbcbbabdccbabbccbcdcaaabaabddbcadcaccabaabbadcdacddcacbaaadcbadcccccaaabccbadbdaccccdcbccbdbbcccbbcacbccaaadbdacdbcbaccbdccdcadbcabcbbcbcabdddbbabdbbadbbcacbabacacdbaacdbacaaacbdbccbcbbaadcabbbcccaccdbddbcdacddabbdbbaadacdcbacbdccdbdbcddadcacddbcabbbcbbdbabaaadacbaabddcbbcabcccabdcdcbdbadbdbdabbdbdbdbcbdcacabbbcbdbcbacabdccadacddbbdcdcaddaaccdadadbbbabdddbabaccbdbccddddbbcccbddddcddcabdccddcdcadacddaaaabaaadbdadccbbdacdcdcdaabbdaddbacabadaccbaabbcabdacabacbcbdacdcdacccccbdadbbdacbddddddcadbbddaddacacbcadacbbadacabadaacddcbdbacccabbdcdacbbcbbccbddaccdaadaaccdcadddcbdccacbabbdccbaadbdcbdacbaaabbbcbbcabcaddbcccacbacabadccadddabadcacabcbadcabdbacaccccdcdddcaddcadaaccbaacabadcccbbcbbaaaaabcbaacabcdabccddbcaacaddaadbaacdaddccdaaadacdbaccdbaaaacbcaacbddabbcdadadaadcbcdbcbcaddccbbcdccabdbadbcdbcbcadbabbcddaaaaadabddbabcababbbbdaaaabccbaabbbcdabbadadbbdbddacadcaacbdaaccbccaabbddcbdbdacdadabcaccacccbbdcdabccccdccacdbbdccbdbadbabaadbacdccdcaabbccdbddbdbddcaaccbadbaddccdcaaabacaaadaaddaabddbdcdbabccacbacdcacddaacdadcbabdbdaaccbbbccdcacbcadaaabdacdaaccdcdaabbdbcbbbcbbcbddadcbddabaaaccdbaaacdacddbccbdadabcabbbdaccaaaaddccaabbbdcadbbacbbbdcbaddccbdadaadacaddbccbbccdbaacddcbabdbddbbcdbdcdabaaabadcababbbdaabbaadbdcdaaddabdcdacbcacaacdbddccaccabbddcdbbacadcaddcbbbcdcbadcdabdcadccccdaabcbbcdaccddaccbdddbbabdcdaabdcddbdcdacabaabcbbccabcaabdccacabcbcadabcbbdddaadacddbbdaadadbabdbadadacadcbdaacbbcabcabbcaddbacaccabaccbdcccbbbcadabdbacaddbcddcdcbdcabdcbacabdbbdcbaadbbbbbbbabccdadcdbcbcbdcabcbdbbccaacbaabdbdcabcccdcccbacbcdcdcccdcaddacbdaadbdabddccabbbbbaababcdbccbbacbddaccabdadbabbaaabdbdddbaccdaddccccbbbcacbaabdbccddcdcdcabdcccbbdcadbbccadddaabdacddabdbcacaaababcdddcabbcdcdadbcababaddbabdcaccbdaabcaabdbcbabcddcddbdcacdcdcbbadddabcabbadcbabcccacbdcaaaadccdaddcadbaadcdaabcdaadaacdadbdcaacbdadbaabdddcddcbcbcbbbabdbdcbacbadbcccdbaaabddcdaabddbaccadccccbddaacbcdacbdaddcabacbabacbbadadbbacdcdbacaaccbaacdbbacbccabacdaadcbdbcabacaddcbdaaaacacbadbdcadbccdbadcbcbdbbabcbdcbbacbacabdbcdadbacabadddbdaddccbdbbbbcadabaabdcaacbbbaacabacadcbcbacbabdcbcdccdbddbaabacdbbabacccbdadddacaaaaddaccbcddaaabacddcadbabccdcddcbbdadbddbbbbdddbccaaccaacdacabacadbccbdcdabbabbadddcaabbdddddbacbbadcacbbbbcdadbbbabbdbbcbbcdaacadcdaccaaabdbabbccadbddacacddddcbcdacacbbdcaacccdbcbdccabcccdbaabdbbcddadddbabacacdcaadbbbabccadcaacdbbacadddbbadcdddcbcccdcadbcabdadcccdcbcabaddcbdddcadabadbcdbbadcacaaadbbbadbabacbbdabdcbbaabaccaaaccabbddbcdcaacddccdcabbdabcbbaddaacbabdaaadbaabadccbcbaddcadaadcccbbabbcabdcbcdcddaacdbcbacacdabacddabccdbbbbddcdcadabadbdddbbbddaacababbcdbdadadbcdcacbbddbcbabbddbccddaacacbbcbdcdbaaabdbbccddbcacdcadbcdbcbdcabbabaddadaddcdcbdbcddccdaaaddcbccadaccacabbaabdbbaddccdbaccdbabaacacbcccddcbabbaaaababcbcdcddbabadddcabbccdadacdcddabdaacddadcacdbadbacacaadcdbaadadcacddcccbdcbbdadcbacdddaacbdbbbaabccacddbbdcaaadddbbabdacccadbddacaaccacddbbbdbaaadccaadcbbbbddbddbccdabdbbcddaccccaacdddabcbdaddbbbbaaacadbbccbbadabdcbbdcdaadaddbbcadcadcaacacadbcbacbdacaddccadbbbbbbbccdbdaabccbababcabbbadbaddacccbacdcaccbacbbaddadddacacabaddbbaaacaacaacadcacadaddcaddcaaaacdcdbdabcbbadcabbabaddbcdbcbaaabcabbbdbbccaddbcbadcabacaabddbcabdccccbdcccbadbadaabccbbcdcddcbcdcbbcabcbadaddcdbbadcdcabcccccccbaddbcabcddacaccdcbbcacadbddabddaadbbcacbcdcadcdbdbcdbbdacbbaadccaccddacbcbccbcdcddadbadadadcccbdaaabbaacabdcacbcabaccdacddbdbaaadddaabdbcaabddcaddcbbdadbbccddbbadabddbacaaabcaaddadbaabbabbabcbbbbcbbbaacbdbacdccdcacaabdccababddaaaacbccccbdbcacdbddcdadadbccaddaaddaaabdcdccbadcccdaabaaaccdabadbccdadcddcaacbaddbacbcabddaaccddccdddbccbabdcdcbdabdbadaadabcbabcccddbcbdcacbdbcbabbbcccbcbbbbaddadacbcdbbcdacadadcbacaaabcaccddbabacbbbdabdcdbbbbdabaacabadbccadbcdadccdbbdcaabccbdbadbcbddccacbadbbcbccaccadbccdaddddcbabdbdcbcccbabaccdacdbaabdcbdaaccbcbdaddbaaaabdaacbabdcbacbbdbccbcccdcdbadcbabdaccdbcbccacbaccabcdcaaddbcaadcbbbbadabddcddadbbdadcaabbbdbcbcdcbddcaabccbcbaadddcbbcdbcadbbcaccbdccbdbdcbbadaabdabaddbcdcaadbadddcababcdddbcddadddcbcbcdadddbdacadccdccddaacaccddacaaaacbaccbdcddacdadddcacabbbdbccbaadabcacbcddaaabbbcabaaaaacbadbdacadcbbbdaacddcddcaaccadadddbbdbabcbcdcccdbbadbcdbccbbccbdaccccccbdcaacbbabbadbcbbcdbbdcadacbcbacccddadaddbaacbccabcdbacbbcbababcaaadacbbacccbabacbabbccdcdccdbcddddbccdcdbdbdbbbdcbcbadabccaabddbbddaabbbdcdaccabbacacdbbbcddccacddbcacdddcccccaadaaccabbddaddccbbdadbdbacadcddcbacbadbcaadcbcdcadbcdcbdddaddaacbbbbcadddddaddcdbaacdcdddcdaaadabaadbcbaccaccdadacbcbdadcdbccaacbdddddaccacbbaadcdbaddacdacddccddbaaaccabbbddacbcdbabcdabbdacbddbddcddbcbacacbdbdbbdcccaaacbcaaacbadbcbbbccbdcbbdcbadcbbcbbbccdbadcbddddcabadcaccaccdbdadabddacabbacbdcbcdddbcddddbaddcacacbbccddbadaabacbbbdcccbdadbcabdbacbbcccbbcbbadbbbdbdcbbdabdddddadcbabbdbdabbabbadcbadcccbccdaabdcbcbcdaadacbccadacbbbbcadbdcabbdcbccacdddcdacdacadcbcabccddccacbdcdadbcdacbcbbcaddbccacabbcadbdbddcdbcbacbacaaccdbbdabbaaaadcaacdaabbdbdbaaacddccaaaabbbcdadaaddcdcacacdbcbcddcdcbaadbaacdacaabbacaaccdcdcdddcbcddaacadabacadaacddcabdcaccddbbdcbaadbadaadbcbbdacadcbdabddaadcbccbaddacccdaddbbcdabaddabadadddadddbbddddbcdadcdbbddddddcdcbdbacddabcdddcdcbcabccaaaadcbccbaabadcdbabdcbbaabdcbabaabddaccbadbcdaddaaccbcabccbbdbdadbbdaabbccacbdadbaaccbbbcaadbccbacdbbdabcddabcbdcdbccadadcbcdcdcdbcccaddbddcbaaddabdbcbdddbcdcbaccaabaccbbabaccddbddadccdbbddccccdcdaaaaaccddcadaacbdabcacadbcccbabacdccccccadcdadcaabbbaccccdcdadaabbcdbdcdcaaabbddcadcbbcaacabcbacdacadbbacacacbcbddbbacddddbbabdcbbdacdcacbbcdadbdcccdacbbbddcccdbbbdbdbcdddabbbdbdcbcccddaaccaccbccdbbcacbbadbbccadccacccabcaddcacadbddabbadacadacdcdbadaacbabdbbbadbcddbbccaabbadadbcdaabdaaacdbbaadabdcadcadccabbcadcccdaddcbacaccaabcdcadadddbdabcadbdadaccdbcbbbdaabbbdaaccaccaacddbbddcdcbcbadddbcdabddbaaadcabadbdbcdcbcbaabaddbcbdccdbcdabdcacbaaaddaddbacaccbcbdadddaadaddcccddbdcdaabcaacdbabcdaaabacdacccdaabdcdccbcbdaaaadadbacbdabcdbcdacccbbcadcdabbbabbaaadcbbabaacdababbacabdacacabbdcdcbbddaccbacaddadacaccdbbaadcbbbcbacccaadaacdadccacccaabbcaddbdcaaccdcbcadcbcdcbabdcdddbddadcacabddcaadcabcccdabdbcddaacadcddcdcaabbaadccdaccdddcdbbdbbbadbdccbbdcbccbabbaccbacaacaabcccacbbacbdaababbabbdbbdccccbabaabadaacdcdacdddcaadadacdbbaaccdcdbdaacacccccddabdbbacbabbaadbaaaadcbdddddbcdaadcddcadbcbdaacdddbcbbabadbaccccbdcaacbacbbcbacaaadbcdbcbcacbabbbddabdbbbabdacacdbdbadbdaabdcabaabacdcbbdacbbbdccabbbabcbbcaabddcadbccadccdababdbbccddabcaddadaccccdcdbababcddbbbccdbbabbbddddbbccbcbaacdccabdabadacdbdbcbdaadccbcddbcbdddccbbbacbdddbcdccacadbadadcbaccaabbdcdbbbadcabbddbbcddbbcadcadddbccdcdbdcbdabbbadaaabdbcdcbaabcaabcdaadcdbaaaddabcadcdacaccabdbaccadaddabaaaababcdacddbdcbaabbacababdcbdacdbbbaccdabacbcbaddbcacbdbbbacccabcdcbcbbdbbadbdcdcdccbbadbadcccbbbbccabacadccccbacccaadddcdabdbbaadddccabccaddaaadabdcdddcabddbbaacbcdcabacdbabdbaaaddabbddcacbdcacbaabcaadaabadbcabbdccaddadcdbaaaccadddccddddcbcbadbccbcbcddaadbbabacaadaaadddcacaacbdcabcdbbadabbbaabaaadbbdddbddcdccddabaccadcadbbacbcaacbaaabacdabbdbddcddcaacabdabaabdcbaacabddcbbbbcdbdaabdccacbcabdbadaaacbaacddbabbbbabbaadcbcabdbdaacbcdcbabacdbdcdbdbadbbaacadccbbcccddaaaabadbdbdbdbddcddddcbcaacbbbdbcddabbaddcbbbdddcdbddabbbaacbacdcdbdccddbbaacddbdbcbaabcccdadcadcacacaddbddbdbdadbcddbabbdcacacbccbccdcbbbbbcdaadcbbbdcbcdcdaaddaaabdcbdcacbabcbdcaadbcaabbddcdbbccccbadababbcbdbccabbabccbddcababdccadbddadcdbacdaaabbabccbbbcbccccadccbbbbbabaccdbbdcaacbacdacaacddbbcdccbbacddcdcbcabdbaddddaddabdddccdccbabccaccdbdddadccacdabbcddbadbcdbbcccdbcaaaccaccaaaddbdacbbdbcccbdbcabdddcddbabbabacbadaddcaacdabdcbddbbcaadabaccadcdabbbdbbcbdabcbbbddbaaabadadcdcdbabdbdacabdcbbdbacdcbdaccdabbbdddaacaaabccbaabccadbbbacdddbbbdddbdbdbdddddcccbaddabcadbcdcdaaabadacddaddaaaaaaadacabaddadcbbadaadbccbdcccbbacbbdddadaaaacbdcacbddaacacacabccbddcadcdcabbabbdcbcacbabdadddccddabacbabcadcdcddaabacdacdbccccbdccbccaccdbbdbabdabbcabdcbbdcabdbdcaddcbdcbadcabcdacbabbdbcddaadcbacabbbdbcccddcabaacddccbacacdacabcbbaadccabadccacaccbbbabbbbccccbacbbccdadcdaacdaddbabdbacadbddcbddbbddabddbddddbbbcaddcdddbabaaacbbdbacdbaadadddaccbccdcdcbbbcdbababbbddcadcbbdbabcbccddcbdbddbacbbaaddcdddaabaaaabdccbbcdcdcbaababcbbababbdbdcadcddcbacaacabacdcdadccddacdaddbdddbdbdaccabbbbcaccbabbddddcbcabababbdbdbccbcdccdaaabdcccccbadccaccdcddccbabbadbaaacaddbaadccbdccccaacbdbccadacacaacdbbbbacdabbbddacababababdbaddabadbaccbcbcaddccbdccbcdccaaaadcaaccadaccaabdcccabddddbbdacadbdadcbbbdbaacdddcdcccbbbdccdddddabdbdaacabcdacbadcdaddbbcadccdbbacdccaaaccbaccccbadcaaccddcdacdadbacdacdbacbdbbbdadbbacccaadadbdcbadcdddadcadbccabaccdcdcccdbdcdcdbaccddcabdaabbadcdbcddbcbbabababcadcabacdccadaababadabdcbaadcdbccadaababaaddcaaddadccbbaaaccccdddadaacddbaabbdababcddcaddbbbccbddccadaaaccddbbdbbbabccabacdbccccdccddbacbccbddacbaaadbcacdbdccdabcbbcbdcacacacbcddbbcaacddbdbdbcadbaacabcaaaadbccbaccbbcbdaabaacdddadddaccdaddabdccbdaccdbdaacbaabbabaacaddbbbcdbacaccacacdcccdcadbbcbddaccbaddaadccbbdcbbadcbadbbacdadbbaaddcadcddbabcccbcacaacadbdbcabbbdbcbdbccaadadacbdbadabcaabbacbadaaabdbcbcbbdcccccacaaccdaacbddaabcbaaadbdbabddaaddcaaddbbdccbdddcabbcbbcadcaacbacccacbbdcbdabababbaccbddaadbadbcdbcacdbacbabcdacddbadadadabcadbcddcccacbadbbdccadacdbddcccaddddbbadaccacaddbddacddcaccddadbadcabacdbdacacdcddaaaabacccaadccdccaccdbbdacaccdabdabdabbcbbdaccaabddccbcbbbbbdccaabaaccabdcbdbcddaacbadbccbccbdacdbaaabcabbbdddbcadbdcacabbdcddbddbbdaaddacbbddaabababcddbcacdadcadadaaacdddddbaccdacdbcbdcbacbcdddbaabcbcbcddcddddddcadaabacccbddcddcbbbbabdbccaacccdddadcdabdacbadcdcacabbdbacaddcaaababcdcbbbcacdaadbdbcdadbdbadcdcabdddcddcbaadaddcdadbdadcddadbbcdaddcddaaccadcccccdaccbabbdbdbdadacacdddccdbcdaacbaabdcadacaccacbdabccbabdcbbaaccabcbdabaccadbdcdcdcaabdacbdbaaddcbcbdacdbbccaadcdacaadbdaacddbbdaccdadbddddaacddacbdbbaddbbdccdadbabdccabbaabcbabdcbbcdbacbacbcdbcccdcaccdabacabddcbaabdadbbbdaadbdbacdcabbccbdcddbddbcabcdbddcbdaaadbbadbdbcbaabaabcaaaadbcaabcbbbdabbbcacaadbbbabdaaacdaccadaacdccbdcbdbbdcccbcabccddbddbadccddaabbdacdddcdbdbacaaacdcbcddadbcdaacbcbabaaccdcaccdacdbdcabdadccaabccdaabadccbbcbbbabaabdccbddccadccddddadddddaddaccccadcaccaabccbccaaacbccdadabcaabaaaaabcacaaaddaaabccccbdadcbadacaaddaddcdbdacdbccbaadaddadabbbddabdcdabdccaaaababcbbbdcadccabdcddcaabdbccbaacdbaadddbbadcbabbcaaccdcabacbaccbaadabbadbaabbaccabcdadacaaaabaaccdbccdbbdcdcbddccbabdcbbabbacacddcddacaddddabbaadaaccddaacdcbbdbbddacbccaaadcbcdbdccdabbcdabcdcdbdaabbbdbaabaabdaaabbdcbbbcbccccaaccbabcbddccbadbcabaccdbdadcaadccccdbadabaddcbddbaaaccdbcbaddbbdbcddbacbadaddddbcabbabcbdbabacdaacacbcdddbbccbabdbdaccabcacbcccccbccbdbbccddacdcaacbcaadbbaaccabccadccadbdccbbdcdaddcbabbbcdadaaadbdcdcddcbccabbdcabbdbcaacacabddbdbabbaacadbbccdadcbbcdadddbdbdcdbbcbcbbcbcddcbcdbdaabbddaacbddbccddddccaacbbccadabddacadaaaaacdbdaccaadcddcdbddcddabbcbbaacdbdaadbbdcbdabbaababacabcbcccaadabbddaacbcddccacbbadcccbaadadcddcaadddcdcbaadaddadbdacbaadacdcaaccbcbcbcdbcccdbbbadccabccdabaaabdaddccdddabdccdbbcbdadcabbbcbbcccadabdbaddacddabaacdbadcacbcbbcabcbabacbddcbdacbbbaadbdaacbbcdccdadaabccabbdacbbaccdddbbadbbdbbaadacacacacbabbccddcabaacbaacdddbcacdcacccdcccaaacbbcadbcdcccbbbaddababcbcabbacdaabbddcaadcacadacacbccbddccbcbadaaacddbdccbaabadbccbcdaaaccbcccabaccaccccdacaabadabbacacadcddcdaccbdddbbbbbdcdaabcbcdcaaaddabacbbcccaacdaacdbbcbccdcabcaddcdcabdcddcbaacdddcbacadbabcbbbdbbcaaabcabaabcbddaacaabccbdccaddadcbadaaadbdbabdbabbccaacaddbddcbdddaacccbaaabccabadbaaadccbbddcacbbccdcacacbacccaacaadaacaddabcdbadbcbdcdbbccccbbccddbcbadbdbaaddadcdabcdbdabaddabdcbddbcdcdabdadabbcdaabbccaabdbcaddbcbcdbbdbdddbaaacadabcaccdaddcdddaaaaacdcaadbbbbdccccdcdbdddcccbdbbabacdabddcbadaabddadbaabccbacbddccdbdcdcabdcdadaaaaadbadddbbbddccbadbdddbabdccbcdcbabbdccaacddabdbcacddcbbabcabbdbbcccdcaaadabdacdcbabaaabbacbcacaacaabcaacbbbdbcbabddacadabcacdcbdcbabcdaabbdbbacdaababcdaaadaaabcbaaaccadaaaacdcccdbdddbdacaaddbbcccaccacadabbdccbcbadbcdbccadcbdbaaddbacbaaaadabbdcacdbbcacacdcbaaacbacbcaacbabbaadccbbcddbdbdbabcddabdddbdaabadbcdadddabcadcccdadbbbdacddbdadabdbdcdcbcbddbacdcbbaaaddabcdacbcddaaadddddcdbdbcbdcbdcdddabbccbdaccbdcdccadaaacadcadbcabddddadcacbbdcbaacaabbcbbbdcadcbccdbcacaaadabcabdbcdcccabadbcbbbcacabcbdacbabaddbddcccabacadbddacacdbbcaddbacccacddcaccccbcdbddcacbadcbbbbccadaabdacaadbbdccabaacacdbacccabdbdcbbcbcddddadadadbacdacddcacdcddcacbbbdddcbcdbbadaadccdaddcdcddbadcbddcddcdcddcaacaadaccaccadadaaddcbadbbddbaccbbadbdabcabaddddaabddadabdbacdacaabdbdbabababcdaadababbcadbaccabcccdcdbbccaabcbbdddaaabccabcdbcacdbbbbadbacbcccdcdbcadbbacadadaaabcddcbbaddcddacdbdbcbdddcdbabddadddbcdacccccbdbadabdbaabdcbbacabdaababbbbbcaadcadabcabbabdbccdaccbaaccbdabdbdcacbbadccdbbdbabdbabdbabcadcccbacbabdbbcaddcbaabbcddcdadacaccaadcbddaabddcdcbcadbcaabbbccdacacdadababbaccadabddcaabbaabbbdcbcbaccaaaccacbcdbdccdcdcbbbacddbcccadbcbabddddbcadcbdccbdabccddcdbabccabadbdbcaabddcacdabdccadacddcdbcdddaabccbabadbbbccaadcccccadaddcdcbcadacadcddaddbbbdbddaabbcdaccccbbdcabdaaacdcadacaccbbaadcddabddaddbdbbcbcadcddbbccaabdddacbbbdcdaddbbacbbcdcdadaadcadaacbaddccbadddccdaacacbdcbacbbbbdcbcdacadcdbdddccadcccccbdccdabdddbbccddccabcbbdadccbdbacccdaacaadbacabccddddddcddbbcacadadcdcabcbbabbbdcabcaccacdbbacccbcdbcdcbddadcdddcabbadbdcadcabcbcbdbbcadbbabdabacbdbbbdabbbbccddddcabdabbaccabbdbacbddbcbbbbddbdabdddacbcbcaaddbccbcacdcdabcddccaccaccdcbcddcbbbabbcacbbccbdbcbbbddddaddaddcbbcdaaddbbcdaddbabcdcdcccdabacdcbcadaccbadddaddbcbabdbabcdbaababbdaaddbaaaabababcacdddccbccabadbadccaadaabbcacbaddcdcdccbddacabadcbbabcdcbdcdbacccbcdacdbadbddaaacbdcdabbcabadadabbcbbbbddddddbcdcabaaddabcbbcbcdbbacadcdcdababcbbadaadbbaccddddccbacaabdbdabadcbadcccdddcbccacbcabcaddbcabddcbccbdacdcccccddaacaaadbacadaabbbbcadcaccacbcadcdbddbddbccaacaaaaaaacbabaabacbdcddbcdcddcacbddcbcccbdcdcccbabbabbcdddbdcddcaccdadcdaddbdddbdacbdacadacdcbccccbdbbadcdbccdabdccdacccabcbcdcbabdddacdacbdcbaaacaaaacbdadbdccdbaaaacabbbcdcccccddacccadacbddabdababbbcdaddabbcaccbadcbbacccacbdbacaadbddacbccbddbdcabbcbccdbbbdbdddcadcddddcabadbbababbbaacdaaaabcdadddcbcccbdaaacaddbaadcdaacadabccdaccaccbcdcdacbbdadcbccbbbadddbdcccccddabbdccacaccacdcdacbddbddacaabbdabdbacbdaddbdddbcbacdbbcdcacbdcabdcdaaabcbcdbcdcbabbdbdbbbbbbddcdacadcadbaabbdddadabdddcbcaccddccadbdbabccbdadcdbcdbbbcbcbdababaccbbbddbaadddcbadccaccaaccaccddbcabcbaabbdbdbbadbddbaacabdbdddcabbbcbbbdcbaaabbaccbcadaacacbcaaacddcaacabdcaaacdcbabdcbdccdabbadadcdacaabdaacdbbcdaccdbcdbdbaaaddddcdadcbcbccacabcaccaadaabbaddcdaddcbbbbbbcaaaccdabbbdbbbdabdbaddacaacdddcccddbdbbbccccccddbaddbbcdaaabaaadbddbdcbdbdbbbbaaddcdbbabccbcdbdaabdacaaadddbbdddaccddbbacbcabaaccbdcbadcacbbccacacbbbdcaadbcbdbbddbbcacbababccccabdadbaadbcdabaadbdcdacbbadadcadcbbcaadccaaaaabaadccacbdadadbadcdcddcbaaddbbccdacbcdaaadcdbadacababdadcdbcbccddbaccbaabbdddabcdcddddacdbabadaadbdccbcaacaabdababbcbcbdbcbbbbdccdadcacbabddcbdbccaacdabccdcbaaccadcdcbdcdccadbdbbdbacbaccdcdbababcbdddabaaadacddcbabbcadcadcbddabbdbccdaaadacaadaaabbadcdacadbcbcbbbcdabddacaadbaaccbaadbdbcdbdddbddaaabaadcdbbddbadccabccbbadaaadcbbabcbddbbccacaacbcccddacabcacbaaabdccdbcbcbbabccdabdbbcabcbacadaadcabaadccabbcbbbcddcbbdaacddbdddabacaacbdadbbdcdcacbdccdcadcbaccacadbaaaaadbabcddbdbaaaabbbddaccaabaacccabcdbdcaadbaddbbcdbbccbdcdddcdbaacbddccaabdbbbaaabbdadaddbbcdcdabdabdaacadbdcdbdabdcccbcdbdadbcdbcddbaacbcdaabdaababdbbdadbbccdbcbdddcbdddabdccdccbbbdaaacccbabbbaddbcbcbaacbddabbabdabbacbabcdcaadcbcdbdcdcbbccbaabbbdddcdbcdbdaabddcaddccbbdcccbddcdccadacdadadbccdbdcadcdbaadcdcddaadcbbbcbdaccbdcacbbcdcaccaddbbdbcddabddcacaacbabcaaadcadabcdcdcadaaddbcdaabdbbbabddaabacbabcbcccdbadbbbadcbbbdddcdbcaaadadabdbbddacaaddbcadddaababbbaccdaadabacbccdbbcdacbdddbbdcbacdbbabcbabacbadabcdbadbcbcabdccabaaadddaccaddcaacccbabddbadbdbacbcbbcacccbbcaabcabdcaaabbddadabdadbbbbdcbccbcddacabdabcbdabcaccacbddccbaadadbaabdaddbaacdccadbccbacadabcabccdcaadacbcadcdbdabbbdcbcdadcdddabadcaccdaacbaaddbbacdbcddcbbdbcccccbbcccabcacdcadcdabacccbdbabcadcdbbdcaacaaabccbcccdcdddddbdcdbaddadbaabbcbdbdaaabdccbbcddddbbcdadcaadbdbdaddadbabdbaabcacadccdacdbbdcdcaddbdddbdcdcdacabbccccabbadbbbcaacabdbbdbaaabdcacaccacddccaacdabaccbccbacddcbbdaaacabdddaccdaccadabcabbadcabaadabcddccddbacccaabdadadaccdaaccddbdadadbccbabbbddbbbbcaddccddbcadcadadcddabddbcdadddcbbdaddadbbdaabcacbddbacdbbbadcabadbdadacbaabadbdbcbabadbbabdadcacddbcaaadabcabddadaacbabcadddcaaabdddcbccccacddbabbddabbaaabcbaabbdbaacbaacadadbadcdaddcdbdbbdbcdccbcdaaabacbbcddbdccdbbcbdcbbbdcbabdaaaaaaccaabacdcaabcdddabaaaabcbcdcbcccbbdcaadbacdcdadadaabacaddadbcddddaadcbbacdcdadbbcbabbbdcdbdbdaacbcabdcdddccdabbadddcacdcdbbadcdbcbcacaabbcaaabcccbcddadaabaccadababaaabcabbcbcddacccbccdccbcbccbbcbacaccddccabbbadaacbbbbcdbbcdddbbbacaccaccbdcaabccacadcabbababcddaaaacccddccccbdabadaacadcdbbdcabbddbadbbbdddaaddbcacccdabdbcadcadcdcbbacdcdacabcadcabbccccabcbadaddcdcccbddaddaabbacbbbcbddabddcabcbbbaaddabcaaaddabdabaabdcdbaabdcbaaaacdbaadcddbbadcbabdbcadbacddadaabccccabaadacadcacdaaccbccbbcbcbdbccabbabbaabccccaccbbadaabcbcbacbdabbbccbbdaddbbddaabbcacaccdaddaadcacddbcbbacdabcdaaddaaaacddccddbdcdccdcbcbccacbacadbbcaabdaaacabacaccacbbadbdcdaddccbcbbbddaddddcdddbcaaabaadcbdccbbdadacdccdbbbddcdadcdbbccdaaddacadcdabccdabaccdabadadddcaacbcbcbbdbccdcabddbddcbbddbabaacdcaaacdaacaadcdbbccacbbbdadcbabdcddacaadbdaadcbabcdcccaaacdabbbcacdbddbadbabbccbcbabbdbaabaaabbcbdabbaabcbbaddabaaddbdcbbabbbdbcabdbbdaccacacdbdcadddbaadacbbbddabccaddddcdddcbaaaaccbbddabcadacbcbdbcddbdaabbbbaccbdbbbccbadaccdacaaccacbbdccdddaccbbbdcbcdbdacddaaaadbacbcbacabdbcacdcbbabbdbbbcbcbdabadcaddcadaadbbaddccddabdcacdcccaaacabbbacabbcaadbadcdaddddcabbbdcdddbbaccbcdadaccabcbccabcccdcadadcbaacacbcbbabcccbbadacadcdabddbcbaacabcbaaababdacdcbabababdabdabdcdacdabbabaacddbdcdcddddbcddcbccdbdcbabaacddcdbdcaaddcadbaccbccaaabbbcaadcbabcaaaddbbccaabacccccbddababdbbababadacbdddcaadadccbcadcdbbdadcdcddddaccabbadcadacddadddcccdcddaaacabbbbdcbaaccccbaabdcdcdbdccbdbaccbdbadbadcbdbcdbdbbccacddbbdbaaababbdddddadaaacdbbacdcadbaccbbddcbddbbcdacaaadbbbdcaaccacaadbcbdaabccdcabbabddbcacdaaddbabccbdccadabcabdcabdbbdabdbbdababacddbbadbcdaccababccaabcddabcbccdacadddbcaaddcbdbddccaddbbbddcacbdbbdbacdcdccbbdccccaadcddddbdadcbaadabdbbaadcadbbbcddcaadbcababccdbadaabacdddaadbccadaacdaabbccdbdccadbacccdccbcdcbabcaadbdbabdababbacdcdcbdaddcbdddcbdcacabddcbcbdbddabbcddbbdbaccbddaccadacdbbcabaccbabdbabbcbcadadbccacadbdabacbaccdddaaccbbcbbbbdabcabcdcacdcabbcbdbdaadbccbbccbdbcbaabaddaaacabaaadcddaaddbdbdaadcdaaddbdadcadacdaaaaddccbdbbdcadbcdccadcbaaadcbdcdbddaaaacbabddadabaccdadabbbccbccdbccaaddcdaaddabcbcaacadcdddaadbbaadbcadaddadcddbcdaccbcaaadbabdadabadcacdabadbbdcdbbbdbcdaacbabdacbdbdddcddaaacdbbabaaccabbddcdbcbcbacdababdacbcddbcbcadccabcdbddcbbbdddbbaadabdbbcdbdcddaadbadddabcbbbabcdaadbbddcdcadbcaddcddbbabbbbbdbdadcdddabdaaaadadacddccdcbbdcdbcdbdadddddbdbbcaccdaddabcbbaacbcadbadabcdcddcaddccbadaaadaadbdbcabbccadbbbdabbddacdaabdbcdddbcaaacdbdddccdcadbcdacaadabdadaccaadbdaccaccbbbcbdcdbdbabbdcbadcccccabcacaaddcabcccdcbddcbccddabbbcadcdaaccbabcdccaabdabcadddbbdaabadbbdabadcbbbcacacbbbaabbacbdddccddbcdddaacaaabccdacbbccadcacdcacbcdbbddadbdbaccaaabcdacbbdcbcadadabacdabaddbcdaabbbabdaaacdcabaddaaacdbaccadcbbababbbcdbdabccdcacacbaccbcaababddccdbdbbacccdbbdcdbcacbaddacaaacbbdcbdbbabbdbbabbddbabccacbbacadabdaacabacdbbdcdabcabccddbddaacbdcabbdccaadbcddcccaacacdbcbccdddcdaddabdbacccccaaddbbabddcdbaacbcbdacbbdbbabadbbbdcbddcbbcbdcdcbdbbbbacdddcbcdddadccbbbadcbbddabacbadcadcacbaccdddabbaaaacabbccccabaadcccccaddccbcaccadcdddddcbccadcbacbbcaaacccacabbdabbcdbdbbddaddbacdadcdddddaabddaaacbadbcbdabbbcbdbabbbcbdacaccccacaabccdaadbcadbbdadbddcaaaabdaccbdbccaaadcdcdbacdbaaacbdbbddaaadacabdacdbaccacbaabdabcabbaaadadaddacabcbcdbbaacbbccdbbaabcdcdcaaabbcdcadacbbcdacdcbabcbacbdcbaadacabbabddbccaacdcdcacbbdcdacaadabdddcbabaadcbcccbcccbdddadabaaabbcdbbcccbcddaaaadbcbbabcbbdddbdccaddcbbadcacbcabbbaccbcdbbdbabbbadcaabcdacbcbabbbdbaacbadcbcdcabdacdcbcdabdcccabccabccbabbcaabdbcaabdcddbbbabdcaccdaaddadcbcbcbbcabbdacaadbadcbcbbaccddadccaacbacbdadbcadabdbcdbacbabbcacaddacbacdadcaddcaadddaddcddacbccccbbadcbcaacaccdacdabdbbdcdacbbabacbddcadbcbccbbbddddbaaacbbadaacccabbabcabacdbcbdbcccaadbbdbdcaacabaccaadddaccabbdaccadacadcaacdcbccccbabdacdaabdccdaccacacddbabcaaccccbdbbdbcbadbdaaaacbaddcabdddbdccbcaccbdbaddcdbbdbcddadabdabbcadacbadacacabcadbcacbadddbdcacdadaaacbdbaabcdbabcdccdadabadbcdbdbccdaabaabcaacbacdaaddadcddbdacdbcabdbbbddddadadaaccbbddabaccacaaabacadcadcbadacaacdbaccababaadaadbdccacbdcddabcbcaacbbbabdcaaaccaadcbbbaaabcbcbcbabadcbbbaccaaabbdaacdadabaacaababadbddabbbdcbdaaccdaadacabbbcddbbcbadcadcdbbdddacadabdcacdaccbacaddbcbaaddbbaddccadbdcbcdabbbacaccbacacddccbbababdcbabddacaddbcdbbdaacaacbaaddcacbbcadddbadbadcaabbadbcaccbbcccdbcaaacdccccccddacacdbbdccbcaaddcbadcdbbdbaccdaddaabccbccbccbcaaaadcbadcdaabaadccdbdbddbdadcdcbbdadcbdacddbbcddabddaaddcabadcdcdabacdcccaddaddcacdbdbcddcddbdbbdaddabacabbccdacadcaaadabbdddccbcabadcabadbdacbdbacacacbddadadddbcbbbaddcdabbbbccccbaaadcbbbbcacadaaaccdccdcaabbbdcbadddadbcdabacacbbddadbcaabbdcbcddbdcabbbdbacbbdaacccbdcddbadcccddccacddaabadbccaaddddaabcacabaaaadabdcacdaaaadcdabcccdbdabbcdcbadadabcaacbbaaccadbbbaaccabbddbdbbbbccabddcdaadbacbbcadcccdcaabcadcabddcadccadabbccbdcddbacbcdccacccdacabddcdbbdbdcccccbbdabcabddcbbcbcdabcacadbcdababdcacabbcadbddcdbddcbabbaacabbacaababdbdccdabcbadbccccaacddbcbaacdabccaacdbcaccaacdddababababcabcaaddbbdacbdbacdbcbcdbdacdacdcbbdcccdcddbcbdabdbcacaadcddbcdbdadabdbacbbbcdaabadbdbbdddcddabbdaabadcddabcabccdbaabdcbabaabaacaaaaddbdbbbbaabaaacdcadccddcddaaadbadaacacdbddcdbbcdacdbaddcbdaddcbcaacccdabbbbbcbbbabadaadbababadcbabbcdaadbdcdcbcccaabcdcbbaaabbaabbbadbcacaccbaacdbbcbbabdabbcdbdddcbdaddddaaccdbcadadcddddcaddcbcbdbdddcbbdaabbadcdcadcdbaadcbcdaddcddacaadbabaabbcddcdccdccababadbadbbdcbbcacdcbaabaacaaacddabacbcdcddbccabdccddcdaddccbcacadbbadbabcdadddcaccacccbcbabcabccadaacbacadbdbdacbcaccabcbbdbbdbdacadbbccdacbcbdbcdcdabbdcdccdcdbabcdabbbabdbaacacddccacdddaaaababbacddbdbbbaccdadccbccaadcbadcaacddbdbcddcdadabbdbaaddbdbaccaaaaddbdacdabdbbacdbbaaaadcdbdacdcbccaabccccdbccbbbadcdababddadddccbcdacbabdbbccbcadcdcaaacadddbdbabbadccdcabaddabdcaadddcbdcddaaaababccaaaadbaddadcadcbbaddddbcadaaacccacbaaddcdbcaddbdbaddccabcccbbbdcabbbccdacddcddcaaccbddaadccbcccaabaababbbacabbabcaacabcddcccadbbddcbdabbbdcddcccbacadabdbcdcaaaaabbdabcdccbadcbbacacdcccabbbadbadacacdccdabbccadaacddbcbbdbddddabcbaadbdcaadcdddbbcaccbcbbacdbdacdbbbbdacbcbdaaddcadacbddddaadbadbbacbbcccbaccbaacbbabccbabbcbdbbcbbabdbaddababacaacbdbacaacdbdbccaacacbdcababaccdbabadcbccdcdaddcdbadbdabbdbacddacdbcdbccbdcacbcaabdababadadbccccccddaddbccccaabbadddbcdcddbdabddbdbabbccbdcbddbbabaabdacbbadddadbbbdbcbabcbdddadbcadbcdcbacdbbbccbbcddcbddbcdcdaadbbcbcbadcabdddbcabdacbbadbcacbdbddacaaaabbbbbcdddbccdbdcaaabcbbcdbcacacaadddcbdaadcccdcdaacdccdcdabadccaaabacaccdddbcaadacdbccddabcaacdcaadbcababcbddbacbbcddcacacccdadbdcbabcaadaaaddacadcbdcbaabdddcbddadcbcaaaabbddbccccbbbdaabaabdbaccbabbbdacdbcadaddddbcbbbccacdbabbdadbbddddcdadddcbdaddcdaccbcbbddcbbcddabcdcdccdbbdccddbbdccbdcbaddaacbdbbbbadcdbcdabcacdcabdaabdbacbcaccaccccacdbcbaaadbadbabcbbddbdaddaadcabbbbdadddbbabdbbadadaacaddccadbcacabcaaaadadccaaaabaccabadcbdcabadbacbdacbcdbacdabccaccbdaaddadacdcbbbbcbcababbabaddacbdcbaddbcddccaaaabccccaaabdaacacbdccbcdbbbaadbaccbbdadbdbddabaabacdabacabacaabbbbcabbaaaaaddcccadcbddcbabdaaacdabaadbadcbbbacbdcccdcccbbdddbcbcaabddaabadbbcbcaaadcabbcddbcbcbdcdbdacaccbcdcbdbdabacdccabdaccbccdbaadccbdadbcccbbacaccdaaaaabbdaddbccdcccaccbccccdbaccccbddbddadabaabadcadadaddcbbddaddaccacaddacbadbddcbdbabcddabddbaaadcdbbaddddabdaabdddabbcbbdaddbabaadaaadcbaaddbadccdadbcacbadabddddddcddadadccddcbabbdaadcabcdbdaddbbdadaddabdacaddcaadaaadadbcaabcadbcbddbbbcccbbdcdcbabbccbdbbbcdcddcbabccaaddbcbccdbcabcbbcbddcbdbacddbcadbbdcbdabacdccdcdbcbdbccccaabdbdcbbcbbcdcbcadabbbcbabcdddccaddddcabdccaacacccabcdabbcbcbcabcaadcadadcdcabbcacadacdcccdcadcaacdaaaccbadcaaacdaabbdcdcccdccaabddacbbdbcbbabbbcaabbddabadabacabcaacccadabdadcbcdcddbacccdccbdddcdbdbacddbaadaddcabcbdcabccabbaabdcaacbcddcadcbbcdaadbaadbaaaaabdcacbacdadcaddbcddcccdaddcdbbccccbabddadcdcbabccaddcdcbddccdaabbdbcadadbdadccabcdddcbbaabacabddddabbcdcbbcbbbddbdabaddacaaacbcbcaaaccccbbcdddbdddcccccabdcdcaaddbbdacbcdabacbbddcccaccddbbdbcdbabcacdbacbbdbacbbdbcbadacdbacbbddbcbaaddbabaddbcccbaacdaacaccbbacbdadaaaabbdacaacdbacabaaaddcaadddbbbcacbadbacbdccacddabddadacbaccbadcdabbbbbbdbbdaabdbbcacacaacbabbacacbccaddacbcadcaddbbccaabddaccbddbacabcddaccccaabaadddcdccdacdbaabacccccddabddbbcdccdcabbcbacddabdbcbbbdacdcdabdcdcaadbccbbcaabbbcccccdcdaaccbcdbcbbdbabdaaaaaadbbbddacdbadccdadcadaacdccdacccbddbbaabcacbadbbaaacacdbbddcabbdadccbdbdbbaccdbbcadcddcccddcbcadaccdbddddabdbaabcbabaabddccdabaaabbacdbbdabadacccdaddaabdabdabdcbdbabdcddadbbdcbcdcddcadcbbadaadbcabbdaacccdaccbaabdbcdcdaccbbacacbdabbbbaddbbdccbdcacdcdabacccadabaddbabaacdcabaadcacbadaaccbcbccdcabbdcbacaaccabdddbababbdaccddaaaaabddbbccddcccaabbcdbdadcdbcdcdabcbcacbdabacabcababbdcdbdaccdccbbbcbbccbbaadbcddbacdbcaabdaacdaaadcbccddcdbddadbdabbcabdadcbacbdddccabdabaddacccacccaaaabcbbbaacdabddbbcdbbabdacbbcaadaddaabbccddbbacdddbddaabaadcbcbadcdbbccbcbbdbdabbcaadaccbbcdcbdccdacadcbcdbdbcbdcdcbbbbadaaadadaabdbcdcaaddaadbdbcccabdbcacddcdbacabbaddcddaaccddbdcbcbadbcadcadcbaaddabaabcaaaacaacdddcddbbdbdaaabbccdabcbadadadccdbbcbaddaaccdabaadababcacaddbaacdbcabbacdbbcdbcddacaababacccbdcdadccdbacbabcdabddbababaacbaadabcabaabcdcaadacadbcabdbcbbacdddcdabbaddadcddadcaccaaddbbcbdadabbcddabadadcbccbbdddbcdbcbadcdcbabcbcbcdbbabaacabcbcdbbaadaaadcdddcdcaaddabdcbcabccaddddbbcbcdacabcdaaadacabcbbccabcccccadabddacddcdbdbaacdbaaaaadcbbccbdcccbbadaaacbcaccbabaacccccabddaccccccaccddbdcacbcdddaacdaaacacbabdccbcadadaabbbdbaacabcddccddbbcbbdbbbcbccbdbabaddaaddabdacbbbcabbdaaccbacdbdbdcbacbadbbdbbdbbbaadaadccacdbbdddbbbbacbaccbcdbadabadbbdcccddbbacdccbddaabacbabdaaccabadbadbcabbcbdabaacbddbabcacbcaabdbaccccbddbaaccddbacabdbbdcdccbabdaabbaaacacbbcaabddbbacbddbdccdbcadbabbbbaaadadbcaaaabbcabddddbddbdabdccbaaaaadabaacadcbbcddaddbbbbaacddddbbbbabddccadcdaddaabdabadaaaccaaccacbaddcaaadcbadddbcccacbabcabccbabadbabbadbacccdddbbcadbaaccaababcdacaccbaabacbbbaacacabbcbacdaddaccbcdbdcbdabacbabaddacbbbcdadbcdbacdbcaadccaccaadabcbbdabccdbbabbdcdbdcabaacdacdbcbdbddcadddbbcdcaacdacacabbddddddaabddbcadbcaaadaabadacaabbbbaabbcdbdbcdbdbcdabbabcddacdacbdddbcbaabbdddacdadcababadcdbaddccddcadbdaacabccdcadcbaddaadcddbbbaddbdccdbbcddbabdabdaadcdabcacddacdaccbdadababcaadbbdccbdcddcabbaccbbdbdbcacbddacbdabddaadbbddcacbbbddbacaaabbdaabcbdbbbdaddbdaaadbcbbcacaddbaddddddbcdcadcdacbbdcdddaadbdacabadadcdbbcbdbcdbcdddddcbdbbabdbaabbcbdbadacddcaccbdbbaaabacdccbcadaaabbccdbaccbbabccddcadbcbdcbcccadccbccdadbcacbaabaaaacbabbbdadcdcbacbbdccaccddacccabaddaadbdcddcaddcbdbbbbbdcddaabbaadbaaadbcbdbcacccadbcabcabcdacacccdbcacbabbdccbcaacbbabbddbdddbcddaababdbcaabbabbddbdacbcbbbbadcbdbacaadadbcbccdcaadcbdbddcdcbadccdadbbcbccdabdbaabacabcbcdacabacdbdaddbcdcbbadbaddcdcdbacdbdcbbbdacbdaddababbabbccbcbcbbbcdcdcccaababcacbbccbbdcaadaddbdaccdbacccadaccabbdccdabbcbdccaddccdbbcdbacabcdcbdcbabbdcdbdbaaaaadbdcbadbbdabdaabddcaccbbdcaabdacbabacacbdbcbbadcadbabbbabdaaadaaabcaabcacdbadbcbcbccaadaaacdbbdcdbaaddbcbcabbbcaddcaccbacaacdaaddacbbdddbdadbdbcbddbaabadcddcccaaacbcdcdadaadbabadbadaabbcdacabddbbadcacbaaaadcbbadaababaaabacbaddbabbbbbcbdbdccdaadbacccabadbcbdacddbcacbcddcdcaacdbdbcddbbaacbcdacdadaccdcbaabbabcbcdbabccaccaabdacabbcadbbcabdaaccccadacddbadadabcaacaacdcddabddbaabbdcccdaabdbbddbbaaadaaaddbbdbbbbbabcdaacdccadadcdabcacddbaabbcabbccaacadbadcaccaccabcaacadaddbbdcbaaaababdddbcaaccdabcdcacadbcdbccbadcddccccbcdcaaacdcacdbdddcddcbadbadddddacddbabacccbacccbdddbbbcaaccaabcddaacabcdbdbbbdcbbddbaadbbbcadccdcbddaadadcbacbcbbdcccaddbaabcdcbbbcbcaacadbddacaabbbcabccddcdbdccdacacabbadabddadcbdcacbcacabcadcddadcdbbcbcdbbcdbdbbaccdcabdbadbcdbcdacadcccccbcadbacbabcabcacabdbadbccbdccaacdbbccdbdbcbcdabdbcddcadadddcaaacaccbbcdcaaacbdcbcacbbaacbcabbdbcbdbddbcbacbbaccdbbabdddcdbaddacabbdcababcdbadabbcdccdbcacbaadbabcadcddbdcadbcdcbbbdcdbbddddcabdcdbabaabdadbbacccddbdbdddddcbdbaadbcbabbbcaaccccddabcabbabcdadccccdaaccabdbddabcccdcdccadbccbaccbbcddadadcddddaaaccdcadcbdbcddbadcadacaaaadbdbcbdbacbbbacbadbabccbcabcabdbaddccdddddacbccaabcbbacaacdbdaddabadbccbacbdcbaadbbcddaabbadaabdaaacbaabddbdddddbbdacdcaadbbdccbbcadbacabcdbcbdabbdadccaadcacaddcadaabbbbdbcccbabcaadaaddbcbabdcccdabadaabaaadbbabdcaadabdcccbbdcddbcadccbbcbaaadcdadadbcdcddaadaacdacccccbadbbdbbaadccdbadacabaccbadaaadcbcddaaabdacdaccdcadaaaddbadcadaabdadacabcabbbadbcccabbaaddacdbddbcddbacdabcccbabadcdaabcdaacbbbabcbbaaddabbbacbaacccadbacaacaacabbbabbdcacdcbadbbaabddbdacbadadccadcdbcccccccbdcacdaadbcbaadbbcacbcdbcbacbacdadbdadccacaacccbadabdccccbcadcccaadcbccddcadcbacbddbacaaaccdaacccaddacdcbadbcdbadcbbaddaabbabcdbcdbacbbbcddadbabcbcbddcabdadbbdaadaacadabbdddadcddaadacdcdcbaccdbbdcdccacbcbacabbdababbcccaaccbacbdabbcccdbcccbcabbabcbabbcbdcadadababdadcccddadabdabbbaaaaabdbcdabbadbbbbbdbcacbdddbcdcaacdabacccdcabcbdcddcaacdcdcacaccddbbbcccabccbaccdcbcacbabccdccbacaadbcbadcadadaacacdbdcbcbadccadabcadcbadadabbcacdaabcdcdbcadcccaabdbbccccbdadbaacabbdbbdaaadadbdddbdacdcbdbabcbbcdcdacadcdcbbbbcaddcccddcdbacbbccbcdbdbbbbccbbdcaaaaadaadbddacccdcdacabadbdbcdcdbdbbbcbacabdcdbaccbbabcbaadacdcdaadaaddbcaaccadddcaabdbccbdbcaddbbccdacbdcddadbacbcccadcbbbbdbbcabcaaddadbcaaccacbbadabcbdcadadbbadadabcdcbaaaabacccccaabddbbcdbacadbadaababbacabbcdbbbaabbbdadaddbabacacdddacadbcdacdbcbbbcadcbcabacbcbddcaaacbacbbdccbadcaaccddbbdaccbadcbccdcaaddacdacbcbdadbbabcdcccddacbacdbabaacbcbcbcdcbaabdacbacdcabdbbdacadbacadccabcababaadccadcbdbddcaaaabccaddcbbcccbcdadbbbdacdbbcacbbaaaddacbadbddbacbbddbddaddbdbcbbabbcabccadcadbcddbaaddbdacadbbcbbcaddadccddddcabacdcacbddadddacbadcbbccbabbbcbcdadaacccdbaadccbbaaadcbbddbdadbcdcbbabdbdbdaaccccdcbabbcbaacaddabdbccdcaccddcbbbababcabcdbcbbcdcddcdbaddacbdcaddadddcdbbcadccdddbcdabbcacdbcabdbadadacaabbdaacdcdbcbaccadacbbadbbcccbdcdbbdbcacadacadadbadcdadcdbdaccdbccbccdbaaaabcbbbadbaaaabbddccccaadcbbddacbcccddcbbcccacadacbabacdaabcdbbcacbaabacbbabdbddbabcadbddbdcdcdabaadbddaaccbaacbdddabadbbcddcdcdaaadacabcbdccbbcabdacbcdcbacbdddbdcbadbcdbaadcdcacddcaddacddcbcbdddbcdacadcacabcadccaaacdcdddcaadaddcdcacdddbbcaddaacaccdaaaacabcabacdaacacbadcbddabcdbddabdddabccdcbbbadcbdbdabddabcddbaddcbaadaacbdcdccacabbaaaadacaabacbdbbdcbdbcaaaaacacaccadacbadadacdaabbaaacbbaaaadccadddcbaadddbcababdcaabccdbbdaacadbdcaccabdacabadbcaddadaaddabdaaddcdcbacaaadbccccccabbaddaaadaabdddccdbcbccababaadbdcabccadcbcddacdcacccbacbbcaacdadaccddcdaaadacdabdcbaabdcaaababaacaaaaabddcaadbdcacccbaaacdcaacabdbdabaacccacccabddadddcddbbdadabacabcbcddbacddaadbcdbabadcbcadccccdbbbbbcaabbdbcaddcccbadcbcdaccacbdbbddcdacbcdbbbbccbbabacabcbbacdbdccbbbddcccdaabcbcdbcdbcbdabcaadcdcbdbdcabbdcaaddcadabacacdbdacddbcdbbaccbbaaabadbabcbcacaccbbcabacbadddbcadabcadbbacdbacbadbcbdabdadccaadbbbcadbcddabcbbdbdbcbccacdcbadbbaacabacadbdbaacdabcbacabaabbcbdaacdcbbadbdcdaaaabadadadcccbcdbaadddbaabbbacadbccbabdccccdacbadcabbddcabcbaaacddcabbcbadddcadcdbcdddbbbdadcdddbbaacbadaabdccaabdaadccdbaddcacadbbbacadccabcddadbbaabbbacdabccaccccbaddabaacbabdacdbbbdbbacbadcabdcbaaacccbcdbbcabbabaaabccdaaababbacbaaccbdbbccbadaadacdaabaccbbbbcdcdcdabdabbadaabdcbcbccdcaddcacbddbabdaacccaaabcaabacbcbbdcdddddaaccccdadabdcccdcbbcbcbbbadbbabdabbcaccdbacbcbbccaacbdccbabcaacdaabbdacacdbcbccdadbcbcdbcdddcdccadbbcdccbadaccaaadabaadbbdcbcbbdccccbdadcbcdadbbdcdbacbdbabaddbdcabbaccdabcdddbccaabbbdbddbbaaacbaaabdaddbacaddbaadcdbdcbcbbcbdbababdcdacbadbdccdcaacbaaabddadcadddaaccddcdcccbcdaacdbacdbdcccabcadbcbcdbadcdbbaadadccbcbaadbddbbcbbdbcbbdbadabacdbdadabaaaabaccccbbbddabcbbadcaddcdadadadcbdbdaabacbbddccbcdcdcddbadacbbdddcdabbccaabcbabbbddbbaacaadbbbdbaacdcbcbdbdabacbcccdddcdcacadadbcdabcdcadcdcbcadbdcabbbdbcabbdcabdadcdcbbadacbadacdaabbdbcddcadcdacbacbacddbbacdabdbdbacaddcadbdaddbddbcbcbcdbabcadcacaabdbbbddbadcdcaddbcababaacadacaabacbadcdaaacbccdababdaccdbcdaabbbbabbbcdadddabbabddadbcdccbbdcddadddddbbabdbbacdabdaaadcdbcddacbaaaadcabdddcdbccdddcaacaadbbdaaaabaaccadaaabdddbdbaadabccaaacbbdbdbacabccbcbbabbcbcadbcdaabaacacbabcbcdccbdbdacabababddbdbcbdadcdabddcbccddcbabcdddabdbadcddcbacdbacabdcdabadbdcdbcddcacbaabadcbbddddddacddcbdddababbdbcbbababbddbadcbccabacdddabbdacdbdbcbdcacbbbbdbdacaaabbdbccaacdddaacdddaabbccdcbaaaaadcbabdabbaddadccdcadadbaccdbabaaaaacddddccaadaabacccdddbadacdbadddddddcbbdcaaabbaccbbbbabbbaaadcccacaabcaabdbdcbbbcddbdadbdbdbacbbdadcdaaabdbbaabbbdbabbdbadccbcaddbdabbbdbddaabddaaabbcaacdcdbdddaacccccbbdbccbddcbbdbaddbabcaadbadcdcabcbcabddcaacacaabadababaaaaabaccbbacababdcbddcbcabbcbddcacadbabaabccaacbccdbacacdcaccdcaadddcccbbbdcaddadbabdcdbcbbacdbcbccbddcdcabbacbdabcbccbacacccbbdabdcbcbdaaacaabbabaabddaaacddbbcadbbdaaacadabbbcbbbcccdaacdaccdacdaadccdddaadbbbbbcbcdddcabaacbdddbacddcbbabbbdcabdaabbcbbdbdadcbdddcbdbdabccacccabacccaccabdbacbdbddaadacdccabbabbabacbcccccdaacccacaaaaadabdaaacdbbacddbbabcabbbacabbbcdbdcdbbbdaccdcddacaacddddbccacbbadbdaabdbadaaaaababdbbdabdddcbdabacccdaaabccddbdddbbcdbbbadbbdbbdddcadcbdbbcacdcaddbabcbddbaadbcdabcaaaaacbaccdddccddbcabcddcdbcddacddcbbdbdbcbabaabcbacbddddcccaddcbbadbbcbccccbbabbbbcbddabbbbcbcaccacddbaccdadcaaccaababbcdaadbaabcdbdccadbdcaacbdccbccdccddcabdadcbaabcbacbdbcbaddabdcadcabdccdbbddbdcacaddadacdbaddbccbbcabcacbaacaacbbbbdacbbbcddddcacaabbbbacacbbcbcddaaabbccbadbddadcdacddbcbbdacddababbbdddccaaaadcbdadccbdbcdabacccbaabbbbbddcdcccccadadbccacdbabcabaaadccacacadcddcabadbabbbacbbdbcabbccbcbabdadcaaaabdcdccbbbbdcadbddadbcaabcbcdcdadbbbbbcbabdbcbadabcddddaddaccbadacbbdbccbccdbbadbdbbbdadadbcadcaabbddbadbbaadaacbddbdbcdbbcaabbdcaccbadaadbbbcddabbbacaddabbcbbbcbcadbdccdbbdadcaccadddcaaddbdaabcbabbdddcacacdaababaacdcaaccdaaaabcbcbcdbacadadcabdbaabdabaaddbacbdcacddbacacdddbbdabaacbcbbacaabcadcadaddccdcbbccbdacaabdccdacaccbcaddbaaddbddbddcadaacccdbadcacdcaacbdccaaaccaaaccccddcbbdabddbbcbabacddadacdcddcccddddddccbbdadbcadaaaabcbbbcdcbacdbcabccdbbddacadbbadbcdcbbacdbdbcaddabbbbdcacbbdcadbdccaaabcabbdcaddcbbacccbacbabdbdccbbcbdcddcbabbdddacdacdccdcbbcbdcdbcbcacaddbcbadbcbddcbddadadcdddbddddaadacacdbcaccccabcdadabcbcbaabdcbbcdabcbaaccbdbcbccdcdccdcdbdaabbcadbddcadbabbaddcbbcaacbbcbbabacaadbabbaacacbbbccabadadbbddbbbbbbaddaddbabcaaabdacabdadbbcbcbdabbcdbbcdbbbdddcddcddcaabadbacdcabdcabaccccccbadbbadcbbdabaacbdadacbcdcabaabadaccbbcdcdadcacdadccdbddaabbacbbbdbbbdaabdbddcabbbdddacaabacbdbaadddcdcddcdbdcddadbccbbabaddacacaaaaabccbbabcdcabaababdbaabcabcbbccdcbdaabadbcdbcaaddbbacabddaccdacccbddddadbdbaaadcccdbccbbccacdbcaadacddbbcabcabdcbddccdbcaccbadadbacbdbdcdcbdbdaccaabbcaaaadbbdcbbcbbcaacaccaaccadddcaddbddbcbdbddcabdbaadaabcaccddcaaacbdcababadddacacbddbdbbbdadbababccbcddaaadbcabcbabbdbdcddacaccdbcdbaabddbcadadccbcadbbcbdccddbdcababbbbacbdabbaadbbdccccdbdcdbcbbdbccabcccbdcbaddcbbbacaaccabdbadaadbdcbbdcbdcabcadbcbdbadabdbacdacdaaccdabcdbbaadacbbaccbbbbccbacbbddacdabbbaabbbcaabaadcdcacddcabbadbcddbabbdaacadbdbdaadccaacdcccbdaabadaddacdaacddacddbdbbaddacbcbaddbaabdcddbbcdbabbabcaababcdccbaccbcaabbacaaacdcacbdbaaabcbaabacbddcdacdcbaddcbaabbbcacaacdacdbccaddbcdbdbdaccbdcbbbcbbdbddabdabcaacdacdcdcbcbaddaddabdaaccdadcbaccacdcacbcabababaadcddcdbaaacabddbdabcbbccdcbdaaccbcacdabcbaadcabcbdcadacdabbbdabcbbdbaababcaaabacccbcbdadaabddbbcaaacdddbdbbaadccccccaacacabbcacbbddcbbbcacacccaaadbababbccbdbaabcdddaccdabcaddbbbddcaccaddaddcdbbdcbccabbbcdbdbacaadacbdadadbbdbaaccaadcdddacdadcdbaabbcddcdacaaddcdbdcdcbdcacbaccbbbbbabacacacaaaccbbbadbaaacabbadbcbdbddadbdbbcddbadaccaccacdbaacbcdaadddcaddacdcaaddbabbbddadcacbacbbdcadcbaabdccbdacbcddbaaddddabccdabcbdacbadbdaabcdabddaccaadccddcadcaaabbbaabbacaacdaddcbcddadaaacacdbbcdadbbaababdbbbccabbabbccaddcbdacbbcdbdaacabcccdacdacbbbcbcbaccdcbaabbbbbaabdaadabadccabaaaddaadccabdcabcaaccbdcbbbcbddccadbababcdaabbddaddbaadcbccbcaaaadcacccbbacbbabdbcadcbddcdcccdbdadccccdbbbdaaacaabadabbadddadadcdcdadaabdbcbadcbbbdbacacdaabcbddcbbacddbaacdadddcacdaadcbccbcaaccabcbddbccbaacdcbdbdaaddacacbbdaaacbcccbaadcbabbbadbadacaaadbcbdbbdccbcaadaadccacaabbdbcbdcacacabcdbdadaddadcbaccbcdadacadcaacaddccddcaabbbabcbcbbcddcbaadbacdbbabbabbcdacbaccccadddabdcbaaadbdbcbddadcdaddbdccbdcdbacbbabbbaccabcabbaadacbdddcdacdccaadcbcdcccccddaccbbcddcbdcadcadadcacbdbaccadbaabbaccdaccdadaacbdcaaaadbcacccdcbcccccaccdbbaabbcbcdabaabbacababaadbabdbbccadbcccbcaaabdaaadbbbbcddcddcbdacdaababbbaabacddbadbcbddcbbaacabdbaababddabbaadacdadcababdabdccccbabadaaddabdabccbbcabacddababddacbadadabbcdbdaaabacacaaaabccbbcdaccbbdaadcaaadabcdbdbbaacacccbacbbbdaacddcbbbdccdadbccaabccdcbccbaadbbbadcaaadcbcabacdaccccacddbbdbcacbdbbaadaabcaddabdbdacbdaddcaddcdacaaaabdccdbcdacbabbaddbbccbddddbdbdbbcddbbcacbbabaccdcabdbadadacdbcabadbdbdbbbcacbcdbbdbaabdbcdbbcaccccbcdbbabddcdbcdadcdccbcdbdbddcdbababacdabaacbababcaccbbaaadcbccbccddbbdbdbcbacccbcbabbbcadaddcbabcadbdcbbaadcadddcdbcccbaddcbbabcbcacccdadbdbadbabdbcdbbcdcaacdbcabaccdcdbdaccdcddacbdbbaddddbadbdadbdaabadaccbddcbccdcdacababbdcdaacdccacabbbaccacaaacccdacddddcbbbccabababdbbdccbcbadbadbcbbcadcdddccbdccbacdcbcdbabbdcccdcdddcacbdbcddcdcdcddbbbbaabaacbadcdbbacbbbcddbdbcbbdaccdacccabcaadaccadddacacabcaddccabbcbccdcadbccbaddcbddccaabcbdacdabaababaadddcdbcbadaaccdcdcbaadbbddabbcaccbccbcdbcbabdacdbbcdbabbbacbbaccdadaddcbcdacbdabcacbbbdbbccbbdbbcccccacbbaaabdbabdcdddadbcabddacddbbbaadbbabacdadcdaabbbbcdcddcddaaaadcadbcdbaadabcbdcdcadbbabccabaaabcdcacbcccddcbacbcdbccaaccbdcaacbbbaabbabadccabadbcdabcaaabccdbddbacbdcabdcdaddacbbdbaaccccabccabccdcbadaddcccdcbacdbccdcaabcbacbdaacddbdccacdbcdacbacbabdacdbcdbcacadacbdcabbbaabdbacbadccaabacacccbdabbdbaacabcdccdaddaabbbdaaaccddcdcccbbcabdccaddaddacbcbcccdbdaacaabdaacbadcdcdbddcbcadcbcacdaddcbddcbbbddaccbddbbdbbaacccbbbacbbdabbaccacbadbbdadbbabbcdcbbaaaaccaabddabbbccadaabcadbcadaaddacccaadcbcdacddabbcddcbcaaadadcbbbaaddacdbcdaabacdbbbabdccabdbcbdbbcbcbcdbaaabcaaaadcbdbdbadbdddcaacbdbddcbdbbaabdbbdcaadbabddcacdbaabbcacbbbbcbbbaabaacabdcadbbcdbbacddaadbbbdacdddddcacbcdadbaadaabcbcabdabacbcdcddadbacadacdabacabcaaabdbabbadddadddbaabdbabccabbdaaadbdcdbbdbbabbdacbccbcaccacbdadcbcccdddcabcadacabcacbbdcacddbbbaacbdcaabdadcdabbcbabdadacddbadcbabddddbddadacbaacadcdbdddbbbdbbbdaaaccacaacdcbdbddbddbbcccddadcdcbdddabbcbbdcccccbdabbccaccdaaccddbddcbbdbcdaadbbcddbcbbccabcdccaaacccdddabdaabcbadaaaccabababacddcbbaccbbbadcadcdaaadbcaaadbcadadcadddbacbbdbdcddddcadbabbdcadbcddbcdbdbbdaccacdbbacbdadbacdaaabacbbabababdababaacddcdaadbbbdcbbcddbcccbbbbcccdddaabbdbdcdbaddcbbcbaddcbadabadadbccbabbcbcacdaacddabcdbdccadcbbaddcbaccbccdaadcdbbcddbabbdbaddadbaaabcdbbaadbbbbcdcdaccabdbcdaccbbcacaaaaddabcabcdcbabdabaaabbdccaabbcadbcbdbaddcdccbdcadacababaaabdddcacadadbabbdbdabbbacadabdaadbccaacdcbcdcbabdbadabdaaccbbddaacdcccccdbbcbaacdcacbaccbdadabcbbaaaabddacbbcdaadaddbdbbdadbbcdcbcbabbbccdcaccacacadbcbccbadabdacadbabbcbdabaaaabddaaaabcacaaccaabcccaacccaacdbccddcdcdbaaddcadaaddcddbdcdabcbaacdacacdabdcdbacdcdbdbcdcdbbdbccdaddbaaddcabbbcdddbaadbcacbdbddbaacdcdbbdddadbbcaacbbddaccbabadccadbbcbcbbcdaddcbcccabbccddbaaaaaddddabdadaabacacabbbbbaadddadbbbbddadaaabccdcbaabdaadbbbcbcbbdabdbdbdaadddcbbcddddaaccdcccaabbddabcccdacabcadaccbbcadadacbabddcbbaddbcdababbdadccbdacadbccbbbcdbabcccacaddbcbcbcdcacddccccadcbccacababdadcdacddbbbdaddcdccabbabccabdbaaadaadbcacaddccbdbddcaadabcabbacdcadbcaaaccaaadbbdddcbbdabccaacdaaaadbdddadacdccaacbdcdbcaabbbcddbaadaacdcdbbababbcdcccbdabdcbbcbadcbdcdbbbaaaadabadbabdbcbdbabacaadcdabcbcbddbddacbbaccbcaadcabdbdcbbbbdadcadaccdadaaaddcdbbdbcccabbacaadabaacdcbdcaacbdbcabbbcbccccdbcccbaaadcbcbcabbbdbcccccaacddddbccbbaaccadcccacaddbaaaccadbddababdbbdccccbaddbdcaacbadbcdccabdcacacdabcaaaabdcbdbcbdcabdcccbcbdbdacdadaabcabbdabbdcdccacbcdbaccdddddbbcdbccbacbbacadaccccbdbcdbadcacbabbcbbdbcbdacbdcbbcddbbbcdcccddbbaacbdddbdacddcbdbccddcbccdacddaaaacbccabacddcdcacddabbcbcaaddcaabccccdccacbdadcbaaaaacccababdcbcbadccbdaaaabacaabaacbbbddbdcbacdccbcadbbdadcdcdcbdabbabbddcbcdcaddcacbbbdddaadcdbccabcacddbaaccababbabdaacacbbdbdbaccdcbccddbdacbbacbadadcddbbbdadddbbbcccdbbcbcbdbccbdbccabbbdddbcdbbaaaadabbdcabcabbaababadccdaaabbbcbdbcdcbdcbdacdaadacacdbaccdaaaaabbbaadcaabbcbacbddbdbbabdccbdadacdbacdbbbbbdcddaabbacdccccbdababaccdbbbcdabcdcccbcbbadadacadddabdddcaccccbcbbccadaaddaccbcaacdccdcdbcdaaddbdaadaaaabdcdaccdcbdbcbbadacbccdbcddcaccdcccccccdcadabacbcdbaacaacadacbcabcadadbcbbbccabdcdcaddbdcbaaccabaddbacbdbbbbcaaaadcdcaacdaabbbadadccadddbdbcabbabcacadddddabdadbbbbbccacccaccbdddbddcbcaaddcbccddddbbabacdcdbabcbbacccddaadddcbaccadbbccaabdccbbabcbbaacbbdcbdaaadddccabdbacbdaadddaddbdabbdcccbddabddcddcdbcddaabcdadaddbbbdbbdcaabbccbdcbcddacbcbcdccbbabcdaaabdccbdaabbbbbcccbbcdcadabccadabaadcdddacdcbabcacdbcadadbbaaddcdcaccbbadbcbacbcbbcacadaaccdababacabdadacbbbadbadcdbbcaabadbbdcdaaacccabaddbcdbdbabdbbbcacabdcbbcddacccacbcbaabaabbaacbadbadccaddacbadccdcbdaacbaaccbbaaadbcacbcccddcdaadbdaaccadcbdcaddbacccbabbcacdcadabdcddddcaddccadaadabdcaaababdcaacddcdcccbccdacbcdaccadbbdbdbcdbdcbbccdcaadcabcccccabbbbadbbabbacadaaccdcddaccdadbacdbbbaacdccddbdcdbddaccbcaccdbbcddbbbdbbabcccbbbabdbcbbbdabdcdcbdaadabcaccaaaccacababbccabcaaadcdcdaabcacddbdbaddbaabbbacbdcddbbbabbccbccdbabdcddddaaabbbbdbccddbdadcbbbadbacbdacbbdcdbdcacbcaccbacccccbddadbcaabcabdcddbbaddbbcbbdbbbdabbacddcbcbdbcaccdcbaabdcaaddddabbdaabdbcadadacddbbcbcbbdaccbbccdabdbbddbccaaaaacbcadcddcdccbacacaacdaadabbdbcacdbdcababaabcbaaadaaccdbbcbadbcdbccaacdbdcddacdaaaadbbadcddabcddbdccacdcddcbcaaaabbdcbbacbaaaccbdadacbbcbcbdcdbbbdbcbcbadcbcabbbddaddabccabddcdbdddbadaccdbbdbdcbcbbbadadadbbcabcbbcdabacabbbbbbbbadbbacbddddbadaaaabbcadddcabaccddccbacabbadaaadcacbbbbbcbbbbbaacdcbbbaaddcabaabcdacaccadbabdbabdadadbcacaaacbadbbaccdaabccaadadbdbdbdaabcaadcaadacbbdccaccdcabdaadbbdbcdbbbdbbbbdbaaaaaaacccabcadacddadadbbcabbdcaabddbcbddcbcddcaaacdddadacadacbcdbddcbdcbddbaaaccbcbbdbbbddcccadbaddbbbbabcabdabaccccbaaddbcacacbccadabccbccdaabbbdaaabdbaabdadcacbccbaaabadabbdbdbcacbbcaabddbccdacabcbddcbbbbabccdadcdadadbdbcacabdacdddddaaddbbbccbccbadacccaaacccaadabccbbdddbbdcacccabdabbacddaccdcabcccabdaadacbcbbcdbddaaddbcbcbbbabcdcbaaddcadcbccdabbddcabaabbcadcadaaccddabadadcdcdddadcadbbaacdcdcacaadddabcacaaaccbadcacbaadbcbcacdbcadcbdccabcbaaabdacdbbabababbbadaddbdabaccdaadddddcadddbcadccadadaabccccbbdacbccabbcbaccbcdbbdddaadcabcbdddbbcabaacbadbaddcdcbcdbcdcbcccbcdcddadaabbbbacddacbcadadbdaacbaabacccacdcbcdcaabcbacdacbdbaaaadcbddbcadcacddababbcadbcdddbadabcdbaaaaacbbddcacdaababbdadabddabcbbccabddaddbcbbabadacbccbbcacbcdaadddcbbcdadabdcccdcacaaaadbddacabbadaabcbddcdaaabbcaddabccdbabcdbbdaaddddcdbbdcdbbcccacdbbcdbabaadaaabccaabcdbcaadccdbbdcbdabcccddbdddcbcabbdddadccbbdcadcbcadadabddbbdbdddbccccdcacbadababcddbabdbacababcbccbadddacddccbbbcbcbcbcaacbbcdcadbadccbdcabccaaaadbdddbaacbcaddccbabdbcadbdcadaadbcbaadcaacdbadcbacbdbcdcbabccacbabcdbbdcacdbacbddcccdbadbaccabacbadcdbddddcadbaddabbdccdbdacddcabbcadccbbbcdccbdbbbccccbbbcbcbacdbbccacadcbcacacbcbaaadcadbccbbcdadbbdaddabbbcbdddddaacbcbcabdcadadccaacabbdbabcdaacabdcbccabdddaaccbcabacddacbabcaaabbccdababdbbddaccccdbdadcacbdbbcbcbacadaaddcdaaacbcbacbcdcddbbaddcddaadbccbddbddbbdddaabddacdacbcdaabbaacdccabcadacdcdcacabdadccbbacbcbadcbddbbacbcaadbadabcdbadaabcdbdcaabbbabcabbaadbdaaabaabadacdadddadbddabccdddaccbcddcdaaadcbcccddcddbcaadaaaccacababbccacdbdcddcdbdadacbcccddabbdbaddddacccabdbabbcdccdcabccbbaccddacdcddbcababcdbaabbcdabdcddadaabdcadadcadcdbdbacbccadabdbbbbbaadbadcdddababdccdaacaadadbbdcaabdbcdbdbdccdddadbdaccdbdcdaccdbcadccacabadbbbddbcbcbdcdcbdcaaadaacbcdadcacabdbbbdabdcbcdbcdcccddddaadbdbdbaacbdbdbbdddbdabdcacbbbacabbdbbcbdbaadadcdddcbabbcadbbdbdddccbdcaaabbcbdbbbadbcbdabacbaccadccccdadcbabbabdaccabcbbdcbbdaddbabdbadadbdadaaddcdbdadbadbcddabdbdbbbacdbdcaabcdbcbbbcdbbabdcbdddbdaabdcdbcaacdccbdbabbcbbcbdbbcdbaaabdabacbbdcbacbabcddbdaaacdccdddcbcdaddaadbabcdbbdcadbcccabadcbbbddcbddbdcccccacacdbcbcdccdcddccbcaddcaabcbbaacadbaacadddcacabdddbbabcbdccdcdddbacadadcdabddabaddcbdadcadabacbbddadccbcbcabddbccadddcaddcbbaddbcccddcacdcabcddcdcaccabaaccadaadbcbbcdbddadbabdbdaddabbbddbcddccdababbacddbaabbdacccbdcacdacdadcdbabbaddbbbbbcbcacbbdcadddddcbcddababbbbbdcccdbddccacacbcddbccbacabadbcbabacadacbcdadddadcabbbbadcdbdbccaabbaabbcbdbabcaddcadbbcadbcdccadabcbdadddaadcdcdbdddbadaaccdbbdabcaaddcccdcabcdbbbdcdcdbcbccbdadbcccabcdacbcadbddbaadadbbaadbcbdcbaccbabdccdaadabcbcaaabccaacdddbcdadabccdcabaaacaddacbabcbacabadcdcadabddabddbcdbdbbacdcccdaaccbabdddaadbbacbabababdccaabaabbadbccdaadbdbcbcbcbbbbdcbdbaadabdbdbcacacaccadbabddddcdccccbdbdacaabccdabbccddabbcdadaaaadadadbaccacddbbccdabcbacdbddabababaddbbaacabddbddbdadcdcbbadcccabdaccabbaaaaaacdaabaddbacabccdcdddbbacdbcbddaacadbbbbddddbbacddddcccbbbbbcadbddcdbcbadcababdbadaccdaadcaddadbabdaaadccaacabbbdbbbcccbadbcccdcabcacaacaacabcddbbdacbbdccbcddbdbccddddcaabbcdaaaaddbddcbabaaccdbdadcabbacabaacacdbdcabbadabdbbddbccccdddaddadddbcbcbbabcabdabcdddcabbcaabcaabacbacbaaacbaccdbcbbabbbcaaadddbbcaaacddaddbccdaccbcdddbcabbadacaccddaaccdacbdcaccbdbcaddccbbbbbbbbcdbadaacadaacaadddbcadaabdcddccdddbcabbbdbdaddaddbdbdddddddacacaccaabcbbaabbcbbabddadcadaadadcabccacddbbcbabdcaadccddcbcbdcabdcdbadcbbaababdbaaadcbcdaaacaacaaaddabadbddddcbbbdbbcbbaacdbbbbbbcacdaacbdabdcdcbcdcadbdadddaacadcdaacabdaddcbdacdaacaacacdccbacbcabdcbccddbbdcbaacbdcadcbdbacbcabbdbadcdbcadcdbabdcbadbdabcabccddcabddabdddbccadcddcccaabcdcabdbbbcdcacbbdaabaddcdaaaadbdddabaadbacbabaccbbcbcdadacadcbaccbbcbbabbaccaabbbbadaccdacdadbaccdacbcbadbbbadabcaddccdbddbaddccadbbaccabdbbbdadbbbcabbabacdbacbacbabcdabaccdcbcbaddcddaddcabcaddddbadcbaddbacbacaacaaadaddaaddccbaacdcbcbdacdabbcccbdcadaadbbaddacbaabccbdaaccdbdccdcabbadcdccaccbacacbdacccbdabbdcadcbcbbcadcbdbcccacbbdbbbbddabcadbaaccaddccbcdbddcddaabdbdabbaabbccdcbacadaacdbaadadadacacaadcdcdcbabdbccaccadacabcbddaccbbacbaaacabaacddaaaddaccddacdcaaaacaacbdbcdcdbdcbdadadbdbadababcdcaabbaacddcbccadbbabbaacaccdcaddaabbdddcabcabcaacabdbadaccaddadbcbcacabaadaacdcacaadcbddabddaabcdddcdbacaaabcdbccadcaaaadcacadabadabdcacddacabcacabaacbdccdcadbaadccaddcacbdbcbbddccaadddccdcbcacadaddabdbddcaadcccaabbbdadbdbaaacdadbccaaaddbbabbbbbdddacacadcbbccccbbcccadbcbcbaddabdaaccbbbdbcacdccbacaddabcdacdbcddbcaccaacadbcbaaabdabdddcdbcccabcdadabbcdcabaaacbacbddaaadcdaabdcccdcddaccddcdbbadddadabdbdbaaaacbddcdcdcccccbddddccbadcccaacadcbacaddabcccbbdcacabdbacdbaacacaaccaaadbddbcdddbccbcbbdaccbddadaaaadbbdbccccaacaabbdacaddcadbdadbcbbdaadcdcbcacaadccbdaabbcccbbadcaddcbdcbdccbdaddcbcacbdacdbbabbdbdccadadaccaaaccaadbbcdbdcbcddacaaacbcacacccbbaccccacaddbbdcbabccadbbbdbbbbbabcadcbbcabdbacaaabbdddbddccccadaccadbdbccccbbcbdbacaabdacbaddcbdbaacbcabcacabcccaccbdbabdabcdbccadcddaacccbacdabacabdbbddbbababadaaddabccdabcdcccbaaddbbaacdabbabdbdbdabaaadbabcbbbbcbacdacccacdbdccccadccbadbcbbdbadcacdaabdacbacacbacabccabcdcddcacccdbcdaccacbacccddcbccdddddcdbddccaacbdaadbdcbbccbaaaacbabcddccaddbbaaacacaaaabccbdbadadcadbbdcbdaddaabaaccabcdbcdadbdccabadcbacdcdccabaaaddadcccbabdadabaddbbbbadddacaaabddbbbcdadbbdaaacdaddacccaddabbccacacbdbcddbcadaccacccdbccdcdbdcabaaabccadcbdccacacccbbadbababaaadcadbdccdcabbccabbababbbdcadbbadbdabdccabbaaddabdaabcccaacdbcdccbbdabbbabdddcaabaddcbdaddddddbcccaacdbacbacddbbacaccadbaccccddcdddcdadabdbadbbddcbddcddbddcdabcdcddcdbcdddbcabcdbbbadabbacccbdcadacbccdcacaaddbdcabdcacdcbddadddaacacaababcdcdbbbdabcdbdccbdcbacaddabcbbdbacaccbdbadbcdddbdadbaccdcbacbbcaabcccadbccaabaccadcddbcbdcabcabbababaabaaccdabaaaccddcbbbbcdbccbadbcbcbabdddbaadddbccacadbcccbdaccbdbabababcabbadbcdcddbdbdacdbcbbbcdbdcacaabbcdcabddaadadacdbaddddaacbcadbcacaadbdddadbcadabdcbddcdabbdaacddacbbcaabbacabbdccdbbcdccbbbacdadadbacccbaccdcdbacccadddbbcaddabddccdcccdccadbcddaaaaabcdbabbcbaadaccbcbbccbccbbcbccccaaddaddcdbdcdcdcacbdcdaacaacdbdbdabccadcabdbdcacbacddcccddbaacacdcadbdaabccbabdbcdcabcddabcbbcaaacccbcdbabbddaadbbdadbcaaacdbcadbcddabaacbdacaccbbaacbcdacdbcbdbbbdaadaaacddddbbaabadcccbbcadbbbbacccbcabaabdcddbadcdadbbddcbabcaaabbbcdadbbdcacabcabcbccabadbbbbadbcbcccbaddaabdaaacdbcababbbbdccacaadcaadaddabbbaaccaccbadbabcdddadcbccbdbdcbccbcaadbabaaccaaacdbaaccdcdbbacddbdabbbbabdcaaccbaacdcbdcadbcdaababdbdacaabdbdaacdbdaaabbbddbbdccccbdcdcbdadadaaadcbcdadccbacbaddcadbbdadadccadadbdcdaaaacbcaddbcddccacbbcaaddabddcdccdbbabdcddbbdddcbabbdbacbbabcddcbdcdcdcdaabbacdbbbbadccdbdadcabddaaacbaddcddbcabccccbcabccddcdbaadabdacdbddcaddddbcbababbcccadbbacddbbaadacdbdbcdababbbaccdbadabacbdbcacdcbabacbbdadabcdbcbdccbbcbbdccbadcdacdcbbcbdaaabacbccdaddacbbabaccdbdddddcabbbcdbcdacdacbaadababcaaadabdbaacdbadbaabaacdabaccbcaabbbcaadadabcddcaacddaccabbcbadaaacaaadcccababbbbdbcbcacadcbbaaddddbcddcabdcbccaabcdddddcbbcabcadcddbdbccbabbbbddddacacaadcadbcbbbbaadacbbaaadbdddaabaacaadcababbbabbcbcbdbaabbdbadbbcbcbbbbabbcbadaaccdbacddcdcbdabcdbdbbaccccccadabbabdddabdacdccdddbccabcbcdddaadbaccadcaaadcccdbbdcdcbbcdcbbcaddadadadbdccdcdbaaadaaadbacdcdddcbdddcadbbcbcdbdddadadbbbcdcaccaaccdcacddbdcbbbbbcaabcdaaddbcbcdccbadbcdababaaaddabdcbbacbdaccbdcccadbddddadcbcdbcbbabdcbcdddadcdbbaddccdcdadbcddddbbabcaccadcbacdcdabdbaabcdbdbdabaadbabbddaaabccdbcdacbaaacacddbbacdbdcdccddbdcbddbdbbdbabdbbbcaabcaaacabcacacbdbdcaabaacbcaabbdbcdbabcddabbaddcdbdbcdbdbacdddacddaadddadcbbdbbddbcadaccabdbcbaddbcbbbbdcabbacaacadbccdbbdcdaaacbcdccdcbbaccacabddccaaabcddadddbbbdadddaddcbcabaddccbdccdbccadcccccbcccbcddbdbbbbddabaccadccbcbbbacaaabdaddddccccbdbbcddbddcdcdabdacaabbdcdadbdcbaadccabbcddaccaccdbbacccbbaaccabbcdddaddcadcddadbcadcadbcbdbacdcddcabccdbbbdcdcdcbcddddbbbbbbdccbdaabdbdbcacbadbbbaacbcbbbdddbdacacddcadbcbcadcbcabccaaabaddcbacdbdddddddcbaabcdcbcccdbabccddddcbcdbcdabccadccabdbcabccdcbadbbbdbccbccabbccbbdacbbadbdacaaacddadcdaacaaaaadddbdbcbadaabacaabbacbdbacabcbadcddaababaacddbbabcdacacbacbbabdcacbcddadcbcccbdccaabdbcacacdaadbbdaaaaccccbcdacadababccaaadabcdddcabcccdaddbdabdcddddaaccddabcbddaaabbbdacbadcabacdcdccbbbcbababcdcaccadbbabbdcabdbdaabccbbbdbbdcbadbbbcdbbdddbdadabbbbadcddbcdcbdacbcdddcdaaadddcdcdcacbabbacdcdaddabdbadccdcbdaccbbdbcdbdbbcabaaccabdbccddcdccbdbccabbbaddcbcadaddbcabcccddcdddcabddbaaaccadacbaaccdccbabbcabbbcdcdacccbabdddbcbcadddabdacdccaaabbcabddbccaaaaaccbdaadbdccddaaadcaddcdcaccabcbbbbdaabdbbadcadcaccddaaccbaacdcadaabcbbccbdbbcadcddcddcbbabcddbaddbcccbddcabadabbabacdcdcdbaacbbbddbaabbddcadadaddbacabddbbccdbcbdbbcddcccbcbaadbdbacaabbabadcabbbcacccadbadbdbbdadaacdbdccbacdbcadaccaddaaabcdcdbccadbaaaddbddcdccdaccbaadadadcbbbccacbdddaadccdddbbaccbaccabadacdcadabddcccbaadacbacddbacbcbacacbaadcdadbcaacbdddcdcbbcadacbcdbbbdccbdbcbadbbcdaadcddbabcbddbcbaaaccacaadbbccabddcdbdcddbccaccdaddbdbbbbdabddbbdacaaacadabddcaacabddddbcbbcaccccaccbcddcbdaaddbcbccaadacbabdabcabcacbcdcdbaacacdcabaabbaaacbbdddbccbdbaaddcabcdaccbaabcadbdabbbbcddcdccbbdbcaacabbbcadbddcbcaddccddabdbcbabddddcbcaccdddacacabccdcadbdcbcaacdadaabccadcbbababddaccdcbbdcdbbbbcadcabbbddcdbacadccabadccdbcaaacdbcbcadbcdcccaaaabbdbbaacbadddadcaaaaccbaaccddcbcdcadccababdbbbdcbddabcbdbbacacdccdcccbcadbccaddbcdbacbdaabadddbadcbcdababaabbadacdaabbabadabdddbaabcacadbcadbababcdddaacaaccdcdabacabbdacaccdacccacdadadccabdadbaadcaaddbbabaccdcabbddcacbdaaaadaabbabacaccbbaabaabcbcabdcbababdadbaadadcdcadbaaaabbddcdaadabadacbbddddcbaadbdaccadccbadcdaabbbbbcbdadccaadaadabdddaabbacbcadbdccaddcaaadbabdbbdcbcadababdbaadabaabdcccabdcdbbcbbdabdbdbaaadabdcadbccbcacaaabadcabcdbacaabbdccbbababdbccacacbbcbabbdccccdbcbddbbaabbdbbcbabcbbddabacdabaacdaaacbdcbbdddbbcacaaaddcdcadabadbcadcdcdcddcdcbcbbaabaadaaaadabacdabbbabbcaabcaccabdcadabddcdcdbbbbaadcdaacadbbcabacabbdabdaaabaccbdbdabbcbcabddaaaabdcccaabadbdacabdbbdbadcadcadbadadcbaccdacdaccadacdccaadcdadcbabadaaccdbdccdbbadacbadcbcacdbbacbdddcddaddbcbbdccbbddbbcaaacdcaacdadbaddddccccdbcbdacccbbcccccaaaddbaaaabcaaccdaacdcbdabddbacbcbbadbaddbdcdbcbcabbddbbccdaaddbdadabcbadabddbdaacbccdcccdddcbbadbaabcdacdbccbcdbbdaadcccabdadcadbddcbdbbcddababbaadbddcdbabcbbdaadddabddbbcdabbbcdcbbccaabdabdadaddcaaccbbcababcdcbbdaadbdcdbddbdcdddaaddbaaccccaabcdcaddaadcdaddbabdddbbbbdbabcddaadbccacccdbbcacdbdbbdcddcaddacadcbcadccbbdbababdbdacaaaabdabbcddccbcadaddcdcddcabcbadcbaddbbadbadbdbbacbaccccdcabcbadbabcbcbacccddccbdaaddadaccbcbcacbaddccdbbbaddbcddbaabcdcacabaaaddccbaacbcbcbaaacacbcdcdcccaaacaddcaabdbbbbbdcbcdbbabdaacacbdadadcbddccddbccbdcddaacbabcdaaccdabddabcbadbacddadbcddbbddabbbdacbbbbabcadaadacdababcdbdcbcaabbadcadbdcddbdbcbbdcdcdcaacacdcdccccccdcdbdcacdbaddbbdabdabdcdcadaaaabdcdddbbbaadbddcacbdbdcadacddcbdbbabaccdbddabbcbdcbdbbccbdabddaaadabbbcbcbcbdbddcbcbcabbbadbddaaccaddadaaccdcdccaacbcddbbbacbaacdddbdbccbdcbabdcdcbaccacbcadbabcadbbdcccccabdaabbbccdbadcbbcddabbaadbdccbbdbdbbcacadbdabbdcdccdadacdcdbadbcbcdbacacabdbcddcbacadaadcdbaddbdddbaabadacdaddddaaddabbcaddbdcadbadbdbccbadacbbdbcccbcdaabcbccddbcacabdacaaadddcdbabdcabccacbbbabdaddbccdacbbbbdbbdabdcdacccbaaacdddddbcbbacdaddadbdadcadbadcdccabadcaabccbdbdccdcbbcbacbbadbbdcbcbcabdabccbcacbabcdbccdacbabbcaabcccdbccdcaaaaadaaabcddaccbacdccccdaacacbbdcbcadaccabbddbaacbaacbcdaddabbdaddacaabcbabacbbdbbadddcbaacccbdabddaacbddbaccbcbdbaacbbbdbccdabacbdadcbaabbbabbaaaadccabbccdabbcacbaccabcbbbbdcaaaadcacbbbddbbabaacdddbdaadcbabccacabbbdacdaadaabdcacbdbbccdabababdccbacbbdcdddaabbbabbdbaadaacbccbdbbcbccaccbdccaabcaccbdabcdbcddbbadccabccacabcdbabdbbcdadbccdbdccbbdddaccacacbddcbbdbcbdbacbbdcbcbaadacbdaabdcaabaccdaacadccaabdcddddbdcdabbdbacdaccdbbdcdddccbdbbacbddabbacdccabcbbcbdcdaabaacbadddddbdddcdbcbabaddcbbcbbcacbabbbcdadddaacacadadccabcacadacccabadcdbbaddcdcbdcadcdaacacdacdcacdbcbddbdaddcadddaaaccbaccabcbabcbbbdddcaabdbdbacdcbbdbcdcbdcdcbadbcbaabbaacddddbdbbcaadcddcbbdbbccddacdbbdaccbdcdbdabcdabadbdddabbcdaadcdabbccbaaadbabacdaaacbbabcacbbabcddcdadcbaccccabdcccadadcdacadbaacdcadbcbbaccbdcabccabbaaacdacdbcbdcacaccacabccccbbcabcccaabadbaadcccdbacddddabaddababbaccadaddaaccccbbdaaaaccbacbacacdcdbccabaaaddadbcdcbdcadaddcaaddbddccddcdabcadaddacdacddabbaacabadcabcbcadbaccbaadabbbdabdddbabbaababcbddcbbdadababbbccaadddbacccaabdaccacaacbbcaababadbadacdccacdbcbdbbdcccaacdacadbbbcaabdcccbcaccddcccbbbccbcccbcadabcdcdbbdaadccaaccbcdcbadbbbaccacbadbbcacdabbdcacacbbcdacdddcdaacdadadadaddddaccbbdcaabddacdddaaabcccdabcdbdaacdcdddbaacabcbdbcddcdcccaadaaaadadbcddadaddcabbbdabbcacadabbcbcdbdbbcadcbdabcdbdccdaacdacdcbbdbadbcdcdabcdbadbabaabacbaddabbadaabccacbcbcdabdcdbbbbddabbbbdcbadbcadcabcbabbcbdddadbddbacdbabcaabbcbdcacbcdaccdaccccdbacbbaabccadbcbdbdbccacabacaabcdcbdddadaadbccdbaaadacbcbbaabbbcdbdcdcbdaadbcdcacbadcbdabdbcabcbbdaddccadbdcadbcccbcacaabdbbdcdcdcdbaacaaabcdcaadbcbccbcccbabddcddbacacdabbdadadbdccaacddcbbcacaacdccacadacacaccdcccabdacdabcacdacacbdbcdaddcbdccdbbdcddacadbcbcbcbbdbdadcabcabdcadccabbdaabdadbcddaaabcdbcddcabddbbadbbadbadddadbabacdaabdabcadbabaaaccdaadddbaacbcdcbddbaddcabaddbcdacdaddaaaaccddacbbcbdacdccbbadaccabbcaaaccbcdbaadaccaccbabbddadbbabacaacaadadabcaabdddcdcaccdabacbcbcadddababdccbcdbdaadddcddaaadbbabaaacbcaadbbcbdaabcabadaacbadaaadbdbaabcbddbdbadaacbabccdcdacbcaddaadbabaacbbbdbbcdbddabcbbabddacdccacadcdbadcbcadddbbdcaddbabdbccaccadcdbbadcbccacacccdbbbcadcbcabdbbbbdaadadaccccbbbdacdcdbbcddcdabdbcbdacccacdcacaddabddbcabbcdcddbadbcdababdabccabadbddcbaddbbcdaadcbccdaaadbddcabdbbdadadcabbadabdccbdcbcccabbbdabbaabaadcbdaabbaadcbdacbccdbbcabadcbcdacdcbdabbbaccbddcadcbcaacacbadcbcbaabccddaacdaaabcadaabcbdaccadaaadadadddabbdccddacabcdadcddbccacdbcaadcddcacabcbbcbccbadcadcdadcacddbcddacddcbabbbaaadddbaabcbbaaacddbbbbdcadaabaabdbbcddcbacddaadacccbbdcababddcaacbcbddccddccaacadacddacaacacbccbbdcbcbabbdbbabcbaababdadcbabadccdddbbadcadaccaddbbcabbacbbacbaacdbcbbbcacadcddbcccddcbdcdcadbdacbbcbacdacbaaacdbcdcbbdaadabacaacdcdcbcdaadccccdbdcdbdbcccddadabbbadadbdbbdbddcdbccddcaccbbabcaaccacdadccaaccdaadbdcbacdaacaacbabddbcabddabddbccbacdcccacdcbcbcdcabacdbcacadcabaaadacdbabacdddccbbcddacbaacbadcdaadcabacbabaddbcccbdbbbabbdcbadbddcbbabacabdcbabdbabddbbdacccbdadbdcadcdaaccddabacbaacacbcbcbbadcdcbbaddcabccadacaacabdacbaacdacddbdbbcdcdbacccccdcaaaadcaadbbdacbccdcdacacbcacdcdbaabaccbbccccabddbbbdbcadbacdadbdcdacabadbdadaacbdbcbacbcdaaadbbbbacbcbaccccadcdcaacaddbaaddabcccdbccdbcaadbacaaaacacdcdadadbacdadbdacadbaadccbdcdadaddcacbcbabdadddcacbdcbddabbababcdcadddbcbbcddbbaddbddbccacccaccacdbcdaababdddbcacbcaaacdcadacadbadabdbccbacbcddcdadcdbcccabcdacacbcbbabdbaccaabddbddbbbcbdaabcdaadcbbcbcabddaaacbbabddacdaccdaccadcbacddcdadbcbcadbacbcdacabddaabbdadcdcbcdcadbccacaccabccdccbcaddaccdbdbbcbaaddabbdcbdcbabbdddcddabcddcdacbbccdaddacbdaccbbcdcadcabbabcadbaacaaabbabdaaaaaaacbbdbbddbbbddcdcbdaaaabbdcacddcdadcdbabcbddadddaddccaddcbcadcbbccadccdccabbcdbacbcdbbacabddbcbdaabcddbacbacacdcbdbbcbcddddacbdbdadcaabddbcabacddadaccaaabccbbacaabcbbdddbddabcccaaccaabdcaabacbadbbacddbcdacbaadbbdbdbbaadacaacccacddbbbcacaadacabbddcaccbbcdbddaddcabbcdbcbabcdbacdddbccccacbdadbdcddcadcdcbdccccbddcbacbbdadbaccdcdcdbdccddccadcbcdcaadccbbaaaabdddbcbdbadbccdabaaaaacdaacacccabcbadabadbdadabbdabdbbdabaabadcdbbdcacacbbbadcbdbabacaccdccdaacddddbcbcaaaadcddbccabacaddcbbdcaaadcbaaacdccadbcdabdbdaabbbdacbabbbbaacdabdbabcccccdaaaddbacccdbcadbbcadbacdccdbccbbbaccbdbdbbbdacbaabbacccabdadabdadcabcdcacbbaacbbccdcacbacdadacacabccdaadbdabccabccbaddabccdcaaddaacbdcaacccadbabbdcbdcbddaacdacbaaccbadacdcbddbcaacaabbbddadaaaadbaacdcabcbcdbacddacbdddcdabcdcabddbdaadadcbcdbcdcdbdcaacbcbbbbdaccabccadddacaabbdbbadbaaaaababacdaadabbdbadabbabcddcaacabcdcdacaabdbadbbdccbacdbbbabccbabaddbbccbabbcddbababacbccaccaaccadddbacaadbcbbbdabaaabadbbcbabadbccbcbbacdacccacacaaacbbbdbcadaddbdcadababccccabdcbcacbacddbaacccdaacccadbbabbbdaacaabbbcbdbddbcbababacadbbdacccbcaddacdaadccacdbcccdcdadcacdaacdcbcaabbbaccbddacddacadccccccdaacdadbdcdbadadbbaaccccabaacbdcacabbccccddbccabddaacccacadcdbcadcbbcbcbdbadbccbdacbdabcaabdacaadabbbdcaabbcbdaadccdadbcabcdcaacccacdabddbdcdcdaadbbbdbccbadababaccbbdcbbdcccaddbadbdcdabdcddacbcbcbcdabcaddcbacbbcaccbcbadcabdccaccdaadaccbbcdabaadaabcdcbbabbdabbdcadbdcbdbddaacbcbdbcaaadbbacbbcccaaababcdbcaaadddadcacbadcdcbaddacccaadaaacabbdbcbdcbcdbaccbbadaddbcdcacaaacbcbbcbbcdcdbbdccdbbabdacacadbbbbbcaabbbddbbdbaccacaaaddbacabdadaddbddbcabadbdcaaadcbdacbdbaccbdcddbccacbcdabadccbaaadcacccdabadbcaacadbabdbababbabddbbcdbcadcbbdbabaaccdacdccbabbcddbadbdbdaabadcdcbbcadabacacbacbbbccdbacbaaddbaaccccbbabcacaccbccdddaaabacdcddcbddadcbcdcbaccbaddabbdcccddbddcdcdbbbacdcdacbccbcbaabbaddacdcdbcacabacaacbbddcaddccbcbcdcaacbdccbdccdbdadaaddbbbbacaddaabbcacdbadbbddacbdcbdbdcccadaddccadbcadbaaaddccddabbbdbacdbbbddadccabadacabccccacddabaabdadccbdaccbdbcdcbdacdddbaddaccbadccbdadadccccabdbaaccabdcbbacddaaccdaacadacbddaacabadbccddabbabacddacdaaadcbbadddbaabcacabadabaabccbccbdcacacdbbccadbabbdbadbcbbdaabcadcdccdbdacbcddcdaaaaaddcdadddacbdadabdabcccbbacdccdddbaaddbaadababbabadbbdbbabbacddadbdbcaabaabdddbcbaadddaddadbaabaaacacbabadccdacdaddcdaaaababbddadccccdadcbaddbbccbadcbcdcbcaccadbbabbdaaddabdddabccaccbcaadcabcdbddddcbddbbdacbaaabcdabcacddabbacabdddddccaadcddcbcbccacdbcadcbdcdcbcdcddcacaaaccacdbbabddbacacddccacacbcdbbcacadaadddaabbcbdddaabccdaabadbddbdcbbddbccadadbdadadcddababbbcaccbaddaaddbdbadddcacbcacaabaabdbcabacabcdcacabadbcbaaadddccaddbddcdaacbbdbcdaadccdbcdaabbcacbadddcacdaacbbabcccddacaccacabbaddbbbcbcdaaddcbabaaaaddaddbbadcadcaadcdabaaaadbaadabacbccdbacdacbdbaaabbccadcabcdbcaaaddbabcbcbdbdcdabcaaabbaddcdcbcbdbcacadacbddabdddaacbdccbabdcbcdabbdcbcccaacbbdbcbbbbacdddbabbaddabdadcccbbdbcdaabdbbcbccaadcababcdbacabbbdbdadadababbdabdcaaadbabdbdbdaacacaaaacbaadabbbdccdbbdcdcdbcdddbaaacdcccaaacbaadbcabacbbcaadbbddbcbcacccabacbcbbcbccbaadbbaaaaabddcdbddabccaaadbcadadccdccaaddbdbccdabbcababccccdbccdbdddcaadcaaadabbcdcccacccacccadcabbdcbbabbccbbabdabdccbbdcbdbbdadbdddccddccaabcbcbccacbbadcaddbdbcbbcbbdadacbcbbdcaaacaabbaccdacacddacbccbabbdbbaccadcabacddcacddbcdcaddcbdcbdbabdadccadaaddababcdaadbbcdddbaadccdcaabbbdccccacbcdacbdbacbdacdccbcacabbbaaacabddabababaabbbabbcaccdbdbcdddccdbbdbadcbacccbbbddbbacbbabdcacacbcccababdadbdcacddadcbaddbcadddacdcccdcbdcbbdbbddaadbaacbaccdaaaacdcdaaabdbdabdbcabbdadadddbbdacdaabbaabddbcccdccaaaccddabcbdabbcaccbaccccaabaddccdbaaacbdacccccdaadbddccabadbbdbadccdabacabbabaacabddbadadbbabbbbccbabcaabdccdadcddacababaaaacaacdcdbbbcabcbdccbacadaababbddddacabbdaddbaccccbdbabadcbacbddcadddbcccbaddbcbaabbddccaabbbbdbddadadbcdcabdaaccdbbcadbbbdbbddbabccdaaadcaabbbcdddbbacdbabaaabbccbabbacbcabddabbbdcdadddbcacbccbccdbccbaacdcdbcbcdbacbbbccacbbdbbadaaabccbacbbccddaaaabcabcdbbbadabbadacbadabcbbcdcacdccacccccabadcbbbbcdaabdabddcdbdcadcdabacdaddddaddcababdaadabdbabcaccdacbcbbacacdbbcabbbcadddbdccccbacabdabdddcbbbdcadbdbccbcdbcbbdbbbcbaaddcaaaabcbacadcdcdbbbcbbbbbccdcaddddabcbbdabcdadacdbcdbbcdbdcaccbdbddababbbabcadccdbccadcabdacaaccdadbcbbdcddcaabcddbddaacaabdbcdaabddcdabacbaadcbbddcaccbacdbaadcccbdccccbbaadbcbbdbcaabdcbddbdaacaaadaabbdbdaabdbbddcbbbacdccbddbcdbbdbbdcadbbdccddddccabbbaddddbdbbaabcdbabacbddcbadadcdcaadacdbcbdcdbdcadcbbdabaacbbabbdddcbacaddbdbcaddadaaddaddcabcdadaabbbaaccabcaccccadaccbadcadcdaadccbdcabbcdcbcbaaabcdddbccadababaaacdcabacbddacbbdbbaaabaaddabaddbccacbbaaabbbbcadcbadacabdaacbccacdaadabdacdcbabcdaaacaaccbbaaadabbdcdcbdbdbdbadcdbbadbddaaccdaddabddadcdbabacbacbbadcdaccdddbcdacbcbbaccdbadbbadacbccbadbaabdbaccdcaddddbbadbabdddbdadaaacddbdddbadaabbcddbccbdcbaddcdacbacdbadaaddcaddbbbdbbbbaddcbddcbabdbbaacbaccccdbccbdbcaaccccaaadabbcdbbabcbabcdddcadcabbdadccbdcddccadcaaccdccdcabcaaaadbaccbaadbbaadbdacddbadacbccdacdcccadacadbaaadcadcdbbaaadbacdddaadbddadbbbccbdbdcdcacbbdddccaacaccddbdbccbacbdcbdcbdccdbcdcbbbcacabadbccaccbbbcbbcddabccccbdadcbdbabbabadcdabcccdaccadadaaccdddbcddbccbcddcdadbcbbaadcbbcdbdccccbddbdbbaadadabdabaddadbddcdcadabaaacccaadbcccbcacbccabcbabadddccbbddcabdccbaaaabcacddabcddbbcabaaacdbadabdabdabadadddacdadbbbdabbbababaadaabdbaadbbdbcabaadbbdaabbbdacccbcaaccaacbdcadcbbcacccddbdddaabacbdbabdcdbdbccaaddadccccbcadbabccdbddbabaaddbacabdbcaaabdbaccdbbdbcbcdcbbcbbddabbdaccacccbaadbbacaccbbaaacbcabbadabbaacbbdcbdcadcbbdcbdbbacdcdaccdbbdcdabaadccaabdcacbacdacdbbbbcbbcddabaaadcbacaaccddccdcbdcbaababdbbbccbbcacadbcbbdbbaaddabcdbacbddddbcbaccdabbaddcaddbbbadabddacbdddaccdbcbcddaddbcbdacacbacaccabcdbddccadaadbccbddccadbbadcdcbddaddaabcccccdcaadaccadadcccdcaccddcdccdcaddddbcccaddcaaccbddbdabdccdacaabdcadacadaaccdddaabdcbcbaadadadbbadccbbcbbdcbabcbcbacdcdabdbbbaabdcbdbdababccdcbcdaddaaacbbacddbabaaadcababbdbbdcdddddaacbcbdababcdaccbbdbdbabccaadabbacabccaddbdcdcddbabbadcaaddccacbccacddcbbdcacabbbbadcdbdadadddcbcaaccacbdcdccabccabcbcabaddbcbadababcadabddcabdcccbddcdaabbdddccbaaaababacabaddcaccabaadbcacccabacbdccdbdbccabcbddcccabaddcdcbadddacaadacdabcdcacdbbdddbdaddbdcbadcdadcaaccabadddcbbcaabaddccacdaccdbcadabbdabddbdcbbddccdbacaacaddcdacabbbdbbbbdbadadbabcbabbbdadabdbadcbabdacabcdaddcdbacddbbaadcbbcabdacaadabdbbdbdbbbaabaabdadbabbabadadcbadaccadcacdcdcabcdbaabcdaadcbaaadaaccacaaccddbadbcdddaaaadadbcadadbbbcbadbadbacccbadacdcabbbccbbcbcbabbdddbdcadbbbadddbcdbabadbbcaccddcaccbdadddadccaabacaabadabcdcdabcdcdccaccbdbaabbaaddcaddddcccacabdbadbdbaccdacdbdcbcbddaadbdcbccbbddaacbbcccbacaaabbdcaddcdcddcddaddacacaaabbcdcbbadccdcbccdcbddadcacbadbbaddcdcabddadbddabcdadcababdbdadaaddcccbdbcbaddaacadccaaccccdbdccabbadccdabaacbbcabddcbddbbdabbabdddcaacbbdccaadbdcbcdadbdcbcccdbdabbcaabdacbcbcabaaabacacacdbbacaabcabbcbbaacbccaacbcccbdcdccdabccdbbdbadcddbbcaadddbdbadcbdaddacababbbacdbaadbacdcbadddbaadddcdbdadabdddadacdcbbdbbbbcdadadbadaacddccdccdabccdcbdaccbdbdcaccabcbccdaaddabaacabdddcdbcccbaaaccdbbcdcbdcdcbbdbadabacaccbdadadcccbdacbaacccbdaabdcdbcdcbbcaaaadbdadbdcbdabdaddccbdddacbbbcdacbbdabaacbadabaaabbacaaaaddaadcabbadcbabaddcaaabadaddabcdacbdcbcacadccadcbadcabbaaabadcbaadbbbadadbdabbaabaaaddbddabadbdcbbdbbccdadadacddbbcdaaabdcbccdccadbdcdcaadccbddbdcbbabbdcbbdbdbcaaddccbcbdddcbddcbbbcaadccdcdbabddddcaddabbdcabdcbccdaddadcbccbdacacbcbbbabacbccbaccacacadcbdccbcdaddacccababbcccbbaaaabbbcbddbabbcdddddcdcdcbbdbdcbabbdbcbddcadadbbacdabbcbbabcaabbdbaadbbcadddabbacadadcccabbcbcadadccaccaabcacdcbbabccaddbaaacaacadcbbdbaccbbbdddabcacbabaccdcdcabbbabcaacababbacaadbdccbbacdcdbaaabbabccabbbcacbadbacddaacadbcabcababdbdccabbdcdcdcbadadabdbdaacdcabdcbbaccdabaabaccdaadaddccbcbaacbadcacbaadddcbdaaadbccabcdabbdadcaacbccabddcdbbcacbbdbbcbdbadddbcbddaabbacccaabbacaccaaabbacbaccadabbcbdaaadbbdcbcdccbdcaadacccaccdabcacbaadabcadacacbbcbccbabdbccbbbbacccdcdadadbbcbdbcbcaadcbcdbadcbaaaddcbdadccdbdcabcbcdccadbbddadccdcdbdbcadbdacdabcbbabbddcacbababcddadbacadcccbcbbaacabcdbaddbabcaadbdcbddacbbaddacdbdddabdcddabbaaacabadcaccdbbbadadacdbacacccacadbabcdabbbabddbbbdcbdaccaadcdacbaccddccdcabaccacabbdccaadddddaccdccdacadcdbdaacaabadcbaaaacccaddbbcccddaabbddddddbdccccbbbacadbcdbabdaacbccbcdcbbbbcccdbbdcbababcccdbacbbbccaddbdaababadbcdbddabcdcdbbaadacaabdaaacddccccaacdbdddccbacbbabdacdcabcaabadbacbaaabccbbabbabbcdddddabdcaaabbcbddcbcbdccadbcababdbdbbbadabbcacdcabccaccdbccadcdbcaaaabaccccdbaddabdcccdaaaaacdcaccdbbdbbdbadcccccccdadcaaadabacbadadccbcbbcbdaadbdccdcdbbdabbcdaaddbbbcabaaacbdbdcbcacdabddccbbdcacdacdcabdaacdbcadbacbacacaccbcbddbcaccdccbddadcadbcaaabccadcbdddbdbaaccabbcaaddddcbaaabcdadcbddcccabaaaabdcdcccddcbacccbabdcaacbdacbbacbadabaacabcdbbbccbacccdadacbdcbdadcabdbaabbbccacbabbbcddcbabaababcbcaccdadcdcbabdaaabdbddbacacbdadcdccdaadcdacadacdbbcbbcdcddbccadddddddacabaacbadbaaddbadcabccacabcddbcbdccbccccbbbaddddadcdbccdbcdacdcaadbacbbaddddacdaabcdddccbdcdbbbaaccddccaacdcddabbbcdcdcadcacbdbbddccbbccdaccdcddcdbcabddcbcaacdbbacdbdbaabccbcdacdaadcdadcdcacdadbcddbdcbaadacbcdcaaabbbbdcbadbabcbdcbcabcdbccaddaccdddddcaddddcbdbbbddadbadbabaaddbdbdccddddcabadbdcbaaadabbcdaabacbbbbdddcdaabaccdadabaaaacacabababdacacccbdccbdbdcbdbaabdcbdbbbbadbbaddddbdbaaccbccbccddccaccbabcdaaaadbcccdcdcbbcaadcbcdaacddbccacddbbababccccacbdcaaadacdbabdcddcdbcdacbaaddbdacadbabcbdcaadcaabbabbdbbdabdacdbbaccbbdbbdbbdacaacbccbcbabdcdcdadadbdbdaaddcdaaddbadabcbdacdbabdcaddabaddcddabcbadbbdddaccbaaaddbbcdbbdaccdcacdbacdbbbcacdddbccdadcababacbcbadbcdacbacacaacbcbdbacbccbbaabcdcdabaadcbacdaaaabbbbdbaadbaddcbacdadbbdcccadcbbcbcdcbdcadaaccabbcacbacdbabbaaabdacabcaddcaccdadacadacdacbcccaadaadddbbbaadcaaccbaadbcdbcaabbdbabcdbabdaaadbadbabbbbacbadddcbcddabababbcbdddbcacabcdbdaaccbbdcbccadbaddabaacdbadbacdabcbdbabcadcaddabcacdabcdbbddccaaadccddbbdbdccddbcbaddacacdababbcccbccbcccaccdcbcdcbdbabddadacbdbaaadbbcdcacdadbcddccdcccabdaabacabccdacbabdcabaaabcddcadadcdabacbccdcabaddabaadcdadbcbbddcadbaaaaacbdabdcdddbabaddbdadcacabcadbcdcdacdadcaacaadbadcbdcadabacadbbcddadddbacacdddcdadbacdbbaabcaaccaccabdbdcabacccbbbabddbbbccddaccacdbcaccadbcabdbbaaaccddacaadcaccbacacddacdadccdbccbddcbcaabbdbcbbacbddddbcdaadcabbdcadababaababcbdbcaadddacdbdacbbaabccadadacccdacbcbddadabcccacaaadbcadddaabddddbdcbbddcbbdabacdbaddbcaabbdbdadacbbcdddcccbcabacdddcadbddcbcbcdbbabcbbcddabbbccdcbadaacaacaccaadaacbbaacacbdddcbcabccddcdbaaabdbcbcccdccaccbabcdbcbdcaccbaccdddcdccabccbbdcacbbaadcbcadcadbcbabccbccdacddbdccadcdcdbccddbbcbbbdbddddccccdbadbbbcbccccabcabccbcbabaccbbddbbbbaccdaaadbbbaadaabbcbacaadacccaaccdbcbadaabaaadbdbcbabdcabbbbbbbadcbdaddadbbdbcbabbdcccddaddbadcadaccababdccaaadcbccabcacdbccabccbaccdbbbcbbdbbcdcbcdbbbcccdadaacbcdaadbbacbbbabacadccbaaccbdbaccaacadabdcacdadbabcbbbacaccbcaadacdbdadbdddcdbacbdbaacbbdacbddcabdcbdacdbbdbddbabcadabcbaaababcabcababbabacaabcaccbaacdcddbabacbcdcdabdbccdcabbabcacbacbabbbbcdcccbabbcbcdabdacacacbcaabdcadabbacdbbacdcbcccbdcdcabacadaadcaabdddbcadccbccdbdcdaaaccadabdaddacdcdabcdaabbacbaacbdcacdddcdcdbdccbccbdaaabcbcbdbdacbcddaacabcdddbbadcbbaaaccbbccadcbcacabdabaacddaddccbdacbaddbcbdcadbddbccaadcdbcadddcdbdaaddacdbcbbbcccccdcabcccbbcddaccdcabbcbdccbdaacbcdbabaabbcabbccbcccdcbbdbacdbbbcbbdbaacbbacadbcbcbaabbabacddccadcacadaadabdddabdbcadbbaacbbadcbbbdbabcdddbbacabaacccaadacacaaacbaddbaadcbabcaccaaadcadadccabcbcdaababbacbcccddbccdacaaaabacdcbdccbcadadaadaabcbddbbabadacddababababbcbbdcbaaaccdbdddcdbcdacdadbbbbcddcbaaadbbccabdaaaaccbccbaaacbbccdadcdbdddcbcddddccbaacbdaddcbcdcaddaadbbddcbbdcdcbdcbccaccadabdaccadaadbadbbbdcdbddbddbdccbaaadaabcaaccdbddcadacaadbddadddbbcbdacbbacacdddddbacbdbcaaaccccabcaddadadddacbdddddbadbaccbbbbdcbdabdacadadbdbadcdabbdcbbaddcdcabdabcbacdbcabbadcdddcaabcadbcadbdcdadaddaadabddbbbddcddcabdccddcbbddcddbcdcabbbbccbbaadacbdcaacabaddccccbacbaddbccadbddbcbacabbaabdaacdddcaadcacaababccdcacbadabcaacdbbbababccbdcabacbccaaddadbaadaccccdcddacddadadbcbcdbcadabbbdccadadabbdccbcccbbcbdcabacddadbacaaaaabddbbccdbbddabacabbdadddbbbddccadccaadbbababbdbbaadcdaaacacddbacaacadcbdbcccacabdaadaabbbdcabadadababdcdbbcbcbdcabddcddabadbadbbdaaabcddbcabddbcbdcaccadaaabdcbdccababbdcaddbcdacbdcacdbccbcbdabbddbddcabccbccdadabbbbbdcadabddddccbdadbbbaaacbcdcadcbabaccbaddcadcaccbadcababdabacaaccdaabbabaddadacadaaddbbcccbcddacabbbbbcbdcacacdccbbbdbcacabbdbcaccacacdabbddccccdadcddbdddacbcdabbbbddaddcacdbddcabadbddacdadbbdaadbbdbdcdcccdbbbcddcabccbddaabcbdcccaccaddcddcdbadabadbddddadaccbcdbcacbabdcbcaabababbcdcbbadcdaccdbcdcaaacadddbdcccbcdaacadcccabacaabbacccbbacdbaabcdabcaacddbaabdcacbbacccbbcaadcabdbbcdcdaacbbbbadbcbbaabacbccacadcccccabdadcbdbcbdacbbddbaadccdabddcbdbbbdbdccdddccdabbbddcdcdbbabdcacccacadccbaadcdcbbbabbcaadddddbdacabdbaacbcadaaccdccdadcbdcccdddbdddbcaaabbcddbcaddadcaabdcdabbbccdbbbcbcacaaddadaaacdbbcddcaadabcaabccccdaccdcbabcbbdcbacddabbbabbddcbcbaadbbdbacbaaabdcbdcabcacdbbabbdcacabdabaabdccbdcbddcbbdacddbcdccccaaacdcdbdcaaabddbcbcbcadbccccacacdddcbbaccaddcacdcbdcdcbdbaacacdaddbddbaddaabaabbcccdcbddaabcbcdbaaaacaddcadcabcbdddccaddbcadbacaaadbadcacbddbbaaaacddbdcbabddbbdacccddbdcbddaabdcabaaddaadbdbbcdaabacbcddaaadaaddccacdacacddbaaacadcbdddbddbabdabbaacbbdbaaaddcdaacbdcdabdaccddbccaabbbdadbcdbbcadbabbccdbdbabbcbcaacbddadcdbbadcbaaacbdbaccddcabddaacbdadcaadcdbbcbbcdabccbddaaaaddcbbcddddccbdacacbcbbdcadcabdbcdaaaadaccabdcbabbcdbbdbdcadddbddcbaadcbbdcdbdacaacbaabddcdcdaddadcdcadccaacdcadadbacbcabcacbccbadddaacccdaddcbbcbcaacabbcadadaaababddcacccadcabdacccdcadaddcaccaacbdddabcccaccdabbcacabdbcbaaadbbaacabdcdcdadbdbacaddbdaddcccadccdbcccbccccbdcacaddaacdbcadbccbdabccaabaaccdababdccbaccddadccccbccadaacbdcbaacabbabbccbaadbdbabaacbbbaaabbdbdaddbdbcdcbbdbacdaadaababaccaddacbddadabcabdddcacdccbdadbbabbacadbcbcbbbdbddabbdabacddaaaabbbbdadcaaadacbcdacbdcdcadbaaadbcaaaddbbbcaabbcacadccddabcabbbacdacaabbbbcddddacdbdbcdabbddacdbababcdabccbbcbdcddadbcdbbbadbbdbcacbcadcdabdabddabcccaaccbcacadbaaacccbccbaddbcccabababddbbcbaacdaddbddcbdcccccabaabaddcdbaaababdbcacacdacaddbcadbbacbadddccccbccbcdcbacdaccdcbccdaaaabbdccbdbabdcbbdaacdbcbcbbcbbbcaddbdccddbccdbdcdbabcdddacaadabcbadcdabbbdacdccbadcddcbacdcdadccdbbdcbbbdaabcacbcdddabdcdcdaaadccdaaaabdaaadbcdcdccbdbcbcbaacaccdcdadddacbccabcbbcdbdcdbbccddadcabaddcdbddccabbcbcdaabbadccacabaadbdcacddcdcdccbadcbbabacbcbccdcbbcbcbdddddbbbbadaaabaadacaabccdbbcbaacbdcbdbabdbbdadabadccdbadcabccbdbdbcabbdaadcdbacccccbaccdbdbbbcbcadddaddabbbcbdacbddcccbabdcbdbbbbccdaccbaaddaabbcbcbababcadcbbaabbcdabccdbababdcaaddbddacccbdddaddddbabccbdabcdaadabaccbaacbccbbcbcbbccdabdcdcaddbcadcabbccbdcdcdaabacdbcbabdddaadaddcacdaddbcabacddaabbcdcabcbadccbbaaadadbdcdadacacbbbdcdcaddbcbddbdbabbcdcaaaddcdadadbaaacadacddbddbddaabdcdaccacbbdcaadccdaabbaadccacccccaababdcaaadbdadbbdccabacaaabadccdcdcbcddacadadacdadbbbcbcdcbbbbdcdadabbcbdcaddbdddbdaabbaabdbcdbdbcbdcbacabcccaabbbbbcacbbbabcacdcdcbbbaddcacdcddddbcaddacbcdaaddadabbbcacccacdddcbccacddadcddabbccaadbcbdcaccbdbccdbddaadacabbbbadddadcdbcbcbcbbbabddcbbbbbbbcbcdccccbaacbccdaccadbddabbdadbcbddccbadccbdbadddaabcacbdbdcabbcadbcdbdadcaccddbdacacccbcabbbabbccdbcdbbacccbbaddddcadcaaadabbbbddaabcdbbddbacdaabcbdbbccadcdbdbabddcbdccbcbbddccdaaadadadcbdaacccbbbbbdcdaacccdcbcbddccdcdaaccbdcdbadaabddbaabadacbbdddcdadbcacdbaddababcdbbdbcdcdacaddcbcbdcdcabbabacaaddbdcccadacdababccacaddbcaaabddddcbccadddcccacddaacddcadacbacbdddaaacbadbadbcdadbacdadaabcddddacdababdacccbbcaaacbabacadccbcbcabbccbdaabcbacddbccbcbddcddbdddbcaacbbaabbacbaaacddaddaadcbbdddcaaadcaaabdabdabaabaaacaacbbadaaaaadabcdacaabbdacbaccddbdababacdcbcbdbcaddcbcbadaaabdbadcaacbccadcacdbbcbdaddabbbdbabcdcdcbbccccbacbaabcbbdabbdbcbcdbbdccbdcdbddcacaccddcdcbbdbaacbbcabccbddbaaddabcaabccdabbbaadabccadddccbbbdcacddbbcdadbbcccddabcadaacbcdaddbdacacbcbbcbbbbaccacdbbcdbdcdaabcbdcdcaaaacabaacbbcadcdbcaadcbbcdcacbbbddddbbccacccadcdcaddbaaaaaddcaaabadcadbbccaaabaadbcddccbdbabcbbcddadbcddcabdabdbddabcdcaacadbbdabcacdaaaadbadabbadadbdbccbbdacabadbccbcaacbadadbaadaaddbacdaadaabbdbbcabdbdaccadcaddaadcdbabdbccccbccbbdbbcdadbbbccdcdcbadbacadadabdcbabdddabcccbbccbddcbcbccaaaccdcabacdabacbdaabadbcbbdaaaadaacdddcdcdaddcbcadcdbbbbcbbcbbabadbccacdbdaadbbdbbacacdbdddabccdddddcdbddddddbddccbbadcacdcdbdbbadacdcaadbdbadabccdbaacbdbdcaabcbdddbdbcacccbaabdbadcabdcdbaddcddbbdcacbbacdbbcababbddcdccdcbccaababdaabdaddbdaadcadcddabbbadbbacabbabcbcaabcdbccacdaaabacccccdcaabcaadbbbcadaccabddabccbbadbbdccbadaadcdbdaccabddbaabbdbaaacdcbccdcbacadcccbccadbacdcaacadcdacdccbddbbdabdabbddcbddddabacadadbddbdcbbcadcbddbddaaabbabdacaddddabdaaababdbbbbbcdbdbcdcdccdcbbbaacacaabbcdbacabddadadcadabaababcdcabdbadabdcdadcdaabacdbcbadbddcaddbdcdabcbbcacccbbcbdbacabaabdabccccbaabbcbccddbacacbdadacadddcbbcabbcbdbbaabbbcdabcdddbcccacacaddababcbaddbddbbdadcddcccadbccdbaccaddcabbadbcbcdcdadaccbcaacbacaacbcaabcdabbaacbaabcbacbcbdbcacddbcbcccabdbdcdcbccccabdbaabddcaadaaaaacccaabbbadbccdddbcabcdacdacdbbdddcdacdaadcccadcdcdcbccdacbddabdacbdadbbddacaaabaccdadbacacacbbbccbbbacbbbbddadabdbbaaccababbbacbcdccbdddcabadabdbcabdabdcbccddbdbaabaccaaadcbddbcccdddabcdcbcddaacaddbcbdddadcabcccdcbcaabdcbcccdbcbadcaacbacbdbbabadbddcadbadbacbdcaaaccbcacaadbbacccbbbcddbbbcbdcddddccdbbdbbbdadacabadadbdbacbdbbacccbcccdbabcabdababbdcadbcabaddabdacadcdbdddcbccabbbbaacadcbabadccbdbcdacdaacbccdcaaacdaabdacaaddcdcdacadaadcaacdbdacbcabcbcabccdccdddaddcadacbaacbddabaddbbadddccdacadddbccbacadcbbbdadabcacaadbddacaddbddaacbbaaabbbddcacacadaadbddbdcaaaaaaccabdcdbcadabaccadcaadbadadadabccaccabadcccaadcbccaacdbadcdddcdddabbcbabaddaccbbdccdaaaacabbddbbabddadbddabcddadddaacddcdabbaadcaddbaadaadcbcdddbabdcbaacaacacabcbbdbbcdbabdcadcdbbdcbaacdaddddadadabbcaccdbcccddcdbbdadbdcaddccdccadbdbdcbabddcbbddabadadbdbddcacaaaabbdacacccacabdaaacbbcccddcbdabadbbabadadabadbcbabcbcacaccacbacbcddaabbbdaddccaabcddbcdabacddcabbcaadbabaddbabdbbaaadcabcbdabdaabbdabcadbdccababdaadbabdbbdaadadcacdcbaaacdbbadbabcdcaddaacdaddcbabddddcbcdadbdbbbacdbdbdccadacbbbcaaaaaccccaaaaddbaacbccaddcbdbbadcddaadaddcdcaadccbccbbcbbaddaacdcdcadbabbcbdccbbdbbcaabcbdcddcdabdccdcbdbabbacdaaadbcabbcadcaccabbcbbcdabadacdbbcacbbdbdbdcbbacdcadaccbabccaadcbabccbbcaabccdcdddbaddccdbbadcbddbbabdadbbaaddbbdbccdddcbbdabdaadaccbccadcaadadbddcdbcdaaccbaddacbbbabddcaccdacbaabbaccadabbbcdacdaacaabccadadddbddabbaccacacdbbdcbdccbdbabcdccdcdbabbbbcbcbacbccaacdaabacadcdddbaccbdcbabcddbbbbcdacdbcbcddaccdccaadbaaacbaaaacccccbaddcacdddabdacccabdddcabcaaaacadbadbcdbadbadbdcadbabaccdaaadddbdddcdcbcadbcadaddbbbacbbabbdcadadaabcacdddddcbbaddbacbcacabdbbcccdbcddadbdbbadcccbccdbabcbbbbdcccddbabdbbcddccabddcccdcdcccdcbbacaaabbcbdbbdacadbdadcbacdaacdbaadcbdddcbcaacababbadcdadacdcdaacdbcaaaabcdcdddcdaacdaaadadbaaddcaabcbccbbdbcbcbcddaabccdadcadcdcabdccdbabacbcabddcbdadcdcdbdcbccaadbcbbabdaccbbbdcbbbbbabccdababccacabbbcdbbccbabcdacbbbdabbbadccadbadacaabcbcbacaabdcddbbadcbdacdccacdcbdadbbccbbdababcdcdadbadbdccbaccbdaaaddccbcabacaabbaacbdadadabcbccdaaabcabacdadccbcdbbbbbdbcbbabdabccdbddcbdccccacacabcacbaaabbdbaaaddbbdbcaaccaddbccbdccbaabbcdbadadbbcbdacddbbbdabdcbbcdaaddcdcbaaadbbcdcdabaacbcaababbbdadddbbdacdbccbcabadbadbbdddbacaadbadcaadabababcadcdbbacbdbdcacbbdcdbcbdaababbcccacadcbbabbcdabbabcababcadadcdddbcdbcbadcdccbadbbdaccccabcaddccaccabdaacacccbbdaacbcabdacbcdbbcccaacbbbddbcabccaddcdabdbbcbcaddcdbcabcaddaaddccbdbbcddcbdbcacaacacdbcdcdbadabddbacaadaddbadcabcbdaaabacbcabdaacadddbbbccdbdaaacdcbbaaccadddbbcccccdddbdbbddaaadcbcacddabbacbdcbcddbcccababcdadbbcbcdabcbbbbbaddbcdbcccbadbcaccddcbaaccabdabccbcdbbdbcbaacbbbdaabddbbcbacacabaadccdcdabccddbcbcabcdadcbdabbaacacbacbcadbcdbbbccddadaacaaccacaddabdcaaccdbcbadaacdacaccbcaaaaddcaaaacacbdcdccbbbabbbbacbadbccbbaddbcbbbdbddcdaacddbaddbabdcbcdabcbaacdadacdacabdccdabcadaabaccdaadcddbdaabacacbdadbddbccabacbabbbdadadcbddbbdddadbabdadbdbbbccacbbadbddbabbdcadcbbcbbabaaccbbacaabdddaaabadcdabbdaabdbbabcdbddcbddacccaccadaccbcddabbccccbcccdcbdddbbccbccdbccccabcadabdcaccccabcdcbbbddcbcabbbadadacdccadacdbcbdcbbaacbbabcadbadaaacddddddcbbdcdbdddbdcbbadddcbaabddacadbdcbcdbdcaabdbbddbcababcaddaaddaaadbccdbcdbcccabcaccdbcccdcdddbcacbadaadaacccabbabcdabcbbaadbbdbbbdaadacbacccacdbbbddadbaabbabcbcdbbccadbccadbcccbdacadbcabaaabcaaabadbbacbcdddddddbbaadbbbacaacbcccbacdbcbbaaacababaabddcacbbacbdcdbabbccddbabdddadbbbbbcccdbaccddbacdcbabacaccdbcbbacaacaccbabbabbbdabadaccccabddacccdddabcdbcddcdcbdbdbdbaddabacabddcaccbcbdacddcbbcbdcdcacacdcaabcabcccdbcbabbacdcadccabdcbddadddcbcbdadaacbcabaaaadcdaabbdbdbbaccaaabcdccabbddbaddcccabdbaadddddbbaccbdadccaaacbacaacdbcabaaaadbddacccbbdcabaccbbbdbbbabbddddaccbaccddcbadbabcdaaabdaabbcdcdabdcbdbacdadbacaaabbcccbdbbccacbdcbccbccdadacaabcabddbaacdadaacbbdbccddbadacdddaddbcadbbbdacaaaadcabaacccbbbdcddccaaaaabcdcccccabdcdacdbcbccdddaaddbbcdadcadadaacbcbabcaddbcbbdacaadcdcdccabcbbabccabbdccacabccbbcababbdccddaadcbcddccacbbbaabcaabadcccccabacbbdcbccacbcbbccbacbbbddcabadadbcbabddbbcbbcccabcddabddbdddabddccaabdbcddcaaacabbaddddbcbadcddbaacdcccddcccadcbbaadbabddbddbcdccdabdbdddbbdcddccabbbaccbddcdddbdcaaacaccadcddcbabbdccdbbcbdbaadddbcbcabcbdbacdaabbcacdaccbabdcdcacaacaaadacbacccbaddcbaaacdabcddbcddbdaddccabcbddabdcddaadacdabbcccaccbcadbdbdcbbddcdbdbbcabccdbadbacdcddbcbdcbbaddcdbaabbabcbcccdbcdacdadcdddacaabdcbccaddabaabbdcccbbacabcddbdbabcddaabaaabcccbcadcdadbddbdacbccbadaccdcddcdaaacbbdaadcacbbacdaadbdaabacbddcdabcaccdcaaaaabbbbabbddbabbdcdaccbddacbbbdaacaadaddddccbbaabdddddbcddabbbcdbadddcddddddadacbcacdababcdcdaccaabaabdbcddaacabcabadcbacbabccaaccbbdadddcdaacdbaabcdaaccbababaccddcdcdcdabdabdbcadadaacabccdcdabdccdcbadaacdabcdadcdaccbdacaaacddddbddbbcacddabaddcadcdaacbcdbaabbdcacbbcabdbaaabdabcbcddccbdcaddbadcadacbaabdaaaaccbabdbaaacadacacdacaccaddbccbbbcbdcdcaddbcadcacdbabcccbcabcddcabacdbbbadccbcbbdacbddbdbcacdadbadacbaabbcaccacabbbaadbdddcdaaacacbadaadddcbbbcddcaddcaaabdcbdadcbdcdccacabdbbbcabdcacdbacadacbcabdacbaaacbdbadcccacaccbbdabcdbdbddbabadbbaadddbabccdabbaaacdcdacbcbabddbadadccbcbcabadccbaaacbcddbcacaccacadcbbcabbcdbbdcccccacdbdadccbcccbcbddbddbdbcacdaccdaccbccccdabcadcacdcadbcbbbababcbdcdcccaadabbcbdacacbdaaabbdcdcdbaccbbccbdabcacdaddbdbcddcadcdbabbadbbcbcbdabacadacbaccccbbaddbaadccddabcabbadbcacbddaabcdcadddbcbbacdaccabccdbcabdccbaabcddcdcdacdcababdacdadbddbbbabbbcaaacaaacccbdbcbbbdabbccdcaabbcadaabdccaccdacdaaabacdbcccdbdcaacadddcbbacddabbabcbcacacbbcdccdabbbabddbaaccabdbdcccbcbcadbddaaddacdabdadbbcaaacadacbcbbadddcdcddabbccddadcdabcbaacbcddaadbadcaabbcababcccadadabadbbddabcdcccacabaabdaaaabdcabaaacdcbabbccbbbccbadaaaabcdbbaddaadcdcbdccdcdcaddbbadddbdddddbbaadbdcabcdddcdabddccadbcbddbcabcdbaccaadabcbcdadcddddcbdbababbbbabbcabcddddacbbdcabdabbcdddbaccaadcaacadacadbaaaddbcaaddaaddaacbabbbabdcdbacdccaadadbabcaddcbabdcdababaaadcdadbdbbbbacaccaaaacdcdbadbcbbdbbbbaaabacccacbdccccbaaacbcdacbcbbbccdbabddbdaacbabaddbdcdcadccdbabdcdbddaaabbacddadbcddacaccbcccdaddddbdacdacdccbdbdadbacbcbbdabbbdccbcacaaaabbccadcdccaaadcaccabccaccdbddaaddcdaabcbdadbdadcccddabaaaacddcaadadddbbbabaddaaaddbbddbbcccbdacbabdaabdbbabbadbdcdadcbbccbbaddadcccccdacaaddaabbabacddadbabcccacbcccaddddcdbbbbbdabbcdbacdccbabaaabccbaaddbcdadddbabacbaabddbacaabccaabccadbcccbadccdcbdabbabdacabdbccdddabccacadcacbccbadaccccaccdccadbcabbdcdacdbccadabadbbdaddacbbbccacaadabadbcccdccdbdbcddcdabacbcccabacbdacbdbdbcbdcaabdcbbadbbbacaabbcbdabbbcbaccbcdccadcbaacabddabbdadddbacacbbcdcacbacbdbabcaaccbccbbbdaddacabdcabdddcddbddcbcddcaabaccadaabbccaaadcacacbdaacaaacaacacbabadabbbdbbcabaddcaabdcddbcadddaacbddbdcabdcdcbcccdbbcdddabdaccddcbaddbbcaadbdddaaabaaabcadadddcaccdbcdcbaddbabccdaccdccbbcdcccbaabaaadddddaccbcdaaccccbdcbcdbadbbcdabcdabcbabdaaadccdaacbbcdaacdcadadacbacacddadcadbbcbbcdddccbdacccacbddabcddcbbaaaaaddbcdaabcacadcadcaddddbcdcbbccbbcdccbdcdadabdbbbdccbbdddcaaccaadcdcadbdbaaadcbacdcdcaddacdbdabcdcaddcabbddccabcbdccabbdcdcdcbbbaadbbdddddcbadbccaadabbdccababbbbabbdcbcdcdbccccbadccddacacadcbdccbcaabcaadcbadbdcaabdaaadcccbcddbbdbabcdbdbdcbcdbddbabaddaccaabbcdcdcbdbaadacbbdbdccadaddbdbccdcaacbccdacbcdcdcbbdccbdcdabdabbcdbcbcddcbaabcbcadcdbddbbabbdcacabcdaabadbaabbcacbdccaabdaddddadaddccbdddbcbdbbacdbaccbabddadabaaadbdbabddcbbddbacdabdbbdbabccbdccdbbaabababddcdadddacbbdabcababbcadacaaaadccacadccdcbadccadcdadbcdbabadbaaaaaabcabdaadbdcccdcbabcccaddbbdccbdddbddaddbabbdcaacaadddbcdcaddbbdcbcddbbbabcaacacbbcbdcabadcbaddaaddabaddadbccdbdcadcccabdcccaadbacdddabdbbddbdabdccbdddcacdadacbbbcdddadddcbdbbadbddcdabbbcbcaccbbdbcadbbaddcabdabdadacbcddbbbdbbaaccdabdddcdbdadabdbdddcccbaddbaddbddccdcbaacacbcbcabcadacbddbbdcadbabdacdcbabcadcccabbbabbcdccbaccbaacdbbacbdaadcbccdcbddbadabdccadaccbcdadadbccabbabdbbbbbddbdbcddcdcaddcbcadddaaaddcbdcdcbbccacdddcbbdacddcbabbcddacdcdccddccccdcadbabcccbacadaaabcaabbdacacddcddcdcbababcacabababcbdabcbaadcddaadacbcbadadbcbdcbdcdabadbacaaddbcdbbabccacbbbadabaabacabdbaaabbbbdbaacccbcdcdbdbdbadacdacbaabdcddaaabddaccaccbbdadcbddaddaacacbaadabbbcbdabcacadacbcbacbdcdbbcadadcbcbcbbdbbdcdbcadbdbbdcaaaccdacbadbcbbaccacaaccabacbabbabcdaaaddccdbbbddabdbaacbddcbbbacacdcccaccddbadbabacbddcabcacaccdccaaccccdabddbddbbaaaabadabdcdddbabddcaadbcdabacacdabadcdbdbdbbadddcbbcccbadbbccbacbbdbaabdcbaaccbbbcadcdbbdddabdccdacacdcbabdcadaaccbbdaaccaccadbbbdaabddadbbadbacbdaccbaccdbaaaabdddbaabbcaaccbbddbcaaccabdbadbcbacadbdcbbdcacacaccbcdabaaaacbdcabbcbccabadaabcaadcabdcbdabbacdcdadbcdbabaccddccdabaddbbbadbbdcbadaabacdcbddaabbbbddadbacbbdbadcdacddaaabaabdcdcdddaaacdbcdbcadbccaaacaacaddbacbaadadbaddcccddccadbbbaaadaaabcdcbcdaccbacaabcaddcdabdbadbdcbbabdacabcbbcadbaccacbcdddaabdbcbcdbccbdadddcaccaaaadbbaaabdabbbcdccdccbcddaacbcbbacacbbcbaccaccaaaddababdbabdccdcddbaccddddbcadbadbbcabccacdabbaabbdbadbcdadbcdbaacdaaddcaabdcdacbdadbcaadcccbabdccccadbbacaadacddadcdddabbdbccbddccdadbaddcdbdddbbaadcadaddacbcbdddadccdbaddbddbbdacdcbabaccdcbdadbdcbdbaabcddbacadaddabbcaadadabdbcacbcaadcdbaaaabddadbcbabacabbdccbdaccaadaccbaabbcbccaacbcacbcdcbaabcadccdbaacdbacacacddbdababadccddbbbaabbbbbadaabbbdccabcadcaadcddcbdbdddbbcddbbdcadcdbcbadcbdbaccaabddbdabbccbadabcdcacaddadaddddcdadddaabbacddacacdcbaccdbcdccadbacdbadcbacaccbaaaaccacddbacdadbcdcacacbbdcdaaadacadcabdaaadacababbcddbbbcbccddacddbabcdddccddddcbdcaacbbadadacbdabcbacabcaaddcaccadcdadacdbbcaacddadcddacdbaaabaccacddadcddcdaabadbdacbcbbcddcadbdbaacaaddcadbcdcbdbadbadacdcbabcddabbcbbbabddacabccbdaaccaccaaadcabbaacaccbbdddacaccdcacdbcbdcbadaabcdabdacaabcbdcbcbdaccaacdcccabcdbddbdbccdcdabdccabaaacbcabcaabdccadabcacdbbddcbcdacadcaaadbbaabacbdcbbbadaabdababdcbbcdbbdbacaaabdcdabbbcbdbaddabbcdcddcbabdccbdacddcdccdbbdadcdadccabbbcbdbcdcdadcaddbcbdddaaacbcccacdbadbbbdbbacbdaacddccadbdaaadbcabbccccccdbbbbdbbababadcdbcccdcddaadbcbaacbdaccdcababadcdbaaddaaaadabbbadbbcacdcaccadacdcbacdcbbadbbadccbddbcbcdcbbbcabaabcbdcabbaaabcbabcaadbcaacabcdccabbcdbaacdccaccaddacbdcddbbbbcddccbdbbabcccadbacacaddaabdbdbddbdabccabacbcaaaabdbacbbbcddbbdcbcdadbccabcdbabadaccdbbaadcdabddaddbadcadbacdaabcadadadddaabcaddaddbbdbdcdabdcdbaccbddcddabdccadcdaaccccbdbbaacdcbcadaacaabcdbbccababcdaaaddcbcacdacccbcaacaccdcdcacccdacbbbabcbbbdbbdbbcdcddadbcaaabbdabcccbbdadcbdabbbbbbddccbbdcdddaaaababddcbdaacdddbbcbcdccabdabdabbdabdcccacdbdaccadddbbdadadababbdacaabaacccccacbccbaacbccdcaaacddaaababaabbccdaabbdcdcdbaadbaabbccdbdbccdcbbddaabdbaccddcddaccabdcaddbaadbbccccadbbdacdddccaaadcdababbcaaacbccacbdabdacabbcacabdddbccabbcbccdbdcbaccbaadccbcbcbaadbccaccabddbdabcabbacadabdddbaadbbbcdcbbbcdaacdcdbcbababdccdcadddbcccbccdbacbcdcdcddcbdacadbcbdaaabcacbdddddbccbdaccbddabccbaccddabcdbdaabdbacbddabccaaabbaabdcdbadccaabcbcacddbadadbaadaabcaadaccdbccdbbadcdbbabaaaabcdbcadacdddcbacdacabaabaddbbbdccaacadccbdbdaabcbbaacccbcddbdcaaadbddacbddcaaabacdccdbcdcbddcbcdcbabccabbadcdabdbcdbcbcacdcdbdabaacccabddadaddbdddacabbbbdcbbbbcbcdacdcbcdabbdbbcbadbabcbadadadbbbbbababdccabdbddbadaccdababdbdadcdacdaaddcbcadcbabdbaaadcdbbaabcbdbbccaaaddcbcbbbbdddaaabcacccdadccbdabdacaabcbadcbdacbddcdabcbbcdbbccacabcdababbcddacbbcccccdadcababbabbbddcbdcabcaaaabaadcbdcdcabaabdcbccbbcddbdcdadaacabbddbacccbcddbddcdcbbbdcdacaaadddbbccbdbaabddcaccbabdcabbcccabcabbcbbbbbdaddaacbbaadadababdcabaaadbccbcaaadddddbdadccdbdabaaadbbccabbbcabddbbacbcbdabcacddaadbbbccabcaddbbcdadbbcdadcabaccdabbcbcabcacdbacdcbdaacbcbacadcacccdacbcadbdabbcbdbdaddacbcadacaaacbdbcbdcbddbacdcaaaaababbaacaacddbbbcdadadaacdbcddbcaaabcabcdcbdccabbcbdadaaccdcdbacbccbcabddcadabdbbcaadbabbbabccacbcbddcbddadbbdbcdadcccccadacadbadabccbdaddacddbcaaaadbddacdcbbbadbcbddaddccabcacbdacbddbdbcdcdbbcddabccdccaabadcdbbabdacaababbccaabddbcabcabcacbddacacdcaaddcddcdbbabcdbadbacacdacacbbacacbbcacadccbaacbbdcbcbaccbcaabacddbccaccadddbcdbcbaccbaddcdcadacccdabbdacbdbbcccddacbbbaabbdbcbdbdccbaccbcdbddaccbabaabdbdbcdccbcaaadcadaaadaadcdabbbcaddbcbdaddcaccdbcdddacbaddbbcabdaddabbbcaabdccadcdbaadbdbcdabbccbcdcdccacaddcababdbbdacdacbcdcacdabcacabacabcaaadcadaabdcabbbdcddcababbbdddabbccbddcaccdaccacdccdccccdaabdacbcbbbabbdcadbaaaccdcccddaabdaaccdbcaccdbcdbddaccadcbbddaadcddaacdbaadbabcdbbbacbabadabbbcbbbadcdcabcbcdbdacaabaaacaaadaaacaadccdabbdacbccdbcdcabddaacabdbcdcbaacacccaacccdccbcbadbadacccccaccdabcdcacdbbdaccbbbccbcacbdddbadadcbabdaabcdcdbbadaaddcbcadbabcbacccaaaccbaadbbbadadbaccbcbdcbdaaadacaabcbdadabcbbaccdbddcdbcbddabbbabcacbcacbbcbdddcacaacaddbdccdbbcddbdadaabdbbdcdcdbdaabaabaabdbacaaadccaccabaadabbbbdadbcdcadaccabcdaababccbaabadbcbbbdcacdaaadddcbcabccbccdaaaccacacaacbdbcdcccccbdaabbcddcccadbadbddaabacbacaaadbcbcdbbddcddcbadbbcccabbdcdacbdbabcccbbcbadbbabdcbdcddcabdcbcaabcdbaacbcbcabdddcdbbacadbabadccdbbaccdbbacaabaacdacaddccbbcdaadaadcbdcccbbaacbdbddccbadcbaaccabbbdabdacdbcbbdaaabadbbddbddcaacccaaddaabdadbcbaadccabbabdccabddabbdbdcabadbddbcdddadbcbdcdcaacaaaddbdbbbcdadcabcabbabadcdddcabaccddbcdcbcccddabbcbadadbcbabadbabadbaccbdcbaccbcbbdabcbddadbddcbbbbcccacccdcdaabdbbdbcadacbacdcdaddccccdabbcbabcabcbcddcaddaaabcbdccaaacdcabdddcccbccacbcbacdbadbbaaaccabcabcacccbabdbcddacccaadbcaacbccdbaadadabdbbcabcaaacdbccadbacdbbcadbcdbabbdadbcaddccdcadabccacbccaabddabdacadbbadadadcbacbbcbbadbbabbcbbadbabcabbadaaaaabdddddabcbacbccbaddbcdacdbcddbbdcbadcbadaaadcccdcdcabdababbadaacbadcddcadcdadbdabcbacbcbacccdcdbcabaaccbaccacacdcdabdccabbaccbbbadbcacdadbccabbaaccaaadacbadbabdbbbdddbdbbabadadbbdcbabcaccddccdbcbaacdcdddaddbdbbacadadbabbabdddbdaacbdddaadbcabddddbdacccbbaaadbcccbdcbdbcadbdcbbcbdccdbbdbdabdaaaadcaabbaadccaccdddbabadcabadbabcaabcddcabbdabadadbbdbcadcddabdcddbdacbabddcabaaaccabccbbabdddcbcadcaccbbcabcbdacaccbcdaacbabccdcbbcdbadcadaadbddacdcbcdccdadabdbacbadabcdacadaaccdbabbbdacbbcbaaccbbadddaaadcdbadcbcacbacdacaccbdcaddabbaddcaccbbcbbcdcdbdbcccaaadacabdcaddacaadcdcbdcabdbbcbabbccabbdabdccdadacddbccacabdadcbadcbbcbbcbabdccdccadabdbbbbabcacababcbcccdccdbabadacbdbdbbcbcdaacccbbcdcaabccbbbadccccbdbdacbdaadcabcacadacbaccadbbcabbbaabdbdbcbddbbbcdacbacddacdbbbbbadbddadacabbdddaabbbbbcbcdbcaadbccdbccaadcdadcddcaaabdabbbbccacabbdbcdcbcccaabddcdbaacdadaaadcdaadabcbcdacdbcdcdabbacaacdabbdcdaadaabcabaaabbcaaadddaddcabbcabdcbddbacaabcbbccacabdadaddcccabdccaadbdcccacaabadacacaaaacbbcbbaabaabbddccbccbccabbdbcabcbcabcdccdccdbbbaadccbcbbcaabdcbcdadcbcbcaacacacbabbddadddaadacddcdadabccaadcaaaabdbcdacbaccbccdacbadbdbccaccaaacadbddaaababddccdbbdcbcabacdbbddbbbacccdaaacbacbbcccaaddbbbbccaddacbdacaadbbbcdbbcbbbbbbcdaccabbcdaacaddccdbccdbddcdbbbaacbabadddbcbbcadbcdbdcccbaddadcabcbabadbdbaccbbdcbbbdcabdccbcacaacdcddcabcaaadcaccdbcadaadacbbdadbbbaddcdcbbbabcaabbbacdacbaddcbbadcbcabcbbcdcaacdbbdddddcaaaddbccdcabbdaabdbdccaddbacddbddbcbabdaaddcaacbaadaaaaadadaaadbaaabacbddcaaddcadbcbbbccadccdcbdbbcbdbbcaddccbacacdaacdbabddcbdbbadcadadcccdbcacbcbaacbcabdbcdbccdcdccddbbdabacdccacbbacdbdbacbaacddddcdddccdacdddbbcbacdbacdadacdcdcbabbadcbbdcbbdbadadadddabbbbcabaaddaaccdbabcbabcddcdcccddbcbdaddcadbacdbabaabdbcbbdbbdaaaabaaadcdcbbadbabdcbaabaccdcccbddccaddbbaddcdcadbbadabccaadbaddabdcdcabcbcddbbdbcabaaacadcdcabccaaaaddcaccbbbccadcdbdbaadbccabacdcbaaabadddabccbabcbdacadbbdcbbbdbcbaaaddacacdccbaddcabdabadbcacdcccbcdbdabcbcabbadaaccdadaddaccbcdadbdcbbbbcdcacaaacccaadcaccbcbbdabdabccaaddbccbbcbcdabaaaadabdadcdbccdcbcacbdbdbdbbcdaaacabbccaabcadbdcccaddbbaacaababdbddabccbcdabdcdcdbbcbdaccaacbcaaccacdaaabbddadbbbaccddacbaddbdbabcadbbcbdccbbcadbdcdbbabcccaabdcbbbcabbaaababbccadacbdcbcccaacaddbabaaddabcabaddccaabcbbdbabbdcbcdccbccabaacbbccdadcdbabaaaacacbdabcbdbadacabccbddaccbaabcbdcacabacbacbaaababadbacaacaddcacbaadcbabacdcaaabaddabbaabaadaadbbbacdacbddaabcddbcbdbbabbccbdbccdcddadcdcacbdabccdbcaaccadbcadaacbaccacdbaccdbabbabdaacddbbbaadacdbabbcacbbaccbdccbdcacbdbddccaacbaddbddcddbdaaccdbadcdacddccdcacbcbdbacdabbcdabacccaadcddacabaaadcbdbddbaabdcbddcdcbdcbddbbcbacbdbdbaddddcbcbddadbbbcdaacdcccdcddccabcddaadbbaacdcdaaacdcdddabdbcccbddbdabacdcdbdbaccaadddcdacdabbbbbdabbcabaaaddbbbcaadbdddbaababddbbcaaacadacbdcaacaaadddbcddabcdbcbdccdaaddbdcbcabacdababadddaaabbbcdcbacabcdddbbdaccaacbdacbbdcbcbdcbaaaadbabdbddaccadbadbbbdacdabbaacacaccdcaabacaccbcccccaaaadcbaacccbdaccddcadddabdccccaacbbcdddbddbbdcbcdacacbbdbbbdacbbdadaccccdaabbdbdbddcabcabdbcaaabbbbbccdbcdcdadaadbabdcdcdabdabbbbdadbcbbabcdcdcaddcabdaabbcddcdaddddccdadaaacbbbaaabcbdbbbbdcddcbcbcbdbaddacbbbbcdbcbbcacbacacbabcdbcbcbbbacadbdbdcbdcbbcbaadaacbacbadbdbbabcbdbdccccdadbcdcbbabacacaacbddccbddbdadbabadcdbabdaaddbaddaccdccbdcddddcdbacccdbaddacbcacbdbabadddcaaabccaaddaddbddabdcdcadbdbdaaabaabbdabacdabbddccdccbbbbbddbdbddbaadcbcccbcadbacdaabacbacbbddbbdbcbaccbbcbacdbbaadabcbbaabbadaddccdabdbdaadcbaadadbcadadcccacdabaaaaadadcaabbdbddccdadccbcbadcdcdddabcabaabacbabcadbccbabacbcccadcbcaabdbbcbabbabcacdcadabaacaabccdabadaccbcbdccadcacadcacabdacdbacaccaaccabccaccdcacaacacabbabccadaadcabdaaabbababdaaddaaccbbbbddcacdadaacdacdbaabbdaabdccbbaccaaadddaddabbdbdaabbcdbbdcabddaddcadbcabadccabdbddadbadcdabdbcaacdbdadccbaaaddbcddcbbaaddcbdddbcddaaccbddcdcbadabaadacccaabdbdadaadbdcadcbaacdaddbcaacccdcbcbcdbccaaacadccaddcbdddbacaadbbdabdbaacbbdcaadbddadaddabbddacbcadcdddddbdcdabaddddabaddbbbadcbcccadddaacbcddcbcddcbdbdddccacbaccbcccdaaaddcddcbadcaacddbdadaacaddbcdcdaaabcbdaacaddccdcdcbcbdcabaccacbbdaacbdbcabcbbabcdbcabaaaadacbbcaacbbabbdbbbbdcbabbdaaddcbcbadaadcddacbacaaaabcdcdcbaabdbdbaddabbadbcbdacacaddaaaacccababaacdbdcbbacdccccdabcbdadacdbbcabbaccbacbbdcddbcbcdabcccaababccbcaaaacbdddabaadacadcbcdbcbdddadbdcadcbdcdadabcdacababbdacbbacdaadbdccabcdabdacdabdbccbacccbaabaabadacaacbdabacccbdbcdabcccbacaaaddabdcddaacdcdbbbadbbaaabbdbdacdabacaaddabccaabdabbbdaddcbbdcdbcbbbdacadbbcbdabdbabcbcbdbcaaabacccbbabccdbddadabdcdacddabdddbbbcbbcdacdcacbbacbbbabdbbdcccabdcdadddbbbdbbcbcdbdcdbcccbcaaabdddabbaccbdababacaaaddbdcdaaaadadaccaababbbbbbbcadcdcdaccbbaccbaadbbdcacaaababddbcbbbbdcdcbaaaccaababccbddbcdacdaccaabddccacaabdcbdcdbadabdcdbadabaccbddbababdbddcaddacaacaddbdcaadbbadcadbdabddadaaccadbcbbadcacacbcaadcadbcadaabdbbcbabbcbdcaacaaabbccbbbccbdbcddbbdbcddaadadbcdcdbccbadbacadabadbcaadbaddadddccdbdcbadcdddaacccdadbaadccbbbbdcdcabdbbcabbbbadbbbaabaaddabcbdadccdbcdbccaadbdcaaacaaacdbcabbcbddcdabbacadacaaddaacbaaddacdcbaaadccaccdaabcddacaabbbddccccadccbccbbcbcabdabacbadbdccbdcdaadacdbcabbdddbbadccbcaccdabbcbaabdacccccdcbbbcbbabbcacccabdccaccdaddddabaaaabacddcbcbadbaadbbadcadacbdacdbdcbcbdcdacabdcbcdaccdaabbddbadadcbbcabbcccdbddccbadbcabccbbbcaccadadcbaacbabbdcbccadcddccddbaddbdbbbcbbbabdadbbadbacbbbabcaacdabbabcbacaaccaadcdbcaddacbaadbaacddbcdacbbabdaccdadbbadcbddcdbdcbadbdcdcacbcdbccdadbcbaccacabdbcddcdbbbbadadcbcacdcdbcbdcddcddbadbdcacacddbdcbcdcaddbbdbadbcadbcccbbbbccdbbccccbcdcbadcddabacbbdcdadbadadcdccbacccccbbddcbddaaddcabdacdcdcdadbdacbaabcdbdcdcddaaddbcbcbdbdacccccdcdaadaadcadacbdcaccccbcdcdbacaabcacbbdbaddddadbabcadddddbcdbcdcabaabbbdcdadccdbbddadabddcaaaacaaddddaabcbadaacccccaacacbccccbcdccabaacbbbaddbdcbcbcbbadbbcbaaabbbcdaadabdacacbaddcdaacbdbdabadcadaddbdacbaabcaccbaadcabbdaadbbcbaadcacaddcbcaabdaccaacdbddcdabcacddabcdaadbacaddcaabdacdaccdbbbadaacdcadcacbbacabdaccacbcddabcbdbaccdddbccacdbbaccbbddcacaddaadabcabacbacccbadbaabadbcdbbcaccbcadbbaaddacaacacaccccddcaccaccbabadbbbbdabaaaadaabacdcddccbabbbcaadcababccbdacacbbddddcdacdcaadbabddcabadcbcbaaccbcccccccabdcdccbacdabccaacccdcccdbdbddcaddaaaccbdaccabcababbabdacbcccaaadadcbdbbbcdbdaaabddbbdabcaaddccbddaabcbacbbcbdaaacdbbddbbbcadbdadcacbbbbbcbddcacccbddbbddaaadcddaacadaabaccbadbbddbdccdabcbdddbbbcaddbbabbddaabdacdbacbbcbacadcdbbabadbaabddbdadcdcabbbcbcbcbcbcadaccdaabddddbccbcbddbbaaabdacbababacddadadaabccaadcddbbadbadcdcacdcdccbbccabcadccaadbdcdddcbaacccddbbaccddccbcbdcdaaaaddbaabbadddaddcdbddcabcbdcacacaccdcbaddddbbdddbcbabcdddaccbccaaadabbcacadaddacdabbbcacadbbbdddadcbadaaacbcdcbbdcbcadbbccaaccbdbbcadcbaabdcabccbabccbcbaabddcdcdabadaadaaccadbbcaaccabdacddadabcadabcccccdccbaaaccbbaacabbdacdbacabbadccbcbbdcabbbccadcbdaaccbcbdaddacbabbdacddcddbdaccbccdbabadaccaacbbbcabdbcadbdcaaaadbaabadabdddddcdccbbcdccbadcadcddbbaddddbaadcdabaabddaacdbbaccaabadbaddcbacdbddadcbcccaaadcaccbdbacbcddabadabdadbbccabcdcdcccccaddcbdbadcaddbcbbdbdbbbbbcdbcaddbbaacbabbcbcabaaddcddcacabcdacbcdcddcccbcdbbdaadbbaccccdbbadadbddcacadabcbdbbddcdaddadaccabddbacbdaacccacbaaaabcbbbdddbddacaabbcbabdddccabccdcaacdadbcbacccbbdadbcdaabcadacbaadcabcbcadacddcbbaaddaacdabdabdbcdcdcabaabdcbbacaacccccdddbdbaadbdbacacbcaabddbacadacdddababbdbaddaadddcaacabdcdcadacccadbcbbddacdcccccbccdbccaaabdabdadcbbcaacadbabcaaddbbddcbaaaccbcbacdccbaccbdadadadbdcdccbabbdbbabdaaaddbaddadbaccddccddbacaababdccddacbaddaadadadbcaacddaaddbbbdadabaddacbbdcbaaabcabcbdccbddbdbabdbcababccbbbdbdaadcaddaaccaccdcbdbabbbdcdbcadbbbbdbddabaaddbcbddcbbcdabcadadaddacdbdbdccddbbbadbdddcabbabddcccacacbaddacdccddbabbbcddbabbbdbdddbcacadacbdddcdacadddcdababbadcdddcbbbaaaabacbbabdccbdddcbcdddcbdcbdbccbbadcbddaaaaaccbcabcdbaccaabcbddbbaaddabbaaadabbdcdbbccabcaaccdcccbdbddcabdbcabaabbccbcdbbbacaddddadaccabdddbbbddbddbbdacbdbddabbdadadadcdabcadddacacbabdbcdaacdabdccaaaadddaaacbdabdaaadddbbacccadadbbaaddddadcbcaddbccbdcaadacacccbcdbcdbacaddaaccacdbbbbdcbabdcacbdaacaaaabdddacadddcdabdadccdccbcdddbcaccdbdcadccaadcaadbbabcdbadbdbbccdbbdadcbacadaacdcaadbdacacaaabcddbdaaaadacddbccccacddccbbbdddccbddcbcccdaddadabbadaacbcbdcaccdbabbadccbaacdbacdadbcaabcbccbbcbabcadababcdcbbadaddabbbaabdcabccbdbccbadaddbdaacbdbbaabadacdddacbbdcbaabdddaddcdcbcbbcddaadccbabdcdddcbcadbddbacdcabacbaabdcbbbdaabcbaabcbcaabddddcadacdadbdaacdaaaaabadabacacdbdacdcdbabcbabdbbccbbdcabcacdbddaddabdcadadbdccdbdaacbabbdcddbccacdaccaaabacaadadcabdcabdcadbbddddacaccbbbcdcdbddaddabcacabaadcbaddadaccccdbdaadccabacbcccaccbcaaadacdbaaccbaabbbbabccadbbaacdbbdcdcaadbaabdabdbbaacdbcbbcdbdccbbbccdcadbcbdbbdcbccbbbcbddadcdaccdacadcadbbacbbabdbaabacacabbabcdcdabdcabaddadadbadcccccdbcaaadbddabbbaabcccdadbcccbdcacadbabbbbbcacacaaacdbcababbabbccaabbbacdbdadabddaccbabcbdcaabbaabdacaabdbaaacdbadadadbcccbbdddbccbdbbcbccacbbaadbcbadbcccbddbadbbabbcaadcccbddaabaddcabcdabcdcbcdcccacadbaabadcadadbbaacbaaaadbbbabcabcbdbdbdbcbddbaabccbaddbccabbadbaabbcabacbdaccdabbbcdabbbdccdccadaccdcddbdbbaadadacccabcacacdadaadadbacbaadaaaabcbacaacaccacccccaccadcaabbbbccbbacaabdcdbadbdcbcabadddccdcbabbdacbaddacdaaaccddaccadbcddbccbcbdacddcaabdbcabdbdadddccacdbbaababccddcbccabdddcacaddacaccccccacbcaaccdbcacbdbbacadabcaccacdccabbcbccdddcccdadcbaaacccbdbdcdbabcccbaaaadbccabbdacbaadcaacddbcbcdaacdbcbdccaccddcadddcacbcbccbcaaacdbdcbdcbabcccbdaaacccabccbbccdacdccccdacbbcccdcbacadcbaddcaabbbbdbdbdbdbddcccbadbbdcdbdabacbcabcbabaaabccadcdbbaadabaabcbaabcbbccdbbddcaaacabdcdcdbcdcdadadbdcccadadbdaddcdbdbccbbdbbaaacaddbcbbccbacbbbbababbddcabdadccadbbdbdbcadacbdbcbacbcaaddcddbbbbacdddacaabcabccadcaddbbbbcdbddbbacdcddabbacaadaadbbccddadabababddabcddacbadbbacacbaaabbcbddbdcabcccdccdbddacabcdacdabdadbdbdcaabbdcbcaabaaccacdabbdbacbdccdccbdbabbddcaacbadacabbcaacbddabdcdacddbacccbdbbdcbdcddbabdaddaaabdbcddbdcbabbcdbaacdacaacccabbbddacdbcdabaccbdbccbdbacacaabcaadccdbcdddcabaadbacccdacabcbaabdcbbadadbccbbaacabcbacadbcabacbcdaaacbcccabaaaaccccbdbccbacbccbbbddbcbcaabcdaadbcdadadcbadddbcdabbbbcbaabdbadbbdcbbdabbcdddcbcdbdaddddbbadcddcbaaacaabbcacacdcadcbcdcddccdccbbbaacdcbacaaabadccacadcddcdaddbccaccdaadcbcdbdcbbbcaddaadcccdbdabdadaacaadbdbbdccaccbdbbdaccdacccbccaccdccbbbadaaaacdbdbbdababdacabdadadcbabcadaaacbbbadbcbbbbcabdbddbadcbdacddabcadbadccaadcdbddbaadbddcdabcbdadcbbbaadccadbbacbdcccccbdaddbabbabbbadaadaccabddbdbadadcdbbbabddcaccaddcdaadacbabccbaaaddaabbbbcbacdbadabcdcbcacadbddadbbbccdacadaddaadbcbbddddadddbbcbbacdadaaccdccdabcadaadadbccddadbbcbacbbbddabbddabcaadcccddcddbbabadbdcdadacbadabadaddcbaabccbbcdbcdcacdcbbababadaaaccbdacccccaadbdcdcddbdcbbabbbcbbddcddbdcaaabaabcadaadadabddbbdabdaaccccdcccadddcabadbcbcadacbaddccdbcbcdddbdaaaacaaacbbbddbdbaddaadacdaaddddbaaacbabaaddbddddcadccdbaccbbcaccbaacddadaddcbcbcaddadbdbbaaadcdaadbcbbaabccbaabbbaaabcdaccbcabaaacdbdcdaacbbbddabdacddbcdbbacdbbddbabdbbcbaabcdbcabdcddbcabacddadcabbddccdaabcadbcbdcadabcdaacbbadcccdabccdddcbbababdcdddcdaabacdaaccaabdbbbdacbadcccdbaabdcbcbbbbdcdcacbaaadcaadcbbcabdbacdbaddaaacdabcbadcabaaadadddaddddbabcadbacacdbacbbdbdadcbdbdacdcacaadbaababdadccdcbabbbbbaaabaccbddaadcbbccbacaacdcaccbcbbaaacaccbcccddddcdaaccbaabcbaabcdaadabadabdbaabadcacccbdaccdcaaddbdbdcbacadabbaaaadbdadcaadcdaccbcbccabcadabdadbdccdaaaacacdcdcbdcccacaddddbdbacdddacacaccacbaacabccacbbacbccddacdbabddabcbdccabbccdbcdcdbcadadcbadbbdaaacaaaabdabbaacccdbbcdbabcababaabdbabbbddcccdacdbaabccbdccbdcbadadbcbabdbbbacbddbbdbbabddbdacbabaaabadbbdcbbbdcdbaccacdcabdacdcbdddbbbadbcacbdbacccaccbcbbabadbbbabbbacabcdabcabaddbbcddbbdcaabbbbddaaacaccccdabdabbadbacddadddddacddbcaadaabaddadcdbbdcdabdababdccabcddbabbaabdbbbdcbdcacdcaccbacacbddbbddacbbbabbcddddacaaacdcbbdbacadbbacbbdccabcbcdccacdccdacbcaadccbadddaabcbdabacacabbacabcccbbbdaddbdaccbcdcdabbcbbccadcbdcbbababaacbadbbccdabdacdbddcabcbccdcadccaaccdbbdadaccdcacbabadadbbdadaabaccabdcdadcbccdacacdbcdadaadcdabddcddaccdbbddaaabdcdabccacbcbadcddadccaddbbbbbccbdbcdbbccaacbbbdddcbdccbddcdaabacaccdbbdddacaabbbbbcccbaacababdccbcdcaacbbdbbaaadbaabaddcbccbabdbbaaddccdacbcdccdadbdbbacbaaddbcbccdaddbbbdbcdbdabdbacbddbbdcdbdbbcdbaacbbbadbbbaaadddbbaabccbdbcdcbacdcacbacddbbabacbcccbcbdddcaabbdaaaadcdabaaddcbaccabbacbcbaabaccaadcadbacbdaccdaddbcddbadbbadadcadddabccdacbbcdacddabcbbcaddbbabccccdabadacadabaddacddddbbcbbabbcacbaddacaccccbcdabcdbbcccacacdadcbadcbcdcaaccbdccaccccbdcbaabddbbadbcbddabdabdaaddadaddbadabccbdcdaaaaaacbbcbadddcbacccabdcbadddcacbdbaddbdbcddcddbdccdbcdacaabaadadddccdbbccdacbaddbaaaaadacbbbbbbcbbbbdacddcadacbccdccbbacdcbdababcacddbbabdaaabadabccaaaaabcdccbdbcbaaccabddadcaccaabcbbcaaddbbadadbddcaaabdadbcbbdcabaaabbdcbcddcdbdddcbadaaacbbaacbbbbddbbdbaccaaabaadcbbdacccdccaabccaabbdaacdaddcabaaddacaccaaabdacaacbbddcaacadadadccdbbcbcbcbbbbbdacaabdaacddacbcbcdadbdbcddaaccccbccbdccaacbdaddbbddadcbaaadccacdbcdadacdaadcccacabacbbdaaddccccbdbdbdaabdbbdcccbadbbbbbbcbaddacabacdaabbdabadadadaccdbbddddbcdaaccacbabccbbbcddadccdcdbcabbcadbccadbabadccbabaacbdbccdadabbaacddaabdbcbaddadaddaadcccdbbdbdddbcabdddddbaccdbacbdcdacdbabcbdcaaadacabbdbdbccdaadabbcadadddaaabdddcdcadaddbddcaacacbaadacadcaadcccdcbcabcbadaccdadaadbcabddaacadddcacbaaabadbacdcdabccbccdaacadcbdbcddbbddacacdacbccacdabbcbaaadbaccdbbabbccaabaabcbbcabcccdcaaadbabccbddddbbadbaaabcbabcabcccdbacccadbbbddacdadaacadbbbaccdddcddbbccdcdabdaaccbacdcbcbacaadbdbdcbbadccabbddddacaadcbaaccdbaadbbabbdccddddabcbadcddabcdcabcacaaaacaaaaabcbdccabcabbadaadcaddacaaacbdccabdcbabdcaacbbdbabccbbcabbaacdabdabcacbbaccbcbbdbaaaddbbbddddbdbcabdbcadbdcdcbaaabadaabbbddcbdbbacbabdacabcacaaacacaadbbdbdaabacabaaadcaaddacbaaaabdddcadcddaccaddcacccdbbacbdcbadbaaddcdabacdaacacaacadbacbaacbdadabbbadabbdbabdbbdcaabadddbaadcbcbddddadacddccdddddacdadcdabbadbadadbdabdcdaadadbdcdbccacbdadbccddabdbcdbacbbbccccabbcadcadaacbcacdddaabcbddabdbcdbbbdcdbbddacdbadacaaaaaccdcccaccbdbdddadbdcbcdbaccdbccccdccabbcacbaddaabbbaabdddcdbcbcbdcbccbdddbdbacdabaaabcadcdbdddddccbadbabcdadcccddcddcaccabbadbabcbbabcadbbaabaacdcadcdadcbcddcdcaddbdccdddbcdaacbcdadbbdbdbdcaadcdbacdacabddbdcaddcccdcddbccaadbacccadbccbcbccccabccdbadcbcbbbaadcbacadcadcdbbbdcaacccbddbdaadcbadcdcddbadddddccbdbabcaaddbbadcbcaddadabbddbdddadbcdcbbcbbdbaacbdadbbccddbaaabbabdacccbbcccdbbdaacbcdaddbbdababbccccbaabcdcbdccaacbcbcdbdcabdcbdbbadbcdcbddabbbbdbbaddcbcbbbcbcaaaddcabcabddbcacdaaadaabcbccdddbccbddaaacddadaddbadcabadbdbdbcaadcadadcbcbdbbcabbccaaadbcabadccddbacbdacdabacbadbbccaacbabdcbadbabbcacccbbdcdddbbababbacaabacbcdabdcbdcabcdadcbbdddadbddbbabaacbcbccbdccabcdbcddbcddcddaaccbadbdcaddcbdcbabdcbcbdddcddabbcdabadabacccddacdcbacdddacdabcdddccaadddbbbcbccaccabaacbaaaabbcababcdabdcbbaadcabacdabbbdccacbaababaabdccdcadaaddabdcdbcddbdbcbcbbccabdbabdbbdddbccbacdcadbcaacdaadbdcaacddbaddbcaadbbbadcbcadbbaaadcbbbbdcdabdaccdddacbcabbdbaddcadcabadcddccabdbddbbdddbacbbccbdaababdccbdcacabddaabacdcbabccabdaaccddadcccddcadaadddaddabdbcbbdccbaabacbbabbdcabdcbdcdacacadccacabaaabccdddadcccbbdccacaddadbabaaababdabbcdddbcbddbdacddbdaabadcbccbdbcabdcdbccdbdcbcaacbdaacbbaadadaacacdddbdddbdcaddbcdcbbbaabcbbacacabdcdbbdcaddabbbaaddaadacaddadcccddadacbddddbccadccbbadaabbdaadadcdcdabcddaccbbddbabdacdbabccdacbadddcadcdaacabbbdcdaabacaadbdbcadbababdcbaadcbbaadabdaabbbdbcabbaadbdbcadcbbcbdcbcdbdcbcbbaccccbbdcccbbabaaacccccdbccdcccabbcacdddacbbcbdbdcbacdcbcabddaadcbcbbcccddcaddcbabacdacbadcacacdbcaadcbcccababdcbbabbbddcbabadabccbaccabbbccbacbddcadbbaaababbbbcaacdcddaadbaabdbdaaabbbdabcbddcaaaadcddddbddaaaacbbcaaaddcaaacabbadbcacbcdcadabaadabcbdcbacbababadbddcdcccbadcdabdccdacaaacaadcaccbbdacbcbdaacccadcddbcccccdadabcdccaacdccccdaddbdddbabbcacaaadddcbcbbcdabacaaccddcaadbdcbbdbaddbabbdabddbbbaccaaacaccabacdabcadbcbabcadcbaaadcadbdaccccdabcddcdbacbbdadcaddaadabdcdabcdcccdaaaacbaaccacabdadcaaadbacabcaaaccacabbdbdbcdddbaacbcdbbdbdcbacbbddcadaacaaadabcacaabbbdcacabccdbbabcbcdaddcacddbcdddcbbcacbaacadbacabaddcbcabbbbcababbbaccacabdccbbbcbadbcbadcbcddccbdcaaccccdababcdaaddcacabcbcaddabccbccdacaddcdbbadddccdbaadcbdabdbdcaaddddbcbbccbddbcacdbcddcacabdaddacaacddaddddabdbbbdccccdbdabaddbbdbdabcadadcdacaadcdbababddadbaacadcbadbbbbbcdadbdcaacbbdbabacdcadbddbdbdbadaaddddcabcadcaacdbdcddbadcaaabbabcbabbbdcdaccbcdaabddcdacaadcacddaaaabbcbcbdcadadcbcdadacacdbaddcacabdcbddccabdadcdbabbaadbaaaccbaadcaaccbdabbdcbbdaaddacaddabadcdcaacdcdacdbbbbabbddcbaccdaccddcbcdcbadbdbcabbcbddbbdcddbabdbdadbbdaaabbacdcbdbddbbcddccbaacdddcaaddcccabadbbbbbabccacddaaddbddccbdddbabdcdbcccbcccddbbadcccacbbcaddbdabbddcdbcdbabddbcbcacacbcaaadcccabaccadbcbbddabdbcababaabacaadcabbacddbbabcdbadbcbaacaabdbbabacadddbbccbbabdccbbbcbdcbbccddcadcaacbbdacbabbcbbbdaadcbdcbabdcbdbccabbbccdbdaaccbdccaadcadddcbcadccbdacdadaabbddabbcbaddbbcddccccbbcbdddcccdcccdddcbbbdbbcadccdabbcbcbbcbbbdbcddcdcacaaddddabdaaacdbbcbbbdbcddccbcdcbababcbcbdcdccccbcaccabcdbbadccaddbdbbadacacbdbbdddbdaabbbaacbbadbacbdaddbbbdaabdbadbcadddbdbbdccbbccdadcbdbbdccccdcbabaabadbdabbaddbbdbaaacbdbbdcbcdbbbcabcddcbbcaababacbcbaaadbcacadbadcbbccdbabbcaabddbadddabddaccbdbcacbadbccaccdadaaaaccadadcddcddcacabdacaddacbabdccadcbabdaabbaaaaaacbdccabaabcddaddcdaacdacdddbcbcbbcbcdabcdaabbbdbbbbaadabddddadaacadaaabdcbdabcdaacbbbcabcacaccdbcdbbaacbcdaccdcdcdbdbddabbdbaddacbadccdccdadbdcacbdbdccbbdbcabdbadaddbdccbacacbababaaaddcdcdacaadadccbbcdbcbadbddaabdcdcdcdacdcdcacbddaacddbdbddaccdbbcdcdaddadadccbbddbbdccbcddbbdccdcabcabcdccdadacbcabadcabbacdaadaaabbabbdadadcbdaadaccccdacbcbcddbacddaaaddcdacacbababadbadccbdadabcdbadaadabccdaaddbcdddbacbcabbdbcddcbaadbdadbabbbcdaccacbabcddbcadcacbccdadbdbbaaaabddddddbccdccddbcdcadcaadcbcabccaccdddaacbddbddbdccbadbdaacadbdabbddbbdaaacbabbdaddbcadcdcaddbdbccbdbdbdabcccdacdcdddacabbcaccacbbdbbadcddcadbcbcdcccaabcbccadcaddababadcbdcdcbbbbbabbadbdcddaacadbcdcaabbbadaaccbbacdacabacbdbacadacdcccdcbabcadbdbcadddbbdccccbbdbcaaadcccabcbcccccbaddbabddabbacaccacccdaccabbadbacabdabcbdaddbcddbdacccddabbbddddcabccadcadbccadddacbccdbcabaddcbdcccbdcdbcbadacdcbbbabacadbacacbdaaaaaddbbcadbadaaacbdcaacdacbcbaaacbbcccddaacbdcadcaacdbcdcccbdcbcaaaaddbacbcaabbdaabacacbcbcdaacbdabcbababcadcacdbdccaaccabaadbbbccbdaaabadcbbcdddcaddbbddbabbcdacbcadadbaaaddbdddbbdacaabbababdcbbddbaabccddadcadbaddbdaddcbaccaacdbdcbcddddcdaaaccdacbbdcbcdcacdaaacadccbbdadcacbbaccaadadcdabbcbbbdaadbbddbcdbadbdddccdcdcccbccabbabaccbccaadcadbddacaadcdcdbacdcbdbcbbbadabbacaabdbcaaddababbaaabbbcbdabdacadbabbaaacaadaadadbdddadddacbaaaaddbbabbbaabbdbdbbabdaabcbcbcdbbddbdcaacbadccdcddddcbdaacbbaccbdacbdbdcadababdbadccccbcaddaacaccbbbdcdcddccacbddaadadacadbbcccabccabbbccdacadcacbaaabccaaddbbcddddaaaaaacabdcdacadcbabaccdaaaadadcdaadababdbcbbbbaabcacbddbacabcbadadbaacabcdcaccbaacaaabcdcdbbdaaaadcdbbdcdbbcddcdddacdacabdaddbbdbaabcaaabbdbddbbcdbadccadbbbddcabacbdacdabbccccbbbdaccbcbbaddacadbdaaabbabbdcdcadcaccbcdabdcadddbddaabadcaabcacdddbbadbadddbdaadcbcdcbaadbcddaacddccabaadbcdabcbcdadbadddbcddaacdbadcdbbccbddbaadccbadabbaacdcdcaaddbddcaddbacadbaabddacbcdcbabdadcdbadaaaaccbdcacbdcdacbabbdabbcdbabbcdcbdbaaacaccaacccbbabbbdcccdcacccbccbccbaadbbbddcadbaaababaabdbcbcddbdbccdbddcddddbddadbbbdbccbcbcabbbbddaaacccccbddcdbdaadbddbbacadaccdcabbddcddcbccadadbaaccbdcaabbdababaadbacbbdbcacdddcaabdabdcdababbdcacadcbacdaaacccbbdbadcdbcccadabccdbdacccbadcbdddcaadabdbddddcacbddbbbbdacaadbbdabcadbbacabcdbccbbadaddbbaadabcbcabddbaadbaabaacacbbcbacbcbbacdcdbadabcaacbddaddcccdccbcacdcdbddbbbcbdaaaaccdabcdaaadacbbbccadaaabbacddbbaddbdddcdbcaaddbaaacaabbbbbadabacccccdaaddbcdbadcdacdacccbbabaabdaabdcbdbdaabdaccbdbadcacbdcdabbaddabcaadaabdbcadadcababcdcabddcaadabcbdadcaabbbdaaaacdcbcaadccbddacadbcbbdbaaabdcbdcaaadacdddddabdaacdaaaddcbbbbddbbaccdabdcdbaaaabdbcaddcaadcbddcabbbbcdddddbacddbbccbcccdabccaaacddcdaaadadabcccabbdcddcbabababbdadbcddbbcdccdaddcccbaaddadadcddbbbdcabdcdadcacbcccbbabbbcaaaabacbddabbcdcddcaabcdcbabadcadcadcbdbcddabcdacbcbbdbcdbaaddbbdbaaccdcccdbdccbbcbdabaacbabbdcdcdcdababbdadadacdacaacbbcdcccdcaabccbaadbacdacaddbacdcbcabcdabbddcbccaabdaabcccaabaabdddccdacccadddbbbdcdbddbabaacdbabbadcdddccbcbdbbcaddaccabacdccbdbdaaabadbddadadadddcbcccacabcdbdbdccaddabcdbbbdcadaaccbbdadddbabadbdbbbbdcaccdacbaddacbcadabdcabbcbadcacadaccdbcdcbcdadbbbddbabaacabaaacbdaabbdccddcccccccacabaadbccdaadbcddbacbbdcadbababcdbbdaabcdacbccadccbbddadadcabcbbdcabddcddccadbccbcbbdaccacdcdabbcadbbdabcdcaddcbcbcdcbddaabdcbdcbbadadcbababcaddcbaddccacdcddaaabbdabcacbcbacdccddcdbbaadacdbbbcbddacdbbbcbaccbdbccadbcbcbdcadaabdaadaaaddbdadcabdabcabccadaccadabbdcbabcdcbdabbbdbdcccbcbddcdcadbbbbddabcdbaacadcacccddddddabdacdbdacbbaccabbbddbcdbbcbbcdabaadbdbbadddbcaccaaddbadcbddcbcbbcdcbababbbcbdcbadaaacbbbddcaaaabaacbbbaccbbcadaccbbdcccbacbdabbaabbdbdcaadccabbacababddccdcdacaccabcccddbbbadaacdbdbaacdcdaacbdaabcbdcdbbabccabdaaaddcbccddcabbccbbbdbaddcaaaaccabdbbdcabadbdbdcbdbaaadaccccbdbabdbcbdacbbdadadacdaacaacdbdbcacadadbbdbbbaacabacccaaadacbdccdacccdbccbdbaaccddaadbddcadcbdccbcbdcdccabdccabcdbcadcdcbabddddcadbdddcacdddcabbddbdbdcbbdbdcbdbbddbcdcaaaddbbcadcbabcbadbdcabbdcadabacddbcddaaccdcadcbacaddadbbcbdcacdcdcdbdcaabbadbabdabacccacacdabdbbbacaadcdcaadcaaaddbaddbbbbbcbcdaddcbdadcbbaddcbdcdaddccacdbbacabdbcabdcdadbcbdbbcbddaddcbddbdcbdbbaccaaccaaaadabddbbabcadababcadbabababaddcaaddcaaabcccababdabbbacacaabcbbacddccbdbddcabbcbbaadcddaabcdabdbbdbdacbcbbaacdacbdbbcdaacaaadcabbaccddcdbcabbadbbdadccccbcdcdbcdcccddcdccaddaadddadbcbaabbbacaaaabcbaabcaddbdaddcbcdcdbddddacaaccaadadabdcdbcaaccdccaabdcdbbacbcaaccbcbdadcabdacdcdbabccacdaddacadddcccdbabcaacdacabbccddddcdadcbcdcdccaccabcbbabbccaadabcbddbaddbcddabdbdacdbdacbbcccddddcdcadcacbbcdabbabdcaddcbabaacbcacbdbdcacbccbdcaddcbabacbddbbdccbbcddacddbbdabbbaacaccbbbbcacbdbacddbaccabdcaaabbccdacaadabcdcccdddcbdbcdcaababaadcbcaccdacddbbdbbbdacdaabacbdabaaabbaaddddbccbaddbdddcbcdaddddacbaadaaaccdacdcaacadcdacabcbccaaaacddbdaabdcddcccdabbabdacbdcdaacacbbdcccdacddaaccaddbccccccdaddccddcdddcabbabaddaaadbbcbdcbabccadcababbbdbabdaddacdcbdcdbdabadaddaaabddbaabbacdddcddaddbbdbddddbcbbacabcadacacbbacbbbcdacacbcaaabccacaccbcbbcdcaadcdccadddacbbddaaaaabbdbabbdcccbadaaabbcdbdcadcaababbbcadbcadcdbddcabdbbdbaadcacacbaabccbbbcaaccdcbbaddcadababcbdbbcacbbcdbdbbdbcbddbdacdacbdcbaacdadbddbbdaccabbdddcadbcccdbcdbbaaabcadcacccadaccbdddbdcaabdbadadadadbdbddbdddcddccdddbdcdbadcbdaacbdbdadaacbbcddcbdcbcdbcaccaacabddddddcbcdadaacccbaadcaccbbbbbadaddbababbabcbacabcbacbbcccbdaacbdacbbccdbadcdbccccbbbdaddbcacdcdddddbcbcdccdddbdbccbcdbbdcbbdadcaadddcbcdaaadbcbdaabcacadddbbddddcbbddbacabdbdbaddacbaaabaacbbdbcdcadddbbccdddbdadcdaabaccdaddcabbdababcdddaaadbcaddbdaccabdcccdbcdbbcdbcdddcbbccaaccabaabcacadbbaacbdcacdcbbbbabbdcbcdcdbcbcaccbbdbdccacbcbaabacdadccdbbcdcbccbcaabdcbbbbbadbdbbccdaaadddbbbddaccdbddbccdcbbdabadcababbdbacabdabadacdcdcdaacacdacbbaabbdbbcbaccccbcbbcaabdcbabbabdddbccaaabacdcdbacdcaddbaccbdabacbcdacddcbacdbbadcbbdbdccadaaddadcccbbccaabbabcacdbcddccbdaaddccdcdbcddcaacaacdbabaddababcbabbdbbacaccdbdcbadbcdcbdcbbbbdccabdacabccaaabcbccabacbaaabbcccbccabbaaccdcaddbbcadacaabaaaaaddadcdbdbcdcbadbacdcddaccdccddaaadbbbadabbbaddbbbbcbdabbabadcbaacabbdbcaabadbbacbcbcabacadccbddcddbcacbdbdcbaacabcdbcaaacdadcbaadccbdbabdcbcdacbabcdbcddadcabbbdcbadccaadbdbbadaccccabdcbbabcddcbcacacddbdaaaadaacdacbadbdadacabdbabdbcadadadadbacbacbbbdcbcadddcaaacabbabaacddbddabaaaaabccaabdbddcbccaddaacbadabbdbdcdbbacadcbcdbadabbaddbaccdbbdabbbadadbaddbbabadcbcaaaaadbabdbbbddaaabbaadaabadcaddaaddcbacabcbaabbdccbdbabddbbdadbaadbdddbcddcadaabbcbcaacdacdccccbccbbbcdbbbcaaccbaaddbddbdcccbbaddacabdadacddaaaccccaabccbaadbcabbcaaadadabdbdbbddabccadacbbdcaabbdccbaababdadcbcbddcdacacddadabcdabacdacdcdcbbddacaabdbbdbbbbaccbdaadaabbcacabacadddddcbdccaacdcacadadaddaabbcadbaacdabddabbddddcdabbbcbddadbacabdccbcbbcbbdaaddcdbabbdcdcabccabddcadabdbddbccadcbbbdaddbcdadcbaadaabacaacabdbcccddacabbabbabcbaadbdaaaabdbbbccaaaabdbcbaaddacbcddabbbacdacbaacbbaaddacaacddcadabacccbcdadcbbadbcdaaddcabcccbbaccdbbbcbcccccacbcdddcaddaccbaadaabbcbccbabadbaccbbdbdbddcabbcdadabcbdaacdcbacdbaabdcbddbbccdcaacaabcaccbccaaaccdbcbbddcbdccaabacaddaaacbcacdbaabbdacccbbbbdccbaabadaddbbdcabcdbdacacacccdcbabaaabdbdddcbabcabcbdbaabbcdaddbcdcdcaaababccddbcbabadbdbccbcbbdcbacaaaddaabddbaabaccddcaaaadaccbdadbddaddaccdadbdcddcbbccbcbcdcaaabaccdaacdabaadbbacdbcccaabaddbcadbccbababbaadccbbacbdbddbdadddbacbaabacdabbabccaacabaaccaacbacacdcdbbbbbbddbdadbcdddccaaddcbcccbbdcbcaadcaadbdccdcabadacddcabacadcbcacbbdababcbabbabbbaabcdcccdabcbdcbcbacacadcadabbadabccabaabbdaddaaabbccababdbbbbabdabcbbbddcbccaddbadbadacadbdcbadbcadabcadabbdbbbcacaaaadccdacbaaacddcdcaacacacdcdabdacdaacbdbbdacabbadccbccbaddbdbdcadcbbdadaabdbbabbddddcbddcaddcccdbbbdcdabbccaddbbbbcccdcbbacbadcbbbccaacdcdaaccbcdbddaddbcadabaddbaacbacdbabcdcdadcddddccaddbdadcbdacbaacdcadccabacdcdacadbbbddbccbaadccbdcadadabbdbccdcdbaccadaabdcabbdcaaabccddababcddabcacbabdacaacccdcdbcdbabccbdbddcbcabcbdcbdcdabcbabcacddddbcacdbdaaacdbcddbaabdbccacaccbdbdbbbbbbbacabadbddaccadacbbadabbaaccacbaaddbbaabdbcabcbcabcbacbccdcaabdaacbbbacbdcdcddbbacbdcbdcbdabaaadcadabaddabdbbacacaddaacacbadddcabcdacdbbacbccabcaaadaadacdacabaddbcabcbcabdacdbbbccaaaccadadcabcabbadcadbbbcdcdddbcdbbbbacabbcbbddabbdbcbbdadddcaacdbccbbccccadcbadadbdccaadbdabbdccaaabaabaccbcabbbaddaacbcabdcddbcbccbaddcbbcdcdadccbaacccddbbdcacdadbabbaddbaaddbcaabcabcadadcaadcdbcbbcaabbcbcbaabbbdababaabbbbcddddacdbcadcccdaaaddddcababaaaadacddacdaddbdadacababdcdcacabdcacadcaaaadbdadcdcbcacdbbabcddacabcbdadddadaddabdabbbdcacdbbddabacdacbddaddcbccdddadcdacddccbabdbdabcadcabdcddcddcdacdcddabdaaacccacaadddbbccababbcaddddbbbbbbdbddcccdbdbaaacdaaaadcdddccbbadacbabcadacdaadcbdaabdcdbaccbdddcaddcdbbbabcacabbabdbcdcbcdaabdddaadadccaacbcacddcbdaaacbbbdddccaadbabdaacdcdbadadbacbaabccbbbbcddbccbbbcbabaabcbdaadaddbcdbdbbdbdbcddbbaadacdbabcdbaacbdaabbbaccdddcdcbdabbccaccddbadbabdcdccbbcbcbcadbabcddbbadcbbaccdaaaaadbdcdadddcdcbcccccbcddcaabddaabbbcdcbaddcdcddcbabcadabcbbdaaadccbacbaddcccadabdbaabaddcabcccccdccddcaaaaccaddcaccccadbccdacbcbcabbdcadcbaccadcadaccdccadcdacbbbacabdaaccbbbdbcadbabacdcbbddbbcbdbbcbaaadbdddcccbaabcbddbadbacbdaccaacadbaabcaadcccbacdcdaabbdbcaccbcbcbdbdacbdacdaddaaadcbcaadaadadaacdabaccaabbaababacbbaddbcdcabcbdbddabdcdbbddbdbbbbabbcbbabdbbcbddbacaacbacbbbacacadbdbaaadaccbcdccdadaadacddcabaccabdbddbcadddbcabddadccdbadcdabaccdcacbabdabacabbcacabdacdbcaccddcddcacdaadbcdacbcbccacdcdbcdbbcadcadbbaabccabbddabaadcdacddbddcdbbaaaddadddddabacdbcdaccddcccbcaccaaaccdcbcdddddcabccccdccbcaabadcdbaacaacccacadcbaaaacbadbcabcbdcbbcddaccbabdbbdcbacbbabacdbddacabdaddddbabdaddaaaadcbcabcbddcbcadcccabaddabaaabacacbaaabbcbcdbbccdbdacdcccccaacbdcaaaadbcbdbbcccdbbbdbcdbdbddcbdadaadbccbbdaaaaadcccbdaddddcaacaadaadaddccdabcdbaabcdcccadcbbccbadaccdbccdbdddcabcbcadccccbaaaaabbbbdaaadcdcccacddcddbcadcabcccdbadacadcbddcababadccacdcdbcaabacabbdabdddbcaabaaccabccbdcbdcabbdccdddbababcbabdcdccbbbbdaabbaacaaacacbcddbbbbdcbbbdadcadaaaadacdbcaacddabdbdbcbdcbcaaababdccbdbdcacbacdcbadcbaccadcacddddabacccaabdbcaddacacbbddcaaaacacaacbbdcdcacabbabbcbdbaddbbbcbcbcdbdcbbbddbadcabbcbaccdbabdddadacabbaaabacdbaadabacddcdcdddbaadbcdcdcbccdcabcabaaaaaaddabccbddacdacbdaadadbdbadcbbacdbcbaaabbdadbbaacbaabadbdcdbcdbaaacbbacaaacaaacabbddacabddccdadacabadcdcaabcdbdddbacaccddcadbabbbbcbcabbdcbcbccdaabccdaddbcdbadcdbcbddcaabddadbdcdbdabddcaccbcbccddddcbcbbabbdbccbacccdacadaaaccabadcdcadccccdbddcdccacdaddddcbbbabccdbccaacdccaabbdbddcdbdacaadcdddcccdbabdbcddcabbaddacccccbcadccbddaabccabacdccabbcbbbacbaccaabacabaddccabdccccbaadbaadcabdabacccbdbcabccccddacbbbdbcbcdccadbaacdabbacbcdcddbdcccbbaadaccbdcbccaabdbdbdbaccbcdaaacadcdcadbbcabaabccdbbaacdaddabdddaccabcbbdacbddadbcaadbbacadbcbdbbaaababdbdabcdcabbcabcdcddacaddacabcbbccdcaabcaadabcdbdaddbdaccddbbbbaacddbaadadaabcdcaabcdcdbbaaaddbdaddcaabbabdccdcadccabcbdcbbdaddabdbcbbccbcaacccccacabbcaacbbbcacdbdddddaabbddaaaaadddbadcbadcddbcadbccdcdbaacbcbacabcdacdccadcbdaacaddcacbadbacabbdacdbacadaddababcbbdabbccbbbbdcbacddaccabbcdacdcccbcbbddbdaacabdcdadaacccaadccdaccdabdddbddbbdccaaccacdadcdadbaaacbabccdcccaaccccacaadaabbaadacaacdcdadabdbadcddacdbbcbabbcbbcababadbbacccddddabbdbbbbbaacbabbdddddbbaabdddccbbbdbdcbddacbaaacdddadaaaadcdcdcbdbacdbcdbcbdacbcaabdabcdcacaacdacaadbccccddadbadbadacdabdcbdcbbaaacdcbcdabbaadababdbcdddcadccaddcdacaacbbcbdaccabdadacdbbddbdbabbbaabbaabcbbbbabdacbbaddaacccaddbcdabcdbdbabcdcdbcbdbcbbbaccbbaabbcaaddbdacbccdadcbcdaaaccbcddbabadacccacbadaabbcadbdbdabdcdcdbbaabbaacccbcdcbcbbdbacddddcdacbabdabcadaaaacdbcabcaabbcbbadcdccccdddbdbbaadadaaaddccdddccdbadcdbabdadcaaddcccbabdcbbabccdcbbaacddadbbdaccbdacdabaccadacbbadcddadddbbadaadabacabbdbddcaaabbdddaddcbaccabbddaabbaabddabbccbcacaaacaddadcdcaaadbcccdcccdaddaadbdcabaaacdddcdbcadccccdaaccbcbacccaadbacaddddddbcbdcdcdbdabacddcddadbabbddadbcccadcdcacccbcdbaaabbbbcaccdaccbcbbccdbabdcadcacdbbadccdbbdbcbbcaaaddbaacadacccbaccdcbbdaccbcbdadbbadaadbbddbbcabdabbdadabacadacdcbcddccdadbbbbcdbbbaadbddbbcadbbbabdcdcaccaadabdcdaaccdddddddbccdccbdaadbcabdcddddbaaddcabbdbcabdcbbdacbcddaaabcdddaadbacbcaaababddcacacdbabbadcdddcdcadcbdadcdaacccadcadcdadddcaaaacabccaaaadbdbbaabcbdaabccaabcbacdaaabbcbabcccbacbadaaccbcdccccdbcbdcbaadcbcbbacbbadccdcacbcabbabbbdcaddccdddbacbcbbcbdbcacdabbbbacdaaaaaaadddbcdddbddaabadcbacbabcbdccadbdaaaccddcdbaadcadcbccdacbabcddadddcaccbbdcdbcacbbabadddcdccbbcddadcdacbacccdcaaadadadbbbadbabccbbcaaacdcbddcdbbcbabbbcbdccaacdabcbbcbcbbcdacdaaacadddbadaccdbabdabaacdacaccbcbadddddaddbbbbbacadabdbdbbdbdcdccbcaadbccdcbcabbddcdaccabdbcaadcbbdaacaabcacdaaddbdcddcbbcccbcbbbbaaccabdababaacbdabcbcbcdabbdabbacbbbbdcbbcacbcacdadaabcbcacdccadbdbcabdaaadcadadcbaacaaadcdbaaabbbacdbccadaccbabdaaabcccabdbbaaccbbbacbdaddcccbcbddbcdcabacbdaddddcaadabbcdaacdbbdbdbdcbcccbbbadccbcaddaddbaddbbaccabdbccbbacbbacacacbaaaabbbaccbdabcacbdddabcacaddacaabcacdabbbabccabdacbdabaabccbccccabcaaabcbabbacbdcbcddbaccbbddcddacdbcdcddaadbcccbddaaccacddadcddcbdaddcadbacadccaacacdcbdccddbdacbcbbddaadccacbddbabbacbdcadbdbcbdcdaccccbccaaddadddaabbdccacbbdbdbbaaddbbbcabcbbabcdbddddbbcacaadcabcbbabdbddbcaacabcbbdaaadcaacbdadbcbbaccadcaababbbaddbbcaabccdcbdcdbcabdcbcdadddbdabbcdbcbdaaabbcddabddcccdaabcbcbcbdaccccccdadabababdcddcbabbcacdbbcdacbcdccbaacdcbdcbddacababcbcddbcabccaddcadabaabbbaadaaacabdaabbcdbbcdadcacccbabaaadabdbbdbdddbabdbcacbdaaadacdaccbcaabbccccbbdbbcbcbcabbaccbacdbaabdadddbcdacdadaabcbacdbcbccdadcaddbdbcddcbdbbdaddabbbddcbdbdcaacaacbaccbbaadacbdaacdbddddcdbdcabaddbadbbcbbbadbcdacacbadddddcdadcacabadabcbbdbbaacacadbaacbabcdcccbaddbbaacadaaccaddbacabdbcbbbcccbabbcabbddbcdbccbaddccacccdccacbadccbbabacbbbaaccaddabdcdabbaacdcabbabaabcdbddbdcbabccabaadddabcdadabbcacbaddabcadacaaccbacbdadbdadcbadbadabcbbbcbcaaaccdcaccdacbdabbabdbdbaabdcbaddacaabaddbccdbbbadbdcaabcbdadbbbacddabdccbadadadaddddacbdbadcdabaddaddcaaacaccacbbbcccbaccabcdaacaaacbaabbacadbbaaddbdbbdbbdbdbaacbabccbdccacdbbadbaccaacccbcabaddacbcbbccbabbbcbdaababadcccbcbbdabbcbabbccbbabcacbdcddcbaaabbaddaaddbadacbaaaadaabcacbccbcbbcbbbcacbbdcbdaabacabcddcbdddbcddbbadcacdbcbcbbabddbbbbabbaaaaaadacbaddaacaadbdacddbddbacdabaabbdbabddabaccdbcccbcadcdaacbdcddbbcacadcaabdcbaddbaaccbccdacabbccdbdbdbcbaacbccdabdcabbbbaaddacdcbabcbabbbbadbababcadbdadddbbcaadddaacaacbbdccbadbcbdbbaccaadabcccababbcabcdbccbcbacddabdbbbadcbdacdadddbabacbcbdabccdbcbbdbdcbdcabadaccdbbcdbdbcddadbaccacabdbdcacdadbbabadacdacdbaacbdcccbbdbbcccdbacaacacacdccbcaccdddbcbdddbddaccddcdbdadaadddbdcdbbadbdddcabaddbbacaccdcabbbdadbbaaabcabacddbdadcacbcadadacdaabbcddbdccbbaddbacbbbdacadabbbbcbaccccbdadddbbbbddcacacddacdbbddbdadaaddcaabbdbccdcbbcddbdcbaaaccdbaabdccbaacccdbbacbddcddcbaaddbcaaddbcdddccbdadbdcdbdccdadddddbbddbdaccbcbadddccccdcddbcaacadccbcdbabbaacbcccdcadacadabcbbcdabbddbaccbdcdcdddbdcdccdaddbcacacbcbaccaacdbdadaabacdbbccbcabddabcbaabccdacabcbaaabbadacabdbbcccaaccbacabccbdaaccbdbacbbbbdddcacbcdbaabbcdcbbbdbcbaaaadbdbbddaddacdddadcdcbcadccdaabaabdacadaabbddaabcdcdbcdccbaaadbcabddbcdcaacbbdccadbacdbcbdabbbbdcddabbdccbdccaddaadadbddddccaabdbbacaaacdccabbbcaaabcadccbbbababaabcbbddcdcdccaacaddbcdcaddacabcbcdbcbbdadabdbbaacadcadabaabbadaadcacbacdbaacdcadbbadbdccccdabaccbadbcbbaccdadaccdadddaddcbaabbdbddcbbbbadabdabaacdadcbbcbadbbdcbcdcabdbbaacaababcbdccdacbadabccdbdddadbbcbbdcbdbdbdddbdaabdaccabaaddbcaacdcabaddbdabdbabdbbdabddbadbababdbcacaaadcdcdcadbabbdbbcddaabcacdbdacbcbabddbdcdbadaadbbadddacacccbbabcccbdcadcddccaaabacbddcbbcacdddbcbcadabaddbddddbbdcaacbadcddbbcdbbadddbcdccdcccbdcadbacbddccadbddcbbddcdddabacabcbbacddbbcbdbddcabbdcdbacaaccaaacaccadbabbbdabdbbcccacbbabadccbbdacbabbcddacacdbdbdadcbbacbdaaddaddbbbcdbbcccdaabdabbcbacccbaabccbbaddcdcddcdccdbdabdccdbaaacbcaacbcbaaacccdbabbddddabbaacddaddcbcccdddddacddbcdddcccbadcbdcbcdadcdbbbddbccacdbddbddaabbdccddbdbaddcdacddacbcbbdacbbcdaccdcbddabddaabddabaccacdbbcbbbadbbabddcaabcdcdccdddbaddaddccdddcaccdaabdcbccbdbabdbcbaaabdbdaabbadcbbbbbbdababdabdabcbadbabccbaddaadbcbdbbccabdbbaadcadbddacacbbcadcbcbadacddabdbcabacbbadcaccabcbddbccddbddadddcdccbdabcabdbcdbbabdccbbdccaaaccdbdbdadddbacbdbcdddcccddadcbababacaadbbbccacccccabababbbbddabddcbbbdcbddcbadbccbacbdabdbddccccddacdacbcbddabdcdaaaacbccdbabacbaadbbcdadcbdcdaadccdbcaadbbdabcbcccaacacdcdaabdccbaddcbbaaaabaadbbbcdabccaadcdaaabadaaacdadaccbcabbacadccbcccaababbcccabbbbbbddcabdabbbaccdbddbbdaaddbcbaacaddccbcaaabcbdbbaaaaacadbbddbadbbaacccbdbcaadbcbcdabbdcbddbcaacacbaaaddadadacdbabcbdabcddadacddbaaaabdadcbcdbcbacbdabcbdadbcaaadacdaccddacbddabdbaccabaaacbabcccabbadccaaacbdcdccddccddcbabdabdbdbcccbadbbadbadacdcbaddbbdacdaaaabcbbacbabdccacacaaccacdaccabdbcadaaabdbccbaadccacdbdbdccddaacaaddcccbadbbbdddacbddcaccaaccbaddbdadcbddacabcdcabadbadabccbaccabaaacbbacabbaaadcdacbcadaacaccadaabcccaaaaacabbbbbcaabdbdddcddbaaaadddbccadccaddbccdbbdbcacbcbbbbcabbbdcdbcadcbaccbbbbabccbbadcddddadcacdbbccdaaccddddaadddaddcaabbcbccdabdcbddbccdcbdaaabdcbbcddadcabcabcaaccdacddbdadcacddcddcadabccacaabddbacddccdccdacddbbdacaaacddabcccdacaaaccbbccdcabbcddbccbccacbcdacddbdaabbcbbabcddaaccbbbcdddcdacaddcacdcdbcbcacaaaddabdddaabbbdccccdcbcccadccdcaaabdbdbaaccabcbbdbdcbacacbcaacdadabcddbdbabacaaabbdbaaababaccdadbbadcaabdbddcaabbcadbdbabbaaadaaacddcdaaaaacacbccbcbbbabdbcaadbbadbcbaadbbacccccccddcbbbbcdbccddaadddddacdbdabcdbcadbbdbbcdccadbbbacbbdbcccdcdcdaacddddccdbddbbbabadaabcbdbbdadcaccdbbddbbadcaaddabcbaaccbcdbccdabccccaaabbacdddbbbcbccdbbababdbdabbccabbcccabbdadaaadbacbbcccacaaadbbdaaccdbdadabbcbbdadcbaccacddbcdaabcdababacdcabcbbadbaccadadddacdbcdabcdcadcbaaabadbdbccbbcadabccbacbaabdcdcacabadddbddaddbabcbabaaabcacbcbbccddccccadccaccbdccaaadccbcdcccbadcdbadbbcbadbdcabddbddcbdbccccbdddcccddabcbdbcdbdbcbdadccccbccbcacbdacccbdcbabcaaaabcacdbbcdcdbcabcddaadccacdadbacdbdabacdadabaaadccdbccdbbabdacccdbaabbaabdccbcdababccdcaabccdcadbaabbddabbcdbcccadcaccacaccbbadbcbbbbdacddabdaadabccbdadcbadadcddabacbbbadccccaaacdcddbcdabaddcbdaccbdddadbaabadacbaabdbadcbdadbddacabbacaaabaddaadbbbcccadcacccdbdddadbabadcdacdadcdbcccaccaccdcddabbbcababdaccbbcbccbcdabcbcdacbabcadbcdcccadccacddaacaaaaadaccbaacddcbbdcacdccdcbadbbddabacaaccdbddddccbdbbcbaaadcdcbcdabddaccccabacadcadbbbccbacbcccbcaddbdadbddcadbcbcdbacddbcaccacbdadabbabcbccaacdbdadacdcbccdcbacacbaacbbccddabdcbbacbcbdccdcdabbbdaaadcaddccbccaaabbbccdbdaacabdbbcbadbaabaccddadddddaacabdbbdcddddcdabdacbdbbccaccddcddabbddcabcaadcddbacccbdcbacdcddadacbbbdcaaaabcbbbbacadcacdadbbdbcdddaaccacadbdcbdadacdbacccdadbccdadbbccabbdadacdcaccaabbbadcbcbcbdccdbcaaaabddcdccddbcdacadbdcabadbbbcdadadaabcbcdcccbabdbaaabcddcbdcbddacaacbdbbbacaaccdcbdbaaadcccbdadcdcdbaddbdcddadcdaacdcadccccdadcdbcaaccaddddbddcbccadbcaadbcacaaadbabcaadacabcdbacbadbcacadcaaacbbddbcccdbbabcbcabdbcadcadadccbcbadbbdaaabbdcbbdcbbaddbccacddacbcddbdddddbbcdbcbcdccddccadbcabdbbaccaadabcbdbacdaabdbbbabdbabadbdbcacdddccabacadcccdaacbdacdaabddaabddcbbdbcbddbbbcdbacaaccbccdcacdaadcabacdcabdcccdbacaacddbadbcdbdaabadaccbbabcddaaacbbbacaadbddababcccaccbdccadadaabcbacadbaccdaabaaadcddbddcaaddacbcbcdcbbbdddddddababdaddbddaccccbcbcaaabbbaaaccbacadaaddbbcdcddbdbcdcabbcbbdabbbbdbcabcabaadcdbbdbcdbdacadddaabddbccaaddbabadbacbdaaaacaaadaaaaccadbbacacdcbdcbcaadbddcbaadbbacbbbbdcdbcdbababacadcbdabddcdcccccbbbbcabdbcbbbabcbdcccacbcbcbbdbaaacccdccbdcabcccddacddcacbdcbccdcbcdbddadcaaaaaaacdccbcdccabaacbbadcadcbbccccdabdadbacadbcdbbdbdcccaaaaaababcaaaddadbbacaacbdcaacdbbacacbbbbcdbdbccbaacdbabbbbcbddbadbcddbbabbbbdbdbacacadcbabaabacdddacdcdabababbdcdbdbaadccabbcbacaddacbcaaadadcbcdaddaccabcaabcaddbdcaaddadadaddcbdbbdaccbdbacdcddbcadccbccabbcddbcdccaabcacbacabcbdabbadaaaabacdbddbbcbbdddbdcaaabacdabadbcaadbaabacbdbadcdaadadbdbcaccabaaadcddcacadabddcbbbbcaabcacaaacabccbacabacdddbabdadbdccdababadbbbacddbabcdadaabcbacaacbcbccbdbacbbbcccdddaabadcbacabcdabdbaababccdddaddcbacddcbabbdacaaaaaaabcbdabadcbbdddcbbbccdbbbadacbaacaaaacadaccdccccabadbadaddbadddbbaabaccccbcddcddbaccdbcdddabbdcadcccaaaaacabbccbdabbdccaaddcbdaddacbbacdaaacabdcaabdacabcbadacdadbdccdddcaadcdddbabbbadadaddaadcbaadbccaddcdbcdbdbadcccdbdaadbbcbbcaabaddaabcaccbaaccbcbaddcbabbbcbaccdabaacabccacbcbaacddaabdbbcaccabbcbadacdbbdcdacdcdbdadcabcdbbdaadccacccbbdcabcdadcdcbdbbacbdacbbddbacbcbdadabdbaccbacbdccadabbdbcabaccdbbbddadcdccbbcbcbbbcadcbbdbcaadadbbcaccdbcabdbbccdcaddaccadbcbcacddaacaacaaabadcbcaacdccdbcbbdbdbccabacaacdcccbddcbaadcaccbcacbcaccaabdcdccaadbcbabcddaabaadadaddcdbcbbccccbcadbbbccbdbdaccacddbcadaadacaacacdababccdadbddcddccdbabaacbcdcccaddaabbdadabccbccdabdaabddbbccdcccbdcdcabdaabbaddadcbdcbcbabdccdddadcccbacdaccbbaddacaabbddadcbccbdcaabaabbbdcaababbbddbbbddacbbbadccbbccaacdddacbaabcaaaddbbdbdababcdbbbaadcdbbaabcaacabdbaacdcdaadabbbdbabcbaadaaaabdbcddccabcbcdcabcabdddcaccaacbabddadbddaccddddaacdbccdccabbaadcbabcbbdbabbccdcabbcaaccaacbccdcacabccdcdbbdbbcbacdbdabbbaddabcbbddadddcbdbabaabdaddbbbdbabcdcdcdadbdddbcaadccdddcbcdddabacdbbbbcccdaddabaadaadcabddbdbabababcabacabcdbcbcccacbcadccccbddccbccdbcbbcdcbdaddaadbacacbbccaddaacccbbcccddbadcaddabbbbaccaccddabbabaaaddabdddccabbcdcdbdaddcbbcdddcddddacadcabdababdbbdbdbaaaacaaabcdcccacddcaddababdacaccadcbdcbbdbdddcbadbdddbbabbbaacdbdcdadacabcbaddbccacccdcbadbddabacdcdaacababaccccbcbccdadbdabbbaccdbacddcddcbbcbabccdbdaccabddabcabcdabdcbccbccaacddaaadbbbddcbdbccddbcbabdaadbadaabddaaddacbcdbaaacdabbcbcbbdcacccdbbabcbcdcddcacabcdbcdcadbbdccddadbaddcdbbbcbaaccaadbccacdaaccdcdcdbbacddaabcddaccbaadcdccbbaddcbbbaabcbbaadbbacdccaaaadcbabcabccaaabbccacdbddbcdcbddcabadaacdbcdcccaabadddabbacabdaaabaacabbaadccacdcbcdacabdadcbcddcaadbcbbcbdabcbddbcbdcaaaadacccbaddacbbccaccdbabaddaabdadcccdaabbbbbbcabddbcbdcaddbbcbbdbabddcddcdbccdbbabcaabcbaaacaccccadccbdbdababdcccddccadbbdbbaaddbcbabacdbccdbdcdbccacccbbdcdacdadcdaabdcdaddaddcadcbddcdcadaacadbccadcddbddbbdaadabbccbadacadaabaddaddbaccacdbcdcdccacabccdcaacdabdbcddddacbbbddbbbcdbadddacdbdaacbdbbccbbbadbcccabaddcaacdacdacabaadbbbacdadaaadcadbddaabbcccabdbcbbbadcaadacacbabbabadddcdbdacdadacbbabaabaabbcbadaacabaacadaaccccbcaddbacaacdaacbaccbcbdabbbcbacabaddddbbcacdacabdbdbddbaddbccdcabaabdddaaccbaacccacabbddcaadbadaaadcccaddadcbdcdaabbcdbdabdaaddababadcbcbaadddcccacadcbbcccdcacdddbccaacccccaaaabdbcacdccaacdaadababaddaadcbccbbdccaaddbbcbdcbbcbdbcbbaadcabaaccdddbbbdcccdbaccddbdadbccbbcddacccadabaddcabcbaabcabbcbcacbacdcbcdaadacaddcadcbdbcdabbbabaaddcadabbcadbaddccbacccbaabdccdabdbddbdaabcdddddbbaaabdbbdcabcaddcdbdbcbaacaaddbcccbdcaabdcabbbcdcbdabbdbbdcbddbbbccdcddbccdbcdbadcbcdcbacadadbbcdccaccbccacdddadcabcbdcacdcaaaacdcbabdcbcabdbdbbddbacbcabdcabcaccaaadcdbbddbdbbddbddccaaddbdabddbacbcdcbdcacaacadddcdccbbacbbddaddcbcccdbbcccaadaaadcaccdcacbdbbbdabbacdccadaadcbabccacadbaddadccaabdcdabbaacdbcdcdaaadbdabcbdcccdaccbbadabdacbadbaacdccabaaabdbdabadcddacbdcbcbccbabbcacacadddccdcddcbcbadbaddabbdabcccccbdbcbacbbcbadcdbdadabaccaaaddddaadbabdcbdabdbcadadcaaddbcbbaaccdcacbbcaaddcbadadadaaccdbbcadccbbdabcaaddbbbccadbcabcddacacaaabbbaadddddddccabdbdddbbdbdabcbbbacdbaddcccbbbbccccdacdbdcabdcbbdddaabddbabacabdcaabadbcddbcddaddbadadccbabbdaddaaabbdbcddcdcdacdcbaabdbaadbddadbacdccbdbcbaddacbacccaadaccbccbacdbcaccababaaabbbcaacbccdbbdbdbcdacbcddaaccabaccbcdadbabbababbbccddacbabdcdbddaccbcbdcbdbddababbccbbcaabaacdbccbddbdabbdaacdaaacdcccaddbaabbbbabbbddcbdabcccccacacbbdddbaaddadabcabcacabdadbdcdcadaddacabaabcaabacdabbcdcdabcaccbcdcbaccddaabdadbadbdcadacddbbcaddaccaadabddbcdcaadcbbdacbcccbbcbcdacbadcadabacbadabbbdcbdabbbcadbacadbcdbcbabbcdbbddcbabbaacdddaacacbaddddbbcdbcdaacccaadaadccbccdbababdccbacacdcaabaabdbdbddadacbbdcbcbbdaabacdddaddaddccccadaadcaadaddbacdbaccbddcbdcabbddaddbdadddadacadbadbcacaaadcbdcadcdbabbddadbaababcbabbaaccbcacdabcacddbdcbdbaddbbbdaabbababaabcbaaccaaaaacddbbcbaccaaababacacbdcbaadccbbbadadbccdbcbddbdabbcdabdaccdcadacacbbbabdcaaabadbddabccddabcdcbaccbdbcbcadbbddcdabaabcdcdacbcdaabcbdadabcbbdbdddddadbbaaaaddcacdcccbadddacaadbdcdcdcccaabcbacccdadbccbbcabbdbadbbbbabacbcbcbdbaacdbaaabbababcadcbabcabadaadcbcadabdcbdbbcbdcccacacdbcadddcacabccaccaadcacccbbcddaaaaadcbbdccacabcddaddcbbbabccaddaddbbdaacbbccccaccdaaddaccadccbccbbaaccababaaadbaaaaaabbbcaabcbabdcacccaabcacdbbdcdadcdcabccaaccdccadaadacbcbdccccbbbadbcbdcbcaaccdbcadbaabccbcdabcabbcbdcbdbbbdacbcdadacababcbbdcabdbaaaccbbbabadbcddacddcddabbcacaccacbacbcaaddcbaaaaddcdcdbccadacbdaadbabadbdbabccccaccdabcaabcbcabdacbdbcaaaaacbaaabaacabbbadddcbaddcdcabaadddbdadbdaddabbcdadaadaccbadaaaabacbdddcbcaaacacadcadddadcbbbaabdbbdbbaadacbadadbcbaddcadaaadcccbdcbcaccbcaacbdddbdacbccddbdabacacabbcdabcbababadabdabddbaaccadbdadadabdcdcbccdcacccccbacbdbcacbbbaccddcddacadadcccbcbadaccbabbdbddccddccaaadcdbbacacadcbbdcadadbcacbcccdaacdcdbcbbdbaccddbddbdccbdbccbbcdaadccaccdcddadcdcdccbbabcaddcbaadbdccdbdadbbbdcddacbdaccbabababcdddddbbbababdbdabbaccccaaaddccdbdcdccabddcaabdcaabccddbdcaccbacaaacacdaacbcbcddcadbbcbabbcadccabdbdbdbacbdaaaabdbbdbbddddbbadaaadbdcbcccccdddcdbddcccabacddbbacaaaccacbabdcdaddbdcddcccbcabbbcdbdccdddbdcabbddcbacbaaacbdbacdbacbbbabdbdddcddabdacbdcdbddddbadcccadbdcbdacacadaaacabbabbdbadabaacaaacbbdbbddbaacddbdccbabbcacbdadbaacadcbcccbaddbdadddbabccaabbacdddbddabadaaaaacabbcccdacaacbaabdabacbaddbadbcdbcbbbcddabddbbbbccbbdbbaaabadbbcbddcccccaabdbcacbbcabddbbaddcaaccccdaccccbccbdccbbbabccdcbcacabdabccddaabdaabbcccaaccdbdccdbacccbcddcdcabdcbbcadadabbbaaabbbbddcdaabdcbcaccbccddbddaaccabbaddcdbcdbabbcdabdbadacdcabbbacdddcbaacdbdccbcccaccacabbdddaddcdadcaaccaadbacdcbbaaabccddababaccaaadddbdcdddbcdbbcbbdbdacccdbccdbbbbbbaaccbbacbcdaaaababaadcccaaccabbcbbbcbdddcacdcadabbccaacdcddaacbcbacadcaadcbcbbbcbacdbbbabdaabbccbbbccbbbaddacccaccdbabbdcdadadbadbaacaccbdbadbdbbdddadabacabbcacabadcacbcdccbccdaacdddcbacbdabddbcaddcabadbcbdcadbacbabcadcadbbcadabbdaccaacbbdcbcccacbdaddcddcacaadcbabcaadabdadacdbaadbadbbcbddaddbdabccaabaaaddadadbcbbdabbccbdddaddbdbbdddcacbcddbabcbbdaccadbbbcadbbbcaaacccdabacbadcacbccbdcdcccacdbbacacbccccacbadbaabccbcbdbcdaadcdbbdadaaabccdccaaccadddacbdadbddababcadabcdabbacdadbcaaddbcdcddbddaaaccaccbcabdcadccbadcdaaadbcaabbdcabadddddddaddbdbbccccdccabbdccabcdbdcbadabbcbdbcbbbcdcbacbbbaaddcbbabcccabcccabbaddbcbdcbbaaacdcdbbadbddaaaacdadcabccdcbdcbacbdbdacbbcaddacbccdcbcdadbbcacabcdadabcbaabbbcbdcdcababbaaddacddaddacbaaddadcbbabcadacaabadadbbbabcacabbbadbcbbbbaabaacddccaddccabaacbbcadcddddbccaccaddcdaddcdaadbaacddabdddbbcaaaabccadbbdddbddaaccbdcabccbcddaabacaaddaaccdbacddaabaaadcccbdaacacdcdbababadadcabcdaaddcabdadbbccabbcacaadddccdcacbbcddddcadcaabbbcddabacacabacaacccaacabcdbaddbbbcbacccddbbddcadabdddccbaadccaadcacabbcdcbbbacdbdddaabaabdaaaacaccacdaacaabcbbdcccaacddacbdcabdbaaabadddcaadadadcaddaacbacabdaddcbdadbddddcbdabdbcabacadbacbbccbdbddcbcbdddbcdaddcdbbadabdbcbdddbadbbbdacbcbddcdccbcbdaaabbccdbccadaaddbbbcaccabcbdbacaaadababbbbaadaadabbababdacaabaacdabddbdbababaddacdddbdbbcccdbdcdbbcadcdbabdbccdcadaaccbcbcabacbbbaddbcaddcbaabddcbabbcbcbbbaccaacbadaadccbdbabdddaacbbcdbddacaddccbadbdacabaabccdcbcadcbdddabbbbadacdadabcbddcaaacbaacbdcbbdcaccdcdabdadddddaabbdddcabdaccaabbbbacddbaabdacbbabaacaddaaaddcdadbcabbcabddcddcddcbcadbdaaadbacadaabddcccddcdacdabbdabdcadcdadcdbdcddbcbbcbdcdcaacdabaadaddbadcbcbcbdccaaaaacabdaabcbaaccbbdacacdddaccaacdddacdbbdbaacddccddadbacbcbdccbdcaccbadcdaabbdbaccdcabcbbbdabbccddabdaadcaacadbbdbdaacaadbcaabbacadaccbacadabcbcaacababbaaabcdbcabddccaadcabbdacbdcdadcccabcdcaaccdbaabdcaabdcddaaacbaabdaababaaaabccacadacbccbdabacaddabddaccccddcdbcdacabadabcbdabcadddcabdcbbaddbbcadccbabacdaaaccdcdddaddbcaacbbbaaccbcacdaddddcabaaaadaadbcaababaddcabccdcbcdacbaccdbcadbccccdcddccbbdcddbcbabcacbdbdcdcabcdbbdcdcadbbdaddcbdccdddbdaddbbaabdacbcbbcaaacbcccaccdaccbcadbaaabadbcbdbbcbbabdbadbaaccadacdadaabbddddbcdadacacccbbcabdbdbccccbdcaaabaacacddbcdacdababcadadbbbabdbcdbbadddddadaaaabdcdabcadbccdcabadcaabcbcdbcbbbbcbcdabccccbbaddcdbddaacddaddaddbddccccddddaadcddddacaadaaadbcbcddaabaacacddaccdccbcdaaadaacddbaaccdaaddcbbbdcadaadcccdaadbdcbcaadccdbcbacbbacddcdddacaacbbcbbbbdacdcdbcdccaaabdadccbbcbbadbcbcabbaccdaacaaadcdadbdbcadcddabcbcdaacacadaddcbbbadbbcadbccbbbcadaacabcaaddababacbdddaaacdccbadbbacddbcdbbbcacdccbddaababacbacabdaaacbbcbabbccabcccdbcaaccabddbcbddcaccdbdcadcabcdcdbdadddccdaaadaddacccddabcacdbcdacabaacabcdaaadcaaabcbbcbddacdcbacbcbbadddbcbdaabbbccaadabbcbdbcdccdaaacdbcccbcadccccbbabcccaabccabdcdacdcbcdccadbbbbcaabcdacabadabbacbcdcdbbbdbabacaaababcbabbcaacdddacbcbabbcbcbacbaabcdaaacccddacadcbadbbaacbcbadbadabdbbbcbadcacbdcacdcdcdbbcbccaaccdcbdabacdddbcddbbbdddaabbadacdbabcdcbddcbacacdddaaaaddbbaaaddbacadcbbbdacdacabaabaabcadbbadbacbbdccdaadbcdbcbabaadcbcdadbaadbcbadbdaccbabadbdadbabcaacaabcbbdcbbdaaadccbddcbddbddbdbdbdbaaabcabababdbbddbbbbabcddacdabddacbadcbdbdbbccbcbdababbaddbabcddbaaaacdcddccdacdcaaccdcdcabcacdabdbdbcddbdcabaadacbcabaaacccbbbbdaadaabddabacdadabbcbbcccddddbbbaadddabaccdaddbcccacadcacdabcddbadbadacdddadadccdcdcddbdadacdabcddccabcbcccbdabddadbbcdbddbbbdbbdbacabddaaadbacbaabacdcabacabbcbadacddbdcbbdccdcbddbacdacbbbdddcadbdacdbbbcaacbbccdccaccbadabdacddbcddbbcabdcbbcaaccdcbbdcadacddaadbdcbcbabbdcbdbcbaddcbadbdaadbccabdccaacaddddcdcdaacbcdcbacbbdcdabbcacacaacddadddbdabadcabababaacbcbddbbcbbbbcbcdaddaabddadbdcbbbacbcaaabdaabddabaacaaaadaacaadddcdbcacdcbabbdbaadbddabcaabcdacdcaccacccaccacbbbbbbccccabaaadaadacdabaabbbdacaaccdbabadbcdaabbbdabdbdccbbbbcaccaccddcbdcbcbdcdcabbbcabacaaadabbaaabccabdcabadaadddcdbbaccbdabacaaccccccddabacdbbcacccadcbbbcabcbcbcbacdcaddddcabbcaaabaaadcbddbbdbcbdccddbddcacabcbbababbdbbbddbdcbaadcddbbbdaabccbdcacdababdabbddacaddaaccccbcdcdbcddcdbcccbaaabbdadbcdcabbadddddddadabcdbaddddcaddacdccaadcdaccbcbbbaadbbbbbccbabdddcbbbadcdabcdbcabcbabdaacbcbbacbbaccddccaadbabbcdabcbddcbcbbccdabbcbcbbabbaddaacddbabaadbccaadbcaadcbaaccdbdadbbbaacbdddacbdcccbdaaadaabbbbcbccacadcdcccbbdcddabbcaadbabdabbabcccbcdabbbbddbaaccbcaaaadaadbdabacdcdabcbcaddaadcaacbabdbbdcbacdabadbbbdbbabcdcdaacacacdadbbbdbbdabdcbcbcacbdabaabadabdcdbcaabbbbccdbbddccadababcdbccdccbddadbdacdcdcadbabdccbbbabbbadcdcccaaabaabbbbbdcddaccbddccbbabaadbcabcadabddccccacccccbabcaaddaccabacbdddbccdacacaacdacbccdadcdcbcdbdaccdcdbbccdcdbdaacccaabcddadbaddcbdddacbcdacdcadaddbbcdcacdcbcdbacdcacdcbcdcdcadcaaddcabbadbddaaddaddbdcddbcccbdbbdcaccbdccbbdacddcbddcaadbcbaaddacdcadbcdacbababbdabaadddddbcdcddccababbacadcaddbaacadbddbbcbdbdbcbdbbaccbddabadddcdadbdaacdabbdadddbdcbdddcabdccddcdabdddbcdbcabcdacadbacbbcbcadcacddacddbdabaabdbccbddbbaadbbaaacaadbcaccaaddacaaabcabcbaabcdccadbadbaadcacddcabdbabdddbdbacdccbcbcdbcabccdacdbaaacdcbbaddcdcadbbbdddccccbadaabbccabddbdbcdaddcdcbabbadbdccddcacbcdacadddbbacbddbaacdcadcabdcaacbbacddadcbcbbbccddadddcdabbadccacacbadddcaadbcabdbdddddbdcbdcccccbbabcbdadadcbacabcdabcbdcadbbcadccdbacaabdbbaccdddaaabacccaccdbacaddcdcddcabddcbbcdbddbbbcbbcacadcadcdabbaadbdddbdbacdcbaaadacdadddbacaaacbabacbdcddbabddcdbacaddbacbacbbcbbddcabacbcabcbcdbbcabaadacbcddbabaadcbcddcabcdcabdcbbccbcdbdaabcddbacadadbacbccababadcbaddbdbbcdccabbaabcdacdcdddbcccaacdabacdcddcabacbcbdcaabcaadddaacddcbbcccddcbdbbbcbdbdbadabdcdabbbbcadbbbbcbccacacabdabbcdcbbcddbacdabdbccbabbabadcadabccddaacccaabababbbabbaddabbddaccccdabdcbaacabacdacdbccbbadcccacbbdcccddaaccacaccdddbcaadaacdcbbccbdcdabbacadcabaabdccdaadcaddcbdbbdbccbddccadaabbadcadbbbbccccbacdbaadbdbcdaddacabcacabdaddaccacdbbcdbcabbcbddaaabdddcbdbdbbbbaacdacadadaabdcbcccbcbabbcaccdbbdbadcaababbdadbbbaccacbaacabaacaccabcabbcbbcbccdcbbaddabcbcaabcaacbdadabaadacadabdbababbdbacdaadaccdabdcccadabdbcdcbcdcaabdacbadbcabdaadaaadcaacabadccbcbabdaaddccabcadbccddccababacccbddbbbbdaddcacbbbdaacacadbbbbaaadacddcbacbbcaadcabbdadcdbcddcaaaddcabcdadccdcabbdacdbccdccbabdcddadcdbcbccacadbadabbacadadbcccbcbbcdcaaadccbbdaaccdaaddacdabbbcbadbddccbdddcacbdddccddacabccdcddcaadddddbbadcdcbcbcdaddcadaaacaaddcababbcadcbbcbdbdcaccdadbbdaaacaabdbbdbbbadbdbbdddadbbabdbdbadbcdbdaccaddbaaabccbdcaacbcbcdbaacdcacbdcaabbbadbadccabbccadddaddadcdddabdacdabdbddbccdabacaddcaacbaabbdbbaacbcdcbcbadddbaabccbdcbcadbadcacaaabddbadbcbbdcccdcaacbcbaacddbbbadccbcbbddddbacbbdcccacdaccdbcaaccbaabbbbccbadacbcdcacaddddbcacdadddddadccbdcddbacbcaabdccbabcbabacdbbdaabacadaabccccdccdbcbadbbcdbbaabcbacddccdbccdabbcabadbadacabcbabbabcadadacadbcdcccaccbcabaccadbccbbabcbdbcdddacbcdccddadacadabbddcdbaabcdddadcbadcbdacbbcbdccacbcdacdbdadcbcdbacccacaaadaaaddcddddcaaadbabdccbdccdbbbbbaaccabddaadadddabaacbcabdadaabcacccabacacbddaccddcbcaddcadacdccddbcccbbaddcdcabbcdabbaabcbbadcccadddbbaddbacccdbcdccbbdccdbaccbcbdcbdcabbcbadcbdcbbbabdcadadbbbaaaaadbdbcdbdddcccdcddddddacbddcbbbbbcccccdacabddccaccabcdccdaddacabadbdaddbbadcababbbbbbdddbbacbbbbbadddbaadccdadbdcdcbdacaabbabaacdcaadabdacbaaabdcaccbbcaddbbaaabdbdcbcbadbbdacbdadbcbacadacabaabbddadbbadaadcbaadadddadbbbdcaccbcdddcaaddbcdabbabbccbcccadbccddddcdbcdaacddcddaaccdaadadcbabccdbaadbdbbddbbdadcdbaacbdbddcacbdcbccbdcaccbbccbcabaadadcdabacbcbabbccabdacddbdcbacdbcbbbaaabbdbbacaaccdaabdccdddabdcaacbdddbbdbdacadaccabcdbaadbadbcacabacbaabdcbcdcdccdddddddcdacdcdbcbbcdcbbadadccbdabdbdccbddccbddbbbadaadacdabbcadaaccabdbccddbccccabbbdacbdadbbbbdadabcacabaadbacdbcddbddbabdbdaccacbacadbcacaccbcdbadbacdadbdaaccddababbdabaccdaddbababcabdbdaadcbcaadbadbaabacbaaaadaddbddcdddbadcdddbabdddbbdacdccbcadaacabbddbbcdbdbbcbddbbcacacccadcdcadbbdabbcadaaaccabccccacdbbbdabbdbcddcacabadabcdccccdcbadbaabababdddddbdccdbdcaabacbbbadcdacabcbaddabbaadaccaddcadcdabcababdcacadacbababbdccdddacdbcdcbbdbcbccdbdbccbdaddadddddabdbbddbccddbaacbbaadbbbaacbbbacccbababcddacbcacdbaacadbacdabaacbbbdcaddcabadbcbddddcaabdcbdbdddcaddcbddbaccacadbdcaaddcdbabcddacbcabbdbcbaccddccbabcddcaddcbddbccabbddaddcbcbcbcbbbdcbdadcabbbbdddacdaacaaddacbdcbbdabdcbaaadccddbdbdccdbacabbabdbcbbcddbabccbddbacbabbabbabacadcddaadddaaccbacdcccadcaabbccdbbddcadcabbadcaabbabadcadcbaadbbabbacdabbbabacaaacbaabbbdbdbccddcdbabcbcbbacccbadaddbadbcaacbddbbbcccbdbcadabddcbacdadcddcddacddbcabdbcbcccbcaabbbddbbacbbcadbccbabaaadaadbdbabddbadccbdccabbcacacdadbcbaaadbcaddbcaddbcacbbaacadabbbbbccadccbdccacadaabcdcdbdaabcacdbdcdbbccbbcdbdddadbcacaaccbbbcdaaaadddbbdadddbbbdbcccadbcbabdccdabdddbabaddddbbacabdbcabdadcbcadaacccbcacadcbacbdabdcccddaacccbacccdaddbacacacdabbaabcccddbcbbcbaddcdacadcdaddbdaccccdcabdbbaabaaccccaadabdcdaaccdcddccadccdddbacaddabcbaabdaadacaccaabaadabccbccbbaadadacabddbcdbcadacdbdbdcdbdbbaccbaabdcdccadcdbddddcdcdbbbcdcccccaddaabdaccdbaabacadabcccdabbbdabaccdbbbbacdcddcacbbccadabcbbdbacdccccdbacbccacbdbdaababccaababcccddddabcbcbcbdbbbbcbbcdaaabadcaddaacaadddadadabdccbdaacdbadcddbabbaddaaddaacdddcddaaacabbbcdcadcdbcaadaaaaaaabdaaccabbdadacccbbbddbcabacababdccaddbbccbdbcdbcddacbabdddbbacabdddaadadabdccbdadcbccaaaccdddbddcdbddddbbcaabddaacacaacbbbdbdbcddadcaadbbdaabbabbcbcacbdbaadaccdbbbabcbddbaccdaddcccabaacccdaababbacbddbbbbbadbcadababacadaacbbbdbcaccabbdabcabaabbaacbdcbbddbaadbcbaababbadcccdcdddbacddbdcbdadcbddcaaaaaabdaddbcddcdabaccccbdccddbddccdadbacbbcdbbabbbadcadaadacbbdddcaadbdacababdacddbbcdcbcddacaddabbbbaacaddacabbdacdcbcdbadcddbbdbbbddcabdabcdacbabbdbcdcdcbdcacddbabdbccdbbaccbbabbcddaadccbadbabdccddcbdadddcddaddbccddaaccaaacbbdbcdbccdcdacadaccacadbbadcaabbbdabcbddcbbdaabddbdbdbcaaaccbdacaacddbdbcabccdaaccccaaacbaccbddcaccdccbcaacdbcaaaacccacbaaccccdbcaddbccdbcbaabbabaabbcaccbcddadbbcabccaaccacddadadbcccdabadaccadcacadddbdaacdbbddadcadaccdccadacdaaaaaababbdbbddcbbdddcbcbbbcbcacdaddadbdaabacadababcdbdddacbbbcdabbccbabbdbadccdadbcaacbccdccabaaadccdadbccbadccdcadddaadacdcbabdababcbcadababbbabadbdbaababbabbbcbaabccdddccabcadaddccdabcdcacbabccdbaadbdadcdcdcdcddcbbcaccddaacbddcbddadcbdcdbcdbccadbbdbdabdbbbcdddbbcbacbbdbacabbddccbbadaaccdbaabbdbbcaacbbabaabaadcaabccabcbdabadabcbdacbcdcdcccddbcacccbddacbdaccacccbcbdacbbbccacbddcdccccbdcaccdabacabcbcbaadcdbdbddcacaadbbabbbccdccbdddcabaddabdccaddbddbbdbbbccadaabcabddcaacabbaddcbcabbacddcbbaacdaaccaabacdcadbaddabcacbcdcbbdaaadbdbdaadadcdcdbcabacddcaaddbccdaddbdaadaaaadcdacabbbdddbabbbdbbbadcdbaaddddaaaccdcbaadcdcdbbabbddaacddbdcdacbdadcadcaadbacdcccbaaabccbcacdbbcdbbddddbccbaadaadadbabaaddcbcbdbbcabdbbbbbbcacdbcacdbdcdcdcdbcaaacdaccddacadaddcbbccdbdaadabbdbddadadabddabababddcbbcdcacaadbbccdcbacccaddccdacbcbabddbdacbacbbdaadcacbbbcdccadaaababdbdbcccdbdcbdbababacccdbaddddabddcaaacaadadcadacdcbcadcccacdababaccbdaadaddbadbcdbdacaacbcddccccddbabcbcbaadadbbbaaacddaaccdcdccdbcabccddbbbbbacbbabccbdcddddcabcddbacbaadddccacdcbdbbcabbbabbcdbacbbbdddaccdaacddcbaadadadacbcabcbcdaccddcbdacbaacacdcdbaacdcaaaacdcacbaacbdcbbbabdadddbdddbdddbbcabaddddcbaccadcbbaccdcbabadacbbcdddcbcdadadaccccaaadcdcbbdbadabcdbabcaaccdccbaababbbcabaabacdcbcbacddadcdabdcaadabcabbcacbacbcadddabaadcacacabcaacbacaabbcdbaadaadadbabcbaccbbddcdbbcbbcbcbacdcbabaddcdbcabaaaddbacbbcbbcadddadcaaccadbdcdbdbcddbbddacaaccddbcaabacbacddbaaacdbdaddcddbccaabbcbaddbdddabcbbcbcbdcdcccdcabcaadcbdbdcbdabbbdccbcabcbccdacbbbdddcdaacacaaadddbccdcaddabdcaaacaaddaaaccdbbdbdbcbabbcdcbddaaaccabcacdddcdaabadcacdbaddcabadaabaaaabdbbdaacdacacdabbbadbacdddbcddbdadacadddddadccdaabbcdddbdadacabdccbabacaacddaacdbbabbdccddbbbaacbbbbccbbcbcdcdbdcbbdabaccbbacdbadabcdcaccbcbdbaabaaddbcbccababcdbcddcbdbbbddbbdddacbcacadbcadbdacacdcacbaccdaacacbacdbaaabcbbbacacbddabbdabbcbdadaccbcbccadbacaaccdbaaccadcbaaaabaababadbdbbabddaabbbbbbccbbcbbbbadaabdbcbaabaccdaabbcadacadcadaddacaaabddbcdaababbdabdacbdacddbdddbcccbdbbacdaccbadcdabcddaaddbacdddbddcabccbcddcadadabdbaabaadbcbccccbacbbdbababdccbbaddbbddbbaabccadccbcabdddcbddcdddddccbdcbbabcbcadaaacacadbabcbcabbdcbaccdadcbdccdccbdccaaccabadbccadaabadaacdaaabbbadbbdcbbbadcddaabddadbdabbadcdcddddaaaacddcdcbbaccbacabccbbabbbacabaaabcabacdcdbbddbdbddbabdcdcaaacddbbdcbcbdcccccabacddcdcababbcacdabacdacacbcdcbcddcbabbdbaabadacbcbddbbdbcadcdcdcbcaaddaaaaacbccdbdacbccbacbcabbababbcacbccaccadabddcbdbcdddabddddaabcbaaabdabadaabdbbdaacdbcbabcaabccdbcaaabdddabaaacdcaddddabbdbaacacbdccaaaaccbcddacbdcbaabacadccbbbcaaabdbbbbdaadbbbbcbbcbbbbaaabaacacacdbddababcbbcadabdcbbddddbacdcbbbbcabbdabccbdaddcabcbaddacabbbabcccbcddbbddcaabcbbdacdcabcaddcacdcccadbdcadcdadaaacddcdaccaaddacbbbabddaadadadadacacaaaccdddabccbcacadaaadddccdcabcaddbcbdcbdadadabacbdcccadacbdbadbbbbabdbccdaccacddbcddcbdccdbabcaddaabbcbabdcdcbddcbdaddadbdaaadacddaddbacaddcdadbddbdcaacdbdbaabaaaaaabbcaacbddaacbcddcddbbbcdcddaccccabaabbbdaddabddadcabbcbbcbcdaacbddaaaddadbbabbddacbcccaddccbabddcbcbcacbcccdcdddbdcdbbbcadbacbaaaddadcddddadbcbadcccccbcbdacadbdadcddcacaacccbbccddbcbaaadbddcbbbcbaabdbcccdcdddadbcbaddccdddadadaabdbcccaaaccabaddaccbaacdaabbcabcccccabbbdaccdaaccbbccccccbcbdcadabbbcdccdddcbbdbbddcdacabdcccacccaababbcabdccaccabcdacbaacbaabaabddadcdddacdcbbddabadadbaaacacdbbdbccbcddaccadcadcdacadaaadcbdadadadabbdccbbbdcddcbbddbacdbabdbaacaacbbccacdaadbacdaccbaacbdaaddaaabbbdbdddddcacddbcbdbcdcbcbbabadbdbacbccabacbdaccccddcacdccabdbacababdcddaadbbdcbaaaccbccbcbbbbcbdadbadccbbadbbadcdccddcacabddbcdbcaddaabccabcbcaadddabaddbbbbbcacaacdcdacbcbcdbbbbddbcaddabcbaddcbabaadabcadbddccccbccdccbaacccdaadabadadbbbddbdcdbacdbcdbcbcaabadbbbbbbbbdbbccadbaacdbcbabdbaadcbbbddaccdabcccbcdcadaabaabcbabccdcacbccccabdbdccabacaadbbadbcdbcdbdcbabdadbbdacdabdcdcbdddacbcdddccadcacadabdaabbbbdabadddbbabcdaaadabbacadccdddbdaddccabaabdccdacbbcabccbbacacabdbbcbcdabccccbbcbaacabbddabadcccdaddcdbaaaaaacccdabccbcdaaabddbdbddcddbdaadaccdbcbabbdcddaabbbabababbaacbbcadcaaabcdccadadcdbcdbdacbddaabbcdbccddcdbdacaaaabcdacccdaadddcbbcbabbbabdbaccbdacdabbacbcacadadbddadbbabadbadddabccdddbaaadbbbcdbdbbdcbbccadcbdabcabdadadaaacadacbbdddbbaccbacaacacabcbdcaddabacadaccbbbdacdddcdcaacbadddbadddabadadacaadcbaccabdadadbadabddbddbbaaacbbbcaddadddcdadbaadabcbaaacadbadbbddbbbcddbbbaadabcabcddbdaabdaddbdcbbbccdacdccccaccbccaacdababcabdcaaaabababdddadbdddbbcbaaabaddaabccbababdabbdcddaabdddbbcdcddbddcbdbacdbcdcbbbabaacbdbcbdcadaacdbaddddbdadadaadcdcaaadbdcdcaccabdcabdaacaabdacadcaccaabbccdddcadcdbcddaaaccbcadbaadccdcdcdcbbabcddacaabbbaabbdbdaacbabcaccabacbccbbacddaadaccdcababaddcbbcdbadcacbadcdadddacdbcadcabbadadadcabbdabcacabacbbdabbcbbaabcbadcbdcdaabdccaabdadcabbbacbacccdbadabbcaababccbcadabbdddddccccdbbcacbaacbccbbcbdddcdccbdbcbbacbcaadacbacaadbcbabdcdadccccbadbcaacdaccabaacabacabcbcdabcdabdaaccbbabcbdbabbaacdbaaaddcdbddabbbdcdcbdcabbcdcaaddaaddabdcadcaaababcdcccbdcdcbabdcbdadadbbbabccdcbcbdccbdccacccadbcaccadddbcdccbabdadacbbdabcdcadcdadcbbbcbcccaddacacabbcdbccbddcadbddbadabaaaddcdbccdabaadaacbdaddccdbdddbabbdcdbdbbccddadabaddadbcbacbccadcddadbdccbacacbbcddccbadcdcaacdcbcdacddaacabdaccbadcddcdadadcbaddcbbcdbdbdbaccabbdcbbcdbdbbbdaacbbcdbddbccbabcadcaddccbadcbadbabbbcbadbaaddcdbdcdcdacdcdccbbcdbabdacbabcaaacddbbbbdacbaaaddbcddbdbcabbcbbcdcdcdddbcddacdccbdbdcaacabacaababbccaddbdacbcabdadadaddcaabcccadcabbbacdbbbdcaaadbbcddacbacbabadacdbaacbdbabdddaddcaadcaadcaccaadbaddcdddcacbcbdcccdbdcbcdcdddbcdadbcaccacbccaabccbcdcabcdabddbdcabdacadaccbdabcdddcacdddabddbbdbcbdccbdadabaaadcddbbcbacbbcdbdbacdbabadabbacccbacbdbdaababdaaccadcdccbaddccbddacdadcccaadadbccadcdccbdbcdadaddcdbdcbccbbcdadcabcbbbcadbbdabcdabdddccccccdcbcadaadadbcbcdbcadcabcdabdbdddddcccbcdddacabaabdcbadaabcabcabcddaaadadbadacdaacdadbcbddbddddddbbbbbacbbaaccdddadddccbdbcbdbdcaaccddaabbadddadbaddbcabcbaabccabdabaadccdcadcbdbdbaabccddddbdcbccdccbbdcccaccabadccacdbacccdabdbccbdcabbadddacaaaccccbadabddbcdbbbcaddbaacaddbadbddbdddbbdacdaabbdcacacacbcadbdabbadcadccabbaabbcacabadabbddbdaccbddaadddbbbbbdcbcacdcdcdbdcdccbbaaadcbadddbcdadacbacababdcbbbbdcdaabdcabbacadbadcbbbbabddacdacbdaacabacdbccabdbbdbadbdcabbbcaaadcdbbdccbdbcadbbcaddcddddcdcadbabdaddbaddbcaaccbcabcbccaccbdccdcdbbbbddddcbcdbdccddbadbaabbaaaacdaacddbbcbcbaacdbddadccdbcccbaddcacbccacddccddcbaadccdbdadabbccaddabcbbbbbdbcacaccaabdcbbcdabdbdbcdbbcaadddbacdabdcdcbddadbbcadbcaccbbcbbbdcdabdbcdcdcbdadcbddabccaccbbddddccaddccbaaaccabbdacdccdccbdddaabdcdcaaddcbbccccdcdcaabbabacaccdcaaccaaadcadcccccdccbdcbaccdaaadaddddcbdcbddccdcadbcacababdadcdbcbdacacdbaacbaccbbcbbbbbdcdcddacdadbbdbaacdddacaccaacbdccccaddcdabacdabbdaabbbdbbabaaabdcaadbbcdaabacabccadbcaadadaaacabaabdaccbcabdcbbbdcdbddabaaddaadaaaddbbacbbadbacbabcabadacabbbabacaccddaababbbdaaabcacdccccdcccbccbcadaaddcdabbcadbaacdcdabaaadcdbcdabadadddbddbadaabcabadbcabcaddbadcbbabcdbacdcccbbadaddadbdcbcdcacbddccccbbcbbccdbddccbcbbbdcbaacadabccadcbbaaacbbbdcbcdbcacdbcccabcaacaddaccbdaadbbddcbdbabcdcaacabdcabcaadabaddabbcaaadadacdadbddaabddbdadbbcabacddbdcdbddbaaccdbdaadbbdaacadbbabccbbbbbbdcdbaaaacaaddbdccdcdacaacadadccaccbcbcdddbacaccbcabacbbbcbcbccbaccadaadddaabdcbbabbcbcdabddcccbbbddaaccdbacdaabacdcdcbbdccdaabacabbbcaddcccbdbdadbadcdbbcdbabaadbdcabbdbbbaaadbcbbbbddbbbcaabbdabdddacdddacdbaabbbcacbdababdccbcadabcdaacabdaabcbadbdbbcbdbbabcdadabdaddadbccddabcaadadbaaadadccbabcacaddbbdcaabccaacdabbcbbcbdbbdacccaccbcbbddbdcddbcddbbcaccaabcaadccddddacbbcadddabcdbcbbaaadabdcdacabddccbcddcccbabacdcbcabcbbdaaacaadcbcddcbdbdbadcdddcddcaaccbacadaacdbbdaaadaaddaddaacadbbcbddbdcbcadbdddaadbdbbbbacddbccccadbccbccdbbdddcadbddbbbcacaadaacbbcadababcadabbdbdbddbbcdbababcbbbcccdcccabcabaccadbddddcbcddbbddbaacdaaaaabbbabdcacdabdbccddcbcacdbcdaacccdaccbacbadbdbbbddbababcccccddbccddbadddbcdcaaadaacaacbaadddccbbababccdddcaddabdcccacabbcdccbcabcbbacacddcbddabbbddcccdcdcbbcababcbccdcacbacbbcaadadbccccdacdbaaacababbdadcdabcdbaabcbbbaccdccbcbcbcbbcabbbddcabcabaacbaadacccbabbbdbbcddadcbbabcdbaddadbbaabbdcbccdcdcddadaddbddbdccaabbacbbadabccbadccbabdbabbbcddaabbaaccbcdcadbbccbdddacdbdbaaacdadabdbaabacdbdacdbcdbccaddbcdddacbccbadcbddddddccbdcddbccadbabdcabbdbdbcdcbaddacaaaddddcbdabbbbbccacbadcddcbadbddcdbdacdaacdddabbbabcbdacbabdcdccaabbaabcdbcdaabababdcdacddadadacdabddcbcdbaabccbcbcddcdcccccdbabdbdbbdbbabbdacbddcabdcadaabcacdcaabcbdbbdddcdbaccabacccdbdaacbbdaddaccdacddadccbccbbcdbbcdaaabccabacaccccccbcadbaaaccaabbdaaabbadabdcbcbbdbbcdbdccccbbbadcbcbddcabcbcdcbbbaddccccadbbdcbcadbdbbadbcadabcbbdabaadcddcdcbccbaddcdccaddbcddacaacccdccbcddcaccdaabadbdaadcbbdaadaaacaabbddcdbdadddaacddbaddcbdccdbaacbbadbdabccaacdcbdbaddababadaaaddbccadcbbadaccdacdbabbdabadbbbacbacadbaaadbaabacbdbccdcacbabcdcabdaacbcbaabdadbcbddbaabdacaadaddbdcbccdabddabbbdddcadcaacaadcbdbdcddbdccdbbbdcadcababbdbcbddcdcaddadadaddbbbccaddcdaabbccbbddbcbcbbdcdddcabcdccbcddbaaabaaabccbbdcaadadcdadcabaacadcaccccdabdccdbdcbdcababbddadbdccdcdcacdbcbaacbcabdbccacbdaaaabbaaadcbcdcbcdbbaddccabccddbabbadccabcdaccddbbbcdadcacdddabadbabcdcbbadbbccdbbaacbbdcdaabcbbbdacbdcdcacddadaaaacdbabbdcdbbdcaabbbacaccbccddbdcbaaddcabaacbdaccbddaaacdbbaaccbadbabcccccaccbbdcbcacacbdaacbbcbbcbcdccbdddbbabacbdbaaaabcbdbbcacdacadbdcabbbbacdaaaddadddbcddcbbbbbadbbdacccaadbbcddddadabddbdcddaaccaaddcbdabdcacdccbcccbbbbbacccbbdccccbabaccaadcddbddbbcddcdbccaababcddabdcdbbcacdaadaacccabcbcabadccddacddcdbdcacbaaadacbbaacdddcbaadcdbbdcccacbdbabbaabadabaddbcadcccbbccabdbccaacccbaaaabadcaacababacbdadcbbcbbbacdbdcaadbcdbbbaadaccadabdccabcbcccaacdaabcdcdabcccbabddacdaadbabbdabddcdcbcdbcabcbaccdaacbdbabdadadbdbdcbacdbcabdbdcccbccdccccdaabcbcccdccbbacdacaaddbaadcccccadabcbbcddbcdbdcaadbbacbcccdbdcacbacbcccbbacccabacabccbaddbdbadacdacaacadbbdaadaddbcaaadadabdccbdaacadbbdbbcdaabcaccbdacababbadabdcbbdabcaaabbbbabaaabadabbdccadddacabcdaaadababcbcabbcaacabdacababaadadcbaadcdcbdacacaabdadcbdcdbcadbbbdabdccbcdacdbddcdbddddcaaccccadbadbbcbcdcadbcaacdcadcacdbbddbbacbbccdbdbabcdcdcacbadacdbccadbabdcdaacccddbcaddbbccdbbbdaaacdddccbdaacbaadcabadccdcddcbaadacbbcbbbaabdddbbcdcbabccdadbdadaccddcdddcccbbbbacbbdcaccaabdbcccbbcbccbabdbacddbacabbdcbcbdbdaabadaccaacdcddbbabdcdcacabddcadccaababbabccacdbbcadccaadbdabbbdacddbddaadabccbdcbbdbcabbbdbadcabccdbabddacaccacdddbddcddccabdcbaddcabcaaddbbcbbcdaddbcacbbddadaadcdcdcddabcaaabbddccacdaaccdccbbdaaddabbaaaaccbbbcbdccbdccbbdccacdbdbbdadcaddbbdbcacbbacdaccdcacbddbcddcbbbdcaccdcdbcadaccdcaacddadcbdadabbabcccbcadbccdaacdadbacadddaabacbbcabbdcacbcabdddcadbacabcbdddcbdcdbbccbabcbadaaabdcaacacdcbbaccdbbdddddaaabddcabbcccaddabbddcbdddccbadcbacccabcabacdcdbaaacbbacabdbddbabdadbbdabcdccbcaacbcabbbcdccbadacbcacccdaabcabcacddbcabcdabcdcbbbbddbdabaaaddbddabbbdccddbdadbcbccaadbccddbabcdacdbcacbdbdaadddacabbababacccddacadccddddababbabaabbabbddddccbadaacddcabcccccaadcdadcbaaababcababdbddcadbaaaabdabbdcbaabaadbdddbaabcdbdcdccddacdaadacacdbdaabddcaccbdaacddcccbdbbbddcbbbacbcabbbabcaaaddbcbbcdaacaddacccdbcadaacbabaddabdbdcbccdcdcacbdbbaacdaddadcbdacabbcddbbacabcbddbcdccabaaddabbbbbdbcdcdcbbdaaabbaacdcbbabddbdaccddabadadcbbbbababdadcdacccaccadacabdabccbbcbcaacbbcbcdccdacacabbaaadacaccddbdbcacdcabdabccdacdddabdbaddcdbccbbbcbdcababacdccadaadadddbdcabccccdcdbdbaddbabcbbbcbcccbbccddcbdbbabcdcddbcaaccbbdcaabadcbdcbdbacdbbbddadcbbddccbbcadabacadacdbbcbbabbcdabaddbbbbabddbbdcdcdcacaccaabddbdabbccbacabcacbcbaaabcacaadbbcbaacadbabacabdbbccadddcdcddcadcbaddccdadcdcdcdcdabdcdccdcbdbaabddabbdadcaadbbdddbcdbaabcdddbdbdacaaaacdbccbdcdbdabbdccabbbdcabcabbcaadaaccdabbcaacaacbddcabccbadcdbbdcddcbdcbcadbaacbbdacabbadaddadbbdddccccacdaaaddcccbacbbddaadccdaacbbcbcdaaadabbdbdbabdadbbbcdcddaddcbbaaccdbcdbabbddaadadbcacbccdaabbabadbaabdbcdcdccdcbacbbacdcbddaacbcbabcbdddbbcccbdcccdddcbbdbdbdbdbbcddcadcadcaadbadccdcdbabbcbccbbbdddcdacbdccdcbabddbdccdbdccccaadcdbccbcabdcdbccaadbddabdbdcdcabcbbcbdddbdadcbacadcdaabdbbdddcaacacaacadccdabdcaaddbcdddbdcddadaddabcdcdcbccabcbbabaddbaaabdadacdbadbcacbaaaccdbdbdabbdbabbbccaddcdbbabbcdadcdbbbbbddbbcbcdbacdcddaccccaabcdaadcddcaccbdcbadbadbcbbcaabaadcacbbdddbabaccddacbadbbbcbbdabbaadcdaaacdbaabbbcccaaddbbdcaaaaabdbddacddabacadabccdbdcaaadaddccddaaadbdaddcdbccabcacdadbdacabadcaacaddcabdddccbadadcdacdadacbdbaacaaccbddbccddacbdacdaddbaaccccddbabccddbdcadbcaadabbdbdbbadbddacabbcacabaacbcaaddbbaccabdbaaaacabbaccdaaccccccccdcadccaabcdcdbcbaaacdbcacbdabbdbddbdcbcbcdabccbbdcdaacabcabdaccabacddcabcaccabdacaddabdcacbdcacbbbabbbcdababacbaabadbacdbcbcaaaacbbbdddbcbcaddbcdbccaccabcccbcccddbddadbcaadbbdcaddbcbacabadacbccbccdabddcbcaccbbbdcaaddacbcdabdbbcadbabcdacbccbdbaaabdabdaacdddcdcddbcccbbcbcdbdbccddbdcdaaacddbadbbbdadcdccadcbaabbadbbdaacacccbddadbdcaddddccdacacdbabbdcabdacdaccbabcabbabcdabcddbcbbdaaaabccadadcbabcdabababcdcdbacdcacbdbaaddabcbbccdbabaaddbacbbddcbdbaaabacdcccbbacacbdcbbcaabcccbdadbdcbbdacdbabcbbcdbdddbdcabdbdcccababbdcdacdddbabacaabadcdbdccabacdcadcbcabdbadabbbccbccbccaadcacbbabbccbcdccabcdcacbaccbccddcbdcccdbbcacbadcabbadadddbadaadaacbcbbddbbcacbbddabccadcbdcdbbcddccaddbabbdabacbccadabdccbacbaabcccbdaabadaccbbacabbccbdacaacadcccbcdcdbabccdabddddbbaddcacacdccadaddaaabcddacbcacccaddbdbdadbbaadadaabbcbabdaccdacadadaaddddacacbcbdbbbbcdbddacbbbdbbacbbbcddcdbdbcdabacbadacaccabdcdaadddbacbcbdabaababcadcdadbcbbadbaacabaccababacbbddbdacbdbdabbdcdddadcbbdccdcddaddbcdadcddcbcccccdacccdcbddcadbcbcbbcbccbababcdcbbdcadccacdccdbbcbdcbbdbabccbdbbacbbdbcadbacacadbcadaabacbcacbcdabcbcbadbbaaccddccdcdcadaaabcdacadccacbddbaaaccbdcbaabdaadbdcadbaabcadbcbcadbcdadbdadbacaccbabaadcdcaabbcbaaacdcaddabcbbdcdadababaacadddacaadbadabbdaaabccbdbddacdbbadabadacdddbacbdaadcbaaaacaabdacacaddcbabdccdbdddcddbabbbbbbdadcddadcdacccdaddabcccdbccadddbddbcbaccdbbdccdadddadccaadadcacbacaaaabdaacdadacbbbaaacccbdbdbdbbddadcaacdddccaabbccabacaadabcbdbdaccdbdddcbdbadacbdacadaadcaddbcdadbcbdcacabccdacabadacbbacbbbdacbdcabccddabbadcbcdaddacabadaadccbaaabadbddadddacaccadcbadddddcbdccdccccabaadcbddddcdddcaadddcacabcdadabacaaddbbcbcbdbaddcdacddacabdababdaaccbcdbbcbdacaccabcbababddcaabccadccadbbbacddcccaacdccadcddbbaacdccbaccacdcadcabbdddcdabbdcbdcaadabccacdcdccaddcdcbcddcabadadbdcacdbbbdaccabccbbabbbadacaaaaaaaddadcddcbbcddcbbaccbbbdacbddabdaaddbbaadaacdddcdacbccadbdadbcbbcddabcdcddacbbdadbbaadaddbaddbdaaccadcaaabdbccdacdbcabacdddcddddbabcdcabcaabcadaaadbbbdccabcaabdbdddacbcadbbcacaaadbcacacaadbcddccbaabcdcdabbacdbabbdadbdaaacdcadbdaddbadcaccbacccaadadbaababbaadddbabdcbbacddcbddcdbdadccddddcbddddcdddcbddaabcbaddbdcdbccdbcacbbddcbabbccdbbbddcdaddbdcddaaacdbdadbcbcdcacdccaadcdadabaadcbcbddcdbbdadbdbcddbbabbdcaacdcbdadddddaabaccbbbdddbdbbbddccbacdcaddcaabdacabccdadcccdabdaacbcddaaabbddbddcdbcacacdadabcabcacbbbbacacbcacacaccacaaaaddcacbcdddaacbcaadaabaabccbbabbcbcddcdcbddacbabdcdadbbdcbdbacbdbdbaacabacdaccddcbdbddcdbcdbacdcbadbdcaddadcbbdccabbaacdcccabdcaccaadbbdaadbdccbadccccdccbbabcbadaaccdcdcbbbbbabdbbdbbbccaadabbcaadbcdcaadaaacccccccbdacbccacddbadbadbdaabdbdccadbbcabdddcbacdcdbaccabccdaccccbbddbccbcddccdbdcabbadbdcdbdcbaccbbbbacddcaaabababbcbddbcccddbbabadadbaccbdbbcaadadcccaaddcbdbcdbabccdcbbbddaabaddadcdcbdbdbdcbcbbbabbaddcacacaaccbdbabcdbccccbcaddabbacbcaacdbbbbdabadbcbbbababbdcccaccdbaaccacbbdabcccddbddcccdcbbbdbdacbaccbcdbcaadacddccbdcccaadaccababcacaccddacbcaddccbbdddaadbbaddccabcbabdcbccbabcadadbbcbcbbdbcacddaccbdbdaaccababaacbdacbbdddadddacbabcbdccddcadacdddbdaabcbaacdbdbccabbbccadbadcbcbaccddadabacdaccdaddcaaaccccbdbbdacdbdaacdcacddaabccbcacabbccbcacdbccbbbbdabaaddcddcdbddbcaaadadaabcabbdacbbbcbabcadaabdabcaacbbccbadbdcbaccbcbdbdcaaabacbddcbbbaacbbbddaaccbbdddcddacabbdcdbacddcacbabbddbcdcbababcadccaacbbdccccccacccadaadacccadaadadaaddbbcaaaadbbbadadabdacadbdcdabcbdcbdcdaaddcbdbddaadcdbbcbdddcdccaaadbbcabcbbbadaacbabdcbdcbccccaaabacbabbdcabdacdcdcdbdaccbaaccbbcdcabddccabadababdddbbcadabccccdacdcadcdddcadadbaabddacadbadadadcccbaaabaaaabdcddacdcbbbdcbdbacdbcddcbacbababdbabbdabcabcadaacaabcaccdcddddcddcbdccdcbcdbcbbcaddcaadccaacbabbcdbcdcbdbbadbcbbababacabdaaccdadaaddaacbcdbbdcdbabbadcdbaacbbbabbbdadadcbbaddabacdaddcddbaccacbacaccdbacdbbcbadcacbacdcaadabbdadbbbdadccabbadcadcadbcbadbdabbdadcdcabcdbbbabacadcdddccbddaacadcbddbdabccbdabacadbdccaadbdbcaccabcadddbabacdcdbadbdbcbcbabdbcdadbdaaabcbdbcdbddbbbccbbbdccaabbccdccabbccccbbabdaabaddccdddcddcaabcbdbbabaacbddbccddbaadbbbbbddacbbbbbdaabbddcdbdbdccbbabdbabbbbdddabbdcdaaaddaacadddcababdbddbabcadccdacdcccbccddaddabcdadcdbbdcabdcaaadcdcdcccbcbacaadaaadbddacaacadacdbbabbddadbbadbdbdbcccbcccadbabccdcbcbadaddbbabcbcacbdbdbdbcccddacdcbcbddcaccdcbdcacdaabbadcdaccdbbdbacadbcdcaaaabbcacbabdababcdacbccdddaaaababccaabcddccabbccadcbddacdbbbbbacbadabdccaadccdadbbcbbcbabdcabdaddcbddbbcccdbdaabcabadbcdcbdacaabcabcaacaaaaccbaaaddbcbcbdbddbcbdcaabbabdabdddcccaacaacbdacbcdbccdcdbacbaaadddbdabbbcadabdddadcbadcadadaaddbccdcacabcbcbccabaabbaccabdacdbcabdbaaacbbdcbdddbcdddbcdbdaabbaddcdcddbdbdcaaaaaccdabcadaaabacbbddabadabbdbacbbabdacdddccacbbdcccbdbbdcbcbccbbbcdcadcbbaabaaddbccaccbbadcbddcccabdbdccdbddccccdacbadababbbcabcdbbbbcbaadcbbcadbabdcbcaaaaacacadbabddacccadcbcbabbacabddccbcdabdaaaccabbccaaacbbddaccbccaabdadbaccbccbbdababdbabaaddcddcbdbdbbaadbdccacddcacbabdcacdbacacddcbdcbcddbdcacadcdbcbacadabaccbaddcbacbbbadcacacbbcaacdcacacddccbcabbbabccdadadbbbcbcadbcbbabacccdccbadcdccdaaccdbdaccaabbbdbcaadbcccbbacbdabaccaabdbaadcbccccbdcaccbbbabddabaddcbdbbacdcbabbbdbabbaacabbbcbcabbddbcbbabcbacadaddbccbddacbcaaddcaacccadadbabaadacaacbbbbcdbbcadadcddcaaddaccbaddddddaccccbadddcadbabbcadcbbacbbaabacbdacccacacbcddccacbbdcdcbdbbaaddcabbcdcbbccdbdcaccccddacccbbddcbbbaacbbcbcabcadbabacaadddaccdbddacbdcacdaabaddacdcddadbbdbaadbdddddcadcbaddbaababdddcdacdbcbabdcdbbdcdbdcddbadcdcadacabdacaaddabaaaaacaabdcddcbadabdbccbbdddacdbaaacdccdbcdbabbdcbcbbcacaaddabdbddabdcbddadcccdcbdbdcbbccbdabdaadcdbbbccdcacacacbbdbdcdbcdcbdbaccdcabbccccbbcaabadbadddbbabbddbabbbdbadadabbbacadacdbacbcccbcacbbabbacabadabcdacabbadabdacdbaadcbaddccaacbacadbdabcbcbdcdacbaaabbdbabcdaacabcdcccbdcdaaadbbabbccdcbadbddbadabaaaacbbcdadadbdbacadcacdaccdaddcdccbcbcbddcabccbcbdabccbacbdccdabbccaadbacccabccaabaacaadcabccccabbcabcacccbbdcdaaddbdcbbbcaacadccabddaaccdadcddacdbacbddabdbddcadcbcdbddbcbbcdadbbadcdcbcdcccdacddbdbabaabaabcaaaadbdcdbacabbbcbbacbaabbadbccaaaddacbadbcdddacddcdbddaaacacbabacdabdcadbbbbbdcaaccdabcddadaaddaadbdbabcccbdcdadabcbdcdaadcadddbaadaadcabadaabaaadaaadadbacccbacbacdcdcdacbdabbbadcabadacabaddbadaababbdcbdbdcacadcbaccaadcdabadccdbcdcdbcabbddadabddddcccabadbdcbcaaccdaabadaaaacbccccdcaddcdacccadadcbdbadaabbcdacacacdcbabbccbbaddccdddccadbdaaccbcdbcdbbabbddcbdcaaaccabbdbcaabccdabcaddbadabcdbcdbccccaaacbabbaddadbadbadbacdcbccddbdbbcbddcbbababadacbbbadcbabbcdccadadbcdcdcaadcadddbaaadbcdcbbbacddcaddbbbacbacbababcaaaabddccccdbddacbcadbccdbaabbaccccabbdcdadbadcaabdadadcdddaccdacbdadaddcdbcdbacdaaaaadacdbdcddcdcdbbdacbcbacbccbcddbabaabbcabccdbdccdbdddbdadabdddacccbacdadacaacbddaacabaacbccdbacbbdbbdaacaaaadcbadbbbcaabbdbaadbcccdcdbdbacbccaabaaaaabcddabacbdcbacabccacbbcdcabdbbbddaadcbccabcdacbcacddddcbbdacdbabcdbdaccdbaddaccdcdaadabccbbacdddbbdcccacbabbaadbabaddbdddabbacacbbacbbdaaccbcdbacdcbacabcdaaadbbbbbadbcdcccdbacbadbbadacabadaadddbbbdabcccababaadbdadacbccbaaabddcbcccdcacabadccaadabbcacaadadbddbadabdcddbdddacbdbbdcaabcadcbdbcdddccbaccbaadaadacbbdcaccdacccdacddbcbdddaccdbbacbaccdaadbbdcaccccbbadcdaccdbcdaccaddbbaabbaadbdadaddbddadbdabdadbdccdddacabaaddaacacaaaddaacbacdaddddbcbacdbaaabbbbddbdcdacaadcdcaabbcadcbddbabbbbbabdccabdcbbddcbbcdbdcddcdddbbbcacccdcbaddcaabcaddbbcddcbddbccccbadadaabdacaadadbdcdaacdbbdcbcacdcdbaccbcacacccbcdcbacddbaadcaadddbbcabacbbacbbddaabcdacdbbcbcccddcdabaabaddadbcaddcadbcdcdadbddcdacddcbbacdaadbcabacbcdabcaacbcdbcaadbcbccbcdbbcbdcdcbacacccbacbcdacbcbcbaccaaabbaccdadacadaaaadabdaccdddabcdbacccadcdccaccaadabcacdaacddaaabbdaabcabbdadbdbbccacaadddcadcdaabdcacddaddabbadacbdabbacbbdaccdcaccbbccaabbaacabcbdcccaadcdccdcbaccdcdddbaaaccdbcdbcadadadcdbbdaadbababdccccdbabadbbdbbacacbddbbccbbccadbdacdaaddddcbbdcdccadbdbaddbaddadbadbbccbcdbabaccdbddcbbbaaadccccadbbcadcaccdcbddcbcbcdbcaddbdcddcccdbbdacbaabcccddcaccdbadcddacaadbcbdacabcadbbdaccbbadddbdbccdbbacdadcbbdddbcdbdbdbacadabcdbdaadbdbdadaaccdbbbcbdcbcdadddadaccdbacbaabbcdcacbcdbadbacdddababdcccbccabcccbcddccadacadacdacacaccbaaaccabdcccbacddddcbaaacdbdcddbbcabcbbdcdbaadaaaabdabaddccccccabddddabdddcbdcdacdddccaadddddbcddccbbdbdddccacacdaadabcaacbacabacdcdaaaccbccbabdabadaddbdddacabbcbbaccbabcaaacddbbadaaddcacbbdccabbbbaababcbbdabbdbbbadbabccabaabbccbbcbdbdbbbbbadcccbcbdddadcabcaaadcddacbbaaabcadcccabddacdaccbbdbbcadbbcbbdccdcaddbbcccacdbadccabdbcbbabaaabbbadcaacddcdbcbdabaaabddacacacbadadddccaacddbbcccbaaababaccbacadcbabcdaacddbcbadcdbcacccbcbbaadccbbcddbdbddbaabbbbcdcbdcbaacadacadcdadbddbaaaabccdcdabccddacaacbcbcdbdbdbabddccdccbabaabadacbbbcbcccaaabaaaaccadbbcbdcdbcdbdddcaddacbbbdbaabbcbcaadabcbabdcbbdadccbcabccbadaabcdadcbbcaadbcadcbbbcbbaccadddaddcbbcddbdcbdbbbcaccacdbdbadbbaaabaddbcbdaabcdcddabcbcccddcbcccccadaddaabaabbdccbbacccadaadbcdbdcabdbababaccdcbdcdacadadcdbbbddabbdddcbbddbdabbcdcabbcaabdccbcacdaabbdcbccbababaadcacacbbbcabdcbccbbbaddaaddcdbbaccabbbdcaccacdcadaccdddbcbdcbaacddccabcddcbbabddbcbdddccaaddcabbccdcbbcabaabcbadcabcdaaacccddbaccdbdcbdbccddacaaaccdaabdbabdbcacaaacbdcabaaccdadbbadbacdcbcbadddbbdbabdcaddcbaadddadddcdcdbaacdabbccdcbdcbbdcbbbcdcdcaccccabdbacdacaaccaabdcbbdddbddaccaadbbccbabdadcbadadbdbdacdbccddaacccdbadcbbcaccbadacbdaadaabacdcdaaabdabbabddacbbbcddbacaacbacdcabbcacaccdcadcbcabbabcbabdddabacadcdccdbcbbcdadaaadbdabdbcdbddcacddbbdcdacaddcabadbbbccccaccaddbddddcdccbaaddbaadbaadbbcadcbbabccdcdcdacbabbddaccbacdcbbdbdabdcabdaaadcdddcabdbdcdccdaacdccccbaabdcbabaaccdcadbdabddacadaddbdcbddaddacbbabcdcdcccdadaaadbdbacaadabbcdddccbdcbcbddadbcdabacacacddbdbcabdbbbcdabcacaaccacdaccbacaabdcbdbbbadbbdadddcaddacbdbdbcbadacbcccdbdacadbbcdaacabacddbbdbdbbacaaadccdbadbaaaacdcacadcbcbccdaaacadaabbbdadccdbbacbacacccaabcddaddcddbddababdabdcdcbacbbacabbacdbbabbdbcbbcbaabcbabdacacbdcdadcacdaadabcdbadaddaadaadaaaabdadbccbcadcbaaaddcabddacbbaddadaaaabccbcaaacbdccbdadcabcbccacdaababbddacdcaacacaadbdbbdcadabddbdaaccaabaabddbdddbcdbccbadadcaaadcaadbcbccdcaacbadaddccdddbbccabdabbddddadacbdaccabadcadaabaccbdbcbcdddadaabbadacbdbaddacdcbddadbadadcadddbdaaddadbdbadbbcddbddccacacadbaaadcacbcadbabbabbadbcdccdbcbdacddcdcacdcbdddbdadbbadaadddcacbbcdbdaabcbabbdcdaddcbbdbabdabcbaddbdbcbccbccdcadddccdadbbaaacdcadabddadcbdbdcdbcbcbdbdcbdcadbbbaadcbbaddaadcaaddcccaddccdcaacacadaabacdbaaccababdcaacabcddabccddcadaacdacdabddbcdcaaacacccdcdbacacdabacbdcbbbbccadaaacdabdbddcabcabacaabcdaaadddbbcbdacabdcdccbddaabcaccabbdaacddbdbbadbdbddaabbddcbcaacbbbacadcccdddbaabdacddccccaabccabcbacddcbcbaabdacaadaaabcadcacababbabbdbbacbadcdbccbabbbdbdbbcdbbbcdaaadbdcddccdbccbdaabbacddbbcaccdcababcaabbcabcacbcddaccdbabaaccbbbdcbcadaddadbcccccdadcddcaacaddcaacaccdacacacbabcdbbbdcbadabdcdabccdbdbdcaaaddabcbbcdbacabdabcddbdcbcdadbbdcddbcddcbbddccacbbcdaaadccdcccadddbbdababdddaacbbbbdbbadaabdaaabadbcdbbdadddcdbcddacabdccccdadbcaaaccccccdbbdabcbabababadaddbcbddbccacdbacbabacdabbdadddcabbadaaddacccabbddcacdacccbabacabcddddbbcddccbcdadddccbacacbbccbaddbdbadaadadacacbcdcbbcdcdacaddcaccdbccbbbdbdcccabdbadbdaababccbadaccdacdaadbbdabdbcccbadbbdbdcddbadaabdddbbdbcbadbdadabadddadcddaabaddcaadadcabbdcabbcddaccacccbaacabdcacbcdacdadaccaaacccaccbbabcabcdbbddcacacdacaabdcdddbbaaaaacacdcccaccdabbcaddcddacaaddcbcbacbdccdccddcacbdccddcbbdaacaccddcbcbddadadbdbbacdcdbabbbdcdacdaccbadbbbabbdbacccbdccaddacadddccdaddcabaddaabcdccbbaddcdddddddbdaacaadcdcccbccddabccaaaabaabddabcbdbadccbdacaaadcabbccbabcdadadacbdbdcabdabbcdabaddadbccbacbaddbcaacdcacdbacacbbbddabddddacbbcaccbcdcdcdadccadcbaacdbdcdabdcacdbcabbcbcccdcdadaddacabdcabccbcccdcdccdcadaabcbddcdbbdaabdabbcaabccadddadccaabbbacaacccbbccacaaaaccbabacbbddccadcaaaaaabbbaaaddcbccbbbcdcdadadcdcbcdaaabcccdbbcbbbacddadbcabddbbbcccdddbdaabcddbbaabdcbdccdcdaaadaadddcdbbbdaaacccbcdacccdaccacbaaccdcaabaddcbaddcadaaabadbccabdbacbdbcbdbbbbcaabadddcdcdbcdaacaaabdabcdbddccadacdddabbaddacccdbacaabdcbbdbdcadacddcadbccababcdcbcccdcacbbcaabccdabccdadbbdbbccdaadddcadcccddcaacdabaabbcbbddadaaccbaadbcddcaacbadaabcbcabcbabcccabdadabcabbdaabacdbbdbbcacddcabadbcbcbabacabaddcdddcdccddccbdabaaddbadcdaadcbaccbacdccdcbcbccdcbbdabcbcaacbaacccadbcdbcdcdabbcaadbdcaaaadcdadccbdbacbccdbaadbdabccacaadcdbcdccbdbadcabdccccbbcadbbbdcddaaabdddaddabddacbbddacdbdaaaddbddcadcddcbdcbccbdccaaccbbbdcdaddddbcdbabaccadbababbcbacdadbabbcdacadadbbbdcbdbddcdacaddadccaddcbdbcbbcbdbcdcdbcaaabacbaabdacbccbcaabdabbdddadddccdacddaaacbadacaaaaadbbbbacddcadccbaadbcbccbdadbdadddbdadcadcadcbbccdbadbbcdbdcbbcddacabadbbdcaadabbadbdaadcbbdadbdaacbaaaccbbbdddbcaabbcbcbaddaaadbacbdcccaabdbcacacadcadccacbbabdcbbcddacbdddcaaaadcdbabcddabbabadaccccdacaaadcdababdbcbbbccdcaaaabaaabcacadbbdacccbccadcdabccdbababddcaaccbcbccabdbcdcdbdbaaacbdcacdabbbdbacccadaaacabadcdcadcbdadcacbddbcacdbaabdbacacbcbccbbacbbacbcbbddaabbbacadbbadababaacbacbacdbdacdabbacbbacbaacbbacacacdabbacdabdcbabbdbdbdbddddacbdadadaaabcbbdbdabcdbcacdaacabcaacabbbbaadabacbbadabaadcdabcaaaccbbddddcdbabcdcbbbbcdacdabddcccbbddadaadbaacabbdbdccbcbabdadbcbadabadabbddbaacabbdcabccbcbcccbcbdccadcadcaaddcdcbdbcbacadbcddabacacdaaaddaccdcacbdcaaadcbcbaacbcbbbabcbaaaacbcaaacdbcbdbadddcadaaccbabdbdddbbbbacbcabcabdbacdcabccddacabccaacbdabdcacccacaccccdbcbaadbbabdabaddddabdcdbddbddbdcccabddddbbddaddaccbdaccccbacccaaddcacbcccbcbbbadbcccdadbcacadaccacaadbcbadcbcacdccbacdddcccbcabaacdbcbdadbcdccdcadaddcdbccacacbcaadabadabcbaaddcbdcddcadcabcdbbbbdadbabdacbbbabdacccddcbcbbadbcaccaccccdadabdbcdacadaddbcccabbccdacdbacdadcddcaabdaadbbbbcddbaddbacccbcddccbbccdacdabbabdddacbbacbabacdbccdbaccabbbadbbcdaaaacdbcaababbbbdccadbabaccbacdacdcabacaaddaacbcdabcaadaabbdaabacccbbaaccccabaadbccabdcaddacbddbdbcaabddadbbbdabaaacaadcbadbadabddbcbcddcadbababadbacccacbbaabbcaddcacdccdabcabdcbbaaccccbcadcadbaabcddbdaabcdddabbdcacaaabddaadaaddddaaddbccbcbcbdbcbcdddbbccacccadcbdacddbbcdcdcbccdbdbbbdacaddbbabcaacdadddadcadababcaccabcbaacbacaaabccaaddccdcbdbadbbaabdcacbdacacbccddacacbcdcbabbacbbbbdcbaccbbadcdaccbaacacadbabccaccddcadbaabbadaacacbdcabaadbbbdcaddbcaccdbdadabbbcdbababaadcaddababbacacbcdbbddbcddcbbdcdbbdbbcaaccccdddbbbbbcbccaadcbabddcacdbadcbcdbdcccdccbccbaccacdddbcadbbccdbcdbabcbddbccadccddddcacacdbbbbcdadcddbcabacccacdadabadbbddbdbdacdcacdadcdacbddddcaabaabadcbcbadaccdbbdabdcabbdadcacabdcacbacbdcadabdaccccaabdbbbdaacdddbddbcaaccbaaccdaccaaddcbabbdacbbddaaadcdddccdadcccabdcdcabcdadbbcacbdbccbadbdabbdbaacacbadccdbccbccbbddccbabdcdaaddbbdbccdddbdcaccbbbaacabcbdcabaadcbccddabbcccbbabaddadabcaaaacabbcbbbdabbacadabadccbadaadacccaaacdbadbcaaccdbdcdaaaabdddccbdacbbbdcdbaccabbdbcaadcddaacdcadcadbbcbbdbdcdcadaddbbabbdbaddadacbdddbcadbcacaddcbbbadabbccbadbddccacbbcdcabacdbddbddddabdcdcccdbbacddcacddacbcdcbbbddccadabbababdccdcbbdacddaadcaaabacaaccadbdcacacbdbbcdccaabdddbcabcdcadbdbdbcbddbbbbdbabadacadbbaccaaabcbbcbbadabcdcddbdccbdbcaacccadaccbbaacdddcaaddaacabcacbcbdccacbbbbdddbcabbcadcdbaadbacdadbadbbbbbdcbbcabaccbbcdabddbdaaacdbcccdddbcdbabbcccbbccabacacaadaaccdcdbabcbabcdbabddbccabbabbaccabdaaddbadbcccdbccabbdcdbadadaacdcddcccddaddbdbdbbbbbabdbacdcbdacbacabbbbbdadcacdadadcaacbbcabacbdcddadbdccbbaacbacddabcbaadcacccacdaddbcdbaaabcbabcbbadccbacacbaddbcdabdacabadccbcdacacbaacadbcdacbaadaadcdcccbdaacacbdabadbabbbbcadcbdadcddaaddbdcabdabcaabddcdbaaacdcabdabdbccdbbbaaabdadbbccaabcddccadcccbcaacccbbcbacaddbbaccaabbbbcabbbbddcaadbcbdacdbccbdcdaaacdbbcbcccdbaaacdabbcdcdbdbaccaaadbdabdbccbbbdbdddaacbbaabdcaadaabbcbcaabddaaadcdbadacdacbcbdbadaabccabcadbbacccadbdacdbcadcbcdddcbddccabbadccbadddbcbcbacddcdcdcbcbddcdddabdbddbaaaccbdcbababadadacbccdcdcabdcabddaacdcaccabddacdcdcaccccccbbddbadaaddcbaaaccbccaccccbdcdbdcadadcbbdacbabdaacbbabbccbbabcaaabccbccdcaabbaabacbcdaaababbccaddccdcadcdaccbdbddbbaaddbcbabdaccbbbcaaadaadcccaabcaabccaaccadccbbdaaadddcdcaddbdabaccdddaccbbdacccccddbdcbddcddcdcccaacbdbbbdddbaaaaadadbdddccdbdcaabbabaabdbbcbddbdddbbdacbddbbacbbdbacbbdbcdabadacbcddccdcaaccdccdbaabcabbdddcccbccdacdbddcabcddcdacaccadaabaadadbdbdccbaddbcccbcbbddcadaabbdaabbcbccdbbabbdbdbdbcacacbcdccaabdbadbdababbadddddcacddbdbdbadcbcadcccdcccdabacadaaaaaacdadbcbcdbbdbadadcbcdddaccdbbbddddacdacccdbacbadacdbbddbcbbcdcdcadbadbbaadadcbbbcdaccccddbacdcbdaacbdbbddacdbcddddabcacdbabdaddccaabcdcdaccbdcbcabddabadbccdcacccdbddabccabbbadbbcdbaccddbacddaadcbccbadccddcccdaabbcdbaddacdcdbbbddbadadabdbccbaabaadbcabdabbdcdbcdccbddddbbaddcabadacdddaaddadccaddabcbddbddbabbacdcabcbddbcaccdadadcdccdccbadadbbdabbbcdddaadcacccddddaacbbaddcdddcbaddddbccbcadbbdddbdbbcccdacddcacddbccbbdaccdbbaaadccbccdbcbbdcbbbbcbaaaaadbabbadacacdbaaaacdcacccbccabaabaabbaabbbdcdaabbabdcbbbadbdbdcadaccabddbcdabcbcaddddadbbabacbacaaccacddbbcdcbaccbdadbabcddaccabcdcdaaabcacddbaddddcababdbbccdcadcdbbacaccbadccddaccdbaddbdbadccbdbacadabcacabccbbabbdbcacdcadddddbbaccacddadaabdadddbadddaddcaabddcdbaaaacbaabcacbbcdcbdbcadddbbddcaabddbabaaacbcabcacddaaadbddbdcbbadbccbacccdbdbacbaddbbbcdcbbadcadccdaabcdbcabacccdbcdddaaaaacdcbacdabccaaaadddadcbdcbccbdcbbbacbaadadbddccaadacadccbccdcbadcbdcdccbddbadabacddadddbdddcddbccbbaaaaabcabbdcababadddaadbadbabcabcaadccddaadabdbbcbbdddcdbaadacbddcabdccccaaadbaacccacbcdacbcbcabcabababdbadbabdbabbcdcaddcaccddcdbbddcbbcbbcbaccddbddaaccbdbbbcbadcccddbcbccbcdacaaacbadabcdbbdddbadddcdbbdccdabbcacbdabbbacdaccadcccacdcadabdaabbcdabdadbbcccdacadcdbabbcacbadbcadaaadcdcadbdbaabbcbcccdadbbccccacaccccbcaabcbbabdcaddbccbcbbbddaadbcccbdcbddababaaddddabdddccccdbacdaaddccccadcaaacaabadcacddbbdcddbccacdcccdccbbcbaadddcbabbbaccdabcbaccbcacbbcbcccacabccabcacbbcdcbbacbcdcbdbaabdcbdcaacbdaacdcccdbbbccccadccbdabbbcbcabbdbabdbbcacaababcbacdbabacdcadcddcdbadbabcaccdcabcdacdbdddcacbbadacbaadcadacccdbddabdcbadbbbcbbcaadccdcbcaccbaddbcddabcbbbcddbaccbabcaaddcabacccdbcaacdbabbcbbbdcbcbbcbadccbacdcddcdabcacdcbaddddcadcdcadbabbcaaadccddddabddcbacadbcbabcbadddcddbdabaaccaddbdbbbcdcdbacddbadcbabbbdcbbcdaddcabcabbbddadbccccbdbbdcaddacdddacbdacdccaabbacdddcddacdbdcbcaacbdaaaadbbcaacaaaadabbbababbddbbdddbadbbbadcbbbdadabdcadcaaddacdaadbabccbddcaacacdcbcbbccbabddbbbccbdbdbabbdacdacdddcbbbbcddcbabaacdbabcbcdbcdcdaabdaacadbdbccacabbdcabadbbadbdcdcbdadbbcdcbbbbbdaaddddbcabdacaadddaccadddcbdccaddcdccdcbaaaabbcdbccdbabcaddacbcdbcaaacaaadabdcccbbaabccddbbdbddaabdbcababccbbddbbdddcadacbcbbcbbccdccddcadddcaadccbcadbbcadcabbaabcdacadcacbbdadcdbddaadcbdbadbacdadacabacadadbabdbbbddcdcbacacadaaadbbbcdbacbbaabbcaddacdcdaaacccbdaaadadbbcdcdaadcdbaacccaddccacdbccdbcdcaaacccdcabbbccaadacaabbdcddcaacadcbdbdbadbdbcdadaaccdbdbdabaccbbabaadaadcacbdcccddadacadccbcbcaacbabddcbbdadbddaddcdcadbcdadacdbdcadcbacacbbabcadbcbdbadcdaaaaccaacdaabdcdaddbccacbacaaaccdcaaacabbdabaadadadcaddbbdabbacdaabcaacaacacbdcddccbbdadccdbcacccadbdcadcaaacabacadaaabbdabdbaddadbbdccdbacaacbbadaabcbadabdaabcabddcdbcaaaddddbbdddbcdaaaaadbcabdacbadccbcbcbbcdbddcbabbadcadbadcccbdabbdacadabddbdbbddbdbacdbdcabcbcbdbdcdaabbcaababaccdcbdbbcdababdbacbacaabbcaabddcccdbcaaaadbbccbbdacbbbbbdcabdcacdbbabbacbacacadcccdaddddcddabcadbabaacabadadbbbcbaadaabadaadcdccdbaadcadcccababdadbcbcbbbadcbdcabdadaaddcbaabbdcdcbacbcacdaadccdcadcacaadadbabadacbabcdbbbbdcccbbbcdbcbcbcbbacdcadbdcbaaacbadddbaacdbbbbddaaaabadbccbbcdabdccabcdcbbbbcbbbccaddddbabdbddccbbdaabbcacddbcdcbcbadbbccbabaaabadcbddcacbdbdcbabadbdcdbbbcdcccccccbaabaaacccdaabcdcbdacdccbbdbbcdcaabaadcdadccacacbdbaddbccdccabadbddccbdcabaccddbbbddddadaaadabdcdbcadabaadbbddacaabbabaddadacddbdaddaabaddccccbcdabdbabaadcdbaacacccccccccaabddbdddbbdbcccbdcdcdacdbbaccdaccbaabdbcbdbaabaaacbabdbcbdaccccdbcdcdbaddcddabdcbccdbadccdbcbbbbdccbbbddccadbdacdcaaaaddaadadabbaadccacbcbdacaddcaddbdccadadcbbababcabacdccabddaacaacadabbdabdaddacdbdbbcaabbdcbabbabdcbbccdbdbabddbdadcddbdcbadbcaddbbadddadddabacabbcaddabdadadcaacdbbddccdddbbdbbcbcdcbdddddcdbbaccaacbbcbddcbbaaadbaacbdbdbccbaddcbdccdacddcbdbbcadddabcdaadbdbbcbddaccaacabdbcbcaabbcbacbbbaccbcbcbcbcdbbcadadbccdaaacbdcacbdbcbccdddcddcacddacbadbdcbadddbcabccaabbabcbdcabbdbdaabaabbdbbcadbaabdbbdcccbdcabccbcabbbbabbcddabbbcabbabdcadaadbbbdbabbaaabdcbdddcccacdadabaabaddbbaabcbddcddadbddbbdacbdbacacdbcbdbbdbdcaaccaaccbcadcccbbbbacabaddbcccdcacaaaabcbcbddbcdcadbacbbdcbbadbaadbbadcbcddcbbcbbadbbcabcdbcacaddccccaacabcdcdbbaabacbbdbaaaacccccabdadbaaddddacbcbbcddbcbdabcdbdaaaaddacbcdcbabacdcbbcdbdbcbacdcccdbbcbcccbdcbadbbcbcacadccbdbdcbdbdbbdbbacdbbbdabcacaddabdcacaaaddddbcaaccdcdbbbacacdcaacbcdcdbccdaaccacbbcbbbccacaabbcbaccbacbcdccbdbddbacacbddabaacddbdacdddcbcbbacadbbddcdacbbacdcaaccdbdaaabbdadbbadacdbadaabbacdaddacbaaccbadbdacabaaababccccabcabacacddbccdbcdabbbcababdddacbcbdddbddadabddcacbabbdbbcbcbbaddcaaacbdbcccabbdbccaaadbcdaddbbaabccbcbaaaabcbadacaddcbcbbdaacbbbdcccccbbbabcaabbddbdcaddbcbdaddaadadbacbccdabccbcadadddadbcacdbcaaacdcccdacbccadacbdaadcbcbaabcbdabdcccabcbadadabdbddadcadbdadbcaccdcdbcbccdcdadbbdacacbaadccadccdddadcadbaacaddcdcdcddbbaaadcabaccbbabaabbcacdbbbbddabdabaabbaddacbddcbcdcbcacbddbdbddaababcdcadbdddcbccdbcccdaabadbcdabccacbcabdcddacaccadccabbcdbcbcdbadcacdacccaddccccbdcddcbccbcaacdcbaaadacbbbabcabbaaabcabddadaddccdabbabccdcbdccddcacdcbadbdbdacdaacccccabacbcdcaababbcddaadbbacbaadcbcdaacacbbadbabbaccabaadbcbbadcaaadccabdbdddaaccacabadaccadacdadbadaabbacdbbbdbcbabadcbaaaacacdcadcddabbacacdcbcddabcaccdddbcbbcabcdabdbcdbbbcdadbabaccadaaadddaaccdadddaabaddcdbddbdddccdcdbaacbcbbbababccadaaaababaabcacbcdabcdbbdacadacabdddbcababacabcdcdcdaabcdcdddcdccbcbacacaadbabcdaacdddccdbbddbbadbadcbdddbcacbbdbbbbabaaacddddccdbadacbcadbcddcaccbacaacdaabacbdbbcbaddcdbbaaabbcadadcdabcddcabaddcdcadaadaadcbbcabcdbcbabadbcadcdacbcbdddbcaaddabbdcdaddbacdcdadabadbbcadbbdccbaabccbaccdaadabbccddcddddccdcdcbcaaadbcbcbcddaccdcbdacbacaaccdcdcdbadcbbdcddaacddccbdbbcdbccdadaababddcaddabbacbbbdbdacbdabbbabbaaadcdcaadacccdccccdcabbbbcaaccbdacabbabcbbbbaddcccccaadacabaaaadbabdcbaaadbdcdcccdcacdacddccddadcadacbacacddbbdcdabcadcbccccbbdbdbddadacdbcbcdbddaaccccabbbcaacabcadbdddddbaddcbcacbacdccabcdbabaccadbddbcabccdcddcbccbcdcababcccdccdbbccbabbcadbbdddcdcdcdbdbabcabbbbaddbddcbbcabaadbbdbcdbdccaabadaddbcccdbaccacbbcbdccaaabdcbabcbcdbdbcbaadbcddbddbdccaccdbdcabbaccabdcccdcabbcabdbbccdabcdbabddbddbbbaaabbabcaddbaacacabadcccabdadadacaacaddcaacacdacabbbdadbadacdcdabccccbbdabcbcdacccdbaacbcbdacbdbcbaacacdbddcabdbabbbdadabbaaacbabcbcabdbbdccdbcbcbdcdbadcbbddaabaddbdaaacccaadbcadbbdcbcbadddbcddbbbbcadaadbadcdddaadcbbaaacababcabdcdaadadbcdadcaabacbdacdacccabcccbbcbbcdccdabcbbabbcbabcdcbccadbadacdcbcbcccaabbbcbccaccdcdadadcdadbbbdddcdbabaddadacdddcccdddbbacdbaabadbcdaacbbcdcbcaabadbabbabccdcacbccbaaabdcccbbcdddcdadbdddddcdaccaddcbcbdbabbcddacdabdbabbddadadcdaddccdcaaacabcdddbcddcccddbbdcbddbddbbdddbbccaddacbbcdccadabaaaabaabdacacdcabcdababbbdccdcbcddccdcdbaadbdbdbbcccdacaddbcbbabccacdadcbbddbcdbbcdadbcbbbbcadadccbaabccdaddadbaaaaadacdabddcdbcbbddcbdacabdbddcababcaabddcabadcdcdbdbddaabccdbbcdacdadadcbadccbcccabbddadbcccbbccdaccacabddcdcddcadcadaccdbabbabdbadaccddcdbccaababdabdcaadaccbbaabdaddddcdbbbcddccbdbccdbcdaaccddddadbadcbdabaabbdbbbdabbbdbcdcbccabaabdaabdbccdaaaabbbaccabbacddccadcbacddaddcbdddacaabbddabdbaabadbbdcccdabddbcadadadccdacdcbcabbaabdcdcbbadcdbbbdddccaaccddacacdbdccdcbacbabbcbbccdcdabdbcbcbddadcddbcadcadaacccabadcacacadbdcaaaabbcbbbaacacabbbbccdaccdbcbcbdccabbdbabdabcdbcacbabcabccadcaddccadabbbaacdbadbadbbaaababbacdbcacadadcbdcbbbbdaacdbaccabcabccccabbaabaddddabacdccadcacbabbaadcccbadbcdbbcdbbcdcaacbdbbdbcaccccaddbdbdbbddadacabcacddaddccdadcaaaabcaaddabbadbdbccadbaccdabadbdabacccdbbaccbaadbdadcdbcdddbbdcdabaccaacadbbabacaabccbadcdabccadbcbcbdbcaddbdaddabcbbdcabdbdcacbdcaaccacdbdbaadbbbdbbadccbabbaccaccacdcccadaacbdcadcaabcddbbaadddcadcaccbbdcbdaccddcdbacbaabdccadabbbcacadbdcdddcacbbacabacdaaaddaacdcdcbdbdabcaccbcadaabdcbaaccbbabaaabbdcaddaccccccaaaddaddddaccaaadcdcbcacbbdbcccbbdbbbcaabdbcdcaddcccbcbaaaacabcacadcabcbcccadcbcddabaaadacbcdbabcbbbcbccadbaabddbaaabccabbdcddddbabcaadddbcaccadbccbaadaaacddccabbadddbdaaabcaadcdcccbcbcacaaaabdddaaddacbccccaccbaddbabcbabbbabbdbadbcccddbbcabcdadadcadadbabcacbbaacaacdaacbacbabacbddcccabaaaaadcbacabccaddbadcbbccadbccababacbddcdbbcddcbccdbccdaadbdbcdcabdadccdabadbbccacacbbdcbadccaadbabcddbbabcbbdaaccbadaaadabbadccabccdbdccdccdbddcdbbbccdcbdbbbbdacdccaabbadbdadcdbdccdccbbcbbddcbaaabdadbdaaccacbcacdacdcbbbdcbbaacccbdcbacaddcadadcaaacbacdacdccbaadbbacdabbdbdbadcaadaabbccbdcbccacbcaaaddbabccbcdbccaaddadcddddcbdbbbccabbdaaddacdcddacaddcabadbaadaabbaddacadaadcacadaadaabdbcacddcdddcbaaabcddddddabbabdbbccaabcbacaacdcbbddaadaacbdbbdccbbcdcbcbcdbacabdddcccaddcabaadadbabaccbabcccaabaaddccabddbcbadddcabdddababbbabcdbbccadddadbaadacdbbbbcdcadaacccabaaccddbdcdcbaaddddaaabaacdcadacacbaabaaaaccbcabadbabbdbaccbddbcdbdcdbbadcabadaaacdcadddcdaaadcdaadababccdcddcabddcbccabdccaabccabcdaccdbdcaaabaaaabbacaddcdcbdcabacacbadbbdacabdacdbcaacbcacbbdcdacdccadbdcbccdcccacbbccccaddcaccacbcabaddacdbadadbcdacdcacddbddabcccacadcaaccbdcbbbaacabdbcbcdbbacbacabdaacabdccdbcaadcbbacbbcbabbddbbdbcbcbddbadcaabacbbaadcdbbcbbaadbbbabbbbabcacddbbbaabcddbadcddbdbbadaabdcbbaadbacacdcaaaddadcdbadcddcbabbbaabcabcabcadcdadbabbcbdabdabadabccccacbdbaabcaaadaaddabbdccbdaabcacbacbdcadadabbdcbcccacbddccbadaadcdbdacbdccbbdcdbddcdcaddaacacdaddbbdadcadcbddddddacaadbbdbbadbddcdddbdbcbacdcadbaaabcdcbccaadbdcabdaaddbadaddabcbacabbcabcccdcadcdcdcbbbcccdbdadabcabbacdabadcaadbbccdcccbbdcacaabadcbdcbabbcadbcbcccabdabdbacdadcabcdcdabccbbadadbdcddcaccdbdbcccdcbccbabbbaadcaabadacdaaaddaaddddbadbbcaaccdbbbaaccbcbbacbbdccdcbcdaabbddabcbbdcdaaddbbdbcbcccaabdcdbabababdbdabbbdbbbabacdacbdaabdbaddbbaacbcddbbcbccddaccaccadbcbdbcaddbccabccdbcaaacbddadbddccccabadaadadcbbbcddbcccbbbbabcadacddcdadbbccdababcbcacacbdadccddbbdcdcdbababdacbcdabaacbcabaadcdcabaabbdabacbbbcbcdddddcbbaddbdddbababadaddbbabbacdadacacacabdcaaadabbcbabcccdabbdcacaddcaddcbacdbdcbaaaccacabcadddaaaddacaaacbbdbadbaadbcdadcbddddadbbcbadcbdcacbbbdaabaacdcabdbdbaabddaaaaddadacccdacbdbbbbbdbdbbbbbbddadbcbddaddaddccbccbabadcaaadcbbbabbcabaabbcbadcbdaccbacdacabadadcbccbdbbababcdbaccdcabdccccbabbcabdbdbaaacddacbcdbdacaccbddcbcabacccdbddddabcccdacbbabbdaacbbbcdbabdadcdccaacbcdddccabdcadbcabbccbdabbdcaaddbccccabbaccadcdabadacadadacccabdddcdbdcacbcadddddcdadcdbcbddbbbcadcbbcadaddabacacddddbaaddabbbbdbbacacaaddbdabbbdddaacccaccabbcdadbccdcdddacbdadacdacdbdadacaabdbdbcbccddacababcddddddbbddbadbaaacdacaacbbbadcdbdabbcccbbacdaabdddbdbcdbdbabbcbaacbcdddabbccbdccbaaccbbddbaddccbccacabccabcdddddacacadbcbdaaaadccabbccdabbaddaadadcdaddddccddadcddaaabbabdcdcbcccdbbbddadbbacaabbbbdbdbabadccdaadaabcdabcdaabbdddaabacabcbdbcabbdabdbdbdbbaddcbbdcbcccbabdaacddbabbccddabacaabbdddbcbabdccdbadcccadcabaaabcabaacdadcaadabdaabbccdacddadccbbbcdadadbccacddcaccddcabddbcabaadbccbbddadbddbddbaddbacabaccdbacbdccbabcdcdbbbdcbdddabbdbcabbccadcdaabaaacaadcdbcbcbddccbaaabdcbacabbacbdccbbdbdbaaacacbccadadcbaabccbdcbcaccdcabdddbbcacaddbbbbcabdcdbdddcabbcbabbbdabadddacdabaadcaacacbacaaabaacbbdabbbddbaacbbbacbabadbbcdadcdcabdabdbdcccdcbbccabaaabcddadaaacbbbcacacccabadbdacddcaccadcddbdbcdaabaacbaddadcddccbdabccacdcdccacadadccbbcdabbccbdbbbcdcddcdabacdcaacbcbbbacddddaaacdcaadbbcdccaacaccbccabdabcbcadacabbddacbdbcbacddaacdcaadaabbddbcdacabccaabdabadaaaaabbcbbaadacdacaabbdcaaccdbabdbcacbcdabdbaabbcbdbcdddbaadacdadacdddddbdcbbacdbdcccdbbbdbbccdcaacaacdcaadaabaaacdbcabbdbbcbccdabddbddaaddbdbabcdddbbccdddadadbcccdadddbcddbbddadadaaaadcadccbddabbbdacbcbbacdabaaabaddcdadabadbdddbbbdcdaccacaaaacbabdaddabccaddbdadaaacdabbcccadbcdccacccdcacbadbbcdcbbadddbdaacaabbadcdcdcbcabccacdaabcbbacbadbcbcbabcabcbcbcabbbdaabcdbbaccbddaddcaacdddccdbbcddaaccbaddddcdacababcacaaabbaddbbcdbbbbcaaadddadccbcaccaabddcdadbcdbabbcbbaccbcbdacbbadacdaaacdbcbdbbaaaabbbcdadabddcbcaddadabdccbdadcbadcaccbbabbbbbddcbbbbcbabddbcdcbbbbddbadccdcabcbbcdbabbcacdbbdadaccababbcaabddabaddbbbcbcccacbcabaaaacadbcdcaacbdaddbaabcabbddddaddbdaaaabcdcbdcacbddbbbcabdbccdaddcadbbdbdcaccdacdbaacdadadcbccacdbcddbbcacbbcdaccccabccdddbadcbbbcacbbbdbabcdadcadddaccdbccadaaaabaddbaccaddbbabcbbcdcabdbcaccdcbdbddcccbacbcddbcbcabccadbabadaccbbbbdcdbdbdaabdcdbcccaccbddbaabbbdcbdbdccaaabcabbccaacbcacbdbdbdcdbbcbaadbccbcaaddcccbdbcaadaddaaadbacdbcdbadccdabacadbddcabdcdcdbdddbbccbadddcbabdbcdbdcccdaabadadbadaababbadcbcccbdaadbabbbbccdaacdcbcddabcddbabaabaabcbbcdabdaaacadcdaddaccddcbadcbcdcbcdbbbcacbccacaacadacccddadabcaabbdbaabcbdddccdccacaacbaaabccacbcabaacdaddbcdaabaabbadbdbcbccaacbbbccbcddcadbcabbdcdcdbcbacaaccddbdcccacaadcddcacbcccadccaabccabcdcacdaaadbbcdccccacacdcabcadddddaddbacccbcabdaabbdcdaadcaacccdccbbdbcaabbbaabbdacdbbabbcdccbaaddcbcabbddabdacadbabdbbbcdaadbbdbabddbbcacbabddbadddadcbdabadcdaddbbbabddbbcdbdbbbadbcaddcababcacaabaadddaddbbadccabacbbbcdcdcdcbcdadadaddadacdcdccbdaacbcddbabcccdbccbdcbdbbdadacdbbdabcccdcdbaabddbdabcbccdbcbaacdbdaccacdadcbacbcbbabbadcbcadcacbadbaaaaabbccddbaaabbacabbabcddbdabbccacbdccbcbabacdadbbddbbcaaadddcbacaaadbdadacbaaabacddbababbdadbcadbccdbbbaacdbbaababbbcbbbaabdbddcbbaccdadbcdcbbcbccccddddcdcccbbcbdbbdbbcaddbbdcbbbbbcdcddacddcdbbacdcdddbabbdbbdbcdabbacadccbbacbcaaccacddddabaacccabdbddbdccaddbbdacacacbcdcadddcaaadacbdccdbdbdcbbadaacbdcdbbabbdbcaaaabacbbbaadbbbbcdbaabaddccdbbaaacccdcddbbdccdcadbbddcbdbbcbacaccbdcaadbcdcccaacaadcbcdddddcddbdabbdbbcdcacbddbcddabacaacaaaabacabddbcbbbcccaddddccbadacbdabdbbbaacdbdabdbacbaacdadbbdababbaadaaadcbcbbaccbdaaacaacbdccbdbbbaadbadcbaabaaabbdbbcdabccbdcbdacdaaaacabbacaddaadadddddcadacaabaccbaaaacdbbbadbbaaaaaccdcbddadaadacacbcdbcdaccaabaaacbccddadbbccaddbcaccacccdbcbcabcdaccaababbbacdbdaacdbaaadbbbacddadcdcacbdbbacacddcdddcacbadccdbabbbacaabdbacabababbacadcbbdccddccdccaabbcddccdccabaacbbaacbdbabbdadababdbbbacdcacdcccbbaddaccbcbdcbdccbbacddbacbcbdcbccaaadbddbbbdcbbdcdbdccdcaacbbbbddddaaaadadcdadcbacabcabdbcbbddadccbaadcbbccdddabbbcaacaabbbbbdbbcdbdcbddbbaaaaadcbdbadddabaabdaacdbbccdacdcdadddaaacbccddbcdadadaccdbcdddbaaaabdabdbabcadcbccdbcdbbbdadbacbbcddddcdbcbaaabcabccadadcaddcacadaacddbbacaaddbdadcbbbccaaadbdbcdcadbddcacbaddbbaddbcaabdaabcdcdabbbbaddabadbddcaadcdbbcdcdaaacdbbabbbdbaccdcabdbaccbdaadacdbaabdacbacbddcadccabadadddbdbdcbabcbacdaddadcacbcaaacdaabadcbacaadacaadbbaaabacacbbdadacdbbbbbcdbcbbccaadabaaccdaddbccbdaabbbbdacdabcabdddcbabdbacddbcacddabdbdabbacaaabbbdbaacbcbcdadcaccaabbbcdbcddacdbaabaaabddacdacbccccadacaccbdcbabdbddbddbacdcabbccbdbbddbccadddcdbbcbaacadacbcbcdbccddbddabccbaacdccdbccbbdcaaadbcacaddaabaccaaabaadbdadaacacaacbccddbaccdacddcbbcdabddabcacdccbcbbdcbbaaacbabcbababadacbcbcdaabcbccaadbdcbbcccbcadbcdccaadacacdbdddacdbcdaabbcbbbdaaccaaccdcdcacabbcdcddcdabacddbddcabadcadbdbadccadbaabcddddcccbdbabaabaaadacddbbbcdcbcdcbacacbbaaaaababbcdbbaaaaccaaadacadccaccbbadbdbdcdaddacbcdcdcababbdbccacccbdccabbbbcbbddcbddbbccddaddaddbacdddabddbbaddcddadaccabcddaacabbdcdcbdacabccddbdcaaadaddcbdcbdadadccbccdabbabcbdabdbbadcddadabbacdbcddcacddabbdccdcccccdbcadacccdcccddcdabacccdbaaadddddcaabdcbcacdccdbadbabdadcbaccddbcaacadaaacdbddcbdacdaaadcccbdbdcabbacdbddcdddadcaacaddcabddaddadaaacbbababccbbccdbbcacbcdbadacbacbbabdbbcbdbdacdbadccdcbbdcdabbdbcacdabdcccaddbaddacbdccdabdacdabbbdaababdccddddcadbacdbdbdddacaccddcbccccabadbdbbdbadddabcabcdbdcdcdabbcdaddcbbabddacadbbbacacacdabdbbbcbaadacbadddabbbcacdaddcdadbbdccbccddacbaddbcdbbdadadbbacbcbacdcadaccbcdbaadbcaaacacccdccabdbaacaadcccadbadadbaabdadabcdadaacccababbcccacdbbaadcacdacdcaabcbaaabdacccbaddaadbdcaadaacddabdcbdcbbccbccbcaaccbadbccdacaacccbababcabddaabbbbdbdabacccdbddcaacdcaadaaddcbaaadcdcacbacbbacaaacccbbbadabcdadabcdccbbdacbccaaabddbcdabcdabcbdbbccacdaadabacabcabbaaddbbadaddcbdaddddcdcdbaccabbadabdccbcbcdcabcdaddadbacaddadddccddadcbadaaaacdcabdbcabbabdcdbaabbbbbadbabdcdabddbcadaacbdaaaadcdcaadbdbcabddddcabadbdbabbdacbbaabdcddaadbabbccacacddcabacbdbdbadbaccddbddaaddaadcdccccdadadcbbaababacbbcbbbdcdcbaadcbbcddbdcdcacccdcbacdddddcaddcaddbcbbbbdbbccdbcdbbaaaadbdaddcddbcdbdcdbbcdccdabccdcabccdbcabbbabcabcdbdaccbbaaddbaaababdacdabbbcbdbbadccdbcdccabbdacccbdcadddbbbacbbcaacaadbadadbddbddcabccaabdcbbabbabcdbddbcacacdcddbababddacadcddacbcddcbccbddabadabdbcdbcaaabaaabcabbdbdbcccbaccacddadabbcbbbabdcdbbccccddcdabacdcadadadabbcdbacbbbcdadcadddcdbbcdbbbbbaaddcadcbbcadbaccdbcbaaabbbddabbdbcbbcbdaadaddabbcaadbacdcacdaaddababbbabddbcdcbbdbadbcacccccbddcdbdcadcddcbdbcbbbdaddddabcdccbbccaaddcbdbdbcbdaacdbdcdccadcadcdcaccbccccdaabddcabacbdcdcdcbadccbacbcccbdbdcacacadcccbbcaacdaadcaacbacaadbabaacdcdaadadadcdbcddbcbbaacbccdaddadddddcddadcddaaabaacacbaaccccaabdddcdadbcbcdddbdcbabdccacbcbdbddddcdabdbbcdddddcabbaddbbdcdddcbcdcddcbaacaacbdbbdbdcdaaabdacabbabaabdbdaabcacccdaabaabcadbdbcdabbbdbabdddbbcacaccacbadcbabacabcdcbbbddcbaccadbacbdababbdcdcabacdaadcccacbbccadbbccdbdbaaacaacbdccddcccdadddadcbcbcbabccdcaddbbbabbcabbbbbaabdddaaacaadcbccaabcbabddbcdaaccdbaadacbacbdabaacdcbdadcbdbdbadccbbcdabddbdbccddbbcdcacaaccabbddcabcacbbbbccbdbacbbadacaddacacdadbcacabccddbccbdccddbabadabcbaccacbaacddaccdccacdbbaddbaabdcabadabdcaddbcbdbcadcabadbbaddcbddcabbdcabdabcadccbaaabbbbdaaaddbdddcbdbbcdabbddddcabdcdacaacccbbadbbdbabcbcadbdcccbacccbddaadbaabbdbbdcddaabddaaaabcbcdbdcdabddcdcdbbbbdacadccddacdddccccadcadcaacdccabcadcdadaacdacbbcbbdacbadbbdcaaddcbacccdbcababacdacbcdbbdbdabcdcabcdacababccbacbdbcdadacaddabbaccabddbcccdabdbcdbcdddadcbacbdaaaccbbbabdaddaaadaacdabbaacbdcabdbbacdcabdacaadbbadcadcacdccdcdcbdcabbaabcbdaccdadaccdacbddcddcaaaccabcdacdcdcbadcaacaaddcbdcbbccbdbacbaccdbbcacbbddaddccccbaddcadabdaabddbbdabbdcdbbbcacadbbbbbabdaaccbcbcaabbabbbaacbcbcbbcbbababcabadbdadbadcbabcddadcdcdbccdcccdabcddbcdcbdadaababdcdcadabbbdabcaadbaaacbbdacddcbcccabdadbcabcccbdbddadbaabcbdccccdaadbccbaddcbaaaccccbcddabbdbabdacdaabbccabddbdcabbbbcbdddcbbcabdcabbbcbacdbabbaadcdbdbabaabddcabadccccbbcabacdbabbddaacccddcdaadbdddbcdcbdbbbbabbccaaaccaacbdbbcdcdacaabccbdccbadabbabddacabddcacaacccdbdddbbdbcbdbddbaabbdcaccbcddababcdbbbadbccadcbabbbabccbaaddababaabcdbcabbdbbacbbbcbdcdccabdcccaaabdddddbbbabadbcbbcdcadbbabbddbbcbddddbdbddcbcdacbcabbbdcccbaadabbcdadaabdbccabcaccdadaadcabbcaaccbaddcccaacabbdaccacbdadabdbacddcddccccadbaaccdcadcabbbdbabbbbdbbdbababbcabdaacbaaabacadacabcdbdadbbababaccacabddaaaaaabdadabbcdddccadaaadadacdddadbdbbbbbdccbddacdcbabcdaacccbabcccbacccaaaddbcadcbdccadcccbabdbdbdacdbcbbbcdbabbbdbccbccdddcdccabbaccdbcbadadbaabbaacdadccbdccdbbddddbcaadbdbbacbdaaaadcbdabcaaacbcddbabbbbadbbbadddaaaadbcdaddabbbbabbbddcddbdbccaccdcadccdaadcadacaaadddacddbcacaabccdbdaabbbcbaabcbddabdbdadbbbcaaccbdbcadbbabccaabdacbadddacbcdbcdcbacdcbcaadbabbdacadaadddbdaadbbcddabadcbbcddcdbdbbbcddbcbbcadacdaddabacbadcdbcddcdbabccdbcdbccaddccacbcadbaddbaccbcbddcdbbddcacccacacababadcadabcbcccdcbdcdcccdaccaaccabcdbdcaacdbbcabdabaadbbccbdbdbccdddcbbcabccacaacdbcacadabddbddaaadaabddccabcccbabcbabcdbdcdbbbaacbacccacadcbabccbdaddadccbabcdcacaaadbaacccdcacaddbacbaaddabaccdabadbcccbbddabddbbdacadaadbcabbccddcdbcbbabccbdabbdbcdbdaabcdbcdaadddbbbaabacbbbddbdabbdbddabdccdbcccddcabcaaccbaacbdbbbaccabcbabbacbcaadddbdaccdabadabadcccabdadcbadadbccadabbcacdcccbccacdadbdccaddbbaaabccdccacbcccbbacbddcdddaddaadbcbcdaabdbdbaadcdbcdbbbabbbddcbcacdddcacccbcabbbcdbccaadcddddaacdbbddddccdaadcdacccdbadcddddcdacbacccbadacbbbbbdacbbccbccadbdbccddbdcbbacddddcabbbdbcadcacaadabcaddadbdbdcccadbbcadbabcbdccdcbcdbbaaacabdabdadadbcdcaaabacacdaadbbbcbbdcadbcabddcdbabdadacdadbdbabadabdbbcbbcbdddccccbcaacddadbcccddcabadacdadbbadddabcdaaadaabbacccdbaacddcbadacaccabdbadbdcbcbcacdbacadcbbabcadbcaddaabbadadcbadbabaddabddcdaabdddbaabcadccddaacaabbcbddcdbdaaddbbadcccacbbbdbbcbcbcadadaaddbcdbcbccbcbddbcbbaaacbacdaacadacdaccabaababacddddcadabccbcdbadcbddadbbbbdaacbbacabadbabbbdddbcabcabadcaadabbcbbdadbdaabdbbcbaaaadbdccaaacdcccdadcbbabaddbbbdacbabababddcbcdbacbbadbabdccdbccdcacdddbdacdddcdbdcdaabbdcabaaddabacdbacccddaabcddbacacacbdccbdadabccaaabacbccbdcbdabababccdbdbbaabbbaaddabacdacbccaaabdbddcddbaaccbaccaccccbabdabacacbdacbbabadddddcddcccdccabcbbacdcbabbcbcbcabaccdbbbddddabcdbbbbdbbbaddabdcdcacadbdcbddbccbcddbbdaabdbdcadadaddaaddaaddbdabbabbccadbcbaddcccbdacbcccdabddbbdbbcaccdabdaaaccacdabdcbbdddcabcacabbcacddccabacabaabcccccaaacabcdbbcbbbaddabacadcdaabcddbbdcdadccddcccbbdcdbaadadcabbdaddacbaccbbadadababdaccdcaacadaaabbcaaabaadabbccbadabbaaacbdcbddddcdadcdabcaabdcaabbdcdabdbdcbdacdddcaabccddacddcdacddbbcdccddbcaccbddadabcdadadabaabdbabbaacabddddcdadabcadcbcbaaacaccddccdaaabcadbaddcdbbababdccdbbabbdaccbbcdabaabdabbddbcdddbbcbcbadddcdbbdccabbbabddbdaddabdccdabdbdcdadbdcbadcddbcdbadcacadbbdbabddaacdacaadadaadbdaddcdcacdccccdabcccbccabacbbdabccdddabddadbacccdaaabbbaddcbcaababcddabdbddaabbbbbdadbbbacadabddaabadbaaacdbdcbaacdaababdbccdbadaabdacbcbddccdcddcdadccbcdaacdcbababdacbcdacddbccadddcddddcbcdbddbccaaaacaaccbaddbaacbcacbdbccbbbccdccbcdbbdadcbbbabbcdbcccdbcbcacbbdbdabbacacbacdaaaabbbddbdbadbcbaacdabbbcdacdccdbbcdaabbdbabdcaaccabacbbbbbabccacdadcbaccdadcbbbdcbbcdccabaadabadccababdbcbdcbabbccbadabdccccbbbcadcbdbacbccbbbabdaacbdcdbdadadbcaabcaccdbdddcacdddbccccabbdabcaabcbddbcdabbbcbdbbbddaadbddcccdbbadbadddbacdddbdbcdaaadacddacacbdadaabccdbabbbcddaaadcacadacbddbdbccdbbcacccbdbbbddccdbdacacdbadaddabdbcdbdacaadccbcaaccccccababddcaaacbbccaaddbdaabdaadaadddddcbabcbdcaabcbbbadaadbcdcbababcbadadddacbccccdbcdadccdcaaddacbadbdaabbdacadddabadcccbabbcbdadaaacddbcdcbabcabadddcbbdabaaddabbccccccabacdacdddbbadbdaaddaddbcdbaaacacdbcddcbdaccbdddbcdaccadcdccccacadbdbbcaaaaabbacdbabcbadbcbdcdabadbddcaccbacbaddbcdcacbdadcabcbabdccdcbadcbbbcddbcdadbaccaadcdcdbcbdcaacbdcdcbddaccadacddcdbccbcacaccccaabdbbbadcadbcdaacbdcaaacacbcdcaddbacabdcadbcbbacaabadccbccbaaabaabdacccabdddcaddaccddcadbbdcacabdbddadcaaaabbaabdccdbabbdcbbdbbbdbacadbaaabcbddacdbabaabcdcddbdbdadbbcdcdababaadbdaadaddcccbbddbdcabacdddbdabbccccddbacadaadcbbbbaadcbadcbcadcbaccdddddaabaabbbcbdbcdabcacddcdddbbbbaadbbdbbdcbbadcdcbdbbddaabdcbddbcabbabadccdaacdcbdbddcddbbbbbddbddbaabbabadacbadcdccbcdadbadabcacaccdcbabccaccabdacdaaacdccbaadddbabbdddacaacdaadcddbcaacdbacdacbcacccddcbdaddbddcdaccdbcbdacccbccabcbaadcbbdcacdbcdaadbbcdbbbdcbdcbdcabbcaabdbcbbcdcaadddacabcbddcadbcbcbdbaaababcdddbccbccdcabcbdacadccabbcccbdcdbdcdadddcbdabbadcabaadbccaabaabbdbaacaadbadbcdbbdcdcccabcaabbcccbacaabacddbbacaabdddbbadabdcddadabaddacddcaddbcabcbaddbddcddabcbdddccaccdcbbccabaabdcaaccddbbbdadcabddadbcabdadccdacbcadbcccacacbcccbddabbccbdbbcccdcadcccdcdddabcacddcaaabbaababcdcdbdadabbadabcdbbabbbcdcdadadadcabbdcdaccddaaccabdbabdabcccdbacdcbdbacabcacccbbbdaddacbbcbbacbdbddcddcaccbacbddddadcddcabdbacdcabcaddaadbacbdacbbddbbdddcbcbcacdbaadccbccbbdcbcdddcaabbbbbdbdacabdacababbcadddadcadbbbdcdaddbbacdabbdbddadaaaadacccdccbdbacaadcdabddbbbaaadcadadacaacdbbabacdddabbcbaadacadcbbdbabcdabcaaaddbbddcdbdacadbccbcadbdbccadbdbcbddcddabcabdbbcdaccdbbdccaaadaabcdddacdaaaddbacdbbcdcdacacdccbcdadaababdddbdbdccabaabbbcddbcbbdabadddbbbcabbacccddbcccbcccbbbacaadccadabccdadcabbddaadbbbddcabddbdcddbbdcaabcbbbbdcacbdbdcacacbdddbabadadbddcbbcdaabccbddbdbcabbddcababccaadabbbcbbddbadcbdabccbdababbdccaabcbdcdadddbcdaddabcddaaaabcacbddadabbbcbbcdabadbcdcacddabbcabcccabaddbacbabadccbbdcbccadcdababaccdbacadabddabcbadddaaaddcdbabcccacdaabdbbacbddbcabdcdcbaadcdddadccacbabcdcdccdadbbaadcbccccbddbaacccdcacbcdbdbcaadcbcccabbdcdaacccbccddbddaaabacccbaabcaacabcbdcdcbcaaaaabaddbadaddbccdbaaadcbdcacaccbacdbaccdbcccbbcacbbdcacbbcaadadbdbbadacadbcccbbbdbdcbbcdcaadaccbbaddbaaaabbccabdbdacabbddcbadadddabadcbbaccbcadccdcddbaabcacaaaccbadcacadcdaabcccacaabdaabaabadddbbcbdcaccdccacaddabdbbabcaaacbdbbbcdadbbadbaabddcacacacaabdaadbbbaaabdcdadddabccdcabccbabcbcdbbdaaaabcbaddccaddcbdcacabdaabcdcabbbdbcaddccacabaccbcbabdadadcdbbcbcbaadbddddbdaaaacacadbcddccbbccdbcbbdbdabcdcabcbacbdddcabadbddbadcaaabcdbbccddcabadcdaddadcbcccdbddbdbbbabcacabdcbacccbcacbcadcdbcacadbbaacddbbbacbaacddcaddbdcbcbbdcdadddbddcaabcaddccaacaddccaadcdcbabaacbbacbbacbbacdddccdacddbdbdbcbbcbcacabcadddacbcddabcdbabababbdadbadbbdcdcadbddadbadcdcabbdbdddadcdbdbbcabcbccaacbdddcbaabddccacbabbbabbdbabacdbcccdcccbbcbddbabdbbdaaccdacccdbccaadbcdbacbcabcbccbcdaacdbccbbdaddddbcbadacbdbddcdbbccaadddbcdcdbaaabcdbacdbcbcbbcdbcaadbddddacdaadbbdadbbadcaacacbbbcabadaaadbcacbcaadbbabccbaabdabacacdccabaabbcabcaabcdcaaacdbbadddacbabcbacbcddcabdbacdbdbcddcdcdccdccaaacbcdaaacacacacccdbaaababcbadcdcbcadabdcbbdbcdaccdddadadadacadcabadcacbbbaccbdbbcbaadcdabdcdcbaaabddaddbabcccbbcdbabdbaacdcbddbbbadccbddcadcccbcbdccaabcaacaccbbadcacbccaddbbdababbcdacabdbbabddcdcbdaacddbbdabcaddbaadacacbcddccdadadcbbaacdbcccddddcbbcccdacbdccacdbddccbdddaddcadcdadadbcdadccababbaccadadacbcaddbbdaccdcaaadacbcbacbadaaddbaccdaadbbcbcaddbbdcddbddddbccbbdbcdbdabcdbabcbbabbddbaaccdcddadabaaabccddbabaddcadaabcbacdcabbbadbdacaaddbaadbbcdabccbbcccaabdcadcdadcacbdaccdcbcbcdccddacababbbbdbbabddcbabcdbddbaccabcaadccdacacabcbbcbabaccdcbccddddbbaacbcabbbcacbbbacadcdacaccbabcbcdbbcbbbabdddadcadcbddbbbabbbbbdcbdccaadaaaaddbacaccaaabcccdabdddcbabbcdabcbbdaaabbbcdcbbbabbadbaaadbabdbcbbabaacbbadddabcadbbdddbbccacbdbdcacddacadbcbbddacccddbdcacacaddcccbacabadcbbcaddcbdadcdaacbbaadaabadacaabaddcdccaddbdcccdbcccaaccadbacdacddcdcbabaababbacabdbdbbbaababbcbaaadbbbcdadbccbaaddcdbcccaadbbadcdacaaabcdbbdacadbcdbdaadcacccbaddccddcabadcccddbadaaadadbdcccaabcbbbdcbcbcbadcdbddddaccdccdbbdabbdcbcabbdcbbbdbacdddabbcdbccdbdadabaaaababadacbadccbbcbbdbbdcacddaacbacbbddbdbacdcdccbddccbccccbaadabddaccbbadcabbdaadddaccadaabbddaccadbadbaabdacacdccaababadbbbabbdacdabaaaddaacaddbcaadacdbcddacbcacbcacbaddadbdadbbccaadcbcacdbacabbbbcdccaddadddccbcbdccccbdcaaddccaaaddbbbddddbccaacbcccccbaacaaaaadbdcbbdbbdddcaddadccabcacbcadbccaaadacdbacaccdadcbdcdcabccdbbdcdaaabdcbdbcbbcbbbbbdddbccdacbaaaadabadabccdbddadbbccbacdadbcdcaadbcaabbbcadbcbdbcdacbcadccbddbaaabaccabbdacacddbdcddcbdacdcababcaabddcccdadcbacbbcabcdddaacbacbcdbacbdcacadcccabdcdbbdddbbdabaddccdcadbdcdbcaacbbdbabddcbdaaaddcdbdabbbbdadcddaacddcbbcdccbcdabbaddadccabbabdaacdbaccabbcabccbbaddbcbdbdddbadcccdcccccadaadabcaadadabdbaaabaadcbaaabadbaabccaabcaadcadacabcbcaacddcdbccdabadcadddbbaaacbcaabccdaddbbcdbaaadcaccadcaacdddbbccddccbdbbdbbccddcadccdbdbdbcdbcdbaabacbcccbaabdbadddbbdaccbcbcabdbaacdacadacbddaacacbabbdbadbdbbaadcaacaacddacbaaaacbccbadbdcdcccbdbdabcdbcacaadbddacdbcdbcabdababcbcbddddbbcaddddbbbdddcacdbbbbddacccdaadacbbcccaacbbdbccaadcabadabcabdbbdcbbcddbdcbdaddcdadcdbbababdbaadaaaaddcabbcddcccbacdaadcccdbbbccbdabaaaadcaccbbccbcadadccdbabcddbaccbacdadaadabdcbabdcbddddbccdcabaabaabdddddcaccaddacdacddcadbdcbaabacbcdaddacdbbaddddadbcbbddbcbccaaddddbbdcdaacaabdbacdcabcaaabbacacabbaacaacabddbdcccacabcadbadadddababdbaddbbabbbcaaaddddcdcbbdcacadbaaacdccaaaccbdbbcabaddacdcaccdcadadabcdadadabbddaaddbabadccbccbabaadbaddaaabbdabcbdbadbbcdbcadaaddabbbdadbcbabbdcbddbabdddcddcdbcbabcddccdbdbaaaadbdcbcabbcddcbbabbaacabdbabcccdabbddaddaccaadcbabcbcbcccddacabcbaabbdbcbbccacbdddbbbccacccbbcdcddccdbdbadadcccbbabdadbcadadadccbaabddadaabbbbdabadacbbcbcbadccccabbbbbacabcdadbdadbcadabbbaaddbbcbcabaaadacddbaabcacadbcababaddbcaaaddccddaddacdcddcdbbdddaabcccdaaacdbcbdbadcaddbacdbbbaddbdcddaabaccddabadcbcdaaabddaadcabaddbaacbbacacbcbbdcbabbcadbbddcdacddbdacdcdddbcbdaacccddcbdbaccccdcacbbdbadbaacabdccdaabccdddbabdbcbdabcacbaabacbbbaddcbccabbbababccdbbacddadcbcccabcbbcabdbdbadaaacadbabbbdbadcaddacacdbcbbbdcdddbdcdbbbbcccdaccbabddbdacbdbbbbcddbdaaddabbdbbaaddbbbcaadcdddcddacddacdcbacbcbcababddabaaacacaaddbacbdbdbdbacdaaddddbaabbbbaaaadddadadabbdaaaabdabaaabbbbbddacbbccacacaacaddcddbabddcbcdcaddcaabcbbbbcaabdbcaaaddadbbadadcdcdcbdaccdadabbadaaddbdacadcbdcdacccabbdcdbbbbacdbcabdabcbaaddcbbbacabbbacbdaaadaabcabcddcdaddddabdcbacccbdbcdbaaabcbbdabdbbbabadaacccaccbbdcbdbddbbbbcccadbcdbdccdbccddcbdbbbdbabbdbaabbaaaaccadabdbcaabdbcaaccbabbaabdccacbdadbabddcdbccbacdaccbdbacacbdacbcddcbdbacdbdbddcbabddbbbcadbdccdacadcbdacabdacdadbdccadcaddcddaaccdccbdadbcbdbdddbadcbaccaacbcdbbcbbddbcdbdbddbbadcaacbaadacbdadaabcbccabbddcadcdbdcabbddbadccdbbdbbcbdbbcabaddcdccbbcbcaacbdbbaaadcdddadbbaabbadccdabccbbdaadcabaaccabccdcbbcacccbacdcccbcdccabbbccbabbcacddbcbddacacdadcccdbbaadaabcdcccdcccdbddadcbccacbcbbbaababcbbaabdcccbacdcaabadacaacccdddcbacabdbbbdccacaaaacaaadcdabbcbdcaadcddcbcbbaaadbcdbbbabcccacaabacabbaaacadcdadacaaddabaccadddcacbaddbccadbcadadcbccdddbaaaaaacabcadaacaaacbcdccbabbbbbaccdcbdadbadcdcacddbdddcdadbcbbdbcccdabbadacaadbbaaccbcbcdbbddbcdbcbacabdccccdaabbcadcdcdbcbaddaacdbaaaabbddacccabacbdbdcdabbddabcdbddbacbccdadadcadaacbbddbcdccadbbbbcbcdbacbbdccbccdccddddaaccbcdabddadddcdcdbbaccdcbabaadddaccbbbccadccdaaaccdbdbaadcbcbdaaabbdccacbaaccabcdbcbbaddacbddbaababcadbbccdcbabccddabdabcbaabdabadcbbaaaccbadaadbacdccdabcbccccbcdbcbbdadbcbdcdbddcadcdbbaacbcaaddccaadccbadbdbccaabacbaabdacbddbbcacacdcabbaccadbdbcccadbccddbbcadcdbadadcbabcbadbbbadaccdbbbcdaaaddcacbbbcdddbacbbccacaadcdacdddbddcbcdbdcaacbaddadbcbabbaacdcaccdadadcdbcbabcdadadbababdacbdcdccabaaddbdcbcacbacabdbdbdaaccccbbadddadadaddabacdbababbbbdbaccbacaaddaacbababbbcacdadaadbcabdadcacbcbbddbdadcadbcaddbdabdacdbacaaababaaadbcdbdbaddabbbbcbaadcdacbadcbcbacddbbccdcbdccaadaddaadccdbcabbdcbdaddbccccaababcdaadabdccbccabdbcbaaacbababccadbadbaadbdabbbabbaacbbbcddbbadddbbaddaddbcdcbccddaaabccdabccacbcbbababcaabbacccddbbabcdabadcdbbbbaaaccbcacdbcdaddbaaabacbaaccddaabcaacabaadabbbbaddbacabaadacaccabdcbbdbacdbccbddbadbadcbacbbaabdcdcddcdcdabaccbabdcbdcbabadacbacbbacdacdcdbabdcaabcabddbacdacbdccabcabacdccaddbabdabbababbddbcbdbbcacacdcccbccbaabbcdbdddcddccbccbacbdaaaadbbcddccbbaabaddacabdcbbccddbbcabbbbdabccbbccbcdccbabcbbdbbcbdaaddbabadccabaaadbaaacaddbcaabdcdbbacbbcbabadcddabbacadbdacdaadcccabacaddcdadbadbaabbbaddadcbaacdbddaddadcabbdddbcbdaaacdabbccdaabcababbbabbddbabcbcddaccddcacbcbccabdcaaacabbcdbcddadbccadddbbbadbbacabbccabbdbcaacbaabacadacdbaaaccbcbcdaaacbdbdcbabbdabccabddadbbbbcaabccaccdcaadbaadcbbcbcccbbacaaabbdbcdcdbaacaaaacdababcdcbbbaccdccadccccadbaacdabcadabbcdcbdddbabcbbdadcbbdbcdccbcbdcbbbdacddbdaaccbdbdbadbccacbdbbbabaabcadacadaaccddcbaaaadabdcccaaadddabaabdabdadcbaabccbbbdcdcbddbbdcbdcacbcaabbdacbdddaacbddbbdbbddaddcbaadbbdaccddddbbacdbdaacbacaacdcccdcdaaadbaadbcdaddadccaacbabdcdccdbabcddcdbacacaadaaccbabcdbbbcacbaddabcdadbcbcdbaaadcccdbabababaabdbdcbacdcdabcbcaadcadbcdcddcdccddbbdddcbdbbddbbdbabdcdbabbadbaacbbaaccbabadcbdaadaddcbbbcaadbdcacddbbdabbdbddcadbdaccbdaaabcdcadbbabdcddaccdbdcabaddbbdcaaadbccbbbdcadbbbdcacdabddabbdcadbdbcabacdbcadabbcdbbcaccacaccabbbddcaaaddabacadacadbbabdcabcdaadbccddddcccbcdbccacadccbddbbdbcdccddbdbbccadbcbacadcddadddbacdaccccbdaaccdacabaddbbaccdcbccabbbabddcbaaacbcdbdccdabbdabbcbcccbbcdbcccdaaadaacccbbaddbbcbcbbaccbcdabbddcabbadadbbbbbadbaccbaabcccabbcbbacdcadbabbbbbcbbccdbabdadaadcbabacbdcabbccbdaacdbacddccdcccbaccccddbaacaccccbaacbdacbbbdaaabbddccddcbadcadcbbbabddcbacabbdabdaadccdbbcabacbbaaaaacbadcdacccbabbcabaccadabbbddccaccbadabdbcdccccdbadbbbdbdcddbabbadcccdadcbddabbbabbdabcccbaaacbaddccbaaccdacdcbbddbcddcbcbaaaabbdbbbadaaabcaacadcdccbbbabaacabccddcbadcbbdaaabcabacbdbdaaabdcdcdbddcddcaabdcadbccabbddbcdddcdcadcbbdcbcbbdcbacabaccdddbcbcccdbaddaccbddccdcabcdbbbcaadddbabbbcaaabbacadcbdbbccaabacdabbacccddadaccbabacacddaacdddbbcbbaacbdcbdadddbdcbaadbcdcacdbcbacabcddacbcadccbccbcaddccaaddaddcbcadaadacbdbacccadccccccadabdbcabddadabdbbdacbccaabacbddccaababbcaabacaccaabdabccabdcacacdbdcdacbccaabaddadbdcdbbbbcdadcaccdcbabddcdcbbaddcabacdcaabddccbacbdaacdbdabdcabbcdcbdddbdbcddacbbcdabdadccaaaaaddaccdadaabaabacbaacdabdadcddacdbcdabcdaaccddcabdcbdabbdcdaadbcbddbabdadcbbddabadbacdbccdaccdddbaadbddadbcddbaabdcdbcdaabbbadddbadccabdddaaccbdcbaccbadacddddacdcabbdcbcbdaadcddcaaccaccdbddcbbabaadddbadbaccbdddbdacadadabcbadbdbaabdadcadbcacbdbdbccacbabaddbcdbddacbadcdcdcbcddcdaabbcdddcdbdacccddacadaaaccbbadcdccbaaaaadcccacbcbbcddcadadccababdacbdbddddaacabacbadadbdacdadbdbbbddcbccbacbdbcabacbdbbdbbbdbbdcddcdccadbccdcacadcbadcbdadadabbaaccdabacabaacadabaabbaddcbbbccddacbbbcaadcaccbacbbbaaabacbbcabaadaddbbcbaacadccdadcbdcaacadaddacdbcccddadbddddcdbbdbaccbdaaddaaadcccdcaabbbddbcbdccaabddbdddbcdaabdcdaacbccddaabbbcbababdbcccabccadccbdbabcabdbcacbbbccbddcaacadcabcdbcbcbdbdbddbdaacdcabbddddacdbbddcddacabddaadacddacabbdadacaaadabbcdaabbdbddaaaacdcabdcddbbccaacdcadabcadbabaacddaadcbddaaacdddaabdbcbaccccbbcbcccbacbcabaadcbdbdcdbaabbadabccdbbddcdaddaabbbcabaddacddcbacacccbccdbbacabcbabbabccdacbcdcbbaadbbaacddabcaddacdcbddabdcadcbcbaccbadabaaacdbcaacdabccaccabbcdcacbcdcbccbdccdbcacccccdaddabbbcdbadccbcadaacbbcaaacadadcddaaadcbcddcbbbdbbadbaccadccabadbacdacddbcabbabbbadcdbdadddcbaacbadcdddbcbabcbadbaabdcacdbaccbbddcadaddcbdbcbdcdacbdbaabadbbbaadccddbbabbacbabbcdbdccccdaabdcdacadcbbcabdccbdcdadabcbbacdabcbdaabdbacadacdaabacbdcbadcbababdbbacdcadabccbdabbbbcdbbbccaacbcdccaacbdbacdabadadabbdbbcdbbdbbabbaaacdaacbaaadbbbbabcadbcbaddcbcdadbdcdcdcadabccdbbbdbabccbccaacacdaacdcbcabbbcbadacbbddcaabbdcddbcbdcbcadabbbcdacdaddcabddabacccdaacdbacbbdcbdacbabcadabcccbbabaabdcdcbbdcdccabadcbcadabdbdbccbbacdcdacdacdaacacbccccbddcbadddbbacaabcbadaabdabdccdccbbbdbccaabadcaabcacbacbacabdcadaabcaddbccbdcabdbdacabbaadcdababbbdbbabadabaddbabddaacaaacbabcbbbdbdcaaccbdacccdaaddcbbbabdaabdacaaadacaddbcddabcdcbbacbbbaadcdbdbbabaccbcadbbababddbcbbcbccacbbcbcacccddcaacbbcdccadddbbbaccbddcadaddbbaddddbbaadcddabacbcabdaccdbccaaccdcbabdddbabcdabdaacdbabddcccbbbaccbbbdbcaabadcdcbaabaabcdaabddbbbadadabadcacccbbbdccccbccbddcdbddabcaadaddbbbcdaaccdadcacaccdbaabdcbcaaaaaabddbaabdbbdcccbdcaacacadcaadadcdcbbdbdccddbcaadcadadcdadabaacdbbbdccdbabdadaddcaadaccddccbbcddacbbbbadbdddaabbbcdbbabdbdbbcdbcccdaabcbacbdbbdcbbddabcbcdcdcaaabdbcbbddadacbdddcacdacdaadbdbccaabcddacadbcbbbadcdcdbaccbaaccabcbdbadaaacbcdaadadbbbdacabbacbbadbbbdaccacdcbbadaacbadaccadaccdacccdcccacadccadcadabcaddcabdddacdbadbbdccdbdabccbbdcaabcccbbaddddaddacbccaddadbdddaccddacddcdddcdaadabcabaccaadcbaddcdddcdddacdabbccadabadacbccccccaaddbadaddcaccbadcdccacccdbdbacdccabcbbbbcdabbbdbbdddbcccdbcddccaadcaacbcbbcadbdcdbacbaccbbaccbcdabbdbbbacadcbdbcaacbcabcddbdbabbbddcbcaccccccbbdbbdaabbccbaccbaabbdbaaaddcdabccbdcbbcacabdcacbdaaaaaabbdadbcaaddaabcacabbdcdbaaadbcbcbddadbccdcbabcddabbddbdcaaadccacddccdcdcaddcabcbabbdbbacbccbbcabbabcdacaacabaaaabddaccabbabbdbcdacdccabcdbdaaddababadcdaababbdcadddcdaccddbcabbaaccbdbcdaaddbcbcdbcaadaaacabdcabaaddbbdacbdaadbaccdbadccaccbbbddcaadbadaaaadbcbddabdcbacbcbaadaaaacbadbcdbbcdaaddbcdacabcacbbdbcaaaadaabcbcccaacdcbacbdcadddbbbaddcbdbacbaadacdbcaadacbdaabccbaddbcabaaacadddbdbabcbaaccdcacadabacdbabcaabbdcdbbdbacbacbcbdaadcaabccbdbccdabcdbdcadcabadadcbdaaccbccdbacccccaadaccabbaaaaacdaadacbdaccddbaabcbbcbbcdabaccbdddccaadbcdadbcddddbdaacaddabbbbbdabcbdcbbcbbadbdbacdcccdbcaccbddccaacbacbddbccdbddcaaacadccbabdcdadaacabdccbbdacdbdddabaacbddacbbaaddcddbddcbaaddcbcbadcdcdbcaaadabcabbdabdacabbaccccacbbccabdcabbbcbadbbbcdbacaadcabaccadddbcdaacbccadbdbbadcccdacdaaaaacdaadcdcbadbdbbcdaaabdcaccaaabadaccbdbcdbbdbaddcdccdbabbbacacbbaadccbaadddbcadddbbdababacbdcabbabcdbdcdabacdcacaccdbbdcacbbddacbdbbdbbcdbacaaaccddccabcacbbbddababdbbddcccaaddacaabcccccbbdccbabbadcddbabbcccbdcbbbdaabdbbdbcbaacbbacbccaabadaacdbaaccadcdabcbbdaadabbaaaabbcddaabacccbccabbdbaabddbddcbdcadaaaaaabadbddcccadabdcdbdcccbccbbddccaadcdcccbdacdacdccdbabbddaacbcbccddcdccdadddcadacaccdbbbabcaabddcbcbacdabddbcdbbcbabcbdcaacdcdbdddcdbcdbbcdbcddbbabadbdaabdcbbdbccbbcaddcbabbbddddbbdabbdbadadcdabacbabccdacccdddcabacbcdacbbdaabbadabaababbcacabdcdcccbbadcaadcbdbaaaaddbacababcacadadaaababcbaaaadccdddbaccbbccddbbcdacabbacdbcbabbbdacbbaabbdabdcadabdaacdbdcddcdddbaabcbcacdaccbdbacdcdaaaacdcccbdcdcbadababacbddadcbdcbdccdadabacbdacdacaabbcdadcacadcdbbdcdddbbdabcabbaddbbdcadacaaaddbdacbadcbdcddbdbdbbcbaacdbbaadcbaacbcbccbbdabadddaaddabddabcacdcbcbbbadcdacddbcdabbcbbbcdddcbacabcbdcdbbcdbdcadabdcadacabbabddaabcadbaddbdbabdaadcddcdbbccdddbcaccdccaccdbdbdacdabdccaddbadcaddcdbcddbacacdbbbacaadabaadbddcbaccddabdbaddbdccabdccadbbbccbacccbdcbaccccddadcbaacbbbbcadbaddcacbdbbadcdccbbddcabbddbaacdcadcbcadbcdbcdccbccbbaddcddbbcdbbdbabcabaddabcbcabacbbdbacbbadaabdbccbacbcacccdadbccdddbbddaccdcabbcababccdaaaccccccbdadbbbbdcbaaabacdcddcbbcbbbabdbbdcdaaaacdcacbbaadcdcdabaadcadcddabaabadcaabcdaddaccdcddbcaaacdcadbcbbcbbaadadcadcacdbaaaabccbacdcaaccbadbbaabcccdbbaaccabcadbbccbdbccdaabaccabcccbbadbbcccccaacdacacdbcacddbddcbdddbbdbcdbbbacacbaadcbcbbacaddbdbbddbccbbbcddabccbabdbaacbadbbbccbadbdaaddddbaddacddbdaaabaacaacacddaaaccddcbbabdcccbdcbabbbbcccbdabdcbcaabddcbbddcccdddcbabbdbcbddddcadcacbbaddadbbaddabbbbddadabcaacddccdbcccbcbcdadacdaabdccaadbcacbcacccacaadcdcbbdcabbbdabcbbdbaccbbadabaacbcacaabcaccacbbdddcaaaaaccacdbcbbbcddbcaddacaacabaaacbdbcbcbdcdcbbdddddcaccbabdcacaadbbbaacaaccddacdabcbdacdddadcccabdddcabbaccddccbdcacaadadbaaabdabbbdccacbccbaabbcbaddcbcbaddcdababcdccdabbdcdcccaccbddbbdccabcbdbcadbdbcaccccdacadabadbdadcddaddbabdabdcbcacdccdcdcacaacbdddbccddbdadddbbaaacdbddbabdcdaaabbcbbacbdbababadbcbbbdcccbbdacbccdbdadcaabbababcbbbdcbacacbaddbbadbdbcaabbddadbbdbbcadbacaccadacbcbdcccbddbbdbadbacdbbabcaddcbcddccaacdadcdcbddabacddaddddbaddbcdaddcbdbcbacccddccbdadddcaacbdabcadbcbccaddaacdbcdaadcccaccbbdbcdabcabddaaaccdaaaaddddbacaddababadabcdacdbbdaabadbbddbcbbaddbbccdccadbbbbbdddcdccbdbdcbccbbdbadbacbadddadbbbcccaabcddaddcccbdbdaccccdabbadadbadadaabcaadcdcddbadaccacbdcabcabdaaacdcbdbbdadbbbcabdccbcdddaaddbddbcadbdabbababbdbdddacbddccaddccadbcdabcbcdbbbcdcbabbabdbcabbabacacaddcadacabcacccaadcabcbadbaabaddbdbdcdadadbcbcddddddbcbadbccabdadcbccdaacabdadbacadcdddbbcbacdbccdcaacbadcbcdbcacadbbcdadbddddbdddddbbccdcccdcbabcadddbbdaabacadaabcdcccddbbbdbcdabcababaaddadabddbbbbdcaaabdadbbcddaacabcdddddcbcddcdadbcaabbcadcbcadcdcdabbcbcbddbbdadcdcbbcbcccdadabcdccbdddcaaccabbdbcbdbcacbbcccadaaaadbbdbbaddadddcaabcdbbcdabcccbabbbcacacdadddddcaaddbbabcaaaacbbdcabadcdbcadccdddbcbbddbcaabbacdabdaaaadacccababdccdcdaadaacccaaadccbcdadccdcbcacaabbabdcaaadacbaaddadbabdbaacdaabaacbabacdbababcdabcbcdaccaacacabbccbacbabcbdadaddcbbcbbacbabadddcddbdddabbcdacbcabcbcddcdabdbcaddaabcdbcccbbdcbbbcbbcbbbbabaaddddaacdacbcdbdbbdbabbbbddbbcbdccbcbcccacbcbcbccdabbbaacdcddcbdbddbcdcddcacaacadbcbdbabaddaaaddaddddcabdacbcadbdabcbcccbabbccbdabdaadcddcabdbadcdcbdaccddbacaccacdbdabcdbbaabcdacdabdbcbdabdcadddcacddadbdcaccabacadcdcadcccddcadcbcdbdabaaabbdccddbbaacacccdacddbbcbccccbacbaadbcadddcccbddcdaabaddbaccbaddbccbddacdcbdcdadaddcddcbdabccdccbdcddaabaaacacabcddacacabdbcdacaabccbcddcacdcdbbbdbabdabdddbdacbcdabaaadccddddbbccbddacaccabccabdacdabcccddaaabbadbbaacaddabcbcbddabdbcbbaaccabbcbdaacaadccdccbabbacaaacadcdcbdbabdbcdccccdddbbdddcddcdcabccbacdcddbdbadbddcbaadcaaddbabcbcabbbbaadabdadbcdcdabcbbbcbbaaaabddccadcaddbdabdbbdcacddaabccbdadbdaadcbaabcdabdaaacdccdacaaabddbacbdabbbbabbbdbddbdddabcbdadbcccbbcdadacaccadadaaadcabbbcdbdbadcdcdcabdabaaacaabdbdddabbadbabbdcabddcadcdddcacaddcadbdbbdcbbcbdbbcaabddbdccbcbdcbabdcbbabbdbddbcdcbbadbccbbbcbccaaabdddbbaacccbdcbbabbbdcaacddbadcadbdaddcbbdbdccdccabbbccdbacbcdadcaccdabbaddbabdcdcdadcbccbbabcbbdaaddbacaccaacbcccababadaadabadbadaadadaadccbccaaabdaaddbcccddbddbacacdadbadddccbabcdbcbdadbcadbdabdbdbddcacddcdbbabbbaccbddaaaaaacdcadcbdbcbbbacadaddcabcabacabcddaacbbdacaaaddddaccbacbdcbadccadaabcdddabbbbaadaacbdbccaabbaaccbdcbdcbcaabccbbdcbddacacbcbcdaababaddbbcbbcacdcddddbabcadbadddddbcbcaccacbadaadddbacbaadbcbdbbdbcdacbdcbacbadbbbdcdbdcbcbcbbacbacacacbcddbadcaaddbdababbaaddcbaccbbabcacddacdddcadbbcbaddcadabcddcabadbdbdaddbcccbbdcbccbaccddbddcacadbadccaababadcdaadcbcadcbabbdcacccaaccdabcdbadbccbadbcbababcccccabcbbadbbccccbdcddddbacabbcacddbdcdaacaaaaccabacaaacdabcdaddadbdaabbbadbbbabbacacbdbaaacabaaaddabbbdadbcddbcbcabadcaccaacaadcddbbccdccccdbaddaadacadabbcdbbbcadbadbdccaaabbdbadcabddcdabddbadacdabcacaccbdcbcccbbabbddadacbabcddabcccddbccdbddbbcaacbaddadcdcbbadbbbcabaaccbcddcbccabdadbdbdabccdaccdaabccdcababcacbcbcbbdababaacadbdaacabbabdcccadaacbdacbcdacddcacbbadaacacccbbdabdaaadcabdacbccdcdcbaabdccdcbcbbcbdcccdaabccdaabaaccdbdaaacdadbbbdcadcbdcaccaccdbacbdbbabaccdccbaacbaabbabcbbbabdbbaaacaacdbdccdacbbdddcdccbdacdbbdadacabcacadbcddcbbaccaddbbabadcbcbbabbbdcaaaaaddbcdccadaacdccaadaabdabcadbbaadcacaacddbabdddaadcddacccddcdcddacccbcbdbcdacccdaacabdadcabbbddcdabaddaaaccbacdcddbbdadacdaaabcdcbbabbccbbadacacdcdbbddbadaacabaddadddacccbacdaaccbdababcaacdbbddadbdaddbddababaacdcbcddcbdbccdccaacdabdcbbbcccadabbbcccbbbabdbbacdbdbbdcadddddbbccddaabacaddccabbcdaccbaaaabbdaaccccddbadcadddccaaadbabbccaaaaaabcdaddbbcbbbbdbdbbbcdadbbdbbacdbcbdacbbacaacbbbcbcbbacadcbcddcacbbadcbabababadbbadaccbbbbaaaddadabadbabdcbabdcbcbaadcbaddbccbcadcdbcbddcbbbccaabddddacdcbcbacbbbcdbddcacbabbdcccbacdadaaabdcdcadaccbbcabbcccadbaccabcdacbdbacbdacaabdddabddadadcacbabdabcaddbaaabccddccdaabbdcddababdaacddabddbddcbcabdcaacbddbadcacbbbcbcabadcdcdccabdaadacacaadcbdbabdbccabcdadaaadabddddacacbaadbbadaabadbdbcdabbcccadaadacdaacdbacadbccdadacabdacccbabcacaddbdcabbcbcbcbaddddddbcbdddbddbacdcddcaddbdcbcacacbadbccaacdddbddbababcbaccdccababdaadccdcbbcaddddcbccbaadbdbcdbdbbbdacaabcdbdadcbbabddccbbdddacbcadadcdbbaccdbccdbcbccaabddacdbaaabdbcbddabbbdcbadcdbdcdddbccbbababbadddcdaacaadccccdcacbcdcdbbdbccaaacdadcdbbdbdbcdcddaddcadccbcbccbbccdaabbbcaababdccadabcbbcacccaaaaacbbbacaccbcbbdabcdaccdbaadddaacbdbcdcbaaacbddcbcbcbabcbbaadbaaadcbadabbbbdaaabbbabaacbabddabcdbacbadbadcadaaabdddbaccadbadddacdaadaabadcbccccaacabcabdaadbcdcbbdbdcddadbaadbdaddbccdaabdccbcadbbabcbacadddbacdccaadbbadbdbbdcbdacbbababbcdacbbaddcdaadbdcaabbdbddcaabcacbddabcacabcddadcacbabbdbaadbbdbabcbcdcaabdbdacadbadddcbbbbaaacadbbcdccaddadaacaacbacccbdabdacdcbcdbabddccdbdcbaadacdbdddabbaadddaaadbddcddaddbbdccadabbcbdadcbaddadbbddbcaabbabaabdbaaabbabdcdbbccaaaacbbaabddbcccbadcddbdacbaacddcaacbbbccdbbdcababcbababbbdbbaabccbdadbdbddbaddbaabaaadaabbdadbcbcaccbbbdcccdddcabcdabdacdcddddcdbddcbcdcacdbddaaadbdcdabbbcdaddaacbacddccbadddccadbddcacdbddcccbabbadccbcccddbacdbcadcaaccccadcccaabadbbbbaadcacbcababddcddbbaabadcbbadcddadccdcaaacbaacabcbdbccbddacbddbaacbbacabdbcbaaabdcbdcdabbdbbdaccccdccbbdbcbbdaaacbcbdccaadcadcccadadabcbdadacaabacabdaddbbaacccdcccbabdcdcabdaabbcabccddaccadddbbbabdcbaccddcdccddcddcabdadcbbcbdbaacbabdadaccacbabcbcabddacabcaccccbabcbadbcacbbcdbacbcaabcdaadccccadcacacbaaacbdbadcddabbdddddbbbcccddaddabdcbabbdabbacddcadbddadddbdbbaaabcbcddbaaccdcbadccbacaabdacbcabbacccdbdcddacadaaabdaabaaabacdbccbdaccadacddddadaaadaadbdbdcdbbaabbbcbccddccdccbacbcabccbccdcbacacaabbccbbdcdddacddbadbdbddaadadccbbdcacdcaabbacbdaddccddacbcabbacabaddcdddddcddbabadbacabccccbbbbadddacacbadccbbcdbdaccdcbcdbadaaabcabbdbacabdbabdccbdabaacbcbbbbccbcdbccbcddbcbbabdbacacddcabbdcdcaaadccaabdacdbcbbbbcabbaaddaabababccdddcddabbcbdadabdccdacaddcbacdbcdccdcadadbcaacbdccbcddcacadbbdbadbdcdbbcaaddaaaccadaaaadcaabcdbcbcaccccdacbbbbdbadbdcccdcbbacddcdcaddaddcdcdccdacbbbdaccdbbacabaccbaabbdabdabadcaabcbbcbdadddacaddcccbdcacdbcdbbddadadbaccccdcdcddccacdaabbcdcaccbdbcadbbbdbbbdbcbcccbdaccabdcaacabbddaabdacddccabdbaccdbadcdcbadbddbdcaaadcdbdddcccccccabcbaabccddddbddccadacdbacbccacdcaabaddbcddabbabcabdcadbdcdccbadaaccbddadcdcdcdddcadbbabccdadacaacccaacaacbaddbdddadabdaaaccbcacaadddaccbaccbbbcccadccccdddaacacacaaabaaccbabcaaccdddcdcaaddddaaccbaccacbdaacdcccdbcaadacdabcaddcabdbdbcddcabaacbbdcdcbacdaddddaccccdadaabbdcbcbdcdabbacdddcddddccdbadabdbdbadcbacdddcccabaacdcdcbaacddcbbdbdadcccbccbcdccdbaaacbbcbcbdacadcddadbcbbcaddbbbaccbbcbcacadcccabcbdbddabbccbddadcbaaacdcdcaadbbcddcdacdbddcccdadabadbbababcccaadadcdbdbcabbaddacdcbaaccbcbadacbddbbbdbbbccaabbdbbacadcdabddcbaaadbdbbdbaccbadbbcbbbabaaccabaccdbdabddcaaaaaadddccaccdcacdadcccdcbcdabccbaddddaacbbdccadbabcdcdcaaadddcdaadadaacbababcacdcdbacacbdbbcabdacdacccdacdbdaabbdabbabbbcababcbcdcbcbbdaadabdaabdbddbccaccabbcdcccaadaacbdaaaadddbcaadccdadcbbdddcbabbccdacbdccbbdcadbdacabbdbdbcdabbdabcddcccadaaadadcdaaaadaddacbbabccdbbccbbdcbccbbdaccbaadbaaaddcbbdacbcdbcacbaaddaacdcbbdcaaadabbabcaaadaacabadcaaccbcacbaaaaacbbaddccabbbcbdcccbccadaadbaddbdddccadcaddbccbaabbdcbdacbbcdaccbaaddbcccddadddcbbccdcaabadcccabbbcbccadcaadcddcdbababcdadabdaacbabbbcdccdcbbdabaabdcbccdadbccdcadabccdccaaadababdccccabbadbaaddbccddaaadcccadccadaddccdcacdbbcbcbdbcbbaddcbbdabbacaaadccbbaacccdaabaabaacaaaaacacbabaccbbaadbdababadbadcdcccbccadbcababdadbbbbcddbccdbbcbbacadcdaddabcdbaabaabbccbbaabdbccccdacabddcbcdccbacadbaddbccbdacabcdabccbbdcdcabadabdcbbbaacbbadddccdbabbcdbaabacddaccdbaabcaddcbaaaacadbbbbcddddcabacdbbacbccaacacbddbdddbdbcddacccbbaabbabadcdbabcbbcdabcaccdbbbacccbbaacaccaccccddcdaacdabcdbbbdacbdacccbcadbddddbbddbaccdaadbcbaccbbadabcbbbbcacacacccbaccdabbbacdbbcddcdaaadcbdadadcabaaaaaabddbbbbbddbacccbbdbaddbbdbabbaadddcdbccdcbbddacdaaacacdaddbcbddbdddccbdbccdabcbbadcdadddadbabcdbbddbabcdccdbacdbbcdbdaaaddacdadbcacdabcbbcacabcdacccaddbdddbcdcadadbdccbbababaadacbacbbcddbdaacdbbbcbccabadbdcddcbabaddaaaccccccbcabdaddccabbdddbbcbddddadbdcdddaadcccadbddadbccabcbbdaddacabbcdddacbbacbbcdbaddbdacbbddabaddbadbdbacdababaabdbdbcddacabdcbbbbaabccdbbdbbacdbbadddbbacddcbbbcbdacbbdcbcbdaddcdddbcdcccababaabbdadcbdadbacccbddbbabdcacaddadccdcabdccacadadbabcbabbcdddcdbadacbbabdadbddaacccdcbbabacabdcdcacdbdcdaddcdcabdbbadbadbbbcccacdadbbdbdacdbdcbbbadaaadcaddadddaadcbadbcbcbccaaaadbddbaaaadadbccdcbcdacbcddbbdacdcaadddbccadccaaccaacaddcabdbdaaaccacdadadadcccabdddbdbccacabbccbcbdddbacbcacacdaadbcdccaadbdcbcacdacdbbbacadcdaaabdbcbddbcadbdadaaddaccabaabbcadacdabdbddadddcbadabdcbbabacacdccdabaabacbaddcbbdadbbdadaadadbbaaaccaaacadcccbcddabadccacbcbbbcddcdbbdbbdcbadbdcdddbcdbdbbcdddcdabbcbbbabbbbacaccaddbadbcbbaddddcdbdccbbbbddbdbabcbacaaadbaaaabaabcbabbbdcccbadcacaacdcbcbdcccdddcaddababcbcbdabcadaadbaaccabadaadcaaacdddabdddabbccabcdbdcbabdcbdbbcdcdcbcbadcbdbdcbdbcacdbcdbddddcacbdbcddadabadcaaddcbacbacabcbbcdabaaddbaabdddbbbdadcbbabddccddcaabaababdaaddbcbcdddacabcbcadbbcdaccccbddddadbcbbcacddbbaddacbbcbdbcbbcaaaaaacddbabdddcabbcdbbdccbacacabcbbbcabdbaadacbcaccddbcbabacddddccacadddcddcabdacabbdcbbcadaabdaccdbadbbdabbbadaadaacbbbddaccdaadbdcdbcaaccbacdcddcdadcacacacaacaaaaacacbaadcccbbdbbbbcabbbccbcadcdbabdbbbbacccdacbccdcdadbdadcbcbcdbddbcdbddabdcdabbabbabbcacaadadcaaabbaddcdadaccbbccbccdccbaccadbbaabddbbcdddcaabbbadaaddaadaddbbaddbcdaaaaabccddccacbbdaaddbaccdddabaadbdccddaaddababbbbddbcadccdcbdcbdbcbaadaabadccabcdaddbddaacaadbcadccdcbccdacadbcacdccccdcbcddcdcbdbcacccdabbbdacdcbbdacbcdbdcabbdadccdacdcabdcacacabbabccabbaccbbddabddbaabbbcdcaaabadbaadaccccdaaadbcdcabcaabbcdadabcabbbdabdcaacadbddbcbcbbadcaaadcaadbadabdabccbccbdcbbdcbbadabccaddcaadadaddaacadbacacbaddbbdbadcdcbddabaccabbbbcdcabcbbabdcdbcadbbcdabcadddaadbbcdccddcabddbacbdcddccdbaadaddaaccdadbddcddccdabadabcbcabcabaaccccacbbbccaccabbbbbdadcccbdaddbdcddabaaacddcccbdcbbabbabcbcbadbccbdbccbcddacddaabcddcbbdccacbcbacdbabcaaabbdddabcdbcbdccddcbbaaacdcdbdaadcbcbdbbcbddacabacbccacbdadcccddccdbbdbbaabadaaabbaaaadbaddcdaacdcdbccabbdaccddbabbdcdcadaaacdccbdbadbcdbccdacdccdcccaabcacabbbbdacbdacaacababdcaaadcbaaabdbbbdbdbdccbbaaadbaaacdbbcaddcaaddcaabccaadbbbcccbdabdccaddbbadbdadbbbdddadcddbadaabbadadcbbcabbcbcdddcbcacdddddccccaaaddaadcdaccbacbadbbbdddccccdacabdddbddcadcabbdadcbbbcddbbbcddbabaadccbcabcdadadddcbbbbbdccdbbdbbbdbbaacadbaddbdcaaabdcdcccddaacccdddabaacbccbdcbcadcdacbacddbbccabbcdcabbddcabbdcccdbbcabddddcbddbdbcacacdacbdcbdcdbaabbdddadcaacbacaccdbaccadcdbbccbdbdabbaddabddacbbbaadbbcbdbaaccdbcdacbdcdbbcbdbcbcaacdadddcacccbbbdadddcdabbdbddabdcbdbdbbbbcacadcbabacbdbcabccdabdbadadcaccaaaaaacabcbdcacaccbabcccacbaacabaccbacadcdccdbdccbbccabbdcbdddbacbdbbabcabbadabdcdcbdacdbbddbdddcaccabcdcadaadcbacdbdbccdccaabadbaccbbdcdbcdcdcaabdcaacbdcbbdcbccccdcdddcbdcdaddccbbbddbdabdcabddddbcdcababcdbcbacadccddcbbccabcbbddaddbacbcbadccbacaadbaacaaccacdacbcaddbaddbdcaacdcaabcddcbbddbbcbcbdabacbadccbaadaaaccddcbbdddbcabddddacbdaadbbadaacdbdacaccdabcddbbaacbaccdccbbccaacbddcdbccdddcaddccccadcadcaaddacdbbbbbcbdcbddbbbdbbacbaacadacabcbaddbbbddbcdabdbdaccbbddbbaacccdddbdcbaccddbbcdcacabbbbcacdbbadacacddbdbadadaabcbdabbcaccabcadcdadadcbddcbaddbbdabbacacbcdcbdabadcbccadcbdabcdcdbacaadcdbbbacbdabdabadbdcadbcccbcdbcacdcbbcddbdcbccdaadbbcbadcadbabbabdadabaadcacbcdbddbdcccacbcaaacbcbbbadadddacabdcbadaddbdcdcbadabcbbddddcbbcbcdcdbbcbbcadbbbabdabadbbabddacddaadcaadcdaabacabdddddbbaaadbbaacbccaabdadcdabbcabcbabcdbcddaadccdbacbbcabbcdcdccadbaabaabcbdaadbdcdadcbaaadadacdacccadaacaacabdcbbbbcdabdadcabbcaadcadadaabcbcbacdacaccbacaaaccddccabcdbcacddacdabbadaaaaaccbccacaaacaddaabbcbdaadcadacadbaacbccdbccaabbdccbbabdbaabacdddcdddcbacacbbdbdccddbaacabdacbadcdbabacdccdcdcaddcaddbdabbcdbababcbbaabacbddcdbdbdddbdbcbaacddacccadbbbaacbdcdadccddbabcaddccdcaaddaaaaaadaaacdbcddaaadcbbcbababaacdcaccbbdccbdaddabdcbcbccdddcddddcdbddcacbbdadadbacaadcbcddaabddbbacbddbddcdadbbbbddccadbdbbaaacdbdbbbcdbabdcadabadabacdaaadcacabdbbcabbbccccaaddddbabdbdccccdacccaccaccbabaaacddaaababcdcbacdbaccaddabbcddbadbadbdabbadabcabababddbcccadbcbbcbccadcdadbdbbacddbaaacdcadaadaabcddacdbbcdddadcdcbacbcbbacccdaddbcadccdbbcbddcdbdcbcbcbabbadabcbcacbdbdbcdcdadbabbcddbdacbaababaacbcbbbabaadbdacccbbbdababcbdacdcbcddbcccdcbabdbaaabbcbdbadbcbabbaacbadddbcaccbdbadbdbcabbcccaaaccbacbcaaccdaababbaacadaaccabbdcdbdcddbcccaabcddcdcbcdadcdbbbbbbbbccbdddbbddcabdaddbcddcccacadaabdbacddcbddadaddddccabbcbbbbdadadadbacbbdaacbddbcadcbadddcbcaccdccaabcdaccaaaadddcdcadbdaaccababbccccbabdccaddbdbaadcdbbcccccdbadddadbcbdabaacdbbbbcaccbbddaaddcbabbcdbdccccdcdbcbdcbddacabbddaadcdbdbdbaaddacbdbcdbbcdbdaccababcdbdaadabaccccadbcccaadbbadbcabbbcbbddccbbdbadbadacbccbcadcddadabcabccdbcddddabaadddcbcbacdcaadaddaaacbddcaadcbcbbcddcbaacdccbacccaaacbddccadcaccbbabaaaaadadcbaaabcaaadbcaccaacdcbdabbdbdbcabdcbcaababbadbcdaccdcdcdacdbbaadcbadbabbcbcadaadbaadaddcdaabdacddabbdaddcbbaaabdcbcdaacdcccbbdcdaadcabdadadabadcbacddbcbaaacccacccdaddacccbacabbcdbababbcbcddaccdcdcbdcadacadcdbdddbaacabbcadccdaabcddcddcacddcbdcadcabdcbbabdcdcccdcbacaadbadbbbbaadacbcbadccbbcddbbbadcdacccbaddacdcabbbaaaccccbccabaaacdcdabdadccbcbbcbbbdabbdcdaadddaabddbbaaccbbccdcdbddddddaaabdbbbcadbddbccbdadcdbcdbbcdbbcacdabadbcbabdacaddadddddbcbacddaaaaddbbcabbdaacabbdacacccbbcbccaacddbdadacbdcadcacabcbbcdcacddacdbbcaadabaccadbdaccdbddddadbadcbadcadbbcbabdbaccdacababbabcdcdadadaabaccbaddacdadadccdcbbbabbaddbabdcccbacabadcbbbbbbacccadcbdacadacaddaaabccdacbadaacaabaadbbacbcdacbcaaaaaacbcccaabdacccdddacdacddccbccadbbacddbccbccacbdbcbbcdaacbcbdabcbabcadacbacddaccacbdcbcdbbdacdbcbaacaabababdddabbbdacdaccbcaccbcdabacbcabbadaadbbadccabaaabddaccbabdacdbdbaabdaaddbbdaccddabbcdbdcdbaadcccccbdcbddaadbbadaddccdbaacaaacdbdabdaabaacbbbcdacacbdcbadccdcbcdbbadaaababccdddbdcaddbdccddbbcbcadabcaabacaadbdaacbbddbbbbbccaccdbbbdbabbdbbcdcbbbdaaaddcaddcaadcbabbbadbdbdadbccbaaabacdbbbcbbadcddcbdbbcacacdbbaddbddccdadabcbbabbdadccccdddbcdbcccaacadbdadaacabddabccdbacdbcbcdbdbccccbcbdbaadccdcdcdbccbcdacbbcaabbcaacbaabcdbadbadbabaaabacacdcbcdbccddbacddbcdaddcbbddcdacaddaabaadaacddbdaabaaabaaacaabddcdbdabbdcbaccdcbcbdacbabbcdddbdaaddbaaaadbbdabcbcadbcbbadcbbcbccdaadacabacccbccbbcabaadccadddcaaaadccccabaddcdabddcaaaccbbadbcacadadaaabbbddbacacdbbbdadbccabdbbdbcdcbcdccdcdbbbabcadaddbbbcccdbccbcdbbdbdadcbbabddddadcdabcacbdbbcabacdacbbcaacbbdababacbcaccbbcbadcacbddccdadcaabbadbbdaaaddacaccbabbaacbbdccdadddabcadcbbbccbbddabbcdccbcdbccbcabcbcdacacdbbdaadcbcdbcacbaddddbdbabbdbbbababddccadadaadcabcadcdbacbccbdcabaacdadbcaccaddbdddacbbbdaddaaacccccbdbdacbadbbdccbddbbbacbdcddaaccbdcbbdcbbdabbaccdbaadcbdabacacbccbdadbbddbabdabcbbdccaabbbdbbcbacddccbbcbadbcbcbdddaddddccbccacbdbbaccaccbbbbaccbdcbbaaddacaccdadcdbdbcbbcddddcbbccbbcdccbcdabcabbdaadbdbcbbabddccbacccddacdbbddbadabcbcadabaabccabdacaddbdbbdadacdbdcadacdaadcdcacbbbdbcabcbcdcdaaadbcbbdcbdbbdbdccadcaabacdcabdaaaadcabcccccabbacabdcdccaadcbcdacdbabdcababdacdacdccdadbdbbdbadacaddabcccdacbddbbdbadcbcdddcbbdccadababbccdbddbddaaccdbcdcdaadccbcbdabbdacbcadcdacabcdaacbbdacacbdccbcabcbddbbcbbcaabccdcbdabddccccbdbabcccbcdddaccbabcbbbadabbaddaaacccbdbccbdcacdbadbabdcadaaacbadcbdbbccdcccacdaccabaadbbddcddacacccdbbcadbddbcbbddababcbbdbdbacbcccbbbdabacbacdaaadcaadcdabdaddddcdadbddbbccbbaaadadccdaacdddcbbcaccdcbdacbdbbdadbabcacccdcacabbaccdbdccccbbabbcbcacaccbabdbdabaaaaccaabaccbabadcacccaacddaadadbacdbcabaadbcababcdcbabddadddcdbcdcaacdbcbacddcbbabbcdccbcadacdbdcdaccddddcccdcadbdadbadadbbadbabcdaaaabadcbcddbbccbabacbbccbcbdabdbdcbdaadcbdcaadbaaccbcacabbacdabdacaccdcbbdabaabbcbdcbadadcadbbbdadbabdcadcaaaadcaddcadcdcadbaabbdbbaadcccbadbccbaaacabdbdbbccabdccbaaadbadccbccdbcbcbacabbdadcacabaacbbdbaccabcdabbabadaaaadbdacdcddcbbbdccbccadcbdabdbadabbcbcddcaacdbdaaaddaddbdbbdbadacadcaaadaacdacbbcccbaadcddccddacadabddccababbacdddbdbbabbdacbbbacadcbaacbcdbaabccddddbaaccccdbdaccddccbccddcacbbacaccccbdcbdddcdbacccadbbaccbaadbccabdbdbcdddddccdcbadaadaabdcbbbddcabcabdddcccccbbadcacbdcdaddaccccabcbbddbadddbbcdccbabdbdccddbaabdbbdbdadcdacbdabdbacbddbdababcddbbddbbccbbdcdcbaaddbbadcbddccabbdccbbcbbbacacbbcacbccbcccbcbaddbcccabccdcacaacaaccbdddacbdcbabcaabbaccbcacaadadcacbccaaacbdcadcbddbcabdadabbcdbcdacdbbacdacbbaacdddabcdaccddcacccdcdccdbbdacdbbbbbdccdbacadbadcadbcbcbdbcbadcbaaabaacbaaacadbccbbdccccccdaccbbdacbbccaabdcbaacbdabccaabbcaadcdaaddabcdcacccccdbdcdcdcdccabdcbbcdbccadbbbadccddaaccdcdbdabbddacbbaaacdcdadcacbcbbabadbadaaaabbbcacacadbacddacacaacbaddccbdabdddbbcaccbcaaaabcdcabadbcbdbcabbdaccadaabdcbcbcabadcccaaaddccdcddcbbaadbcababbbdbaabcbcaaccaabdddbdccdbaccaacbbcabbbdcabdabaabdacabaadcbcbdcbdbccadcbccbaddccabdcdacbacddacaccadcdcaaddabcbcddadaabdcdcacdcdababddbbccabbcacacdaacccbabbabccadacbacddccbabdcccbcacacababbaabcaabcbdbcddcbabcaccbabdcbcaaaacccdabcaaaaccdacdccadbbaddbbabccbbbadccbdbacaddbdbcdacabbacabaadabacbadaabadbbabaabcabdbadbbbcdabbdacbbcbbbbbbcdaacaabbdbdbacdaabcbcccddbddcdbadbaccdcbbbdacacacabcbbabdccdbdcaabbacacabadcdacbdaaccaababcddadbcdbbbacdaddddabbdaacbdccadacaaccbdccabbadddbdcadcbaacbcacddbdbaddbdcbdbadcccddabaaadccccbbccccaccbbdbddbbdcdbcbadbdccabadddbbbaccbbbbcadbdacadaaaccadcbcdadacdbcdadbcbcababcdcbbdbbccbddbacdcccddacbcddddaccbdcadbabcabbbcddbbaacbabcddcabadaddcbbcdbdabbadcccababaaadcbaabcdbbcdbbaaccdadbccbabaadbaabcddbbabcdadbdacbcdaaccaccdcbabaabcbabaacbcbdaadddbbbabadbcbbdbacaccabacacdaadddbdcdabbadbacaacacddadccabcabcbabbccdcdbdadccacabaabaaabcaacbccdbabadcaaacaccccbacbbbcdbdadcadbdaaccaadabacdddbabdcbcbaabdcaacbcdbcdadcaacaadadaaabcaccadbccaadddacabbbadaaabbbdabdbcdbaadaddccababcddaabbacacadaadbdbbdaadbdddcdcbbbdabbaddcbbbccadbdabbaaacdcdcdbddcdbcdadbbbdbcbbadabcbabcdbddadaccabbcbdbaabaababdbcddddcdbcbabdabdabcbcbdbddbdaccccbcddcaddabbbcddcaacacccdbcadabdcbdaaadbbadabbabcbdadcdbddbacbcdcbdbabdbbcbacaadbddabddacbddcbbdcacdcccaabccacbababbacadddadaccadacbaccddcbdcbaccbbdacbdaddbbddcdbdcbbababacbcdbdcdadacbabcccabcbccadbaccddcabbccdccdabcadcdddaddddcddaaabcccbabcbdadcbabccbdcbdabdabccdbadabaccacbcacdbdcaadcabcbbbadcdddbddddaabacaacbcbcbaadacdcaaacbabbdaacbbbaabdbcaaadacccddccbbcdabdbcccdcccdcabcadbabbacdcaaddbabdabbaabbbbbdadcbdcdbbdcdbdaabcdcdcdbdbacdcdaabbbdcddddbaaccaabbcabaaadcccbcbbabccaababbdcdcbbcdcadbbccddaabdcdbdabccabcccbccddcbcbdbdbbcadcaadabbabddacccdacdbcdbbdbdacacaabdbcaaadadcdbcabbaacaacdbbccbddbcddaccccaccacbbabacbdbaaabacdcaaddbcaacadbabcacadcaadcbdccabccddabbcdabcbbadddbbcaadddaacadacbcadacadadddabdccbaaaadbbcabcccccdadabbacacdcaacbbbaacbdaacbabcbbbdccadadbbcbdbbdcbcddcdaccbdabdabdbccdadaddaadbccabbbadccdcbadadbababdbdaadaaabaabacdbccaababbabdbccbcdbcdacddbaaabbbadcccddbcddbbacadcbbcdbcdcbdaabdccaacdbddbcbcabdaaabdcdbacccadddcccddadbbabbdbadacdbaabacaddbacdbcbdcbbccdbbcaddabcdadbcddcdbdcddabbcdaabbcdabcdcaadcdccdbcdccbddddbbaaaaacccbbbccaddbbcaaaaddcbbaaccaabbdadcccdbdcadcbcacaaddaddcabbbcabacddaaacaccbbbdadabbdacbbabacdcabdbaabcdcccbcbdbacacaacbcaacaaaadaccdbdddcccbaddacadcddcccabaaaaaadbdadbbbddcbdacbabaabccdbaddacdbdddabcccccbccbcbbdbabdadcbabcdcdbdcaacabbccbaadbcbccacbaadbacdccaccacaaadaccddbbbdbddadadabcdbcccdadaddabcacbadbbdbaabdcadaaacccbdaadbddadbaddddcddbccdcabaacadcddbbbbdbaaacbbcaaadccdacdaaabbbcbdbdcbccaaaaadcaddcbabddbdadbaacddaacbadccbbcdaaddbbdcbadaaddcacacbabddbdcbdbadddbacbcdaaccdadcbaacddbbabadcddcbacadbaaddadacdbcadbcbabbbbdadcddcdcaabdcbadddbdddddcddacdaaacccaaabcbddacdccccacbbaddcabdddaddddadcdbcddbdccdddabaccdcbccdcadadbabdccadabddcadcdccababcbdbcabdbdabcdaddcbaacadbdccbadaabcbddbacbbbccdcbabbdcdddbdbcabcddabbacbaaddcdbacacdaaadcbbccabcaccbcbacbabcadbccbadabdddaddbbadbcabcbdbdaadabdabdaccabddabbdbbcacaaaabbbddacbaababacdcccdabaaaababbddaccdcabccadabcdbadabcbdccdbcccbdbbcaabaacabcbbcbcbbdbddbbdaaddaabbabacacacccabdbcacabadccddccdddacaaabcbdbadacddbcacdcdaadabcddcaadcdbdcaaaddccdcaddcbccaccdcbadcaaabdcbababadbaacbbbdddaaaacdcdbabcdaddadcccbaabacacbbcadabdccccaaddbbccdcabdcaabdddadaddcbcadbccaaacbddaacbbbacdcdddbacdbdddcbaaacdabadbcabdddbbaacddbaabacdadcdadcdcbcdabacccaabcbddbabcaabbbcdabdddbbddccdccaacabaccabbcadaacdcdcadbbdcbadbcbabbadaccaacadcdaaaabdaadcadbddacbddbbcaacbbdabbaaadbbcddaddacccbbcabadbbacdaccdcaddcbcdcdabbbacbbadbbbccdabdacddbaaabcdccabddbdaddcccccbacbbacaadbaabaabdddaccacdbadcbabacdbbcaaddaccabddbcdbcaabdbacdbbabaadbbdaaaacbdcbabababcbcabccacdaaabdacccbdddddcdcbbddbcaccdbccabadcacbbbcbcbaabdaaddbddddbbcddcdbcdacddbbaadbbbabbaddacbcdaccaacdcdbbcadcaadcbbdcdcbadbbdbdaabdbcdbdaccccccbaaacddbdcdbcadcbbbabcbadacbdaabdbcdabbbabbaddaadccbdcddbcbacacdccabcbdbdadcccdddaddcaadbbcacbaabbacadaccdbddbcccdddacddccbabacadbbcbabcdbccddaabacbbaadbbdacabdacaadcacadddcabddabdcbadbaadddbbdacababaabcdbbdabbabcdbccbdbdaaccbabacdcccabacbabbcbdbbbdabbbabcccabacbcbaadcbcbabcabdbaacadabbbacddaccbcbdbdccbbabbcccbcaaadcbcdcaadbccbccdcabbddbcdbdccaaaddacdcbcaacbcbcadcbcadddabcbbbadbcabddcbccbaacccddbcbcbbdbcdccbdacacbaabccdadaccbdaacdcbcabcdccbcbbcbccaccdcddbcbacacadcddbaadaabbacbdaacddaaabbbacccbbdbaddbbabadcdcdccdccbcdcdacccccaddbdcbbabadcbbcabbabbdabddbddcaacabdadcbcdccacdcddbbbccadcacdccccbdadaacdbadabcbacaddcabcbaabdacdbaacdcabadcdbcdabdddaccadcababccbbdadcddbbaaabcdaabdbbdcdccadbdbaacdaababdaccdaaaaabaacdaddccbbddbbccdacacdabbbbdadbbddcaabbccbabcdaaddadbcccdbddaababcadccbaacbdcaaacacdcdddacbadbcccadccbdcdcdbaadbbabdacddccadabdaabccbcdaddcababbdbbdacbcbaadacadbcbbdddccddbcdcaaddcaacaaabaadccdaabbddbcaddccddcabbdcaadacdaddbdcbcbdcabddaddbbabbcbaaddbabcbdbbacccbdaaaccdccadccbdcbcbadcdbdcbcbabaaadcaddcdcaacbddadacdccacbcacbbacddbcabbbcccaccbacdaaddbbbdabccadadaabdcbbbbccbbcdcdbaaacdcccdcdbcdbddaaddbadcdccbbbaddbcdcccdaccabcdcccccacadcadacabaccddadbbacbdcbbdbdcacddabccaabaccbdbcaaabbdbdbbaccccdababbcbcbcbacabdbcdccababcacdbdabbaaacbcbbcdbccacadbacdbcbdbcbbdccbbdbbbdbabddbaadaddcbacccdbcbccabcabaddcccabbdbbabbcdabdbbacbdcddabddaaadcddbddbbcadabdbbacccaddbabbddcbbcbcdabccbabcbdbabbbddbbaabcdcdacdbcabcbacdcccadbacabaacdadbacdabbdacdbadcddcacabddbcadcdbabccbbbdaaccddcccdcdacccacdcadddbcabbdcddacdabbcbcccababcdcbaddacbcdabcdcbabdcadbbaadacadbdbbcbacaadbcbcddbadaddaacbcabaddaccbbabdcadddabadacdbdcabcbbbcbdddcdabdbcdbaabccbabbdaccbdccabaaacbcdcbadddccacabacdadbbdaaabcbcbdcaccabdbcbdcdcbdcabcbbdbbddbbacadcadadcaddaddbbcdabdbbcdabaababadbcadcadabbcabbdbbccbbbddbbccbbaccbbbcbcddbbcdccadabccdbbdccbcdaccbdadaaacaadbdcbacaababcdddcdcbcacccdbadababdabaabaacdcaabaddadccbcadbabbbdaaccabbadcdcdaabaccaddcaddcccacbacccabcdbdacdcddcadbaabaacacbacaddbacbdbbbabbacbdbcbbccacacbacccdabbbdccbbbbbccabbccadcbcdabbccabdcdaadbcadcbcdadadcbcaacadcacbdadacadbbcabddccacddddcabdacdddbcccbbcdbdcadcaacbadcdccdccdccbadadadccdccdabccdbabdddaadbaccbcacccacaadddcdaabbacdababbdccbcacbacabbbabdadbbdbddddbcbdacbdbbcbccdbbcababcdacccdcaadccdbcacdbbbaccbcbadbdbcbccdbddacbadcdbbcbcaabccddbbacddcddcaddcbacbcbaaddabbdccbbacbbabaacdaddbaaadbdadcbccacbcbbccaaddbaddbbdcddbbcaadbcaaadaacadccccbdddccccaccbccabccccdacbbdbdadddaaabcccbcbbcdbddabbadadcbdacaacbabbccadabdaaddcdddadbbadcaccbacddbaaadcadccdbbbbdcdbadaacabddbccaaadacdcaabdabaddabcdccabdcbcacabcbaccbbbddadccbbbccdbbabadccabdddbadbbbcdadbbddcabdadcacaaabbcabaccdddcabaacdbbaccbcbbbbdbbdbbccdaacaadabcbbbacdccbadbadadcbabccdccdbaabcbacabaaacdadaacdbddcbdbcbbbccbabbabdaacdcccaaabbdcabbbbaacccacdbbdacbcccccbcaadaccbaccbbbdcddaadaadddcabddbbbabdbbdccccdbabbabcbccadddaabbbbbdaddbbcacadcbbaaadabcbacadddbcaabdccbdcdbccbdacdacbaadbacddbaabcbdbaaaddcbbadbabbdcdaddacdcbdddcabcadabaabaccdcdabbdbdabddbdcabdddcccaaadbabaabaababaadcaddbbbdaadccadabcdbccbbabaaabbddbaabbacdabbbdadcabbdbcbacdcbbddcadacdbcdbaadcbbadaadcabdaddbdbbbaacadccabacdadabcccccdcbddbccbdcadaaaaadcdbbbdbdcdbbddaaabbdaacbbbbabccbbbabcabbcabbdcbcdadcddadcaabcbacdddbbddbddbacbdbbbbcbaabddbacaabadabdbdbacabcddccbbddcbdcaadddcadbddcacbdcdbaaaccdccdcbaddccddaacacaaabcacdacbabaabcaadbbcacaabcbdbababccdbcaddabdcddbabadacaadbbbadabdbbcddbcaabbaabccdacbbbcbcbcbcbacbabdabbdbbdbbdacacbcccdccbcdbacaabcdcbdccdbcdcadbaddddcabcbccbcdbccddbbcdbdcaaabddbcdccdcbcbabbababacdaabbabbcbcdbdabdadbadcdaaabbccccbaabbdbdbbadbdcacacbdcbaaadcbbbcaacaaabcbabddcaacababbcddbdbbacacddcbcaaabadbdbaaabcadccbdaddcbaccadbbddbaadbbdacccbbdccbbacbacdccbcbcdaccaaacccabcddcbabbdbbaddbbbdcabaccabcdbdaacdabaabbddaaddcaccbaaccdddbcdadadcdacdbcdabaccdbbdbbbbbcaabddbdabbbbcdbcacdacbadbbbacbbabccbbbababdbdbdccacdabddadbdbabccbdccbdbababdbbaacaacdcbabacaccbabacdaadacacadbdcdcdbbccabcacbddadcbddbadbaacdbbadbccbabcbbaabaacbcadcaabcbababdcadbdbaadaacabbddcdcbdbaaacbbadcbaacbacbaacccadcaccbaacacbabbddbcbaaadaadddadcacadacccbabcccdaadadaabcbcabddabdcdcbdccaccddbaacddbccacbacbbccbcbdbacbbcaadddbbbdadbbdcdaacbddbcbbdbabcddacabcbbcbdcdcaddcbcadbcdcdaadccadaccabcacabaccbacbabbcacccabcdbadbacbdaacabdcaccbddabaaaaddccdcbdccbddabbbbbdadadcabbbccbadcadbccaadcaabcdcbdabdabccbdcbdcbbdbbcbcadbcdbcadbccbbcbdcaaadccaabdaaccccdbabdcabbbabaacaddbaaddcadbccdcaddddbcdbdaaadcacbdddcbbbcacadcbcdddbbddababbdcbaabbacccdaadbbbbdabdcadbbbbacbdcbbdbbacdcabaabbbadcccaccdaaabbbddbcbccdcccbcdcdccaadddcdcdcadabdbcdbcabddbcbaadbbaccbdcccccaccdacdabdcbaccbcbdbccacddadacdaddbabdbaddacbcdbbccaddbccdabddbadabccddbadcddddbcdbaddababadacbcccdacccbaadcaabdcbdaaacbcdcaaaabbdcacaddcbacddccbaadcbadbadbacadbbcdaddabcdabdcdccbcbbbadccbcbccacdbdcdcadadadcadcbbcbdcdcbadbdbabddcadddabaabdcacabcddbcbdabdabcabbadccddbbdbcdbaaacbddddbcadbbdabcbdcbdadbcdcbbbcadddadcbbddbddbcbbbdabcccbbbcbbaabdbaaabacccddddccddadadaaadcaadddbcdaadcaadadcacacbbaddaddaaccddbddbaddaaacccddcdcbccacabaacddbbadccdcbddddbaddcadcbdccdcbdbddbcacdbcabaddddadccbdbadacabdcddbacdbadacdbcbdddcdddcccadbadbadabbbaabaddbcdacaacdbdaaaaaccadbaddadbccbbdbbbdddabbbdbccdccbdbadbcaaccddcbbbabcaaacbdadbacdacaabadcdabbcbcddadbacacabcdacccbbbbcdacbddbdbacbdcdcccabbaacbacacdcaacdddcccbcddadaabdcbaabcdbdabbdcbacdcbabbbaabbbdcadaddccdabdbbbbabbdddbaaaddabdabacbaccaaaadadbdcaaddccbcdabaadcbbcbcbadabcaaddcbdbcdabdcbbdbababbabdbccabbacccccadbcdbdacddbbbddbdbbbcddcacdddbcbdddabdbddcdaaadabdacdbcbdcbbadabddadaacaabbabdbacbadaadddcacaaabdbbbdbcacbbdadaadcbbcbacadaaaabbdcbdcaacbccbdddccbaacacaadbadcdadcacbbccdcbadbcccacacbcdbcdbadacbbcbbbbacabbcabdadbcbcddcccbccbaaadbbacaddbbaabbababbcccdbbabdaacddbbcdaccaccababaddccccaacbabdbdcbdcdbddcabccdababadcddbbdacbcddbdcdbbbbbdaccadbabcdadbbbbbdbccbbaacacbacdabbddcbcbcbbbdbdababadddaacdbadbcccaccbdaabbbcccadaacdabbdbdbcacaacdcccabddaacaacbaabcccaacddabdcaadbcabadccbcbdaaddaacdcdadcdbddadacbddacdbacdbdadadadbacbdcdabbccccbaccdacaaddcdbdcaccabbdcacdaccdbbbddcccbaadcabbccadadddddadbdadabbcababcbabdbcdadbcbccabbadbdcbbabdcaadaacdbbaadddbbadbdbdabcbcadbacccccadbcbcdcdbacdadddbdadcaaaaacbbabddddabdcdbddbbdaccdaddcdbddccbacbadadbabdcdadacaddcacddcdcccddcaadabdbacabaaabddbacdacaddbaddccddbccbdcdcdccdacdbaacddbdbbaaabaacbadbdcacdccacdbbdcdadbdccdaaaddadabbcadcbbaabcdaddbaabadbabbbcaacaacabcbbcdcaacbbcacbabcbacbcbdabdbbbddabdabdccbbdbbacdaddbadbabdacacdabbbbaaccabbcaacaddadbbdbbddccadcdcdacacbadddbcddddabaadbddbcdccccbacabddddbbbabdaddccbcbbdbdbbcdacacabdbdaacacddcaadbcabddadaddbadabacaccdcdcbccacbadadccdcdcacbbcbacccdaabbaaadcdbdaccbaddabbaacabdbdcaaabbbbbddacaabdccbbdaababdaccabacddbcabaabaabaaaccdacbcaadaabdddadbaddaaccdabbddacadcadaadaddbaaaabdbbdbaadbbbddaaadabbddcbdaaccdbcdbbdbbaaaaadabcddcdddbdabbabccbccbccbddcaddbccccdcdcdbacbadabbadaacacaababdcbccaacbccbacdaddcccaadbcacadbdaabdaddaacbbbbbddacbaddbdcbdbcdcbdacdbaadcddddbdaadccbddcbacddccadbbbccabbacddaccadbbddacacabbacacdcccbacddacaccddaacbaadbbccccbabdcacbcaccaddddcbcacaaabcdcacdaacdbdcdaccddddcddcbcaadcbabcdabbbadadbbdcccdcbccccddcdcdbaaddadddcabadcbacddbbbcabbadbdbabacaaddddcdbbabcbaaddbdcdccdbccbddbbaddcadbbbcccbbadddccbaddbdabcadaccaaacbbacadcaaacccaacbbcdbbacdcdcacadacbabacdbabbdbbbbddbbbccddcbccadaccabaadcdadbbccdddbdcdcabdbbdcbcccccbdcbcbdadbaabaccbaaabbdbcdcbdbbabddcdcaacabddadcdadccaabdadbadaabbbabbcacdcccdadcdbccccacbccdbcdbdddbcbbabdabcaacbbddcadbadcdbbdaabacbabbaccbdbdbdbcdabbbaaabbaddcdcddbcabbbdadbbcabadbcbaaabaccdabacdbcabcdccbcdddbabcabbdbaabdbbccabcadccdaddcadabbadacbcdcbbcbdbbbababcacbacddcbdcdcbbaadadcabddacbaabbdacbdbacdcdddccccdcddaccbacdcccbccdbacacbaaccbcaccbdacabbcdddacaaacbcbadbcbbdacbcdaabcacbdcdbdabadcabdaacadddbcaaccccaccbdadcaadbcbcadbcdcddbbdbaddcddbcbcacdadacbddddaccbabbaaabbdcdbccadaccbcacbcaaacabdaaadbcbbadacaaadbcbcdcaaaaabcddcabadccddbbdddbabdbbccccbdddabacabaccdacbcdbddbbbaaddaddcccddacdcddadaccabaacbcdcbabacbbcbccbbadbccdabdcdcdabdaababbaacdddcdaabdabbbccbdbcbcacaccaacdabdbddbcbadacadaddccbacdabdddddcbaabaabaabdbabbbdbccdcaaadacbbccdbbacadcbcaabddbbcccbbbbcbcccbdbcbbacaddaadbbccadddbcbacacadbbcabbcbddbadbcdaaaabccacabbddabcdacadabbdbcbcbcbaccbbbdcddbcdcddbdadbcbadcbadbdccbbacdbddadcdcbbababcdabdaddbbdbdcaaddaabcadabdcbbbcbdbcbadccccabaadddaacaaccbabdadacbcbbcddbcbccdacccadcacacddadcdbcdddddcbdadaddcdaaabdddadacccabdbbcbddccabdabdbbdccbaadcddccddadaaddacccbabbbaabdbabdcaccdcccbbbabbadabbbcdbdabadcbdabbabbcabcdaaadcaccbccbbbccabacbabdcbcddbcacdbadcbcddaabcccddaaccaadbddaadcbaccccacabdacdadbdbbabcbbababadaccaddaddaacaacddcadbaaabcbbbdccbdbccccbcabaacacdcaabacbdcccdcabcccaaaaccdccbcdcbbdcbdcbbdbccbbbbddcadcdababacaabcbbccaaadaddbaddaccccbdbbabacddccbddadcaadbcabdadabaadbbdadabbbccbdbddadcdbbadbdaccacdcbaccbbbadbaaabbbcddcdaaaaaccdacaccccbabaaaaadccdbdddadbabbddcddcdbdadadbbadbccdbddbcdadbaadbcbdcaabcadbbcdccdbaccdcdbdcdaadcdbddaccbaabbadcdacacdbaabccbbabdcccacaaaadbdacbadbdabacdccadbdccbccaaabdbababcaadabdcccaaacdaaaccbdbbccbcdbacbcaadcadbbbdabaaabdbcabdbadbadcbbadbdadaadcdbdabddcbcdacdcdddbcdcdacdbdcbabaabadadbabaaabadbbbabaddbdbbadbabcdddbdccbadcadaaacbbbaadcbcdccaaaaacdcdaabdccccabbabdbccddcbdcbdcbbbbddbddaabdabcdddddbbcbbaaaaabaccacdcbabbbcbcbadbabbbbbabaddbcbdabdccbcdcaacddabcacbbddbabcbcbdbbcdbcbcabadcddbdbacdacadccdcadcaabdaddabaabbbdcadcbacacaaddbcbcaadcbabbcadacbdaadcccacdccaddabbacbddcbcddcbcddbbbcdcdadcbbccdbaddadcdbccbdbdaaaddbabccaaccdbacacadbcbadcccddbcddbcaadadbbabdcdacbdbaadcccdaabcabbcbaaaadcaadcbbcdababcdcabbacbbdaaccaacacbacdbcbabddbcddbadcaaaacaddaddbbdbaddacbababcacaccadbccbdcdcabdaddbdcbcabbaccdbccbccdcaaabbbbbdbcccbabdcbbbdcbdcbaabbbbdcbbadbaddbdbcccacbcbbddbcddcaadcccddbddaccabccccadacacdabdbbbbabcacadbcdacbcddcbbdcadcdaadccbcccaaddccaaababbadbbadbddcccadaabcaabddcbdbaacaabcadcccccbaaababdcabcadadcdcdccadcdaaadbbadcadbbbcbdadbdbcaabbddaccabdbbabbcbcdbddacdbacdbdabccacacbbabdbbdbadaddcddbbaadcaadaabdabdcdcbbbadcbcadddccddbdaabadbaaaddddbdcabccadaddcdaaaacbdbdadcdcbbccacaaaddbcdcdcdbacddcbbdbabdcdddaaaadadabbcdaaddccdcdcddbccdabcaabddbaabcdcdcdabbccadabdbdaadbaaabddcacaddcccaccbddacddbbbdadccadaaacdcddcdacccacabaadbadddcadcdadccaababcaddababcabababdcacaabcabdcbcbcabaaaacadaddacacdbadcacddacbddaaccddcacbbbcaababcdddcdcdcbcbcdbddbdddddccaaaabbadbdcaddcadcbdcccdbabdcbcdcddaadccacbadbcdcaacdababccaabacbbacbddddcbdbadbaccacdbbaaacdbabbdacbbcaaaacaababcbbddbccbcbbdaaadacbbcabbbcdbbadbbcddaabaccacbbcabdaacabacddbbcabbcdacabcccacddbddadbcdcdcadbccbdadddabbdabbbacdccbdaadaaccaabacdaababdaddbbdbacbdaccbbbabcbaccbbdbdcdbbdbdcabacccdaabcacabddbcccaddadabacdbacabcbcadcabaadadbcccaddbaccabcccddcaddbccddbadbadcbbcbcdabcdaaaabcccbaddabdcbacddaaddcdcaacbbacccdaaacadbacdcbcccdbdadcabaadacaaabcddddcdcbcbbaaddbdcbcdcccbbbabdaccacbbbbcdbbbdcddccacbdadadcadabddcbcdaaaacccdcdbcdcddddbcdbccccacbdbaabccaddbcdcadddcddcaabacbddcacdcdbacbddbdbcbbcbbadbcdadcadadbdcababaccdacbccdbabbdaabadaaadbdddcdacbcccbdbadbdbaccacbdbcbdbaadaaddcbcdabacdbdbcbbbdabdcccbbdcbadbadccbcbaddcacdcabdcacbaaacabaaaaacbcbcdbddbbdcaddacaacbddcdddcddcabaccdddbabdcacdbbdcdcacbabacacababcacaaccbbabddaaaaadcdbadcbbbbbddbdaaccadbcbadcbdabaaddccbadaddbdaccdaaabbcbadcaccdccdaadbcdbbaabbbdcbcbcbbcbdbbadccbdbccdbaacbbcadddbbdcbabdabccacacabdbbbaacdcabdcbcadcaddaddcdcdcbcaccdbabbcadccdcaaadcacacbbccbacacddcbdccabdcbccbaaabbcadcaaccccbcadbdbbcadabdadccdaabdbbcddcaaccbcbcbdcdcaadababbaadcacddacabbbbcdbbcdcaccccaadccbdbddacbcaacbddadcadaddacbabddddbadcbbaccbbaadbacdbccdacddccacbbbdbabbccbbbcadbddaacdddaacddbcbabccdaadcbbddbadabacdbbadbccadbaadccdcddadbcabababddadadccadbaabbdaccdacdacdcacbcbadabbcbcddcbddbdbcabccabadccbbabdcadbacccadacaddabdccccacbbbcccabadbdbadccbddaaaadddcdadcdcbdccbbcaacbdadbadababacadcbccadbacacdabdcbbccaababcaddcadaaacbabbcbcabacccbbaaccccdcadabccddcccdcabadaadacdbaaaaabdaddbabcbdbbcadbcaacdcadddcabcdcdbdbdbcadddaaacbbbddadbcadaddcbbadddadbbcbbcaaccaacdbdbddccddbcbcbaababcabbbdbaabccbcddabdcababcdccaaaadbdabaccccadbcbddbaddbcccbadcdabdaaacacdcddccdabbabccbbbdbbdaaadbccdcbdadbbabcdabaabbbcacacbdcdabacccdadbbbcdbddbdabadadcbcacbcbcbbaaddcbaddcdddcbaccaababaddabcdadcaccdcdbcbdaabbabcbddabdddcadcbbcabdcdbdcbdbabbcdccabddccbaccbcdacddaaacddcadaccabbdaddacacbbadccabacddbccdcaaabdbdaccabdddacdcbdccbcbcccbbcaacbcddaaabbccddcdbabaaacdcabdccbaadccdbcbbcccacbbcdcbcdcacadbbabbdacddaaabddcdbddbcaddcdcbdabaacadacaacdacbdbbcdcdaabddbbadbaaabbbabcdaadcbacabcccacabcdabcacacbcbacadaddacaaaadcadacaabdbadbddcaddcdcbddcbcbbccccabaabdadcdcacacbbcdccdaddaacccdccbdabdcdcadcbdbbdcbbdabddccaaaccdcbaadcbbddcbbcdaddaacbdccbbbbbcbaddabcacaabadcccaaccbdbadccabcddadaacaaacccbbcbadbcdbbcbbaddaaddcbcbaaddcbdbacbacbbbaaadbdaabbcacddcadbcbcbbdbcacddacbcdadadccbdbcbbdbcdbcaaadbacbbcdaccdacadcdaaacaabdadbabbcabadccacbacadbabdbbacabdccaadccaccabbcbbdbdcbcbbbadbbcbcdcdadbbcaddbdcadcdaadadcbaaccabbabcaaaaacdcdbdadbdcddacdacdbcadbaddcddcdaaccdadcbccddabcdbbacbcbdccbbbcdddddccadbcdcadbaadcbadabaabbadcbdacdabaddbdcdbadacccbdadaaccdcaaacadcdbddbdbdaabbcbaaadbaaacacdbabadcbcacdcddddbccdddadbcbbbbadadcbbccbcabcddccdabadaadbaccbbbcacaaadbbdbbdbdcbbdcaddcaadacadbcacdadaadbdccbbddadabdacaccaadabaacdcbcbaddadbcddcbcadcddcddbdbbbaccabcaadbadcbdcbbbaddcabbddaacaaaddcbbbdbdbbaddacbbbbdbbadbacbccddbacadcbdacbcbbbdacdbcdadbaadbbdaacdbbddddbaccdbacccabccbdbdadabbbccddcbcbdaadacccbaddccddadddccdcccabddccbaccdbdcbaadbcdacaaaababccaacbbbdcdddaaadababccacddcdcdbcddbbdcaddbdbccbdddadcdabacdbcacccccdbbdcdaaddccadcbadcbdbaddcccdbbabcddcccdddbddbbcbdadbcbaacaabbdccaddcbdbdadbbdcbbccaacbacbaaabddcbdcdadbccdbabbdadbabdbadadadddccacdbadaddbabddacbcbdcbbcadbabdccbcaaaadaccaccbdcdccacbacabdbcbaddbcdbbbdddbbabbbbbddcabdacbbddacdadccabbdabbaaabcccdcabccccddacbcdacabaccccadccbccaccaccdaacaacdcbcdaadadddcbdadbcacbbacbbddbcccaccaaaccbacacccadbaabcdbdadccaaabbabcbdcbdbbaacbadbacbbadadcaaabcbaacbacbbaaaadbbcddbbbdbdcbadcbabbbbadaacbaddddbddcdbdaaabaccababadabadababadccacbcbdcdbdbaadddadbbdcbadddcbacbbddcddaccbcbbdcddaaccbbcbdccbcddddcbcddbacdbbbbbccbcabdddacdaddabbcabbbababbbddcaacabacbbabcdccbadbdccdbbbaadbdbccdaacdcbaabddcbcacaccaacdbaccdcdadbdddbbcbcdacdbcaaabbbdabdcacdddbdabbcdacccbaaddaadbabaabbcacaccaddccadacccbbadbcacddacddccaacbdcbcaacdbaabccbdaaaccdbcadcbcabadbdddcccbacdabcdcccabbbdaaaabcdcddbdbdbadbdbbbdcdaadadccaddaadcabbacbddbadcbbddddccbbddcddcbadaaaacabadcabdacaabcadacaccadaaccacaabbcaaabaadddaccbdabaaccbbbbcddcacccbbbdcdacdaadadcdccaddbcbbacacdbcabbdddcdaabccdbbdadaccaaaadacccdbdcbcbbacdacbddbddbddcdbbddcccbbbbabdbccbbbabdbbdbabadbcbdacdadacbbabddcbddacdbddbdddaaacdaadbdbbbcbadadacddddccbadabcdacaadbaaabcacddbdaacaddaddbdaabdbdadbadcbccddcbaacdcdbacabbcabbbdacabcbbdbcdaccccbacacdadcaababcddbcacbdaaccbdabddacdcddcdacdbdbaaadcadcbbcdaaacddaaabdbdbbdbacccbddcabbbaddacabcbdabbadddacacdbbadcbaabdaacadddcbcddbcdbaababbcdddcccaacaacdadacbdcbdadbcacdbcbcabadbddcdaaadbccdaaadaacdbbbbdbbcbbdbdaaabdbccdacdbcddcccaddccaabaadbbcdddccadbdcbababdaaadbbadbccbbabdaddcddcdcbdbdabdccccdcbabacabcbbdcbabbcacabaadadcaaccbcdaabdbccbdabccbabaccaaacccdcdcbccdabcdaadbbbcaccbcbdcadbcadbacbbcccbccbbdcadcaadbcbacabbaabaacabaabdadaadcccbbabaccdadccdabbabcbbccbaccadacbbdbcccddaabddcbbccdaacdaccdababacabdbcbcacadbcddbcdaabcdadbcdabbccacdcadddcaabbacdbacddddbaaccbccaddacbbabbcadddacddaabdcacddadcdadcdbabadadcbababbdacbbabcdbccddbbcdcdaaaacaacaaadacbcbdabcbdddcacaaacbdbabdbcdcbaaddcbddcdcaadcbdcbaacbddaccbaabbbabaaadbacccdaadadacbdadbcddccacbdbcdadaccdccddbaddbccddbccdaacaccaadacdcbcdadbcbadcdadacdcbccbdbdbcaadabbbdbbbacbabdccdacbabaddddbbcdabbdcdadbadabdbcdaacbccaacbbaadccdacabdbccaabcdbbabbadcdcaccbdbccbdcbdaadadcbdacbbadacaccdcacbcabbacaabaaccdbbddbacdbccacdbcbdcdcabbcdbddbabacccbcbaacdddaddcacbdabadabcadbcaccdcacddaaacdbbdaccbbcaaaacaccdbaadaaabdddccbcdbddbacbcdccbacbacbdbbccacccacacddcddbdaaaabcaabaabaccdbdbbcbdbabacdbacbdbdcdcbdcadcdcbcbaccddbcbcacbdadbaadcbdbadcabbcbaacdcaabbcbbccaabbbacccdbbccbaadaddacbcdccdccbadcddadaccbaabadcdadbdbdaaadcbbdcccbbbacdabdbdabbdcccbccbdabaadbcacccdaabcdcabcaacdacdcdabadcbcdddcabcbcbadbcaaccbbaccbbdccacbcdcdddcadcadacccdcbbbaaddaadddbaccbbcaddbdcabdbacccbacbadadabdcbcdacbdcaabccabdaddacabcdcbadacabadcadddccaabcacaccaabdaabcaabddccabadaabdbbdddccdadcdaaaccdacddbbabcbadbbbabcbacddabdcaabacbacccdcbdddabccbcbbaabdcadcbbabcbbcbddbdcdcaadabcbdcdcddabdcadbbbdbdbadbcaaadcabbcddbbcaaddddccabbabbabadabcacdbdbbccadacabbdbabcdaabbaaadacccbcccbbcbbbacdddbcadacabbcdbdabdbbadbaaabaadbdbcaadaadbcdacacdddcdbddabbbdabbbabbccdcbccbcccbcccbaadacbabbbadcdbbacabacbacabcdbabababbddadabbddcdcdacaaddcdcccbdcccbcccddcacdbccddccdbaacbacaabaacbcbccbaccccaacbdbcabdbccbacbaabbcadbcbcbccbcdbbdbcadccaabadddbdadaaccaabacccbaddcdabbcabacaadbabcaabaadcbbadccaadbcccbdbcbcdacdccbaabcdcbaaabacbaacadcddbcbbadababbaddaadcdbbbbdacdcbabbabbdcdcbcddaadcbcdbdbabaddabaddaacacacdcadbcbabbddcdaacbaabcdbaccddacaddcddacbdbbabcdbcabbcbcaadbbbbccdbccabbccddbadbdcbdcbcdbababaddbcdadcdbcccdababbdbcbbdcabcbadddaccbbdddbcddbacccacbbacabbcdcacbcaaababaacbbdcabdbbabadacbddcdddcbbddcbdbacdabcdaaabbdaaabbbaaaddcdbcdadbccccabccdccadbcabcbbacabdaabdbacacddabacddbbddbadbbbccbbbdcdcbcbcddbabbcbcdbacddacbacaacabbbbbdadcdddcbcbcdbadbcdbcdacbacbcbbcbbadcaddbacbcbdcbcabacddbbabbdadddbcdadadadccbdccadcadbabcbaaabadddaadbadaaaadcacdadbcabdbaaddaaaadabcdbabcdcaccbbaacbddcdbcbabbbcadbaddbddcbbadcbddcdbccddabcabbcaaaccdcdbaaadcbbbbccabacdbdbaabcddbdcbabdacbadbaccdbbadcbddcadcababbdbccadbbacbcbdccacdcbcdacbabcdbdcbabdcadacbdccbadadaccbaacdcbaaddacaaabdcbdabcccddbbcadbcccaaaccdaaddddaadcbddddccaccccabbcacacdbdaadbcabdcbacbbbccdabcdabdbbbcdaadbacabcdaddbdcccbaaacdcadbdaccacbbbacaabbadabdccabadbdadcdcbcbcbaddbcabbdacacbccdbbccdadcccabaacdbcacdcbbdccacabcbcdaadbdbbabadcbccbdcbcadbdacddcacbbadaabbddaadabadaacdcdbccdccaaacdcccbcdbaabbadbcadacadbbddbacdddbdadcccadbcdddacccbabaacadcdcdabdbdbbdabdcdbabdacdbcdacaabdbcaaddcbbdcdcdaaccbbcaccccddbabbaacdcbadaacccaaaababaddacdabaadacbcbbabcdadbadbbaddacabbdacacbccdbadabadccbbbccddaabcaddbaacacaabbcbdaadcbdabacbbcdcacadcaadccbbdaacbadadcddaacbdcddccabcadadcbaabbbcdcbbcdacdccbdcaaacacdbbcaddddbabbdcaccbddaccbdabbdcdacaadddbcabcbbcdcacbdadbaacbdbddbbcccbcdacbabbadccbbabcacdcbcdabcbabaccbacbddbaaadacabccdaacddabcdbcbdcacbababbdcaaddacccbaacccbddbbddcbcdabbddcaabdaabadadcbaccaadcbcccdbacbaacadbdcddaaadadaacdadcddbacbbcdbaddaacaccdadbdcbbdabbcadaaacaadbababdcadabbdbdadcaacdbdbcadbcadacabdddbaddadcddddcbddacaccbcdcdacadddaabddccccbdabcbadcddacbdabcdccacadccbaadaacccaadaaabadccbbacbdbaacacdaacdaddddabacbabcbdcbacbdbcdabcccdbcbdacdcbdcbbcddaacbadaaabdcbadaddbddacaacaabddacbcbbacdacabbddcdcdcdadbdacbdabbabccbcccddbcbcdbdccdadcbaaddbddcdbaadddaabdbaddcaaaaadbacdddcbabdcbdaadbacbcbbcccdcabadcccdabbddbabdadaadcdbdbbaccbbbbdccaccabcddaccbaabbdaabcddabcabaadcbbbdadadacabcddddbababbaaacbbacbbdbabacaaabdbbaddacbabbbbabdaadccccdabaddcaaaddaadcbccadbdcacbcacabbbbcdcddaacbdaccdabdcbbdcbcbcacddaacccadcbdbcbabbbdddbaaccbbbaddaacbbcddacabbcbcbddaacacdcbababcdbcaaccbbaabdadaabaddcdcabbbcbaaccdacadbcbbcdacdaacadabbadabbacdcacdaacdddbaabdaaadcdcacdcacaacaaadcdacadccacbdccbcacbaabdbdccbaadacccacbdbdbacdbdcdabdccbaadbaaabccacbbcbaaacaabbdcacdaaabdddcddabddccbabbdcbdbdbdbbbbbacadcccbcadadaabdccdbcdcdcabdcbbddcbcaccbddcdabbdaacaadbbbccbdcdcdacacbdbddbccbacacbbabddadccaacbabdccbcdbcdabbbcdccdccadacdbabaaaacdccdbdabdcbacdcbcdccccdbadcabddbdbbdddcacabbbcdccccaacabdbdccacdbabbabadabcdaababbbcbadabbaacbaaccbcdbccdcaddddaddbaccbacdbcccaccbaaccccbddbdbbcdccbaabacccbdacbdbcddbcaacbcabcdbdbbabdcbbaccdaaaddabdaaabaadbabbcdaddbaacdccbccdabbabcbdabdaacbdbadabbaaabdadacabcdbdbacdaaabcbabaabcaaaacbdbacbaabccdbaaddccabadaaabcdbdbcbdcdbbadbbcddccdaaadadabaaabbdbdbbcadddbdabdbbbcaaabcbbcabcccbacdacbdbcccdadddddccacbdcaccbcaccdababdbcdccdacabcacdccdacdabdcaddcadcdbdccdcacbddabbcacdabcccdacdccbcaddbbcacaacbdabbdbaacbcbddadaadadacaacdcaccbbabdcdcababcdcbbabdadcbddbddbbcbcddbccdcddcabdaaddbbccbbddcadaabcbbdddabcacddbcaadcadcbccabadcbaacbbbbcbddddccddccdbcbccbcdccbbabdcbbadcbadcdccbaabcbbcdccbbbcbbbdbadaadddccabbdaadcdaadaacdccbadabbacaadaddddaacaacdabcaaccabdcccabdbcbdcdbdaacbabddcdbccbbdcbdcacdbcadacdcbccababdbdddbacacacccabbcabbbbcccacbdccbabcaadacdbbcdbaacbdbbadbcdbbacdbabbdaaabdbcddcbdddcaccddaccbcbddbccbcabccdcbddcddcacababddddbacdccccaabacbaabddacaacabababddbadccbcbcddbcbcbbdbdbccacddbbdcadaaddddcbddccbabaddabbcdcbdadcabbadcbacdaaaabcabcbabaccbbaaabdcdbbacccadbdbccabbacbcbcbbcdbbacdcbddaacdbadcdbddabbddabccabaadcaaadccbcbaaadbdcdabbdaadabcdbcadcbcadaabaaaadcabcccdababbbbbdabdcbbdccdbbbcbdaacadabcadcbbdccbdadbcbcadacabbbdabaadbcccacdadadaacbddbbbbddbbbddaabbdabcdddbcdbddbdabadbcbacdaaaccbddcacccdcdcaadbcadcbacbddacdddbbcbaccbbaaacdaadacccbbdcaadaadddbaabadbaaddacccdbabcbcbccaadadadbbdcacdbdbdccbdbccccddcdcccbbabbdbbcdccdcdaccccacbcdddcdaadadcbcacbabdabbcacbcdbdbbbcdadabbdbaccadcddbacbacdaadcbbdbdbabbcdaacccbbcdbacbadddbbbccbcaddbaadcbdddbddcbbdacaaabccabaacdbbacadcaadbccbaabddabcabbdcdcbcdbabcdccadababcccdcdaaacadadcdbdadcaabaaccacccbddcbcdbdaacddabaabdbccacbdccaaaddcdacbbdbaaaabdbcbdbdbbccbccddbaaaaabacbbddbcaccbccbcbbaddccbbbbdadbdbdcacbbaadcadbbcacdaddbdbdcbddabbbaabbbbcbddbbacdacabaddddcbcdacbbdbccaacdaaabccdcbbccdacdcbdababacdbbcdbcbcddacdcacdacaccbacddbcabdcabddacaaabddaacbdcbcaabbbacdcbbadbaddcaadcaacaddacbbbadbddadcccababcbdcccddcdacbbcabacaddcaccdcbadddddcabcdbccdabaadcbadcdbbdadcbdabacbddbdbbbddacadabaaddcdcddacdddccddaddacbabcdcbacccbbcddcdbaaabbbaadabcbccababbcdaaddbbcddbaabbcbcabdadbdbcbbcbcaabadcdaacaccbccddddabddbbbdababcaadddcddaacbaaacacdbcbaadadbdabacbcdbdbacacaddcadbaaacaaadddadddcdbaddcbcacaadbabbadadabbccbcadbabdcadbcacbaaabdacabdbdddddacdacdcddabddabadcbccdaaabdabcbaaccccdcbccbabacaddadbbcdabddbdcdaaccabcaadcdbbacaaaccccdbcddbccacbbccdabddbccdcdddcabbbdbbdbaaadbacbcacbdacbcbbdbdbcabddcbdbcccbcbbdaaabbbbdcaddbbadabbdaadcbcdacbcbdbcabcbdcdacbaccbdbbdbcacdbacaccacbaccbdbcbcabcdabaacddcaddbcddacaaaacaaadbaaccddbadbcdbcbadbabbcccdaddbaaddcccabaabbabbdabcadadabccdbbbacbcabaadbcaacaccdaccbadcabbbabddbcddbbadbdddbdbcbaccccbbdbdbccbddcdabaacabbbacdadbbcdaacacbccdccdbccdcddaabdadabbccbaddbabaadbdcaddadcadaaccbcddaaacadbbaabdcddbaaccccadccadbdbacbccdcddccbbbcacbabacabbbdbdcdbbabdccdddabbccaabbdbacaabcbcabbbacaccddaddcbcdcdcdbdacdccabacacccbbadbdacdcccaddbcdddcdacabacaabcacdbbbbdacbddcaddcdbbccdabccdbdbdcaddcabdbcccaaddaabaabbdccbccddadbdbccaaaddaacabbccdabaabacddddcccdcabcdaaadccbadabacddcbccbdccdccdcacdddbdbbaddbbccbcccbcccdddadcccddbdadbaadabacbbdcdcadbacdbaababdcacddccbccbbbbbbaddbcddddccbbbbaadbdbdccdaadbcccdadadacddaaabbcbbaadcaaaaacaacbdcbddbddddacabdbcccbbbbababbbabcaadbcddbdabbdbdbddcbaaddaddbddbdacdddccdaddabadbbdaabcbaadbccbaaaccdcccacbabbacbdcaddcbccbccadacbbdabaaccddcacacccbdddbcaddcbbcadcbcbbacaabadbcaabbdabdbcddacacdbcaaadbbbbdcaadccbadaaccdbdbdcdbcadcbbaaccaadaddacddbdacababccbcbdacaabababbadabadaddadccddbacbbdddaddbbccbddbcaddbcacabadaacabcdcaabadccddddbdbdddadbabdddcccdabdddbcccacbdcbdbbcbcbbdcaddcbcddcdbcbabbcbbbaacbbabdcdcbcddadaabddadabbdbdaabdddcccbadbcbdadbadbddbbbdccccaacbcdbdcabaaccbbacdaaaccdccadadccabcccddaccbaadcbcbdbbcaadbbaccdbcabbaaacbbdbbbccbdbdbcdadcabadbcabbadaacadaadbabddcddcccbddbdcaacdbacdccccadcabdcdaabbadbaabbccdccbdacacbaddbbababadcdbdabdbbdcbddbccacbdbabdbdbadccbbbccccadbcdcbcdcbcdcbbacdddabccbcccadacbcbbbbddcddcdbdabaacaacaadccbaabdbcccdacabcabdccbaababbacddacbbcdcdabccbcadbbcbdccdcabcbcbbbbcaadacdaabaaacadadadddcaddbccbbbadcacaaddcaccbdcdacddcccddbabbcadcdaccdbbcbcbbbbacddcadacbdbccdbbdbbbcdccbbbdddabbbababcbbabccdddcbddbcbadaaddddbcabcbccddbacacbabaadddbbcabcbbadadadccabdbbdcabbbdccabcdcacabbdadbbcdbbabadacbcdbcdbbdabbbdbbdadbabdcaabbbccabbdababdbaaccbbbbaccaaaabdcbdadaaadbcccccccccbabdbbbddcabbdbdacadbbdaacdccbdcdccbbaccbdabddddbdccdbaabacbadacadddabcaccbbbcaccaaddbbaaabadaabbacbbbcbdbdacdccdaadccccdaadbdabadabccbdcabcbabadbcccadbbabbbbaaabaabcccaacdbcddcddcbaabaaaaabaaadcdcdbacbbabaaccbbcdbdabddcadabadbdbdbcdcbabaabbbadadddcbcddccbcccccbbabacddddbdaddaabcdabbdaaddaccdccdadabdbbdcbcdbaddcbbadabddbcddccacaccabdbddcdcadbabbabacacadcadbcaddbbacdcbcddbdccccadbbdcaabbaddccdbcccacbabdbacbbdcbcccabdababcbdcdcbccaaccccabddcadbabcbbabdcddbdbcaabddddbbcbaaaaaccdcabacbadcdadaabcadaacdaacbcdadbddcdcddcbdcbdbddbbacccbdbbbbbdbcdddacaadcabbdcadbcdadbcccbadcdccacbcbcbcdbbabaddaaabcabddacdcbcadcabdcdbaaaadcdcddccdbdddaacdbdaaccbaacddacbcaacadabccadadaddcbcdbacadcdcbdcbacacaaacddadabdbdddbbdbbbdabacabbbadabcbdcaadabaaadbcacdcbdbdcaadbacaddacadcdadaaddbdcbdbdccabdcccabdadacacbddbdaaddadadcbcacbbdaaabaaacddaabbdbdddcbdcacbbdabbdadabccdbccccacdbdbcbbdaccabbbcbacdbcccadcdbadddcbcbbdcddadcbadadbaaddcdbcdbbcccdbdadbdccabccccdbaaabcbdcaacbbbdbaabdbadaaacdcbaadaacdcbcabccbbbacbaddbbcdbddcddcdbacdcdbacbdaddbbdbdabcdbbacbccbadccbddbaddbdbccdbdabbdbaaabbcacccbdadbdcdbaadbcbcbaacacdbabcbddcbbdcbabcdacababdbacdcccdddbdbcdddababcdaabbdabcbdaccdaacccbcbacaccdadcbcbcbcaadddcdbddaaacbaccabbcccabcaacbabbabbbadbbcdbaaaaadcdcbdbccdacbacabaccddbdacbadabaabcbbccacccddbbabdaabaccdcadbdbcacadcdaabdccbaadcdcbdbacccbdacbdcaacdcadcbbdcbacbdbddbacdabaaabddaabbdbabbadccaacabbdddcbdbbcbccacddccddaadacdcacddcbdaadaddcddbbadbcbcaccaddbacdccadaccacbaddabaabdadbabaccdbcaaaaadbdadcbabcbdccadcbbbbaaadcadbbdbbaacbabdcccadcdddbacbbabaddbaaaccddcbdacabcddaddcdaadbbacaddcbbabcddddcbcdbcddababdbcbdadcaaacdddbdbbdbcabcccbbaacacdabccbdbdcdabbbaadadaccbccadcbcbacbadacabcabbacbbcacbbbdbcdbabcabbbbbbacbcabdbaaaaccadabcdcabdbdabdbbcddcbaaccaadbcaccbddcbddbcddabdabbdcbacababaadcccbcbabdbabdbcdabbabccadababcbdcbbbccccccaabbcacbddacddbdcccccbcdbdacdcdbabcbcbbbccbcacaccbbabcdbdabddaccbcbbddcadacbbdbaacbdbbccaaddcccccbbdaaabcabcdbbcbbdadbdcbacdddbbacdcddcdabcaacdcbacccbdadcdabdcaabbabbddcbaadcdaddbadddbcabcdabcccbbdcabcdcdccccccddcadcdbacbacacbacbddcaadabaabcbbbacbaccdcababcdadbadacdabbccbdacdabbadddccdadabcacabbcaddbcddcdacbbdbbaddaaabcddadabacbdcbcbcdddacdcbcabdbdcabbbdddcccdbaabcaaadccddcbcdcabcabaabdbcbcddbbdbaaabbcccaccdbdabbdbaabaaccabdabbcdcaddacdccdbccdbdabadbdacaadabbcacbaccabbdcadbbcbdddbddabdcddccddcbcaaaadabdabaaacacddbccababbdddbcdbdddbbaaacdcdbdccadadadcacddcabacbcddbccdcbdbbcdccadcaabaaaacbadcabaddbccabdddbaaddacddbdbdbcbbdadbbabbcaadabaacdddddccbdbcbcabdacbdbbaccdcbcacddbdcdaadacaaacddcaacdcbcaacaacabacacaddbabbbabadbaccdbdddbbadddbcbdcccbbccdadcabbbbdbbbacaadcddcddddadaaaccdcbcbaacdaadbbbbdcbccccccdcabbcdbcdccbcdbcdabdbdbbbcbaadcdaabbccabdaaabcdcadacdaabcabbbcddcdbbbdbcbcabdbbaccddbdabdacbdcbcccdbbbbcddaabbdaddadccdadaaacddbbccdabbaccccbabcbbcacbbabacbcbdbacaabcccdbccdbabdddbadadacbabbbdabdbbabdaccdcbcdacababcbaccdbcadaabdbcbcaadcadcdbcdcdacdadcccbcacdadbaaacabbadbadaaabbbacaaabdadcbaacbdbcbdadbabaaaddaaccbcdbcbdbdcacddcabcacadbcbccccdabdaacbddbbcbcbdddcccdcaadcdbbdbabcbadbaaaacaadccacaacbddcdcdddbccbcbdcbbdbabbbccbabddcaaacaabbaabacdcacdbdbbbabbbcdcabdcdaaaabdccabddbcbddaaddabdddbbdabbdadacdddbbaadacabcccaddcbcdccbcaadaadbacabccddbcadcacbacccaacdbdbbccdbadcaaababacadadcacbabbaaabddbcbdaacbdddbaaabdcaaddcdbcccabcbacadbddbdcccddcccddaaccdcbcacadbacadbdcccdaacadabaccabdcaddbacbdcabcbaabddbdcdcdbbdbdaadbcbcdadbabcbccbccbbbaacdabdadaabbbddcbbbacadbcbaaabbdbddcabdabddcbacddabccadadbbaabcdadbdacadbbbdacbccdbadacabacdbddaabdbbbdacadbddcddcddccaacbdddbccdaaaacbddcbcaacaaccaabcdabaccaccbacddbcabadbddbbcbdcbabaaabcdbbbacacdccacbaddbccabbbbbcbbbcababbddbadbdcdbdcdccdbbaaaccbdcbbdbabdcabdbcbcaddbccadbddbbbcbbacdccddbcabbbdaccdcdbcdaddcbbabaabdbacbcadbddadacabacabaccccacdbccadacdcbbaaccbbbddccdcbaabdacccbccaaadcaacccabcdddccacdbcababaacabccaadaaadcabcddbdbacbdbdbabbbbdcbbadcbdbdbbccbdbaddacbcdcadccdcaddbbbadbdcbdcbabbaccbdcbcdabadaadaaadbccaadadaccdddcbadddcbbcbddcbcbaddbcbabdcadcacacddddcddcdacaddcadacbacbdcdacbddbbaacadacbbccabacacdcabadcbcaacdbbcdaaacdadddadbbbacbbacabdbadabadbcbcabbcccdbbabbbcbdbaabbaccbabbaacdcddaabadddddbccdcabbbccbadaccdcdabdababdbabbbccbcadddbbbccaddbdabacbcabbbddcdacbdbdaaacabacbcaaccbcacccbbcbdacabdbbddbdaaddacbbdabccaaccadbaadcdddbcbcccbcdccbdababdbbcdcbbcdaaaddcabcdddabccbadaabbcaadcabddabbbbcdaadadcdabddbabddacabacbacbbddbccbccdbccdcaabacdddbcaaadbdbcddcbbbdccdccacdbbcbabaccadbbccdbbccadacbdaacabccccacadbdbcdbbbaddddadcdbbccadbaabbcdaadbcaaadbcaadbabaaabdcbadccbbdbbaadadacadccbccaadbcdcdabbbaabcaaabdacbdbdadacaddaabccacdcdcaccadbcdababdbcbccdbbdbbbadbcdcbdadbcdbcdadddbcdbdcdbdbbddbdbbbacbccdacadbdcadbcdaaaccdbcadacadcccabdcbdcbaadcdcdccddcbabbdcbacbbcccacddbdcdcbcacdccaabbaddbccadaacabdcbbabcdcbdabbbbbaddbdcadbabcadbacdddacdbdbbaccaadbdaddadacabdbdcdcabdaddccccaaacacaaaadddaccdcdbccbccbccaddabbaabadacccddbbddaaacacaacbaddaddadbcdbdcbdccacababcabdbbadcdbddbbdcbabbcadddaacccbddbdddbccbbaddbaddcdadcdbccccdabbccdbabdcdaadacadadbaadcabddbbdacdacabcdcbdcbdcbbbadcdbccbcdbabaccabacadadadbbdcaabdaddbbdcdcbdaacddcabaccbacbccadadacadacacccdcbddaaacccbdcabbcbbbdadcddabbdddadacbdbcbbbdbdaaccdabcacadcdcccbbcaccabdbbccaabdccacacbccdddbaddddbccbcaadcbbadddbcabdcddcccadddddddaabbdaacbccdcadbabdadadddccddbbadacbccccdbbcbcccacbdcbadcbbbadcaccaaddabcbdcbddbdabcadadabbabacabcbaccdaaadabacdcdaaccacccbdcccdabbabdbddbccdaddadaaccabdbddcbbdccdcdbadbddaacbcaabbccbdaacdbbbcddcbcabccdabbddcbcbabbccccabbdabbbdbdaadcbabcbbcdcbccccdccbdddddddddaccaadbbaadbaaacbabbadabacdbcbdccadcbcabbacadbcccabacccdbcabadbcdacaacccbbbcaaadababacbaddcdbcabacbabccbcabdbcadbddcbaabcdbbdbcdacababddabaadbabdacbdcabcaddbcbcdcdabcbaddbcabbdaddcaccdcdbdcdacaadaccdcbbadbcccbdbcbbaaacbcdbbbadccacacbcdcbcddbdcdcbddcdabdcbdadbdabadbcacdccacbcdcccacacacddadbbacddcbabccdacbdaabbabcacddcbcbabbabbddccbabbbdbdaabbcabacdabaadaaacadbaadcbdacdcccccbbcbbadbabbabbdcdacddaacdaadddbbcbdcbbadbdccbcbabdddccabccabcbdcbacdcbbcbcbdcdabddccbbdbadaaacddbbdcccdbdacdbbddbbaccbacccbaaaddcaadaaadabadbcaabccaaacdbbaadabdbadbdbbccadcbcaaadaadacbdabaccbbcacccbddaddbdbbbcbcbddacaaabdbadcdaaabaccadcdcaaccacddadabcadbabccdcbbcbddacadcdccabadaaadbacdcdcdaddaacccaaddbdccaaabadbdddcacbdacbdabbbacadbcbaabbdabcaaacbaacbaadcaddddadcbcbccacbacbabbbdacdcacbcdcabcbcddbccdbccacbaadcbdadaabddcabbcbcccdbddcbaabcbaddabadaaababaddaaaacabdacabacddccdaaaabcaabadcbbccaacabdbaabdbadccdbcbcaccddbdbddacbcdacbababadbbccbdcdbbdcccdbaacbbcbadbcddadbdcbbcdcdbccaaaabdaaacdcacbdbacabaccbbaccbccbdbddccccababaddabbccadabbcbacbdaddaacdcacacdabadcdddddbcbcbcdccddabaabbdbccbbabcddcbbcdddbdcabcbdcabacbbaddaacabadaccdcdacbdbcdcdcbccdacddbbbdccaaccbdbdabdbcbbbbcadaacbddcccdbdbbbcdcbbacabbdcbcccddbaacbabaabbaaddabbcbdcdbbbdcbaddcdcbbbdddabcdddcdbbdcacbcacdbccadcbccaacaccdbbcbcacacdbbcabdcbdbccbdbcdabdcdbbbdcdbbbcdbacdcbddcabdbadcabcddbdcbdacdbadcdddcddacbcdabdddcccdcccaabdcacbcadadddadcdcdcbccdccccadacbbcdcadadcabaadddadaccccbdcbccccbaaaaaddddbcbbddcbdcbcdddcddcbbddbabdbcbddacbaacbccdbcbabcaabdcaaacdcbbccbddcacbbbbbccbabcbbbaabdcacdcdadbdcbbdbaaadbcaaccdcdabacbcbcdadcdbccbacddcdbbacabdccbbdaccbcccccdabccddddbacdcbaddcddaacbcdaccccbddbbadcacdbccbaccddacbbadbbabadccbbdcddcbabadaadccbadddadcbbddbbbdabadddadbcaacdbcacddcdcbbbbccbbcccdadbacdadadadddddcbaddcbaabbcdcdbaddcdcbccccbbbbbaabbbbbdccadddcdbdcadbabcbdabcadcbabbbdbaddbadbadcdabcdaaacbccbdabbbcccadbabacdbaccabbbabbcbcbbabbacdaccbcddcdccdabacadbcaddabbbbadbcccbddcbaaaddadccabcdabaabdbdcabaabaaadababbaddadcadaaddcccbbadcabbbccdadadacbcdbdbadcbdcbdadacaddbbcaadaccddbabccaddabdcbbbcadbcbbcacddabdaaddcdccbdadaacbacabbbbcaadcabbdbacdcbaddcadbdcaccbdcaddabdddaccbbdbcaaabbcbacaaaaadaaaddccdadcdbcadcbcaacccaaadddbaaababbcacbbcdbbbbddcdcabcdbabdcabdddbabbbcaddddabbabcaadbdcdcadbddabcccdadcaaddadcdacaabccbadadbbadcbadbcabaadbbaddbdacbcccdacacddadbaaddbcabdccaaacbdcbaacddacddbbcabaddddbcdcdbabbcaacbcaacdabbcdaaadbdaabcdcbbdbadaddcdacdbbcdddcbbbccdcbabcaaabbddcdadbdddacabadbcbcbaccbcacdddddcacbbdbaccbabbbbdcbbadbacbbacccddcdabbbdaccbbddbadcccadabbdbabccbdbaabcbbabcdbaacadcbbccdbaacaabdadddcddcaabccacbbbdccaaadbcbbccdbcaadbbacddcbbcdbaddacadbaddccdcabdcddccccdabbcccaacacdaaadccdddcbdbcbcadddbbcddcaaabbbcdbcabcdabbcaabcadabdabaaabddcabccdbdcabacabdadddbdabcbdbdcabbadcbaddababccabdddcdcbdacadaadabacaaccaccdcbdccdaabadbcdacaadbcdddccdadbababcccbbccabcbaabcddababacaabbaddacabbacacdadbbdbabdddcbbbccacdddcadcabaddbbcadbdbddadbbbdcddbdcbbaccdbdbdbdacddaccacdabbdcccabccbcddbbaadcdbadbbbabbbdacbbcaddddaaabdcbaabbddacbddcccbabbacddccbadbdbaadabdcadbddadaabbcabadadddadcbbdbcacabdbcdabccdcadbbcdababcdbcdcabbbdaadabddbabdabbacccbccacbccbdbbbbbbadabaacaccbbbbadcbdddcbddddbdadbadcbbdabdbdddccccdadabadcbccbdbbccaaaddacddcbcbdbbdabccbddcdcaddcbbbcdacbcdbddbbdddbadcccbcdbaddcaddbbdcbbbadddbaddaabdcaccbbcbaabcbdddadadbbabadbcbdbbdcaadaacbdbddabdbcbcabcbdcdddccacbdaadccdbbcddaccddbcccadcbadcbacbacaddbbccbabdadcccadadbcaacabaabbcdadadddbddbddbadbbccadacacbcdccaabcaadacacbacddcdccccdadcdacabadccbbadababbcaaadbaabcbccdcddbaacacabccabaabbcdbabbcadacaccabddbdddaaaddcccdcccabbbbdacddbcbcabdbbdbabadddbadddcbbbbbdbdabbdcdbdcddcabacddadcdbadcabdaabadaddcddbdadbbbcbcbcdcccdbdadddaaaddcadaadbccbadbcaaadcbcaacdbaacbdabacbacbcaabacabcdcdadcbbbdcabcadaccdaaabadbaabcdcbacdcddcccaddacaacbacccdabcccbacbbbacbcacaaaaacdbaaccaaaadcbaadcbdadcdbaddddbcdabdccbbaaaddaddcabccbbaddcbadaabcadacadababbcacabaabababbaaccbbbdcdccddbacbdadddadabadbdbbbbbacabaadadbbccddbdaaaaccbbabadbbbbdcbcdbdadcddcbdbddaadbbdabaaaddabbdadadbbdcbbacbcbcbbcbcabcbcabbbdccdbaacbdcdacbadcdbacacadbcacadcccbcbabbaddddcaacdbabaacacbdcdccbbdcddccacddcabcdaaacbaabcbacacbcabcadcdaadcaadddadcdbdbbacadababbadcadcbdacbcddccbacbacdccaccabdaadddacdabadacaaacdababbccdacddacccbdaccbacbdabbccdcbbaabbccacbaaabbbdabdcdcbcccadddcdcccbbccacacbcccbdccdaccbacadcaaccbcacddbcbcbdbbbcdcccbbacdbaacaadccbbdbddbdbbcbdbdbabdddbdbdbbdacacabbcccdcdacadaddbbcadacdcbbabbaddbbadcadcbdbccbcdddaabbabdbbaadcbbdcdbcbbbaddabcacbddaadbcbaadbdbabbcacacadddacabcaabccddcababacadbcbddbbdbacccabaddaaccbdcbdbdaccbdabcacdccbbbcbcbcbbdaabacababbcaddcdcbddadcbabcdacdbcaacdbdcdbbbcabcccbcaaaacbddbcdcdaadaccaabcbdacbdaabbdbcdbcbbaadbcbcadaacababacabcdbbbdbbcccaadabcbcddacdcbdcbbbbabcacaccababbacdacbbabcadaadcbdbadbbadddddbccaabcacbaddadbbbccabadbabddcccbabcbdbaccbbcabadcdcadcbcaabdcbdbbcaccaccbbcbbcaaccabdbccacddbaaddacbadbaddbccdbacbbbaddcdadaccdccddabadbdacaabddabbbcbbcadbbcbdcacdcaddddbbdcbcaadccccabbadbcbbadbbababdabdadddabccbcddbbbbdddddcbbcacbabcddaddccbbdaabdddcabdbcbbadddddcbbbdabbaadadbdbbaadbbadbdccdcbdbaacacbdcbbccbbaabcbbdadadaccaabcadddcbabcaabbacbbcdaacacacccddbcbcbccaaacbcabdcbbbbaababacabdbabbcccdcdadddcdacaddcdacdbadddbdcdbbbcbcacbdcddbdbaccccdcbdbcbacbbcabbddadccbcccdddddcacdcacbbdddbaabadbadabcccdbdcdbbaababdadddadcbcbbdbdaacaddddbddbdcdcdababcdabbcadadccdbaabdcaaacddcdccaaccddbbbddacabdbdbcacbdcbbcdcacbcdbcacacbdbdaacabbdaadbdbcbbdbdcbacbabcacccddabbbdbdabacbbbcadddbcacbcacdababdabaccdbbbbabbdddadcbcabadaddbdabbadbbadbcdddbdaadbccbbcdbcdcddbcccccdbaccbdabadccbbbccdccadaddaababcdabbccdcdccdadcbaddcabbcbcaaacdcbaacdabcadaaabdbaadbcabbbbdaabcdddacdbcdadacdbddabbbaadadbbcadbabaacdbbabbdacbadddadcbccdbcbbdadadddaacaadccbbdddccdcaccacddccbbacbbcabcaadccadbccdcaaccdccaadaccbabacdbdbcdbccbddcaddacddccccbaaadddbabbbcdcadaaddcaadcdadaccaabdadbbabddaddadaaaccccaddadbcbbaabbaaacaabcddbbdabdabaaadcccadaccaabdabbbbddcaabbcaccacccaaccabcddbadccdcdcdbbcccdaabaacbadbdddbdacbbccbccababcccbbbcdcddbcdacaabcacddacddbbbcbddddbccacbbbdbbacabbaaabaabbdcdbcdaabbbbbbbcbbacababbcaaddaddcddaaaabbcddaacdddaadbcabccdcdbcdcbcacbdddddbabaadacddbaacdcccccdbdabcbbcdadccddddaabaacdacaaaccdbaabaadadbdcadabbadbbbbcdbacdacaaabdaddbaaaadccadbccccbbcbcbcaabbdadbdbcdbadcdcaabaadbddcdbbaacdcdcdbadbddddabcdcdcdaccddddccadaadcacdaadacabadcaccadbccacccadbbbbddacaadacaddbddadcdbaadbdcbcdacddbdccaddbdabacbcabcbbdddadaaacccbddabbcbcccdbddadaddaaadcadcbdddaaabcbbaccdcbabcaacadaccbbbacdcaddddbdcdbaddaadcadcdbbcdcabdbaadaaddbcdcccdacdcbcbcbbcddadddacadbcbdbccdabbabadbbadcaabcddbdccdcabdacadccdcdcbbbccaaabbcddcdaaabababdabbdccbdcaadadaaadacdcddacaacadcdddaccccadaaccdcddbccaadbabdddcabbcbacaaaacbdbcbaacdbabcbdcbaabaddbbdacbdadbcabadcdcdcaccaccbcbdcddbdadbbabddcabbbbcdbccdabadcaccbbbbacdabbbadbcdacccddbbcdddabbadddddbbdcaadccdbabbcbdddddbacbbcdbdbbbcdddddacdbbccbdbbddbabdbdbcddabaadcaddddacdaaaabbcbaaaacadcaadcccaabbdcacabaaddaabbaddddccbbdaabaaadbacbbacdbbcdaccbabdcdddbcddddcdccbadcccdddababcdcabccbaabaccdabaccaccdaaccaabbccbccddbdcabcadbbcdaccbcacddaabcbabdacaacbdccddcdadcacdccbdbbbcdbabccbccdadaadcddbdcbbaaabadcabbddccdbbdaddaaaccacbbabdacdbbccbcabbdcadccdbbccccabccdbcbbcabbccbbbadcbdddabaccccabbcdcdbaddcbacbbdbbbbcbdccdbbccbdcaddddbcacacbaacbcbbabdabbcbbadcacccbcbcdcdacaddcbaababaddbdddaddbdddbaadccdbcbacbbcdadbacaddbbbbcdbababaaccadccbabcbadbcddbdbbdcdddbddabdbaabadbdadbdaaacbaaacbcbcabcddcdbdcadcacccadcddccbabdcbcaabcdccccccdcbbaddbbdbaccdadbcccaacbaabbabadbbacdacbcbadacdaaabcddddabadacabacabddbdcaddcbcadbccbcdbbbaaacbbbdcadadacbdcddaaddaacaabaadddcbbddcbcdccccaabadadcdaabbcbbbbbbccbacacccaacbddaacdbdbbdcdbbcdbbcdaddddcabdddacbdbabbbdcabbddcabcbabcabdcbdbcccbbcdbabddacbdbbcaababcbccdabacbcababbbbbabcccdddbdccadbacbbbcbcddcbcadcdabbcdcabccdcbdbdcccbbadddbbcbbdcccadbdccbcdbdaababcbcccbbddacbccbccaccbaccdabdcccbcbbdacdddcdcbbaaadcccaabdcdcbdbbaaadcbccabbadcaadcaddacdcacbddcdcadaabadbabdccadacdcdbbbcbcbcdcddddaaddddcabcddadabddabdbbcdcbbcbaacaabdcccdbbcacdbdbaabddcddacabcdabbdcbbcbdcdadcbaccdbbacacbabdbcbabaadbbcddabddadaabdddacabccbdadbabbadccdbbbacadbbdcbdcbcadaabcabacccaaaabbaaccbcabacccdcbacdabaddacbdcddbddabadabcdcdcacdaaddaaaaaaccbacdbacddbbaaacdcbacbbccddbcabcbaacbdccbbdabbadbdccdcbcbcacccdbdcbbcddbbaabddaacdaccbadadcccacacdbadabdcbddadccbbdcbdacaccdddaacddcccbbdcbbdbabcaccdaddcdacdbbbabbcbbdbaaccaacbacdcbbaacdbbbbaddaabaccacadcaaddccccbbdcabccacdcadbcacabdaaccacbdcadcaddbddbbcabacbadbccddbdbbbbbdddcbcbadcccdbadbbbcdabbbbddccadabdcbabccddaccbccddaddbdccdaacdbbadbaccbccccbcabdacbddadbaccdddbaaaccbddabcbdccdccbdadbdacbccabdcabadadacbacabccbdbccabdbaccaabaadacbcaababbabddcdacbaadbcdaacbadbabcadbbcbaccaddcddcbbbabddabbaccabdbcdadcadcdacaddbbdcadabccddaaaadccaabdccbcadaadddaabddccdaabdaabadbaacbbcdadccababdbbccbbdcdabaccbdbabacacbdcdccbabacaaccbbbcbddcbcbacccccbcbacdbdccddccccaaccaccadcbdbdbcacbcbdcbdcbbccaadbcdbacbcbbddcdcdcbaacbcbbbbdbdbccdacdbbbadaabcddccacbacddabcdcadddcaccbcbbacdadacaacbcbcadcdabaaaabbbbbcdaacadabaaccbaddcdbadcbbdaadcdbbbdcabaabddbacbadccdabbabadaaacacccbaccabdbbdbabacabbbadaccaababaaacdcbbbcadddbacabdcbabccabccdbacccdcdacbcdbcbddcdaadacbcdcdadabdcabccacaababadcabcbdaabcdadccabdccbdcddcadabdacbdbacdccbdbcbdbccccbcdcaadabbccddadccaddddadbcbbacaccbdbbaadacddcaacbbdabbbacaccbbacbabadcccbcccddacdcaadbdbcdadcbcbbcbadbdccadcbaadbccacddcdccbcbbdcaccaaddacbcbdaabcadcbbacbadabdcdacadcacbbbdaddbcbacabaadcbcaddabcdabddadbaaadddabadbacddcdbdbdadcbdcbdbdcbccdaababcdaaaaabbbbbcbbacbccaacdabccaacacabccdcaccddacccbccadbadbdabaccbadbbaccbdcaabcccbcddbbdadadaddddcaaabadcbbbbccccbbcbdcdaccbcadbbcabccaaddcacdcacacdaacabcdcaadcacbaadadadbdaaccbddbdadaacbcbbdabaaabcacadabdaaadccbdccccdadaddbacbadcdadaddacbbcdbbbcdbadaccaacbccbadbdbbaadddcabccdaccaaaaadbdcacccdacbbadacbdacdbdcaacdcdcadcccacbacbaababcbaacdbcdaaabacdbdaadbabcadcbbdbabdaaaadadaabcbbccadbccbacddcdbdbacdadacdcabbadadbdcaadaddabaaaadcbbcaababcdadaaaabbaaaaaccaaccdabbbcadbcaaadbdccbacbacbccaacadcacbcbabbdaadcbdaddbbbacbcabacabbabdabddbcabbbbdbbbbacdccbcdabdcaaacccdbbbddcdbacdcbdaddaabaddcbdadacdabbcbddaaacccbbabcbbabcacaaaabacaabddbadbccdbbbaccbadbdddbbadaacacaabcabaccccddddbdcddcdbdadddcacaacadcaaacbdbaacccccaaaccddaaacbacccbaaacabcabcadabacdbbabbbccdbbcaddbdccdcaadcabccdccdaaaacbccdabadcabbdadabcdcdcaccacddbddaccabcadabbabaddbacbdcbccadaacaddacaddcdcbcaacbdbbdcabaaadddadddbcbdccdbcaacbacaabaddbbcbcbaaaacadccaabacabcdabdbddbadadddddaaddbcddddbacacbbcababaaccddcccbcdbdcbcdadcdbbaccaacdbadbdbcdbabababbcddaaccddcacddcadadcccbcbaaacdddddbcdcccdbcccabcdbdbcadcbbbcaccabaaccdcbbbcabccacddbbaacabaabdabddbdacacdbdabdddbbddbadcaddbddbddbacbacbcccadaabdacbdbbbcbabccbdbcbcaaadbdabbabacaabcdacbbbdbccbabbbaaaddcacbcdabbabaadbddbcbbbbabadcbcdbdacaddcbbdddabcdadbdcdcbadcdaddcbabcabaddcdbdcddabacdacdcacbdadbcbcdbdaaabdcaddbacacccabbcdbdcdbcaabbdbaabddbdbcaddbbaadacacacbcadaadaacbcbaddbcabdccabcdaaabacbbcbbddcaaaabcbcbdaaabcbcabacddaabbacacccbaddacbdaacaaaaadbcacaabbcabbdcbdbdccbcdcddacdddcadbdcdcaadcaddcabbdadcdaabcacabbbbdabbaacdbbbaadabcdcabaccbdddaddbdbcddbbaabcbdccbbaadacbaaadabbcbccdacccccacdbaabbcbcddcbccbdbccccabcaadcdacdbbacbabacbacadcbccbccabccbbacbddbdddbabcaccbadcbaddbaaabbbabcdabddcaabaaddddcbbddcdcbdbcaabadbdcabdabaccdbcdadacbaddabaaaaadadcccaabbbdabbbdbcaddacddaabaabaabbaddccbabddbcdcaacabdacddbacbcbdaabaaadcbcacccbddadaabcddccaacccbcccacccaacadbdddabacacbdbcdaddddccbcbddddcbdacbbbcbbddbabbadacbdddcdccbbadaccadcdbdbadcbdacabaabdbccdcccaabaacdccdbcbbdccdcacccbddddaabadddbbbbdcbdbabadddcccddbcbdbadcbcbbbdadaaccbbbccdaacdacacbbabdaddbdbbccaadbdcccaddcdabacaacacabbccbddadcdacdcbababccabbdbdbcbcbdddbbdabdcdbcabbadcaababdbaadabbcdaccbccddcbabdbbacdddadcbdbacdcadabccdbbbaabdacbccaabbddabbccccbdaadacaacadacccadcdddabbdbbdadacadbacccabdddacbadbcdcccbbbcabbadaabbdcccbddabccacccabddaccbaaaaaaabbcbdbdbaaacaaaaaccacadbbdcbabaaacddcccacacabcbcdbbdbadabaccbbdbaccabbdddacabbbacacbddadbbacaccabdadccacaaabdadcccdddcacadcabbcccabaddbaacaccacdbacacddbddbddddabadadbacbbdcdbaabcbccadbcbbddabaccacbbbcdabcbcddaddabddbadcdcdbadacdadaaaccbccbdacbdbcababccdcaaaabdbcdaddbbcbbddabcacdaadddcddcbdaaddccccdcbbbdcbccbdbdbbdcbbadbcbaaacbccbdbcbbcddcdbcbbdadadcabcdcabcbaabcddaacdcadccabadccccabbdbcadabbaadcbaadcdacdcbcbbaacadabbccaddbdbcdabbbabbaaacbbbdadccbaaddbacdddababdbbcababbaabccbccbabddacadaadbdababcdbabdcddcdcabbbbdaccccddcbacdddacabcbbaaabacbddddbbcaaccbbdccbaaacbcccbaddcbbcdaaabdbdaaccaabdbdccccabaccacdbcbaadccdadbbdabcdccaaacabdaadbbbdbdacaabcacbbbacbcadacabccdadbacddcdbaccbaddacbbbbccdccccbdbccadcdaacbbcbccbcabbdadaaacbbbbacbdacdbbabbbbbcbdcacadbdbaadcccbdacdbddcaccbabaadcccabdabbcbdcdbbbbacabadabadbacaadbdaadccbcadccaaaabbccbcbaccbddbbdddbbccbdbbdaaccdccacbdcbbadacdbbbacbbdbcadaccabdcbacaddababccabacbccbddaacddadbdccdabbabdcbadadbacadbacbbdccdadaaaccadcbbabcadaddaaaddacbaadcacacaccaddcbacbaacddcbdcabbbdbbdbbccdccadcdbbaddbadcdcadbddadacbacaaccadbcdaccbacacdbcddcbcdcdddbacbcddcaabcbadabaaacbdbbadcddaadcdccddacbaadcbadadcaadadaaccbdacbbcaabbcddbbdbbcadacaabcbdcbcccbdbbbcdcbbbbcbdccbadacacbbaaaadacddcabcccdcdcbdaaaabacabdddddcabacaddccdbcabaaaabcabcabbacbbbcbdbbbdbdcddbcdcaadaadcdacaaddbbddadccabbbdcacdcaccbbdbbccacadddbbbcadcadcdcbcacabadacbdccaabadcbbbcaaabbabdaabacdcdcabbcdbaacbdbbcaddcbcaaaacccddaabcdbdbadbbdbcdcbabcddccbdcdbbdaabbdabcadaadddbdaaaabaccaabadaacbddbadbdbcacabbdbbcaaacccaaddddbacabcbacabcbcdbcbabdadcdbdcabdadaddccdadbbddccbacbabccddbbddbcbaabddcbdcaababdccaddbbbbababccdccadabaaddbbdabababacabbbcdddbcdaddddcabbcbdcaabaaacbbdbabdccbbcadbaadbccadddbdbacbacdbbcacdadcaaadbdddbaaabddddadaacabdccaabadadddadbbdaccdcdcbdcaadcdaaccbcaddaababbddabccbaabddcbccbcddbaaaacdcdcabbcacbcdbbbbdcbdbddacaaadbabaabbacdbcbadcabadcacdcdacacbbcaaabacbbadbdbbbccadaccbdccacddbbacaacaabadabddbcbbacabbaadcbbcbcaadcadbcbddcaacccdbbbabadcdbbaaddaacadadacadaddbbacccbbaaacdcbbcadacbcddccaaddbbcdaccacdbbaabbacabdbdccdcccdabdaccbbcdccabdddcacddcdbbccbdabaadabcbdaddbddabacaddacbabaacaabbaaacbdccbdcdbbdadcacbdbccbbadcdaacbbcbbdbcadcacdaddaddcccdadaddbaaadcacabddacbddcdbbdadabccdbbdadaddadcaaadaaaacadbbbdaadcbddbcabcdcacdbbabcdaaaccbbccabcbbabccabbadccabbaacbbddbcbbadbdcdbbdbdbdbcacdbaccbcdbaacbcdccacdddcbabdbdabcabdabdbcccdaaacbcdcbabbccdacdcbbdbcabaacdbbccccdcccbdacbdbdadcdcdcaabcdabacaaaacdabdddcaddbbdcbdabaaacbcacbbcdacccbaabcdabbbdabddbadabdcaabcbcbccdababaabcaabadcddddadadbabaaaabcabdabbabaacdccccdddccddbbbaddcdbcbcccacabbcbcddadacbcbabdccdcbbddaccbcdbdbaacdcdcbddcbdcacbbdbdddaacdcbdddacbdcbdcccbcabbdbcbaddabbdbbbcbbbacdcdcbbacbdddbaacbcbcaccaccdccadcaccaaacbaadbdbbabdacaadccdbcdbccbddcdbbddbdccbdadcccacbbdbdbbcbdaccbbbcdbbacccddccccdaacbcaddcbcaabadcbcccbbddcbcddbcbacddbbaacdadcbbcacabacbabaccbdaaabbdbdbbccaddaadddccaccdaacbdabbcdacdcdcbbabbbadcddcbcbbdadaaabbbcbccdcdacdacbdabbdbbbbdbcdabcbdbdccaddabdadacbdbaadcaadccdbbdabcaadbbcadbdadadaaabbaccbbcdbcaaadddacddcaaccbdbabcccadcdabcbaacddcbbcdabdcacddcdddbcdaddadacbcacadacdbccccadcabdbddbcabbdcdcbadccaabacccccabadcacabaabdaccbdbadbbadcbdabccdcababbdacdddabdadbbcbddcadaadcbbbaadaacdabccbccccdcdcaccbadabcbdbddcbbdbbbcdbdcaababbbcdbddcdcccbaaacdccdcccaaaaacbcdddbdcbbcbccdabdbabaccadaccbbbdbbaaaddcdcabcbdddcbbacbdaaadbccddabbacacacabadabaacadabcbdbbadaaaabbcbbccaaccdcaddcdadacddcbadaadbbdcbbbbacbdcaddbacacbacabbdcabaaaabddabbcaabcbadbabcddbcbacabdbabbcdcdaddcbcbbbdadacbabcbadcaabbcbcdbcbbadcbbcdccbbdbcbcbccdcabacbdcacdabacccdcadbdcdbcddcacdaaacccbadcbbababbbccbdbabcccaabccadbabcbdbcbcbbdddbddaababdbbdbcdbbdbbadabcdbdbcbbdaaabadadcccabaadaadaccaddabdbcbadbbadbddddbcadbbacadccadabaddcdacadcddbaabdbabaadaddddddcccbdbdbbcbabcbabbaacbdccccdddabdbcbcadaacdabddadbccadabcbabaaccdbadbcbcddbcbaacdadaabbbcdbdcddcccaddbddbadbacdcdabacddbacdcbcbdacaddbaacaddacbbdadabdacbcaddaccbabbabbacccaabccdbbbccabcddddbbacbbcadabdddcaabadcaabcccabbddddddbacabbcabaaaacdbbdbdadadccbacdbbddbbadabbbcbddaacdbacadbbddacbcabdcdcbdbddbdabbcbdaabcdbddabccabcbcdcdbcdabdaddcacadabcdbcddaabdabdcdbdabdcdaccbcbdcbdddabcaadcccddcbbaabaccaacbadaaddcccbdbabcaabbadaadcbdcacabadcdccabcbdcddaaaddaddcadddcdacdabaccbbbadcaddacabcbdccaaaccddccdabadbabdbbddabcacddbcabcbabbdbcadccdcddadcccbabacddcadcaaadcacabdacdbcbdbbcacdccdadbcdbbadcdccbdacdabdacccbaccddbbcdaaabdabadccbbcaddabccddddbcdadcddddacbbacababacacdaaaabcadbadddbbcdcabbddbbbbadbbcbdadbcbdacccdacdbbadddaddaaddccabbaaadcaabcacdccabaaadcdaddadaabaacacaacdaabcaccbabcaccacccabccabadcdabbaacdcacaacbacdaccbbcbddadccabbcdbbbbabcaabbbbdbcdacbdbddbdabbbabaccbadaabbabaccddadbacccccaabbddabdadadadaadcbcdcacdddadddcbbbaadddadccdbbcddbccccaaaaabaabdbbdbbaacdccabaadcddcadabbdbbdaaabcddacbdcadbdbdacacabdaabbaadacaddccaddbbcacdbacabcdaddbcddcddbdaaadbabaccabadbaddaababbcabbaaadcbccbbcbccbdbadcabaaadcaccadabaddbddadacdaadbadaabaaadcddccacaddbaddcdaabacadbbdddcabcbbbddacaabdccbdbaabccaabccacaaccadbabdacbbbabbbdbabddcadabbddaccbccabaababcbbbaabdcbbacddcbcaddacbadbadccddaaaabcbccdddcababadcbdabbacdbabbadadaacccbcccadbacaccadaccdabbacbadbcddabaaccaabadcacdcabcddcdbaadcadbbabacdabbbccabcddadcdbbbcdbccbadaaaabbbcdbbbcabbcccddcdcadcababdcdbdccababbacddcaccdbdcdaadcdcbdaddbbbbbdcbcaabcabcaccaddcabdcbcaacddbdaabbaabaadcddadaddbabacdbcddcadcbccccabcaaccabbcdaacabbcaaabcdadabdaaaaaacbddddaabcdcbcbcdbcdaadccdacccaaabdbddcaacadcddcdcbdcdcdcaaaddcaaccdcbbdbdbcadabbdbcdadabbddbabbddbbadddbccdaacbdcdbbdcabaacbcbaaacaacdccdbdadbdbbacccbbcdacdccbcaacdbcddcdccaadbaadacdcbbbbdbacdbbddccbacacaaadcbbdddbdcbcabcbadbbdaccdacdbcbcbbaccbdbbdaabadbdddbcdcdbdddbbbdccabbcdaaaddbbadddbdabbccdcbabbdbcbddbbcaddaaacabdacadcbbaacdadabddbadbbdadbbcacdadcbbdccccabaaddbaccaabdcbdbbcdddbbdabbbacddddaabbabcddcaaaaadbaadbcdcdccccdaadccbddabbdbcddcddbdabcabacccacdbadccaabaddcbdcbaddccadabbabadaaaaaabacabcacadcaaccaabcabbbcadcbbdbaddcbbaddaabbbddbdcdbcbcbccbddbdddcbcadcdaddcbadaccdbcdcadaaddddcbdacdbdcdabdbbacdabaadbbbdccacdacadabcccdccdbadadccbacbdabbcbbbcddbacaaabbcbbdcaddbaabbcaadaaddbcbdabaabdcdcbbccaadbdbdcdbaabbaadabcddaccdcdddadcabbccaddabbdddaaadbbbdbbcbcbadcaccdaccdcbdacadaddabbbdbbbccdbdbabbdcdccbaccadbabbaabbcbcaacacbccbbbbaacaadcbacdaacdacbcbcbbbbcbcddbdaacaddaaccdbabcbbbbaacbddcabadbbccaaadcddcbcccabcacbcabadabaacdbbbbddbbdbcdddcbcccaadaabdabbaaadaadbbaadddddaaaacaccbdcbbddadddadacdadacdccadabaddcdbdbabababcaccacabbcdccaccdbdbadcbbadcadaccdbabcccccbaabacccbdcdcabddbdcaadaaddcbaddbccaacdbcbdccdcaabaccbdddabddbaccbadbbbbccbacbcdadddacdaabcbbacdbdaabdbabdaaccacaaabadccccacbcbaddbddaaadcacaccbbdaccbddcdacacbadcdbccaddcddaabdcddbbcdcabcaacdcbdcccddcbbccdaccccbcaaddbccdacaccbacabddbabbababacbbbacdcccaddccbadcbccdabbcaaaabcbaddcaabdbbdbaaaababdbaddcccaaadcccaabaacbccbbbacdbadcbddcacaccccbcdbdabadaadbdbbcacadbdcdbbcdcaddadaabcbdcadabbccbcabbdadacabdadbdbcaaadbccdcdacdaddcccacacccccdbabbccdabadcccbabbababdababbbbbcdddcaacdcccadddacdadbbddaddcccbdccabdbbbbacdbccdaababcdbcabcdcaabbcbcdaadabaabcddbbacaacbdacbcddbccabcabbabdddacdbcccbbdbbbdabdbccddcaacaabbaaaadbddcacdaddccdbdcadccbdbabcdcbbaabbcdcbcbdbadbcaacbbaccdbccbdaabadcabcabdcdacdbaaccbddbaddbdcabbdadbddabbbdbdcaaaaabbdccacdacbdbcdbabddcddcdcdbcbadccdbaabdcaaacbbadabbbbddadaabbabcbbdcdacbbbbaccabdbcddbdbbdbdcbcdbbccbcadbdbbadabbdaadcdbdbdddbbbcabadddcbcdabbcabcacabcdccddcdbaadbdadabadacdcbabbddbbbabcbcaccacdddbacccaaaacbcdbaaaaacddcdcbcbcbddbbccadcabbacccccbacabadcdcdcccbcaaccabbdabdaabcdccaddbacaaaccdcaabcccacdacdbdbbcabcacdcbadccdbbaccabacaaaacabbbccbcbcbacdacacdadabdabaccddcbdbbbcaacaccbaaacdcccddbbdcaddbcbdddddbabbcddababdadcddaddbbbcaaabdbbacbcbbabdcddddcbbdadbddbdaccbdcaddabdbdbdabdbbcabadbbdabbababdbcbacaadcdccdbacbabcdddabcbacbdcaccbbcaadccdbcdbddaabdbaadadbcddcababddbddbdddbbdbdacbbbaadbaddacbabdcacaadcdaaddacbbbdcaacdcddbadbbabbbdbcbacccacbbcbdaababcccdbdbcddcabddbcdbbaadcdcaccdaacbaabbdbbdbacdddccdbdcdcdadadcddacccbcbacddbcbabbddaababaadabcbacbbabdddcaaaddadcbcccbacccbbbbccaccbbadccdcdccdbacdbccadcccbadcabdcbbadcadcccbbaccabacdbbbddccddbbdbbbcbddbdcdddccccdcdcaddddbacacabcdacaabccbcadbddcaadabaacadbcadcdadcbcbcadabbbcaaaacbdcbdabacdbbdbbbaabdccccddabcdbcadbabcdddbbcabbbcdcdcdccdcdbacacdbbbbdddacdacdadabccacddcaadbcdacdadcbdaaacdbadbdccdbcbccaddaabaaacbaccadabcdbaabcddaddcdddcbdabcccbbdbadacddabbcbdcdaaaaadadbdbccdcbaddacccaddabdcaadacabbccbbdddcbbcbcddacdcacdddbddaddbbdbbbbbaaccdcdddccbdacababadcacddbdababbaccaccdcccaacaddbddbccbadccacccbacbdddbcacdddccabcbabdbacdcabdabbbcacdbcbcacbcbdabcbbdccddcabddbaaccacbbdabbbdcadcbbadbaabdcbddddaacdcddcbcdcdbabdbaaddddcdcbdbbdcdcaabcabdacacaaadbcdbbabbaddddaadcddabdbdbcacbcdaacdacabdbbdddaacabcdcacacccbdcbddabaddbccaadabacaacbdcbcddcbbdbdbabccabbdbcbddabcdabccabacadadcccddbcabdcdbacaaaadbcdcddcacadcbaaaaabcccccbbaddcabbdacbabbaabdcdabddbbdbadcabaadcdddcabcbddcbacaabadcbbcabdbaacbbaddcabbadccacadacbaacbdbdacacaacbbbbdbdcadddbaacdabbdadabbbcddbabdbaaadadaaaaddbddbbababbaabdbcbbbaaddcaababddabbbbbaadabaadacdbbbcbddacbcaabacddadaacabdbbcdccdcdcddcdbddaadadabbbbadbbdbbcbdababacddbbdacdbdcbadbbbabdbccdbbcdabddaacabbddadccdcdddadbacbaadadddbcbcacbbabacbccbabaabbadbdcbdcbdaaaacbdaaaabbadaaabaabccbdbcadaaacccaccbbcababbaaadccddbbabcbbbadaabacacdbbbcdbdcdadbbcacaccadbcaabadcbccdbdbcbbdabccdccbdccadadbaaabbdacccacabacacbcbadcacccaacacbcdbdcdcdbccdcbacaabdcaddbacaabbabacdcddbcadcbadcbaaaabcddbccacbcdbbcabdcdbaacacdbcdcccbadbcdcdcbcdbbccabcadcdabddcabcabbaaaacacdddcaabdbaddaaccbcadababbacbcdccddbbdbbdbccbdabaabbddcaadcadbbbdaddabbdbbbcaacccdabcabbdcbbbdcbbbbbcdabccabdccccccabddbadcbcbdaaacddddbabcdbcbdcdbdacddabcdcddbcacccddccaabbaddcabccbaabbcccbbbabadcccacdcbaaadaabcbbadaddabadccdcbdccbcbaabcbcdcbabdbabadccbdcbcabcdccdbdaadadabbdbdabddcdbcadcabbcdddddbcaadbbdabacaacadcdcdbabdbabdcaadcaadaabaaccacdbaddcccbdacabbbbbadccdccbccdccddbdadadbdabdabdcdcdbbbcbbccbdbdbcbacbadcabccdcadaacacdbddddaaddbdaabdabdacddbccddcaadbaadaabadddadbcabadcbbacdddccdaadbccdaaadadbadadddcdadcdcabacdcababbdbcabdbcadddccaddacddaccaabbcdcccadcaadcaaddccaccdadccabbccbacdabbcccaddadacbdbdcadabaacbdaaccdaddabdbbabcccadaacadadbabaddbdadbadadaacbabddcddbddbaddadcddcbaabcbccabdccdddcbcacaccccaddcdabbbdcbcbddcddababdadbdcabbdaabcabcdadaddaabaabacbdacdaabcdcacdccddaacbbacdcaaacbccaadbbddcdaddccadbabbddcbddcdcbadcacaadacdaaccdbbbdddccdcdddcccbccddccbdbadbdccdddadcddcbbcddaaccbdacccacbddbadcacccddcdbcbcdcdadbbbcaadadbbadaccdaccdaccdaaabcacacadacdadabcacbdcdddabcbaccdccaadaaddaabcccddbbcbcacbaccadacdabdcbadbbaadbbacabbacbcacbaadbaacbadabbdcdcaddbaccdcbdabadbccdadbbcbdcbacbdbdaddbdadccabcbadcaddbbdcbdcccbddbbcaccdacbcbaaadbddddbdbdaddaabbbbbacdbdbdbbcaacdaadbcbdbacddcdcddbbdbbbdcbbcbcbcbacbcaccdabdcadacbabbabaabddaadbddbabcbcadcdadbadbdadcbaabadabbaadbbcccdacdccdadbdddbccdbdbbbababbcaaaaadaccadbbadcadadabcdbbbaaccdaabbdbababacdbdbcabaddacbbaacdcacadabaaabcdbcccddccdcdcadcdbadacbccbabbbccabaddaabbcdcdaaacbabccdbaaccbbdcddddbaadcababdcdbbcbdbdaaaaccbbbcdbbddabdddabbbdcbddcbbcdcbdabbdddcdabdbdbabdcadbdbcddbbdbcbbcdadadbcdacbaaddbadbddbcabcabcdacbbcbcddabbbddadddbdbdaadbacbcacadacaadccccaddcbabdcdaabacadacdcdadddcbdddcabbdcbdabbbcdddbdabbbaccccbdccbdaadabbbbacdbbcdbdadbccbbbdcdbbbbbcadbddddbdddddbddcdabbccccccdaabbbaaaaccbdcdddcacbbbcaaacdcacbbbccbbbddacabbcdaacdcacbdbbbdccabbabdbadbacacddddbadcbddbbcbacaadabbccbbccccadaadbdadaddbdbdcacbdaaacdadbbcccbbbcbaabcdcbcbcdbbdcdcdbaaadadacddcbddaccdccccabdbcbadadbcdbcbaabccbcbdddcdbaacdccbcaacaccdbdbdddccdabaccdaadbdcdcbacbcdcdddccdabdcbaaccaaccbcaacccdbbdaaaddcacbcccacbdaaccacdcdbadbbadcdbbcacbcdbdacaaccbdcbcababcdbdcbbccacbbbcadbcaccbbadddcaabddabbbcabcccbcbabccadabcdabcaadcaabdccdbddcaaccbddbabdbacbacddaccbbddabcbddbadabacbaaddbcaacadbbaacdcaaccdadbbbcbdbdaddcbbbaacaacdacaccbccdacccbbacadabacdbddccdddbccbbbbaabcadccddddcccadbcccbaadbbccbbdcbcdcaadcbdcccbdbdccccabcdabbdbbdbdadbadbaacdbbdacbcaacaccdbddcabbdcbbabbdabbcadbacbdacccadbcbcbbacaddccbbdcdcccacdbadaaccddadcbacaddacacbccddababacdcaaaccaadbbdcdcbabacbddbcabcbdbcadddcbdddccdacdcbadcccaadacccdaccadbbadcbccbcabbcbbcbcdcbadcddbbcdbbbabdaccbddccdbdbcdcbbcdadccaccaaadbbbbcdbbabccdcdcaccdccadbddccabbabdcdacadabacbbdddcabcadddabcabadbbddcbacaadaddbbccddadacdcdcacbddaddbadbbaabcadadbdccbcddcadcdcdacccbbbbbababadbabdadaabbbcbacbaaddccbabaaccbacbccbdbaadbaadccbbcccccadccbacadacdacddbbbdbcabbadccdaaadadbbdaccdaaadddbadbabdabacdabcaabadaaadbbcabbdddbcdabdaaabacacbdddcbaddacaadcbbbbdbddcaacdddacadcdcbabcccddcccadbddbbbccbdacaaacdbcbbacabadbbdadadcdddccaaccdaccccdcdcddbadbbddcdadbbbdbaacbadcbdacdcdbaadaccdccbcbdabdaddcaadcbaacbaabdcdabbacdcacdabbaaabbabdbcbccbdbaabdbbcadaadccadddbbdacdcccabdaabdddccddcacaabacddbaababdbcabdadababcddbddccacbbaddccbacbbcbbbabbbdddbccaddababdaadbdcbdcdabccaddbadadddcaddccaaccacbcadcaccdabcdbbbcabddbcbdcbcbddbcbdadbabbcccbcabaaaaadbbacbbccabccbccdadccaaddbaadcccababababcbdccccadabdbdcabcccdcabbabdddddabbccbdccdcccdbacbdbbaabcdccadadaabbbbabdbcbdbcaaacccbbdadcbabdbdaacadcacdacadddacaabbbccbadcdaaaaabccbadabcdbacbdaadcccccabbcbbcababcdbbcbabbdabaccaaacbbddcababcdcbdddbbccabacbbbcdcadbaaaabbaaaaadacbbbccaabacbcccadbdaabaccbababababdbaadbdacbdddadcdbacbcbcabadcadcadacbdaaddcdcdbacbacaaaadbdadcaacbccbabdbdabaccdabbccdaaacaacddcdcccadbdddbbcbbdabdaadadddbdaddcaddcadddbacbdbaabbaabadcdcbaabaadbaccdbacacdbbcabdadbbadaacacbaaabcacdbdbdcadaabaccbcdabccbcbdbcadcabcacccbddbcacbcbcbbdadcbcddcacabcdcacdbadcbdcdcbbcbdbdbdcdcccbddbbcaddddbbdacdcdabdbadcaacbdadbdccdacaccbbbcbbbcbbbcaaacadaabaddbdbcdbdcbdbabdacbaabbddaddbbcadbacddbcbaacabbdabccbddcdbbacacadddcdbcadbdbacbacdbddcbcbdcbababacbbccbdbbaabacccbbdcaccabdbabbdcbbbabdccccadcaacbadbccaacbaabacabaccccbdacdbacadabcadadddcbaadcccbddaadabbacdbdcccbbdbcdccbdcbcccbabdccaaccbadaacdbcddcabccdcbbbdaddadbaadcdcbbbcdabbbbdbccbbaabdaaaabbcdbcdacbaadadabaddbdccbbdbbcdbbbbadcabdcdcddadbcacbaaaaadbdbdcbbaaacdabccabcbdbddadbcabddbadabcaadddababaddcbacacabcbacbdccdcddcaacdcdbdbadbbbbacbcbdacaabcccabbdacdcadcbadddcccbcaacbdbdcbcddbdacbadccdbabdabcbddcccaccbcbcdbbdaddcbcaaadaaddbdaadaaacaabcbccddddcbcdbaccadcddabccbadbabdbabcbaacbabbacdcaccdccbbbaabcccaabaaccdabaadcaccacbbdaadcaabaacdddccaabacbccbdddbcddbbcaaabcccdddaaadababdddbbdbdccacbaabcbadadaaddbbbbbdcdacbbcdacbcaccbaabbdcdabaabddccbaabcdddcadbdbbbdadbdabdaccaabdcaaabdbddabcadbbbacdbdcbbaabbaccdbadcccbadbcbcddbdaddcdadcdcdcabbbccadacddbbbcabdaccccdbbbaaccaadadcccccbbdabbcdaaaaaacacabbcdcddddcbcddabdabbdcbcdaabccbadcdbdbabcacadcbcacccbcadcdcaaaabbdadacaaaaadccaaccaaddddddbabcabccccdcdabcaadcdddcdccdaabdcbbcabacccabcbcdbccccaddbbbcbbdacaddbbccaacaadcbbabadccccbdabcbbbccbbdccbabcadcadcbdbabcdcaadababcbcbaacdcadcbcccabdbadabbaabcdbcccbdcbadabadbbdaaaadcbbdcdcbaaacccdabcdcdbbbcacbaaccbdbcabcaaadacaabcdbbdddbddcbcbadadabdbdcccccacdbcbcaacbdadcabcbbcaccadadddcaabbddbcdcabdacddbbddabcabaccdbddddcadccababbcbbdadcbdaababbddbaddbcddcaaabacbdcdbdaabdaddcccaaddbabdbcabccdcdadbaaaadcbabacbdbbaabaadabdacccababbcbacbbbdaaacccaaddabacbcbabdacdadccbbcbdcbcdcdabdddbdaddabababbaadccbdccdccbdddcdddcdacadcbbbcddddadabdcacacbcbdddcbdbaddbadbdaabcabcbcbbadbaccacabcdbdababdcdccdacccaabdcccddbaabcccbadadbddabdacdccbbaddccbbbcbbbbddadbbbabcababdddabbababddbdaacaabbdccacbbbdadbccbabdddddbcbadbababbabddbdcdacdbaaadbdaaaabcddbbbdacbbcbabcabdaaacacdcbabbdabadddadbbcacbcbadadddbdbcdbcbccbaccaccadaaccbbabadabccbaaccbaddaabacddbbacabdcbcdbaccbddabbabadaaaddacaddbcaccabbacdcbddbccbdbbdbbddbcccadddabaaddcadcdadcccaacabddbdddddccdcacbccccbbcbdcbdbbbcbbcabbadababbaabdacdbcccbccbacbaddcadbdadaddbcbbddbddadccbbdacbcbcadbdddbcccdadbcbcaadaadaacbcabdccbbbaaaadabbcbbcbbccdcacacadccacbaccddcaadcddacdbbbadcabbccaacccbdbdcacdddbcbccaddababaddbbddaadbbbddcbcbaddaddcbcaddcabbadddcbabbbdbdaacbbcccbcadbbccaaaacbdcdababacbbcacaabaabacadbddccbdadbabbccbdaddddcddcaabbabbccaadabdbcaddbaacdbcaacaabbcbbbbbccdbabcdaccdbbdcdaccbbddaaacdcaccaaaadcadbacccdabdaaaaddcdabbadbddaabbdcaaddbabdbddcdcdddacddddccdaaabaddcdaacdbddbcdadbcbdbaadbaabbcdbbabdbcdadcabbacbddcdaadabbacabcacdbcabcdddbacdccbcabdacdabbdcbaacccdbdcaacaddbdadcccdccccbcdcccbabcaadabccdddabcaddcdadcabaddaabddcbadcdbdabbcdcbabdcdcbaaabaccdccdaacaaaabcdadabbbcaaccbabdaaaabccacadabbdddbcddcdddadbbbbacdcbaddcdcbaabdbcdbcbbaddabdaaabadcbabbddacccabaacdbcaccbccabdabdaccdcbaaddbcaabddcabbccadbbcadcacddbbacaaaccaddbacabdccddbbddadbcccbdcabccacadcdaacddaccadcccaadddcbbbcdddacbbcadadddbbbddbbcbdcacacbdcaddcaacdcdcbdccccaaddccbbaccdbdaaadbbabaaaabcabcdadadaabbacddaadbabccdbbddbbcdcbdaccbdacaccdacddbdddaadddcccddbdacddcbddbaadbdadababaddddacadaccbbbbbdccacabdbaacbdcabacacbcbcccbcbbabbdddaddbddbccdacbabdabcabcbadcdbabddbbbcdcdadcdbaacadcbcbadabadbacabdbcdabccccbcabbdadbacbadccbdddcccbdbbaacbcbbcdccbcdabbcaabcdccabaddadacdbbbccbcaabdadbabaacdadcabcdacccbcbbbddbcabcacddbccdabacdabdbcddabcdbbaacccabdcadcbdcdddbcdbcdcddcddccdddcacabcacdaadbbdcbabcbcaacccbabbacccabccccbdaddbbdbbbcbacbadbbadabccdcaacabbbdcbbdcadddacabcdbbdcdbcbbccccabddbadcaddcaacbadccadcdaaadbacbbddacdcbdaccadcccadcdbcdabdbcbabbbacadacdbbbaadcacdacbcdbaacddccdbabccbbdabbbcaaddbbabddbcaabcabbcbadbdcadcdbccaabadcabcddbdabcbcbbaaacacccdddbbdcbaadaadcbbadddbdaccbacddacbadcdadcdcdbaddbccbdbadddcaabdadbcabdbadabcaddcabaccbdcbdacadcbdabccdabbcccbadcbcbbcbacbdbddbbaddcdbdddacdddaadcdbcacdacacdbccaaadcdbbaadacbaaaccabbcabcbccacbbbdcdbbdccacadcadcbabcddbdadbcddaaadbcaacabbdbdbabdbbcaccddcaadbbbdccdbacbdbaccccbdddbdcbabadadadacbbaacbbbbbdbaabacaddbacdbdbabdbdadbbcccdddadadcbcbddabddbdaddaabcabacaabbbabbdabccdbaaabccdadbbadbaadaacaaaabdacaacbcbcaaadadbdcddcdacbacdbabababbbcaccdcbbcdbaacdabbcacacaadcdddbcdadbacabbdabcaacacbdcadabcacadccadbaacabdaadacdcabcccddccddabbaadaabbbbacddcbdcbddcaabbcdbbcabdabbdbaccddbbdccdcacbdcbdcabaaacacdbabcacdcdacadbbacddcdabbabaaabdbacadacdabcdabcdaaabbdddbadacdaabadbcdbbdcbbadaccbddccdcddbdaccbabccbbaacabdccddacdaccaabdbdbcbdbcacaddbcbacadaaadbdbaabdcdccdabbabcbbdcbbaacccacdbbbdddbddddcacbdcbdbcbdcacdbbadacbccddcdaddccbacdadbaadcacacabccbdabaccababbdadddaccccbcbdabcdcbdaaddbbbbbcddcdbbcdbbaacbdabcddbbbddcdcacabcbdccdacdbdaacaddcacdadcddccaabbbbbaadcbcacbaadcdabccbcddaccdbcabbbdcaaccbccbbaccdabaaaccbccaaadcdcbadbadabcdccdbdaaaabdbbabacaddcccabadaabdddccdadaadcdaabadbbddacbcbadaaddbddaccdcbcddadaadbbaabcbbaaaccacdaccacacdbcaacbadabdaadbcbbbdcacabdddccbbdabcbdabbdbcbaacdaaaaaaaacabcabddaccdaabbacbcdcdddbadcdbabdcbbdcbadbccadbcbbdabbccdadbcbbbdcbabbbccbabdbdbdbbdcdabbddbdabdbacdcaabcbbcdabbdddbabcdddaacbcadaddabbacadacadcdaadaccabcaaddbcdbbdaaccbdacadaaddabadcdcddbddbaadcbdddbcdacdbcbdcbbdbcbadbbcddddbccbdabdddaccaabddbbdcdddbadabbaccdcabaaadccacaabaabbaaaadddbcccccdadbddadbdaaadbdabcaccbdbdacbccccacadbbbbcbadbbcdaacadcaddcbbadaaccbdcdcbcdcdcdddadcabcbddbddaccabdbbdbadaccdababcbacdadbdcbbdbbdbcbdcaccbbccacbddddaddabbaaccccadbbcbbbabcabbbbcbabbbdacacdbcacacccbdacbdaabddbababbababbccbcddaddbbbabbbccadcdacacbaddacccbacdcddbbdbbabddadabbdaadccbcacacdbbddadcdddcaddbacdabbbccdddddbabcadbcdcacadbbdcddbabaadbdbcacadccababcbacdbdaaddabcabdbdcdcccbbcadcdaabbdabbbccabbcdbdcbabddbcabcaaaabbbabccdcdcaacbcacbcbdcdcbbbadaadadcdcdccbbbabdbabbccbdbcddacaadcabbddbabccddcaadcaaacbacddadcdabdccddbdcbacdbacbbdddbbcddbccbadbcdbbaabcbbcbbcddccbadcbdbcadbbddbdcbbaccddcaaacccddbcdcddcccacccdcddaaccddcbdcbbdbabbacdcacbccacdbdcdbabaaabdbdbcaaccdadccddddddddbbaadbbbdccccbbaddbdaabcbcbddddbabccbdaddbddcadacadbaaadccaccabbbdbbbacbcddcdbdadabcbbabcbcbdaacbbdcadbdddccbabcacdbcaadadaadbbbddacdbcbaddcbdadbcbdbbdabadcddacadccabcdbbbabadcdbcacccdacbcdddaddbccbccdcdaccbbbdddabdccdabcdbdccdcbbadacaccbaccadcdaddddbabdcdbadbbdbdabcccdbddcaddadaaabbaadbabcbcdabdacbadabdbccdcabdabbabbccdccbcccdbccadcbdaabbcdcccacaccdacddcccccddcacbaccadbadcadddbaacacacbbdacadacbccdcabdcdbcaacaabbbcbdaadbbadcccbacdabcdccbabddbaddcbdcbbacdbccddadcddbbdadddccaddabacddbdbacdbbbccbadbdcabbabacbdcdaabaadbcbadcbdbdbcaddbabbbbabacbbdbddbccbbdcdbaadcabdcbbbaadaaabdadaccabdddadbdbdadcaabbadbbaccbcddbbdabdaddcddbdadbccbbabbcbdbaaddaabdaabbdbccadabcdcacadddbbccbcacbccddadabcdddabcdbcdbaadbbccbcdddccbcdbaacbacdbaaacacaaadabaaabaccacdcaccbcdcccdcabcddcaccdaabbacdcabcbdccaaabdadbcadaacadacbaaaaaaadbcdbadcbbdbabbccdcccdcbbdddcbdadbadaadabdbadbcdcbbdaabbabbddbcdbcbadadbabaadccbcddbaaabbccbabdaaadbacddbadddcbbadabdcbacbacbcdbbbaccaaaadbbbdadcdbaacaadbcdaacabaadbcdabcbcbddaaacdabddccdbbaaabdaaccdbbaabaabacbabacddbccadbababbadaccbbddacdccdcbcbdadddcbababbddcddbbadbadbaccdbdaaabaddadcbcdcabadcbddaacbcdcbdbcccddbcabbbddcdadccbcdaabddbdcaadddacaaccdbbcadccabcadddadadcddbbbddaacaccbacdcaaaabcbcabbddacdcaccbbbdcbcacadbabcadbabdaddacbccbadcbbddaccccbcbccabccabaacbaaccbbcacbcbacdcbddadadcdaabbdabdcaaccadcbcbaddddaaccdbcabaddbaddcdcacddbccbadcccabdbadbcbdbdbcbaaccdbdcadccaaabdaaabadaaabdadcdaccdaacabccbcadbcabbbdadcdcccdaabcdcaaccbdbcbddacaddccacddcadddcdddcadddbddbbccaddadaacaacabbdbadacdacaccbbbcabaccdadccdabbadaadadddbcccbdccdcbcdcbdcdaddcacdadcbaacacadbcccdbdbaadcdaacacbdcdbcddddcbcccddcddcacbabbcdccbdadbcabdaabcacadaaacaadddadaaddabdcaacbabacaadbdcaabbddccdcaccaaacacbccdbbbaaaabcdbdabdbddacdcdbbcbabcbbaacbbcaccddcaabcdbcccbccdadcaddbcabddadaaaccadddcbcbbdbccbdbddabaddbaabbcdaccdadbccacbccacacacdcbdabacaaadabdbbbddcddcdcbdadccdbaadaaacacdcdaacdbdaababbacbacddcacabacacdcdacababbcbddccdcccdbbadbcbaaddbababdacccacccddbabbdcddacbdabbbddbadcbbbbdbbcaabcbacddccdbcdddbbcacaabdccabcbddcacbadabaaabdbcccdbdbdbdabcababcbadbbcbbcaaabbbccabcdccbbbccdcabcbccdbbbaddacabadaddacabbdbcbbadcddcdaadcdddccbacdbdabaaacabbcabccbcdccbbbdbacadcdddacbcaccabbdcccacbaaddbbbbbddccababbcbadaddcbdaccabddbccbdcccbbcbadabababbcacaacaaabaccbaddacaadcadaaccdacacccadddbddacbabbbccdcbddbcacdababcddcdaacdccadaddbcddacddbdcbcbadaacbddddbadccbdabcdadcdbbdccaddcbddcbadddcbddadaaabdadcdbcadbabcadadacbbabdccbababdacbbbacbbaadbdbabdaccbdcadbcababaaaacbdabbddccddabacabdbbbbccdbdcabaadadcddaabccdcadabdbdaacaccbbcdcadcdbccdaddabdcbbbbbccbbbadcbbbdbbacdddddaccbadacbaccbdbccbabddacbdaadaabcbabdbdcdcbcbbdcbacbacbabacadbbccbdcdddddbbbddccdaacbbbcabcdddadbadccaadddcbdcbaaadcaacdabddcacbdbcadcbdcabdaaaacacbbbabbcaacaadbaccacabdcdadacbaaccaddddcaacbcacacacbacbcaacbcacbddccdadacddcbddbcccabaabdabbbbdabdaccdaddcbddcadbacabdbcaadddbacadaccdcacccacadcabacbcccbbdbdaccadbbdcbdcacbcaabcadcadcaaaabccbabcdccdddbcacadadbddacbcdccbabcdaacbdacddbcdaddbcaacadbddcdccabadadccabbcaddadddcbaddcdacccbccbdaabaccacccacbbdcddaabcbcaacaddbbdcabcaabcabccdcbbddaaabccbabbbadbdbdbbaaaabdbbbcbacaaddbbbccbacdbbccaaaaccacbbcadbbbbdcaaccbaadbcacbcaccddadcadbdacbacdbbcbbaaabadacdabbcddaddacdcdddddcdcbbbdbdaaadcdbbaaaaadadabdcdbbbcddadaccdacbdcbbaccbbccbbdbdabbcdcddabcccddcbbcabccabbccabacddacdcdaccaadbcccdbdcabaaddacbddbbadccddaaacadacdbcbcdcdadddcaccacdbabbabcdbacccbcbbcabdadbabbbadaddbadaaabbcdaacabcabcbacbadbccabbcdaabbcddbabadcacdaddabacbddbadbccadbbaacbddadacacabdaabbcddacdddcaacaabadadddcdadadcbcbccddcdacacbadcbddbacccbaacbcadbbccacdbdbbaaacbdddaaddbcbdbbdabaaaadcabdcccbdabbdbbbabadddbdbbbccdcddbbbbccdadcadcdcbddcbabacbdbdcaaaacdaccdcdcdbcddcdcddbbbbadbbcbbcacbaacddbabddccbdddbadadabcbaabccdbacaaccddbbbbadbaccdcaaddbdabaadbddbbcacaacbbcddcbbbadcbdaadabbadbcaccabdcadabcbcbacdaaadaaaabdacadcdaadabdcdcccbcddbbcbbdcbcdcdcaadbdccaddbacccdbcdcaadaccdbaaabccbdbdcaadddabdcbbaabdabacbaaacbcbbaadcacdbbcdddcaadadccdccaadddccacaccdddbddacdcadadbdbbdbacccbacdcccccaddbaddcbbbabbabbdcdadaadcbbacbccdddcdbbdcdbcbbddbbccbdbcccbabcabdabdaabcbddadcbacadcadddbadcaaababbcccdbcacbabcadaacccbabdcaccbbcdabcbddcaaabbadabdbcabdddacadbaacdbcabaddcadadcdaaadadbcadadadbacabcdddbbbbddcdbcaabdacbdbbccdbcbbcbbdccaabaacabdbcaaccabcdacaacdbccbbbcdbabddccbdcdaaacbadcdcdccbaabcbcbcdbbdcccddbdcabbdaabcdcaccbaadbcbcdcbabacbdbbbbabcabacdbbacddcbabdbbbcdbabcadadcbddcddddaadbdbbacddbcacdadddbddddadddddadaabbadabaacdcadcbbdadbadbdccabdabdcaaabcdcaddbaaacbcccdbdcbdababbaadcdbcaacaadabdddabaadcbdbccccdbabcaacadccadcbbacbdaddcddcdbdcaaadcbbabdbacaaccaddbadaadaacabdcacbacaaacacaadddaacacdbabbdbbaadacaadcaaabacadcbabcccbdbcbacdbccbaaccbbddbaacbaaabbdbabbcdbadcdcdaddabdbcaadbdbdadbbccaddbddbcbcbccddbddccadbdacadccacdbbbdbcdadcaccacbadaabbaaadccddacbbdddabcbbbcdabbdbbaadbccdabadaacbcbbcabdbdbbbacadbabdaadacbddccbcdddaccacdbccdcbaaaaabdbacddabaacdcaacadccdcccdcbdcbdbcddbabccdbcdbadaaadddaaddbdadadbabddadbddcbdbcbccbcddccbcbbbcbbbcadcacccdacbbdccbababdaabdcccbabacbaaaddadaaadbbbbbdaabbbbdbbdbaccccbabcaacbcdccccadaadaccbdccbcddccdaacdabacaddacaacacbdcdacccdcbdbbacdbbbdabcbbddddbdadadabadcbacdcacabdcaaccbaacadccdacdaaaabccacbbacaadabcccccaaacbbaadbadcbbabdbdabddabaaabdcaacdbaaacdaaaabdccbbccddccabadcbaaaaacabcaabbdadcdddddbcacabdaddddccccbdcbdabccaccbdcbdccadbddacdcbcbcdabcbdcbddcadadacbdccaccddcbbbddcaddacbccddabbbccbdcadcbbcadaddbaccdbbcccdcdacadacdbcbabddddcaddaaaabcbcdcdbccccaabccdcaaddabccadbadadadadacbdababcdadccaddcdbcbccdabcbcdadbbddcbbadcbdbcbabaaacccbaacabbbacccadbadbbcbbcdacaaadddadcbbcaadbdddcdddabbccabbdaaaaacadadbbcccbcaddbacbdadbbcdcdbccbababcccaccbdcdabdcdddddddcdccdbdaadabbcdacacbcbcdcaaabbdcdabdccaadbadabbdcadddcaaacddabdaaacadaaabcadbddbdabcadaccadcdbcbaaacaaadddcaadddcdbcbacbacbccbcabcddcaacdacadbddaabddcccbddcdaaabaaadaddbabaabcbdddddbabcabbccdddcaaadabdabbadcbaccdbacccbdbbdabcbbaacdabbdacbbacaddbbbcdabcbcaababadbbcdbcdabacacbacbbcbbccadcbbabbbaadbccabbccbbaccdcbbdddcddabaddadbacdcabcaacacbadcbdddcccadcadcadbdccbaabcbcaacabbbdabccacddababdadccccdbaabdaccabaccdacddaddacacadacabdddbacadbcadbcbccadddcbbcbcbccdccdabbcdbaccddaadcabacddbcdbdcbbacbcddbccdbacbdcbaabadbbcadcddcbaabacacddccabdbbdccadadaccbbddbbdacabdabbcacdbadbbcaabbcbdaacccdbacbaacbcdccddbadabcabacaaccbccdcacbdcacaccbbcbbdbabaadababbcccdbcaccbdabcadbcbbadbcccaccaaaadacadcdbcccbabcaacaabbdaabdcaaddadbacdcabccdbddacabcbcbdcbbbbddddcdcdadbabddccccacbdcbdcabbbcbcabbaaaabdbbdabdccdadbbbbdcccabbabaccdcddddcbbdabbdcddbcbacaaddcbdccacbdbbbdddaabcdcbbabaabbabdbcacabbbadcbadbcccdcccaadbdcacccdbaabbdaccabbddbbbacaddccabcdbcacacbcdcaddbcbddcdcdbdcaabacbbdddddcccbcdcdddcacdcadcbbbdbdaaddbabbaabbadbbdcbcbbcdacdccdabacbddbaddbdccbadabdbddacaadabacdbbacacacccdbaaaacbadcccbcacddcbcaacdaccdadacdbdbbacbbbacbabbcbdaccbcaacaaaacbabdbdcaabcbbcddbbcdcdcaabaadcccadaccbbdcacabdbcbacaacbbadaadacaabdbabddbcdbcddaddbcaddcabbccacccaacdbdacbcdbadcbabaddcadcbdbcaaccbadbaacdddcbacccbbdacbadabaddcdbadaddadaddaaacdcccbccbbddcaacdddcbcbcdcaddbbccbddbadddccbbbccbcbcdabbcbadcaddddcbcadbdacdcbacbbdcaccadddbccadbdabbbabaabdaabbaabbddcbbbcaabacbbbcdbdaccacdccadcdccbccaccdaddcdbaabbadabbcbbbdccbdcbcbdabcabcbcdbddabdbcdbddadbdbcdbdddddbbcccbabacbdbaddcddadadaccbadacdbcabadaabadddacdaddacadbcbacbdcadbdabbabbbccaacadbdbbbdbdcbdaabaacbadddccbdadadacadddbddacaddcbbcdcbdccabddccadadacdddbcdacaccabdacdbbabdaabdbaababdbbcacccaadbacddaccaddccddabadaabdcacaacbadbcddcabcaaccaaacccddbbadabdbbaaadaaacddccbdcdbbabcadddbdbbaddacaaccacacdacdbabdaacbdaacacdbadacaacababbdaacbdcbddbbddcbbadccdcadaccacccddbdbcadaabbbbdbddbcabadddbddcabdaddabdacbbccaaddacbbaadcccbdcaadabaddccbbcdbdaadbbdcbacdaababbabdaabccddcdbbbcdbabcbccbdbbadbaadaddccadbbabdcbaabdddcddbcddabbdbabdaccbccbcadbdddcbabcadcadacbdbabacaaaadbdddcacbddbdaccbcbbcacbbaddcbdaadbabbadddbbbcaaddabccbaacbababbccabbcbdbdcdbaaabdaaaddcbccaaccbcbdddcbddcbdcdbbaaddabccdcabcaacabbdbaadabaddbcabcacdbbacdbabcbddccdbcdcacbdbdbadadddbddbbaccbaaabaadcdbcaccababdcdcaacabaadcdabbcdbdddbddacccccaaaabdbcbcbbbaabbaacddadabcbbcdcdcbbbccdaadbccbdacbbacaadabababcaccbdcbcdadbccaaaabcccaccdcaacbcdccdbbcdabbaddacdcaddcbacbbaabaccbcdbbccddaacbadbbdcbcabaadaaccaccbdddcdbbdccdbcbcbcadabcdbaccdcaddcbbbcdcbaaaadadbbbcbbcdaabcbaabddccaaaddddcadbbadbddaabdacbbabdcbadbdbabcddadddbcadcccbbaddbcdaabcaaaaaaddabaaadacacbacbadaabccddcbaccabcadcdcdadabccbddabaabacddcccaabcbdbdabaddacadacccbdcacbbaaadacacabacdbcadbcbbbdabcaddbddddadadaabbaddccaaacdbaabdddbbdddbdddbadaadabdccbdbdbdcddbcadddcbcccbdbcccddbbccdacabbccbdcbcdcabcbaddbabddcaadbcbccacbdddadacbccdcccdccdbdadacddbaaddabcbcbccaabdacdcacabbaddadcbbabaadccbbaabdbbcabbbaddcaabcdcddaacddbbcbdbdacbcdbdbababdcdbdddcadaacddbacaaacadccabdbbaaddacdbbdbbcaccbaabccabbddcdcabbbacaadadbabbdbadcbbbdbbcbaacdcbcdaacbdcbcdbabdaaadddaddcadacccdaaabddacddbaaccbadcbabdabcdcabdddcdabddbdacdbcacaadbaddaaaccdbdbcbcacaddacbdadbbdadacacdcddbccababbddabaaccbadbdcbcbdccadaacaabbbddbbdaacbdbccaccccbbacbcdbdaababbadcbadcdbdbdbacadbccdadddbcbbaddcadaaaacdbccadccacdabaaabadcdddbdcbdadccbddcbacdadcdbdcbbccaaacdbdabcabccbcaccbcddaadbbbcbcadddcccadbabcdbbdacdbcbadabcddbbbdddccdcddadddaabcbacbbdbdbdaccbcdbbdbdaaccbaacddcaaacaaacbbbaccdabaccdccabcbcccbacbbaccdaaabbabbdacccaddbbbdaccadccadcdccacdabccbcbbbccbbcdcdcbcaadcbbcbdaccacdaadbdbddbcbcabcbaabbacadaaacbbadbababcabcbcbcbcbcdbcbcdcbbaadacbbdbadabadbdcbcacadaccaabdadaabbaacaccbddbdcbdaabbcacaccccbdcbacbbddcaabbbbbcddadbbcaccdaaacbbabbcbadbcabdbabcdddacabddadcdcdaddddddbcacdcaacbccbcabcaacadbcdbccbdacbbbcdbdcdabcabbcdbcacbccadcacdcdbdcadcddbbadaddbbccccccccdadaccbcadbdbcbdcccabaddcddaddddbcdcaccabdadbdbbdcbacdaaadccccccccbcaacadaacbccbdcdacaacadddbccadaabcaadbbcadcacbddbaacdccdbaabbacccbdadaaadbaccbddbdaaaccbdaaaacacadbdbabcbddcddaacadbbcabcabaddcacbddddbbcbddbdbabcadacccadbaccdaccdbdaabdcdcbcadadadbbbdaddcbdbcadabbcbdcacdbddaddddcacabbdddcdddaaadccacaacadacdcadcdaadaabcbabdccacbaabcabbccaaacdbdbdadaaaaabbbacbcacaddcdbbcbcbcddbadcbaabbddccaadacaabcadbddbabdddcacddbabbabdacdacddbbbadbabddaccaaddccadbabcdbcacacbaccddddaadabbbcbbcdbabcdacdcccacadabcbdbcdaddcdabbcbdacbdbacbcbdacacbacccdbdcbacdddcccddbaccbdbbbcbbadddbabbdaaddaabacbbbdddcbbbbccdbcdddabadbccbabdaddbdddabdacbcdddddabdcbacccddccbbcddbadbbaccaabaacddacbabccadadabbaacbabcdcbbdddddbcdddbccbccbabadbacbcbbcbcbaccacbdadbaccbccacddcbaadadccaadcbadcdccdaabbdcdbdbccadadaddddcacccdbbccadabdaddbddbccbcdaadadccadacadcdcdcccadcbaaccbbcbddadcdbadadcccccbcdbccdcbbbbaacccbdbcacccdcbcabcacbcadadaadcadcaadadaddcccbcbcdabadbdbabbdbcbbaccbbaaadabbbddadcbbabadbdaaccdabdccddbdcadaaddbbdabbbbdcaaccababccadcdabbcccbdcccadcbdaadbcbcacbadbacabbbdbdbcdbbcbdcbcdaacacbabdabcdaaddbaadaccaadacbaccbdccacddddbdddadbcaadcaddabcadbcdacdcacccaabdcadcaddcdaacbdcbaabcdcdbdbdbcadadbbbdabddcbcbcdccbdaaaddadddaaaabaadabbdaadaabbdcdcbdccabadcdaacdbaaccaadbdbcadadcdbbbcdacddadccbdbdbccdbacdcbddcbacddcdabdcdbadbcbdbcdbdcadccaabcbbbadabcbcadbadcbdcdabbbdcdccbacdcadabdbabddbcbdacacdcdcbabdcbbcbdbacaaabccccbaddcbbadbdbcbdcddbcaccddadaddccabacdbbbcdbbcaacaccaddbbcdbdacaaaacddbcbdcdabdcbdccbdbcdcaaacacbddddbbbbdcdcbddcaacbbdacadbacbddadcbababccdbbacaccbdaabaabcdbabcdabbbdcbacddbddbbbcbaddbcdaacabcbbddacdbdadcabcacdbabbacbccbbddaddccbcbbacbadbabbcabccaddabcababbaddabbabccadcbdbadcdacbcaaadcbdbcbacaaaaabbacabcccbcbcaaabbbaadcacddcbbbcdbcdaadbadaaababbcabdaacdbacacbbdbbcbabababadcdbbdaaacbddaddccdcbacbdaaddccabbdccbccbcdbbbbcabadcdcaddaaaccaadaccaccbdcaadddcdddccabbbcacdccdaacaaaadbabdbccadabbaaadcaabbbbcddadccdbdaaaaaadbcbddbaabaacababcdaadaadddbbacccbdbaacbddcdbbabdbcaadbcddbdbbcdcbccaacdaadaccdcaccddacdaabbcbcabbcbddbaddbdaacdabdcbcbbbbbcadaccdbdbcbaaddcbcdaaaaaadddcbacbddcacbccbbdbacabdcaaccaacabacdbdbbccdbbabaabdaadcadabbabbbbcdddcbaabbcabcbdcabbcddaccbcdcbbdcbbcccbbcaaadbacabcacabaddbbcbbdaadbcbccbbbcacbccbccddcbadcabbccddcbcacbccbcabbddcdbbdbabbbccabacdcbcabcaadccdcddaddcddbabbcbcbbadaacddbadcdaaadcaabadbadbaabdddddbddcbcddadcbcbcabbacbcabbcbbbdbaabcbaaaabadbdcbbcdaddcbadbdbcddcababbbdaabcddcdacbcaadbaaaaddcbdcaadabbcbdcdbaaddcaddbdabbddbbbcdbbaddaaacdcbbacdaddcbbbacdcaaadacabaaabdaddcddaddbbaabbccacdadadcddcacbbdbdcadacabcadddcdbaddbccbbbdbadaccdcbdcadbacaaccccddcbbacbcdcdccdcbdadddbabcdaabdcbcbacadcadcabbbdcaaaccababdadacdddcdadadbcadacddaabbdbcdcadddacccacacbbadcbacbcdbccdcdcddcccacccbdaacbccccdcaccadcadaddacadacdbabbbdddbcbbddacaaabadccbabdbcacbbabdacbcaacbbbddbbacbbcbbaccdcbcbacdddbccccbddbdbbbbddcdbdaacdacdaabbbaaccadaabaddabdcdabdccaacdababcbacbbbabbdbdbaccdadbcddaabddbadccccbbbcdcbcddadacbcbdbddadaddabcacbaadacdddbcadbcaadbabcdccbdbbcdcccabdaccddaccbdddcacadadcdcbbcdaadbcdbadbbdaaabacaddbdabcbbdbccddcdbbddbcbdcbdadcbcdbdabbcaacabcccaaaddabccccdcdcabdbddbababdbacaaccccacaacacccdacbbdbcaaccadccdddddcaacbbaacdbaabcbbbddabdcdaaaccbbbccddcabbabcbbbadacaacddbdbcbabbddadbccdbcadbcdacabcdacbbcbadaaccdcdaadadcabbbbcbbaadbcbdbabacbdbdddaabbcbcaadbccddbbcdbdadcdbadabbbbddbcacabdaaddccdadddbbccccaadddccdcdbabbddbdabaaccacdaadbdcddddacacdddcdcacbaacdcaaadacbadadbabacdaadcbadcadbcadbcccabcdbbdcabdbabacdddcbcbbdaccbdddcdbcdddacaccbaadabdbdccabdcacdbcddccccadadacdccdadddcccdabbbdbbcbacabaaacbdbddadbcbabbdaaaccddbabdccddacabbbabbdaabbdcbdcadabddbdccaaaacaaaddccbdbbdbbccddbbbabcccdcaddbccdcdccdbccdacdcabcabdddccdbdaaaababbabbaaabccddccaccadcdabdbbccbdaadacadabdcdabbcdbbaddbbdadcddbbdaddabbbccabcaddcbbbdbcacbccaaaabdcdbcdaddaaaccacccbadbbcbcbbbdaabddbdcdddddbbaabaabbbcddaacacabababccbcdbadccacdccdddadcbcdcacacacbcdaaabbdccddbbdaaadaddbcbbaadccadccbddcacbdaccddbcbdbadbdcbabccacaddbcbbbdacabdacdcdccdbcdccbbbacaabdddaccddbdcaaabccdbbbbdcdbacbbabccadddcddbbcccadcdaaacbaacbdddcbbcdccbdcadcdcbaaaabccabaaabbbdcbcdddabdbadbaddbdbdcbbbdcbabcaadadcbcdcdabacadbdcbcddcbbbbcaababccdcdbadbdccbaabcbddcbaadcbdbbdabdbcabaaaacbdbcdbdaccabcbbcccdddcccabadbadbabbcbaaacaadbcccbddaacdabbaadbbcdcbcbdabcdddbddbcbddbabdabcbcadaabdccabdbbddcdcdcadabbdccddcdcdadcadcdacbcbabaabcbabcbbcdaadabdbacabdcdddbdabadbddcdacdcbbadbaadacbcbcdbdaaaabdcbdabcdcdadbbbdbcdbaacddaddcbbbdcddccbadaddccbdadbbddbdcadaacacbaadbbbbcbddddbbdcabbacadbbcddcabacdabdbaccdbcaddbcaaaccadaacabcbaadbdccdcccdcdaaadccdcacadbddbcbcdbbacabadaaacddbaacbaaadcdbcbddcbaccbadddcaabbccbbaddcacddadacabcbdddddbbcabacaadcdcabddcbddbbddddaaaabdccbdcabddabdadbbcbcaaababcaccbbabdcacaddbadccddcbabcbbaadbcdbaabdbbcbdddccbcacbbbcdbbbbbaacdcaccbdacbadcdccbcdddaacdacaddddcdccbabcdacbabcdacbdacbadbaccadacbdddcabbadbbbcdbcdcbbadbcbcaaadccaabdcabaccbccacbcaaddacdbbccaacbcbbacbdbdcbcbbabaabcadcbacdabdbdccdbcdcddbabcaaccbbcbaabaaabdbbbacacadaaccadbaacbcaabbdcddaacdaadacdcbcdaaacdcbcaaccacccbdcdbaaaabcbabbdbdbbbacdabbbdbaaabcccbbbdbdadabdcdbbdacccbaaccddcababacaddccabdbabadbddabbbcadaabddcccbacdcaddddcddcdabadabdbcbbcdbbbbccdbbdadccbdcdaacdbbddbbbdbcdcaddcdbaacbcadddbdcddcdcddddcacdcadbddacbaaacacbcdbccdbccdbacccbabccbabbccabcaccaaacdddaabddcdaaabbadbdcbcdbdaaccbbcaaddaacdbadabacbdcadccacaaadbcacdcdbdadaaaaadcdaacbbcccdbbadbabaccacddddcccddbccabbaccbcdadbbbadbaabbabadbadabbbcacdaacbcdaacddadaaacbcddbcbbabddcccbdcdadbddccadaaabbdbcbcbbbcbddbcbadbdbdaadcaabcdbdadcccbcbccdbaaabacbacdcabbddbacbacbddddddcaccaacdbabbcbaabacbbcddabbcddbbcbcdbcacccaadaacbddabacbbcbbaadbcbcdbcdbaaabaccaadcddacbcdbbabbaadcbdddddadacadbbbdcdbdacbbcadcbcdacbadbdbbdbdadddcbdbdaadbcadbbccbbbcabdcdcacaccdbaabaaccccdddabadbdadbbadabdadddaccbdcadacaccdabbdddcbbacadacacdddbdcdaaaddbacdaacacbcabbadabcddbcbbacadbdccdbbdcdcbadadbddabcaadaadbaddadabcdbaccccbbbddcbdcccdabcacccbaadbdbadcbcdcaaadadcbabadbabccdcdcdbaabbccadcdabacdbbdacdbabbddcbaabaaccbacadadcabcbabbcdacbbddadacdbaaacccdbacaadbbbcdcbaadccccdccccdabbccdcaccabcbbcdcabdcbbacbbbabdaccacacbadbbddcabbccaaaadbabdaddaddbcbcccdbbaaccccadbaadabbddcddddcadcabadadcbbabdaacadabdacbadacbbcadbcadcbcbdbbaaacdcdccbdccaababddbbcacaaccbaacdbcabaaacbdabaababadcabcdbccacbddcdbccacdcbdaaaaaacadaaddbabcccdaadadcabcaaabcbbbdbbdcbbbbbbcdbbbadcccdbddacbcadbaacdaaccbbddbcdbbccdaddadbbaaabbcdcdcacccbcbbddbdabacddcaaabacdbbaccbdddbaaaccdbadaccbabbdbabbbdcabbbcadbcbacccadbddcabccccdabcaadabaabcbadaccdcabbdbaddbbbabbacbdcddcccccbadccdbbaadbdaaacaddbacabbdacbadabaaaabdcbaacdddcdaabcdcbcbabacabaabbdbdbbbdddbdaabbaacbabbcaabaddddbccdccddcccbccbdcacbcdacbcdccbbcabdababdbdbccccabcbaadabcbccaaddbcbbcddccbaaacdadddcdcddbdcbaabaacdaaddcacaddbdbadaadcdbaccaccbacbaaadbbdadddacbccacbbbdccdbcbabbbaababcdcdccbbdbbcdcbddddacbaddcccdacbcabbadddddacabababdbbccacaadddcdcbaccbadccbbacccdbccbcbdbaddbabcccccbbbcccaccbdabbcccbacbaaacaadbcadddaadcbcbcaaaddbbddcbdbbcadbcbbcdbdbadbbacccccbdddadaccbbaddbaabbdabccbdbbadbbdadadcccaadcddbccacacdbaacadcbdbccdaaaadddabadacddacbaaaddbdccbccbcadabcacbdbccacaaadbbccbbdadbbbcddcdcaabbcacdbaaabbddacbdcdbdccaaccaddcbcacbccdadababdadadcadacbaaddbcbdabadbaadcaccddaaaaddbcaadbddcadaccdcdcacaacabaccdadcbcbbcdbbbbaaacacccdaddcbdacadcdbadadbbbaadaabcccbabbdacabdcdacabbdcdcdddacabbddbdacadccccbadbabbbadabdababbadbcbcbacaacbbadbbbdacaacbdccadabbcbcdabcbdacbdacbdccbdadaacdddbbbbcdbabbbdbcabdacbddcccbbbabdabbacbdacbcdbbaaaddccbdaaacdbcadbbdddacccaacdccbdcabadbdcdbcdcccbcabaaccdaadadbaaaabdaabcbcabbdacaadbabaadddbcbccdbbadacbbabcacdaacddabacdaddbdaadbcbbabaddadabaaaaddcbcdcacddcbadaccdadbdaddbbabbcbccbacabaadaadabadabbbcbcbbacbaddabaccaccadacdabddbdccccadbcbcbccaacabbbccadabbcabdcdddbdabbdacabbdccbddabcdaddbabbadadbcbbddccbabbcbacadcbababcbcbaabacccdadabdcaacaadabcdbcadccddcadcbbbdcbbbbccbbbadddacadddbbababbacacacabbccdbdcdcaacadadcadccaacacbbdcdababdcdcbccbadcbbcdbadccdbddcccaacccbaaacabadbcacbcdbcbbcccbcaccccdcaddadacdbadacadcbcacadddaabddcdaabbddadbbabdbdaacbcdabdbbdadabdcbbbaabcadbbbcbbcdbddadbbccbdaddccacabcbcaaadabcabdcdbcbacddacbdbdcdacbbabbbcdadaabadcbacdcabbbabbbbbbbbccaddbbbacdbdbbbaabcdbbcccacbaddbdddcbdbaccbdcacccddbbcabdacdccbdacacaadabacbcddbbbcbbadaddcacdaddbacaacdbbaddbdbaaabdbdbdccabcaccdabcaadcbadcbcdddcdbbbdcaadaacbcbcbaadcdbaccbdaacddcbacdddacbadbaabadcccbdadbababaacadbbdbaddbdbdbbabcadcaadbbadcdbbcbbacadcdcaccaadbccdcdcddbbdcdcabacbaaccabacbcbbbdbdabcdaddddabdbbacaaaaabbdbcaccdbcbbaadadaddbcbdacbdaccbdbaacbddcdcddccaacbbccdbdcbaadcccacbbdadaabadacddcacabbaadbdbccbbcbaaddddbcbddbadddddbbbbddabdadbcaadacdacaaaaababbbcdbdcbabcbdabcbdbbddddcbabdcbcdcabccaaddababcdcadcbbaaddaccbcadbbccadcdcaddcabbaabdcdbabadadaaacadabcbcdcbdddbaddcdbdacaddadddbdbcdddbccdbaabbdbdbcbbddccacdccccabacccabdaccadcaaabcdbcdbdbcbccdacbbacccacacabadaacdabdcccccbcbccdddcddcbbabddbaaacdbdccacdbdbbdaaddbddcbbdcbaddabadcccabdbcaacabcdcbbacdcadcaaaccdddcdcababcbdcbacabacdcddbdcabdacbadcbbdbddacdbabdcccdcabdddcdabccbbcccbdcabbccdbaabbabdccbcbbdccdbdddbacabadcbabddccbddadabcbcaacadcbbccabbdbbdcbcddabacdcacdabdacbccddbacdbbdcbdbbbbdccdcbbdcbdcbaccaccabbddddaccaddddbaabcdcddcbdbaaabbdccbabcabccbcbbcdcdaaabccacdacdaabaadbbcacbcbdbcdbadaadcbadddbbbdaddbcdacacdabbdadbcadaabbbbddcbcdbdcaddccccaaacdddcdccabbbdcddacccbcacdabbadbbcdcccccdaabcaaacdcaaaabbccabdbdcadcdcbcbbccccdcbcddcabcccbbcdddcaddcbabbcbddabcbbbccbcacadbdacccaabdcdbbccbcbaaaacdccdaddbbcdacabaaadbdbbdccaabcbddbbaccaacdabaadadadacbbcaccaaadddbcadaabbbaaacddaaadddabcbdacbaabadccadaadcbabadacaadcdbdaaadcdbdbaabadaddcacadbaaccbdbbdddadcddbbbacdabcabbccbbbdbbcbaabbddccdddbdcabccdbcccacbacacbbbcbdabbdcaabdcdcdaabddbcbbcbdbcaddaabdcabaabbddbdcabcdcacaabddabbdbbccbbcccbaaacadaccdbdbabddadcbacbbcaabbdaccdaddbadbadcbaadcaccbdabbbcacddacdaaaaacbddcbcbabcdcdaaaabbbababdadbcbcddcbcaccaadbdddaabaacbbdbadcabbaacbbcadadbaadacccddabcddddddbdddadcabcacdddbbdadaddabbdacbabbdbbcaaabcabbdcadabbcbbcbdbcacbbcbcacbaacdacccbbcdaadcdacdabdbbdabdaaabddcdacadaddbdccccddcdacddaadaddacdbdacbbacabddbbadcddaabaddbbdabdbdcdbaaacdabbdadaddaaaabdccabaabacabadcdabbddabccbdddadaaccadbdabccdabdabadbddcabadbcbcaddbcaddbcbdbdbcabcbcccacadbddacacbcaabacbdbabdabcccddcdcacbdbadaabbcbdbdcadcdcadbbcaacbdbccbddbcaccbacdcbadccadccbdbadadaadacdbbcbdbbcbdabadcdcbcacabcdabbbddadcbadcacdbddbacaddaacaadbccaacdadbdbcbbcabaccbbdaacdddbdacaddbdccbbbbcbabaddbbdccbaaacadaabcadbadbaacdacbaadabadcccddcbcabccaabbcdcaaabdbacaddabcbdbdbbaaccdbdddbdcdbccdcdacabadacabdcbabddbcdbcacbbaaabcbddbcbcadbabcacdabddbddcbbbdbbdbdacbddddcbcbabcbaadbcbdbabccaadcdaaabbcaadbddaccdddabcdcddcbcbcbaabdccbdcdbcbbcdbdccdbcbccacaadababbbbaacddccdbabacaccabdccdbdacdbaabbaabdacaaaacbccbcaccbcdcbbdccaccababcaccccbcaaacbcadbabccaaacbddddaabcbaababababaccbbbcadcdcaacabbcdabbccccacadccabaccacdccdbbcdbacbaadbabbcabccbbcadacbcdcbcccaacccdbdaddaaacdbdadcbcbbdaabddbcadbcdbcacdaadccdbbdadbcabadddbcabccdaacccbbdcccdbbdadbacadbbbadaaaadddcdcbbbdcaaaccbabbccbdadbdabcddcadddcbbabbcadacbaadddcadcaaccdbbaaaaccccdccbaaadcbbacabcabaaadbdbbcbaadbcbbcdbdccdbcbcdbdacbbaccbdabbbcdcdacdcccbdcdbcccadcbbdbdadcacadacbacdbcbcbdadcaccbdadcaccbdbbcaddaddbbdacdccacadacabcccbbcccdbdcdbbcabdadadcaccaadabddacbbaabcbdcadbcdaadadaaadcbcaddddbadaaacddaacddadcbadbbdbaccabacdcacacdbbcbbcddbccbdcbcdbabdaddbccdbdcaddbdacbbbaabacbdacaabdbbadbcdcaaabdbbdbcaabcbabbbccbcccccacbcbddddabcdcacaadaccbbcacacbacdbbddccacdbcbacabadcbbbdaabdcacbddccadcdabdbacadbcbdabbaababccbddbdbdddadccbadddccaacbbccadbbdddcabbccadbccbaadcbadcacbadadcbdcbbdcbcadcdbacccdcabacddddaacdacacccbcbadbadbdccabdcccdbbcccbbbbccdaacbbcddbdacdaadabbbbdbcdbcabdabaabaabaddcbacdacaabdaabbcddbdbdbdccdbbcadadadabadabdcdddcdabcbbcaacdddaddcccdacaaddbadddddbcccccbcdaddddabbbcadbacccdcdbaadbacadacbadbdbbddaddbcabbcbcdadabdabddcaaaddaaadaccdccdaabbcabdddaadacdddcccbdcbdbbdbbdbbcaccaabaabbcbadacbbccbdcbddbadcddbcdacbadacadbcabdbbdbaabacddcbbbcccdadbabaddbbbdcdddaaaacbacbadadcbabbaaadacbbbbcdbacdccccabbdabdaaaccdbdaabcabdbbbccadbcdccbbdcabdadbdadbccccddacbdbcacbcdbdacdaabaccddcaabdddbddbbaddbdcaddcbbadddddbbdbdbcbcadcddccbadaccaadddabdabdbccdcddbaddadddddbbcbbdbbadcccdcacbbadaddbbccaccadacacbdbbbccddcbdbddbcbadbbbcbadcababbdbcbdcbdbcdccdbcaadadddcddbbddbaabbcbadcccdccadacacbdaadacadbbcbaadadabbaddadbddacbdddbbccadcbdddaccaaabbddbddbdaacabcbaadddbcacdcbbdcccadcabcbdcccdabdcbcacdcbcaaccdcdcdbdbabddbdcdbccadcdddaacccbdddbbdaadacddcdbdbdaadcdbddacddacbccabcbcbdcacbdbdcaabadcdcaccadccbbabbacbddcdccbaabbccaacacacbbcbcdcdbbabacdbcbdcbadbbccbcbadcbbdcadbdbdaabadbabddbcaddacbbdddbcbaaabaabaacccccdddcdbdaaddcbbadccadcaddadcbbbadaadcddcabdbabcabacaccacdcaaddaababacabccdabacddbddbabbbcbdbaacdaadccbcdababccbadacaaaddcbaddcbdbdaacdabdacdbadbabddaabbcabbbbbacdcdddbcbcdaddcbaaacbcbccbaddbcbacddccccadcabdbdbdaddbdccddaaabaacbadcabacaddaacbaabaccbcbcbbddabdbbdbcbcbccdadddbacaabbccdaddabdcadbacacbaadabdcbbdacabaadbdccacbdcbcdbbdcdcbcaabadcbbadbddcdbacdabbdbcddbccadaadacadbcbbdabcbccddaccbabddcdaddbaaccaabdcbabcbabccadaaddcabaacdadcdbbbddabbbadaacacdcdbaaabacabadbbaabcbabaacdcadbdadabbabadcdbbbcdddbbddaaaadbbdaacacaddcbadcacbbcbcdbdbbadbbcadcabdababcddcbcdcbcbabddcacadcdcdcddcccdddcbbdaddabacdacbccddacdcdddabcababbcddbaabcdcbacbadddbdcdbdbdbadacadbdbcaaaabcaabbccddbbdbaccbbcdbdbabccbbcdccaabcbaacdbbcbabcdcaabbdbcccbcaadbdbaabaaaabcbdabcddcdaaacddcdddbaacbadcbdadcdbaacacccccbbadbdccdaaadbadaaadaacccbdbbcadcaadadbdacabcdbabdbbacbcddaaccaabbbaaabbbcdacddadccacbcbcdbaadbacccacdaabaabbcbdbbbabdaabaddcadcddadadcbbadcbbadadbcbaccadabdcaabdbaddbcdddaaacbddbbadabadddaabbadadcccbabaacccccacbacbddacdcbdcccadbddacabbabccddbdabaccddacbbddcacaddbcbabacccabcccbbbcaabdbabbcdbdbdbabcababacbcdddaabccabadabbbdcdbdddaccdadadacbcdddcacbdabdabdbadcadcaacbdbddadcddcacdbbbccdbcccbdabbacdbcddadaadaacadcbcabdcdccdcdadcbddbcbccdaabdbcdacbacacacbdbcdaadcdddacbcaddabddaaccadbddbccadcaccdacababbbdbcbddbdcbdbaadbccabbdcccdadbcabdaabdccaabccbaabdbcdcadabbaabdbccbbbaadbcaaaddccdbdddbbadcdabccabaaabcdadcacacdbdbabcababaaddbdbaccbdcbbaacccccaddcccabdabacdaddaabbcdbccdaaddddacccccacbdbadbbdcbbccddcccbcccadcaabdccbdcabaaacbcdbadcccaaddccdaaadcddcaababbccbbbaaccbcccbdccadbdaadcbbcdcdadccbabdcabbbbdcbdccddbdaaadcbadbdbababcbabccddddcdcbbbacdcdddcbddacacdacaaccaccadadddbccdcabbacbadaaacbdcdccdabbccbadabdabbcccdabaacbaccabaddbdddbabbcdcaaacacddacbbddcacabcdcbadccaadcacccdbdbccbaabbdbdbadddbaadbdbabccdcadadbaacaddabccacdadacacbdaddaccccdababcddacbbccdaacbacccdcaabbbacddacbcacddcbabdbaaacacbcbbaabbacabdddabbcadcadcbbdbdcaadccbaaadcbbadbdaacbddbdbcbaaccabbcbdcacdcabcaadcaabbcddddccbbccdacbdbcdcccbaacbcaabdddbcbcccbacbaccdacacbbcaaabccababcdabbbdbcccdbcbdbaaaaaabbcabcbaddcdcacaddcbaccbccabbbbaadbbcbaccadaaadababdcccccdbaccbbaadbbcdcbdccccbcbaabdaabcbbcdacabdddaaabdabbdadbabacdadbaaddddbbdcdadadaaddccddbcaccccbdbadddbacdbbbbcddaddccbccdaaadcabbdbadddbdabdcbbbdaddaaaadacacbaaacddbdbcddbbccaabbcccbcabdacdcbddbcdabacababccdaabcdacbabccccacabababdaaccbbcdadabdabdaadbaaadccacbbbadbacddbddaaccbccadcdbbdadbdcdddadbaaaaddcbabdcaaaabbcbbcacbcbdbddccaabddccccabbdcabbdadcbcccdacdabddbdadadaccacdadcacaddaabadccbddcadbdccbadabaacccaacaabcababdcdbddcacbdacbacadcbbcdddcddcdcbbabcbabadcdbcbdbbbddbdaabcdddbbbdbaddbcdccaccababbcdabddaadbcbbcadcccabddaaaadbaabdbaccccdabacbdadcddadbdbbcaccacbccdacbbdbcabccccabcacddaaaaacddadcdcbbdacaddabcbdbbdcbccbcbaccbddbdacdaccddcdabbbdbbcabdcdbdcbbcaccbcddbacdabddcadcaabcdacddbbbdacbcdcaaaabddaccbaaaddcbaddccacddccacadcacbccbccadaddaadbbcaaaadbcadacabaacaaabaaccbadaadbddbbabbdccbdcbcbccbbdccabcadddcadcaabddcbacabccdabddccabbbdaddabcabcdadbcbababbaddbababdacabbbadddacbbbcbbdaadbccbbbbbdabbbcabadabbccacabaddaddccccdcabaddbcdcbddcbdacdbadbcaaccddbcdbcaaabaaaaccddaacaadcdcccccadacdaacaabbdabbccddcaacdccbadabbdcddcbdbadbcacbbdabccaadbcadbdbbabbadcabaaabbbabbbbdcdddcbaadaabbacbbbbddaabbaadbdadcaccccacbdadadacbaaccacddacabdabaaaccadbcabbccdbbaaddbbcbcdaccaccbadcdbabcdcacabaabadbdabadcbdccabbdcbbbdabadaccbabbacdbbbabacbdbdbbdacaaccdbdcdbccacdbccadaddaaacacdbdacddcdabbdadcbdaabbcbbadaddaaaabacbbdcdcdbcbaadabaccabcabacddaadacbdaccbdabbdbdccdbdbbcdacdabadbcdcddcbadddbbbabaabdaddccdadccccccddddbcabccaadbaccaccacbbdcabcabdbcdccaaaadabacadacabcdccdacbccdaacbacbdccadaddacabcbcddcbabcccadadaabdabcabcaadcabcdaccaccddbbacacbbccbdcbdcaacacdbadcdacbccaabaddaabccdbabcdabcaccbcccaaccccaacbbcacabcbdaabacaaccdabddbcaacdaaaddabcaacbacbdaabaaadabdbacdcbcbbdaadbdbcadaddbdbddbdcdabcdcbbcbbcbcbddabbadbabaacbbacdadbcbcdcabbbddcbcbbaccdbdddbacabddadcbcbadbdacacbadabaccdbacacadabcdbacabdbdcaadadbadbdccdbcdcadaaccddbcdbdcbdbabcacccacabcabccabbdddbaaadabcddbadbdadadbacbadbbcbbddaabcabcbaddcdacbbcaaddacbdabbbddbbaacbaabcaaddaacddabadacababccadbacabbccbdbccdddbaccdaabccaadabbdccddacbcdccdbbcbabccaaacdbabaacdcacbccdcbadbababdcbbadcddadcacaadbacbaabbadccdbdabaccbbcccbcacabcaddaaacaacccaccabbdcbdbdcbabbbbcabbdbdccdcdcbbddacdddcdaaddaacdbdaabcabaacbdcdbccbacdcbadcabdadadccbdcabacbdaddbcbbbccaacccddcabcbccccccaadcddcccacacaaadbadabcdacbcabdabaabaddbbdbbdbaaaccaacbaacbddadcababcdcacadbdbaaacbbdcabcacbcccbbccadddbccbbbbbcbccdcdcaabbaaccaadabaaddcdabcbcabdcccacbadddabaaaccdcbddbccdcabababdbabdbcabcbcddabbddacddddbadadaaacdaaacbccbbaabdabdadbbcdddacccbacccbcdcbdabdabadcccccbcdddccacacdbbadababaacdacddddccbccaddbdbaaccdcbcbbabdbccdcccdcaccdadbabdbdbddbacbbdbbcbdcbdaaadbcbdaddaaacdabbcbacdbdcadaaaadbaabdddabcccbdacccaddbbacdbcabacdababdcddccbdcaddcaabdbbdcddbdbccbaabacdacabdadccddbdbdbdbbbcddbcdabdababbbbcacdadbddcdbdadddcdbabcdcccbccadbbbccaadddcbabacddbdcdddddbdcdccabadadccdacccdbcdccbcdccbdaddddddcaccbcaaadcbaccdbaddcdcbdcddccccbdddddabbccdaaadbaddddcbdcccdcddcdbaacadcbbbcdacadaccaccdbbadbcdbdbbaacbcbcddcabdbaadaabdaadadaabbcbdcdbccbdcbccdbbdbdbbbddbcdbdbcdbcdccbdacbadbcbccbaaaacadabaacccbcacaabaaaaacbabcbabaacbcbccccaddbbadaacbccdbaaacccdacbbadccdccbddacdbbabbcddbcdddddadbddccbadaacbabdbdbacbccdccbdddabccaacbcbcdabbdaabcbacbdbdaaddbcbabcbacdbababbdcabcaaccccabddaddbbbbbaccaaababadddadcbcbbcdddcbcdbabdadababccdabbabdababdabdbccdddaccaaddbbdcbcdaacbbabadadbcacabbbaaaccaccbcadbdbbadacaabcbcccbccabcbbbcdcdcadbbdbadbaddaaaabbdddcbacdadbabdcdcdacbddccacbcdaaadcbdbbdcbabaddbabbacdadbccbccddbdccabcaaddabaccacbbabdcccddacbbdadcaabbbbbcabddaacadaacbcbdddcbcccdacabccccbcadbabbcccdadbdccddcadccdbdaddcaadbbdddbadbaaccbbdbcbcdacccbcabacababdadbadcccbabacacdddbbcaaccaabccbbccddbbcaaaabddbddcadcaabdacaaaadbdddaabadabbccaadbcdbbbbadbbdacbacbbcbaacbcdcdaadbdcaadacdbcdadabadcdbdcadccdbabcacbadcccdbbbadadcbacaadbcdddbbabddabacdcadaacbbadbbdacadaadababcdbcdaccacadbbddbdccbccbcdddaaccabddcdbdcdbcbadacabbdddaadccadabdbccddaacccadacdbabbccbbcdcdbcccabccbcccbbaaaadaadddcacddabcbcbbaaabbacdacbcbbadcdddbccccacbaaaacccabccaadcabbbcbacbaacbbadabaaadbabccadbbacaaddbddcaaccdbabaddcaddbdccdaadcdadbbcccbdaabbacaaabcaabadabbdadcadddccbacbabdcbbaaaadddcbadcccddbaaabdcbccbddbcabadbcbdbaabdbacddcbaababdccbcddaacdbacddccdadcbbcbbbaaaccbadadabbbdcbbabdaadcdbadacdbddaacbbcacbccddcadcdabaadcbacabcbbbcdccdaabddccdddaccaaadcdabbadbaccbdddbababaadaadcbccbdcbcdacacabcddccbbbdddacbdadcbacbbcbddccadabcbacabdcdbdddaaacdbbdadacddddaadccbadbbbabcdaddddbabdcacdadccbdbadcdbcbbbaaddbbddbbcaacaabcdbdbcbdcbcdbaabadaadbddddcbcdabccdabcdcbbaacabaccaadbaabcdabccdbcabdddbadccaccbcaacbccbdddbabcbdaaaababbabacccadacdbcabdbbcdadcdcdddbdcbdcbcbdadbdadccdabbadbccddadbccabacdaddbbddbcddcddacadabadaaabcdddcbcbddabbbccbabadbadddcbcbaacdcdcadbbddcadbbcdabddcadabccbacbbabbaadbaddbadbbccaddaacbbdacbdbaaccaddaabaadababdccdbcbaddbdbcbabbbacaacbcccddacdbaadcdbddbccacccacdbdddacdcaddbdcdbaacbcdcdcbccbadadabaadacddbdabbaadaaaacbbcddabdacddbabddcacaaddbdcaaaadcccdaddbbbbcbdddaabaabaabdadcdadbcbcbbcaddabbdcabdcddbabdabbaababdabcaddabddaccddccadbdabdaaabcdbdcbdbbdbbdaaaccdcaaacddcdccbbddaddbaccaadaddacbacaaaadadbddbbbabcbdadcdbaddbddcbccbabaacaacabadbddcdccbbbbacabdcaadabbdacbbdabccacbbdcccdcabddcbacccdbcaddabbcdccbccdbbbabccbcddccdddbbddababddcbcdcaadaddbdcdacaadcbcabcabacccdadbbcbaccacabaddaaddacbacabddaccadccbabcacccdabddadbacabcaadddaabbbbbbdbdbbbadbdcaadbcaaccdccaabbddddaaaabacddaaadcbaacaaabbbbdbaddabbbccdbcbbadbacaccddaaacdcabcacadbcbbbcaacbacccabccdbdcabcccbdddbddbcaacdacdbbccbacbacdddbccadabcccccdcbabacaaccacdaabababdcbbddddcdaaccdadbdcdadcdacaaacbbdccadbdcdbdaacaaabacaaadccdcbcbadcbabbdaabbadbdbcdaadcacacaaddbadacccaadbcadddcdabacbdcbdacbcddabcccdbabbbdaaaabbcaaccdaaccabccababccadcccaacacaccaccabadbdccddbacdacbacdcbacccbcdabdabbbbcadddabaacbacccadcacbdacaadcaacbcabdacbaabcdbabdcadbcdbcdcccacbdabccbbbcdccbacadcaaccaacabcbcdcbcdbdadbccdddbdbcddadaadcbcdcbcdaaadcabdcddcacdaccabbcbdbbabcaaddacbbbcaabaadccdbbbcaaadddcbaccbcabaadddbdbbdcbdadcdcbaabbabbdccdcccabcbcccaabbadaccbabaaadabbcccacbcabcbdcabaabdcacaddabbcadccabdbbbdccabacadbadcbadbaddbaadcabccbdadcaabccadbcbadaddacbbdddabcacbabbacadbdbbaacbbdddcacbaacbcbdbbabdacaaadbcbbadacbadbccdabdaddbcacdcaacddcbdcdabddccbabbadaddacdbdbbaabbccdbbcaabdcdcdacabcbabacccdbcbbaaddbbbcdaddacdaadcadbdabccbadbcdcadabbcdcaccbacabccbaacbacaabbaacdddadcbbdacabddcbacaadcbaddaddadcbddcbdcabbbdbacccacccbbaaabdababcbbdbdadbdaaaabddbaaacadccbccddabbbabcaaadaaabdccdcdcdacdbdcdadcbdbccaaadacbadabccddcbacababaddcaabdbbcdaccccbcacdaadbacddcbcbcdccbdaaaadacccbbdcbacabddadbadabbdaccdbacaddcbccbdbdcdcaadbdacabbbdaddaaabadbddbbbcacbcddbdaacddbcdcacbaddbcbccbcdacccaddabdbacccbdbbcdabacadaddddbcbaaddbbddccbcdcccdbccbdccacdaadabcacdbddbdbbcccdbababbabbccabbbbbcaacddbcdcbccdbbbdbbcabbbbcbbdacbcddbdbcbcadbdbdbcddbbcdabbabdadbdcdcddbcbadacdccccbaddabcbaccdcbdaaacaacaacdabdbabcbaaabaabdbdacdddaccaabbcdbcbddbaabdbbbaacaabcdcadccabbaacbbcdccacccbdbacdcdcadcccddccbaadaababbcbadcbbbacbbbbbcbbbdabdacbdbacacdbcdacccdabaabcadbccbdcbdbabdbdaaabdcaddacbaaaddaaacbaacbaaaadaccacdcbbacbbbcdcdacddbacbcddaaabbbcbdbbbabdbbbcbccbaabcdcdcabcadcbbcdbdaddcaadadabaacdcdcbaabdaaddbbbccbcbccbacccbccccdbcaaddcdbbcdabbdcadbbbbdbddadbcbbbbadcaaadcacbabbdccacbcddacbdbccbabcddcbabddaadcccccbccbaaaadaabacdadddacbcbdabaababccbbccbdcdabdcbddbccacacaaddbcaabddbacdaacccdbadddabddbcbcbddaabdacacaacbdacbbdaddadcdbaabcbcaaadbbccbccacadcadcaccaadaacbbbcdbabccbcccdaaaabcadcccdacabaabcddccdadbddcddaddccbddbdcdccbaabcdbccababdbbcbdbdddcbbddacaaccbbbbadbbacadacacabdcaabbacaddbcaddabcdbddbdcdaccaccbbbbaddbbcccccbcbcdadcbdcdcddbcdcbdcabaccacdadabbdbabbcdaabbccbdcbadaababaadaabbabcbaacbbaccbdbbcdabcabbdddacbaaaabdaacbadcaaaadcdabcddcbdddcddbbcbdcdbcbdcabddbbddbacaccadddbbbbbdcabbaabcbcdaaacbbabbbcaaaaddadbdaabcdddbabdcdbaccdcdbbbabdbddcbbacacdadbabbbcbbdaabdbadabbabccdbcdbabbcddadcdaabcadaaddcdbdbabbbdddadcdbaadacdbdacbdbbdacdbbadddbabcccddacbddbbcdbdbcaddcdacdbccdcadbabccaccccdccdacaacbdcacddabaabccadddaccbcbbdaabbdcaabbabbcbddacccdbbdaacbcacadcaccccddcdacadaddaaabdacaabadcbaaaddbcbccbacbdcdcaacadccaaabbdbaccacaacaccdabaddbabdbdaacdbdbddbcdcddbaccaabdcbccdcbbdbacdbabbaadbabdcbdacaaaabdaaacbcddaadbadcdddbadcbbdddbbcaadacaddaacacadbbdbdbaddabdbdadccddacccbdbbcbcbccdabccbddbaddcdbacabbcbccabadbabaadacbabadacdbcadddaaddbcadcadbdaacbbdadbadbcaabbbbcaabcccdccacbaddacdccbcbaccabcaaaabadaccadddbdbacccbadddcaadbcdabcabbdcbcdddbdddbbdccbabdaadabcbccdddcaaddccdacaadbccbbdaaadaaccbbdddcaaacbcdabaacccacbdcabcbbacbbcbbcdaadbacbccabcaabacdcbacacdcacbdcaddbcdcdccadbcbbbbbcbcbddbbccdbcdbdcbbabcbabbaccabcdcdbaabbddaabddccaadbcdcdcbbcbaabdbbabdbdbadbaccabbabbbcdddccbbacbcabcaacdaddaccbacdaaacbdcaabdcbddbdcddadbdadaadccdcdbcdddbcdcacbbcdccaaddadcddbbbbacbdddaddacbbbbdcbdabbbaaacdaddcbbddccaaddcddaadacdadaacdadbbddaabcbdddddadacdadaadbcbadbddcacdaaacbcdbdbabdbdbdbabbcbdbdbddbababacdccaadccbcccbcbacdcacdbadcccccccdbbabbdbccacbbadcdcaadaccdbcdcacbbadcbddabacbcadccbbdbaaacdddacdbccaadddcbadbabadabbdcaccdccdddaaaacbbaacdabbccdacddcdbabccaccaccbaacbbbacbadadcaddbbdcddabcacdcbdabdbbcabcbccabdadaabbaadcdccaadcbbacaabbbdcabbbcadbbbcdbbbcaddbacbabcccdbbcccbcddddcccbcbddcbdbaccdaabdbdaaddccbdacdbabdadaabddabbddcdbaacbbcbbdcbabcaadddabcabcbbbdbcdccadcbacbccaadacdcbaacdbdadadbadccadbbcbbdbbabdacabacddaabdbdabdadabaddbbbadbaabcaabdcbcbaddabaccbddacdbbcbaccbdcbacabdccadadcaabadbcaadabcdbbdbbabbcbddbddcdccaccaaaccccdcbadaaabdbadaacbbabdcdbbaaabcbccbdbbcbcccddbcabbbabadabcbcaacdcaaadcdabbbadbccabadcaccacabddcadbdaddbbadabcdaadacdaaaaccadcbdbbaacbbdcddbaabcbbdadbddccacdcadbacadcdcdcdabacbaaddddabcbaabddbabbcacdbbaaaccccbbbaabadbacbbdcdadbadbddabcdbddababbbdbabaddcbdccdcbbdabdaccabbcbadbdbbbdcadddabadbcbdbdbabbacdccaaaccdddbbcbddcdbddbdaaddaacbcbadcbaccaaaacddabacabaaabbcdcadcbdbcddbbbcacabccadacacbbacbbbdaabcccddadcbacdbcccaacdbabcdbbdbbabadabadacbaacbccabddbcadbdccccaccbcccbbabbbcaccaadbddcbccddbdcabdabbbbdabbdaddcddcacccbbadcddbdbdcadaadcbaabaadadacabcdbaddccdbdabaddabcabbcaccdcddacdbcbdacbacdcadddbabcbcdaccabcdccbbbdabbacbbbabbdacdabbbdadbbcbdbababcacdddcaacbcdbdaadbacaaacbdcbaadbdaadaddbcabacdbdcdcbddbaccdbbbacdaabdadaababdbabcdacbadbbdadabccbbbddbcbbcaabbcadcadcbdcbcabcbcdcbcbbdbdbdcadabcccbdaadbaabcdcddabcdaaadcdaddddbbbdccccccabcddbdadbdcacbabbbbdccaadcaaaddccccadbadddcaaaaaacdabdcbdbadababcdcdaacbcbadddcbdcabcccadacbccaaddaccdcadcacdbdaabdadcbcbccbccababccdacacaabbcabbaadbcdbbdacbdadabcdbcabadccadabdaddbccacabdbdcbaddabadcccacccccadbcaaccbbbddaccacbabadccbbaaadabacddabaaacdccbcbacddccbddbddacaabababdaacabbcbddacddbdbdcbbbcbadacddadcccbabadcadddccadcdbaddadddabbdcbdaccdaccbdbdbdbdbdcadcdaabcaabaacddcccccabdbbcacdcddacdabcabccbdccccccccbabacccabbdcdaaabccdddabacaccabcbacaabbadacacdbbbadcbbacbcbbbdcbaabdadadddcbbacbcaadacbaabaaabdcddbbbcccdddccdaaaabbacbdabaabbababaccdddbcaaacddccbcddbabbcbbbacdddbaddcbddbbddabcdacabadcbbbcbddddbddccbbdabdddbadddbdbbadcccbacdbaacbdaccbddbdacdabcbbccdaaaabddadacaadbbaadcdabadcdcbdaccdbdabccbcbbaccdabaaabbcacbbbdaadaacbacdabbdadcacbaddadbbddccababbacacbcbbadcadcdaabccdabbbbbbaababdadcddaddbbcccddbdcbccccbddcbddcdbddadaddcddaddacabacaabdbacacaadaadcddbcdacaaacbcaddcbbaccaacbccdcdcddbdadbbbddaabdccccbcaccbdbcdbcdadddccadbbbcaaadbdcccdcabaabccdabbdaaaccdddddadbbdcbcbdaacabbacbcbbcaccabababbbbccddbaabbdaabdaabddabbdaacbdddbacacdddbbcbbacbbcbbacddbcdbcbaadcbddddabbdaabbcacdcbacacbabccbacbddcbcdbddbddacaabcabdddbabbbddcccaaabdccbadacaadbdbccbdbcccdadaaadcbdbbdcacaadadbbbcadcddabbaabcbccbabcbabbdcbacbbadbccaadcacbcdaaddbaaccbadcddcbbccccccabdaaccadcbccdadcccacadcbbbadbadbabaccddacdacddaccdcccdaabbadacaccabcbaccdcdcabadcddbacbadacaaabbaadcbdaacadbdbbadcdddcacbcaacbbbabadbcdbddadccdbbccdcddcdbbbbbcacddadcddddadddddbcdadacdcccccbdcccdbbdddbbcddbbdcbadaabadcaaaddcdcadcaabdabdcababacbddcaadbadadbbdacbdadcbacabdbdcadcdabcddcaadbbdbcbdabacdcabccdbbabbaaddbdbabbdcaaabdcbbdbacdacbdbdacabcdaacabadddabbbbbcbdcdaddaddbbbacbbdccbdcdbbcabbcbccdabcadddbaacdadabacdacdbbabcdcccdbacaccbacaacdacdbbabdadcddbdcdccaacbacabcddaadcadddaabbbaddacadcaabccacabaadcccacacadcbbcbabccacdcabcbababbccadcaccabcdbdcadbcadcbacbcacaacacccccbbaaacdadcbaacbdacdacaacdccbdcdcdccbdbcbbbcaddbbcddcbcdacadbacccadccbbaaddcbacadccbbacdccacdbdadaadadaadbabcabaccdacddddacdddbadabbaaddbccdcbcbbadaddacaadcabdabcaaadbcbbbdaadcbdaacaaccccaccabccdcbaccadccaacbdabaccadddbbcaacbdbdaacdabcbbadccdcddbcacccbcdaccdacdddccbcdddddbaadcacbaaaacacdbdcabdcbcbccdcdcbbcbcbbadddcdccabdcaddccacbadaabbbaadbaaacccbdddcbddabcdaabdcbaaaadcdacbaaccdadbaddcbcdcbdbcbbdaddabdcdcbbbbaacbaaddbcdcdabacccbdacbcababababbacdccbbbdbdbbaadbabccdcbdaacbbbaacbddddcddbbdbdacbabccbcbcccabbdcaaccbcbbdbcccbbacbdbdbabccbcaabaaaabdcbadbabcddbbcbabadadccbabbdcbdcadbcddcdcdacdbbbdcaaaaadddaacdabcddbabacadadbaddabddcccbbcaaddbddadcaddcddbadcbacdddaacccddbcddccaadbacccbacaabbbcbbddbbccadacdcdcbcaddddcbbbaababdbacdadcbcbaabbdbacbdadddcdabdbbcaadccaccabcbdcdbabdbabbdbdbbbabbbdbddbbbbbcadabbbcdaabacbdccacacbddccbaabbabbbdadccadaaccbacaccbcbddccacddcaaaadcdddbbbddabdaacaadcadabcdbbcacbdcbcadbccbcbabbbcbccabddccdcaacbaacacdbdadcacbbbcdacdbbbddcbcabbdbbacbcbdbadaccbacaadcccdadbaccabdaadcadaccaaacdbddaaacacdbddcbbdbbcdddadbbddacbccbcdcbdbbabcddaabacddbaccbdaccaccabadadcdabbcdbbbadbddcaaabaabcaddcbcdbbcccaabbaacdadadbcadabdbddcbaddbcbbcbacdadcdcdbcbbdbdbdbadbdbadcccccdaaacdccbcabbbdcadadbbbcbbdacdacdbabddadababdcabbbcadbcabddddbcbbbcabccababbdacacaaddcccbabcccbadccbabbdcababdcaacaadaabdaddcbcadccaacbbabccaaabdabbadbadbddbddabbbddbbbdddadcdccadbacaadcacdbbababbddbbdbbbdabccacdabbbbdbbbcbcabcacababbcdccabcacdccbbdaaddcbcadacdaddcbacadbbbaabddbdbbaaddcbbccbadccbdbddbbaddacbbdbdbcddcddbacaaaaadabdcbdcacaaabbdadbddbdabccacbbddacdacdaddaaccbacbcdbacadacdacddcaadbdacaccbddbbcbacbacadbddacaddcdcbdbcbacbbcbdcdbaacdbdbcdadddbadabdcbbaabccdbabbdcbdbaaacccddbcccdacccdccbdccadcaacbcdacaccdbdadadacdcabbccdbdcdcdaadcbaadbbcddaadabbcbabdccabcaadbccaccaadaddcdbdcdbbbbabdcaadadcaabbcddcdbababcdbbcaccacabcaccababbabcaddcbabddbabccbbbbdbabddadabbdccdaadbaaddcbadabdbacabddcdabcadccbacacadccddbcdbabbadaacabcdaabbcbdaaddcababbcbbdcaacdaccacaddacccbdcaddddaababcbdcddaddaddaccccacabaaaabddabddaabbcaddaadbaadabcddadbddadcdbbcaaabcacdbadaacdbabacbbcabacbbbaddbdabdddcccdbaaaccbaadccdaabbcaaadbcaacbbbaaddbaddabddaadbdadcaabbdacddbbbadacbaccacbdacddcdcbdcddcadbbcbccdcdbaccdcbabccdbddbdbadababcbacdadbadddbadbacacbacadbccdbbadbaaaccabaabacddabaaacacacdbdabcdbcaababddbdcdbbbbdcdbcaacabcadabdbccbabcccdaaaaabbacbdbacdacadcdbabccccdbdacdcccbcdcadacdcabadabbcbcbcbcccacbcacccababaddacacacaddbaadabbdcbddbabdccdbaadadbbadbcabdadbadcadcaccacadaaaadadacbdccaacabaaadadcadadbbdbcdbcbaddbcaabaddbcbbacdacbacaccdaccbdccbdcbdbaabbdbbbdaacbabcbcdadcaccbcbdabbaabbcadcacbdacdcbdaaaabddcabbbbcacdcddabdcdddccbdbaabddbaadbbbccbaacdcadacddddbdbaddabcddaacddbdcabbaaadacdadddabbadccbbabdccbddbcdadabdaaddbccbbdcdbabdaccdaabbdccccdaaccadbddbdbddddcdbdacabdaddaaaadcdcaabdacaddacaabaccdabddbacbbdbabababbccdcbbdbdadaacdbbabdabadadaccbadaadccaacababcdbcacbdaddcdbaabaabcacbbaabbdcdccacbbcddcadadbbbbdbdacbdddacaababadadaadaccddccdbcbcacddacddbcaabbbaadabbddddaadccdbaddaddcbcacacbabdcbcaacadcbddbadbbadbaddccccddbbcdaadaabadbbccbbcbcdadacbcabaddcaaadabadbdbdadaccdcadbbadbacacbacbdddbcddbddabbbccdaddddbcbccabddddcbacabcdcbbabbddaaacabcbbdaccbccddcbbbbaddcdcbcddcabcadadcdcdcbdddabccdbbbbdbbcaadcdccbcdbbbdcccccccccbddaccadbddacdbbaddbadcdbcbdbacaabbcbdbaccabbacbbadbddcdbcbdbdcabbdaddacadbdccdadcacabbacdcdbcdbcaccdddcbddcabcdbddbacdadbbbbcdabbaabcaaaccbddbbadaadddadabcacbaaacbbbbadabbadaddadbaacddaababdcbdbaabaccbcccaacdcbaddbdaabbdccaadcdbadbdbccbccdcbbaddcccadbbbcccabcacbdbcccaaccaabbdacdadaaddbbacbcbdcadaccdcbdccadcddacaabcadccdccbdcdcbdbadcacadccddabdbcadaaadabaaadbcacbcaacddbddabcdcadbaadbdadacaabbaabdcbcaaadcbadbbdcbccacaaacdbadccaacbadbccddadcdbdddbdbbdaddcadbdcdbbdbaddddcdcbabbdbacacabbbbcddacdbacdbccdbbadacbadbdcdcccbcdadadadbabdbaacbcaadbddcdaabdcbdcaadcccaadaaddaaaabbaabcacdabbadcddcbcdbdbbbaaaccabccdcbbdbdccbdacabacbaabacacadbbdccacabdbcdbdabaacadbcccdaacbcdccdacddabaadabcbcdcbacabacabdaccabdcddcaacaaacbaacdabbdbdccacccccaddadcddbaccbdaaadaadccdcccdaabcababcacaddcdccbbcdbadcdabbabaccdbbccdabaaccbcacbbdccccdccbdbddcadacccabdabbdabcdcbdabcbacabddcacbddaabbacccbdcaaccdabdccdbdcaccaabaaccddadbdaabbdbbdbcaaddaadaaddcabcacbdadaaadddccadacdbbdcdadbddbddbdccccaaabcaababcbcacdbbbcadbcbbdcbdccacabaabcbadccbadcbbbbaaacbddcdbdddaacdbbaacbdacbaacddccaaaabdcabdbbacdabbdcabadcccacdbbdccbacdddbdadcaddbabacdabbbcbaabcbdcccdbcbcbccacacbbddccbaadcadcbbcdccadbacbbcccdcbadaddabcabcbadcdabbbacabbbddbccacdbbccddbdbddcdaccdccbdddbaccabcdaccaabacabccacbbdbbdbcdbcadaacdabbccbbbddcdbdcdcdaaddadccddadbaddaccbbbaccaaacddcadbcbcbdaddbacbccdbdccbdcdacbaadacbddcadbbccbabdbaccbadacddaccbacababaacacdaccabbccaaabdaaaabdbbdadcdbbaccdbabadcaaccbcbcccdaabdbabbdddaccbcbadbdaaabccdaacbcabaadbdcbdddcaddddddcbbddcbddbbdaadabdcbaddbcadbaddbacdcacdbbcbdcbccadbcbdcbaaaabbdcdddbdadaadddcdcbbcdcbdddbdcccabaabcdabbcdcaabadaaadacaaacaaaccdabbbcacdbdbccdabdacdbbdacacaddabbabadccdcbadbaaadccaaadadaddbabacbdcddcddcdddabbacddcbadadbbcbdbaacdcbdbdcdaddacbabacbdddadbbcbcaccdbcbcaaccabbadabbcdcaddabaddcbadabdddacabaccabccbbaaddaaadccbccdbdadbcabacbaddccbbdcdabdaacbbccadbacadbdbaaccabdbabbdaddaccaacbaadcccaddbddcacdaacdaabdbbabcbdadbaadccdbabadcdbababdcccdaadbdabcccdcabcdbdbdcddacadbdcccbabcbbabadacbddbdbdabcaabbbaaccbdabbcabbabacdccbdccbadaabdaacbbacbbdbcdddbcdcbdccccbcbabcccdbdabcabbcadcdbadbadddcddbbabcdbdddaacbdbddccadddabdbadcbbccaccbcabcccabdcdccacbbabbdbbaaaadddcdcacacacaccacdbcadcacabaabbccdccddcbddbbcdaaabddcccbccadcacdadbcbbdcabcabdbbbbabbbcbabcddbcddcdbddaacdbbccacbcbbddcbbaaccadcdaccbaaaacbcabadbdddccbaddbbcbdbdbdbdbbaabbbbccababbccdaaacbcdabddaccacdadccadacbbbcdccdbdbaaaaabcccccbacdbdbdaadbdbdaacdcbdbccccacdcdbcaadcddaddaabababaabcdbcddbbddbdaccccddcdbbbddcbcddcbaacccbccbabdbbcaaadccbadcbabcabdcabacdacdddbbaaddadacdcdcdbabbccbcdbddcdbacbdccacbcabccacdbcdbdcddbdddcacbdabaaacaaabddbdbcddacccabccbcbadaacacbabbdcdadabdabbdaccdcbabcbcdddbbbbaccccaacdcccbaadbadbacbabdacaabcaacdcdaaccbdcbbabadcdabdbbdbaddcadaaacccdcbbcddbacbdcbdacaabbbbdaadccddcddbadbcdbabbcbbcbcbbbcbbdabaaaabdddbbaccbdbbbcbccdddcbabbbdbbddcbaaadbbcacbcddabccdbababbaaabbbdbbddbcbaccbdbdaacbacccbdabbabddbaddacabdadcdaccadbcddbdddbacccadacdbcccadabcbadabbcaccaccadbbccacddcabdddbabbdaddacdaabaabcdcabadcacadbcbabaaabcccccbcbcacccdaacdaddbabcdabddbaabbcdbbbccdadaabcabdbbdabbabbabcbaaabaccbdddbcdbbdcbbaacdadabdbcabbabddcaadccaaabcdcbaccdaadcdaccadbcbabcaadbbaaadddaaadbbccdbaccaaaddadbddcbaaaddadaccdcacbdbabacaacbcdddaaabaddcbaadabadcbcddbddaddcdcbbcbdbbdbcbcdcccddacbcdcccbbbdccaabadcabadbdadbaccddddabdacdbddcbacadabbdacdcbcdbbdbcdbaaadabdacdcdccdaccddcddcdcbabdbddacccdaadccabaabdcabadbbcbccbcadcdcbabcadccacaacadaabbdbcdbccadaccaddcdbcadbcddbbaaabbdcbbdcbcaddcadaabbddbadcddcadaddbbdadaabcccbddccdbdccbcaabbdcbacccaadbabcacbbaddcbaccdccddddbcdccbbabdaddcdccdaadcacccdabcbbcbcacbcbccdbcdddaadaaddaacadadabacaaaccbcddbabcbbabbdabbacabcdcadaabdadcdccddabcaabcdddabbacdadcccbbcbaacdcdacadccddaacbdaacacccaadddcabddbadadadcabdbcabddcccbddcbbbddbcbdbcaaaabaaadcccaaddaddbacbcacaccbbabdabdcbdaacacbcddcbcbdacbacaabcbaabdaddddcbaabccadacdaddbbcdabcabdbdcddabdcbbdddccabdaccbdadbbaddcdbaccabbbacddadbabdabdabbcbadbbcdcbdbdbdddabcbdcccdadbccabddcddbaccbddbbacccccdbdcabaadddbddbbadadbcacadccdbaadaabacbadbcbdcbbbbdabdddbcaaaccabbaccbbcddbdcdddabbcacaacbabcddaddabbcbbbbbaacbdabccbbacddbdabadcbbadaababcacbcccbaacdbcddcdddbcbdacabbcbdabcbaabcadccddcabdaadcbacaccbdbdbadcddcccccaacbcabdcdbcadddcadbdaaacccddcbccacabbcaadacbaaaadaabcdbabcbbabdabdcccbbdbabcdcbccdccbccddcabaccbdddcdcbcddcabcbcdbabdbdacbaccdddabcabccdbbbdabcdbbbdccdcacbbdabdabccccbbbdaacacacbcbdacbabaacdcbbacdcbabcdcdcabbdcdcbbbdddabddbcbadcaabdcddbbabcddbaddcbcbadcbccddbcababcdacbaacdddbdcbdddabdbacbddcbcacadcacbbabaabdbcabbccababaccaadbddbccbdbabacaacccdbcccbabdbcadbcddbccdadabddbccacaadbdbcdacbbccadcdbdcddbdcadbbddbdcddcbbbcbbabbdbdaadbbcdbbdaacbbadcabbdbabbdccacbabacbbdccaacadacdddaaaabadcddababadccdaaaccbacaabdddadccdabbddbacdcdacaabbcaadaccbaababaacbcbdcbcbdbbccabcaacbbaaacaddaddaaacacbdadbabcccdbabadadcaadcdbbdbcdbbccaabaacbbcbbcaadcbbdcbbaabddabadcdbaabddcbdadbcbaadbbbbdbdbaacdcaaddabcbdacdcddadaabbdcaacacdbdddadaaabadcaabbdcbacadbcdbadcabccbcabcdbabbcbcdccbcdaacccdabadabbbccbcbacdccdabaabcdcdbddcdcaaacdbcadbabbadccadaabcdadddcdbaacacadadbbdabcdccbaadbbbccdbadacadadadbdcbcccddaddacacbccabdbbadbaacbcccccaababbdbbcdbbdbbcbbcddccdcbbdbbadadbbaadbbbaaadcabbdacadddbdddbbcbaccdacdddadadaaacbbbcaacbaacbaddcacadddddaacacacbabbbbccbddacaccadccdcacbbcabbdcadcbbdbacacbbcacadccbcacbadadcaccaabdbdaabacacddddacbdcdcbdcdccdabbbcddbaadbbbddbcadaccabaaadcbcccdcadaccbacbccddcabaaccabcaacdddcbaabbdbdabdbaaabbabdbbcdcbdbcaaadcabaaadbbccdccccbbadbcdbbdbccaaabaabdabbdcadcbdbbbddcbdddcbcacdbaabdadcdadadcdccbabcabbadacaacdaadcdbabaaabbabdcbacbbcbcdabaadcbdaccabdcbddcccbdcbcccbbadaccdababdcdacdcdcbdddadcabcbbbadbdacbbbdbadadababbacbbadbbddbcdaacccbbabdcacbbdaddaddacddacdcccbcddaadaccccbddabdccbccdbcbcccdbcabbbbcdadacabdbccdbcdcbcadcdbbbabbacbabbcaccbbdcadcacbacddacbbacabccdbbbdadaacabadcccbacadbbdcadabbdcdcbcaccbbbbcdcdbbcbcdbacbdadddbbdcdacbcbbccbdbbadbbbcabdaababcbccccccaccdccaabaaacabccbbbcdddcadcbdbbbbcadabbdcaacabbcadccdbcdcaaabacbcbcccaddbcaacbacacbcddbdaabcaabadbbcbcddbbcdcbcacddcbadadbabacbbbbacacdabaacabacdabbdbdcadbabddacaabbdbcdcdbdddbbaacababbbdcbcabcdbaacdabccdbdcbdbbcaccddcdbdbbdbbbdccdacbdccabaaacddcababbcdcbcacbbdcdacddcbdddbdadacdbacbaacbaacdccaacbcaabbcaddaaccaacddacbcadcbbabcdaaccbbddaabaddaabacdcaadccacdabcadacddbdcddcdadcbbabbaacbcccbdddbcddbcdccdcaaababccdbddacbddbbacddbdcadacaacadbdbbcdbacdddccccccccccbdcabdbcacddaddccccabcddcbccdcabcdadcbaddacccccbacdccdbddcdbddabbadaddbdccbdaacbbcbbabcdcbddacdaabbabaddbadaacbaadcccadbccbcdbabbcabdbbbbddacbdababcddbbbbccaaadcbbadbcbabcdaddbdcccdabdcaabdcdaaccbcbabaadaaabaddccadccaacdadbdacbaadaddcdbccdbdcaadcdccddbaaacddcaadbbcbccddabbbcacacbdbcacddcbcdaccaaaabaddccdaacdaaccbbdddcadbbddadbbdbbbcbccadbccacdaacadddcbccdbbcabbdaaacdddacccdadbddcdcbcbdaaccadcbacbdbbbdcdaaadccbababdcadababbacbdbadacbbabddcacccdbcdacccabcbcabbdcdcbabccdbbdbaaabddcacadabbcbacdbbaddbadbdaacabbbcbbbababcbccadccbccddcabcacadacbdbabbbabcccdbbcccabdbbcabcdbdbadadcdabbbdbddcbbdaccaadbcccdacddabbacacbdabcbcccdbbcdcdacbcaadcccbbcbccbccdccadbcdbcacdacababdbacaaaadacdbacdbdaccbabbbacaaccdbcacaaacdccbdabdccdaccdbbcdcbbdbcabdcdcabacaaabadadbbcacbbadbcdbdaaabdcdaadaadbbaaccdabaaaddbbadbbddccbabbdacdbcccadadaddbabdadcdbabccbdccabdadadcadcccbbbacbababacdcbdbadcccdccacccbccdbabccadbabdcabdcbbddbddbadccbacabcdadcacddbcdcddcabbbbbcacdbbdadbcccaaddaacbaaaddadcbdbccdabdaaacaacbddcaaaccbcabaddbbdccabdabbdabbdcdddbdbacbdcbaadbbdcabdbabbdabdacacdcabadcacacdbbadcacddcdbcbbbddaddcdbacbddacddadddcbdaabbaaddbdadbbbddbdacbcaddbabadbddbcabcccbbdbcadcdcdbbabbabdabdbbabadabbbdbcbdbaccadaaaaadaddadbdaadbcddaacbdbddbbdacbbbacaccbadcdbacbccabbdaddbddadacddbdbdcaaabacbcabaacadddaccdcbbdabcbabdabcdccddbcdbabadcadbdcdcbabbacaaaacbbabbbcacabcccbccdabbbaacbabcccbdbabcbbcdbbdddcabbdabccbbddacdccdabcccbdcadbbbadccbcbbcbcbdadaadacaabbdcadbbbaddccadabdbbbbddddaaacdaaadbbcbbbdacdbdaddcdabbaacacbacbdaaadbdcbbbaaabbdcacadabddbdcbbbcaacdbbddabccbbabbcbcdbcbacbbbccbcaabbdbacacdcbacbbbdccbcbdadcddbcdcaddbcccbdcadbbcabcbccdaaacabddaccbccdbabbddcaaaddaacdabdbaadbcacdacabdbbddbdcaabbbdbacbdacbdcbbdaccaaddaaaacdbcadbadccacbbcabddaccbabaadcbbacadbcddabbdcbcbdadacaacbbdbcdbcbacacbadbaabdcbadcbdccbddcccdcdcabbaaadcaadcccdbcbcdcbcadcddbdcdadddaacaddccaacadbcbdacacdcdcdccaddbbcdabdccbbdabcadbbbcbdbaadabadbdbbbaacabbcbbadaddbbdaadbaccdabcbccaccadcbdacbcabaabcdaaacabdadcbdcccbccadaaacadbdbcadbcdcbdaccbdaddddcbcaccbdddbbbabbcaacbbcabdcdcadbcbddddbabadbdaadbbaacdadaabaabbbbcadabcbcabaabcacdcbdbaacbdbdcbbbbbabbadcddbbdbbcbccadbbababccdbdabdccaccbddaabadbdbbdcabbabbdadbdcbcdbddabdabccddbdcdbaddacadbbbbadaadddadadbcbccbaaaccadadcbbbccacdadcbdccaaadacbdcccadbbdabcdccbbaadbdcaabcdbdddbaadddcabbbaacbccbbcccddbaaddbcdabdbdcaababdddbbcabdcbabcbaabbddcdcadcaccbaccdacccdaadaacaadbbbcbcbacccdadbaadbadcacadacacdabbbbbdbcdccadcdbdbcdbbdaacabbdacbcccddcbdadadddaabdcbcccacdbcdbcbbbadbcbacdcddbbabadcbadaaacadadaabddcabcccabdabdbdbabacddaaaccaaddbcbabbdbccbabbddadacadccbabbbdbbdcbcaadbaccbabddcdbddaabadbbabbcdcddbcaccababadcaadddcddbccbacbbacbaacadbababcacdddcdcccdaccddacbbadaaaabcabcbccadacddddbccbbabddbbaaaccbbccbaaabdadaabdcdddddbdbabddccddddaccdbdbbdacabdddcbccccdadbcbbadbdddbbcadabbacccaabaddbdbabbbaaacbbbbbbcdbcadddabdacbcaadabcdddcbbdaccdddbdabadbbbbacbdaacbbdacbcadaccabbdabdbdddcbbacdddddcbcdbdcadacaadcbddcbbacabddcacabacabaaabaccddcbbcdcddccbbbcbadcbdcbabcacccdacdcadddcddacbcdcaadcadbccbaacbdcbdabcbbdacdddcdbabbadbbbcbaabbdccbbadbbddbcbdbbddbccdbadbdabdbcbbbbbaadbabddbddddaaabdadddbdbccacbbddaaacdbdcbbcacdcccdcdcbdaacaabbcacacbcccbdbcdbccddddddccbbbcababcdcaaddbcbabadbbacaabcacbadadacdaaadbaddadddcabcacdbbccdcbcdcbddabcdacacbdadcdacdcccaccaccccaadbbcbdcaaadabbcdbadbbddadcabbdbddbcaadabcbdbddbbdbdcbddbbabbcdbbdccadbbadaacdccacabbccabdcdcdabcdddbacbaaacbcadbadccdadbaddaccbabaaabdcadccacbadababdcadccadddabbdcacbdcddabaadbabccaddbdcddbdbadbadbcabbcbbdcdadacbbbabcdbdcbccbbcabcbadadabdcadacbaccccaaadacadcdcdddbaacaababcbcbabbabdbabdaacddcddcaabccbdaddcdbabcdccaacbbbcdabadabbcaadcdcbcabbdaccccdadcdaccdddaabcdbbcaabbbddbabdbcbbbccbcaaccaccaccdddccbadaadaccdcacccadadddcaccaadbdaaacabbbadbbabadadabccbbaacacabaacaabaddcddcbdbacaaabcbaacdadcdaaabbabbcbacbdcccbcbacdcacdccaccacddaccddbcbadabcdbdddcaabcccdaccbcbdcbadddbabdbdadcbdbdbadcabbadabbaddbdcbbcacbccbcdaacbddbbbbcbaabdaccacccabcbcadbbadcbdadcccdddddacddaddaaabbdacabccaacabdcdccddacdcbcabdcdcdcbcadddbaabbbadbdaacbabdacbabcccbcccddbdaaddcddbdcaccdcaacbcbbbacdbbdbbcbdadcbcabbcdcdaabbbdcaacadddabcaacbdababdddadbdabacdabacbcbaddccbacabcabbccdcbaaccadacccdadbbcdbbcdcdcddcaacbbcdabdcdaaccbdabcbcdccbbcccddbbdccbbbddddcbadbbbcbbababcccdddbcdccbdaccabddadccdacbcbcbaccbddcbdcbbddabcbbbcdaccadbddabdcccccbbcaabdddaaaababbddcdaccdabcbabaccbbacaadaabdabddbbdabbaaccccaadcdbdcdccadcadaababbcbacdbaadbbdaaaacdcaadaccbdcdacdaaddcacbbbdadadabccdddacdcbdbcaadcccaaabdbcdddcccaadbddabcadcddbaccbdbcdbbcaddbaabbbbbbccdccddabcdbddcaddcdaccbabbcabbcadcddbabacadccdadbcbcdbdcccacbdbbabbddbcdcdbbaacacabcddbaaacadcacbcabbddbaacaacdcabbbbdbaabddccbdcdbbcbddbccbaccabcadcdbabbcaaddddabcdddbdabcbacbcaacbcdccddbaddcbdddcbbaaadbdddacdacabbcccaaddacaabdcddadbdadbbacbdaabacccadccdddddcbdcdbcdcddbacdbabaadbbacccaaadcdacbbdbbaacbddaacadadbdadbcdbabadcdcddbdbdadaadaabcdbbbcdcdaaabbabdcdacbbcacdaabbdcbdacbbccdadcdbaaccabbcaccdaaaaababcacccbdbbddacacdcaddbbadaadaaaadddaababccacbccabdaacbabcbcacadbadcccbbadaadcdcabcbbbbbadabaccccbdcbdbbbdcdbbdcbbcadbdbacdcbbadddbadadcbccbaadabbbbbbaccbabcaccbddadaddbabaaccdbddadbcacdbadbddcabaadadadcddacbbbddadcbdaadbbcacabbbabddcdbcadabacacdcdcaabddcabbbbaccbdddddaccccccdacddbdcadadbacdbbdddbbaababbddabdababccabcacbaadccacbbcbdbbbddbbcaaccaabcdbbdcbbcbddbdadcaddcadcbcdbccdaacaadbababbaaacdbccadbbbbcbbaacaadbdbcbabcaaddcdaadcadbccdbbcdbdcdacbcbdbaabacbabddcdcabcadbdccbacabbcbdabdbbbccdacbdbbadbbbcbdabacbccacccbbaabbadadbdacdcddbdbcadacbacbacdcdbdabbabbdacdcabddbacbaddcccdcbcdbdbbcdbbcadbdaabcbccddbcbbadbdcbbdcdabbbcbabaabadbaabbbbaadcbcaadbacbcccbadccdadadaacbcabddababdaaacabcbcddcaaadccacccdbaaccdcbadbaccaddabbdbadcacdccddcadaddaddcaddcbdaacadcbaddbbcaabbddbadabbbbacaaabcdcaadbcddacdbdbcdcdcabdbacaddbbdbcddadacbddacabadbaababdcdacaabadcdddbbaddacbbcdbdcacbdbacbdcdaaaaaaccadbcadacaddcadadbbbbdbadbadcbcbadcbcbdacbdcaadcccadcadaacbadbbbaccbadaacaababacbacddabdcadbdbccbbcddbccacabcddcdadabaccbcbcbdcaabcdcdbcdadccccaabdcdacddccdbcaaadaddccacbadcbbbcddbbdbcbaddabcdbbbababdcbcbcdcaabccdaccbbababaccaadcbcbbdabccdacacacbbbddacdabacbdcaccabdcccdbbadbddbadcababccdcdbbbcdcabdbdbbcacddbccdcacdbacbbcacccbdcbbcdbbbcbbbdcacacdbadbdabdbcabdddadaaddacddabaadababddbadaddbbcdcacbacdbbabacdbcaaddbdcdbbcacaaaadcbaacaacbdcbccbdbadcbddbadcdbaabbacdacdaddaddabcddcccdabdaddcddaaababddaadcbdbdbbbbdcdbacadabdbaabccaccbdcdabdbddcbbadadddbbcadadddaaababdbddacabccdcabdabbaddddccadcdbddcbaabcdbcbaaadadbbccbdbbaabbdaadddabbbadadccbcdbadddabdcbddabaacdadbbacbbccddadbcbacbdcacabccccacadbabacbabbbaacabdccadbcddcdbbdaadddddbddcbbacbdbacacbdccadbcabbbcaaabdcdacababadcdbbbbadbcdacabbbbdbdccaccacccdbcbbbabababdbdabbbcdaaaabcbdccbbcbcbbabcdaccabddcaacbacbdbdabbaabdcdddcadbaaadbadacadabcbbacdaaddadddabbbbadbdcddadccaabbbaaccadacacbacbcabcbcdcbcaddbabbaaaabbdbbbddddbcddbacccababcdcadccbcdcbbbbcccdaccdbbcdaaabdacabaaccabbaddaaddddccdcccddbaaccaccccdbbbacbccbacdbbddcbacaccadddcabbdcaadbbaacdbdabbbbccbbdbbdabdbddcbabdaacabdaadbcdccdcbbdcdcbbbbdbdbbbbcdbddbbadcbaccbdbdcdcddccdbdadbbdbbddcdacacabcddbabcacaabbccbddbbdababaabaaccaabcdababbdbccaccbcacbccdcbabcbddadabacdbdbadbbbdbcdcddcbbacbdcdcbaddcbaaadcdaddcacadbcaacbbcbdbabdcdacbcbadbabacdcdabdbacaacaabaadddacbddacdbbaddcadabdbdabddcdccacdbacbcbcdbdacbcccababababdcbdcbcddcdbdaaaccabbcccacccccddabdaaccadbbdbdddcacdacbdcccbdacdaadabbadabcbadcaabbdbacaadcdbabbaabdcbaadcccabddadbacdaaacbadcaddaabdcdaaccdddbdcacdcacbcbbdbcaccdcababdbcadbaadaddbcaadbbadcacbbbbbadbadccbbacaaccdbadcabaabdccaabcbbaaaccdadababdcdcbdbaccbcccddaacdddbdabcbdcbccdcbdbaacadabcbcdbabaadbdbcdcdcbcbcadaabccabbbcaabcbdaccbabaabcbbaddddaabbbaadbddabcdcabaccacaacbacbbadbabbacbacbbcabccadcaccccddbaaddcccaabddddacadabcbddcbccaacdacdadbcdbadcdabcccbbdcaabdaddcabbdddcaadbdcdbddccbdbccddcdacdcabdbdbdabbadbbdcbdcdacbddbdbadcaacbdcbdacdacabdbcdacaabacaaddbcdacbbcdbdcddadacbccddcccdccdabdaabcccabbdccadbcaddababbaaaaaadaaadbbcdaaddaacdcbbccabdacddbadaaaadbbbbcacaabacdaccdcbdaaddddadccaabbbaccbcabcbaddacabbabacdadcbcabbddcddcbdccbdbadddbbddbbcdbaabbbccdbbbbdaddbbddccdaadbcdcdadcadcdacbbacabdacbbadbcbdccdcdabdcabcbadadcdbbabdadbccdddbddbdcbdcddbcadcaadcadbabbcaacaddabcbcababbbddcaabccdbdadcdbacbdcdccbddcaddabadbdcacdbcdccbcdbbdbcdccbbbcdbddbbacbbcbbbaabdbcdcbbabcddcdcabccaadcbddbcaddcbdabcdccaddcccdaabaaddcbbcabdbacbcaaabacdbcaccacddbaabccddaacddbabbabcbdbcdccdadadbbccccbaddcaccbacdbbdcdaacdbbaadbcabbdacdabacbbbdbdaabcdaccbbbbabdcdbbddbbcddcccaabddbcbcddccadccacdadabacaddbdaadcaaacdcddddbdddadcbdcbadccdbddadbcdccdaaaacbaacddabdddbdbaccadcdbbaaaacabbcdcabcacdcacacdddccacdcdcddcaaabbbccccbdaadcadabdabaccadadacdccdbdcbacbadcddaddbbcbaacccbdaccddddadacacaccbbabdbdcddbcdcbdccdaaadbabbcdbddccaaabdabddbbbacccabdabaabbcccccbcbddababccccbddacdaddabbadcdbbaaaddaaaaddcccbdaabdcdcdabacabdbbacbcacdacadbcbcbbcadddcbcddaacbbbdaadadbaacadacbccbacddaaacdbddbcdbbcdacabbcbbcdcacaadabdbbaabbcbcabbbabcbbcacaddaacbccacdaaccccccdadcbaddcabaabdbdbcbadacdadbadddcabadbdcbdaaddaddabcdcbdadbddbcdacddbdcadbdbbadcdacacccadbaadcccbcdcccaadcbbbccabdbdadcccbacaddbcaaabacaccdccacbdaaddcbbcacccdadacdababdcccbcbabdadcaaddbbbacdacabccbcccddcabcbcabdbcacbbaacaacaaaacdabdacabdbabbcaacdaabbdbdacdcbabaadccddbadddbaabcbbabbbcbcacdadddcdaccbbdaaaaaaabdcbcaadabcbbaabaabddcdcaacdcdbbbdbdaabddbdccdbaacbbdbbbdbabdbbacadadacacacbcbabcbbddccabbacdcaacdbabbdacadbaaacbddcbdbccccbcbcddddabbdaacdadaacdbbbbbbcccbabcadbdcacdacbdabcdadccbbbdaaabcacabccccadabccbdbbbdbddbabcddacaadcbcbaaabbdddbdbccbdaaacccddddadddcddaacbcdbdcccadccabcbdcaccccbaabdcddbccddaaadbbbdccbddcbbcbaadbaadccabcaaaadbacdbbaabbbbdcdcaaaddcadabcdddbbcccaaabcbadaadababcbbbcabbbdbddcabcaadddbddbaacdabcaabcdbaaaaccdaccddcbcbdcbbcdcdccdbdbbaababcdbaabbadbacddcaaccabbcccbdcdadadabaacbacddadacdbadddcbcdaccddbcdbbbabdcbacddabbccbaacccabbcccaabcaddbbcdbaccadccddcdddbbdbcbcdadddadacacbcbbddbbcabbdabdbcbbcadadbabdcccadbbbadbabdadbbdaccaacaaccbdcbbbccadbaddbaaccddaccbabbdbccadbaabdddbacbcaacbcdabcdcdabacbcbddabdddadccbbcabdcbacbacbccabccdcdbbcdbadccddadabcdadcacaddddbcacbabcadbcbbcbcbbdccaccacabdaacdadcbcbbcadaddbbdacbdddccadccdabdbacccccabdcbbabcbaabaaabacacaabdaabccbaabbdcadaacdbaddbdadabdbdcbabcdababaccbabcdbacabadbcbbacdaccdaaabdaccbabaacbacabdbaabacccbaaaaacdcadbcbacdcccbddadcddbdaccccadbddabbbbbdaabcddadccababbddcbbbdadcdacdcacadadcaadcbdddacbadbacadadbaddabdadccbbdbcddabbbcdbaddcdbdadbddadaacbaabccaddbdbbaaacdcbaddddadbaaccabccadbbdccdcaaccbbdbaaddbbcaaaaccdbcbaaaacbbaadbbadabcbccdbddabacbcabaacdadaabbdddcdbacabcbdbccccdabababacdaacbdcabdbacbbcddacacbdcbabdabcbbddabbcdcccdddccbcdcaaddaacabbcbdaadadccaccddcdadcccbadaabdcacabbcbdbdbccadacbabcdaadaabcbacdcdddbcbcbcdaaaabcaccabdbbadcccccadaaadbbdbbdaadaccabbccadabacccdcdabaccabbabacaacdccababbcbadaacccbbcacadcccbaddaccbcccbdcdcabcdcadcdbbcdabcbabcabbbdadddbbddabcbbacaaaccbdbdbbadccdaddbcababaddbabcdcabccdbaabbaabadcabcaadcbddcdaccbccaaadbdcbaacbdbabbccccdacbdcbdaabbdaadcaaaadbdacccaacccbbacbadbdbbcaabbaabbbccbbaabdcdcdbbadcbbdbacccaddbcddacbcdadddabdcbabcdbddacacdaacadbbbccabddcdacaaaadaacbcabbddaacacbadcdbdccadbccccbdabdacaacdcdcbdddddbacaddadcbacdcbcddbadcdacdbddbdaccccaaacacabbdbdbbcbbccbbccdcbdbcaccddccadbcdacbadbdbcbbdbbabbbdacbaabababdadcbcbcbcccbcdbabcbdadccabbbcdaaaaadabcbbddccccdbcddcacdbcabcabbadcabbcbdaccbbdbaaaabbadddcbcbbccbbbaccdadadbbbbabdadbbcbdaddabdacdcbbdcdcaaabbccacadbbbdddddcbbddacbadacaacccaaddbdcbaaabaabdbdbdbddabdcbcddacadddadadcdcdccdacbaccbcabbbaaabccbbacaaadcdbacacdbdabdaddbddbdaabcadaacadcbacdbbbddcdaadadbbdcddaccccccdbdaddbadaaccdbdccbaaaddcdaadccbbdddacbbbddbccdddcbdcccabaabcddaabccdcbdbbbacddcababcaccbacacccdabbadaabdabdbdabcaddddbbdadaaaaaccaadddcabbbdadcbcdabcadccabbacacabbdbcdacbdcdbbbbbbdabdbbddbcacaddacccdaccdbacdbcbccbbddbbabccaccacbbabcddbabcaabcccadcaddbaacdbbcadbbbbabccccaddadabddabcdcaddcaacdcaabbcadcbbdbcdcacdbaccbbcddddbcccabddbaaaabacbdddabcaabdcdcdcbadddbbabdaacadcccbddaddaadbadadbcabbdaacdbcbcccdddbaabcaabbdddbcbbdbabbdcabccacbbbadbbdabbabcadcdcbcbbabdcabacbbadbccdadcbabbdbdaaaabcacaaacaadabcbbbcabbdadcabcacbaaccaacddabaddcabcbaaccabcddbbadabbdaacabcbacabdcabbabaddbcbdacddbaaaddcdbaaaacacdabccaabadbccccbbcdcacacbbccacaabbbaadccbabcacadbcbdabbbbddbadcdcdacdacbdddcadbaabddddbcdadaddbdbbbdabdaccbdbbaadddbdbbcabcabcddaccbcabaaaabddaabcdadcaadaaaabddaaabbdbbbaaadbdadcdaddacdcbacbdababadbdaccbdbbbbbbdcdaaabddcddbccddcadabcbccbdacdcbdbddbcbdacaddddddcabcbcbaddbbdcdbddbbccdaaacbaaabcbdddadbdcdacadbbdcacdbcdabcccaacbcbbddbbbdcdaaacdbadbdbccdaddbcbbccaacbbdcdadbdacdaccabacdbccbdbdbacccdabbdbbdbbaddbbbabcdbcdcbaaaabcdddddcacbbadbabaaaccbddaaadccddbbbbdabccdcdbccaabcdddbdadbdbddadadacacabbaccbaadcdabcaadddbadccbcbdcdddbaabdbbddaccbcbdbacadbdddbabdbdbcbcdbcabdbadaccbcdbbbadaacadcbcabcbdacbabcbaccbdaaabdaadbbcdddddbcaabacdbdabacadacdacaddcdaddaabcabacaabcacdbcbdaccbbdacbcddddcdcacadcbcaddadbacbdbcdabccbacdddaaaabcbdacaababbbadcdbdacadccddabbcabbbaddabacdaccbabbbcbcdcaddaddddaadcadccdcdbadcbcaddbbbbcaccaabaaadbcabdcbdaddcbcdcdbbddcdcacdbcbdcbabcbcaddddbaccbbbbbdadacdabbbdbadadbcdbabaaadacbdaaabcabaaddadbddbbaddaaabcaaabacaaabadcabddcbabcbbbcbdbdcbccbacdddcadabdbdddbdbbbbddabcacacdddabcddbadcaccabaaadbcddbccaabcdcabcbbacbbcbdbcdddbbdddbaabdccadadccaaacdcdaadaacbdccbaccbbbcabdbccdacddbaccdaabbaadabdbbcaadadbdabbdddcccccdacabdcbabbbbdcadbbbcabdbcdcdcbacacbbaadaccdbaccbdcbbacbaabcabbaddaacdacdcadcddcbbcccdabadaddcdcdbabdcdbbdbcbbacaabccddbdccbbccadddbdccdacaddddbbccaccbacdaacbdadcbbddbbddbbbddbbccdabcaabacbaaaabdddadbbbbbdcdbcaadcbacadaabbdcbdcbadbadacaccbddbabbbcaddabcbbbdcacdbcccabbadbcdcbcdddbcbdbcaccbbaabbcdaadcbcbcbcadccbdabdaadbbbdcadccabbbdadaddcdcbbabbdcacbbbacbaddaccccbacbdbddadacbbbbcdcadcccadcdaaabcddbabdaacacaccbbbdaabacccbbadbacaabdbadddcbdcdabdabcddaacdcbacabbabccdcbcbabbbdcbddaaacbcdbaadcabcacbdadbcdbdabbddbbdbbbabaabbcabddcdbbadccccbcdddaadabadcccacdbdcdbdacccbbabadbdbdccccdadabbddbabadbbdadcbddbbbbcaaabdcbadbabcbcbaabdababbaacbcbcdcaddacaabdcaddcadabdccbcbcaccbcbccbbbbdbcbcadbddcabbdbbbbaccccddddbcdcacdabbadcbaddaaddccdbcadbaacdcacdacdbddcdcbcbcdddbdaadabadbcababcdbabdcbdbbcadccbcdbadbcaabcabadddcdcbadcaabaabbbbaaaaadabbccadacabdcbdaadddbabccdaaddcbccbcbcdcaaabdaccacdadabbcdbaacbacdbdadbacbdadbcdccaaacdbadbcaabbaccbddbacbacdbaaddacbbcabccddcbaacadbaddadcbbddcbaccbddbabbaccabaddbaddbbcdbbabbaacdcdbddbabbcaddcdabdbdbdccdcdbaacbadaabcbcbdcaaadcbdddaacabacaccaacdadddccdacdcccdddbdaabbcbbaacdcdabdadacabccccbdbabdadacdbaacadcacccaacbdacbcdcaadaddbcdabcadbdcbcdbdddcdaccacbdcbbdbddbcaddcddcadadddaabacacdccbdbdaaddddbbdcaadacbcccacaaadbaabbcbcbdcbcacbdcdbbdcbdcccdbdcbccccbcccaacadcdadadcacdcbcaddcddaacababbccacbababdbdcddccdaccbcaacbdadcdcaddcacbdabcbbdcdadbaacacdaaaadcdcdbbbdddadacbcadbaabdadbcaadbdccdbbbaacdcbddababdaadcdcacaabbccccdcaaddaacaacddbddacbaddabaaabdbcdcaadcccaacabccabcbcddaaaaddaaaddaacbdddccdbdccabbddccdcbbdbdbddabcacbaaabddbcaadcbdbbbddcbddcdddbddbbbccaddabbacacdbadcaaddcdcdccbcdcdcaccbddcdaaacbabdbcabbbaadcaaabacbabbbacadddaddadbbaccddaaaabcbcdccaaccddadccbbdcaabbdddbcbcbaabbcaadbaacdbaddacdbacabcddcbdaabaabbdaccadcadbcdbccaadccddabcbddbddccbcdbbacbbbaddbccdbbabdbacdaaccbddccacbcdbdcdcdacdbdbbaaabaacadacbdaccccdbbcadbbcbdbcccdbcdcabbcbcbaddbbbbccbabbbcdbadcabdbdadbabdbbabbdacbbbbdacadacdbbadbddcbddbbdbacccbaacbbbbdccdddddbcbcbbaacdccdcaddbbdbabcdbbbadbdadbbcbaadbdbacadbdcddbbcddaaccccdaabadacdacdaddbacccccbdadcaccacdadacadcacdcdacbdbbdbbabbcacaccdddacaacbbdcbadaadbbcddacbcccadaccbabadbbacbcddcbadbaadcabbabdbbbbcaadbdcccdbbcdaabbbaaacbaddacdcdcaacbbcddcbdcacbbbadabdcaacabbabdddbccadbbdddbbcdaaabcccddadcbabbccbaabacadcdccadcdaacdaddbbddbdcdcaccacdaacdacadbaabdadcdcbaddccbcdaabaaddcdccdacacdcabdadbdbadababdccdcdaaccdddbaabaaadcabbbcdaadccacbbcbcabbbaccbadaabbaccdbaacdcabdabbdcabbbbcbdaccdcdcabbabddcbacbdddcabadbcbbcddcaaccccbcbbacaccdcddbdcbbababacbdababdbbcdadabadaaddcbdbcbcbbddccdcabaaddcddaaaacbbdabadcbdddaadbdaabdaadbbdbccddabadbbdcdcbcbbbdbcbcaaacdbadcacdccdacacbaadddcdacadacbabbaddbadcbadbdbcaddcacdcdaccabdadcbcaccccccbcacbbadcbddadaaacacbadbacacbcdcddccabbcaddddbdccaadbccbddabccacacacddcdcdddcadbbadddadcadcccaabaccbcabdcadabbdcdcdcbbccdabdccdbcacacbbccbadadcbddabacadbcccacddbadccbadcdccccaccabbcdbddbbdddbdbcbddcbcacbddcaaacddcdababcccacdccaddabaadaccbbbaccbbccdccdacadbadbbacaababdbbadcaaacbcaaadbadbdaabdbadddcdcbcdcdaccbcbcbbdcbbbddbdaabaccaadabcdabbddcdddccbbbadccbcccadbbaabbadabdbdbddcaaddbbacdcadabbbddaaabcacbdcbacbcbcabadbbdbbddaddaadbbdadacacdbadbdbbdbbcadbdbacbbbccababccdbcdcbbbdaccaacbabccdadcacdbbbbdcacadddacadbdddbbbcbbdcaacccbdaabaadbcabdddcabbbabbcccbcdacbcabddabadaccdadbbaddaccddadcabcdcabaabccbcabccdcabaaaaacbacadbadcbccadbbdadcaddacbddccaabcccacbcbddabbadbcbbbcaadbaaccdcbaaabdbdbcdaddaacdbacbddaacaddbdaadcbdcbacbababacbdccbddcaddbacabbdcccdcacacadbcccabbbcdbadcbccbdabdbabadbacbcbbbaacddaccdbabdcabcdcdbbcacabaacdbbbcbbdcadabcdcbdabbbbdbdcaacaaaabaaaabdbadbbaabacdadaadaabababadbcbabdaabdacdcdadcddaadadabcbcbaccbaadbbccdbdaaacbacbdadbadacbdcddadaadcbdddabdcddbaadabbcaabccccbbccadcaaabcbbdabdacdbadcabcbbbbddabcbaaaaccbdaddddabbdacadbcaaaccadddaabbdddadaaaababbcccadbbababcdcdddacccabcccdcabbadbbcdadabbdabcbbbaadbacbdddcdacccbdddbabacdaacdacadcabababddcddadbbcacaaaacaacbdabaddbcdcaacabdadddcacbcacbdcbaccbbbbbbacacadabcacdaccdbcdcbaddadcbaadcbbbaacbbacbccbcbacbbbcdabaadacbbcdcbbaccdcbdbbcbdaabaacccaddcacacbddaadbdbaadaccbddaacbcbcababacabddcbacccabaabbdccdaabcdbbcddcbdddcdbdbaacabbcacccccddddacdcabcbbdabbaaccbbdcdacbaccbdadcaccdadcbbcdbaacddbcbddbccdbdaabdaddcccbcbbbcbcccccabbddccbbabbbdbcaddacbbcbbbabccbbcaacbadbacadddbaaccbbcdabbcacbabbaabdbccbbaacccddcadaadddbabbdcbcacdbbbadaaaccdcdaabdccbcaadccadcccdcbbcccdddaacccbccbbaadbdccbcdddddbdadbcbdcadccaacadacaadbabadabdaaccacbdccdbdabdbcaccbacccbbdddcdacbbcdcdbcbcbcbddadacabbcabadcbbddddabddccacdbcbbaaabadbcbaadabbdbcdbdaccdcadcbbaddababaabaaccdddbbcbdddbdabadddaacddbcdbbbbaabaaacabaacabccdddcbbccdbacadaccbbdcbbbcacaacacccacdddaccbdabaaddbbcbabcacdacdbabbabbbaddcbdadbbdaabdbcaabcaacdbbbabccdcdcbdbccbababaddadcbdbacaadabcbcddcadcabbbcabddcdaccddbcaabadddcacdabadbdcacdabdbabcabbccbaccdadaaacbdcdbacccacccaacdbbdcdcdccabacccaabdbdddcddcddcacdacdcbcbabbbccddbcbbaccbaccaadaadbabbcaaacddcbdbbabcddcacbaaadccaccddbdbcaccddbadbbaabdbdaadaabacbdabaccbcabbcbbdcbcdcbccdbaadbadddbdbdbddbaacadaabbcbcdbabbdbcdcdccaabcbbbdddaccaabaadcacbbdbacacbcdabccaaabdcdabcdabcbdcbabdbaddcadabacabccdcaccacddbdcbddbdacdaabbbbccadbbdbdadaccccdadaacadbdaabcbdacbcbbbadaccdabacaaacccbccacbbcadcdadcbddaabbdccbcaadcccddcdddaaabcbcbaadaaaabdbcbabdababccbcddaccabbbcbddcbbadcbbdabbddcabccddaaadcbacbdacacbabbdbbbadbcabccbadabaaddaadbdbaabacbccbdbddadadcadaccbcaacacbabcdddcdbadabccaaddaaadbcdbccabbdbbbaccbaadccaaccadcaadcdbabbaccaacddddabdbcaacbaccdcbcacaddddacdcdabbcadddcaacddbabcdadbaddadbbccbcbddcddcdabccacababdbabbdbbddaacdcccddbcadaddcbbdcdbbcdadccccbbdaacddaacddccbbcbdaadbbacdbcdabccbccbdababdcccbacacacbccdccdcbdbbdbdbacbadadbacacaacbbcabbcadbaabaccadddaaaaddbbbcddcadcbdddccccbbbaddbaccadaadababbdbbbcbddbbbcbbcbacccddcbdbcbabaaccbcbaacddadddddabcdbbaadcacacbdcbcabbdadbbbadaabbdabddcbdcaaacbdcdbddbbabbacdaadbabadcbabdbbcccdbccdabcccbcccdaccabababccadacbbccadababbacdbdbabdddaabdacadadddbdbccccacbdabbccababaddcbcccaccbbdadabbcdadbaadbdacdaadbbbcbbaaabbadabcbadbacbbadcadddcdaaccbddbcdbbabdaacbcdcccdbbccbaccbbddcbaaadbbaabdaddadddbddaccbadcbcdadcdadacbbaadbaacccbcdbabccdbdabacacdddccacccddcdbacaccccdbabcddaddcccacbddaacbacbcbdddcbaadccdbbbddacabccabdcdbbdadcbabbadaabacdccdaabdbbbdddbbaadadabdcdddcbdbadbacaaaddbdabdadbbbcbbbccbcabdcbddbdaabcbbcaacdcaaadbabbccddaabcbbcbdaaaccacdccddbabbddbacabaabdddbcbddabbbadbddcdbabbbadccddabdcbbddcbddcddabdcccdbaabaacacaabdaabccccbcdddcddbcacdbcbddddacbcbdddabbcbcbcbddbdbbcbaabbbdddaaccadaadabdbbccddaaddcabcbcbcbcdcaaadcabdccdcdadaacaadcaabccdccbddacbabaadbdddddacbccdbccddabdbcccdcaccbdbcacbcbdabacacaacbcdacdcbabbdcacbbddabbbabdbdccdacbcbacdaaaabcbcbbbccadddabbbaaabdbbdbaaaddabdbcaaababcdbcdbccdbbbcdaabaabbadabdacacbbbdacccbddbaacbacbaadcdccbbddacbabdccadaabdaadcadabcaaaacccbdcdcbaccbcaddddcaabadbadaacbcadcadaccbcbdabbdbcacbdacdacdbbdcccdbacaacdbcdabbbbbbabccdadcccaadddbbddcdccdcdcdaadbdabaacaaaabacdddbdbbaadacadddbadddbbaccbcbbacddbdcbaccbdaddcdccdbbbdddaccdaadddadabdcdaabccbbbaaccadbbbdacbdacabbbcdbadacaccccbcdbaadcababcbdaadcbdbcabaabdaadddabcbacacdbcbadbdaabdcaaddabdaddadbacbacbbbcbcccbdbbdadcdabccdaabdccabdcbcbbbbadbbcaaacaabccacdbaacddcdccdaccabddbbbbabaaddbbabbdcbbbddaccbcccdbadbacaaddbbdddccbcccdcaacdadbcddbadbcdddbcbcadbcaaddcdcbbadccccbccadcacdddcdcabaaaadabdbaddaaabaaabaadcbbcdddcacdabbbadddcaadbbcbdbddadcdabaddcacdcdabbbbcabbbbbbbccdadcccacbaccbcabcabbbdbdbbccaabdcdbcbbcdcabcdbbbbbaaacacbbacadbadcacbcaadbdcbddadadcaaccabdacdcabcbadbccbabaabcbcbdddacdadddabbadcdbbcdbacabcbbccabcadabadaadcdacdbabdbccdbccdaddabddcbcbdabdababbdaabdbdddcaddcdccaabbbbacdcacbcdabbbcddbcbabdadcabaddccabbcdcbaabccdcdacbcbcdddaacbbbcaddacacaabbcdaaaddbadbccddddadbacdaaddbcdbabcbbbdcdacabbcdcccacbbaaadccdbbdaacddcddabbadaadadbacbcdabacbddacccdbbcabbadadbaccbadcdaabdbdbaaaaadbcbdbcbdcbabadadaadcacabddabbbbaccdcaccddddccabbdddbbabaaddbaccdbcbabbddbababdbaaacacaddcbddabdbbbbaddadccaabcbcdddbaacaabcbabacdddddbcdabdccdcdbdbdbbbcdcaccdccadabaacccabaaabdbbccdbdacaababbddbbabbadcdbbcabaccccabbabacbdddbdddabbdcbddbbcadcdbcccddddcdabdbadadacadadbababcabbcabcabdabcadbcddbadccacdcdbcaaaacdaacccdbccaabacbaccabcacacbdbcbadadcdcccbbabddadacbddbdcdcabcbbaaadaccccbdcacbdadadabdccbadcddcdcdddcdaaaaddccdcdcdbaaabddcabacdccbdadabbaadcbcbaddcbccaadcbadcddbddbdccdbadccccdcdbdaaddcbbacbdaacbbdababcdacacaaaddaaaaadbbccabaabbcbaaadccadbcadbbcdbaabcbdbdbdcbcbabddababcccdbabbaabcddbbbdbdddbcdbdcaadbbbbadaccbabaadacdadbdaccbbdcbababbbbdacdbcdbcbbcccbcdacadaacbbaaaddadadcbdddabdbbcabdbacdcddbccadaaadbcbdddccdcadbdadbcbcddcccabcbbbbdaaddcdcdacdccbdacdbbabaccaadbbbadbbaabaddbcdccdbbddbdbbbabdbaacccbdccccbbaabdddddadbcbdaababbcddcabdcbdbdadbdacacdabdbdbdbaadccbccaaabccbcbdddcadaaaddcdcbabbdbdbddbdabadadbadbdabababbbcdaccababcbdbcbcaabacbdcdccbccccdaacaccbcadacdcddaaaabcddbddcdaabbdabbdadbabacdccaaaadababbbadadabcaadbcacdcdddbacbbdccabdbccddabadddcacbdadaabcbcccddbccbcabbcbbabbccacaacabaadaaddbcdbcdcadacdadcbabaddcbdaccbbccbcbdbbacaaadacdaccadaaddaddbdaadbadcaacbabdddccadabcabdcdbabcadcdddbcdbdabcdbacabdaddabdacdbdabbbbccbdbbbcbbdcabcbccacddbddbbbdbcacaccbcababaaccbbcdadccbdcbcbaddcddcabbbbbcdccabcacccbcdbaaabbbddabdcabbadddbacdccdbcddaddddccdddbcdcbdacddadbccddabcccacdcbdadccacdbcbaddddadacadababdabdacabbdcdbdcdbdbbdabacdabbabacdacaadcdbcabdadcbcaaccdcddbdcacaaacdcbccacdaddddccddaaacacccabcdddbaabbdbdbdcbaaaaaabdabcababdddbdbbcddcddadabdccababbbbcdacadccdbaaccbbbbdddaaabbadcbbdcdbdadcaabaadacdddadbddbcdadccaadbbccbbbadcbcaddbddcaaddbaddbacbcbaddbaadcbccccdbdcaacadadcbdbcbdbbbadaabbddadbdadccacbabadcbbaddbbcaadacbaadadbacbdbbbbbabbdccdcdcacbaacdbddcdbdbcbdbbabccacdcbbcabacabdaaadcdbaadbcabdbdbbacacbbaabcadcccdacbdbaadccbbcddacbabbaccababcbbddbabcdbcbccbaabcddbcaaccddccacbbabccaadbccbcacdacbbdcababaccbdaccccdcdbccbabddccdaabbaaaddbadbcbadaaaacaadadccaaccadcbacacdddbdcbbcabcaaccaabaabbdaaabacbcadcaddcacabbdbcbbbabbadbdadbacbddcdcbcddddadcdbdcbabdcabbcbcadcdaadacadaacbdddadcddadcbcdbcacaccccdbbbcdcadbdaabcddbcdcccaadbdcbdbaabdbbcdccabdaaaadcdddacababdbccacaabacacaaccdaadbcacaadbcacdcdacbdacddbbdabcbabdaddcaacdadddcdbadacbcadaabbbcbacdbbdabddabcaddbcabcdbcbbdddcbdadacbccbbbdacdccbccadddcaaccacbddbcdcbddaabccdcaacbbddcdcbbcaccddbccccacadaaabcccbcdccabaacaddadddbaacdbbddbbcdbacbdaaccccabadbbddbcddddbabddccdaabadddaabccdbcacbdbadbabbcbdbbdbccdbdacdcdadbbadbbcccdcbbdcccabbbdbcbdbacccbabcbdcaacbbaccababbddcbbdbcbccdbbbbbccabcbcdadddaaddbdacadcbbdbadaabadbbbcbbdcbacbaabcbadbabbaddbdcdcbdbbdcacdbdbacbabdaaaddcaabaddddacacbccbbccbddbcbbadabbccbccbbabbcccbbdbacdbdddbdbaacaacccbdddadbccabddbdbddaabacabbbcbdbccaabdcaacbaadababdbddabcadacacbbdbddcadcabbdddabccacdbcddbcbcaaadbaadabaccdcabbdbdccbcccbdadbcacacdabcbabaddcbacbacdcdaaadbabdadaabdbbdadddbccaccdccdacacbaaadcbddbcdbdbcdaddacdcbbbaaacdbddaadacdabdaabbdbbddacaaaacccbdaccbacbaacdbdbabcdadcccddcacbddcadbccdbbcdbdbabddadcdccbccdaaacbbdccdabbdbadbabbbabdabaacabddbcadbbbbbdacadabdabdadcbaacbdddbabbabcadbcbbdbcdbcdaaddaaaddbcbbadbccdbdadbbdccbbddbcdcabccbcbabcaaddbabcadadbbdbbcdcdddbddcdadabdcdccbdddacacbcccccbcaabdaddbddbdbcdcabbccccacbdcbddbddccbddaacbbabadadccbcdaacccccbcbbadcbccadaacbdabbabdaacbaabbccddacbaddbbdddadabddbabcddacdbbcdadcdadaddcccbddbaacbbdcaaadbccdbdcbbcadbbdbaddacdcbdddadacdbcaddddccbbbaddacdcccbacadcbbdabdbabbdacdcacabbcbaaacdcaccdaaadbdacbadaddabbacaadcbbccbbaaacdadbbacbbaaaababbacdabdcadcdcaaccdbdddcdbcadbcbccbdaaaaacbacbacddadabaadcaacabbdbdaccbddbaadddacccdacacdcdbdccabcbacdacacdbabaadadcbddcdadccacddbcbddbcadbbbabbccaadaadbbdddbcaaacaddddcaadcdacccbcbcaaadacddaadbddcdbcdaccdddcbcadbcabbbacdbdbddcabdbbacbaacdbcdacccbadbbacddcccaddacdbbccdaabaccbbbadaacbabdbcaccdbabcabddddadcbdabbcaacbaaadcbadcbbdbdabbcccdaccaaddccbbdcadbdaadccadbcaccdccbcbcddadddddacaddccadaadaaaaaadbcccdddcacadbbabbcddbabcdcdccbbdcaacacabadbcbbdbccbcaddbacadaccbdbbcdaaabbabddcbcdcacdddcabacbbdcbbcdddadadbaabcabcbccabcbadaacdacddbdcbdbacddcdbdacacdaadcdcbcbdbbabbbdacdacadcacdbaccbccbbddccdbcdaabbdadadcddaddbccdcbaddbbcddadcbcbddbccbabdbacbbaaaadcdacbaaddadacddbdddacccddaaddbccadbdcadcacdbcabbddccbcbdcadaccabbcacadddadbbcbbaabacdbdbacbddadcbaadcbbabcbbbddaabbddbdbacdaaaacccaaddccdcadabccbdddabcabcdabbaadabacaaaabccdbdcbdbcabaacbdcdabcdcbdbcdddcadddccaccbabababbcdbcabadbabaabacbbdccabbadcddaaacccacddbbadabbbadabcaccaabddabdabbaddcbdcababdadaccdababbadbbccabdadbdcabaaaabbcdadbdbdcbdabbbbddbabdaaccbaaacdadcbdabbaaddbdabbcbadababaabcacaabcddbbcaadbddcbcbbadacaddcdcaacdbbbdacaacbababadbcdcabcdadaabdbadbcdabcbcbdbbdcbacaabddbcadbdadbbaddcbbadcddccdcddccddcaabbdbaadbddbaaadacccaaddaabccadbcbcccadbdabcacababdcaaaadbabbadcadcbcaccbbcbcabcaaadadddadaabcdcbbbabadbdbacdcccdbcdabdcdccadcabdacbdadaddaaacdbbcbbdddaaacdddcadaaccacdcccabbcbddbbbddacdbbccdbddbcccdcdcacbcdbcaaacccddbccaccdbcbaadaabadacacdcbcdcbabdbcbbcdccbccdbccdacdadbbdcdbcbdadbbaccbababcccdbadaccccbdacbddbabacdcdbbcbbacdaacadaccdbaccdcbbccaccabdccdddaadddcaaacddbabddbdccbdacddadbccabaabdaccbbcadcbccaddcbbccacabacaddcccdbbccbadbabaacdcaabdcbcbddbbacbbadcbbadaddaaabbabaadbaadcdccbcddcaddcbccccbbdabaadbdddabadacdbbbbaadddacaccadbacbccacdcacabadcdcadbaadaacdbbcadaaabaacccccdbcadcccaabdcdcaaacaddadbadaadbcaadabcddbadddbdcaacabbdcddadcbacabccabcdcdabaabbcccababddcabdbacabcacbdbddaadddabcababbbabbdbbccaaddcbccabccbcdbbbabadcdcdbabbdbcbcdbcbaaabcadaaddcabbbcaabdacdcabbdcddaddcacbccabddcbbcbdaddbcdbdcdbadbdcadbbdbddcdcadbbcdcdbacbbdccdabaabdcdacbbcaacabbdbcddabbdcabbbdcbccbcbabcadccacacabccdcddcbaabaacdddadddacabacaabdaabbddbddcdcdacacadccdcdcdbbcccadcdcbbdaabbaadcadacbdaccacbbacbbbababbcaddcbccdbddacaabccbcdbdaacbdbabaaadbbbbbabadcbbddaaddcababccadbdbccaccbdcaaacacbcdacdcaddbaddcdaaacbbcacdaabdcdbbbaccddabacaddddadccdccbcbbadacddddbdacbcdadabacbaabaadacbcbbacbbdcabcbdbcdacdbcccddbadadbdcbacdcbdaccccccbdbcbababcaaccdadddccdbacddaddddbadaaaaadbdbcacadbaaabcdbabcacdcdbacdcbaccbddabbccbcbcacbbccdbdcaccaddbbaaccbaccacdcadcdadbdadabdadccdccdabbdbacdddddcdbdcdadcaadccacdccddaacbcdccbddabddaabaccacbdddacbcddccdbbbacdabbddbbbddbccbcabbccbbaabbadbbbdcbbcbcdaccdcddcababaaccdacbdccbddcdabccbdcadcbabdabaacabddacccccadbcbcaadaaacddadbcdddbcbbdcdcdcdcacbbcdbacdabccadbdaabaabddbbcbbaddadbccdbcbcaaabddbdbdbcdabdadaacabbabbbabccacaaacdcddacdcdbbacdaddaaabdabbadabacaddbbbdbabddddadccbddaaacabbdccbdaddaddcbdbcabbdabdcbdadbdddadccbddbbabcbadbcbdcacdcabcbdcbcddaddaabcdacbccddcddacccacabdcdcacabddadaaabacbabdadddabdcbddcbaaadbdcdcddabdaadcdbbdbcdcabaccadddadccbddacaabbacabbbaddcdaaddbadddbdadbaabdacaddaabbbadbbcddaadadaaccbbcdcdbdadcccbbccbcacaccaabdaacbaddabbcaaaaadbacaaaccbbcbbbcdcbacbbbddddabaabccabbbdcdbacccccaadbabcdacbddacdbccdacbadbcddabdabcacbdacdabdcccabadbabaacdddaabcaadcadddadbbbcdbdccbbbbbbcdbcdadbcbaccdbbdabcaddaaadccabbdcdbdbccadcdddcabddccadccbccdbaccbdbccbcaccbdcacccdbabcbbcbbaadcacccbdcbabcbadacdbbddababacaaccaccadccdbaddaadaadcbccdcbdbbcbbaaccacaaacddcdacbcaddcaabcaccaaadacaabcbdddcacacbddcdbbaaadbccdcbcbabaabadabaaabbbdcdbbbaaadabacdacacaabdababaccbadababdaabdaacacacadbadacadbadcdaacccdbccbdbaaaaabbbdbabdcaddacdddaacaccbcacbbddabcadadbdabcdacdbdbdbcbdbccbababdcacbbaabdadcdabcdababcaadacddbaabddcdcdacaabcdabbaadacadddbdaddbbbadbcdcacdbcaabbadacadadbadddbaccdbdadbdcdbcdadbccddadadbdbccbbbbddcbacadddcccdcccddbabbcaddaccbaabdcacabaacbbcacbbaabacadaabcbbdddabbccaccabddcddcdcadaadaccdbbbccbabbcdbbdaadbccdbadbddacbcdcbcdcbaddcbbddbabcccbcdaaaacbbccdabcabaadbdadacdccdbdcbbdadadadbccdcdacadacdbccddddccaadabdcbcadbdbacabcadbcbabbadcbbaadbcdbabcdcbaddbcacdbcabddacbbddbcadcbbccdabacbcabcbcbacadbcdddcbcdbbbcdddddcdccadbcdcaaddbddcbadddbbadbababbaccdccadddbaccbbababbacbcabaaadccddaddbbcbabadcadcadbbdbbddbcdabddbaaddaccabbcbdbbdcaaadadbadbcbabacaaadbdadaacaddcdcbbabdcbbaccbabcddbabaabacbbdcdcddaddcdcadcbddcaaddabaacbbcbdcddadaacdacddbcdbdcbacadbbddccabddcdabacabaadcadacbdccdccabcbdcddbabbccaababcddaacbcccddbdcdaadccbbbbddbbbadcbcbddbdbbbbddabdadbcaacdabcbbbdabadbdadccdbbbbadacccaadabcbbaacbcbbbaaaacadbabdcabbddacdccacbaabbccdccabbbaaabbaacbbdbdbbcdcdbcadcdccbababaacacdbbaadbacdcdbdacbcabbcccbcabdacacbbaacadbbbbccdcccabdcccbcbccacdcdcdcccbacabaadcaccbbddccadcadcbabbcacdacdcdbcaabadcbcbdcdcdbadcdbdcddcacbddabdcdbdbdadddbdacbcbdaadacdacabbdcbaabcddbccddacadbdcbbbaaadbaabdcbbacccbbbbcbabcabccbcacabddaaadccdccaacdbbaababcbcabbbccddabadabddbbbcddacaacdababdbaccdbcbcbcacbdcbbcbccbababaaccdccacabcdcdaacbadbbbabbbacccbcdbddcdaccbbcbddcababcddaabccdcdbdabbdcdbadcbaccdcaccbcccaadccabddadcbccccababcdcbddccbddcbccbcbdaaabcdcacbcabbbccbddbaaadaaacaabaddabcabaadbbdadaacddabaddbdabdaddaabbaaaaaadbacccacadbbbcddddababddccdbdacbaaaddacacbdccbaadbbdaaacaccdaaccbcaccdacdbabaabbbabcdddbbbbcddcaccddcbdbdaaccdcdcdacacadccbddcadadabdaccaaaadcddadaaddadcacbbcadacbdcacbbddaccbabbadacaabbbaddcabaaccddcbcdcaaaadabbdabaddcbababbcbaadddbcbaccdaacbcdacabddccdbbcdcddbdcacccbbccbbbaacacabcdbcdccdabaaaaaadccbabacaaccbcacdbbaabdcccadcdabbbcdddbdbacbcbccbcccaabadcbadddccccacaddcbabdadaccdaabdbbcadababbbadddaabacdccacddabdcdddabdabacbdcbbdaddcdbbbddadddcaacbaccbbdbcddadbaccbaacbdbdaaccabddaccacbdaddbdccbabbcadbdddabdaacbdbcdababbdbdbcabaaaaddcdbcbaaaccbbacadbccddcbdbccbdaadbacdddbabbddbacadbdabcaccbcadabdcabcbdadccbcbabbaadcaabbacacacddbdbddbbdcccdccbadcadaaccaccbccbacacababbccabcddcaabcbaadbbcadcbaabdcdadcdddbbcccacdcdababcdabdccabdcbabcdadccccccaddddbccdbaabcccddcbbacdbaaadbdbdcbcddaacbadcdbdbaadaadcdcbdcacbddaaacdcbaccdbddaacaabcadbaddbdcadbbbbdaadabbdcaddaddcaaadabcbcbccccacdcacdacdbcddbdddbabadadabbbcdabaadcbacbacbaaaaddbbdadcaaaabbccbadbcbbbaccabaacdccdcddadbadbabbdddcdadbadbadcbaccbbaacbcdbabadddbcaaabdbbdabbbbcbcabbccadacaddbdccbbaaaabadddcdbbadabddaddaacbcacccdcdcdabcdabadcdddcaacbdaccacccbbcddbbcbccbabbacbddbbdcdacbdacddcddadadacccddaaccbbbccaaabdaadacaaccddddcacbdaacaaadababbcccadbadbbddbcbcacdbacaadacadaabbacbbaddabbbdbcdbaadbbddbdbaaacaababdadcbacdcdabdbdbcddbabbadadcdbacdbaaadbadcacbaacbdccdcadbcddcbbaaaabdddabdadbbadccbbbbbcacbddcaddcdaddcdaacddacbadddbdbdaabbdbababdaacbcabaadcbbaaadbabaabdcadabdabaaaaacacdcdcdabdabbabaabbdaacdcdcdddaddbbdbcbaadbdcadaacabacdbdddcbcdaccadaadaaabdcabdbcaadcdbdccdbbccdacddddcdbdabbacaccdbabccaacadddcbadaacbbaddbaadbbadbbdcdabaaaddccdbdbddacbcabddacbbadccdbcbdccbbacddbdbabbdadaddddadacabddbcaadcbaaaadacdbbbadbbbaccbcdcaddcaaabaccdacbcaaabdbacaadabbadcdbadccccaaacccbbcbabdacadddbadaddcaaaabdaaacabdbbcddbcdbbbcbdcbabdbcadcddbdbabcdddaddacbadbabdbbccabddcadbcadbaabdadbacabbbbbbcddbbadbdabdbdaddcabcacddaadcddccacadbaacadcccbddabbcbbadccccbbdcddddadbccbddacadbbbadbbdcbbdbdcaacddaacdcbabccdbcdcadbacdacbabcccbbacadcbbdbdacdbcbbbbabbaccdacdbbddddabcdbdcdbcccadcdcaaadacabcabbdcdbcbdccbcbaacbcadddacddacddccabdcbbbddbcdddbcabaddccbaaddcabaaaabbddcbaadbccbddcacbcdccadcddbcdddbaaacbddaabacbdcdadbbdbabccdbddddacdbdbdacbcbdaabaccccabbcbaabbaaabcbcbaaabdbbadabbabadbcbbbcbbbadcbbdaabaacbcdadcaaaaacadbbdcdbdaddaaadaabbccabdadadbbcbaabdccdccbcdbbdcaadadbccbdbdacbdcbbbadcbbbcdaaaaabcaaccabbbdddcbcbcddbabdbcccaacbdacadbabbccdcccdaccbdbcbadbaaaccbcabcdadbacbdabcaacabbabaddacacccacbdabdcbabdbddcadacaacccdbdcbbabbdbabdabdbdaabcbbbdcbaabcbbadaacccaadddacdbbdabbdaabdabababbadbcbcbadbcbbccbbaabbcdaccbaaaadcbcadadcbcccdcbcdaaddcbcadcaccbbccaaacbbadbcddaddabcacadacadddccbcacccdbbaccbdcdbdbbdcbcadabdcdbccddcacbbacbbaaadbadacdaabcccbdbbddaaaddcbaccabbadadddbcdadaaabcccbaabbadccaacbabdadbddbcaadacaabcdccbdbdcababddccaddbadbcdabbaaaacbdbdcdbcdababbbdacbdcbccdbadbaacbabdaaaabadaacbcadccccdadddddcabbabccddbbbbbaddbcbbccadabdbbbddcccbccbadabcdbbbaaabaaaacaacbdbbbbbacdaacbdbdbaaabacacaddabcdccadbaddbabdaacbaabcdaadadbdcaacabcaabaacbdacbbacbacbddccccbcccdaacadbacdaaabcbdbbaadddbbbcbcbaacdbcbacdaaadbabbcdcdbabbdccccbccabadbbddaaabcbdbcabcbbaaddcbbacabcabbcbdbbabbadbbcdcbddbabcacbcccacacabcbcbccabcbcaadddddaadccdadbbcabaaabbcbccbcbbcabcdabbbddcdccaccabccdbcacbaccbcaddadcdccbbccdbaadbabbddcaddddbbaadbcbcdbdaabcacdcbdcccbabacbaccadbcdcaccabcbbddcccddabbbadacadaadddaccabcdadabbadcddabddbccddadabcdbadaacadccadcbcdaabcbbdacaaabbcacaacbdaaacaacadbbcbacacbcbdaacbadacdbdbadabacadaababdacbbccdcccdabdbcadaacdddccdbdcbcbbcbadacaaacdaacacadbdbcadadbdbbbadbbccbcbccbaabcdbdbdadbccabbcbbccbcbccaadbcbbbbcacdbabbbacbdbdcabadccbbddabcddaabcaddcadccaaccdcccdbbdbaaadbcbadddabbdbbadabdbccacabadbcccbbbdadcbabaacbbadbdcaddbbdbcdbbbbdaadccbaaabaabbababadacbbbadcbdddadaabcadddddaadddaaaacdcccaccbbcbdaddccddbabccbbacadddcdbcddabcaaddadbbbdccddcabadcdbcbbadccccabcaacabbaabccccacbcaccbdcabdbadcbdbbaadaaabdcccbdacddaaabdbbbbddbbbbccabdbdaaadbadcdacbdadddddbddaccddaaadcddcbdcccccdbabdadccbccbdcbdbccdacccaaabdcacdbcaabbadaaddccbddcacdabaacbddbaabdbbcaadadccdbdccacbddbccddbccdbbccbaddccbaccbbddcbcbdbddcacacdcbcbccadabcabdabbccdcbdbaaabccdcadbbbcabcccdaaaccbbcdccaaabacbaddadabaadbdbcdcccccdaabdaddbadbcadcbbabacaddcccdabacdbcadacdbcaddabcdaabaaccbdacabdaacbcbbadbddbadbdcdadbdabbdcacabdbcdabdbadbdddacdabdacacdcdcaddbaccbcccbaccadcadabbadccacaabddccbddbbcccbacaaddadadddccbaaddabacbbdddcbddaadcdcddabbbaccbdaacdacdaaadcbdbdbbdbdccccaaddbddcdabddabbcabacadcbaaabbdacadcabbacbabbbbbbcbbadbbdadadacaaabdadbcacadcdbacabcacbcadcaccabccccbbbcbcccadbadaaacdbdcbaadacadbbaccdddadaaacabbaacabbadcaaabcadabacbdcddcccbabcaadadaaaabcdbbdabddcbbbccddcbaddcdacdcdaaadabcddabbaccaddacdbbbbbabaaccddbdddadacdddbaddadbdcdcbdadbcdbcbcdccbbbccadcdcdcbbaaabdddaabaabdabdababdabcbbcadddcbcbbbcaccbdaacadcacaccbadddcdcccabdaaacaadadbbddadcadcdcacbbabddbcbbbdcabaccadccadbcdabccbddbadbcadcdcababdcbdacdcbdbbddacaddcacbccadbabbbdcadbdcadaddccddabccbcbdcddbacacdabaaaccbbcabcabbbabbdababbccacddaddadbadddddbdddadaabaaabbddbabbaabcaddbababcbacbaccddbccbbbabaccdcdabcdbcddbddbaccddacbccbbddcabdddbbdbbdadaaacbdabbdadcaddcbbddaabbbbddccbaddcbbbbbdccddccccbddaacdcdabcccddbabbbccdadbbddcbdabdccbbdbcadabaacdcacdcdaabbbdbadaddbacddbbdacaddcbdbbddacbaadcbbcaacaabaddaaddaadcdbdbcabdddcdcbaccdbdabbcaccbbdaabdcdabadaccbaababaddbbccdcacddbacadbcbaddaabcbccdadcabcaddbbaabbbbccddbaddbcbdadddccaabddcdcdaddccccbcabaadabcabdccdaaaaccadbdbdabcaadbdccddddbdcdacabaabdbdacacdddaccabdcaadaccadcaacccbdaacbbdacabbacadcbadbccabdbddaaddbcbdcdbcabadaadaabcbbcabdcadcbbcddccccbbcccddbdcaccabacacdbdabbdaadbdbadcddcaaddcadcabcdacbddabcbcdbabccbdcdadabcabcadabcabbccaacccbddacadaadaddcaddbdbbadaabddcdbbbddcadcddacabccdbbbddacbdaddcbcbacdcbabcdbabbabcbacccbcabaacbdcacabcddddbdacdaabbabdbcbdcbbbbcccccadacdbaacbabcbcdacaddabddadbdaddcabbddcdddabaaccdbcbcbdbacadabdaacdcabacadbbdabdadbbbbdcdcbabcddcdbbbbdbbadaccdcadaaabbacaccacdbbcddbaddbbbbacbaaadcdbacdcaaddacbdcadcdaaccacbacabcbdccabcdddadaccccbbcbbbbdacddbccadbdcbbcccdcbddcccdcccccbdcabdbcdcccaacdddaabbbcdbddcdaaccddddbbbdbdacbddcbcbbcdbbcddbccdddabbbbbcbacddacddabdcaddcacadcaddbcbadcaccccbbbabcbacdbbcbdaabbbccabdaccbbcbcdabdddbcddabaadbabaaadabdbbbaddcbcdabcdabdabbaacabcaaccddbaadbabbbabaaccdcdcdcaccdacbdbcdbbcbadcbcccbbadccbbbacddddcaaddbcbccabcdaabcabdbaaddcdccdbcbddcabaddccbbbbcdbbdcccabbddaadddddddacacbdddadadbdacdbcbaddadaaacddacccddacbbdbbddadbcdababbaccabbcbddcacccdabbbdbadacabccaaccdacabccccddbcccdcdcabbadabbbadcaddddcbdddacadbcabdcacabbbabdbdcdbaaccdbcababbbbbaacddcabbbaccbcbbaacdaabcdbcbcaacadcccbbddaaaaacadaacabbcaabddbaaaadccababdbabcbaccadbcdbadbbdacababdacbdaacbdbbdcabcdcacbbccdcddbcccbbdacbdbbdbcdaabbacadabcadaddbacabaddcdacdbcbbdaccbbbccabdbbdcdddbcdbadbadcdcbcadcaddbbbdbdcbbbaadbadbaddbbcaaccabddcbdbacddcdbabdddccdcbddcdaccaddbdaabdcbcccacdddbadccbdbcbbaadacaacbcdbcddcddcdadbbbcdbbadcbabccdbcdbdbcbdbbcdbaccacadbaabbddabcaacbddcdcddbccbabcddacdcabccaacbacbabacacbabdaacabbdababbccbadcacacccbdbbcddbcaacbaabaddcdacbdacbcbcbbcccdbbcbddbadabddbbdbadbdcdbdbdbdaaabcacbbdccabcdccbadacbcbaadbdbcdacabdbbacbcbababbdcbacdababaadaadbdcabdbabddbdbbcbddbcaaaccabcbcbaaabbddabaaacadccbbddbdbccbcbdaaabddaadbacaacaacacaabaddacdbdcdcadcadccccccbcaadcaddcacdbdbcbcbbbbbcabdacdaabbdbbbbaaddccadbbcbdbbbdcabadadbcddaaccbbcbcabbdddbaaaacbddcdccbaaaddbbdabddabacbcabddbdccccaababdbdaaaabcbdcaabbdbbdcddcadccdbdccccaddaaccbbbbdcacddadbbddddbbbcccdaccbaddabcdbdacabbdbadaccacbccbabbbaabbcacccaabadbcadcdcaababdabadbbbbccabbbbcdaaabddddcdbabbdddcbacacacccbacccacbbabbbaadaaadabdaaddddcbabacbadadbcbbadcaacdbaacbacbaabdccccbcbcdbdabcdabadcbbdaacbcbadddaddcbccabaddcdddabbaacbdcbddababdbcbaaabcddcadddcbaacabbdbbbbcccbcdcbbdbcbddcaadaabcccaaadbcbdcdbcabaccbbaadabdaacbdacccbaadadadabacabcbcbbdbbaadadaabdabbaacdacdbcbadbbabbabaabadbcababdadbdccbdcdacabdadaacababbabcccadddcccacbdaacacabcccadbaccdddbaccbabbdcaaaccdadbbaddacacdbcdadbcbacaabadcaaccaacdddaacaabacbaccbdddbdbddbddbadbcabbdabcbadabcbbdaaaaadbbbcbababcbabbbacbbcccabaadbacbbaabacaddbdcbccbbbacbcdcbdbdcdacbbaddcdaadccbadcbdadaacbacbcddbccaccaadddadadcdcdbacdccbaddcaacbdddcddbabbbdbddcbaabdadbcaabdadbabacdcbaaabddccdabbbacacdccddabccadcabcdbaaaaabcdcdddddaaabacbdbbdbbddacdcaccbcccdaabcddacccccacadbbacbbcacbadaadcdcabbaacabababdddadbcabcaddcadddadbadddcddabbdaacacbaadcabcabbcbacbbddcbdddbacacdaabbdaddacdccdabcdccabacddabbbddcabdaaccbcaacacadbcacabbcaccdbbdbdcabbdbabbdabdaacaabdcdcdddbbbcbdddbaadaccaddbcbbcdddbbccdcadddcccbccdccccaadbdbccdccbbdcbcbcdbadbadaccdcacabdbdbabbcbccbcbdcbdabdbcababdaaacadbdadadddabbcadbbacaccbdbbadcbdcabdcacaccabcabcbbbaccccbdadadbcbdaadbdbcabcaddcaaccabccdabdacaaadbdccdbcbdadbdaddcdcbddccddbbbacdaadbaacbdddbacbaddbcbdddaadacdaacdabddaccbbacbccbddbcababddabccdaabdacdddbabdcbdabccddabbcdbabddaadaacaadcacbacbdbcdccaadcdbdbbabbadcdcddaabddbdddcccadacddccbdacbbbacdddcddbbdbdacdccbcadbaddddccdaabbcadbddccddbcadddccccdbbdcbcdabbabdabbabdcbbdaacdbbbcdddaccaacbbddaabbbacbcbdcbcbbbdcdbbdcdaddcadbacdbadbadbdaaccdbbdddaadbdcdcabcdbcdbadcdbaadbbbadccbbbdcbbdbbcdcdbdccaaabbaadcdccdacacbccbaababcaaaacacdcabcbdbdbdbcdddccacabbddaccbaccabbdccbdabccccdbaaabdaddababdbcddabdcabdabddaadbddcabbabbaabdaaaaadbcdbdcddbaccdcacbaaddbbdabddcbcbbadbddbaaaacccacabadacdadbabbbbbcbabdbbdddaaadccdcccccdcdbdcacbbbbbdabacbccbdaddcdaaccdbcadacdadbaccbbbbddbddbacdbbddcddbdadbbbcbacdbaccdabbacbcabddddbbcbccadabcabbaaccaaacabdbdcdadcacddccdbcaccccddbbacabcabdaabbdbbcabdbbabacdcdacababcdadccdcbddbbbddcabbbdcbadbacbadbacaadbccccadbbdabbcaaccdcdccccbaccacbbbdccbbddaacdaaddaaaddacbaabddddacaaaaabbacabdcaabbcadcaadbdbbcdbcddcbcadbdbdddcacaddddbabaaaddbdddcddababbaaccdadcccabddacadabbdbbcdbbcaadbacdababbcbbbbbbbbddcaacbbdbddcabacabdbddabcbaabababbcadbdbacbbdccacdddbbdcdabdadadbbdcddddddaaccccabdabcdbacbbccabacbbcbccbdcaddcbbdaccdbbdaabadcddcdbcbdcbaaaddbacbcdcdcadacbaabababcbaabbdaddacdccdbcbcacbaaaccbadccdbccccdabcddbcbdadbdadadadbbcbbaadccbacaabccdbcdbcacbaddcaddaaaadacdabcddbaccdacacabdacdadcdbcadaacabbcdabdadbdadacdaddbacdcdcdcdcddccacdcaaadcaacdadccdadbcccbacaacbaabacbddbabcaacdbbcbdbadbbabadcccaadcddadabbccdcdadbddbabccbbbccacaaaabcddaddacddbcccdcaaadbccbadbddacbacbcbadabaddbcbccdbaaadacddbabbacbbccabdadadabbadddbcbdddbbacdadbaadaabdaaaacdbcdbbadabadbcdccddbabbccacdcadadccabdccdbdacbdcbcccbccbaabbcbbadcaacdaddcdcdbaddacadcdaaaabbcaaaaaacdbccacbdccaddccbdadbbdbcacbcdcdcbbddddaaaadabbdadadabaccdbcdcadddaddddbdaaaccbbaacbbcdaaddadcabcbcbbbdaacacdcdbacbbcddadadcbbccdacbcbdcdabbbdccbddaaadaaadcbcdacbaddbaddaacdaddbcccabcadbacabbbaadacdaddcccdadddaaabbaddcbdcadddbddbbbdbdcaccabcabbcadcdcaaabddbdabccadbcdbbdbcaadadccdccccddcabbadbdadabccbbaabccbbbaadcaaacbcaacbcccbabaabddddaccabccbdbdbdcaaacbcadadcdbcbcacadccabbcdddbabdcaddccbddcbcbbbcadabddccbdabbbadcbccddaaddcdcaddbcddadadccdaacadccbabbbbccdddddbdcabccabcdbaadbbcdcdaacdcaaadaacacabadacdddbbdbcbcbcaaadcddbaadddabccabacbdbbaabddcbdadbacccaadbdddbbbdccdaccddccdccdcabbccbbbbdddbacdabdcddcccdaabdaacaadaabbcdcbaaadbbbadadacabaccaaaacbaabbdacccdbaddcaccbaaacdccdcacdbcddcabcdcbaddcbabacaaddbdbbbabcacbcaccaaddbbccbccbccacddbbcacdadddbcababbabcbdbdadabdbbbccadababadabbaccbbdcdbabbbbbbcaaccbaaaccacccabccacdbbcacbcbaccbbdbccdbaaccdbbcabbcdbbbcbbaddbcaaabdcdabcccdddabaddbacccdcbdbdbdcbabadbababdccdbddbabaaadadbbcdacbadaacdabaaadbcdcaddbdbadbbcdadcbdaaacabbbcbaadbdcdcdbdbdccacaaaddbbccadbbcacbadacdcbdbabccbcdaacabadbaccdaaadbaadccbadddcbbbbbcbccbacaacbcabcbacbcbbbaddccdddbaaacbaacadcccadacdcdbccbbdcabdcdbcbdcddabbcdaadcdadbbdaaabcaadcbaabbdcdbdcaddcccbcadcdcbaadbaaaccadbcbaaccdccabcddaabdcbdcccccbaddbcddcaadaddcdabadbdbdbddcabbdcbcababbacadbadcbddcdcdabccdccdcaddccbcaddccdbddabdbdbcaacacadabacbbbdaacaabacadccabdaddbbdcdccbbccdaabadcacdbadccaddcadcabcddaddbcbbaaddddadcaddabdcbcaabdbdabadbbddbbccdcabdcccadbadbcbcdabccbcabcaddddadadaabccbbacdbcdcdcbcdacdbcbbdddbaabacccababcbaadcddddddcbdabadbadcacbbacbdadbaadcddccdbbddbaaccbcdddbccbabddccadcdcbbadbcddbaddadaabaabacdacbacbcccbadaccccccbabbcdcccabadcadaaccddbbabbbdbcabaaaddcabdaadadbccdbdbabdbbbbcdcbaaacaadbbdccddccacdddbdaadbdccbcabbcbbbadadcbdcccccbcdbdbbdcbacbbadcaddbdcdbabdbcaccccddbaabbcdbccbccabbcaddcddbacdacbabaabdaacabbddccbbbbbbbdaddadcbcabdabdbddbcabaccadbaaabdadbbbccbcadaabcabcadabbabddcabbbbcaacabdddcccdabccccaabbcdbbabdcaaacddabccabbcbaccadcdcdcdabbddadcddcadcaddcacabdcabcaabcbacdbccdcbabdbddbcbccacadddbbbaccbdadbdcbdbbcdaabccbbbcbbccdbddddbadbbbdbbbaaaccdbcbdadabbdbcadacbcadccabaccbdadbababbacbaababdccabdacabbaacdaaacbacdaacbdccbabbbcadcccbdccdcddabbdcaaccdababddabdbabcabacbcbadbbabacdddbddbabaddcdcdbabbdbcddddcbdbaccbabdaacaaaddcbaddcbabbbdbdccbaaadcccddbdcabacaacbabdacbbbddadddbabaccdadddbcbcbcaadcbcdddadbdcbdaddabbacbacdaacacabbcbdabcbdbbddbcbaacababaddaadacabbbcdbcabdbddcaaacbcbcbababcdbacbbcaddcbcdbbdcdbadbccbcaaccdacaccbbbddaaaccaabadacadbacccacadabadbcabcbdbdcbaaabbddddadbabcaabcacccccacbcdbccccadacacccddbcdbdcbacddddababbdabbdbaadddbbaacbddacacdabadcacbabcdbacbadcdccccacddbbdbbbababdaacbadaacacaaccbbdacaabbbcbdaabacdcdbadbcdbbcbcbdbdabbabbccbadcbdbaddbacdddadddddaacdadbdbbabdcdbaadbcdcdaaabcaddacbccccbabdbcdcadbddcbacbcabacdbacdcbdabcbbbcaaacbabdaccdddbccadaccbdddacbadabcdaddccadaccabbbddabaaddcbbacbabbdacacadccaabbdcabadadabadcabacdbdddaacbacdaaadbbacbcdcdccccbbcbbacbbcbbaccbcdbccaaccadbadaadbcabbdcbdadaaddbdcbbcbdadbbdcdcbabbadccaaabaaccbcdcddbbbbadbadbadddcccbdcaacbbabdadabdccdadbdddddbdccccbbaadbaddbccbcacddbbccabcdabdaddaacabbbdcacacddccddbaadabdcbcbbadbbacaadaadcddbddabbadabdbabadcaacccaaacaabdbbaacbbbabdabdddcdcdcddbcaadbadbcacbbcaccaadaaddbbabccabbdaadccccadbcaaabacadccadaadcbcadaabcbaadbaaaacadbcacdcbaadadacdabaabdaaabcdacccdaaacdacccadaacdcabcddbcbdabcbcacdbcdcbdababbaadacdbcbabbdcababdaabaaadaabcbbdaccabcaabcbaacabaabddaccbddadbbaaddbacbbbababbbbbcdcddbdbabbadbdaddbcccbdbbbaadabdbbcdbdabcbcdcdadadcbaccbbcdadbcbbddbcdcddabbdcccdbdababadcdddccaccbcabdaadaddbbacbbcaaaacaadcdaccdcdbbdadaadbbaccbabbaaadcbbbccdcbcbbccdcaaacdcbbcdcbbdabcbadbcacaddbbdacccaccbacdcbbbdbbacbcbbbabaccaccbcabaddabcdacadbbaddbaddaddadababbcccdbddddcdcaacdddccbdbbaacdacdcbacabbcdbccabcaabdaabadbbbbacbcabadabcdacbccdaaccbdacbdbadccaaccdadabccdbcdbcdbbbacdababbdbaaddbbbadcabadcdabbbbcadccccaabcabbdddcbddacbabdcaadabbadbdacadcbabdaaabaabaababdbcacbdbdddadbccaacbcbdccadbacbbacdaaaaabccbbbbbdabadcadccacaacdccdbaaadadcdccbcdbcdacbacbcadcababacbdbaabbcbdbadddbcccacaaaabbadbdcbcccccbdbadbcadcbcddccbccadddcbbacbcdddbccadcdabaddbacaccacccacabaadcadcdbccdcdbddacccaccaacdddacabccddabddccabcbcddddacacdcdddaabbbadbbbacaaaccdddadcddaabdbdaaccbcccccccaabccadabdcdcdadddccbcaadcbdddcbbccbaacddacbadccbdacccbacbdbabbadcbdaccbbddcdabdbdcdbdcaaacdcbbbcacadbdccbacabdcdabcaacddcbcdbddbabdbacdbbaacbbcbbddbbdbdbcadccccaadbcbabcdadacccbdaccbdcbbcdacdbbbcbbcacadbbbcbabcccdaadbdcccdddbcccacbbbcddbccabbababababacbaabdbdaacccacddadddcadcddcbadacbbdaccddbbcacbbdccdbdacbcdddbaaccabcbbaaacbbacdcdcadbccbadbdbddcbdcacadbaacbddacbaccbbdbddcbcdacabadabdacdcbdbcccabccbbaaacdbdaadcacbbccccbaaccbbdaccdcdadccddcbadabbdaccbccbcdacabbcbdabdbaabaacbaddcdbcdbdbdbababccacdccaddacbccbcaabbbaadcbcbdbbcdabdadaddccbdacdaaabbbcddbcdbbcddaaadaddaadbbdbabacbdddcaaacccdddddcacdaaaaaccaccbadbdbccbdaddcaadbdbbacabcabddbcddaadcaddadaadccdddbdcadddcdcbdcabcadddbdbdbadbacbbcdbcddcbcacccacbdaacbbddaadccbccccdcbdadaadaacabadbbbcdaabbbdddcacaacdbcabacbdacbaadacdbbcddccadadcccbcdcbbbbdbcbbcaabdcddbbacacadcdcbbbcadcbbcadbdacbdcddcbcdaabacbaacbaabccccccaabaacaaabdccbddbbadbcaaabbbadaadddddabcadcacbdddaaaccbbdccbbbbccaadbdcaccabcdddadbbabcdadccaaabdccabdccabdcdcbacbaacbaaaadcacadcddbacccadbdbabacbddcaaadcdaccbaddacabcbbaadbcacbcccdaabdbbcdbdcaddabcbbccdcdcaabbbbaaddcaccadaabdabaaddbbbaddadabadbccadabdbddcdbbdcaacacbbbaabadabbccbdddcddcccacabcdbbbdcddabacdccddbaabddadaddddadacbdcaaadccadacabbcbdadbdabdccbccbbdacabdccdabdcdabbadaddbcaacadcbaadacabdaaacdabdadaaddbaacabbdbbddbdcadaadcdbdcdaccddcabcbabbcaccaccabcdbbdccbbdcccbbddcccabacabccabdaabacbcccacdbbcbdbcadcbaaaaddbcbcdcdaabccaddcabacabccdbdabdddacbbbaccdabacacbccdacbbdbccdbccacddacaadccddbbcbcdccbcbcaddbddaddcabababbbaccbbbabdbabbbabccdbcddbbcbdcdadbcacaabaaacdcadabcbbcdbcdadcbdacdcbcbdbcbcdbcdcbabdabcddbacaddadbddbcbacddddccbbccdbbadddbbcabadaccadabbbadbbaadcabbdccabbbcbcaabbbdbbacbcdddbdbacabbbbcbadddabacccbdbbbcbdccdadbdcccdcadbdadacddddccacbaabcacdadcdaacabccadbbacbcaccdbbbcadbadbcdabcbbadacdcaccdddbddbdaacddccadaabbbdaccadbdbcabaadbabcabbbaacbbaabacdbccdaddbabadaaabbddaccbbbccdadbcbbacbacbaaaccabbabbccbcbaaabdaaaacabbbbbacccddddacbcbdadaaadadcabacbbbdbcdbccdacbbcbadcbccdbbdadcddcdbcbdabbcccdcbccdddbcabbaaacbcccdcbabccbdbabddddddbbdcadcacaaadbccbababcadbbdaacbaabccadbaabbdbdbcdbbcccbadaccdacaadabdaacdcacbcdbcabccddccbdddcbadbcbbabcdcdaaaacdacacddcddaadbbcbabaddabccbbbbcacdacaadbdccbacbbaadbabcddbbdaaddbcaacbccdabccbddacddccbdbdaccabdacbaacbcdacabaddcccdbbabaadbdaaddbbcaacabbbadcbbadbdacadbccdbbdaaabccbaccbbbdbbcaaccbdadbcbdbaabccdaabdadbcbddbbdacabcacdcaccdaddddcaddaaacadbbcddcdabdcccbabcaadacbccbdbddccbbcadaabaaccaaaabaaccdcbaadaaccaddbbbacdcdaabababcbdbddadacacabadcadcdacbdbcbbbdcadbbbbccacbbadcdbcacccbcdcddaddddbcbccccdaaacbdcbcbadcbaaabdcddbdbbcabcaccdbbbdcbabaacddbbbaacaaaaddcabbdaacabadbdbcabacbcddbaababbccbbbcddbcbbacaabccbcdbdadbbbcdacddaccdababdcbbbdbaccaaddbbdcddaccbccbcaaccdabbbadabddabbbccabdcbaddbcbccacdacddcdbbcbcddbccdcbdacddccacbddcbcabccdbbbbbdcabbbdbbacbbcbaaddbbcdacabcacacdddcdbdccccbbacbcdbbadacdcbadbdacbacadadcddabbaccbcbcdabdcbccacdadbcaccabbbccddddcadabcbdadcbcadddaddbbddbbaccdcdcdddcbcbbbabbbbaadbcbaccbabadadbcdaadbdaddcbddbbbbdcbbddbcdacbdbaddadaaaddbaacdccdcdcabddcdddccccddcabccbbcacdabbdddbdddbaacaccddacbbdbcbaacaacbddaddaabbdcdbadaadcccccdcbadcdcccbbdadbaabacbcddaaaacbdabcaaddbbdbbbaabacbbcddbddbdadbbabaccbaccbdcadccdddbdcdcaddcdccbdbdbcbdcabbbbbaacaccdddbaddbcbabbdbdbbbabcadcaabccaddbabbddcdbbdddaabbadbbdadcdcacdaaaabaaabccbababddabacccadadcaddaabdcdaddcbcdddcababaaadadaaddddbabdadcddabdbddcacbaaaadcadddaacbdadcadcabdbaabbdbbcccdcdaddcbbddddacaddddddadbcaddadbcdbdcdcdccaddbadcbcbcaccbdbabdaabbabdccaadcaabcbddbcadbbacbcbddcbabdccddddaccabbbaacaadddabdcaaabcbbddbdbdbbdcbacccaacbbabcabaddcaccbddcadbdcdbdddcdabbadabadcddadbcaccaaacbccaccadadddccaaabdccbbcabaacdaacdcccccbabcbbdcacdabcdaddcabacadcbcaabbbaadbbadcddccbcbadbddbdbbdcbdbdddbacbadacbabbddddaaaccdbabccbabdccacddaaabadddbdacadbbbbddcccabdbdbddddaccbabbadcabbcbaccaacdacdaaadccdadddcbcbaacccdabdcbbbbddadccacabbcabbcdbacdcbbabdbdbcdcbbccdaaaabccbbabdddcccbdaacbdcadacaaaabbcbacaabdacbacbbddaddcdcbdadacbcbccabdbccacbbaddcaccaadbacdbbabbacaaadbdbcabcdcbbbdaddbdcdcadbbaccdbdbbbbbdacbbacdaddcaaacbcbcaaabcbbdbddaaaababcdcbbaccbadadabbddbbdcabbacbbcdcaaadaacabcadbaabbdbaabbbabcbbbacbbadcccdcbacdaaaadcdaddaacdbdcabbddbddacddbacdcdccacabdcabdddabaccbdcabbbcabcddbaddabcaccbaccaddcdddaccaadacddbcaadadcadbccbdaacdbdabbbdddbcdbddccadadcbabbacbcdabaadacdabcbcdbcabcaccbbbccadcdadabbdbcbdababaacbacaabdcaadaaabcdbabbbadddaacdacdcdacbacbbdabaaccbdbcaddaccdcbbdbaacdcdacadddabcccdcdbaabbbdadbdadcaacdbbaabaddcccbacbbbabbddbabddacaddcacacbabacbabdbbcabbcdbcbcdbabcbdbadabccbccacabccbdccadcdadaadacbacacdcadbcddbbaaaaddaaacbbabcddbaaaccaccdabcbbbacbdabcbabadaddcadcbacbcdbacbdbcdcbdaccdccbdbabaacbbddddccccabcaaabdcaccbaaaddbbaddadaabbdcdadacccacbadaccddaddccbcbbaddaadadaddabacbcacccdbdbbdbccbcabcaaddbbcdcacdabcdcccacadccbccadadddaaadccdcbbccaddaddccccaacccdaccbcadbdbcdcadbaabccabdacaddbadcdadcabbbbccacdacabccacbdbbabdbabdaddbcdabdcbddccbbbabdbcbbbaaaacbbcbdbbbbddbaabbcacbdcdcacbdbcdbaccbcadccdccbacadcadccdbcacacababacdcbacabdddbabbaabcacabdcbcccbabaacbadaccccaaccbcadbcbddbbaddcabbbabbcddcbbbcbcbdadadbbadadccbadacaabbadbaacaccadbdbddcbccbcccbcbbbbccbcbcccbcaccaadccadcbdaaaddcadaabbadbabcabbcbaadccccddbcaabcaadccdbccacacbbbcbbbacbdcadbbbccaddcbaccabadddacdacabddcccbbdbdbdcbcbabccaddacbdddcaddacadccddaaccadbcddadabddaacdabdcaadaacaaabbcbcacddcbabadacccaacccbbabddabccaddbcacccdbdccabddbccbcccaaddcbbabacdcddcacccbcaaacccdcaaccbdcbacbbcccddbdcccadbcddacbabdccdbaabcbdbbabcbcbccddcddacbbbccaddabccddddddabbaaabbccacbbccbbababbbadaddabdbdcdbbacdbacbbcaddcacddbdabbaccaccbdcadbcbbaadbcdddbacbbadcddaacbdaacdabbcdcddcbbaccadddabcbcccbddddbdadbacddcccadbcadcbbccdbaadcbadbcbbdaacbaccdbabdcbddcababadaccccdcacccacabbdaacbaadddbadacabdbdcacbbacdbdbcbcacdbcaddddbabbacbbdcbddddcdbacabbabccccbdcccabdbbabccdaadccdcabaacdddcdacaccbcacdbcdbcbadbacdbdaadbbdbcdacddadbaabcbcbdbcaaaadcbacacdacabcaccbabddabbbaddacabdbcdbabcbddadcbbcdbbbbbbbadbbadbabddddcabddccbccccadddcbbadadbcdcdcacabacaaaacbdbcbaadcadccbacdcababdbcacbbcbddcdaabbdacdbccdcbabbbadcdbdaabcadbdcdaaadaaaacbddddabacdacbbccdcacbdcacbbbcbacdaaddbbcbcadadadcccbacbbcacaddbabaacadcbbccbddcdcaabccbabdbdcbdcddbbbdbcbcacbacdaaaadaccbbdbaccaacaadbbdcbcbdabcacadcccbcbbacdbcbcccadddcaacdadacbdccbdbabcbcbacdaadadbaacdbadbaabcdbaaaabdbacbbccdcbdddbabaadadadcbdbaddbdabaaacdaaabaabaddbcaddbdccdabdadbddaaabcccdbbbbddcdddcdddbccbbdbbddbacbbbcddddcdddcabdabdbdbacdacbccaadbddcbdbcbddcbdaccbaabadadadcbacddabdbacddacdaaabacdbbcdacbdbacbaddbccacabbbadcbbadbbdaaddacdddabdaaadcdaaccdbdbbbdabadddcdbcddaaadcdcdbbadbddcbdabcbcacbcaaddadcadabbbcdaaaaddccdcaaaddbaccbadbccaabbbaacdbabbcbabaacccbadbdbbdcdaadcbccdcdcdbabccbdbddbcabdbbccdccbddcdcbdcadcacbdcacbcadbbbbddacdbdbccbacdabaacaadabcbacbdcddcdbaacbddbccbbadbbbccaadcbcbabdabdcbbddcdcdaabdabdddcbabcccabadaadcccbaaacbaaacccbcabdcaccababccdaadccdadbdbbbadbcbbbdcbabcacbaadadcbbdddcbcbbdacacdbadaaabaaacccdbbcadbbcaacccbcacabcbbbacadcdccaacdcadcdbaacdaddcccadcadaabbabcdabcacdddbbbccdbbbdbbbcccddbbcccbabcbccabacaadabbaadbcbddbbcdbcbadbaaadccaabbabccaaaabbbaacbcccaccbdbdaddabcdadcbabacaabcadbddcbdcacadaccbbdcbacccddbadaacdddbccbcdaacbcaacddaccaccaaaddcbaabcacaaddbdcdbcdabdcbddccbabadbbbabdbabddbbccccddcddddcbdcbbcabdabbccbcbbadbbdcdaacaadcdcccacbdabbddacabadbcacbbbbccbacdcacbabbaccbdacbcccbdabadcbcbdbddbcbdcabbcacccdddabadbadaabcabcdaccacbdbbcadbbdbdbbdcbadcdadbdbaddbdabcadcbdacdabccdbcadadbababdadbcadadbdabaabdbbccccdcddaacdccaabccdccccababadbcbadcadaacdaccbbdcccabdccaabcbabcccacdcaccdacabbccbdbcbacbdbdbbadcadaacddddcdaccbdabacbabcbcbbdbabcbadbbbabcbbbbddbdaaccadcaadabbddbcbcddabdbabdddaabddbcabaabbdaaacbcccbccbabcacbcaabcabdbbcbaddcacccbcbcbbbdbcbbacddcaaddbbbaaaabcbaccbaddccacbbdbaddcbbddadbaacdaddaacddccccdacdbadaababacbbdcadabddddcddcddadabcdcdabdbbaabbbcbabacbbabbdcdbbcdadaababadadcbabbcbcbaaadcbaaaaddacccddaadcbddcabddabbacbbbaaccdddddbbdabadbadbabaaadaadbdcabadbdaccacbabcbaaabdcbbcaaadbcbcababaddadabdcddacdbcbbdabadbbbcdbcccadbabdacbacacaccddabdcabddbcbabdbbdadabbabaadabdbbcaccadcddacacacbaabccbdbbbdaabcaaacdadbdbcdacdabacaddbddabdcaadbcbccccbcdcaabbabdacbacadccabdccabadaaacbabccbadacdbcadbcabbbacbbcaccacabababcbbcaaddbdcddbcadbbcadddbbadbcacbcdacabdcadbdbcbabacacadcaadbdbcaadcdccbcbaadcdbcbcadaccacccacbcacbdccabdacbbcacdbdacddcaccdbbaababddbbaadcbdaddcbddddabcbdcbbabbadbbccabdbdbdddccdadbdbccadbcaadbbcdadccdbdcddaccabacdcddccbbcbdbcbbadabcabccdacacccdbbaddddbcbadbcbabbbdaccadddadddcdaacbdacccacaaddadddccbabacdabdcbcbbdcbdbccdcacdcdbcdbbbcbacbcccdcacdacccbcaccddaddbdbcbbcdbadddcdcdbadcbdabbbcaddaabdaddbaabdcbabcbddbccdbdcaddbdbbddbcaadcbacdddbbabdbaddaaabddddcbadacdcbcdacabdddbcabbdbaacdddaaaadcaacccbbabbccaadbaddacdadcaacdbdbaddcbbbabddaabbacdbaacdcaddbabaaabbaccacdadaabdcaabcacbddabdcaccdbdccdcbaabbdadadacacbaccbdabdabaccdabbdabbcdcbdbbbddbcbcdabcdccccbbddccaaddbddbbdbdcdddaabdacdcccbabacdddbcbdcbdcccabdaaadbdbdaaddccddababbaabdbbabaadbdddbbdddccddbdbddcaaabcdcdbaaabdcabbbcbabcaacabbbdbbaccabdbcacccbadbaccbadbcdadcaadbcabdbddcacdcbbadbcdbbbdaddcbbaababcadadbcccccddaccaddcbbbbdcabcacbabbabaccbbbacdbbdbdaacddcdbccbbaccbaaaccaabcdacddbaaddadccbaabcabaaadcdcccdcbbbddddcacbbbaadcabcbadadaadbddabacacbaddbbcccbdcdbacbcbaaaacaaccbacacbccccacdbbdbbaabdbdaacabaccbdbbbaacacdcccddcdbdbaaddddadddcbadaabcacaddbbbabbbdabcaabdaaccdbcdacdcaaadbacdbddcbbcacbabbdacaaabccaadcbaaabbdcacdbcdcddbdaddcccbababadccabcdddabbabdbadbbacacadcbaadabdadacccccdddcaaccbbaaadcaccbbaadccbddbaaacdbcbbbbbcdddddaadbabcdbbdcbbddadbdcacacabcbcdadaddccbcbccbbdcbddcbbdacdbcacadacddbcadaabcabdbbbcdabaadcbdaadacddbbbaddbdbacaacdabcabccdcabcdbddbacaaacabdcdacacdabdddabcdccbaaabaabdccbdabdcddaddaabdbbbabcaababbbcabaccbadacaadbacdbccbbaaaccaabacbadcbadabddababcbacadcacadccdadaaabacbbdbadbacbccbdadccdcbaaccbdcccbdcdbbcdbbdbccbaacdabcdaccaddaccaaabcaabbcddadddadbdccddcbcaacbbdaadbcdbbcbbdbdabbccdadbadcbdadddabbdacddaabdaabcddababdaabadcddccdddcaaaadbbacbadaabcacbbcccdbcaababcbcdcbcacccbcdaccdacdaddcadbcabaddcbbacdcbacaabbdbcacdbdacbadbacddbcdcdacccccdacbddadcbbadcddbbbadcadadbdcbdbaadcbababbbadcbdadcdbbddaacacdcabdddccbabaccacdddacddddddaaadacbdbbbbaaaacbddcaadabaaddcbaaacdddbabccadbcdaacdacabdcacdccbbabddabcadddacacdcabdbadbbbbdbaacbdbbaaabadabbbcddddcabddbcddbdaadbababbdacccbaacdbbbcdcbdddababdabaabaaabcaabacddccdabbbddcbcbbbcdbbcacaddcbadbbaccaadacbcadabbcbcaccddadbaaadbdcddaddcacdbdadbabcaacabdbbbddbbdbccbbbddbaabbbdbcaddbcdcbcadadadbdaddadcdcbdacccbdadaddccbdbaacdabcacadcabadbbdcdcbddcbdddcacbccdabbcddcbddabcbddaadbcdcabbbccddcaabadababacbdcccbdbcdaddcdaaaddcaddcdcbbabcdccbbccabcaccacdababbcbdddaaddaabbacdcddabddbccdaadbcacaabcccadbdaaaaadbdabdbbacccddaccadbcaadadddddcbbdbdcaaabbdcdadadbcdbaccccdcddbbbdacadbaabaaaadabcadbbdbadbcacaaabccacbaaacaacccbdabdcadaaaccddccaabbbccadbcccaaccabadcbbccbdcccddacadccdbadddbdcadbdadabcdcacabdbcbdadbbdcabbcdadadadcdcbadbccbadabdcbbbddbaabcbaaaababcabcbcabdbddbbdcdbdacdcadbdccdbdacddabdaacdacbacdccccacddcaddabddcacbbacabcdcabcaaabddadbbbdaabaddbdaadbbcabdabaccacbaccadccabacacdabaadddcddccbcaadabdccbabdaabdcaacabcaccaccdcabbdcdccaaccdbcbcdddccacadddddaddcaacddccbdbcdbdadbdbcdcbcacccabacccbadbacddbdaaabccdadaddbcbdcccdcaabcdbddbbddadabdaaadcbbaddcdadbabacdadadabddabcabcaadccbdabbcaaabbbcdddbbcdaaacabdddbabdbcdbdcdbbacacdddaacaabcacaabcbaadbadadabaadadacdcacbddcbddcaaababdabcccbcdbaaccaabdabaaadadcbaaccaadddccccabcdbddddaaaabcabbcbacaadcdbbbccddcbabdbcdcdbcbadbccaadadbbbdbcaaddbcabcbbdcccbdaccaaadcdacbacbccacacdadcbcbcbdaacdbabbcacdcbbcabdadddcbdbacddcadbccaabaaabaacabdccadcbbdbccabcbacdbadcdddababbcccbacbcdbddcbccabdacdccdddaccabababbcaabcbdacdabccbaccccbabccdddbaccccccdddbdaaddccccacacaaaccbcdbaccadbbdbbcaabababbabcbdbaaacccccadbacddadbcbdbbdaaccbccaaccbcbcbbbbaaadabbdadabaccdadddbadbcaadcdbcdddcbbccddbdbadbabbbcbcbdbdacdbcaadcbdaaaaccacdcacccbdcabacdabacbbccaadcdaabadaddbcdcdcdbcadcbdccbaacacdddcaabdcaaaacbdacddcadbbddbbddaabbddcdcbcaabaacdaccdcabdcbbdbcababcbccdaaccbddadaaccacaabbdbaadbbbddcbdbbdadddbaabbcbabcaadaaadbbaabddbdadabbbdadaaaacaadddcbccbbdcdbaababdddabbabcdccbacccdbdaacdcbddabdbcaaadbadaddcccddcdabcdddadccbbcacbdbcbcbdcacaaacbdabcccdbbccbdcbbcbddbbaaadadddbabdababadcddcbddaabbdacaccbdadccbbcddbdacdbacccacdcdcadacccadabbabbcbaaacdcdccddbacbdcbaccadacbdcdabddabdcadcdcccbaabcdbdadcddbcdbddaadaddadbdbaabbdabdadbcdacaabccdddaccbbacbacbabddcbacbdccccbbaaccbabaaadbcdbbbaaadccdaabdbdadbcdcaddabbcdbcaccdddcabdcbcbbdadabccddbddbcbbaddabdbcddcabccadadbbcddaacdccccabcccdccdbcadadcdcbcaadbbabbcdcacbabbabcabddcaccbbbaacdcdbbbbbbbdbbcdaabbddaadbdbabdccdcaaaddbccdbcdddbcdbcdccabdcbacbdacdcadccadbcdcaddcbadcbbddacbdacdddcbbaccaabbabacbddbcacdcdcbadbbaddcddacdcacbcbdaaadbccaccbdcbacdddabaadadccbdcbabaccdbdbcaacbccadaccabdbdadabbcddcaddabcbdbcbbaabcacbcadbdbbdbcccaddbcbacbacbcabaadbaaabababdbacbadaacadccbdaccddddababbdbbbcabbbadadabdbdccdabddaaacaaaabadbdaddccbbbbdbbccdbdaaadbbdbcaddbdbcccbaabdcccbcccaddbababdbadcdbaaababadaabcdddbddbbacbdddbcaccbaacaaccacbcbbbbbcbcabbbcdbaaadddaddcaccccabadcacccbcaacabcdaadcbccccbadbcaadbbaacdbcbccccaddbbbadcdbdcabbbcdddaaacacbcabdbcacdadddbbbdbdaadddbdcdcdbbccdbbdddbaadbdcdabadcdadcbabaaddbcdcdabcdabbddcaabcbcaccbbbbdbcbcacccbdbaadbaadaabcadcdbbcdacabaddabbcbdabdbdcdbdbdbbdacccbbaddcbdccddcbbbbadaabcdbcbcbbbcbdacdaacccddbcaabcacdcbcdcbccccccccbcabbddbabdabcaadadbdaacddcbcaaddbbabcdcbacbccbaaabaaadbbbbaabbdcccbcadcdadacaabcccdbaadaacdadaabbbbabccadcadbbcdbbadccccabdbaaababcdcacdbbccaaacabbcbbcaccdabccabbdbcadadbcadacaccbcbbbddbdcadcbcddcdaabaaccdbcaaacadabcadabbadcabbabbbcdbcabcabbacbdabbbcaddbdcbaccacacbbddabadbbcdacccdbbaddbcddddcccbabdcbdcdcbacbcdcddbdbdbdbdadccbdaadcaadcbdbbadadadcddcadacccbaccbadcbacdaabcadaadcbcdacabbdcbddadbaacbaadcbbabddcbbbcaacbcaaaaaccbdccbcbcacdbadcbaaababdaccdadbdbbbabbabacccaaaaadddaabbcdacccdcbdcdabdbcdcdadacadcaabddcacbbcdacbbdabdadabadbaaabddcdbdaacdbdbddcbbaaaabddaddbcbcbabdadaabdcccdbbccaddddccdcaabbacaacddbbaaddcacdabaadbcdaadbdbbcdbadcbddcbbbcdbabbccbddccdbdadbccdabaabcccacabbabcbbcbcdbcabbbcddcbcaacdbbdddacdcdccdbbcbdcdababaccbcdbcbdcaabddbcbadbdddabdcccabaddabaadccdbaabdaaaadcaaacacdcccacbdbcbbcaccabcdacbbaacdadccbbacaaaacdbcdcdddbabbabddaababaabdbbdcccbdacdaacddabcccaadaacaccbbccccbdddccdbdbddcbdabacddbcdcbbccbcacbcadcddddbdbcbddadbdbbadbabdcbcbbdaadbbacbcddacbaaccddcbacdbaacdcdacdaacabbcaccbbdaabdbabaacacccabbcdbccacaacdbccdddaaaabdbbabbdbcaabaabaaddbdadadaccdadacadaababcbbdcbccbaaadaaaaddbdbdcbccaabdaddacaccddaadbdbadbbbabacaabcaccdbdcccccbaccddadccbcabdbcacddaaaabacdabdcbbabddbaabccccaaabdcddccddddbdacdbaadacacabbdddadccbddccdcdcbdabababcdacacbccddccaddcabcbdcccdcdcdccbabccbbbcdaaccbdbcdaabdcccdccccabbbaacddaabaaacaddbadbcddbcaddcdbbbcccacbabdddcbdddcabdddcdaaadbbbabcdbdabacaadcdcaacbadbcadcdbccdbcdccddbcdabcbbdbdadbcdaabdcbcabaadadbcadddccddbbbddcbaadbdcccadcdabbddbaccbcbadbadbababcbbbbdacbdabadbbdacbccabcdabdcacacdabdbbcbdadcbabcacbbdbabcacbcdabcaadababcdbbbadcdacddbbcabbccaacadccdcbdcaabbaddbcccacbcddcbdbdaaabcdbcdcadbaabbaccabacdbabcadcbbbdccaccacacbadbdabcdddbcccadacabddcbbacbaddbdbaddbbaacdddccadbbcdbabddabadbdacdcdcbbadabcaaadbcbcbaaaddbabaccbbddcadcbbabdddbbbaaacabbdabababcdadbaccdaacabdcabbdcacdaaaddbaccdcdcadababacbabaabdcbcbbccdadcdbdaccbbdabbabcacdbacbddcbcbbdcdcddbdaabcdaacbcbcdbcdbddcbacdcdadcdaaddcbbdadbccccabdccddacdaaccbcdddbadbcdbcccbdbcdaccabacdadbccbdbaacddddbdcadbcacaaababbddddbddadccaabdacddaacadadcaccdbbddcabdaacbaabcccdcbdcbbbbcabcccadbabdacdacccbccbabaacddbdaaaacadcacdbddadbbdabccddbbabaabccccbcdbbadcddbcacdcccdbabbababbbbbdbdabdddaccaadbabdcadbbabaacbbccabdadddbbdcdadbcacabbcdbaaadccaabbbdbcaadcdcbccadabaabcbcdacacddabdbdcadaadaddcacbcaabddbccdacbdaadaaaaaadddbabcdbdddcbbacdbdddbabdacdbdbaaacdcbacddabdacaccdbaddbacaabdbbccdcdbbdcdaaabbdabdbbccacadabadcaaccbaabdabcdddbcbbbbcdcdcbddcbabccadacabacccdbdcbbaacbacabdccbbdcdaabbcabaaaccacccdaadcddcdbadbdbdbdcdddadccdddbcccacbdbcdaadcddcdbdaccdbddbcdbddacccddcabadccbdbaabacaddadabbcbcbcddacdaddcdcbdddcdccdccabddbdbcdcaccdadcaacddccbcabadbdbaaacbdabdcacacccccbaddbabdcdbbcdabcaddbbbdcbddcbabccaadacbaadccaaaaacadbbbbbcabaddbbbdcbbabddbbadaaaddbcdacabbddacaaccabdacbadbacdbcbcabacdddaadddcbaadcdbbbccdacbadbdaaaabcddcaacbbcdbdcadbacbbdbdaadabbddabbdcdabcabdccbdbcbccabadabcdddbcbcabbcbdbabacccadbadddaacadbccacdbdabdbbcddbccccdacbacadadbccbcbcbacbbddaaccacababacccadbcdaabdabcbbdaadbaadbbdadaababacbbaaacdbcdbbbdbabaaccdaaccbcaacaccbcdaaddcbdbadccdbbdacdacacdacadcbcccbdbdbbaddbddbcdacddbbbbbcaddccadbabbdbaccaaaacaacbddcdcddacbabdcdccabaddbdbdbbacbaabcbaccddacbbbcdcbbaccdbbcaabcaabacbacbacdcadabcbdabccbbdabacbdbacbddabbbbcdcabcdcadaacbbbadaabdbbaaccbaabbbbaadabcbcacaacddbcbbacccbcbabcdcaaacaabadcaaabbcacadbdbbbadbabbcdadcccaacddbabcbbbcbaacbcdadbccbadbbcddccaaaacabacabaabbcabacbabacddacbbccadacadcadaccaaabaaaababdbdacbdcddbaccaccabbcbddacbbabcdabddbaabbcaddbcbcbbccbcaccbabbdbdbcaddacccdcdbacbcaaaaaccbdadbacbaabdbdaaccbababadbaccabdccdbaccacacdaacdccccaaabababbadabddacddcddddccdbcbdcbbaaddcdddaaacbaabadcbcaddaaddcddacdacddcaacaccccccbbddaadabaacccccacdabbbbcaadaaddadadcdbaacbdcaaddacaacdabaacbabbdcdadcddbdadbcdadcdcdabadacbaacbbcddbdabbbcbabccaadccadadbccbcabdcccdddbdcdbcdbcacabdccaaaaaabbbdadacabbbaaababccdabdcccccbbdaadcabcddccbadbaacbbbacbbcdaabdaaaadbbbbdacaccbccdddadcdbdbbcbdcacdcdcdddccdddadbccdaaaabdadccddcdaaccbaabcacccbcbaacadbddcdccdbaccdcbdabaabdcbddcdcaadbaaccadadcdaccacdaaadccddcadbcbbdadbddbdabcaacbadaddbadcdcdbabbbddcdcaadadbbbdadaaadbbdcbbdcbabddcbadaadcbacdadbcbaacacdcbacdaaddbadadcbdacabcaadabdadcdcacddbaaddbbabdaacdcaccabaadbbdbadcbabababccdccddcdbbabbbbbdbddcccbdcadbbadabdccccdadaadbbbbcacbbcccadddbddbdaccddddadcabcbaddbcbbabddbbcddaaadcaabcbbaccbdabbcdcddbdcdaccaadadcaabbcaacbacbacbcccaccdaaadcadbdcbcbabaaacaabbdcbccbabcdbccbacdaabbabccbacbaaacdbdaacdcababbacccadbddbddcacbbdbdcddcccddbbbddbbabcbcccdddcdbcbddbcddbdabdbdddbcbaaabcbbcdbacddcdbadaddacdbcaadabacdaccaaaaccadabccddbddbcacdadadbacaabdccaccddddddcababbaddaabadccaaccabcabbacbbcbcbbabcbacdabcabcabdcabaabdaccdaddcbcabcbbdbaadccadacabbadcccdcdacccdbcadbbccbdcabbdadbbdbcbcdddddccdddaadacbcdbbdacbbadbdbdcccdccbaddaccddcbadcaadbbddccacdbaddaabaccacadadcbabcddaddaddcbaaacabbdcddbdaaacaaaadabadabbdbbacccabaadcacbdaabcadcdbddaddcadccaabdabaabadbadcdabbbabbabbadadcbbcdaacbdccadddadddbaabdaddbcacadabdacabdbcadddacabaaabcdddacdcabdbaaccbaccbdcddacdcabdadacdaacdbaacbbbccadbcdaaacbbcbbdbcbaabadcccccdcadabcdadbaaccbddcaabbadbbbabbdbadaadacacbcdabccdcddbbbaacabddadbcdbacdabbbbabaadbcaacdbcabccdacdcdcacbadabbaccabdbdddbbadcbccbbacaacdbdbacacbddbcabbcdabcdbccacdaddcacbdbacdbcaaccdddaacacacbdcdcdbdbbbbcbbadcadccccaddcbacadcbdadcdcacbdabbdbadbdabdcbbbdcbcaccbaadadbbbcdaddaddadbcbdadcccddcbdbcadbcbadbabcbcabacbabcbbdaabccccbbadbadbaadccdaccbbcdabcadadbdaaabcbddabbdbdbcadbbbcbdaaaabdcacdaacacadbddbdadcbcddddddbbcadbaabdbddadcbacdbacdbbbdcccddbdccbbcaabdcddbadabacbdcabcaadbaaaaaaccbdcaacccbcccccbbdaadccaacbbcadbacabbdbccccacbbabbdabdaddbaddccadcbcbcabddccddcadbdadbcbbcdddcaddbbddbcdcabaddbddccdcbccbcacadcabcabadbbdaadbcdcadddbdbccbaccdadcbbabdcdcbacbcbcacdbcddabadcdccdadcdaccbbabaaccdbbaccdbadbdcabcddaaccbcccbcacaccccbdacbabcacacbdcdddccdcddbdaadabddcaacbbdbadcbbabcddaccadaadbbbcbcabbcbdddacbbcbcdcabacbbacdbcaabdbcbdaababcdacabccdbcccadaaadccccbbabbacddcaabddcbdbbaadadadaaaddaaadabbccdaabcdbbaabdbbacdbcabcdaaddadcababbdacabaaaacadadbacddcbdaaccbcaaadccdbabbcbddcabbcdadcaaaadcbdbcdbdbaabdcbcabbccdbabdabcbddacdcaabcadccdddddaaacbbccbcbbdaddaadcabdddbdcccbaddbdaaaccdddbabddcbaccabddaadaabaadbcdbccddcddacbabacdccdaccaaddcdbaccbaabbbccccaccdaabadabbcaaadddccccbcacdaadbbaccdaacddddcadacccdadccabdbabccababacacbabddccaaaadcdadcbcadadadadabdbcdcacaaacbccacdaddbcbcdacaaddbddbaabacdacacacabadbccacbbddaccbdaaabadaccdabbdcbbabcdaccccdbccdcbacacbddaabddabbadcbbdaaabdbdabdabaddababbbccbdcadddbcbdaacbabdbcdbbbdccbccbbcdbcddbadbaadcabddaadcacbbdcdccaddcabbacacbcadaaadbbcadbcdddcabbbaccbcacabaababbdbadbababdbcbbadbbdcadcbcbcdbbacdbdddcadbccaacbcbbababdbccbbddcbbbbdccdaacbbcbccbddcaccaaaaacdadddbcacdbdbcaaadabaddccbaadabdddadaaaadcabacdbccaddbcbcccdbbacaadaabaacacabcdadacbbabcbdbbbcccbabccbcabbddaaadadbcbdadcaddadaabcaadbbddcccbcddabddacdabddcccbbbcccdcdadcabbcadcddcadbaccabcaadbdccbbaccbaacdbbbacbdccaddbdbdadbbdcdaabbcacbbbcaabbbabcaadcbddadbcbdbdbaaadbdcaaaadaaadabbadcdabcdcbdbaadcaadbccbcbcbadcdbbcddadccccbcabacaaabaddbacbbacccdcabcacdadadaadcdaacabcdbbaccbaadaccabbbadbbddcdccbcaccbdbdccdbbdbcaacbddddcdbaacababaaabbabdabdbdcabbbbdbdccbadcccdbddcccaaadbddbbccdaacbddbcaccddcabddacdddcdbabaabcccbcbbdcdadaacacbcabbccddcbadbaabdcadabacbddddbbdadccbcdcbbdaacbbbcdbdaaccccaabdaddbbdacbdbcddbcdaadbbbdccaddaabcbbbbadcacabdcaadcbbdacacdbdaacaaababccaadabdbcbaababadcdadcaaddcaaccdccbdbcadbbabbaabadbcadaccbbabddbbabadbccaaaabdacdccbbbbabadccaadbcdcdbbdcbddababdddaddabbbbdccdbccbabaccdadadaaddaddccbbaadccacdabbdbccdbabacacddabccdcadaddcdcbabcdbbccdddbaabdbcabcadbbadcbdabcadbcadbbbdaccabaabbdcadcbcccabcadaadaddccbcbcbadacccbcabcddbcbccbabdcbabacdabadaabadbcddcbddddbbccaccbcdabcccbdcbbbbcbcccabccbacacbcdbcacddacbadbaaaccdbdbcbccdcccdbdbbbacccacacacababcaadcddccbacdbdcacaaabddbabaacdbabccdcdaddccadaaacaaccaaacabdbcbacabbcdddbcdcddacdcdbaadbbaddccacbbddcacbdbabdddacadddacbcbbacacdddcbdbcbcdbdddcccaacdaaddabcbbbabadccbcaabcddcdddbcbbbdabcbbaacdacababbcddbaaaaddcdacdabdbcccddcbdcddcdddbdacbcdbbaacbaacbabacbdababbddadaacdadaadadaacbadaadccacaaabcdcacdbbaaddbabacaaccaccabbcbcccbabcabccddacbcbacababaccacbcddbacbddcbbabaacbcbdcaabbccdaddcddbbbadaccacdbbcbcbdddbcdabbdcaadbaaaadaabccbcbcaaacccbbcbbabaaddcaabaadddbbcccbcddcbbbddbbcbaababbbcbddbbadabdbbaaabcaaacddcacdcbaddacdacddaaddabcacdcabdbcaccdcaadbbcdacbaabcaadabbbdcdcbdbbbbddaddbdddabbcbabbbbddcabbdbacccdaabdaccbdcadadaabdccbddbadccdbddccbdbacbbabccdadbcdadabdddccddddbadbcaabbccbcbcdbbcdabdaaaaacddacadaadbabdaabbccbdddabcbbdabccaacdccbaaaaabcdbcdacbbdbaadccbddddbdcdbbdcabbdbcdbbbddcbbacbacdcbbddcdcacdaabdcacddcbbdcbdbbdabddacdabdcaaddbccbdcadaabadcbbdcaccbdcbacbbddcbbbccbcbddbdddbdccacadabccccabcdabbdddcdddbcacadacdbdcbddacddbddadbcdccadcaccdddcaadacacaddadbcadbaaacabbccdbadcabddbbcbdbdcabdddcaacdababdacadcacdbddabadaacaabcdadbcbabbcdcddaadbbbcadcaccbbccbcccacdadccdbaabbaccdbdcdadbdacdddccaaacabdcdddacdcdbcbbbdadaadacdabbbabdaacaccbdcbabbddbbabbcccabaaaaaaabdcabcccdbddadcabcdddbdacaadbddbcadcabcbbccddadcdaaaabccbdaacbabaccabcdbdaccbcbcddbdadbcaaacbaaadcdbaacbdddcdddacbcdbadccadadaabcbbcdcdccbbbdacbcdcbacdacdaaabddbccddadabcdbadcadbcbdcdbbbcbdbabddaaabdbabdbcbdcadadabccdaacbbcabadabaddcdbabadddccddbbdcadddabcadbaabdcccbaccacdccbdabdcccdabccccabaaadabaccdbaaabddbcbabdbdcbcdcdccbabcacdabbdbbcbcbdacbcbaaacddbddadbccdadaacbdbcdddadaadacccbadabdddbcbcabcadbbbbbdcbcccadadccdbcdcbcdbbbbbccdcacdcaccaccadddadaaacabdacbdbcdddbbdcbbbdbdbbcbabdcadcbbbcddbacbaaacdcdccacdbbaccdbddacbbbdbccbdadadadbbabcdaabddacdacabddaacacababaaacbbdcaccbaaabbdbadcbccbdbbbddbddaabddcbacaacbcadadabdbcdbddccbcbcaddaaaddcabaaadbddccaacbccdacdcdccbcbcbdacbbbadbcdacccbdcacbcdbbbcccadbbdababdadcacadbddcbcabbbbaadcabddadcbaddcdccccadacbbacbbaabbcbcadbdbccbdbbcbadbddcdababcdacbdcdcbdcbadcadadadcaabaabccadacbabaaaaaccaddaddacbbbbdcccacdccbbabadacdcdaaaacdcbaadbbcabdddbacacaadcddbdddaccabbcbcacbcbbcccddbabbadbdbbacdadacbbdabbdaaabbcbbbbbbdddbabbbcccdbdbdcaccdbaacdccaccdaccdbadadaaabbddbbcabdadacbbbdbdaadcbdddcdacacdacaccababdaadacbbabaacbcadacbcacbacbbddbbdabcabccbdbdbcadadacabddcadbacaccacacbadbbbbacacddbbcaaabbadbbcccbacdbaabdcdadddddaaddbbaccbdaadbbacbadbcdbbcddddcddacbabbdbaaaabdbdbbaadbaaacdbccbcbdcccbcdcdacaadaaddcadabdcdcccddcdaaadbccdcadbacdcbccabbdcaadbccdcbbcabcdabbdbabcdacbbabccaabbcabdbcbacdabdcdbadbbcbbbcbdbdbdbaddacdbdddadbaacaacccdbaadbbbcaaabdbadcdcdbcbcdcdbccababdddcaddbaccddabbbcacabbcacbcbabcdabcaadccaaacccdcbabacacbdbcbbbcaadbcadadadcaacacdcacdacbdaddbccacadcabdaabcbbbcdbbbcdbdadbcbacdabbbacddbdcaddabbcacaaacbdbdadbabcddcbaccbcccbadcdcbacbcdcdcddabbbcdddaaccaacbdadccdbbbbddbbabbddaccaaaacdcbdbdabcdcaaccbababbcabddabbbaaacacdbcabbaaccdbadacccacbdbdcbaadbbcaaaabddcdbadbabbcaddcabbcdcdcaabbbddcbacbdddccddabdbadbbacbaaaaaabbcddcadadccbbbcacbbcabaacbbdbacacbaadcbbacbcbaaddabcbcdacbdbdbdbdddacabcddabaacadaccdbcddccaccdaabaadaadbbaccabdadacdbcbdcbaacadbcacddbdccddddabddbbcaccdbbabbdbdbdccacbacacbacacbdabbddbbcababdddadbcccaddbbabdadcabaddbdcacaabdcddcbccbaadacbaacddcdccbaacaadaaddbdccbcaaabbddddbdccdacacaacddbddbcadaaaccdbcbdadccdccabdadbcabdadddcccaabcdbbdbbaccadadbcdabacbacaaddadcbacbdacdbbbbaabbbdacdbacbcadcdaacbabddcaaacdcaabcbccacbbccbbaaabcabddadccbabdbaccadaccbcabbabdddddaddcccdaccadbbaabdbcdbdbddcccdaabdddcddbbdaadaddcadcbacccccbbccdcabcdacaccdbbbcdcaccbbbcccbbbacbbaabcacadbabadddcdcbddbcbbddcacdbbcbacbdbabcabbcaadbcbcbbcacaaaadacbcadadbbbdccaabbdbdddabaadabdbbacbaddabaabccbadcdcbabababcdaadcddbbacaccdacddccabaabaacdcdccccdbddccdcccabaacbdcabdddbdddbbabaadcadabbdcbacdcbdbdbcbbabbddaacdbcbdacbdccadcbbbdcbccddbaddaadcdcadacadbdcdbaaddbdbaddbcacdbbadccdddcbbacbdbbdcdcaaabacbbbadcadacbacdbcbdccbbabcabcadcdcacccbdabdacabaddcacadbbdbabcaaaacaacbccccaaadbcdadcaacaabcabbacbcbbdcbbbdcbdaabcdbabdaddbaadddbdbdddaabdcbcdcaddbbdbdcbdbbdaddbbaccdacacbadaadacccacbbabcaaddabbbbdccbaacabacbdaadadacdacdcddcddbacaaddcdcdcaabcbdcaabddcbacdabcdabccaacdbddadcdcbabbcdbddcadbcacaddcbbcacacbdacadccbbccabccdabdabdadadcacddbabababadbdacbcabccdccbacddcaabdacbabdababdcdabdaadbbbddadcdbbbaddcddbbbbddbdabadacbcdddaabcdbdcbaaaccdbcddcacbcdabcdbbcdccabbcbadcbdddbddadabdddccdbadcacdacabbacbbcabcabacdbcdadacbcadaadadcbccbcbcccadbdabcbdcdcdbaacccccdbbddbcbddaabbbaacddcdbdbbcdcacacabbaacddccbdacbcccbacdddcaadcccacddcdaadddcddcbcdcacdbcaddbcaaabcacadcdcdcbcbdcacddddbaacbdadbddddbaccbdcaacacbdbcbdaacdaccdbaccaabccbcacbcaacdccbbaabdbbdbcbcabbcdcadbacadcdcbaaabbadddbcddddccdabaccccaaadaabcddababacdadbccdaaabcdccadbbbbdbaacbbddbbbabbcddcadbbcccadccbdccacacbbdcaabcbdcadcdbdcadcbdbdacaadbadcbaadacbaadacdaacdbdccaccaaadacadcbbdcdbbabacddaaacbaaacaaaaacaacccdabcacdbbddcbdbbdcbabbbcbbcdaccaadcbaaaaddcbbaacbdccbbdbaadababbaccbdcaacbadbbbcaaabbcbbacbccbbdcbbaababdbdadccdccbdddabdcbcdbaddccdcddacbabbabccbcbcdcaadbdcdcabbdacccdcaadadabbaaccacdaadacdaddccdbcdddbacaacbdddddacaddaacabdbbcacabddddbbadccaddaabdabdcdbbbdcdabddbbcaaabaddbadbadbdbcaadcbdbbcbbdcdbdbbcabcabdcdacbacadbbdabcbbacbababbdaadabadcdbadacddccbadabbcdddcbabadaabdcccbbabbdccdbddabccbcadbcbcaddcbbbbbbdbcdcdaaadcbcdbaddbabaacaacdbdacbddbaaadbcbbdaacdabcabdcdbbcccdadabacbbabdbcdcdcdadcadaddadabcbccadadcddccbccddacccccbdbaabcacdbabdcccbadbcbcabdddacdcbdbcacddccccbaccdaaaaddaabddbbbadbabdacbacdaccaadddcddaacccdbcbacbabadababaaaabbdadbaacbacbdaaabbdccbbbcadaaadbbdcdabdcbacaccadacbbdcadbcbaadbbbdcdacadcbaacddbcdccbdcacbdccaccacbdabbdccccadaababcdcdaacaadbabdbbcbaaddacacbbaaccaccaddadbaacdbcdbbcbaccabdbcacacbabaaacbaccdbaaddddbdbcbadaacbaaccaacacacadbabadcadcdddbcacbacdbbdacdcbccdabcbcabbcacdbdbdcdbcccbabccdadddbcbadadbbdcdaaccabaabcbaccddacbbdaddaccbcccbccabcddccccbdccacdbdacbbbdacaaaacdddaaccadbcbddadacbbbdabbdccbaabcccbccbbabccbdcdaaaaabacaadaaadcaabdaadcbadbdbacaacdbacddccddbbcdadcabbbdaaddcbcddcbdabcbcccadadccaccdbacbadcaaababcdccdddccdabbaccbdaacbbdabccdbabdabacaacdaccbcbacdabaddccacacbdccaacdddbddbbdcccdbbcbadbddaaccdbcccbaacaddcdcdbcaabbddaacbaaaadbacacdacbdbaaaabcddbdadcbbddddaadaccaaaccaaaaabdaadcacccdcacbcdcacddccaabdcacabacdadbdadbdbbabaaabaadbcadcbbdccbbddadadacbbccccdcdabcbcbdaacbacbbccbddabcbddadadadabacbccdaacccccdcbdaccbacdbaddccadbabacadcddbddbdbdcbbcabadaabbccdccbacaabcbccbdbadbacccdcaddacaabaababdccddacaacacaccdbaccbbdaacdaabbbaadababaaacbaadcbcbdbaddbcdaccbdcccbcddcaadbddccacbdbcdadacdadabaabbccccbdcbccdacddbddccbbcadadcdbbaacbaadaaccacccbaaadcddbbcaadbdaddbcabcadccababddadbdddccddabdbccaccbdbddcddcdaaacdaabddbccadbdbabbbacccbddbcadcbbaababbdbbdadcbdbadadcabcbbaaabcdcadbdcabdbdaadcbdcbaccccdbbadaadbcdbcbdbbaccabaddbdadbcbcdbbaadbadbcddadabcabadababadccbdccbcbcbddadcbcdddccdbbdbbdbdacabadcccbabaaacadbabadbaaddbdacbdbbadbaccccbddccbcadbacbaacbbbbadaadcbccabdcdbccbdacacbbdbaabbbaddbaabbcbbdadaabbccadbcacbcccbbaaacacccaacdcacccbccdbaadcbbbaabdbabacabdadcadcdbaccabbbddacdadadabdacbcdaaabacbbbcccacccbbdddabcdccbbbaadbbcdaddcdaccccdddbcdaacccadcbbdacdadabcdbddbdaabdccadbcadabdadccdddbaccabadaadcccabcacbabbdbcacbdcdccbbaaccadcdadbcdaccdccccaaddcbabcdacbcabadbbcbdcdddbccccdaacabadbaddbbabdbdbddbcdbcdcbbcaabdcabcabddcdddbabdbbbcbbdbabdbaabaabcdbadcdcadcaddcbdddbbadbaddccddcdadbbadcdaccccdcaaccccabadadcadbbcdbbdbaabacbabcbdaccdbdacdccdabcbdccccacadbacaacadcccccabdcaaabbbbdcccbabccdbbdbdbbaabbdcdbaabbdcddcccddddcaaacddbdaddddaadabcabdbccbbbabcdbbdcdccaddddcdbbabbdbaaacacadbacaddcadabdaadcdcdabdbbdacaacbaccdcaaadccddbaadddbaddadbcbccdabbacdcbcabccabcabacccaadbadddcccaaddccbbbaababccdaacabbbbbbbcdaccabdbcdaaabcccacddabbbacaaddddbdbbabadbddcdbacbdacbacacdbbbbaccaacadcdbcbacaabaaaaadbcbadcbdabbdbbcadcabacccaddcaacccabcaddabcbdadbadabaccacaacaadaccbdcbbcabbabaccdaccadcacdbadbccdacacbacddbccdabaddcadbcabacdbbbcbaddbdcdbacbdaabcddbcacacddcabccddacacacddbabaadccddacadcacdddcbabbacdbccaccdbadcaababdadddcdaadcbdcadccdcbbccbddccdabcbddcbadbccacddbacbaadbbccaddaddaabadcadcdcbbadaccbadccbcdddbcaadabdddccdcabddbbdbccabddaaabdaabacbdaaccdbcbdccbdadaddcdabcbaacdbadbcbcaadaccdcccddbcabcdcacdbccdcddaaaccddadddcdbbccdaacdbdbcaadcadaadabccbbbdcdadbdabbabbbcaabbbdcbddaccadabddadddaccbdaadbddccbcaadddcbccaaaabdcacbcddadcccddaabccacbcdaaccaaaabcccbaabababdbdaacdcbabcaddaccddcadabacbdababccbdadacdccaabcddccbdddddbbcdabdaccdcbbabacbadabbcabbbbddddacadbdddbdbdbcacbbadacdcbcadaabdcdbbbdbdcaccdbdbddabcbaaccaabbdcabacdadbcbdbaaadaddbcddaadaccbddbdcacbdabbddccacccaabbaadaaabdbdacbcacbbaacbaadaddbdadbddcadcacacbdbbaccaaaabdcabdadddaaacacacddcbdcccacadaabdddadbbbcbdbdadaaacccccabcacaadcddcdaaacbacdbadbdbddbbcadcccadbccbbcabbdaacbaaaacdcbaacdcbcddbdcdbaaacdddacbcacdbdabccdbaaaabbdbdbbcabbdcdacbbabbdbaacdbadcdbddadaaabddaabbabdcccddcabaabddaabdaccbacbbcacdcbaddabbccbcdddcddbbddacabdbdadbbdcabddcddbdcdcaaccdacbaaccbbdcbbabcbcddbbbacabdcbccaccbbcabbbdbbbccbbcaaaaacbbadbbdbadabdaaacbddbdacdccdabbbcdddbdbbbaaaaaddbaaadabaaddabbccaacabdabcbdbddbaacaaddaccacdbcdbcadaabadaacabdddddbdcbdbbacdaadbdcbaabababdcccdcddababbacdcbdcaccdaabbdaccbacdaaacababdbbabcaacabdcbcdaababbdbdbbbaacbcdbbdabbaaadbbaddcbcaaccddcbaadaccbbdccbdabdaccabbacabbbbddcbdbaaaddbddbdacdcbdaabddbbbbbbcccdaabadaacdbaaddccabdbdbcabdddacaaddadccbcddcabcdbcdccdacddbcacaadadddabadbcccdbacdaabdacaccbdabbbbddcdacbabdcdddcbbacabbbcbdbcbabccbccbbaccdcbcbccddadcabdabbabcadbadcbdcdcdbcbbcadbdcdcdbabadadaccdcabccdaddcbdadacbbabcdcbdaabaccdcbcacabbdcccbdcaacccdcdcadaacbabccabcbadbcacdacbcdcbdbaddcdcdddcccdcbbcbdaccbacaabdbaddabdacbbacbacddcbdaacadcabdbcbddbcdcdcbcdcaadbbdbaccdaacdcbcbbdccbccdcbbdabbcdbcbbabbcacdcbdcbcccbcbaadddddddabacdcbdcddccddaaddabcadbdbccbacaaccddadbacadcaadcdcdadadaddacdcccdbbbbadcbacabbcbccbccbbbdcdbbacdcdbdbbdcbcaccaabbccaddbcbdcbbdbabcddcbcdadcbbdccdadbaaadaadbadbcccbabacddbdbdddcdaddddbbadabbbabaadaacbcbaadbcdabbbacabbccdabbccdbbbbbcbbdbcacdcacccdaaddaabbadbbaadcbaabdadccacdcbadaabbdaaccddcbbcacccdccaccbbdbccdccaaacbadddcbccabccdcaccdcaddccbabcacbcadacbdadabdddbddabdbacabdcccbabdbccbbcacbcdcbaacadbdcdbddadabacbaaadbcdcbdbbbbabdccaacbcdbcccbdbcccdcdabdccbbbdbabcdbdbaaaddaadcadaaaacaadabdccbadcdbbdaaddcadabdacaacccdbccccccdcdbabcdcbababbdddcbbacbcdbdcdcbdddaddbbcacbcdcbaabbbaaaaddbdbccccdadbbddddaddadacbbbbdcbbaddcadccdcbddcbdbbcacbbaabdbdbcbccbbdbbcdbdcddbcaabdadbaaaccbdbcdddaaabdcacabddcbcadcdabdaaadadbbccccbadcdddaaaadcccbdddddcbbbcdcbadbdbdadbbacbabdccbaacbabdabbadacbbcaaadcadcacaccccccccbaabaacaddbcbaabcaddbcabaddbaabacbccccadaadbdabdbccddddacccaacbddbcacdddcadcbacbbbcbacdccaacdadcbdbdddabbaacdacaabdcddbddaabbdacbddadbdbbababcacbcbcaaddaabacdaadcdbaaadbccbdcbbcabaaabaccadacbdcbddaaaaabaacaadcbbdbacbcacacddaacbcbddbdbbdcccbcdddaadcadcbddbdbabbccbddabddbdabbdbabadacdbbacbdcddaaadbcdddadadcdccadcacadcaacdaaabcdcbaacdcacdcacbcaccdaacdbbdabbbdbdcbaccaaccbcbaaadbbdccddaaadcaddbbcabddcadbdbbcabaaadbbcdcacbcddbddddaaadcbcaacabbdddbacddbcaabdbbaaabdcdaaabcdbcdcbbcdcaadabdbcdccdbcbcdadaadbabccabbbdcbcdbcdddcbadacbddaabaddddbacccdadbcccbdabdaacdcccdbbbbbdddabcbbacdcbbdbadbddcdadbddaddbadbdabbacdbdcdcaacadcbdbccabacdbcbadcdbdacbcccbdaaadbcadbbbcadaaccbdacacacdccaddaabbddddddaabcdcbccdabdcbdbccdaddaabdbccdcaaadbbbaacaacaacdbccddaaddccdbacdbddbdbddbcccacabcadcbcdabcbccdcbcddcabdddcdcadcbdadcaccdabdcddbadcbcdadddbadddabbbdddcacaacbccabcbdbcdddcccacbcbcadcbddadcbdbcbdcaaabacabbadaaabacccbadcdbbacaccccabcdacbbaaaacccadaaddbbbabcaddcadbaaacddadcbbccdadaddcdaddbacbbbbddacccacddcdacbbaddacacdacddbdddbbdcdacdacdcacadbcbdaabccabdabdccbbccccbaaccaacdddddddcaaccbdcbcbbdcaaaabdbdbadbacabddbccbabbddbaccaddddaaccbacaccddcbbacdacbddbacabcccdbccbbcbbadbcabddddddbddcbdcabddcbcdbdcadcdabcbcabbbdacacaaaddabdcdcccacbdccdcacaadbbdbcbbdaaabcabadbbbbbdbcbbdbcccabcbadcbdcaacadcdadbccadccdcdbacbadcdcbddcbddcdbdbcabdcbdabbaabdbcdbcbbbbbbddaabaacbcacbcdbbbdaddabacbcdbaaababbbabcddcaadadbccbdcacabddcbdadbbbbbbacadcdcdcbbbdbcbbddcccddbbcbbddcbdbccbdaccdddaabddacbcddadabbcaddacddcdacdadadacacddaccacbbddbbaabcbcadccaaaacccdbdbbdbbdcdbccbbbccbcadaaddbcddbabdadadbddbcaacabdcdcacbbbcaccacabdaccdcbdbdcaadaadbddbcabcdbbadbacadaadabbdbccacdcccbcbadbacadcaacabbccaccccbbcbddbcadbadccbaacabadabaaccacbaccabdbabbdadbcdcadbcdaabdbccbbbcdccbbbbdbbcdcdbdadabccdabbaabdabdccaabbaacabddaadbddccddbdbcdadacdacccbdbaacadcacbbacdacdabbbbdbcadcbacaacaabdbbcabcadcccdbbdccdbadadbdaacdbdadacababbcccaababadbcccdacbadccddddadaabcacdddcaddaacddbdadadacdcaacccddabdbdadbabbabdbbbcdddbadcaaaadacdbcdadbbdabbcabcabbacdadccdbddacacccacccaacaacdbdabbcdbbddaacbcbbbadcaaccacabddcddbcdbbdacccbcbabcdabcbbabbdcbdcdcaccbcdaadbcdccdcdadaddccbbcdbccbabaaccbdbccbcbcdcbaabdadaacabbcbccadbbaabbcdadbbdbddbdcdbabcbcaadddaaadabddccbaaaaaccdbdadbdcbdcddccddbaaacadbbccaadddccddcdcdcacadbcbdadddccdbaccaaabadaddbbcbddadbbbbdbcbbcabaabaadcdccababbcacbdcbcccadacdbaadaacbcaddbdaacacdcadbbbacaaabcdccaccbacbbaacbccdbbaacdadacaccaacaddccabaacdcbdccdcbddbcdcddcabdabbddaaacadcbcbcaadadbbccbddcadabdabccbccbbcddccdcbdaaabaaaaabcadacabaaaabcccbcbccdaaabdaacccccddccccbddaabbdbcdaababdabdbaaabdbbaacdcababdadbdddcdbbcaabbcacbcadbbacccdcaaadcbbbbabaddccdbaaacdaacadcababcccccbaabbabccbcbbcaacbccbdcaaccabdabddcaaabbbabbbdaadbcdddbcbcdbcddcabacbbdcacddaaccabbadacabcdcdcababaacaadddccaddddaababbbacdbdbaaacaadacbcaddcccaababdccdcdcbbdbbcbddbdcddbccbaabcddcaaadbacacaccdaddacaaadaadcbdbbddbcccabcabccaddabbccbadadacaccacdcdaadbbdbcddccdbaddcaadddbbababcdacacaabccacabdcccbadaaadcbbdcdbbcadcacadabbaddadbacdbcadbabdbdbaccbcabdbbcaddbacbbbbcaccddcadbabcdcbdbcdadabbdabcababbcabddaaccdbabbcbdcbcccddbdacadcabcdcaaacaadaabccdabaabcddbdbacaacbcbdacaccbcbacddbaddcdadacdbbddaccdadccdbcbdcdcaccccadddacbccdaabbabbddabccbdccbdbddcacabdddbaaabcdabddbbdcbaccadcbdcaaccddddcbdabcabbaaabddbabccacbdacadbadabdddcddcaccbaaccbaadacbdcccdbbdcdacdcbdacdabbbdccacaaacdcacddbbcaadbacabbbaccaacbdbaadacdaccbcdaacdabdadbcdcdaaadcccadadbaacdaadccadccadccdbadacbdcbccdcbdbcbbddbddcbabdadccabbabbacbcadabdbadbbcacaadacbddcddaadbddbdbcaaddacacbdcccacdbbccdcbaccadcbacbcaaddcbccddaddbbccdadabbbdcbcdacacaddcabdcddddcdbdabdabadbcdcdabaccabccbaaacccacadddcdddbadbbbaaabbcbaabcbaadccdabadabdacbdcacacbbcbbbdaccdcacccdababaabdbabdadbccabccbcabdccbbcbbcaaaddaadccacbacaaacccaacbbbadacbacddbbadabbcadbadbdaacadbdbdccdaabccdbcadcaacbccbdbbaadcbbacddcdbaaccddaddaabccccdbdcacccccccddabaaadabcdaabbabcaddbcacbddbadaacdbdaacaaacccacdbbbadcccdbcbcddbabdcbacdccbacccdcacaccdddaddadbbbcadbccdadadbdbabaaaaddbdbaadaccdadbbcddaacdbddaaabddbbddcdddadaacccaaacbacbbaaaaccbbcccbddaabdacdcbcccdcccddaabdcbacbddbdcbcbbdbdaddccbbcbbdcbbadbccbbdcccbccacaccdcdabdcdcdcbbabbcddbbbccdccadadbcaccacabcbbcccdcbbaddcacacbbbbabccaaccbdcadacddbdcbadcabdbbccccaaadbccbcbcbbbdbcadddddabadcaacaadadaacddacdacbbacccadbbdcbaadcbadaccaccadbbcddadaadabddbcddabccdbddcabdbacbdbadacdcbdccdccabcaadbdcdcbcdadbbdadcddccadcaaaabadbbbdcdaacdcdcaddcccaaabcdcdbbcadbbdcdadbaccbadcadadccbbcacdaaddaabbadcbabaaaadbdabddddaaaaacbadbcabbbbbcdcadccdbcbcccadbacdacbaaaaabacbddddadacbbabbdbbabccadddaacaadbdaacbdaaabbbccadbbcbbbccbabbccdabaaacdabdacbcdccdcbbacbccacdaccccacddddcbbdaadabdcbdbcbbbcbddaccbdcdaccbbdabdccdccbaddccbaccbadcadadcbdaddbaaccccaaacbcdacabdcadbbbacddddadcaabbccaaccccbdbacdadadcbbbdbdbbdcdcdbdccddadcbddcdacdcccbcdcddbacddbbbacabacddbbdcbbabcabddabddcbabbacbcdadbaaaccdcadccbdcaabadabdddbdbdccbacdcccdcabcbdcabdbdcddabdccbadbaccdbabbaadccabcbbbdcbadddabdbcbdcadbcacbbadbddbcbacdbabbbdcdccbccdcdcbcbdbdbddcdddcacbadabaaccdabdbacbcaacbcabcdbbcbabbacabbbabbaaaadccdcccdbbdcdaababcbacabacddbbabddddbbbadaacddabddcaacaddabbadbbbccdababcabdacbadcbbbccbcbaaacbccdadacccccdbcbbcbaababdcbdcdddaaadccabcddcabcdacacdabdabbcadacacadcccbcbdabbbdcdbdcccabccdbccccadcdabdacdcccdaacbdadcbbacbababdbadababcbbcddcacabccdcbcabdccdaadccbbcccacdcdbcdcdccbbccdddcddaddcabacadcdbddbdcaaacaaddcacbdbbbbaabaabadcbcddabcbdcbcbbdcaaacdaccbadabaadcbdcdcbddbddcbcbdbcbdcccbbddadbdddabccdcddddbadcbcbabcdabddabbacabbbbdcaabadddcaababbababdcdcbdbadccaaddadcdacbabbaddbccabccdddaddccacadbcdddcdabaaddddcccbbbbcbcdadadbdcaacaacabcabcdbddbcabacdabdcacdbddaacacdddbdbdcbddabdadbabbacccbdabcaaabdbddaabcabadadbbdbadbdcdbadcddbacdbcaadaabcbbbbdcaacddddacabaadcbddcbbdddbcdddcddadcbabdbbaaaddadaccbbdddaccadbadbbdaadadccdbdaaacdbcadbccbcdacbddddcdacbadcacbacbadaddbccdbcaddbdadcdbdbdadccbddcbddbdacbdcadbdbdacacdaaaabddbcdcbddcdaaacccbacbdbaccbccaccacbcbbbbbdddabcbbdaaaaccbdcacbbabcacdddbaaddaaacaadadaabbdbcddcabdaaddcbbcdaaabcacdabacdcccadaabdaacdbddccacbbadddaccbcaabadacbaacdbccdcbacaabcbaddbcabdbaacbddccdbcbcbcdaaaacdbccdacdcadcdbdddabbddcbccdbdddcbdcbcadcbadaacadbddccccddcbdadadacdacaccbdbdaaadabddaddddadadbccbabcacaabdaaacccbbcdabcdcdbabaddadcdbbdcddbcacbcaabcdabbbacbbabbbcdcdbddacdcadacdbabaccabacacddbabacaadbccbdbbddcbdacdbdcaddccaacdacdcabdcadccacbcbcdbddcbaadacdcccabaadabddadcaaadbccaacabccaddcdaaacabbbacacdddccabcadcdbabcaacadbbcabbcdcdcabbcadccddabdbdbddcacbcbbadcbadacdbddacbccdcdbaccbaabaddbbbbabcdacdccbacdcbcaabadcbabdbdcdcddbadbbcccdbaaccccdbcadbaddadcbcaccddadbbcbcbaccabbbabbabccbdddbbcbaddcadbcccbacdddbadccaacbdcbdbddaccbaaadbbcdbdaccdddbaddacdbbaabcdabbdbcddcacdabcbdadccabcbdabcabaadcbdcbdcabaddacddacbbaccaddbcbbaabcccaaaaacbdbcddcccaacaaadcbdadabbabaacadbbcbcaabcbbdccadadaabadcbcdbadaddcacbacdccdcaacababccaaddbddcccadaaacddabdcacbcabadbcaadcbbbdadbaccdcdbbbcdbcbdcbcabaddbcbaaccbbdcdbccbccbddddacbcacbcbbabacabddbdbdcdcdcdbcdacdabdcaacadaddbadcddbcacdadaaabccabaadaacacacccadacabacdcbdcadaaadbbddabcbaddbdbcdcbbccacbaadddbaddbaacabdabaddcbddabddddbdabbadcacdbbbbdcdadaadabdbabddbdbbcbabdddaaaacaddaccdabbbccbaaacddadcccadcbaadadbacdbbacddaaacacdbbadadbdcaacbdddacddaadaccddcbdcbbcbbcbdacdaadbbbdcaabdcaaabacacaabbdcaaacdabbdabcccbaabdddccdbabdadcadcacbcbdccaacaabbbdcaadbacbdcbdcbbbdccaabbddbbacababbbaacbdbacccdadabdbdbdacdacdaddaadbcdcdddabacbbbcacbddcdccbddacaaaaddbbbcabddcaacbabccadcabbccaadccddccdadaadcdcdaadacdcbabdbcdbcacddcabbaddcadcaccdacdabcacdaadadcadacacdaccbaaadbaccbbddaabddcbabdccccabbcdcbdcdaddadccabddddbbbcbccbcadabaaaabadacbabddaddbdacaaadcaaadbdaddcdcbcabbdabdbcbdcbabcbccbcdbbacbacabcbdcbdcadccbddacdcbdbddbcdabbcbddcbacabcbcbdabacbcbdcbddddccbbbaccddbdbbbdbabbacacdbadaabaabdccadbdbdaacdccddbbadcdbdddcddacbdaadbcdacdcdddabbdbcabbcddccaddcbcdacdabaaddbbdbabbbadbabcbdaaadddbcddacdaaabaabccbaaabcaccbbccbacaddcadbbbdcadbddcccdabddaacbbcadcbacddacdccbcaaccabccacbcdabcdcbadbcdcbbddbadabdbbddccdbccbaacbbbdddcaaabbaaacaacacbdabbaadcbdcaadaabbbbbbbcadbddcbcdabbdadcbbaccbddddbcdbbaccaccadbcaacabadcaababacccdbdbadddaabadddacaccabdbdaadbcddadbcbacaababdbccaaaadaacaadbdccbdcdaadadbdbdcaccbddcdcdcccdadaaadcdcdbbcdbcdbbaadcbbbdbbccbccaaabbbadddaacacaadbccdaddadcbbcbdbaccbccccdcccbcaadbaabdddddbbdcaddaabcbaaaddccbcabccabbbacacbcbdacabcdddbbbdaacdcadbddbcabadbccccdcbbbcadacbbdbbaddddcccddacabacaacdcbbcabcdddabbccacaacdcaacdcbbdabbdcbbacacccddcdaaaaccaaacbadacdddabaccbdacddbbcbbcddbdacacdcdbcdddaaabdabbdbbbacdadcabdaadaaaddbbccdcddcaacddcaddbabbbcaaacbcbaacaaccccabdccdcacaabdaccdccabddcdcbacbacbccabaddaaadcdaccdacacdaddcacadabcbdcccdcddbcbbcabbcabdaababddadcbdabbadacbdccdcbdbadaacadadbddacddcccbbaccdacacbabddcadacadaadbccdccccabaaddcbcbadccadbaccaddabaacbcdbccdddccddbabbbbdcdddddccccbcaabdcbcccabbbbdbdacaccbddcccadacaacacbbabdbadddaaabbdaadcaadddcdccdcbcbabcdbdcaadadbccaadbcdcccadbbbbdaccddabdacdcabdadcbbbdbbcdabdabdcccdccdcacabaabadbdcabbdcbdaaccbbdcccabbccbcdbaabcdcbcacbdadbdcaabdccbcddacdbaadaacbdadacbbddccbcdacaaadadccdbccabcadcdadbabbacaddbdacdcdbcbccdadbaccbcbabbbdaabdbccbcdbcdacabdbacaddbcaccbbbabddbddbcbdbacdbdaabbdadaadbddccccaadabdcbaacdcbdabbcbacbcdabccadcacbdadacaddadcaddbcccaaabbbbccddbdbbcddbccabbbdbdcdbdbdbdadaddacbcbabbddadadbdbacacbdaacdccddddabdbbbcdaaabdbdbcbabcdabaddccaadbcbbbbabbbdabccaddadacbbadbbdcbbbdaaacaadbddabcadcbaaccabddcdaccbcdaacbdbaadbbbddcbcaddacccbadbcadbbcabccdcbbdaccdaacadbbbdabbdcbddcaaadddddccabbaaaaccbbddcdabbbacdbdabacaadbdabccabaabccbdadbcaccadbcabdadbbbacbacdcadccdcdabbacdbbcabcaadcaccacdcdbcbbcbbcdcabbbccccccbababcddcadcabadcddabbacadabddbdbcaccdbaccdbdaacdcdbbbaaadacbdaadddccabadcbaacaaddddcadbcddadbbdaccabacaacadbcbbdcbdaaabadabcccdaddddcbacbdadacddabbabdcaddaabaaadcaacdacddacccacccadddbddcacbcccacadbcaacdadacaddcaaabdcddcaadcdbccabdcbcaacccbadbdbcbadddbbcbcabbcdacaabbcdbabcdbaadaccbaaccbabbbbcccadbcbcbbbadcbdbdadbbaaaabcaaccaabcddddabcdcdbaadbababdcacbdaaaddaaccbacbcdbdccdaddabcdcbcdadbddccccdbcbdcbbdbbaaabdaabdcdadcddddccccbdbbacddaadbbbdabbdbdbaacbabcacacbbbabdbcaabdaccdccdbcdaabacdbcbdcacadbbdddbcbdabddbabdcadabdcbbbdbbadbbabcdaacdbdaaaadbdaaabcdccdacdadbdbabaaadaacdddaddaacaadcadacdadbacdbbcbbcaaaacbcddcbbdccbabcdddcccdabbdabcbdabbaccdbdcdaabbbdccbacabcabcdccaacabdcbbbdaadcabbaddaaabcacdcbdaaabbcdddbbaabdbbbbddbcaabdaadbdacabdacbcbdccbdcadacbbdcabcbbbadbddacccabccbdacbacacaabdadacdaabbdcbcbdadabddddbaaadadddbaabaaaadabcacbaccabbddbaaabddaaddbbcbccabccbbabcbcccbbbdaadbacabbacbdcbacbcdcdbabbaacdcaccdacabbcadaadcdcabacabdbddbcaaddccadcdbadadddcdadbabbdacbbcbaaabbddbdddcbcabaabdbdacabdadbcacaccbbdbdddccbbaadcdddbdcabcadabdabbcdbcabaddccdddbcaddbcaadbbcccbdadcdbacddaaddddbacbacabcbbddcacccdccdacadddbddbbdccdabcaacdacadbddccababddcbbbacbaadbbdadadcddacbadaabbdaabcbbbcdddbcaabbababdbabcabdbcbcdacbacdbbcdacbdcaacbbcdccddbaddbdbbdbdbdcbcabddcaaacbcaddbbdbacbbcabbabcddacbcaabbdcabacabccbbaddcabcabbcadbadccbcdddabaacaaaddaaddbadacdadabaccbddbcddbcbdadccaddbbdaadbbcaaaadabaadcbcaadbbacadbcbacddccacdadbcaababacdddcbdcbabacdaadbdddadbaaccbddacbddacacdaadbdccabcdcbadbbccdaaadddaddaddbbbbaddadabbdcbcdcdcaadccabbcbbddddbdaaccaccdcadadadccdbbabcdaaacbcdadaadabdbbaacdcbdaacbddcddddbcbbabadbbdadaacddaaaccbccdddbcbcbcaacbbdbccdbdbbbdaaddadbbaaaddacdacdcdacdbadccadcadbdbaddcccdbdaadbacaccbccbddbdcdbcaaadccaddacdaaadaabcaccaddcabdbdaabbcabaaadccacacbcacbaacabdaababccbcbbadbddcbbbbcaadaaddcccbdbabdabcddaaddddbbbbccaddcccaaccdddacacbadbaacaabccacdbacaababadccdacabcacabbadabaabbccabaabadaccbbaaccbdabbabdabccbbbacabddcaaadaaddacdabcdddacddaadcbbaddbcccacabccabbdcbdbccbdaadccbadbdcabdddbadcaaadaccdbacdbaaccbcccbdcadaadbbccdcdaddaacdcbbbccadacbabcabdbbbacaadbbdcabaababcdadbbcbbadbdcddaacabcadcaaabdcabcadacdaaadcbcbddaabadabdabbbbddbbabcbcccbbbccccadaabbaddbddadbbbddcbacdbbdcdacccdbbcbbabadcaabbadaabdccbaccdaacbbcabbbabdbbcacccaacdababaacccaacddabcacacaaabbcaaaacabdcbcacdbadcabdacacccdabacadcddbbbabbbcddccbacaabaddadacaadddaddccabadddbdbdbdcbbadbcdadadabacbdbdddacabcccddadadcadadcaccadcbaabaabaaaddbcadabdbaaaaaababacdaacacbcdcabdcdcaababcbbdadbdcdbabccaddcadcddacdddbdaabadbdddcdddbbaacaaabadacddacabdcddcbbdbadabdbaadbbadcdcdcadbcbdbababbaaddbadcabdcbbcacdccdbadcbbcbacaaabcbdccdbacacbaccdaaadbccdccdbdbccbbbbdaccabacabcabadacddcabbbaaaaccabacdabdcbadcaadababbdcbddbdbccdbbcacbbacbbbcdaadcbcabadaababcbdaccbbabcbdbadaadaabbbbabddcdaabdcaabdbdccbadacdcababdddabdababdcddccdddabddcbacdcbbcdabddacdccdddbbdaadabbcbbaaaccdbdcaddcaabaadccdcbaaacacbabdabcaadcabaadadcbccdddccdaabbccdaacbdddabaadcbcadbdbdacabbcbbdddaaacacdcdcaacdabcbaadddbacdbbddacbdcbcdabcccbbccadbbaddaaadbdaadcadcdccbbaacbbbdabccacaacaacadaabadbdacdcbabbdcccacabdccbccddbaccabcdcdaaaaadbddacdcadbbcbbaaccbaacbcaabdbdbdccbacddbbaaadcbdaddddccaccacacadadcabccdccdbaddaadcbdaadbbddddabdaaaababdcdcadadccddcbaabcacccdbdbbbacbcbbababbdcbdccbabaacddcabdbadbaddddbbcddcbdbcbdddcddccbcadddbcbdbcddddaccbdcbbbaabaddabbdadbbcdbdbdbbbbaadbcbbccadcbdccdccaabcaccacdaddbcbbbddbdcbcdcaaaadccbddbcdbdcbccbbcadbbbbaccdcccdcbccaabbbbcbbbdddcbbabddccbacdddcbadccdabaadddddbcddddcbaaaabbbddacccddcadbccbacaabdcdaabbbddcdcacaabbbcbabdacccddadababbaaabdbaddbaadbdddddbbbccbddaaadcdabdbccdddbccbbdacacdbdcadcbcadcdbaabdbcacabbabcbccadbddcdbcadaccdddcbaaaddcbddacaddccdccdbcdccabdacdacadddcccbbcbaddddabbcacaacabbbbdbcaacababdccbcccadbaabbcddacdddccbbaadbdabcbdcddcaccadabaddbbdbbdbbbadbbbcbabbdabbadcaabdcdbccbdabcbdddbbadbaacacaddbbbababdaabdcdaadbcacacacdaaaccaacbabcaccbcdbdbbddabccaabacddcdccdabdbcdadacaaadadaabcbccaaaabddacdbbdcbdddadadddabdcbdcacbbaddcbaacabbaacdcacdbaddaadbbbccdaaabaccdbdbddbbbbbbdacacdbdbdbcacacadcaaadaddcdadabcaccddabdabcbccadbcbcdcabaabccadcbbdadcaaaddddbbabdccabdbdccacdbadbcaabadbbaacaadadacdadacbdcaaddccdcccdcabdddbbdcccbacdbdbdbcdcccddbaaddbabbaacaddcdbbcbacbaccadccacabbbccacbdbbdbacccbcabbdbcacbdbcbdcbddcdbdcadcaddddbaaacbaaaabdcbcdaaddbadbaaaddddcdbcdbddacccdccaccbaadbbaababdaaaaadaababbcbbdccbbcccbbadccbcddbabbdadaacbdccddacacdbaabaacabdadadbcbdbdccdcbcaaabbcaaacdbacaacccdcdaccdcbacccccbbdcdcbdabaaddddabaccdaacbcaddabcbcdaaadccbdcbabccbaccaaadadcbaadacbbcdbdbbbbcababdccabddbcbcadccdcadbcbcaddbcbadbbaabbcaaccbaaddaddcdcdbcdbcbaabbabcccccdabddbccbadbdaacacadacdbbcdacddbbabddaaaacbcaddcbbadaccbcaabbacbdcddaadcbdbbcaddddbccaadcacaaaacbaabaaababccbdbddabcbdaccabcabdbcdabcaccabbacdbddbcccaccddadbaccabcbabccadabcddbaadabddcccdcabbbddcbdaaaadadcbdbacccbddcddacdabaddabacaccddaddabbdacacbcdabccbbbaabaaadbddbabdcccbbdadabbdabbcddbaadadcabbdcddbbabcbdccbbdccdcbdbcaaadbbacccbdbdbaddacdabdadcacdaddaaccdcccdabadcbddddbcbaabaabbbbbdbaabdccdbaacbabbadcdbaabbbababadccbaacccbaaadccabbbddcabcabcacbadcddcbdcccacacdaaccbdcdabbdbddcddcbcaddcbdabddcacdbdadbcbcbdadacddabbcbdcccdcabbcacdcadaabbbdaabcbbaabbcadcdcbcaabcbdacbcacbadabdaadcbbbdcdccbcbbabbbbcdbcaabbcdbbcccbbbcddbbcdaddbdaadaddbacdcdddadabadccbddaaadcdaabbdbaacadddccacddbabccbbacacacadaddcddbcdbcdadaadacacbbdcbddcbbcdcacaadcdbcaddcbdddacdcbdcdbdbbbcacdaadaaccdcdabbbcbdaddacdabaddadddacadadaabacadbbbcbdbddcddbaaabdacdbdcccdcdcbbcdcacdcaaccbcaaadddccdcdbdbdccdabccacbacadaacdacacdbddcadbcbbabacaaadccaaaccaaabdcbbbabadcdaaacbdbdbcbccbccdacaaddddccadcddcaddbadbdacadcaadcdacdccbccdcabbbcabccadcadbadcbbabbccbaaccbbccddcbababcabbcbabaccdccababddbccccbcdaaccdccadadccdacdabcacdccccbcdcacbcccbbbcbbcdcdbcbcdaacbcbabdcbdaaddaaacccccbacdbbcabbabaabadcacdbccacabbcadbcbbddbbabacbbabbcaccbdadcdccbcbbaacbbdcbaabcccccbadcdabcdddddbbaddbdcccccddbcbdcddcccdaacddadcccddacbddaccacbcbbdabbacbaabadbcdcadbbdaccaadbcaacaccdcccadccdbcbbcdaaddacbdcbacadccaadbadabcdcdccbdabcbcabdaadbcbbdcddddcccbaccbaacaaccbadbdabcbcbccbbbbdbdcdcbcbcbdcddbbdcbcbbbdadacdcbccacddbbacadddbbaaababdabadbcbdabcdbcbdabacacddacdabaadcababcdabbbccbadaadabadaccbbbadccadaacbbbbaacdacadcbabbcdadabcbbdabbbbcccadaccabbbccabdacdbbccbccdabadaddaaaddcbacdbaacbcddbbddaacdbddcccbdacdcabcdcbabbcacccdbcaacabddcccddaddcaabbddbddbcbbaacdbbbabcabdabcabbaddabdddccccddbabaadcaaaaabbdbdcadabdbaaadcccddbacdadadbbcdaaaccdbbcddabbddaddbaaaabaccdddccaddaacacdabddbcbcdacabdbbdbdacbcbbbcdbcbbcaaabdcddabaadaddbbdaabdabaddaccbacbbbdcacdababaddacbbaacdcbdcddddcabdcdddadadcdabadcabcabcadcddcbabacdbddcbbcdaccaadcdbdbdbdaaadcabddcbdabccbbcdbdddccddadbcadcbcdbdbddadaadddcddbbbcbdbbabbcbbcabcbcdbbbbbbbdbdbdadbacacdccdcdadadbcbacdcbbbadbccdacdcabcaccccbdcdabdabccbdcbbcbcbdabacaccaddbaababbacbccbabbcccaabccdbcaaacacdabdddbcabbbbbcdbbabbadcbaacbdcaaacbadbcbdddbdbbacdcccaccbdaabbcacbbabdbbbcdbdcadaccadbdabdbacccaabaabdadcbbccddacadabcbdcaaddadddaaaddddbcdbccdaacccdaaacdddbcacdcaabaacaddbaaabacbdcccaccdcdaaadccbccabaaccdcbbbabdabdcccaccddcabaadccbbcbcddddacbcbacbaadcbbbacbdddcbaaaacdbccdccddbdbdcbdbdbdddcddcbbbcccaabbdacccccbdbddaadbbadaacacacddbccbbaaddaacddcbadbcbdcdbdcbddaaaadcdaabaaccadadadaaaadcdcbcbaddbdbbcdcabcacdacdadcabccdbbabadaaddcddddbcccabbcdbcadadbaaccbcbdacbcbbacbaabbdacbaaabdcbcddaabdddadabdcadcbadacccdacccaabbbbccacdcbabbbdbbacabbcabbcccbbdacbbbcdddcddcdcccaaddcabdabddbccbbddcbaddcdbdbabcaabbaddcbadcaadbabbbabacdadaadadddbcbbbccabbcdbbcdbbbccdbcbadcdadababbcbccdbdadabacbadbbaacdacdabcdbaabcbaccdacbcacadccaacacacdaddaacbdababbabccddbdaadadacbbaabccbdcbaaadadbadabbdaacaabbcdcdcaddcacaddddaccbcbbcaccacbadbcabaabdcbabcbbdababdddabbbccbcacbbbcaaccdbadaddccadbaccabdbbadccbdaadadcbcbcddbabbaaaabbbbdcbaabbdddbbdbaccdaababdbdabcaacddcbddbccdacddcbcbdbcddcbcbadbbddcddbdddddaaddbcdaaaaccbcbabddcadbabbccaccbbbdcdadcdaccddbdadcdbccaaaadbaaaccdbadcadaabcbdbdcbdbdabccdbbcadbcbadaddbacdbdcdacbdddcdacdabcbbccadaacdbbbbbaacbdacbdccaabdabccaacdcabcaaaccbdadcdaccacdaddddacbbdcbadddbadcbadaacaacdcccddadabcbdcdcdbccccdabbdbbbbcbddbccdbdccdabbaadacdbadbabccccdbdabdabbbacdaaadcabdbabbdcddcbacbdaacdacaacacdbccbacbbadbaadacabaaaccdbcbacbcabcacdcacdcbccccdadcacacdbabadbdcacadabbcdacbbdbaaadaabbadaacddbabddddabcbaacbdcccaaaacbaabdabdcbcdbbaacaddacbdcddcdcabdcbacadbcbcbabcdcdcddbdbabbddcbabcccbccbdcdacbcccdcdbcdcbbdcddadadbcbcbdcdbbbadbdabdacccccababaabadcdcbdddadddcdbcdbabccccbbbbbacababcabbcacaaacbabcbdbbaddddaacbdcbddacabdcacdaddacdaccbaabcbdaccdbcacaadddccaccdabdbaadbcdacadcbbcccacddbddbcacbdbdbadbabccddddaaaadbcbaabdddbcbccddccbdddbadccdcdacdbbbabcabadbcbddacbbdabcccbdacccbbccadaddbcbdabbcccabbbacacbcccbadddddbcddbddcbaaaaabbccbdacbddbddddbcabbbbdbbcabacdbabacdcbbaddcbaabdbbbdbccdabcccccaabbcdcababdaddbacabbadbdcadbccbabbadcaaadadadbadcacadaaaabbabbbbbbadaccdcabcbbacddcaddabccadacccbbcbdbddacaabdbdbbbacccdaabcdbbcaaccdabcaababccbdaadbadadbdaadddccbcbdbbdbcbdcdbacacdacbbbbcbdaaddccbcaadddacbbcabdcddaadcbdcabdacbaddcbadcbbcacaacaadbabdaacacabaababddbdccdccbddbbdbaacdccabcaaaabbccadcabadbbcdaacaddcdacbdbccccadabbdadabcdcbbcbdadcadcdcacbadcbdbbbddabdacdbcdbacdcbadcadbbbbdcbacddddcacbccbcbbbbdaaddcbbcdbdaddddaacbcccaadddaddbdacbabbddbdcaacbdbadcbdbbadcbdbcdbdbdacbcccbcdabdcdadddaaaadadbbbbaacdacdbbacbcabccbbcdcddbcddadbbcdbacdadaaaaadbcacabcdadbcbbdbacdcaaccdccabccdcccabcbacddddadbddaadcdcadcdcbdcbcbadbaaabccddbaccabdacdbcccaccabadbdbcdbbbaacdbacdccaaccbbbbbbdddaacbcadaaaaacddccdbdcddbbbaacdcccdbbddccbadcbddbbcccbbcbacdbabcaccbdcbaddaadacccabccdccdbaacbcaadddbdcababdbccccbbbacbdbabaabdbdbadcbccbccdbbdcdadbcbcaaccabdbbbaccdbbbdbbcdddadaaadbbbccabbabbcdbbbbbbbcbdadcbdbcbdcccbcdacdbcdadcaacdddbaccbcdbadbcaabdbabdbdabdabcbbdbbabaccaadccbcdcbbaadddbdbaadccdbbabbcdacddbdadaacdbdccbdddcdccbdbdaadbbdaaacdbacacbacabcadcccaabbacaabdadcacddbbcbacdcacdacdccdaddadbdcbcdddccaddbaacbcbddccabcacbadcdcbbbdddabbdbabcacbbdaacabdcbaadcdabaddbdccbdabcaaabbadabbbcccdbaccbdbabbacbccbbcccdacdbcbcaacbbdbaccbbcdaaccdddcaccdaabbbcaccbbbdaacddbbdbdcbcbaadbbcbdcbddaaddddcaadcbbadadbbdcaccdcacadcdabbadccddaddbadccdaddbadcdabaaddbbdbbbcaccdcbdcbdddcbcadaadbdbaddabcacaaccccdbdcdbcbcccacdddaaabadcccbbcccdddaabacddbaabdcbaddcdaccccadbabdbdcdddabbdcdacdcbccccdbacaccdddcddcdbbadadaadbbbddcbbbacccddcaacdcbbcabbaacbbbacbaabacaabdddaacccaadacbbacbbcbcaacdacbbabcdccddbcbdaabdcbaacbccddacaabbabdddcbddcbdaaadaabbcdcaacabbbccdccabbcccbcbbdbdbabdbabcddbacabbaaaaddcccdcabacbdbaaadabbccbdaadabbddbdcbcbdcddbadbdaccaacacbabddddadacbdabadcabddaccacdabccbbdadbcacdccbbbdbdaaaabccabbdcbacdbdbdcccbdbbcdccbbcbcacbdbbdbdcdabacbbaaabadcaadaaaaddacbbadbcbaddabccaccaacdbbbbadcbdaacccddcdbbdbcddbacdadaacabcddaadcbdcddabdcddaadbddbabaabadddbdcbcacbaabccdaaabbdcbbaabdadcadcdbabbbbcaccccdbbbbbcbbcdacbccbddcdbacacdcbbccccbbcbbbcbcabaadcdabdaacdbabbbddddddacabbaabdbdcbddcdbbbcaabdcacdcacbbbdbdadaddbbcbacbaddbdaababbbdcccbacbbadcdddcabcddabbcdbcbaccccbaaadcbdddccdacaacbbcaadacbcbbcadbcdaabcaabcbaacacbdaddddcccdaaadadddababccdcdbdcbbacbcdbcdacdccadcadacabddbdcddbadcccdccabdadabccdacdcdbdadcacbdbdaacacccbcaccacabbdccbbaccdbababddaadcabacaaacadccdccdbbcbabdbaacbbddbdcadbcbaccabaabcbcbacaabcbcddcacccbccbaabdabadbbdadaacabdcbcaddabdadcadcdaaacaadbdcacdccdbbabcaadaabbabbdcddacccaadabbaacdabcacdbdbcbdbbbbdddadccdccabbccadcdccbdbaccbbbdbdaaccbabddacdaabbcadbdcbbaaacbcdbddbdaaaabbdbbdacaacbaacdddabdcbddacbdcccacdbaacdacbdddddbadcabcaabddddaabcabcaaccbccbcbadabbdabcbcddbddaddddccbccadbaadadaccadcbcdcdabbbdcadcacadbbabaaadacbbbcbcabbbaaabbdacbccaddcdacbabdcddcabcabacabcdcddcaabdcddcdbbdadbcaabdabadbbbcbdcdbccbddcabcdddadaabbccadbadcbaadbdabcbccacaaabaaaacdabbcccddbccaadabbbaababbcbddacddbacdbcdbcaadacbbcdadcdddacdbacbdcaccbbddaadbaaabccbcdcacadcdaacbaadabadaacdbacdaabadbddabccdbacdcaabbbbcdcabcddbcdbaaddcbcdbbbdcccaabbdacabacddbcabdbbabbccddababbdcccddddbaacbddcbaadbbbacccacdcdaddcadcabcbaacbdccabcbbcdababcddddbdcdaccaacaabbddadadddaaabcbcadccbcbbacbabacbbbbdddabdbdbcccacabbdaadabcadcbadddcbacadcaacccdbacbbdbcbbcabaadcdcbdababcabdbdbddaaadcbaacbddddddcadabcbbbacddddabaaadbabaddbdabcacddcdacdbbdccccdcdbabbbccdacddbdcbcacadadaccdddddaccbbadcbdcaaaabccbabacaadcbdcaacccbcbcdbdbcbdaccbbaadbadcacdddadccbdcadacbadadbadcdbcdbacdcacdadbccbcacababdcddaccbaddcdbdbbbcabadbbacaaaccbdbacaabdacacaccccdccabaccdacaacacdabcdbcbdbbdacdddddcaaadddcaadcbaabcdcdcdbcadaadabacadcdabcdcbbddbaacaadccabbdaaadbadaabbdccdbccddaccaabcdaabbadbdaacdcbbadaccdaddadaacbacaacbddaabbbbacdbaccbbbddbcaddbcabcbabdbbbacabcddddacdcdbcaddacddadabbcbdabaabbddccdacbcaddcddcdcadabccddcabcbdadbaacaacadcadaddccddcddaccbacaacbbddddcbaddbbadaaabbbbaacdacbadaadacccdddcacdbbabcbadacbabdcdabaddbacbbaadaadbdccbabdcdaaabcaaaaacdccbaabcbabadbadbaadbcccbabbbcbbaabacacabddccadbccdcbdcddaacccddcabcdbaadaaaaabddbadbcbccadcbbcbbbccbaaccaccbdccbbcacbccbdadcbabddcadcdadcacabbbbbcbccddbcbcbdcbbdbaddddbabbabcbdaaacbbcbdbdbacabacdcddbdbadcadaaaaabdcbcbcdbbcaabadccbdbaacaaccadbcaacaaaacbcabdcabadacccddcbdbbacdccccdccbbacdcacbadbbabcacdbcabcbbabbcbbdddccdcadaabaadacacadadbbbbacbcbaabddaaaadcbdbdadbbabdaccaaddbdacadaccaaadaaaacccbacbabbdddbadaaaaccaadcacaddcdcadaaacaabcdadcbbdbdabbcddacbbbcbcdcccdabdaadabbcaabdaacdcadbaabcaabcbbdcbdabadcddcccabaabbbaadaaaddcababdcabdaabdcaacdcadadddddacacbadabacabcdbabdbacccddddadbadbccbbadacdacabaaacabddaaadcccdadccaddaabcdcbddbacbabdadcbdcabbabcabcbaaaddbcbcacadcabcbbbccacdcbbcdabbcddbcbabaadbcadbaccaadaadbdbcacbbdaddcbcbacdcbdbbcbbdcccdcbbcbbbcbdaddaacbdbdbbdcccdcddabddccddcaaddadacbdcdadbddbcdcaadcddbcccabaaabaccbcccddbcbddadaccbadcadacabdadccddbcddabaacbacacccddbdadcadcabbdbdbaadadcddadcbcddbbaaabdcacaabcdcadacdacabaadccdbaabcbdcdbaddaacdccacabddaadbaccbcbddaadbcbbaabaabacbabadbcacbdbbbcdacbddddaabdddabbddcccbcaccbdaacdcdbccacbbcacdcddaadbbcddcbdacabcdacdbdabaccbdcbdbccabbbdbcadccabcdddbcbadadbadccdaccbbaaacccbcdacbaccaccdbaacaabdbbcabdbcdaadaaaacbdabddaaaccdcadabbdbbabdadabbcbbadabbaabbacddaacbaaabaaaddcaccbbaccbcbccdcdbabaabadacbbabbaaacdbbbbcaaaabbbacdaacbdcbbdcbcdddccbaddcdacacaaaabadcdaabbaccdcadcaccdcbadcbbbcacddbdcdbbbdcdcbbdddbaccabbacbcdccdaabbccddbbcdbcbdcbcccacccbaadcadcdacadbdbbdacaadbddbadbaccabacadbabdddccacabcdddbcdcabbccbdacaddbbddacaadbbdccdddbadcbccaddaacdadcccbdcbcbcdcabcbabcbccdbcbccbbbbdcdbbddbdacbdddbcdbbdcbbabbddadabdcaabaacdaacdaabdcdaddcddbccbadadaacdbccadccacabadcbdddabccaaabbacaabcbaaadbabdbcdccabadbdbbcacbacadaabcbadcccaccdcabdbbdcdadabbabacbbcadbccbbbcdbdcaabdbbabbbbcdbddddaaacdbcadacccddcccbcaacbbcccbdccccaddbcddccbbddbddcdaadabcdaaadaddccdbccaaadccbdcacdccbbcadabaccdbcaaaaacaacbdcbdadddcdaacbadabbbcbbabacddccabbddbddbdcbbdabacccdddaadcbddbddaccaccaabcccbabcccaacdabdaddbbbbbdbcbaccbacbbdadcaccabadbadadbadbadaccbbbcdccbbbadbcdaacdcddcdbcbbbaabbdabacacadbdaaacbbdbccddccdbabbdbbaabddaccbcbbcbcaaabcababbdaaabbddadaaabbbabcabbaaddbddbbcadadbcddaadcaadcddbbddbdbadcbddadbcdccdbabbcaadabddccaadbbbdddbcddbcdabbaadbbbbbdbadbadbddbadaadcdbddbbdccdaabadbbcaabacdaddaaccccbabacabcdaddbcaccbdbbdbdbadaccabdcbcbddbbbbbadddadabccccbdadabcddcadadacccabdddadabdbadadccbabdaabbbcacaddaaabbcccbbaccadbcdaadcaacddbbcadbacabbcbbcdccdcdbbbaacacbbcdccdbcbabaddbccaacddbadacaadcabdcbddacaccdddaaddacbbddbcbdadddaccbbadccabbbcdccbadcacabaaacdbbcdcbadaaabdcadabcbcdbddbcbaccbcbbadbbdbbbbcabcdcdacdbddaaaaadbcaccddbcbcdcaccddbcabcaabbaabdccdbbddbcbdcbaabcdcdaccabbbcaabcddbadbbdbabcbbbaddaadadbddadbcacabbdbbabadaabbdcbdddcabaabdaddcbcbbbacacdcaabdabbdbdadaaaddadaacbaccbdacdbaaacddbbdacbdccdbcccccacddbaabdbccbcabddbdbdadacdadbabbbdcacdaaadaacccddadadacadddbaadadacaaabacacddbabcacddccaabbbbccaaddcbadacadabacacccdabdcdbbbdcabccdbdbdbddcdcbabcdbabdabbddcbcadbacadbcbcbadbaacbcddcbcccbcdaaacddabcabbcccababadcdbdbdcadcdbcdacdcbbbbbadbabcddbacddacbbbcccdadabcacbaccaddccbacadcbbcddadddaccbdbabbcdbccadadacabdcdaaadabadddcaabaccaacaabaaddaaddcadbacadcbdddcadbdaaadbdcabbccdaadacaccabacaabaddccddadbcbddbdadcdcaaaddababdcccaddcaaacbdaccacbcadabddadacbdaaabcdbadbadbaabcbbabcdcccbcdbbbbccbcbababbadbddbdcddcadcadacbccbabaaaacbadacabddbcdbdbaadbbccaadaaacdcdcabcbbacacbdbacbcadccacdcaaadadbadccdabbcdadcacbdadcbcbabcaaccacabbadcaaaaaddadbdabcbddbbdcaabbacddadccccbadcabbaabbadcdbaadbcbbbabaccbbbaabdcddbaabcbbcccbddcadcabbcacbaccbacbadbaaddcbdcdcbdcddccccdaacdbacadccdbcadcccdbcddcbbcadcbcbdaccacccbacdbadbacaaadcadbdbcbabaadbdadbabbbbacbdbacabcbcadadcdaddaccbbbdcbcacccbbbcdddbdcdbccbddacbbaaaddbbcbaaddbdbbbacccdbcaccadbbbaabaacdabbccaadddbdcccbcdccddbadbabbcbddcdaacbdbbbbbdddcdcdacddcdacccccccaabccbacbabbcdadcbbdabdaaadababcddabcdcbcacabbbdbdaccbdaadbdcdbdcadaddabbccacbdcccabccbbbadaaacbcbccccadbcabadcccdcabcbcdcddbcddaacaacddabdacdcdcbdccadacaabcaacdabccaacaaaddaaccaadaaadcbabaabaddddcbcbbaabbccaadadabbaaadacddcdcccbbcbbcbdcadcccbcacdcaccbdbdbbbcdcabbbdacacadcadaddccabcccdcdaadddcdcbacdaadacdadadbddbdccbcbbadbbabdabcbcdbdccaabccbdbcddcaabbdaacddcbddccdccabcbdbdcbcbabdaaaacacdcccbdccbcabbdcbdabadddccccccdadaadcabdbadadcabdcadbaabdcdcaacdddddddabcdddadbddaaaddddddbcbadabbdaddbbbddcbcdaabbbaaabacdbdccbdabbbbbdbaacbdcbabbdcaddddbbbdcacbbdcabcdbcbbbacdccdaccdccbdaaccadbccdcabcaaaabaccaadcabaccaabcdadcdaaabcdadcdcbdbdbcacbcddaabdbbdacbccbccbabcadbcdbacbdabbccdbdbbccabbbcabbbdbbbcbbccabadccdbbbdcacaccbdbbbcaaacdabcccccccdbaadaacccbbddccdacadddabdcbaddbdcdbbaddccbbcabcdccaddbbddacbbacdcbadddccdbcdacbdcdbabddcddbcccdaadcdcdbcbdabddcadadbabbbcabacdaaccccaaadcbbdbdcbcccdabcccdabbacacbaaaddabbacadbcacaaacacaadbbacbcabadbdccdcbdadbdcbaabdbaadabbcdbbcccadaccdccccdcaacbcbdbbaccbacbabccaadacaabacdcabbbcaccadaaddcdadbccbdaabcbccbaadbdcbaddaabdaccbdbcbaabaddbcbadabcacbdcacbcdaadbcacbbcabdcaacbbaaadcabababcaacdccdbdcaadaabbbabadbddbdcaacaaabdddcbbacddbaccddbaddbdacbccbbcbaadcdbbbcbcaadccccdbadabadcbbaadcdccddcaaccbbcdacbcbadbadbddcaccdabacaccbdccaacbcdabcbacdcbabbdbabaddcacdabcccdcabbaabadadbacaccaacababdadcddcddbddbcbbacadcccaaacadacddaabdacacbcdabacadabbbcabcddcbdbbbddbcdadadcbdacbadbdbbdbaadacccbcccbadbdcbddacdcddccdacadacabbaacdcbcdadacdadcbbcbbccbadacdcadabdcbbccadcdbaddccbdadddccaadbdadcbdddbaddcdddbcccbddbbaaaadadcdcbdcaccccadadcbaadacadcaacdccacadbdcdddcbbdbccbababddcbbbdcddcacabadaccaacaabbaddaaadcdaaaacdddcacbbdbdbacaccdcabbabacdcccbacbcbacdddcdbccbbdbdbaddcbcacabbdbdbdcdaadcccdccbbaacbdaacbddacbbcabcbbabdcbaadcaaaaababbdcdaadbbcdbddaacbdcdcbbcababdcaaaccbaddbbadadabdbbccdaacdaddacadbcdbbbacbccabcbdcaabcaddbaddabdbadbabacdbbbcdbbdacaabcbaadbcdcbcdcdbdcacdaaccaaadaaadabdaabdddaaccbbcacbbbbdccbabbbacbcdacabddaccacbbdcbbadccadaacadbcacbddacccdccaccccbacdddaabcbacbdacbcdbadddabddcbadbaaaacccdcdddabadbcadabaccbbaadbdcbccbcccabdabddcbddbbaacddabcdcababaaaabaadddcabdccbdcbacaddcbacacabacbcabddcddcadabccbccaadadacccccccdddadbbbbadddbbbcccaadacbbdaabbcacbbdacaadbbdabadcacbaddbdddbdcbbadccbddbcbcdcddaacadccbdabbcdddbcacbcccbcabcdcbbcabadcacbcdbccccddadbaaccaaaccbacbdccdbcbddbcadcbdcddbadaadcbbdabcdbbbdcdbdbccabbcacdbbabdcbdcddadcbaaabddddddbdadbdabadaccaccccbdbacbcbcaaadcccdaabddcaacdbdcbcdabaaabdcdbcdbbacacdaabdcbabbdcccacaabadadbbbacaaddbccccbacadacdcdcbbdbbacccdbddddbadaaabacbcababbbcdbadbdbdcdcdaabccbcbdccbdaccbcdbbddabcdbbdbaaacdbcacaccaccadabdcbdcbcddbdacacddcdbbbdcabddacbabddabbdaaccaadccaacdcaacaccacbcdbcbdbbbbcbbbdbbcddcacbcaaddbcbaadadbacbcbbdbcbcacccbdcabdddcbaccdbbaddddabadadaababcacabaaaaadadaadbaddcabbabbdccbcccbdabcaccdcbddadbbdaccdaacdbacbbaddcaaacdcacbdaadadaaabbddaddabbacdabdacbabddadcdbdbdbdcddcbacbbabbaacabdcbacaaacbcaaabdddbdbddddaadddcbdcccbbadaabcbcbddcdcddbacaaabbcaaabdabbdadbbddacacbddabbaddddccbdabbbbaadadaaabcaaaaacbaacbddabdcdddbcabaabbaddddcdcdbaccbbbcbbbcdaccdbdcaaaacbbaadbdccccccbcccccbbbbbaabadbccadabacccbaccdbbbcadbdcbccadbcccadccccadbbacccadcabaddaaadaabccbccdbdcacbcbacdabacabbcddccdacabbccadacdacbdcddacacdcbdacaaabccdabbcdacbcccbcdbabdcdaabdaabcbddcbdddbbcdcaadacbdbabdbdccbbbbbcccbadcccbbccabacbbdddabbaccdbbdbdcdaabcddcaacbcabdbadbaacbddaabdcaacacdddccbdcabadccbacabaadaabcadbdaabcdccdaabcadadbbbccabaaabadcbaccccdaadcbcbccacaccdbabcbddabadbccacaababacbcadadcdacaddaacadbcdaadbacbaaacacdbbcddbccabdadcabdbdccdbacaabbcdaaccabaabdcaaaadadbddadddacaccbadbcbbbbbccbbddddddbcabbdbabdddbacbcbbabaabbaadaabaaaccbbadacacbbbbbaddbabcadaaadbadcacdcbdabdbcbdacadbccdcaccddcbcbaccaadababadcabacabcaabccddbabcbaadabacbbdccbcbcdbddaabdbdcadbaabccdcacaddaabcaacadbcabcbdaaaaddabbbcbabaaccaaccbddaddbbddbbcabcdababbccbcdaababdbcbaaabddabaaaaacaccacbadcadccbabdddacadacabacadbbdddcaacadadbdbcabaadccadcbcaddadabdcdcbadababdbacabbbbcacbbcbcccbbdbcdcdddbcabcadcaddbcabdcbdbabbdbaddbaddacbbdbdabadaaaccdbbcddcdadbbbacacaaccccbabdbdcbdaaccdccadddcadaaabdabdadacbaadcacbcadbcccabbaadbccadbddbadbcacacadcaadabcacdccbabacccababcaccbdbbbbaacaccbbdabcbddaacabddddacccdadddabbacbccdaaaadbccabaacbadbbdcbcabcdaddcbcbdcadcadadcdccbdbcacadccddadcbcddabacadcddbdaabbadccbbcaaadcbcdbaacaaabadcdcbadcacddbcbcabaaacabbbbdcbcacadacacdcddaccbbbbcbbcdaaabadbcbddacdcadbcdccaabbbcccdbddadaddacaddaababcccadcdcccbcdccbbbbabbdbaaccddbbbabbaabdaaddcccbccdaaccbadddaacacdabbaddbcbadcdcbbbabbdaccdcdaccbcddbcadddaadbbddadbcbdadbcbadbccaacbcdcaaddbdcddcabbdbacbbdcbbbcbaccaabcbabdbacadbdbbdddcdbccddacdaadcbdaacbbcddacdddcbcdccbcbcdbdadadadbbcdcabdaacbdbbacaabdbdbbcdcbdbcdbbaadbdcacabadabcbddacdadbabcccabcdadabdccccadccdaacabbcdbbbdbbbacacaababcdabacccbcacadadcbccbaadaadaadaabadbcbbcadddabbdcdcadcddaccbdacdaacbaaaccacbdbdbaaccbbccddccdbabbbccabaaddaabcacadabccadbbbdcbdbaaaaabbdcbcccdcacbddcdbdbcdddbcdddabacddcccabacddbcaddbbbaadacbdbccdaaaabbacdcbdbadbcbbbdadbddbcbbdbddaacbcabbbcaddbadbdbbaaddcdbacbdcbacabaaddbaadbbdddcdadccccaadbdaacaacbbbadbcccdcddbacdabadcabdbccddbacdaacddbdcdabacabcbaacdbbacbdadcbbddccbcbbdcccbbccbdcdddcccacdaadadbbbddaddabbaddaabccbddbcccddbcdacbdbbaabbaddbbadcbaccbdaadbcadbcccbacacdabaadadaaabbccaaadbacaadddbbcdabaabbbabcddaddcaabdbdcddbaccccaaacccaccbbddcdadaabddccdadcddbccbcdabdcbddddabddabadaacbcdcbcdcdbadbabbacdadbadaabadabdabbdcdccbcddbccaddadbcccdacdbcdacdccaabbaadabbbbdccdbbbbbbdadacddcbdccddbdcdddbaaccaddabdbdaacddabbaccbcbdcddbcdbabbccdbacadbdccdbdccbcbbdcdddbdbcadbaddbbcdbabdacdadbcdadccadbabcbbbaaaaaccccdcabacabdabbadccdccacabbaaaabbbdcabbabdadbbaaacbabaddbcaaabcddbabcdcdabccaaacddbdbadabdcadacddbcddcbcdcabbcbbddbcbcbbccbddccbabdaaddbbaadcabcccbcccadcdadbcdddcbdbdbddaddbbdccdcacbaaaaabccadbdcacddaaaabbdcccacbbadcbddbacdbdabaccbdbcdcaddadddcccabdacdbbdddacabdbdddcccabbaacdccbbbbaddaabbbababdbabdaddaddaaacaddcadacbaaacabdbbacdbbbcccacacdbbcdadbbadbadccbaccabbbcbabacdbbcbdbdddbbcdcbbbcbbdbdadcdbdaccaadccdbccadddadccbadacbcdabcbcbbcbdaaaccdcddacdbdcbbdcccadadccdbddaaabdbddabcbabcbdcacdadbcdcadcbbacabaccdadabacacbabdabbcdabaddbadbdabcbdaaccddabddcadabccbccdbaaccbcbacbddccaaaacbcbcddcbdbdaacaacbbaabadcdcbdbbdbccbdcdcabdbaadabadacbcdcbccaaaabcabbdcacbacadcdccaabbbabccacabdaccabbdaccacbacabcbdabccccbcbacadcbaccacccddbdbcaadbdcbbacadbccadbdabddbcdabdbdbdddabadaadaddcbdbccdbbbbbcaadbbdabcacbcbdcadbbcbcccacccacdcadbdaadddaddcaabbbacbccacccbdcaacddcabdbacddbdabaaaacaaddbccacdaaaabdaabcdaaabadcbbbaddbadabaddcadccccdbadccbbcbbdbcddaccdaaacaacabbadaabaacdcaacdcaaadbabdcdcdbcbaaddabbbbcbabbabddabbaabaadbcbbbcbbbcddadcabcdcdbddbdabcccabccdbacadbabdabbbbdcdabdacacdbdacdadabaacbdccccbccdcbddbdcabbdcddddcbaabcadcdbbbbddaabbdbbbcbaddcadacccbbccbacacaccaaacddadacbbbacabcdbbabadaabdbccbcbbabadacbadccccdccbdbdadadbadadccacdacabbcabcacadacbdbdbcbaaabbadbabcadadaaabaadcabcdaddabaaabcddcbdccacbadddbcbbaadcbcdbaaabcabbdbcbbcdadcdbbbcabacdabdaadcbcadccdabadccbdabdbaabaabccbbddcacbbcbddbacccbcacbcdabcdaddbcccddbcbadbdbbacbabaaccacaaabbddadaacadddacbcbcabccabcbbcdacbdaddbccccccbdacdbddbcbdaabdadcadccdbbdddadacaacbbbdcbdbddaacbcaacabdbcdcbccadbadaabddaddbcbcaabbadcdcdbcccdcadccdcbbddcdacbbbcbcaadabcabadbabdcaacbcbaabdbadbabaaccdbcbadbaccacabadaacaabddcbbaccbcbdcbadbcccdccabadcbccdddcddbadcbbbdbcbbbcbabdaababcacadddbacadcadccbcbdbccdbaabcabdbdbdbdbbcbbccbbadbdcdbaacdccacaddbbaaacdacabdadddbadbdadcbddaadaaaadcbbadddaaacbdaccadacbadbcaddacacdadadcdaadcbbbcdaadababadbadddcaabacadcacaddadbbbcacbacdddbccddcdaccdcabbadbccbdccdaabaaabcabcbcccdcbabaabbabbcaaaaaadcdacdbdadcdcccccddccccbdbacbabbaddddccbbcdcddadaccacbbcdaadabadababbabaddcbadabcadcdaccdabcaddabababdcccacddaadddcbcaaccabacacbcbdaddabdddaababccacddcbbadbdddaacacdbccdbbcabccbccabccbdddaccbddbcacdcdbbabacdbbdbcbdbcccbaadbdbcddaccaccdbdccdbdcddadcdcdaabaabdacdcdccaadbbbaddcacbddbbcbcaacdacdbcdcabddcbbadcdcbacacbaccdabbdbabdbacdccdabbacbcbcdcaccabaddbbbdacdccccbabaabbaacddaabdddcabbbbdaaadcdcaccacbbabbcbabdadbbdcdbcaddadccaddcbacababadaacccabdbbccdcddcdcbccaacaacccccccddbcddccadddcdaddcddcddccabcdacdababbddddaaacdbacbbbcdaacbadbcdccadbccacbdacdccaadadcadcaacaabbcababdabdadccadcaddbadccbdbadcdacabccdaccabcadbccaaccdccccddadcaddbbacdccaacdbccccbabacacdacaaaccbccdaaccdcbbcccbaabdacddcbbbaaabdbacbddabccbccbcacabbccdbbaabcbdcdabbbbccdddacccaabbdbcabcacbdcddcdcbdbadccddbaaddddacadbcbbacccabbcadaacbabdabbcbdcccdbbaaccccbaccbbbaccdcdcbaacddaccccbaabdbacabababbbcacdcbcdadccacdbbabdbddcdcbdacdcdbdcccadcacdaccaddbbcccdcdaaacaababcbbadbcdababcddcacadabbabcaabcdbbccababbcdaacaaacddacbdaadcaccaabbcddadabddbcaabdcbaaaccbbbacdaccdbdbccbccbccbdbbbcbcbcbbadddacabcdadbdcaacacaddcccbbcbdcbcdcddddaccaccabadddbbbbaaadcaadddcadbbbdcacdccdbaccbcacbbabdadabbdbcdbbacbbdadaccbcbcbbcbaaddaaaaadaddaccbbdbcdcccacadabbcddcddbdbbdacddabcabcaacbbbccaaacdbdacdaddddbcdaababaccbdcadbdcbdccbaddaabbcbcbdcacbccdbcadbbbccdadadcbdadcacacbacaabbcbadaabacbbbcddbaadadbdbdadcdadcbbbbbdcacaaadcdcdcbcccccbbbcabbcdbdaaaaadbcbcccbdbddbaabdaadcdbcaddbaddbdcbcaaaadbbcbcadccccbcbccacabcaadbcccbcadcddbcbabbbcccdadccaabaaddddbcbaaaabdaacddbdcaddbcbbadaacaabcacccabbaccabbacaacccdacbddbacdbaadcbbbbdcdadbbaacbadaabdcdcaaacbacaaccbacdabbacacccbadaabaabbcbdbbdaccdcdabbacadcabadaaaacbdcbdacbdbadacdcbdaddccadcaabcdadcbcabcdbadccdadbaaddaaadcccacaddabdbabcddcbcabbcdacacdbcdbcdacdcabdbacbabddadbdadddbaacacddbbbdbadcddcbcadacdbcdcbdddbddbacaadabbabadcabacaaacccabdddbbcccaaadbdcacababacbdddabdddbbcabbddbbbdababbcbcbaadbcccaabbcdbbcbababbbdbdcdadbbdcddccdbbbcbaaddbbbddddaabdbdbddbaadccdacbacbcbbabbdacbacbcdcaadaddcbcbabcbbaabacbabdcbaddaddcbabdaaaacddcbbdaaddaadaddbcadbcdddbbbabcbbbddaccbabdbaccbdadaabaabbdbaabdccbbdbacbadabbdacdacacdbccddbcbabdbccaccdddbcbbbccddbcadbaadcabaabccaacbbabacbabcbddaccdbcbabbacbcadadacdabbcaccaacbbbbaacbddcbdaaaddcdcbbcbaadbaaaabcdcbaaaaddaaaacaacbddacdbaadccddaaadabccddaacbbbbcccaacbadcbadbadcbccbcdababbbbacbcdcabdacbbabcdadcddbdbccbbbbcaccaccbcdaaaacdaabdadadddcabdabaacbabbcbcbddadaaaccacbddbacddbdadadbcbcabccacdbdadbcbcdbabdadbcbbdabaccccaacddacdabcbcccbbabcdcdbadcbbabdcddccbcadddccccacdacccddbababccacabcbacccdcbddaaaadddacdaccbaacabcdcaabdcdbddccdabddcaddadcdabccbdcbcadcbabdabcbababdaacacddbaaadbcbaaadadccbdcbdcadbccbbbcdcdcadbadbbcdcbddddcdbaacbbaddccbadacdbbcadbbadcdcbddcbabcaaabccacbcaaabaaabbcbacbdbdaaccddcdccbbbdcacbcadadadacaaadcadbbbaadcaacbdcdacdababddbbcaabddcbbdaacbcdadcadddddaddbcdbcbcacdcdaacaaacadcacdbccabadaadbbabdbbdababbdcdccbabbddaadcddbdaabdaddccaadadcdacbabcccddbcccbaadbdcabccdbbcdccbcdabbcbacaacdcdbbbdacaaaaacacadbaabdbdaddbcccabcccbaaadcdddbbaabbddbaacbacdddaadcdbacdaaacccaacaddbddcbcbbdcdcbcbccdadaabddbacdadbdadaabbddadbbddaddacaddcbdcbaadbbdaababdabddabbcbadababbcacdbabaaacdbdabbabcacddadcabdbacbcadadbaadbdccdcbcabacbacbbbbaacaadadadcddabaabbdacbccadaababaaacbaaadcccbddbcdcdccddccaddcaadccbdadabaadadcdaabaadcbbabdccbcbaacaaccbbcddbccacddcbabbabdbbaccaccdbabccbbcdcdcddbccabbddddccdabcdbcbbdacbbccabdaadcbaabdcbbccaadaccbacbcdcccabccabbccbcacbabbadbaadabdacdccdaddbddcbacababddddddacddddcccbcbdbbcaadadbbacacdaabdcbcbbcdbbabdbabcdcabdabbbcddbbddcbdbaadcabdadddbacdccdbbccdcbdcddcaabccaddacbdadbaaaddccbcbdababddcbddbdbcddbdbcabbdbbdcaacaabadcacdbbddbcaaccbddabdabaaddbaabcbccbdbccdaccaddbabaccbabdbdcdccddcdaaaaaacabababdbdbdaabbbbbacaadcddacababaadadcaccbccaabcccbacaabdcbadbbdbaaadccacbbddddacccbcaaaadbcdddadccabdbabcbadcbbdaccbdddadcbdacddbbacabcbbddbbdddcddcdbcdcaabbadaaadcbaacddbddaabcbdcacadaaaaccddacadcbcdcbadcbdddbdadcddbbacbaaddacabcccacaaccbbadddccdcbacdbdbadddabacbadadcdcdcabdbccbdabaadddbddcddacbbdbaadcbadcbccbaaacaabbacdcdcdbdacbababcadccbdbbacbaabddccddacbaaddcbbcbdccdcbdbccacbdcdccacccbdcccccaabcabbacacacccdaadadbbdaaabadddabbddbacbddbccbabccbbbbdcaacdacaadbabaccadcadbbadbcdbccddccaaaabdccdbaabccddbddcbcdddddcdbbabadccacdaadcbddaadcdabddccdccbbcaddaddccccaabbdbbcabccacabaccbbcaacbdcdcabcbcbccbbadaaabdbbcddcccbcbadacabbdbabddcccaccccbcbcabaacbddbdbbcdcbbbdccccaacacdddacaaadbbbdcdaaddccbdbdccacaaaaaacbdacccbbbbcbdabdbbcabdabdccabbdadbcdddddcdcbdaacabadbdabdddadccababaddbaabcccacacaddaadcdbaabbaaccacddadcbbcdcbacdcdbddcbacddcdaaddccbdbdbcddcdadcddbddbccbcbcccacabcdcccddccccbabbccadadcbcbdcabaadbaaabaddaddbaadacdbcdccdccbbaaaaadcbabcbbbbcccbabdbccddababddcbbaccadbbbdbcadaadcabdcdacdadbcbabcbdcdacacbcadbbbaabcbacccaadabadaabcbbdbdcdcdbaabadbdcbdbdaaccbccadaadbacadadbcaaabaadcacabdabaddbddaddbcddadbdbbbddcdcbabbcdbdcaabadbddacbbccaaddaaabbabdcddabcdacdcaccbaabdaaccdbbdadcdcabaacdbcdcacaddbcdaacdcbaddbaacbccbdbddaaaabdcbcccacadbadadbacdabbccdccbcacdcbbdbadbbadbbdcccdbacabcbabaaabcdcccccdbbbcddbcdabddbcbdacbddabacbdbaadabcaaaadbdcdbcbcbbdadbacbaadaacbbddcdcabaacbdaabcbadcdbacdbcbccadcbbcbadbcdbaabcddbbcdabbcbbaacadbbabcacaacacadbadacadccbacbcbccdcbadacbbddacddadbcaddabaabdddadcccabdadccdcabdaccccbbaacadcaabbdddadcdadcaccdacabaacccdcabddbdcbbcabadddcbbadadddcccbccddacabacbcdbcdabbdccdadbbcdaaadbcddcbbcccdaacdabcccdacbbccdcabcdaadbcadaabbcbabaccabadcdcdccdabaabdcdddbaaabacadcbacdddbcbacacddbdbccadcbbcbcadddbbabbaadcabcdbdcbdabcbdcbaabbbcaccacdcacbaddbbbdcbbadccddbcbbccbaadbbadadccbbabcaddcaddbbcaabacaccaaacaaabdcccbacbacacaccbdbbdacadbaaacbaddadadbacbdbbcdddbcdcdadbcbadbacbdcadbccaadbddaacadaaccbdadabbabddcbdcccccdbacdacaadcdaaabbacacbabdcbdacaccacddccaddadcbabbabcaadbcdbaabcddaabdacccadaabbbcaccabdcbdadccdbbccbaaabdacdabbdcdaaaccdcbdcaccbaaccddacadbadbaddabaccbcddcbbaaadcadabdadaadabcbdababcdacaddcbaacaddaaccbbbaaacabbdbcddcbdcadbdbbddaabbaddcdbdcaddacdddaacbbacbaccadddccddacdadbacdcdcdabcaabbbcddaaacddaaccddcbdddaacccadcdbaabcdddabddbddccadbcccbbcacbabdcbcddabbbadbbadadadaadbacadaadbcdbcdbcbacdababaabadbaadcbdcbcadabcbabbacdcccdcdcccabdabdbabcbcbcdabcdaadacbacdaacacdabaaabacdcadbbcdaacbcbdbbdcbbabdbdbabcdabddacbdbbcdbbcaddbdcbdcdbdbcccacacbabccadcaababbadaadbcbccbdbdbddbaadbcabcbccabacbbddbcaabcddacaaabcbbadcbbddacdcabdbcccddddbaaabddcdcbbbcadbbbbadabbbacabbaabdbbcbdcddccacbcccaabbdabbdccbadddcdcabacbdcbbcdaabcdddddabcccbbccbaddcddbcccbacbcccbddcbadbacccbbaabbbdaddabcaacbbbbdaacadccbdccbccbbcdcbbadddabababcacdbccbccabcbaaccccbccdadcdbcddabcdabbbadccbaadadbcabacadbccdbbcabbacdcacddbdcbdddcabbdacdbaaaacaddbdccaddabaddaaccbacddaacaddaadacbbadacabaddddccddcaacbdccaccdddbbdccddadccbbdacdcdcadacabdabdddabdabcadcaddccccdbadcbdbcabbaaaaaccabddcabcaddadcddacdaaccbbaabdcbcbbccabdbbdbaacdbcbdbbdbadcddbbccbaccbabddaabdcababcdbadacadbdcddadabbbdcaabbbabbdddaaabcdaaccbbacdbdaddacbdbccacbadbccbdacdcdcbadacacdaaacbdcabbcddaadbbadabdcdaacaccdbaadbabbdcadcdddacbcdcbabcdcddcddcdddcccdcaccddbbcacdcaacbbbdaabddabdbbdabbabaadcdbbbbccbaccddbcccbdbbabccadbbdddbdadcbcacccbaaaabbadcdadbadccdbcacacbcbdacbdaadbcacddcdcaaabaccbdddcccdccdcdbdaadccccdbddadcbadabbadccdabccdbbdccdabdbaccddbccbdabaadddcdabcadcdbdcdcbbacbbbbddcbabddaabacbbbcbcbddabcdccabacdcabacbccdccbbbdcbacabdabbddaaaadddadbddcdcbbcbaaaddabadcaccbbbcdabaababcadbbcaadbacbdbaaadbcddaadcddcdcdbacbbddaacacadadbaaccadaadcaccbdddbdcaaddbbbccdcbdaddccdccabcaddacdbddbabbbaccadcdbdcadcbbadabbcbcbdcadacabbbdcaaabdbbcbaccaabdbacddbcdbddcbcbcdcccccabdcdbcbbcbabbbdadbcccccdaabcdaddddbccbadacdbbcddcaabbcdcdabdccacbacbaccdcbccbbacddccbdccabccdacacbcacbcdcacbdadbdcdcabadcbcaabcabdacabbaacbbacbdbabbbabaaadddddbbacaaddcbacdcdabbddadaaddbbbbcdacdaaccaacdcbccbddbcabadcdbddcddbaaddcbcabddcbbdbcacbcdccbbacbccbcccdbddcbaaabbaddbbbcacdcbbaddacddabcdcaddddddcaddbbcbdbadcdcdcbbabbbdabaaddccadddaaabdbbcccabcbcadaadbcdaaadabbcacdacabbaabdbadccbcddbdbdbcdadadbabbacdabcdadddddccbcadbbddcacaadaaaadcdddbdaabcbccddacdcddcaaaadadbbcccbbcbdcadbcaaddcadbcdadcacdbccaabddddacdbaddabdadacdcabcddabdbbbcbaccbaabddbbbbaccbaccabaccaccabbcddccaacdbbbccbdddbdbbbdbbbbcdbbbabdcdbbcbacdabbaddbbaabcaccbdadacadcbcacccbcbbddccddddcadabddcaaccabbdaddbbdcbcaacbaaccbcadcdcbaaabbbddddabbaaccdadadbacaaaabcbdbdbbcbccbdcbccbdabdcbacbadaaadcbdbddaccdaccbddbbadbddcbcbccadbcdbdadbcabbbdaddddabcddbaacdaadbcddddabddabcbbabddbdbcaacbacbbccbbbdaddaadcdcacbcdcdbccaaacbcabdcbddcbaaccaaabacbcdaaacacacacdcadbbdccbaddbbccabdadcccadcdccbcbdcddbdcdbdbaaabdcaaacdbcbaacdbbdcabcdbbbdddadbdcdbdaadaaccabccbbacbcabacbcaabbdaabbcdbaccbbdcabacdcaaddbaaaddbaabdddcbcbabcdbdcacdbaddadbbdbdccbaccabaccdcaddaaaaccdaadbbcdddadadddbaaccaacaabbcaaadcdccdccbabcdadbaaddcadcbbabcababcbcbdbbaaacaabdacdcbdbcdddbddccdbaabbadcdbcaaadccdbbbcbacacaacbaacbbbbabcabbbabcddbdabbaaaababdbbcdaabdbccbdcccdbbdababddadacccdbcaaaabccbacbbbccabdbdddcbdaaccaadcccdccacdcccbdcdaacdaadbcabdddacdbdaaddabbccdcdabbcbaddccabadaaaddbcddcabdcbcbddadbdcbbcddaddcadddbbadaddacccdadddcacccbdaaadbdccaadabaccdacadabbbcbbbadcbddbbbadabbbbcddcabcdccabbdccdbccdcccbabdcddccddadbaadbcaddcacbcccaccdbcbcddccaccbabbdddbdcddcabbcdcdcbbdbabbadacdbddacacbbcbcacabbcbccadabccbdbcaaacccbcdbcdbbdcacdbbaabdbbbcdadbdabcddaccdbddcbacccbdbdbddcbdbabccdadaddccdabacbaddbabbcaabaaccbcdbabcbdbbbcbccddacdbbdaaaadcbababcbdbcadcddbadcdccacbcbdcbcbbdcbcdbcbadcddadadcabccdbdccaaccddaccdaabcbacbcddccabdaadcbbaabdcbcbcbbccabccdcabababbbdbccbabdddddcccdbbcaddaaccbbaddcaacdbddabbadcbbcaaccaaabddbbddacdccbbccaacdcdbccccdbdadbcdaacdabcddddacaddbbdbaacbbacddddacacaccacaddabaccacdccaacabaddbbccaddbaddccddabcababcaddcbaadbbcdcccbdbdbbdcbaaababbdacccaddccbadaabadddccbacdbbdabdbbacacdabbccdbdcbbbcdbdddcddccbadaacbdbcdabcdcbbddcddbdacbadbddcbdbdacdbcdaadaabddbcabccbaadcbccdcdddcadbbcdccaadbcdcabadbdabccabdcdbddddcacdddbdcccbcdcaaadcbadadbdcccccbbbcbdddaccbadbaacbbaabdbdcdabcdbddcacaccabbdbcacbbbcacaadcdbccccccdbbacacdbdbbbdccabbcbcabaabcbabcbcccbdadcbdaccadaabbccacbdddcdcabbaadbacabddddcaacdcdbacbdadbdbbdabdccaccbacabbbbdbabaabdddaacbadaacabbdabcdcbdcaccbbcdadcaddcbcbdbddbbdbaaddacdbdaaabbdcadadbacbabcbccbdacbaaddcddaacdabccdaddbadbdabdcacccadcbdcdccccacbaabccbdbaadbcaaadacdbcacaabadcbdbadcaaadbbdadccbabbbcbddcdacbccdbdddacaabbbcabdbdaccbddadacbddcaadbbaaccbbbbacbcbbcccbcdbbcbcbbcbacccbddcdcbdddcdabcbdbcdbcbbdcacbcabcdddcbccddacbbbbaaaaaddbcbdccdcdcddbabaacdcabcdabbcdbbddccbbcacaacbbacdacdadbbcabdccacadbaccbcbbbbbdaaddbacdaaaadbbbbbcdabcbbbadddcccacaccbbaacddbbbabcdcacccadadbdadcbdddcaaaaaabadabacaabcbccbbbcbccbcadbbdccdbaddcdaabcaccacbdbccddbccbbaaacbacccdcdccbdbadcaabdaacdbaabbdddbacdadccadbabaaccbaacdcbdbdacbcacdaaacbddbcdcdcacccbaadadaacabcbbdabdbadcdabcdbbdbbbaddbacabccddcccabdabbcdbcacaacccbdbbcadbbdddadbbcaabbdcddacdaccddcadcadadcbdbbbbacabcaabcbaacccbddbdcadcbddaddacdbbbddcadacdbaacaaddacdabdddabdbdbaaaaddcdddbadaddabddcdbccccccdaaaccdccadddcdcaababdabcdbdaddaccacbcdbccbdbccbcacbbbcbdadabbaabcbcaddbbacabcdccddbdacbcdcddbcddcbddbbddbacdaaddabbdddacbcadcdcbcadaaabddabdbcacacbadbcadcbdccbdabcadddcbbcaaabdaacaddbaabdacbaaaabcbabaadcaccdadddccbcdcaadaabcabdbcaababdccbadadbcbaaacabaaaccaaabbdadadadacdcddccdbbdcbdccbdcccddcabbcbabcdbdddbdacbbbbcbcadddbdbcdaacddcdbcbccaaacbccccadadcccbcbccbabaaaabdbcbbdddcbabbccbcdbcddaadabbbacdbbcdadbcbdcadcbbadccbadddddcdccdadbdccbabccccaadccabcdbbababacccabbbbdadccbadddccbadddabbdacadcddbcddbbdabaadbcdcbcbbbabaccbcbdbaaaadadabbaabdbccbdbcabbbddbbdcbdadacccdcbbbadcbbacdbaccabcbdaddccdaadadcddccacdaddccbbddaccdacbbbdadccdcadbddadadaccddadadadcbccdacacaabbbaaadaaaaaccdabddcdbbbbbdcacaccdcacacccaacbccaabdbcbbadbabccbccdcabdaaacdbaadbbcabdcdacdbcccccdaaaaaaddadadaacaabadabbbccdcccadbbcabcbdbbaacadbcdcbbaabbdababbdbbabcdcbdadaaaabadbbbbadbaccadaaddcadddadcdcdacccdcaddbadaaabadbbbacbbabbaaaddbcbcddbbcbcccbcdaaaacdaccddbbdcbadaabbdccadaaacbadaccaadddbccabcaccbcbdadacdacbabddadababdaaddcddaccdabbddccadbadccccdabccccddcaabbcadcacaadadbadbcbbbbdcabacddabbcbdabcacbaabdbdcadcdbadbbdadbddbdddccdbccbcdbadbddadcdcbbddabcdcbdaadcacbccbbaaaaccadddaacbbccddadcaaccbbdcacaabaaaadccddddbdcccbbcacbdaabdcadbdccbbabddcccccbaabbdcdaddadbadcabaaacbbbccbccddbdbddaadcacbcdccbdbacbbaabacbccdaaaacddbacaabddbdddcbdbbadbaabacdddbbababcddacddcbacacacdadaaaadaccbaccbdabbcbdbbccdbadababacabcddbaaddcdadadbbbdbcccabdaddddcbcdccabaacddbddaaccacababccbcdbdddbbdacdadaccdcbccbddacabddcbdbdbbcacbccdbadcbcabdbbdacacbcbcddbdcabdccbbabcbaaabcccdcabaacbbcdcdadcbbddccadacadbbcbddbcdbbcabadccddbcbbbcaddbbaaaaabdaccacbdcdaddabdbcddaddcacbabcdcaacbdbbaadadcddbcccccbcacaabcadbcdbbaacddccccaabacaadcbccabcabccbcbababdacacbccddcaaaddadbcbdabbdddbcabcbddabacadcddcbaccadbddbadabdadbbadbccdbacacdabddbcaacbccbaadcaddddccaabcaddcccacadacddaddddcbadccaaccdbcabcaacbccadacbdcadddddcabacbdbccbacdabbcddbbcbcbdcaadadbbbbcdcdaaaddabdcbaccadaaccadabdbcbaadabaabcdcadadbccabcacacaacabbdbabbaaddcaabdccdcdacddcdbcdbddcbcbdddbcdcaddaacacbdbaabcbbdaacbdcbacdcddcbdcbabbbcbdacccdadabbcacaccaddccbaccdbcbbcabddaacbcbcbcacacdadacddbbddacacbcacdbcaadbcbbcbbdcdadbbccadcbccdaaabcbbccbacbacdbcdcacddcdaaccaacaccabdddadbadcbbbcbdaaccabbcccbdadabbccbadaadbddcbcbdcddccacabccbddadbabdababadbcaaadcaccdabbddcdcbcdbbbdccdbcabccbcdadcccbabdbdddadbbaaacabbacccbbadaadcbdcddccbcbddabdcabaacddacdcccbbcbbbacdccaabaaccbdacccabbaabbdddabaddaababcabddbbccbddaabbbadbacbabacbdbbaababdbbaaadbcbdcadaaadbcdbdcaabcbdcaaadaabddbaadbacaabcabcacbaadbccabdabccbdccbdbbcdacdcdbabdaabaaadbbacbacddbcaabdadcbccbadacdabbdcacbacabbdacbabcdacabdabbabaaaaabdbcacdccccccccdaddbdddaabaacbcdadaabcdddabbdabbdbbbaccdacaacaddabcacbadcccbddabbcabddabdbbcbbadbccbdcbabdabbabddacbbdadbdbcbccdbadcaaadcbcacbacbaccbbcdacadbccdcddcbdcbdbbbbaccaabbdcbaaaaabacdcbdbcbdbcabaaadbcbbccbdbbdcdaaddaaadcbcccdaddacdcbddaaabbddbcddadbddacbadacdbaadadbcbbbbcdadcdcadadbbdbaaaacccacdbabccaadddadcbdbaaccbabadcdacddbbbacbbcccabbadadaabdacbddcdadaddcbdbdbcdaababaadbabbbccdcccdaaccdcbcbdaaaabbbbdaaaadccaabbcdccbcdcbdbdaccbadccbaccbaabbdabaaddcabbddacabddadabacabcaadaddacdbdcaccaababcbdadabbaabacaaddcddbcaabbddadadcababcddcabcadcdccaabdabddcaacaacabcbabdcbcadbaadccccabdaccdddcbdccddcadccbddccbabababdcdaddabbadbddcdaacdbccbddddaaadadadcbccdcbadaacbacadaacddccdadcacaacacddbbccaaccaadcbccbabddddcbabababadabcbacdabdccacaabbcbdbddccdddccacdaabbbacbddcddacbbccadcccbaaaabbacabaabaccabbddacbbbaadcbccaddacdbdacbacdadabcdcdbdcacabbadbccdbaaadcbbabdbccbccadbbbacdbbcbbaaaacdcbcabbbbcabacbbdcdabcaacbdbbcbdcbbaaddabbbcbbbbccbadcadaacdbbdbdccabcaabacaababbdacdccdbbcdccdbddbcbdbbcccbcdbbacbccbbcdbcacaddbbddbdaadbcbcdcacbccdbcdbdcaddccdccacadaccdbbbbaabccdabbdbbccacabcbbbadbadabacadcadbbadcbdcadbbbbacdbbccadcccbddacaacbdcababbbacdbdbabbcaadcbbacaadaaacbaabbccccaaacdaaabbcabcbaadcddadcbbbcaabcdbdddaabbdbbacdbaaacadcabdcdbadabcadddccadcdabaabbddbdadcccdcccddbabcabdbdadbcdcbddcdadccacccbdcacdddcbacacdabcdaadbbcabddbdacabacbdbcadadbddacbcdbddacbccbcdabdaadaddbbcdddbddcaaccbccbddbacaacbadddcbacaddcddcbdbcddcdbbadbddbbbbbdcdbdddabbcbbdadccabcacdaabdbaacdbcdbbabadaabbbdbbacdcbbcbacdbdcbbcbddaddcacccacbdacbadadabbaacdcbacbdaabacbcbdcbdacaabbbbacabcadbbcdbdbbacadbbdaddcbcadccaddbccbacdbaabacbadbdbdbddbbdacaacbcabbcbdbbabcbacccadcbbbadccbdaaaddbbabcbcaaacacaabcddadcbcccbdcccabdbdacdadbbcdcccabdbbadacddbcbdcacabbcaacdcdcdacbbbdcddddccacdacbaaacbbcacbcddcdddccaacbcacdcbbddbccdbbcadbadcdbddabbcabccaadbcdbadbacabaaadacaacbbcccddbdaadbcdbcdbdcabbccabcabddbcaadbbcbddacadccdcaadbbbddaccaddccccaaadccddcabddacacccbacccdacbbbccdcbddadddcabbbbaaaddacdbbadddaadcdaccabcbdbcdbbadbbdacdaddabcdaccacdbaabbaabdcbbccaddaabaaddbaacbbdbbbbccddaddcccbdcadaddaadaadccddaadcbdabaccdbcccbadbbcdddbdadbdabadcbcbadadbaccbbaadbdccbddcbbacbdcbbadbbbcbbdbacdacbdbcadacbdbacacccccadbbdcccadbdabcdbdcbddcbbccacddcdbdcbbbcbdadbcabccbaaaabdaddcdbccdbadcbcdbaabcadacacabcbdccaaaccbdaacddddcdccbdaadabddbabdbdbacdddabaaacdabacbacdabcdcadcbadbddacadbcabbddaabccaabadbbaadccdcabaabacbacccacdcdaddabbdaddbccaacbccbbaddacacbcdddccbdbbcbbbbcbabbcbcdcbbdcababdcbbcaadbddbabaddcdadbbbbbabbdbdbbdbbcbbcbaaaabadbdcbabbaaddcbddbcaacdbbabdbbbcdcbcababcccadbabcbaaacdbacddcaccabcaacaaabbcaacaaccdababaddbdcacaddacdcabddbbcdddcdadddbbbcccdbbbbbdbababbaccacabdabcbbdcdabcaddcaccacdaddbcdabddcbbdaabdbbdadbbdcbabaacbbbabcdbcbdcdcaacbacabacdbaabaaabbbadbcacdbabaaacccacdccddacccbaadbccabdaacbcddccabcdccadcdbbbcdaaadcbddcdaadbababccdadcabaabacddbacbcdbaadbdadbababbbdbdbddabccbabdaadbcbadccabdcdcabbdddacaaacabdaaddaccccdbaaaaabbdcabdbdbdadccbcdccacdaaaadbbadabbbdaadccdcdbaddbdcacbacaaddddaccadbcaabdbcdacaabbcaacccccbdccadccabaabbbcbabcbdacbaabbcdbbadccdcbbbccadbadccdcbadaadbbbccbddcabcbdcdabcdcdccbcbbdaaacbbdbdcbdbbabbadccbabcadbdbcdaccabadadbaccdcbdcdccaadcbbcdcdccbbcdccdaabbaaccbdabdcccdaabdbdaaabccdcbcdbabbabcabdabbddcdbaaadddccbacdcbdaabababdabbbdcdccdacbababccacdadabdaabcdabccbdcacbadadcacacadaadcccbacddbaabdacbddcbabbbddbaadcbabbdcdabbbcababdbcbcacdabbacaabaabdbccacaadcaccaaabdbdcaaabaaaccbccbcdaadbcabaddabddcdbccabcccdabcccaccdadcbdabdabaccaacbdcacdbbdcbcdccdbcadacbbabdbbcdcdcdaddaacbcaadbbcdddcdcabdadbaddadabdbdacbdcadbabbcdbccccbbbacddaabcadabdacabcaabaaacabaddaabbaabcdbbabcbdbdbbdabbdcdbbbdcbddbcabddcdddbacababddacdbcbacabcdcdaccdcdcdccdbcaabbbbccdcccdcdacbbbabacddbaacbbccdbdacccbbcdcccdcdbaacacddbbadccccdcdadcdbccddacccddaccbdcaabcbcdccbdbcdcccaaaadbddcbaabaabbdbcbddcabbbacdaabadaacdccbdcaaacabbadacaadcbdbaaacbaacbdddadbddccdabadbbabcacaddcacabacddabbcddcbadbcbbbbddbadbdbdadddccbacbadadcbabcaadbdbccacbddcabdbadcabdcdabbddbdbbbdcadacdbbbabbdbddcaaacbbbaacdcbcbcaccdcbccdbabccabacdcbcbbcbcabaabcbbdbcabcbbdccdbabbadcbddaddadaadacbbbcadcaddbcbcdcbbcabcabdccbabbacddcdcdbcaadcdcaadcdaacbdbdaaccddbacacdcbdbaaacbcadbbaaabccdbcbcbbbdaabcaddbcbcdcacbcbbabcbaabacddcdbaddabcacdcbbdcbbbcddcdbbaaaabcbacdcbcdadbcbaadababbbaadbdbadcacaddcabcacbbbaaadddcabcdbbcdabbdccddbbddaacdacbacbccddccbdcacccabadadcaacacccdbbababadbccbddaaaacaddabbbcaabccbbcbaaccdacaacbddaaacabccdcbaadcdccacbdcccbadabcbdbadadabdcccdadabaaabbcccaccaabacddaddabcbccabdbaaacbaccdbbcdaabcddaacadbbbaabddddcdccdcaddcaadbbaabacdccbdccdaaadaabbbaddbbcabbcaabdcbaabcbaccadaadacddddbbdcaaaadacbdcacbbaadddddacdccbbdbdbdaacaadcdbdbaacdacbbcdcabbdcaddcdbccdaaadbbabdadcccdcdbdcdbdcccdbccaabdadcddcdbbcdbccbccbcaaddcdcbdddacaddcddbdcadaabcadadbcddcccccdbdccacabbcccadddbdddcddccabaadbabbcadbbacdadaddbabcbdcdadacddaccbdbdacabbcdcbddadbaddcbdbdcdbdbadccdadbbdbddcaccaadddcaacbcbdbcbbdadbccccbbdcacdcaadacbdabbddcdcdaadbccdaddcbddcbdcbdabbcaadbbdacbbcbadadaaccbddcbdcdcbcbcdcacccdadbcadcddddddbbcbbbbdcdbbbcaaaaadddddcdcaaabacadbdadddabacaababdbcccabdcdcaddddacbddcbaabaddcccacbdbcadcabadddaddaccbbaacbaaabccbdabdbbdbccdacbddcddccdbdbabdbdbddbccdbcacdacdcbadbdccaabbaaabcacccdbaacbdddbdccccbcbbdbcacbcbdaaabbcbbddcbaccccbacddcabcaabbdadddcddaacbdcdbdabddcbccaabdaadadaddabcdbbaadcaacbcbdccacdaadcdbaabcaadcabacdddacbaadbcbcdbbcdadabbdabacdbbadbbdaaacdcccbcbcbcdbbbbadbbacdccbabadcdcddbccdbdbbaadbcdacdbaccbadcacadbdbccaccadcdadddabcbbdccbdaacaddcbbbdcabccbadbcaccaadbdbbaadbbacdbdbbdbbbabcdddaaddaadaabbbdcccdbacdbacdccccbdadddcccccabacbcdaaacabddbbacaaadcdaacdbcdabcdcaadabaabddaddcbbabbbbbddbdbbaddddddbbacbaacbadddbadbcaccbbbcccbbadadbaabddacbaaadacdbacadbaabcbbaacaabcbaacbbddbdccccdcacccbcbddcddddabdadbbcddacdcaaccbbcbbdabbdaaadbddbdbcbcaabbbaabddbaabbdcddabacacbdacacbaadbbdbcbbbccddaccdbcaaaaabbaabbcdddcdbacbccbddacdbbbbcdcaabaccbaaadccacdccdccdacbdbaabccadbbabbabaddcdcdabdbaddbbadbabcddadcaacabbaabbbbccbdbabaadaabaccadcaddbdabadbcbdacdcaaddaccbbddabddacabbdadabdbdadbadbbddcccaacaacbbcbbdadbaaddbdccacbabbdbadcbbbaadcbcacdddcaaadbcaadabaacdbaacaacadcdabbaadcadaadbabaababaadaacdbbaddddacbcdcadbbddbcbdbbbaacaabdbdccacddcbcaaabdbcbacaabcbdbacddbdcbcbacacabadddbadddbbadddbabdabbcadaccaacdcabcbbadcbcdddbbacadddadbcacadacaddcbbacbaddaabaddccdbdcddcabcdcdacaddaccbacccadcbadbccdbbabdaddcddaabbdccbacadcddcdbbcaacbcabadcbaccccbbcbaccccaadcbaaadcbaaccbcadbacbdccadcbabbcbababbdcacdacacdabaddaaacddbbdcbcddbdcdadaddbcbdabcbbbbcdcccddbbaacdbabcabddbbdbcdadbccbabcadccdbccaaddbcdcbdcbdaadadbddacaaacdcbbabaababcbdacbddabcdcdbbacbbdcaaccddadaacdacddbbcadbabcabaccabccdababaacdadaddaccdacbacbcbdccbbccbabcbccadaddbbbcbcddcacbdcdaddaddcccbbdabcdbabcacabbdbadcdcadabccdcdaddbabadababdccacacaadaadabbadccbdcbabdbbcbdcdcdcccaacbdbcaacccbcbccadcbbaabadcbccbddbabcabadddddcbddaadbccdbdcdbbbcbdabbbdbbdccabadabbbbcacbcbddbbacccaccaccadbdaabddbccaaadbadbababdadadadbbdacdbcdacdcacdabadaabdbccdcbbcaccaddaababdadccadbcbbacbcdbddcccccccbdabadbccaaacadccbcccbdaaacabbdbccbaacababdcdccccbaabcbbabcbcdccbabddbccccaaccabddbccbbadadcdadbbbacbdaacbccaaaaccbbacaabbaabdcddbcbccbcddacbddcadbbacadccbcbbacbadabcacdbbcddbdbbcccabbbabaaddbaacdbdaadbcadddccadbdadbaabddcadbdadcdacbdcacddcdbadcdaaabdabbbaaacdadcdacadadbbccbdaaccaddaadcbbcbdbcaaacdaddddaaddccbdcaaccdbadbbabdbbdaabccaddbddbabdacdddcaacdadcddabdbabdcacbddaaddadbdaacdacabababdacbddddadabdcdcdadcbaaccaabbacdabdbbaacdcdadaabbaadddbdddbdcbdcbdbadbbcaadbaacdbcaacadddcbddbccccbbbddacacaaddadbdabbbdccabcabadccaacbaadbcddcdadddbabbddcdddcadcadbcbddadaaccccbaabcaadabacbabbbaabbadcdacdccaabadcadbbcaabdccddaaaadbdbabaababbcadacbbaddcbbaccbacadacdbcdddcbbcddcdcababbbdaabbbbccaccaaacbbcddcbaddaabaaacddabdbabadcaabddccbbaadcdacddcbaddbdbbadaacbdadaabaccbbddbbddbcdbdcacdadbcdacacaabacbbbdbbbddbbcdaccbbcdacbacdbdddcddabdacacdabdacacbacddbbcdcacacbbabcddbacadcbddadaadbccacddcabaabcdabbcbddabbcaabddccacccacbcccbcbabbdbadadcdadddddaaaddbcaccccbcdadaacdccccdbdbcdcccbccabdabbabadcdababadbcaabbdadccbdbcacaddbacbcadabaccbdcabaadcbbddcbcdbabccddbbcddcddddbbdabadccbacaaabcadbaccbbabdadaaacadbcdaabddabbabcbcabdbabbbcadbadbcacccadacddbaadddddacaacdabacdcabddcbbcdcaadcdbcabbdbdccccbcaddaccacacabaadcccadcdababbcdddabbddcabdccdaccacddacbbccdaacccaccabcabbadabdddcaccdbbaaccdbdabcadddbccccdccdaccbadcccdbadbbdcbacbcbcaaaccbccacccbaaaadbcaccdcdbabbcdbdddcbcaddaabadcbbbdbcdcabddbacacbadcabcbbcbdbdbabadbbadaaaacccbcbbdcdaddaabcadbaccbaaadaddaacbdbcbbcadcbaccdbbcabdacbaabcccddbcbdcadabaccaddccddadacaddaadacdbadabcbdccabaabdcbcaaabbaaaacdcdabbaabddcddcadcddcdaccdbbbbaacbdcadaddcadadaadcbaabaadabadcddbbcdccdacaadcccbbdacbadcdaaadbacaddaacadaccaabcddaaddbdddcaaccbddcacdabbcadcdcddddbdbbdaddccccbcdbbdbcbadbcdacdabacdbdcbbbdbdabccddcdbdbdbdcaaadcbcdbbaccacabdbdddbabbccbabcabaabdaabdcaaabadbbcccbbbcddbdacdcabbaddabcbdacbbacacddcbabddadcbdbacbaabdacbcddabdcddbbaacbcadcdcacbddaddcaccaaccdabbabcbdabaaabacabaacadbbabbacabacabbacadabcaabdbbcaddbdbcbaacdacbccdbaacbabaddbadcacacdbadbbcaaaaddbbcacddbcadadbacaaabcdbdcddaddbdcabcadaaaaaacdaabdabbaabcdbbcbcacaaaabbccbdbbccdcbcddadabaaaaacbacacbdccdbcdcbabcabcdbaccbbbbdbabcadaadbddccabadcdaabbdadddaadbbdcadadcddadccccdbdcbcccdadabbabdadcadbdcdbaaacbaadacccaaaddbadcddbacdbadcbcabcccdcbbaddcbdaacdccacbdcdcacdcabbbddbcdbbcbcddabcdaadddbbbacdbdbabbcdbbddaacdaaccbdabddcabcbcdababcbbbbbcbdabacddaddbdcbbaaacacbaabbacdbdbadcbadadcddccddaacbcadcdacbbddacbdabccaccddbbdcdddcaccaccabbddcadbbcbccacababcdbbadaddbcdcaadacbbdcacdcbaddabbcaadadcbcacaaadacacaabbacbcdbcdbbbaddcbadadadbadadaaccdbadcacbdddcbbbccbabbcdcbcbdbdbbbcdbbccaaaabddabcdbbacdddbccddcacaabddaabcbdbbacbbabcdabbcacaaabcdbdacdddcaddcabccddbacdbcdcaacdddbdcbdcbbccbdaaabacddabadcaddcdbcdcdcaaacbbaccdbbddbbcdabbbadaccbdabbdddcdbcaccdcbdbacdaacbbbddbbcbbdcacabadbacbdabdbbbdcdaddcdcbbcababbcadacaaacbabacbbbbbabcacdcbdacdabcccbbbdabdbdabbbcbdcacaaadababcbbdacccacabdbdbbadcccacbcbdbaadbcdaaadacbcbbcccdddabcbbbdcbdacaaadbaabaadbacadabbbcdcadacbcdbadbaccadbaadbbababccacdaabbbcccbbaddddccddbddaacbadcdccdcddbcccbbacddaccaddbcbdaccdbbababbbacdacabbbbabdcbdbacbbacbabdbadaabbacbbddccaabccddcddabbdddbaccbbcabdbcdcadaccddadacabbdccbcaccbbbdcbddbbcdddbabbccdaadbbabacadcbcbbbaacaabcaabbdaaaddacbdbcdcbddacaaabacaaaccadadbdadcbdbccbabacdbadddbbabbacaccbdbbbddbcdbabacccacabbdbaadbcadbbbdbbbbdcddadcabaacbbbcaadcddadcbdbacdaaaaaabccabbcccdccbcddbddddaccddddbbdadbadacabcbccacdbcccbcaddbcdadaddabdadbbabcdcababccdcdbdaabaabcaccbacdcabdabbabdadabadaccdaaddbdacaadaadbbcbcbdaadcdcdaabbccbcbccbcdbabdacadbdabdcdcccbcbcdaacabcadbdbcbccbcddadbcaacadbbadbaaaaaacdbcdbbacbababcdcabcacaddaccbaccccaddcddccbcdddbdbcdcbcdddccbdbcbadbddbbddbbbcaabbbddaacaacbdadcdacddcbbcacbbcdbcaaadcbcccadbbabadcbdcaabaaabbabbdacdcdbbcbcdbbaccbacddcbbbabbbcbcbbccacbbaccacadcbdabcadadbccabcacacbcdbbdbbbabacbbddabdcdbbcdbdbbcacbcdcdaacddacababcaaabadcbdabccddcabddcbdccccdccccbdcdabcacddcdaacccdccaabbdcaaacdbbccdcdbbbbaccbcaabdaacbaccccadabddbccdbccbaacbbcadccddccbbbadcabdcbbccacaaacadcdaadcaacaddcdbadabbacbadddddcdcbdcdabcabdcacbbcccbcbdbacabdabbddaaacdbadaddddddacbcbdddccdddaabddddacbaccdbbbacbcdabccaadbcbcbdbcadabdbbddccddddabaacdcdbdaddacbcddccdababddacbabbbdcadbbcbcadbbacdbbdaadccdccbdbcdcbaacbddcaabadcbadcadddcdddbbbbabddddcababaddbdaaaaaaaadcadbdadbacbcdabddcbcdadadbbddcacacacdcdbdbadbbcbddbbccdbaadacbcaccdcdabcbabcddccdabdbacdadacddddaabccdaccaddcadabbdccaaccabadaacbdcadcaaccccddabcbccdcbdddcdbdbaaacbcdccaadbcdcdcdddcdcbaabdcaadcacacbbcddcabaacbdacdaddcabddaabdacabcdbcbcdbaadbcdbcdcbbbabddddacabdcaaabddcbabbcabcddabdbbaaccccaacdadddacccabcccaababcddabcbaacdcdbacaacdddabacbaaddbdccdbcdbcccbadbcbbaccdbcdabacbcdddacbcadddadbacdddcacaacbdbacbdbabadabaabcaadcdccaccabbcaabaaddbcbbbdbbbdcdcdabdaccbbaadbcadbcbccdbcddddadbdcdbdacaacbdbdabdaacccacbadbbddbdcacdcccbdbacabccbadbaddcbcbdbacddbdcacdacccadbdddccccacbaacdbacabbbddcddcbccbbddbdcadbacddccbdcccbabcaadccabdcdaadcbbbdacadbbbbabcaddbbabdbbababaadcccacdabaadbcacdcbadccbbaaabacbdaadccabbcabacaccbaadddaadddbbababdcdaabbacbddcbbbbcbabbdccdbbacdacdabdaadbcaabaabcdadcddcdcddcbbbdacbacdccbdcdccbcdddbcdbcbbbdacbdcbddbdbcdbdadbbbdcddadbbcbdbacdaccacdbadbabbacddacbdacabaacdbabcdaaddcbccbdabcdadbdacdddbaaacdbcddcaccadadbabcabbacacbbaaddbccccaadacddccaabacddbcdabacaadadbbdbdbbaaacacaadbdbdbdbbcdaccbdcccdbbdcacaadccbaccdbbaabdccabccbbacccbcbbbdbccdbccabbaababdaadaaadbbbbddcbdbaabdcadabbbadcaddbcabaadbcaccbacacccbbcddbdbaaadcdddaabdacabcdccbdddaadcacacbddadabbbbcbcaacdcdaacbabcdddadbdbcdadbbabbbacdbbbbaddbdacbcbbaadaaabaacdddbdbaccabbcacdcaaccbcaadbcddcdcbcacdbbcacabdddcabdcdbacdbcdbdbdabccdddcabaabbccaabcacaabcbcdbcaadacdaacdbaddaadcdbdcdcdbdaabddbdcbdcaacadcbadbdcbdcdccbdabcccdcbccbcdabacadabbadddcaaaaccccdddadbadcbddaabdacbaccbbdacaddcbcbbdaccaacbdbbcccbdadcabbdadaadbbbcadaabbcaadddbacacbdabcbacbcacdccbacaccabcddadbbcdddadbaccadbbddbadcadbaacaaaabaadcbbcdaaacacaadbdbdcdadcdbabcdcadaacacabddaadcdcdacaacdcccbdbaccdddbdbccdbdbbddaddadbcabddaaacbabbaaacbddabcbcbdbccbdcbdbbddcadbdabcbcabaadadadadcabbdcdbaddbbdccbcaddcbdababbbdcdbdadcaadbbacbacacaadadadababbdabadcacbbcbadbadabbddbabdacdcbaddbaabdccdacdadddacdbacdbadadcdcccabdccdbaacaddbabbddaabdcdccdbbcdcccccaadbcbdaddcbaaaddbddababbbddbcbdcdbdbadabddbbadaccdcddbdcdcbbccddddbbddbbbbadccdaccbccdbababbbacadcbcbcabdcddadddbcdbbbdaacdaaaabcbaaabcacdbcdcdccddccbabcacbbaacacacbadddaccbacacdcdbacbaabbdaadcacaacbcddabadcdcdacaddbcbccbbbaaaabbdaaacabcabddacdabaccbabdddbdcaacddabacaddbacbcbaddcbadacaaaaabadadccdbcabcbcbcdbadbaaaadaaadddacccbccbcbacbddadddbacaacdddbcdcdcbdbadcbdabdddaaccccababcdaaaaadccddbbdbddcabababcdabdbbaacbabacbdcacbcbabcacbadbbabbbabcccaccdccdbcbbbdcdcbadcabadbcaccaaacaaabdaabddccbccaddbcdaadddbcababcbbbbcbadbcabcbbcbdcabbaaacbdadaabcadbbbbcaabdbbdadbcacdadccccbbccdadbdbaccdaadaadbcbdbdbbaababaaaddbbdcdcddbbdabdaaadbbbdaabbbacabbdbccababdaadbdcdadbccccaadddcdbaabdddbadabacdaaaabdcbcadadccdcdcbdddbccaaddbdcdbaaaadaccbabcdcaaccdabbdbaddcbcdadcacdbdacbabdacbbccaacdddadbabcacbaccdbbcccadacaabddbcbacccdcdacbdacacaddadcbabcdabaaddddcbcaddcdbadcbdadaaccbbbccbcdcaaaabbadcdcdaabcacacbbddacdccabdbdcabdbaacdaacacbadabccccdbbbbcccdcabcaaaabcabbbdcdbbbcdabbbcccdabcdcbadbbbaccdbccdbdddcaaabdbdbaadcbdcdccbddabbcabccbcdcbccdcbcbadabcdcbcbdbababcbacacddacdccabadabccdcddcabcbaddccaabadabbdbaacbcdcbdaaadbdcbdcacbcdccabcabddaacdaadcdcdadbcdbdcbbadadcbacbcdbdadadbaaaadaabcabdcacbdadbadaadcaadbddcaacacddbadacccaadcbcadbaadbccccddacaabddbacbbbabcddbdcddbbacaccbabdbdcddcadccdbbbbccdcbcdabbdaccccddabcbdcaddccadbbaadccbcbdcabaacbcbaaabaaaacbcbbddacabddaccacababddabbdcadaaccaaccddbdadbdabcbdcabcabbcdbccdbbbbbcbabbdabdacacbdbcbdbcadcbaabcdabcaabbccadaacabdacbcadaabdcbccddcbcccbbdccbdabdabdcddcbabacdabaddcdbdcbdbabccbdaaacaaaccadbaaabdccbdabdbccdcdcdbbdbdcabccdbdcadbcbdccddcdcbbdbbcadbadcbbddcdbccdddcabbacbdbccadbcdcbacccbcbccddbdbabbdaacdbababbcddbbcccdddaabadcdabbcacaadcdcaaccbabcacacdbabcbdaadabacbcbaccacbccbcccadcbacdadcbbbbcabadcacacdacbbdcadcccbccacdbccbdbccccdbdaddddbcacbabaacccddbdcccbbdadaabaacacbbaadadadccbaacddaacabcdbcdccbbaccdbbacbcacbbdbbbbcdcccdadcccaabccbdacdbabaadcbdaccbacccababdbdcbccdbaccdabccdccaacadaddccccbcbcdacdbcbcbacabbcbbbdacddcacdadaacabdcdbccbadbaaabadbabdbdcdbaaacababbbacccbadcaacccbbabdbcccadadddcdbbcdababcacddcdbdcaadacbadccdbaccacadbcadccbabbcdcdbacdbacabbbcbbaacbdbcbdbababcacaddadaabddbacccaaccbdbbcccabdbcddadbdaacbadbdabaaaacaccabaccbdaadacbddbdbdcccbbdcbabdcbdacbaabbabacdabdccabbaaabbabdaccadbabcadcdabdabbbacdbdbccbcdacaccdddabcbcdbcabcbddccbaadbdacdddabccbdddcccddbbbcccdaadabdbbbadcbdddabaabcacacbdaabdabdbcddbcaacabcbbdcaaacaadacbacdabccccbacaacbaacbbcacdcddccbadbcdcbdbcaabbcbbbcbdabadcbacabadbabdcaaacccaaccdcdbdcdadcddacccdacbbaabcdbccdaaaabdbdcdbbbadcbcccbdddcdaabaaadcadabcbbccbcccaaccdaccaccddcdcdabaabbddcbcdacbacdcbbddbbbbcddaaccaacaccccccdacbbdacccbacbddddabdcbcdbdbbdbaaadcbdbadddabddbcccdbbcddbaaaccacdcacbcccbabcbbadaabcacbccbadbbbabdabbcbbdccdcbcabccdcbdaccbccdbbccbcbabccdbbacbccacbaddaaddddbdadabcddcaadaccdbacbccbdcacbaccabaabccbdbbdadaadcdbbdabbcdbaddbacbcbadcdbcbbbbdadacbbabcbbbcaddbbadbabaacccdbaacacbdaccdbccacbcdbccacbccbaaacacdcdcbbcbcacdbbbdcdbdaabdaabdbbaabaacaadddbdbcbcddcbadaabdcddbdadbaabcaadabcdcdaadcdaaccdbdcbdbbdacdddbddcacaabbcabbbcccaaaccbccaccbbbcaccbbacdbbcddccbacbadbcdddddcacaacaaaacaacabcdbcadcabdababaccdccaabcabbcbbbcddcdbccbcbddccdbaccadacdbabcbcabdabcaacaaabbacdcbcddbaaddababacdbdbabbbaddccccabdbadacddcabdcbbabdabdbdbacaacdacccdacbbcacbdbbdcbdccbcaccadacbdbaaaacdadbdccbccaabdbbccbddcbabcaabccaabdbabcdacccdcaaddcacdcaaaccdcbbcaddbadabbcbaddaadbddbbdcbcbbdabcadaabcdaadddbdcabadabbcabadabbdaacddababdcbdacdacccacbcddadaacdbaacbadddbbacddababbcdcadbcdabacdbadcdacaabdcaddccdbdbaccdbccdbbbbabadbaadaabcbcccaabadbbdccbdbcdcccdbbacacadaababbbcbdbcbcabbdcbdbbdcabccbddddabbcddbacaaccdccbbccbdcdccabacadddbaabaddbdcdbcbcbcaccdddaaabadbaccadbabbaabddaacbadadadbbcbadcbdaabbbccdabddcbddbcbabdaabddcbaaddbcbdbddabdadcdbaacdadbbbdbaadbddcddbaacbdadaabdbdccddcaacdccbaabccddbddcacbacbbdbbbbdbadaaaabaabcbaddbcaddbbdbaaccbbabdcdcabdacacbacbdaabadcbaacbacdcdadadccccdcbcaaddcadabbbdcbbbdadbddbcbadbccccccbbcaacdbbabdcbbbcbbbcaaacadbdbdccadbdaddbbbccacadadadbccbbacbabbccbbbabbdabbabbbbbcdbabcbcbaccddbbddcdbdcddaccacbcbbdabbdcbccbbbadaadadcbcaaabbbccdbbdbadcbccaaccdbacbcdcbccabbdaddbdaadcaccccbbbabbddccadabddbbcabcdadadadbadaaccbaddbdccacacdaadaadababaabcacbbaabaadbadcdacccbcbbbdaacbacaddacdabacbbbaccbdbcbdbaadbddbaabbcacdcadccccbcdbbcbbaacaabccabcdacaaaddddadaacbacaaabababcadacdcabaaacbcaccccaacabcdadcaddcccbccabdadadadbbbacbabbadbaabcddabdabadddcbdbdddbcbbbcbaccbdacbbbcbacdacbcccdbbdccadccadaddddbbbcadcdaddcccbbcabbdaddaddaacdaabdacdbbccccddaddcaadcdababbbcccaabbcbcabbacbacabbdbdddcdddbbbcdbabcadbdddcaaadcccabbcdbbcddbcbbadcaacccccaddcdaadcdcaddbcacbbbbaadbbabcacaddbadaabccddcdbadcddddbabccacbababccabdaacbdadddbcddbadbbbaadccacacccacbddcadcddbcbcdbccbacdadbbabdddadaccccbcddcccabaaaccdaaacadbcaaacdcbcbcaaaadddacaaacdbaacdbaabaddacbcabacbaaacabbacdaddbabbddcccdbddabcabbbdacdddddbdddcccabbacdadbdaccacbbcdaaccbcbcbddbddcdabaaaacaababdbabdabbbcdaddaaabaaacadaaddcddbbacdccdbdacdbcabdaaddcccdbbbcaccbabcccccbbbbbcbdcbdbabadacbcadbdaabdacbdaccdddddbdccadadadbbcdbcbadbadabddacccbabddabcaaaaacbabbadadaacdcdabbabbcdbccabbacddcdbcccdbcbbcbacadbbcdbcbbccdccdaaccbdbacbbbdccbaabbbbbaacbdadbaaabcbacabdadabbdbaabcacddcbcaadddbbbcaacbddbaabcbbbccccdadadbbbbddcdadddbccdbacabdacaaddabcbccadbbddbdcadaddcadacccbaacbddabbbbcaacdcbcdaadbcbadbcababcdddbacababaabaababbdcddcacbaccdbcdbdaaddbbbbcddbadabddaadacddabdabddabbcccddbbddbcaaccabdddbbadbbdbbacbdbbdcdcdddbbcabcabdcbbdaabacddcacaddadbbaaabddbdcddcaaacdbdbccdccbbcabaddcbdccabacccbaacdadbccddcadccabdcadbadacaadbcccbcaacdaabbdbadbacccacaddccbcdbdadadbbcadcddcacdbcbabdddaadcbaaaadbcbbbbcdddbddcdcabbdcbdbccdccadbcacddbccdddabdaddcadadcbbccdddcacabbdaadababadbdacbdaaaadcbccbddbbcacdcbcdaddacdcdccbaabbdbabdacdabbdbcbbbdadcabdbddadaabccbadcdbccdbccadcdcdaaddbdadadbdadbbcdaacbbcdcaaaddaabdccadaadabbaacdbbdcabaabdaccbdbabcbbadadcbcbadaadbbcbdabcaacbbabdcdcdacdabddcdcccccaabaadccadcddbccbccbccdcbbdcbdcdbbacdabdbcbdddbdcdddacccbabcbccadcdaabdadbabddcadbcadabcaacccbbcddcdcdddbdcacbbabbcccaacadcddddaddabadbacadbcacacbadabaadabdabcccbcccadcccdadacdddbddbcacbdbbacabbbabbacdaacdadddbadaaccaaaadcbbaccbcbacacadccacacaccacadbdccaddcdcddadadbcdbcdbdbaadcdcdccdbbaccaabaadccbbdacabdadbbbddaddcdaaadddbdbacacbabddbccdcaadbddbbdabaacdaccbbcbbdaabbbbabcacddbabdbaadddaadbadbdadacacbbaadacabbabaadabaaddbabbadacbddcabadcbddaadcaabababcbdacbccbcbcbbaacadbadcddbcddcaacaaadcbdabdcbcdaadbbdbcbddcbdcabdadcbabccbdadbcccadddaabccadadcdaacbddbcacacbdbcdcadbccadccddcdcadbcdcacbadbcbddcdccdadbddcccbcdbdadbabddccdcccacacdcdcdcbaabcdacaabcbacadddcdcbdaaabaccccbbddbabadbbbccddadabbbabaaddbaadbabaaddcccaaacdaabcdabcccdddbbcdbadaddccbbabbbbabcabddacddcbaabbddcadcaabcbcaaddadcdbbaaaabbcbccabdddbaaadbccdacccaaddbcdbcbbcabcabaccdcabaaaaacabdabbcdacabaccbdcccdaaabcbdadbcbcdccacdcccbacaddbdabaccbadaabccabcbbccaaccbaacbbdadbadabcaaddacabddacbbdbbbbdaabbbcbbaccbbadcdccaaccbacacdbaccddcaaabcbadaadbcadabaacccaadadccbddcbbacccbdddddacadcaacaadabcaaddcabbdcdcacbdbdbdacdbbdddbdbacabcaddccbacbadacdabdabbbbbdacbbaaaaadbcbdabdbbdcdbdcccbabcaddadaaacaccdbaaddccdcabcbcaddcddabcbccbbbaababacbcbadacdcabdacbcbddbcccddbaddcbdcbbcbcccadadccddacccabcacdddabdacdabcbadabbcaaabbdbadabbcbdcdaddbabdddbbabadbbdabdbbcabbbbbdcaadddbaabbdacdbdcddbbdaabcdabbbcbcbcaaadcdcdbcadaaacaaddcddcabacabdaadadbccccbadabbcacbbdccadadcbcdcdcacbabaadcbaaccbaabcdcdcacdaacadbcbbcccdbdddcbbdbccbdadbddbbbdacdcbdaabcdcbccbcacaabbbcbbddcdbddadbbcacbdbbccddcbaabbdbddbdaaabbccdcaacabddcddabcddddabbdbdabdbabbbaaaddadacabcbbbabddbaccccbadabddcdbbbcdbcbadbbaaccdccadcbcaccadaacbbadbdaaaccaadcbddbcdadbbdbbbaadacdbdbbbcacdbdbdddbbbcccadddadbccdbaaddabaadbaabcabcacbabccacbcadcaadadbbabadadcbbaadcdabbdbcccbdcccaadcabacbcccdabbcbcaabaadcdbccaacacdcddcdcaccccdcacabdabacaabbccacdacaacdbcbbcddaddbacadacbadcbaabcbbadcabbcbdaccaddbdbccaabcccbbbbbbacdcbbcbbacacbaddaccdcdbadbbaaadbaacacaccacbacbccccdaabbdcbddadbbbcbccbbbbaaadcbbcdcccdbbcbdabacddcdbbbdadcabddbabdcdadabcadbcadbdbabdaacdbdbacdbddaabdbcdbacdcddddcdaaabddcdcaaaabcccbdcaaddcabdbccadcbddbbacddadbdbbdcbbdaaccbdcccbdcaabbbadbbcaacbddaaccdbdaadcbaddbbbabdcbcdadcdaadabdaaadadcadacabcddbcabbdbbbbcbccaacbbbbcadbbdababccdcadabadbcccbccccdbcbccabbabdccccaadddbbacbbdbaaadabcadbdadabcccdddbdabdaccccdacdbddaadaaddabdabcdcadbdadcbccbbadbcabdccbbacaaaddbdadcaabdbaddcacbaabcaabcbbbaccbcadabaadddcdcdadacbdaacaccbacaaaadcaabbbcbbbdddacabbcdcbcccbbcadcdcaadbbdaabbcaaaacbbacbdacbbcdcacadaddabbcbdbacaaccaaccbcbaddbccdbccdddbdcaabccdacdabcaadddaccddddcccbaddccbcbcbcbbabacaadbbbabddbacbcabdabbddcdcdaacdccabcadbaadccbdadbadadbbdacccbbabcbdaabbdcccbdaacaddbcbcdaccccbdcddddddcdccadbcbadaacbcdaccacbddbdcddaddbaaddbddcbbcbabdbbcccdbddcdbbbbbadcdccdddcbabdbdaaabdabdbabcdcdabacadcbddaabcacdcbabaaaacccadddbbccdbbbccdabaccbcbabaddcbccdbbdcbabbddbabbddbdcaaabaabbcacabbcddcdaccbdaccaccabbdcdddbdabdaddcdbbcaccadbacddcbccdcabaadccbadcdbbacdbccdcbbdcbdbddacbaabaadbbbbbadacabddcddbdabcddddcbcccbcdbadbbacddbaabdadadbdcbbdbdbbdaaaddcddcddaaacdddadcadccddcaddaabbdddcdaaabaddcbdacacaacdaabcddcbcabbdccbdcbbcabbadbbbbbacaabbdcbdacdcccbbccbcdbadaaddcbdbbacdcbdbbddaaacacccdaddaaabdbcbbdbdadddbccddaccbabbbbbcdcdbabccdcadabbcaddacaccbaaccacbdcccadccddbcccaaddaddabddbaddaabadbdadbbbbcbdacaaaadacbcaaddaaddcadcdcddadccaacbbdabaaccdcbdbaadadccbbdacccadcdbbdbbaacadccbdbdddbbcccccbcddccabbcdcabbccddcacbaabadbdbaacccccbcbcbcbcacbaadcbaccdbdacdadddbccbddcdadbbcaccacddcddccaaacdcacdbdadbababcbdaacdccaadcbccccbbcbdddaacccdbdabadaacdabaddbacdddacadccaacdbdaddbcacdccbcbcdacbbbbdddccaccaaacbaaccbcdccbdbaabadccadcccbaabbadbaadadddcbcaddabbacbdcabbbcbcdbaccdbccdcccbdcacadbdccbbcbdcbdabddbcabcacbaadaaacdcbbcbbadbbcaabadbacdcdaacbbabaaccccadabcbccdadccbababcbaaadcaccdcbbbccbbcdccadaaabdbcadadaddcbaadabbaadbbdbbccddccacadbdcadaaaacbdbadcdbbbacdbbadcaaabbaadcbbaccbdacddcadcbbcbaabcbabadcdcacdbbdaadbaaaacadbdbabcddaadbddcccdcbdcaaddddddccbbcbcadcdcccdbdccdcacccbcdbacdcdbcaaaaddbcbcbcbbabbdcdcabcabbbccdccddbbcbddbcbaaccbddadddbdacbccbbabacdbacdadabcadcdabbcdaaabaccddcdabaacdddabdbbdaddacccdbabbcbcadbabddcabbcbccadcacbccacdcbdbadbbdacadcbdadacdcaadaabccdadacabadabdbddacabdcccbcbcaaaccbbdadccddbacdcccbcadbddaccbcdccadaadacbccccddbadbaddbdddbaabbadcbadbcabbbadaadadbbcaadcadddadacbdaaddccbdacdadbcdccbdbbbbbdadadbcbcbcaccaaaccbadcbcbabbbaaabdcccbcbbdccbcdbabddddaabaabbcbadadcbdacbbacaaabbcaaaaacaaaacbcbbdccbadcbcbcbbaddcaaadbaaccacacbbbdbddaddbbacaabcbcbabcaaaccabadaacaddaccdcbcbacdccbbaddadbdbadadcabcbaaabbdabcbdadbbbcadddaccbdbabdadbdbbcbbdabbbabbcdcbbbcdcddabddacbcbacbaacbbadbdccdbabddbdaacbbcabbdacacaccdddcaccdaaadaadccdddacbadbaccbbccbabdcdddbcbbdbdabddacbbdddcadabadbdaabbdbbccdadbbddddbcddadcbdabcdbaacaabcddbabcabbdbdbcacdbadaabadcdccdaccddbbbaccaabaaaddccabdadccdcddaddcbabcdaccaaaddcaaccaaacadbdaccaccbdaaabadbccaaadbcadaddcaaaabdacdcbdaabaadaddacddbcaabaaaccbdbaadaccddabbabdcdbbbbcbdadccbdccddcddbadcbdaaacabcbaaaddcbcccbacdcabbadbccddccbabadbdadbabcdddcdbbbddababcaddbbbcbaccabdcccdadcbcaccbcbcccdccaaccacabdabbcabacbddaaddbcbddbdaacdddaacbbadaacaadcdadacdacddadcdbdacdadbbdcbacbaabcbcdacddacacbbcdcabddbbcbdccdddbcabaadabcbdaccdadcbdacadcbabbaacddccdddcdbddbadbcbbbdddbcdcaaaacddccbbbbaacdabbbadaccbcbbdaddbacbcacdabdadadcdbcdbcdbbbdbcabcbaabbabaaabddcbbbbdbdabacdacccbbaaaccdabbcaacdcbabdaababbcbbdbbacbdcddadacbccdcaaddddacabdabbcdababadaabbddbdccaccaddabadbbdabcadcbdddbaadccabddcddbcdbbaadbdcbaddccbbdaccbcaadcabbbcdaacddbcddcbaaddcbbadaabacbcabcbdbbbcdbdadbddbbaadcddbddcdbbdbcdcdaabdadbcadacbbccacddabadadccabbbccaacdddabddbdacbcddcacdbbccdbcdaabcadcdbcaabccccaaacaacadacadbdddbbcccbdbcdabdcbcdabaddbdcaccbddbccdadbadddccdabacdcababdcdbcdaabbbddbcabbaadabccdadcdbdacdcbdcddcabddbdccdcaaaacbbcdadacdbcadcdadaddccbcaadcadacddaacdbaccdbbdcacaaddbdbbdbacacdddbadcaadcdbbbdcdcccaaaabcbbbcbccccdcbdcbcbbbaabccaadbccadddabccdacdbcbadbbdcccddabadbddbcccdbdbbcaddaccadcacbdbaaacddbadbcaddbbdcdbacadbbddccbdabcabdbacdaabcabdbcabbabacdaacdacbddbbabbbddcbdbddcdccdddacddbdcaacbbdbcadddadbbbadacddaababbdcbbddcbbabaccaccbacacdccdbdbcdadcbaaaddaaaabcbbbcacccbacddcbbdbbdabbcdaabccdcbbdbdcbabbaadbdcdcacddbabcdccccbbabdccbbbbcccbdaddcdcbbdabddbbabbaabddddbacaaadadbddcbcccdcbdaadcdccabdccbdacdaddbabbaccbddcadbddbabccddddbadacdbbdddbacdbcdcddcdaabbdadccbbaaadddccddadaaccddbdacccdabadbcacdacddcadddadcdcccbcacbcbadacdbcbacaaddaacbdaabddccaaacbdadadbacdacaaccdcadccdaadadabccadbadcddadadbccdcbcaddadcdbaadbddaaacdababcaabacdabbabbbaddbabaacdacadbbaddbcdcadbbbcdccbcdcbbcabbadaaacccbadbacadddbdbabccaaaacddbacbdadaddccbbccbdbbbbacbcbbcdacdacbaccbbccbacdacdaadbddaddbcddcbbbddadbcccbbdbccbaccddaccbddadacbdacccbacbdaabdbdcdcadaacaaabbbccddddddabacaabaadcdddbadaabbdabbbdaccabddaddcdadacbbccacbbbdddbdacadcacdbcbaacbdbcdadbbbdabacabcdccbbdcddccbcdccdbacbadcbadbdadcbddaddbbcbdcdbcaccadadabcadcbdadabbdcaaddabbcadcacabcccbbdccabcdbabbcacadddcaaaaabadcdcbcabdbbdddcbaadadaadcdcccaaddbdcabdbaabcbdbadcdabadcacccadabccaddaabcdacabddcababdbdbcccbdcababdabacbccbdbababbbccabaddaabacdcdcaaddccbaabccacdbbbababddaccacbbdadbcdbbaaddcbcaddabdcacaccccabbcdcbcdcabcdacbbacdcabdbbdbabbdcacccccbdbccdaadbcabdddccbddbbccbdbdbacdacbcacacaaabbddccbcbbcadcbabbabcaabbdbbccaaddbaacaabacbbcbcdcbccbacbadaaddccdaadcadabacbdbbdccabcbdccadddcbacaddaabcadddbabdcdccaccaddbcacaddccccbdcbcddbadbabbcacadddadcacaddaddabccacbdddbddcabbcccdbddbaadaadaccaabadabdcdcdcbcabacdbdcdddddddaaabbadadccbcbddbdbcdacccaddaaabbdcbdaaccbacbbddbbcbcbabbcadbdcdcadabcdcacddadcacccbdacadcbdbcccaadadbbbaaacdbcacbabbdadacdcdcabaacbabcaacabaacbddbdbcadbddcdacbbaddcddcdbbccbcdbbbcaacacdcbdaadacddbbaaaabbcabdcbdddbbbabaaddcdacbbbcbddcdadbdcbbcbcdaddbcacdcccbbaaaccabaadacabcaddbbccadbbdaadccdcccbdabbccdaaabcbdbbbbcbddbbcbabbccacdbaccadcccbbbaddcdbccbdababbdabdbcabdaddbbbcacabbdddbbddcddbaadbbcbcbbbcdacacaddbdacbdcbaabbadddbaccbccbacbaadcaadaddaddddadaddcddddabbababbababdaccdcbcacdacabdcaddacabadbcacbaadaccddabcccbaabcdbbabddcccbcbabadbbdbddbaacdabddadddbccdbccdacaadcdbbbcdcdaadabcbbcbacccabdabaabcbbbbbcadadcbcccaaaadbbcaadadcdbddcabbbdccdacbddcbadcbabadcbdbaccacdabddacadcbacadcdacadcdaabbcadbdcddbdbaccbcabccbcaddcbcabbccabaacccaadacaabbbbcaddbcacbadddaabcabccdccddabacccbabdabcdcdcdcbacdcaaaddcbaccdadacddcacccdacbaaadddbaaccdaacaadcccbdbbbbcccabacadaddcdccaddababdbaadacabadbcbbdabbaccbacdcbacbaaaaacbcacacacdbbaadbbcdcadbdadadbdbdbcbacdabdaadcddbbdcbaadabaaddaaabdadacccddcbbcaadbbbddcbbaacbbbdbaabddcaaddcdaddbbdcbdccdcddacacabaabcbaddcbadacacbabcacdbacbddcaacaaccdababdadcdbdcbcdcbcacdbcdccabbaacdbdbbaaddbdbcdabadcdbccdbabaddbdaaaacacadcddabbbcaabdaadadbcdaccabdcabcdcabdccdcdcadbadbaacaabdabaccdacbabcccdacdcaadabababadbddaddadbabccadacdaabbabddadbbddcdbbbbbcaaadcdabbcdccabccccabddddcccdabbabbbbdacbabbbacaacdabdbdddbbdddacbbaaaccbcddddcabbabbbcbaadcabdbdaacacbddccccdbdcabaacccdadbcccddcababbcbcdbbaacccdaaacbacddbaccbbcdabdcadbbdccaacbaabcabcdbbdbdcbbbccdddaaabdcbbdbbcdbabbdaaabaddabadadddbaccbacacaadbbcccbbbccdcccccacadcbbcbdbdadbbdabbbadbddababacabccdcbaaddcbcbbbdacdcdcccaaabdbdabbacdacacbabbcadbcaddbbabbabbabcbcbaacdddacbabbcacbcabcbcdcbdadcdbacadddabcdaadcdbcacbabccddcbddbdaddccbdaddcbddddddcdbacbdcadddaadddddaccdbcbdbbcbaaabddbaaababdbcbbacbbbdadadccbdabbcbaadabbddddbccddcbaadadbbaddbcbaabbadacdababcaabcadccdcabcdbdbbabacbdcabcccbbdbaacacdbacbbcaacbbcdbdcbdcbddddbdcbdabbaacddacbccbdbdbcbbddacbddbadbdcdcabbdaacccdbadbddbabcddcadddaacccdbcaacccbdcdbaacbabdbbdddabdbddcdcbbcacaccbccaadbcbcdcdaaabcadcdacdccbccccabcadccbaacbcaaadadacbbccdbaabbdaaadccacccdcccbcccbaabcaabdbaaaddbdbbbbaabbdbcbcbbadcadbbcabaabbdbdcacbbcbdbacabbddbacccdcbdbbcdbddabdbcdddbbacbbaadacababbabbccdbbbbadddbbcdbcdcacadbaababcccdbbbcdbccaaadcbcbddcdacaaaccdabacabacaaaabadcddaddbcabdacabbdddbcabacccbabccdcccabcbdadcacadcbbdaadcbdbdacababbddbabbabbcabadbcabccbacccabacacadddcddabbbaccbacbdbaddabccabccdbddbcddcdbcaaabdadaddbcdbadbcadcbdcbcabbabadbcadaadcbbababaabbabdbbacdaacbbbdddbbccdddbcdaadaabcadbdcbcbcbbdbabdabaaadcbbabdbdabbbaddaaacaacacbcdabbcbaaddaacbddcdccdccbbbabbbbcacacabaaacadacdccdaabddcdacbccbabccabcacdbabdbdccaccdabdcbaaadbabaaabbcdbdcbdadadcdbddbbabcdcbbaadadcbcacadddcaddbbaadaddbcccccddcacdbdacaccadabddacbccdbcbdcadcdcbaddbbadabdabccddcdcbcdaadbdddabcdcaadddcbcbaddaabbaabcdccaccbaccadbdcdddccaaacabaccaacddcaadcaddadbbaccbcdbdccddddbcdacadbdbccbdccccdbbacbdadbaaadcbdbabbababdaaddddcccbbcdcccadaabdadcdbbcbdcdaddcbcaadcababaaaaccacdbadcdcbcdbccccaabcddabcabcddcddaaccaaaadcbdccacdbcacaabddcbdabdbccabdcdbbdbbcabbdcbacddccaabaabddbaaddccdbcaadadbddabdadcddcdcaabadacccaacdccbbdbcbbcdbdabdddbccdcbddddccacdcbbcccdaacdddccaacbccdcdcdbaddcbcbdaabcaddcadddbacddbaddaadaddcdaaaaddcbbaaacabcdcabadaacaababdabadcbccaabbcbbbbbadbddddbcdbbdcdbacbacbdbaaddbcbcdbaaaddacaabdacaddadadcdabcaaacbbdbacddbbbabcadddbbbbcdbdbacaaaabccadcdbbdadddcdadccbadacacdbcbcabdabdcaaabddcdddcaccacccaacdccccabbcdbcdcdbdbacbddaacdabcaacbabdbbbbcbcbcbbcdccadcdcdabdcccbcdaaadbdcbccdccbbaccdadaccabbacbbbcaddacbabddacabcadddadbbdbddbaacddbadbddbabcdbcdadbcaabcaadbccbabcdddcabababaabcbadabacdaadbaadadaadbcdccbccacacbbcdddabacacdacdddaaaddacccdbaadadcababadcaddabdadbcacdbdcdaddacaadcdadabadcdbcdbadcaadaccdbbacaaacdccbdccbabaddadbdbdbcdccbdcdacdbccccdbcadabcbacdabccaaacbdccccadbbcbbbbbadbaabcacbaaabdddacbbbbcabbbcbcdddbaabdbdddcdcdaabcaabccbbcadabcdcdaccbdaccbadaccbddcadabcbcdbbaadadbbbddbbdddddadabbdaaabdacbdcaabcacdaadbdccabccbcaaaacadadbddadcaddaddadabcbbccccaccdbaccdccaabbcddbbddddddbccabccbcaccddbdbcadbacabcaaccbabbbdbbdbbacdcbddcdbdbcbcbadcacbacadcdbaabdaddcdaacaaabadcabdbdacbdcacbdacdbaadbddccaaacdbcbcaaccbcbdadaacccdaaadbcdcddbabdcaadccdbccddbbdcadbdbcabbcbbdabbdabdbcccdadaaaabdaadaaabbabdddaacaccaabaddcbabcabaddcdddaddcabadbdcddacdbbaadbcccabbdccadbbccbccdcacadacbaddccdccaabcdbadccbbabaccbadcbacaaadbcbddbbbdccccccdadbaddbdbacddcbcbbabcacdbbabccdddcccdbbacbcbdcbdcabbacbcaadcbdacacacccddaddaabddbccddbdcdbadbcddabdbaadcaddcccabadbabbdadccccadccadaccacadaabcbabdbadbacbbdcccaaacababddccbbacbbadaabbaccbbabdaabcdbdadaaadbcddcdaabbcdbaaddacadbcabcaadbbaddbaaaacbcdbcdcadaadbcdbcbddaaddacbbbbbacdcacaacbaacbacdacdbcacccccabcdaccbcdccbdbaaadddaacadcccdacabbddaaacdcaccccddbbcbbdadaccaadbccbcadaddbbbdababdcdbbbcddcaddddbdadbbddcdcdaabbacddadcaaacddbdbacaabdacbdbaccadbbccbbadbacdbdabdaaabddbabcbbdccdbdaabdcddaaababaacddddbadadddddacccbdbadabadbabcccaccbdbabdbcddaabbcdbdabdaacdabacbadbdababbdddcbcddcbccbdbcddadccacbdacacbdabdbacdbcbacdbddcbdccadabdcbbbddbcbbabbaabdacddbbaccdaadbdbcddbcaddddddccdcacbacadbbdcbbdcaadbccbdddcddaaccdbdaddbadacaccaababdabbbdadaacbbbbbbdccabddaacabdabcdacccbbcaccbacbccdabddbccbbcadcbaabcadbcbdabdcdbbdbacdbccabababccaaccbbdddacccbcbbcbdcccbdbaccdaccdbddbacbdcccaadcddccccdbdabbaaabbcdccdaccbacaaaadccadbbdccbdcbbdcccdddacbcdacdacbbacbadabccacdbbcbcabaaabdbdcadbbcbdbccdbdacbcdddcbabbadbbacdacdbbcaabbadcbcccaaaccbbadaadcacdddaadaaaabbdbcabbccadadadbdcdbbcbadbcdcdddcddbdcbdcaabbaababdacacadbcadccdacbbbadcdccbccdacddccacbbaaddcdcaabddccbcddbaabaccddccdabcaadadaaadddbccdbbcdbdaadccdacdbcdbcbadddaabadcbacbdabcbacacdaabbbcbacdadcbcaddaadcadcbacadbbcbaddbbaababbdbbbdbcaacbacbbdbbabacbbbaddacdbaabbcddcbcdbaaacadaaaaaacdbaddbabadbccdbbcaddcabadadadadcbdddcdadbddccdbcbbbcdbdabdadbcadccddbcdababaccdccbabcbbdccbbabcdaaababdccdccddcbbadcdccdadcadbadaacabdbbddbabddaacbcddabbdabcbccccadcddcdbcaaddcdcacdcdbdaddcdcdcbcdbcdabcbcbadbdaacaabdadbcbbcadbbbabcaacacabbbacdbccbadccbdcbabddbbaacbbbdcdcabaccaabdbdaaacadcdaaabdccadcdadccdcdcbbbadddddacbbddadaacdddaaccdbacbaaadaaabdcdbadcbcacaccbcdacdaaacbadcbbdbaacccaadadcbbdbccaabdbaabcbcbbcdcdcbcdbbcdcbabbbbcbcdcdbdccbaabaadddbccbadccbacaacdbdacddbacaabbdccabaabbdbdcddadacbdabccaddabdcdcbdddcbdddcaccbbbbbabcdcdacbbcdcbdcacbcababbdabdbbadcdababbadddcabcaccacbddbdbdcdabbddbcababaaadbdaacdabdbaacbbdcabccabcadbcdbdccbadbabacacccddabbdcbdacccacbcddadbdcabadabdaacabadabacbdbccdbcbadacbbcccbdabdadbcccdccddabbcaabcdacdacbcbcdcbbbcacccacbcddcbccdbaacdcbcdbbcdccdcbaababdcccccaaadcdddaabcbbaacabbbaaaacdbbaadcbdbcacabdcdcacabaacdccbacadcddccbdbaaddddbaacaacacbbaacacacdacacacddddacbcaabdadbbbbdddbddddcddcabacbabcbccdcccabbdbacdbabdcbcbbdcbbabacbabadacbbdbbdbadaddcadadaddacbbaadcbbdcbbbabbccddcdbacdccbdccdbabddddcacbdcabbdaccabcacbbbbddbddabadcabaacbbbdbadcbbbacdccbbbccadbcbdbaadadaccbcadbdbccbabcbaccddcadbaaddcbcaccaadacdddbabadcaaadacbaacbbcdadddbcdcddbbdadbbbbbdbcddbacacdabbaadabacabcdabdbaacacddabdabdcbaaadbcacbaabacbbbabcdacddbabcacacdbbddccabbcdbdbbcacabcbcbaacacadbaddcdcddbcbddbabdaaadadcbadabddccdacddcacacacacdcbbaabdbdbdadaacccdddbcbcccbbdcbbabacbcccadcbadbdbaaacadadcbcdcbacbdcabbddcadadbbaaadabadbaaaccdabaddaaddcbdaaacaaccbddcaadcacddabccbdadbcaaadadabbdddadcdaadacdbdbaaddcbddaddcdddddbdaaacabbaadababcabacabdbabddbbabbbcdbdadadaddcbdcadcaacabcdcccdaacdddbbbbddadacadbccccdbdcdabddcdbddcbaabdabbbdcabaabccddbbcbdcaddabcdcbacaddcaaaddacdbcbbbadbcaaaddcacbdbbadabbbbdbcacbdddcadbabbbbcbabdcdcabdcaaddcabcbaadbcbdabcdaaacdadadcdbcbddbcccccaadabdcaccdaaabbaaaacbbacbdadabdbccbdbcccbcdccdcabadaddbdccaaccbcabbbdbacddcdadacbbbacbbcdccbdccccdabacbdbaddcbbcabcdbbadbbbabbabbbccddbdaccacdbbdcdcbcadbabbddcccdadadbdcbdcdcacdbbaccdcbbcbbbcaccdbbaaadcaaadcbbdbccccaacbaacabcbcbbbdcbcacdbacaadabcaaadcbabbccbdbacddaacdbaccdaacdccdbadacbcabccbcabdbacdddbabacddddabadbbbdcdadbbbbaaddabcbbadadbdaacddcddbbbcdbcdbbcbddbddccbabcddcaacadccbacadaddccababddbacaccadbddcdbdbcadababccdbdacbacdcadbbcdaaadbbaabcdbdabbadaabddacabbdaddacdcbbaabadabcbdbadcbbbaccbbcddbabdcaabdcdaaabbbcaccbadcdcddbdabddddddcbdddbbccdddbabbbaabcbacdcbccacacbcaacabbcadaabbcbacbdcddcadaccacbacbcbbddadcdabcadacbbbbaabddbaabddbadbbadcaaacabcaacccacadbcaabdcdbccbcaabccabbbdbadaacbccbacbccabdaccabdcbcacaccaabaccbaccabbabdbbcbdadcdcaddcddadddabbadbdcadcdbbdcabddcdbdacdacccbdcccccbacbcaabaabbcbbccbbdadccacbbcadadbbacbbabdbcadcccabaacabdabadaaccbddaaaddcacdcbabcdccadadaaabadabacaddaaacaddbddbacddbbaabdacdbdadbdbdcacddbdbdabdbbdabccddadccccddddbbbcadacbdccbbcbbbdbbdcbaaccdabaaccdcababbbaccdbbbbbbaddbbdacbdccabaaaccdcdccdacabbbadcccdabcaaacababcbacdacdbaddccdcadacccbcbabbddabcdabacbaacdbbddccdacbdccaccdaaacbcddbcdbabbaabaccaaabcaaabcbcacbcbccbcadcdbcadabddabbcacacdcdadcdabbddaccababcabcbbbaadccdcbdccddbadacccdbaaadabbbabbaabcdbcabadacacdbcddcbaddbccbdbdcdcbbdaadcccdccbaadbcdbbabcdbdbdaadbdccdddcaaaabcadadacacabadddabcbaacaacadbbbbacddcabcbddbdbdcddcadddbddacddccadaccbbbaabacacbabbbbdaccccdbabaacdbddacbcdcbddcdcdaccccdacbcccadcadaadbcaccaadccbbdbbadbaadadbdddaddacbacbabcdbadbbaccaadbbbddbdcccdaaabdcacaccbababcacddbdcbdcbbdaadbabbcbcabacabcbbabddbadcacadcbbacdbddcbbabdbaddbbcbcaddcdaadbcbdcdaabcabccdddbbacabbdaadaadaacdacacabccaccaccbdadaaadabdaabddcdbbababccaacaacbcddcddadddbbaccabdcccbbdbccdddbadcbcacccabbabdaacddabcbddabdabcaadcbaabadacdadbacaddadabdadaabdbbdccadbcdccbbabdcaddaccbcadbaaccaddcdaabcddbacacdbccaabbcadcadacbccdbbdabbdbaabcdacbbccbbcccabaccddbadccaddcbbcccbbabdadcdbcccbdadaabadccddabaadbbdbcbddcacadcdcaaabaadbbbbcdbaaacccabcabbdabcaddacaabcaddabbcadbdbdcaaaaaaacabcbbdabadbdaccbccacccacdacbbcbcdccaacdbcdadccddadabcbcbdcadadccdcaccababdbbaddaacccaccacdcddcdbabdacdccbcbdbadcabbcabbcadaccbbdcadbcdcacdacdbadcaaacccdcaddacdbabaaddadaacdacdbcaccdbdbbdadbbbcacbdddcdcccaabaddbababcacacdcacaadcdacadbaabbaddadadbdbbdbabbbddcdbbcddcbcccacdbcdbacadcacdddcdaabdaadcddcddbdbbacddbdcccbaacdbadcbdabccccccaccacddbaddbbacdaadccdcbcbbdabdbabcdddbdacaccbbccabbacbbcbacaacabbacdabddacadbcdcbacbcabcdbbdbccbcdbbaabdaacdddcdbacaaabcabacbcadcadacdadaddcdbdbbcbcaaacdabcaacadbbdabcdbbabcaacdadbbbbdadcbbadcdbacbcabbcddadddbabcddcbcdbdbcbbcbbccadaaacdbcaadcadbdcacbccdcaaadcbcbacddabbbbdccadaddcacbdcdcabdddbcaadabcdbabccbbddcaabcbaddcccccaccbcbbaacbddccddabaadacdaadbabcbaccabccdcdacdacdccdacacdcbcddadaacadddbaabcddbbddccabdccdadbbdbbcbacbbcdadbaadacdcabbacbdacbdaabaaccbaacadaacaddaabbaddcabaacabdcdcbcddcabaccbdababccabcaddbadddbdbbdcddaadcdacdcadcaaadddadacbbcddcbbbababbadcabdddcbdaccdddbdbababdbdaccdbdcccaaaadcaacbadaddbbcadbdcdadaddcdacdbacccacdcaddadbdcbacdbdbdaaaccdbadbaccbcadcbbbdddaaabbbbbadacaacccbbbbcdcdadbacbdabbdccdadadcadbadadbccdbadcdcddadcbcdcdbccdbdcabacddacacacccaaaddbacddccbbcacbadcabaadcadbaadccbbdbbaabaacadcbabaccacabcbbadcadbcbabddbdddbadbadddcdcddcdadccabbcaabcdaaaccdcadbdddadcaadcbaadaccdcccadaabbbdbcdadacbcadabdcaccabcaadbbcbccddabccbddccabdccddbbbcdbdbdccaddddbacbdbcbbcccdbbacbdcdbcadcbccdcabdadaadbadbdcdadacbacbabdbbddaadaaadbcbcbbdbccaaadaabcabacbdcddcbadaabcbcbddcdbbabcdaaacbbdcadbbcaacbcabdabddcacbacabaccdddaacccbcacdcbbddddccccbacbcabbdcacaababacbdbabcbcbccddaddbbbaabdabbbcabcccdabdcaaabdbcdbbaacbcdcaccbacbaabbdcbdddababdababbadacdbbcdddddaacdddbcacdcccccdccccacdadacdddacdbcbbacbdbbaddbabdaddcbadaadbadddaabacacdccadccaaacadbacdddddcaadacadadbbdccbaddabcccbacbdcddabacbcdddcbcadbbcbbbdccbdaadbcacdcdbbcbdbddaaacdbbacbcccccadccdabbcabcdabadcdababdabdcabccbbadbcaaabdaddbcaadcdcadcabdcdccdabadcbdadadcdaddaabdddcbadcdccbdaacdddddaadcbaddddcddaccbbcadbababcaaccbaaacadcacdacbccaaaaaccbbbadbcbcbcccaccdaabdaaadccabbcabddddbcddbabbcbcbbdabdadbaabdaacccddadbbcdaaccbaaaadbdbcaddbaabbadadbabbcaadbcbdcbaadbcacdcddccbbccddabcbaccadcbbbadbccdcbcdabcccdcdccdababcbbdbabcdaaddcaacbbaaccadaacaacaacbccacdaababcbccbdadddadcbdcdabbacdbcbcdabcdbbdbadacadacbbbcbaccbbdbaadbabacdcddddacadadacaacadcabaabdbaacabadadcdbadddcbbcbccbbbbcbdcadccddadddcddadcdbbbbadadaddacdbadacaaadbdadabaddccbbbcdbcbdbdaccabcdcdcaadabdbabbcabbadddaaddccabdbabdababddbcabbbabbcadccaccabaaaadadabbddddadbadccaddcdcdbbabccdcccbbdbadaacccbadcbbbcbcabbacabbabdccbacdbdadcaccbdbdbcbddddddcccbacacccbbcddbacbddacabcdbdcccdabddccdcddaaaabddbbbadcdcddabbdcccccbdddcccdcbaaabddcdabdadaccddbaadaaaaadaaacbccbbdccccacbcadbbacdbdbbaddbcbaacdbabaaabcdbdacacbbdcdcabbacbdccbbbccdabcababcbaacbcaadbdbabbabbaadababbacbdcdbcdadbbabdbccadddaddcbbacbcabcbbcddaccddbbbababbbabdddadadabbbdddccccbdaaaddbbdacaaadbcdabddcdcbadccabababccdadbdcbaacdbbbddbaacbaadddcbadaccaaadacdcbcbaddabaaabccdcdaddbbacacaabdbdddabbdcbccbcbbbbadcbadbbccdcabbdbdbbaaaccacdcccccaacbcabdaadbbdcbbadbccabccdaddcdbccbaaadcadababcbccdbcbdbdcdbcdabadabdcdddabcdbbbaadcbadcdcddaacddbadcdcdaacdbbddcbbbbadbdbacadbcaabddbddcbcdcadaccadbadadaaadddbbaccadbbaaacbcdcdaccbaababbbcdaacabcdbddcabddcdcdaaacdacbcdccadcadbdbcabccabcabccddcbacddcbdcaabdcacaccdbbacaaacbabdcdacbbdbabbcbdacdcddcabacbdddadaddaabbabccbccaadbabbaabaacadcaadbacdddcaaacbcbdbdadbaadaddaaddccaddbacccbdacdababdacddbdcadcbbcadcdadbadbbdabaddbbabbbacbbcbdabbddcddddbabbacdaabcdbacddadbcdbaaabcaadababcbabbdaddcabadabbabcddaddbbdbaabbadabdccbdbcbcbbacaaccbaccbbabbccacaddbabbcbddcdadaaabbaaaccdadabadccbababcabcdadbdddcdcccaacdddbacdaccbcbccddaccbbcadcbdcdadcbcabdcaddbcdacadddddcaadabdbacbabacbbdbcbcdccdcbccbbadbcabdcbaadadddcccbbccaabdacdcbddbddcdcbcbdacdccdcacdaadcccccadcaababdbdcdcabccbcadddcddaabbdbacadbdaabbacdaabbadabaddcdbdbbddbaadbbcdcacdbbaaaddadddaabcabcbabbddddbccdcdccaacbbcdbdcbcdcdacaadddcadddabbabadabbcdadbdddabdabcddadbabdabdacbabbdcdbabacabcbbcacaaaaadabdcddcdbbdccdddbccdbddcbcdaaddbcabacbdaaaaadcaaadcacaaabbcdbcbcbbbdbddbbccbcadbccccbcaaddadddcaaabdbcbcbabcbcbbdaacaccabadacadddbbdcdcdddcbdddacbbcdababddacacabdbacadcddccacabbdddbccdcdcbcbbdccacbcadddccababcbabadbddddbbcdacdbdabcdddccbddcbadcabdbdadaabdbabbcbabbaaccbdddababbddbcdbcbaacdcabdcadadcacabadcdbdaddbdcdbabadbacccabcabddaacaaabacdcaddadadbcdbcdbbbabbdcdadbadbacddbbabcadcbabbccdbbbbacaaabcddbabcabdacaababbccdaccccaadabcbcbbddadaacbbaabbbbdbbcbbbacddbcbabcddcbaacdcccbbacdaccaabdbaccababacdbddbbbdabcbabcbbdbbaabacbaccbababddcdadcbdbaabccbabdaabcbbbccdcdacabbbdccdbbdbdbccdbabbcdcacaabcaadbccbbcbaacbdabcadcadbabcbddbbdabbbabccdbaacacabdbdadaddccdbdcbdabccadcbadbddacaccdaaccadbaaacbaddbcbcdbcabdadcaccabcacdbaaaaadaaabbacdaabddddabbabbbbdbbbdbdcbbbcddbbddadadbcbaacbcbcdadbbdcadabdcbacdbcabccddcadadadccbcdbdcbddbacbcaadcacdbaaccbabcdcdbbaadcddacddcadbbdbdbbababaccccddcddcdbabbadcbadaabacadbbbddcbbbccddccddabdcccababbaaddabadbbbacddabacbabaddaabdcaadcadbababbbcbcbaabaaccdcbbbdadcdaccbbdaccbdbdcbbcabbcdccaccdcbbaaabbbdaacaabccabccbccacbdcbaaaabdbcddcbbbbbbacbacbbabbcbcdababaacabaaddbabddacdccabbddadbbbbdccdcadabcbcbaacdbdbcbdbdacddbbaadccacddacdaaaddccadbacaabbabccdcabcdcddbacbddbadbdbbadabdcdbcdbcabbbdddbcadabdaddadcadbbddcbdaabadcdbddcdbabdbcadbaacbbcccbcdcdacabbadabdcabaaddadbcabbdbbddbbcacacbdbbdcbbabdccacbadbcccaabadbddacccdccaacccdcadadbaabaccdcddbbbacabadaabcadcccccdadbcdbcaabbaacbccdbddbdbbdcabdccbdbabbbddaddabcddabdcbabcdbbbbbdacabbaacaabbdccbbdcccbbbcacbcccddaabcbcaadbbdacdbabcabaababcccdbdbcbddbcdaabddabaddcdcdcdadbaccbccdbbcdaabadaadcbaaababbadbbadccbacdddaccbccbdaabdbbdbcabadaddddbbabdaabdddaaccabacabdababcdabbcabbacbacbaccbbaccbacbbdaadcbcbcdcaaccdccddcbacddbbddddbdacdabddabcdbcdacdabbcbbaccbaadbaaddbabacabbccaddcddcacaabdbccbbabccbcbaabdabcadbcdadaadadbddaadccbadcdabcabbdcccaccacdbbbcdcadacbcdbbabaaacccbddacdddbddccdcbcadcabadddaacabacacdddcdbbcdacdbdcbcdabdbbdcadbcdbcdcddadccaccaadcdaadabadaabdccabcbcdbccdacaaacacbcbdcbddccabaababbbcbcdabadbccaccbacdadabdabdbaabbbbdbaacdbcadccadccaaddbacbacbbbccddbdaccdcaadaababcddcdcdcbcccaacadbbdbbbaaacbacdacabcdadbdadcabccdcbaaddccccbddccbaabbaadccbaababbbacdcdabbaccdccbdcbcccbdaccbadadbdcacaabbbabadabdcdbdbaaddaaabccacadaacddcdcbacabcddddcbaaddcbccaacaadcaccdbccacbcbcddadabbacbacaadddcddcacbaacacadccdcbdaccaccaccdaccaccabdcdccdabaabccaacaccbdbcbcbbcddbcdcccaacacadabbbacbcacaadcaacdcadbddcdaccadbacdbddaaaccbbdadabcbccdddcbdbddacbddccbccbbcabcdaddbbbbcbdaddcbccaaccbcabbbdabcacdcbddbdcbdbdbbddbbbdddaacbccdcddabcabaaaabaadbcbaddaddbdaaddacaccadddbdddbaccadaaaacbcbbbbcbcccacdbacadcbccccacdbaacacccdadaacccdabcbcdbcadcbcbabdcbcbbcabbbdcbcacbaaaddbccdcaddbbddabaccdbdcddbadbcdddcdcbccbcadddbdbdacddaccbbbbaaccdcbcdcddbbcaadcbddddbddbbdcabbabddadcdabdbaccbdadabbcdcadaabbbdacabcddabdacccbadddbdbdbbabbddaadbdaacaccbcaccbbdbaaddbbcadbcacaccdcddbdaacbbdacadaccdbcabaacacadbcacccddccadaacbadacbbdddbccdbcdcdbaddbdbaacdbaabbdabcbcabaaababbdcccdcdbccbcdcdcabacccabcabbcdbdcdbdaabdbcaaacadccabcdbbcaabbbcbacbbaccdacbdcacbdbcccccabdcbcacbbaadacbcadcabbacdacacacbcabdbabdcbcccbdbcdcdaccccccadcdbdacdbcaaaddaccaacdbccdcdccadbacaadcddcdababbbbcdcdacbdbbadbdcccdcdccddbdbcbadcaddacddaaaaaaaccdcbdcabacbaaabacaddbcbabbdcaddbcbcdcbccbacaabadabbacccdacaddacbddadaacdababacdaacbaddacdaabacbadaabcacccbbdcdbaaaaabacccaddabcdcadcbcdddaddbddbdcabbdcabbcbddaddabbabadbbdaddadddbbcbadacddddabcaacccaccaacccadbdddbbcbccdbbcbccbbadabdabcddbcbabadcbdaaaacacbaddaacacaabcddbbdabcbcdadaccdcdddbccbbbadbaccdbabdccaaaabccbacccabadbcdaccddadddbcaccbcbcdacabddadacbaddcacbdbcaacabdccccbcdcdbbcdbcacbcddadcbbabddaabcdccabacbbbbcbcdcdbccccccbaabbabadbabacbbdbdabddccbcccabdadddbaccccbdaabccdaddbbbaabbdaaaaddabcbdbbbabcaaadbcdcccccaaacdcdbbbdadcdcacdbddacbdbdddcaaaadcdabbcadcbadaadcdaadccdaaadcdbddccdbbdabbdcabaacbbcabbadaaacdccbcaaacbbcbcccccbdaabddabbbadaaabcbaadcabdddddcacbbccadbccddacabbacdbdbbcaadabdaabaaabcdbddcddddaadaadbadcadcccacadabbbccaabbdbadcacbdbdbccadababdcbdaadaaddadabdbdbccdadaabcbbddadbacdddaacabbbadcbbcdcdbdaabbccdddbcabdbabcdacbbbdadbbcabcdcdabbbdcacbcddddddcdbaddacbadcbcacdbbaccddacaaddbdccdaccccdaadadddbaabaabdcadbaabdaccbccbbbbcbadcabdbbccccbddddadcdbbdcbbbabbdddccabcdcacdcbaaabcadcabcacdbccaccbbbadadcabddcbbccbcdbaabcabdaabddcccbaaadcacbcccadaaadacaacdccdacdcbcddadccacdddaddcdacccbbcccaddacbddbbabddcccdcabcdadaaaacdbadbbadacdbacbaccbdcddbbacdcaddbaacddaaccacadcbcbcadbadcabbbacbbdbdbbcccbbadcbccaabacdccdacbbabbcacbdccdabcaaccabdcaaadbcaccababbabdbbcaacbabdaaabbdaacbbbbdbcdcdcaabbdccbdacabcacddbbddcccacccabdcbdaaaaabbbccbbcdbbbbbdcaaabaabadddabbddababadbdbcabbdbddaaaabcbcbdaabcbacaaaabbdbdacabaadcdcdbdccbddbbbcaadbbaacdadcbcacadbdadcdbddcacacaabdcdcabdcdcbaaaacbacdcccdabcadbbdbdbdbabcdcacababdadccabdcddabcbccdaaaaacdddacbcaddbcddbddbacbdaabaacbbcbacdababaadaadbacddcbbbaaccdbbcacacbbbcbacacdacdcdddcbadbaadaacdcacdabbccabbdaadaccaadbcacbaccbccdadbddcbbabacbcbbbbabbacbadcbaacbddabdcbdbdcdabbbbdbdbbabadbdacccbacbbcacbdbcdabdccadaaacacacdbcbcdcdbdabbdbadbbccadbddabbccbacaccbbabbbbdcadacbccbcdcbcbcccaadababdcbcdabbbddabcddccdabdcdbbbdcddadbdbadbaaaccccbdbccdccddbccbacdddadcddabbbbccdbbcdadaaaacccacdadbbcadacaaacddbdbddbccbcdcdbbdacddbdbdaddaacbabaccdcbdcbadbabbcbcadccbbdcbabbadbcbcccdcccdbaacddbcadccbabaccabaabdaccdaabbbbdddddbadacaaaaabbddaccbaadbaacbcaabccabbdadcbddccacbccabbacccaaabddbddacaabcddbdcaccacdbacbbbabccbdbadacbdddcaadbbcadadcbcbcddacbaadcbccbdcbddadcbccadcbbbdaabbdacabdabcabcaddaaabccdcbaddabdabbbcbdcdacbdaabbbbbbbdbaacaacddabaabddccacacdbaccdccbcabbcdccdcaaccdcaadbdddbbdabdbcdddadbabaabcbbabbadbacbacacbddbacbcdaaadbdabddbdcccddbcbadbaddbacdaadbcadcbbdcadbcdcaabdcccccaadbdbdbacbcacbcabacccdcddacbdaaccbbbadcaaaadadbdaaddabccdddacbcccabadcdcaacdccaadacbabdcabaadbbabbbccabdabcabbcdbcacdacbcadcadbababbcbbbbacabdbcbbddccdbbaabbddddbbbbdabdcbdddcbcbbaabadcdbcbcabbcdcbabcacbcbacdbbabcbbaccdbdbacbccddadbcccccddddabddcaabdbbababccacaacadcaccabcabbbbdaaccbbaabaabcdddabbdadcccbbabcaadbadccaaaddacbbbbcabdccacdcabbacdabcddbddadddbcadbaaacbcbcaabdbbbaabddbaccdaaacbabaacdabaadcbbbaccbdbdbadacbcadacdbdaddaabaadcddbcaaabbdcadcdcdaaddacadddaaddaacaabaadbdcabacddbdacbbbbaabcaabdacbcbbddbaddaabaabcdacadddbaacacddaddbcbcbaccabcccabcccaaabdbacabcaddcdbdadabdddbabcadccddbbabacdcbaabdcdbbcbaaabdabadddcbbcabbbacbdcbcbbccabddbdabdabcddadabdabbbdccbbaccbcdcccbcadddacccbbcccddcacabcbadbaccadaddadbcccadddcaabcdaacaadacabdbcdadcbaccdcadabcbbddabadbcbbbbbadaccbabcadbddacbcadcdacdbabcdbdbabaacdddcddabaccdcacbbdcddaddbbbaaaccababdcbadcbbadcacacabbaddbbbddcabdcbdaacbdbbdbdadcdbbbddabbdadcdabddabbbccdddbcbbcbdbccdbdaadddccacacabdcbdcdbcbbaadabcaddaaddcbaadbdbabccdcbdacdcbcdbadabddddbaadcccababbcacbabadbcaadcbdbdcccbccacdbbacaacabaaaddadabaddbbaddcbbccbddbddcdbdcabcbcabbdaaadccbbdcaddabccbcaaccadbbbccbcdaaadbbaabbdddbdcccbcadbddadabaccdcadadabcbccdbcdbddcddbcbacabcdadbdbbcdbcaaacbabaddcccddbdabcdabdbcababdbcabdbacbbbbbdabbaaacdcacbaabccdbddbdddbddbabdadcbdbadbdbaddbdcadbddbccabadcadaaabdbcbddbcbacbdacaadbbddccddbddcdbddcddacddbdadbaacdabbccddddaadbdcbdddadabcbbdbbdbddbcdddaaabdaddbcaaaaacdbabddbdabcddabddbabdcbcddddcdadabdbbcbbbdadadcaabbabccacccdbabababaadcbcacbbdabcdaaaabdbdbccbaaabbccdabcadbdbdadcdaddabadacbdbacdacabcaadcdcaaaadbbacbacbbbcdcdababbabbcccbddaacaaadbddacddbadbbabbddccbddacddcadbbccabcadaaacdbcbdabbaaccbcabadaabcacdddccdbbdddddbddaaaabcccbcdcaaddacabdcdacbcccabbddacabbdaddcccdaacbcccaaacbdbddccbabdcbdbaaacdbdcdaadcddacaaaccdacbaacbdcbaadacdcbccaaabbbcbadbcadccbabcbaddbaccbcaddaaaaaccadddbbcaaabdbbbaabccaacabdcbcbaacdbbbacbccdcadbacbbacbabcaabcbacccacadbdcdbdbdddacabccdddcbddabbbbcdaddbbdddadcbbcacdacbdbbdabaaddbcaacddaddadaddadcacbbdacbcaadacbacdabbaaababdbadbdbbcbdddccaacabccbabdcdabcacccaabdcaaaccadadaacaddcbbbdbadddbdaaaaadcdabcadbcacddadcacadcbbbcadcabdbdadbccacdcccacdccbbddccadbabdddbcadacbdcbaccdcbccdaacddaddcdcccccadcbbcdadcadcbdcdbadabacaaadbdddaadddddaaabcadbdcdcbcbadbbcabbaadadcaccbbcdcabcbdcdbccbaabbddbcdbccdaabbcdcddabcbddaabcddbbbcdbadaccbbdaddbadcdacdbaccdccdbcbbcdaccababbbbbcabbcdcbbcabcadcbcbabbcacbacbdcdcabcacddadbbddcdddddadabacabbacaaadcddaddbdabbdbdbdabddadbaccdadcaabbbcdbaddcbbaabdddcdccbdccdabdccdbdbbcadabbbcdbaaccbbccbcadcdbdddadccccbadbdbabadddcaddddbcdcccddabbaacdcacacccdbacdabbbddcddbddadbccccdadabccccdbcbadddbdddacdccdcabcccacdccccbcddbdadbbacaadbbddacccabadbbdcabdcabdbccbacbaacbcddcaacbaddbcdbbdccddadbaddcbbbaaababccbadaccddacccadbbaabbaccddbaaabacbacbcccccbadabbcddaacaadadadabddcacbddcbbbbcacbcdcbaaabacbddabacdcaadadcaccbadaacccbbaccbcbbbcbbcabbbacadccdddadccabccbddabdbbbccacbdbaadcbbcadcbbaaacacbddddddbcdcbadbbcbdadaacaabbabccdadadbaabdababccdddadbadabbbbbdcadddaccdcaddcadaaacbabdccbdddabccabdadcaacbcbabccdccadcadbccccdbbaadccabcccdbbdbcdabdcccaddccdcaddcabbcbabdbabbbabadbabdcbabbbdabaddcbbccaacbdcbcbaadabdacdbabddabaabbbadbbccddaadbbbccddadcdbcbbdaadbaacdcbacabadcddbcacdaacadacabccbadaaccaaacbadccbbddcdcdbcbbbcddcdaabbbddddacbbbacdacabccbaaacaababdccababbdcacdbbdcadadddabccdcbcacaccadabadbdddabdbbbadddcababadadadcbdbadbdcabbaccaccaacccccaaccbbabbabcdbccaabdabdacdbdcaddabdaacdabcbcabbbdabbaadbcbdbacacbaccbbbddcdbacabbcdbaabddbcdddabbbbaccdbbbdaaaddcccddbbdcacacbdcabdbccadddbbccdbccabccdcccaacdadcbacadaaaadaadabadbbddbbcdccdccacdabcaccccccbbdbaddbddcdaacdcdaccacdbbadbacacbddccbbcaaccaaccacabdbdddadcacaacbacaaccdadabdacdbddbdbcbbcdbcddbbcaadcccbbbabbcdbadbdbdacdbdadcddabccadabbcddaabacdbaddcaabbacccaaccccbbddacdadadcdbbcadacaaddccabcdcabacacbddbbdacacadbbddbccdcacccbcdbaaaddcdaddccdcccccbacbcbcccbdddbbcdbddcbcababcaaccccaacacdbdbdbabdaacbabaccbbdaacbdcdddaabcbcbddbccadaadcdbdcdcacacaacbcccbbddadbadbdbdddbbbbabcaddcddaadadddccbbbaababbcadcaccbcdccacdcccbccddbbbbcddaadabbbadccabbdaacbabadaadbcdbdacbabbaacacacbdaaccccdbdbddcddcdccdcdacdaabacdbccaccdadcddbcabaddacaaccdabbbdbbccccdacadcdabaabacadbaaacadcadaacaababacdcdbaabdddaabbdababbbcccdadbcadbabcbcdcdddbbbbdacdcdbdbdbdccaccabbbdadcdacbbcbccacbccaadbcddbdbacaaccbdacbadbdcbdbaccabcdccadcacbbabacdcbbaadbbacabdbddbdaacacdbaacbccbadcccdbcabddcdcbdcbabcbacaabaddddbdbadbdbbbcdaaacddbacbdbdaadcbbbccaabccdddcdcbadbcdcbcbcacaabacbbddbcacbdaccbdbdcaccadaabaabbdccdabcccdcaacdaaadadccccadacccacccacdabbcadaddcddcdaaabacbccaaddcdccdaacccabdaacdaaacaadcbdaabadddaddddcbcaddcbcdaccdccdbdadbccbcddccddbdcacddacdaabaacadddadbbdbaabadcdbabaacbbadbbccbccaadaacbaaddccdbbcccdbbdbaccbccbdcddbbaddabaaaaccbbdaddabaacccadadbaddcdbdcbacabadaabbaccdaaacdabbbbadadcbdbbabcacacaacdcccbdadccdacddadcbddbccbcadbabbdacacbcbddccbaaacbbcddddacabbcacbddabacadbbbacdbccdcdcadbcabaddcbcdbccadcbbabcdccabadbcdbdbacddaabddbbbbccbbaabbacdbbcaddcaaaadadbccaaaabbbdccadcbdbcccabacaccaababaccdccbbdcddcbddaacddbdbccbadddadbabbaabbccdadbadcaacbacdddacacbddcaacaadacccacdbdbadbdabcabccbccaccbdaacbdbcdcdbdbdabcacadbbdddbbcdbabadcdaacaaddcdaacbdbbcbcddaadccccdcbdaaccbbcdbdbdbcdbcbbdbbdadcbacdadddcadbccdddabbabcbcddcdcabbccbcdcbbdcacddabcbcccdcaabdbbdaccaabbcbadacddccabdadddbccdcbddbaaaabdbccaaddddadabdbabbdbdcdacccbabcbaabbccbcdcadcbdaadabadbaabbbcadbdcdccdcabddcacccaabdacaadbadadddadccabdbabaabcbccaddcadbdabadccbdbadadcdbacabbcdcbbdbadcdbaabdadcacadadbdbcdbdccdbdcabdbbacccbbdccdcccacdbdcddbbadabbbbcaaddbbcabdbbabbbababddaaaaabbaddaabbbabbdcaccddcabbdcdabbdddddaccccadbbdbdacadbdbdacdbdabbbcdadacabdaddbadbdcadbdbcaccacddcbacabddadbaaabaccadbcbdbbdccaaaddccabdaabbddabcdccccdcbcccabcdddbaadbddadcddacbababaacbabbdabcccadbdbbdaddddddddcadbbbabcbacaacdbcbaabbadccbacccccaadcdbadccddbaddcbcbcaababadcbcdbdcdabdcbaabbddadbcabbbbbcbbbbbadadbdbdbcaaaddabbacdcbccbcaabdbabdddbcbcdccbabcbdacaacddbcbacadacdacccabdadcbcababdcaabaaabbdddcaacaccccadbcddacabcabbadabdacbcddcbbcdadddaababaccabdbbcbdccaaababcdaccadddbdadabadcbaaccacdbaabcabacbddddbcbcabbcadbcccabdbddabadbaccbbbdccabdcacbbcddacccdcccdbaabadacddabbadadcabccbdadcbbcbdcbadcdcbbcadbbaaaacbbcabdabdacaaadccccdccadbdacabbcaddccabadcbabbdcdcdccaccadabbdabbdcacdbaabadbaaadbccdaadbbddaccbdacdcbacccbccbdddaacaddcbcaaabadcbddcdbbddcbdcaaacadddbdbbcdbbabbccacbcaabbbbdabcccbaadbaadbbadccbbbdacaaadcccadacaacadaacbaaccababdcbdbcaaababbdacaccdcbbadcacdbabcccbccdadbabbbadacdabbaccabacbbcdadccacddadcaabdabbbdbbdaddacbdacdccdcbbccdadccaabbaccbdaaacaaacdadbbaabacaacaccabbabccbadbdbbcdbdadddcbcbdcbddcabcdacdbcdcccccabadaddabcdadcbdaccbdbabacaddbdadcbbaabcbadcabdacdacacacdccadcbbadddbadaabadadbcacccdaabaddadcccdcaccaddbdcbacadbbdadaccdcdbdaddbacbbbdbdaccadadbbbdaddccbadaabbcddaabaccdcacdbdadccccbcdcababaccdaacbdddaaacbccadabbdaccdcabacddaaaaadcdabacdcabbbcdacbbaccadddcdaadadcdbdbabaabaccacdbbdacbdadccdbbbdbbccbacbcbddadaacbcdcbbabdbaddccdccdbcddcacbcbccdcbabddadabbdbddabcdbcdabacccacaabadcbdabccacdcccacdadaddabbbccbaaddadcccbaccdadabadbcabcadcbaabadbcccdbcddbdbdbaddadbbabcdadabbbbcbcabadddbaddbaddbbbaabcaddbadabbdaddbbddbbccababcadabaaaccbbbdaadacdbcbcadadbcaadcbdcdadabbbbcaccdbcbabaaadbccbcdddbcaadadbdbdcbaacdddbdbaacdbbbbacdaccbbdadddccabacdcdaaacbdbcaaccdddcacaacccccdadbbbbdcdcdaddcccacbccccddbbabbddcaabcccabbaddbabcbcdcdacbacdadbbbabaabbdabddcdabccbaacabdadbcddbabbdbdaabbcacdacbbbcdddcbcbbccdbdbbbdcccddddcdccdcbbdcddbdccacaabbcdcaccaaaccdcaccdabcacdcddaabdccaabadddbdbdcddcdbaabbcaccaacccdbcbacbdbdbabaddbdbcdcbbaccacadcddcddcadddcdbdbcdbaddacaddccbccbdbaddbbacccddbbbbbdcdbacacbcabdcbdddabbdbadbccccdcdacdbddbbcccdcadabaabaccdbdacccbacdbaacbdbadcbbccacdcabdabccadddbcddaaacbdbabbdcbbaacddbbdbacbcddcabddcccadbadccbbabdbcdbaccccbddacbcbbcdbaabcdbcbcaadccbaabcabcbdcbbacdddbbdacdbccdacabbbcdbcaddbaabdbccbaaddabadbbadccdbbdaabdaaaddbdbaacdccaacadbdcdbccddbbcbdccddbcdccdacddacbbacaabdbbcbdbcabcbcdbbadddacbacbdaacbcaaddcadddaacddcbbbdddcbbbacacacadcbdccdacddbdddbccbcaddadcbcddcddacaacabbdadabbddcccbbbaadbbaacbdcadccdadbcadbcdcbbdccbbbdaccbaabdadadcbddddccdbcabbacbdbadcbdccaacdbaabbbdcdcddaabbaccabcdacbaaaabaccbadaddadddcabbadacadbbbdcabcabdaacdcdacdaadddddabdccbadddbbbbbdaabcaaadbbdbadadbbdaacdccbaaadacdacbddcdcbdccdbdcdcbddacdaadbcbbaaccdbdcbbbdabcddbbccabadabdbdacbbdcbdaacbcccaddabddccddcadaacbbcdbdbabadccdccbaddcacacbbbbbcddabcdbdabacdddacbdbcabaacbadadbabcbdcaddaabbabdbbccabcdbdcbbaaccdbccdbcabcddbcadaccdaacaabacbbccadaccbdbdacdacaabaacbbacdcbacdacbcbddcdbcdddbacbdbdabadbdabddbdbccbbccaabcdcacdaaacddddadbaccddcdcbaaabaccddabdaacbabdaacdbabddbadddbdcdbacddadccdadcadadbaadcadaabbbcacabcbbddaccdbdcbcdccccacdadcbcbcaabccbbacaabdaccbcddcccccabadaacbddadadacbabcbbbdbacbcdbbdbccddcdbcaabcabcdadcaaaabcdaddbcdcabbccaaabbabcbbdbaabdbdaccacbabcbbbbdacddbcbaadbcbcccdcaaaccdbddcdbaaaadcaabdcbabcbcdccadaaabcccacadbbadacadabacacabbbbdacdadbaddbacbcbbdbdcccdbbccadaacddcbddbbbabbaaaababbdbcacdbadbcdcaaaaaaaccbaccdbcbbaacdcbacaaddbaaaacdbbbcabddcddddcbdccacccacccbcdcacbabddadbdbbacacbcbcccbabdadbdaccabbcdcbaccadcbbdbdcccbadcbabadacbcccbdaaaadbbcddcacabddccbdbddcaccbddbcddbdddbdcaabbcdbaadbcabccbadcbbccbbddaabcacaddddbddbaaabdacdcbbaccbaabdcdcdcdbdabbccdcaadbcabdddadcccbdbdbbcaddbcbadccccbdcbcbcdbcacdabcdbabcbadacdbdcbbadacabbaaabbdcaacaddacabcddaccddadadadacdcdaccdabcdddbccdcbdcabcababaccbdcccbacabadbcacaacabbaccdbcdcbccdabbaddcddaccadabaaadabbcabcacddddacdcbcacbddabccdadccaadacdcbaadaaabaccadcbbcacdcabbbaaddbddcdcccddcacccabcbbdabccbbaddbdbdcbbbbabcaaadcbbaddbbcabbccccdcbabaabdaadacbddaadbbbadcdabcbbcbaadcaacdcabacdbccacccadbddcdccbbccaccdacdbabaadcabbddacbdadbadbdccbbcabcddbabdcaabbbaddbdadadadaddbdbcacbbcdaaddcbbdcadbdaacbbcbdcadacbbbdadcadbaabdddddaadbcccadbbcbdadcadadbcccbcbbdcdacdddabcbcabbbaabcbdabcbdbabdcddaddddcccccaabdcdabdbcabbcadabbdcbcacbadddbddaaddddcbbdbdcccbdcbbdddcddaaadcbbabcbddccdaaabbccddccabadaccdddbdbdcbbbddabacdbbccbdadcdcbabbdbcddbdbdaccbbbabdcccbbacbbacaadaaacabaddcdcbbbbdbdbbbcbbdccbadaabababbbadbaadbdcdccaadbaddaddcaccbabcbcbadaacbadcaaabdadbacabbadcadabdacaccaddddbbcccdbbabbcadacddccbabbbadaaaadbabaaddaddcdbdbbdbacbcdbddcadbbcabddbccbaabccadadadccdcaaccccdbaddbaccbabadabcabcbacbcadcdabcaabcbddcdbddbabaadddacccbcbaaadccaccadbcdbabbacbcaccbdbabbbcdadbccadacabdccccccbbbcdbccdcbaaadacbdbcbbbbbcadabdbabbcccbdccccababadcbbaaadbabbddcaaaacccbdaccadcbdbaacddbaccadcccdddbacccdcdbcdccdbbbccdadacacdcdaaadcbaccaadbdabbcbdcababaadabbaddababcbdaccaabbadabddccacbbdcdbccaaaaadbbcacbcbabdcdaadbcbcbcbbcddbabdbacacacbabcdcdcbdbbbdabcdacabcdbaadccbddcbbdcdbdacddcacaddcabaccdabdbadadcbdcbcaacbabdcbbbacadbcaddadabdcdbddbcdbbddcbdacdcbaadbbbdcabdabcbdcaabcbcbadabbcacacaabddddacacbbcccdbacacdaacaabbaabbdcabcabbdccaccabbbcabbdccdcadbdcacbcbaddbabaabcbddcccaccdacaadbdabcadbbbdacddbcbdcaabbbaabacbccbabcbbcbadcdcbaaacadbbbbcaababdcbcdccadbbbdddadccdbbadadaabbaabbbdadcacbcacaaadcbdccdacdbdcbbbccdaacbcdaacaccccdcabdbbdbbdbabbaddaacaaaabcdadbacaccbdbcbbcdbabbaccaddcadcaabdabccddbcddbbdcacccbababaabbaabdbbadbdabbbdadacaaaacdcbdbbbbdacdcbcddabddbddcbbbaacadddbddbdaaacbaabcbacdbbdcadacccabbbdacbbbccabccaacbcdaaadcaacbaddcdbdbcdcaacadcbdddabdabbddcbbdaabdddbcddaadbbbdabdadcdccdbcccdaacbcaabbcbddacddbddcdddbbaadbbdacbddadaacdaaccbacbcacddbdcbacabacccbcdbaccbccdcbaabdabacbbbbabbdadadbbbabbdacbcabadbacbacdacadadbbbdcdabdcbccdccdccbdaddabbabcbabdccbcaadddaaadadbaaaabcbddcbbbcababbccaaaaacbacaabbccacbaddcbabacdbbcabddbbabddcacccddbbcadccccdbacaaadbddbcbabaacacbadabaabdccbbcacdacaaababddddccbbdccacabcbdbacdbdaaaadacccdcdddbdbdccacdaddaaaadcbcbabaaabddabacdaabcdcbcbaaaacdabadacccccdcdbcabcbaacbaccacbaabcbcccaddbacdaaabbbcbaddcaddcadbdbbbcddacdcddcddbbdcdccbaacadbacbdaabbdbbbabdbacadbcccabbbbcdacbccacbdabdadaabcccbcbbdcaaadcadcdbbbcdbacbacbacbabcbbbdacdaaabbabdadcbbbbdaadcbdbcdabccaaddbbcabddbddaaabaabdbdaaccabccccacaabbbdcccdcdcbadaaacbbbddcaaaaadacdccccbcdcabcbccadccbddadcbdcabacdddbacdcbdaacadbacddbddadbccbdcadacdcbcacdbbaddcacbdaaabcabadccdcadabcacaabbcadaddbabddcbbabddbdabcdaacadabccaacaaacadbbbbcadcdcdcbcdacacdcbdacccddcccddcdbccdcacdaacddacbddaddbdacbccdaddbdbaccddbcaabcddbbbbdadcdcccdbbbbcbaccacbbddbdbbddadaaaaddbadccbaddbbdccdcbcabadadbcbdbaabccbbacaddddabaccdcdbbcccbacbbcbdaabdcbbdbdcbbcbacbcaaccdabcaaacdbabbcdaddcabdbdcaadadabdcaabccbbcbdbbcaabcdabadccbdbccdcaadbaadbdddbddcdacbcdcaacadaaaaddcbccaacccbadcdcccdcaddabbdabcccddbdacadcccaddbdbccdbbabbddbaaddbccbaabddaacdbcaabbddbcdaadbbddbbbdbbbdcddacaabaadcbbcdadabccacbbadbccaacbbabbadadbbbaacdbbdabdacbacaadadddcbcbcccbdcaccdcbbbdaabbdbacaabcabdccddaaabbcaacabaaccdbaccbdcaaccbbccccdabdcbbbddcbdbdadadbbcbcccccccbdbdbcaacdddcccbdccdcacdabcadcbdbcadddbbbdadaabbdadbbcadddcaabddccaacbcbddcbbcabbdaaaddcacbdcaacbcdccbabbcdaabcadcaaadcddbacaaddaabcccdacdccaccdddccbcbabbaddacbbddddabacccdaacbadaaccbbcbdbdaabacdadaacaabcccdadbbacbdaccacaddaabbbcbaadcacdacddaabadabccbbabaabaaaaaccbbaaaddadaccbbdbadbbabcaaaacbcccbdbdccbcbcdbbbbbdbabaadacccbdaadbbbadcddcbaacbdddacdcbabbccdbbdbbacbabdabbdcdbcccddabdbaaaaddadacadaacdadcdbdbccdbbbcddbcacbbdbadaadbbabddcbdbcbcdadaadbdcbcacababcbabbcadcacddaacabcdbcadcbaaababaddcdbacadbbaacdaccbcdddaccbbcdcbaaacadcbdbdcccadbcadcaaabdacdccbbbcdcacacdbbaabaaabdadbbbdadaccababaddbadbccdacdddbdccccdddbbccdcbbbabacddddccabbcaaacddadbaadabcadacccccaccdcdacbbcabbacdcaccdbdbbcaaddcbddcccbbddbcbddcbcbbdbdbbccdbbcbbaababdacbddbdacbdacaaddbabadcdaaaccadbdaaaaacbacddaaadacabacacccbabdcdacddcdcadabbbcdbdabddabdddcbbcabdcbcddcadbccccadbabdcadaddcccdbacaaabcdcbbdcabdaaccadccbbbabddccaccccbcccbaccaadadabbdcdbbbacbbaacdbdaabbabcdbaadbcaadbcadbaabccabcdddbcbbabcacbcccbcacbbabbacaddacadbdcabdcabcaddadabbcadcbbbacddcdcddcaddcaccbddcdadaacddbbbddbbcccddddccbdabadcabdccbccbbbadadaccabaacbadbdbbbacadcdccaddbcadaddddaaaccadaacadccdcddcaddcabddcadcddadddacdbacdbbccadddbbbcbccbbdbdadabacdbdadcadcabadaddbbbbbaabcccacdaabcadcacdcbccbdaddadcdcdcbdcdabddbbdcdcacbcacddabbdaddcbdcccddcdabadccabccbccacbcacadbabdbcdaddaccdbdcdabdccdadcbccdddcddacbdadddbddbcbbddbdbbaadddbbbcbcbbcbbbaadaadddbccabbbbdcadaddbcdcdcabbdddbcbcbcdbacaddcabcbcbdcaaabdadbddcadbbcaadacdacddddadadaaddbcadaddbdcdcaccbcadaddcbbbcddabdccdbcaadcaabdbadbdaaddaddcdabadccbdccdadbdbdbddcbdcddccaddcdabdbbbcccccaddaabcddbbdcccacbddcadbacbbabcacaabbbbacaadddacadbbbaddbcaabcbaabcddabbacabaadcbbdbcaadddadddcdbdbbddcdabbcbaabbdccacadbcdbcdaaaaaccbbcbcaccccddbabbcabbbcabcaadcdacddddcaacdccdcddabddadacbcbdddcadadcdccdcdaadaabcbcbbcbacaabbadcacabbcdabaacdaaaaccadbbdcaabadcbbacdadbddcdaadcabaaccabcbbaaabaacbbcddbaadadcbabcbdaabdbdadabbcdaddbccdaacdcbdacabbcccddddaabbabaaacacddbdcbcbcadadcdadbddbddbcbbcdbbbacdbbddabddccdbbdadcbddddacdadbbabcbbbacaccbcdcabcddabcdbaaddcbabdcacccadabbadabcdaaadadbaabadadcbabddbdcdbcdcccddcacccbbcddadaddddcdbbddbacdcdcccbadbcbcdcdacccdaacabdacabcacbbaadadbcdccdcddddcbccaccbcbdbabddadcbdbbbbbbcbdcdacbdbbcbdabbacddcabcdcbdcddabadadbdcadaadbddbdddacadbcbaadddaabdccabbabbdbdcbcacadaaaadddccdabdadaccbabdadadbabadbbadabbadbdabccaaaaabbabcabdbbcdddccdacdabbcccccdacbcdcbdaabcdcbacacccaccbbbcaaccdabbbddccdcdbcaccacbadcbcbdccabaacabccbdadcbddccbabaddacdaccdbaabbbcccacbcabacccbcbdaacccdbcbddcabaaacdbadcddbabbdcdacbbaaacabdddcbdbabcdaacccacacbbababaddaacadbbbcaccbaabdbbcbaacabcdcddcabaabdbbaccdcadbcccacbbdadbbdcaaabdadcdbdcacdcbdbcddbdbbbccbcddbabdbcdbdaacbcabaadabadacacaadacaddacbdacccacaabaaababccaabddddccadaaabdbcadcaccbccbaabdadbbabdaccdddcddbbdddcaacccbcccdcbbbcaccddabbaacacacdbccdbdbaccbcddddbdaccbddabbacabdddaddbcccabbabcddcacdacbdcddcacbcdbcaadbcdcccdddbbaacdbbbdacbadcadcdcabcbbadaacccacadabbcddcdcdbdbcabddcbacabcbaacccabcdddcacccccdbccacaddacbdbdbcbcccbaaccccbcbdaaddabbdaccdddddcbcdacdbdabbaadbbcadddbbbbcabacccbadbdcbabacaccddcbdcbddbcdcadbdccaaddbdcadabcaddabccbbcbbdcccbccbdccaadccccbbbcdbcdabadaabdbaddbccbcaababcdbcbbccdddbacadcbaccabdbdddcddaaadadbbacbdcbadadbdbabbadbbaddccdcbbdccccddabcdacbdccacddbabcaaccdabccabaacbdaabcddcaacbbaabbcddbdcbadbcccdddddbccaadbdbbdbadccabcbbdbcbadcbabbcdaabbabccdbaadcbccccdaddbcaadabbcdcdbbabadcadacdcccbcdbdddaaabbaacbbbbbabcbcbcabdbbbacddddaadbacdacdabcbcbdabddcbaaaabbbddcacadbaccdbdabdcabcdabdcccdbcccadabddbbabccddaacdbdabaccdadcbabbadbcddcbbbacdccbcddabaccbbadcadddadbbacadacbacbbaaadcddbadacbbaadccdddaddbcdbbdaabcbacdbcbdbdbabacbbdcbdbcdbbadcbcacbadaaaabacccabdaabbcbdddbddbbcaadcaabdbdacbcadbddacaddcddbbbcadcccaaccaadaaacacaabbbdabdaddcddaaababcabbddcbacbcdcccdddcaacbbabbdddcbaccacdccaacbbbbddaddbdbcadcaccdbbcbdccdcddcabdccbcbacdacccbbdaddbaadbdcdadddcacbbbababdbbaaaddbbdbddcbcdcacbabbdbdaabadbcdadcdcddcacbacacacdccaccdbacdadaadcbdbcbcabbdabcddcaccccabbbbcabacadcabbcdadcdaccadaccaaddcccdccadbddccbdabdacaaacaaaabdbaaaaccaacdddcaacbbbcacdbdaddbddabbabddbdbdabcbcddcdcbcdababdabbbbabbddbdadaccbcddaddcbcbdabdddacbaccbcdddbddbddddddadacadabcddaaabdaacddaabaddbdbbdbdbabcdbaddbcadcabdbbdabcadbdadbcaaaacbdcdccacddcadaaccaddcdcddcbddcadaddadbcaaddccdcbcaacadcdcbddacaabcbcadbcdbbbaaccdbbdaaacabaaaaccbdcddacdbacabbadccdacbdbcabbcaccbbdcbbbacbcccdbabadddbddbabbdcabaacddcdcddaddabbccdaadcbddabaabcbcabbddacdababccaddddabbcadacccbacddccaaabbdcacdddbbbdcbaaabcbbddccddbaacdddcccacbcccabdaaccbaaaadcdbabcabbccdcbdcdbaccdddabbbcaddacdabccacdabbaabccdbbcadcbbbdccccaccbcbdaaccdbcdaaaccccababdcbabcdccabadcdbddcdccbdababdccababcacbccaabdcbacbcbabcbbdcaaaadcbbdcdbbadbdcbacddbaaddadcddccdacccdbadbabddabbdcbcdaddaadccaddadaadbbadabdabdaadaabdbbaccaababcddadbccddaabdaccbaaaccbadcacdcbcbabdabadaccacacdcbcbcdccbadacccdbbadcdcdaabdbabcabadbcbdcdbaddbbabdbadddccbbbccbbddcdcdcadbdaadbcbddabbccddddccabaacccbabdcacbdaccdacadddaaabbbcbacbcdaddbcbcdbdbaaaccbbaddbadbbabbcbddaacdccaddccdbbabdddbbdacaaacbdcabbaadcdcacaabdadcbbcaaacddcbdbdddadcaaccbdbadababbdadbaddaadcdccbaacdbbabddcadadbbdbaaddaabcbbcaadbcbaccabaacabaacbcdaaddbbaddbaddaacdccdddcabcadcdbabaacddaadcadbacdaacbcbbbabcadbbaacdbcaabddbdacbcacbdacccbcdbacaddddacabbdacabcddcbacabcdcdcadbacdbcdaadbadccdcbbbadcbdbcdcaabdaadddcdaaabcbdcbbaaaccdddddaacaddbbddcacdbcacddcddccdcccabdcbababaccbbdaccbbbacdadcccccabbccaaadcbbdcdacababdbabbbcddcdaccdddaddaabcaabbdabdcbdbcaadadcdadcaacadbacadcdcbbdccbccbbbbacdaacaadcbdbbcadbbcadbddcbaadddccccaddcbcbaaacadbbdbddddbaaadbcaddddbabddcabbccbabdaadcaabcdaababbadcacaacabcacbdaadcbcbadabaabbbbaaacabbabacddbabbdcbcccbbccbdcbabaaabbbbcaabdbdcdbbaabddcaaabbacadbbcccaacddbabadaddabadaacacbadccbcdabcbbcadbdbaccdadbdcddabdacdadbcacaddaccdbcbddcaabbdaddbbcadbdaacdcdbabacabadbcdbbaabaaddaccdabccdadddbbabddabbdddbdcbdbbccacbcdcadbdadbaccababdaddabacdadaabcbbddccacbaaacbbbaaabacbdccadaddccaaccbddcbdaaccdaccdcaabbcdadbbcaaccdadbaabbabbbaddcbccdcbadbbabbddaaddbdcdaacacbbcbadbbcbccadddbdcabadbdabccdbdbdddacadadddaddcbbdccdabdcbaabacdacabdddcdbbdaaccbdadababcbcbcbcdadcaacaccaadbddaadcaaccdaaaadaabaacbadbacaacaccbacbacccdaaddddacaaabdabcabbcbbacbacdcacbbdabdadacdbccccaaaddaaadccadbcbabdbbcaddabccabbdcaaabbddcbcbdabbcbadacaaadadadaaabdbbcdabaddccbbdadddddcbaabdbcacbaddadcbdddddbcddcdcaddbccccdadabcddacdddadcabcddbbbdddccabddbddabcbddadabacbcbcbcccbacdbcbcdcbcbcaabababdadacbdbcabddcddddccdccabcbabccbacadcbccacdcdaabdccacbadddababcaabbbabcaacadbdddddaabcbcacdcddcaccdadbabbcddbbbcbcbdadccaddaadbaccbabbbcbbdccbbbbccbcbcccaadddcdcdacbbdbdcaaddaddadabdabbdcbaddddaabacbbcdbcdbbcabcdacdccdddbdacaacaaabcadbbcbdbabdcacbbaadacdbacddabccacabcbbadabaaabcdcdabcbdacdaacbaddadbdcddddbaaaacdbcdbaacdccadddaacabbdbdaaaaccdbcbcaacdcbbbaaacaaddaabcbaccabbddadcdaaaadcbccaadbaddcdcaadccccacbbdccbbacccabcddbbaccdadaddadadacdbcacacdcdbbaacdcadcbbaddddcccbacacacbbcdadadaabdccdadabcabcccaccbddddbcdabbcaddbaaabddbccdaabdcdbcbacaadbcddddabdbaaacdbccaabdbcbaaccdccdabcaaaacabadbdabaaddcccdabacbacbddbabdadbdaacdddcbdddacacdccabcdadadcababadddcacabcabbdcabcadcdaddaadccdabbbdccbcdddaabbbbcacddcddccccdbdacdaacbaccbbbabadbcbabbcbcccdbdbcbdbdcabdaaabdcbaaacbccbadbdbccadddabbcbdbdbcdabccccdadcdbccbbaaabaaaccabdbbadbbbcbcdaddaaccadbcdbdcadbbbdbdbdbbacbbabdabacdcbcddbaabdbcaabdbadabddcddababcbddbadcdaabcadaddbcbbcddcdbadbdbbaddabdbbcacbddccadacbbdcdcccacaaaadabbcacbdbbddacbcabaacdbabbbaccddcdaaccbacacccbcdbbdccbddcdcccabbaccbddcbbdabbadacbdbddbbddccbabdcbadacaabcabdddddadadaccacaacbbaacbbcdaacbccbbbbdbbabcdaddcdbcdaaabcaccbadbbdbbccddbcdccacdcacbbdacaabbcbbbddbccacabaabbdacbabaacbaaabadaaabccacbbcaabcacbddaccbbaadbbddbdbdbbcadbddacacdabdcbaccabbdddaadcacdbacdcacbdcdacadcbdcbbbdbccbaadaabaaabcbbccabccacbcccaddbbbbadabddadbaadbbcbddaccabacabbdbaaacbabdabaabdaaabddcccaacabbabbcbdcacabddbcacbbdddddcdbcddcacaccadccabcaabbdbcbababdcabacabcbbcadaaaacdcdabbcbadbadadadcddcabcddaacdcdbacccaccdcddaddcddbddacbbacbbbbaddcadddccddddddcbcdcdcabddcbbdccbbbadadcdbdbcdaccdbdaaddbccaadbabdccbcdcddccadabcbaacacabbacdcccdadbdaaacacaaabbdabddccdccddbacccababbcbbccabbcccbcdccbdaababdcbdcdaacaccddaccccacdbbdaacbdddbbbbdbaddbbdbbbdaddddccddcbcabbcbddcadaadacbabdabbcaababddccccbcaaaabdcbbaddbbbdcbcabcabcdbcdcbcaacaabbcadbaaabbaaadaddcbdbcddacaaaabddbddaadbdaabbcdbcdcbadaccabccaababdcacaadbcdacbaaddcdaddbaacccadabdcababcabbddbacbbbbcccbaaaccccbbdbbddcccaadcbdcbddccadcbcaddcabcaddcddabcccabcdbacbdabbdbcdddbdacbccccbbcaacdcabaaadcbdcbcbbdcdccbddcabcbdaddcccbcdadbcacdcbabbabcadabadaacddbacadcaaaabdcbdaccabdacdacddbbabacabacdbdcacdbabddbbcccdaddadccdcccddacbbabccddadabccddbcccdcbabcddccabacaccccdccbadbddcccbacddbbbabbbadacdbbdbabcbaadddbbbdccdcbcaddddbbaddadabbcaabcbcdaccdadbacdddbccbcbacdbabccbacbdccdcdddcbadbaccaaccabaacabdcaaacadaadadcddddccabaacddaacbadcabbbcaabdbbdbbacdbcdaadbaadadbaadbacdbbcdccbcdccbcccabdcacbcbbdcaccbacdaabcabcaacbdbacdbcbaabdaaabbdccababbddccabadcbbaddaabdddabbbbcccbdbbdbcdcbccacaccbdbbdbbcacdbbbdcbdacbabcbbddbdbdbdcdaaddcbdbaddcacabdaccbbbaccbadaccdddabcdcaddaacbccdaaccbbabadadbbbcdbcbcabcbdcaacacdacaabdddddcddabcdcbbcdabdabadcbdcadbabbdcbdbdaabbadabbbccddabddbbcabbcdccbbccbbbbaccacbcabbaabadaaaadbbabdcaaabccdcabddadbcbabacadcbabbcbaaccbbbbcdcaddaaacdbbcbdacccccddaacddcccddadbbabbabdcdadbaccccacadddccdaccaaadaadbbddccdbbadadccdccccaabcdcdcbacadabbbabcdcbaabccadddddddbddcbbdcaabccddacbdbdcdccabadacabdbcdabdcdcdcdaacbabacddbacbabdbcbacadadcdcbadabadcabbccbbbdcbbaabcbbcbadabbdadcdadccbddbdcccbbddcddacadbdcdaaaadcccddbcacadaaadbdbccddaabcadddaacbcbbccaacccdddcacbddcbacbcbabcdabababadcaddbadacdcabdbcdaddbbccacccbcdddbcdcbcbbdadbbdcdcaccdaabdcaccabddcddacbcadccddddddcabacbdabdcbdcadddcdbaddcbbdccbbccddbbcbcabdcdcccdaaaadddabbbadcdacacbdaddcdbaccaaacddacbabcbbdbaaaaddbabaacbadcbabadbabcbbdadbacacbbabbabbddddbbbdabdccdcdcaaacdbabdbbbdccbbbdccbbabbdabbbbcddddbaacbddbdaddaadcbaabadcbcaacdaacdcabbcbababdadbbddcccbacdacabcdaabcaacddccbacbabbbdabddadbacdddbcbacacacacdabbadaacbccdcbdccaaadcdbbacabdcccbabaacbbbcbcbbcddcddbccccdabdbcdbacdbdbbcacaccdddbdcccbdbcbdacbacdbcacdccaddacbbdabcccccbbcaaaaddbddbdabdbbadbbbdbbcbdcaccbbbbbcdbcbbbacbaadcaaadccbadbacdaccddbdbbadcddadbddcabccdbdabaccaddddaaccacadadababaccaaddacdaabdacdaaacdbadcbabbbcbcbadadacadadbdbbcbaabbdbcacbdcadddddccacddabdbcbaabcabaadddccbbbbbbadbddbbacdcccbbaaccdcacbcabccacbadcbbcbccdcacbbddddbbbbdaacabdbabacdcdcadbadabbbabacbdbcbbbabbbcccacbcabbbaaadbadcbbddddaccaadadcddadbbadacaddcbdcdaaabdaababccbabdccbaacbdcbccacabaacadcbbaadaadaddbaccbbddbcdabcccacaaacdadcbccaddbccddadcacadaaacadadaaaaabbcbdcdaaadcdcaabdaababdadaadcaccdcaabaacbaaaccbbdaaaaaadaddbdddcddcdacddbbddabbdbbddbbacdbbaccaaadccdccacccdacbbcadcdcaddccbadcddccbccacabcccccbdadcdcacaadcaddacaddbbbdbbbdaddddcabababaabdadddcaadddcdccccadbccdbdabccdbdcbccccdbadcddcdccadaabdbcbdbdddbcdcddcaababadddccdadabbbdddcbbdbcbadbcadbcacbbbdcdcbcbabddccadabaddcbcaacbdabaccadacbaacbbbccaccabbddabccbdbcabdcabcaccbcacdabbdcdcadbbbdaddbdabdaabacbcdcababbcdabddbdabccdbccadaccacdbdcabdbbbccbacbcdaabbbdadadcadbdadddcddbbadccccdaaaaacadbbcbcdcdcaadcbabaadcbaddbccdcccbcbacbbdbbadcbccacbdccabbadcdbbccabcadbaaadbbcbccbcadabccbbcaaccabcdcabdccbadbccbccadcdacdcbbdcbbdbabaacddaabdcdbddbdaccdaadcacdbbcabbdbbbbddcbbbadddaccddbadabcbcbbbadbcacbabbbaaaabbdcdaabcbccbdccacacdadcaaccbcbcbcbccaacdcccaabbbccaabdcccbaabddcbbbcaccbddcbdbddbaadabbbcdadddaccbbababbdcdbdaaacbbbbbadccacdabacbbcacdaccdabddcabdbddbdadbdacbbcadcbababdcbcbdcbacbbcbbdddbdbbbdbabccaabccbdbabcccbcbadcdabcbbcaccbcabbcadacdcbcddbddbdabbccdaabacaccacdcbccddccdbcacccdcbdbdaaabadddaabbabcdbbadabccdbcbcabdcddcaddddadcbababdaccbccdccddcababdadbddbabaaaddaaababcdbccbbdbbabdbdabbccdccdbddcbcbdbddbccadccbdaadacaddbcabaaccdbaccbbdcbcacababcbcdbbadcaaaccccdddddadaaabbbcadcdbacbabbbcabbbaacbcbabadcbadbabddcbacdabcdaddaacbdcddadbaabddbdadaaadcbcdbdaacdaaaccccddaaacbddabbcadacbcbdbcbbbaabaabbbcbadbcdcbcdbddbdbcbabbaadcbaaadcbdbdcddaddddbbcdbacbddbdbdbbbbbbbddcacbbdbbabccddcbdbbcbdcacdabcdaccbcbacdbbccbadcdbcbddabcadccabbdbdaaacbadcbbbddaacdddaacbcdcbbbadcaccdddbdadcddcdbabadbcdbbcdbdbbbdcdadcabdbdacccaadbcdcabdcadabcbbbacccdadbcbabbaacbaccadbbdaababcbcbbacddcdabdcbdcacbbbaccaacadccadacbaccaaccbbdccbdccbbbacdbcdcbaadccdaddbbddbbdcadaacbddccdbddddccbacdaabcbbbaabbabbdabacbbdaaaabcbbcbcdcbdbcccbcddadacdbbcadcddbadcdadbaccacabbccabbddccdbadacddabcbcadaaaacddbabadadcdcccbccdaaaaacacddbabcbabddcdddabddcbcbbcdabbacbbbadadaacabcdacbdaccdcdabcdbaacbadddaacabddadcbdcacaadbcdbdacddbadddbaadcdcbcdbcacbadcacccbcbabaddcdbbdcdbcdddadcbdbbcdaccabbdccacdccccaacbcbadadaacacaadbbabbcccbdbcddbbcdbcdcbabdacbdbcbabdcccdacbadbbdccadbdbcddbaadcbcbaddcdbbcbcadddbcacacdaabdccabdbcdcadbcbdcccbdbcdbccbbadbbdcdbccbacaddbaadcbcbcdabdaddaddaccbdcdddcadcbbcddacababccacbadbbdabaaddcddbaadcbacadbabcddbddbbddddabbcdbccaaadbadcdabcabbdbadaddcababdaababdcaaaabaacbabccaabdbbbaadaacdacadabbaaaaccbadbbbcbcacddbbdacbbabddbaddcabacaddadbcbdaadaabbbdbbbacdbcdacdaabbdadddbcdcbcdbbabdbacbdbcaadcaabdbbabbaababdbbcbabcbcbabcbbbcaadbbbdbaadaadddcaccdcdadddccbccbbcdcdadccdbdbdcdbaaccbcdbcadbddcaddabaadcdccbbcdbcbddbddaaaaccacbbcdddadadcbcabbcddabaddbcdcddbddcabdaaaccaccdadabaabbaddbddbababbdddddbcbaccbcdcadaaccbaabbbaddaddcaabbadadcabdccbacdbbcabdbcbbbadbdddcdadbddcbcbcdccdddacbbabbcaccbbabdacbaabbcdbcdccdcdabbdbcbacacadcbdcabdddbdccdacabbdbdadaaddcdbcabbcdaaabaacddabbbaaabaddcbaddaaadbabbcbadcdddcdbaaabcbdbcdddcbdcadacbccbdbcadcdbccaabbbdcdcbaccddcbbccababbccbcbabcddcbbacbcadcdaacdccccccdadcdcccdacdbbcdababcbadcaaaacaabcbcbacaacbbdbdbdacbabbbbddabacdcdcccaddacdbdbcbabcccccadddcddbbadbdaabbdccbbbbbdaadaacddbcadcbdabbaaddadadacdcbacbdabbbbbcdbacdadabdddbbbbbabbcbadbdacbddcabcdbadccabcbdaadcccdacdabdbdbabbbabacbcbbacbdabbbbcadcbaaaaaabaccaccadcddaadabddaabbdcbdaaadcabbddbbccabdcdadddcbdddbbcbadabbdbadccaccbbcbbaaddbacabadcbbacddbbbdbddabcacadacdcadaaabadacacbaccdcadaadcaacccdadcbcddabbcadabdaabacadbbababdddccbbdabddbddaacabcbddaccccbcdadbddacddabababbdbabbdbaccbbccaadbcaaddcdbbabadabcdaddcbadbbccddddddbbbbccaccdaaadadbccddbbadbdccbaddacabbcdabcbabcbabbaabcbbdccbdbdcacbaabddbabaadcaddccbbbadbcbbbcccacbdcbabbdabdadaadcaacbcddbdddcdcddccbbcacddccabbdbcccaddbcacdccbdabddcdadaaccbcbcbcbadadddbaacddaacdccacbaaabcdaddcbcbdaabdabcdcbcadcacacbdddbbddcddabbbddcdcabcaacbbbdadcbaacacacacbcbcacadbcdcdcabcdbddbbadabdabacbddbabacccbdbcbbcccbadabdabddcadcbbaadbcabdbbbccadcddcacaadccbdadbcadbcdabadcddbdacdbcbbbacdcccbcdadaadcdcddcbcaadcdbdadadacbdccbccacdcccbcbbbaaaccdbbdbbcddadabdbbbbcaacddacccdcaddbbddacdbdabbadbaacaddaddbadddbacdabcbadbbacabaccbbdbbbdaadbdcacbbbcddaabdbdadcadbcddbdcacbdbdabacbbbdaaccaddbcbbbabbbcabbbbcdcbcadabcccadabdcdbadbabcdccdcccabcddbddcddbcbabccadcaadbcdccdbdabccdaaaacddccaccbccbaabcaabcdbbaadbdbbdbcbaabcadabcdddbdbdabcaddcbbabcbdbddbcbcbddbdaddadabadbaadbabacabbadacbddbbbdbdbcaabbccccbdabdcdddbccaddccdacbaddccdadacdccdbbdcdaacadbcaaacadcaabbbdcbaddaacccacaccdbcdbaabacbbacdbcbcddbbdcbcbbbbcabdccabaadadadbccbcaaabcabcdcddaccccdcdaddcbaacdbbadccbdbdcadddbbbdccdddbddaccbcbbaacacadcadbdadbabbcbccadddbdbccaadbacbabdcdacccdbabacabccacdbbccdcaadabadbabdcdadcdabcabddcdacddcbbcbbbdbcddccdddaaaabdcaccbcdcdcbacdbabcaadcbabdbdaaacadbaacccdcabdaaacddbbacbaaaabababcccccdddcacacacbbaabbbacbdcacbdbcaadaacbbbdbdbdbababadcaacadccddbccdaccabaabdccbbcbadaadcabbbacaabbdcddcddbacdccbccacbbcccdbaaadaaccbcccdbcdadabbcabbaabaadccbddbabcbdcdbbbcdbbbbdcaabddcddccbadbdadbbddbdabdbacbbbbdcabcabdcdabdaababbacbccaaccbdadcbbdaadacdacddbadcdbdbdabdbcaacdccbabbccccdbadcddcdcadbaccbdbccbaadbacacbdccacbdcdcdaddbcbbcdcdcbbbbccbdcacadcbacdacbdcddcacbdaabcbccbbbabaacddcaadabacbbdadaaacdcadaddbadccbbcaaabaacccbdababaaacdbdbcdbcbaabcbccbcdbbdcccccaadcbaaacabaababcdcccacbaddacdbdbbbcabccabddcccbddcadacacbaabbdbdbddcdcabdbadcaaabddcdbcccbadbbbacadacdbccdacddabccbbdbdabdadbcacdcbdbbaaacacbddacaaacccbcabccbdbbabbbadcdbbbcdaacdcccadccdbcabdcdaaacaaabddbccdbdbaddaaadddddcdbaddabbdbbbaacbbabcadacacdaccbdcccdbcdbbcadabdcbacacbcadbadabadadabacbaaadcdaababcdbaaadbccabadadbccbdbbcaabaaabdacbddacacaccabdccbaabcdabcbacacdcaacaaccbdbddbcdaadbdbaadbacaabbacbcccaabacbbdccddcaaababcdaaccdbcadbddacbddaaccbacbcbbcaabccabbaadbbbabbdbcaabcdcbcadbcaaadbdbcbdbdcccacaccdbcaaaabccdcabacddddcdbabaacdbcccddbdabbdcdddbdccadacbabacbcccaababcbdacacddcbaccaabcbdbdbdccbcdbaccacccccdcbdcccccbdbabcbbadbabdbabcbdcadbccdbccdacabdacdccbabbdbbdcbabdddbbaadbacdcbcabdbbaddbdbdcacbccccdcbdbccdccccbadbabacccbaadbbbbdcbdcbcdaccaddbbaadacbdcbadacdddcdcdaabcaaddbcacbcdccbbdacdaabdcbbaddabcdcccbdaaaabdababcaacadcbdadcadcbdbbbcdacaddabcccabdcddaacbcdbbdaadacbacacbacccaddbbcaaabaadacdabdcabdabdbbacbddbddacaccbcbdcbbcaabcbccbdcbcddddbbdadbaaadacdaaadbacbcdacaacbdcbdbddbbdccccccbbbddbccdcdbadcdddbabcccddbcbbdacdcabcacbacbbbcdabccabdbccaadbbdacbdcabdcadbbcbcccaabdbabbddaccdbbcdbdbdbacbbdcbbccdaabdcbbbdcbdaaaabcdadaabbadbaabbddcbcabbdbdaddcadccdcdcbbabbbaaadbcdaadbaaacaaacccdbadaddbdbabaccbdbcaddbbbbcccabadbabbdacdddbbdadcaabdcbaacddcbcbabdcbababdaaaaddddccaccbdaadcddabdbddddbabaabddcbbabcacdbbcbccdacdcdbbaabcbdacabcdbabadadbbacbbbaaadbddccddcbbcbbcadaabbccbdddacbdbccaaacdadabdcccddcccaadbddcdccaaaddccadbacbcabdadbddbddbcbbccdabddbcadbdbacbcddbbcabaaccaccadaadccbdacacabdcadcbbdddbdbaacabdbbabdbcaddcbcaaabacdaacdddbbbddcbbdadaacbbaccbabdbabbacbacdacacbbcbdcdcbabbdacbdcaaaddbbcbdbdbcdbdcacaaabdbdacbccbdcccbdaacbdbbadbdbbaaddbdadabbabaadacccdaacbbddbacdcdddddbabadcdbdcddcdcbabaabbdbdbaacbcacccbcdaabccacdccbddabcdcbabddcaddabbbabcbcbbdcbdbbcbcadcadddbaacdbaddbcccaddaaaabdbcaccacdabdcadbabcdacbbcaaabbcdbbcaaaacbccdadbdbdbabbccbdcacbbbdcbcdaddcdbabbcddbcbadabadbbadbddabcdcccdaabdaddbdadbcaddaacbabddcdbcbbcccaaadcdcddbabccdacdddddbccdcadbccdbdacadcacabbdaccdcabdcdbdacdabcbcccbddbbddccacdcddadbdacabdcccdacddbbaadbabbddaadcbbbcaabcabccdcbddbbabacbddddddcaaccbddddacabcdbddbcddbbccbabbcaabcbccabbccadcdcccbdbadabcbdcddbdbdccccababcddbcccbcabcbcdbbadcddabbacabbdadadcaccddcacccacabaacadcbcdddcbacbaadddbaadaddacaacbdbdabbcccbbacddddcbabcbacdbccadaadbabcbbbbaaacdcadbdadacbbbbcbcdcbbadbacbababacbbcabdbbdbbacdaadccadaaccaabbcaadaabcdaadcbaadacdcdacbadcaabdcababcdacdcccbadcccddabdbaddcdbdcacadbcbbddbdbababbacbddacdcdddbaddddcabbdddbdaacacccbbcacdbacdacbddaaabdcdbaabdbdbddacdabacbcacbbccbbacddcdadababacbcacddbcbaaaccccabbcabadbabbadabcdaabdbaabddbaacacaddcacdbdcbadbadadadaccdbdbdcdbbddddacbbacbddcbbbbbaaadabcbdccbadccaccdbabcdcdabacdcbbbcabbabddabbbdcdddcaadbdbbaaabbcacacacbbabbccbacabcabcbdabddacddddaabacddcdbbdbadaaabdddcbadacadbcadcdbdadadddbbbadaabbdadbabbccbbbbaadbccabccabdddcbbaadcbadbdcccccdbddabbbdbdadbdddbabdddcbcbccccadaddbbcbdcdbabbddacdcdddababdcaccbccababcaabacabacbacddbdbabdcadacbacacabccacdbacbccaacbddaacacaacddaacdbbddadbdaccbbdaabcabddcccbbddaaabcbbdcdcabcbbddaddcaabdbcdbbcbccaaacccbbabcccdabdcbdbcccacddbccbdbcacadaaddbddddddaabcddaadbcbbbcdadddaabbcdbaadaaccaabadccdcbddcbddcadbbcadccdbaabcbdcdbbacaacaacbcdbaabdcaccabdbbcadaadddddabbccbdaabcaacdbdcddddbcdbdbadcdabcabcdcdddbbaababcddadddbaabaacccbabbdadadaabbddcbadccdcdbcabcbcdadbaabbdcccbccacacaccaaccdbadcacbacacabcabacdcdaddaadbbdacdaaccdcaaabdcdbdddddacdaaacdbabddcbabbbadbabbaddaaacdaadbbddbabbdddbbbadbdbdddbdcdbbcaabdbdcddbccbdbdaadacbcbdbbdcdcbcbabaaaaddbbdaccdbdbccdabdcbadbdbacccadcbaabcbdbacdbabbcadcaabddddcbbbabdadbbbabbdbdbaccccbbaadcccbcbcacacddbccbddddbbdcdbdcbcdaccdbbdaaadddbbabbcddcacddaacbdaadbacdacdbabadbbccaddbcacadaaabcbbcdaadbcaadabbcccbadcbbbdccbaaabadbdaccccbabdbacabddbddaaabbaacbdbabccabbbdbdcabcbaaddcaabdbdcadddcccabccdbddbdaadddcbcddbcadaddbddcabcdcbcacaaccacadcabbcadabbccacdadcdbbabcddabdacaccdcbdbabcccdbdabbbbdccddbacbbddabcdaacabacdddcaddabdabcbccacdddaaadacadcdadccbcadcadabacddadbaabadadbcaccccbdbbdddccccdcdbbdddbcddccdcdbcabbccbcbbbbcbbdbaaaddaccadbdbbcddccdbacadbccbbdabbabddbadabdacbcadbbcdcbadbbccacbcadbadabbaabadbdcdbccadbcabbbbdadcaadccdddbcacacbaccbcccaadbaccaddbacbcbbacdabcaddbcbbaaddbdbbaabbbabdbbbdabbbcbcabdacbbcdccbcbbbbddcbddcdcbcacccccaddbbdadcccdacdbabbbaaacdaccccaaccdbbaccadcddcaaacbbbbbdddcaadaabacdadcdabddadacddaaacacbbacbdccabbbdbadbaddacbdddbbbadabdabadcbcdcbbdbcdadacbcabaaacbcbadbacaaabcaadbcdcdbcddaccbbcaaccaadbaabdadabdacacbbaacdccdcbccabbcaaaccbbbacacbcaccdadaadbcabbbbbbbdccbcacacbcacdadbacbccdaaccbbbacacabaaaddccadbccdbcabbadbadaddcbcabbbbbbdcdcbddabacbddadbbcdabcdbdbcddcaaccaddbdacccccdcdcddcdddaddcdbbccbababdacbaaabdcbbaaaaacdcbdaddadabcddbcaabaabbbcbcddcaabcbccdcacbcabcdcdcdccccbdddbabccacadbabdabdbdadaccbbdbddaacdadaacdbbcddbcbdbdadcdaababaccbaadcccbaababbaacaaaccbbdccdaabaccabcbbadcddcdaabcccccdbcdbbccaddaadabcdacbcdbadcbaabdacbcbccabdadbcbddbadbccbddbcbabdadcbbbdabadcdabcbdabaabdcadccbbabbbacbdcccbabaabcbcbdbcacdcadacbbaddcbcaabadadaccbcbaaabcdaabacdbbdbabacbbbadcadabddadaabdaddadcdabccbabadcbcbdbbdcdabbbbadbbdbdadcdbbdcbdacadbbaccbbddddbbacbbcaabbabddcbddacdbbcacabbadddddddabdaadbdbadacaaaaddaabaddcddaaacddadabbbacccdcaccdabbdcaadcaabdaadaadaaaadbbbbdaaadbdbdacdacbdbadcccadddcccbcdaaadcbabadaabbdbacbddbdcbdaccdbcccddcdbbccbddaadbacbaaabbcacdbbadcdcdacbcbddddbbcdbadbcbadcdabbabaddcdaaccccacabbbadccdbcaacbacbccaaddcaabbaadacccccdbddadccddbbdcbdcbbadcdacabdcaadacaaadbaddcbbaadadadddbcdcbabbacabcdbbaaacdadcbcaabbcdddcddcacbcccccbabbacddbdadacdbbbddddbddbbbcbccacacbcdcaacddcbbadaadcacccadaaddddadabbcadacaaaddadcdbacaacdaccddddacabdaccddcddccbabdabaabdbadddcdddbbddaaabbcaadbdccbacbabacbbdadddbadadabadcbdabdaaacddcdcccdbdbcdadcdddbcbcacdbdddcbdaddadaadccaacadadcacdcddaabcadcabcbcbcbbaaadccbaccddcacdbbccccbdcdbcdcbdadacbbdbbcaaaacbdbcaacbabaacbcaaccacabaaadcbcdbdadcdaadbaabbcbadcdaaccadbbbacbcdabbdbcdcccdbbaaaacddabbbddbbbdacbdaabbdddaddbadccbcbdddbdcbdbabdccabacbbdbbbacaadddbdcdaaabdcdbdbdacadaddacdbccacabbadcdaaaadccbaababcccaadcbbdaadcabbbdbcddcdcdbbcdbdcadddcaadcddcadcdddbddbadaaacdcbacbdbcbacbbbaddcdbdddcdccaabbadaabcdcacbccdadcbacdddbcdbdaabcaacacacadabdabacacccbaababdccddaddccbcccddbbbdbaabbdbdbacbddcacbddddbbacbbadbadbdacacbdbcbbcbbbddbabcbdaaacbadddbdacdaabccdcbdaccaacadabbbcccddababbdbdaaaddaccdbbdcbbddbdbbbdbbcabcabccdcbdbddcabacaccbdadccbadaacdacbdcbbccacbadaaacdcacadbccdadacadbbadcacbaabacdcbbccacdcdccbcaddbccbadbbabdaaccbcaccdddbddbcddadacabcaacacbbbdcbaccaadcabccbcabcaadabaaacdbcdddcccbabddccadaacdcbdcbcabbdadcccadcacadbdbabcbbcbcdcdbbcadbbcddbddcbbccdcbbaabbbdcbdbcbcbaabbacacbbdabccabdaaddddccdbabcaccaabdddcbcabcdcabdcabcccbdbdabbacdaaadacdabaccccdbccdcaddcadacdcccddcccabdaccdaaababaacddcdbcbaadaccbabbacadcdccacddacbbcdbaaaccddccddcbdbdbaadbbddbdddcabaaccabdbbbaaaddabdbdcbccdabaccdabcbaadcdaabaacaddcddcadccdccabc